LMFDB - Embedded newform 930.2.bg.b.751.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 195x^{12} + 892x^{10} + 2229x^{8} + 2923x^{6} + 1685x^{4} + 213x^{2} + 1 $ x^16 + 22x^14 + 195x^12 + 892x^10 + 2229x^8 + 2923x^6 + 1685x^4 + 213*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			751.2
Root			$-1.63422i$ of defining polynomial
Character	$\chi$	$=$	930.751
Dual form			930.2.bg.b.691.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.978148 - 0.207912i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.577823 + 0.257263i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})$	\(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} +(0.577823 + 0.257263i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +(-0.978148 - 0.207912i) q^{10} +(-0.246108 - 2.34156i) q^{11} +(-0.669131 + 0.743145i) q^{12} +(4.74783 + 5.27300i) q^{13} +(-0.0661149 + 0.629041i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.153234 - 1.45793i) q^{17} +(0.669131 + 0.743145i) q^{18} +(-3.50246 + 3.88987i) q^{19} +(-0.104528 - 0.994522i) q^{20} +(0.618684 + 0.131505i) q^{21} +(2.15090 - 0.957644i) q^{22} +(6.48654 + 4.71275i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.54776 + 6.14490i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.618684 + 0.131505i) q^{28} +(0.281152 + 0.865295i) q^{29} -1.00000 q^{30} +(0.409338 + 5.55270i) q^{31} +1.00000 q^{32} +(-0.727568 - 2.23922i) q^{33} +(1.43392 - 0.304790i) q^{34} +(-0.511708 + 0.371778i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.69387 - 2.93387i) q^{37} +(-4.78181 - 2.12900i) q^{38} +(5.74040 + 4.17064i) q^{39} +(0.913545 - 0.406737i) q^{40} +(1.97423 + 0.419636i) q^{41} +(0.0661149 + 0.629041i) q^{42} +(-7.93538 + 8.81313i) q^{43} +(1.57544 + 1.74970i) q^{44} +(-0.104528 + 0.994522i) q^{45} +(-2.47764 + 7.62539i) q^{46} +(0.894321 - 2.75244i) q^{47} +(0.104528 - 0.994522i) q^{48} +(-4.41622 - 4.90471i) q^{49} +(0.669131 - 0.743145i) q^{50} +(-0.153234 - 1.45793i) q^{51} +(-6.94047 - 1.47524i) q^{52} +(4.10907 - 1.82948i) q^{53} +(0.809017 + 0.587785i) q^{54} +(2.15090 + 0.957644i) q^{55} +(-0.316253 - 0.547766i) q^{56} +(-2.61717 + 4.53307i) q^{57} +(-0.736064 + 0.534782i) q^{58} +(13.2045 - 2.80670i) q^{59} +(-0.309017 - 0.951057i) q^{60} -8.58340 q^{61} +(-5.15444 + 2.10518i) q^{62} +0.632506 q^{63} +(0.309017 + 0.951057i) q^{64} +(-6.94047 + 1.47524i) q^{65} +(1.90480 - 1.38392i) q^{66} +(-0.848614 + 1.46984i) q^{67} +(0.732980 + 1.26956i) q^{68} +(7.32463 + 3.26114i) q^{69} +(-0.511708 - 0.371778i) q^{70} +(-3.14262 + 1.39918i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(-0.547529 - 5.20939i) q^{73} +(2.26684 - 2.51759i) q^{74} +(-0.669131 - 0.743145i) q^{75} +(0.547138 - 5.20567i) q^{76} +(0.460191 - 1.41632i) q^{77} +(-2.19264 + 6.74824i) q^{78} +(0.820502 - 7.80656i) q^{79} +(0.669131 + 0.743145i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.210974 + 2.00728i) q^{82} +(1.34900 + 0.286738i) q^{83} +(-0.577823 + 0.257263i) q^{84} +(1.18599 + 0.861669i) q^{85} +(-10.8340 - 4.82359i) q^{86} +(0.454913 + 0.787932i) q^{87} +(-1.17723 + 2.03902i) q^{88} +(1.63062 - 1.18471i) q^{89} +(-0.978148 + 0.207912i) q^{90} +(1.38686 + 4.26830i) q^{91} -8.01781 q^{92} +(1.55486 + 5.34625i) q^{93} +2.89408 q^{94} +(-1.61750 - 4.97816i) q^{95} +(0.978148 - 0.207912i) q^{96} +(7.93389 - 5.76431i) q^{97} +(3.29997 - 5.71571i) q^{98} +(-1.17723 - 2.03902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 14 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{21} + 13 q^{22} + 7 q^{23} - 2 q^{24} - 8 q^{25} - q^{26} + 4 q^{27} - 2 q^{28} + 13 q^{29} - 16 q^{30} - 21 q^{31} + 16 q^{32} - 4 q^{33} + 6 q^{34} + 9 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} - 20 q^{41} + 12 q^{42} - 2 q^{43} + 13 q^{44} + 2 q^{45} - 3 q^{46} + 23 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} + 13 q^{56} - 18 q^{57} - 22 q^{58} - 26 q^{59} + 4 q^{60} + 24 q^{61} + 9 q^{62} - 26 q^{63} - 4 q^{64} - 16 q^{65} + 11 q^{66} + 45 q^{67} - 4 q^{68} + 11 q^{69} + 9 q^{70} - 39 q^{71} + 2 q^{72} - 19 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 6 q^{77} - 2 q^{78} - 20 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} - 86 q^{83} - 3 q^{84} + 8 q^{85} + 3 q^{86} + 9 q^{87} - 7 q^{88} - 13 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} + 12 q^{93} - 72 q^{94} + 14 q^{95} - 2 q^{96} + 67 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 14 * q^13 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^21 + 13 * q^22 + 7 * q^23 - 2 * q^24 - 8 * q^25 - q^26 + 4 * q^27 - 2 * q^28 + 13 * q^29 - 16 * q^30 - 21 * q^31 + 16 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 - 20 * q^41 + 12 * q^42 - 2 * q^43 + 13 * q^44 + 2 * q^45 - 3 * q^46 + 23 * q^47 - 2 * q^48 - q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 + 13 * q^56 - 18 * q^57 - 22 * q^58 - 26 * q^59 + 4 * q^60 + 24 * q^61 + 9 * q^62 - 26 * q^63 - 4 * q^64 - 16 * q^65 + 11 * q^66 + 45 * q^67 - 4 * q^68 + 11 * q^69 + 9 * q^70 - 39 * q^71 + 2 * q^72 - 19 * q^73 - 2 * q^74 - 2 * q^75 - 2 * q^76 - 6 * q^77 - 2 * q^78 - 20 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 - 86 * q^83 - 3 * q^84 + 8 * q^85 + 3 * q^86 + 9 * q^87 - 7 * q^88 - 13 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 + 12 * q^93 - 72 * q^94 + 14 * q^95 - 2 * q^96 + 67 * q^97 + 9 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{14}{15}\right)$

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
$7$	0.577823	+	0.257263i	0.218397	+	0.0972364i	0.513019	−	0.858377i	$-0.328527\pi$
$7$	0.577823	+	0.257263i	0.218397	+	0.0972364i	−0.294622	+	0.955614i	$0.595194\pi$
$8$	−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
$11$	−0.246108	−	2.34156i	−0.0742043	−	0.706007i	−0.966867	−	0.255281i	$-0.917832\pi$
$11$	−0.246108	−	2.34156i	−0.0742043	−	0.706007i	0.892663	−	0.450726i	$-0.148835\pi$
$12$	−0.669131	+	0.743145i	−0.193161	+	0.214527i
$13$	4.74783	+	5.27300i	1.31681	+	1.46247i	0.790927	+	0.611910i	$0.209599\pi$
$13$	4.74783	+	5.27300i	1.31681	+	1.46247i	0.525884	+	0.850557i	$0.323735\pi$
$14$	−0.0661149	+	0.629041i	−0.0176699	+	0.168118i
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.153234	−	1.45793i	0.0371648	−	0.353600i	−0.960098	−	0.279663i	$-0.909777\pi$
$17$	0.153234	−	1.45793i	0.0371648	−	0.353600i	0.997263	−	0.0739364i	$-0.0235562\pi$
$18$	0.669131	+	0.743145i	0.157716	+	0.175161i
$19$	−3.50246	+	3.88987i	−0.803519	+	0.892399i	−0.996041	−	0.0888942i	$-0.971667\pi$
$19$	−3.50246	+	3.88987i	−0.803519	+	0.892399i	0.192522	+	0.981293i	$0.438333\pi$
$20$	−0.104528	−	0.994522i	−0.0233733	−	0.222382i
$21$	0.618684	+	0.131505i	0.135008	+	0.0286968i
$22$	2.15090	−	0.957644i	0.458574	−	0.204170i
$23$	6.48654	+	4.71275i	1.35254	+	0.982676i	0.998881	+	0.0473011i	$0.0150620\pi$
$23$	6.48654	+	4.71275i	1.35254	+	0.982676i	0.353657	+	0.935375i	$0.384938\pi$
$24$	−0.913545	−	0.406737i	−0.186477	−	0.0830248i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.54776	+	6.14490i	−0.695773	+	1.20511i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−0.618684	+	0.131505i	−0.116920	+	0.0248522i
$29$	0.281152	+	0.865295i	0.0522085	+	0.160681i	0.973761	−	0.227572i	$-0.0730786\pi$
$29$	0.281152	+	0.865295i	0.0522085	+	0.160681i	−0.921553	+	0.388253i	$0.873079\pi$
$30$	−1.00000			−0.182574
$31$	0.409338	+	5.55270i	0.0735193	+	0.997294i
$31$	0.409338	+	5.55270i	0.0735193	+	0.997294i
$32$	1.00000			0.176777
$33$	−0.727568	−	2.23922i	−0.126653	−	0.389799i
$34$	1.43392	−	0.304790i	0.245916	−	0.0522711i
$35$	−0.511708	+	0.371778i	−0.0864945	+	0.0628419i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.69387	−	2.93387i	−0.278471	−	0.482326i	0.692534	−	0.721385i	$-0.256494\pi$
$37$	−1.69387	−	2.93387i	−0.278471	−	0.482326i	−0.971005	+	0.239059i	$0.923161\pi$
$38$	−4.78181	−	2.12900i	−0.775712	−	0.345369i
$39$	5.74040	+	4.17064i	0.919199	+	0.667837i
$40$	0.913545	−	0.406737i	0.144444	−	0.0643107i
$41$	1.97423	+	0.419636i	0.308323	+	0.0655362i	0.359475	−	0.933155i	$-0.382956\pi$
$41$	1.97423	+	0.419636i	0.308323	+	0.0655362i	−0.0511515	+	0.998691i	$0.516289\pi$
$42$	0.0661149	+	0.629041i	0.0102017	+	0.0970631i
$43$	−7.93538	+	8.81313i	−1.21013	+	1.34399i	−0.287755	+	0.957704i	$0.592909\pi$
$43$	−7.93538	+	8.81313i	−1.21013	+	1.34399i	−0.922379	+	0.386286i	$0.873758\pi$
$44$	1.57544	+	1.74970i	0.237507	+	0.263778i
$45$	−0.104528	+	0.994522i	−0.0155822	+	0.148255i
$46$	−2.47764	+	7.62539i	−0.365308	+	1.12430i
$47$	0.894321	−	2.75244i	0.130450	−	0.401484i	−0.864405	−	0.502797i	$-0.832304\pi$
$47$	0.894321	−	2.75244i	0.130450	−	0.401484i	0.994855	+	0.101313i	$0.0323043\pi$
$48$	0.104528	−	0.994522i	0.0150874	−	0.143547i
$49$	−4.41622	−	4.90471i	−0.630888	−	0.700673i
$50$	0.669131	−	0.743145i	0.0946294	−	0.105097i
$51$	−0.153234	−	1.45793i	−0.0214571	−	0.204151i
$52$	−6.94047	−	1.47524i	−0.962469	−	0.204579i
$53$	4.10907	−	1.82948i	0.564424	−	0.251298i	−0.104630	−	0.994511i	$-0.533366\pi$
$53$	4.10907	−	1.82948i	0.564424	−	0.251298i	0.669054	+	0.743213i	$0.266699\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	2.15090	+	0.957644i	0.290028	+	0.129129i
$56$	−0.316253	−	0.547766i	−0.0422611	−	0.0731983i
$57$	−2.61717	+	4.53307i	−0.346653	+	0.600420i
$58$	−0.736064	+	0.534782i	−0.0966500	+	0.0702203i
$59$	13.2045	−	2.80670i	1.71907	−	0.365401i	0.760301	−	0.649571i	$-0.225051\pi$
$59$	13.2045	−	2.80670i	1.71907	−	0.365401i	0.958774	+	0.284170i	$0.0917181\pi$
$60$	−0.309017	−	0.951057i	−0.0398939	−	0.122781i
$61$	−8.58340			−1.09899			−0.549496	−	0.835497i	$-0.685180\pi$
$61$	−8.58340			−1.09899			−0.549496	+	0.835497i	$0.685180\pi$
