LMFDB - Embedded newform 75.2.i.a.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(4,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("75.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.i (of order $10$, degree $4$, 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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.3
Root			$0.0898194i$ of defining polynomial
Character	$\chi$	$=$	75.64
Dual form			75.2.i.a.34.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0527945 + 0.0726655i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.615541 - 1.89444i) q^{4} +(-1.27125 - 1.83954i) q^{5} +(0.0277557 + 0.0854234i) q^{6} +4.36070i q^{7} +(0.341004 - 0.110799i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.0527945 + 0.0726655i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.615541 - 1.89444i) q^{4} +(-1.27125 - 1.83954i) q^{5} +(0.0277557 + 0.0854234i) q^{6} +4.36070i q^{7} +(0.341004 - 0.110799i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.0665563 - 0.189494i) q^{10} +(-3.55235 + 2.58093i) q^{11} +(1.17083 - 1.61151i) q^{12} +(1.16479 - 1.60319i) q^{13} +(-0.316872 + 0.230221i) q^{14} +(-0.640580 - 2.14235i) q^{15} +(-3.19696 - 2.32273i) q^{16} +(-0.948224 + 0.308097i) q^{17} +0.0898194i q^{18} +(-0.417468 - 1.28484i) q^{19} +(-4.26741 + 1.27599i) q^{20} +(-1.34753 + 4.14727i) q^{21} +(-0.375089 - 0.121874i) q^{22} +(1.38512 + 1.90646i) q^{23} +0.358553 q^{24} +(-1.76785 + 4.67704i) q^{25} +0.177991 q^{26} +(0.587785 + 0.809017i) q^{27} +(8.26109 + 2.68419i) q^{28} +(2.46551 - 7.58806i) q^{29} +(0.121856 - 0.159652i) q^{30} +(-1.13645 - 3.49762i) q^{31} -1.07204i q^{32} +(-4.17603 + 1.35688i) q^{33} +(-0.0724490 - 0.0526373i) q^{34} +(8.02171 - 5.54354i) q^{35} +(1.61151 - 1.17083i) q^{36} +(-0.844681 + 1.16260i) q^{37} +(0.0713231 - 0.0981678i) q^{38} +(1.60319 - 1.16479i) q^{39} +(-0.637321 - 0.486439i) q^{40} +(4.83992 + 3.51641i) q^{41} +(-0.372506 + 0.121034i) q^{42} -2.68554i q^{43} +(2.70280 + 8.31838i) q^{44} +(0.0527945 - 2.23544i) q^{45} +(-0.0654066 + 0.201301i) q^{46} +(10.4039 + 3.38042i) q^{47} +(-2.32273 - 3.19696i) q^{48} -12.0157 q^{49} +(-0.433192 + 0.118461i) q^{50} -0.997022 q^{51} +(-2.32018 - 3.19345i) q^{52} +(-10.5102 - 3.41496i) q^{53} +(-0.0277557 + 0.0854234i) q^{54} +(9.26366 + 3.25369i) q^{55} +(0.483161 + 1.48702i) q^{56} -1.35096i q^{57} +(0.681555 - 0.221451i) q^{58} +(5.41147 + 3.93167i) q^{59} +(-4.45285 - 0.105163i) q^{60} +(7.64982 - 5.55792i) q^{61} +(0.194158 - 0.267235i) q^{62} +(-2.56316 + 3.52788i) q^{63} +(-6.31602 + 4.58886i) q^{64} +(-4.42988 - 0.104621i) q^{65} +(-0.319070 - 0.231818i) q^{66} +(-12.2894 + 3.99307i) q^{67} +1.98600i q^{68} +(0.728201 + 2.24117i) q^{69} +(0.826326 + 0.290232i) q^{70} +(2.26280 - 6.96418i) q^{71} +(0.341004 + 0.110799i) q^{72} +(-0.249694 - 0.343674i) q^{73} -0.129076 q^{74} +(-3.12661 + 3.90184i) q^{75} -2.69101 q^{76} +(-11.2547 - 15.4907i) q^{77} +(0.169280 + 0.0550023i) q^{78} +(1.96390 - 6.04425i) q^{79} +(-0.208626 + 8.83372i) q^{80} +(0.309017 + 0.951057i) q^{81} +0.537343i q^{82} +(0.700939 - 0.227749i) q^{83} +(7.02730 + 5.10563i) q^{84} +(1.77219 + 1.35263i) q^{85} +(0.195146 - 0.141782i) q^{86} +(4.68968 - 6.45479i) q^{87} +(-0.925401 + 1.27370i) q^{88} +(-7.91814 + 5.75286i) q^{89} +(0.165227 - 0.114183i) q^{90} +(6.99105 + 5.07929i) q^{91} +(4.46427 - 1.45053i) q^{92} -3.67761i q^{93} +(0.303628 + 0.934470i) q^{94} +(-1.83281 + 2.40130i) q^{95} +(0.331279 - 1.01957i) q^{96} +(0.0320583 + 0.0104164i) q^{97} +(-0.634365 - 0.873128i) q^{98} -4.39094 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} + 10 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 8 q^{71} - 30 q^{72} - 20 q^{73} - 52 q^{74} - 32 q^{76} - 40 q^{77} - 20 q^{79} - 4 q^{81} + 10 q^{83} + 12 q^{84} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 26 q^{96} + 40 q^{97} + 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 + 10 * q^17 - 2 * q^19 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 8 * q^71 - 30 * q^72 - 20 * q^73 - 52 * q^74 - 32 * q^76 - 40 * q^77 - 20 * q^79 - 4 * q^81 + 10 * q^83 + 12 * q^84 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 26 * q^96 + 40 * q^97 + 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.0527945	+	0.0726655i	0.0373314	+	0.0513822i	0.827275	−	0.561798i	$-0.189890\pi$
$2$	0.0527945	+	0.0726655i	0.0373314	+	0.0513822i	−0.789943	+	0.613180i	$0.789890\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.615541	−	1.89444i	0.307770	−	0.947220i
$5$	−1.27125	−	1.83954i	−0.568520	−	0.822669i
$5$	−1.27125	−	1.83954i	−0.568520	−	0.822669i
$6$	0.0277557	+	0.0854234i	0.0113312	+	0.0348739i
$7$			4.36070i			1.64819i	0.566451	+	0.824095i	$0.308316\pi$
$7$			4.36070i			1.64819i	−0.566451	+	0.824095i	$0.691684\pi$
$8$	0.341004	−	0.110799i	0.120563	−	0.0391734i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	0.0665563	−	0.189494i	0.0210469	−	0.0599232i
$11$	−3.55235	+	2.58093i	−1.07107	+	0.778180i	−0.976105	−	0.217300i	$-0.930275\pi$
$11$	−3.55235	+	2.58093i	−1.07107	+	0.778180i	−0.0949680	+	0.995480i	$0.530275\pi$
$12$	1.17083	−	1.61151i	0.337989	−	0.465202i
$13$	1.16479	−	1.60319i	0.323054	−	0.444646i	−0.616343	−	0.787478i	$-0.711386\pi$
$13$	1.16479	−	1.60319i	0.323054	−	0.444646i	0.939397	+	0.342832i	$0.111386\pi$
$14$	−0.316872	+	0.230221i	−0.0846877	+	0.0615292i
$15$	−0.640580	−	2.14235i	−0.165397	−	0.553152i
$16$	−3.19696	−	2.32273i	−0.799240	−	0.580682i
$17$	−0.948224	+	0.308097i	−0.229978	+	0.0747244i	−0.421739	−	0.906717i	$-0.638580\pi$
$17$	−0.948224	+	0.308097i	−0.229978	+	0.0747244i	0.191761	+	0.981442i	$0.438580\pi$
$18$			0.0898194i			0.0211706i
$19$	−0.417468	−	1.28484i	−0.0957738	−	0.294761i	0.891681	−	0.452665i	$-0.149527\pi$
$19$	−0.417468	−	1.28484i	−0.0957738	−	0.294761i	−0.987455	+	0.157903i	$0.949527\pi$
$20$	−4.26741	+	1.27599i	−0.954223	+	0.285320i
$21$	−1.34753	+	4.14727i	−0.294055	+	0.905009i
$22$	−0.375089	−	0.121874i	−0.0799692	−	0.0259836i
$23$	1.38512	+	1.90646i	0.288818	+	0.397524i	0.928630	−	0.371008i	$-0.120988\pi$
$23$	1.38512	+	1.90646i	0.288818	+	0.397524i	−0.639812	+	0.768532i	$0.720988\pi$
$24$	0.358553			0.0731893
$25$	−1.76785	+	4.67704i	−0.353570	+	0.935408i
$26$	0.177991			0.0349069
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	8.26109	+	2.68419i	1.56120	+	0.507264i
$29$	2.46551	−	7.58806i	0.457834	−	1.40907i	−0.409942	−	0.912111i	$-0.634451\pi$
$29$	2.46551	−	7.58806i	0.457834	−	1.40907i	0.867776	−	0.496955i	$-0.165549\pi$
$30$	0.121856	−	0.159652i	0.0222477	−	0.0291484i
$31$	−1.13645	−	3.49762i	−0.204112	−	0.628191i	−0.999749	−	0.0224173i	$-0.992864\pi$
$31$	−1.13645	−	3.49762i	−0.204112	−	0.628191i	0.795637	−	0.605774i	$-0.207136\pi$
$32$		−	1.07204i		−	0.189512i
$33$	−4.17603	+	1.35688i	−0.726954	+	0.236202i
$34$	−0.0724490	−	0.0526373i	−0.0124249	−	0.00902722i
$35$	8.02171	−	5.54354i	1.35592	−	0.937029i
$36$	1.61151	−	1.17083i	0.268585	−	0.195138i
$37$	−0.844681	+	1.16260i	−0.138865	+	0.191131i	−0.872785	−	0.488105i	$-0.837688\pi$
$37$	−0.844681	+	1.16260i	−0.138865	+	0.191131i	0.733920	+	0.679235i	$0.237688\pi$
$38$	0.0713231	−	0.0981678i	0.0115701	−	0.0159249i
$39$	1.60319	−	1.16479i	0.256716	−	0.186515i
$40$	−0.637321	−	0.486439i	−0.100769	−	0.0769128i
$41$	4.83992	+	3.51641i	0.755869	+	0.549171i	0.897641	−	0.440728i	$-0.145280\pi$
$41$	4.83992	+	3.51641i	0.755869	+	0.549171i	−0.141771	+	0.989899i	$0.545280\pi$
$42$	−0.372506	+	0.121034i	−0.0574789	+	0.0186760i
$43$		−	2.68554i		−	0.409541i	−0.978810	−	0.204770i	$-0.934355\pi$
$43$		−	2.68554i		−	0.409541i	0.978810	−	0.204770i	$-0.0656447\pi$
$44$	2.70280	+	8.31838i	0.407463	+	1.25404i
$45$	0.0527945	−	2.23544i	0.00787015	−	0.333240i
$46$	−0.0654066	+	0.201301i	−0.00964368	+	0.0296802i
$47$	10.4039	+	3.38042i	1.51756	+	0.493086i	0.945082	−	0.326833i	$-0.105982\pi$
$47$	10.4039	+	3.38042i	1.51756	+	0.493086i	0.572480	+	0.819919i	$0.305982\pi$
$48$	−2.32273	−	3.19696i	−0.335257	−	0.461441i
$49$	−12.0157			−1.71653
$50$	−0.433192	+	0.118461i	−0.0612626	+	0.0167529i
$51$	−0.997022			−0.139611
$52$	−2.32018	−	3.19345i	−0.321751	−	0.442852i
$53$	−10.5102	−	3.41496i	−1.44368	−	0.469081i	−0.520639	−	0.853777i	$-0.674306\pi$
$53$	−10.5102	−	3.41496i	−1.44368	−	0.469081i	−0.923043	+	0.384696i	$0.874306\pi$
$54$	−0.0277557	+	0.0854234i	−0.00377708	+	0.0116246i
$55$	9.26366	+	3.25369i	1.24911	+	0.438728i
$56$	0.483161	+	1.48702i	0.0645652	+	0.198711i
$57$		−	1.35096i		−	0.178938i
$58$	0.681555	−	0.221451i	0.0894926	−	0.0290779i
$59$	5.41147	+	3.93167i	0.704514	+	0.511859i	0.881399	−	0.472372i	$-0.156602\pi$
$59$	5.41147	+	3.93167i	0.704514	+	0.511859i	−0.176885	+	0.984231i	$0.556602\pi$
$60$	−4.45285	−	0.105163i	−0.574861	−	0.0135765i
$61$	7.64982	−	5.55792i	0.979460	−	0.711619i	0.0218719	−	0.999761i	$-0.493037\pi$
$61$	7.64982	−	5.55792i	0.979460	−	0.711619i	0.957588	+	0.288142i	$0.0930374\pi$
$62$	0.194158	−	0.267235i	0.0246581	−	0.0339389i
$63$	−2.56316	+	3.52788i	−0.322927	+	0.444471i
$64$	−6.31602	+	4.58886i	−0.789502	+	0.573607i
$65$	−4.42988	−	0.104621i	−0.549459	−	0.0129766i
$66$	−0.319070	−	0.231818i	−0.0392748	−	0.0285348i
$67$	−12.2894	+	3.99307i	−1.50139	+	0.487831i	−0.940423	−	0.340006i	$-0.889571\pi$
$67$	−12.2894	+	3.99307i	−1.50139	+	0.487831i	−0.560968	+	0.827838i	$0.689571\pi$
$68$			1.98600i			0.240838i
$69$	0.728201	+	2.24117i	0.0876651	+	0.269806i
$70$	0.826326	+	0.290232i	0.0987649	+	0.0346894i
