LMFDB - Embedded newform 224.2.bd.a.109.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.11
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.480321 + 1.33015i) q^{2} +(-0.758838 - 0.988936i) q^{3} +(-1.53858 - 1.27780i) q^{4} +(0.171111 + 0.131298i) q^{5} +(1.67992 - 0.534359i) q^{6} +(1.01488 + 2.44336i) q^{7} +(2.43867 - 1.43279i) q^{8} +(0.374296 - 1.39689i) q^{9} +O(q^{10})$	\(q+(-0.480321 + 1.33015i) q^{2} +(-0.758838 - 0.988936i) q^{3} +(-1.53858 - 1.27780i) q^{4} +(0.171111 + 0.131298i) q^{5} +(1.67992 - 0.534359i) q^{6} +(1.01488 + 2.44336i) q^{7} +(2.43867 - 1.43279i) q^{8} +(0.374296 - 1.39689i) q^{9} +(-0.256834 + 0.164537i) q^{10} +(2.10346 + 0.276926i) q^{11} +(-0.0961237 + 2.49120i) q^{12} +(3.53590 + 1.46462i) q^{13} +(-3.73750 + 0.176348i) q^{14} -0.268851i q^{15} +(0.734477 + 3.93199i) q^{16} +(6.24315 + 3.60448i) q^{17} +(1.67829 + 1.16883i) q^{18} +(-0.462645 - 3.51414i) q^{19} +(-0.0954963 - 0.420657i) q^{20} +(1.64620 - 2.85777i) q^{21} +(-1.37869 + 2.66490i) q^{22} +(-1.34605 + 5.02353i) q^{23} +(-3.26749 - 1.32443i) q^{24} +(-1.28206 - 4.78470i) q^{25} +(-3.64652 + 3.99978i) q^{26} +(-5.12039 + 2.12094i) q^{27} +(1.56063 - 5.05613i) q^{28} +(2.56271 - 6.18694i) q^{29} +(0.357612 + 0.129135i) q^{30} +(-2.46695 + 4.27288i) q^{31} +(-5.58291 - 0.911655i) q^{32} +(-1.32232 - 2.29033i) q^{33} +(-7.79321 + 6.57300i) q^{34} +(-0.147150 + 0.551337i) q^{35} +(-2.36083 + 1.67096i) q^{36} +(-2.06576 - 1.58511i) q^{37} +(4.89654 + 1.07253i) q^{38} +(-1.23476 - 4.60818i) q^{39} +(0.605405 + 0.0750265i) q^{40} +(4.31161 + 4.31161i) q^{41} +(3.01055 + 3.56233i) q^{42} +(-4.15699 - 10.0359i) q^{43} +(-2.88250 - 3.11387i) q^{44} +(0.247455 - 0.189879i) q^{45} +(-6.03550 - 4.20335i) q^{46} +(4.71097 - 2.71988i) q^{47} +(3.33114 - 3.71009i) q^{48} +(-4.94002 + 4.95946i) q^{49} +(6.98015 + 0.592868i) q^{50} +(-1.17293 - 8.90930i) q^{51} +(-3.56879 - 6.77158i) q^{52} +(6.20584 + 0.817015i) q^{53} +(-0.361725 - 7.82960i) q^{54} +(0.323565 + 0.323565i) q^{55} +(5.97579 + 4.50443i) q^{56} +(-3.12418 + 3.12418i) q^{57} +(6.99861 + 6.38050i) q^{58} +(-0.990748 + 7.52548i) q^{59} +(-0.343537 + 0.413650i) q^{60} +(-0.817471 + 0.107622i) q^{61} +(-4.49863 - 5.33376i) q^{62} +(3.79298 - 0.503144i) q^{63} +(3.89422 - 6.98821i) q^{64} +(0.412729 + 0.714867i) q^{65} +(3.68162 - 0.658791i) q^{66} +(-2.72913 - 3.55667i) q^{67} +(-4.99981 - 13.5233i) q^{68} +(5.98939 - 2.48089i) q^{69} +(-0.662680 - 0.460551i) q^{70} +(-2.53740 + 2.53740i) q^{71} +(-1.08867 - 3.94285i) q^{72} +(-11.7032 + 