$62$	−5.15444	+	2.10518i	−0.654614	+	0.267358i
$63$	0.632506			0.0796883
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−6.94047	+	1.47524i	−0.860859	+	0.182981i
$66$	1.90480	−	1.38392i	0.234464	−	0.170348i
$67$	−0.848614	+	1.46984i	−0.103675	+	0.179570i	−0.913196	−	0.407521i	$-0.866393\pi$
$67$	−0.848614	+	1.46984i	−0.103675	+	0.179570i	0.809521	+	0.587091i	$0.199727\pi$
$68$	0.732980	+	1.26956i	0.0888869	+	0.153957i
$69$	7.32463	+	3.26114i	0.881782	+	0.392595i
$70$	−0.511708	−	0.371778i	−0.0611608	−	0.0444359i
$71$	−3.14262	+	1.39918i	−0.372960	+	0.166053i	−0.584653	−	0.811284i	$-0.698769\pi$
$71$	−3.14262	+	1.39918i	−0.372960	+	0.166053i	0.211692	+	0.977336i	$0.432103\pi$
$72$	−0.978148	−	0.207912i	−0.115276	−	0.0245026i
$73$	−0.547529	−	5.20939i	−0.0640834	−	0.609713i	−0.978687	−	0.205360i	$-0.934164\pi$
$73$	−0.547529	−	5.20939i	−0.0640834	−	0.609713i	0.914603	−	0.404353i	$-0.132503\pi$
$74$	2.26684	−	2.51759i	0.263515	−	0.292663i
$75$	−0.669131	−	0.743145i	−0.0772645	−	0.0858110i
$76$	0.547138	−	5.20567i	0.0627610	−	0.597131i
$77$	0.460191	−	1.41632i	0.0524436	−	0.161405i
$78$	−2.19264	+	6.74824i	−0.248267	+	0.764088i
$79$	0.820502	−	7.80656i	0.0923137	−	0.878307i	−0.846154	−	0.532939i	$-0.821088\pi$
$79$	0.820502	−	7.80656i	0.0923137	−	0.878307i	0.938467	−	0.345368i	$-0.112246\pi$
$80$	0.669131	+	0.743145i	0.0748111	+	0.0830861i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	0.210974	+	2.00728i	0.0232982	+	0.221667i
$83$	1.34900	+	0.286738i	0.148072	+	0.0314736i	0.281351	−	0.959605i	$-0.409217\pi$
$83$	1.34900	+	0.286738i	0.148072	+	0.0314736i	−0.133279	+	0.991079i	$0.542551\pi$
$84$	−0.577823	+	0.257263i	−0.0630457	+	0.0280697i
$85$	1.18599	+	0.861669i	0.128638	+	0.0934612i
$86$	−10.8340	−	4.82359i	−1.16826	−	0.520141i
$87$	0.454913	+	0.787932i	0.0487718	+	0.0844752i
$88$	−1.17723	+	2.03902i	−0.125493	+	0.217360i
$89$	1.63062	−	1.18471i	0.172845	−	0.125580i	−0.497999	−	0.867177i	$-0.665932\pi$
$89$	1.63062	−	1.18471i	0.172845	−	0.125580i	0.670845	+	0.741598i	$0.265932\pi$
$90$	−0.978148	+	0.207912i	−0.103106	+	0.0219158i
$91$	1.38686	+	4.26830i	0.145382	+	0.447440i
$92$	−8.01781			−0.835914
$93$	1.55486	+	5.34625i	0.161232	+	0.554380i
$94$	2.89408			0.298502
$95$	−1.61750	−	4.97816i	−0.165952	−	0.510748i
$96$	0.978148	−	0.207912i	0.0998318	−	0.0212199i
$97$	7.93389	−	5.76431i	0.805565	−	0.585277i	−0.106977	−	0.994262i	$-0.534117\pi$
$97$	7.93389	−	5.76431i	0.805565	−	0.585277i	0.912541	+	0.408985i	$0.134117\pi$
$98$	3.29997	−	5.71571i	0.333347	−	0.577374i
$99$	−1.17723	−	2.03902i	−0.118316	−	0.204929i
$100$	0.913545	+	0.406737i	0.0913545	+	0.0406737i
$101$	8.22478	+	5.97566i	0.818397	+	0.594600i	0.916253	−	0.400601i	$-0.131199\pi$
$101$	8.22478	+	5.97566i	0.818397	+	0.594600i	−0.0978562	+	0.995201i	$0.531199\pi$
$102$	1.33922	−	0.596259i	0.132603	−	0.0590385i
$103$	15.4119	+	3.27590i	1.51858	+	0.322784i	0.890361	−	0.455255i	$-0.150452\pi$
$103$	15.4119	+	3.27590i	1.51858	+	0.322784i	0.628216	+	0.778039i	$0.283785\pi$
$104$	−0.741684	−	7.05665i	−0.0727281	−	0.691961i
$105$	−0.423229	+	0.470044i	−0.0413029	+	0.0458716i
$106$	3.00971	+	3.34262i	0.292329	+	0.324664i
$107$	0.926410	−	8.81421i	0.0895595	−	0.852102i	−0.853861	−	0.520502i	$-0.825745\pi$
$107$	0.926410	−	8.81421i	0.0895595	−	0.852102i	0.943420	−	0.331600i	$-0.107588\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	−1.32504	+	4.07804i	−0.126915	+	0.390605i	−0.994245	−	0.107128i	$-0.965834\pi$
$109$	−1.32504	+	4.07804i	−0.126915	+	0.390605i	0.867330	+	0.497734i	$0.165834\pi$
$110$	−0.246108	+	2.34156i	−0.0234655	+	0.223259i
$111$	−2.26684	−	2.51759i	−0.215159	−	0.238959i
$112$	0.423229	−	0.470044i	0.0399914	−	0.0444149i
$113$	−0.419452	−	3.99081i	−0.0394587	−	0.375424i	−0.996376	−	0.0850625i	$-0.972891\pi$
$113$	−0.419452	−	3.99081i	−0.0394587	−	0.375424i	0.956917	−	0.290362i	$-0.0937756\pi$
$114$	−5.11996	−	1.08828i	−0.479528	−	0.101927i
$115$	−7.32463	+	3.26114i	−0.683025	+	0.304103i
$116$	−0.736064	−	0.534782i	−0.0683418	−	0.0496533i
$117$	6.48208	+	2.88601i	0.599268	+	0.266812i
$118$	6.74973	+	11.6909i	0.621363	+	1.07623i
$119$	0.463614	−	0.803003i	0.0424994	−	0.0736112i
$120$	0.809017	−	0.587785i	0.0738528	−	0.0536572i
$121$	5.33729	−	1.13448i	0.485208	−	0.103134i
$122$	−2.65242	−	8.16329i	−0.240138	−	0.739070i
$123$	2.01834			0.181987
$124$	−3.59495	−	4.25162i	−0.322836	−	0.381807i
$125$	1.00000			0.0894427
$126$	0.195455	+	0.601549i	0.0174125	+	0.0535902i
$127$	−11.8222	+	2.51289i	−1.04905	+	0.222983i	−0.700016	−	0.714127i	$-0.746824\pi$
$127$	−11.8222	+	2.51289i	−1.04905	+	0.222983i	−0.349035	+	0.937110i	$0.613491\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−5.92962	+	10.2704i	−0.522074	+	0.904258i
$130$	−3.54776	−	6.14490i	−0.311159	−	0.538943i
$131$	−18.4617	−	8.21969i	−1.61301	−	0.718158i	−0.615463	−	0.788166i	$-0.711031\pi$
$131$	−18.4617	−	8.21969i	−1.61301	−	0.718158i	−0.997546	+	0.0700078i	$0.977698\pi$
$132$	1.90480	+	1.38392i	0.165791	+	0.120454i
$133$	−3.02452	+	1.34660i	−0.262259	+	0.116765i
$134$	−1.66014	−	0.352874i	−0.143414	−	0.0304836i
$135$	0.104528	+	0.994522i	0.00899638	+	0.0855948i
$136$	−0.980918	+	1.08942i	−0.0841131	+	0.0934170i
$137$	−11.9711	−	13.2953i	−1.02276	−	1.13589i	−0.990652	−	0.136410i	$-0.956444\pi$
$137$	−11.9711	−	13.2953i	−1.02276	−	1.13589i	−0.0321113	−	0.999484i	$-0.510223\pi$
$138$	−0.838089	+	7.97389i	−0.0713429	+	0.678782i
$139$	−0.845511	+	2.60222i	−0.0717153	+	0.220717i	−0.980490	−	0.196571i	$-0.937019\pi$
$139$	−0.845511	+	2.60222i	−0.0717153	+	0.220717i	0.908774	+	0.417288i	$0.137019\pi$
$140$	0.195455	−	0.601549i	0.0165190	−	0.0508402i
$141$	0.302514	−	2.87823i	0.0254763	−	0.242391i
$142$	−2.30183	−	2.55644i	−0.193165	−	0.214531i
$143$	11.1786	−	12.4151i	0.934799	−	1.03820i
$144$	−0.104528	−	0.994522i	−0.00871071	−	0.0828768i
$145$	−0.889944	−	0.189163i	−0.0739058	−	0.0157092i
$146$	4.78523	−	2.13052i	0.396028	−	0.176323i
$147$	−5.33946	−	3.87935i	−0.440391	−	0.319963i
$148$	3.09486	+	1.37792i	0.254396	+	0.113264i
$149$	−3.63467	−	6.29544i	−0.297764	−	0.515742i	0.677860	−	0.735191i	$-0.262908\pi$
$149$	−3.63467	−	6.29544i	−0.297764	−	0.515742i	−0.975624	+	0.219449i	$0.929574\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	10.9294	−	7.94066i	0.889420	−	0.646202i	−0.0463065	−	0.998927i	$-0.514745\pi$
$151$	10.9294	−	7.94066i	0.889420	−	0.646202i	0.935727	+	0.352726i	$0.114745\pi$
$152$	5.11996	−	1.08828i	0.415284	−	0.0882713i
$153$	−0.453006	−	1.39421i	−0.0366234	−	0.112715i
$154$	1.48921			0.120004
$155$	−5.01345	−	2.42185i	−0.402690	−	0.194528i
$156$	−7.09552			−0.568096
$157$	−5.71441	−	17.5871i	−0.456060	−	1.40361i	−0.869887	−	0.493252i	$-0.835808\pi$
$157$	−5.71441	−	17.5871i	−0.456060	−	1.40361i	0.413827	−	0.910356i	$-0.364192\pi$
$158$	7.67803	−	1.63202i	0.610831	−	0.129836i
$159$	3.63891	−	2.64382i	0.288584	−	0.209669i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	2.53566	+	4.39189i	0.199838	+	0.346129i
$162$	0.913545	+	0.406737i	0.0717749	+	0.0319562i
$163$	−15.2996	−	11.1158i	−1.19835	−	0.870655i	−0.204232	−	0.978923i	$-0.565470\pi$
$163$	−15.2996	−	11.1158i	−1.19835	−	0.870655i	−0.994122	+	0.108268i	$0.965470\pi$
$164$	−1.84384	+	0.820932i	−0.143980	+	0.0641040i
$165$	2.30301	+	0.489519i	0.179289	+	0.0381090i
$166$	0.144159	+	1.37158i	0.0111889	+	0.106455i
$167$	−1.37042	+	1.52200i	−0.106046	+	0.117776i	−0.793831	−	0.608138i	$-0.791917\pi$
$167$	−1.37042	+	1.52200i	−0.106046	+	0.117776i	0.687785	+	0.725915i	$0.258583\pi$
$168$	−0.423229	−	0.470044i	−0.0326528	−	0.0362646i
$169$	−3.90376	+	37.1418i	−0.300289	+	2.85706i
$170$	−0.453006	+	1.39421i	−0.0347440	+	0.106931i
$171$	−1.61750	+	4.97816i	−0.123693	+	0.380689i
$172$	1.23963	−	11.7943i	0.0945207	−	0.899305i
$173$	−1.61230	−	1.79064i	−0.122581	−	0.136140i	0.678730	−	0.734388i	$-0.262531\pi$
$173$	−1.61230	−	1.79064i	−0.122581	−	0.136140i	−0.801311	+	0.598248i	$0.795864\pi$
$174$	−0.608792	+	0.676132i	−0.0461524	+	0.0512574i
$175$	−0.0661149	−	0.629041i	−0.00499782	−	0.0475510i
$176$	−2.30301	−	0.489519i	−0.173596	−	0.0368989i
$177$	12.3324	−	5.49073i	0.926958	−	0.412708i
$178$	1.63062	+	1.18471i	0.122220	+	0.0887981i
$179$	7.60872	+	3.38762i	0.568702	+	0.253203i	0.670883	−	0.741563i	$-0.265915\pi$
$179$	7.60872	+	3.38762i	0.568702	+	0.253203i	−0.102181	+	0.994766i	$0.532582\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	3.21857	−	5.57473i	0.239235	−	0.414366i	−0.721260	−	0.692664i	$-0.756437\pi$
$181$	3.21857	−	5.57473i	0.239235	−	0.414366i	0.960495	+	0.278298i	$0.0897702\pi$
$182$	−3.63083	+	2.63796i	−0.269135	+	0.195538i
$183$	−8.39583	+	1.78459i	−0.620637	+	0.131921i
$184$	−2.47764	−	7.62539i	−0.182654	−	0.562151i
$185$	3.38774			0.249072
$186$	−4.60411	+	3.13085i	−0.337590	+	0.229565i
$187$	−3.45154			−0.252402
$188$	0.894321	+	2.75244i	0.0652250	+	0.200742i
$189$	0.618684	−	0.131505i	0.0450027	−	0.00956561i
$190$	4.23467	−	3.07667i	0.307215	−	0.223205i
$191$	2.14506	−	3.71535i	0.155211	−	0.268833i	−0.777925	−	0.628357i	$-0.783728\pi$
$191$	2.14506	−	3.71535i	0.155211	−	0.268833i	0.933136	+	0.359524i	$0.117061\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−8.76279	−	3.90145i	−0.630759	−	0.280832i	0.0663506	−	0.997796i	$-0.478864\pi$
$193$	−8.76279	−	3.90145i	−0.630759	−	0.280832i	−0.697110	+	0.716964i	$0.745531\pi$
$194$	7.93389	+	5.76431i	0.569620	+	0.413853i
$195$	−6.48208	+	2.88601i	−0.464191	+	0.206671i
$196$	6.45571	+	1.37220i	0.461122	+	0.0980146i
$197$	−1.75310	−	16.6796i	−0.124903	−	1.18837i	−0.859958	−	0.510365i	$-0.829510\pi$
