LMFDB - Embedded newform 930.2.bg.e.691.1

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			691.1
Root			$-1.93590 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	930.691
Dual form			930.2.bg.e.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.731733 + 0.325789i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.731733 + 0.325789i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(-0.351475 + 3.34406i) q^{11} +(-0.669131 - 0.743145i) q^{12} +(0.273056 - 0.303259i) q^{13} +(-0.0837254 - 0.796594i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.447463 + 4.25733i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(-1.52677 - 1.69565i) q^{19} +(0.104528 - 0.994522i) q^{20} +(-0.783478 + 0.166533i) q^{21} +(-3.07178 - 1.36764i) q^{22} +(0.181209 - 0.131656i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.204038 + 0.353404i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.783478 + 0.166533i) q^{28} +(-0.936222 + 2.88139i) q^{29} -1.00000 q^{30} +(3.62365 + 4.22719i) q^{31} -1.00000 q^{32} +(-1.03906 + 3.19791i) q^{33} +(-4.18724 - 0.890024i) q^{34} +(-0.648008 - 0.470805i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.33958 + 4.05226i) q^{37} +(2.08446 - 0.928061i) q^{38} +(0.330140 - 0.239861i) q^{39} +(0.913545 + 0.406737i) q^{40} +(-1.28186 + 0.272468i) q^{41} +(0.0837254 - 0.796594i) q^{42} +(0.0590918 + 0.0656281i) q^{43} +(2.24994 - 2.49881i) q^{44} +(0.104528 + 0.994522i) q^{45} +(0.0692157 + 0.213024i) q^{46} +(-0.284594 - 0.875891i) q^{47} +(0.104528 + 0.994522i) q^{48} +(-4.25462 + 4.72523i) q^{49} +(-0.669131 - 0.743145i) q^{50} +(-0.447463 + 4.25733i) q^{51} +(-0.399158 + 0.0848436i) q^{52} +(6.74800 + 3.00440i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-3.07178 + 1.36764i) q^{55} +(-0.400491 + 0.693670i) q^{56} +(-1.14086 - 1.97603i) q^{57} +(-2.45106 - 1.78080i) q^{58} +(3.08716 + 0.656195i) q^{59} +(0.309017 - 0.951057i) q^{60} -3.72863 q^{61} +(-5.14007 + 2.14003i) q^{62} -0.800982 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.399158 + 0.0848436i) q^{65} +(-2.72030 - 1.97642i) q^{66} +(-6.54793 - 11.3413i) q^{67} +(2.14039 - 3.70726i) q^{68} +(0.204622 - 0.0911036i) q^{69} +(0.648008 - 0.470805i) q^{70} +(4.54481 + 2.02348i) q^{71} +(0.978148 - 0.207912i) q^{72} +(-0.333691 + 3.17486i) q^{73} +(-3.13096 - 3.47729i) q^{74} +(-0.669131 + 0.743145i) q^{75} +(0.238505 + 2.26923i) q^{76} +(-0.832271 - 2.56147i) q^{77} +(0.126102 + 0.388103i) q^{78} +(0.281609 + 2.67933i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(0.136985 - 1.30332i) q^{82} +(8.21325 - 1.74578i) q^{83} +(0.731733 + 0.325789i) q^{84} +(-3.46322 + 2.51618i) q^{85} +(-0.0806764 + 0.0359194i) q^{86} +(-1.51484 + 2.62378i) q^{87} +(1.68124 + 2.91199i) q^{88} +(8.37618 + 6.08565i) q^{89} +(-0.978148 - 0.207912i) q^{90} +(-0.101006 + 0.310863i) q^{91} -0.223987 q^{92} +(2.66559 + 4.88821i) q^{93} +0.920967 q^{94} +(0.705092 - 2.17005i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-10.7049 - 7.77759i) q^{97} +(-3.17921 - 5.50656i) q^{98} +(-1.68124 + 2.91199i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$3$	0.978148	+	0.207912i	0.564734	+	0.120038i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	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
$7$	−0.731733	+	0.325789i	−0.276569	+	0.123137i	−0.540334	−	0.841450i	$-0.681702\pi$
$7$	−0.731733	+	0.325789i	−0.276569	+	0.123137i	0.263765	+	0.964587i	$0.415036\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	−0.978148	+	0.207912i	−0.309317	+	0.0657474i
$11$	−0.351475	+	3.34406i	−0.105974	+	1.00827i	0.804288	+	0.594239i	$0.202547\pi$
$11$	−0.351475	+	3.34406i	−0.105974	+	1.00827i	−0.910262	+	0.414033i	$0.864120\pi$
$12$	−0.669131	−	0.743145i	−0.193161	−	0.214527i
$13$	0.273056	−	0.303259i	0.0757320	−	0.0841089i	−0.704088	−	0.710113i	$-0.748644\pi$
$13$	0.273056	−	0.303259i	0.0757320	−	0.0841089i	0.779820	+	0.626004i	$0.215311\pi$
$14$	−0.0837254	−	0.796594i	−0.0223765	−	0.212899i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.447463	+	4.25733i	0.108526	+	1.03255i	0.904282	+	0.426937i	$0.140407\pi$
$17$	0.447463	+	4.25733i	0.108526	+	1.03255i	−0.795756	+	0.605618i	$0.792926\pi$
$18$	−0.669131	+	0.743145i	−0.157716	+	0.175161i
$19$	−1.52677	−	1.69565i	−0.350266	−	0.389009i	0.542106	−	0.840310i	$-0.317627\pi$
$19$	−1.52677	−	1.69565i	−0.350266	−	0.389009i	−0.892372	+	0.451300i	$0.850960\pi$
$20$	0.104528	−	0.994522i	0.0233733	−	0.222382i
$21$	−0.783478	+	0.166533i	−0.170969	+	0.0363406i
$22$	−3.07178	−	1.36764i	−0.654905	−	0.291583i
$23$	0.181209	−	0.131656i	0.0377847	−	0.0274522i	−0.568733	−	0.822522i	$-0.692566\pi$
$23$	0.181209	−	0.131656i	0.0377847	−	0.0274522i	0.606517	+	0.795070i	$0.292566\pi$
$24$	0.913545	−	0.406737i	0.186477	−	0.0830248i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.204038	+	0.353404i	0.0400151	+	0.0693082i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.783478	+	0.166533i	0.148063	+	0.0314719i
$29$	−0.936222	+	2.88139i	−0.173852	+	0.535061i	−0.999579	−	0.0290083i	$-0.990765\pi$
$29$	−0.936222	+	2.88139i	−0.173852	+	0.535061i	0.825727	+	0.564070i	$0.190765\pi$
$30$	−1.00000			−0.182574
$31$	3.62365	+	4.22719i	0.650828	+	0.759226i
$31$	3.62365	+	4.22719i	0.650828	+	0.759226i
$32$	−1.00000			−0.176777
$33$	−1.03906	+	3.19791i	−0.180878	+	0.556684i
$34$	−4.18724	−	0.890024i	−0.718105	−	0.152638i
$35$	−0.648008	−	0.470805i	−0.109533	−	0.0795806i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−2.33958	+	4.05226i	−0.384624	+	0.666188i	−0.991717	−	0.128443i	$-0.959002\pi$
$37$	−2.33958	+	4.05226i	−0.384624	+	0.666188i	0.607093	+	0.794631i	$0.292335\pi$
$38$	2.08446	−	0.928061i	0.338144	−	0.150551i
$39$	0.330140	−	0.239861i	0.0528647	−	0.0384084i
$40$	0.913545	+	0.406737i	0.144444	+	0.0643107i
$41$	−1.28186	+	0.272468i	−0.200193	+	0.0425524i	−0.306917	−	0.951736i	$-0.599297\pi$
$41$	−1.28186	+	0.272468i	−0.200193	+	0.0425524i	0.106724	+	0.994289i	$0.465964\pi$
$42$	0.0837254	−	0.796594i	0.0129191	−	0.122917i
$43$	0.0590918	+	0.0656281i	0.00901142	+	0.0100082i	0.747634	−	0.664111i	$-0.231190\pi$
$43$	0.0590918	+	0.0656281i	0.00901142	+	0.0100082i	−0.738622	+	0.674120i	$0.764523\pi$
$44$	2.24994	−	2.49881i	0.339191	−	0.376710i
$45$	0.104528	+	0.994522i	0.0155822	+	0.148255i
$46$	0.0692157	+	0.213024i	0.0102053	+	0.0314087i
$47$	−0.284594	−	0.875891i	−0.0415124	−	0.127762i	0.928153	−	0.372200i	$-0.121396\pi$
$47$	−0.284594	−	0.875891i	−0.0415124	−	0.127762i	−0.969665	+	0.244438i	$0.921396\pi$
$48$	0.104528	+	0.994522i	0.0150874	+	0.143547i
$49$	−4.25462	+	4.72523i	−0.607803	+	0.675033i
$50$	−0.669131	−	0.743145i	−0.0946294	−	0.105097i
$51$	−0.447463	+	4.25733i	−0.0626574	+	0.596145i
$52$	−0.399158	+	0.0848436i	−0.0553532	+	0.0117657i
$53$	6.74800	+	3.00440i	0.926910	+	0.412687i	0.813965	−	0.580915i	$-0.197305\pi$
$53$	6.74800	+	3.00440i	0.926910	+	0.412687i	0.112945	+	0.993601i	$0.463972\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	−3.07178	+	1.36764i	−0.414198	+	0.184413i
$56$	−0.400491	+	0.693670i	−0.0535178	+	0.0926956i
$57$	−1.14086	−	1.97603i	−0.151111	−	0.261732i
$58$	−2.45106	−	1.78080i	−0.321840	−	0.233830i
$59$	3.08716	+	0.656195i	0.401913	+	0.0854294i	0.404433	−	0.914567i	$-0.367469\pi$
$59$	3.08716	+	0.656195i	0.401913	+	0.0854294i	−0.00251985	+	0.999997i	$0.500802\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	−3.72863			−0.477402			−0.238701	−	0.971093i	$-0.576722\pi$
$61$	−3.72863			−0.477402			−0.238701	+	0.971093i	$0.576722\pi$
$62$	−5.14007	+	2.14003i	−0.652789	+	0.271784i
$63$	−0.800982			−0.100914
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.399158	+	0.0848436i	0.0495094	+	0.0105236i
$66$	−2.72030	−	1.97642i	−0.334846	−	0.243280i
$67$	−6.54793	−	11.3413i	−0.799957	−	1.38557i	−0.919643	−	0.392755i	$-0.871522\pi$
$67$	−6.54793	−	11.3413i	−0.799957	−	1.38557i	0.119686	−	0.992812i	$-0.461811\pi$
$68$	2.14039	−	3.70726i	0.259560	−	0.449572i
$69$	0.204622	−	0.0911036i	0.0246336	−	0.0109676i
$70$	0.648008	−	0.470805i	0.0774517	−	0.0562720i
$71$	4.54481	+	2.02348i	0.539370	+	0.240143i	0.658295	−	0.752760i	$-0.271278\pi$
$71$	4.54481	+	2.02348i	0.539370	+	0.240143i	−0.118925	+	0.992903i	$0.537945\pi$
$72$	0.978148	−	0.207912i	0.115276	−	0.0245026i
$73$	−0.333691	+	3.17486i	−0.0390556	+	0.371589i	0.957485	+	0.288483i	$0.0931508\pi$
$73$	−0.333691	+	3.17486i	−0.0390556	+	0.371589i	−0.996541	+	0.0831065i	$0.973516\pi$
$74$	−3.13096	−	3.47729i	−0.363967	−	0.404226i
$75$	−0.669131	+	0.743145i	−0.0772645	+	0.0858110i
$76$	0.238505	+	2.26923i	0.0273584	+	0.260298i
$77$	−0.832271	−	2.56147i	−0.0948460	−	0.291906i
$78$	0.126102	+	0.388103i	0.0142783	+	0.0439440i
$79$	0.281609	+	2.67933i	0.0316835	+	0.301448i	0.998876	+	0.0474032i	$0.0150945\pi$
$79$	0.281609	+	2.67933i	0.0316835	+	0.301448i	−0.967192	+	0.254045i	$0.918239\pi$
$80$	−0.669131	+	0.743145i	−0.0748111	+	0.0830861i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	0.136985	−	1.30332i	0.0151274	−	0.143928i
$83$	8.21325	−	1.74578i	0.901521	−	0.191624i	0.266241	−	0.963906i	$-0.414218\pi$
$83$	8.21325	−	1.74578i	0.901521	−	0.191624i	0.635280	+	0.772282i	$0.280885\pi$
$84$	0.731733	+	0.325789i	0.0798386	+	0.0355464i
