LMFDB - Embedded newform 930.2.bg.e.661.2

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} - 27x^{14} + 345x^{12} - 2652x^{10} + 13244x^{8} - 43398x^{6} + 89940x^{4} - 107433x^{2} + 58081 $ x^16 - 27x^14 + 345x^12 - 2652x^10 + 13244x^8 - 43398x^6 + 89940x^4 - 107433*x^2 + 58081
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			661.2
Root			$2.08547 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	930.661
Dual form			930.2.bg.e.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.15704 + 0.458493i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(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} +(2.15704 + 0.458493i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.104528 + 0.994522i) q^{10} +(-2.16880 + 2.40870i) q^{11} +(-0.913545 + 0.406737i) q^{12} +(-2.32360 - 1.03453i) q^{13} +(1.47559 + 1.63881i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.97811 + 3.30752i) q^{17} +(-0.913545 - 0.406737i) q^{18} +(2.74185 - 1.22075i) q^{19} +(-0.669131 + 0.743145i) q^{20} +(-0.230509 + 2.19315i) q^{21} +(-3.17039 + 0.673888i) q^{22} +(-0.889117 + 2.73642i) q^{23} +(-0.978148 - 0.207912i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.27175 - 2.20273i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.230509 + 2.19315i) q^{28} +(2.29693 + 1.66882i) q^{29} -1.00000 q^{30} +(-5.53804 + 0.574529i) q^{31} -1.00000 q^{32} +(-2.62220 - 1.90514i) q^{33} +(0.465226 + 4.42633i) q^{34} +(0.681454 + 2.09730i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.584942 + 1.01315i) q^{37} +(2.93574 + 0.624011i) q^{38} +(0.785983 - 2.41901i) q^{39} +(-0.978148 + 0.207912i) q^{40} +(0.671688 - 6.39069i) q^{41} +(-1.47559 + 1.63881i) q^{42} +(5.34023 - 2.37762i) q^{43} +(-2.96100 - 1.31832i) q^{44} +(-0.669131 - 0.743145i) q^{45} +(-2.32774 + 1.69120i) q^{46} +(1.23575 - 0.897826i) q^{47} +(-0.669131 - 0.743145i) q^{48} +(-1.95220 - 0.869177i) q^{49} +(-0.913545 + 0.406737i) q^{50} +(-2.97811 + 3.30752i) q^{51} +(0.265867 - 2.52956i) q^{52} +(6.72715 - 1.42990i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-3.17039 - 0.673888i) q^{55} +(-1.10262 + 1.90979i) q^{56} +(1.50066 + 2.59923i) q^{57} +(0.877349 + 2.70020i) q^{58} +(0.699465 + 6.65497i) q^{59} +(-0.809017 - 0.587785i) q^{60} +1.12977 q^{61} +(-4.81807 - 2.79038i) q^{62} -2.20523 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.265867 - 2.52956i) q^{65} +(-1.00159 - 3.08258i) q^{66} +(-4.73251 - 8.19695i) q^{67} +(-2.22536 + 3.85443i) q^{68} +(-2.81437 - 0.598212i) q^{69} +(-0.681454 + 2.09730i) q^{70} +(-4.24717 + 0.902764i) q^{71} +(0.104528 - 0.994522i) q^{72} +(-2.15000 + 2.38782i) q^{73} +(-1.06874 + 0.475834i) q^{74} +(-0.913545 - 0.406737i) q^{75} +(2.00828 + 2.23042i) q^{76} +(-5.78256 + 4.20128i) q^{77} +(2.05773 - 1.49503i) q^{78} +(9.54950 + 10.6058i) q^{79} +(-0.913545 - 0.406737i) q^{80} +(0.913545 - 0.406737i) q^{81} +(4.29976 - 4.77537i) q^{82} +(-0.568903 + 5.41275i) q^{83} +(-2.15704 + 0.458493i) q^{84} +(-1.37535 + 4.23288i) q^{85} +(5.71787 + 1.21537i) q^{86} +(-1.41958 + 2.45878i) q^{87} +(-1.62061 - 2.80698i) q^{88} +(1.97482 + 6.07787i) q^{89} +(-0.104528 - 0.994522i) q^{90} +(-4.53777 - 3.29688i) q^{91} -2.87724 q^{92} +(-1.15026 - 5.44765i) q^{93} +1.52747 q^{94} +(2.42812 + 1.76414i) q^{95} +(-0.104528 - 0.994522i) q^{96} +(-3.16588 - 9.74357i) q^{97} +(-1.06848 - 1.85066i) q^{98} +(1.62061 - 2.80698i) 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} - 5 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 - 5 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} - 10 q^{14} - 4 q^{15} - 4 q^{16} - 22 q^{17} - 2 q^{18} - 3 q^{19} - 2 q^{20} - 11 q^{22} + 9 q^{23} + 2 q^{24} - 8 q^{25} + 11 q^{26} + 4 q^{27} - 3 q^{29} - 16 q^{30} - 15 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{34} + 5 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} + 28 q^{41} + 10 q^{42} - 28 q^{43} - 19 q^{44} - 2 q^{45} - 9 q^{46} + 9 q^{47} - 2 q^{48} + 19 q^{49} - 2 q^{50} + 22 q^{51} + 4 q^{52} + 2 q^{53} - 4 q^{54} - 11 q^{55} + 5 q^{56} - 2 q^{57} - 12 q^{58} + 24 q^{59} - 4 q^{60} - 40 q^{61} - 25 q^{62} + 10 q^{63} - 4 q^{64} - 4 q^{65} - 7 q^{66} - q^{67} - 2 q^{68} - 3 q^{69} - 5 q^{70} + 39 q^{71} - 2 q^{72} + 81 q^{73} - 8 q^{74} - 2 q^{75} + 2 q^{76} + 28 q^{77} - 8 q^{78} + 64 q^{79} - 2 q^{80} + 2 q^{81} + 32 q^{82} - 40 q^{83} + 5 q^{84} - 14 q^{85} + 13 q^{86} - 9 q^{87} - q^{88} - 7 q^{89} + 2 q^{90} - 46 q^{91} - 36 q^{92} - 20 q^{93} - 4 q^{94} - 6 q^{95} + 2 q^{96} - 17 q^{97} - 9 q^{98} + q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 4 * q^13 - 10 * q^14 - 4 * q^15 - 4 * q^16 - 22 * q^17 - 2 * q^18 - 3 * q^19 - 2 * q^20 - 11 * q^22 + 9 * q^23 + 2 * q^24 - 8 * q^25 + 11 * q^26 + 4 * q^27 - 3 * q^29 - 16 * q^30 - 15 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^34 + 5 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 + 28 * q^41 + 10 * q^42 - 28 * q^43 - 19 * q^44 - 2 * q^45 - 9 * q^46 + 9 * q^47 - 2 * q^48 + 19 * q^49 - 2 * q^50 + 22 * q^51 + 4 * q^52 + 2 * q^53 - 4 * q^54 - 11 * q^55 + 5 * q^56 - 2 * q^57 - 12 * q^58 + 24 * q^59 - 4 * q^60 - 40 * q^61 - 25 * q^62 + 10 * q^63 - 4 * q^64 - 4 * q^65 - 7 * q^66 - q^67 - 2 * q^68 - 3 * q^69 - 5 * q^70 + 39 * q^71 - 2 * q^72 + 81 * q^73 - 8 * q^74 - 2 * q^75 + 2 * q^76 + 28 * q^77 - 8 * q^78 + 64 * q^79 - 2 * q^80 + 2 * q^81 + 32 * q^82 - 40 * q^83 + 5 * q^84 - 14 * q^85 + 13 * q^86 - 9 * q^87 - q^88 - 7 * q^89 + 2 * q^90 - 46 * q^91 - 36 * q^92 - 20 * q^93 - 4 * q^94 - 6 * q^95 + 2 * q^96 - 17 * q^97 - 9 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{15}\right)$

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
$7$	2.15704	+	0.458493i	0.815285	+	0.173294i	0.596639	−	0.802510i	$-0.296503\pi$
$7$	2.15704	+	0.458493i	0.815285	+	0.173294i	0.218646	+	0.975804i	$0.429836\pi$
$8$	−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
$11$	−2.16880	+	2.40870i	−0.653918	+	0.726249i	−0.975345	−	0.220685i	$-0.929171\pi$
$11$	−2.16880	+	2.40870i	−0.653918	+	0.726249i	0.321427	+	0.946934i	$0.395837\pi$
$12$	−0.913545	+	0.406737i	−0.263718	+	0.117415i
$13$	−2.32360	−	1.03453i	−0.644450	−	0.286927i	0.0583706	−	0.998295i	$-0.481410\pi$
$13$	−2.32360	−	1.03453i	−0.644450	−	0.286927i	−0.702820	+	0.711368i	$0.748076\pi$
$14$	1.47559	+	1.63881i	0.394367	+	0.437989i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.97811	+	3.30752i	0.722297	+	0.802193i	0.986757	−	0.162204i	$-0.0518603\pi$
$17$	2.97811	+	3.30752i	0.722297	+	0.802193i	−0.264460	+	0.964397i	$0.585194\pi$
$18$	−0.913545	−	0.406737i	−0.215325	−	0.0958687i
$19$	2.74185	−	1.22075i	0.629023	−	0.280059i	−0.0673606	−	0.997729i	$-0.521458\pi$
$19$	2.74185	−	1.22075i	0.629023	−	0.280059i	0.696384	+	0.717669i	$0.254791\pi$
$20$	−0.669131	+	0.743145i	−0.149622	+	0.166172i
$21$	−0.230509	+	2.19315i	−0.0503013	+	0.478585i
$22$	−3.17039	+	0.673888i	−0.675930	+	0.143673i
$23$	−0.889117	+	2.73642i	−0.185394	+	0.570583i	−0.999955	−	0.00949452i	$-0.996978\pi$
$23$	−0.889117	+	2.73642i	−0.185394	+	0.570583i	0.814561	+	0.580078i	$0.196978\pi$
$24$	−0.978148	−	0.207912i	−0.199664	−	0.0424398i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.27175	−	2.20273i	−0.249410	−	0.431991i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.230509	+	2.19315i	0.0435622	+	0.414467i
$29$	2.29693	+	1.66882i	0.426529	+	0.309891i	0.780259	−	0.625456i	$-0.215087\pi$
$29$	2.29693	+	1.66882i	0.426529	+	0.309891i	−0.353731	+	0.935347i	$0.615087\pi$
$30$	−1.00000			−0.182574
$31$	−5.53804	+	0.574529i	−0.994662	+	0.103188i
$31$	−5.53804	+	0.574529i	−0.994662	+	0.103188i
$32$	−1.00000			−0.176777
$33$	−2.62220	−	1.90514i	−0.456467	−	0.331643i
$34$	0.465226	+	4.42633i	0.0797856	+	0.759110i
$35$	0.681454	+	2.09730i	0.115187	+	0.354508i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−0.584942	+	1.01315i	−0.0961638	+	0.166561i	−0.910094	−	0.414402i	$-0.863991\pi$
$37$	−0.584942	+	1.01315i	−0.0961638	+	0.166561i	0.813930	+	0.580963i	$0.197324\pi$
$38$	2.93574	+	0.624011i	0.476240	+	0.101228i
$39$	0.785983	−	2.41901i	0.125858	−	0.387351i
$40$	−0.978148	+	0.207912i	−0.154659	+	0.0328737i
$41$	0.671688	−	6.39069i	0.104900	−	0.998057i	−0.807808	−	0.589446i	$-0.799346\pi$
$41$	0.671688	−	6.39069i	0.104900	−	0.998057i	0.912708	−	0.408612i	$-0.133987\pi$
$42$	−1.47559	+	1.63881i	−0.227688	+	0.252873i
$43$	5.34023	−	2.37762i	0.814377	−	0.362584i	0.0430897	−	0.999071i	$-0.486280\pi$
$43$	5.34023	−	2.37762i	0.814377	−	0.362584i	0.771287	+	0.636487i	$0.219613\pi$
$44$	−2.96100	−	1.31832i	−0.446388	−	0.198745i
$45$	−0.669131	−	0.743145i	−0.0997481	−	0.110781i
$46$	−2.32774	+	1.69120i	−0.343206	+	0.249354i
$47$	1.23575	−	0.897826i	0.180253	−	0.130961i	−0.494000	−	0.869462i	$-0.664466\pi$
$47$	1.23575	−	0.897826i	0.180253	−	0.130961i	0.674253	+	0.738500i	$0.264466\pi$
$48$	−0.669131	−	0.743145i	−0.0965807	−	0.107264i
$49$	−1.95220	−	0.869177i	−0.278886	−	0.124168i
$50$	−0.913545	+	0.406737i	−0.129195	+	0.0575212i
$51$	−2.97811	+	3.30752i	−0.417019	+	0.463146i
$52$	0.265867	−	2.52956i	0.0368692	−	0.350787i
$53$	6.72715	−	1.42990i	0.924046	−	0.196412i	0.278767	−	0.960359i	$-0.410074\pi$
$53$	6.72715	−	1.42990i	0.924046	−	0.196412i	0.645279	+	0.763947i	$0.276741\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	−3.17039	−	0.673888i	−0.427496	−	0.0908670i
$56$	−1.10262	+	1.90979i	−0.147343	+	0.255206i
$57$	1.50066	+	2.59923i	0.198768	+	0.344276i
$58$	0.877349	+	2.70020i	0.115202	+	0.354554i
$59$	0.699465	+	6.65497i	0.0910626	+	0.866403i	0.940747	+	0.339110i	$0.110126\pi$