$71$	2.26280	−	6.96418i	0.268545	−	0.826496i	−0.722311	−	0.691569i	$-0.756920\pi$
$71$	2.26280	−	6.96418i	0.268545	−	0.826496i	0.990856	−	0.134927i	$-0.0430800\pi$
$72$	0.341004	+	0.110799i	0.0401877	+	0.0130578i
$73$	−0.249694	−	0.343674i	−0.0292244	−	0.0402240i	0.794155	−	0.607716i	$-0.207914\pi$
$73$	−0.249694	−	0.343674i	−0.0292244	−	0.0402240i	−0.823379	+	0.567492i	$0.807914\pi$
$74$	−0.129076			−0.0150047
$75$	−3.12661	+	3.90184i	−0.361030	+	0.450545i
$76$	−2.69101			−0.308680
$77$	−11.2547	−	15.4907i	−1.28259	−	1.76533i
$78$	0.169280	+	0.0550023i	0.0191671	+	0.00622778i
$79$	1.96390	−	6.04425i	0.220956	−	0.680032i	−0.777721	−	0.628609i	$-0.783624\pi$
$79$	1.96390	−	6.04425i	0.220956	−	0.680032i	0.998677	−	0.0514225i	$-0.0163755\pi$
$80$	−0.208626	+	8.83372i	−0.0233251	+	0.987640i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			0.537343i			0.0593396i
$83$	0.700939	−	0.227749i	0.0769381	−	0.0249987i	−0.270295	−	0.962778i	$-0.587121\pi$
$83$	0.700939	−	0.227749i	0.0769381	−	0.0249987i	0.347233	+	0.937779i	$0.387121\pi$
$84$	7.02730	+	5.10563i	0.766742	+	0.557070i
$85$	1.77219	+	1.35263i	0.192221	+	0.146714i
$86$	0.195146	−	0.141782i	0.0210431	−	0.0152887i
$87$	4.68968	−	6.45479i	0.502786	−	0.692026i
$88$	−0.925401	+	1.27370i	−0.0986481	+	0.135777i
$89$	−7.91814	+	5.75286i	−0.839321	+	0.609802i	−0.922181	−	0.386759i	$-0.873595\pi$
$89$	−7.91814	+	5.75286i	−0.839321	+	0.609802i	0.0828599	+	0.996561i	$0.473595\pi$
$90$	0.165227	−	0.114183i	0.0174164	−	0.0120359i
$91$	6.99105	+	5.07929i	0.732861	+	0.532455i
$92$	4.46427	−	1.45053i	0.465432	−	0.151228i
$93$		−	3.67761i		−	0.381351i
$94$	0.303628	+	0.934470i	0.0313168	+	0.0963833i
$95$	−1.83281	+	2.40130i	−0.188042	+	0.246368i
$96$	0.331279	−	1.01957i	0.0338110	−	0.104060i
$97$	0.0320583	+	0.0104164i	0.00325503	+	0.00105762i	0.310644	−	0.950526i	$-0.399455\pi$
$97$	0.0320583	+	0.0104164i	0.00325503	+	0.00105762i	−0.307389	+	0.951584i	$0.599455\pi$
$98$	−0.634365	−	0.873128i	−0.0640805	−	0.0881992i
$99$	−4.39094			−0.441306
$100$	7.77219	+	6.22799i	0.777219	+	0.622799i
$101$	3.19390			0.317805			0.158902	−	0.987294i	$-0.449204\pi$
$101$	3.19390			0.317805			0.158902	+	0.987294i	$0.449204\pi$
$102$	−0.0526373	−	0.0724490i	−0.00521187	−	0.00717352i
$103$	−8.13479	−	2.64315i	−0.801544	−	0.260438i	−0.120532	−	0.992709i	$-0.538460\pi$
$103$	−8.13479	−	2.64315i	−0.801544	−	0.260438i	−0.681012	+	0.732272i	$0.738460\pi$
$104$	0.219565	−	0.675753i	0.0215302	−	0.0662630i
$105$	9.34214	−	2.79338i	0.911700	−	0.272606i
$106$	−0.306730	−	0.944017i	−0.0297922	−	0.0916910i
$107$			2.22136i			0.214747i	0.994219	+	0.107373i	$0.0342440\pi$
$107$			2.22136i			0.214747i	−0.994219	+	0.107373i	$0.965756\pi$
$108$	1.89444	−	0.615541i	0.182293	−	0.0592305i
$109$	8.90108	+	6.46701i	0.852569	+	0.619427i	0.925853	−	0.377884i	$-0.123348\pi$
$109$	8.90108	+	6.46701i	0.852569	+	0.619427i	−0.0732844	+	0.997311i	$0.523348\pi$
$110$	0.252639	+	0.844925i	0.0240882	+	0.0805604i
$111$	−1.16260	+	0.844681i	−0.110349	+	0.0801735i
$112$	10.1287	−	13.9410i	0.957074	−	1.31730i
$113$	−1.00524	+	1.38359i	−0.0945646	+	0.130157i	−0.853678	−	0.520802i	$-0.825633\pi$
$113$	−1.00524	+	1.38359i	−0.0945646	+	0.130157i	0.759113	+	0.650959i	$0.225633\pi$
$114$	0.0981678	−	0.0713231i	0.00919426	−	0.00668002i
$115$	1.74618	−	4.97157i	0.162832	−	0.463602i
$116$	−12.8575	−	9.34152i	−1.19379	−	0.867338i
$117$	1.88467	−	0.612365i	0.174237	−	0.0566132i
$118$			0.600798i			0.0553079i
$119$	−1.34352	−	4.13492i	−0.123160	−	0.379048i
$120$	−0.455811	−	0.659574i	−0.0416096	−	0.0602106i
$121$	2.55877	−	7.87510i	0.232616	−	0.715918i
$122$	0.807738	+	0.262450i	0.0731292	+	0.0237611i
$123$	3.51641	+	4.83992i	0.317064	+	0.436401i
$124$	−7.32556			−0.657855
$125$	10.8510	−	2.69365i	0.970543	−	0.240927i
$126$	−0.391676			−0.0348933
$127$	7.38079	+	10.1588i	0.654939	+	0.901447i	0.999301	−	0.0373905i	$-0.0119046\pi$
$127$	7.38079	+	10.1588i	0.654939	+	0.901447i	−0.344361	+	0.938837i	$0.611905\pi$
$128$	−2.70605	−	0.879248i	−0.239183	−	0.0777153i
$129$	0.829877	−	2.55410i	0.0730666	−	0.224876i
$130$	−0.226271	−	0.327423i	−0.0198453	−	0.0287169i
$131$	5.09006	+	15.6656i	0.444721	+	1.36871i	0.882790	+	0.469769i	$0.155663\pi$
$131$	5.09006	+	15.6656i	0.444721	+	1.36871i	−0.438069	+	0.898942i	$0.644337\pi$
$132$			8.74646i			0.761282i
$133$	5.60278	−	1.82046i	0.485823	−	0.157853i
$134$	−0.938972	−	0.682203i	−0.0811149	−	0.0589334i
$135$	0.741001	−	2.10972i	0.0637752	−	0.181576i
$136$	−0.289212	+	0.210125i	−0.0247997	+	0.0180180i
$137$	−5.68231	+	7.82102i	−0.485472	+	0.668195i	−0.979545	−	0.201225i	$-0.935508\pi$
$137$	−5.68231	+	7.82102i	−0.485472	+	0.668195i	0.494073	+	0.869421i	$0.335508\pi$
$138$	−0.124411	+	0.171237i	−0.0105906	+	0.0145766i
$139$	10.9482	−	7.95430i	0.928611	−	0.674675i	−0.0170416	−	0.999855i	$-0.505425\pi$
$139$	10.9482	−	7.95430i	0.928611	−	0.674675i	0.945652	+	0.325180i	$0.105425\pi$
$140$	−5.56422	−	18.6089i	−0.470262	−	1.57274i
$141$	8.85007	+	6.42995i	0.745310	+	0.541499i
$142$	0.625518	−	0.203243i	0.0524923	−	0.0170558i
$143$			8.70133i			0.727642i
$144$	−1.22113	−	3.75825i	−0.101761	−	0.313188i
$145$	−17.0928	+	5.11090i	−1.41948	+	0.424437i
$146$	0.0117907	−	0.0362882i	0.000975809	−	0.00300323i
$147$	−11.4276	−	3.71306i	−0.942535	−	0.306248i
$148$	1.68255	+	2.31583i	0.138304	+	0.190360i
$149$	−13.6843			−1.12106			−0.560529	−	0.828134i	$-0.689402\pi$
$149$	−13.6843			−1.12106			−0.560529	+	0.828134i	$0.689402\pi$
$150$	−0.448596	−	0.0212008i	−0.0366277	−	0.00173104i
$151$	−11.3204			−0.921237			−0.460619	−	0.887598i	$-0.652372\pi$
$151$	−11.3204			−0.921237			−0.460619	+	0.887598i	$0.652372\pi$
$152$	−0.284717	−	0.391879i	−0.0230936	−	0.0317856i
$153$	−0.948224	−	0.308097i	−0.0766594	−	0.0249081i
$154$	0.531455	−	1.63565i	0.0428259	−	0.131805i
$155$	−4.98932	+	6.53689i	−0.400752	+	0.525055i
$156$	−1.21979	−	3.75413i	−0.0976614	−	0.300571i
$157$			8.56070i			0.683219i	0.939842	+	0.341609i	$0.110972\pi$
$157$			8.56070i			0.683219i	−0.939842	+	0.341609i	$0.889028\pi$
$158$	0.542892	−	0.176396i	0.0431901	−	0.0140333i
$159$	−8.94048	−	6.49564i	−0.709026	−	0.515138i
$160$	−1.97207	+	1.36283i	−0.155906	+	0.107741i
$161$	−8.31349	+	6.04010i	−0.655194	+	0.476027i
$162$	−0.0527945	+	0.0726655i	−0.00414793	+	0.00570914i
$163$	−2.69505	+	3.70942i	−0.211093	+	0.290544i	−0.901413	−	0.432959i	$-0.857469\pi$
$163$	−2.69505	+	3.70942i	−0.211093	+	0.290544i	0.690321	+	0.723503i	$0.257469\pi$
$164$	9.64080	−	7.00445i	0.752820	−	0.546956i
$165$	7.80481	+	5.95707i	0.607604	+	0.463757i
$166$	0.0535552	+	0.0389102i	0.00415669	+	0.00302001i
$167$	−6.86465	+	2.23046i	−0.531203	+	0.172598i	−0.562323	−	0.826917i	$-0.690092\pi$
$167$	−6.86465	+	2.23046i	−0.531203	+	0.172598i	0.0311206	+	0.999516i	$0.490092\pi$
$168$			1.56354i			0.120630i
$169$	2.80372	+	8.62898i	0.215671	+	0.663767i
$170$	−0.00472785	+	0.200188i	−0.000362610	+	0.0153537i
$171$	0.417468	−	1.28484i	0.0319246	−	0.0982538i
$172$	−5.08759	−	1.65306i	−0.387925	−	0.126045i
$173$	−2.73326	−	3.76201i	−0.207806	−	0.286020i	0.692374	−	0.721539i	$-0.256565\pi$
$173$	−2.73326	−	3.76201i	−0.207806	−	0.286020i	−0.900180	+	0.435519i	$0.856565\pi$
$174$	0.716629			0.0543275
$175$	−20.3952	−	7.70906i	−1.54173	−	0.582750i
$176$	17.3515			1.30792
$177$	3.93167	+	5.41147i	0.295522	+	0.406751i
$178$	−0.836069	−	0.271655i	−0.0626660	−	0.0203614i
$179$	2.22597	−	6.85082i	0.166377	−	0.512055i	−0.832758	−	0.553636i	$-0.813240\pi$
$179$	2.22597	−	6.85082i	0.166377	−	0.512055i	0.999135	+	0.0415819i	$0.0132397\pi$
$180$	−4.20242	−	1.47602i	−0.313230	−	0.110016i
$181$	−1.17557	−	3.61804i	−0.0873797	−	0.268927i	0.897813	−	0.440376i	$-0.145155\pi$
$181$	−1.17557	−	3.61804i	−0.0873797	−	0.268927i	−0.985193	+	0.171449i	$0.945155\pi$
$182$			0.776167i			0.0575333i
$183$	8.99291	−	2.92197i	0.664775	−	0.215998i
$184$	0.683566	+	0.496640i	0.0503931	+	0.0366128i
$185$	3.21246	+	0.0758687i	0.236185	+	0.00557798i
$186$	0.267235	−	0.194158i	0.0195947	−	0.0142364i
$187$	2.57324	−	3.54177i	0.188174	−	0.259000i
$188$	12.8080	−	17.6287i	0.934121	−	1.28571i
$189$	−3.52788	+	2.56316i	−0.256616	+	0.186442i
$190$	−0.271254	−	0.00640620i	−0.0196788	−	0.000464755i
$191$	−17.4377	−	12.6692i	−1.26174	−	0.916711i	−0.262903	−	0.964822i	$-0.584680\pi$
$191$	−17.4377	−	12.6692i	−1.26174	−	0.916711i	−0.998842	+	0.0481112i	$0.984680\pi$
$192$	−7.42493	+	2.41250i	−0.535848	+	0.174108i
$193$		−	3.15029i		−	0.226763i	−0.993552	−	0.113381i	$-0.963832\pi$
$193$		−	3.15029i		−	0.226763i	0.993552	−	0.113381i	$-0.0361682\pi$
$194$	0.000935592		0.00287946i	6.71716e−5		0.000206733i
$195$	−4.18074	−	1.46841i	−0.299389	−	0.105155i
$196$	−7.39617	+	22.7631i	−0.528298	+	1.62593i
$197$	24.8071	+	8.06032i	1.76743	+	0.574274i	0.997927	−	0.0643637i	$-0.0205018\pi$
$197$	24.8071	+	8.06032i	1.76743	+	0.574274i	0.769507	+	0.638638i	$0.220502\pi$
$198$	−0.231818	−	0.319070i	−0.0164746	−	0.0226753i
$199$	24.2662			1.72018			0.860092	−	0.510139i	$-0.170406\pi$
$199$	24.2662			1.72018			0.860092	+	0.510139i	$0.170406\pi$
$200$	−0.0846324	+	1.79077i	−0.00598441	+	0.126626i
$201$	−12.9219			−0.911437
$202$	0.168620	+	0.232086i	0.0118641	+	0.0163295i
$203$	33.0893	+	10.7514i	2.32241	+	0.754597i
$204$	−0.613708	+	1.88880i	−0.0429681	+	0.132242i
$205$	0.315842	−	13.3735i	0.0220594	−	0.934045i
$206$	−0.237406	−	0.730662i	−0.0165409	−	0.0509076i
$207$			2.35651i			0.163789i
$208$	−7.44756	+	2.41986i	−0.516395	+	0.167787i
$209$	4.79906	+	3.48672i	0.331958	+	0.241182i
