LMFDB - Embedded newform 930.2.bg.e.691.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 27x^{14} + 345x^{12} - 2652x^{10} + 13244x^{8} - 43398x^{6} + 89940x^{4} - 107433x^{2} + 58081 $ x^16 - 27x^14 + 345x^12 - 2652x^10 + 13244x^8 - 43398x^6 + 89940x^4 - 107433*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			691.2
Root			$1.93590 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	930.691
Dual form			930.2.bg.e.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.45430 - 0.647494i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(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} +(1.45430 - 0.647494i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(0.440265 - 4.18884i) q^{11} +(-0.669131 - 0.743145i) q^{12} +(1.87422 - 2.08153i) q^{13} +(0.166401 + 1.58320i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.361964 - 3.44386i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(1.94032 + 2.15494i) q^{19} +(0.104528 - 0.994522i) q^{20} +(1.55714 - 0.330980i) q^{21} +(3.84777 + 1.71314i) q^{22} +(3.96840 - 2.88321i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.40049 + 2.42572i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.55714 - 0.330980i) q^{28} +(1.24981 - 3.84651i) q^{29} -1.00000 q^{30} +(-5.09490 + 2.24544i) q^{31} -1.00000 q^{32} +(1.30155 - 4.00577i) q^{33} +(3.38716 + 0.719962i) q^{34} +(1.28789 + 0.935710i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.48374 + 6.03401i) q^{37} +(-2.64906 + 1.17944i) q^{38} +(2.26604 - 1.64638i) q^{39} +(0.913545 + 0.406737i) q^{40} +(8.36533 - 1.77811i) q^{41} +(-0.166401 + 1.58320i) q^{42} +(-1.54207 - 1.71265i) q^{43} +(-2.81832 + 3.13006i) q^{44} +(0.104528 + 0.994522i) q^{45} +(1.51580 + 4.66514i) q^{46} +(1.95372 + 6.01295i) q^{47} +(0.104528 + 0.994522i) q^{48} +(-2.98819 + 3.31872i) q^{49} +(-0.669131 - 0.743145i) q^{50} +(0.361964 - 3.44386i) q^{51} +(-2.73977 + 0.582357i) q^{52} +(-5.30978 - 2.36407i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(3.84777 - 1.71314i) q^{55} +(0.795962 - 1.37865i) q^{56} +(1.44988 + 2.51127i) q^{57} +(3.27204 + 2.37727i) q^{58} +(0.257219 + 0.0546735i) q^{59} +(0.309017 - 0.951057i) q^{60} +9.30105 q^{61} +(-0.561132 - 5.53942i) q^{62} +1.59192 q^{63} +(0.309017 - 0.951057i) q^{64} +(2.73977 + 0.582357i) q^{65} +(3.40751 + 2.47570i) q^{66} +(5.10514 + 8.84236i) q^{67} +(-1.73141 + 2.99890i) q^{68} +(4.48114 - 1.99513i) q^{69} +(-1.28789 + 0.935710i) q^{70} +(3.70982 + 1.65172i) q^{71} +(0.978148 - 0.207912i) q^{72} +(0.630323 - 5.99712i) q^{73} +(-4.66215 - 5.17784i) q^{74} +(-0.669131 + 0.743145i) q^{75} +(-0.303107 - 2.88387i) q^{76} +(-2.07197 - 6.37688i) q^{77} +(0.865551 + 2.66389i) q^{78} +(0.736328 + 7.00569i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.893950 + 8.50537i) q^{82} +(-8.94511 + 1.90134i) q^{83} +(-1.45430 - 0.647494i) q^{84} +(2.80149 - 2.03540i) q^{85} +(2.10535 - 0.937363i) q^{86} +(2.02223 - 3.50261i) q^{87} +(-2.10596 - 3.64762i) q^{88} +(-6.87490 - 4.99491i) q^{89} +(-0.978148 - 0.207912i) q^{90} +(1.37789 - 4.24071i) q^{91} -4.90522 q^{92} +(-5.45042 + 1.13708i) q^{93} -6.32239 q^{94} +(-0.896075 + 2.75783i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(5.55940 + 4.03914i) q^{97} +(-2.23289 - 3.86748i) q^{98} +(2.10596 - 3.64762i) 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
$7$	1.45430	−	0.647494i	0.549672	−	0.244730i	−0.113058	−	0.993588i	$-0.536064\pi$
$7$	1.45430	−	0.647494i	0.549672	−	0.244730i	0.662730	+	0.748859i	$0.269398\pi$
$8$	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
$11$	0.440265	−	4.18884i	0.132745	−	1.26298i	−0.701933	−	0.712243i	$-0.747679\pi$
$11$	0.440265	−	4.18884i	0.132745	−	1.26298i	0.834678	−	0.550739i	$-0.185654\pi$
$12$	−0.669131	−	0.743145i	−0.193161	−	0.214527i
$13$	1.87422	−	2.08153i	0.519816	−	0.577314i	−0.424885	−	0.905247i	$-0.639685\pi$
$13$	1.87422	−	2.08153i	0.519816	−	0.577314i	0.944701	+	0.327933i	$0.106352\pi$
$14$	0.166401	+	1.58320i	0.0444727	+	0.423129i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.361964	−	3.44386i	−0.0877891	−	0.835258i	−0.946480	−	0.322763i	$-0.895388\pi$
$17$	−0.361964	−	3.44386i	−0.0877891	−	0.835258i	0.858691	−	0.512494i	$-0.171279\pi$
$18$	−0.669131	+	0.743145i	−0.157716	+	0.175161i
$19$	1.94032	+	2.15494i	0.445139	+	0.494377i	0.923399	−	0.383841i	$-0.125399\pi$
$19$	1.94032	+	2.15494i	0.445139	+	0.494377i	−0.478260	+	0.878218i	$0.658732\pi$
$20$	0.104528	−	0.994522i	0.0233733	−	0.222382i
$21$	1.55714	−	0.330980i	0.339795	−	0.0722257i
$22$	3.84777	+	1.71314i	0.820348	+	0.365242i
$23$	3.96840	−	2.88321i	0.827470	−	0.601192i	−0.0913728	−	0.995817i	$-0.529125\pi$
$23$	3.96840	−	2.88321i	0.827470	−	0.601192i	0.918842	+	0.394625i	$0.129125\pi$
$24$	0.913545	−	0.406737i	0.186477	−	0.0830248i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.40049	+	2.42572i	0.274659	+	0.475723i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−1.55714	−	0.330980i	−0.294271	−	0.0625493i
$29$	1.24981	−	3.84651i	0.232083	−	0.714279i	−0.765412	−	0.643541i	$-0.777465\pi$
$29$	1.24981	−	3.84651i	0.232083	−	0.714279i	0.997495	−	0.0707380i	$-0.0225354\pi$
$30$	−1.00000			−0.182574
$31$	−5.09490	+	2.24544i	−0.915071	+	0.403293i
$31$	−5.09490	+	2.24544i	−0.915071	+	0.403293i
$32$	−1.00000			−0.176777
$33$	1.30155	−	4.00577i	0.226571	−	0.697314i
$34$	3.38716	+	0.719962i	0.580892	+	0.123472i
$35$	1.28789	+	0.935710i	0.217694	+	0.158164i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.48374	+	6.03401i	−0.572723	+	0.991985i	0.423562	+	0.905867i	$0.360780\pi$
$37$	−3.48374	+	6.03401i	−0.572723	+	0.991985i	−0.996285	+	0.0861181i	$0.972554\pi$
$38$	−2.64906	+	1.17944i	−0.429735	+	0.191330i
$39$	2.26604	−	1.64638i	0.362857	−	0.263631i
$40$	0.913545	+	0.406737i	0.144444	+	0.0643107i
$41$	8.36533	−	1.77811i	1.30644	−	0.277693i	0.498468	−	0.866908i	$-0.333896\pi$
$41$	8.36533	−	1.77811i	1.30644	−	0.277693i	0.807977	+	0.589215i	$0.200563\pi$
$42$	−0.166401	+	1.58320i	−0.0256763	+	0.244294i
$43$	−1.54207	−	1.71265i	−0.235164	−	0.261176i	0.613999	−	0.789307i	$-0.289560\pi$
$43$	−1.54207	−	1.71265i	−0.235164	−	0.261176i	−0.849163	+	0.528130i	$0.822893\pi$
$44$	−2.81832	+	3.13006i	−0.424878	+	0.471874i
$45$	0.104528	+	0.994522i	0.0155822	+	0.148255i
$46$	1.51580	+	4.66514i	0.223492	+	0.687837i
$47$	1.95372	+	6.01295i	0.284980	+	0.877078i	0.986405	+	0.164335i	$0.0525477\pi$
$47$	1.95372	+	6.01295i	0.284980	+	0.877078i	−0.701425	+	0.712744i	$0.747452\pi$
$48$	0.104528	+	0.994522i	0.0150874	+	0.143547i
$49$	−2.98819	+	3.31872i	−0.426884	+	0.474103i
$50$	−0.669131	−	0.743145i	−0.0946294	−	0.105097i
$51$	0.361964	−	3.44386i	0.0506851	−	0.482236i
$52$	−2.73977	+	0.582357i	−0.379938	+	0.0807584i
$53$	−5.30978	−	2.36407i	−0.729355	−	0.324730i	0.00824673	−	0.999966i	$-0.497375\pi$
$53$	−5.30978	−	2.36407i	−0.729355	−	0.324730i	−0.737601	+	0.675236i	$0.764042\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	3.84777	−	1.71314i	0.518834	−	0.231000i
$56$	0.795962	−	1.37865i	0.106365	−	0.184229i
$57$	1.44988	+	2.51127i	0.192041	+	0.332625i
$58$	3.27204	+	2.37727i	0.429640	+	0.312151i
$59$	0.257219	+	0.0546735i	0.0334870	+	0.00711789i	0.224625	−	0.974445i	$-0.427884\pi$
$59$	0.257219	+	0.0546735i	0.0334870	+	0.00711789i	−0.191138	+	0.981563i	$0.561218\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	9.30105			1.19088			0.595438	−	0.803401i	$-0.296978\pi$
$61$	9.30105			1.19088			0.595438	+	0.803401i	$0.296978\pi$
$62$	−0.561132	−	5.53942i	−0.0712638	−	0.703507i
$63$	1.59192			0.200564
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	2.73977	+	0.582357i	0.339827	+	0.0722325i
$66$	3.40751	+	2.47570i	0.419435	+	0.304738i
$67$	5.10514	+	8.84236i	0.623692	+	1.08027i	0.988792	+	0.149298i	$0.0477015\pi$
$67$	5.10514	+	8.84236i	0.623692	+	1.08027i	−0.365100	+	0.930968i	$0.618965\pi$
$68$	−1.73141	+	2.99890i	−0.209965	+	0.363670i
$69$	4.48114	−	1.99513i	0.539466	−	0.240186i
$70$	−1.28789	+	0.935710i	−0.153933	+	0.111839i
$71$	3.70982	+	1.65172i	0.440275	+	0.196023i	0.614888	−	0.788614i	$-0.289201\pi$
$71$	3.70982	+	1.65172i	0.440275	+	0.196023i	−0.174614	+	0.984637i	$0.555868\pi$
$72$	0.978148	−	0.207912i	0.115276	−	0.0245026i
$73$	0.630323	−	5.99712i	0.0737737	−	0.701910i	−0.893653	−	0.448759i	$-0.851866\pi$
$73$	0.630323	−	5.99712i	0.0737737	−	0.701910i	0.967427	−	0.253151i	$-0.0814671\pi$
$74$	−4.66215	−	5.17784i	−0.541964	−	0.601912i
$75$	−0.669131	+	0.743145i	−0.0772645	+	0.0858110i
$76$	−0.303107	−	2.88387i	−0.0347688	−	0.330803i
$77$	−2.07197	−	6.37688i	−0.236123	−	0.726713i
$78$	0.865551	+	2.66389i	0.0980043	+	0.301626i
$79$	0.736328	+	7.00569i	0.0828434	+	0.788202i	0.954525	+	0.298130i	$0.0963629\pi$
$79$	0.736328	+	7.00569i	0.0828434	+	0.788202i	−0.871682	+	0.490072i	$0.836970\pi$
$80$	−0.669131	+	0.743145i	−0.0748111	+	0.0830861i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	−0.893950	+	8.50537i	−0.0987203	+	0.939260i
$83$	−8.94511	+	1.90134i	−0.981854	+	0.208699i	−0.670756	−	0.741678i	$-0.734030\pi$
$83$	−8.94511	+	1.90134i	−0.981854	+	0.208699i	−0.311098	+	0.950378i	$0.600697\pi$