$59$	0.699465	+	6.65497i	0.0910626	+	0.866403i	−0.849684	+	0.527292i	$0.823207\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	1.12977			0.144652			0.0723260	−	0.997381i	$-0.476958\pi$
$61$	1.12977			0.144652			0.0723260	+	0.997381i	$0.476958\pi$
$62$	−4.81807	−	2.79038i	−0.611896	−	0.354378i
$63$	−2.20523			−0.277833
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.265867	−	2.52956i	−0.0329768	−	0.313753i
$66$	−1.00159	−	3.08258i	−0.123287	−	0.379440i
$67$	−4.73251	−	8.19695i	−0.578169	−	1.00142i	−0.995689	−	0.0927501i	$-0.970434\pi$
$67$	−4.73251	−	8.19695i	−0.578169	−	1.00142i	0.417521	−	0.908667i	$-0.362899\pi$
$68$	−2.22536	+	3.85443i	−0.269864	+	0.467418i
$69$	−2.81437	−	0.598212i	−0.338810	−	0.0720163i
$70$	−0.681454	+	2.09730i	−0.0814493	+	0.250675i
$71$	−4.24717	+	0.902764i	−0.504046	+	0.107138i	−0.452915	−	0.891554i	$-0.649616\pi$
$71$	−4.24717	+	0.902764i	−0.504046	+	0.107138i	−0.0511311	+	0.998692i	$0.516283\pi$
$72$	0.104528	−	0.994522i	0.0123188	−	0.117206i
$73$	−2.15000	+	2.38782i	−0.251639	+	0.279473i	−0.855708	−	0.517458i	$-0.826878\pi$
$73$	−2.15000	+	2.38782i	−0.251639	+	0.279473i	0.604070	+	0.796932i	$0.293545\pi$
$74$	−1.06874	+	0.475834i	−0.124239	+	0.0553146i
$75$	−0.913545	−	0.406737i	−0.105487	−	0.0469659i
$76$	2.00828	+	2.23042i	0.230366	+	0.255847i
$77$	−5.78256	+	4.20128i	−0.658984	+	0.478780i
$78$	2.05773	−	1.49503i	0.232992	−	0.169279i
$79$	9.54950	+	10.6058i	1.07440	+	1.19325i	0.980265	+	0.197686i	$0.0633427\pi$
$79$	9.54950	+	10.6058i	1.07440	+	1.19325i	0.0941376	+	0.995559i	$0.469991\pi$
$80$	−0.913545	−	0.406737i	−0.102137	−	0.0454745i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	4.29976	−	4.77537i	0.474829	−	0.527351i
$83$	−0.568903	+	5.41275i	−0.0624452	+	0.594126i	0.917897	+	0.396820i	$0.129886\pi$
$83$	−0.568903	+	5.41275i	−0.0624452	+	0.594126i	−0.980342	+	0.197307i	$0.936781\pi$
$84$	−2.15704	+	0.458493i	−0.235353	+	0.0500257i
$85$	−1.37535	+	4.23288i	−0.149177	+	0.459120i
$86$	5.71787	+	1.21537i	0.616573	+	0.131057i
$87$	−1.41958	+	2.45878i	−0.152195	+	0.263609i
$88$	−1.62061	−	2.80698i	−0.172758	−	0.299225i
$89$	1.97482	+	6.07787i	0.209330	+	0.644253i	0.999508	+	0.0313746i	$0.00998847\pi$
$89$	1.97482	+	6.07787i	0.209330	+	0.644253i	−0.790177	+	0.612878i	$0.790012\pi$
$90$	−0.104528	−	0.994522i	−0.0110183	−	0.104832i
$91$	−4.53777	−	3.29688i	−0.475687	−	0.345607i
$92$	−2.87724			−0.299973
$93$	−1.15026	−	5.44765i	−0.119277	−	0.564895i
$94$	1.52747			0.157547
$95$	2.42812	+	1.76414i	0.249120	+	0.180997i
$96$	−0.104528	−	0.994522i	−0.0106684	−	0.101503i
$97$	−3.16588	−	9.74357i	−0.321446	−	0.989309i	−0.973019	−	0.230724i	$-0.925891\pi$
$97$	−3.16588	−	9.74357i	−0.321446	−	0.989309i	0.651573	−	0.758586i	$-0.274109\pi$
$98$	−1.06848	−	1.85066i	−0.107932	−	0.186944i
$99$	1.62061	−	2.80698i	0.162877	−	0.282112i
$100$	−0.978148	−	0.207912i	−0.0978148	−	0.0207912i
$101$	2.73721	−	8.42427i	0.272363	−	0.838246i	−0.717542	−	0.696515i	$-0.754733\pi$
$101$	2.73721	−	8.42427i	0.272363	−	0.838246i	0.989905	−	0.141731i	$-0.0452669\pi$
$102$	−4.35346	+	0.925355i	−0.431056	+	0.0916238i
$103$	0.520193	−	4.94931i	0.0512562	−	0.487670i	−0.938539	−	0.345173i	$-0.887820\pi$
$103$	0.520193	−	4.94931i	0.0512562	−	0.487670i	0.989795	−	0.142497i	$-0.0455131\pi$
$104$	1.70193	−	1.89018i	0.166888	−	0.185348i
$105$	−2.01458	+	0.896949i	−0.196603	+	0.0875332i
$106$	6.28286	+	2.79731i	0.610245	+	0.271699i
$107$	−0.543499	−	0.603617i	−0.0525421	−	0.0583539i	0.716301	−	0.697792i	$-0.245834\pi$
$107$	−0.543499	−	0.603617i	−0.0525421	−	0.0583539i	−0.768843	+	0.639438i	$0.779167\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	10.0868	−	7.32846i	0.966137	−	0.701940i	0.0115690	−	0.999933i	$-0.496317\pi$
$109$	10.0868	−	7.32846i	0.966137	−	0.701940i	0.954568	+	0.297994i	$0.0963174\pi$
$110$	−2.16880	−	2.40870i	−0.206787	−	0.229660i
$111$	−1.06874	−	0.475834i	−0.101440	−	0.0451642i
$112$	−2.01458	+	0.896949i	−0.190360	+	0.0847537i
$113$	8.66236	−	9.62053i	0.814887	−	0.905023i	−0.182046	−	0.983290i	$-0.558272\pi$
$113$	8.66236	−	9.62053i	0.814887	−	0.905023i	0.996932	+	0.0782669i	$0.0249386\pi$
$114$	−0.313724	+	2.98489i	−0.0293830	+	0.279560i
$115$	−2.81437	+	0.598212i	−0.262441	+	0.0557836i
$116$	−0.877349	+	2.70020i	−0.0814598	+	0.250707i
$117$	2.48791	+	0.528822i	0.230007	+	0.0488896i
$118$	−3.34581	+	5.79512i	−0.308007	+	0.533484i
$119$	4.90743	+	8.49991i	0.449863	+	0.779186i
$120$	−0.309017	−	0.951057i	−0.0282093	−	0.0868192i
$121$	0.0516882	+	0.491780i	0.00469893	+	0.0447073i
$122$	0.914001	+	0.664061i	0.0827498	+	0.0601212i
$123$	6.42589			0.579403
$124$	−2.25776	−	5.08945i	−0.202753	−	0.457046i
$125$	−1.00000			−0.0894427
$126$	−1.78407	−	1.29620i	−0.158938	−	0.115475i
$127$	−0.723679	−	6.88535i	−0.0642161	−	0.610976i	−0.978549	−	0.206013i	$-0.933951\pi$
$127$	−0.723679	−	6.88535i	−0.0642161	−	0.610976i	0.914333	−	0.404963i	$-0.132716\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	2.92280	+	5.06244i	0.257338	+	0.445723i
$130$	1.27175	−	2.20273i	0.111540	−	0.193192i
$131$	14.6202	+	3.10762i	1.27737	+	0.271514i	0.796159	−	0.605088i	$-0.206862\pi$
$131$	14.6202	+	3.10762i	1.27737	+	0.271514i	0.481216	+	0.876602i	$0.340195\pi$
$132$	1.00159	−	3.08258i	0.0871774	−	0.268304i
$133$	6.47399	−	1.37609i	0.561366	−	0.119322i
$134$	0.989365	−	9.41318i	0.0854681	−	0.813175i
$135$	0.669131	−	0.743145i	0.0575896	−	0.0639597i
$136$	−4.06593	+	1.81027i	−0.348651	+	0.155229i
$137$	−0.231931	−	0.103262i	−0.0198152	−	0.00882230i	0.396805	−	0.917903i	$-0.370119\pi$
$137$	−0.231931	−	0.103262i	−0.0198152	−	0.00882230i	−0.416620	+	0.909081i	$0.636786\pi$
$138$	−1.92525	−	2.13821i	−0.163888	−	0.182016i
$139$	16.5483	−	12.0231i	1.40361	−	1.01978i	0.409396	−	0.912357i	$-0.365739\pi$
$139$	16.5483	−	12.0231i	1.40361	−	1.01978i	0.994213	−	0.107425i	$-0.0342606\pi$
$140$	−1.78407	+	1.29620i	−0.150781	+	0.109549i
$141$	1.02208	+	1.13513i	0.0860746	+	0.0955955i
$142$	−3.96666	−	1.76607i	−0.332875	−	0.148205i
$143$	7.53129	−	3.35315i	0.629798	−	0.280404i
$144$	0.669131	−	0.743145i	0.0557609	−	0.0619287i
$145$	−0.296773	+	2.82361i	−0.0246457	+	0.234488i
$146$	−3.14291	+	0.668047i	−0.260109	+	0.0552879i
$147$	0.660355	−	2.03236i	0.0544652	−	0.167627i
$148$	−1.14432	−	0.243232i	−0.0940624	−	0.0199936i
$149$	3.31030	−	5.73361i	0.271190	−	0.469716i	−0.697976	−	0.716121i	$-0.745916\pi$
$149$	3.31030	−	5.73361i	0.271190	−	0.469716i	0.969167	+	0.246405i	$0.0792493\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	3.33970	+	10.2785i	0.271781	+	0.836456i	0.990053	+	0.140694i	$0.0449332\pi$
$151$	3.33970	+	10.2785i	0.271781	+	0.836456i	−0.718272	+	0.695762i	$0.755067\pi$
$152$	0.313724	+	2.98489i	0.0254464	+	0.242106i
$153$	−3.60070	−	2.61606i	−0.291100	−	0.211496i
$154$	−7.14764			−0.575973
$155$	−3.26658	−	4.50882i	−0.262378	−	0.362157i
$156$	2.54349			0.203642
$157$	−8.37345	−	6.08367i	−0.668274	−	0.485529i	0.201173	−	0.979556i	$-0.435525\pi$
$157$	−8.37345	−	6.08367i	−0.668274	−	0.485529i	−0.869447	+	0.494026i	$0.835525\pi$
$158$	1.49178	+	14.1933i	0.118680	+	1.12916i
$159$	2.12525	+	6.54084i	0.168543	+	0.518722i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−3.17249	+	5.49492i	−0.250027	+	0.433060i
$162$	0.978148	+	0.207912i	0.0768505	+	0.0163351i
$163$	2.26745	−	6.97850i	0.177600	−	0.546598i	−0.822142	−	0.569282i	$-0.807221\pi$
$163$	2.26745	−	6.97850i	0.177600	−	0.546598i	0.999743	+	0.0226842i	$0.00722121\pi$
$164$	6.28547	−	1.33602i	0.490812	−	0.104325i
$165$	0.338800	−	3.22346i	0.0263755	−	0.250946i
$166$	−3.64178	+	4.04461i	−0.282657	+	0.313923i
$167$	−0.780596	+	0.347544i	−0.0604044	+	0.0268938i	−0.436716	−	0.899599i	$-0.643859\pi$
$167$	−0.780596	+	0.347544i	−0.0604044	+	0.0268938i	0.376312	+	0.926493i	$0.377192\pi$
$168$	−2.01458	−	0.896949i	−0.155428	−	0.0692011i
$169$	−4.36985	−	4.85321i	−0.336143	−	0.373324i
$170$	−3.60070	+	2.61606i	−0.276161	+	0.200643i
$171$	−2.42812	+	1.76414i	−0.185683	+	0.134907i
$172$	3.91147	+	4.34413i	0.298247	+	0.331237i
$173$	9.04931	+	4.02901i	0.688006	+	0.306320i	0.720801	−	0.693142i	$-0.243774\pi$
$173$	9.04931	+	4.02901i	0.688006	+	0.306320i	−0.0327950	+	0.999462i	$0.510441\pi$
$174$	−2.59370	+	1.15479i	−0.196628	+	0.0875444i
$175$	−1.47559	+	1.63881i	−0.111544	+	0.123882i
$176$	0.338800	−	3.22346i	0.0255380	−	0.242978i
$177$	−6.54540	+	1.39127i	−0.491982	+	0.104574i
$178$	−1.97482	+	6.07787i	−0.148019	+	0.455556i
$179$	22.7461	+	4.83484i	1.70013	+	0.361373i	0.952920	−	0.303220i	$-0.0980618\pi$
$179$	22.7461	+	4.83484i	1.70013	+	0.361373i	0.747205	+	0.664593i	$0.231395\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−6.10763	−	10.5787i	−0.453976	−	0.786310i	0.544652	−	0.838662i	$-0.316662\pi$
$181$	−6.10763	−	10.5787i	−0.453976	−	0.786310i	−0.998629	+	0.0523519i	$0.983328\pi$
$182$	−1.73327	−	5.33447i	−0.128479	−	0.395417i
$183$	0.118093	+	1.12358i	0.00872968	+	0.0830573i
$184$	−2.32774	−	1.69120i	−0.171603	−	0.124677i
$185$	−1.16988			−0.0860115
$186$	2.27146	−	5.08335i	0.166552	−	0.372729i
$187$	−14.4257			−1.05491
$188$	1.23575	+	0.897826i	0.0901265	+	0.0654807i
$189$	−0.230509	−	2.19315i	−0.0167671	−	0.159528i
$190$	0.927461	+	2.85443i	0.0672851	+	0.207082i
$191$	7.59241	+	13.1504i	0.549367	+	0.951532i	0.998318	+	0.0579754i	$0.0184645\pi$
$191$	7.59241	+	13.1504i	0.549367	+	0.951532i	−0.448951	+	0.893556i	$0.648202\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−17.5948	−	3.73989i	−1.26650	−	0.269203i	−0.474791	−	0.880099i	$-0.657476\pi$
$193$	−17.5948	−	3.73989i	−1.26650	−	0.269203i	−0.791711	+	0.610895i	$0.790810\pi$
$194$	3.16588	−	9.74357i	0.227297	−	0.699547i
$195$	2.48791	−	0.528822i	0.178163	−	0.0378697i
$196$	0.223372	−	2.12525i	0.0159552	−	0.151803i