3.13587i) q^{73} +(3.10066 - 1.98640i) q^{74} +(-3.75889 + 4.89868i) q^{75} +(-3.77853 + 5.99796i) q^{76} +(1.45814 + 5.42056i) q^{77} +(6.72264 + 0.570996i) q^{78} +(-2.02495 + 1.16910i) q^{79} +(-0.390585 + 0.769241i) q^{80} +(2.22575 + 1.28504i) q^{81} +(-7.80603 + 3.66412i) q^{82} +(-1.12785 - 0.467172i) q^{83} +(-6.18445 + 2.29342i) q^{84} +(0.595009 + 1.43648i) q^{85} +(15.3459 - 0.708973i) q^{86} +(-8.06317 + 2.16052i) q^{87} +(5.52643 - 2.33849i) q^{88} +(-16.0470 - 4.29977i) q^{89} +(0.133709 + 0.420355i) q^{90} +(0.00994050 + 10.1259i) q^{91} +(8.49006 - 6.00914i) q^{92} +(6.09762 - 0.802767i) q^{93} +(1.35506 + 7.57270i) q^{94} +(0.382235 - 0.662051i) q^{95} +(3.33495 + 6.21294i) q^{96} +10.3954 q^{97} +(-4.22401 - 8.95308i) q^{98} +(1.17415 - 2.83466i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−0.480321	+	1.33015i	−0.339638	+	0.940556i
$2$	−0.480321	+	1.33015i	−0.339638	+	0.940556i
$3$	−0.758838	−	0.988936i	−0.438115	−	0.570963i	0.521152	−	0.853464i	$-0.325503\pi$
$3$	−0.758838	−	0.988936i	−0.438115	−	0.570963i	−0.959267	+	0.282501i	$0.908836\pi$
$4$	−1.53858	−	1.27780i	−0.769292	−	0.638898i
$5$	0.171111	+	0.131298i	0.0765231	+	0.0587182i	0.646315	−	0.763071i	$-0.276309\pi$
$5$	0.171111	+	0.131298i	0.0765231	+	0.0587182i	−0.569792	+	0.821789i	$0.692976\pi$
$6$	1.67992	−	0.534359i	0.685823	−	0.218151i
$7$	1.01488	+	2.44336i	0.383590	+	0.923503i
$7$	1.01488	+	2.44336i	0.383590	+	0.923503i
$8$	2.43867	−	1.43279i	0.862200	−	0.506568i
$9$	0.374296	−	1.39689i	0.124765	−	0.465631i
$10$	−0.256834	+	0.164537i	−0.0812179	+	0.0520313i
$11$	2.10346	+	0.276926i	0.634218	+	0.0834963i	0.440778	−	0.897616i	$-0.354702\pi$
$11$	2.10346	+	0.276926i	0.634218	+	0.0834963i	0.193439	+	0.981112i	$0.438036\pi$
$12$	−0.0961237	+	2.49120i	−0.0277485	+	0.719148i
$13$	3.53590	+	1.46462i	0.980681	+	0.406211i	0.814678	−	0.579914i	$-0.196914\pi$
$13$	3.53590	+	1.46462i	0.980681	+	0.406211i	0.166003	+	0.986125i	$0.446914\pi$
$14$	−3.73750	+	0.176348i	−0.998889	+	0.0471310i
$15$		−	0.268851i		−	0.0694171i
$16$	0.734477	+	3.93199i	0.183619	+	0.982997i
$17$	6.24315	+	3.60448i	1.51419	+	0.874216i	0.999862	+	0.0166201i	$0.00529058\pi$
$17$	6.24315	+	3.60448i	1.51419	+	0.874216i	0.514324	+	0.857596i	$0.328043\pi$
$18$	1.67829	+	1.16883i	0.395577	+	0.275495i
$19$	−0.462645	−	3.51414i	−0.106138	−	0.806198i	−0.958869	−	0.283848i	$-0.908389\pi$
$19$	−0.462645	−	3.51414i	−0.106138	−	0.806198i	0.852731	−	0.522350i	$-0.174945\pi$
$20$	−0.0954963	−	0.420657i	−0.0213536	−	0.0940618i
$21$	1.64620	−	2.85777i	0.359229	−	0.623616i