$210$	0.696196	+	0.531376i	0.0480421	+	0.0366684i
$211$	−13.2503	+	9.62694i	−0.912192	+	0.662746i	−0.941568	−	0.336822i	$-0.890648\pi$
$211$	−13.2503	+	9.62694i	−0.912192	+	0.662746i	0.0293766	+	0.999568i	$0.490648\pi$
$212$	−12.9389	+	17.8088i	−0.888645	+	1.22312i
$213$	4.30410	−	5.92408i	0.294912	−	0.405911i
$214$	−0.161416	+	0.117276i	−0.0110342	+	0.00801680i
$215$	−4.94017	+	3.41399i	−0.336917	+	0.232832i
$216$	0.290076	+	0.210752i	0.0197371	+	0.0143399i
$217$	15.2521	−	4.95570i	1.03538	−	0.336415i
$218$			0.988224i			0.0669310i
$219$	−0.131272	−	0.404013i	−0.00887052	−	0.0273006i
$220$	11.8661	−	15.5467i	0.800011	−	1.04816i
$221$	−0.610541	+	1.87905i	−0.0410695	+	0.126399i
$222$	−0.122758	−	0.0398866i	−0.00823899	−	0.00267701i
$223$	−3.34035	−	4.59760i	−0.223687	−	0.307878i	0.682393	−	0.730985i	$-0.260939\pi$
$223$	−3.34035	−	4.59760i	−0.223687	−	0.307878i	−0.906080	+	0.423107i	$0.860939\pi$
$224$	4.67486			0.312352
$225$	−4.17932	+	2.74469i	−0.278621	+	0.182979i
$226$	−0.153610			−0.0102180
$227$	−2.14174	−	2.94785i	−0.142152	−	0.195656i	0.732004	−	0.681300i	$-0.238585\pi$
$227$	−2.14174	−	2.94785i	−0.142152	−	0.195656i	−0.874157	+	0.485644i	$0.838585\pi$
$228$	−2.55931	−	0.831569i	−0.169494	−	0.0550720i
$229$	−0.513355	+	1.57994i	−0.0339235	+	0.104406i	−0.966584	−	0.256348i	$-0.917481\pi$
$229$	−0.513355	+	1.57994i	−0.0339235	+	0.104406i	0.932661	+	0.360754i	$0.117481\pi$
$230$	0.453450	−	0.135585i	0.0298996	−	0.00894023i
$231$	−5.91693	−	18.2104i	−0.389305	−	1.19816i
$232$		−	2.86074i		−	0.187817i
$233$	7.47434	−	2.42856i	0.489661	−	0.159100i	−0.0537719	−	0.998553i	$-0.517124\pi$
$233$	7.47434	−	2.42856i	0.489661	−	0.159100i	0.543432	+	0.839453i	$0.317124\pi$
$234$	0.143998	+	0.104621i	0.00941344	+	0.00683926i
$235$	−7.00748	−	23.4358i	−0.457118	−	1.52878i
$236$	10.7793	−	7.83161i	0.701672	−	0.509795i
$237$	3.73555	−	5.14155i	0.242650	−	0.333980i
$238$	0.229536	−	0.315929i	0.0148786	−	0.0204786i
$239$	−0.458956	+	0.333451i	−0.0296874	+	0.0215691i	−0.602530	−	0.798096i	$-0.705841\pi$
$239$	−0.458956	+	0.333451i	−0.0296874	+	0.0215691i	0.572843	+	0.819665i	$0.305841\pi$
$240$	−2.92818	+	8.33690i	−0.189013	+	0.538144i
$241$	15.3779	+	11.1727i	0.990578	+	0.719697i	0.960048	−	0.279837i	$-0.0902804\pi$
$241$	15.3779	+	11.1727i	0.990578	+	0.719697i	0.0305304	+	0.999534i	$0.490280\pi$
$242$	0.707337	−	0.229828i	0.0454693	−	0.0147739i
$243$			1.00000i			0.0641500i
$244$	−5.82037	−	17.9133i	−0.372611	−	1.14678i
$245$	15.2750	+	22.1035i	0.975883	+	1.41214i
$246$	−0.166048	+	0.511043i	−0.0105868	+	0.0325829i
$247$	−2.54610	−	0.827278i	−0.162005	−	0.0526385i
$248$	−0.775065	−	1.06679i	−0.0492167	−	0.0677410i
$249$	0.737011			0.0467062
$250$	0.768609	+	0.646283i	0.0486111	+	0.0408745i
$251$	3.02533			0.190957			0.0954787	−	0.995431i	$-0.469562\pi$
$251$	3.02533			0.190957			0.0954787	+	0.995431i	$0.469562\pi$
$252$	5.10563	+	7.02730i	0.321625	+	0.442678i
$253$	−9.84086	−	3.19749i	−0.618690	−	0.201024i
$254$	−0.348527	+	1.07266i	−0.0218686	+	0.0673045i
$255$	1.26746	+	1.83407i	0.0793716	+	0.114854i
$256$	4.74604	+	14.6068i	0.296627	+	0.912925i
$257$		−	19.8613i		−	1.23891i	−0.785032	−	0.619456i	$-0.787353\pi$
$257$		−	19.8613i		−	1.23891i	0.785032	−	0.619456i	$-0.212647\pi$
$258$	0.229408	−	0.0745391i	0.0142823	−	0.00464060i
$259$	−5.06977	−	3.68340i	−0.315020	−	0.228875i
$260$	−2.92497	+	8.32775i	−0.181399	+	0.516465i
$261$	6.45479	−	4.68968i	0.399541	−	0.290284i
$262$	−0.869621	+	1.19693i	−0.0537253	+	0.0739466i
$263$	−13.4191	+	18.4698i	−0.827456	+	1.13890i	0.160935	+	0.986965i	$0.448549\pi$
$263$	−13.4191	+	18.4698i	−0.827456	+	1.13890i	−0.988391	+	0.151930i	$0.951451\pi$
$264$	−1.27370	+	0.925401i	−0.0783911	+	0.0569545i
$265$	7.07907	+	23.6752i	0.434864	+	1.45435i
$266$	0.428081	+	0.311019i	0.0262473	+	0.0190698i
$267$	−9.30833	+	3.02446i	−0.569661	+	0.185094i
$268$			25.7395i			1.57229i
$269$	−4.58346	−	14.1065i	−0.279459	−	0.860086i	−0.988005	−	0.154421i	$-0.950649\pi$
$269$	−4.58346	−	14.1065i	−0.279459	−	0.860086i	0.708546	−	0.705664i	$-0.249351\pi$
$270$	0.192425	−	0.0575365i	0.0117106	−	0.00350156i
$271$	−1.98920	+	6.12214i	−0.120835	+	0.371893i	−0.993119	−	0.117106i	$-0.962638\pi$
$271$	−1.98920	+	6.12214i	−0.120835	+	0.371893i	0.872284	+	0.489000i	$0.162638\pi$
$272$	3.74706	+	1.21749i	0.227199	+	0.0738214i
$273$	5.07929	+	6.99105i	0.307413	+	0.423117i
$274$	−0.868313			−0.0524567
$275$	−5.79111	−	21.1772i	−0.349217	−	1.27703i
$276$	4.69401			0.282546
$277$	−3.94390	−	5.42831i	−0.236966	−	0.326155i	0.673927	−	0.738798i	$-0.264606\pi$
$277$	−3.94390	−	5.42831i	−0.236966	−	0.326155i	−0.910893	+	0.412642i	$0.864606\pi$
$278$	1.15601	+	0.375609i	0.0693326	+	0.0225275i
$279$	1.13645	−	3.49762i	0.0680372	−	0.209397i
$280$	2.12122	−	2.77917i	0.126767	−	0.166087i
$281$	−6.33074	−	19.4840i	−0.377661	−	1.16232i	−0.941666	−	0.336549i	$-0.890740\pi$
$281$	−6.33074	−	19.4840i	−0.377661	−	1.16232i	0.564006	−	0.825771i	$-0.309260\pi$
$282$			0.982560i			0.0585106i
$283$	−10.8589	+	3.52828i	−0.645496	+	0.209734i	−0.613427	−	0.789751i	$-0.710210\pi$
$283$	−10.8589	+	3.52828i	−0.645496	+	0.209734i	−0.0320688	+	0.999486i	$0.510210\pi$
$284$	−11.8004	−	8.57347i	−0.700223	−	0.508742i
$285$	−2.48514	+	1.71740i	−0.147207	+	0.101730i
$286$	−0.632286	+	0.459383i	−0.0373879	+	0.0271639i
$287$	−15.3340	+	21.1055i	−0.905139	+	1.24582i
$288$	0.630131	−	0.867300i	0.0371308	−	0.0511062i
$289$	−12.9491	+	9.40806i	−0.761711	+	0.553415i
$290$	−1.27380	−	0.972232i	−0.0747998	−	0.0570914i
$291$	0.0272704	+	0.0198131i	0.00159862	+	0.00116147i
$292$	−0.804766	+	0.261484i	−0.0470954	+	0.0153022i
$293$		−	28.5505i		−	1.66794i	−0.551812	−	0.833968i	$-0.686063\pi$
$293$		−	28.5505i		−	1.66794i	0.551812	−	0.833968i	$-0.313937\pi$
$294$	−0.333505	−	1.02642i	−0.0194504	−	0.0598622i
$295$	0.353140	−	14.9528i	0.0205606	−	0.870584i
$296$	−0.159224	+	0.490042i	−0.00925473	+	0.0284831i
$297$	−4.17603	−	1.35688i	−0.242318	−	0.0787339i
$298$	−0.722455	−	0.994374i	−0.0418507	−	0.0576025i
$299$	4.66979			0.270061
$300$	5.46724	+	8.32491i	0.315651	+	0.480639i
$301$	11.7108			0.675001
$302$	−0.597653	−	0.822598i	−0.0343910	−	0.0473352i
$303$	3.03758	+	0.986969i	0.174504	+	0.0566999i
$304$	−1.64969	+	5.07723i	−0.0946164	+	0.291199i
$305$	−19.9489	−	7.00669i	−1.14227	−	0.401202i
$306$	−0.0276731	−	0.0851689i	−0.00158196	−	0.00486878i
$307$		−	20.5417i		−	1.17238i	−0.810175	−	0.586188i	$-0.800628\pi$
$307$		−	20.5417i		−	1.17238i	0.810175	−	0.586188i	$-0.199372\pi$
$308$	−36.2740	+	11.7861i	−2.06690	+	0.671577i
$309$	−6.91986	−	5.02758i	−0.393657	−	0.286009i
$310$	−0.738415	−	0.0174392i	−0.0419391	−	0.000990477i
$311$	−14.1979	+	10.3154i	−0.805090	+	0.584932i	−0.912403	−	0.409293i	$-0.865775\pi$
$311$	−14.1979	+	10.3154i	−0.805090	+	0.584932i	0.107313	+	0.994225i	$0.465775\pi$
$312$	0.417638	−	0.574830i	0.0236441	−	0.0325433i
$313$	1.75491	−	2.41543i	0.0991935	−	0.136528i	−0.756535	−	0.653953i	$-0.773109\pi$
$313$	1.75491	−	2.41543i	0.0991935	−	0.136528i	0.855729	+	0.517425i	$0.173109\pi$
$314$	−0.622067	+	0.451958i	−0.0351053	+	0.0255055i
$315$	9.74811	+	0.230221i	0.549244	+	0.0129715i
$316$	−10.2416	−	7.44097i	−0.576136	−	0.418587i
$317$	15.3794	−	4.99706i	0.863791	−	0.280663i	0.156580	−	0.987665i	$-0.449953\pi$
$317$	15.3794	−	4.99706i	0.863791	−	0.280663i	0.707211	+	0.707003i	$0.249953\pi$
$318$		−	0.992598i		−	0.0556621i
$319$	10.8259	+	33.3187i	0.606134	+	1.86549i
$320$	16.4706	+	5.78502i	0.920737	+	0.323392i
$321$	−0.686438	+	2.11264i	−0.0383132	+	0.117916i
$322$	−0.877813	−	0.285219i	−0.0489186	−	0.0158946i
$323$	0.791707	+	1.08969i	0.0440518	+	0.0606320i
$324$	1.99193			0.110663
$325$	5.43903	+	8.28196i	0.301703	+	0.459401i
$326$	−0.411830			−0.0228092
$327$	6.46701	+	8.90108i	0.357627	+	0.492231i
$328$	2.04005	+	0.662852i	0.112643	+	0.0365999i
$329$	−14.7410	+	45.3682i	−0.812699	+	2.50123i
$330$	−0.0208217	+	0.881641i	−0.00114620	+	0.0485328i
$331$	−4.03900	−	12.4307i	−0.222003	−	0.683256i	−0.998582	−	0.0532356i	$-0.983047\pi$
$331$	−4.03900	−	12.4307i	−0.222003	−	0.683256i	0.776579	−	0.630020i	$-0.216953\pi$
$332$		−	1.46808i		−	0.0805711i
$333$	−1.36672	+	0.444075i	−0.0748959	+	0.0243352i
$334$	−0.524494	−	0.381067i	−0.0286990	−	0.0208511i
$335$	22.9683	+	17.5307i	1.25489	+	0.957806i
$336$	13.9410	−	10.1287i	0.760543	−	0.552567i
$337$	15.7555	−	21.6856i	0.858257	−	1.18129i	−0.123725	−	0.992317i	$-0.539484\pi$
$337$	15.7555	−	21.6856i	0.858257	−	1.18129i	0.981982	−	0.188973i	$-0.0605159\pi$
$338$	−0.479007	+	0.659297i	−0.0260545	+	0.0358610i
$339$	−1.38359	+	1.00524i	−0.0751462	+	0.0545969i
$340$	3.65334	−	2.52470i	0.198130	−	0.136921i
$341$	13.0642	+	9.49167i	0.707464	+	0.514003i
$342$	0.115403	−	0.0374968i	0.00624029	−	0.00202759i
$343$		−	21.8721i		−	1.18098i
$344$	−0.297555	−	0.915780i	−0.0160431	−	0.0493755i
$345$	3.19701	−	4.18865i	0.172121	−	0.225509i
$346$	0.129067	−	0.397227i	0.00693867	−	0.0213550i
$347$	−24.2385	−	7.87558i	−1.30119	−	0.422783i	−0.425196	−	0.905101i	$-0.639795\pi$
$347$	−24.2385	−	7.87558i	−1.30119	−	0.422783i	−0.875996	+	0.482318i	$0.839795\pi$
$348$	−9.34152	−	12.8575i	−0.500758	−	0.689234i
$349$	28.0435			1.50113			0.750566	−	0.660795i	$-0.229781\pi$
$349$	28.0435			1.50113			0.750566	+	0.660795i	$0.229781\pi$
$350$	−0.516572	−	1.88902i	−0.0276119	−	0.100972i
$351$	1.98166			0.105773
$352$	2.76687	+	3.80826i	0.147474	+	0.202981i
$353$	−13.9489	−	4.53226i	−0.742423	−	0.241228i	−0.0867054	−	0.996234i	$-0.527634\pi$