$197$	7.63282	−	8.47710i	0.543816	−	0.603968i	−0.407113	−	0.913378i	$-0.633465\pi$
$197$	7.63282	−	8.47710i	0.543816	−	0.603968i	0.950929	+	0.309409i	$0.100131\pi$
$198$	2.96100	−	1.31832i	0.210429	−	0.0936891i
$199$	6.40479	+	2.85160i	0.454023	+	0.202144i	0.620990	−	0.783818i	$-0.286731\pi$
$199$	6.40479	+	2.85160i	0.454023	+	0.202144i	−0.166967	+	0.985963i	$0.553397\pi$
$200$	−0.669131	−	0.743145i	−0.0473147	−	0.0525483i
$201$	7.65737	−	5.56340i	0.540109	−	0.392412i
$202$	7.16611	−	5.20648i	0.504206	−	0.366327i
$203$	4.18943	+	4.65283i	0.294040	+	0.326565i
$204$	−4.06593	−	1.81027i	−0.284672	−	0.126744i
$205$	5.87034	−	2.61364i	0.410002	−	0.182545i
$206$	3.32998	−	3.69831i	0.232010	−	0.257674i
$207$	0.300754	−	2.86148i	0.0209038	−	0.198887i
$208$	2.48791	−	0.528822i	0.172506	−	0.0366672i
$209$	−3.00611	+	9.25184i	−0.207937	+	0.639963i
$210$	−2.15704	−	0.458493i	−0.148850	−	0.0316391i
$211$	−4.78285	+	8.28414i	−0.329265	+	0.570304i	−0.982366	−	0.186967i	$-0.940134\pi$
$211$	−4.78285	+	8.28414i	−0.329265	+	0.570304i	0.653101	+	0.757271i	$0.273468\pi$
$212$	3.43872	+	5.95604i	0.236172	+	0.409062i
$213$	−1.34177	−	4.12954i	−0.0919365	−	0.282951i
$214$	−0.0849029	−	0.807797i	−0.00580384	−	0.0552199i
$215$	4.72919	+	3.43596i	0.322528	+	0.234331i
$216$	1.00000			0.0680414
$217$	−12.2092	−	1.29987i	−0.828815	−	0.0882412i
$218$	12.4679			0.844435
$219$	−2.59947	−	1.88863i	−0.175656	−	0.127622i
$220$	−0.338800	−	3.22346i	−0.0228419	−	0.217326i
$221$	−3.49818	−	10.7663i	−0.235313	−	0.724220i
$222$	−0.584942	−	1.01315i	−0.0392587	−	0.0679981i
$223$	3.63675	−	6.29903i	0.243534	−	0.421814i	−0.718184	−	0.695853i	$-0.755026\pi$
$223$	3.63675	−	6.29903i	0.243534	−	0.421814i	0.961719	+	0.274039i	$0.0883598\pi$
$224$	−2.15704	−	0.458493i	−0.144123	−	0.0306344i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	12.6628	−	2.69156i	0.842317	−	0.179040i
$227$	−0.561713	+	5.34434i	−0.0372822	+	0.354717i	0.959938	+	0.280211i	$0.0904045\pi$
$227$	−0.561713	+	5.34434i	−0.0372822	+	0.354717i	−0.997221	+	0.0745054i	$0.976262\pi$
$228$	−2.00828	+	2.23042i	−0.133002	+	0.147713i
$229$	24.3075	−	10.8224i	1.60628	−	0.715164i	0.609313	−	0.792930i	$-0.291445\pi$
$229$	24.3075	−	10.8224i	1.60628	−	0.715164i	0.996972	+	0.0777658i	$0.0247786\pi$
$230$	−2.62849	−	1.17028i	−0.173318	−	0.0771660i
$231$	−4.78271	−	5.31173i	−0.314679	−	0.349486i
$232$	−2.29693	+	1.66882i	−0.150801	+	0.109563i
$233$	−4.05788	+	2.94822i	−0.265840	+	0.193144i	−0.712718	−	0.701451i	$-0.752536\pi$
$233$	−4.05788	+	2.94822i	−0.265840	+	0.193144i	0.446877	+	0.894595i	$0.352536\pi$
$234$	1.70193	+	1.89018i	0.111259	+	0.123565i
$235$	1.39542	+	0.621279i	0.0910269	+	0.0405278i
$236$	−6.11310	+	2.72173i	−0.397929	+	0.177169i
$237$	−9.54950	+	10.6058i	−0.620307	+	0.688921i
$238$	−1.02593	+	9.76109i	−0.0665013	+	0.632717i
$239$	−4.83110	+	1.02688i	−0.312498	+	0.0664235i	−0.361491	−	0.932376i	$-0.617732\pi$
$239$	−4.83110	+	1.02688i	−0.312498	+	0.0664235i	0.0489930	+	0.998799i	$0.484399\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	−7.84282	−	1.66704i	−0.505201	−	0.107384i	−0.0517411	−	0.998661i	$-0.516477\pi$
$241$	−7.84282	−	1.66704i	−0.505201	−	0.107384i	−0.453460	+	0.891277i	$0.649810\pi$
$242$	−0.247245	+	0.428240i	−0.0158935	+	0.0275283i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.349117	+	1.07447i	0.0223500	+	0.0687861i
$245$	−0.223372	−	2.12525i	−0.0142707	−	0.135777i
$246$	5.19865	+	3.77704i	0.331454	+	0.240815i
$247$	−7.63385			−0.485731
$248$	1.16494	−	5.44453i	0.0739738	−	0.345728i
$249$	−5.44256			−0.344908
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−1.04652	−	9.95693i	−0.0660555	−	0.628476i	−0.976600	−	0.215065i	$-0.931004\pi$
$251$	−1.04652	−	9.95693i	−0.0660555	−	0.628476i	0.910544	−	0.413411i	$-0.135663\pi$
$252$	−0.681454	−	2.09730i	−0.0429276	−	0.132117i
$253$	−4.66289	−	8.07636i	−0.293153	−	0.507756i
$254$	3.46164	−	5.99573i	0.217202	−	0.376206i
$255$	−4.35346	−	0.925355i	−0.272624	−	0.0579480i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	1.33745	−	0.284284i	0.0834278	−	0.0177331i	−0.166009	−	0.986124i	$-0.553088\pi$
$257$	1.33745	−	0.284284i	0.0834278	−	0.0177331i	0.249436	+	0.968391i	$0.419755\pi$
$258$	−0.611032	+	5.81358i	−0.0380412	+	0.361938i
$259$	−1.72627	+	1.91721i	−0.107265	+	0.119130i
$260$	2.32360	−	1.03453i	0.144103	−	0.0641589i
$261$	−2.59370	−	1.15479i	−0.160546	−	0.0714797i
$262$	10.0014	+	11.1077i	0.617888	+	0.686234i
$263$	0.280946	−	0.204119i	0.0173239	−	0.0125865i	−0.579090	−	0.815264i	$-0.696592\pi$
$263$	0.280946	−	0.204119i	0.0173239	−	0.0125865i	0.596413	+	0.802677i	$0.296592\pi$
$264$	2.62220	−	1.90514i	0.161385	−	0.117253i
$265$	4.60191	+	5.11094i	0.282693	+	0.313962i
$266$	6.04641	+	2.69204i	0.370729	+	0.165059i
$267$	−5.83815	+	2.59931i	−0.357289	+	0.159075i
$268$	6.33334	−	7.03389i	0.386870	−	0.429663i
$269$	−1.61353	+	15.3517i	−0.0983789	+	0.936013i	0.828332	+	0.560238i	$0.189290\pi$
$269$	−1.61353	+	15.3517i	−0.0983789	+	0.936013i	−0.926711	+	0.375775i	$0.877377\pi$
$270$	0.978148	−	0.207912i	0.0595282	−	0.0126531i
$271$	−5.48730	+	16.8882i	−0.333329	+	1.02588i	0.634210	+	0.773161i	$0.281326\pi$
$271$	−5.48730	+	16.8882i	−0.333329	+	1.02588i	−0.967539	+	0.252721i	$0.918674\pi$
$272$	−4.35346	−	0.925355i	−0.263967	−	0.0561079i
$273$	2.80450	−	4.85753i	0.169736	−	0.293991i
$274$	−0.126940	−	0.219867i	−0.00766873	−	0.0132826i
$275$	−1.00159	−	3.08258i	−0.0603983	−	0.185887i
$276$	−0.300754	−	2.86148i	−0.0181032	−	0.172241i
$277$	−0.217397	−	0.157948i	−0.0130621	−	0.00949019i	0.581235	−	0.813736i	$-0.302570\pi$
$277$	−0.217397	−	0.157948i	−0.0130621	−	0.00949019i	−0.594297	+	0.804246i	$0.702570\pi$
$278$	20.4548			1.22680
$279$	5.29757	−	1.71340i	0.317157	−	0.102578i
$280$	−2.20523			−0.131788
$281$	−9.22635	−	6.70333i	−0.550398	−	0.399887i	0.277534	−	0.960716i	$-0.410483\pi$
$281$	−9.22635	−	6.70333i	−0.550398	−	0.399887i	−0.827932	+	0.560828i	$0.810483\pi$
$282$	0.159664	+	1.51911i	0.00950788	+	0.0904614i
$283$	−0.652925	−	2.00950i	−0.0388124	−	0.119452i	0.929773	−	0.368133i	$-0.120003\pi$
$283$	−0.652925	−	2.00950i	−0.0388124	−	0.119452i	−0.968585	+	0.248681i	$0.920003\pi$
$284$	−2.17103	−	3.76033i	−0.128827	−	0.223134i
$285$	−1.50066	+	2.59923i	−0.0888916	+	0.153965i
$286$	8.06387	+	1.71403i	0.476827	+	0.101353i
$287$	4.37895	−	13.4770i	0.258481	−	0.795523i
$288$	0.978148	−	0.207912i	0.0576379	−	0.0122513i
$289$	−0.293605	+	2.79347i	−0.0172709	+	0.164322i
$290$	−1.89977	+	2.10991i	−0.111558	+	0.123898i
$291$	9.35927	−	4.16701i	0.548650	−	0.244275i
$292$	−2.93534	−	1.30690i	−0.171778	−	0.0764803i
$293$	11.0392	+	12.2603i	0.644919	+	0.716255i	0.973619	−	0.228179i	$-0.0732772\pi$
$293$	11.0392	+	12.2603i	0.644919	+	0.716255i	−0.328700	+	0.944434i	$0.606610\pi$
$294$	1.72883	−	1.25607i	0.100828	−	0.0732555i
$295$	−5.41364	+	3.93324i	−0.315194	+	0.229002i
$296$	−0.782805	−	0.869393i	−0.0454996	−	0.0505324i
$297$	2.96100	+	1.31832i	0.171815	+	0.0764969i
$298$	6.04822	−	2.69284i	0.350364	−	0.155992i
$299$	4.89686	−	5.43852i	0.283193	−	0.314517i
$300$	0.104528	−	0.994522i	0.00603495	−	0.0574187i
$301$	12.6092	−	2.68017i	0.726783	−	0.154483i
$302$	−3.33970	+	10.2785i	−0.192178	+	0.591464i
$303$	8.66424	+	1.84164i	0.497747	+	0.105799i
$304$	−1.50066	+	2.59923i	−0.0860690	+	0.149076i
$305$	0.564884	+	0.978407i	0.0323452	+	0.0560234i
$306$	−1.37535	−	4.23288i	−0.0786233	−	0.241978i
$307$	0.659947	+	6.27898i	0.0376652	+	0.358360i	0.997080	+	0.0763622i	$0.0243305\pi$
$307$	0.659947	+	6.27898i	0.0376652	+	0.358360i	−0.959415	+	0.281998i	$0.909003\pi$
$308$	−5.78256	−	4.20128i	−0.329492	−	0.239390i
$309$	4.97657			0.283107
$310$	0.00750162	−	5.56776i	0.000426063	−	0.316227i
$311$	−28.4512			−1.61332			−0.806659	−	0.591018i	$-0.798726\pi$
$311$	−28.4512			−1.61332			−0.806659	+	0.591018i	$0.798726\pi$
$312$	2.05773	+	1.49503i	0.116496	+	0.0846393i
$313$	−3.49053	−	33.2102i	−0.197296	−	1.87715i	−0.427512	−	0.904010i	$-0.640610\pi$
$313$	−3.49053	−	33.2102i	−0.197296	−	1.87715i	0.230216	−	0.973140i	$-0.426057\pi$
$314$	−3.19837	−	9.84358i	−0.180495	−	0.555505i
$315$	−1.10262	−	1.90979i	−0.0621254	−	0.107604i
$316$	−7.13575	+	12.3595i	−0.401418	+	0.695276i
$317$	−28.3086	−	6.01719i	−1.58997	−	0.337959i	−0.673853	−	0.738866i	$-0.735362\pi$
$317$	−28.3086	−	6.01719i	−1.58997	−	0.337959i	−0.916119	+	0.400907i	$0.868695\pi$
$318$	−2.12525	+	6.54084i	−0.119178	+	0.366792i
$319$	−9.00125	+	1.91327i	−0.503973	+	0.107123i
$320$	0.104528	−	0.994522i	0.00584332	−	0.0555955i
$321$	0.543499	−	0.603617i	0.0303352	−	0.0336906i
$322$	−5.79643	+	2.58074i	−0.323023	+	0.143819i
$323$	12.2032	+	5.43321i	0.679003	+	0.302312i
$324$	0.669131	+	0.743145i	0.0371739	+	0.0412858i
$325$	2.05773	−	1.49503i	0.114142	−	0.0829292i
$326$	5.93626	−	4.31295i	0.328779	−	0.238872i
$327$	8.34267	+	9.26548i	0.461351	+	0.512382i
$328$	5.87034	+	2.61364i	0.324135	+	0.144314i
$329$	3.07722	−	1.37006i	0.169652	−	0.0755341i
$330$	2.16880	−	2.40870i	0.119389	−	0.132594i
$331$	−3.59276	+	34.1828i	−0.197476	+	1.87886i	0.227680	+	0.973736i	$0.426886\pi$
$331$	−3.59276	+	34.1828i	−0.197476	+	1.87886i	−0.425156	+	0.905120i	$0.639781\pi$
$332$	−5.32363	+	1.13157i	−0.292172	+	0.0621031i
$333$	0.361514	−	1.11263i	0.0198108	−	0.0609715i
$334$	−0.835797	−	0.177654i	−0.0457328	−	0.00972080i
$335$	4.73251	−	8.19695i	0.258565	−	0.447847i
$336$	−1.10262	−	1.90979i	−0.0601526	−	0.104187i
$337$	−7.20447	−	22.1731i	−0.392453	−	1.20785i	−0.930928	−	0.365204i	$-0.880999\pi$
$337$	−7.20447	−	22.1731i	−0.392453	−	1.20785i	0.538475	−	0.842642i	$-0.319001\pi$
$338$	−0.682638	−	6.49487i	−0.0371306	−	0.353274i