$84$	−1.45430	−	0.647494i	−0.158677	−	0.0706474i
$85$	2.80149	−	2.03540i	0.303864	−	0.220770i
$86$	2.10535	−	0.937363i	0.227026	−	0.101078i
$87$	2.02223	−	3.50261i	0.216806	−	0.375519i
$88$	−2.10596	−	3.64762i	−0.224496	−	0.388838i
$89$	−6.87490	−	4.99491i	−0.728738	−	0.529459i	0.160426	−	0.987048i	$-0.448713\pi$
$89$	−6.87490	−	4.99491i	−0.728738	−	0.529459i	−0.889164	+	0.457589i	$0.848713\pi$
$90$	−0.978148	−	0.207912i	−0.103106	−	0.0219158i
$91$	1.37789	−	4.24071i	0.144442	−	0.444548i
$92$	−4.90522			−0.511404
$93$	−5.45042	+	1.13708i	−0.565182	+	0.117910i
$94$	−6.32239			−0.652104
$95$	−0.896075	+	2.75783i	−0.0919353	+	0.282948i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	5.55940	+	4.03914i	0.564471	+	0.410112i	0.833093	−	0.553134i	$-0.186568\pi$
$97$	5.55940	+	4.03914i	0.564471	+	0.410112i	−0.268621	+	0.963246i	$0.586568\pi$
$98$	−2.23289	−	3.86748i	−0.225556	−	0.390674i
$99$	2.10596	−	3.64762i	0.211656	−	0.366600i
$100$	0.913545	−	0.406737i	0.0913545	−	0.0406737i
$101$	1.88615	−	1.37037i	0.187679	−	0.136357i	−0.489978	−	0.871735i	$-0.662995\pi$
$101$	1.88615	−	1.37037i	0.187679	−	0.136357i	0.677657	+	0.735378i	$0.262995\pi$
$102$	3.16345	+	1.40846i	0.313228	+	0.139458i
$103$	−7.22831	+	1.53642i	−0.712227	+	0.151388i	−0.549756	−	0.835325i	$-0.685279\pi$
$103$	−7.22831	+	1.53642i	−0.712227	+	0.151388i	−0.162470	+	0.986713i	$0.551946\pi$
$104$	0.292782	−	2.78564i	0.0287097	−	0.273154i
$105$	1.06521	+	1.18303i	0.103953	+	0.115452i
$106$	3.88917	−	4.31937i	0.377750	−	0.419534i
$107$	0.608987	+	5.79412i	0.0588730	+	0.560139i	0.983708	+	0.179771i	$0.0575358\pi$
$107$	0.608987	+	5.79412i	0.0588730	+	0.560139i	−0.924835	+	0.380367i	$0.875798\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	4.39260	+	13.5190i	0.420734	+	1.29489i	0.907020	+	0.421087i	$0.138351\pi$
$109$	4.39260	+	13.5190i	0.420734	+	1.29489i	−0.486286	+	0.873800i	$0.661649\pi$
$110$	0.440265	+	4.18884i	0.0419776	+	0.399390i
$111$	−4.66215	+	5.17784i	−0.442512	+	0.491459i
$112$	1.06521	+	1.18303i	0.100652	+	0.111786i
$113$	0.804157	−	7.65104i	0.0756487	−	0.719750i	−0.889302	−	0.457320i	$-0.848809\pi$
$113$	0.804157	−	7.65104i	0.0756487	−	0.719750i	0.964951	−	0.262430i	$-0.0845238\pi$
$114$	−2.83639	+	0.602894i	−0.265653	+	0.0564662i
$115$	4.48114	+	1.99513i	0.417868	+	0.186047i
$116$	−3.27204	+	2.37727i	−0.303801	+	0.220724i
$117$	2.55882	−	1.13926i	0.236563	−	0.105325i
$118$	−0.131483	+	0.227735i	−0.0121040	+	0.0209647i
$119$	−2.75628	−	4.77402i	−0.252668	−	0.437633i
$120$	0.809017	+	0.587785i	0.0738528	+	0.0536572i
$121$	−6.59291	−	1.40137i	−0.599355	−	0.127397i
$122$	−2.87418	+	8.84582i	−0.260216	+	0.800863i
$123$	8.55222			0.771127
$124$	5.44170	+	1.17811i	0.488679	+	0.105797i
$125$	−1.00000			−0.0894427
$126$	−0.491932	+	1.51401i	−0.0438248	+	0.134879i
$127$	−5.06607	−	1.07683i	−0.449541	−	0.0955529i	−0.0224226	−	0.999749i	$-0.507138\pi$
$127$	−5.06607	−	1.07683i	−0.449541	−	0.0955529i	−0.427118	+	0.904196i	$0.640471\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−1.15230	−	1.99584i	−0.101454	−	0.175724i
$130$	−1.40049	+	2.42572i	−0.122831	+	0.212750i
$131$	−4.30038	+	1.91465i	−0.375726	+	0.167284i	−0.585907	−	0.810379i	$-0.699261\pi$
$131$	−4.30038	+	1.91465i	−0.375726	+	0.167284i	0.210181	+	0.977663i	$0.432595\pi$
$132$	−3.40751	+	2.47570i	−0.296585	+	0.215482i
$133$	4.21711	+	1.87758i	0.365670	+	0.162807i
$134$	−9.98716	+	2.12284i	−0.862759	+	0.183385i
$135$	−0.104528	+	0.994522i	−0.00899638	+	0.0855948i
$136$	−2.31708	−	2.57338i	−0.198688	−	0.220666i
$137$	−11.2799	+	12.5276i	−0.963709	+	1.07031i	0.0337760	+	0.999429i	$0.489247\pi$
$137$	−11.2799	+	12.5276i	−0.963709	+	1.07031i	−0.997485	+	0.0708779i	$0.977420\pi$
$138$	0.512735	+	4.87835i	0.0436469	+	0.415272i
$139$	−4.54626	−	13.9920i	−0.385609	−	1.18678i	−0.936037	−	0.351900i	$-0.885536\pi$
$139$	−4.54626	−	13.9920i	−0.385609	−	1.18678i	0.550428	−	0.834882i	$-0.314464\pi$
$140$	−0.491932	−	1.51401i	−0.0415758	−	0.127957i
$141$	0.660869	+	6.28775i	0.0556552	+	0.529524i
$142$	−2.71728	+	3.01784i	−0.228029	+	0.253252i
$143$	−7.89406	−	8.76724i	−0.660134	−	0.733153i
$144$	−0.104528	+	0.994522i	−0.00871071	+	0.0828768i
$145$	3.95608	−	0.840891i	0.328535	−	0.0698322i
$146$	5.50882	+	2.45269i	0.455913	+	0.202986i
$147$	−3.61289	+	2.62492i	−0.297986	+	0.216500i
$148$	6.36510	−	2.83393i	0.523208	−	0.232947i
$149$	10.1802	−	17.6326i	0.833995	−	1.44452i	−0.0608520	−	0.998147i	$-0.519382\pi$
$149$	10.1802	−	17.6326i	0.833995	−	1.44452i	0.894846	−	0.446374i	$-0.147285\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−7.26534	−	5.27858i	−0.591245	−	0.429564i	0.251516	−	0.967853i	$-0.419071\pi$
$151$	−7.26534	−	5.27858i	−0.591245	−	0.429564i	−0.842760	+	0.538289i	$0.819071\pi$
$152$	2.83639	+	0.602894i	0.230062	+	0.0489011i
$153$	1.07007	−	3.29334i	0.0865102	−	0.266251i
$154$	6.70505			0.540308
$155$	−4.49206	−	3.28959i	−0.360811	−	0.264226i
$156$	−2.80098			−0.224258
$157$	−6.79203	+	20.9037i	−0.542063	+	1.66830i	0.185809	+	0.982586i	$0.440509\pi$
$157$	−6.79203	+	20.9037i	−0.542063	+	1.66830i	−0.727872	+	0.685713i	$0.759491\pi$
$158$	−6.89035	−	1.46459i	−0.548167	−	0.116516i
$159$	−4.70223	−	3.41637i	−0.372911	−	0.270936i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	3.90437	−	6.76256i	0.307707	−	0.532965i
$162$	−0.913545	+	0.406737i	−0.0717749	+	0.0319562i
$163$	3.94156	−	2.86371i	0.308727	−	0.224303i	−0.422623	−	0.906305i	$-0.638891\pi$
$163$	3.94156	−	2.86371i	0.308727	−	0.224303i	0.731350	+	0.682002i	$0.238891\pi$
$164$	−7.81284	−	3.47850i	−0.610080	−	0.271625i
$165$	4.11987	−	0.875706i	0.320732	−	0.0681736i
$166$	0.955908	−	9.09485i	0.0741928	−	0.705898i
$167$	0.793962	+	0.881784i	0.0614386	+	0.0682345i	0.773081	−	0.634308i	$-0.218715\pi$
$167$	0.793962	+	0.881784i	0.0614386	+	0.0682345i	−0.711642	+	0.702542i	$0.752048\pi$
$168$	1.06521	−	1.18303i	0.0821824	−	0.0912728i
$169$	0.538792	+	5.12627i	0.0414456	+	0.394328i
$170$	1.07007	+	3.29334i	0.0820708	+	0.252588i
$171$	0.896075	+	2.75783i	0.0685246	+	0.210897i
$172$	0.240896	+	2.29197i	0.0183681	+	0.174761i
$173$	−11.6639	+	12.9541i	−0.886793	+	0.984884i	−0.999962	−	0.00869219i	$-0.997233\pi$
$173$	−11.6639	+	12.9541i	−0.886793	+	0.984884i	0.113169	+	0.993576i	$0.463900\pi$
$174$	2.70627	+	3.00562i	0.205162	+	0.227855i
$175$	−0.166401	+	1.58320i	−0.0125788	+	0.119679i
$176$	4.11987	−	0.875706i	0.310547	−	0.0660088i
$177$	0.240231	+	0.106958i	0.0180568	+	0.00803942i
$178$	6.87490	−	4.99491i	0.515296	−	0.374384i
$179$	−1.68565	+	0.750502i	−0.125992	+	0.0560951i	−0.468764	−	0.883323i	$-0.655301\pi$
$179$	−1.68565	+	0.750502i	−0.125992	+	0.0560951i	0.342773	+	0.939418i	$0.388634\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−10.5573	−	18.2858i	−0.784718	−	1.35917i	−0.929168	−	0.369659i	$-0.879475\pi$
$181$	−10.5573	−	18.2858i	−0.784718	−	1.35917i	0.144450	−	0.989512i	$-0.453859\pi$
$182$	3.60737	+	2.62091i	0.267396	+	0.194274i
$183$	9.09780	+	1.93380i	0.672528	+	0.142950i
$184$	1.51580	−	4.66514i	0.111746	−	0.343919i
$185$	−6.96747			−0.512259
$186$	0.602840	−	5.53503i	0.0442024	−	0.405848i
$187$	−14.5851			−1.06657
$188$	1.95372	−	6.01295i	0.142490	−	0.438539i
$189$	1.55714	+	0.330980i	0.113265	+	0.0240752i
$190$	−2.34595	−	1.70444i	−0.170193	−	0.123653i
$191$	−3.40414	−	5.89614i	−0.246315	−	0.426630i	0.716186	−	0.697910i	$-0.245886\pi$
$191$	−3.40414	−	5.89614i	−0.246315	−	0.426630i	−0.962500	+	0.271280i	$0.912553\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	11.2583	−	5.01253i	0.810391	−	0.360810i	0.0406566	−	0.999173i	$-0.487055\pi$
$193$	11.2583	−	5.01253i	0.810391	−	0.360810i	0.769735	+	0.638364i	$0.220388\pi$
$194$	−5.55940	+	4.03914i	−0.399141	+	0.289993i
$195$	2.55882	+	1.13926i	0.183241	+	0.0815842i
$196$	4.36819	−	0.928487i	0.312013	−	0.0663205i
$197$	0.603648	−	5.74333i	0.0430081	−	0.409195i	−0.951745	−	0.306890i	$-0.900712\pi$
$197$	0.603648	−	5.74333i	0.0430081	−	0.409195i	0.994753	−	0.102305i	$-0.0326218\pi$
$198$	2.81832	+	3.13006i	0.200289	+	0.222444i
$199$	11.5924	−	12.8746i	0.821761	−	0.912658i	−0.175659	−	0.984451i	$-0.556206\pi$
$199$	11.5924	−	12.8746i	0.821761	−	0.912658i	0.997420	+	0.0717934i	$0.0228722\pi$
$200$	0.104528	+	0.994522i	0.00739128	+	0.0703233i
$201$	3.15515	+	9.71056i	0.222547	+	0.684930i
$202$	0.720445	+	2.21730i	0.0506903	+	0.156009i
$203$	−0.673004	−	6.40321i	−0.0472356	−	0.449417i
$204$	−2.31708	+	2.57338i	−0.162228	+	0.180173i
$205$	5.72255	+	6.35553i	0.399680	+	0.443890i
$206$	0.772444	−	7.34931i	0.0538187	−	0.512051i
$207$	4.79803	−	1.01985i	0.333486	−	0.0708846i
$208$	2.55882	+	1.13926i	0.177423	+	0.0789936i
$209$	9.88095	−	7.17893i	0.683480	−	0.496577i
$210$	−1.45430	+	0.647494i	−0.100356	+	0.0446813i
$211$	1.17699	−	2.03861i	0.0810276	−	0.140344i	−0.822664	−	0.568528i	$-0.807513\pi$
$211$	1.17699	−	2.03861i	0.0810276	−	0.140344i	0.903692	+	0.428184i	$0.140846\pi$
$212$	2.90614	+	5.03358i	0.199595	+	0.345708i
$213$	3.28534	+	2.38694i	0.225108	+	0.163550i
$214$	−5.69872	−	1.21130i	−0.389557	−	0.0828028i