$22$	−1.37869	+	2.66490i	−0.293938	+	0.568159i
$23$	−1.34605	+	5.02353i	−0.280671	+	1.04748i	0.671274	+	0.741210i	$0.265747\pi$
$23$	−1.34605	+	5.02353i	−0.280671	+	1.04748i	−0.951945	+	0.306269i	$0.900919\pi$
$24$	−3.26749	−	1.32443i	−0.666974	−	0.270349i
$25$	−1.28206	−	4.78470i	−0.256411	−	0.956939i
$26$	−3.64652	+	3.99978i	−0.715141	+	0.784421i
$27$	−5.12039	+	2.12094i	−0.985420	+	0.408174i
$28$	1.56063	−	5.05613i	0.294932	−	0.955518i
$29$	2.56271	−	6.18694i	0.475884	−	1.14889i	−0.485639	−	0.874160i	$-0.661413\pi$
$29$	2.56271	−	6.18694i	0.475884	−	1.14889i	0.961523	−	0.274726i	$-0.0885871\pi$
$30$	0.357612	+	0.129135i	0.0652907	+	0.0235767i
$31$	−2.46695	+	4.27288i	−0.443077	+	0.767432i	−0.997916	−	0.0645260i	$-0.979446\pi$
$31$	−2.46695	+	4.27288i	−0.443077	+	0.767432i	0.554839	+	0.831958i	$0.312780\pi$
$32$	−5.58291	−	0.911655i	−0.986928	−	0.161159i
$33$	−1.32232	−	2.29033i	−0.230187	−	0.398696i
$34$	−7.79321	+	6.57300i	−1.33652	+	1.12726i
$35$	−0.147150	+	0.551337i	−0.0248730	+	0.0931930i
$36$	−2.36083	+	1.67096i	−0.393472	+	0.278494i
$37$	−2.06576	−	1.58511i	−0.339609	−	0.260591i	0.424850	−	0.905264i	$-0.360327\pi$
$37$	−2.06576	−	1.58511i	−0.339609	−	0.260591i	−0.764459	+	0.644673i	$0.776994\pi$
$38$	4.89654	+	1.07253i	0.794323	+	0.173987i
$39$	−1.23476	−	4.60818i	−0.197720	−	0.737900i
$40$	0.605405	+	0.0750265i	0.0957229	+	0.0118627i
$41$	4.31161	+	4.31161i	0.673360	+	0.673360i	0.958489	−	0.285129i	$-0.0920365\pi$
$41$	4.31161	+	4.31161i	0.673360	+	0.673360i	−0.285129	+	0.958489i	$0.592036\pi$
$42$	3.01055	+	3.56233i	0.464538	+	0.549679i
$43$	−4.15699	−	10.0359i	−0.633935	−	1.53046i	−0.834635	−	0.550803i	$-0.814322\pi$
$43$	−4.15699	−	10.0359i	−0.633935	−	1.53046i	0.200700	−	0.979653i	$-0.435678\pi$
$44$	−2.88250	−	3.11387i	−0.434553	−	0.469433i
$45$	0.247455	−	0.189879i	0.0368885	−	0.0283055i
$46$	−6.03550	−	4.20335i	−0.889886	−	0.619751i
$47$	4.71097	−	2.71988i	0.687165	−	0.396735i	−0.115384	−	0.993321i	$-0.536810\pi$
$47$	4.71097	−	2.71988i	0.687165	−	0.396735i	0.802549	+	0.596586i	$0.203476\pi$
$48$	3.33114	−	3.71009i	0.480808	−	0.535506i
$49$	−4.94002	+	4.95946i	−0.705717	+	0.708494i
$50$	6.98015	+	0.592868i	0.987142	+	0.0838442i
$51$	−1.17293	−	8.90930i	−0.164243	−	1.24755i
$52$	−3.56879	−	6.77158i	−0.494902	−	0.939050i
$53$	6.20584	+	0.817015i	0.852438	+	0.112226i	0.544068	−	0.839041i	$-0.316883\pi$
$53$	6.20584	+	0.817015i	0.852438	+	0.112226i	0.308370	+	0.951267i	$0.400217\pi$
$54$	−0.361725	−	7.82960i	−0.0492245	−	1.06547i
$55$	0.323565	+	0.323565i	0.0436295	+	0.0436295i