$339$	10.4733	+	7.60929i	0.568831	+	0.413280i
$340$	−4.45071			−0.241374
$341$	10.6270	−	14.5855i	0.575487	−	0.789849i
$342$	−3.00133			−0.162293
$343$	−16.3010	−	11.8433i	−0.880169	−	0.639480i
$344$	0.611032	+	5.81358i	0.0329447	+	0.313447i
$345$	−0.889117	−	2.73642i	−0.0478684	−	0.147324i
$346$	4.95285	+	8.57859i	0.266267	+	0.461188i
$347$	−11.5389	+	19.9859i	−0.619438	+	1.07290i	0.370150	+	0.928972i	$0.379306\pi$
$347$	−11.5389	+	19.9859i	−0.619438	+	1.07290i	−0.989588	+	0.143926i	$0.954027\pi$
$348$	−2.77712	−	0.590294i	−0.148869	−	0.0316431i
$349$	−4.17884	+	12.8611i	−0.223688	+	0.688441i	0.774734	+	0.632287i	$0.217884\pi$
$349$	−4.17884	+	12.8611i	−0.223688	+	0.688441i	−0.998422	+	0.0561540i	$0.982116\pi$
$350$	−2.15704	+	0.458493i	−0.115299	+	0.0245075i
$351$	−0.265867	+	2.52956i	−0.0141910	+	0.135018i
$352$	2.16880	−	2.40870i	0.115597	−	0.128384i
$353$	−12.1013	+	5.38784i	−0.644087	+	0.286766i	−0.702669	−	0.711517i	$-0.748009\pi$
$353$	−12.1013	+	5.38784i	−0.644087	+	0.286766i	0.0585825	+	0.998283i	$0.481342\pi$
$354$	−6.11310	−	2.72173i	−0.324908	−	0.144658i
$355$	−2.90540	−	3.22677i	−0.154203	−	0.171259i
$356$	−5.17015	+	3.75633i	−0.274017	+	0.199085i
$357$	−7.94038	+	5.76903i	−0.420250	+	0.305329i
$358$	15.5602	+	17.2813i	0.822380	+	0.913346i
$359$	29.3167	+	13.0526i	1.54727	+	0.688891i	0.989952	−	0.141405i	$-0.0451619\pi$
$359$	29.3167	+	13.0526i	1.54727	+	0.688891i	0.557323	+	0.830296i	$0.311829\pi$
$360$	0.913545	−	0.406737i	0.0481481	−	0.0214369i
$361$	−6.68598	+	7.42553i	−0.351893	+	0.390817i
$362$	1.27684	−	12.1483i	0.0671093	−	0.638502i
$363$	−0.483683	+	0.102810i	−0.0253868	+	0.00539613i
$364$	1.73327	−	5.33447i	0.0908482	−	0.279602i
$365$	−3.14291	−	0.668047i	−0.164508	−	0.0349672i
$366$	−0.564884	+	0.978407i	−0.0295270	+	0.0511422i
$367$	−4.30921	−	7.46377i	−0.224939	−	0.389606i	0.731362	−	0.681989i	$-0.238885\pi$
$367$	−4.30921	−	7.46377i	−0.224939	−	0.389606i	−0.956301	+	0.292383i	$0.905552\pi$
$368$	−0.889117	−	2.73642i	−0.0463484	−	0.142646i
$369$	0.671688	+	6.39069i	0.0349667	+	0.332686i
$370$	−0.946456	−	0.687640i	−0.0492039	−	0.0357487i
$371$	15.1664			0.787398
$372$	4.82557	−	2.77738i	0.250194	−	0.144001i
$373$	−12.7340			−0.659343			−0.329672	−	0.944096i	$-0.606938\pi$
$373$	−12.7340			−0.659343			−0.329672	+	0.944096i	$0.606938\pi$
$374$	−11.6707	−	8.47924i	−0.603476	−	0.438451i
$375$	−0.104528	−	0.994522i	−0.00539783	−	0.0513569i
$376$	0.472015	+	1.45271i	0.0243423	+	0.0749180i
$377$	−3.61069	−	6.25390i	−0.185960	−	0.322092i
$378$	1.10262	−	1.90979i	0.0567124	−	0.0982288i
$379$	−31.9727	−	6.79601i	−1.64233	−	0.349087i	−0.708195	−	0.706017i	$-0.750490\pi$
$379$	−31.9727	−	6.79601i	−1.64233	−	0.349087i	−0.934131	+	0.356929i	$0.883824\pi$
$380$	−0.927461	+	2.85443i	−0.0475778	+	0.146429i
$381$	6.77198	−	1.43943i	0.346939	−	0.0737442i
$382$	−1.58724	+	15.1016i	−0.0812105	+	0.772666i
$383$	−13.8287	+	15.3583i	−0.706611	+	0.784771i	−0.984414	−	0.175867i	$-0.943727\pi$
$383$	−13.8287	+	15.3583i	−0.706611	+	0.784771i	0.277803	+	0.960638i	$0.410394\pi$
$384$	0.913545	−	0.406737i	0.0466192	−	0.0207562i
$385$	−6.52970	−	2.90721i	−0.332784	−	0.148165i
$386$	−12.0362	−	13.3676i	−0.612629	−	0.680393i
$387$	−4.72919	+	3.43596i	−0.240398	+	0.174660i
$388$	8.28837	−	6.02186i	0.420778	−	0.305713i
$389$	−4.99762	−	5.55042i	−0.253389	−	0.281418i	0.603007	−	0.797736i	$-0.293969\pi$
$389$	−4.99762	−	5.55042i	−0.253389	−	0.281418i	−0.856397	+	0.516318i	$0.827302\pi$
$390$	2.32360	+	1.03453i	0.117660	+	0.0523856i
$391$	−11.6987	+	5.20858i	−0.591627	+	0.263409i
$392$	1.42990	−	1.58807i	0.0722209	−	0.0802094i
$393$	−1.56237	+	14.8650i	−0.0788112	+	0.749838i
$394$	11.1578	−	2.37166i	0.562121	−	0.119483i
$395$	−4.41014	+	13.5730i	−0.221898	+	0.682932i
$396$	3.17039	+	0.673888i	0.159318	+	0.0338641i
$397$	5.11765	−	8.86403i	0.256848	−	0.444873i	−0.708548	−	0.705662i	$-0.750650\pi$
$397$	5.11765	−	8.86403i	0.256848	−	0.444873i	0.965396	+	0.260789i	$0.0839828\pi$
$398$	3.50546	+	6.07163i	0.175713	+	0.304343i
$399$	2.04527	+	6.29468i	0.102391	+	0.315128i
$400$	−0.104528	−	0.994522i	−0.00522642	−	0.0497261i
$401$	−31.0785	−	22.5798i	−1.55198	−	1.12758i	−0.942218	−	0.335001i	$-0.891263\pi$
$401$	−31.0785	−	22.5798i	−1.55198	−	1.12758i	−0.609766	−	0.792581i	$-0.708737\pi$
$402$	9.46503			0.472073
$403$	13.4625	+	4.39431i	0.670617	+	0.218896i
$404$	8.85780			0.440692
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	0.654453	+	6.22671i	0.0324800	+	0.309026i
$407$	−1.17175	−	3.60626i	−0.0580813	−	0.178756i
$408$	−2.22536	−	3.85443i	−0.110172	−	0.190823i
$409$	15.9473	−	27.6215i	0.788541	−	1.36579i	−0.138319	−	0.990388i	$-0.544170\pi$
$409$	15.9473	−	27.6215i	0.788541	−	1.36579i	0.926861	−	0.375406i	$-0.122497\pi$
$410$	6.28547	+	1.33602i	0.310417	+	0.0659812i
$411$	0.0784533	−	0.241454i	0.00386981	−	0.0119101i
$412$	4.86782	−	1.03469i	0.239820	−	0.0509754i
$413$	−1.54248	+	14.6757i	−0.0759006	+	0.722146i
$414$	1.92525	−	2.13821i	0.0946209	−	0.105087i
$415$	−4.97203	+	2.21369i	−0.244067	+	0.108666i
$416$	2.32360	+	1.03453i	0.113924	+	0.0507221i
$417$	13.6870	+	15.2009i	0.670253	+	0.744392i
$418$	−7.87009	+	5.71795i	−0.384939	+	0.279674i
$419$	13.6619	−	9.92592i	0.667426	−	0.484913i	−0.201737	−	0.979440i	$-0.564659\pi$
$419$	13.6619	−	9.92592i	0.667426	−	0.484913i	0.869162	+	0.494527i	$0.164659\pi$
$420$	−1.47559	−	1.63881i	−0.0720013	−	0.0799656i
$421$	20.5759	+	9.16097i	1.00281	+	0.446478i	0.841402	−	0.540410i	$-0.181731\pi$
$421$	20.5759	+	9.16097i	1.00281	+	0.446478i	0.161405	+	0.986888i	$0.448398\pi$
$422$	−8.73870	+	3.89072i	−0.425393	+	0.189397i
$423$	−1.02208	+	1.13513i	−0.0496952	+	0.0551921i
$424$	−0.718888	+	6.83977i	−0.0349123	+	0.332168i
$425$	−4.35346	+	0.925355i	−0.211174	+	0.0448863i
$426$	1.34177	−	4.12954i	0.0650089	−	0.200077i
$427$	2.43696	+	0.517991i	0.117933	+	0.0250673i
$428$	0.406123	−	0.703426i	0.0196307	−	0.0340014i
$429$	4.12201	+	7.13953i	0.199013	+	0.344700i
$430$	1.80639	+	5.55950i	0.0871119	+	0.268103i
$431$	−1.10476	−	10.5111i	−0.0532146	−	0.506303i	−0.988370	−	0.152066i	$-0.951407\pi$
$431$	−1.10476	−	10.5111i	−0.0532146	−	0.506303i	0.935156	−	0.354237i	$-0.115259\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	−16.0356			−0.770619			−0.385310	−	0.922787i	$-0.625905\pi$
$433$	−16.0356			−0.770619			−0.385310	+	0.922787i	$0.625905\pi$
$434$	−9.11341	−	8.22801i	−0.437458	−	0.394957i
$435$	−2.83916			−0.136127
$436$	10.0868	+	7.32846i	0.483068	+	0.350970i
$437$	0.902660	+	8.58824i	0.0431801	+	0.410831i
$438$	−0.992911	−	3.05587i	−0.0474431	−	0.146015i
$439$	6.87153	+	11.9018i	0.327960	+	0.568044i	0.982107	−	0.188324i	$-0.0603054\pi$
$439$	6.87153	+	11.9018i	0.327960	+	0.568044i	−0.654147	+	0.756368i	$0.726972\pi$
$440$	1.62061	−	2.80698i	0.0772596	−	0.133817i
$441$	2.09026	+	0.444298i	0.0995360	+	0.0211570i
$442$	3.49818	−	10.7663i	0.166392	−	0.512101i
$443$	−17.0129	+	3.61620i	−0.808305	+	0.171811i	−0.593487	−	0.804843i	$-0.702249\pi$
$443$	−17.0129	+	3.61620i	−0.808305	+	0.171811i	−0.214818	+	0.976654i	$0.568916\pi$
$444$	0.122286	−	1.16347i	0.00580344	−	0.0552161i
$445$	−4.27618	+	4.74918i	−0.202710	+	0.225133i
$446$	6.64466	−	2.95839i	0.314634	−	0.140084i
$447$	6.04822	+	2.69284i	0.286071	+	0.127367i
$448$	−1.47559	−	1.63881i	−0.0697150	−	0.0774263i
$449$	−6.72432	+	4.88551i	−0.317340	+	0.230561i	−0.735040	−	0.678024i	$-0.762837\pi$
$449$	−6.72432	+	4.88551i	−0.317340	+	0.230561i	0.417699	+	0.908585i	$0.362837\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	13.9365	+	15.4780i	0.656242	+	0.728831i
$452$	11.8265	+	5.26549i	0.556271	+	0.247668i
$453$	−9.87314	+	4.39581i	−0.463881	+	0.206533i
$454$	−3.59576	+	3.99350i	−0.168757	+	0.187424i
$455$	0.586299	−	5.57826i	0.0274861	−	0.261513i
$456$	−2.93574	+	0.624011i	−0.137479	+	0.0292220i
$457$	−4.40421	+	13.5548i	−0.206020	+	0.634065i	0.793650	+	0.608375i	$0.208178\pi$
$457$	−4.40421	+	13.5548i	−0.206020	+	0.634065i	−0.999670	+	0.0256900i	$0.991822\pi$
$458$	26.0264	+	5.53209i	1.21613	+	0.258497i
$459$	2.22536	−	3.85443i	0.103871	−	0.179909i
$460$	−1.43862	−	2.49176i	−0.0670761	−	0.116179i
$461$	3.42950	+	10.5549i	0.159728	+	0.491591i	0.998609	−	0.0527230i	$-0.0167900\pi$
$461$	3.42950	+	10.5549i	0.159728	+	0.491591i	−0.838882	+	0.544314i	$0.816790\pi$
$462$	−0.747132	−	7.10849i	−0.0347597	−	0.330717i
$463$	−13.0994	−	9.51727i	−0.608780	−	0.442305i	0.240204	−	0.970722i	$-0.422786\pi$
$463$	−13.0994	−	9.51727i	−0.608780	−	0.442305i	−0.848985	+	0.528418i	$0.822786\pi$
$464$	−2.83916			−0.131805
$465$	4.14267	−	3.71998i	0.192112	−	0.172510i
$466$	−5.01581			−0.232353
$467$	18.9717	+	13.7838i	0.877906	+	0.637836i	0.932697	−	0.360662i	$-0.117449\pi$
$467$	18.9717	+	13.7838i	0.877906	+	0.637836i	−0.0547907	+	0.998498i	$0.517449\pi$
$468$	0.265867	+	2.52956i	0.0122897	+	0.116929i
$469$	−6.44998	−	19.8510i	−0.297832	−	0.916634i
$470$	0.763737	+	1.32283i	0.0352285	+	0.0610176i
$471$	5.17508	−	8.96349i	0.238455	−	0.413016i
$472$	−6.54540	−	1.39127i	−0.301276	−	0.0640382i
$473$	−5.85491	+	18.0196i	−0.269209	+	0.828541i
$474$	−13.9596	+	2.96721i	−0.641188	+	0.136289i
$475$	−0.313724	+	2.98489i	−0.0143947	+	0.136956i
$476$	−6.56742	+	7.29386i	−0.301017	+	0.334313i
$477$	−6.28286	+	2.79731i	−0.287672	+	0.128080i
$478$	−4.51203	−	2.00888i	−0.206375	−	0.0918842i
$479$	−6.54314	−	7.26689i	−0.298964	−	0.332033i	0.574882	−	0.818236i	$-0.305048\pi$
$479$	−6.54314	−	7.26689i	−0.298964	−	0.332033i	−0.873846	+	0.486204i	$0.838381\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	2.40730	−	1.74901i	0.109764	−	0.0797479i
$482$	−5.36511	−	5.95856i	−0.244374	−	0.271405i