$353$	−13.9489	−	4.53226i	−0.742423	−	0.241228i	−0.655718	+	0.755006i	$0.727634\pi$
$354$	−0.185657	+	0.571393i	−0.00986754	+	0.0303692i
$355$	−15.6875	+	4.69069i	−0.832606	+	0.248956i
$356$	6.02452	+	18.5416i	0.319299	+	0.982701i
$357$		−	4.34771i		−	0.230105i
$358$	0.615337	−	0.199935i	0.0325216	−	0.0105669i
$359$	−11.8283	−	8.59373i	−0.624272	−	0.453560i	0.230139	−	0.973158i	$-0.426082\pi$
$359$	−11.8283	−	8.59373i	−0.624272	−	0.453560i	−0.854411	+	0.519598i	$0.826082\pi$
$360$	−0.229682	−	0.768146i	−0.0121053	−	0.0404848i
$361$	13.8948	−	10.0952i	0.731305	−	0.531324i
$362$	0.200843	−	0.276437i	0.0105561	−	0.0145292i
$363$	4.86708	−	6.69896i	0.255455	−	0.351604i
$364$	13.9257	−	10.1176i	0.729905	−	0.530307i
$365$	−0.314780	+	0.896217i	−0.0164763	+	0.0469102i
$366$	0.687103	+	0.499210i	0.0359154	+	0.0260941i
$367$	16.8279	−	5.46773i	0.878412	−	0.285413i	0.165114	−	0.986274i	$-0.447201\pi$
$367$	16.8279	−	5.46773i	0.878412	−	0.285413i	0.713298	+	0.700861i	$0.247201\pi$
$368$		−	9.31212i		−	0.485428i
$369$	1.84869	+	5.68967i	0.0962388	+	0.296193i
$370$	0.164087	+	0.237440i	0.00853049	+	0.0123439i
$371$	14.8916	−	45.8317i	0.773134	−	2.37946i
$372$	−6.96702	−	2.26372i	−0.361223	−	0.117369i
$373$	7.18821	+	9.89372i	0.372191	+	0.512278i	0.953495	−	0.301409i	$-0.0974570\pi$
$373$	7.18821	+	9.89372i	0.372191	+	0.512278i	−0.581303	+	0.813687i	$0.697457\pi$
$374$	0.393217			0.0203328
$375$	11.1523	+	0.791329i	0.575902	+	0.0408641i
$376$	3.92231			0.202278
$377$	−9.29333	−	12.7912i	−0.478631	−	0.658779i
$378$	−0.372506	−	0.121034i	−0.0191596	−	0.00622534i
$379$	−8.68186	+	26.7200i	−0.445957	+	1.37251i	0.435474	+	0.900201i	$0.356581\pi$
$379$	−8.68186	+	26.7200i	−0.445957	+	1.37251i	−0.881431	+	0.472313i	$0.843419\pi$
$380$	3.42095	+	4.95024i	0.175491	+	0.253942i
$381$	3.88031	+	11.9424i	0.198794	+	0.611826i
$382$		−	1.93598i		−	0.0990533i
$383$	32.7481	−	10.6405i	1.67335	−	0.543705i	0.689748	−	0.724049i	$-0.257721\pi$
$383$	32.7481	−	10.6405i	1.67335	−	0.543705i	0.983603	+	0.180345i	$0.0577213\pi$
$384$	−2.30190	−	1.67243i	−0.117468	−	0.0853458i
$385$	−14.1884	+	40.3960i	−0.723107	+	2.05877i
$386$	0.228917	−	0.166318i	0.0116516	−	0.00846536i
$387$	1.57852	−	2.17265i	0.0802406	−	0.110442i
$388$	0.0394664	−	0.0543208i	0.00200360	−	0.00275772i
$389$	10.9399	−	7.94834i	0.554677	−	0.402997i	−0.274830	−	0.961493i	$-0.588622\pi$
$389$	10.9399	−	7.94834i	0.554677	−	0.402997i	0.829507	+	0.558496i	$0.188622\pi$
$390$	−0.114018	−	0.381319i	−0.00577350	−	0.0193088i
$391$	−1.90078	−	1.38100i	−0.0961265	−	0.0698400i
$392$	−4.09741	+	1.33133i	−0.206951	+	0.0672423i
$393$			16.4718i			0.830892i
$394$	0.723974	+	2.22816i	0.0364733	+	0.112253i
$395$	−13.6153	+	4.07108i	−0.685059	+	0.204838i
$396$	−2.70280	+	8.31838i	−0.135821	+	0.418014i
$397$	−34.2136	−	11.1167i	−1.71713	−	0.557931i	−0.725639	−	0.688076i	$-0.758456\pi$
$397$	−34.2136	−	11.1167i	−1.71713	−	0.557931i	−0.991495	+	0.130145i	$0.958456\pi$
$398$	1.28112	+	1.76331i	0.0642169	+	0.0883869i
$399$	5.89112			0.294925
$400$	16.5152	−	10.8461i	0.825762	−	0.542304i
$401$	4.35977			0.217717			0.108858	−	0.994057i	$-0.465281\pi$
$401$	4.35977			0.217717			0.108858	+	0.994057i	$0.465281\pi$
$402$	−0.682203	−	0.938972i	−0.0340252	−	0.0468317i
$403$	−6.93108	−	2.25204i	−0.345261	−	0.112182i
$404$	1.96598	−	6.05065i	0.0978110	−	0.301031i
$405$	1.35667	−	1.77748i	0.0674136	−	0.0883237i
$406$	0.965680	+	2.97206i	0.0479259	+	0.147501i
$407$		−	6.31003i		−	0.312777i
$408$	−0.339989	+	0.110469i	−0.0168319	+	0.00546903i
$409$	−14.6543	−	10.6470i	−0.724610	−	0.526460i	0.163243	−	0.986586i	$-0.447804\pi$
$409$	−14.6543	−	10.6470i	−0.724610	−	0.526460i	−0.887854	+	0.460126i	$0.847804\pi$
$410$	0.988466	−	0.683097i	0.0488168	−	0.0337357i
$411$	−7.82102	+	5.68231i	−0.385783	+	0.280288i
$412$	−10.0146	+	13.7839i	−0.493383	+	0.679084i
$413$	−17.1448	+	23.5978i	−0.843642	+	1.16117i
$414$	−0.171237	+	0.124411i	−0.00841583	+	0.00611446i
$415$	−1.31002	−	0.999883i	−0.0643065	−	0.0490823i
$416$	−1.71869	−	1.24870i	−0.0842657	−	0.0612226i
$417$	12.8703	−	4.18182i	0.630263	−	0.204785i
$418$			0.532806i			0.0260604i
$419$	−0.163120	−	0.502031i	−0.00796892	−	0.0245258i	0.946993	−	0.321254i	$-0.104104\pi$
$419$	−0.163120	−	0.502031i	−0.00796892	−	0.0245258i	−0.954962	+	0.296728i	$0.904104\pi$
$420$	0.458585	−	19.4176i	0.0223767	−	0.947481i
$421$	5.76583	−	17.7454i	0.281009	−	0.864857i	−0.706557	−	0.707656i	$-0.749753\pi$
$421$	5.76583	−	17.7454i	0.281009	−	0.864857i	0.987567	−	0.157201i	$-0.0502472\pi$
$422$	−1.39909	−	0.454593i	−0.0681067	−	0.0221292i
$423$	6.42995	+	8.85007i	0.312635	+	0.430305i
$424$	−3.96239			−0.192430
$425$	0.235336	−	4.97955i	0.0114155	−	0.241544i
$426$	0.657709			0.0318661
$427$	24.2364	+	33.3586i	1.17288	+	1.61434i
$428$	4.20823	+	1.36734i	0.203413	+	0.0660928i
$429$	−2.68886	+	8.27546i	−0.129819	+	0.399543i
$430$	−0.508893	−	0.178739i	−0.0245410	−	0.00861958i
$431$	6.48668	+	19.9640i	0.312453	+	0.961630i	0.976790	+	0.214198i	$0.0687136\pi$
$431$	6.48668	+	19.9640i	0.312453	+	0.961630i	−0.664338	+	0.747432i	$0.731286\pi$
$432$		−	3.95166i		−	0.190124i
$433$	−12.9952	+	4.22239i	−0.624508	+	0.202915i	−0.604141	−	0.796877i	$-0.706484\pi$
$433$	−12.9952	+	4.22239i	−0.624508	+	0.202915i	−0.0203675	+	0.999793i	$0.506484\pi$
$434$	1.16533	+	0.846665i	0.0559378	+	0.0406412i
$435$	−17.8356	−	0.421224i	−0.855153	−	0.0201962i
$436$	17.7303	−	12.8819i	0.849130	−	0.616929i
$437$	1.87124	−	2.57554i	0.0895134	−	0.123205i
$438$	0.0224273	−	0.0308686i	0.00107162	−	0.00147496i
$439$	−3.50578	+	2.54710i	−0.167322	+	0.121567i	−0.668295	−	0.743896i	$-0.732976\pi$
$439$	−3.50578	+	2.54710i	−0.167322	+	0.121567i	0.500973	+	0.865463i	$0.332976\pi$
$440$	3.51945	+	0.0831190i	0.167783	+	0.00396254i
$441$	−9.72092	−	7.06266i	−0.462901	−	0.336317i
$442$	−0.168776	+	0.0548385i	−0.00802783	+	0.00260840i
$443$			1.60742i			0.0763707i	0.999271	+	0.0381854i	$0.0121577\pi$
$443$			1.60742i			0.0763707i	−0.999271	+	0.0381854i	$0.987842\pi$
$444$	0.884567	+	2.72242i	0.0419797	+	0.129200i
$445$	20.6486	+	7.25244i	0.978837	+	0.343799i
$446$	0.157734	−	0.485456i	0.00746894	−	0.0229870i
$447$	−13.0145	−	4.22867i	−0.615565	−	0.200009i
$448$	−20.0106	−	27.5423i	−0.945414	−	1.30125i
$449$	13.8291			0.652634			0.326317	−	0.945260i	$-0.394192\pi$
$449$	13.8291			0.652634			0.326317	+	0.945260i	$0.394192\pi$
$450$	−0.420089	−	0.158787i	−0.0198032	−	0.00748530i
$451$	−26.2687			−1.23694
$452$	2.00236	+	2.75601i	0.0941832	+	0.129632i
$453$	−10.7663	−	3.49818i	−0.505845	−	0.164359i
$454$	0.101135	−	0.311261i	0.00474649	−	0.0146082i
$455$	0.456219	−	19.3174i	0.0213879	−	0.905613i
$456$	−0.149685	−	0.460682i	−0.00700962	−	0.0215734i
$457$			20.1345i			0.941850i	0.882173	+	0.470925i	$0.156080\pi$
$457$			20.1345i			0.941850i	−0.882173	+	0.470925i	$0.843920\pi$
$458$	−0.141910	+	0.0461093i	−0.00663101	+	0.00215455i
$459$	−0.806607	−	0.586035i	−0.0376492	−	0.0273538i
$460$	−8.34351	−	6.36823i	−0.389018	−	0.296920i
$461$	−25.5054	+	18.5308i	−1.18791	+	0.863064i	−0.993041	−	0.117766i	$-0.962427\pi$
$461$	−25.5054	+	18.5308i	−1.18791	+	0.863064i	−0.194865	+	0.980830i	$0.562427\pi$
$462$	1.01089	−	1.39137i	0.0470308	−	0.0647323i
$463$	0.0265501	−	0.0365431i	0.00123389	−	0.00169830i	−0.808400	−	0.588634i	$-0.799666\pi$
$463$	0.0265501	−	0.0365431i	0.00123389	−	0.00169830i	0.809633	+	0.586936i	$0.199666\pi$
$464$	−25.5071	+	18.5320i	−1.18414	+	0.860327i
$465$	−6.76513	+	4.67517i	−0.313726	+	0.216806i
$466$	0.571077	+	0.414912i	0.0264546	+	0.0192204i
$467$	31.2278	−	10.1465i	1.44505	−	0.469525i	0.521582	−	0.853201i	$-0.325342\pi$
$467$	31.2278	−	10.1465i	1.44505	−	0.469525i	0.923468	+	0.383676i	$0.125342\pi$
$468$		−	3.94732i		−	0.182465i
$469$	−17.4126	−	53.5905i	−0.804039	−	2.47458i
$470$	1.33301	−	1.74648i	0.0614873	−	0.0805592i
$471$	−2.64540	+	8.14171i	−0.121894	+	0.375150i
$472$	2.28096	+	0.741129i	0.104990	+	0.0341132i
$473$	6.93119	+	9.53996i	0.318696	+	0.438648i
$474$	0.570830			0.0262191
$475$	6.74725	+	0.318878i	0.309585	+	0.0146311i
$476$	−8.66035			−0.396947
$477$	−6.49564	−	8.94048i	−0.297415	−	0.409356i
$478$	−0.0484607	−	0.0157458i	−0.00221654	−	0.000720198i
$479$	−2.31323	+	7.11938i	−0.105694	+	0.325293i	−0.989893	−	0.141818i	$-0.954705\pi$
$479$	−2.31323	+	7.11938i	−0.105694	+	0.325293i	0.884199	+	0.467111i	$0.154705\pi$
$480$	−2.29669	+	0.686729i	−0.104829	+	0.0313447i
$481$	0.880003	+	2.70837i	0.0401247	+	0.123491i
$482$			1.70730i			0.0777654i
$483$	−9.77309	+	3.17547i	−0.444691	+	0.144489i
$484$	−13.3439	−	9.69489i	−0.606540	−	0.440677i
$485$	−0.0215927	−	0.0722145i	−0.000980475	−	0.00327909i
$486$	−0.0726655	+	0.0527945i	−0.00329617	+	0.00239481i
$487$	−14.9471	+	20.5729i	−0.677316	+	0.932246i	−0.999898	−	0.0142956i	$-0.995449\pi$
$487$	−14.9471	+	20.5729i	−0.677316	+	0.932246i	0.322581	+	0.946542i	$0.395449\pi$
$488$	1.99281	−	2.74287i	0.0902103	−	0.124164i
$489$	−3.70942	+	2.69505i	−0.167746	+	0.121874i
$490$	−0.799722	+	2.27691i	−0.0361278	+	0.102860i
$491$	8.95323	+	6.50490i	0.404053	+	0.293562i	0.771190	−	0.636605i	$-0.219662\pi$
$491$	8.95323	+	6.50490i	0.404053	+	0.293562i	−0.367137	+	0.930167i	$0.619662\pi$
$492$	11.3334	−	3.68246i	0.510951	−	0.166018i
$493$			7.95479i			0.358266i
$494$	−0.0743057	−	0.228689i	−0.00334317	−	0.0102892i
$495$	5.58198	+	8.07733i	0.250891	+	0.363049i
$496$	−4.49084	+	13.8214i	−0.201645	+	0.620599i
$497$	30.3687	+	9.86739i	1.36222	+	0.442613i