$85$	−3.46322	+	2.51618i	−0.375639	+	0.272918i
$86$	−0.0806764	+	0.0359194i	−0.00869956	+	0.00387329i
$87$	−1.51484	+	2.62378i	−0.162408	+	0.281298i
$88$	1.68124	+	2.91199i	0.179221	+	0.310419i
$89$	8.37618	+	6.08565i	0.887873	+	0.645078i	0.935323	−	0.353796i	$-0.115109\pi$
$89$	8.37618	+	6.08565i	0.887873	+	0.645078i	−0.0474495	+	0.998874i	$0.515109\pi$
$90$	−0.978148	−	0.207912i	−0.103106	−	0.0219158i
$91$	−0.101006	+	0.310863i	−0.0105883	+	0.0325873i
$92$	−0.223987			−0.0233522
$93$	2.66559	+	4.88821i	0.276408	+	0.506884i
$94$	0.920967			0.0949905
$95$	0.705092	−	2.17005i	0.0723409	−	0.222642i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	−10.7049	−	7.77759i	−1.08692	−	0.789694i	−0.108044	−	0.994146i	$-0.534459\pi$
$97$	−10.7049	−	7.77759i	−1.08692	−	0.789694i	−0.978877	+	0.204452i	$0.934459\pi$
$98$	−3.17921	−	5.50656i	−0.321149	−	0.556247i
$99$	−1.68124	+	2.91199i	−0.168971	+	0.292666i
$100$	0.913545	−	0.406737i	0.0913545	−	0.0406737i
$101$	1.93844	−	1.40836i	0.192882	−	0.140137i	−0.487153	−	0.873317i	$-0.661965\pi$
$101$	1.93844	−	1.40836i	0.192882	−	0.140137i	0.680035	+	0.733180i	$0.261965\pi$
$102$	−3.91069	−	1.74115i	−0.387216	−	0.172400i
$103$	0.972301	−	0.206669i	0.0958036	−	0.0203637i	−0.159760	−	0.987156i	$-0.551072\pi$
$103$	0.972301	−	0.206669i	0.0958036	−	0.0203637i	0.255564	+	0.966792i	$0.417739\pi$
$104$	0.0426555	−	0.405840i	0.00418271	−	0.0397959i
$105$	−0.535961	−	0.595245i	−0.0523045	−	0.0580900i
$106$	−4.94261	+	5.48932i	−0.480068	+	0.533170i
$107$	−0.337340	−	3.20957i	−0.0326119	−	0.310281i	−0.998653	−	0.0518918i	$-0.983475\pi$
$107$	−0.337340	−	3.20957i	−0.0326119	−	0.310281i	0.966041	−	0.258389i	$-0.0831917\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	1.03009	+	3.17028i	0.0986644	+	0.303658i	0.988191	−	0.153225i	$-0.0489659\pi$
$109$	1.03009	+	3.17028i	0.0986644	+	0.303658i	−0.889527	+	0.456883i	$0.848966\pi$
$110$	−0.351475	−	3.34406i	−0.0335118	−	0.318844i
$111$	−3.13096	+	3.47729i	−0.297178	+	0.330049i
$112$	−0.535961	−	0.595245i	−0.0506436	−	0.0562454i
$113$	1.25023	−	11.8951i	0.117612	−	1.11900i	−0.763406	−	0.645918i	$-0.776475\pi$
$113$	1.25023	−	11.8951i	0.117612	−	1.11900i	0.881018	−	0.473082i	$-0.156859\pi$
$114$	2.23186	−	0.474397i	0.209033	−	0.0444314i
$115$	0.204622	+	0.0911036i	0.0190811	+	0.00849545i
$116$	2.45106	−	1.78080i	0.227575	−	0.165343i
$117$	0.372795	−	0.165979i	0.0344649	−	0.0153448i
$118$	−1.57806	+	2.73328i	−0.145272	+	0.251619i
$119$	−1.71441	−	2.96945i	−0.157160	−	0.272209i
$120$	0.809017	+	0.587785i	0.0738528	+	0.0536572i
$121$	−0.299577	−	0.0636770i	−0.0272342	−	0.00578882i
$122$	1.15221	−	3.54614i	0.104316	−	0.321052i
$123$	−1.31050			−0.118164
$124$	−0.446919	−	5.54980i	−0.0401345	−	0.498387i
$125$	−1.00000			−0.0894427
$126$	0.247517	−	0.761779i	0.0220506	−	0.0678646i
$127$	−12.9643	−	2.75564i	−1.15039	−	0.244523i	−0.407032	−	0.913414i	$-0.633436\pi$
$127$	−12.9643	−	2.75564i	−1.15039	−	0.244523i	−0.743361	+	0.668891i	$0.766769\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	0.0441557	+	0.0764798i	0.00388769	+	0.00673367i
$130$	−0.204038	+	0.353404i	−0.0178953	+	0.0309955i
$131$	2.69819	−	1.20131i	0.235742	−	0.104959i	−0.285466	−	0.958389i	$-0.592148\pi$
$131$	2.69819	−	1.20131i	0.235742	−	0.104959i	0.521208	+	0.853430i	$0.325482\pi$
$132$	2.72030	−	1.97642i	0.236772	−	0.172025i
$133$	1.66961	+	0.743360i	0.144774	+	0.0644575i
$134$	12.8097	−	2.72278i	1.10659	−	0.235213i
$135$	−0.104528	+	0.994522i	−0.00899638	+	0.0855948i
$136$	2.86440	+	3.18124i	0.245620	+	0.272789i
$137$	11.0039	−	12.2211i	0.940129	−	1.04412i	−0.0588190	−	0.998269i	$-0.518733\pi$
$137$	11.0039	−	12.2211i	0.940129	−	1.04412i	0.998948	−	0.0458507i	$-0.0145998\pi$
$138$	0.0234130	+	0.222760i	0.00199305	+	0.0189626i
$139$	−1.94648	−	5.99065i	−0.165098	−	0.508120i	0.833945	−	0.551847i	$-0.186077\pi$
$139$	−1.94648	−	5.99065i	−0.165098	−	0.508120i	−0.999044	+	0.0437269i	$0.986077\pi$
$140$	0.247517	+	0.761779i	0.0209190	+	0.0643821i
$141$	−0.0962672	−	0.915922i	−0.00810716	−	0.0771345i
$142$	−3.32887	+	3.69708i	−0.279352	+	0.310252i
$143$	0.918144	+	1.01970i	0.0767791	+	0.0852718i
$144$	−0.104528	+	0.994522i	−0.00871071	+	0.0828768i
$145$	−2.96347	+	0.629905i	−0.246103	+	0.0523108i
$146$	−2.91636	−	1.29845i	−0.241359	−	0.107460i
$147$	−5.14408	+	3.73739i	−0.424276	+	0.308255i
$148$	4.27462	−	1.90318i	0.351371	−	0.156441i
$149$	−2.17096	+	3.76022i	−0.177852	+	0.308049i	−0.941145	−	0.338004i	$-0.890248\pi$
$149$	−2.17096	+	3.76022i	−0.177852	+	0.308049i	0.763293	+	0.646053i	$0.223582\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	2.29725	+	1.66905i	0.186947	+	0.135825i	0.677322	−	0.735686i	$-0.263140\pi$
$151$	2.29725	+	1.66905i	0.186947	+	0.135825i	−0.490375	+	0.871511i	$0.663140\pi$
$152$	−2.23186	−	0.474397i	−0.181028	−	0.0384787i
$153$	−1.32283	+	4.07126i	−0.106945	+	0.329142i
$154$	2.69328			0.217031
$155$	−1.84903	+	5.25177i	−0.148517	+	0.421832i
$156$	−0.408075			−0.0326722
$157$	2.25450	−	6.93864i	0.179929	−	0.553764i	−0.819895	−	0.572513i	$-0.805968\pi$
$157$	2.25450	−	6.93864i	0.179929	−	0.553764i	0.999824	+	0.0187493i	$0.00596845\pi$
$158$	−2.63522	−	0.560133i	−0.209647	−	0.0445618i
$159$	5.97589	+	4.34174i	0.473919	+	0.344322i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−0.0897046	+	0.155373i	−0.00706971	+	0.0122451i
$162$	−0.913545	+	0.406737i	−0.0717749	+	0.0319562i
$163$	12.1708	−	8.84260i	0.953290	−	0.692606i	0.00170707	−	0.999999i	$-0.499457\pi$
$163$	12.1708	−	8.84260i	0.953290	−	0.692606i	0.951583	+	0.307393i	$0.0994566\pi$
$164$	1.19720	+	0.533029i	0.0934857	+	0.0416225i
$165$	−3.28900	+	0.699099i	−0.256048	+	0.0544248i
$166$	−0.877698	+	8.35074i	−0.0681226	+	0.648143i
$167$	−5.82915	−	6.47393i	−0.451074	−	0.500968i	0.474122	−	0.880459i	$-0.342766\pi$
$167$	−5.82915	−	6.47393i	−0.451074	−	0.500968i	−0.925195	+	0.379491i	$0.876099\pi$
$168$	−0.535961	+	0.595245i	−0.0413503	+	0.0459242i
$169$	1.34146	+	12.7632i	0.103189	+	0.981782i
$170$	−1.32283	−	4.07126i	−0.101457	−	0.312252i
$171$	−0.705092	−	2.17005i	−0.0539197	−	0.165948i
$172$	−0.00923105	−	0.0878275i	−0.000703861	−	0.00669679i
$173$	4.37887	−	4.86323i	0.332920	−	0.369745i	−0.553322	−	0.832967i	$-0.686640\pi$
$173$	4.37887	−	4.86323i	0.332920	−	0.369745i	0.886242	+	0.463222i	$0.153307\pi$
$174$	−2.02725	−	2.25149i	−0.153685	−	0.170685i
$175$	0.0837254	−	0.796594i	0.00632904	−	0.0602168i
$176$	−3.28900	+	0.699099i	−0.247918	+	0.0526966i
$177$	2.88326	+	1.28371i	0.216719	+	0.0964897i
$178$	−8.37618	+	6.08565i	−0.627821	+	0.456139i
$179$	13.0152	−	5.79472i	0.972799	−	0.433118i	0.142108	−	0.989851i	$-0.454612\pi$
$179$	13.0152	−	5.79472i	0.972799	−	0.433118i	0.830691	+	0.556733i	$0.187945\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	8.16087	+	14.1350i	0.606593	+	1.05065i	0.991798	+	0.127818i	$0.0407974\pi$
$181$	8.16087	+	14.1350i	0.606593	+	1.05065i	−0.385205	+	0.922831i	$0.625869\pi$
$182$	−0.264436	−	0.192124i	−0.0196013	−	0.0142412i
$183$	−3.64715	−	0.775225i	−0.269605	−	0.0573063i
$184$	0.0692157	−	0.213024i	0.00510265	−	0.0157043i
$185$	−4.67915			−0.344018
$186$	−5.47268	+	1.02458i	−0.401276	+	0.0751260i
$187$	−14.3940			−1.05260
$188$	−0.284594	+	0.875891i	−0.0207562	+	0.0638809i
$189$	−0.783478	−	0.166533i	−0.0569897	−	0.0121135i
$190$	1.84595	+	1.34116i	0.133920	+	0.0972983i
$191$	−0.554226	−	0.959948i	−0.0401024	−	0.0694594i	0.845278	−	0.534327i	$-0.179435\pi$
$191$	−0.554226	−	0.959948i	−0.0401024	−	0.0694594i	−0.885380	+	0.464868i	$0.846102\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	12.6259	−	5.62140i	0.908831	−	0.404637i	0.101567	−	0.994829i	$-0.467614\pi$
$193$	12.6259	−	5.62140i	0.908831	−	0.404637i	0.807263	+	0.590191i	$0.200948\pi$
$194$	10.7049	−	7.77759i	0.768569	−	0.558398i
$195$	0.372795	+	0.165979i	0.0266964	+	0.0118860i
$196$	6.21948	−	1.32199i	0.444249	−	0.0944280i
$197$	−0.889879	+	8.46663i	−0.0634012	+	0.603223i	0.915983	+	0.401217i	$0.131413\pi$
$197$	−0.889879	+	8.46663i	−0.0634012	+	0.603223i	−0.979384	+	0.202006i	$0.935254\pi$
$198$	−2.24994	−	2.49881i	−0.159896	−	0.177583i
$199$	8.46001	−	9.39579i	0.599714	−	0.666050i	−0.364491	−	0.931207i	$-0.618757\pi$
$199$	8.46001	−	9.39579i	0.599714	−	0.666050i	0.964205	+	0.265157i	$0.0854238\pi$
$200$	0.104528	+	0.994522i	0.00739128	+	0.0703233i
$201$	−4.04684	−	12.4549i	−0.285442	−	0.878501i
$202$	0.740418	+	2.27877i	0.0520957	+	0.160334i
$203$	−0.253661	−	2.41342i	−0.0178035	−	0.169389i
$204$	2.86440	−	3.18124i	0.200548	−	0.222731i
$205$	−0.876896	−	0.973892i	−0.0612451	−	0.0680195i
$206$	−0.103904	+	0.988577i	−0.00723931	+	0.0688774i
$207$	0.219092	−	0.0465694i	0.0152279	−	0.00323680i
$208$	0.372795	+	0.165979i	0.0258487	+	0.0115086i
$209$	6.20698	−	4.50964i	0.429346	−	0.311938i
$210$	0.731733	−	0.325789i	0.0504944	−	0.0224815i
$211$	12.7601	−	22.1011i	0.878441	−	1.52150i	0.0253887	−	0.999678i	$-0.491918\pi$
$211$	12.7601	−	22.1011i	0.878441	−	1.52150i	0.853052	−	0.521826i	$-0.174749\pi$
$212$	−3.69330	−	6.39699i	−0.253657	−	0.439347i
$213$	4.02479	+	2.92418i	0.275774	+	0.200362i
$214$	3.15673	+	0.670983i	0.215790	+	0.0458675i
$215$	−0.0272897	+	0.0839890i	−0.00186114	+	0.00572801i