$483$	−5.79643	−	2.58074i	−0.263747	−	0.117428i
$484$	−0.451738	+	0.201127i	−0.0205336	+	0.00914213i
$485$	6.85524	−	7.61351i	0.311280	−	0.345712i
$486$	−0.104528	+	0.994522i	−0.00474151	+	0.0451124i
$487$	−23.7805	+	5.05470i	−1.07760	+	0.229050i	−0.712324	−	0.701851i	$-0.752357\pi$
$487$	−23.7805	+	5.05470i	−1.07760	+	0.229050i	−0.365272	+	0.930901i	$0.619024\pi$
$488$	−0.349117	+	1.07447i	−0.0158038	+	0.0486391i
$489$	7.17728	+	1.52558i	0.324568	+	0.0689890i
$490$	1.06848	−	1.85066i	0.0482689	−	0.0836041i
$491$	−14.5566	−	25.2127i	−0.656929	−	1.13784i	−0.981406	−	0.191942i	$-0.938522\pi$
$491$	−14.5566	−	25.2127i	−0.656929	−	1.13784i	0.324477	−	0.945894i	$-0.394812\pi$
$492$	1.98571	+	6.11138i	0.0895227	+	0.275522i
$493$	1.32085	+	12.5671i	0.0594882	+	0.565992i
$494$	−6.17592	−	4.48707i	−0.277868	−	0.201883i
$495$	3.24122			0.145682
$496$	4.14267	−	3.71998i	0.186011	−	0.167032i
$497$	−9.57523			−0.429508
$498$	−4.40312	−	3.19906i	−0.197309	−	0.143353i
$499$	3.05373	+	29.0543i	0.136704	+	1.30065i	0.820782	+	0.571241i	$0.193538\pi$
$499$	3.05373	+	29.0543i	0.136704	+	1.30065i	−0.684079	+	0.729408i	$0.739796\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	−0.427235	−	0.739992i	−0.0190874	−	0.0330604i
$502$	5.00589	−	8.67046i	0.223424	−	0.386981i
$503$	−2.83340	−	0.602257i	−0.126335	−	0.0268533i	0.144310	−	0.989532i	$-0.453904\pi$
$503$	−2.83340	−	0.602257i	−0.126335	−	0.0268533i	−0.270645	+	0.962679i	$0.587237\pi$
$504$	0.681454	−	2.09730i	0.0303544	−	0.0934212i
$505$	8.66424	−	1.84164i	0.385553	−	0.0819519i
$506$	0.974809	−	9.27469i	0.0433356	−	0.412310i
$507$	4.36985	−	4.85321i	0.194072	−	0.215539i
$508$	6.32473	−	2.81595i	0.280614	−	0.124938i
$509$	−27.4089	−	12.2032i	−1.21488	−	0.540899i	−0.303644	−	0.952786i	$-0.598203\pi$
$509$	−27.4089	−	12.2032i	−1.21488	−	0.540899i	−0.911235	+	0.411886i	$0.864870\pi$
$510$	−2.97811	−	3.30752i	−0.131873	−	0.146460i
$511$	−5.73244	+	4.16486i	−0.253588	+	0.184243i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.00828	−	2.23042i	−0.0886677	−	0.0984755i
$514$	1.24912	+	0.556143i	0.0550962	+	0.0245304i
$515$	4.54632	−	2.02415i	0.200335	−	0.0891948i
$516$	−3.91147	+	4.34413i	−0.172193	+	0.191240i
$517$	−0.517508	+	4.92376i	−0.0227600	+	0.216547i
$518$	−2.52349	+	0.536384i	−0.110876	+	0.0235674i
$519$	−3.06103	+	9.42088i	−0.134364	+	0.413531i
$520$	2.48791	+	0.528822i	0.109102	+	0.0231904i
$521$	12.4162	−	21.5054i	0.543962	−	0.942170i	−0.454710	−	0.890640i	$-0.650257\pi$
$521$	12.4162	−	21.5054i	0.543962	−	0.942170i	0.998671	−	0.0515298i	$-0.0164097\pi$
$522$	−1.41958	−	2.45878i	−0.0621333	−	0.107618i
$523$	−3.81541	−	11.7426i	−0.166836	−	0.513469i	0.832331	−	0.554279i	$-0.187006\pi$
$523$	−3.81541	−	11.7426i	−0.166836	−	0.513469i	−0.999167	+	0.0408105i	$0.987006\pi$
$524$	1.56237	+	14.8650i	0.0682525	+	0.649379i
$525$	−1.78407	−	1.29620i	−0.0778632	−	0.0565709i
$526$	0.347268			0.0151416
$527$	−18.3932	−	16.6062i	−0.801219	−	0.723378i
$528$	3.24122			0.141056
$529$	11.9099	+	8.65307i	0.517823	+	0.376220i
$530$	0.718888	+	6.83977i	0.0312265	+	0.297100i
$531$	−2.06783	−	6.36411i	−0.0897360	−	0.276179i
$532$	3.30931	+	5.73189i	0.143477	+	0.248509i
$533$	−8.17210	+	14.1545i	−0.353973	+	0.613099i
$534$	−6.25100	−	1.32869i	−0.270507	−	0.0574981i
$535$	0.250998	−	0.772493i	0.0108516	−	0.0333978i
$536$	9.25819	−	1.96789i	0.399893	−	0.0849999i
$537$	−2.43074	+	23.1269i	−0.104894	+	0.998000i
$538$	−10.3289	+	11.4714i	−0.445311	+	0.494568i
$539$	6.32752	−	2.81720i	0.272546	−	0.121345i
$540$	0.913545	+	0.406737i	0.0393127	+	0.0175032i
$541$	−15.6370	−	17.3667i	−0.672288	−	0.746651i	0.306423	−	0.951895i	$-0.400868\pi$
$541$	−15.6370	−	17.3667i	−0.672288	−	0.746651i	−0.978711	+	0.205244i	$0.934201\pi$
$542$	−14.3659	+	10.4375i	−0.617069	+	0.448327i
$543$	9.88235	−	7.17994i	0.424092	−	0.308121i
$544$	−2.97811	−	3.30752i	−0.127685	−	0.141809i
$545$	11.3900	+	5.07116i	0.487895	+	0.217225i
$546$	5.12407	−	2.28138i	0.219290	−	0.0976341i
$547$	14.2821	−	15.8619i	0.610660	−	0.678207i	−0.355936	−	0.934510i	$-0.615838\pi$
$547$	14.2821	−	15.8619i	0.610660	−	0.678207i	0.966596	+	0.256304i	$0.0825047\pi$
$548$	0.0265377	−	0.252489i	0.00113363	−	0.0107858i
$549$	−1.10508	+	0.234892i	−0.0471636	+	0.0100249i
$550$	1.00159	−	3.08258i	0.0427080	−	0.131442i
$551$	8.33504	+	1.77167i	0.355085	+	0.0754755i
$552$	1.43862	−	2.49176i	0.0612318	−	0.106057i
$553$	15.7360	+	27.2555i	0.669162	+	1.15902i
$554$	−0.0830383	−	0.255566i	−0.00352796	−	0.0108579i
$555$	−0.122286	−	1.16347i	−0.00519076	−	0.0493868i
$556$	16.5483	+	12.0231i	0.701805	+	0.509891i
$557$	−41.6972			−1.76677			−0.883383	−	0.468651i	$-0.844740\pi$
$557$	−41.6972			−1.76677			−0.883383	+	0.468651i	$0.844740\pi$
$558$	5.29294	+	1.72767i	0.224068	+	0.0731380i
$559$	−14.8683			−0.628860
$560$	−1.78407	−	1.29620i	−0.0753907	−	0.0547746i
$561$	−1.50790	−	14.3467i	−0.0636636	−	0.605719i
$562$	−3.52415	−	10.8462i	−0.148657	−	0.457520i
$563$	−15.3012	−	26.5025i	−0.644869	−	1.11695i	−0.984332	−	0.176327i	$-0.943579\pi$
$563$	−15.3012	−	26.5025i	−0.644869	−	1.11695i	0.339463	−	0.940620i	$-0.389755\pi$
$564$	−0.763737	+	1.32283i	−0.0321591	+	0.0557012i
$565$	12.6628	+	2.69156i	0.532728	+	0.113235i
$566$	0.652925	−	2.00950i	0.0274445	−	0.0844655i
$567$	2.15704	−	0.458493i	0.0905873	−	0.0192549i
$568$	0.453868	−	4.31827i	0.0190439	−	0.181190i
$569$	−25.6365	+	28.4722i	−1.07474	+	1.19362i	−0.0945540	+	0.995520i	$0.530142\pi$
$569$	−25.6365	+	28.4722i	−1.07474	+	1.19362i	−0.980183	+	0.198096i	$0.936524\pi$
$570$	−2.74185	+	1.22075i	−0.114843	+	0.0511316i
$571$	42.6926	+	19.0080i	1.78663	+	0.795460i	0.978437	+	0.206544i	$0.0662215\pi$
$571$	42.6926	+	19.0080i	1.78663	+	0.795460i	0.808194	+	0.588916i	$0.200445\pi$
$572$	5.51633	+	6.12650i	0.230649	+	0.256162i
$573$	−12.2848	+	8.92541i	−0.513204	+	0.372864i
$574$	11.4642	−	8.32925i	0.478508	−	0.347656i
$575$	−1.92525	−	2.13821i	−0.0802885	−	0.0891694i
$576$	0.913545	+	0.406737i	0.0380644	+	0.0169474i
$577$	5.99290	−	2.66821i	0.249488	−	0.111079i	−0.278183	−	0.960528i	$-0.589732\pi$
$577$	5.99290	−	2.66821i	0.249488	−	0.111079i	0.527671	+	0.849449i	$0.323066\pi$
$578$	−1.87949	+	2.08739i	−0.0781765	+	0.0868238i
$579$	1.88025	−	17.8894i	0.0781404	−	0.743456i
$580$	−2.77712	+	0.590294i	−0.115314	+	0.0245106i
$581$	−3.70886	+	11.4147i	−0.153869	+	0.473561i
$582$	10.0211	+	2.13005i	0.415389	+	0.0882936i
$583$	−11.1457	+	19.3048i	−0.461606	+	0.799525i
$584$	−1.60656	−	2.78265i	−0.0664801	−	0.115147i
$585$	0.785983	+	2.41901i	0.0324964	+	0.100014i
$586$	1.72450	+	16.4075i	0.0712384	+	0.677788i
$587$	−12.2337	−	8.88829i	−0.504938	−	0.366859i	0.305962	−	0.952044i	$-0.401022\pi$
$587$	−12.2337	−	8.88829i	−0.504938	−	0.366859i	−0.810900	+	0.585185i	$0.801022\pi$
$588$	2.13695			0.0881265
$589$	−14.4831	+	8.33584i	−0.596767	+	0.343472i
$590$	−6.69162			−0.275490
$591$	9.22851	+	6.70490i	0.379610	+	0.275803i
$592$	−0.122286	−	1.16347i	−0.00502593	−	0.0478185i
$593$	−2.60761	−	8.02541i	−0.107082	−	0.329564i	0.883132	−	0.469125i	$-0.155431\pi$
$593$	−2.60761	−	8.02541i	−0.107082	−	0.329564i	−0.990213	+	0.139561i	$0.955431\pi$
$594$	1.62061	+	2.80698i	0.0664944	+	0.115172i
$595$	−4.90743	+	8.49991i	−0.201185	+	0.348462i
$596$	6.47593	+	1.37650i	0.265264	+	0.0563837i
$597$	−2.16649	+	6.66777i	−0.0886686	+	0.272894i
$598$	7.15832	−	1.52155i	0.292726	−	0.0622208i
$599$	−0.690179	+	6.56662i	−0.0282000	+	0.268305i	0.971332	+	0.237725i	$0.0764019\pi$
$599$	−0.690179	+	6.56662i	−0.0282000	+	0.268305i	−0.999532	+	0.0305792i	$0.990265\pi$
$600$	0.669131	−	0.743145i	0.0273171	−	0.0303388i
$601$	15.6054	−	6.94799i	0.636559	−	0.283415i	−0.0629731	−	0.998015i	$-0.520058\pi$
$601$	15.6054	−	6.94799i	0.636559	−	0.283415i	0.699533	+	0.714601i	$0.253392\pi$
$602$	11.7764	+	5.24321i	0.479972	+	0.213697i
$603$	6.33334	+	7.03389i	0.257914	+	0.286442i
$604$	−8.74345	+	6.35249i	−0.355766	+	0.258479i
$605$	−0.400050	+	0.290653i	−0.0162644	+	0.0118167i
$606$	5.92703	+	6.58263i	0.240769	+	0.267401i
$607$	7.44836	+	3.31622i	0.302320	+	0.134601i	0.552290	−	0.833652i	$-0.313754\pi$
$607$	7.44836	+	3.31622i	0.302320	+	0.134601i	−0.249970	+	0.968254i	$0.580421\pi$
$608$	−2.74185	+	1.22075i	−0.111197	+	0.0495079i
$609$	−4.18943	+	4.65283i	−0.169764	+	0.188542i
$610$	−0.118093	+	1.12358i	−0.00478144	+	0.0454924i
$611$	−3.80022	+	0.807761i	−0.153740	+	0.0326785i
$612$	1.37535	−	4.23288i	0.0555951	−	0.171104i
$613$	11.0001	+	2.33813i	0.444288	+	0.0944363i	0.424623	−	0.905370i	$-0.360407\pi$
$613$	11.0001	+	2.33813i	0.444288	+	0.0944363i	0.0196651	+	0.999807i	$0.493740\pi$
$614$	−3.15678	+	5.46771i	−0.127397	+	0.220659i
$615$	3.21294	+	5.56498i	0.129558	+	0.224402i
$616$	−2.20874	−	6.79781i	−0.0889928	−	0.273892i
$617$	3.99951	+	38.0528i	0.161014	+	1.53195i	0.714825	+	0.699304i	$0.246507\pi$
$617$	3.99951	+	38.0528i	0.161014	+	1.53195i	−0.553811	+	0.832643i	$0.686827\pi$
$618$	4.02613	+	2.92515i	0.161955	+	0.117667i
$619$	26.0435			1.04678			0.523388	−	0.852095i	$-0.324668\pi$
$619$	26.0435			1.04678			0.523388	+	0.852095i	$0.324668\pi$
$620$	3.27872	−	4.50000i	0.131676	−	0.180724i
$621$	2.87724			0.115460
$622$	−23.0175	−	16.7232i	−0.922916	−	0.670538i
$623$	1.47311	+	14.0157i	0.0590187	+	0.561526i
$624$	0.785983	+	2.41901i	0.0314645	+	0.0968377i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	16.6965	−	28.9193i	0.667328	−	1.15585i
$627$	−9.51538	−	2.02256i	−0.380008	−	0.0807732i
$628$	3.19837	−	9.84358i	0.127629	−	0.392802i
$629$	−5.09304	+	1.08256i	−0.203073	+	0.0431644i
$630$	0.230509	−	2.19315i	0.00918372	−	0.0873772i
$631$	−19.1355	+	21.2521i	−0.761771	+	0.846032i	−0.991886	−	0.127131i	$-0.959423\pi$