$197$	−1.75310	−	16.6796i	−0.124903	−	1.18837i	0.735055	−	0.678007i	$-0.237156\pi$
$198$	1.57544	−	1.74970i	0.111962	−	0.124346i
$199$	4.12118	+	4.57703i	0.292143	+	0.324457i	0.871293	−	0.490764i	$-0.163282\pi$
$199$	4.12118	+	4.57703i	0.292143	+	0.324457i	−0.579150	+	0.815221i	$0.696615\pi$
$200$	−0.104528	+	0.994522i	−0.00739128	+	0.0703233i
$201$	−0.524472	+	1.61416i	−0.0369934	+	0.113854i
$202$	−3.14159	+	9.66881i	−0.221041	+	0.680295i
$203$	−0.0601530	+	0.572318i	−0.00422191	+	0.0401688i
$204$	0.980918	+	1.08942i	0.0686780	+	0.0762747i
$205$	−1.35053	+	1.49992i	−0.0943253	+	0.104759i
$206$	1.64697	+	15.6699i	0.114750	+	1.09177i
$207$	7.84260	+	1.66700i	0.545098	+	0.115864i
$208$	6.48208	−	2.88601i	0.449451	−	0.200109i
$209$	9.97036	+	7.24389i	0.689664	+	0.501070i
$210$	−0.577823	−	0.257263i	−0.0398736	−	0.0177529i
$211$	10.4252	+	18.0569i	0.717698	+	1.24309i	0.961910	+	0.273367i	$0.0881375\pi$
$211$	10.4252	+	18.0569i	0.717698	+	1.24309i	−0.244212	+	0.969722i	$0.578529\pi$
$212$	−2.24897	+	3.89533i	−0.154460	+	0.267532i
$213$	−2.78304	+	2.02200i	−0.190691	+	0.138545i
$214$	8.66909	−	1.84267i	0.592606	−	0.125962i
$215$	−3.66471	−	11.2788i	−0.249931	−	0.769208i
$216$	−1.00000			−0.0680414
$217$	−1.19198	+	3.31378i	−0.0809169	+	0.224954i
$218$	−4.28791			−0.290414
$219$	−1.61866	−	4.98171i	−0.109379	−	0.336633i
$220$	−2.30301	+	0.489519i	−0.155269	+	0.0330034i
$221$	8.41519	−	6.11399i	0.566067	−	0.411272i
$222$	1.69387	−	2.93387i	0.113685	−	0.196909i
$223$	8.82244	+	15.2809i	0.590794	+	1.02329i	0.994126	+	0.108232i	$0.0345189\pi$
$223$	8.82244	+	15.2809i	0.590794	+	1.02329i	−0.403331	+	0.915054i	$0.632148\pi$
$224$	0.577823	+	0.257263i	0.0386074	+	0.0171891i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	3.66587	−	1.63215i	0.243850	−	0.108569i
$227$	18.3318	+	3.89654i	1.21672	+	0.258622i	0.771167	−	0.636633i	$-0.219673\pi$
$227$	18.3318	+	3.89654i	1.21672	+	0.258622i	0.445554	+	0.895255i	$0.353007\pi$
$228$	−0.547138	−	5.20567i	−0.0362351	−	0.344754i
$229$	17.7361	−	19.6980i	1.17204	−	1.30168i	0.227310	−	0.973822i	$-0.427007\pi$
$229$	17.7361	−	19.6980i	1.17204	−	1.30168i	0.944727	−	0.327857i	$-0.106326\pi$
$230$	−5.36496	−	5.95839i	−0.353755	−	0.392885i
$231$	0.155665	−	1.48105i	0.0102420	−	0.0974460i
$232$	0.281152	−	0.865295i	0.0184585	−	0.0568094i
$233$	6.34175	−	19.5179i	0.415462	−	1.27866i	−0.496375	−	0.868108i	$-0.665336\pi$
$233$	6.34175	−	19.5179i	0.415462	−	1.27866i	0.911837	−	0.410552i	$-0.134664\pi$
$234$	−0.741684	+	7.05665i	−0.0484854	+	0.461308i
$235$	1.93652	+	2.15072i	0.126325	+	0.140298i
$236$	−9.03290	+	10.0321i	−0.587992	+	0.653031i
$237$	−0.820502	−	7.80656i	−0.0532974	−	0.507091i
$238$	0.906966	+	0.192782i	0.0587899	+	0.0124962i
$239$	−10.3007	+	4.58615i	−0.666295	+	0.296653i	−0.711874	−	0.702307i	$-0.752153\pi$
$239$	−10.3007	+	4.58615i	−0.666295	+	0.296653i	0.0455793	+	0.998961i	$0.485487\pi$
$240$	0.809017	+	0.587785i	0.0522218	+	0.0379414i
$241$	16.8661	+	7.50929i	1.08644	+	0.483716i	0.870238	−	0.492632i	$-0.163965\pi$
$241$	16.8661	+	7.50929i	1.08644	+	0.483716i	0.216206	+	0.976348i	$0.430632\pi$
$242$	2.72826	+	4.72549i	0.175379	+	0.303766i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	6.94411	−	5.04519i	0.444551	−	0.322985i
$245$	6.45571	−	1.37220i	0.412440	−	0.0876669i
$246$	0.623701	+	1.91955i	0.0397657	+	0.122386i
$247$	−37.1404			−2.36319
$248$	2.93263	−	4.73283i	0.186222	−	0.300535i
$249$	1.37914			0.0873991
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−6.14894	+	1.30700i	−0.388118	+	0.0824970i	−0.397838	−	0.917456i	$-0.630239\pi$
$251$	−6.14894	+	1.30700i	−0.388118	+	0.0824970i	0.00972003	+	0.999953i	$0.496906\pi$
$252$	−0.511708	+	0.371778i	−0.0322346	+	0.0234198i
$253$	9.43880	−	16.3485i	0.593412	−	1.02782i
$254$	−6.04316	−	10.4671i	−0.379182	−	0.656762i
$255$	1.33922	+	0.596259i	0.0838652	+	0.0373392i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	3.88559	−	1.72998i	0.242377	−	0.107913i	−0.281954	−	0.959428i	$-0.590982\pi$
$257$	3.88559	−	1.72998i	0.242377	−	0.107913i	0.524330	+	0.851515i	$0.324316\pi$
$258$	−11.6001	−	2.46567i	−0.722190	−	0.153506i
$259$	−0.223980	−	2.13103i	−0.0139175	−	0.132416i
$260$	4.74783	−	5.27300i	0.294448	−	0.327017i
$261$	0.608792	+	0.676132i	0.0376833	+	0.0418515i
$262$	2.11240	−	20.0982i	0.130505	−	1.24167i
$263$	4.16609	−	12.8219i	0.256892	−	0.790633i	−0.736559	−	0.676374i	$-0.763550\pi$
$263$	4.16609	−	12.8219i	0.256892	−	0.790633i	0.993451	−	0.114259i	$-0.0364495\pi$
$264$	−0.727568	+	2.23922i	−0.0447787	+	0.137815i
$265$	−0.470162	+	4.47330i	−0.0288818	+	0.274792i
$266$	−2.21533	−	2.46037i	−0.135830	−	0.150855i
$267$	1.34867	−	1.49785i	0.0825373	−	0.0916670i
$268$	−0.177409	−	1.68793i	−0.0108370	−	0.103107i
$269$	−18.1990	−	3.86832i	−1.10961	−	0.235856i	−0.383575	−	0.923510i	$-0.625307\pi$
$269$	−18.1990	−	3.86832i	−1.10961	−	0.235856i	−0.726038	+	0.687654i	$0.758640\pi$
$270$	−0.913545	+	0.406737i	−0.0555966	+	0.0247532i
$271$	−11.0495	−	8.02793i	−0.671209	−	0.487662i	0.199220	−	0.979955i	$-0.436159\pi$
$271$	−11.0495	−	8.02793i	−0.671209	−	0.487662i	−0.870430	+	0.492293i	$0.836159\pi$
$272$	−1.33922	−	0.596259i	−0.0812022	−	0.0361535i
$273$	2.24398	+	3.88669i	0.135812	+	0.235233i
$274$	8.94530	−	15.4937i	0.540405	−	0.936009i
$275$	−1.90480	+	1.38392i	−0.114864	+	0.0834533i
$276$	−7.84260	+	1.66700i	−0.472069	+	0.100341i
$277$	2.72346	+	8.38194i	0.163637	+	0.503622i	0.998933	−	0.0461776i	$-0.0147040\pi$
$277$	2.72346	+	8.38194i	0.163637	+	0.503622i	−0.835296	+	0.549800i	$0.814704\pi$
$278$	−2.73613			−0.164102
$279$	2.63243	+	4.90615i	0.157600	+	0.293723i
$280$	0.632506			0.0377995
$281$	−9.86047	−	30.3474i	−0.588226	−	1.81037i	−0.585908	−	0.810377i	$-0.699262\pi$
$281$	−9.86047	−	30.3474i	−0.588226	−	1.81037i	−0.00231831	−	0.999997i	$-0.500738\pi$
$282$	2.83084	−	0.601714i	0.168574	−	0.0358315i
$283$	−9.15415	+	6.65088i	−0.544158	+	0.395354i	−0.825627	−	0.564217i	$-0.809178\pi$
$283$	−9.15415	+	6.65088i	−0.544158	+	0.395354i	0.281469	+	0.959570i	$0.409178\pi$
$284$	1.72001	−	2.97915i	0.102064	−	0.176780i
$285$	−2.61717	−	4.53307i	−0.155028	−	0.268516i
$286$	15.2618	+	6.79498i	0.902448	+	0.401796i
$287$	1.03280	+	0.750373i	0.0609643	+	0.0442931i
$288$	0.913545	−	0.406737i	0.0538312	−	0.0239672i
$289$	14.5264	+	3.08769i	0.854496	+	0.181629i
$290$	−0.0951027	−	0.904841i	−0.00558462	−	0.0531341i
$291$	6.56205	−	7.28789i	0.384674	−	0.427224i
$292$	3.50496	+	3.89265i	0.205112	+	0.227800i
$293$	1.13784	−	10.8258i	0.0664734	−	0.632452i	−0.909671	−	0.415330i	$-0.863666\pi$
$293$	1.13784	−	10.8258i	0.0664734	−	0.632452i	0.976144	−	0.217123i	$-0.0696671\pi$
$294$	2.03949	−	6.27691i	0.118946	−	0.366077i
$295$	−4.17156	+	12.8388i	−0.242878	+	0.747501i
$296$	−0.354116	+	3.36919i	−0.0205826	+	0.195830i
$297$	−1.57544	−	1.74970i	−0.0914163	−	0.101528i
$298$	4.86414	−	5.40218i	0.281772	−	0.312940i
$299$	5.94668	+	56.5789i	0.343905	+	3.27204i
$300$	0.978148	+	0.207912i	0.0564734	+	0.0120038i
$301$	−6.85254	+	3.05095i	−0.394974	+	0.175854i
$302$	10.9294	+	7.94066i	0.628915	+	0.456934i
$303$	9.28746	+	4.13504i	0.533551	+	0.237552i
$304$	2.61717	+	4.53307i	0.150105	+	0.259990i
$305$	4.29170	−	7.43344i	0.245742	−	0.425637i
$306$	1.18599	−	0.861669i	0.0677983	−	0.0492584i
$307$	−33.2960	+	7.07729i	−1.90031	+	0.403922i	−0.999538	−	0.0303798i	$-0.990328\pi$
$307$	−33.2960	+	7.07729i	−1.90031	+	0.403922i	−0.900767	+	0.434302i	$0.856995\pi$
$308$	0.460191	+	1.41632i	0.0262218	+	0.0807024i
$309$	15.7562			0.896338
$310$	0.754078	−	5.51646i	0.0428287	−	0.313314i
$311$	−32.6647			−1.85224			−0.926122	−	0.377223i	$-0.876879\pi$
$311$	−32.6647			−1.85224			−0.926122	+	0.377223i	$0.876879\pi$
$312$	−2.19264	−	6.74824i	−0.124134	−	0.382044i
$313$	9.01016	−	1.91517i	0.509284	−	0.108252i	0.0538994	−	0.998546i	$-0.482835\pi$
$313$	9.01016	−	1.91517i	0.509284	−	0.108252i	0.455385	+	0.890295i	$0.349502\pi$
$314$	14.9605	−	10.8695i	0.844271	−	0.613399i
$315$	−0.316253	+	0.547766i	−0.0178188	+	0.0308631i
$316$	3.92478	+	6.79792i	0.220786	+	0.382413i
$317$	−7.68374	−	3.42102i	−0.431562	−	0.192144i	0.179447	−	0.983768i	$-0.442569\pi$
$317$	−7.68374	−	3.42102i	−0.431562	−	0.192144i	−0.611009	+	0.791624i	$0.709236\pi$
$318$	3.63891	+	2.64382i	0.204060	+	0.148258i
$319$	1.95695	−	0.871289i	0.109568	−	0.0487828i
$320$	−0.978148	−	0.207912i	−0.0546801	−	0.0116226i
$321$	−0.926410	−	8.81421i	−0.0517072	−	0.491961i
$322$	−3.39337	+	3.76872i	−0.189105	+	0.210023i
$323$	5.13446	+	5.70240i	0.285689	+	0.317290i
$324$	−0.104528	+	0.994522i	−0.00580714	+	0.0552512i
$325$	2.19264	−	6.74824i	0.121626	−	0.374325i
$326$	5.84391	−	17.9857i	0.323664	−	0.996136i
$327$	−0.448208	+	4.26442i	−0.0247860	+	0.235823i
$328$	−1.35053	−	1.49992i	−0.0745707	−	0.0828191i
$329$	1.22486	−	1.36035i	0.0675287	−	0.0749983i
$330$	0.246108	+	2.34156i	0.0135478	+	0.128899i
$331$	21.6169	+	4.59481i	1.18817	+	0.252554i	0.759257	−	0.650791i	$-0.225563\pi$
$331$	21.6169	+	4.59481i	1.18817	+	0.252554i	0.428915	+	0.903345i	$0.358896\pi$
$332$	−1.25990	+	0.560945i	−0.0691461	+	0.0307858i
$333$	−2.74074	−	1.99127i	−0.150192	−	0.109121i
$334$	−1.87099	−	0.833020i	−0.102376	−	0.0455808i
$335$	−0.848614	−	1.46984i	−0.0463647	−	0.0803061i
$336$	0.316253	−	0.547766i	0.0172530	−	0.0298831i
$337$	−3.04543	+	2.21263i	−0.165895	+	0.120530i	−0.667635	−	0.744489i	$-0.732693\pi$
$337$	−3.04543	+	2.21263i	−0.165895	+	0.120530i	0.501740	+	0.865018i	$0.332693\pi$
$338$	−36.5303	+	7.76475i	−1.98699	+	0.422347i
$339$	−1.24002	−	3.81640i	−0.0673488	−	0.207278i
$340$	−1.46596			−0.0795028
$341$	12.9012	−	2.32505i	0.698641	−	0.125909i
$342$	−5.23434			−0.283041