$216$	1.00000			0.0680414
$217$	−4.02872	−	1.91263i	−0.273487	−	0.129838i
$218$	−3.33343			−0.225768
$219$	−0.986490	+	3.03610i	−0.0666608	+	0.205161i
$220$	3.28900	+	0.699099i	0.221744	+	0.0471332i
$221$	1.41326	+	1.02679i	0.0950659	+	0.0690694i
$222$	−2.33958	−	4.05226i	−0.157022	−	0.271970i
$223$	−3.57377	+	6.18994i	−0.239317	+	0.414509i	−0.960518	−	0.278216i	$-0.910257\pi$
$223$	−3.57377	+	6.18994i	−0.239317	+	0.414509i	0.721201	+	0.692725i	$0.243590\pi$
$224$	0.731733	−	0.325789i	0.0488910	−	0.0217677i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	10.9266	+	4.86484i	0.726827	+	0.323604i
$227$	3.16816	−	0.673413i	0.210278	−	0.0446960i	−0.101568	−	0.994829i	$-0.532386\pi$
$227$	3.16816	−	0.673413i	0.210278	−	0.0446960i	0.311846	+	0.950133i	$0.399053\pi$
$228$	−0.238505	+	2.26923i	−0.0157954	+	0.150283i
$229$	−0.0878049	−	0.0975172i	−0.00580231	−	0.00644412i	0.740237	−	0.672346i	$-0.234713\pi$
$229$	−0.0878049	−	0.0975172i	−0.00580231	−	0.00644412i	−0.746039	+	0.665902i	$0.768047\pi$
$230$	−0.149876	+	0.166455i	−0.00988255	+	0.0109757i
$231$	−0.281525	−	2.67853i	−0.0185230	−	0.176234i
$232$	0.936222	+	2.88139i	0.0614660	+	0.189173i
$233$	3.07262	+	9.45655i	0.201294	+	0.619519i	0.999845	+	0.0175923i	$0.00560011\pi$
$233$	3.07262	+	9.45655i	0.201294	+	0.619519i	−0.798551	+	0.601927i	$0.794400\pi$
$234$	0.0426555	+	0.405840i	0.00278848	+	0.0265306i
$235$	0.616247	−	0.684412i	0.0401995	−	0.0446461i
$236$	−2.11186	−	2.34546i	−0.137470	−	0.152676i
$237$	−0.281609	+	2.67933i	−0.0182925	+	0.174041i
$238$	3.35390	−	0.712893i	0.217401	−	0.0462100i
$239$	12.7565	+	5.67955i	0.825148	+	0.367380i	0.775469	−	0.631385i	$-0.217513\pi$
$239$	12.7565	+	5.67955i	0.825148	+	0.367380i	0.0496793	+	0.998765i	$0.484180\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	13.9205	−	6.19779i	0.896696	−	0.399235i	0.0939643	−	0.995576i	$-0.470046\pi$
$241$	13.9205	−	6.19779i	0.896696	−	0.399235i	0.802731	+	0.596341i	$0.203379\pi$
$242$	0.153135	−	0.265237i	0.00984387	−	0.0170501i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	3.01652	+	2.19163i	0.193113	+	0.140305i
$245$	−6.21948	−	1.32199i	−0.397348	−	0.0844589i
$246$	0.404967	−	1.24636i	0.0258197	−	0.0794650i
$247$	−0.931116			−0.0592455
$248$	5.41628	+	1.28994i	0.343934	+	0.0819111i
$249$	8.39674			0.532122
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	14.1731	+	3.01259i	0.894601	+	0.190153i	0.632199	−	0.774806i	$-0.282152\pi$
$251$	14.1731	+	3.01259i	0.894601	+	0.190153i	0.262401	+	0.964959i	$0.415486\pi$
$252$	0.648008	+	0.470805i	0.0408206	+	0.0296579i
$253$	0.376575	+	0.652248i	0.0236751	+	0.0410065i
$254$	6.62695	−	11.4782i	0.415812	−	0.720207i
$255$	−3.91069	+	1.74115i	−0.244897	+	0.109035i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	6.59555	+	2.93653i	0.411419	+	0.183176i	0.602000	−	0.798496i	$-0.294371\pi$
$257$	6.59555	+	2.93653i	0.411419	+	0.183176i	−0.190581	+	0.981671i	$0.561037\pi$
$258$	−0.0863815	+	0.0183610i	−0.00537788	+	0.00114310i
$259$	0.391764	−	3.72738i	0.0243430	−	0.231608i
$260$	−0.273056	−	0.303259i	−0.0169342	−	0.0188073i
$261$	−2.02725	+	2.25149i	−0.125484	+	0.139364i
$262$	0.308728	+	2.93736i	0.0190733	+	0.181470i
$263$	−6.01756	−	18.5201i	−0.371059	−	1.14200i	−0.946099	−	0.323876i	$-0.895014\pi$
$263$	−6.01756	−	18.5201i	−0.371059	−	1.14200i	0.575041	−	0.818125i	$-0.304986\pi$
$264$	1.03906	+	3.19791i	0.0639499	+	0.196818i
$265$	0.772111	+	7.34614i	0.0474304	+	0.451270i
$266$	−1.22292	+	1.35819i	−0.0749818	+	0.0832757i
$267$	6.92786	+	7.69417i	0.423978	+	0.470875i
$268$	−1.36889	+	13.0241i	−0.0836183	+	0.795575i
$269$	7.81402	−	1.66092i	0.476429	−	0.101268i	0.0365629	−	0.999331i	$-0.488359\pi$
$269$	7.81402	−	1.66092i	0.476429	−	0.101268i	0.439867	+	0.898063i	$0.355026\pi$
$270$	−0.913545	−	0.406737i	−0.0555966	−	0.0247532i
$271$	22.4369	−	16.3014i	1.36295	−	0.990238i	0.364694	−	0.931128i	$-0.381174\pi$
$271$	22.4369	−	16.3014i	1.36295	−	0.990238i	0.998251	−	0.0591100i	$-0.0188263\pi$
$272$	−3.91069	+	1.74115i	−0.237120	+	0.105573i
$273$	−0.163430	+	0.283070i	−0.00989126	+	0.0171322i
$274$	8.22256	+	14.2419i	0.496743	+	0.860384i
$275$	−2.72030	−	1.97642i	−0.164040	−	0.119182i
$276$	−0.219092	−	0.0465694i	−0.0131878	−	0.00280315i
$277$	−0.171425	+	0.527593i	−0.0103000	+	0.0317000i	−0.956074	−	0.293124i	$-0.905305\pi$
$277$	−0.171425	+	0.527593i	−0.0103000	+	0.0317000i	0.945774	+	0.324824i	$0.105305\pi$
$278$	6.29894			0.377786
$279$	1.59102	+	5.33560i	0.0952519	+	0.319434i
$280$	−0.800982			−0.0478678
$281$	1.32812	−	4.08755i	0.0792293	−	0.243843i	−0.903595	−	0.428389i	$-0.859081\pi$
$281$	1.32812	−	4.08755i	0.0792293	−	0.243843i	0.982824	+	0.184546i	$0.0590815\pi$
$282$	0.900841	+	0.191480i	0.0536443	+	0.0114025i
$283$	10.6720	+	7.75367i	0.634385	+	0.460908i	0.857917	−	0.513789i	$-0.171759\pi$
$283$	10.6720	+	7.75367i	0.634385	+	0.460908i	−0.223531	+	0.974697i	$0.571759\pi$
$284$	−2.48746	−	4.30840i	−0.147603	−	0.255657i
$285$	1.14086	−	1.97603i	0.0675789	−	0.117050i
$286$	−1.25352	+	0.558102i	−0.0741220	+	0.0330012i
$287$	0.849214	−	0.616990i	0.0501275	−	0.0364198i
$288$	−0.913545	−	0.406737i	−0.0538312	−	0.0239672i
$289$	−1.29613	+	0.275500i	−0.0762428	+	0.0162059i
$290$	0.316687	−	3.01308i	0.0185965	−	0.176934i
$291$	−8.85395	−	9.83331i	−0.519028	−	0.576439i
$292$	2.13610	−	2.37238i	0.125006	−	0.138833i
$293$	1.68932	+	16.0728i	0.0986912	+	0.938984i	0.926073	+	0.377344i	$0.123163\pi$
$293$	1.68932	+	16.0728i	0.0986912	+	0.938984i	−0.827382	+	0.561640i	$0.810171\pi$
$294$	−1.96486	−	6.04722i	−0.114593	−	0.352681i
$295$	0.975296	+	3.00165i	0.0567839	+	0.174763i
$296$	0.489104	+	4.65352i	0.0284286	+	0.270480i
$297$	−2.24994	+	2.49881i	−0.130555	+	0.144996i
$298$	−2.90531	−	3.22668i	−0.168300	−	0.186916i
$299$	0.00955426	−	0.0909027i	0.000552537	−	0.00525704i
$300$	0.978148	−	0.207912i	0.0564734	−	0.0120038i
$301$	−0.0646203	−	0.0287708i	−0.00372465	−	0.00165832i
$302$	−2.29725	+	1.66905i	−0.132192	+	0.0960429i
$303$	2.18890	−	0.974559i	0.125749	−	0.0559870i
$304$	1.14086	−	1.97603i	0.0654330	−	0.113333i
$305$	−1.86431	−	3.22909i	−0.106750	−	0.184897i
$306$	−3.46322	−	2.51618i	−0.197979	−	0.143840i
$307$	−16.3467	−	3.47460i	−0.932955	−	0.198306i	−0.283732	−	0.958904i	$-0.591573\pi$
$307$	−16.3467	−	3.47460i	−0.932955	−	0.198306i	−0.649223	+	0.760598i	$0.724906\pi$
$308$	−0.832271	+	2.56147i	−0.0474230	+	0.145953i
$309$	0.994022			0.0565480
$310$	−4.42335	−	3.38141i	−0.251229	−	0.192051i
$311$	−12.7271			−0.721686			−0.360843	−	0.932626i	$-0.617511\pi$
$311$	−12.7271			−0.721686			−0.360843	+	0.932626i	$0.617511\pi$
$312$	0.126102	−	0.388103i	0.00713913	−	0.0219720i
$313$	−25.3018	−	5.37806i	−1.43014	−	0.303986i	−0.573207	−	0.819411i	$-0.694301\pi$
$313$	−25.3018	−	5.37806i	−1.43014	−	0.303986i	−0.856935	+	0.515424i	$0.827634\pi$
$314$	5.90236	+	4.28832i	0.333090	+	0.242004i
$315$	−0.400491	−	0.693670i	−0.0225651	−	0.0390839i
$316$	1.34705	−	2.33315i	0.0757772	−	0.131250i
$317$	4.77369	−	2.12538i	0.268117	−	0.119373i	−0.268275	−	0.963342i	$-0.586454\pi$
$317$	4.77369	−	2.12538i	0.268117	−	0.119373i	0.536392	+	0.843969i	$0.319787\pi$
$318$	−5.97589	+	4.34174i	−0.335111	+	0.243473i
$319$	−9.30649	−	4.14352i	−0.521064	−	0.231992i
$320$	0.978148	−	0.207912i	0.0546801	−	0.0116226i
$321$	0.337340	−	3.20957i	0.0188285	−	0.179141i
$322$	−0.120048	−	0.133327i	−0.00669002	−	0.00743002i
$323$	6.53578	−	7.25872i	0.363660	−	0.403886i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	0.126102	+	0.388103i	0.00699489	+	0.0215281i
$326$	4.64883	+	14.3076i	0.257475	+	0.792426i
$327$	0.348438	+	3.31517i	0.0192687	+	0.183329i
$328$	−0.876896	+	0.973892i	−0.0484185	+	0.0537742i
$329$	0.493603	+	0.548201i	0.0272132	+	0.0302233i
$330$	0.351475	−	3.34406i	0.0193481	−	0.184084i
$331$	9.12472	−	1.93952i	0.501540	−	0.106606i	0.0498071	−	0.998759i	$-0.484139\pi$
$331$	9.12472	−	1.93952i	0.501540	−	0.106606i	0.451733	+	0.892153i	$0.350806\pi$
$332$	−7.67080	−	3.41526i	−0.420990	−	0.187437i
$333$	−3.78551	+	2.75034i	−0.207445	+	0.150717i
$334$	7.95838	−	3.54330i	0.435463	−	0.193881i
$335$	6.54793	−	11.3413i	0.357752	−	0.619644i
$336$	−0.400491	−	0.693670i	−0.0218486	−	0.0378428i
$337$	−5.95948	−	4.32981i	−0.324633	−	0.235860i	0.413517	−	0.910497i	$-0.364300\pi$
$337$	−5.95948	−	4.32981i	−0.324633	−	0.235860i	−0.738150	+	0.674637i	$0.764300\pi$
$338$	−12.5530	−	2.66823i	−0.682795	−	0.145133i
$339$	3.69605	−	11.3753i	0.200742	−	0.617820i
$340$	4.28078			0.232158
$341$	−15.4096	+	10.6320i	−0.834476	+	0.575753i
$342$	2.28173			0.123382
$343$	3.30644	−	10.1762i	0.178531	−	0.549461i
$344$	0.0863815	+	0.0183610i	0.00465738	+	0.000989956i
$345$	0.181209	+	0.131656i	0.00975597	+	0.00708812i
$346$	3.27206	+	5.66738i	0.175907	+	0.304680i
$347$	−2.13576	+	3.69925i	−0.114654	+	0.198586i	−0.917641	−	0.397410i	$-0.869909\pi$
$347$	−2.13576	+	3.69925i	−0.114654	+	0.198586i	0.802988	+	0.595996i	$0.203243\pi$
$348$	2.76775	−	1.23228i	0.148367	−	0.0660572i
$349$	−9.35377	+	6.79591i	−0.500696	+	0.363777i	−0.809283	−	0.587419i	$-0.800144\pi$
$349$	−9.35377	+	6.79591i	−0.500696	+	0.363777i	0.308587	+	0.951196i	$0.400144\pi$
$350$	0.731733	+	0.325789i	0.0391128	+	0.0174141i