$631$	−19.1355	+	21.2521i	−0.761771	+	0.846032i	0.230115	+	0.973163i	$0.426090\pi$
$632$	−13.0377	+	5.80474i	−0.518611	+	0.230900i
$633$	−8.73870	−	3.89072i	−0.347332	−	0.154642i
$634$	−19.3654	−	21.5074i	−0.769097	−	0.854168i
$635$	5.60105	−	4.06940i	0.222271	−	0.161489i
$636$	−5.56397	+	4.04246i	−0.220626	+	0.160294i
$637$	3.63694	+	4.03923i	0.144101	+	0.160040i
$638$	−8.40676	−	3.74293i	−0.332827	−	0.148184i
$639$	3.96666	−	1.76607i	0.156919	−	0.0698647i
$640$	0.669131	−	0.743145i	0.0264497	−	0.0293754i
$641$	4.08181	−	38.8358i	0.161222	−	1.53392i	−0.552512	−	0.833505i	$-0.686330\pi$
$641$	4.08181	−	38.8358i	0.161222	−	1.53392i	0.713733	−	0.700418i	$-0.247003\pi$
$642$	0.794497	−	0.168876i	0.0313563	−	0.00666499i
$643$	3.15197	−	9.70078i	0.124302	−	0.382561i	−0.869472	−	0.493983i	$-0.835540\pi$
$643$	3.15197	−	9.70078i	0.124302	−	0.382561i	0.993773	+	0.111422i	$0.0355405\pi$
$644$	−6.20633	−	1.31920i	−0.244564	−	0.0519836i
$645$	−2.92280	+	5.06244i	−0.115085	+	0.199334i
$646$	6.67902	+	11.5684i	0.262783	+	0.455153i
$647$	1.21961	+	3.75358i	0.0479479	+	0.147568i	0.972164	−	0.234301i	$-0.0752803\pi$
$647$	1.21961	+	3.75358i	0.0479479	+	0.147568i	−0.924216	+	0.381870i	$0.875280\pi$
$648$	0.104528	+	0.994522i	0.00410627	+	0.0390685i
$649$	−17.5468	−	12.7485i	−0.688772	−	0.500422i
$650$	2.54349			0.0997640
$651$	0.0165428	−	12.2782i	0.000648364	−	0.481221i
$652$	7.33762			0.287364
$653$	−23.5182	−	17.0870i	−0.920338	−	0.668665i	0.0232700	−	0.999729i	$-0.492592\pi$
$653$	−23.5182	−	17.0870i	−0.920338	−	0.668665i	−0.943608	+	0.331064i	$0.892592\pi$
$654$	1.30325	+	12.3996i	0.0509612	+	0.484864i
$655$	4.61883	+	14.2153i	0.180473	+	0.555437i
$656$	3.21294	+	5.56498i	0.125444	+	0.217276i
$657$	1.60656	−	2.78265i	0.0626780	−	0.108561i
$658$	3.29482	+	0.700336i	0.128446	+	0.0273020i
$659$	−11.2559	+	34.6421i	−0.438468	+	1.34947i	0.451022	+	0.892513i	$0.351059\pi$
$659$	−11.2559	+	34.6421i	−0.438468	+	1.34947i	−0.889490	+	0.456954i	$0.848941\pi$
$660$	3.17039	−	0.673888i	0.123407	−	0.0262310i
$661$	−2.28073	+	21.6997i	−0.0887102	+	0.844021i	0.856190	+	0.516662i	$0.172825\pi$
$661$	−2.28073	+	21.6997i	−0.0887102	+	0.844021i	−0.944900	+	0.327359i	$0.893841\pi$
$662$	−22.9987	+	25.5427i	−0.893871	+	0.992745i
$663$	10.3417	−	4.60440i	0.401637	−	0.178820i
$664$	−4.97203	−	2.21369i	−0.192952	−	0.0859078i
$665$	4.42872	+	4.91859i	0.171738	+	0.190735i
$666$	0.946456	−	0.687640i	0.0366744	−	0.0266455i
$667$	−6.60882	+	4.80159i	−0.255895	+	0.185918i
$668$	−0.571751	−	0.634994i	−0.0221217	−	0.0245687i
$669$	6.64466	+	2.95839i	0.256898	+	0.114378i
$670$	8.64673	−	3.84977i	0.334052	−	0.148730i
$671$	−2.45024	+	2.72127i	−0.0945905	+	0.105053i
$672$	0.230509	−	2.19315i	0.00889210	−	0.0846026i
$673$	−11.4851	+	2.44122i	−0.442716	+	0.0941022i	−0.423876	−	0.905720i	$-0.639331\pi$
$673$	−11.4851	+	2.44122i	−0.442716	+	0.0941022i	−0.0188403	+	0.999823i	$0.505997\pi$
$674$	7.20447	−	22.1731i	0.277506	−	0.854076i
$675$	0.978148	+	0.207912i	0.0376489	+	0.00800252i
$676$	3.26532	−	5.65570i	0.125589	−	0.217527i
$677$	6.15283	+	10.6570i	0.236473	+	0.409583i	0.959700	−	0.281028i	$-0.0906753\pi$
$677$	6.15283	+	10.6570i	0.236473	+	0.409583i	−0.723227	+	0.690610i	$0.757342\pi$
$678$	4.00044	+	12.3121i	0.153636	+	0.472843i
$679$	−2.36157	−	22.4688i	−0.0906287	−	0.862274i
$680$	−3.60070	−	2.61606i	−0.138081	−	0.100321i
$681$	−5.37378			−0.205924
$682$	17.1706	−	5.55350i	0.657496	−	0.212655i
$683$	−23.5632			−0.901619			−0.450809	−	0.892620i	$-0.648865\pi$
$683$	−23.5632			−0.901619			−0.450809	+	0.892620i	$0.648865\pi$
$684$	−2.42812	−	1.76414i	−0.0928417	−	0.0674534i
$685$	−0.0265377	−	0.252489i	−0.00101395	−	0.00964712i
$686$	−6.22641	−	19.1629i	−0.237726	−	0.731644i
$687$	13.3039	+	23.0431i	0.507577	+	0.879149i
$688$	−2.92280	+	5.06244i	−0.111431	+	0.193004i
$689$	−17.1105	−	3.63694i	−0.651857	−	0.138556i
$690$	0.889117	−	2.73642i	0.0338481	−	0.104174i
$691$	31.9386	−	6.78876i	1.21500	−	0.258257i	0.444550	−	0.895754i	$-0.353364\pi$
$691$	31.9386	−	6.78876i	1.21500	−	0.258257i	0.770452	+	0.637497i	$0.220030\pi$
$692$	−1.03543	+	9.85143i	−0.0393610	+	0.374495i
$693$	4.78271	−	5.31173i	0.181680	−	0.201776i
$694$	−21.0825	+	9.38655i	−0.800282	+	0.356308i
$695$	18.6864	+	8.31973i	0.708816	+	0.315585i
$696$	−1.89977	−	2.10991i	−0.0720105	−	0.0799758i
$697$	23.1377	−	16.8105i	0.876403	−	0.636744i
$698$	−10.9403	+	7.94863i	−0.414098	+	0.300860i
$699$	−3.35623	−	3.72748i	−0.126944	−	0.140986i
$700$	−2.01458	−	0.896949i	−0.0761439	−	0.0339015i
$701$	−28.2573	+	12.5810i	−1.06726	+	0.475176i	−0.863763	−	0.503899i	$-0.831898\pi$
$701$	−28.2573	+	12.5810i	−1.06726	+	0.475176i	−0.203500	+	0.979075i	$0.565232\pi$
$702$	−1.70193	+	1.89018i	−0.0642352	+	0.0713404i
$703$	−0.367021	+	3.49197i	−0.0138424	+	0.131702i
$704$	3.17039	−	0.673888i	0.119489	−	0.0253981i
$705$	−0.472015	+	1.45271i	−0.0177771	+	0.0547123i
$706$	−12.9570	−	2.75410i	−0.487645	−	0.103652i
$707$	9.76675	−	16.9165i	0.367316	−	0.636211i
$708$	−3.34581	−	5.79512i	−0.125743	−	0.217794i
$709$	9.15006	+	28.1610i	0.343638	+	1.05761i	0.962309	+	0.271958i	$0.0876712\pi$
$709$	9.15006	+	28.1610i	0.343638	+	1.05761i	−0.618672	+	0.785650i	$0.712329\pi$
$710$	−0.453868	−	4.31827i	−0.0170334	−	0.162062i
$711$	−11.5459	−	8.38858i	−0.433005	−	0.314596i
$712$	−6.39065			−0.239500
$713$	3.35181	−	15.6652i	0.125526	−	0.586668i
$714$	−9.81485			−0.367312
$715$	6.66955	+	4.84571i	0.249427	+	0.181219i
$716$	2.43074	+	23.1269i	0.0908409	+	0.864293i
$717$	−1.52624	−	4.69730i	−0.0569986	−	0.175424i
$718$	16.0455	+	27.7917i	0.598814	+	1.03718i
$719$	−14.3246	+	24.8109i	−0.534217	+	0.925291i	0.464984	+	0.885319i	$0.346060\pi$
$719$	−14.3246	+	24.8109i	−0.534217	+	0.925291i	−0.999201	+	0.0399721i	$0.987273\pi$
$720$	0.978148	+	0.207912i	0.0364534	+	0.00774841i
$721$	3.39130	−	10.4374i	0.126299	−	0.388708i
$722$	−9.77368	+	2.07746i	−0.363739	+	0.0773151i
$723$	0.838113	−	7.97411i	0.0311698	−	0.296560i
$724$	8.17360	−	9.07770i	0.303769	−	0.337370i
$725$	−2.59370	+	1.15479i	−0.0963277	+	0.0428878i
$726$	−0.451738	−	0.201127i	−0.0167656	−	0.00746452i
$727$	7.16065	+	7.95271i	0.265574	+	0.294950i	0.861152	−	0.508348i	$-0.169744\pi$
$727$	7.16065	+	7.95271i	0.265574	+	0.294950i	−0.595578	+	0.803297i	$0.703077\pi$
$728$	4.53777	−	3.29688i	0.168181	−	0.122191i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−2.15000	−	2.38782i	−0.0795751	−	0.0883771i
$731$	23.7678	+	10.5821i	0.879085	+	0.391394i
$732$	−1.03209	+	0.459518i	−0.0381473	+	0.0169843i
$733$	2.22220	−	2.46801i	0.0820790	−	0.0911580i	−0.700706	−	0.713450i	$-0.747132\pi$
$733$	2.22220	−	2.46801i	0.0820790	−	0.0911580i	0.782785	+	0.622292i	$0.213798\pi$
$734$	0.900871	−	8.57121i	0.0332517	−	0.316369i
$735$	2.09026	−	0.444298i	0.0771003	−	0.0163882i
$736$	0.889117	−	2.73642i	0.0327733	−	0.100866i
$737$	30.0079	+	6.37837i	1.10535	+	0.234950i
$738$	−3.21294	+	5.56498i	−0.118270	+	0.204850i
$739$	−5.39717	−	9.34816i	−0.198538	−	0.343878i	0.749517	−	0.661985i	$-0.230286\pi$
$739$	−5.39717	−	9.34816i	−0.198538	−	0.343878i	−0.948055	+	0.318108i	$0.896953\pi$
$740$	−0.361514	−	1.11263i	−0.0132895	−	0.0409009i
$741$	−0.797955	−	7.59204i	−0.0293136	−	0.278900i
$742$	12.2698	+	8.91456i	0.450440	+	0.327264i
$743$	4.95238			0.181685			0.0908426	−	0.995865i	$-0.471044\pi$
$743$	4.95238			0.181685			0.0908426	+	0.995865i	$0.471044\pi$
$744$	5.53647	+	0.589450i	0.202977	+	0.0216103i
$745$	6.62060			0.242560
$746$	−10.3020	−	7.48488i	−0.377185	−	0.274041i
$747$	−0.568903	−	5.41275i	−0.0208151	−	0.198042i
$748$	−4.45780	−	13.7197i	−0.162993	−	0.501642i
$749$	−0.895596	−	1.55122i	−0.0327244	−	0.0566803i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−4.46239	−	0.948511i	−0.162835	−	0.0346116i	0.125773	−	0.992059i	$-0.459859\pi$
$751$	−4.46239	−	0.948511i	−0.162835	−	0.0346116i	−0.288608	+	0.957447i	$0.593192\pi$
$752$	−0.472015	+	1.45271i	−0.0172126	+	0.0529750i
$753$	9.79300	−	2.08157i	0.356877	−	0.0758565i
$754$	0.754840	−	7.18182i	0.0274897	−	0.261547i
$755$	−7.23163	+	8.03154i	−0.263186	+	0.292298i
$756$	2.01458	−	0.896949i	0.0732695	−	0.0326217i
$757$	24.8203	+	11.0507i	0.902109	+	0.401645i	0.804757	−	0.593605i	$-0.202296\pi$
$757$	24.8203	+	11.0507i	0.902109	+	0.401645i	0.0973528	+	0.995250i	$0.468962\pi$
$758$	−21.8719	−	24.2912i	−0.794422	−	0.882295i
$759$	7.54471	−	5.48155i	0.273856	−	0.198968i
$760$	−2.42812	+	1.76414i	−0.0880773	+	0.0639919i
$761$	−6.82206	−	7.57667i	−0.247300	−	0.274654i	0.606696	−	0.794934i	$-0.292494\pi$
$761$	−6.82206	−	7.57667i	−0.247300	−	0.274654i	−0.853996	+	0.520280i	$0.825828\pi$
$762$	6.32473	+	2.81595i	0.229121	+	0.102011i
$763$	25.1176	−	11.1831i	0.909319	−	0.404855i
$764$	−10.1606	+	11.2845i	−0.367598	+	0.408259i
$765$	0.465226	−	4.42633i	0.0168203	−	0.160034i
$766$	−20.2150	+	4.29683i	−0.730397	+	0.155251i
$767$	5.25950	−	16.1871i	0.189910	−	0.584481i
$768$	0.978148	+	0.207912i	0.0352959	+	0.00750237i
$769$	3.74290	−	6.48289i	0.134972	−	0.233779i	−0.790615	−	0.612314i	$-0.790239\pi$
$769$	3.74290	−	6.48289i	0.134972	−	0.233779i	0.925587	+	0.378535i	$0.123572\pi$
$770$	−3.57382	−	6.19004i	−0.128792	−	0.223074i
$771$	0.422528	+	1.30041i	0.0152170	+	0.0468330i
$772$	−1.88025	−	17.8894i	−0.0676716	−	0.643852i
$773$	−21.8947	−	15.9074i	−0.787496	−	0.572149i	0.119723	−	0.992807i	$-0.461799\pi$
$773$	−21.8947	−	15.9074i	−0.787496	−	0.572149i	−0.907219	+	0.420658i	$0.861799\pi$
$774$	−5.84561			−0.210116
$775$	2.27146	−	5.08335i	0.0815934	−	0.182599i
$776$	10.2450			0.367774
$777$	−2.08715	−	1.51641i	−0.0748762	−	0.0544008i
$778$	−0.780705	−	7.42791i	−0.0279896	−	0.266304i