$343$	−2.65818	−	8.18103i	−0.143528	−	0.441734i
$344$	11.6001	−	2.46567i	0.625435	−	0.132940i
$345$	−6.48654	+	4.71275i	−0.349224	+	0.253726i
$346$	1.20477	−	2.08673i	0.0647690	−	0.112183i
$347$	−1.00461	−	1.74004i	−0.0539305	−	0.0934103i	0.837800	−	0.545978i	$-0.183842\pi$
$347$	−1.00461	−	1.74004i	−0.0539305	−	0.0934103i	−0.891730	+	0.452567i	$0.850508\pi$
$348$	−0.831167	−	0.370059i	−0.0445552	−	0.0198373i
$349$	−3.49992	−	2.54284i	−0.187347	−	0.136115i	0.490159	−	0.871633i	$-0.336939\pi$
$349$	−3.49992	−	2.54284i	−0.187347	−	0.136115i	−0.677505	+	0.735518i	$0.736939\pi$
$350$	0.577823	−	0.257263i	0.0308859	−	0.0137513i
$351$	6.94047	+	1.47524i	0.370455	+	0.0787426i
$352$	−0.246108	−	2.34156i	−0.0131176	−	0.124806i
$353$	−14.9156	+	16.5655i	−0.793878	+	0.881691i	−0.995203	−	0.0978337i	$-0.968809\pi$
$353$	−14.9156	+	16.5655i	−0.793878	+	0.881691i	0.201325	+	0.979525i	$0.435475\pi$
$354$	9.03290	+	10.0321i	0.480093	+	0.533198i
$355$	0.359580	−	3.42118i	0.0190845	−	0.181577i
$356$	−0.622841	+	1.91691i	−0.0330105	+	0.101596i
$357$	0.286529	−	0.881846i	0.0151647	−	0.0466723i
$358$	−0.870595	+	8.28315i	−0.0460124	+	0.437778i
$359$	18.0188	+	20.0119i	0.950995	+	1.05619i	0.998356	+	0.0573094i	$0.0182521\pi$
$359$	18.0188	+	20.0119i	0.950995	+	1.05619i	−0.0473612	+	0.998878i	$0.515081\pi$
$360$	0.669131	−	0.743145i	0.0352663	−	0.0391672i
$361$	−0.877866	−	8.35234i	−0.0462035	−	0.439597i
$362$	6.29648	+	1.33836i	0.330935	+	0.0703425i
$363$	4.98479	−	2.21937i	0.261633	−	0.116487i
$364$	−3.63083	−	2.63796i	−0.190307	−	0.138266i
$365$	4.78523	+	2.13052i	0.250470	+	0.111516i
$366$	−4.29170	−	7.43344i	−0.224331	−	0.388552i
$367$	9.52782	−	16.5027i	0.497348	−	0.861432i	−0.502647	−	0.864492i	$-0.667640\pi$
$367$	9.52782	−	16.5027i	0.497348	−	0.861432i	0.999995	+	0.00305935i	$0.000973824\pi$
$368$	6.48654	−	4.71275i	0.338134	−	0.245669i
$369$	1.97423	−	0.419636i	0.102774	−	0.0218454i
$370$	1.04687	+	3.22194i	0.0544242	+	0.167501i
$371$	2.84497			0.147704
$372$	−4.40036	−	3.41128i	−0.228148	−	0.176867i
$373$	−4.57149			−0.236703			−0.118351	−	0.992972i	$-0.537761\pi$
$373$	−4.57149			−0.236703			−0.118351	+	0.992972i	$0.537761\pi$
$374$	−1.06658	−	3.28261i	−0.0551518	−	0.169740i
$375$	0.978148	−	0.207912i	0.0505113	−	0.0107365i
$376$	−2.34136	+	1.70110i	−0.120747	+	0.0877275i
$377$	−3.22784	+	5.59079i	−0.166242	+	0.287940i
$378$	0.316253	+	0.547766i	0.0162663	+	0.0281741i
$379$	17.7708	+	7.91207i	0.912825	+	0.406416i	0.808749	−	0.588154i	$-0.200145\pi$
$379$	17.7708	+	7.91207i	0.912825	+	0.406416i	0.104075	+	0.994569i	$0.466812\pi$
$380$	4.23467	+	3.07667i	0.217234	+	0.157830i
$381$	−11.0414	+	4.91595i	−0.565669	+	0.251852i
$382$	4.19637	+	0.891966i	0.214705	+	0.0456369i
$383$	−1.89274	−	18.0082i	−0.0967144	−	0.920176i	−0.930056	−	0.367418i	$-0.880242\pi$
$383$	−1.89274	−	18.0082i	−0.0967144	−	0.920176i	0.833342	−	0.552758i	$-0.186425\pi$
$384$	−0.669131	+	0.743145i	−0.0341464	+	0.0379235i
$385$	0.996475	+	1.10670i	0.0507851	+	0.0564025i
$386$	1.00264	−	9.53952i	0.0510332	−	0.485549i
$387$	−3.66471	+	11.2788i	−0.186287	+	0.573334i
$388$	−3.03048	+	9.32685i	−0.153849	+	0.473499i
$389$	−1.49261	+	14.2013i	−0.0756785	+	0.720033i	0.889233	+	0.457455i	$0.151239\pi$
$389$	−1.49261	+	14.2013i	−0.0756785	+	0.720033i	−0.964911	+	0.262577i	$0.915428\pi$
$390$	−4.74783	−	5.27300i	−0.240416	−	0.267009i
$391$	7.86482	−	8.73476i	0.397741	−	0.441736i
$392$	0.689881	+	6.56378i	0.0348443	+	0.331521i
$393$	−19.7673	−	4.20166i	−0.997127	−	0.211946i
$394$	15.3215	−	6.82157i	0.771886	−	0.343666i
$395$	6.35043	+	4.61386i	0.319525	+	0.232148i
$396$	2.15090	+	0.957644i	0.108087	+	0.0481234i
$397$	−9.97632	−	17.2795i	−0.500697	−	0.867233i	−1.00000		0.000805416i	$-0.999744\pi$
$397$	−9.97632	−	17.2795i	−0.500697	−	0.867233i	0.499302	−	0.866428i	$-0.333590\pi$
$398$	−3.07950	+	5.33386i	−0.154362	+	0.267362i
$399$	−2.67846	+	1.94601i	−0.134091	+	0.0974225i
$400$	−0.978148	+	0.207912i	−0.0489074	+	0.0103956i
$401$	9.02574	+	27.7784i	0.450724	+	1.38719i	0.876083	+	0.482161i	$0.160148\pi$
$401$	9.02574	+	27.7784i	0.450724	+	1.38719i	−0.425359	+	0.905025i	$0.639852\pi$
$402$	−1.69723			−0.0846500
$403$	−27.3359	+	28.5217i	−1.36170	+	1.42077i
$404$	−10.1664			−0.505797
$405$	0.309017	+	0.951057i	0.0153552	+	0.0472584i
$406$	−0.562895	+	0.119647i	−0.0279360	+	0.00593798i
$407$	−6.45297	+	4.68835i	−0.319862	+	0.232393i
$408$	−0.732980	+	1.26956i	−0.0362879	+	0.0628525i
$409$	−18.7606	−	32.4944i	−0.927653	−	1.60674i	−0.787238	−	0.616650i	$-0.788489\pi$
$409$	−18.7606	−	32.4944i	−0.927653	−	1.60674i	−0.140416	−	0.990093i	$-0.544844\pi$
$410$	−1.84384	−	0.820932i	−0.0910610	−	0.0405430i
$411$	−14.4738	−	10.5158i	−0.713940	−	0.518707i
$412$	−14.3940	+	6.40862i	−0.709141	+	0.315730i
$413$	8.35190	+	1.77525i	0.410970	+	0.0873544i
$414$	0.838089	+	7.97389i	0.0411898	+	0.391895i
$415$	−0.922822	+	1.02490i	−0.0452995	+	0.0503102i
$416$	4.74783	+	5.27300i	0.232781	+	0.258530i
$417$	−0.286004	+	2.72114i	−0.0140057	+	0.133255i
$418$	−3.80834	+	11.7209i	−0.186272	+	0.573286i
$419$	−4.64205	+	14.2868i	−0.226779	+	0.697955i	0.771327	+	0.636439i	$0.219593\pi$
$419$	−4.64205	+	14.2868i	−0.226779	+	0.697955i	−0.998106	+	0.0615154i	$0.980407\pi$
$420$	0.0661149	−	0.629041i	0.00322608	−	0.0306941i
$421$	13.7917	+	15.3173i	0.672168	+	0.746518i	0.978689	−	0.205346i	$-0.0658319\pi$
$421$	13.7917	+	15.3173i	0.672168	+	0.746518i	−0.306522	+	0.951864i	$0.599165\pi$
$422$	−13.9516	+	15.4948i	−0.679153	+	0.754276i
$423$	−0.302514	−	2.87823i	−0.0147087	−	0.139944i
$424$	−4.39964	−	0.935173i	−0.213666	−	0.0454160i
$425$	−1.33922	+	0.596259i	−0.0649617	+	0.0289228i
$426$	−2.78304	−	2.02200i	−0.134839	−	0.0979660i
$427$	−4.95968	−	2.20819i	−0.240016	−	0.106862i
$428$	4.43138	+	7.67537i	0.214199	+	0.371003i
$429$	8.35305	−	14.4679i	0.403289	−	0.698517i
$430$	9.59433	−	6.97069i	0.462679	−	0.336156i
$431$	−35.8154	+	7.61280i	−1.72517	+	0.366696i	−0.960619	−	0.277869i	$-0.910372\pi$
$431$	−35.8154	+	7.61280i	−1.72517	+	0.366696i	−0.764549	+	0.644565i	$0.777038\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	24.7457			1.18920			0.594601	−	0.804021i	$-0.297310\pi$
$433$	24.7457			1.18920			0.594601	+	0.804021i	$0.297310\pi$
$434$	−3.51994	−	0.109625i	−0.168962	−	0.00526219i
$435$	−0.909825			−0.0436228
$436$	−1.32504	−	4.07804i	−0.0634577	−	0.195303i
$437$	−41.0509	+	8.72563i	−1.96373	+	0.417403i
$438$	4.23770	−	3.07887i	0.202485	−	0.147114i
$439$	−14.9247	+	25.8504i	−0.712318	+	1.23377i	0.251667	+	0.967814i	$0.419021\pi$
$439$	−14.9247	+	25.8504i	−0.712318	+	1.23377i	−0.963985	+	0.265957i	$0.914312\pi$
$440$	−1.17723	−	2.03902i	−0.0561222	−	0.0972065i
$441$	−6.02934	−	2.68444i	−0.287112	−	0.127830i
$442$	8.41519	+	6.11399i	0.400270	+	0.290813i
$443$	−25.2439	+	11.2393i	−1.19937	+	0.533995i	−0.906520	−	0.422163i	$-0.861271\pi$
$443$	−25.2439	+	11.2393i	−1.19937	+	0.533995i	−0.292852	+	0.956158i	$0.594604\pi$
$444$	3.31371	+	0.704352i	0.157262	+	0.0334271i
$445$	0.210683	+	2.00452i	0.00998734	+	0.0950232i
$446$	−11.8067	+	13.1127i	−0.559065	+	0.620905i
$447$	−4.86414	−	5.40218i	−0.230066	−	0.255514i
$448$	−0.0661149	+	0.629041i	−0.00312363	+	0.0297194i
$449$	−4.64243	+	14.2879i	−0.219090	+	0.674290i	0.779748	+	0.626094i	$0.215347\pi$
$449$	−4.64243	+	14.2879i	−0.219090	+	0.674290i	−0.998838	+	0.0481961i	$0.984653\pi$
$450$	0.309017	−	0.951057i	0.0145672	−	0.0448332i
$451$	0.496729	−	4.72606i	0.0233901	−	0.222542i
$452$	2.68509	+	2.98209i	0.126296	+	0.140266i
$453$	9.03959	−	10.0395i	0.424717	−	0.471696i
$454$	1.95900	+	18.6386i	0.0919404	+	0.874754i
$455$	−4.38989	−	0.933099i	−0.205801	−	0.0437444i
$456$	4.78181	−	2.12900i	0.223929	−	0.0996995i
$457$	−6.42975	−	4.67149i	−0.300771	−	0.218523i	0.427155	−	0.904178i	$-0.359516\pi$
$457$	−6.42975	−	4.67149i	−0.300771	−	0.218523i	−0.727926	+	0.685655i	$0.759516\pi$
$458$	24.2147	+	10.7811i	1.13148	+	0.503766i
$459$	−0.732980	−	1.26956i	−0.0342126	−	0.0592579i
$460$	4.00890	−	6.94363i	0.186916	−	0.323748i
$461$	−8.99665	+	6.53645i	−0.419016	+	0.304433i	−0.777242	−	0.629202i	$-0.783382\pi$
$461$	−8.99665	+	6.53645i	−0.419016	+	0.304433i	0.358226	+	0.933635i	$0.383382\pi$
$462$	1.45667	−	0.309624i	0.0677702	−	0.0144050i
$463$	−3.25770	−	10.0262i	−0.151398	−	0.465956i	0.846380	−	0.532579i	$-0.178777\pi$
$463$	−3.25770	−	10.0262i	−0.151398	−	0.465956i	−0.997778	+	0.0666238i	$0.978777\pi$
$464$	0.909825			0.0422376
$465$	−5.40742	−	1.32657i	−0.250763	−	0.0615184i
$466$	20.5223			0.950679
$467$	10.8100	+	33.2698i	0.500227	+	1.53954i	0.808649	+	0.588291i	$0.200199\pi$
$467$	10.8100	+	33.2698i	0.500227	+	1.53954i	−0.308422	+	0.951250i	$0.599801\pi$
$468$	−6.94047	+	1.47524i	−0.320823	+	0.0681931i
$469$	−0.868485	+	0.630992i	−0.0401029	+	0.0291365i
$470$	−1.44704	+	2.50635i	−0.0667470	+	0.115609i
$471$	−9.24611	−	16.0147i	−0.426038	−	0.737920i
$472$	−12.3324	−	5.49073i	−0.567643	−	0.252731i
$473$	22.5894	+	16.4122i	1.03866	+	0.754633i
$474$	7.17093	−	3.19270i	0.329372	−	0.146646i
$475$	5.11996	+	1.08828i	0.234920	+	0.0499338i
$476$	0.0969217	+	0.922149i	0.00444240	+	0.0422666i
$477$	3.00971	−	3.34262i	0.137805	−	0.153048i
$478$	−7.54477	−	8.37932i	−0.345090	−	0.383261i
$479$	2.59999	−	24.7373i	0.118797	−	1.13028i	−0.758949	−	0.651150i	$-0.774287\pi$
$479$	2.59999	−	24.7373i	0.118797	−	1.13028i	0.877746	−	0.479126i	$-0.159046\pi$
$480$	−0.309017	+	0.951057i	−0.0141046	+	0.0434096i
$481$	7.42809	−	22.8613i	0.338692	−	1.04239i
$482$	−1.92983	+	18.3612i	−0.0879016	+	0.836328i
$483$	3.39337	+	3.76872i	0.154404	+	0.171483i
$484$	−3.65113	+	4.05499i	−0.165960	+	0.184318i