$351$	0.399158	−	0.0848436i	0.0213055	−	0.00452862i
$352$	0.351475	−	3.34406i	0.0187337	−	0.178239i
$353$	−17.1593	−	19.0574i	−0.913299	−	1.01432i	−0.999837	−	0.0180729i	$-0.994247\pi$
$353$	−17.1593	−	19.0574i	−0.913299	−	1.01432i	0.0865375	−	0.996249i	$-0.472420\pi$
$354$	−2.11186	+	2.34546i	−0.112244	+	0.124660i
$355$	0.520020	+	4.94766i	0.0275998	+	0.262595i
$356$	−3.19942	−	9.84679i	−0.169569	−	0.521879i
$357$	−1.05957	−	3.26101i	−0.0560782	−	0.172591i
$358$	1.48920	+	14.1688i	0.0787069	+	0.748846i
$359$	−23.4383	+	26.0309i	−1.23703	+	1.37386i	−0.334977	+	0.942226i	$0.608728\pi$
$359$	−23.4383	+	26.0309i	−1.23703	+	1.37386i	−0.902050	+	0.431631i	$0.857938\pi$
$360$	0.669131	+	0.743145i	0.0352663	+	0.0391672i
$361$	1.44184	−	13.7182i	0.0758862	−	0.722009i
$362$	−15.9651	+	3.39348i	−0.839106	+	0.178357i
$363$	−0.279791	−	0.124571i	−0.0146852	−	0.00653828i
$364$	0.264436	−	0.192124i	0.0138602	−	0.0100700i
$365$	−2.91636	+	1.29845i	−0.152649	+	0.0679637i
$366$	1.86431	−	3.22909i	0.0974492	−	0.168787i
$367$	−9.73832	−	16.8673i	−0.508336	−	0.880464i	−0.999953	−	0.00965281i	$-0.996927\pi$
$367$	−9.73832	−	16.8673i	−0.508336	−	0.880464i	0.491617	−	0.870811i	$-0.336406\pi$
$368$	0.181209	+	0.131656i	0.00944617	+	0.00686305i
$369$	−1.28186	−	0.272468i	−0.0667311	−	0.0141841i
$370$	1.44594	−	4.45014i	0.0751707	−	0.231352i
$371$	−5.91654			−0.307171
$372$	0.716715	−	5.52144i	0.0371600	−	0.286273i
$373$	−21.3626			−1.10612			−0.553058	−	0.833143i	$-0.686539\pi$
$373$	−21.3626			−1.10612			−0.553058	+	0.833143i	$0.686539\pi$
$374$	4.44800	−	13.6895i	0.230001	−	0.707869i
$375$	−0.978148	−	0.207912i	−0.0505113	−	0.0107365i
$376$	−0.745078	−	0.541331i	−0.0384245	−	0.0279170i
$377$	0.618168	+	1.07070i	0.0318373	+	0.0551438i
$378$	0.400491	−	0.693670i	0.0205990	−	0.0356786i
$379$	21.4530	−	9.55148i	1.10197	−	0.490627i	0.226551	−	0.973999i	$-0.427255\pi$
$379$	21.4530	−	9.55148i	1.10197	−	0.490627i	0.875415	+	0.483373i	$0.160588\pi$
$380$	−1.84595	+	1.34116i	−0.0946955	+	0.0688003i
$381$	−12.1080	−	5.39084i	−0.620313	−	0.276181i
$382$	1.08423	−	0.230460i	0.0554740	−	0.0117914i
$383$	1.86615	−	17.7553i	0.0953561	−	0.907252i	−0.837363	−	0.546648i	$-0.815904\pi$
$383$	1.86615	−	17.7553i	0.0953561	−	0.907252i	0.932719	−	0.360605i	$-0.117430\pi$
$384$	0.669131	+	0.743145i	0.0341464	+	0.0379235i
$385$	1.80216	−	2.00150i	0.0918465	−	0.102006i
$386$	1.44466	+	13.7450i	0.0735313	+	0.699604i
$387$	0.0272897	+	0.0839890i	0.00138721	+	0.00426940i
$388$	4.08892	+	12.5844i	0.207583	+	0.638876i
$389$	1.66719	+	15.8623i	0.0845301	+	0.804250i	0.951863	+	0.306522i	$0.0991654\pi$
$389$	1.66719	+	15.8623i	0.0845301	+	0.804250i	−0.867333	+	0.497728i	$0.834168\pi$
$390$	−0.273056	+	0.303259i	−0.0138267	+	0.0153561i
$391$	0.641588	+	0.712555i	0.0324465	+	0.0360355i
$392$	−0.664637	+	6.32360i	−0.0335692	+	0.319390i
$393$	2.88899	−	0.614074i	0.145730	−	0.0309760i
$394$	−7.77726	−	3.46266i	−0.391813	−	0.174446i
$395$	−2.17956	+	1.58355i	−0.109666	+	0.0796769i
$396$	3.07178	−	1.36764i	0.154363	−	0.0687267i
$397$	−0.937782	+	1.62429i	−0.0470659	+	0.0815206i	−0.888599	−	0.458686i	$-0.848320\pi$
$397$	−0.937782	+	1.62429i	−0.0470659	+	0.0815206i	0.841533	+	0.540206i	$0.181654\pi$
$398$	6.32164	+	10.9494i	0.316875	+	0.548844i
$399$	1.47858	+	1.07425i	0.0740214	+	0.0537797i
$400$	−0.978148	−	0.207912i	−0.0489074	−	0.0103956i
$401$	−11.4156	+	35.1337i	−0.570069	+	1.75449i	0.0823197	+	0.996606i	$0.473767\pi$
$401$	−11.4156	+	35.1337i	−0.570069	+	1.75449i	−0.652388	+	0.757885i	$0.726233\pi$
$402$	13.0959			0.653162
$403$	2.27139	+	0.0553519i	0.113146	+	0.00275728i
$404$	−2.39604			−0.119208
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	2.37369	+	0.504542i	0.117804	+	0.0250400i
$407$	−12.7287	−	9.24795i	−0.630939	−	0.458404i
$408$	2.14039	+	3.70726i	0.105965	+	0.183537i
$409$	−4.22301	+	7.31447i	−0.208814	+	0.361677i	−0.951341	−	0.308139i	$-0.900294\pi$
$409$	−4.22301	+	7.31447i	−0.208814	+	0.361677i	0.742527	+	0.669816i	$0.233627\pi$
$410$	1.19720	−	0.533029i	0.0591256	−	0.0263244i
$411$	13.3044	−	9.66620i	0.656257	−	0.476798i
$412$	−0.908085	−	0.404305i	−0.0447381	−	0.0199187i
$413$	−2.47276	+	0.525600i	−0.121676	+	0.0258631i
$414$	−0.0234130	+	0.222760i	−0.00115069	+	0.0109480i
$415$	5.61851	+	6.23999i	0.275802	+	0.306309i
$416$	−0.273056	+	0.303259i	−0.0133877	+	0.0148685i
$417$	−0.658419	−	6.26444i	−0.0322429	−	0.306771i
$418$	2.37086	+	7.29675i	0.115962	+	0.356896i
$419$	6.93442	+	21.3420i	0.338769	+	1.04262i	0.964836	+	0.262854i	$0.0846636\pi$
$419$	6.93442	+	21.3420i	0.338769	+	1.04262i	−0.626067	+	0.779769i	$0.715336\pi$
$420$	0.0837254	+	0.796594i	0.00408538	+	0.0388698i
$421$	−11.9302	+	13.2498i	−0.581441	+	0.645756i	−0.960059	−	0.279797i	$-0.909733\pi$
$421$	−11.9302	+	13.2498i	−0.581441	+	0.645756i	0.378618	+	0.925553i	$0.376399\pi$
$422$	17.0763	+	18.9652i	0.831263	+	0.923211i
$423$	0.0962672	−	0.915922i	0.00468067	−	0.0445336i
$424$	7.22519	−	1.53576i	0.350886	−	0.0745832i
$425$	−3.91069	−	1.74115i	−0.189696	−	0.0844582i
$426$	−4.02479	+	2.92418i	−0.195002	+	0.141677i
$427$	2.72836	−	1.21474i	0.132035	−	0.0587856i
$428$	−1.61363	+	2.79488i	−0.0779976	+	0.135096i
$429$	0.686073	+	1.18831i	0.0331239	+	0.0573723i
$430$	−0.0714454	−	0.0519081i	−0.00344540	−	0.00250323i
$431$	−29.5230	−	6.27531i	−1.42207	−	0.302271i	−0.568260	−	0.822849i	$-0.692383\pi$
$431$	−29.5230	−	6.27531i	−1.42207	−	0.302271i	−0.853814	+	0.520578i	$0.825717\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	24.2522			1.16549			0.582744	−	0.812656i	$-0.301979\pi$
$433$	24.2522			1.16549			0.582744	+	0.812656i	$0.301979\pi$
$434$	3.06396	−	3.24050i	0.147075	−	0.155549i
$435$	−3.02968			−0.145262
$436$	1.03009	−	3.17028i	0.0493322	−	0.151829i
$437$	−0.499908	−	0.106259i	−0.0239138	−	0.00508304i
$438$	−2.58266	−	1.87642i	−0.123404	−	0.0896586i
$439$	−11.7182	−	20.2965i	−0.559278	−	0.968698i	−0.997557	−	0.0698587i	$-0.977745\pi$
$439$	−11.7182	−	20.2965i	−0.559278	−	0.968698i	0.438279	−	0.898839i	$-0.355588\pi$
$440$	−1.68124	+	2.91199i	−0.0801500	+	0.138824i
$441$	−5.80871	+	2.58621i	−0.276605	+	0.123153i
$442$	−1.41326	+	1.02679i	−0.0672218	+	0.0488395i
$443$	5.34293	+	2.37883i	0.253850	+	0.113021i	0.529717	−	0.848174i	$-0.322298\pi$
$443$	5.34293	+	2.37883i	0.253850	+	0.113021i	−0.275867	+	0.961196i	$0.588965\pi$
$444$	4.57690	−	0.972850i	0.217210	−	0.0461694i
$445$	−1.08224	+	10.2968i	−0.0513030	+	0.488115i
$446$	−4.78263	−	5.31165i	−0.226464	−	0.251514i
$447$	−2.90531	+	3.22668i	−0.137417	+	0.152617i
$448$	0.0837254	+	0.796594i	0.00395565	+	0.0376355i
$449$	1.72184	+	5.29927i	0.0812585	+	0.250088i	0.983430	−	0.181290i	$-0.0580274\pi$
$449$	1.72184	+	5.29927i	0.0812585	+	0.250088i	−0.902171	+	0.431378i	$0.858027\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	−0.460608	−	4.38239i	−0.0216892	−	0.206359i
$452$	−8.00325	+	8.88851i	−0.376441	+	0.418080i
$453$	1.90003	+	2.11020i	0.0892713	+	0.0991458i
$454$	−0.338561	+	3.22119i	−0.0158895	+	0.151178i
$455$	−0.319718	+	0.0679582i	−0.0149886	+	0.00318593i
$456$	−2.08446	−	0.928061i	−0.0976138	−	0.0434605i
$457$	−32.5231	+	23.6294i	−1.52137	+	1.10534i	−0.560562	+	0.828112i	$0.689415\pi$
$457$	−32.5231	+	23.6294i	−1.52137	+	1.10534i	−0.960805	+	0.277226i	$0.910585\pi$
$458$	0.119878	−	0.0533729i	0.00560151	−	0.00249395i
$459$	−2.14039	+	3.70726i	−0.0999049	+	0.173040i
$460$	−0.111993	−	0.193978i	−0.00522172	−	0.00904428i
$461$	−17.8014	−	12.9335i	−0.829096	−	0.602373i	0.0902076	−	0.995923i	$-0.471247\pi$
$461$	−17.8014	−	12.9335i	−0.829096	−	0.602373i	−0.919303	+	0.393550i	$0.871247\pi$
$462$	2.63443	+	0.559965i	0.122565	+	0.0260519i
$463$	3.54227	−	10.9020i	0.164623	−	0.506659i	−0.834385	−	0.551182i	$-0.814177\pi$
$463$	3.54227	−	10.9020i	0.164623	−	0.506659i	0.999008	+	0.0445234i	$0.0141769\pi$
$464$	−3.02968			−0.140649
$465$	−2.90052	+	4.75257i	−0.134509	+	0.220395i
$466$	−9.94320			−0.460610
$467$	−1.34317	+	4.13384i	−0.0621544	+	0.191292i	−0.977312	−	0.211805i	$-0.932066\pi$
$467$	−1.34317	+	4.13384i	−0.0621544	+	0.191292i	0.915158	+	0.403096i	$0.132066\pi$
$468$	−0.399158	−	0.0848436i	−0.0184511	−	0.00392190i
$469$	8.48622	+	6.16560i	0.391857	+	0.284701i
$470$	0.460483	+	0.797581i	0.0212405	+	0.0367896i
$471$	3.64786	−	6.31828i	0.168085	−	0.291131i
$472$	2.88326	−	1.28371i	0.132713	−	0.0590876i
$473$	−0.240234	+	0.174540i	−0.0110459	+	0.00802535i
$474$	−2.46117	−	1.09579i	−0.113045	−	0.0503311i
$475$	2.23186	−	0.474397i	0.102405	−	0.0217668i
$476$	−0.358410	+	3.41004i	−0.0164277	+	0.156299i
$477$	4.94261	+	5.48932i	0.226306	+	0.251339i
$478$	−9.34355	+	10.3771i	−0.427364	+	0.474636i
$479$	2.38599	+	22.7012i	0.109019	+	1.03724i	0.903100	+	0.429431i	$0.141286\pi$
$479$	2.38599	+	22.7012i	0.109019	+	1.03724i	−0.794081	+	0.607811i	$0.792048\pi$
$480$	−0.309017	−	0.951057i	−0.0141046	−	0.0434096i
$481$	0.590051	+	1.81599i	0.0269040	+	0.0828021i
$482$	1.59279	+	15.1544i	0.0725495	+	0.690262i
$483$	−0.120048	+	0.133327i	−0.00546238	+	0.00606659i
$484$	0.204934	+	0.227603i	0.00931519	+	0.0103456i
$485$	1.38312	−	13.1595i	0.0628044	−	0.597544i
$486$	−0.978148	+	0.207912i	−0.0443697	+	0.00943107i