$215$	0.712159	−	2.19180i	0.0485688	−	0.149480i
$216$	1.00000			0.0680414
$217$	−5.95558	+	6.56445i	−0.404291	+	0.445624i
$218$	−14.2147			−0.962743
$219$	1.86342	−	5.73502i	0.125918	−	0.387537i
$220$	−4.11987	−	0.875706i	−0.277762	−	0.0590401i
$221$	−7.84691	−	5.70111i	−0.527840	−	0.383498i
$222$	−3.48374	−	6.03401i	−0.233813	−	0.404976i
$223$	−9.70158	+	16.8036i	−0.649666	+	1.12525i	0.333537	+	0.942737i	$0.391758\pi$
$223$	−9.70158	+	16.8036i	−0.649666	+	1.12525i	−0.983203	+	0.182517i	$0.941576\pi$
$224$	−1.45430	+	0.647494i	−0.0971692	+	0.0432625i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	7.02808	+	3.12910i	0.467501	+	0.208145i
$227$	−12.3044	+	2.61539i	−0.816673	+	0.173589i	−0.597265	−	0.802044i	$-0.703746\pi$
$227$	−12.3044	+	2.61539i	−0.816673	+	0.173589i	−0.219408	+	0.975633i	$0.570413\pi$
$228$	0.303107	−	2.88387i	0.0200738	−	0.190989i
$229$	−8.31209	−	9.23151i	−0.549278	−	0.610035i	0.403025	−	0.915189i	$-0.367959\pi$
$229$	−8.31209	−	9.23151i	−0.549278	−	0.610035i	−0.952303	+	0.305154i	$0.901292\pi$
$230$	−3.28223	+	3.64529i	−0.216424	+	0.240363i
$231$	−0.700868	−	6.66831i	−0.0461137	−	0.438743i
$232$	−1.24981	−	3.84651i	−0.0820538	−	0.252536i
$233$	1.41357	+	4.35053i	0.0926063	+	0.285013i	0.986622	−	0.163022i	$-0.0521241\pi$
$233$	1.41357	+	4.35053i	0.0926063	+	0.285013i	−0.894016	+	0.448035i	$0.852124\pi$
$234$	0.292782	+	2.78564i	0.0191398	+	0.182103i
$235$	−4.23050	+	4.69845i	−0.275968	+	0.306493i
$236$	−0.175958	−	0.195421i	−0.0114539	−	0.0127208i
$237$	−0.736328	+	7.00569i	−0.0478297	+	0.455069i
$238$	5.39210	−	1.14613i	0.349518	−	0.0742923i
$239$	−6.99262	−	3.11331i	−0.452315	−	0.201384i	0.167919	−	0.985801i	$-0.446295\pi$
$239$	−6.99262	−	3.11331i	−0.452315	−	0.201384i	−0.620233	+	0.784417i	$0.712962\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	21.5471	−	9.59341i	1.38797	−	0.617966i	0.429479	−	0.903077i	$-0.358697\pi$
$241$	21.5471	−	9.59341i	1.38797	−	0.617966i	0.958494	+	0.285111i	$0.0920306\pi$
$242$	3.37010	−	5.83718i	0.216638	−	0.375228i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−7.52470	−	5.46702i	−0.481720	−	0.349990i
$245$	−4.36819	−	0.928487i	−0.279073	−	0.0593189i
$246$	−2.64278	+	8.13364i	−0.168497	+	0.518582i
$247$	8.12217			0.516801
$248$	−2.80202	+	4.81131i	−0.177929	+	0.305518i
$249$	−9.14495			−0.579538
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−23.5893	−	5.01406i	−1.48894	−	0.316485i	−0.609613	−	0.792699i	$-0.708675\pi$
$251$	−23.5893	−	5.01406i	−1.48894	−	0.316485i	−0.879329	+	0.476214i	$0.842009\pi$
$252$	−1.28789	−	0.935710i	−0.0811297	−	0.0589442i
$253$	−10.3302	−	17.8924i	−0.649452	−	1.12488i
$254$	2.58962	−	4.48536i	0.162488	−	0.281437i
$255$	3.16345	−	1.40846i	0.198103	−	0.0882011i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−11.0108	−	4.90231i	−0.686833	−	0.305798i	0.0334873	−	0.999439i	$-0.489339\pi$
$257$	−11.0108	−	4.90231i	−0.686833	−	0.305798i	−0.720321	+	0.693641i	$0.756005\pi$
$258$	2.25423	−	0.479152i	0.140342	−	0.0298307i
$259$	−1.15940	+	11.0309i	−0.0720415	+	0.685429i
$260$	−1.87422	−	2.08153i	−0.116234	−	0.129091i
$261$	2.70627	−	3.00562i	0.167514	−	0.186043i
$262$	−0.492052	−	4.68157i	−0.0303991	−	0.289228i
$263$	−3.92290	−	12.0734i	−0.241896	−	0.744480i	−0.996131	−	0.0878754i	$-0.971992\pi$
$263$	−3.92290	−	12.0734i	−0.241896	−	0.744480i	0.754235	−	0.656604i	$-0.228008\pi$
$264$	−1.30155	−	4.00577i	−0.0801050	−	0.246538i
$265$	−0.607549	−	5.78044i	−0.0373214	−	0.355090i
$266$	−3.08884	+	3.43050i	−0.189389	+	0.210338i
$267$	−5.68617	−	6.31513i	−0.347988	−	0.386480i
$268$	1.06727	−	10.1543i	0.0651936	−	0.620276i
$269$	24.9724	−	5.30804i	1.52259	−	0.323637i	0.630751	−	0.775985i	$-0.282747\pi$
$269$	24.9724	−	5.30804i	1.52259	−	0.323637i	0.891842	+	0.452348i	$0.149413\pi$
$270$	−0.913545	−	0.406737i	−0.0555966	−	0.0247532i
$271$	−17.3077	+	12.5748i	−1.05137	+	0.763865i	−0.972472	−	0.233018i	$-0.925140\pi$
$271$	−17.3077	+	12.5748i	−1.05137	+	0.763865i	−0.0788971	+	0.996883i	$0.525140\pi$
$272$	3.16345	−	1.40846i	0.191812	−	0.0854003i
$273$	2.22948	−	3.86157i	0.134934	−	0.233713i
$274$	−8.42879	−	14.5991i	−0.509202	−	0.881964i
$275$	3.40751	+	2.47570i	0.205480	+	0.149290i
$276$	−4.79803	−	1.01985i	−0.288807	−	0.0613879i
$277$	−6.64301	+	20.4451i	−0.399140	+	1.22843i	0.526550	+	0.850144i	$0.323485\pi$
$277$	−6.64301	+	20.4451i	−0.399140	+	1.22843i	−0.925690	+	0.378282i	$0.876515\pi$
$278$	14.7120			0.882368
$279$	−5.56772	−	0.0209689i	−0.333331	−	0.00125537i
$280$	1.59192			0.0951357
$281$	0.151645	−	0.466714i	0.00904636	−	0.0278418i	−0.946431	−	0.322905i	$-0.895341\pi$
$281$	0.151645	−	0.466714i	0.00904636	−	0.0278418i	0.955478	+	0.295063i	$0.0953406\pi$
$282$	−6.18423	−	1.31450i	−0.368265	−	0.0782772i
$283$	−17.4669	−	12.6904i	−1.03830	−	0.754368i	−0.0683462	−	0.997662i	$-0.521772\pi$
$283$	−17.4669	−	12.6904i	−1.03830	−	0.754368i	−0.969953	+	0.243293i	$0.921772\pi$
$284$	−2.03045	−	3.51685i	−0.120485	−	0.208686i
$285$	−1.44988	+	2.51127i	−0.0858835	+	0.148755i
$286$	10.7775	−	4.79847i	0.637289	−	0.283739i
$287$	11.0143	−	8.00239i	0.650156	−	0.472366i
$288$	−0.913545	−	0.406737i	−0.0538312	−	0.0239672i
$289$	4.89938	−	1.04139i	0.288199	−	0.0612585i
$290$	−0.422761	+	4.02230i	−0.0248254	+	0.236198i
$291$	4.59813	+	5.10674i	0.269547	+	0.299362i
$292$	−4.03496	+	4.48128i	−0.236128	+	0.262247i
$293$	1.35648	+	12.9060i	0.0792462	+	0.753977i	0.959924	+	0.280261i	$0.0904211\pi$
$293$	1.35648	+	12.9060i	0.0792462	+	0.753977i	−0.880678	+	0.473716i	$0.842912\pi$
$294$	−1.38000	−	4.24721i	−0.0804833	−	0.247702i
$295$	0.0812607	+	0.250095i	0.00473118	+	0.0145611i
$296$	0.728299	+	6.92931i	0.0423315	+	0.402758i
$297$	2.81832	−	3.13006i	0.163535	−	0.181625i
$298$	13.6238	+	15.1307i	0.789204	+	0.876499i
$299$	1.43616	−	13.6642i	0.0830553	−	0.790219i
$300$	0.978148	−	0.207912i	0.0564734	−	0.0120038i
$301$	−3.35156	−	1.49221i	−0.193181	−	0.0860096i
$302$	7.26534	−	5.27858i	0.418073	−	0.303748i
$303$	2.12985	−	0.948270i	0.122357	−	0.0544767i
$304$	−1.44988	+	2.51127i	−0.0831563	+	0.144031i
$305$	4.65052	+	8.05494i	0.266288	+	0.461225i
$306$	2.80149	+	2.03540i	0.160150	+	0.116356i
$307$	−21.4326	−	4.55565i	−1.22323	−	0.260005i	−0.449358	−	0.893352i	$-0.648347\pi$
$307$	−21.4326	−	4.55565i	−1.22323	−	0.260005i	−0.773868	+	0.633347i	$0.781680\pi$
$308$	−2.07197	+	6.37688i	−0.118062	+	0.363356i
$309$	−7.38980			−0.420391
$310$	4.51671	−	3.25566i	0.256532	−	0.184909i
$311$	−4.68169			−0.265474			−0.132737	−	0.991151i	$-0.542377\pi$
$311$	−4.68169			−0.265474			−0.132737	+	0.991151i	$0.542377\pi$
$312$	0.865551	−	2.66389i	0.0490022	−	0.150813i
$313$	−1.16436	−	0.247493i	−0.0658136	−	0.0139891i	0.174887	−	0.984588i	$-0.444044\pi$
$313$	−1.16436	−	0.247493i	−0.0658136	−	0.0139891i	−0.240701	+	0.970599i	$0.577377\pi$
$314$	−17.7818	−	12.9192i	−1.00348	−	0.729073i
$315$	0.795962	+	1.37865i	0.0448474	+	0.0776780i
$316$	3.52214	−	6.10053i	0.198136	−	0.343182i
$317$	25.9893	−	11.5712i	1.45971	−	0.649903i	0.485229	−	0.874387i	$-0.338736\pi$
$317$	25.9893	−	11.5712i	1.45971	−	0.649903i	0.974478	+	0.224484i	$0.0720696\pi$
$318$	4.70223	−	3.41637i	0.263688	−	0.191581i
$319$	−15.5622	−	6.92872i	−0.871314	−	0.387934i
$320$	0.978148	−	0.207912i	0.0546801	−	0.0116226i
$321$	−0.608987	+	5.79412i	−0.0339903	+	0.323396i
$322$	5.22506	+	5.80302i	0.291181	+	0.323390i
$323$	6.71898	−	7.46219i	0.373854	−	0.415207i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	0.865551	+	2.66389i	0.0480121	+	0.147766i
$326$	1.50554	+	4.63358i	0.0833842	+	0.256630i
$327$	1.48584	+	14.1369i	0.0821674	+	0.781771i
$328$	5.72255	−	6.35553i	0.315975	−	0.350926i
$329$	6.73464	+	7.47958i	0.371293	+	0.412362i
$330$	−0.440265	+	4.18884i	−0.0242358	+	0.230588i
$331$	−7.49203	+	1.59248i	−0.411799	+	0.0875306i	−0.409153	−	0.912466i	$-0.634176\pi$
$331$	−7.49203	+	1.59248i	−0.411799	+	0.0875306i	−0.00264629	+	0.999996i	$0.500842\pi$
$332$	8.35433	+	3.71959i	0.458503	+	0.204139i
$333$	−5.63681	+	4.09538i	−0.308895	+	0.224425i
$334$	−1.08397	+	0.482616i	−0.0593124	+	0.0264076i
$335$	−5.10514	+	8.84236i	−0.278924	+	0.483110i
$336$	0.795962	+	1.37865i	0.0434233	+	0.0752114i
$337$	−3.61886	−	2.62926i	−0.197132	−	0.143225i	0.484841	−	0.874603i	$-0.338878\pi$
$337$	−3.61886	−	2.62926i	−0.197132	−	0.143225i	−0.681973	+	0.731378i	$0.738878\pi$
$338$	−5.04186	−	1.07168i	−0.274241	−	0.0582918i
$339$	2.37733	−	7.31666i	0.129119	−	0.397386i
$340$	−3.46283			−0.187798
$341$	7.16269	+	22.3303i	0.387881	+	1.20925i
$342$	−2.89976			−0.156801
$343$	−5.64038	+	17.3593i	−0.304552	+	0.937314i
$344$	−2.25423	−	0.479152i	−0.121540	−	0.0258342i
$345$	3.96840	+	2.88321i	0.213652	+	0.155227i
$346$	−8.71574	−	15.0961i	−0.468561	−	0.811572i
$347$	−6.02220	+	10.4308i	−0.323288	+	0.559952i	−0.981164	−	0.193174i	$-0.938122\pi$
$347$	−6.02220	+	10.4308i	−0.323288	+	0.559952i	0.657876	+	0.753126i	$0.271455\pi$
$348$	−3.69480	+	1.64503i	−0.198062	+	0.0881829i
$349$	26.7642	−	19.4454i	1.43266	−	1.04089i	0.443142	−	0.896451i	$-0.353864\pi$
$349$	26.7642	−	19.4454i	1.43266	−	1.04089i	0.989514	−	0.144435i	$-0.0461363\pi$