$498$	0.0389102	+	0.0535552i	0.00174361	+	0.00239987i
$499$	−4.68157			−0.209576			−0.104788	−	0.994495i	$-0.533416\pi$
$499$	−4.68157			−0.209576			−0.104788	+	0.994495i	$0.533416\pi$
$500$	1.57627	−	22.2146i	0.0704932	−	0.993468i
$501$	−7.21792			−0.322473
$502$	0.159721	+	0.219837i	0.00712870	+	0.00981182i
$503$	−10.2985	−	3.34618i	−0.459187	−	0.149199i	0.0702839	−	0.997527i	$-0.477609\pi$
$503$	−10.2985	−	3.34618i	−0.459187	−	0.149199i	−0.529471	+	0.848328i	$0.677609\pi$
$504$	−0.483161	+	1.48702i	−0.0215217	+	0.0662371i
$505$	−4.06024	−	5.87532i	−0.180678	−	0.261448i
$506$	−0.287197	−	0.883901i	−0.0127675	−	0.0392942i
$507$			9.07304i			0.402948i
$508$	23.7884	−	7.72932i	1.05544	−	0.342933i
$509$	9.30422	+	6.75991i	0.412402	+	0.299628i	0.774574	−	0.632484i	$-0.217964\pi$
$509$	9.30422	+	6.75991i	0.412402	+	0.299628i	−0.362171	+	0.932112i	$0.617964\pi$
$510$	−0.0663581	+	0.188929i	−0.00293838	+	0.00836594i
$511$	1.49866	−	1.08884i	0.0662967	−	0.0481674i
$512$	−4.15570	+	5.71984i	−0.183658	+	0.252783i
$513$	0.794072	−	1.09295i	0.0350591	−	0.0482548i
$514$	1.44323	−	1.04857i	0.0636580	−	0.0462503i
$515$	5.47915	+	18.3244i	0.241440	+	0.807470i
$516$	−4.32776	−	3.14430i	−0.190519	−	0.138420i
$517$	−45.6828	+	14.8432i	−2.00913	+	0.652805i
$518$		−	0.562860i		−	0.0247307i
$519$	−1.43696	−	4.42250i	−0.0630755	−	0.194126i
$520$	−1.52220	+	0.455150i	−0.0667529	+	0.0199597i
$521$	0.246536	−	0.758759i	0.0108009	−	0.0332418i	−0.945511	−	0.325591i	$-0.894437\pi$
$521$	0.246536	−	0.758759i	0.0108009	−	0.0332418i	0.956312	+	0.292349i	$0.0944368\pi$
$522$	0.681555	+	0.221451i	0.0298309	+	0.00969263i
$523$	23.5954	+	32.4763i	1.03175	+	1.42009i	0.903622	+	0.428331i	$0.140898\pi$
$523$	23.5954	+	32.4763i	1.03175	+	1.42009i	0.128133	+	0.991757i	$0.459102\pi$
$524$	32.8107			1.43334
$525$	−17.0147	−	13.6342i	−0.742584	−	0.595046i
$526$	−2.05057			−0.0894090
$527$	2.15521	+	2.96639i	0.0938824	+	0.129218i
$528$	16.5023	+	5.36191i	0.718169	+	0.233347i
$529$	5.39138	−	16.5930i	0.234408	−	0.721433i
$530$	−1.34663	+	1.76432i	−0.0584939	+	0.0766374i
$531$	2.06700	+	6.36157i	0.0897001	+	0.276069i
$532$		−	11.7347i		−	0.508764i
$533$	11.2750	−	3.66346i	0.488373	−	0.158682i
$534$	−0.711203	−	0.516719i	−0.0307768	−	0.0223606i
$535$	4.08629	−	2.82390i	0.176666	−	0.122088i
$536$	−3.74831	+	2.72331i	−0.161903	+	0.117629i
$537$	4.23404	−	5.82766i	0.182712	−	0.251482i
$538$	0.783070	−	1.07780i	0.0337605	−	0.0464674i
$539$	42.6840	−	31.0117i	1.83853	−	1.33577i
$540$	−3.54062	−	2.70240i	−0.152364	−	0.116293i
$541$	−1.14085	−	0.828873i	−0.0490488	−	0.0356360i	0.562991	−	0.826463i	$-0.309651\pi$
$541$	−1.14085	−	0.828873i	−0.0490488	−	0.0356360i	−0.612040	+	0.790827i	$0.709651\pi$
$542$	−0.549887	+	0.178669i	−0.0236197	+	0.00767449i
$543$		−	3.80424i		−	0.163255i
$544$	0.330293	+	1.01654i	0.0141612	+	0.0435836i
$545$	0.580863	−	24.5951i	0.0248815	−	1.05354i
$546$	−0.239849	+	0.738178i	−0.0102646	+	0.0315911i
$547$	14.7053	+	4.77804i	0.628753	+	0.204294i	0.606023	−	0.795447i	$-0.292764\pi$
$547$	14.7053	+	4.77804i	0.628753	+	0.204294i	0.0227302	+	0.999742i	$0.492764\pi$
$548$	11.3188	+	15.5790i	0.483514	+	0.665500i
$549$	9.45570			0.403560
$550$	1.23311	−	1.53885i	0.0525800	−	0.0656169i
$551$	−10.7787			−0.459187
$552$	0.496640	+	0.683566i	0.0211384	+	0.0290945i
$553$	26.3572	+	8.56397i	1.12082	+	0.364177i
$554$	0.186234	−	0.573170i	0.00791234	−	0.0243517i
$555$	3.03179	+	1.06486i	0.128692	+	0.0452008i
$556$	−8.32991	−	25.6368i	−0.353267	−	1.08724i
$557$		−	18.0445i		−	0.764568i	−0.924045	−	0.382284i	$-0.875138\pi$
$557$		−	18.0445i		−	0.764568i	0.924045	−	0.382284i	$-0.124862\pi$
$558$	0.314154	−	0.102075i	0.0132992	−	0.00432117i
$559$	−4.30543	−	3.12808i	−0.182100	−	0.132304i
$560$	−38.5212	−	0.909756i	−1.62782	−	0.0384442i
$561$	3.54177	−	2.57324i	0.149533	−	0.108642i
$562$	1.08159	−	1.48868i	0.0456240	−	0.0627960i
$563$	16.7711	−	23.0834i	0.706816	−	0.972849i	−0.293043	−	0.956099i	$-0.594668\pi$
$563$	16.7711	−	23.0834i	0.706816	−	0.972849i	0.999860	−	0.0167502i	$-0.00533201\pi$
$564$	17.6287	−	12.8080i	0.742304	−	0.539315i
$565$	3.82308	+	0.0902897i	0.160838	+	0.00379852i
$566$	−0.829676	−	0.602795i	−0.0348739	−	0.0253374i
$567$	−4.14727	+	1.34753i	−0.174169	+	0.0565910i
$568$		−	2.62553i		−	0.110165i
$569$	−5.07011	−	15.6042i	−0.212550	−	0.654162i	−0.999318	−	0.0369135i	$-0.988247\pi$
$569$	−5.07011	−	15.6042i	−0.212550	−	0.654162i	0.786768	−	0.617248i	$-0.211753\pi$
$570$	−0.255998	−	0.0899146i	−0.0107226	−	0.00376611i
$571$	−2.57938	+	7.93852i	−0.107944	+	0.332217i	−0.990410	−	0.138159i	$-0.955882\pi$
$571$	−2.57938	+	7.93852i	−0.107944	+	0.332217i	0.882466	+	0.470376i	$0.155882\pi$
$572$	16.4842	+	5.35603i	0.689237	+	0.223947i
$573$	−12.6692	−	17.4377i	−0.529263	−	0.728469i
$574$	−2.34319			−0.0978029
$575$	−11.3653	+	3.10794i	−0.473964	+	0.129610i
$576$	−7.80703			−0.325293
$577$	−4.95815	−	6.82431i	−0.206411	−	0.284100i	0.693243	−	0.720704i	$-0.256181\pi$
$577$	−4.95815	−	6.82431i	−0.206411	−	0.284100i	−0.899654	+	0.436604i	$0.856181\pi$
$578$	−1.36728	−	0.444257i	−0.0568714	−	0.0184786i
$579$	0.973492	−	2.99610i	0.0404570	−	0.124514i
$580$	−0.839050	+	35.5273i	−0.0348397	+	1.47519i
$581$	0.993145	+	3.05659i	0.0412026	+	0.126809i
$582$			0.00302764i			0.000125500i
$583$	46.1495	−	14.9949i	1.91132	−	0.621025i
$584$	−0.123225	−	0.0895284i	−0.00509910	−	0.00370471i
$585$	−3.52235	−	2.68846i	−0.145631	−	0.111154i
$586$	2.07463	−	1.50731i	0.0857023	−	0.0622664i
$587$	−14.2745	+	19.6471i	−0.589171	+	0.810925i	−0.994663	−	0.103174i	$-0.967100\pi$
$587$	−14.2745	+	19.6471i	−0.589171	+	0.810925i	0.405492	+	0.914099i	$0.367100\pi$
$588$	−14.0684	+	19.3634i	−0.580169	+	0.798534i
$589$	−4.01943	+	2.92029i	−0.165618	+	0.120328i
$590$	1.10519	−	0.763764i	0.0455001	−	0.0314437i
$591$	21.1022	+	15.3316i	0.868028	+	0.630659i
$592$	5.40082	−	1.75483i	0.221972	−	0.0721232i
$593$			28.4653i			1.16893i	0.811418	+	0.584466i	$0.198696\pi$
$593$			28.4653i			1.16893i	−0.811418	+	0.584466i	$0.801304\pi$
$594$	−0.121874	−	0.375089i	−0.00500054	−	0.0153901i
$595$	−5.89843	+	7.72798i	−0.241812	+	0.316816i
$596$	−8.42323	+	25.9240i	−0.345029	+	1.06189i
$597$	23.0785	+	7.49866i	0.944541	+	0.306900i
$598$	0.246539	+	0.339332i	0.0100817	+	0.0138763i
$599$	−16.0387			−0.655323			−0.327662	−	0.944795i	$-0.606261\pi$
$599$	−16.0387			−0.655323			−0.327662	+	0.944795i	$0.606261\pi$
$600$	−0.633868	+	1.67697i	−0.0258775	+	0.0684619i
$601$	−8.09005			−0.330000			−0.165000	−	0.986294i	$-0.552762\pi$
$601$	−8.09005			−0.330000			−0.165000	+	0.986294i	$0.552762\pi$
$602$	0.618268	+	0.850973i	0.0251987	+	0.0346831i
$603$	−12.2894	−	3.99307i	−0.500464	−	0.162610i
$604$	−6.96814	+	21.4457i	−0.283530	+	0.872614i
$605$	−17.7394	+	5.30424i	−0.721211	+	0.215648i
$606$	0.0886490	+	0.272834i	0.00360112	+	0.0110831i
$607$		−	0.434608i		−	0.0176402i	−0.999961	−	0.00882010i	$-0.997192\pi$
$607$		−	0.434608i		−	0.0176402i	0.999961	−	0.00882010i	$-0.00280756\pi$
$608$	−1.37740	+	0.447544i	−0.0558609	+	0.0181503i
$609$	28.1474	+	20.4503i	1.14059	+	0.828687i
$610$	−0.544048	−	1.81951i	−0.0220279	−	0.0736698i
$611$	17.5378	−	12.7419i	0.709503	−	0.515484i
$612$	−1.16734	+	1.60671i	−0.0471870	+	0.0649473i
$613$	23.1565	−	31.8722i	0.935282	−	1.28731i	−0.0224808	−	0.999747i	$-0.507156\pi$
$613$	23.1565	−	31.8722i	0.935282	−	1.28731i	0.957763	−	0.287558i	$-0.0928435\pi$
$614$	1.49267	−	1.08449i	0.0602393	−	0.0437664i
$615$	4.43302	−	12.6213i	0.178757	−	0.508942i
$616$	−5.55425	−	4.03540i	−0.223787	−	0.162591i
$617$	−14.6602	+	4.76337i	−0.590196	+	0.191766i	−0.588863	−	0.808233i	$-0.700424\pi$
$617$	−14.6602	+	4.76337i	−0.590196	+	0.191766i	−0.00133273	+	0.999999i	$0.500424\pi$
$618$		−	0.768264i		−	0.0309041i
$619$	3.29776	+	10.1495i	0.132548	+	0.407942i	0.995201	−	0.0978556i	$-0.0311983\pi$
$619$	3.29776	+	10.1495i	0.132548	+	0.407942i	−0.862652	+	0.505797i	$0.831198\pi$
$620$	9.31261	+	13.4757i	0.374004	+	0.541197i
$621$	−0.728201	+	2.24117i	−0.0292217	+	0.0899352i
$622$	−1.49914	−	0.487102i	−0.0601102	−	0.0195310i
$623$	−25.0865	−	34.5286i	−1.00507	−	1.38336i
$624$	−7.83083			−0.313484
$625$	−18.7494	−	16.5366i	−0.749977	−	0.661464i
$626$	0.268168			0.0107182
$627$	3.48672	+	4.79906i	0.139246	+	0.191656i
$628$	16.2177	+	5.26946i	0.647158	+	0.210275i
$629$	0.442752	−	1.36265i	0.0176537	−	0.0543325i
$630$	0.497918	+	0.720505i	0.0198375	+	0.0287056i
$631$	−5.69664	−	17.5324i	−0.226780	−	0.697956i	−0.998106	−	0.0615162i	$-0.980406\pi$
$631$	−5.69664	−	17.5324i	−0.226780	−	0.697956i	0.771327	−	0.636440i	$-0.219594\pi$
$632$		−	2.27871i		−	0.0906424i
$633$	−15.5767	+	5.06118i	−0.619119	+	0.201164i
$634$	1.17506	+	0.853731i	0.0466676	+	0.0339060i
$635$	9.30471	−	26.4916i	0.369246	−	1.05129i
$636$	−17.8088	+	12.9389i	−0.706166	+	0.513060i
$637$	−13.9958	+	19.2635i	−0.554533	+	0.763249i
$638$	−1.84957	+	2.54572i	−0.0732252	+	0.100786i
$639$	5.92408	−	4.30410i	0.234353	−	0.170267i
$640$	1.82265	+	6.09564i	0.0720464	+	0.240951i
$641$	−10.0546	−	7.30508i	−0.397132	−	0.288533i	0.371240	−	0.928537i	$-0.378933\pi$
$641$	−10.0546	−	7.30508i	−0.397132	−	0.288533i	−0.768372	+	0.640004i	$0.778933\pi$
$642$	−0.189756	+	0.0616554i	−0.00748907	+	0.00243335i
$643$			1.84657i			0.0728218i	0.999337	+	0.0364109i	$0.0115925\pi$
$643$			1.84657i			0.0728218i	−0.999337	+	0.0364109i	$0.988407\pi$
$644$	6.32532	+	19.4673i	0.249253	+	0.767120i
$645$	−5.75336	+	1.72030i	−0.226538	+	0.0677368i