$487$	−9.62179	−	4.28390i	−0.436005	−	0.194122i	0.176983	−	0.984214i	$-0.443366\pi$
$487$	−9.62179	−	4.28390i	−0.436005	−	0.194122i	−0.612988	+	0.790092i	$0.710033\pi$
$488$	−3.01652	+	2.19163i	−0.136552	+	0.0992105i
$489$	13.7433	−	6.11891i	0.621494	−	0.276707i
$490$	3.17921	−	5.50656i	0.143622	−	0.248761i
$491$	−10.7868	−	18.6832i	−0.486800	−	0.843162i	0.513085	−	0.858338i	$-0.328503\pi$
$491$	−10.7868	−	18.6832i	−0.486800	−	0.843162i	−0.999885	+	0.0151759i	$0.995169\pi$
$492$	1.06022	+	0.770293i	0.0477983	+	0.0347275i
$493$	−12.6860	−	2.69649i	−0.571347	−	0.121444i
$494$	0.287731	−	0.885544i	0.0129456	−	0.0398425i
$495$	−3.36248			−0.151132
$496$	−2.90052	+	4.75257i	−0.130237	+	0.213397i
$497$	−3.98481			−0.178743
$498$	−2.59473	+	7.98577i	−0.116273	+	0.357851i
$499$	−14.1429	−	3.00617i	−0.633124	−	0.134575i	−0.119840	−	0.992793i	$-0.538238\pi$
$499$	−14.1429	−	3.00617i	−0.633124	−	0.134575i	−0.513285	+	0.858218i	$0.671571\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−4.35577	−	7.54441i	−0.194601	−	0.337059i
$502$	−7.24489	+	12.5485i	−0.323355	+	0.560068i
$503$	−12.8941	+	5.74084i	−0.574921	+	0.255971i	−0.673536	−	0.739154i	$-0.735225\pi$
$503$	−12.8941	+	5.74084i	−0.574921	+	0.255971i	0.0986153	+	0.995126i	$0.468559\pi$
$504$	−0.648008	+	0.470805i	−0.0288646	+	0.0209713i
$505$	2.18890	+	0.974559i	0.0974046	+	0.0433673i
$506$	−0.736692	+	0.156589i	−0.0327500	+	0.00696122i
$507$	−1.34146	+	12.7632i	−0.0595765	+	0.566832i
$508$	8.86859	+	9.84956i	0.393480	+	0.437004i
$509$	−18.9783	+	21.0775i	−0.841196	+	0.934243i	−0.998579	−	0.0532944i	$-0.983028\pi$
$509$	−18.9783	+	21.0775i	−0.841196	+	0.934243i	0.157382	+	0.987538i	$0.449694\pi$
$510$	−0.447463	−	4.25733i	−0.0198140	−	0.188518i
$511$	−0.790160	−	2.43186i	−0.0349546	−	0.107579i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−0.238505	−	2.26923i	−0.0105303	−	0.100189i
$514$	−4.83094	+	5.36530i	−0.213084	+	0.236653i
$515$	0.665131	+	0.738703i	0.0293092	+	0.0325511i
$516$	0.00923105	−	0.0878275i	0.000406374	−	0.00386639i
$517$	3.02906	−	0.643847i	0.133218	−	0.0283163i
$518$	3.42389	+	1.52441i	0.150437	+	0.0669789i
$519$	5.29431	−	3.84654i	0.232394	−	0.168844i
$520$	0.372795	−	0.165979i	0.0163482	−	0.00727867i
$521$	1.73868	−	3.01148i	0.0761729	−	0.131935i	−0.825423	−	0.564515i	$-0.809063\pi$
$521$	1.73868	−	3.01148i	0.0761729	−	0.131935i	0.901596	+	0.432580i	$0.142397\pi$
$522$	−1.51484	−	2.62378i	−0.0663027	−	0.114840i
$523$	−15.9449	−	11.5847i	−0.697223	−	0.506562i	0.181804	−	0.983335i	$-0.441806\pi$
$523$	−15.9449	−	11.5847i	−0.697223	−	0.506562i	−0.879027	+	0.476773i	$0.841806\pi$
$524$	−2.88899	−	0.614074i	−0.126206	−	0.0268260i
$525$	0.247517	−	0.761779i	0.0108025	−	0.0332468i
$526$	19.4732			0.849073
$527$	−16.3751	+	17.3186i	−0.713310	+	0.754410i
$528$	−3.36248			−0.146333
$529$	−7.09189	+	21.8266i	−0.308343	+	0.948982i
$530$	−7.22519	−	1.53576i	−0.313842	−	0.0667093i
$531$	2.55336	+	1.85512i	0.110806	+	0.0805055i
$532$	−0.913810	−	1.58277i	−0.0396187	−	0.0686216i
$533$	−0.267391	+	0.463136i	−0.0115820	+	0.0200606i
$534$	−9.45842	+	4.21116i	−0.409306	+	0.182235i
$535$	2.61090	−	1.89693i	0.112879	−	0.0820115i
$536$	−11.9637	−	5.32657i	−0.516752	−	0.230073i
$537$	13.9355	−	2.96209i	0.601363	−	0.127824i
$538$	−0.835035	+	7.94483i	−0.0360009	+	0.342526i
$539$	−14.3061	−	15.8885i	−0.616206	−	0.684366i
$540$	0.669131	−	0.743145i	0.0287948	−	0.0319799i
$541$	4.08360	+	38.8528i	0.175568	+	1.67041i	0.627694	+	0.778460i	$0.283999\pi$
$541$	4.08360	+	38.8528i	0.175568	+	1.67041i	−0.452126	+	0.891954i	$0.649334\pi$
$542$	8.57014	+	26.3762i	0.368119	+	1.13295i
$543$	5.04370	+	15.5229i	0.216446	+	0.666151i
$544$	−0.447463	−	4.25733i	−0.0191848	−	0.182532i
$545$	−2.23050	+	2.47722i	−0.0955442	+	0.106113i
$546$	−0.218713	−	0.242905i	−0.00936003	−	0.0103954i
$547$	1.50991	−	14.3659i	0.0645592	−	0.614240i	−0.913633	−	0.406540i	$-0.866735\pi$
$547$	1.50991	−	14.3659i	0.0645592	−	0.614240i	0.978192	−	0.207701i	$-0.0665980\pi$
$548$	−16.0858	+	3.41913i	−0.687149	+	0.146058i
$549$	−3.40627	−	1.51657i	−0.145376	−	0.0647256i
$550$	2.72030	−	1.97642i	0.115994	−	0.0842747i
$551$	6.31524	−	2.81173i	0.269038	−	0.119784i
$552$	0.111993	−	0.193978i	0.00476675	−	0.00825626i
$553$	−1.07896	−	1.86881i	−0.0458820	−	0.0794699i
$554$	−0.448798	−	0.326071i	−0.0190676	−	0.0138534i
$555$	−4.57690	−	0.972850i	−0.194279	−	0.0412952i
$556$	−1.94648	+	5.99065i	−0.0825492	+	0.254060i
$557$	7.28044			0.308482			0.154241	−	0.988033i	$-0.450707\pi$
$557$	7.28044			0.308482			0.154241	+	0.988033i	$0.450707\pi$
$558$	−5.56611	−	0.135641i	−0.235632	−	0.00574216i
$559$	0.0360377			0.00152423
$560$	0.247517	−	0.761779i	0.0104595	−	0.0321910i
$561$	−14.0795	−	2.99269i	−0.594437	−	0.126351i
$562$	3.47708	+	2.52624i	0.146672	+	0.106563i
$563$	−11.4372	−	19.8098i	−0.482019	−	0.834882i	0.517768	−	0.855521i	$-0.326763\pi$
$563$	−11.4372	−	19.8098i	−0.482019	−	0.834882i	−0.999787	+	0.0206392i	$0.993430\pi$
$564$	−0.460483	+	0.797581i	−0.0193898	+	0.0335842i
$565$	10.9266	−	4.86484i	0.459686	−	0.204665i
$566$	−10.6720	+	7.75367i	−0.448578	+	0.325911i
$567$	−0.731733	−	0.325789i	−0.0307299	−	0.0136818i
$568$	4.86620	−	1.03434i	0.204181	−	0.0434001i
$569$	−2.01399	+	19.1618i	−0.0844308	+	0.803306i	0.867592	+	0.497277i	$0.165667\pi$
$569$	−2.01399	+	19.1618i	−0.0844308	+	0.803306i	−0.952022	+	0.306028i	$0.901000\pi$
$570$	1.52677	+	1.69565i	0.0639495	+	0.0710231i
$571$	31.0827	−	34.5209i	1.30077	−	1.44465i	0.475722	−	0.879596i	$-0.342187\pi$
$571$	31.0827	−	34.5209i	1.30077	−	1.44465i	0.825051	−	0.565058i	$-0.191146\pi$
$572$	−0.143428	−	1.36463i	−0.00599703	−	0.0570580i
$573$	−0.342531	−	1.05420i	−0.0143094	−	0.0440399i
$574$	0.324371	+	0.998311i	0.0135390	+	0.0416687i
$575$	0.0234130	+	0.222760i	0.000976389	+	0.00928972i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	23.6467	+	26.2624i	0.984427	+	1.09332i	0.995631	+	0.0933798i	$0.0297671\pi$
$577$	23.6467	+	26.2624i	0.984427	+	1.09332i	−0.0112035	+	0.999937i	$0.503566\pi$
$578$	0.138509	−	1.31782i	0.00576121	−	0.0548143i
$579$	13.5187	−	2.87349i	0.561819	−	0.119418i
$580$	2.76775	+	1.23228i	0.114924	+	0.0511677i
$581$	−5.44115	+	3.95323i	−0.225737	+	0.164007i
$582$	12.0881	−	5.38195i	0.501066	−	0.223089i
$583$	−12.4187	+	21.5098i	−0.514328	+	0.890843i
$584$	1.59617	+	2.76465i	0.0660502	+	0.114402i
$585$	0.330140	+	0.239861i	0.0136496	+	0.00991702i
$586$	−15.8082	−	3.36013i	−0.653030	−	0.138806i
$587$	−7.25271	+	22.3215i	−0.299351	+	0.921308i	0.682374	+	0.731003i	$0.260948\pi$
$587$	−7.25271	+	22.3215i	−0.299351	+	0.921308i	−0.981725	+	0.190305i	$0.939052\pi$
$588$	6.35843			0.262217
$589$	1.63535	−	12.5984i	0.0673833	−	0.519109i
$590$	−3.15613			−0.129936
$591$	−2.63074	+	8.09660i	−0.108214	+	0.333050i
$592$	−4.57690	−	0.972850i	−0.188109	−	0.0399839i
$593$	16.2443	+	11.8021i	0.667072	+	0.484656i	0.869044	−	0.494735i	$-0.164735\pi$
$593$	16.2443	+	11.8021i	0.667072	+	0.484656i	−0.201972	+	0.979391i	$0.564735\pi$
$594$	−1.68124	−	2.91199i	−0.0689821	−	0.119481i
$595$	1.71441	−	2.96945i	0.0702841	−	0.121736i
$596$	3.96654	−	1.76602i	0.162476	−	0.0723390i
$597$	10.2286	−	7.43153i	0.418630	−	0.304152i
$598$	0.0835012	+	0.0371771i	0.00341462	+	0.00152029i
$599$	−27.6633	+	5.88002i	−1.13029	+	0.240251i	−0.734844	−	0.678237i	$-0.762744\pi$
$599$	−27.6633	+	5.88002i	−1.13029	+	0.240251i	−0.395449	+	0.918488i	$0.629411\pi$
$600$	−0.104528	+	0.994522i	−0.00426736	+	0.0406012i
$601$	10.5059	+	11.6679i	0.428543	+	0.475945i	0.918284	−	0.395923i	$-0.129575\pi$
$601$	10.5059	+	11.6679i	0.428543	+	0.475945i	−0.489741	+	0.871868i	$0.662909\pi$
$602$	0.0473314	−	0.0525669i	0.00192909	−	0.00214247i
$603$	−1.36889	−	13.0241i	−0.0557455	−	0.530383i
$604$	−0.877470	−	2.70058i	−0.0357038	−	0.109885i
$605$	−0.0946425	−	0.291280i	−0.00384776	−	0.0118422i
$606$	0.250455	+	2.38292i	0.0101740	+	0.0967995i
$607$	−14.6274	+	16.2454i	−0.593708	+	0.659380i	−0.962864	−	0.269988i	$-0.912980\pi$
$607$	−14.6274	+	16.2454i	−0.593708	+	0.659380i	0.369156	+	0.929368i	$0.379647\pi$
$608$	1.52677	+	1.69565i	0.0619188	+	0.0687678i
$609$	0.253661	−	2.41342i	0.0102789	−	0.0977968i
$610$	3.64715	−	0.775225i	0.147669	−	0.0313879i
$611$	−0.343332	−	0.152861i	−0.0138897	−	0.00618411i
$612$	3.46322	−	2.51618i	0.139993	−	0.101711i
$613$	22.2526	−	9.90748i	0.898772	−	0.400159i	0.0952635	−	0.995452i	$-0.469631\pi$
$613$	22.2526	−	9.90748i	0.898772	−	0.400159i	0.803509	+	0.595293i	$0.202964\pi$
$614$	8.35595	−	14.4729i	0.337219	−	0.584080i
$615$	−0.655250	−	1.13493i	−0.0264222	−	0.0457647i
$616$	−2.17891	−	1.58307i	−0.0877909	−	0.0637838i
$617$	26.1299	+	5.55408i	1.05195	+	0.223599i	0.701269	−	0.712896i	$-0.252617\pi$
$617$	26.1299	+	5.55408i	1.05195	+	0.223599i	0.350681	+	0.936495i	$0.385950\pi$
$618$	−0.307170	+	0.945372i	−0.0123562	+	0.0380284i
$619$	−6.51147			−0.261718			−0.130859	−	0.991401i	$-0.541774\pi$
$619$	−6.51147			−0.261718			−0.130859	+	0.991401i	$0.541774\pi$
$620$	4.58281	−	3.16194i	0.184050	−	0.126987i
$621$	0.223987			0.00898827
$622$	3.93288	−	12.1042i	0.157694	−	0.485333i
$623$	−8.11176	−	1.72421i	−0.324991	−	0.0690789i
$624$	0.330140	+	0.239861i	0.0132162	+	0.00960211i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	12.9335	−	22.4015i	0.516928	−	0.895345i