$350$	−1.45430	−	0.647494i	−0.0777354	−	0.0346100i
$351$	2.73977	−	0.582357i	0.146238	−	0.0310839i
$352$	−0.440265	+	4.18884i	−0.0234662	+	0.223266i
$353$	−7.06112	−	7.84217i	−0.375825	−	0.417396i	0.525326	−	0.850901i	$-0.323943\pi$
$353$	−7.06112	−	7.84217i	−0.375825	−	0.417396i	−0.901151	+	0.433505i	$0.857277\pi$
$354$	−0.175958	+	0.195421i	−0.00935207	+	0.0103865i
$355$	0.424480	+	4.03866i	0.0225291	+	0.214350i
$356$	2.62598	+	8.08193i	0.139177	+	0.428341i
$357$	−1.70347	−	5.24276i	−0.0901574	−	0.277476i
$358$	−0.192874	−	1.83507i	−0.0101937	−	0.0969865i
$359$	2.00410	−	2.22578i	0.105772	−	0.117472i	−0.687934	−	0.725773i	$-0.741482\pi$
$359$	2.00410	−	2.22578i	0.105772	−	0.117472i	0.793706	+	0.608301i	$0.208149\pi$
$360$	0.669131	+	0.743145i	0.0352663	+	0.0391672i
$361$	1.10710	−	10.5334i	0.0582685	−	0.554388i
$362$	20.6532	−	4.38997i	1.08551	−	0.230732i
$363$	−6.15748	−	2.74148i	−0.323184	−	0.143891i
$364$	−3.60737	+	2.62091i	−0.189077	+	0.137373i
$365$	5.50882	−	2.45269i	0.288345	−	0.128379i
$366$	−4.65052	+	8.05494i	−0.243087	+	0.421039i
$367$	16.1872	+	28.0370i	0.844964	+	1.46352i	0.885652	+	0.464349i	$0.153712\pi$
$367$	16.1872	+	28.0370i	0.844964	+	1.46352i	−0.0406882	+	0.999172i	$0.512955\pi$
$368$	3.96840	+	2.88321i	0.206867	+	0.150298i
$369$	8.36533	+	1.77811i	0.435482	+	0.0925645i
$370$	2.15307	−	6.62646i	0.111933	−	0.344493i
$371$	−9.25271			−0.480377
$372$	5.07784	+	2.28375i	0.263274	+	0.118407i
$373$	14.2284			0.736718			0.368359	−	0.929684i	$-0.379920\pi$
$373$	14.2284			0.736718			0.368359	+	0.929684i	$0.379920\pi$
$374$	4.50705	−	13.8713i	0.233054	−	0.717266i
$375$	−0.978148	−	0.207912i	−0.0505113	−	0.0107365i
$376$	5.11492	+	3.71621i	0.263782	+	0.191649i
$377$	−5.66423	−	9.81073i	−0.291723	−	0.505278i
$378$	−0.795962	+	1.37865i	−0.0409399	+	0.0709100i
$379$	−15.9389	+	7.09647i	−0.818728	+	0.364521i	−0.772979	−	0.634432i	$-0.781234\pi$
$379$	−15.9389	+	7.09647i	−0.818728	+	0.364521i	−0.0457494	+	0.998953i	$0.514568\pi$
$380$	2.34595	−	1.70444i	0.120345	−	0.0874357i
$381$	−4.73148	−	2.10659i	−0.242401	−	0.107924i
$382$	6.65950	−	1.41552i	0.340729	−	0.0724243i
$383$	−3.77603	+	35.9265i	−0.192946	+	1.83576i	0.286371	+	0.958119i	$0.407551\pi$
$383$	−3.77603	+	35.9265i	−0.192946	+	1.83576i	−0.479317	+	0.877642i	$0.659116\pi$
$384$	0.669131	+	0.743145i	0.0341464	+	0.0379235i
$385$	4.48655	−	4.98282i	0.228656	−	0.253948i
$386$	1.28818	+	12.2563i	0.0655668	+	0.623827i
$387$	−0.712159	−	2.19180i	−0.0362011	−	0.111415i
$388$	−2.12350	−	6.53546i	−0.107804	−	0.331788i
$389$	1.73717	+	16.5281i	0.0880782	+	0.838008i	0.945987	+	0.324205i	$0.105097\pi$
$389$	1.73717	+	16.5281i	0.0880782	+	0.838008i	−0.857909	+	0.513802i	$0.828236\pi$
$390$	−1.87422	+	2.08153i	−0.0949049	+	0.105403i
$391$	−11.3658	−	12.6230i	−0.574793	−	0.638372i
$392$	−0.466801	+	4.44131i	−0.0235770	+	0.224320i
$393$	−4.60449	+	0.978714i	−0.232266	+	0.0493696i
$394$	5.27569	+	2.34889i	0.265785	+	0.118335i
$395$	−5.69895	+	4.14053i	−0.286745	+	0.208332i
$396$	−3.84777	+	1.71314i	−0.193358	+	0.0860885i
$397$	0.758925	−	1.31450i	0.0380893	−	0.0659727i	−0.846352	−	0.532623i	$-0.821206\pi$
$397$	0.758925	−	1.31450i	0.0380893	−	0.0659727i	0.884442	+	0.466651i	$0.154540\pi$
$398$	8.66226	+	15.0035i	0.434200	+	0.752056i
$399$	3.73458	+	2.71333i	0.186963	+	0.135837i
$400$	−0.978148	−	0.207912i	−0.0489074	−	0.0103956i
$401$	−9.95465	+	30.6373i	−0.497112	+	1.52995i	0.316529	+	0.948583i	$0.397483\pi$
$401$	−9.95465	+	30.6373i	−0.497112	+	1.52995i	−0.813640	+	0.581369i	$0.802517\pi$
$402$	−10.2103			−0.509243
$403$	−4.87501	+	14.8137i	−0.242841	+	0.737921i
$404$	−2.33141			−0.115992
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	6.29778	+	1.33863i	0.312554	+	0.0664353i
$407$	23.7417	+	17.2494i	1.17683	+	0.855020i
$408$	−1.73141	−	2.99890i	−0.0857177	−	0.148467i
$409$	−7.22751	+	12.5184i	−0.357377	+	0.618996i	−0.987522	−	0.157482i	$-0.949662\pi$
$409$	−7.22751	+	12.5184i	−0.357377	+	0.618996i	0.630145	+	0.776478i	$0.282996\pi$
$410$	−7.81284	+	3.47850i	−0.385849	+	0.171791i
$411$	−13.6381	+	9.90864i	−0.672716	+	0.488757i
$412$	6.75091	+	3.00570i	0.332594	+	0.148080i
$413$	0.409473	−	0.0870362i	0.0201488	−	0.00428277i
$414$	−0.512735	+	4.87835i	−0.0251995	+	0.239758i
$415$	−6.11917	−	6.79602i	−0.300378	−	0.333604i
$416$	−1.87422	+	2.08153i	−0.0918913	+	0.102056i
$417$	−1.53782	−	14.6314i	−0.0753076	−	0.716504i
$418$	3.77419	+	11.6158i	0.184602	+	0.568145i
$419$	9.32057	+	28.6858i	0.455340	+	1.40139i	0.870736	+	0.491751i	$0.163643\pi$
$419$	9.32057	+	28.6858i	0.455340	+	1.40139i	−0.415396	+	0.909641i	$0.636357\pi$
$420$	−0.166401	−	1.58320i	−0.00811956	−	0.0772524i
$421$	−13.4971	+	14.9901i	−0.657810	+	0.730572i	−0.976076	−	0.217429i	$-0.930233\pi$
$421$	−13.4971	+	14.9901i	−0.657810	+	0.730572i	0.318266	+	0.948001i	$0.396900\pi$
$422$	1.57512	+	1.74935i	0.0766759	+	0.0851572i
$423$	−0.660869	+	6.28775i	−0.0321326	+	0.305721i
$424$	−5.68527	+	1.20844i	−0.276101	+	0.0586871i
$425$	3.16345	+	1.40846i	0.153450	+	0.0683203i
$426$	−3.28534	+	2.38694i	−0.159175	+	0.115648i
$427$	13.5265	−	6.02237i	0.654592	−	0.291443i
$428$	2.91302	−	5.04550i	0.140806	−	0.243883i
$429$	−5.89874	−	10.2169i	−0.284794	−	0.493278i
$430$	1.86446	+	1.35461i	0.0899121	+	0.0653249i
$431$	19.9888	+	4.24875i	0.962826	+	0.204655i	0.662400	−	0.749150i	$-0.269538\pi$
$431$	19.9888	+	4.24875i	0.962826	+	0.204655i	0.300426	+	0.953805i	$0.402871\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	17.0916			0.821370			0.410685	−	0.911777i	$-0.365290\pi$
$433$	17.0916			0.821370			0.410685	+	0.911777i	$0.365290\pi$
$434$	−4.40279	−	7.69262i	−0.211341	−	0.369258i
$435$	4.04446			0.193917
$436$	4.39260	−	13.5190i	0.210367	−	0.647444i
$437$	13.9131	+	2.95733i	0.665555	+	0.141468i
$438$	4.87850	+	3.54444i	0.233104	+	0.169360i
$439$	9.68439	+	16.7739i	0.462211	+	0.800572i	0.999071	−	0.0430990i	$-0.0137231\pi$
$439$	9.68439	+	16.7739i	0.462211	+	0.800572i	−0.536860	+	0.843671i	$0.680390\pi$
$440$	2.10596	−	3.64762i	0.100397	−	0.173894i
$441$	−4.07969	+	1.81639i	−0.194271	+	0.0864950i
$442$	7.84691	−	5.70111i	0.373239	−	0.271174i
$443$	3.00907	+	1.33973i	0.142965	+	0.0636523i	0.476972	−	0.878918i	$-0.341734\pi$
$443$	3.00907	+	1.33973i	0.142965	+	0.0636523i	−0.334007	+	0.942571i	$0.608401\pi$
$444$	6.81522	−	1.44862i	0.323436	−	0.0687484i
$445$	0.888267	−	8.45129i	0.0421079	−	0.400630i
$446$	−12.9832	−	14.4194i	−0.614774	−	0.682776i
$447$	13.6238	−	15.1307i	0.644382	−	0.715659i
$448$	−0.166401	−	1.58320i	−0.00786173	−	0.0747994i
$449$	−4.44247	−	13.6725i	−0.209653	−	0.645246i	−0.999490	−	0.0319290i	$-0.989835\pi$
$449$	−4.44247	−	13.6725i	−0.209653	−	0.645246i	0.789837	−	0.613317i	$-0.210165\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	−3.76524	−	35.8238i	−0.177298	−	1.68688i
$452$	−5.14775	+	5.71715i	−0.242130	+	0.268912i
$453$	−6.00909	−	6.67378i	−0.282332	−	0.313561i
$454$	1.31490	−	12.5104i	0.0617111	−	0.587142i
$455$	4.36151	−	0.927068i	0.204471	−	0.0434616i
$456$	2.64906	+	1.17944i	0.124054	+	0.0552323i
$457$	9.10143	−	6.61258i	0.425747	−	0.309323i	−0.354199	−	0.935170i	$-0.615246\pi$
$457$	9.10143	−	6.61258i	0.425747	−	0.309323i	0.779946	+	0.625847i	$0.215246\pi$
$458$	11.3483	−	5.05257i	0.530269	−	0.236091i
$459$	1.73141	−	2.99890i	0.0808155	−	0.139976i
$460$	−2.45261	−	4.24804i	−0.114353	−	0.198066i
$461$	27.9224	+	20.2868i	1.30048	+	0.944851i	0.999960	−	0.00892589i	$-0.00284124\pi$
$461$	27.9224	+	20.2868i	1.30048	+	0.944851i	0.300516	+	0.953777i	$0.402841\pi$
$462$	6.55852	+	1.39406i	0.305130	+	0.0648574i
$463$	−3.82335	+	11.7671i	−0.177686	+	0.546862i	−0.999746	−	0.0225395i	$-0.992825\pi$
$463$	−3.82335	+	11.7671i	−0.177686	+	0.546862i	0.822060	+	0.569401i	$0.192825\pi$
$464$	4.04446			0.187759
$465$	−3.70995	−	4.15166i	−0.172045	−	0.192528i
$466$	−4.57442			−0.211906
$467$	6.24585	−	19.2228i	0.289024	−	0.889523i	−0.696140	−	0.717906i	$-0.745101\pi$
$467$	6.24585	−	19.2228i	0.289024	−	0.889523i	0.985164	−	0.171617i	$-0.0548992\pi$
$468$	−2.73977	−	0.582357i	−0.126646	−	0.0269195i
$469$	13.1498	+	9.55386i	0.607200	+	0.441156i
$470$	−3.16119	−	5.47535i	−0.145815	−	0.252559i
$471$	−10.9897	+	19.0348i	−0.506380	+	0.877076i
$472$	0.240231	−	0.106958i	0.0110575	−	0.00492312i
$473$	−7.85292	+	5.70548i	−0.361078	+	0.262338i
$474$	−6.43527	−	2.86517i	−0.295582	−	0.131602i
$475$	−2.83639	+	0.602894i	−0.130143	+	0.0276627i
$476$	−0.576219	+	5.48236i	−0.0264110	+	0.251284i
$477$	−3.88917	−	4.31937i	−0.178073	−	0.197770i
$478$	5.12177	−	5.68831i	0.234265	−	0.260177i
$479$	1.97082	+	18.7511i	0.0900490	+	0.856759i	0.942557	+	0.334045i	$0.108414\pi$
$479$	1.97082	+	18.7511i	0.0900490	+	0.856759i	−0.852508	+	0.522714i	$0.824920\pi$
$480$	−0.309017	−	0.951057i	−0.0141046	−	0.0434096i
$481$	6.03070	+	18.5606i	0.274976	+	0.846290i
$482$	2.46544	+	23.4571i	0.112298	+	1.06844i
$483$	5.22506	−	5.80302i	0.237749	−	0.264047i
$484$	4.51007	+	5.00894i	0.205003	+	0.227679i
$485$	−0.718298	+	6.83415i	−0.0326162	+	0.310323i
$486$	−0.978148	+	0.207912i	−0.0443697	+	0.00943107i