$56$	5.97579	+	4.50443i	0.798549	+	0.601930i
$57$	−3.12418	+	3.12418i	−0.413808	+	0.413808i
$58$	6.99861	+	6.38050i	0.918963	+	0.837801i
$59$	−0.990748	+	7.52548i	−0.128984	+	0.979734i	0.797478	+	0.603348i	$0.206167\pi$
$59$	−0.990748	+	7.52548i	−0.128984	+	0.979734i	−0.926463	+	0.376387i	$0.877166\pi$
$60$	−0.343537	+	0.413650i	−0.0443505	+	0.0534020i
$61$	−0.817471	+	0.107622i	−0.104666	+	0.0137796i	−0.182677	−	0.983173i	$-0.558476\pi$
$61$	−0.817471	+	0.107622i	−0.104666	+	0.0137796i	0.0780110	+	0.996952i	$0.475143\pi$
$62$	−4.49863	−	5.33376i	−0.571327	−	0.677388i
$63$	3.79298	−	0.503144i	0.477871	−	0.0633902i
$64$	3.89422	−	6.98821i	0.486778	−	0.873526i
$65$	0.412729	+	0.714867i	0.0511927	+	0.0886684i
$66$	3.68162	−	0.658791i	0.453176	−	0.0810915i
$67$	−2.72913	−	3.55667i	−0.333416	−	0.434517i	0.596318	−	0.802749i	$-0.296630\pi$
$67$	−2.72913	−	3.55667i	−0.333416	−	0.434517i	−0.929734	+	0.368232i	$0.879963\pi$
$68$	−4.99981	−	13.5233i	−0.606316	−	1.63994i
$69$	5.98939	−	2.48089i	0.721038	−	0.298664i
$70$	−0.662680	−	0.460551i	−0.0792055	−	0.0550463i
$71$	−2.53740	+	2.53740i	−0.301133	+	0.301133i	−0.841457	−	0.540324i	$-0.818302\pi$
$71$	−2.53740	+	2.53740i	−0.301133	+	0.301133i	0.540324	+	0.841457i	$0.318302\pi$
$72$	−1.08867	−	3.94285i	−0.128301	−	0.464669i
$73$	−11.7032	+	3.13587i	−1.36976	+	0.367026i	−0.867391	−	0.497628i	$-0.834205\pi$
$73$	−11.7032	+	3.13587i	−1.36976	+	0.367026i	−0.502369	+	0.864654i	$0.667538\pi$
$74$	3.10066	−	1.98640i	0.360445	−	0.230915i
$75$	−3.75889	+	4.89868i	−0.434039	+	0.565651i
$76$	−3.77853	+	5.99796i	−0.433427	+	0.688013i
$77$	1.45814	+	5.42056i	0.166171	+	0.617731i
$78$	6.72264	+	0.570996i	0.761189	+	0.0646526i
$79$	−2.02495	+	1.16910i	−0.227824	+	0.131534i	−0.609568	−	0.792734i	$-0.708657\pi$
$79$	−2.02495	+	1.16910i	−0.227824	+	0.131534i	0.381744	+	0.924268i	$0.375324\pi$
$80$	−0.390585	+	0.769241i	−0.0436687	+	0.0860038i
$81$	2.22575	+	1.28504i	0.247306	+	0.142782i
$82$	−7.80603	+	3.66412i	−0.862032	+	0.404634i
$83$	−1.12785	−	0.467172i	−0.123798	−	0.0512788i	0.319925	−	0.947443i	$-0.396342\pi$
$83$	−1.12785	−	0.467172i	−0.123798	−	0.0512788i	−0.443723	+	0.896164i	$0.646342\pi$
$84$	−6.18445	+	2.29342i	−0.674779	+	0.250232i
$85$	0.595009	+	1.43648i	0.0645378	+	0.155808i
$86$	15.3459	−	0.708973i	1.65479	−	0.0764506i
$87$	−8.06317	+	2.16052i	−0.864463	+	0.231632i
$88$	5.52643	−	2.33849i	0.589119	−	0.249284i
$89$	−16.0470	−	4.29977i	−1.70098	−	0.455775i	−0.727790	−	0.685800i	$-0.759453\pi$