$646$	−0.0373851	+	0.115059i	−0.00147090	+	0.00452695i
$647$	−37.0683	−	12.0442i	−1.45731	−	0.473508i	−0.530061	−	0.847960i	$-0.677831\pi$
$647$	−37.0683	−	12.0442i	−1.45731	−	0.473508i	−0.927246	+	0.374452i	$0.877831\pi$
$648$	0.210752	+	0.290076i	0.00827913	+	0.0113952i
$649$	−29.3708			−1.15290
$650$	−0.314661	+	0.832472i	−0.0123420	+	0.0326522i
$651$	16.0370			0.628539
$652$	5.36836	+	7.38891i	0.210241	+	0.289372i
$653$	−26.9519	−	8.75719i	−1.05471	−	0.342695i	−0.270193	−	0.962806i	$-0.587088\pi$
$653$	−26.9519	−	8.75719i	−1.05471	−	0.342695i	−0.784514	+	0.620111i	$0.787088\pi$
$654$	−0.305378	+	0.939857i	−0.0119412	+	0.0367513i
$655$	22.3468	−	29.2783i	0.873163	−	1.14400i
$656$	−7.30538	−	22.4836i	−0.285227	−	0.877839i
$657$		−	0.424804i		−	0.0165732i
$658$	−4.07495	+	1.32403i	−0.158858	+	0.0516161i
$659$	−18.0864	−	13.1406i	−0.704547	−	0.511883i	0.176863	−	0.984236i	$-0.443405\pi$
$659$	−18.0864	−	13.1406i	−0.704547	−	0.511883i	−0.881410	+	0.472352i	$0.843405\pi$
$660$	16.0895	−	11.1189i	0.626283	−	0.432804i
$661$	−23.6349	+	17.1717i	−0.919290	+	0.667903i	−0.943347	−	0.331807i	$-0.892342\pi$
$661$	−23.6349	+	17.1717i	−0.919290	+	0.667903i	0.0240570	+	0.999711i	$0.492342\pi$
$662$	0.690049	−	0.949771i	0.0268195	−	0.0369139i
$663$	−1.16132	+	1.59842i	−0.0451019	+	0.0620774i
$664$	0.213789	−	0.155327i	0.00829662	−	0.00602785i
$665$	−10.4713	−	7.99232i	−0.406061	−	0.309929i
$666$	−0.104424	−	0.0758687i	−0.00404636	−	0.00293985i
$667$	17.8813	−	5.81000i	0.692368	−	0.224964i
$668$			14.3776i			0.556287i
$669$	−1.75613	−	5.40480i	−0.0678958	−	0.208962i
$670$	−0.0612751	+	2.59453i	−0.00236726	+	0.100236i
$671$	−12.8302	+	39.4873i	−0.495305	+	1.52439i
$672$	4.44605	+	1.44461i	0.171510	+	0.0557270i
$673$	1.89000	+	2.60136i	0.0728542	+	0.100275i	0.843889	−	0.536518i	$-0.180261\pi$
$673$	1.89000	+	2.60136i	0.0728542	+	0.100275i	−0.771035	+	0.636793i	$0.780261\pi$
$674$	2.40760			0.0927372
$675$	−4.82292	+	1.31888i	−0.185634	+	0.0507636i
$676$	18.0729			0.695111
$677$	27.7711	+	38.2236i	1.06733	+	1.46905i	0.872751	+	0.488166i	$0.162334\pi$
$677$	27.7711	+	38.2236i	1.06733	+	1.46905i	0.194579	+	0.980887i	$0.437666\pi$
$678$	−0.146092	−	0.0474681i	−0.00561062	−	0.00182300i
$679$	−0.0454227	+	0.139797i	−0.00174316	+	0.00536490i
$680$	0.754194	+	0.264897i	0.0289220	+	0.0101583i
$681$	−1.12598	−	3.46541i	−0.0431476	−	0.132795i
$682$			1.45042i			0.0555395i
$683$	−35.4294	+	11.5117i	−1.35567	+	0.440483i	−0.894595	−	0.446879i	$-0.852536\pi$
$683$	−35.4294	+	11.5117i	−1.35567	+	0.440483i	−0.461074	+	0.887362i	$0.652536\pi$
$684$	−2.17708	−	1.58174i	−0.0832426	−	0.0604793i
$685$	21.6108	+	0.510382i	0.825705	+	0.0195007i
$686$	1.58934	−	1.15473i	0.0606814	−	0.0440876i
$687$	−0.976460	+	1.34398i	−0.0372543	+	0.0512761i
$688$	−6.23777	+	8.58556i	−0.237813	+	0.327321i
$689$	−17.7170	+	12.8721i	−0.674962	+	0.490389i
$690$	0.473155	+	0.0111745i	0.0180127	+	0.000425406i
$691$	8.88522	+	6.45549i	0.338010	+	0.245578i	0.743822	−	0.668378i	$-0.233011\pi$
$691$	8.88522	+	6.45549i	0.338010	+	0.245578i	−0.405812	+	0.913957i	$0.633011\pi$
$692$	−8.80933	+	2.86232i	−0.334880	+	0.108809i
$693$		−	19.1476i		−	0.727357i
$694$	−0.707380	−	2.17709i	−0.0268518	−	0.0826412i
$695$	−28.5501	−	10.0277i	−1.08297	−	0.380373i
$696$	0.884016	−	2.72072i	0.0335085	−	0.103129i
$697$	−5.67273	−	1.84318i	−0.214870	−	0.0698154i
$698$	1.48054	+	2.03779i	0.0560394	+	0.0771316i
$699$	7.85899			0.297254
$700$	−27.1584	+	33.8922i	−1.02649	+	1.28101i
$701$	22.4086			0.846361			0.423180	−	0.906046i	$-0.360914\pi$
$701$	22.4086			0.846361			0.423180	+	0.906046i	$0.360914\pi$
$702$	0.104621	+	0.143998i	0.00394865	+	0.00543485i
$703$	1.84638	+	0.599926i	0.0696376	+	0.0226266i
$704$	10.5932	−	32.6024i	0.399245	−	1.22875i
$705$	0.577534	−	24.4542i	0.0217512	−	0.920997i
$706$	−0.407085	−	1.25288i	−0.0153209	−	0.0471527i
$707$			13.9276i			0.523803i
$708$	12.6718	−	4.11732i	0.476236	−	0.154738i
$709$	−11.8357	−	8.59914i	−0.444499	−	0.322948i	0.342921	−	0.939364i	$-0.388584\pi$
$709$	−11.8357	−	8.59914i	−0.444499	−	0.322948i	−0.787420	+	0.616417i	$0.788584\pi$
$710$	−1.16907	−	0.892296i	−0.0438742	−	0.0334873i
$711$	5.14155	−	3.73555i	0.192823	−	0.140094i
$712$	−2.06271	+	2.83907i	−0.0773032	+	0.106399i
$713$	5.09394	−	7.01121i	0.190770	−	0.262572i
$714$	0.315929	−	0.229536i	0.0118233	−	0.00859015i
$715$	16.0065	−	11.0616i	0.598609	−	0.413679i
$716$	−11.6083	−	8.43392i	−0.433823	−	0.315191i
$717$	−0.539535	+	0.175305i	−0.0201493	+	0.00654690i
$718$		−	1.31321i		−	0.0490085i
$719$	8.80627	+	27.1029i	0.328419	+	1.01077i	0.969874	+	0.243608i	$0.0783310\pi$
$719$	8.80627	+	27.1029i	0.328419	+	1.01077i	−0.641455	+	0.767160i	$0.721669\pi$
$720$	−5.36111	+	7.02400i	−0.199797	+	0.261769i
$721$	11.5260	−	35.4734i	0.429251	−	1.32110i
$722$	1.46714	+	0.476702i	0.0546013	+	0.0177410i
$723$	11.1727	+	15.3779i	0.415517	+	0.571910i
$724$	−7.57778			−0.281626
$725$	31.1310	+	24.9458i	1.15618	+	0.926465i
$726$	0.743738			0.0276027
$727$	−25.8663	−	35.6019i	−0.959329	−	1.32040i	−0.947257	−	0.320476i	$-0.896157\pi$
$727$	−25.8663	−	35.6019i	−0.959329	−	1.32040i	−0.0120725	−	0.999927i	$-0.503843\pi$
$728$	2.94676	+	0.957460i	0.109214	+	0.0354858i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−0.0817427	+	0.0244417i	−0.00302543	+	0.000904629i
$731$	0.827405	+	2.54649i	0.0306027	+	0.0941854i
$732$		−	18.8351i		−	0.696166i
$733$	−25.9854	+	8.44317i	−0.959793	+	0.311856i	−0.746689	−	0.665174i	$-0.768357\pi$
$733$	−25.9854	+	8.44317i	−0.959793	+	0.311856i	−0.213104	+	0.977029i	$0.568357\pi$
$734$	1.28574	+	0.934144i	0.0474575	+	0.0344799i
$735$	7.69703	+	25.7419i	0.283909	+	0.949503i
$736$	2.04380	−	1.48491i	0.0753355	−	0.0547344i
$737$	33.3504	−	45.9029i	1.22848	−	1.69086i
$738$	−0.315842	+	0.434719i	−0.0116263	+	0.0160022i
$739$	13.3227	−	9.67951i	0.490083	−	0.356066i	−0.315133	−	0.949048i	$-0.602049\pi$
$739$	13.3227	−	9.67951i	0.490083	−	0.356066i	0.805216	+	0.592981i	$0.202049\pi$
$740$	2.12113	−	6.03911i	0.0779743	−	0.222002i
$741$	−2.16584	−	1.57358i	−0.0795642	−	0.0578068i
$742$	4.11658	−	1.33756i	0.151124	−	0.0491033i
$743$			35.6012i			1.30608i	0.757322	+	0.653041i	$0.226507\pi$
$743$			35.6012i			1.30608i	−0.757322	+	0.653041i	$0.773493\pi$
$744$	−0.407476	−	1.25408i	−0.0149388	−	0.0459769i
$745$	17.3961	+	25.1728i	0.637345	+	0.922261i
$746$	−0.339434	+	1.04467i	−0.0124275	+	0.0382481i
$747$	0.700939	+	0.227749i	0.0256460	+	0.00833290i
$748$	−5.12573	−	7.05496i	−0.187415	−	0.257955i
$749$	−9.68668			−0.353944
$750$	0.531278	+	0.852165i	0.0193995	+	0.0311167i
$751$	46.0748			1.68129			0.840647	−	0.541583i	$-0.182175\pi$
$751$	46.0748			1.68129			0.840647	+	0.541583i	$0.182175\pi$
$752$	−25.4090	−	34.9725i	−0.926570	−	1.27531i
$753$	2.87726	+	0.934879i	0.104853	+	0.0340689i
$754$	0.438839	−	1.35061i	0.0159816	−	0.0491862i
$755$	14.3910	+	20.8243i	0.523742	+	0.757873i
$756$	2.68419	+	8.26109i	0.0976231	+	0.300453i
$757$			36.6482i			1.33200i	0.745951	+	0.666000i	$0.231995\pi$
$757$			36.6482i			1.33200i	−0.745951	+	0.666000i	$0.768005\pi$
$758$	−2.39998	+	0.779800i	−0.0871711	+	0.0283236i
$759$	−8.37114	−	6.08199i	−0.303853	−	0.220762i
$760$	−0.358933	+	1.02193i	−0.0130199	+	0.0370692i
$761$	22.0116	−	15.9923i	0.797919	−	0.579722i	−0.112384	−	0.993665i	$-0.535849\pi$
$761$	22.0116	−	15.9923i	0.797919	−	0.579722i	0.910303	+	0.413943i	$0.135849\pi$
$762$	−0.662939	+	0.912457i	−0.0240157	+	0.0330548i
$763$	−28.2007	+	38.8149i	−1.02093	+	1.40520i
$764$	−34.7346	+	25.2362i	−1.25666	+	0.913013i
$765$	0.638672	+	2.13597i	0.0230912	+	0.0772261i
$766$	2.50212	+	1.81790i	0.0904053	+	0.0656833i
$767$	12.6064	−	4.09608i	0.455192	−	0.147901i
$768$			15.3585i			0.554202i
$769$	−8.19906	−	25.2341i	−0.295666	−	0.909965i	−0.982997	−	0.183621i	$-0.941218\pi$
$769$	−8.19906	−	25.2341i	−0.295666	−	0.909965i	0.687331	−	0.726344i	$-0.258782\pi$
$770$	−3.68447	+	1.10169i	−0.132779	+	0.0397020i
$771$	6.13747	−	18.8892i	0.221035	−	0.680277i
$772$	−5.96803	−	1.93913i	−0.214794	−	0.0697908i
$773$	−16.9092	−	23.2736i	−0.608183	−	0.837092i	0.388244	−	0.921557i	$-0.373082\pi$
$773$	−16.9092	−	23.2736i	−0.608183	−	0.837092i	−0.996426	+	0.0844651i	$0.973082\pi$
$774$	0.241213			0.00867024
$775$	18.3676	+	0.868059i	0.659783	+	0.0311816i
$776$	0.0120861			0.000433867
$777$	−3.68340	−	5.06977i	−0.132141	−	0.181877i
$778$	1.15514	+	0.375327i	0.0414137	+	0.0134561i
$779$	2.49749	−	7.68650i	0.0894820	−	0.275397i
$780$	−5.35523	+	7.01629i	−0.191748	+	0.251224i
$781$	9.93581	+	30.5793i	0.355531	+	1.09421i
$782$		−	0.211030i		−	0.00754641i
$783$	7.58806	−	2.46551i	0.271175	−	0.0881101i
$784$	38.4138	+	27.9092i	1.37192	+	0.996759i
$785$	15.7478	−	10.8828i	0.562063	−	0.388424i
$786$	−1.19693	+	0.869621i	−0.0426931	+	0.0310183i
$787$	14.6160	−	20.1172i	0.521005	−	0.717102i	−0.464721	−	0.885457i	$-0.653845\pi$
$787$	14.6160	−	20.1172i	0.521005	−	0.717102i	0.985726	+	0.168355i	$0.0538455\pi$
$788$	30.5396	−	42.0341i	1.08793	−	1.49740i
$789$	−18.4698	+	13.4191i	−0.657541	+	0.477732i
$790$	−1.01464	−	0.774430i	−0.0360992	−	0.0275530i
$791$	−6.03342	−	4.38353i	−0.214524	−	0.155861i
$792$	−1.49733	+	0.486512i	−0.0532053	+	0.0172875i
$793$		−	18.7379i		−	0.665404i
$794$	−0.998495	−	3.07305i	−0.0354352	−	0.109058i
$795$	−0.583435	+	24.7040i	−0.0206923	+	0.876160i
$796$	14.9368	−	45.9708i	0.529422	−	1.62939i
$797$	−29.8828	−	9.70951i	−1.05850	−	0.343928i	−0.272503	−	0.962155i	$-0.587851\pi$