$485$	1.02509	+	9.75311i	0.0465471	+	0.442866i
$486$	0.978148	+	0.207912i	0.0443697	+	0.00943107i
$487$	−2.15262	+	0.958410i	−0.0975447	+	0.0434297i	−0.454929	−	0.890528i	$-0.650335\pi$
$487$	−2.15262	+	0.958410i	−0.0975447	+	0.0434297i	0.357384	+	0.933957i	$0.383669\pi$
$488$	6.94411	+	5.04519i	0.314345	+	0.228385i
$489$	−17.2763	−	7.69191i	−0.781262	−	0.347840i
$490$	3.29997	+	5.71571i	0.149077	+	0.258210i
$491$	4.99547	−	8.65241i	0.225442	−	0.390478i	−0.731010	−	0.682367i	$-0.760951\pi$
$491$	4.99547	−	8.65241i	0.225442	−	0.390478i	0.956452	+	0.291889i	$0.0942839\pi$
$492$	−1.63287	+	1.18635i	−0.0736155	+	0.0534848i
$493$	1.30462	−	0.277306i	0.0587572	−	0.0124892i
$494$	−11.4770	−	35.3226i	−0.516375	−	1.58924i
$495$	2.35446			0.105825
$496$	5.40742	+	1.32657i	0.242800	+	0.0595649i
$497$	−2.17584			−0.0975996
$498$	0.426176	+	1.31164i	0.0190974	+	0.0587758i
$499$	−36.6321	+	7.78640i	−1.63988	+	0.348567i	−0.933309	−	0.359075i	$-0.883092\pi$
$499$	−36.6321	+	7.78640i	−1.63988	+	0.348567i	−0.706571	+	0.707642i	$0.749759\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$	−1.02403	+	1.77367i	−0.0457502	+	0.0792417i
$502$	−3.14316	−	5.44411i	−0.140286	−	0.242982i
$503$	4.26187	+	1.89751i	0.190028	+	0.0846057i	0.499545	−	0.866288i	$-0.333501\pi$
$503$	4.26187	+	1.89751i	0.190028	+	0.0846057i	−0.309517	+	0.950894i	$0.600167\pi$
$504$	−0.511708	−	0.371778i	−0.0227933	−	0.0165603i
$505$	−9.28746	+	4.13504i	−0.413287	+	0.184007i
$506$	18.4651	+	3.92487i	0.820873	+	0.174482i
$507$	3.90376	+	37.1418i	0.173372	+	1.64953i
$508$	8.08733	−	8.98189i	0.358817	−	0.398507i
$509$	22.7717	+	25.2905i	1.00934	+	1.12098i	0.992638	+	0.121123i	$0.0386496\pi$
$509$	22.7717	+	25.2905i	1.00934	+	1.12098i	0.0167007	+	0.999861i	$0.494684\pi$
$510$	−0.153234	+	1.45793i	−0.00678534	+	0.0645582i
$511$	1.02381	−	3.15096i	0.0452907	−	0.139390i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−0.547138	+	5.20567i	−0.0241567	+	0.229836i
$514$	2.84602	+	3.16082i	0.125533	+	0.139418i
$515$	−10.5429	+	11.7091i	−0.464578	+	0.515966i
$516$	−1.23963	−	11.7943i	−0.0545716	−	0.519214i
$517$	−6.66510	−	1.41671i	−0.293131	−	0.0623068i
$518$	1.95752	−	0.871543i	0.0860084	−	0.0382934i
$519$	−1.94936	−	1.41630i	−0.0855676	−	0.0621685i
$520$	6.48208	+	2.88601i	0.284258	+	0.126560i
$521$	14.1083	+	24.4363i	0.618095	+	1.07057i	0.989833	+	0.142234i	$0.0454286\pi$
$521$	14.1083	+	24.4363i	0.618095	+	1.07057i	−0.371738	+	0.928338i	$0.621238\pi$
$522$	−0.454913	+	0.787932i	−0.0199110	+	0.0344868i
$523$	−10.5846	+	7.69016i	−0.462832	+	0.336267i	−0.794641	−	0.607079i	$-0.792341\pi$
$523$	−10.5846	+	7.69016i	−0.462832	+	0.336267i	0.331809	+	0.943347i	$0.392341\pi$
$524$	19.7673	−	4.20166i	0.863537	−	0.183551i
$525$	−0.195455	−	0.601549i	−0.00853036	−	0.0262537i
$526$	13.4818			0.587833
$527$	8.15816	+	0.254079i	0.355375	+	0.0110679i
$528$	−2.35446			−0.102465
$529$	12.7578	+	39.2646i	0.554689	+	1.70716i
$530$	−4.39964	+	0.935173i	−0.191108	+	0.0406213i
$531$	10.9213	−	7.93478i	0.473944	−	0.344340i
$532$	1.65538	−	2.86720i	0.0717697	−	0.124309i
$533$	7.16058	+	12.4025i	0.310159	+	0.537211i
$534$	1.84130	+	0.819801i	0.0796810	+	0.0354763i
$535$	7.17012	+	5.20940i	0.309991	+	0.225222i
$536$	1.55049	−	0.690325i	0.0669712	−	0.0298175i
$537$	8.14678	+	1.73165i	0.351559	+	0.0747262i
$538$	−1.94481	−	18.5037i	−0.0838468	−	0.797749i
$539$	−10.3978	+	11.5479i	−0.447865	+	0.497405i
$540$	−0.669131	−	0.743145i	−0.0287948	−	0.0319799i
$541$	−3.07862	+	29.2911i	−0.132360	+	1.25932i	0.703625	+	0.710572i	$0.251564\pi$
$541$	−3.07862	+	29.2911i	−0.132360	+	1.25932i	−0.835985	+	0.548752i	$0.815103\pi$
$542$	4.22053	−	12.9895i	0.181287	−	0.557945i
$543$	1.98919	−	6.12209i	0.0853642	−	0.262724i
$544$	0.153234	−	1.45793i	0.00656987	−	0.0625082i
$545$	−2.86917	−	3.18653i	−0.122902	−	0.136496i
$546$	−3.00303	+	3.33520i	−0.128518	+	0.142734i
$547$	3.56853	+	33.9523i	0.152579	+	1.45170i	0.756157	+	0.654391i	$0.227075\pi$
$547$	3.56853	+	33.9523i	0.152579	+	1.45170i	−0.603577	+	0.797305i	$0.706258\pi$
$548$	17.4996	+	3.71966i	0.747548	+	0.158896i
$549$	−7.84132	+	3.49118i	−0.334659	+	0.149000i
$550$	−1.90480	−	1.38392i	−0.0812208	−	0.0590104i
$551$	−4.35061	−	1.93702i	−0.185342	−	0.0825197i
$552$	−4.00890	−	6.94363i	−0.170630	−	0.295540i
$553$	2.48245	−	4.29972i	0.105564	−	0.182843i
$554$	−7.13011	+	5.18033i	−0.302929	+	0.220091i
$555$	3.31371	−	0.704352i	0.140659	−	0.0298981i
$556$	−0.845511	−	2.60222i	−0.0358577	−	0.110359i
$557$	29.7835			1.26197			0.630984	−	0.775796i	$-0.282651\pi$
$557$	29.7835			1.26197			0.630984	+	0.775796i	$0.282651\pi$
$558$	−3.85256	+	4.01968i	−0.163092	+	0.170166i
$559$	−84.1475			−3.55906
$560$	0.195455	+	0.601549i	0.00825949	+	0.0254201i
$561$	−3.37612	+	0.717616i	−0.142540	+	0.0302978i
$562$	25.8151	−	18.7557i	1.08894	−	0.791163i
$563$	14.6808	−	25.4280i	0.618723	−	1.07166i	−0.370996	−	0.928635i	$-0.620983\pi$
$563$	14.6808	−	25.4280i	0.618723	−	1.07166i	0.989719	−	0.143026i	$-0.0456832\pi$
$564$	1.44704	+	2.50635i	0.0609314	+	0.105536i
$565$	3.66587	+	1.63215i	0.154224	+	0.0686651i
$566$	−9.15415	−	6.65088i	−0.384777	−	0.279557i
$567$	0.577823	−	0.257263i	0.0242663	−	0.0108040i
$568$	3.36485	+	0.715221i	0.141186	+	0.0300100i
$569$	1.05670	+	10.0539i	0.0442993	+	0.421480i	0.994087	+	0.108585i	$0.0346320\pi$
$569$	1.05670	+	10.0539i	0.0442993	+	0.421480i	−0.949788	+	0.312895i	$0.898701\pi$
$570$	3.50246	−	3.88987i	0.146702	−	0.162929i
$571$	11.5681	+	12.8477i	0.484112	+	0.537661i	0.934872	−	0.354984i	$-0.115514\pi$
$571$	11.5681	+	12.8477i	0.484112	+	0.537661i	−0.450760	+	0.892645i	$0.648847\pi$
$572$	−1.74626	+	16.6146i	−0.0730149	+	0.694691i
$573$	1.32572	−	4.08014i	0.0553827	−	0.170450i
$574$	−0.394495	+	1.21413i	−0.0164659	+	0.0506768i
$575$	0.838089	−	7.97389i	0.0349507	−	0.332534i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	−0.863435	+	0.958942i	−0.0359453	+	0.0399213i	−0.760849	−	0.648929i	$-0.775217\pi$
$577$	−0.863435	+	0.958942i	−0.0359453	+	0.0399213i	0.724904	+	0.688850i	$0.241884\pi$
$578$	1.55235	+	14.7696i	0.0645692	+	0.614335i
$579$	−9.38246	−	1.99430i	−0.389922	−	0.0828804i
$580$	0.831167	−	0.370059i	0.0345123	−	0.0153659i
$581$	0.705715	+	0.512732i	0.0292780	+	0.0212717i
$582$	8.95898	+	3.98880i	0.371362	+	0.165341i
$583$	−5.29510	−	9.17138i	−0.219301	−	0.379840i
$584$	−2.61904	+	4.53631i	−0.108377	+	0.187714i
$585$	−5.74040	+	4.17064i	−0.237336	+	0.172435i
$586$	10.6476	−	2.26322i	0.439848	−	0.0934926i
$587$	−9.93860	−	30.5879i	−0.410210	−	1.26250i	−0.916466	−	0.400113i	$-0.868971\pi$
$587$	−9.93860	−	30.5879i	−0.410210	−	1.26250i	0.506256	−	0.862384i	$-0.331029\pi$
$588$	6.59994			0.272177
$589$	−23.0330	−	17.8558i	−0.949058	−	0.735736i
$590$	−13.4995			−0.555764
$591$	−5.18267	−	15.9506i	−0.213187	−	0.656121i
$592$	−3.31371	+	0.704352i	−0.136193	+	0.0289487i
$593$	17.9793	−	13.0628i	0.738323	−	0.536423i	−0.153862	−	0.988092i	$-0.549171\pi$
$593$	17.9793	−	13.0628i	0.738323	−	0.536423i	0.892186	+	0.451669i	$0.149171\pi$
$594$	1.17723	−	2.03902i	0.0483023	−	0.0836620i
$595$	0.463614	+	0.803003i	0.0190063	+	0.0329199i
$596$	6.64088	+	2.95671i	0.272021	+	0.121112i
$597$	4.98274	+	3.62017i	0.203930	+	0.148164i
$598$	−51.9721	+	23.1395i	−2.12530	+	0.946243i
$599$	3.06017	+	0.650459i	0.125035	+	0.0265771i	0.270004	−	0.962859i	$-0.412975\pi$
$599$	3.06017	+	0.650459i	0.125035	+	0.0265771i	−0.144969	+	0.989436i	$0.546308\pi$
$600$	0.104528	+	0.994522i	0.00426736	+	0.0406012i
$601$	6.24786	−	6.93895i	0.254855	−	0.283046i	−0.602117	−	0.798408i	$-0.705676\pi$
$601$	6.24786	−	6.93895i	0.254855	−	0.283046i	0.856972	+	0.515362i	$0.172343\pi$
$602$	−5.01917	−	5.57436i	−0.204566	−	0.227194i
$603$	−0.177409	+	1.68793i	−0.00722464	+	0.0687378i
$604$	−4.17465	+	12.8483i	−0.169864	+	0.522788i
$605$	−1.68616	+	5.18947i	−0.0685521	+	0.210982i
$606$	−1.06268	+	10.1107i	−0.0431683	+	0.410719i
$607$	15.0051	+	16.6649i	0.609040	+	0.676407i	0.966247	−	0.257618i	$-0.0829376\pi$
$607$	15.0051	+	16.6649i	0.609040	+	0.676407i	−0.357207	+	0.934025i	$0.616271\pi$
$608$	−3.50246	+	3.88987i	−0.142043	+	0.157755i
$609$	0.0601530	+	0.572318i	0.00243752	+	0.0231915i
$610$	8.39583	+	1.78459i	0.339937	+	0.0722559i
$611$	18.7597	−	8.35235i	0.758935	−	0.337900i
$612$	1.18599	+	0.861669i	0.0479406	+	0.0348309i
$613$	−21.7093	−	9.66558i	−0.876828	−	0.390389i	−0.0815756	−	0.996667i	$-0.525995\pi$
$613$	−21.7093	−	9.66558i	−0.876828	−	0.390389i	−0.795253	+	0.606278i	$0.792662\pi$
$614$	−17.0199	−	29.4794i	−0.686869	−	1.18969i
$615$	−1.00917	+	1.74793i	−0.0406936	+	0.0704834i
$616$	−1.20480	+	0.875335i	−0.0485426	+	0.0352683i
$617$	−23.9565	+	5.09211i	−0.964453	+	0.205001i	−0.663116	−	0.748517i	$-0.730766\pi$
$617$	−23.9565	+	5.09211i	−0.964453	+	0.205001i	−0.301337	+	0.953518i	$0.597433\pi$
$618$	4.86893	+	14.9850i	0.195857	+	0.602786i
$619$	8.18101			0.328823			0.164411	−	0.986392i	$-0.447428\pi$
$619$	8.18101			0.328823			0.164411	+	0.986392i	$0.447428\pi$
$620$	5.47949	−	0.987511i	0.220062	−	0.0396594i
$621$	8.01781			0.321744
$622$	−10.0939	−	31.0660i	−0.404730	−	1.24563i
$623$	1.24699	−	0.265057i	0.0499597	−	0.0106193i
$624$	5.74040	−	4.17064i	0.229800	−	0.166959i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	4.60573	+	7.97735i	0.184082	+	0.318839i
$627$	11.2586	+	5.01264i	0.449624	+	0.200186i
$628$	14.9605	+	10.8695i	0.596990	+	0.433739i
$629$	−4.53694	+	2.01997i	−0.180900	+	0.0805417i
$630$	−0.618684	−	0.131505i	−0.0246490	−	0.00523930i
$631$	−3.44959	−	32.8206i	−0.137326	−	1.30657i	−0.818525	−	0.574470i	$-0.805208\pi$
$631$	−3.44959	−	32.8206i	−0.137326	−	1.30657i	0.681200	−	0.732098i	$-0.261459\pi$