$627$	7.00895	−	3.12059i	0.279911	−	0.124624i
$628$	−5.90236	+	4.28832i	−0.235530	+	0.171123i
$629$	−18.2987	−	8.14710i	−0.729617	−	0.324846i
$630$	0.783478	−	0.166533i	0.0312145	−	0.00663485i
$631$	1.71794	−	16.3451i	0.0683903	−	0.650690i	−0.905605	−	0.424122i	$-0.860583\pi$
$631$	1.71794	−	16.3451i	0.0683903	−	0.650690i	0.973995	−	0.226568i	$-0.0727506\pi$
$632$	1.80270	+	2.00210i	0.0717075	+	0.0796392i
$633$	17.0763	−	18.9652i	0.678723	−	0.753798i
$634$	0.546208	+	5.19682i	0.0216927	+	0.206392i
$635$	−4.09568	−	12.6052i	−0.162532	−	0.500222i
$636$	−2.28259	−	7.02508i	−0.0905105	−	0.278563i
$637$	0.271222	+	2.58050i	0.0107462	+	0.102243i
$638$	6.81659	−	7.57058i	0.269871	−	0.299722i
$639$	3.32887	+	3.69708i	0.131688	+	0.146254i
$640$	−0.104528	+	0.994522i	−0.00413185	+	0.0393119i
$641$	11.1641	−	2.37300i	0.440955	−	0.0937279i	0.0179163	−	0.999839i	$-0.494297\pi$
$641$	11.1641	−	2.37300i	0.440955	−	0.0937279i	0.423039	+	0.906112i	$0.360963\pi$
$642$	2.94824	+	1.31264i	0.116358	+	0.0518058i
$643$	21.3140	−	15.4855i	0.840543	−	0.610690i	−0.0819794	−	0.996634i	$-0.526124\pi$
$643$	21.3140	−	15.4855i	0.840543	−	0.610690i	0.922522	+	0.385944i	$0.126124\pi$
$644$	0.163898	−	0.0729723i	0.00645850	−	0.00287551i
$645$	−0.0441557	+	0.0764798i	−0.00173863	+	0.00301139i
$646$	4.88378	+	8.45896i	0.192150	+	0.332813i
$647$	2.88062	+	2.09289i	0.113249	+	0.0822800i	0.642968	−	0.765893i	$-0.277703\pi$
$647$	2.88062	+	2.09289i	0.113249	+	0.0822800i	−0.529719	+	0.848173i	$0.677703\pi$
$648$	0.978148	+	0.207912i	0.0384253	+	0.00816754i
$649$	−3.27941	+	10.0930i	−0.128728	+	0.396185i
$650$	−0.408075			−0.0160060
$651$	−3.54302	−	2.70845i	−0.138862	−	0.106153i
$652$	−15.0439			−0.589165
$653$	0.00515158	−	0.0158549i	0.000201597	−	0.000620452i	−0.950956	−	0.309327i	$-0.899896\pi$
$653$	0.00515158	−	0.0158549i	0.000201597	−	0.000620452i	0.951157	+	0.308707i	$0.0998962\pi$
$654$	−3.26059	−	0.693059i	−0.127499	−	0.0271008i
$655$	2.38946	+	1.73604i	0.0933639	+	0.0678329i
$656$	−0.655250	−	1.13493i	−0.0255832	−	0.0443114i
$657$	−1.59617	+	2.76465i	−0.0622727	+	0.107859i
$658$	−0.673902	+	0.300040i	−0.0262714	+	0.0116968i
$659$	−3.46066	+	2.51432i	−0.134808	+	0.0979440i	−0.653146	−	0.757232i	$-0.726551\pi$
$659$	−3.46066	+	2.51432i	−0.134808	+	0.0979440i	0.518337	+	0.855176i	$0.326551\pi$
$660$	3.07178	+	1.36764i	0.119569	+	0.0532355i
$661$	−3.73512	+	0.793924i	−0.145279	+	0.0308800i	−0.279977	−	0.960007i	$-0.590327\pi$
$661$	−3.73512	+	0.793924i	−0.145279	+	0.0308800i	0.134698	+	0.990887i	$0.456994\pi$
$662$	−0.975101	+	9.27747i	−0.0378984	+	0.360579i
$663$	1.16889	+	1.29819i	0.0453960	+	0.0504174i
$664$	5.61851	−	6.23999i	0.218041	−	0.242159i
$665$	0.191038	+	1.81761i	0.00740815	+	0.0704838i
$666$	−1.44594	−	4.45014i	−0.0560289	−	0.172439i
$667$	0.209701	+	0.645394i	0.00811966	+	0.0249897i
$668$	0.910603	+	8.66381i	0.0352323	+	0.335213i
$669$	−4.78263	+	5.31165i	−0.184907	+	0.205360i
$670$	8.76284	+	9.73212i	0.338538	+	0.375985i
$671$	1.31052	−	12.4688i	0.0505920	−	0.481351i
$672$	0.783478	−	0.166533i	0.0302233	−	0.00642417i
$673$	−12.5501	−	5.58765i	−0.483770	−	0.215388i	0.150335	−	0.988635i	$-0.451965\pi$
$673$	−12.5501	−	5.58765i	−0.483770	−	0.215388i	−0.634105	+	0.773247i	$0.718631\pi$
$674$	5.95948	−	4.32981i	0.229551	−	0.166778i
$675$	−0.913545	+	0.406737i	−0.0351624	+	0.0156553i
$676$	6.41674	−	11.1141i	0.246798	−	0.427466i
$677$	−0.265437	−	0.459750i	−0.0102016	−	0.0176696i	0.860880	−	0.508809i	$-0.169914\pi$
$677$	−0.265437	−	0.459750i	−0.0102016	−	0.0176696i	−0.871081	+	0.491139i	$0.836581\pi$
$678$	9.67638	+	7.03030i	0.371619	+	0.269997i
$679$	10.3670	+	2.20357i	0.397849	+	0.0845654i
$680$	−1.32283	+	4.07126i	−0.0507284	+	0.156126i
$681$	3.23894			0.124116
$682$	−5.34977	−	17.9409i	−0.204853	−	0.686991i
$683$	43.6789			1.67133			0.835664	−	0.549242i	$-0.185083\pi$
$683$	43.6789			1.67133			0.835664	+	0.549242i	$0.185083\pi$
$684$	−0.705092	+	2.17005i	−0.0269599	+	0.0829739i
$685$	16.0858	+	3.41913i	0.614605	+	0.130638i
$686$	8.65636	+	6.28922i	0.330502	+	0.240123i
$687$	−0.0656112	−	0.113642i	−0.00250322	−	0.00433571i
$688$	−0.0441557	+	0.0764798i	−0.00168342	+	0.00291577i
$689$	2.75369	−	1.22602i	0.104907	−	0.0467078i
$690$	−0.181209	+	0.131656i	−0.00689851	+	0.00501206i
$691$	−25.2204	−	11.2289i	−0.959430	−	0.427166i	−0.133569	−	0.991040i	$-0.542644\pi$
$691$	−25.2204	−	11.2289i	−0.959430	−	0.427166i	−0.825861	+	0.563874i	$0.809310\pi$
$692$	−6.40112	+	1.36060i	−0.243334	+	0.0517223i
$693$	0.281525	−	2.67853i	0.0106942	−	0.101749i
$694$	−2.85821	−	3.17436i	−0.108496	−	0.120497i
$695$	4.21482	−	4.68103i	0.159877	−	0.177561i
$696$	0.316687	+	3.01308i	0.0120040	+	0.114210i
$697$	−1.73357	−	5.33539i	−0.0656638	−	0.202092i
$698$	−3.57282	−	10.9960i	−0.135233	−	0.416206i
$699$	1.03935	+	9.88873i	0.0393117	+	0.374026i
$700$	−0.535961	+	0.595245i	−0.0202574	+	0.0224982i
$701$	−3.60160	−	3.99998i	−0.136030	−	0.151077i	0.671281	−	0.741203i	$-0.265745\pi$
$701$	−3.60160	−	3.99998i	−0.136030	−	0.151077i	−0.807311	+	0.590126i	$0.799078\pi$
$702$	−0.0426555	+	0.405840i	−0.00160993	+	0.0153174i
$703$	10.4432	−	2.21978i	0.393874	−	0.0837205i
$704$	3.07178	+	1.36764i	0.115772	+	0.0515450i
$705$	0.745078	−	0.541331i	0.0280613	−	0.0203877i
$706$	23.4272	−	10.4304i	0.881693	−	0.392555i
$707$	−0.959594	+	1.66207i	−0.0360892	+	0.0625084i
$708$	−1.57806	−	2.73328i	−0.0593072	−	0.102723i
$709$	−25.9588	−	18.8602i	−0.974903	−	0.708308i	−0.0183391	−	0.999832i	$-0.505838\pi$
$709$	−25.9588	−	18.8602i	−0.974903	−	0.708308i	−0.956564	+	0.291523i	$0.905838\pi$
$710$	−4.86620	−	1.03434i	−0.182625	−	0.0388182i
$711$	−0.832520	+	2.56223i	−0.0312219	+	0.0960912i
$712$	10.3535			0.388015
$713$	1.21317	+	0.288929i	0.0454337	+	0.0108205i
$714$	3.42883			0.128321
$715$	−0.424016	+	1.30499i	−0.0158573	+	0.0488038i
$716$	−13.9355	−	2.96209i	−0.520796	−	0.110699i
$717$	11.2969	+	8.20766i	0.421890	+	0.306521i
$718$	−17.5140	−	30.3351i	−0.653617	−	1.13210i
$719$	−2.33035	+	4.03629i	−0.0869075	+	0.150528i	−0.906202	−	0.422844i	$-0.861032\pi$
$719$	−2.33035	+	4.03629i	−0.0869075	+	0.150528i	0.819295	+	0.573372i	$0.194365\pi$
$720$	−0.913545	+	0.406737i	−0.0340458	+	0.0151582i
$721$	−0.644134	+	0.467991i	−0.0239888	+	0.0174289i
$722$	12.6012	+	5.61042i	0.468968	+	0.208798i
$723$	14.9049	−	3.16812i	0.554318	−	0.117824i
$724$	1.70609	−	16.2323i	0.0634062	−	0.603270i
$725$	−2.02725	−	2.25149i	−0.0752902	−	0.0836182i
$726$	0.204934	−	0.227603i	0.00760582	−	0.00844712i
$727$	−1.53250	−	14.5808i	−0.0568373	−	0.540771i	−0.985480	−	0.169794i	$-0.945690\pi$
$727$	−1.53250	−	14.5808i	−0.0568373	−	0.540771i	0.928642	−	0.370976i	$-0.120977\pi$
$728$	0.101006	+	0.310863i	0.00374351	+	0.0115214i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−0.333691	−	3.17486i	−0.0123505	−	0.117507i
$731$	−0.252959	+	0.280939i	−0.00935603	+	0.0103909i
$732$	2.49494	+	2.77091i	0.0922156	+	0.102416i
$733$	2.97768	−	28.3307i	0.109983	−	1.04642i	−0.790778	−	0.612103i	$-0.790324\pi$
$733$	2.97768	−	28.3307i	0.109983	−	1.04642i	0.900761	−	0.434315i	$-0.143010\pi$
$734$	19.0510	−	4.04942i	0.703186	−	0.149467i
$735$	−5.80871	−	2.58621i	−0.214258	−	0.0953936i
$736$	−0.181209	+	0.131656i	−0.00667945	+	0.00485291i
$737$	40.2276	−	17.9105i	1.48180	−	0.659741i
$738$	0.655250	−	1.13493i	0.0241201	−	0.0417772i
$739$	−14.9415	−	25.8794i	−0.549632	−	0.951990i	−0.998300	−	0.0582914i	$-0.981435\pi$
$739$	−14.9415	−	25.8794i	−0.549632	−	0.951990i	0.448668	−	0.893699i	$-0.351899\pi$
$740$	3.78551	+	2.75034i	0.139158	+	0.101104i
$741$	−0.910769	−	0.193590i	−0.0334579	−	0.00711170i
$742$	1.82831	−	5.62696i	0.0671194	−	0.206572i
$743$	−10.5731			−0.387888			−0.193944	−	0.981013i	$-0.562128\pi$
$743$	−10.5731			−0.387888			−0.193944	+	0.981013i	$0.562128\pi$
$744$	5.02973	+	2.38786i	0.184399	+	0.0875431i
$745$	−4.34192			−0.159076
$746$	6.60142	−	20.3171i	0.241695	−	0.743861i
$747$	8.21325	+	1.74578i	0.300507	+	0.0638747i
$748$	11.6450	+	8.46060i	0.425784	+	0.309350i
$749$	1.29248	+	2.23865i	0.0472264	+	0.0817985i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	13.0112	−	5.79297i	0.474786	−	0.211388i	−0.155371	−	0.987856i	$-0.549657\pi$
$751$	13.0112	−	5.79297i	0.474786	−	0.211388i	0.630157	+	0.776468i	$0.282991\pi$
$752$	0.745078	−	0.541331i	0.0271702	−	0.0197403i
$753$	13.2371	+	5.89352i	0.482386	+	0.214772i
$754$	−1.20932	+	0.257049i	−0.0440408	+	0.00936116i
$755$	−0.296814	+	2.82400i	−0.0108022	+	0.102776i
$756$	0.535961	+	0.595245i	0.0194927	+	0.0216489i
$757$	20.3490	−	22.5999i	0.739597	−	0.821406i	−0.249546	−	0.968363i	$-0.580281\pi$
$757$	20.3490	−	22.5999i	0.739597	−	0.821406i	0.989143	+	0.146957i	$0.0469479\pi$
$758$	2.45466	+	23.3546i	0.0891574	+	0.848276i
$759$	0.232736	+	0.716289i	0.00844779	+	0.0259996i
$760$	−0.705092	−	2.17005i	−0.0255764	−	0.0787160i
$761$	−0.866023	−	8.23966i	−0.0313933	−	0.298687i	−0.998941	−	0.0460005i	$-0.985352\pi$
$761$	−0.866023	−	8.23966i	−0.0313933	−	0.298687i	0.967548	−	0.252687i	$-0.0813143\pi$
$762$	8.86859	−	9.84956i	0.321275	−	0.356812i
$763$	−1.78659	−	1.98421i	−0.0646789	−	0.0718332i
$764$	−0.115865	+	1.10238i	−0.00419184	+	0.0398827i