$797$	−29.8828	−	9.70951i	−1.05850	−	0.343928i	−0.786000	+	0.618226i	$0.787851\pi$
$798$	0.311019	+	0.428081i	0.0110099	+	0.0151539i
$799$	−10.9067			−0.385851
$800$	5.01398	+	1.89521i	0.177271	+	0.0670057i
$801$	−9.78736			−0.345819
$802$	0.230172	+	0.316805i	0.00812766	+	0.0111868i
$803$	1.77400	+	0.576406i	0.0626030	+	0.0203409i
$804$	−7.95393	+	24.4797i	−0.280513	+	0.863332i
$805$	21.6796	+	7.61455i	0.764104	+	0.268378i
$806$	−0.202277	−	0.622545i	−0.00712491	−	0.0219282i
$807$		−	14.8324i		−	0.522125i
$808$	1.08913	−	0.353881i	0.0383156	−	0.0124495i
$809$	40.8575	+	29.6847i	1.43647	+	1.04366i	0.988765	+	0.149481i	$0.0477603\pi$
$809$	40.8575	+	29.6847i	1.43647	+	1.04366i	0.447710	+	0.894179i	$0.352240\pi$
$810$	0.200786	+	0.00474198i	0.00705491	+	0.000166616i
$811$	−20.3558	+	14.7894i	−0.714789	+	0.519325i	−0.884715	−	0.466132i	$-0.845647\pi$
$811$	−20.3558	+	14.7894i	−0.714789	+	0.519325i	0.169926	+	0.985457i	$0.445647\pi$
$812$	40.7356	−	56.0677i	1.42954	−	1.96759i
$813$	−3.78369	+	5.20780i	−0.132700	+	0.182646i
$814$	0.458521	−	0.333135i	0.0160712	−	0.0116764i
$815$	10.2497	+	0.242068i	0.359032	+	0.00847927i
$816$	3.18744	+	2.31581i	0.111583	+	0.0810696i
$817$	−3.45047	+	1.12113i	−0.120717	+	0.0392233i
$818$		−	1.62697i		−	0.0568856i
$819$	2.67034	+	8.21847i	0.0933093	+	0.287177i
$820$	−25.1409	−	8.83028i	−0.877957	−	0.308367i
$821$	−6.37524	+	19.6210i	−0.222498	+	0.684777i	0.776038	+	0.630686i	$0.217226\pi$
$821$	−6.37524	+	19.6210i	−0.222498	+	0.684777i	−0.998536	+	0.0540914i	$0.982774\pi$
$822$	−0.825815	−	0.268324i	−0.0288036	−	0.00935886i
$823$	−21.0790	−	29.0128i	−0.734769	−	1.01132i	−0.998903	−	0.0468368i	$-0.985086\pi$
$823$	−21.0790	−	29.0128i	−0.734769	−	1.01132i	0.264133	−	0.964486i	$-0.414914\pi$
$824$	−3.06686			−0.106839
$825$	1.03643	−	21.9302i	0.0360839	−	0.763513i
$826$	−2.61990			−0.0911580
$827$	−2.78400	−	3.83184i	−0.0968090	−	0.133246i	0.757865	−	0.652412i	$-0.226243\pi$
$827$	−2.78400	−	3.83184i	−0.0968090	−	0.133246i	−0.854674	+	0.519166i	$0.826243\pi$
$828$	4.46427	+	1.45053i	0.155144	+	0.0504093i
$829$	8.79981	−	27.0830i	0.305630	−	0.940632i	−0.673811	−	0.738903i	$-0.735344\pi$
$829$	8.79981	−	27.0830i	0.305630	−	0.940632i	0.979441	−	0.201729i	$-0.0646560\pi$
$830$	0.00349489	−	0.147982i	0.000121309	−	0.00513652i
$831$	−2.07343	−	6.38136i	−0.0719265	−	0.221367i
$832$			15.4708i			0.536355i
$833$	11.3936	−	3.70200i	0.394765	−	0.128267i
$834$	0.983357	+	0.714451i	0.0340509	+	0.0247394i
$835$	12.8297	+	9.79236i	0.443991	+	0.338879i
$836$	9.55941	−	6.94532i	0.330619	−	0.240209i
$837$	2.16165	−	2.97525i	0.0747175	−	0.102840i
$838$	0.0278685	−	0.0383577i	0.000962700	−	0.00132504i
$839$	−0.619476	+	0.450076i	−0.0213867	+	0.0155383i	−0.598427	−	0.801177i	$-0.704207\pi$
$839$	−0.619476	+	0.450076i	−0.0213867	+	0.0155383i	0.577041	+	0.816715i	$0.304207\pi$
$840$	2.87621	−	1.98765i	0.0992386	−	0.0685806i
$841$	−28.0384	−	20.3711i	−0.966841	−	0.702451i
$842$	1.59388	−	0.517883i	0.0549287	−	0.0178474i
$843$		−	20.4867i		−	0.705600i
$844$	10.0815	+	31.0278i	0.347021	+	1.06802i
$845$	12.3092	−	16.1272i	0.423448	−	0.554791i
$846$	−0.303628	+	0.934470i	−0.0104389	+	0.0321278i
$847$	34.3410	+	11.1581i	1.17997	+	0.383395i
$848$	25.6686	+	35.3297i	0.881462	+	1.21323i
$849$	−11.4177			−0.391856
$850$	0.374266	−	0.245792i	0.0128372	−	0.00843061i
$851$	−3.38644			−0.116086
$852$	−8.57347	−	11.8004i	−0.293722	−	0.404274i
$853$	−33.0292	−	10.7318i	−1.13090	−	0.367451i	−0.316981	−	0.948432i	$-0.602669\pi$
$853$	−33.0292	−	10.7318i	−1.13090	−	0.367451i	−0.813917	+	0.580981i	$0.802669\pi$
$854$	−1.14447	+	3.52230i	−0.0391628	+	0.120531i
$855$	−2.89422	+	0.865395i	−0.0989802	+	0.0295959i
$856$	0.246124	+	0.757493i	0.00841236	+	0.0258906i
$857$			54.2561i			1.85335i	0.375860	+	0.926676i	$0.377347\pi$
$857$			54.2561i			1.85335i	−0.375860	+	0.926676i	$0.622653\pi$
$858$	−0.743297	+	0.241512i	−0.0253757	+	0.00824508i
$859$	12.8710	+	9.35134i	0.439154	+	0.319064i	0.785299	−	0.619117i	$-0.212509\pi$
$859$	12.8710	+	9.35134i	0.439154	+	0.319064i	−0.346145	+	0.938181i	$0.612509\pi$
$860$	3.42672	+	11.4603i	0.116850	+	0.390793i
$861$	−21.1055	+	15.3340i	−0.719272	+	0.522582i
$862$	−1.10823	+	1.52535i	−0.0377464	+	0.0519535i
$863$	−13.2083	+	18.1797i	−0.449617	+	0.618845i	−0.972315	−	0.233673i	$-0.924926\pi$
$863$	−13.2083	+	18.1797i	−0.449617	+	0.618845i	0.522698	+	0.852518i	$0.324926\pi$
$864$	0.867300	−	0.630131i	0.0295062	−	0.0214375i
$865$	−3.44572	+	9.81040i	−0.117158	+	0.333563i
$866$	−0.992896	−	0.721381i	−0.0337400	−	0.0245135i
$867$	−15.2226	+	4.94611i	−0.516985	+	0.167979i
$868$		−	31.9446i		−	1.08427i
$869$	8.62336	+	26.5400i	0.292527	+	0.900307i
$870$	−0.911015	−	1.31827i	−0.0308863	−	0.0446936i
$871$	−7.91289	+	24.3534i	−0.268118	+	0.825183i
$872$	3.75184	+	1.21905i	0.127053	+	0.0412822i
$873$	0.0198131	+	0.0272704i	0.000670572	+	0.000922963i
$874$	0.285944			0.00967219
$875$	11.7462	+	47.3180i	0.397094	+	1.59964i
$876$	−0.846181			−0.0285898
$877$	−15.9146	−	21.9046i	−0.537399	−	0.739667i	0.450836	−	0.892607i	$-0.351126\pi$
$877$	−15.9146	−	21.9046i	−0.537399	−	0.739667i	−0.988235	+	0.152940i	$0.951126\pi$
$878$	−0.370173	−	0.120276i	−0.0124927	−	0.00405913i
$879$	8.82258	−	27.1531i	0.297578	−	0.915852i
$880$	−22.0581	−	31.9189i	−0.743578	−	1.07598i
$881$	−2.41440	−	7.43077i	−0.0813433	−	0.250349i	0.902111	−	0.431503i	$-0.142017\pi$
$881$	−2.41440	−	7.43077i	−0.0813433	−	0.250349i	−0.983455	+	0.181154i	$0.942017\pi$
$882$		−	1.07925i		−	0.0363401i
$883$	−55.4476	+	18.0160i	−1.86596	+	0.606287i	−0.873018	+	0.487688i	$0.837840\pi$
$883$	−55.4476	+	18.0160i	−1.86596	+	0.606287i	−0.992942	+	0.118599i	$0.962160\pi$
$884$	3.18394	+	2.31327i	0.107088	+	0.0778036i
$885$	4.95652	−	14.1118i	0.166612	−	0.474363i
$886$	−0.116804	+	0.0848629i	−0.00392410	+	0.00285102i
$887$	−5.08205	+	6.99484i	−0.170638	+	0.234864i	−0.885768	−	0.464128i	$-0.846368\pi$
$887$	−5.08205	+	6.99484i	−0.170638	+	0.234864i	0.715130	+	0.698992i	$0.246368\pi$
$888$	−0.302863	+	0.416855i	−0.0101634	+	0.0139887i
$889$	−44.2994	+	32.1854i	−1.48576	+	1.07946i
$890$	0.563130	+	1.88333i	0.0188762	+	0.0631293i
$891$	−3.55235	−	2.58093i	−0.119008	−	0.0864644i
$892$	−10.7660	+	3.49809i	−0.360472	+	0.117125i
$893$		−	14.7785i		−	0.494543i
$894$	−0.379817	−	1.16896i	−0.0127030	−	0.0390957i
$895$	−15.4322	+	4.61434i	−0.515840	+	0.154240i
$896$	3.83414	−	11.8003i	0.128090	−	0.394219i
$897$	4.44123	+	1.44304i	0.148288	+	0.0481818i
$898$	0.730099	+	1.00490i	0.0243637	+	0.0335338i
$899$	−29.3420			−0.978612
$900$	2.62711	+	9.60693i	0.0875704	+	0.320231i
$901$	11.0181			0.367067
$902$	−1.38684	−	1.90883i	−0.0461769	−	0.0635570i
$903$	11.1377	+	3.61885i	0.370638	+	0.120428i
$904$	−0.189490	+	0.583189i	−0.00630233	+	0.0193966i
$905$	−5.16111	+	6.76196i	−0.171561	+	0.224775i
$906$	−0.314205	−	0.967022i	−0.0104387	−	0.0321272i
$907$		−	40.4367i		−	1.34268i	−0.741151	−	0.671339i	$-0.765720\pi$
$907$		−	40.4367i		−	1.34268i	0.741151	−	0.671339i	$-0.234280\pi$
$908$	−6.90285	+	2.24287i	−0.229079	+	0.0744324i
$909$	2.58392	+	1.87733i	0.0857032	+	0.0622670i
$910$	1.42779	−	0.986701i	0.0473309	−	0.0327088i
$911$	40.9074	−	29.7210i	1.35532	−	0.984700i	0.356596	−	0.934259i	$-0.383937\pi$
$911$	40.9074	−	29.7210i	1.35532	−	0.984700i	0.998727	−	0.0504407i	$-0.0160626\pi$
$912$	−3.13790	+	4.31895i	−0.103906	+	0.143015i
$913$	−1.90217	+	2.61812i	−0.0629528	+	0.0866471i
$914$	−1.46308	+	1.06299i	−0.0483944	+	0.0351606i
$915$	−16.8073	−	12.8283i	−0.555633	−	0.424090i
$916$	2.67712	+	1.94504i	0.0884545	+	0.0642660i
$917$	−68.3130	+	22.1962i	−2.25590	+	0.732985i
$918$		−	0.0895519i		−	0.00295565i
$919$	13.3979	+	41.2346i	0.441957	+	1.36020i	0.885787	+	0.464092i	$0.153619\pi$
$919$	13.3979	+	41.2346i	0.441957	+	1.36020i	−0.443831	+	0.896111i	$0.646381\pi$
$920$	0.0446079	−	1.88880i	0.00147068	−	0.0622720i
$921$	6.34773	−	19.5363i	0.209165	−	0.643743i
$922$	−2.69309	−	0.875039i	−0.0886923	−	0.0288179i
$923$	−8.52924	−	11.7395i	−0.280743	−	0.386410i
$924$	−38.1407			−1.25474
$925$	−3.94428	−	6.00591i	−0.129687	−	0.197473i
$926$	0.00405712			0.000133325
$927$	−5.02758	−	6.91986i	−0.165127	−	0.227278i
$928$	−8.13472	−	2.64313i	−0.267035	−	0.0867650i
$929$	10.5605	−	32.5020i	0.346480	−	1.06636i	−0.614307	−	0.789067i	$-0.710564\pi$
$929$	10.5605	−	32.5020i	0.346480	−	1.06636i	0.960787	−	0.277289i	$-0.0894358\pi$
$930$	−0.696885	−	0.244768i	−0.0228518	−	0.00802627i
$931$	5.01618	+	15.4382i	0.164399	+	0.505967i
$932$		−	15.6546i		−	0.512783i
$933$	−16.6907	+	5.42312i	−0.546427	+	0.177545i
$934$	2.38596	+	1.73350i	0.0780710	+	0.0567219i
$935$	−9.78647	−	0.231127i	−0.320052	−	0.00755867i
$936$	0.574830	−	0.417638i	0.0187889	−	0.0136509i
$937$	16.3990	−	22.5713i	0.535731	−	0.737371i	−0.452259	−	0.891887i	$-0.649382\pi$
$937$	16.3990	−	22.5713i	0.535731	−	0.737371i	0.987990	+	0.154516i	$0.0493817\pi$
$938$	2.97489	−	4.09458i	0.0971334	−	0.133693i
$939$	2.41543	−	1.75491i	0.0788246	−	0.0572694i
$940$	−48.7110	−	1.15041i	−1.58878	−	0.0375222i
$941$	43.9507	+	31.9321i	1.43275	+	1.04096i	0.989496	+	0.144561i	$0.0461769\pi$
$941$	43.9507	+	31.9321i	1.43275	+	1.04096i	0.443257	+	0.896395i	$0.353823\pi$
$942$	−0.731284	+	0.237609i	−0.0238265	+	0.00774171i
$943$			14.0978i			0.459086i
$944$	−8.16808	−	25.1388i	−0.265848	−	0.818197i
$945$	9.19986	+	3.23128i	0.299271	+	0.105114i
$946$	−0.327297	+	1.00732i	−0.0106413	+	0.0327507i
$947$	4.02460	+	1.30767i	0.130782	+	0.0424936i	0.373677	−	0.927559i	$-0.378097\pi$