$632$	−5.25238	+	5.83336i	−0.208928	+	0.232039i
$633$	13.9516	+	15.4948i	0.554526	+	0.615864i
$634$	0.879178	−	8.36482i	0.0349166	−	0.332210i
$635$	3.73488	−	11.4948i	0.148214	−	0.456156i
$636$	−1.38994	+	4.27779i	−0.0551146	+	0.169625i
$637$	4.89507	−	46.5734i	0.193950	−	1.84531i
$638$	1.43338	+	1.59192i	0.0567479	+	0.0630249i
$639$	−2.30183	+	2.55644i	−0.0910588	+	0.101131i
$640$	−0.104528	−	0.994522i	−0.00413185	−	0.0393119i
$641$	−33.1926	−	7.05530i	−1.31103	−	0.278668i	−0.501198	−	0.865332i	$-0.667107\pi$
$641$	−33.1926	−	7.05530i	−1.31103	−	0.278668i	−0.809830	+	0.586665i	$0.800441\pi$
$642$	8.09653	−	3.60481i	0.319545	−	0.142270i
$643$	−11.3461	−	8.24344i	−0.447447	−	0.325089i	0.341140	−	0.940013i	$-0.389187\pi$
$643$	−11.3461	−	8.24344i	−0.447447	−	0.325089i	−0.788587	+	0.614923i	$0.789187\pi$
$644$	−4.63287	−	2.06269i	−0.182561	−	0.0812813i
$645$	−5.92962	−	10.2704i	−0.233479	−	0.404397i
$646$	−3.83667	+	6.64530i	−0.150952	+	0.261456i
$647$	−11.0482	+	8.02699i	−0.434350	+	0.315574i	−0.783386	−	0.621536i	$-0.786509\pi$
$647$	−11.0482	+	8.02699i	−0.434350	+	0.315574i	0.349036	+	0.937109i	$0.386509\pi$
$648$	−0.978148	+	0.207912i	−0.0384253	+	0.00816754i
$649$	−9.82177	−	30.2283i	−0.385538	−	1.18656i
$650$	7.09552			0.278309
$651$	−0.476959	+	3.48920i	−0.0186935	+	0.136752i
$652$	18.9113			0.740623
$653$	0.994096	+	3.05951i	0.0389020	+	0.119728i	0.968622	−	0.248540i	$-0.0799508\pi$
$653$	0.994096	+	3.05951i	0.0389020	+	0.119728i	−0.929720	+	0.368268i	$0.879951\pi$
$654$	−4.19420	+	0.891506i	−0.164006	+	0.0348606i
$655$	16.3493	−	11.8785i	0.638821	−	0.464131i
$656$	1.00917	−	1.74793i	0.0394014	−	0.0682453i
$657$	−2.61904	−	4.53631i	−0.102179	−	0.176978i
$658$	1.67227	+	0.744542i	0.0651918	+	0.0290253i
$659$	−25.1448	−	18.2687i	−0.979501	−	0.711649i	−0.0219039	−	0.999760i	$-0.506973\pi$
$659$	−25.1448	−	18.2687i	−0.979501	−	0.711649i	−0.957597	+	0.288111i	$0.906973\pi$
$660$	−2.15090	+	0.957644i	−0.0837238	+	0.0372763i
$661$	32.1326	+	6.83000i	1.24981	+	0.265656i	0.784857	−	0.619677i	$-0.212736\pi$
$661$	32.1326	+	6.83000i	1.24981	+	0.265656i	0.464958	+	0.885333i	$0.346070\pi$
$662$	2.31006	+	21.9788i	0.0897831	+	0.854229i
$663$	6.96013	−	7.73000i	0.270309	−	0.300208i
$664$	−0.922822	−	1.02490i	−0.0358124	−	0.0397737i
$665$	0.346068	−	3.29262i	0.0134199	−	0.127682i
$666$	1.04687	−	3.22194i	0.0405654	−	0.124848i
$667$	−2.25422	+	6.93777i	−0.0872837	+	0.268632i
$668$	0.214080	−	2.03684i	0.00828302	−	0.0788076i
$669$	11.8067	+	13.1127i	0.456475	+	0.506966i
$670$	1.13567	−	1.26129i	0.0438747	−	0.0487277i
$671$	2.11244	+	20.0985i	0.0815499	+	0.775895i
$672$	0.618684	+	0.131505i	0.0238663	+	0.00507293i
$673$	20.8815	−	9.29706i	0.804924	−	0.358375i	0.0373233	−	0.999303i	$-0.488117\pi$
$673$	20.8815	−	9.29706i	0.804924	−	0.358375i	0.767601	+	0.640928i	$0.221450\pi$
$674$	−3.04543	−	2.21263i	−0.117305	−	0.0852274i
$675$	−0.913545	−	0.406737i	−0.0351624	−	0.0156553i
$676$	−18.6732	−	32.3429i	−0.718200	−	1.24396i
$677$	15.9203	−	27.5747i	0.611866	−	1.05978i	−0.379059	−	0.925372i	$-0.623752\pi$
$677$	15.9203	−	27.5747i	0.611866	−	1.05978i	0.990926	−	0.134411i	$-0.0429142\pi$
$678$	3.24642	−	2.35866i	0.124678	−	0.0905839i
$679$	6.06733	−	1.28965i	0.232843	−	0.0494923i
$680$	−0.453006	−	1.39421i	−0.0173720	−	0.0534655i
$681$	18.7413			0.718168
$682$	6.19796	+	11.5513i	0.237332	+	0.442323i
$683$	17.4879			0.669156			0.334578	−	0.942368i	$-0.391406\pi$
$683$	17.4879			0.669156			0.334578	+	0.942368i	$0.391406\pi$
$684$	−1.61750	−	4.97816i	−0.0618467	−	0.190345i
$685$	17.4996	−	3.71966i	0.668627	−	0.142121i
$686$	6.95920	−	5.05615i	0.265703	−	0.193045i
$687$	13.2531	−	22.9551i	0.505638	−	0.875791i
$688$	5.92962	+	10.2704i	0.226065	+	0.391555i
$689$	29.1560	+	12.9811i	1.11075	+	0.494540i
$690$	−6.48654	−	4.71275i	−0.246938	−	0.179411i
$691$	7.53146	−	3.35322i	0.286510	−	0.127563i	−0.258450	−	0.966025i	$-0.583212\pi$
$691$	7.53146	−	3.35322i	0.286510	−	0.127563i	0.544960	+	0.838462i	$0.316545\pi$
$692$	2.35689	+	0.500973i	0.0895956	+	0.0190441i
$693$	−0.155665	−	1.48105i	−0.00591321	−	0.0562605i
$694$	1.34444	−	1.49315i	0.0510341	−	0.0566791i
$695$	−1.83083	−	2.03334i	−0.0694473	−	0.0771291i
$696$	0.0951027	−	0.904841i	0.00360486	−	0.0342979i
$697$	0.914320	−	2.81399i	0.0346324	−	0.106587i
$698$	1.33685	−	4.11441i	0.0506006	−	0.155733i
$699$	2.14517	−	20.4099i	0.0811377	−	0.771974i
$700$	0.423229	+	0.470044i	0.0159966	+	0.0177660i
$701$	2.50864	−	2.78613i	0.0947502	−	0.105231i	−0.693905	−	0.720067i	$-0.744111\pi$
$701$	2.50864	−	2.78613i	0.0947502	−	0.105231i	0.788655	+	0.614836i	$0.210778\pi$
$702$	0.741684	+	7.05665i	0.0279930	+	0.266336i
$703$	17.3451	+	3.68682i	0.654184	+	0.139051i
$704$	2.15090	−	0.957644i	0.0810653	−	0.0360926i
$705$	2.34136	+	1.70110i	0.0881808	+	0.0640671i
$706$	−20.3639	−	9.06658i	−0.766404	−	0.341225i
$707$	3.21515	+	5.56881i	0.120918	+	0.209437i
$708$	−6.74973	+	11.6909i	−0.253670	+	0.439370i
$709$	13.7192	−	9.96756i	0.515234	−	0.374340i	−0.299571	−	0.954074i	$-0.596844\pi$
$709$	13.7192	−	9.96756i	0.515234	−	0.374340i	0.814806	+	0.579734i	$0.196844\pi$
$710$	3.36485	−	0.715221i	0.126281	−	0.0268418i
$711$	−2.42565	−	7.46538i	−0.0909689	−	0.279973i
$712$	−2.01556			−0.0755362
$713$	−23.5133	+	37.9469i	−0.880579	+	1.42112i
$714$	0.927228			0.0347006
$715$	5.16247	+	15.8884i	0.193065	+	0.594194i
$716$	−8.14678	+	1.73165i	−0.304459	+	0.0647148i
$717$	−9.12206	+	6.62756i	−0.340669	+	0.247511i
$718$	−13.4643	+	23.3209i	−0.502484	+	0.870328i
$719$	−3.42389	−	5.93036i	−0.127690	−	0.221165i	0.795091	−	0.606490i	$-0.207423\pi$
$719$	−3.42389	−	5.93036i	−0.127690	−	0.221165i	−0.922781	+	0.385325i	$0.874089\pi$
$720$	0.913545	+	0.406737i	0.0340458	+	0.0151582i
$721$	8.06257	+	5.85780i	0.300266	+	0.218156i
$722$	7.67227	−	3.41592i	0.285532	−	0.127127i
$723$	18.0588	+	3.83853i	0.671616	+	0.142756i
$724$	0.672865	+	6.40188i	0.0250068	+	0.237924i
$725$	0.608792	−	0.676132i	0.0226100	−	0.0251109i
$726$	3.65113	+	4.05499i	0.135506	+	0.150495i
$727$	−2.98483	+	28.3987i	−0.110701	+	1.05325i	0.788296	+	0.615296i	$0.210963\pi$
$727$	−2.98483	+	28.3987i	−0.110701	+	1.05325i	−0.898997	+	0.437954i	$0.855703\pi$
$728$	1.38686	−	4.26830i	0.0514003	−	0.158194i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−0.547529	+	5.20939i	−0.0202649	+	0.192808i
$731$	11.6329	+	12.9197i	0.430260	+	0.477852i
$732$	5.74341	−	6.37871i	0.212283	−	0.235764i
$733$	−1.73372	−	16.4952i	−0.0640363	−	0.609265i	−0.978735	−	0.205128i	$-0.934239\pi$
$733$	−1.73372	−	16.4952i	−0.0640363	−	0.609265i	0.914699	−	0.404136i	$-0.132428\pi$
$734$	18.6392	+	3.96189i	0.687987	+	0.146236i
$735$	6.02934	−	2.68444i	0.222396	−	0.0990169i
$736$	6.48654	+	4.71275i	0.239097	+	0.173714i
$737$	3.65058	+	1.62534i	0.134471	+	0.0598702i
$738$	1.00917	+	1.74793i	0.0371480	+	0.0643423i
$739$	0.627643	−	1.08711i	0.0230882	−	0.0399900i	−0.854250	−	0.519862i	$-0.825983\pi$
$739$	0.627643	−	1.08711i	0.0230882	−	0.0399900i	0.877339	+	0.479872i	$0.159317\pi$
$740$	−2.74074	+	1.99127i	−0.100752	+	0.0732004i
$741$	−36.3288	+	7.72192i	−1.33457	+	0.283672i
$742$	0.879144	+	2.70573i	0.0322744	+	0.0993304i
$743$	−33.5754			−1.23176			−0.615881	−	0.787839i	$-0.711200\pi$
$743$	−33.5754			−1.23176			−0.615881	+	0.787839i	$0.711200\pi$
$744$	1.88454	−	5.23913i	0.0690905	−	0.192076i
$745$	7.26934			0.266328
$746$	−1.41267	−	4.34775i	−0.0517215	−	0.159182i
$747$	1.34900	−	0.286738i	0.0493572	−	0.0104912i
$748$	2.79235	−	2.02876i	0.102099	−	0.0741790i
$749$	2.80287	−	4.85472i	0.102415	−	0.177388i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	−2.02313	−	0.900755i	−0.0738250	−	0.0328690i	0.369492	−	0.929234i	$-0.379532\pi$
$751$	−2.02313	−	0.900755i	−0.0738250	−	0.0328690i	−0.443317	+	0.896365i	$0.646198\pi$
$752$	−2.34136	−	1.70110i	−0.0853807	−	0.0620327i
$753$	−5.74283	+	2.55687i	−0.209280	+	0.0931776i
$754$	−6.31461	−	1.34221i	−0.229965	−	0.0488805i
$755$	1.41212	+	13.4355i	0.0513924	+	0.488966i
$756$	−0.423229	+	0.470044i	−0.0153927	+	0.0170953i
$757$	−5.27535	−	5.85887i	−0.191736	−	0.212944i	0.639610	−	0.768700i	$-0.279096\pi$
$757$	−5.27535	−	5.85887i	−0.191736	−	0.212944i	−0.831346	+	0.555755i	$0.812429\pi$
$758$	−2.03335	+	19.3460i	−0.0738545	+	0.702678i
$759$	5.83350	−	17.9537i	0.211743	−	0.651677i
$760$	−1.61750	+	4.97816i	−0.0586729	+	0.180577i
$761$	2.06848	−	19.6802i	0.0749822	−	0.713408i	−0.890860	−	0.454278i	$-0.849897\pi$
$761$	2.06848	−	19.6802i	0.0749822	−	0.713408i	0.965842	−	0.259130i	$-0.0834359\pi$
$762$	−8.08733	−	8.98189i	−0.292973	−	0.325380i
$763$	−1.81477	+	2.01550i	−0.0656990	+	0.0729661i
$764$	0.448439	+	4.26662i	0.0162240	+	0.154361i
$765$	1.43392	+	0.304790i	0.0518437	+	0.0110197i
$766$	16.5419	−	7.36494i	0.597684	−	0.266106i
$767$	77.4922	+	56.3014i	2.79808	+	2.03293i
$768$	−0.913545	−	0.406737i	−0.0329647	−	0.0146768i
$769$	5.45049	+	9.44052i	0.196550	+	0.340434i	0.947407	−	0.320030i	$-0.103693\pi$
$769$	5.45049	+	9.44052i	0.196550	+	0.340434i	−0.750858	+	0.660464i	$0.770360\pi$
$770$	−0.744604	+	1.28969i	−0.0268337	+	0.0464773i
$771$	3.44100	−	2.50003i	0.123925	−	0.0900365i
$772$	9.38246	−	1.99430i	0.337682	−	0.0717765i
$773$	−5.04759	−	15.5349i	−0.181549	−	0.558750i	0.818323	−	0.574759i	$-0.194904\pi$
$773$	−5.04759	−	15.5349i	−0.181549	−	0.558750i	−0.999872	+	0.0160084i	$0.994904\pi$
$774$	−11.8592			−0.426272
$775$	4.60411	−	3.13085i	0.165384	−	0.112463i
$776$	−9.80683			−0.352045
$777$	−0.662152	−	2.03789i	−0.0237546	−	0.0731091i
$778$	−13.9674	+	2.96887i	−0.500757	+	0.106439i
$779$	−8.54700	+	6.20976i	−0.306228	+	0.222488i