$765$	−4.18724	+	0.890024i	−0.151390	+	0.0321789i
$766$	16.3096	+	7.26150i	0.589290	+	0.262369i
$767$	1.04196	−	0.757030i	0.0376231	−	0.0273348i
$768$	−0.913545	+	0.406737i	−0.0329647	+	0.0146768i
$769$	−7.31760	+	12.6745i	−0.263879	+	0.457053i	−0.967269	−	0.253752i	$-0.918335\pi$
$769$	−7.31760	+	12.6745i	−0.263879	+	0.457053i	0.703390	+	0.710804i	$0.251669\pi$
$770$	1.34664	+	2.33245i	0.0485296	+	0.0840558i
$771$	5.84088	+	4.24365i	0.210354	+	0.152831i
$772$	−13.5187	−	2.87349i	−0.486550	−	0.103419i
$773$	−13.6842	+	42.1157i	−0.492187	+	1.51480i	0.329108	+	0.944292i	$0.393252\pi$
$773$	−13.6842	+	42.1157i	−0.492187	+	1.51480i	−0.821295	+	0.570504i	$0.806748\pi$
$774$	−0.0883113			−0.00317428
$775$	−5.47268	+	1.02458i	−0.196584	+	0.0368041i
$776$	−13.2320			−0.475002
$777$	1.15817	−	3.56448i	0.0415491	−	0.127875i
$778$	−15.6011	−	3.31612i	−0.559328	−	0.118889i
$779$	2.41912	+	1.75760i	0.0866741	+	0.0629724i
$780$	−0.204038	−	0.353404i	−0.00730572	−	0.0126539i
$781$	−8.36402	+	14.4869i	−0.299288	+	0.518382i
$782$	−0.875942	+	0.389994i	−0.0313236	+	0.0139462i
$783$	−2.45106	+	1.78080i	−0.0875937	+	0.0636406i
$784$	−5.80871	−	2.58621i	−0.207454	−	0.0923645i
$785$	7.13629	−	1.51687i	0.254705	−	0.0541393i
$786$	−0.308728	+	2.93736i	−0.0110120	+	0.104772i
$787$	15.5237	+	17.2408i	0.553360	+	0.614568i	0.953319	−	0.301965i	$-0.0976425\pi$
$787$	15.5237	+	17.2408i	0.553360	+	0.614568i	−0.399960	+	0.916533i	$0.630976\pi$
$788$	5.69649	−	6.32659i	0.202929	−	0.225375i
$789$	−2.03551	−	19.3666i	−0.0724660	−	0.689468i
$790$	−0.832520	−	2.56223i	−0.0296197	−	0.0911601i
$791$	2.96047	+	9.11138i	0.105262	+	0.323963i
$792$	0.351475	+	3.34406i	0.0124891	+	0.118826i
$793$	−1.01812	+	1.13074i	−0.0361546	+	0.0401538i
$794$	−1.25500	−	1.39382i	−0.0445382	−	0.0494647i
$795$	−0.772111	+	7.34614i	−0.0273840	+	0.260541i
$796$	−12.3670	+	2.62869i	−0.438337	+	0.0931713i
$797$	48.0863	+	21.4094i	1.70330	+	0.758359i	0.998816	+	0.0486412i	$0.0154891\pi$
$797$	48.0863	+	21.4094i	1.70330	+	0.758359i	0.704486	+	0.709718i	$0.251178\pi$
$798$	−1.47858	+	1.07425i	−0.0523410	+	0.0380280i
$799$	3.60161	−	1.60354i	0.127416	−	0.0567292i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	5.17676	+	8.96642i	0.182912	+	0.316813i
$802$	−29.8865	−	21.7138i	−1.05533	−	0.766741i
$803$	−10.4996	−	2.23177i	−0.370524	−	0.0787574i
$804$	−4.04684	+	12.4549i	−0.142721	+	0.439251i
$805$	−0.179409			−0.00632334
$806$	−0.754542	+	2.14312i	−0.0265776	+	0.0754881i
$807$	7.98859			0.281212
$808$	0.740418	−	2.27877i	0.0260478	−	0.0801670i
$809$	−39.1759	−	8.32710i	−1.37735	−	0.292765i	−0.541030	−	0.841003i	$-0.681965\pi$
$809$	−39.1759	−	8.32710i	−1.37735	−	0.292765i	−0.836322	+	0.548238i	$0.815299\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	12.1780	+	21.0930i	0.427628	+	0.740674i	0.996662	−	0.0816405i	$-0.0260159\pi$
$811$	12.1780	+	21.0930i	0.427628	+	0.740674i	−0.569034	+	0.822314i	$0.692683\pi$
$812$	−1.21336	+	2.10160i	−0.0425805	+	0.0737516i
$813$	25.3359	−	11.2802i	0.888567	−	0.395616i
$814$	12.7287	−	9.24795i	0.446141	−	0.324140i
$815$	13.7433	+	6.11891i	0.481407	+	0.214336i
$816$	−4.18724	+	0.890024i	−0.146583	+	0.0311571i
$817$	0.0210627	−	0.200398i	0.000736891	−	0.00701105i
$818$	−5.65149	−	6.27662i	−0.197600	−	0.219457i
$819$	−0.218713	+	0.242905i	−0.00764244	+	0.00848779i
$820$	0.136985	+	1.30332i	0.00478371	+	0.0455140i
$821$	−1.26663	−	3.89828i	−0.0442056	−	0.136051i	0.926518	−	0.376251i	$-0.122787\pi$
$821$	−1.26663	−	3.89828i	−0.0442056	−	0.136051i	−0.970723	+	0.240200i	$0.922787\pi$
$822$	5.08182	+	15.6402i	0.177249	+	0.545516i
$823$	−1.57522	−	14.9872i	−0.0549088	−	0.522423i	−0.987060	−	0.160353i	$-0.948737\pi$
$823$	−1.57522	−	14.9872i	−0.0549088	−	0.522423i	0.932151	−	0.362070i	$-0.117930\pi$
$824$	0.665131	−	0.738703i	0.0231709	−	0.0257339i
$825$	−2.24994	−	2.49881i	−0.0783328	−	0.0869974i
$826$	0.264248	−	2.51415i	0.00919436	−	0.0874784i
$827$	19.7823	−	4.20485i	0.687897	−	0.146217i	0.149315	−	0.988790i	$-0.452293\pi$
$827$	19.7823	−	4.20485i	0.687897	−	0.146217i	0.538583	+	0.842573i	$0.318960\pi$
$828$	−0.204622	−	0.0911036i	−0.00711111	−	0.00316607i
$829$	21.2614	−	15.4473i	0.738438	−	0.536507i	−0.153783	−	0.988105i	$-0.549146\pi$
$829$	21.2614	−	15.4473i	0.738438	−	0.536507i	0.892222	+	0.451598i	$0.149146\pi$
$830$	−7.67080	+	3.41526i	−0.266257	+	0.118545i
$831$	−0.277372	+	0.480423i	−0.00962194	+	0.0166657i
$832$	−0.204038	−	0.353404i	−0.00707373	−	0.0122521i
$833$	−22.0207	−	15.9989i	−0.762971	−	0.554331i
$834$	6.16130	+	1.30962i	0.213348	+	0.0453486i
$835$	2.69201	−	8.28516i	0.0931609	−	0.286720i
$836$	−7.67225			−0.265350
$837$	0.446919	+	5.54980i	0.0154478	+	0.191829i
$838$	−22.4403			−0.775186
$839$	−5.29689	+	16.3021i	−0.182869	+	0.562813i	−0.999905	−	0.0137737i	$-0.995616\pi$
$839$	−5.29689	+	16.3021i	−0.182869	+	0.562813i	0.817036	+	0.576586i	$0.195616\pi$
$840$	−0.783478	−	0.166533i	−0.0270326	−	0.00574595i
$841$	16.0356	+	11.6505i	0.552951	+	0.401742i
$842$	−8.91468	−	15.4407i	−0.307220	−	0.532121i
$843$	2.14895	−	3.72209i	0.0740138	−	0.128196i
$844$	−23.3138	+	10.3800i	−0.802495	+	0.357294i
$845$	−10.3825	+	7.54333i	−0.357169	+	0.259498i
$846$	0.841345	+	0.374591i	0.0289260	+	0.0128787i
$847$	0.239955	−	0.0510041i	0.00824497	−	0.00175252i
$848$	−0.772111	+	7.34614i	−0.0265144	+	0.252268i
$849$	8.82672	+	9.80307i	0.302932	+	0.336441i
$850$	2.86440	−	3.18124i	0.0982482	−	0.109116i
$851$	0.109553	+	1.04233i	0.00375542	+	0.0357305i
$852$	−1.53733	−	4.73142i	−0.0526682	−	0.162096i
$853$	6.97099	+	21.4545i	0.238682	+	0.734588i	0.996612	+	0.0822517i	$0.0262111\pi$
$853$	6.97099	+	21.4545i	0.238682	+	0.734588i	−0.757929	+	0.652337i	$0.773789\pi$
$854$	0.312181	+	2.97020i	0.0106826	+	0.101638i
$855$	1.52677	−	1.69565i	0.0522145	−	0.0579901i
$856$	−2.15945	−	2.39832i	−0.0738086	−	0.0819727i
$857$	5.87911	−	55.9360i	0.200827	−	1.91074i	−0.175889	−	0.984410i	$-0.556280\pi$
$857$	5.87911	−	55.9360i	0.200827	−	1.91074i	0.376716	−	0.926329i	$-0.377053\pi$
$858$	−1.34216	+	0.285285i	−0.0458206	+	0.00973947i
$859$	−22.6450	−	10.0822i	−0.772638	−	0.344001i	−0.0177400	−	0.999843i	$-0.505647\pi$
$859$	−22.6450	−	10.0822i	−0.772638	−	0.344001i	−0.754898	+	0.655842i	$0.772314\pi$
$860$	0.0714454	−	0.0519081i	0.00243627	−	0.00177005i
$861$	0.958936	−	0.426946i	0.0326805	−	0.0145503i
$862$	15.0913	−	26.1389i	0.514011	−	0.890294i
$863$	17.3299	+	30.0162i	0.589915	+	1.02176i	0.994243	+	0.107149i	$0.0341721\pi$
$863$	17.3299	+	30.0162i	0.589915	+	1.02176i	−0.404328	+	0.914614i	$0.632495\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	6.40112	+	1.36060i	0.217645	+	0.0462618i
$866$	−7.49436	+	23.0653i	−0.254669	+	0.783789i
$867$	−1.32508			−0.0450022
$868$	2.13509	+	3.91537i	0.0724695	+	0.132896i
$869$	−9.05882			−0.307300
$870$	0.936222	−	2.88139i	0.0317409	−	0.0976884i
$871$	−5.22732	−	1.11110i	−0.177121	−	0.0376482i
$872$	2.69680	+	1.95934i	0.0913253	+	0.0663517i
$873$	−6.61601	−	11.4593i	−0.223918	−	0.387837i
$874$	0.255538	−	0.442605i	0.00864370	−	0.0149713i
$875$	0.731733	−	0.325789i	0.0247371	−	0.0110137i
$876$	2.58266	−	1.87642i	0.0872601	−	0.0633982i
$877$	−9.16907	−	4.08233i	−0.309617	−	0.137851i	0.246045	−	0.969258i	$-0.420869\pi$
$877$	−9.16907	−	4.08233i	−0.309617	−	0.137851i	−0.555663	+	0.831408i	$0.687535\pi$
$878$	22.9242	−	4.87269i	0.773654	−	0.164445i
$879$	−1.68932	+	16.0728i	−0.0569794	+	0.542123i
$880$	−2.24994	−	2.49881i	−0.0758454	−	0.0842348i
$881$	16.6041	−	18.4408i	0.559408	−	0.621285i	−0.395400	−	0.918509i	$-0.629394\pi$
$881$	16.6041	−	18.4408i	0.559408	−	0.621285i	0.954808	+	0.297224i	$0.0960608\pi$
$882$	−0.664637	−	6.32360i	−0.0223795	−	0.212927i
$883$	−5.73335	−	17.6454i	−0.192943	−	0.593817i	−0.999994	−	0.00333586i	$-0.998938\pi$
$883$	−5.73335	−	17.6454i	−0.192943	−	0.593817i	0.807052	−	0.590481i	$-0.201062\pi$
$884$	−0.539816	−	1.66138i	−0.0181560	−	0.0558783i
$885$	0.329905	+	3.13884i	0.0110896	+	0.105511i
$886$	−3.91346	+	4.34633i	−0.131475	+	0.146018i
$887$	25.0163	+	27.7835i	0.839966	+	0.932877i	0.998515	−	0.0544740i	$-0.0173482\pi$
$887$	25.0163	+	27.7835i	0.839966	+	0.932877i	−0.158549	+	0.987351i	$0.550682\pi$
$888$	−0.489104	+	4.65352i	−0.0164133	+	0.156162i
$889$	10.3841	−	2.20722i	0.348273	−	0.0740277i
$890$	−9.45842	−	4.21116i	−0.317047	−	0.141158i
$891$	−2.72030	+	1.97642i	−0.0911336	+	0.0662124i
$892$	6.52959	−	2.90716i	0.218627	−	0.0973390i
$893$	−1.05070	+	1.81986i	−0.0351602	+	0.0608993i
$894$	−2.17096	−	3.76022i	−0.0726078	−	0.125760i
$895$	11.5260	+	8.37410i	0.385270	+	0.279915i
$896$	−0.783478	−	0.166533i	−0.0261742	−	0.00556349i
$897$	0.0282452	−	0.0869298i	0.000943080	−	0.00290250i
$898$	−5.57198			−0.185939
$899$	−15.5727	+	6.48359i	−0.519380	+	0.216240i
$900$	1.00000			0.0333333
$901$	−9.77126	+	30.0728i	−0.325528	+	1.00187i
$902$	4.31024	+	0.916169i	0.143515	+	0.0305051i
$903$	−0.0572264	−	0.0415774i	−0.00190438	−	0.00138361i
$904$	−5.98033	−	10.3582i	−0.198903	−	0.344510i
$905$	−8.16087	+	14.1350i	−0.271277	+	0.469865i
$906$	−2.59406	+	1.15495i	−0.0861819	+	0.0383707i
$907$	35.4476	−	25.7542i	1.17702	−	0.855154i	0.185187	−	0.982703i	$-0.440711\pi$