$487$	21.8113	+	9.71101i	0.988364	+	0.440048i	0.836270	−	0.548318i	$-0.184732\pi$
$487$	21.8113	+	9.71101i	0.988364	+	0.440048i	0.152094	+	0.988366i	$0.451398\pi$
$488$	7.52470	−	5.46702i	0.340627	−	0.247480i
$489$	4.45082	−	1.98163i	0.201273	−	0.0896126i
$490$	2.23289	−	3.86748i	0.100872	−	0.174715i
$491$	9.85268	+	17.0653i	0.444645	+	0.770148i	0.998027	−	0.0627793i	$-0.0199964\pi$
$491$	9.85268	+	17.0653i	0.444645	+	0.770148i	−0.553382	+	0.832927i	$0.686663\pi$
$492$	−6.91889	−	5.02687i	−0.311928	−	0.226629i
$493$	−13.6992	−	2.91186i	−0.616982	−	0.131144i
$494$	−2.50989	+	7.72464i	−0.112925	+	0.347548i
$495$	4.21191			0.189311
$496$	−3.70995	−	4.15166i	−0.166582	−	0.186415i
$497$	6.46465			0.289979
$498$	2.82595	−	8.69737i	0.126634	−	0.389738i
$499$	−16.2797	−	3.46036i	−0.728781	−	0.154907i	−0.171444	−	0.985194i	$-0.554843\pi$
$499$	−16.2797	−	3.46036i	−0.728781	−	0.154907i	−0.557336	+	0.830287i	$0.688177\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	0.593278	+	1.02759i	0.0265057	+	0.0459093i
$502$	12.0581	−	20.8853i	0.538181	−	0.932157i
$503$	19.6131	−	8.73233i	0.874507	−	0.389355i	0.0801324	−	0.996784i	$-0.474466\pi$
$503$	19.6131	−	8.73233i	0.874507	−	0.389355i	0.794374	+	0.607429i	$0.207799\pi$
$504$	1.28789	−	0.935710i	0.0573674	−	0.0416798i
$505$	2.12985	+	0.948270i	0.0947770	+	0.0421974i
$506$	20.2089	−	4.29553i	0.898394	−	0.190959i
$507$	−0.538792	+	5.12627i	−0.0239286	+	0.227665i
$508$	3.46559	+	3.84893i	0.153761	+	0.170769i
$509$	25.7068	−	28.5503i	1.13943	−	1.26547i	0.179958	−	0.983674i	$-0.442404\pi$
$509$	25.7068	−	28.5503i	1.13943	−	1.26547i	0.959475	−	0.281794i	$-0.0909295\pi$
$510$	0.361964	+	3.44386i	0.0160280	+	0.152497i
$511$	−2.96643	−	9.12972i	−0.131227	−	0.403875i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	0.303107	+	2.88387i	0.0133825	+	0.127326i
$514$	8.06489	−	8.95697i	0.355727	−	0.395075i
$515$	−4.94474	−	5.49169i	−0.217891	−	0.241993i
$516$	−0.240896	+	2.29197i	−0.0106048	+	0.100898i
$517$	26.0474	−	5.53655i	1.14556	−	0.243497i
$518$	−10.1328	−	4.51140i	−0.445208	−	0.198219i
$519$	−14.1024	+	10.2460i	−0.619025	+	0.449748i
$520$	2.55882	−	1.13926i	0.112212	−	0.0499599i
$521$	5.27269	−	9.13257i	0.231001	−	0.400105i	−0.727102	−	0.686529i	$-0.759133\pi$
$521$	5.27269	−	9.13257i	0.231001	−	0.400105i	0.958103	+	0.286424i	$0.0924667\pi$
$522$	2.02223	+	3.50261i	0.0885106	+	0.153305i
$523$	−28.8700	−	20.9753i	−1.26240	−	0.917186i	−0.263525	−	0.964653i	$-0.584885\pi$
$523$	−28.8700	−	20.9753i	−1.26240	−	0.917186i	−0.998873	+	0.0474670i	$0.984885\pi$
$524$	4.60449	+	0.978714i	0.201148	+	0.0427553i
$525$	−0.491932	+	1.51401i	−0.0214697	+	0.0660768i
$526$	12.6948			0.553518
$527$	9.57715	+	16.7333i	0.417187	+	0.728915i
$528$	4.21191			0.183300
$529$	0.327916	−	1.00922i	0.0142572	−	0.0438793i
$530$	5.68527	+	1.20844i	0.246952	+	0.0524913i
$531$	0.212743	+	0.154567i	0.00923227	+	0.00670764i
$532$	−2.30810	−	3.99774i	−0.100069	−	0.173324i
$533$	11.9773	−	20.7453i	0.518794	−	0.898578i
$534$	7.76317	−	3.45638i	0.335945	−	0.149572i
$535$	−4.71336	+	3.42446i	−0.203776	+	0.148052i
$536$	9.32756	+	4.15290i	0.402889	+	0.179378i
$537$	−1.80486	+	0.383634i	−0.0778853	+	0.0165550i
$538$	−2.66864	+	25.3904i	−0.115053	+	1.09466i
$539$	12.5860	+	13.9781i	0.542117	+	0.602081i
$540$	0.669131	−	0.743145i	0.0287948	−	0.0319799i
$541$	0.205434	+	1.95458i	0.00883230	+	0.0840338i	0.998050	−	0.0624183i	$-0.0198813\pi$
$541$	0.205434	+	1.95458i	0.00883230	+	0.0840338i	−0.989218	+	0.146452i	$0.953215\pi$
$542$	−6.61096	−	20.3465i	−0.283965	−	0.873955i
$543$	−6.52477	−	20.0812i	−0.280005	−	0.861766i
$544$	0.361964	+	3.44386i	0.0155191	+	0.147654i
$545$	−9.51152	+	10.5636i	−0.407429	+	0.452495i
$546$	2.98362	+	3.31365i	0.127687	+	0.141811i
$547$	−3.77615	+	35.9277i	−0.161457	+	1.53616i	0.551038	+	0.834480i	$0.314232\pi$
$547$	−3.77615	+	35.9277i	−0.161457	+	1.53616i	−0.712495	+	0.701677i	$0.752435\pi$
$548$	16.4892	−	3.50489i	0.704384	−	0.149721i
$549$	8.49693	+	3.78308i	0.362640	+	0.161458i
$550$	−3.40751	+	2.47570i	−0.145297	+	0.105564i
$551$	10.7140	−	4.77019i	0.456433	−	0.203217i
$552$	2.45261	−	4.24804i	0.104390	−	0.180809i
$553$	5.60698	+	9.71158i	0.238433	+	0.412979i
$554$	−17.3916	−	12.6358i	−0.738900	−	0.536842i
$555$	−6.81522	−	1.44862i	−0.289290	−	0.0614905i
$556$	−4.54626	+	13.9920i	−0.192805	+	0.593391i
$557$	−24.9255			−1.05613			−0.528064	−	0.849204i	$-0.677082\pi$
$557$	−24.9255			−1.05613			−0.528064	+	0.849204i	$0.677082\pi$
$558$	1.74046	−	5.28874i	0.0736797	−	0.223890i
$559$	−6.45513			−0.273023
$560$	−0.491932	+	1.51401i	−0.0207879	+	0.0639786i
$561$	−14.2664	−	3.03242i	−0.602328	−	0.128029i
$562$	0.397011	+	0.288445i	0.0167469	+	0.0121673i
$563$	−7.58000	−	13.1289i	−0.319459	−	0.553319i	0.660916	−	0.750460i	$-0.270168\pi$
$563$	−7.58000	−	13.1289i	−0.319459	−	0.553319i	−0.980375	+	0.197141i	$0.936834\pi$
$564$	3.16119	−	5.47535i	0.133110	−	0.230554i
$565$	7.02808	−	3.12910i	0.295673	−	0.131642i
$566$	17.4669	−	12.6904i	0.734188	−	0.533419i
$567$	1.45430	+	0.647494i	0.0610747	+	0.0271922i
$568$	3.97216	−	0.844309i	0.166668	−	0.0354264i
$569$	−4.08679	+	38.8832i	−0.171327	+	1.63007i	0.484242	+	0.874934i	$0.339095\pi$
$569$	−4.08679	+	38.8832i	−0.171327	+	1.63007i	−0.655569	+	0.755135i	$0.727571\pi$
$570$	−1.94032	−	2.15494i	−0.0812710	−	0.0902606i
$571$	0.425612	−	0.472690i	0.0178113	−	0.0197814i	−0.734173	−	0.678962i	$-0.762430\pi$
$571$	0.425612	−	0.472690i	0.0178113	−	0.0197814i	0.751985	+	0.659181i	$0.229097\pi$
$572$	1.23317	+	11.7329i	0.0515616	+	0.490575i
$573$	−2.10387	−	6.47505i	−0.0878905	−	0.270499i
$574$	4.20711	+	12.9481i	0.175601	+	0.540445i
$575$	0.512735	+	4.87835i	0.0213825	+	0.203441i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	1.73425	+	1.92608i	0.0721980	+	0.0801840i	0.778162	−	0.628064i	$-0.216152\pi$
$577$	1.73425	+	1.92608i	0.0721980	+	0.0801840i	−0.705964	+	0.708248i	$0.749486\pi$
$578$	−0.523566	+	4.98139i	−0.0217775	+	0.207199i
$579$	12.0545	−	2.56225i	0.500966	−	0.106484i
$580$	−3.69480	−	1.64503i	−0.153418	−	0.0683062i
$581$	−11.7777	+	8.55702i	−0.488623	+	0.355005i
$582$	−6.27769	+	2.79501i	−0.260219	+	0.115857i
$583$	−12.2404	+	21.2010i	−0.506946	+	0.878056i
$584$	−3.01508	−	5.22227i	−0.124765	−	0.216099i
$585$	2.26604	+	1.64638i	0.0936893	+	0.0680693i
$586$	−12.6935	−	2.69809i	−0.524365	−	0.111457i
$587$	−4.22682	+	13.0088i	−0.174460	+	0.536932i	−0.999608	−	0.0279840i	$-0.991091\pi$
$587$	−4.22682	+	13.0088i	−0.174460	+	0.536932i	0.825149	+	0.564916i	$0.191091\pi$
$588$	4.46578			0.184165
$589$	−14.7245	−	6.62234i	−0.606713	−	0.272869i
$590$	−0.262965			−0.0108261
$591$	1.78456	−	5.49232i	0.0734071	−	0.225924i
$592$	−6.81522	−	1.44862i	−0.280104	−	0.0595379i
$593$	11.0165	+	8.00393i	0.452392	+	0.328682i	0.790539	−	0.612411i	$-0.209800\pi$
$593$	11.0165	+	8.00393i	0.452392	+	0.328682i	−0.338148	+	0.941093i	$0.609800\pi$
$594$	2.10596	+	3.64762i	0.0864084	+	0.149664i
$595$	2.75628	−	4.77402i	0.112996	−	0.195716i
$596$	−18.6002	+	8.28132i	−0.761892	+	0.339216i
$597$	14.0158	−	10.1831i	0.573630	−	0.416766i
$598$	12.5516	+	5.58833i	0.513273	+	0.228524i
$599$	28.6194	−	6.08325i	1.16936	−	0.248555i	0.417999	−	0.908448i	$-0.362732\pi$
$599$	28.6194	−	6.08325i	1.16936	−	0.248555i	0.751360	+	0.659893i	$0.229398\pi$
$600$	−0.104528	+	0.994522i	−0.00426736	+	0.0406012i
$601$	10.0865	+	11.2022i	0.411438	+	0.456948i	0.912871	−	0.408249i	$-0.133860\pi$
$601$	10.0865	+	11.2022i	0.411438	+	0.456948i	−0.501433	+	0.865196i	$0.667194\pi$
$602$	2.45487	−	2.72641i	0.100053	−	0.111120i
$603$	1.06727	+	10.1543i	0.0434624	+	0.413517i
$604$	2.77511	+	8.54092i	0.112918	+	0.347525i
$605$	−2.08284	−	6.41031i	−0.0846793	−	0.260616i
$606$	0.243699	+	2.31864i	0.00989958	+	0.0941882i
$607$	−26.6761	+	29.6269i	−1.08275	+	1.20252i	−0.104624	+	0.994512i	$0.533364\pi$
$607$	−26.6761	+	29.6269i	−1.08275	+	1.20252i	−0.978128	+	0.208005i	$0.933303\pi$
$608$	−1.94032	−	2.15494i	−0.0786903	−	0.0873944i
$609$	0.673004	−	6.40321i	0.0272715	−	0.259471i
$610$	−9.09780	+	1.93380i	−0.368359	+	0.0782971i
$611$	16.1779	+	7.20285i	0.654487	+	0.291396i
$612$	−2.80149	+	2.03540i	−0.113243	+	0.0822761i
$613$	−2.96951	+	1.32211i	−0.119938	+	0.0533997i	−0.465828	−	0.884875i	$-0.654244\pi$
$613$	−2.96951	+	1.32211i	−0.119938	+	0.0533997i	0.345891	+	0.938275i	$0.387577\pi$
$614$	10.9557	−	18.9759i	0.442137	−	0.765804i
$615$	4.27611	+	7.40644i	0.172429	+	0.298656i
$616$	−5.42450	−	3.94113i	−0.218559	−	0.158793i
$617$	−37.6949	−	8.01231i	−1.51754	−	0.322563i	−0.627563	−	0.778566i	$-0.715947\pi$
$617$	−37.6949	−	8.01231i	−1.51754	−	0.322563i	−0.889978	+	0.456003i	$0.849281\pi$
$618$	2.28357	−	7.02811i	0.0918588	−	0.282712i
$619$	5.60419			0.225251			0.112626	−	0.993637i	$-0.464074\pi$
$619$	5.60419			0.225251			0.112626	+	0.993637i	$0.464074\pi$
$620$	1.70058	+	5.30170i	0.0682969	+	0.212921i
$621$	4.90522			0.196840
$622$	1.44672	−	4.45256i	0.0580083	−	0.178531i
$623$	−13.2323	−	2.81261i	−0.530141	−	0.112685i
$624$	2.26604	+	1.64638i	0.0907143	+	0.0659078i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.595187	−	1.03089i	0.0237885	−	0.0412028i