$780$	3.54776	−	6.14490i	0.127030	−	0.220023i
$781$	4.04970	+	7.01428i	0.144910	+	0.250991i
$782$	10.7376	+	4.78069i	0.383976	+	0.170957i
$783$	0.736064	+	0.534782i	0.0263048	+	0.0191115i
$784$	−6.02934	+	2.68444i	−0.215334	+	0.0958727i
$785$	18.0881	+	3.84475i	0.645593	+	0.137225i
$786$	−2.11240	−	20.0982i	−0.0753470	−	0.716878i
$787$	−31.6732	+	35.1767i	−1.12903	+	1.25391i	−0.165529	+	0.986205i	$0.552933\pi$
$787$	−31.6732	+	35.1767i	−1.12903	+	1.25391i	−0.963500	+	0.267709i	$0.913733\pi$
$788$	11.2223	+	12.4636i	0.399778	+	0.443999i
$789$	1.40923	−	13.4079i	0.0501698	−	0.477334i
$790$	−2.42565	+	7.46538i	−0.0863007	+	0.265606i
$791$	0.784322	−	2.41389i	0.0278873	−	0.0858282i
$792$	−0.246108	+	2.34156i	−0.00874506	+	0.0832037i
$793$	−40.7525	−	45.2602i	−1.44716	−	1.60724i
$794$	13.3509	−	14.8277i	0.473807	−	0.526216i
$795$	0.470162	+	4.47330i	0.0166749	+	0.158651i
$796$	−6.02442	−	1.28053i	−0.213530	−	0.0453872i
$797$	43.6243	−	19.4228i	1.54525	−	0.687990i	0.555595	−	0.831453i	$-0.312490\pi$
$797$	43.6243	−	19.4228i	1.54525	−	0.687990i	0.989656	+	0.143463i	$0.0458237\pi$
$798$	−2.67846	−	1.94601i	−0.0948163	−	0.0688881i
$799$	−3.87582	−	1.72562i	−0.137116	−	0.0610482i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	1.00778	−	1.74552i	0.0356081	−	0.0616750i
$802$	−23.6297	+	17.1680i	−0.834394	+	0.606222i
$803$	−12.0633	+	2.56414i	−0.425706	+	0.0904866i
$804$	−0.524472	−	1.61416i	−0.0184967	−	0.0569270i
$805$	−5.07131			−0.178740
$806$	−35.5730	−	17.1843i	−1.25301	−	0.605291i
$807$	−18.6056			−0.654948
$808$	−3.14159	−	9.66881i	−0.110521	−	0.340148i
$809$	40.1766	−	8.53981i	1.41253	−	0.300244i	0.562425	−	0.826848i	$-0.309869\pi$
$809$	40.1766	−	8.53981i	1.41253	−	0.300244i	0.850110	+	0.526605i	$0.176535\pi$
$810$	−0.809017	+	0.587785i	−0.0284260	+	0.0206527i
$811$	−0.578519	+	1.00202i	−0.0203145	+	0.0351858i	−0.876004	−	0.482304i	$-0.839800\pi$
$811$	−0.578519	+	1.00202i	−0.0203145	+	0.0351858i	0.855689	+	0.517490i	$0.173133\pi$
$812$	−0.287735	−	0.498372i	−0.0100975	−	0.0174894i
$813$	−12.4771	−	5.55518i	−0.437593	−	0.194829i
$814$	−6.45297	−	4.68835i	−0.226176	−	0.164327i
$815$	17.2763	−	7.69191i	0.605163	−	0.269436i
$816$	−1.43392	−	0.304790i	−0.0501974	−	0.0106698i
$817$	−6.48864	−	61.7353i	−0.227009	−	2.15984i
$818$	25.1066	−	27.8837i	0.877832	−	0.974931i
$819$	3.00303	+	3.33520i	0.104934	+	0.116541i
$820$	0.210974	−	2.00728i	0.00736753	−	0.0700973i
$821$	−10.8331	+	33.3408i	−0.378077	+	1.16360i	0.563303	+	0.826251i	$0.309530\pi$
$821$	−10.8331	+	33.3408i	−0.378077	+	1.16360i	−0.941379	+	0.337350i	$0.890470\pi$
$822$	5.52850	−	17.0150i	0.192828	−	0.593465i
$823$	2.18823	−	20.8196i	0.0762768	−	0.725726i	−0.887823	−	0.460185i	$-0.847783\pi$
$823$	2.18823	−	20.8196i	0.0762768	−	0.725726i	0.964100	−	0.265540i	$-0.0855504\pi$
$824$	−10.5429	−	11.7091i	−0.367281	−	0.407907i
$825$	−1.57544	+	1.74970i	−0.0548498	+	0.0609169i
$826$	0.892515	+	8.49172i	0.0310546	+	0.295465i
$827$	33.1472	+	7.04565i	1.15264	+	0.245001i	0.744311	−	0.667833i	$-0.232778\pi$
$827$	33.1472	+	7.04565i	1.15264	+	0.245001i	0.408329	+	0.912835i	$0.366111\pi$
$828$	−7.32463	+	3.26114i	−0.254549	+	0.113332i
$829$	12.4750	+	9.06363i	0.433275	+	0.314793i	0.782957	−	0.622076i	$-0.213710\pi$
$829$	12.4750	+	9.06363i	0.433275	+	0.314793i	−0.349682	+	0.936868i	$0.613710\pi$
$830$	−1.25990	−	0.560945i	−0.0437319	−	0.0194707i
$831$	4.40665	+	7.63254i	0.152865	+	0.264770i
$832$	−3.54776	+	6.14490i	−0.122996	+	0.213036i
$833$	−7.82743	+	5.68696i	−0.271204	+	0.197042i
$834$	−2.67634	+	0.568874i	−0.0926741	+	0.0196985i
$835$	−0.632885	−	1.94782i	−0.0219019	−	0.0674070i
$836$	−12.3240			−0.426236
$837$	3.59495	+	4.25162i	0.124260	+	0.146958i
$838$	−15.0220			−0.518926
$839$	−3.80199	−	11.7013i	−0.131259	−	0.403974i	0.863730	−	0.503954i	$-0.168122\pi$
$839$	−3.80199	−	11.7013i	−0.131259	−	0.403974i	−0.994989	+	0.0999803i	$0.968122\pi$
$840$	0.618684	−	0.131505i	0.0213466	−	0.00453737i
$841$	22.7918	−	16.5592i	0.785924	−	0.571007i
$842$	−10.3057	+	17.8500i	−0.355158	+	0.615152i
$843$	−15.9546	−	27.6341i	−0.549505	−	0.951770i
$844$	−19.0477	−	8.48059i	−0.655650	−	0.291914i
$845$	−30.2139	−	21.9517i	−1.03939	−	0.755160i
$846$	2.64388	−	1.17713i	0.0908983	−	0.0404705i
$847$	3.37587	+	0.717563i	0.115996	+	0.0246557i
$848$	−0.470162	−	4.47330i	−0.0161454	−	0.153614i
$849$	−7.57131	+	8.40879i	−0.259847	+	0.288589i
$850$	−0.980918	−	1.08942i	−0.0336452	−	0.0373668i
$851$	2.83923	−	27.0135i	0.0973276	−	0.926011i
$852$	1.06303	−	3.27166i	0.0364187	−	0.112085i
$853$	12.1481	−	37.3880i	0.415943	−	1.28014i	−0.495461	−	0.868630i	$-0.665001\pi$
$853$	12.1481	−	37.3880i	0.415943	−	1.28014i	0.911404	−	0.411512i	$-0.134999\pi$
$854$	0.567490	−	5.39931i	0.0194191	−	0.184761i
$855$	−3.50246	−	3.88987i	−0.119782	−	0.133031i
$856$	−5.93034	+	6.58631i	−0.202695	+	0.225116i
$857$	0.394208	+	3.75064i	0.0134659	+	0.128119i	0.999190	−	0.0402517i	$-0.0128160\pi$
$857$	0.394208	+	3.75064i	0.0134659	+	0.128119i	−0.985724	+	0.168371i	$0.946149\pi$
$858$	16.3410	+	3.47339i	0.557874	+	0.118580i
$859$	35.0616	−	15.6104i	1.19629	−	0.532620i	0.290712	−	0.956811i	$-0.406108\pi$
$859$	35.0616	−	15.6104i	1.19629	−	0.532620i	0.905573	+	0.424190i	$0.139441\pi$
$860$	9.59433	+	6.97069i	0.327164	+	0.237698i
$861$	1.16624	+	0.519245i	0.0397454	+	0.0176958i
$862$	−18.3078	−	31.7100i	−0.623565	−	1.08005i
$863$	−7.25189	+	12.5606i	−0.246857	+	0.427569i	−0.962652	−	0.270741i	$-0.912731\pi$
$863$	−7.25189	+	12.5606i	−0.246857	+	0.427569i	0.715795	+	0.698311i	$0.246065\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	2.35689	−	0.500973i	0.0801368	−	0.0170336i
$866$	7.64684	+	23.5346i	0.259850	+	0.799737i
$867$	14.8510			0.504365
$868$	−0.983461	−	3.38154i	−0.0333808	−	0.114777i
$869$	−18.4815			−0.626941
$870$	−0.281152	−	0.865295i	−0.00953193	−	0.0293363i
$871$	−11.7796	+	2.50382i	−0.399135	+	0.0848387i
$872$	3.46899	−	2.52037i	0.117475	−	0.0853504i
$873$	4.90341	−	8.49296i	0.165955	−	0.287443i
$874$	−20.9840	−	36.3453i	−0.709794	−	1.22940i
$875$	0.577823	+	0.257263i	0.0195340	+	0.00869709i
$876$	4.23770	+	3.07887i	0.143179	+	0.104025i
$877$	−31.4631	+	14.0083i	−1.06243	+	0.473025i	−0.862119	−	0.506706i	$-0.830863\pi$
$877$	−31.4631	+	14.0083i	−1.06243	+	0.473025i	−0.200314	+	0.979732i	$0.564196\pi$
$878$	−29.1971	−	6.20604i	−0.985356	−	0.209444i
$879$	−1.13784	−	10.8258i	−0.0383784	−	0.365146i
$880$	1.57544	−	1.74970i	0.0531081	−	0.0589825i
$881$	1.15769	+	1.28574i	0.0390035	+	0.0433177i	0.762331	−	0.647187i	$-0.224055\pi$
$881$	1.15769	+	1.28574i	0.0390035	+	0.0433177i	−0.723327	+	0.690505i	$0.757388\pi$
$882$	0.689881	−	6.56378i	0.0232295	−	0.221014i
$883$	−4.11603	+	12.6678i	−0.138516	+	0.426307i	−0.996120	−	0.0880024i	$-0.971952\pi$
$883$	−4.11603	+	12.6678i	−0.138516	+	0.426307i	0.857605	+	0.514309i	$0.171952\pi$
$884$	−3.21432	+	9.89265i	−0.108109	+	0.332726i
$885$	−1.41108	+	13.4255i	−0.0474329	+	0.451294i
$886$	−18.4900	−	20.5352i	−0.621183	−	0.689894i
$887$	16.7185	−	18.5677i	0.561351	−	0.623443i	−0.393931	−	0.919140i	$-0.628885\pi$
$887$	16.7185	−	18.5677i	0.561351	−	0.623443i	0.955282	+	0.295697i	$0.0955518\pi$
$888$	0.354116	+	3.36919i	0.0118833	+	0.113062i
$889$	−7.47762	−	1.58942i	−0.250791	−	0.0533073i
$890$	−1.84130	+	0.819801i	−0.0617206	+	0.0274798i
$891$	−1.90480	−	1.38392i	−0.0638131	−	0.0463629i
$892$	−16.1194	−	7.17682i	−0.539718	−	0.240298i
$893$	7.57431	+	13.1191i	0.253465	+	0.439014i
$894$	3.63467	−	6.29544i	0.121562	−	0.210551i
$895$	−6.73812	+	4.89553i	−0.225231	+	0.163640i
$896$	−0.618684	+	0.131505i	−0.0206688	+	0.00439329i
$897$	17.5801	+	54.1061i	0.586984	+	1.80655i
$898$	−15.0232			−0.501332
$899$	−4.68964	+	1.91535i	−0.156408	+	0.0638804i
$900$	1.00000			0.0333333
$901$	−2.03759	−	6.27107i	−0.0678821	−	0.208920i
$902$	4.64825	−	0.988016i	0.154770	−	0.0328973i
$903$	−6.06847	+	4.40900i	−0.201946	+	0.146722i
$904$	−2.00640	+	3.47518i	−0.0667318	+	0.115583i
$905$	3.21857	+	5.57473i	0.106989	+	0.185310i
$906$	12.3415	+	5.49479i	0.410019	+	0.182552i
$907$	47.4816	+	34.4974i	1.57660	+	1.14547i	0.920465	+	0.390826i	$0.127811\pi$
$907$	47.4816	+	34.4974i	1.57660	+	1.14547i	0.656137	+	0.754642i	$0.272189\pi$
$908$	−17.1210	+	7.62277i	−0.568181	+	0.252971i
$909$	9.94423	+	2.11371i	0.329829	+	0.0701074i
$910$	−0.469119	−	4.46337i	−0.0155512	−	0.147959i
$911$	24.9057	−	27.6606i	0.825164	−	0.916437i	−0.172482	−	0.985013i	$-0.555179\pi$
$911$	24.9057	−	27.6606i	0.825164	−	0.916437i	0.997646	+	0.0685756i	$0.0218454\pi$
$912$	3.50246	+	3.88987i	0.115978	+	0.128807i
$913$	0.339416	−	3.22933i	0.0112330	−	0.106875i
$914$	2.45595	−	7.55862i	0.0812355	−	0.250017i
$915$	2.65242	−	8.16329i	0.0876861	−	0.269870i
$916$	−2.77066	+	26.3610i	−0.0915451	+	0.870994i
$917$	−8.55299	−	9.49906i	−0.282445	−	0.313687i
$918$	0.980918	−	1.08942i	0.0323751	−	0.0359562i
$919$	−2.87302	−	27.3350i	−0.0947723	−	0.901698i	−0.933845	−	0.357678i	$-0.883568\pi$
$919$	−2.87302	−	27.3350i	−0.0947723	−	0.901698i	0.839073	−	0.544020i	$-0.183098\pi$
$920$	7.84260	+	1.66700i	0.258563	+	0.0549592i
$921$	−31.0970	+	13.8453i	−1.02468	+	0.456217i
$922$	−8.99665	−	6.53645i	−0.296289	−	0.215267i
$923$	−22.2985	−	9.92794i	−0.733964	−	0.326782i
$924$	0.744604	+	1.28969i	0.0244957	+	0.0424278i
$925$	−1.69387	+	2.93387i	−0.0556942	+	0.0964652i
$926$	8.52877	−	6.19651i	0.280273	−	0.203630i
$927$	15.4119	−	3.27590i	0.506192	−	0.107595i
$928$	0.281152	+	0.865295i	0.00922925	+	0.0284047i
$929$	−57.2400			−1.87798			−0.938991	−	0.343940i	$-0.888238\pi$
$929$	−57.2400			−1.87798			−0.938991	+	0.343940i	$0.888238\pi$
$930$	−0.409338	−	5.55270i	−0.0134227	−	0.182080i