$779$	−5.95976	−	18.3423i	−0.213531	−	0.657180i
$780$	1.27175	+	2.20273i	0.0455358	+	0.0788704i
$781$	7.03678	−	12.1881i	0.251796	−	0.436123i
$782$	−12.5259	−	2.66247i	−0.447927	−	0.0952098i
$783$	0.877349	−	2.70020i	0.0313539	−	0.0964973i
$784$	2.09026	−	0.444298i	0.0746520	−	0.0158678i
$785$	1.08189	−	10.2935i	0.0386141	−	0.367389i
$786$	−10.0014	+	11.1077i	−0.356738	+	0.396197i
$787$	44.2933	−	19.7207i	1.57889	−	0.702966i	0.584762	−	0.811205i	$-0.301188\pi$
$787$	44.2933	−	19.7207i	1.57889	−	0.702966i	0.994125	+	0.108239i	$0.0345213\pi$
$788$	10.4209	+	4.63967i	0.371228	+	0.165281i
$789$	0.232368	+	0.258071i	0.00827252	+	0.00918756i
$790$	−11.5459	+	8.38858i	−0.410784	+	0.298452i
$791$	23.0960	−	16.7802i	0.821200	−	0.596637i
$792$	2.16880	+	2.40870i	0.0770649	+	0.0855893i
$793$	−2.62512	−	1.16878i	−0.0932209	−	0.0415046i
$794$	9.35041	−	4.16307i	0.331834	−	0.147742i
$795$	−4.60191	+	5.11094i	−0.163213	+	0.181266i
$796$	−0.732840	+	6.97251i	−0.0259748	+	0.247134i
$797$	17.7068	−	3.76370i	0.627207	−	0.133317i	0.116667	−	0.993171i	$-0.462779\pi$
$797$	17.7068	−	3.76370i	0.627207	−	0.133317i	0.510540	+	0.859854i	$0.329446\pi$
$798$	−2.04527	+	6.29468i	−0.0724017	+	0.222829i
$799$	6.64979	+	1.41346i	0.235253	+	0.0500045i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−3.19533	−	5.53447i	−0.112901	−	0.195551i
$802$	−11.8709	−	36.5349i	−0.419177	−	1.29009i
$803$	−1.08861	−	10.3574i	−0.0384161	−	0.365505i
$804$	7.65737	+	5.56340i	0.270055	+	0.196206i
$805$	−6.34499			−0.223631
$806$	8.30852	+	11.4682i	0.292655	+	0.403949i
$807$	−15.4363			−0.543384
$808$	7.16611	+	5.20648i	0.252103	+	0.183163i
$809$	3.54917	+	33.7681i	0.124782	+	1.18722i	0.860326	+	0.509745i	$0.170260\pi$
$809$	3.54917	+	33.7681i	0.124782	+	1.18722i	−0.735543	+	0.677478i	$0.763073\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	−7.16251	−	12.4058i	−0.251510	−	0.435628i	0.712432	−	0.701741i	$-0.247594\pi$
$811$	−7.16251	−	12.4058i	−0.251510	−	0.435628i	−0.963942	+	0.266113i	$0.914260\pi$
$812$	−3.13050	+	5.42219i	−0.109859	+	0.190282i
$813$	−17.3692	−	3.69194i	−0.609165	−	0.129482i
$814$	1.17175	−	3.60626i	0.0410697	−	0.126399i
$815$	7.17728	−	1.52558i	0.251409	−	0.0534387i
$816$	0.465226	−	4.42633i	0.0162862	−	0.154953i
$817$	11.7396	−	13.0382i	0.410717	−	0.456148i
$818$	29.1371	−	12.9727i	1.01875	−	0.453579i
$819$	5.12407	+	2.28138i	0.179049	+	0.0797179i
$820$	4.29976	+	4.77537i	0.150154	+	0.166763i
$821$	8.01026	−	5.81979i	0.279560	−	0.203112i	−0.439165	−	0.898406i	$-0.644726\pi$
$821$	8.01026	−	5.81979i	0.279560	−	0.203112i	0.718725	+	0.695294i	$0.244726\pi$
$822$	0.205393	−	0.149227i	0.00716391	−	0.00520489i
$823$	20.8140	+	23.1163i	0.725531	+	0.805784i	0.987219	−	0.159369i	$-0.0509459\pi$
$823$	20.8140	+	23.1163i	0.725531	+	0.805784i	−0.261688	+	0.965152i	$0.584279\pi$
$824$	4.54632	+	2.02415i	0.158379	+	0.0705147i
$825$	2.96100	−	1.31832i	0.103089	−	0.0458981i
$826$	−9.87408	+	10.9663i	−0.343563	+	0.381566i
$827$	5.81701	−	55.3451i	0.202277	−	1.92454i	−0.150081	−	0.988674i	$-0.547954\pi$
$827$	5.81701	−	55.3451i	0.202277	−	1.92454i	0.352358	−	0.935865i	$-0.385380\pi$
$828$	2.81437	−	0.598212i	0.0978060	−	0.0207893i
$829$	1.81616	−	5.58956i	0.0630778	−	0.194133i	−0.914551	−	0.404470i	$-0.867456\pi$
$829$	1.81616	−	5.58956i	0.0630778	−	0.194133i	0.977629	+	0.210337i	$0.0674560\pi$
$830$	−5.32363	−	1.13157i	−0.184786	−	0.0392774i
$831$	0.134359	−	0.232716i	0.00466086	−	0.00807284i
$832$	1.27175	+	2.20273i	0.0440899	+	0.0763659i
$833$	−2.93905	−	9.04547i	−0.101832	−	0.313407i
$834$	2.13811	+	20.3428i	0.0740368	+	0.704413i
$835$	−0.691280	−	0.502244i	−0.0239227	−	0.0173809i
$836$	−9.72796			−0.336449
$837$	2.25776	+	5.08945i	0.0780396	+	0.175917i
$838$	16.8870			0.583351
$839$	4.09380	+	2.97432i	0.141334	+	0.102685i	0.656205	−	0.754582i	$-0.272160\pi$
$839$	4.09380	+	2.97432i	0.141334	+	0.102685i	−0.514872	+	0.857267i	$0.672160\pi$
$840$	−0.230509	−	2.19315i	−0.00795333	−	0.0756709i
$841$	−6.47056	−	19.9143i	−0.223123	−	0.686701i
$842$	11.2615	+	19.5056i	0.388099	+	0.672206i
$843$	5.70220	−	9.87649i	0.196394	−	0.340165i
$844$	−9.35667	−	1.98882i	−0.322070	−	0.0684581i
$845$	2.01808	−	6.21101i	0.0694241	−	0.213665i
$846$	−1.49409	+	0.317580i	−0.0513680	+	0.0109186i
$847$	−0.113984	+	1.08449i	−0.00391655	+	0.0372635i
$848$	−4.60191	+	5.11094i	−0.158030	+	0.175510i
$849$	1.93024	−	0.859398i	0.0662457	−	0.0294945i
$850$	−4.06593	−	1.81027i	−0.139460	−	0.0620917i
$851$	−2.25232	−	2.50145i	−0.0772085	−	0.0857487i
$852$	3.51280	−	2.55220i	0.120346	−	0.0874368i
$853$	30.5096	−	22.1665i	1.04463	−	0.758967i	0.0734444	−	0.997299i	$-0.476601\pi$
$853$	30.5096	−	22.1665i	1.04463	−	0.758967i	0.971184	+	0.238333i	$0.0766009\pi$
$854$	1.66707	+	1.85147i	0.0570460	+	0.0633560i
$855$	−2.74185	−	1.22075i	−0.0937693	−	0.0417488i
$856$	0.742024	−	0.330371i	0.0253619	−	0.0112918i
$857$	34.2512	−	38.0398i	1.17000	−	1.29941i	0.224243	−	0.974533i	$-0.428009\pi$
$857$	34.2512	−	38.0398i	1.17000	−	1.29941i	0.945755	−	0.324881i	$-0.105324\pi$
$858$	−0.861735	+	8.19886i	−0.0294191	+	0.279904i
$859$	−14.0047	+	2.97679i	−0.477834	+	0.101567i	−0.440531	−	0.897737i	$-0.645210\pi$
$859$	−14.0047	+	2.97679i	−0.477834	+	0.101567i	−0.0373029	+	0.999304i	$0.511877\pi$
$860$	−1.80639	+	5.55950i	−0.0615974	+	0.189577i
$861$	13.8609	+	2.94623i	0.472379	+	0.100407i
$862$	5.28451	−	9.15303i	0.179991	−	0.311754i
$863$	−9.54990	−	16.5409i	−0.325082	−	0.563059i	0.656447	−	0.754372i	$-0.272059\pi$
$863$	−9.54990	−	16.5409i	−0.325082	−	0.563059i	−0.981529	+	0.191313i	$0.938725\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	1.03543	+	9.85143i	0.0352056	+	0.334959i
$866$	−12.9730	−	9.42546i	−0.440842	−	0.320290i
$867$	−2.80885			−0.0953937
$868$	−2.53660	−	12.0133i	−0.0860978	−	0.407759i
$869$	−46.2571			−1.56916
$870$	−2.29693	−	1.66882i	−0.0778732	−	0.0565782i
$871$	2.51644	+	23.9424i	0.0852664	+	0.811256i
$872$	3.85280	+	11.8577i	0.130472	+	0.401552i
$873$	5.12250	+	8.87242i	0.173370	+	0.300286i
$874$	−4.31777	+	7.47860i	−0.146051	+	0.252967i
$875$	−2.15704	−	0.458493i	−0.0729213	−	0.0154999i
$876$	0.992911	−	3.05587i	0.0335473	−	0.103248i
$877$	47.4267	−	10.0809i	1.60149	−	0.340406i	0.681335	−	0.731972i	$-0.261400\pi$
$877$	47.4267	−	10.0809i	1.60149	−	0.340406i	0.920150	+	0.391565i	$0.128066\pi$
$878$	−1.43654	+	13.6678i	−0.0484809	+	0.461265i
$879$	−11.0392	+	12.2603i	−0.372344	+	0.413530i
$880$	2.96100	−	1.31832i	0.0998154	−	0.0444407i
$881$	−12.5585	−	5.59138i	−0.423105	−	0.188378i	0.184128	−	0.982902i	$-0.441054\pi$
$881$	−12.5585	−	5.59138i	−0.423105	−	0.188378i	−0.607233	+	0.794524i	$0.707721\pi$
$882$	1.42990	+	1.58807i	0.0481473	+	0.0534730i
$883$	−5.18606	+	3.76789i	−0.174525	+	0.126800i	−0.671618	−	0.740897i	$-0.734401\pi$
$883$	−5.18606	+	3.76789i	−0.174525	+	0.126800i	0.497094	+	0.867697i	$0.334401\pi$
$884$	9.15836	−	6.65394i	0.308029	−	0.223796i
$885$	−4.47757	−	4.97285i	−0.150512	−	0.167160i
$886$	−15.8892	−	7.07435i	−0.533809	−	0.237667i
$887$	18.8987	−	8.41426i	0.634558	−	0.282523i	−0.0641394	−	0.997941i	$-0.520430\pi$
$887$	18.8987	−	8.41426i	0.634558	−	0.282523i	0.698697	+	0.715418i	$0.253764\pi$
$888$	0.782805	−	0.869393i	0.0262692	−	0.0291749i
$889$	1.59588	−	15.1838i	0.0535241	−	0.509248i
$890$	−6.25100	+	1.32869i	−0.209534	+	0.0445378i
$891$	−1.00159	+	3.08258i	−0.0335546	+	0.103270i
$892$	7.11455	+	1.51224i	0.238213	+	0.0506337i
$893$	2.29222	−	3.97025i	0.0767063	−	0.132859i
$894$	3.31030	+	5.73361i	0.110713	+	0.191761i
$895$	7.18597	+	22.1161i	0.240201	+	0.739261i
$896$	−0.230509	−	2.19315i	−0.00770078	−	0.0732680i
$897$	5.92058	+	4.30156i	0.197683	+	0.143625i
$898$	−8.31172			−0.277366
$899$	−13.6793	−	7.92232i	−0.456229	−	0.264224i
$900$	1.00000			0.0333333
$901$	24.7636	+	17.9918i	0.824996	+	0.599395i
$902$	2.17709	+	20.7136i	0.0724892	+	0.689688i
$903$	3.98351	+	12.2600i	0.132563	+	0.407987i
$904$	6.47285	+	11.2113i	0.215284	+	0.372882i
$905$	6.10763	−	10.5787i	0.203024	−	0.351648i
$906$	−10.5713	−	2.24701i	−0.351209	−	0.0746517i
$907$	14.6499	−	45.0877i	0.486441	−	1.49711i	−0.343442	−	0.939174i	$-0.611593\pi$
$907$	14.6499	−	45.0877i	0.486441	−	1.49711i	0.829883	−	0.557938i	$-0.188407\pi$
$908$	−5.25635	+	1.11727i	−0.174438	+	0.0370780i
$909$	−0.925892	+	8.80928i	−0.0307099	+	0.292185i
$910$	3.75315	−	4.16829i	0.124416	−	0.138178i
$911$	−34.6533	+	15.4287i	−1.14812	+	0.511174i	−0.890460	−	0.455062i	$-0.849617\pi$
$911$	−34.6533	+	15.4287i	−1.14812	+	0.511174i	−0.257657	+	0.966237i	$0.582950\pi$
$912$	−2.74185	−	1.22075i	−0.0907917	−	0.0404231i
$913$	−11.8038	−	13.1095i	−0.390650	−	0.433860i
$914$	−11.5304	+	8.37730i	−0.381391	+	0.277097i
$915$	−0.914001	+	0.664061i	−0.0302159	+	0.0219532i
$916$	17.8041	+	19.7735i	0.588265	+	0.653335i
$917$	30.1116	+	13.4065i	0.994373	+	0.442723i
$918$	4.06593	−	1.81027i	0.134196	−	0.0597478i
$919$	6.83795	−	7.59431i	0.225563	−	0.250513i	−0.619731	−	0.784814i	$-0.712758\pi$
$919$	6.83795	−	7.59431i	0.225563	−	0.250513i	0.845294	+	0.534301i	$0.179425\pi$
$920$	0.300754	−	2.86148i	0.00991556	−	0.0943402i
$921$	−6.17560	+	1.31266i	−0.203493	+	0.0432538i
$922$	−3.42950	+	10.5549i	−0.112944	+	0.347607i
$923$	10.8026	+	2.29617i	0.355573	+	0.0755795i
$924$	3.57382	−	6.19004i	0.117570	−	0.203637i
$925$	−0.584942	−	1.01315i	−0.0192328	−	0.0333121i
$926$	−5.00352	−	15.3993i	−0.164426	−	0.506051i
$927$	0.520193	+	4.94931i	0.0170854	+	0.162557i
$928$	−2.29693	−	1.66882i	−0.0754004	−	0.0547816i
$929$	29.2130			0.958448			0.479224	−	0.877693i	$-0.340918\pi$
$929$	29.2130			0.958448			0.479224	+	0.877693i	$0.340918\pi$
$930$	5.53804	−	0.574529i	0.181600	−	0.0188395i
$931$	−6.41370			−0.210200