$627$	11.1576	−	4.96769i	0.445592	−	0.198390i
$628$	17.7818	−	12.9192i	0.709570	−	0.515533i
$629$	22.0413	+	9.81340i	0.878842	+	0.391286i
$630$	−1.55714	+	0.330980i	−0.0620378	+	0.0131865i
$631$	4.61339	−	43.8935i	0.183656	−	1.74737i	−0.383300	−	0.923624i	$-0.625213\pi$
$631$	4.61339	−	43.8935i	0.183656	−	1.74737i	0.566957	−	0.823748i	$-0.308121\pi$
$632$	4.71355	+	5.23492i	0.187495	+	0.208234i
$633$	1.57512	−	1.74935i	0.0626056	−	0.0695305i
$634$	2.97372	+	28.2930i	0.118101	+	1.12366i
$635$	−1.60048	−	4.92576i	−0.0635130	−	0.195473i
$636$	1.79609	+	5.52781i	0.0712197	+	0.219192i
$637$	1.30750	+	12.4400i	0.0518050	+	0.492892i
$638$	11.3986	−	12.6594i	0.451274	−	0.501191i
$639$	2.71728	+	3.01784i	0.107494	+	0.119384i
$640$	−0.104528	+	0.994522i	−0.00413185	+	0.0393119i
$641$	−9.12663	+	1.93992i	−0.360480	+	0.0766224i	−0.384592	−	0.923087i	$-0.625658\pi$
$641$	−9.12663	+	1.93992i	−0.360480	+	0.0766224i	0.0241114	+	0.999709i	$0.492324\pi$
$642$	−5.32235	−	2.36966i	−0.210056	−	0.0935231i
$643$	−4.68516	+	3.40397i	−0.184765	+	0.134240i	−0.676323	−	0.736605i	$-0.736428\pi$
$643$	−4.68516	+	3.40397i	−0.184765	+	0.134240i	0.491558	+	0.870845i	$0.336428\pi$
$644$	−7.13364	+	3.17610i	−0.281105	+	0.125156i
$645$	1.15230	−	1.99584i	0.0453717	−	0.0785860i
$646$	5.02068	+	8.69608i	0.197536	+	0.342143i
$647$	−38.0142	−	27.6189i	−1.49449	−	1.08581i	−0.972512	−	0.232853i	$-0.925194\pi$
$647$	−38.0142	−	27.6189i	−1.49449	−	1.08581i	−0.521979	−	0.852958i	$-0.674806\pi$
$648$	0.978148	+	0.207912i	0.0384253	+	0.00816754i
$649$	0.342263	−	1.05338i	0.0134350	−	0.0413487i
$650$	−2.80098			−0.109864
$651$	−7.19026	+	5.18277i	−0.281809	+	0.203129i
$652$	−4.87203			−0.190804
$653$	5.98513	−	18.4203i	0.234216	−	0.720844i	−0.763008	−	0.646389i	$-0.776278\pi$
$653$	5.98513	−	18.4203i	0.234216	−	0.720844i	0.997224	−	0.0744547i	$-0.0237216\pi$
$654$	−13.9041	−	2.95541i	−0.543694	−	0.115566i
$655$	−3.80833	−	2.76691i	−0.148804	−	0.108112i
$656$	4.27611	+	7.40644i	0.166954	+	0.289173i
$657$	3.01508	−	5.22227i	0.117629	−	0.203740i
$658$	−9.19462	+	4.09371i	−0.358444	+	0.159589i
$659$	−1.71661	+	1.24719i	−0.0668698	+	0.0485838i	−0.620718	−	0.784034i	$-0.713159\pi$
$659$	−1.71661	+	1.24719i	−0.0668698	+	0.0485838i	0.553848	+	0.832618i	$0.313159\pi$
$660$	−3.84777	−	1.71314i	−0.149774	−	0.0666838i
$661$	18.0323	−	3.83289i	0.701376	−	0.149082i	0.156598	−	0.987662i	$-0.449947\pi$
$661$	18.0323	−	3.83289i	0.701376	−	0.149082i	0.544778	+	0.838580i	$0.316614\pi$
$662$	0.800626	−	7.61744i	0.0311172	−	0.296060i
$663$	−6.49011	−	7.20799i	−0.252055	−	0.279935i
$664$	−6.11917	+	6.79602i	−0.237470	+	0.263737i
$665$	0.482524	+	4.59091i	0.0187115	+	0.178028i
$666$	−2.15307	−	6.62646i	−0.0834297	−	0.256770i
$667$	−6.13058	−	18.8680i	−0.237377	−	0.730571i
$668$	−0.124029	−	1.18006i	−0.00479883	−	0.0456578i
$669$	−12.9832	+	14.4194i	−0.501961	+	0.557484i
$670$	−6.83201	−	7.58772i	−0.263944	−	0.293139i
$671$	4.09492	−	38.9606i	0.158083	−	1.50406i
$672$	−1.55714	+	0.330980i	−0.0600679	+	0.0127678i
$673$	−3.91126	−	1.74140i	−0.150768	−	0.0671262i	0.329966	−	0.943993i	$-0.392963\pi$
$673$	−3.91126	−	1.74140i	−0.150768	−	0.0671262i	−0.480733	+	0.876867i	$0.659630\pi$
$674$	3.61886	−	2.62926i	0.139393	−	0.101275i
$675$	−0.913545	+	0.406737i	−0.0351624	+	0.0156553i
$676$	2.57725	−	4.46393i	0.0991250	−	0.171690i
$677$	−18.2551	−	31.6187i	−0.701600	−	1.21521i	−0.967905	−	0.251318i	$-0.919136\pi$
$677$	−18.2551	−	31.6187i	−0.701600	−	1.21521i	0.266305	−	0.963889i	$-0.414197\pi$
$678$	6.22392	+	4.52194i	0.239028	+	0.173664i
$679$	10.7003	+	2.27442i	0.410641	+	0.0872844i
$680$	1.07007	−	3.29334i	0.0410354	−	0.126294i
$681$	−12.5793			−0.482040
$682$	−23.4508	−	0.0883191i	−0.897976	−	0.00338191i
$683$	−31.8813			−1.21990			−0.609952	−	0.792438i	$-0.708811\pi$
$683$	−31.8813			−1.21990			−0.609952	+	0.792438i	$0.708811\pi$
$684$	0.896075	−	2.75783i	0.0342623	−	0.105448i
$685$	−16.4892	−	3.50489i	−0.630020	−	0.133915i
$686$	−14.7667	−	10.7286i	−0.563795	−	0.409621i
$687$	−6.21111	−	10.7580i	−0.236969	−	0.410442i
$688$	1.15230	−	1.99584i	0.0439309	−	0.0760906i
$689$	−14.8726	+	6.62171i	−0.566601	+	0.252267i
$690$	−3.96840	+	2.88321i	−0.151075	+	0.109762i
$691$	−38.1023	−	16.9642i	−1.44948	−	0.645349i	−0.477119	−	0.878839i	$-0.658319\pi$
$691$	−38.1023	−	16.9642i	−1.44948	−	0.645349i	−0.972359	+	0.233489i	$0.924986\pi$
$692$	17.0506	−	3.62421i	0.648165	−	0.137772i
$693$	0.700868	−	6.66831i	0.0266238	−	0.253308i
$694$	−8.05927	−	8.95073i	−0.305926	−	0.339765i
$695$	9.84426	−	10.9332i	0.373414	−	0.414718i
$696$	−0.422761	−	4.02230i	−0.0160247	−	0.152465i
$697$	−9.15149	−	28.1654i	−0.346637	−	1.06684i
$698$	10.2230	+	31.4632i	0.386947	+	1.19090i
$699$	0.478157	+	4.54936i	0.0180856	+	0.172073i
$700$	1.06521	−	1.18303i	0.0402610	−	0.0447144i
$701$	19.7696	+	21.9563i	0.746687	+	0.829280i	0.990059	−	0.140653i	$-0.0449203\pi$
$701$	19.7696	+	21.9563i	0.746687	+	0.829280i	−0.243372	+	0.969933i	$0.578254\pi$
$702$	−0.292782	+	2.78564i	−0.0110504	+	0.105137i
$703$	−19.7625	+	4.20065i	−0.745357	+	0.158430i
$704$	−3.84777	−	1.71314i	−0.145018	−	0.0645663i
$705$	−5.11492	+	3.71621i	−0.192639	+	0.139960i
$706$	9.64035	−	4.29216i	0.362819	−	0.161538i
$707$	1.85571	−	3.21419i	0.0697913	−	0.120882i
$708$	−0.131483	−	0.227735i	−0.00494142	−	0.00855879i
$709$	32.8801	+	23.8888i	1.23484	+	0.897163i	0.997243	−	0.0742018i	$-0.0236409\pi$
$709$	32.8801	+	23.8888i	1.23484	+	0.897163i	0.237595	+	0.971364i	$0.423641\pi$
$710$	−3.97216	−	0.844309i	−0.149073	−	0.0316864i
$711$	−2.17680	+	6.69951i	−0.0816365	+	0.251251i
$712$	−8.49784			−0.318470
$713$	−13.7445	+	23.6005i	−0.514737	+	0.883846i
$714$	5.51256			0.206302
$715$	3.64562	−	11.2201i	0.136339	−	0.419607i
$716$	1.80486	+	0.383634i	0.0674507	+	0.0143371i
$717$	−6.19252	−	4.49913i	−0.231264	−	0.168023i
$718$	1.49754	+	2.59381i	0.0558877	+	0.0968003i
$719$	13.2359	−	22.9252i	0.493615	−	0.854966i	−0.506358	−	0.862323i	$-0.669009\pi$
$719$	13.2359	−	22.9252i	0.493615	−	0.854966i	0.999973	+	0.00735709i	$0.00234185\pi$
$720$	−0.913545	+	0.406737i	−0.0340458	+	0.0151582i
$721$	−9.51727	+	6.91470i	−0.354442	+	0.257517i
$722$	9.67572	+	4.30791i	0.360093	+	0.160324i
$723$	23.0709	−	4.90386i	0.858015	−	0.182377i
$724$	−2.20708	+	20.9989i	−0.0820253	+	0.780419i
$725$	2.70627	+	3.00562i	0.100508	+	0.111626i
$726$	4.51007	−	5.00894i	0.167384	−	0.185899i
$727$	1.55126	+	14.7593i	0.0575331	+	0.547391i	0.984886	+	0.173203i	$0.0554118\pi$
$727$	1.55126	+	14.7593i	0.0575331	+	0.547391i	−0.927353	+	0.374188i	$0.877922\pi$
$728$	−1.37789	−	4.24071i	−0.0510681	−	0.157171i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.630323	+	5.99712i	0.0233293	+	0.221963i
$731$	−5.33994	+	5.93060i	−0.197505	+	0.219351i
$732$	−6.22361	−	6.91202i	−0.230031	−	0.255476i
$733$	4.20503	−	40.0082i	0.155316	−	1.47774i	−0.588034	−	0.808836i	$-0.700098\pi$
$733$	4.20503	−	40.0082i	0.155316	−	1.47774i	0.743351	−	0.668902i	$-0.233235\pi$
$734$	−31.6669	+	6.73101i	−1.16885	+	0.248446i
$735$	−4.07969	−	1.81639i	−0.150482	−	0.0669987i
$736$	−3.96840	+	2.88321i	−0.146277	+	0.106277i
$737$	39.2868	−	17.4916i	1.44715	−	0.644312i
$738$	−4.27611	+	7.40644i	−0.157406	+	0.272635i
$739$	−15.3011	−	26.5024i	−0.562862	−	0.974905i	−0.997245	−	0.0741772i	$-0.976367\pi$
$739$	−15.3011	−	26.5024i	−0.562862	−	0.974905i	0.434383	−	0.900728i	$-0.356966\pi$
$740$	5.63681	+	4.09538i	0.207213	+	0.150549i
$741$	7.94468	+	1.68869i	0.291855	+	0.0620357i
$742$	2.85925	−	8.79985i	0.104966	−	0.323053i
$743$	−13.9154			−0.510505			−0.255253	−	0.966874i	$-0.582159\pi$
$743$	−13.9154			−0.510505			−0.255253	+	0.966874i	$0.582159\pi$
$744$	−3.74112	+	4.12360i	−0.137156	+	0.151178i
$745$	20.3604			0.745947
$746$	−4.39681	+	13.5320i	−0.160979	+	0.495442i
$747$	−8.94511	−	1.90134i	−0.327285	−	0.0695665i
$748$	11.7996	+	8.57292i	0.431436	+	0.313457i
$749$	4.63731	+	8.03205i	0.169443	+	0.293485i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−9.61452	+	4.28066i	−0.350839	+	0.156203i	−0.574587	−	0.818443i	$-0.694837\pi$
$751$	−9.61452	+	4.28066i	−0.350839	+	0.156203i	0.223748	+	0.974647i	$0.428171\pi$
$752$	−5.11492	+	3.71621i	−0.186522	+	0.135516i
$753$	−22.0313	−	9.80898i	−0.802866	−	0.357459i
$754$	11.0809	−	2.35532i	0.403543	−	0.0857757i
$755$	0.938713	−	8.93125i	0.0341633	−	0.325042i
$756$	−1.06521	−	1.18303i	−0.0387411	−	0.0430264i
$757$	3.28326	−	3.64643i	0.119332	−	0.132532i	−0.680518	−	0.732731i	$-0.738245\pi$
$757$	3.28326	−	3.64643i	0.119332	−	0.132532i	0.799851	+	0.600199i	$0.204912\pi$
$758$	−1.82374	−	17.3518i	−0.0662414	−	0.630245i
$759$	−6.38440	−	19.6492i	−0.231739	−	0.713219i
$760$	0.896075	+	2.75783i	0.0325041	+	0.100037i
$761$	4.50417	+	42.8543i	0.163276	+	1.55347i	0.702732	+	0.711455i	$0.251963\pi$
$761$	4.50417	+	42.8543i	0.163276	+	1.55347i	−0.539456	+	0.842014i	$0.681370\pi$
$762$	3.46559	−	3.84893i	0.125545	−	0.139432i
$763$	15.1416	+	16.8165i	0.548163	+	0.608797i
$764$	−0.711658	+	6.77098i	−0.0257469	+	0.244965i