$907$	35.4476	−	25.7542i	1.17702	−	0.855154i	0.991832	+	0.127549i	$0.0407110\pi$
$908$	−2.95892	−	1.31739i	−0.0981951	−	0.0437193i
$909$	2.34369	−	0.498166i	0.0777351	−	0.0165231i
$910$	0.0341663	−	0.325070i	0.00113260	−	0.0107760i
$911$	15.5450	+	17.2644i	0.515027	+	0.571996i	0.943421	−	0.331596i	$-0.107587\pi$
$911$	15.5450	+	17.2644i	0.515027	+	0.571996i	−0.428394	+	0.903592i	$0.640920\pi$
$912$	1.52677	−	1.69565i	0.0505565	−	0.0561487i
$913$	2.95124	+	28.0792i	0.0976718	+	0.929285i
$914$	−12.4227	−	38.2332i	−0.410907	−	1.26464i
$915$	−1.15221	−	3.54614i	−0.0380909	−	0.117232i
$916$	0.0137165	+	0.130503i	0.000453205	+	0.00431196i
$917$	−1.58298	+	1.75808i	−0.0522746	+	0.0580568i
$918$	−2.86440	−	3.18124i	−0.0945393	−	0.104997i
$919$	0.749198	−	7.12814i	0.0247138	−	0.235136i	−0.975191	−	0.221363i	$-0.928949\pi$
$919$	0.749198	−	7.12814i	0.0247138	−	0.235136i	0.999905	−	0.0137724i	$-0.00438401\pi$
$920$	0.219092	−	0.0465694i	0.00722325	−	0.00153535i
$921$	−15.2671	−	6.79734i	−0.503067	−	0.223980i
$922$	17.8014	−	12.9335i	0.586259	−	0.425942i
$923$	1.85462	−	0.825732i	0.0610457	−	0.0271793i
$924$	−1.34664	+	2.33245i	−0.0443013	+	0.0767321i
$925$	−2.33958	−	4.05226i	−0.0769248	−	0.133238i
$926$	9.27379	+	6.73781i	0.304756	+	0.221418i
$927$	0.972301	+	0.206669i	0.0319345	+	0.00678790i
$928$	0.936222	−	2.88139i	0.0307330	−	0.0945864i
$929$	−32.3806			−1.06237			−0.531186	−	0.847255i	$-0.678254\pi$
$929$	−32.3806			−1.06237			−0.531186	+	0.847255i	$0.678254\pi$
$930$	−3.62365	−	4.22719i	−0.118824	−	0.138615i
$931$	14.5082			0.475487
$932$	3.07262	−	9.45655i	0.100647	−	0.309760i
$933$	−12.4490	−	2.64611i	−0.407561	−	0.0866297i
$934$	−3.51646	−	2.55486i	−0.115062	−	0.0835975i
$935$	−7.19702	−	12.4656i	−0.235368	−	0.407669i
$936$	0.204038	−	0.353404i	0.00666918	−	0.0115514i
$937$	9.63361	−	4.28916i	0.314716	−	0.140121i	−0.243299	−	0.969951i	$-0.578230\pi$
$937$	9.63361	−	4.28916i	0.314716	−	0.140121i	0.558015	+	0.829831i	$0.311563\pi$
$938$	−8.48622	+	6.16560i	−0.277085	+	0.201314i
$939$	−23.6307	−	10.5211i	−0.771160	−	0.343342i
$940$	−0.900841	+	0.191480i	−0.0293822	+	0.00624538i
$941$	2.42623	−	23.0841i	0.0790930	−	0.752519i	−0.881052	−	0.473018i	$-0.843164\pi$
$941$	2.42623	−	23.0841i	0.0790930	−	0.752519i	0.960145	−	0.279501i	$-0.0901690\pi$
$942$	4.88179	+	5.42178i	0.159057	+	0.176651i
$943$	−0.196413	+	0.218139i	−0.00639609	+	0.00710357i
$944$	0.329905	+	3.13884i	0.0107375	+	0.102160i
$945$	−0.247517	−	0.761779i	−0.00805173	−	0.0247807i
$946$	−0.0917610	−	0.282411i	−0.00298341	−	0.00918199i
$947$	4.58608	+	43.6336i	0.149027	+	1.41790i	0.771982	+	0.635644i	$0.219265\pi$
$947$	4.58608	+	43.6336i	0.149027	+	1.41790i	−0.622955	+	0.782258i	$0.714068\pi$
$948$	1.80270	−	2.00210i	0.0585489	−	0.0650252i
$949$	0.871689	+	0.968109i	0.0282962	+	0.0314261i
$950$	−0.238505	+	2.26923i	−0.00773813	+	0.0736234i
$951$	5.11126	−	1.08643i	0.165744	−	0.0352300i
$952$	−3.13239	−	1.39463i	−0.101521	−	0.0452002i
$953$	7.26987	−	5.28187i	0.235494	−	0.171097i	−0.463779	−	0.885951i	$-0.653507\pi$
$953$	7.26987	−	5.28187i	0.235494	−	0.171097i	0.699274	+	0.714854i	$0.253507\pi$
$954$	−6.74800	+	3.00440i	−0.218475	+	0.0972712i
$955$	0.554226	−	0.959948i	0.0179343	−	0.0310632i
$956$	−6.98186	−	12.0929i	−0.225809	−	0.391113i
$957$	−8.24164	−	5.98790i	−0.266414	−	0.193561i
$958$	−22.3274	−	4.74583i	−0.721365	−	0.153331i
$959$	−4.07044	+	12.5275i	−0.131442	+	0.404535i
$960$	1.00000			0.0322749
$961$	−4.73825	+	30.6357i	−0.152847	+	0.988250i
$962$	−1.90945			−0.0615630
$963$	0.997276	−	3.06930i	0.0321368	−	0.0989068i
$964$	−14.9049	−	3.16812i	−0.480053	−	0.102038i
$965$	11.1812	+	8.12363i	0.359936	+	0.261509i
$966$	−0.0897046	−	0.155373i	−0.00288620	−	0.00499904i
$967$	−19.0063	+	32.9199i	−0.611202	+	1.05863i	0.379836	+	0.925054i	$0.375980\pi$
$967$	−19.0063	+	32.9199i	−0.611202	+	1.05863i	−0.991038	+	0.133579i	$0.957353\pi$
$968$	−0.279791	+	0.124571i	−0.00899283	+	0.00400386i
$969$	7.90213	−	5.74123i	0.253853	−	0.184435i
$970$	12.0881	+	5.38195i	0.388124	+	0.172804i
$971$	22.3776	−	4.75651i	0.718132	−	0.152644i	0.165669	−	0.986181i	$-0.447022\pi$
$971$	22.3776	−	4.75651i	0.718132	−	0.152644i	0.552463	+	0.833538i	$0.313688\pi$
$972$	0.104528	−	0.994522i	0.00335275	−	0.0318993i
$973$	3.37599	+	3.74942i	0.108229	+	0.120201i
$974$	7.04753	−	7.82707i	0.225817	−	0.250796i
$975$	0.0426555	+	0.405840i	0.00136607	+	0.0129973i
$976$	−1.15221	−	3.54614i	−0.0368813	−	0.113509i
$977$	−12.7774	−	39.3249i	−0.408787	−	1.25812i	−0.917692	−	0.397294i	$-0.869949\pi$
$977$	−12.7774	−	39.3249i	−0.408787	−	1.25812i	0.508905	−	0.860823i	$-0.330051\pi$
$978$	1.57252	+	14.9615i	0.0502836	+	0.478416i
$979$	−23.2948	+	25.8715i	−0.744505	+	0.826856i
$980$	4.25462	+	4.72523i	0.135909	+	0.150942i
$981$	−0.348438	+	3.31517i	−0.0111248	+	0.105845i
$982$	21.1021	−	4.48539i	0.673395	−	0.143134i
$983$	13.8613	+	6.17143i	0.442106	+	0.196838i	0.615703	−	0.787979i	$-0.288872\pi$
$983$	13.8613	+	6.17143i	0.442106	+	0.196838i	−0.173597	+	0.984817i	$0.555539\pi$
$984$	−1.06022	+	0.770293i	−0.0337985	+	0.0245560i
$985$	−7.77726	+	3.46266i	−0.247804	+	0.110329i
$986$	6.48469	−	11.2318i	0.206515	−	0.357694i
$987$	0.368839	+	0.638847i	0.0117403	+	0.0203347i
$988$	0.753289	+	0.547296i	0.0239653	+	0.0174118i
$989$	0.0193483	+	0.00411261i	0.000615240	+	0.000130773i
$990$	1.03906	−	3.19791i	0.0330236	−	0.101636i
$991$	60.1578			1.91097			0.955487	−	0.295033i	$-0.0953305\pi$
$991$	60.1578			1.91097			0.955487	+	0.295033i	$0.0953305\pi$
$992$	−3.62365	−	4.22719i	−0.115051	−	0.134213i
$993$	9.32857			0.296033
$994$	1.23138	−	3.78978i	0.0390568	−	0.120205i
$995$	12.3670	+	2.62869i	0.392060	+	0.0833349i
$996$	−6.79310	−	4.93548i	−0.215248	−	0.156387i
$997$	0.856051	+	1.48272i	0.0271114	+	0.0469583i	0.879263	−	0.476337i	$-0.158036\pi$
$997$	0.856051	+	1.48272i	0.0271114	+	0.0469583i	−0.852151	+	0.523295i	$0.824702\pi$
$998$	7.22945	−	12.5218i	0.228844	−	0.396370i
$999$	−4.27462	+	1.90318i	−0.135243	+	0.0602140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.e.691.1	✓	16
31.7	even	15	inner	930.2.bg.e.751.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.e.691.1	✓	16	1.1	even	1	trivial
930.2.bg.e.751.1	yes	16	31.7	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.731733 + 0.325789i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.731733 + 0.325789i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(-0.351475 + 3.34406i) q^{11} +(-0.669131 - 0.743145i) q^{12} +(0.273056 - 0.303259i) q^{13} +(-0.0837254 - 0.796594i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.447463 + 4.25733i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(-1.52677 - 1.69565i) q^{19} +(0.104528 - 0.994522i) q^{20} +(-0.783478 + 0.166533i) q^{21} +(-3.07178 - 1.36764i) q^{22} +(0.181209 - 0.131656i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.204038 + 0.353404i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.783478 + 0.166533i) q^{28} +(-0.936222 + 2.88139i) q^{29} -1.00000 q^{30} +(3.62365 + 4.22719i) q^{31} -1.00000 q^{32} +(-1.03906 + 3.19791i) q^{33} +(-4.18724 - 0.890024i) q^{34} +(-0.648008 - 0.470805i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.33958 + 4.05226i) q^{37} +(2.08446 - 0.928061i) q^{38} +(0.330140 - 0.239861i) q^{39} +(0.913545 + 0.406737i) q^{40} +(-1.28186 + 0.272468i) q^{41} +(0.0837254 - 0.796594i) q^{42} +(0.0590918 + 0.0656281i) q^{43} +(2.24994 - 2.49881i) q^{44} +(0.104528 + 0.994522i) q^{45} +(0.0692157 + 0.213024i) q^{46} +(-0.284594 - 0.875891i) q^{47} +(0.104528 + 0.994522i) q^{48} +(-4.25462 + 4.72523i) q^{49} +(-0.669131 - 0.743145i) q^{50} +(-0.447463 + 4.25733i) q^{51} +(-0.399158 + 0.0848436i) q^{52} +(6.74800 + 3.00440i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-3.07178 + 1.36764i) q^{55} +(-0.400491 + 0.693670i) q^{56} +(-1.14086 - 1.97603i) q^{57} +(-2.45106 - 1.78080i) q^{58} +(3.08716 + 0.656195i) q^{59} +(0.309017 - 0.951057i) q^{60} -3.72863 q^{61} +(-5.14007 + 2.14003i) q^{62} -0.800982 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.399158 + 0.0848436i) q^{65} +(-2.72030 - 1.97642i) q^{66} +(-6.54793 - 11.3413i) q^{67} +(2.14039 - 3.70726i) q^{68} +(0.204622 - 0.0911036i) q^{69} +(0.648008 - 0.470805i) q^{70} +(4.54481 + 2.02348i) q^{71} +(0.978148 - 0.207912i) q^{72} +(-0.333691 + 3.17486i) q^{73} +(-3.13096 - 3.47729i) q^{74} +(-0.669131 + 0.743145i) q^{75} +(0.238505 + 2.26923i) q^{76} +(-0.832271 - 2.56147i) q^{77} +(0.126102 + 0.388103i) q^{78} +(0.281609 + 2.67933i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(0.136985 - 1.30332i) q^{82} +(8.21325 - 1.74578i) q^{83} +(0.731733 + 0.325789i) q^{84} +(-3.46322 + 2.51618i) q^{85} +(-0.0806764 + 0.0359194i) q^{86} +(-1.51484 + 2.62378i) q^{87} +(1.68124 + 2.91199i) q^{88} +(8.37618 + 6.08565i) q^{89} +(-0.978148 - 0.207912i) q^{90} +(-0.101006 + 0.310863i) q^{91} -0.223987 q^{92} +(2.66559 + 4.88821i) q^{93} +0.920967 q^{94} +(0.705092 - 2.17005i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-10.7049 - 7.77759i) q^{97} +(-3.17921 - 5.50656i) q^{98} +(-1.68124 + 2.91199i) 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

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