$89$	−16.0470	−	4.29977i	−1.70098	−	0.455775i	−0.973185	+	0.230025i	$0.926119\pi$
$90$	0.133709	+	0.420355i	0.0140942	+	0.0443093i
$91$	0.00994050	+	10.1259i	0.00104205	+	1.06148i
$92$	8.49006	−	6.00914i	0.885150	−	0.626497i
$93$	6.09762	−	0.802767i	0.632294	−	0.0832430i
$94$	1.35506	+	7.57270i	0.139764	+	0.781064i
$95$	0.382235	−	0.662051i	0.0392165	−	0.0679250i
$96$	3.33495	+	6.21294i	0.340372	+	0.634106i
$97$	10.3954			1.05549			0.527746	−	0.849402i	$-0.323037\pi$
$97$	10.3954			1.05549			0.527746	+	0.849402i	$0.323037\pi$
$98$	−4.22401	−	8.95308i	−0.426690	−	0.904398i
$99$	1.17415	−	2.83466i	0.118007	−	0.284894i
$100$	−4.14131	+	8.99986i	−0.414131	+	0.899986i
$101$	−0.0248310	+	0.188610i	−0.00247077	+	0.0187674i	−0.992636	−	0.121137i	$-0.961346\pi$
$101$	−0.0248310	+	0.188610i	−0.00247077	+	0.0187674i	0.990165	+	0.139904i	$0.0446794\pi$
$102$	12.4141	+	2.71915i	1.22917	+	0.269236i
$103$	0.208871	+	0.0559668i	0.0205807	+	0.00551457i	0.269095	−	0.963114i	$-0.413276\pi$
$103$	0.208871	+	0.0559668i	0.0205807	+	0.00551457i	−0.248514	+	0.968628i	$0.579942\pi$
$104$	10.7214	−	1.49448i	1.05132	−	0.146546i
$105$	0.656901	−	0.272853i	0.0641070	−	0.0266277i
$106$	−4.06755	+	7.86226i	−0.395075	+	0.763650i
$107$	1.16521	−	1.51853i	0.112645	−	0.146802i	−0.733628	−	0.679551i	$-0.762174\pi$
$107$	1.16521	−	1.51853i	0.112645	−	0.146802i	0.846273	+	0.532749i	$0.178841\pi$
$108$	10.5883	+	3.27958i	1.01886	+	0.315577i
$109$	−14.8637	+	11.4053i	−1.42368	+	1.09243i	−0.443068	+	0.896488i	$0.646110\pi$
$109$	−14.8637	+	11.4053i	−1.42368	+	1.09243i	−0.980615	+	0.195943i	$0.937223\pi$
$110$	−0.585804	+	0.274974i	−0.0558543	+	0.0262178i
$111$			3.24575i			0.308073i
$112$	−8.86186	+	5.78511i	−0.837367	+	0.546641i
$113$			1.46473i			0.137790i	0.997624	+	0.0688950i	$0.0219474\pi$
$113$			1.46473i			0.137790i	−0.997624	+	0.0688950i	$0.978053\pi$
$114$	−2.65501	−	5.65624i	−0.248665	−	0.529755i
$115$	−0.889903	+	0.682847i	−0.0829839	+	0.0636758i
$116$	−11.8486	+	6.24450i	−1.10011	+	0.579787i
$117$	3.36939	−	4.39107i	0.311500	−	0.405954i
$118$	−9.53412	−	4.93249i	−0.877687	−	0.454072i
$119$	−2.47098	+	18.9124i	−0.226514	+	1.73370i
$120$	−0.385208	−	0.655640i	−0.0351645	−	0.0598515i
$121$	−6.27732	−	1.68200i	−0.570665	−	0.152909i
$122$	0.249495	−	1.13905i	0.0225883	−	0.103125i
$123$	0.992096	−	7.53572i	0.0894543	−	0.679473i
$124$	9.25547	−	3.42193i	0.831166	−	0.307298i
$125$	0.821534	−	1.98336i	0.0734802	−	0.177397i
$126$	−1.15259	+	5.28689i	−0.102681	+	0.470994i
$127$	21.8084			1.93518			0.967590	−	0.252526i	$-0.0812612\pi$