$932$	−4.05788	−	2.94822i	−0.132920	−	0.0965722i
$933$	−2.97396	−	28.2953i	−0.0973629	−	0.926347i
$934$	7.24655	+	22.3026i	0.237114	+	0.729763i
$935$	−7.21287	−	12.4931i	−0.235886	−	0.408567i
$936$	−1.27175	+	2.20273i	−0.0415683	+	0.0719985i
$937$	−28.6810	−	6.09633i	−0.936967	−	0.199158i	−0.285970	−	0.958239i	$-0.592316\pi$
$937$	−28.6810	−	6.09633i	−0.936967	−	0.199158i	−0.650997	+	0.759080i	$0.725649\pi$
$938$	6.44998	−	19.8510i	0.210599	−	0.648158i
$939$	32.6634	−	6.94281i	1.06593	−	0.226570i
$940$	−0.159664	+	1.51911i	−0.00520768	+	0.0495478i
$941$	−27.1604	+	30.1646i	−0.885402	+	0.983339i	−0.999949	−	0.0100790i	$-0.996792\pi$
$941$	−27.1604	+	30.1646i	−0.885402	+	0.983339i	0.114547	+	0.993418i	$0.463458\pi$
$942$	9.45533	−	4.20979i	0.308071	−	0.137162i
$943$	16.8904	+	7.52009i	0.550027	+	0.244888i
$944$	−4.47757	−	4.97285i	−0.145732	−	0.161852i
$945$	1.78407	−	1.29620i	0.0580358	−	0.0421655i
$946$	−15.3284	+	11.1367i	−0.498368	+	0.362086i
$947$	6.95034	+	7.71913i	0.225856	+	0.250838i	0.845413	−	0.534113i	$-0.179354\pi$
$947$	6.95034	+	7.71913i	0.225856	+	0.250838i	−0.619557	+	0.784952i	$0.712688\pi$
$948$	−13.0377	−	5.80474i	−0.423444	−	0.188529i
$949$	7.46601	−	3.32408i	0.242357	−	0.107904i
$950$	−2.00828	+	2.23042i	−0.0651572	+	0.0723644i
$951$	3.02517	−	28.7825i	0.0980977	−	0.933338i
$952$	−9.60038	+	2.04062i	−0.311150	+	0.0661370i
$953$	1.18868	−	3.65838i	0.0385051	−	0.118507i	−0.929956	−	0.367670i	$-0.880156\pi$
$953$	1.18868	−	3.65838i	0.0385051	−	0.118507i	0.968461	+	0.249163i	$0.0801556\pi$
$954$	−6.72715	−	1.42990i	−0.217800	−	0.0462947i
$955$	−7.59241	+	13.1504i	−0.245684	+	0.425538i
$956$	−2.46951	−	4.27733i	−0.0798698	−	0.138339i
$957$	−2.84368	−	8.75195i	−0.0919231	−	0.282910i
$958$	−1.02214	−	9.72500i	−0.0330238	−	0.314201i
$959$	−0.452940	−	0.329080i	−0.0146262	−	0.0106265i
$960$	1.00000			0.0322749
$961$	30.3398	−	6.36353i	0.978704	−	0.205275i
$962$	2.97559			0.0959369
$963$	0.657121	+	0.477427i	0.0211754	+	0.0153849i
$964$	−0.838113	−	7.97411i	−0.0269938	−	0.256829i
$965$	−5.55856	−	17.1075i	−0.178937	−	0.550710i
$966$	−3.17249	−	5.49492i	−0.102073	−	0.176796i
$967$	−30.4155	+	52.6812i	−0.978097	+	1.69411i	−0.308785	+	0.951132i	$0.599922\pi$
$967$	−30.4155	+	52.6812i	−0.978097	+	1.69411i	−0.669312	+	0.742982i	$0.733411\pi$
$968$	−0.483683	−	0.102810i	−0.0155462	−	0.00330444i
$969$	−4.12786	+	12.7043i	−0.132606	+	0.408120i
$970$	10.0211	−	2.13005i	0.321759	−	0.0683919i
$971$	6.37331	−	60.6380i	0.204529	−	1.94597i	−0.103594	−	0.994620i	$-0.533034\pi$
$971$	6.37331	−	60.6380i	0.204529	−	1.94597i	0.308123	−	0.951346i	$-0.400299\pi$
$972$	−0.669131	+	0.743145i	−0.0214624	+	0.0238364i
$973$	41.2079	−	18.3469i	1.32106	−	0.588176i
$974$	−22.2099	−	9.88848i	−0.711650	−	0.316847i
$975$	1.70193	+	1.89018i	0.0545053	+	0.0605343i
$976$	−0.914001	+	0.664061i	−0.0292565	+	0.0212561i
$977$	22.6489	−	16.4554i	0.724602	−	0.526454i	−0.163249	−	0.986585i	$-0.552198\pi$
$977$	22.6489	−	16.4554i	0.724602	−	0.526454i	0.887851	+	0.460131i	$0.152198\pi$
$978$	4.90983	+	5.45292i	0.156999	+	0.174365i
$979$	−18.9227	−	8.42494i	−0.604773	−	0.269262i
$980$	1.95220	−	0.869177i	0.0623609	−	0.0277648i
$981$	−8.34267	+	9.26548i	−0.266361	+	0.295824i
$982$	3.04315	−	28.9537i	0.0971110	−	0.923949i
$983$	−4.99500	+	1.06172i	−0.159316	+	0.0338636i	−0.286879	−	0.957967i	$-0.592618\pi$
$983$	−4.99500	+	1.06172i	−0.159316	+	0.0338636i	0.127563	+	0.991830i	$0.459284\pi$
$984$	−1.98571	+	6.11138i	−0.0633021	+	0.194824i
$985$	11.1578	+	2.37166i	0.355517	+	0.0755674i
$986$	−6.31814	+	10.9433i	−0.201211	+	0.348507i
$987$	1.68422	+	2.91715i	0.0536092	+	0.0928538i
$988$	−2.35899	−	7.26023i	−0.0750495	−	0.230979i
$989$	1.75809	+	16.7271i	0.0559039	+	0.531890i
$990$	2.62220	+	1.90514i	0.0833391	+	0.0605494i
$991$	−26.6426			−0.846329			−0.423164	−	0.906053i	$-0.639081\pi$
$991$	−26.6426			−0.846329			−0.423164	+	0.906053i	$0.639081\pi$
$992$	5.53804	−	0.574529i	0.175833	−	0.0182413i
$993$	−34.3711			−1.09073
$994$	−7.74653	−	5.62818i	−0.245705	−	0.178515i
$995$	0.732840	+	6.97251i	0.0232326	+	0.221043i
$996$	−1.68184	−	5.17618i	−0.0532913	−	0.164014i
$997$	13.9590	+	24.1777i	0.442086	+	0.765715i	0.997844	−	0.0656291i	$-0.0209054\pi$
$997$	13.9590	+	24.1777i	0.442086	+	0.765715i	−0.555759	+	0.831344i	$0.687572\pi$
$998$	−14.6072	+	25.3004i	−0.462382	+	0.800869i
$999$	1.14432	+	0.243232i	0.0362046	+	0.00769553i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.e.121.2	✓	16	31.28	even	15	inner
930.2.bg.e.661.2	yes	16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.15704 + 0.458493i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(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} +(2.15704 + 0.458493i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(-0.104528 + 0.994522i) q^{10} +(-2.16880 + 2.40870i) q^{11} +(-0.913545 + 0.406737i) q^{12} +(-2.32360 - 1.03453i) q^{13} +(1.47559 + 1.63881i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.97811 + 3.30752i) q^{17} +(-0.913545 - 0.406737i) q^{18} +(2.74185 - 1.22075i) q^{19} +(-0.669131 + 0.743145i) q^{20} +(-0.230509 + 2.19315i) q^{21} +(-3.17039 + 0.673888i) q^{22} +(-0.889117 + 2.73642i) q^{23} +(-0.978148 - 0.207912i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.27175 - 2.20273i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.230509 + 2.19315i) q^{28} +(2.29693 + 1.66882i) q^{29} -1.00000 q^{30} +(-5.53804 + 0.574529i) q^{31} -1.00000 q^{32} +(-2.62220 - 1.90514i) q^{33} +(0.465226 + 4.42633i) q^{34} +(0.681454 + 2.09730i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.584942 + 1.01315i) q^{37} +(2.93574 + 0.624011i) q^{38} +(0.785983 - 2.41901i) q^{39} +(-0.978148 + 0.207912i) q^{40} +(0.671688 - 6.39069i) q^{41} +(-1.47559 + 1.63881i) q^{42} +(5.34023 - 2.37762i) q^{43} +(-2.96100 - 1.31832i) q^{44} +(-0.669131 - 0.743145i) q^{45} +(-2.32774 + 1.69120i) q^{46} +(1.23575 - 0.897826i) q^{47} +(-0.669131 - 0.743145i) q^{48} +(-1.95220 - 0.869177i) q^{49} +(-0.913545 + 0.406737i) q^{50} +(-2.97811 + 3.30752i) q^{51} +(0.265867 - 2.52956i) q^{52} +(6.72715 - 1.42990i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-3.17039 - 0.673888i) q^{55} +(-1.10262 + 1.90979i) q^{56} +(1.50066 + 2.59923i) q^{57} +(0.877349 + 2.70020i) q^{58} +(0.699465 + 6.65497i) q^{59} +(-0.809017 - 0.587785i) q^{60} +1.12977 q^{61} +(-4.81807 - 2.79038i) q^{62} -2.20523 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.265867 - 2.52956i) q^{65} +(-1.00159 - 3.08258i) q^{66} +(-4.73251 - 8.19695i) q^{67} +(-2.22536 + 3.85443i) q^{68} +(-2.81437 - 0.598212i) q^{69} +(-0.681454 + 2.09730i) q^{70} +(-4.24717 + 0.902764i) q^{71} +(0.104528 - 0.994522i) q^{72} +(-2.15000 + 2.38782i) q^{73} +(-1.06874 + 0.475834i) q^{74} +(-0.913545 - 0.406737i) q^{75} +(2.00828 + 2.23042i) q^{76} +(-5.78256 + 4.20128i) q^{77} +(2.05773 - 1.49503i) q^{78} +(9.54950 + 10.6058i) q^{79} +(-0.913545 - 0.406737i) q^{80} +(0.913545 - 0.406737i) q^{81} +(4.29976 - 4.77537i) q^{82} +(-0.568903 + 5.41275i) q^{83} +(-2.15704 + 0.458493i) q^{84} +(-1.37535 + 4.23288i) q^{85} +(5.71787 + 1.21537i) q^{86} +(-1.41958 + 2.45878i) q^{87} +(-1.62061 - 2.80698i) q^{88} +(1.97482 + 6.07787i) q^{89} +(-0.104528 - 0.994522i) q^{90} +(-4.53777 - 3.29688i) q^{91} -2.87724 q^{92} +(-1.15026 - 5.44765i) q^{93} +1.52747 q^{94} +(2.42812 + 1.76414i) q^{95} +(-0.104528 - 0.994522i) q^{96} +(-3.16588 - 9.74357i) q^{97} +(-1.06848 - 1.85066i) q^{98} +(1.62061 - 2.80698i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} - 10 q^{14} - 4 q^{15} - 4 q^{16} - 22 q^{17} - 2 q^{18} - 3 q^{19} - 2 q^{20} - 11 q^{22} + 9 q^{23} + 2 q^{24} - 8 q^{25} + 11 q^{26} + 4 q^{27} - 3 q^{29} - 16 q^{30} - 15 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{34} + 5 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} + 28 q^{41} + 10 q^{42} - 28 q^{43} - 19 q^{44} - 2 q^{45} - 9 q^{46} + 9 q^{47} - 2 q^{48} + 19 q^{49} - 2 q^{50} + 22 q^{51} + 4 q^{52} + 2 q^{53} - 4 q^{54} - 11 q^{55} + 5 q^{56} - 2 q^{57} - 12 q^{58} + 24 q^{59} - 4 q^{60} - 40 q^{61} - 25 q^{62} + 10 q^{63} - 4 q^{64} - 4 q^{65} - 7 q^{66} - q^{67} - 2 q^{68} - 3 q^{69} - 5 q^{70} + 39 q^{71} - 2 q^{72} + 81 q^{73} - 8 q^{74} - 2 q^{75} + 2 q^{76} + 28 q^{77} - 8 q^{78} + 64 q^{79} - 2 q^{80} + 2 q^{81} + 32 q^{82} - 40 q^{83} + 5 q^{84} - 14 q^{85} + 13 q^{86} - 9 q^{87} - q^{88} - 7 q^{89} + 2 q^{90} - 46 q^{91} - 36 q^{92} - 20 q^{93} - 4 q^{94} - 6 q^{95} + 2 q^{96} - 17 q^{97} - 9 q^{98} + q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 4 * q^13 - 10 * q^14 - 4 * q^15 - 4 * q^16 - 22 * q^17 - 2 * q^18 - 3 * q^19 - 2 * q^20 - 11 * q^22 + 9 * q^23 + 2 * q^24 - 8 * q^25 + 11 * q^26 + 4 * q^27 - 3 * q^29 - 16 * q^30 - 15 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^34 + 5 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 + 28 * q^41 + 10 * q^42 - 28 * q^43 - 19 * q^44 - 2 * q^45 - 9 * q^46 + 9 * q^47 - 2 * q^48 + 19 * q^49 - 2 * q^50 + 22 * q^51 + 4 * q^52 + 2 * q^53 - 4 * q^54 - 11 * q^55 + 5 * q^56 - 2 * q^57 - 12 * q^58 + 24 * q^59 - 4 * q^60 - 40 * q^61 - 25 * q^62 + 10 * q^63 - 4 * q^64 - 4 * q^65 - 7 * q^66 - q^67 - 2 * q^68 - 3 * q^69 - 5 * q^70 + 39 * q^71 - 2 * q^72 + 81 * q^73 - 8 * q^74 - 2 * q^75 + 2 * q^76 + 28 * q^77 - 8 * q^78 + 64 * q^79 - 2 * q^80 + 2 * q^81 + 32 * q^82 - 40 * q^83 + 5 * q^84 - 14 * q^85 + 13 * q^86 - 9 * q^87 - q^88 - 7 * q^89 + 2 * q^90 - 46 * q^91 - 36 * q^92 - 20 * q^93 - 4 * q^94 - 6 * q^95 + 2 * q^96 - 17 * q^97 - 9 * q^98 + q^99

Introduction

L-functions

Modular forms

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