$765$	3.38716	−	0.719962i	0.122463	−	0.0260303i
$766$	−33.0013	−	14.6931i	−1.19239	−	0.530884i
$767$	0.595890	−	0.432939i	0.0215163	−	0.0156325i
$768$	−0.913545	+	0.406737i	−0.0329647	+	0.0146768i
$769$	−8.94433	+	15.4920i	−0.322541	+	0.558657i	−0.981012	−	0.193949i	$-0.937870\pi$
$769$	−8.94433	+	15.4920i	−0.322541	+	0.558657i	0.658471	+	0.752606i	$0.271204\pi$
$770$	3.35252	+	5.80674i	0.120817	+	0.209260i
$771$	−9.75092	−	7.08445i	−0.351171	−	0.255140i
$772$	−12.0545	−	2.56225i	−0.433850	−	0.0922176i
$773$	−5.66793	+	17.4441i	−0.203861	+	0.627421i	0.795897	+	0.605432i	$0.207000\pi$
$773$	−5.66793	+	17.4441i	−0.203861	+	0.627421i	−0.999758	+	0.0219884i	$0.993000\pi$
$774$	2.30459			0.0828370
$775$	0.602840	−	5.53503i	0.0216546	−	0.198824i
$776$	6.87179			0.246683
$777$	−3.42752	+	10.5488i	−0.122962	+	0.378437i
$778$	−16.2560	−	3.45531i	−0.582805	−	0.123879i
$779$	20.0631	+	14.5767i	0.718835	+	0.522265i
$780$	−1.40049	−	2.42572i	−0.0501456	−	0.0868548i
$781$	8.55208	−	14.8126i	0.306018	−	0.530038i
$782$	15.5174	−	6.90880i	0.554901	−	0.247058i
$783$	3.27204	−	2.37727i	0.116933	−	0.0849568i
$784$	−4.07969	−	1.81639i	−0.145703	−	0.0648712i
$785$	−21.4992	+	4.56979i	−0.767338	+	0.163103i
$786$	0.492052	−	4.68157i	0.0175509	−	0.166986i
$787$	17.2120	+	19.1158i	0.613541	+	0.681406i	0.967214	−	0.253963i	$-0.0817341\pi$
$787$	17.2120	+	19.1158i	0.613541	+	0.681406i	−0.353673	+	0.935369i	$0.615067\pi$
$788$	−3.86420	+	4.29163i	−0.137657	+	0.152883i
$789$	−1.32696	−	12.6252i	−0.0472411	−	0.449469i
$790$	−2.17680	−	6.69951i	−0.0774472	−	0.238358i
$791$	−3.78452	−	11.6476i	−0.134562	−	0.414140i
$792$	−0.440265	−	4.18884i	−0.0156441	−	0.148844i
$793$	17.4322	−	19.3605i	0.619037	−	0.687510i
$794$	1.01564	+	1.12798i	0.0360437	+	0.0400306i
$795$	0.607549	−	5.78044i	0.0215475	−	0.205011i
$796$	−16.9459	+	3.60197i	−0.600633	+	0.127668i
$797$	−23.7748	−	10.5852i	−0.842148	−	0.374948i	−0.0601196	−	0.998191i	$-0.519148\pi$
$797$	−23.7748	−	10.5852i	−0.842148	−	0.374948i	−0.782028	+	0.623243i	$0.785815\pi$
$798$	−3.73458	+	2.71333i	−0.132203	+	0.0960510i
$799$	20.0006	−	8.90482i	0.707569	−	0.315030i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−4.24892	−	7.35935i	−0.150128	−	0.260030i
$802$	−26.0616	−	18.9349i	−0.920268	−	0.668614i
$803$	−24.8435	−	5.28064i	−0.876707	−	0.186350i
$804$	3.15515	−	9.71056i	0.111274	−	0.342465i
$805$	7.80874			0.275222
$806$	−12.5822	−	9.21408i	−0.443188	−	0.324552i
$807$	25.5303			0.898708
$808$	0.720445	−	2.21730i	0.0253452	−	0.0780044i
$809$	2.65919	+	0.565228i	0.0934921	+	0.0198724i	0.254420	−	0.967094i	$-0.418115\pi$
$809$	2.65919	+	0.565228i	0.0934921	+	0.0198724i	−0.160928	+	0.986966i	$0.551449\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	−22.6676	−	39.2614i	−0.795966	−	1.37865i	−0.922224	−	0.386656i	$-0.873630\pi$
$811$	−22.6676	−	39.2614i	−0.795966	−	1.37865i	0.126258	−	0.991997i	$-0.459703\pi$
$812$	−3.21924	+	5.57588i	−0.112973	+	0.195675i
$813$	−19.5440	+	8.70153i	−0.685437	+	0.305176i
$814$	−23.7417	+	17.2494i	−0.832147	+	0.604590i
$815$	4.45082	+	1.98163i	0.155906	+	0.0694136i
$816$	3.38716	−	0.719962i	0.118574	−	0.0252037i
$817$	0.698540	−	6.64616i	0.0244388	−	0.232520i
$818$	−9.67229	−	10.7422i	−0.338184	−	0.375591i
$819$	2.98362	−	3.31365i	0.104256	−	0.115788i
$820$	−0.893950	−	8.50537i	−0.0312181	−	0.297020i
$821$	−10.5656	−	32.5175i	−0.368741	−	1.13487i	−0.947605	−	0.319444i	$-0.896504\pi$
$821$	−10.5656	−	32.5175i	−0.368741	−	1.13487i	0.578864	−	0.815424i	$-0.303496\pi$
$822$	−5.20928	−	16.0325i	−0.181694	−	0.559198i
$823$	1.93323	+	18.3934i	0.0673880	+	0.641154i	0.975131	+	0.221628i	$0.0711371\pi$
$823$	1.93323	+	18.3934i	0.0673880	+	0.641154i	−0.907743	+	0.419526i	$0.862196\pi$
$824$	−4.94474	+	5.49169i	−0.172258	+	0.191312i
$825$	2.81832	+	3.13006i	0.0981213	+	0.108975i
$826$	−0.0437578	+	0.416328i	−0.00152253	+	0.0144859i
$827$	22.8431	−	4.85546i	0.794334	−	0.168841i	0.207166	−	0.978306i	$-0.433576\pi$
$827$	22.8431	−	4.85546i	0.794334	−	0.168841i	0.587168	+	0.809465i	$0.300243\pi$
$828$	−4.48114	−	1.99513i	−0.155730	−	0.0693356i
$829$	9.91442	−	7.20325i	0.344342	−	0.250179i	−0.402150	−	0.915574i	$-0.631737\pi$
$829$	9.91442	−	7.20325i	0.344342	−	0.250179i	0.746492	+	0.665395i	$0.231737\pi$
$830$	8.35433	−	3.71959i	0.289983	−	0.129109i
$831$	−10.7486	+	18.6172i	−0.372866	+	0.645822i
$832$	−1.40049	−	2.42572i	−0.0485533	−	0.0840968i
$833$	12.5108	+	9.08963i	0.433474	+	0.314937i
$834$	14.3905	+	3.05880i	0.498303	+	0.105918i
$835$	−0.366666	+	1.12848i	−0.0126890	+	0.0390528i
$836$	−12.2135			−0.422414
$837$	−5.44170	−	1.17811i	−0.188093	−	0.0407213i
$838$	−30.1620			−1.04193
$839$	−2.17357	+	6.68958i	−0.0750401	+	0.230950i	−0.981540	−	0.191256i	$-0.938744\pi$
$839$	−2.17357	+	6.68958i	−0.0750401	+	0.230950i	0.906500	+	0.422206i	$0.138744\pi$
$840$	1.55714	+	0.330980i	0.0537263	+	0.0114199i
$841$	10.2279	+	7.43098i	0.352685	+	0.256241i
$842$	−10.0856	−	17.4687i	−0.347572	−	0.602012i
$843$	0.245366	−	0.424987i	0.00845086	−	0.0146373i
$844$	−2.15047	+	0.957453i	−0.0740224	+	0.0329569i
$845$	−4.17008	+	3.02974i	−0.143455	+	0.104226i
$846$	−5.77579	−	2.57155i	−0.198576	−	0.0884116i
$847$	−10.4954	+	2.23087i	−0.360627	+	0.0766535i
$848$	0.607549	−	5.78044i	0.0208633	−	0.198501i
$849$	−14.4467	−	16.0447i	−0.495810	−	0.550652i
$850$	−2.31708	+	2.57338i	−0.0794753	+	0.0882663i
$851$	3.57247	+	33.9898i	0.122463	+	1.16515i
$852$	−1.25489	−	3.86215i	−0.0429918	−	0.132315i
$853$	6.40265	+	19.7053i	0.219223	+	0.674698i	0.998827	+	0.0484251i	$0.0154202\pi$
$853$	6.40265	+	19.7053i	0.219223	+	0.674698i	−0.779604	+	0.626272i	$0.784580\pi$
$854$	1.54771	+	14.7255i	0.0529615	+	0.503895i
$855$	−1.94032	+	2.15494i	−0.0663575	+	0.0736974i
$856$	3.89838	+	4.32959i	0.133244	+	0.147982i
$857$	5.23292	−	49.7879i	0.178753	−	1.70072i	−0.426336	−	0.904565i	$-0.640196\pi$
$857$	5.23292	−	49.7879i	0.178753	−	1.70072i	0.605089	−	0.796158i	$-0.293137\pi$
$858$	11.5397	−	2.45284i	0.393958	−	0.0837384i
$859$	−32.3855	−	14.4189i	−1.10498	−	0.491968i	−0.228565	−	0.973529i	$-0.573403\pi$
$859$	−32.3855	−	14.4189i	−1.10498	−	0.491968i	−0.876413	+	0.481561i	$0.840070\pi$
$860$	−1.86446	+	1.35461i	−0.0635774	+	0.0461917i
$861$	12.4374	−	5.53751i	0.423867	−	0.188718i
$862$	−10.2177	+	17.6975i	−0.348015	+	0.602780i
$863$	−4.72755	−	8.18836i	−0.160928	−	0.278735i	0.774274	−	0.632851i	$-0.218115\pi$
$863$	−4.72755	−	8.18836i	−0.160928	−	0.278735i	−0.935202	+	0.354116i	$0.884782\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−17.0506	−	3.62421i	−0.579737	−	0.123227i
$866$	−5.28160	+	16.2551i	−0.179476	+	0.552370i
$867$	5.00883			0.170109
$868$	8.67665	−	1.81015i	0.294505	−	0.0614406i
$869$	29.6699			1.00648
$870$	−1.24981	+	3.84651i	−0.0423724	+	0.130409i
$871$	27.9739	+	5.94603i	0.947858	+	0.201473i
$872$	11.5000	+	8.35521i	0.389438	+	0.282943i
$873$	3.43590	+	5.95115i	0.116287	+	0.201416i
$874$	−7.11198	+	12.3183i	−0.240566	+	0.416673i
$875$	−1.45430	+	0.647494i	−0.0491642	+	0.0218893i
$876$	−4.87850	+	3.54444i	−0.164829	+	0.119755i
$877$	15.2511	+	6.79021i	0.514991	+	0.229289i	0.647741	−	0.761861i	$-0.275714\pi$
$877$	15.2511	+	6.79021i	0.514991	+	0.229289i	−0.132749	+	0.991150i	$0.542381\pi$
$878$	−18.9455	+	4.02699i	−0.639380	+	0.135904i
$879$	−1.35648	+	12.9060i	−0.0457528	+	0.435309i
$880$	2.81832	+	3.13006i	0.0950055	+	0.105514i
$881$	31.5995	−	35.0948i	1.06461	−	1.18237i	0.0820159	−	0.996631i	$-0.473864\pi$
$881$	31.5995	−	35.0948i	1.06461	−	1.18237i	0.982598	−	0.185743i	$-0.0594692\pi$
$882$	−0.466801	−	4.44131i	−0.0157180	−	0.149547i
$883$	−10.3597	−	31.8839i	−0.348632	−	1.07298i	−0.959610	−	0.281332i	$-0.909224\pi$
$883$	−10.3597	−	31.8839i	−0.348632	−	1.07298i	0.610978	−	0.791647i	$-0.290776\pi$
$884$	2.99725	+	9.22460i	0.100809	+	0.310257i
$885$	0.0274873	+	0.261525i	0.000923977	+	0.00879105i
$886$	−2.20401	+	2.44780i	−0.0740451	+	0.0822355i
$887$	17.6871	+	19.6435i	0.593875	+	0.659566i	0.962901	−	0.269854i	$-0.0869753\pi$
$887$	17.6871	+	19.6435i	0.593875	+	0.659566i	−0.369026	+	0.929419i	$0.620309\pi$
$888$	−0.728299	+	6.92931i	−0.0244401	+	0.232532i
$889$	−8.06480	+	1.71423i	−0.270485	+	0.0574933i
$890$	7.76317	+	3.45638i	0.260222	+	0.115858i
$891$	3.40751	−	2.47570i	0.114156	−	0.0829390i
$892$	17.7257	−	7.89197i	0.593499	−	0.264243i
$893$	−9.16670	+	15.8772i	−0.306752	+	0.531310i
$894$	10.1802	+	17.6326i	0.340477	+	0.589723i
$895$	−1.49278	−	1.08457i	−0.0498981	−	0.0362531i
$896$	1.55714	+	0.330980i	0.0520203	+	0.0110573i
$897$	4.24572	−	13.0670i	0.141760	−	0.436293i
$898$	14.3761			0.479738
$899$	2.26947	+	22.4039i	0.0756912	+	0.747214i
$900$	1.00000			0.0333333
$901$	−6.21956	+	19.1418i	−0.207204	+	0.637707i
$902$	35.2340	+	7.48922i	1.17316	+	0.249364i
$903$	−2.96807	−	2.15643i	−0.0987713	−	0.0717616i
$904$	−3.84659	−	6.66250i	−0.127936	−	0.221591i
$905$	10.5573	−	18.2858i	0.350936	−	0.607840i
$906$	8.20405	−	3.65268i	0.272561	−	0.121352i
$907$	−11.5809	+	8.41405i	−0.384539	+	0.279384i	−0.763214	−	0.646146i	$-0.776380\pi$
$907$	−11.5809	+	8.41405i	−0.384539	+	0.279384i	0.378675	+	0.925530i	$0.376380\pi$