$947$	4.02460	+	1.30767i	0.130782	+	0.0424936i	−0.242895	+	0.970053i	$0.578097\pi$
$948$	−7.44097	−	10.2416i	−0.241672	−	0.332632i
$949$	−0.841815			−0.0273265
$950$	0.333046	+	0.507127i	0.0108055	+	0.0164534i
$951$	16.1708			0.524375
$952$	−0.916291	−	1.26117i	−0.0296971	−	0.0408746i
$953$	45.5848	+	14.8114i	1.47664	+	0.479788i	0.933106	−	0.359601i	$-0.117087\pi$
$953$	45.5848	+	14.8114i	1.47664	+	0.479788i	0.543531	+	0.839389i	$0.317087\pi$
$954$	0.306730	−	0.944017i	0.00993074	−	0.0305637i
$955$	−1.13794	+	48.1831i	−0.0368229	+	1.55917i
$956$	0.349197	+	1.07472i	0.0112938	+	0.0347588i
$957$			35.0334i			1.13247i
$958$	−0.639459	+	0.207773i	−0.0206600	+	0.00671284i
$959$	−34.1052	−	24.7788i	−1.10131	−	0.800151i
$960$	13.8768	+	10.5916i	0.447873	+	0.341842i
$961$	14.1377	−	10.2716i	0.456055	−	0.331343i
$962$	−0.150346	+	0.206933i	−0.00484734	+	0.00667179i
$963$	−1.30568	+	1.79712i	−0.0420750	+	0.0579113i
$964$	30.6318	−	22.2553i	0.986582	−	0.716794i
$965$	−5.79509	+	4.00480i	−0.186551	+	0.128919i
$966$	−0.746713	−	0.542518i	−0.0240251	−	0.0174552i
$967$	19.8607	−	6.45312i	0.638676	−	0.207518i	0.0282614	−	0.999601i	$-0.491003\pi$
$967$	19.8607	−	6.45312i	0.638676	−	0.207518i	0.610414	+	0.792082i	$0.291003\pi$
$968$		−	2.96895i		−	0.0954257i
$969$	0.416225	+	1.28101i	0.0133711	+	0.0411519i
$970$	0.00410752	−	0.00538157i	0.000131884	−	0.000172792i
$971$	4.96713	−	15.2872i	0.159403	−	0.490591i	−0.839178	−	0.543857i	$-0.816963\pi$
$971$	4.96713	−	15.2872i	0.159403	−	0.490591i	0.998580	+	0.0532663i	$0.0169632\pi$
$972$	1.89444	+	0.615541i	0.0607642	+	0.0197435i
$973$	34.6863	+	47.7417i	1.11199	+	1.53053i
$974$	−2.28406			−0.0731860
$975$	2.61356	+	9.55737i	0.0837009	+	0.306081i
$976$	−37.3657			−1.19605
$977$	20.9055	+	28.7739i	0.668826	+	0.920560i	0.999733	−	0.0231034i	$-0.00735470\pi$
$977$	20.9055	+	28.7739i	0.668826	+	0.920560i	−0.330907	+	0.943663i	$0.607355\pi$
$978$	−0.391674	−	0.127263i	−0.0125244	−	0.00406941i
$979$	13.2802	−	40.8723i	0.424438	−	1.30629i
$980$	51.2761	−	15.3320i	1.63795	−	0.489762i
$981$	3.39991	+	10.4638i	0.108551	+	0.334085i
$982$			0.994014i			0.0317202i
$983$	17.5671	−	5.70790i	0.560303	−	0.182054i	−0.0151542	−	0.999885i	$-0.504824\pi$
$983$	17.5671	−	5.70790i	0.560303	−	0.182054i	0.575458	+	0.817832i	$0.304824\pi$
$984$	1.73537	+	1.26082i	0.0553216	+	0.0401935i
$985$	−16.7087	−	55.8805i	−0.532384	−	1.78050i
$986$	−0.578039	+	0.419970i	−0.0184085	+	0.0133746i
$987$	−28.0391	+	38.5925i	−0.892494	+	1.22841i
$988$	−3.13446	+	4.31421i	−0.0997204	+	0.137253i
$989$	5.11986	−	3.71979i	0.162802	−	0.118283i
$990$	−0.292245	+	0.832056i	−0.00928815	+	0.0264445i
$991$	33.6476	+	24.4464i	1.06885	+	0.776566i	0.975705	−	0.219087i	$-0.0703078\pi$
$991$	33.6476	+	24.4464i	1.06885	+	0.776566i	0.0931455	+	0.995653i	$0.470308\pi$
$992$	−3.74959	+	1.21832i	−0.119050	+	0.0386816i
$993$		−	13.0705i		−	0.414779i
$994$	0.886283	+	2.72770i	0.0281112	+	0.0865174i
$995$	−30.8484	−	44.6387i	−0.977959	−	1.41514i
$996$	0.453660	−	1.39622i	0.0143748	−	0.0442410i
$997$	30.2792	+	9.83830i	0.958952	+	0.311582i	0.746348	−	0.665556i	$-0.231806\pi$
$997$	30.2792	+	9.83830i	0.958952	+	0.311582i	0.212604	+	0.977138i	$0.431806\pi$
$998$	−0.247161	−	0.340189i	−0.00782376	−	0.0107685i
$999$	−1.43706			−0.0454665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.i.a.64.3	yes	16
3.2	odd	2		225.2.m.b.64.2		16
5.2	odd	4		375.2.g.e.301.2		16
5.3	odd	4		375.2.g.d.301.3		16
5.4	even	2		375.2.i.c.199.2		16
25.3	odd	20		1875.2.a.p.1.4		8
25.4	even	10		1875.2.b.h.1249.9		16
25.9	even	10	inner	75.2.i.a.34.3	✓	16
25.12	odd	20		375.2.g.e.76.2		16
25.13	odd	20		375.2.g.d.76.3		16
25.16	even	5		375.2.i.c.49.2		16
25.21	even	5		1875.2.b.h.1249.8		16
25.22	odd	20		1875.2.a.m.1.5		8
75.47	even	20		5625.2.a.bd.1.4		8
75.53	even	20		5625.2.a.t.1.5		8
75.59	odd	10		225.2.m.b.109.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.3	✓	16	25.9	even	10	inner
75.2.i.a.64.3	yes	16	1.1	even	1	trivial
225.2.m.b.64.2		16	3.2	odd	2
225.2.m.b.109.2		16	75.59	odd	10
375.2.g.d.76.3		16	25.13	odd	20
375.2.g.d.301.3		16	5.3	odd	4
375.2.g.e.76.2		16	25.12	odd	20
375.2.g.e.301.2		16	5.2	odd	4
375.2.i.c.49.2		16	25.16	even	5
375.2.i.c.199.2		16	5.4	even	2
1875.2.a.m.1.5		8	25.22	odd	20
1875.2.a.p.1.4		8	25.3	odd	20
1875.2.b.h.1249.8		16	25.21	even	5
1875.2.b.h.1249.9		16	25.4	even	10
5625.2.a.t.1.5		8	75.53	even	20
5625.2.a.bd.1.4		8	75.47	even	20

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0527945 + 0.0726655i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.615541 - 1.89444i) q^{4} +(-1.27125 - 1.83954i) q^{5} +(0.0277557 + 0.0854234i) q^{6} +4.36070i q^{7} +(0.341004 - 0.110799i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.0527945 + 0.0726655i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.615541 - 1.89444i) q^{4} +(-1.27125 - 1.83954i) q^{5} +(0.0277557 + 0.0854234i) q^{6} +4.36070i q^{7} +(0.341004 - 0.110799i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.0665563 - 0.189494i) q^{10} +(-3.55235 + 2.58093i) q^{11} +(1.17083 - 1.61151i) q^{12} +(1.16479 - 1.60319i) q^{13} +(-0.316872 + 0.230221i) q^{14} +(-0.640580 - 2.14235i) q^{15} +(-3.19696 - 2.32273i) q^{16} +(-0.948224 + 0.308097i) q^{17} +0.0898194i q^{18} +(-0.417468 - 1.28484i) q^{19} +(-4.26741 + 1.27599i) q^{20} +(-1.34753 + 4.14727i) q^{21} +(-0.375089 - 0.121874i) q^{22} +(1.38512 + 1.90646i) q^{23} +0.358553 q^{24} +(-1.76785 + 4.67704i) q^{25} +0.177991 q^{26} +(0.587785 + 0.809017i) q^{27} +(8.26109 + 2.68419i) q^{28} +(2.46551 - 7.58806i) q^{29} +(0.121856 - 0.159652i) q^{30} +(-1.13645 - 3.49762i) q^{31} -1.07204i q^{32} +(-4.17603 + 1.35688i) q^{33} +(-0.0724490 - 0.0526373i) q^{34} +(8.02171 - 5.54354i) q^{35} +(1.61151 - 1.17083i) q^{36} +(-0.844681 + 1.16260i) q^{37} +(0.0713231 - 0.0981678i) q^{38} +(1.60319 - 1.16479i) q^{39} +(-0.637321 - 0.486439i) q^{40} +(4.83992 + 3.51641i) q^{41} +(-0.372506 + 0.121034i) q^{42} -2.68554i q^{43} +(2.70280 + 8.31838i) q^{44} +(0.0527945 - 2.23544i) q^{45} +(-0.0654066 + 0.201301i) q^{46} +(10.4039 + 3.38042i) q^{47} +(-2.32273 - 3.19696i) q^{48} -12.0157 q^{49} +(-0.433192 + 0.118461i) q^{50} -0.997022 q^{51} +(-2.32018 - 3.19345i) q^{52} +(-10.5102 - 3.41496i) q^{53} +(-0.0277557 + 0.0854234i) q^{54} +(9.26366 + 3.25369i) q^{55} +(0.483161 + 1.48702i) q^{56} -1.35096i q^{57} +(0.681555 - 0.221451i) q^{58} +(5.41147 + 3.93167i) q^{59} +(-4.45285 - 0.105163i) q^{60} +(7.64982 - 5.55792i) q^{61} +(0.194158 - 0.267235i) q^{62} +(-2.56316 + 3.52788i) q^{63} +(-6.31602 + 4.58886i) q^{64} +(-4.42988 - 0.104621i) q^{65} +(-0.319070 - 0.231818i) q^{66} +(-12.2894 + 3.99307i) q^{67} +1.98600i q^{68} +(0.728201 + 2.24117i) q^{69} +(0.826326 + 0.290232i) q^{70} +(2.26280 - 6.96418i) q^{71} +(0.341004 + 0.110799i) q^{72} +(-0.249694 - 0.343674i) q^{73} -0.129076 q^{74} +(-3.12661 + 3.90184i) q^{75} -2.69101 q^{76} +(-11.2547 - 15.4907i) q^{77} +(0.169280 + 0.0550023i) q^{78} +(1.96390 - 6.04425i) q^{79} +(-0.208626 + 8.83372i) q^{80} +(0.309017 + 0.951057i) q^{81} +0.537343i q^{82} +(0.700939 - 0.227749i) q^{83} +(7.02730 + 5.10563i) q^{84} +(1.77219 + 1.35263i) q^{85} +(0.195146 - 0.141782i) q^{86} +(4.68968 - 6.45479i) q^{87} +(-0.925401 + 1.27370i) q^{88} +(-7.91814 + 5.75286i) q^{89} +(0.165227 - 0.114183i) q^{90} +(6.99105 + 5.07929i) q^{91} +(4.46427 - 1.45053i) q^{92} -3.67761i q^{93} +(0.303628 + 0.934470i) q^{94} +(-1.83281 + 2.40130i) q^{95} +(0.331279 - 1.01957i) q^{96} +(0.0320583 + 0.0104164i) q^{97} +(-0.634365 - 0.873128i) q^{98} -4.39094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} - 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} + 10 q^{17} - 2 q^{19} + 20 q^{20} + 4 q^{21} - 30 q^{22} - 20 q^{23} + 24 q^{24} - 10 q^{25} + 12 q^{26} + 30 q^{28} + 16 q^{29} - 20 q^{30} + 6 q^{31} + 10 q^{33} - 36 q^{34} + 10 q^{35} - 2 q^{36} - 10 q^{37} + 30 q^{38} - 8 q^{39} + 10 q^{40} - 14 q^{41} - 10 q^{42} + 26 q^{44} + 16 q^{46} + 40 q^{47} + 20 q^{50} - 32 q^{51} + 40 q^{52} + 10 q^{53} - 2 q^{54} + 10 q^{55} + 10 q^{58} + 12 q^{59} - 30 q^{60} - 10 q^{62} - 10 q^{63} + 8 q^{64} - 70 q^{65} + 16 q^{66} - 40 q^{67} - 12 q^{69} + 30 q^{70} - 8 q^{71} - 30 q^{72} - 20 q^{73} - 52 q^{74} - 32 q^{76} - 40 q^{77} - 20 q^{79} - 4 q^{81} + 10 q^{83} + 12 q^{84} - 20 q^{85} - 36 q^{86} + 40 q^{87} - 40 q^{88} + 18 q^{89} + 30 q^{90} + 26 q^{91} + 10 q^{92} - 38 q^{94} - 40 q^{95} - 26 q^{96} + 40 q^{97} + 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 - 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 + 10 * q^17 - 2 * q^19 + 20 * q^20 + 4 * q^21 - 30 * q^22 - 20 * q^23 + 24 * q^24 - 10 * q^25 + 12 * q^26 + 30 * q^28 + 16 * q^29 - 20 * q^30 + 6 * q^31 + 10 * q^33 - 36 * q^34 + 10 * q^35 - 2 * q^36 - 10 * q^37 + 30 * q^38 - 8 * q^39 + 10 * q^40 - 14 * q^41 - 10 * q^42 + 26 * q^44 + 16 * q^46 + 40 * q^47 + 20 * q^50 - 32 * q^51 + 40 * q^52 + 10 * q^53 - 2 * q^54 + 10 * q^55 + 10 * q^58 + 12 * q^59 - 30 * q^60 - 10 * q^62 - 10 * q^63 + 8 * q^64 - 70 * q^65 + 16 * q^66 - 40 * q^67 - 12 * q^69 + 30 * q^70 - 8 * q^71 - 30 * q^72 - 20 * q^73 - 52 * q^74 - 32 * q^76 - 40 * q^77 - 20 * q^79 - 4 * q^81 + 10 * q^83 + 12 * q^84 - 20 * q^85 - 36 * q^86 + 40 * q^87 - 40 * q^88 + 18 * q^89 + 30 * q^90 + 26 * q^91 + 10 * q^92 - 38 * q^94 - 40 * q^95 - 26 * q^96 + 40 * q^97 + 60 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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