$931$	34.5463			1.13221
$932$	6.34175	+	19.5179i	0.207731	+	0.639330i
$933$	−31.9509	+	6.79137i	−1.04603	+	0.222340i
$934$	−28.3009	+	20.5618i	−0.926035	+	0.672804i
$935$	1.72577	−	2.98912i	0.0564387	−	0.0977547i
$936$	−3.54776	−	6.14490i	−0.115962	−	0.200852i
$937$	−31.7374	−	14.1304i	−1.03682	−	0.461621i	−0.183504	−	0.983019i	$-0.558744\pi$
$937$	−31.7374	−	14.1304i	−1.03682	−	0.461621i	−0.853313	+	0.521398i	$0.825411\pi$
$938$	−0.868485	−	0.630992i	−0.0283571	−	0.0206026i
$939$	8.41508	−	3.74664i	0.274616	−	0.122267i
$940$	−2.83084	−	0.601714i	−0.0923318	−	0.0196257i
$941$	0.665058	+	6.32760i	0.0216803	+	0.206274i	1.00000		0.000827892i	$-0.000263526\pi$
$941$	0.665058	+	6.32760i	0.0216803	+	0.206274i	−0.978319	+	0.207102i	$0.933597\pi$
$942$	12.3737	−	13.7424i	0.403157	−	0.447752i
$943$	10.8283	+	12.0261i	0.352618	+	0.391622i
$944$	1.41108	−	13.4255i	0.0459267	−	0.436963i
$945$	−0.195455	+	0.601549i	−0.00635816	+	0.0195684i
$946$	−8.62840	+	26.5555i	−0.280533	+	0.863393i
$947$	−2.48221	+	23.6166i	−0.0806608	+	0.767437i	0.877185	+	0.480153i	$0.159419\pi$
$947$	−2.48221	+	23.6166i	−0.0806608	+	0.767437i	−0.957846	+	0.287284i	$0.907248\pi$
$948$	5.25238	+	5.83336i	0.170589	+	0.189459i
$949$	24.8695	−	27.6204i	0.807299	−	0.896596i
$950$	0.547138	+	5.20567i	0.0177515	+	0.168894i
$951$	−8.22710	−	1.74872i	−0.266782	−	0.0567063i
$952$	−0.847065	+	0.377138i	−0.0274535	+	0.0122231i
$953$	28.3616	+	20.6059i	0.918723	+	0.667492i	0.943206	−	0.332209i	$-0.107794\pi$
$953$	28.3616	+	20.6059i	0.918723	+	0.667492i	−0.0244826	+	0.999700i	$0.507794\pi$
$954$	4.10907	+	1.82948i	0.133036	+	0.0592314i
$955$	2.14506	+	3.71535i	0.0694125	+	0.120226i
$956$	5.63774	−	9.76485i	0.182338	−	0.315818i
$957$	1.73303	−	1.25912i	0.0560210	−	0.0407016i
$958$	24.3300	−	5.17150i	0.786067	−	0.167084i
$959$	−3.49681	−	10.7621i	−0.112918	−	0.347525i
$960$	−1.00000			−0.0322749
$961$	−30.6649	+	4.54586i	−0.989190	+	0.146641i
$962$	24.0378			0.775010
$963$	−2.73874	−	8.42898i	−0.0882548	−	0.271620i
$964$	−18.0588	+	3.83853i	−0.581636	+	0.123631i
$965$	7.76015	−	5.63808i	0.249808	−	0.181496i
$966$	−2.53566	+	4.39189i	−0.0815834	+	0.141307i
$967$	6.40424	+	11.0925i	0.205946	+	0.356710i	0.950434	−	0.310927i	$-0.100639\pi$
$967$	6.40424	+	11.0925i	0.205946	+	0.356710i	−0.744487	+	0.667636i	$0.767306\pi$
$968$	−4.98479	−	2.21937i	−0.160217	−	0.0713332i
$969$	6.20786	+	4.51027i	0.199425	+	0.144891i
$970$	−8.95898	+	3.98880i	−0.287656	+	0.128073i
$971$	−20.1503	−	4.28309i	−0.646655	−	0.137451i	−0.127103	−	0.991890i	$-0.540568\pi$
$971$	−20.1503	−	4.28309i	−0.646655	−	0.137451i	−0.519552	+	0.854439i	$0.673901\pi$
$972$	0.104528	+	0.994522i	0.00335275	+	0.0318993i
$973$	−1.15801	+	1.28610i	−0.0371241	+	0.0412305i
$974$	−1.57670	−	1.75110i	−0.0505207	−	0.0561089i
$975$	0.741684	−	7.05665i	0.0237529	−	0.225994i
$976$	−2.65242	+	8.16329i	−0.0849017	+	0.261301i
$977$	12.4562	−	38.3361i	0.398508	−	1.22648i	−0.527687	−	0.849439i	$-0.676941\pi$
$977$	12.4562	−	38.3361i	0.398508	−	1.22648i	0.926196	−	0.377043i	$-0.123059\pi$
$978$	1.97677	−	18.8077i	0.0632101	−	0.601404i
$979$	−3.17539	−	3.52663i	−0.101486	−	0.112711i
$980$	−4.41622	+	4.90471i	−0.141071	+	0.156675i
$981$	0.448208	+	4.26442i	0.0143102	+	0.136152i
$982$	9.77262	+	2.07723i	0.311857	+	0.0662872i
$983$	55.1635	−	24.5604i	1.75944	−	0.783354i	0.770067	−	0.637963i	$-0.220223\pi$
$983$	55.1635	−	24.5604i	1.75944	−	0.783354i	0.989374	−	0.145391i	$-0.0464440\pi$
$984$	−1.63287	−	1.18635i	−0.0520540	−	0.0378194i
$985$	15.3215	+	6.82157i	0.488184	+	0.217353i
$986$	0.666884	+	1.15508i	0.0212379	+	0.0367851i
$987$	0.915262	−	1.58528i	0.0291331	−	0.0504601i
$988$	30.0472	−	21.8306i	0.955929	−	0.694523i
$989$	−93.0073	+	19.7693i	−2.95746	+	0.628627i
$990$	0.727568	+	2.23922i	0.0231236	+	0.0711672i
$991$	9.62805			0.305845			0.152923	−	0.988238i	$-0.451132\pi$
$991$	9.62805			0.305845			0.152923	+	0.988238i	$0.451132\pi$
$992$	0.409338	+	5.55270i	0.0129965	+	0.176298i
$993$	22.0998			0.701317
$994$	−0.672370	−	2.06934i	−0.0213263	−	0.0656356i
$995$	−6.02442	+	1.28053i	−0.190987	+	0.0405955i
$996$	−1.11574	+	0.810635i	−0.0353537	+	0.0256860i
$997$	−17.2192	+	29.8246i	−0.545338	+	0.944554i	0.453247	+	0.891385i	$0.350265\pi$
$997$	−17.2192	+	29.8246i	−0.545338	+	0.944554i	−0.998586	+	0.0531689i	$0.983068\pi$
$998$	−18.7253	−	32.4331i	−0.592738	−	1.02665i
$999$	−3.09486	−	1.37792i	−0.0979170	−	0.0435955i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.b.691.2	✓	16	31.9	even	15	inner
930.2.bg.b.751.2	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.978148 - 0.207912i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.577823 + 0.257263i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\)	\(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} +(0.577823 + 0.257263i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +(-0.978148 - 0.207912i) q^{10} +(-0.246108 - 2.34156i) q^{11} +(-0.669131 + 0.743145i) q^{12} +(4.74783 + 5.27300i) q^{13} +(-0.0661149 + 0.629041i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.153234 - 1.45793i) q^{17} +(0.669131 + 0.743145i) q^{18} +(-3.50246 + 3.88987i) q^{19} +(-0.104528 - 0.994522i) q^{20} +(0.618684 + 0.131505i) q^{21} +(2.15090 - 0.957644i) q^{22} +(6.48654 + 4.71275i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.54776 + 6.14490i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.618684 + 0.131505i) q^{28} +(0.281152 + 0.865295i) q^{29} -1.00000 q^{30} +(0.409338 + 5.55270i) q^{31} +1.00000 q^{32} +(-0.727568 - 2.23922i) q^{33} +(1.43392 - 0.304790i) q^{34} +(-0.511708 + 0.371778i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.69387 - 2.93387i) q^{37} +(-4.78181 - 2.12900i) q^{38} +(5.74040 + 4.17064i) q^{39} +(0.913545 - 0.406737i) q^{40} +(1.97423 + 0.419636i) q^{41} +(0.0661149 + 0.629041i) q^{42} +(-7.93538 + 8.81313i) q^{43} +(1.57544 + 1.74970i) q^{44} +(-0.104528 + 0.994522i) q^{45} +(-2.47764 + 7.62539i) q^{46} +(0.894321 - 2.75244i) q^{47} +(0.104528 - 0.994522i) q^{48} +(-4.41622 - 4.90471i) q^{49} +(0.669131 - 0.743145i) q^{50} +(-0.153234 - 1.45793i) q^{51} +(-6.94047 - 1.47524i) q^{52} +(4.10907 - 1.82948i) q^{53} +(0.809017 + 0.587785i) q^{54} +(2.15090 + 0.957644i) q^{55} +(-0.316253 - 0.547766i) q^{56} +(-2.61717 + 4.53307i) q^{57} +(-0.736064 + 0.534782i) q^{58} +(13.2045 - 2.80670i) q^{59} +(-0.309017 - 0.951057i) q^{60} -8.58340 q^{61} +(-5.15444 + 2.10518i) q^{62} +0.632506 q^{63} +(0.309017 + 0.951057i) q^{64} +(-6.94047 + 1.47524i) q^{65} +(1.90480 - 1.38392i) q^{66} +(-0.848614 + 1.46984i) q^{67} +(0.732980 + 1.26956i) q^{68} +(7.32463 + 3.26114i) q^{69} +(-0.511708 - 0.371778i) q^{70} +(-3.14262 + 1.39918i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(-0.547529 - 5.20939i) q^{73} +(2.26684 - 2.51759i) q^{74} +(-0.669131 - 0.743145i) q^{75} +(0.547138 - 5.20567i) q^{76} +(0.460191 - 1.41632i) q^{77} +(-2.19264 + 6.74824i) q^{78} +(0.820502 - 7.80656i) q^{79} +(0.669131 + 0.743145i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.210974 + 2.00728i) q^{82} +(1.34900 + 0.286738i) q^{83} +(-0.577823 + 0.257263i) q^{84} +(1.18599 + 0.861669i) q^{85} +(-10.8340 - 4.82359i) q^{86} +(0.454913 + 0.787932i) q^{87} +(-1.17723 + 2.03902i) q^{88} +(1.63062 - 1.18471i) q^{89} +(-0.978148 + 0.207912i) q^{90} +(1.38686 + 4.26830i) q^{91} -8.01781 q^{92} +(1.55486 + 5.34625i) q^{93} +2.89408 q^{94} +(-1.61750 - 4.97816i) q^{95} +(0.978148 - 0.207912i) q^{96} +(7.93389 - 5.76431i) q^{97} +(3.29997 - 5.71571i) q^{98} +(-1.17723 - 2.03902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 14 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{21} + 13 q^{22} + 7 q^{23} - 2 q^{24} - 8 q^{25} - q^{26} + 4 q^{27} - 2 q^{28} + 13 q^{29} - 16 q^{30} - 21 q^{31} + 16 q^{32} - 4 q^{33} + 6 q^{34} + 9 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} - 20 q^{41} + 12 q^{42} - 2 q^{43} + 13 q^{44} + 2 q^{45} - 3 q^{46} + 23 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} + 13 q^{56} - 18 q^{57} - 22 q^{58} - 26 q^{59} + 4 q^{60} + 24 q^{61} + 9 q^{62} - 26 q^{63} - 4 q^{64} - 16 q^{65} + 11 q^{66} + 45 q^{67} - 4 q^{68} + 11 q^{69} + 9 q^{70} - 39 q^{71} + 2 q^{72} - 19 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 6 q^{77} - 2 q^{78} - 20 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} - 86 q^{83} - 3 q^{84} + 8 q^{85} + 3 q^{86} + 9 q^{87} - 7 q^{88} - 13 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} + 12 q^{93} - 72 q^{94} + 14 q^{95} - 2 q^{96} + 67 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 14 * q^13 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^21 + 13 * q^22 + 7 * q^23 - 2 * q^24 - 8 * q^25 - q^26 + 4 * q^27 - 2 * q^28 + 13 * q^29 - 16 * q^30 - 21 * q^31 + 16 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 - 20 * q^41 + 12 * q^42 - 2 * q^43 + 13 * q^44 + 2 * q^45 - 3 * q^46 + 23 * q^47 - 2 * q^48 - q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 + 13 * q^56 - 18 * q^57 - 22 * q^58 - 26 * q^59 + 4 * q^60 + 24 * q^61 + 9 * q^62 - 26 * q^63 - 4 * q^64 - 16 * q^65 + 11 * q^66 + 45 * q^67 - 4 * q^68 + 11 * q^69 + 9 * q^70 - 39 * q^71 + 2 * q^72 - 19 * q^73 - 2 * q^74 - 2 * q^75 - 2 * q^76 - 6 * q^77 - 2 * q^78 - 20 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 - 86 * q^83 - 3 * q^84 + 8 * q^85 + 3 * q^86 + 9 * q^87 - 7 * q^88 - 13 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 + 12 * q^93 - 72 * q^94 + 14 * q^95 - 2 * q^96 + 67 * q^97 + 9 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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