$908$	11.4918	+	5.11647i	0.381368	+	0.169796i
$909$	2.28046	−	0.484727i	0.0756382	−	0.0160774i
$910$	−0.466087	+	4.43453i	−0.0154506	+	0.147003i
$911$	16.9337	+	18.8067i	0.561037	+	0.623095i	0.955205	−	0.295943i	$-0.0956340\pi$
$911$	16.9337	+	18.8067i	0.561037	+	0.623095i	−0.394168	+	0.919038i	$0.628967\pi$
$912$	−1.94032	+	2.15494i	−0.0642503	+	0.0713572i
$913$	4.02620	+	38.3067i	0.133248	+	1.26777i
$914$	3.47644	+	10.6994i	0.114990	+	0.353904i
$915$	2.87418	+	8.84582i	0.0950175	+	0.292434i
$916$	1.29848	+	12.3542i	0.0429028	+	0.408193i
$917$	−5.01430	+	5.56894i	−0.165587	+	0.183903i
$918$	2.31708	+	2.57338i	0.0764751	+	0.0849342i
$919$	−1.62679	+	15.4779i	−0.0536630	+	0.510569i	0.934368	+	0.356311i	$0.115965\pi$
$919$	−1.62679	+	15.4779i	−0.0536630	+	0.510569i	−0.988031	+	0.154258i	$0.950701\pi$
$920$	4.79803	−	1.01985i	0.158186	−	0.0336235i
$921$	−20.0171	−	8.91219i	−0.659586	−	0.293667i
$922$	−27.9224	+	20.2868i	−0.919575	+	0.668111i
$923$	10.3911	−	4.62643i	0.342029	−	0.152281i
$924$	−3.35252	+	5.80674i	−0.110290	+	0.191028i
$925$	−3.48374	−	6.03401i	−0.114545	−	0.198397i
$926$	−10.0097	−	7.27244i	−0.328938	−	0.238987i
$927$	−7.22831	−	1.53642i	−0.237409	−	0.0504628i
$928$	−1.24981	+	3.84651i	−0.0410269	+	0.126268i
$929$	−41.9267			−1.37557			−0.687786	−	0.725914i	$-0.741417\pi$
$929$	−41.9267			−1.37557			−0.687786	+	0.725914i	$0.741417\pi$
$930$	5.09490	−	2.24544i	0.167068	−	0.0736309i
$931$	−12.9497			−0.424408
$932$	1.41357	−	4.35053i	0.0463031	−	0.142506i
$933$	−4.57939	−	0.973379i	−0.149922	−	0.0318670i
$934$	16.3519	+	11.8803i	0.535049	+	0.388736i
$935$	−7.29256	−	12.6311i	−0.238492	−	0.413081i
$936$	1.40049	−	2.42572i	0.0457765	−	0.0792872i
$937$	29.1860	−	12.9945i	0.953467	−	0.424511i	0.129772	−	0.991544i	$-0.458576\pi$
$937$	29.1860	−	12.9945i	0.953467	−	0.424511i	0.823695	+	0.567033i	$0.191909\pi$
$938$	−13.1498	+	9.55386i	−0.429355	+	0.311945i
$939$	−1.08746	−	0.484169i	−0.0354880	−	0.0158003i
$940$	6.18423	−	1.31450i	0.201707	−	0.0428742i
$941$	−0.0385412	+	0.366695i	−0.00125641	+	0.0119539i	−0.995132	−	0.0985496i	$-0.968580\pi$
$941$	−0.0385412	+	0.366695i	−0.00125641	+	0.0119539i	0.993876	+	0.110504i	$0.0352464\pi$
$942$	−14.7071	−	16.3339i	−0.479184	−	0.532188i
$943$	28.0703	−	31.1753i	0.914096	−	1.01521i
$944$	0.0274873	+	0.261525i	0.000894637	+	0.00851190i
$945$	0.491932	+	1.51401i	0.0160025	+	0.0492508i
$946$	−2.99955	−	9.23167i	−0.0975238	−	0.300147i
$947$	−1.86554	−	17.7494i	−0.0606218	−	0.576778i	−0.982102	−	0.188352i	$-0.939685\pi$
$947$	−1.86554	−	17.7494i	−0.0606218	−	0.576778i	0.921480	−	0.388426i	$-0.126981\pi$
$948$	4.71355	−	5.23492i	0.153089	−	0.170022i
$949$	−11.3019	−	12.5520i	−0.366874	−	0.407455i
$950$	0.303107	−	2.88387i	0.00983410	−	0.0935652i
$951$	27.8272	−	5.91485i	0.902359	−	0.191802i
$952$	−5.03597	−	2.24216i	−0.163217	−	0.0726688i
$953$	9.56913	−	6.95238i	0.309974	−	0.225210i	−0.421911	−	0.906637i	$-0.638641\pi$
$953$	9.56913	−	6.95238i	0.309974	−	0.225210i	0.731886	+	0.681428i	$0.238641\pi$
$954$	5.30978	−	2.36407i	0.171911	−	0.0765395i
$955$	3.40414	−	5.89614i	0.110155	−	0.190795i
$956$	3.82719	+	6.62888i	0.123780	+	0.214393i
$957$	−13.7815	−	10.0129i	−0.445494	−	0.323670i
$958$	−18.4424	−	3.92005i	−0.595846	−	0.126651i
$959$	−8.29278	+	25.5226i	−0.267788	+	0.824166i
$960$	1.00000			0.0322749
$961$	20.9160	−	22.8806i	0.674709	−	0.738084i
$962$	−19.5158			−0.629214
$963$	−1.80034	+	5.54089i	−0.0580153	+	0.178553i
$964$	−23.0709	−	4.90386i	−0.743063	−	0.157943i
$965$	9.97013	+	7.24373i	0.320950	+	0.233184i
$966$	3.90437	+	6.76256i	0.125621	+	0.217582i
$967$	−11.3066	+	19.5836i	−0.363596	+	0.629766i	−0.988550	−	0.150895i	$-0.951784\pi$
$967$	−11.3066	+	19.5836i	−0.363596	+	0.629766i	0.624954	+	0.780661i	$0.285118\pi$
$968$	−6.15748	+	2.74148i	−0.197909	+	0.0881147i
$969$	8.12363	−	5.90217i	0.260969	−	0.189605i
$970$	−6.27769	−	2.79501i	−0.201565	−	0.0897423i
$971$	−26.5259	+	5.63826i	−0.851257	+	0.180940i	−0.612825	−	0.790219i	$-0.709967\pi$
$971$	−26.5259	+	5.63826i	−0.851257	+	0.180940i	−0.238432	+	0.971159i	$0.576634\pi$
$972$	0.104528	−	0.994522i	0.00335275	−	0.0318993i
$973$	−15.6713	−	17.4048i	−0.502400	−	0.557971i
$974$	−15.9758	+	17.7429i	−0.511897	+	0.568519i
$975$	0.292782	+	2.78564i	0.00937654	+	0.0892118i
$976$	2.87418	+	8.84582i	0.0920003	+	0.283148i
$977$	−19.0607	−	58.6629i	−0.609806	−	1.87679i	−0.459571	−	0.888141i	$-0.651997\pi$
$977$	−19.0607	−	58.6629i	−0.609806	−	1.87679i	−0.150236	−	0.988650i	$-0.548003\pi$
$978$	0.509266	+	4.84534i	0.0162845	+	0.154937i
$979$	−23.9496	+	26.5988i	−0.765434	+	0.850100i
$980$	2.98819	+	3.31872i	0.0954541	+	0.106013i
$981$	−1.48584	+	14.1369i	−0.0474394	+	0.451355i
$982$	−19.2747	+	4.09697i	−0.615082	+	0.130740i
$983$	50.6285	+	22.5413i	1.61480	+	0.718955i	0.997691	−	0.0679230i	$-0.0216372\pi$
$983$	50.6285	+	22.5413i	1.61480	+	0.718955i	0.617109	+	0.786878i	$0.288304\pi$
$984$	6.91889	−	5.02687i	0.220566	−	0.160251i
$985$	5.27569	−	2.34889i	0.168098	−	0.0748418i
$986$	7.00263	−	12.1289i	0.223009	−	0.386263i
$987$	5.03238	+	8.71634i	0.160182	+	0.277444i
$988$	−6.57098	−	4.77409i	−0.209051	−	0.151884i
$989$	−11.0575	−	2.35035i	−0.351608	−	0.0747367i
$990$	−1.30155	+	4.00577i	−0.0413660	+	0.127312i
$991$	44.7644			1.42199			0.710995	−	0.703197i	$-0.248245\pi$
$991$	44.7644			1.42199			0.710995	+	0.703197i	$0.248245\pi$
$992$	5.09490	−	2.24544i	0.161763	−	0.0712928i
$993$	−7.65940			−0.243064
$994$	−1.99769	+	6.14825i	−0.0633628	+	0.195011i
$995$	16.9459	+	3.60197i	0.537222	+	0.114190i
$996$	7.39842	+	5.37527i	0.234428	+	0.170322i
$997$	−28.5748	−	49.4931i	−0.904974	−	1.56746i	−0.820952	−	0.570998i	$-0.806556\pi$
$997$	−28.5748	−	49.4931i	−0.904974	−	1.56746i	−0.0840229	−	0.996464i	$-0.526777\pi$
$998$	8.32171	−	14.4136i	0.263419	−	0.456255i
$999$	−6.36510	+	2.83393i	−0.201383	+	0.0896615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.e.691.2	✓	16
31.7	even	15	inner	930.2.bg.e.751.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.e.691.2	✓	16	1.1	even	1	trivial
930.2.bg.e.751.2	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.45430 - 0.647494i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(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} +(1.45430 - 0.647494i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(0.440265 - 4.18884i) q^{11} +(-0.669131 - 0.743145i) q^{12} +(1.87422 - 2.08153i) q^{13} +(0.166401 + 1.58320i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.361964 - 3.44386i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(1.94032 + 2.15494i) q^{19} +(0.104528 - 0.994522i) q^{20} +(1.55714 - 0.330980i) q^{21} +(3.84777 + 1.71314i) q^{22} +(3.96840 - 2.88321i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.40049 + 2.42572i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.55714 - 0.330980i) q^{28} +(1.24981 - 3.84651i) q^{29} -1.00000 q^{30} +(-5.09490 + 2.24544i) q^{31} -1.00000 q^{32} +(1.30155 - 4.00577i) q^{33} +(3.38716 + 0.719962i) q^{34} +(1.28789 + 0.935710i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-3.48374 + 6.03401i) q^{37} +(-2.64906 + 1.17944i) q^{38} +(2.26604 - 1.64638i) q^{39} +(0.913545 + 0.406737i) q^{40} +(8.36533 - 1.77811i) q^{41} +(-0.166401 + 1.58320i) q^{42} +(-1.54207 - 1.71265i) q^{43} +(-2.81832 + 3.13006i) q^{44} +(0.104528 + 0.994522i) q^{45} +(1.51580 + 4.66514i) q^{46} +(1.95372 + 6.01295i) q^{47} +(0.104528 + 0.994522i) q^{48} +(-2.98819 + 3.31872i) q^{49} +(-0.669131 - 0.743145i) q^{50} +(0.361964 - 3.44386i) q^{51} +(-2.73977 + 0.582357i) q^{52} +(-5.30978 - 2.36407i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(3.84777 - 1.71314i) q^{55} +(0.795962 - 1.37865i) q^{56} +(1.44988 + 2.51127i) q^{57} +(3.27204 + 2.37727i) q^{58} +(0.257219 + 0.0546735i) q^{59} +(0.309017 - 0.951057i) q^{60} +9.30105 q^{61} +(-0.561132 - 5.53942i) q^{62} +1.59192 q^{63} +(0.309017 - 0.951057i) q^{64} +(2.73977 + 0.582357i) q^{65} +(3.40751 + 2.47570i) q^{66} +(5.10514 + 8.84236i) q^{67} +(-1.73141 + 2.99890i) q^{68} +(4.48114 - 1.99513i) q^{69} +(-1.28789 + 0.935710i) q^{70} +(3.70982 + 1.65172i) q^{71} +(0.978148 - 0.207912i) q^{72} +(0.630323 - 5.99712i) q^{73} +(-4.66215 - 5.17784i) q^{74} +(-0.669131 + 0.743145i) q^{75} +(-0.303107 - 2.88387i) q^{76} +(-2.07197 - 6.37688i) q^{77} +(0.865551 + 2.66389i) q^{78} +(0.736328 + 7.00569i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.893950 + 8.50537i) q^{82} +(-8.94511 + 1.90134i) q^{83} +(-1.45430 - 0.647494i) q^{84} +(2.80149 - 2.03540i) q^{85} +(2.10535 - 0.937363i) q^{86} +(2.02223 - 3.50261i) q^{87} +(-2.10596 - 3.64762i) q^{88} +(-6.87490 - 4.99491i) q^{89} +(-0.978148 - 0.207912i) q^{90} +(1.37789 - 4.24071i) q^{91} -4.90522 q^{92} +(-5.45042 + 1.13708i) q^{93} -6.32239 q^{94} +(-0.896075 + 2.75783i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(5.55940 + 4.03914i) q^{97} +(-2.23289 - 3.86748i) q^{98} +(2.10596 - 3.64762i) 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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