$127$	21.8084			1.93518			0.967590	+	0.252526i	$0.0812612\pi$
$128$	7.42486	+	8.53647i	0.656271	+	0.754525i
$129$	−6.77035	+	11.7266i	−0.596096	+	1.03247i
$130$	−1.14912	+	0.205624i	−0.100785	+	0.0180344i
$131$	−5.89963	+	0.776701i	−0.515453	+	0.0678607i	−0.383766	−	0.923431i	$-0.625373\pi$
$131$	−5.89963	+	0.776701i	−0.515453	+	0.0678607i	−0.131688	+	0.991291i	$0.542040\pi$
$132$	−0.892071	+	5.21353i	−0.0776448	+	0.453779i
$133$	8.11677	−	4.69685i	0.703813	−	0.407269i
$134$	6.04176	−	1.92180i	0.521928	−	0.166018i
$135$	−1.15463	−	0.309382i	−0.0993746	−	0.0266273i
$136$	20.3895	−	0.154976i	1.74838	−	0.0132890i
$137$	−2.30349	+	0.617217i	−0.196800	+	0.0527324i	−0.355873	−	0.934534i	$-0.615816\pi$
$137$	−2.30349	+	0.617217i	−0.196800	+	0.0527324i	0.159073	+	0.987267i	$0.449150\pi$
$138$	0.423114	+	9.15839i	0.0360179	+	0.779614i
$139$	−0.998247	−	2.40998i	−0.0846702	−	0.204412i	0.875874	−	0.482541i	$-0.160286\pi$
$139$	−0.998247	−	2.40998i	−0.0846702	−	0.204412i	−0.960544	+	0.278129i	$0.910286\pi$
$140$	0.930900	−	0.660250i	0.0786754	−	0.0558013i
$141$	−6.26465	−	2.59490i	−0.527578	−	0.218530i
$142$	−2.15634	−	4.59387i	−0.180956	−	0.385509i
$143$	7.03203	+	4.05995i	0.588048	+	0.339510i
$144$	5.76748	+	0.445743i	0.480624	+	0.0371453i
$145$	1.25084	−	0.722173i	0.103877	−	0.0599732i
$146$	1.45014	−	17.0732i	0.120014	−	1.41299i
$147$	8.65326	+	1.12194i	0.713709	+	0.0925363i
$148$	1.15289	+	5.07845i	0.0947673	+	0.417446i
$149$	8.94508	−	11.6575i	0.732810	−	0.955016i	−0.267153	−	0.963654i	$-0.586083\pi$
$149$	8.94508	−	11.6575i	0.732810	−	0.955016i	0.999963	+	0.00863800i	$0.00274959\pi$
$150$	−4.71049	−	7.35281i	−0.384610	−	0.600355i
$151$	1.80749	−	0.484316i	0.147092	−	0.0394131i	−0.184522	−	0.982828i	$-0.559074\pi$
$151$	1.80749	−	0.484316i	0.147092	−	0.0394131i	0.331614	+	0.943415i	$0.392407\pi$
$152$	−6.16326	−	7.90695i	−0.499906	−	0.641338i
$153$	7.37187	−	7.37187i	0.595980	−	0.595980i
$154$	−7.91052	−	0.664069i	−0.637448	−	0.0535122i
$155$	−0.983141	+	0.407230i	−0.0789678	+	0.0327095i
$156$	−3.98853	+	8.66784i	−0.319338	+	0.693983i
$157$	−1.09817	−	1.43116i	−0.0876436	−	0.114219i	0.747473	−	0.664292i	$-0.231267\pi$
$157$	−1.09817	−	1.43116i	−0.0876436	−	0.114219i	−0.835117	+	0.550072i	$0.814600\pi$
$158$	−0.582455	−	3.25502i	−0.0463376	−	0.258956i
$159$	−3.90125	−	6.75716i	−0.309389	−	0.535878i
$160$	−0.835598	−	0.889018i	−0.0660598	−	0.0702831i
$161$	−13.6404	+	1.80942i	−1.07501	+	0.142602i
$162$	−2.77837	+	2.34335i	−0.218289	+	0.184111i
$163$	−13.6305	+	1.79450i	−1.06763	+	0.140556i	−0.643805	−	0.765190i	$-0.722645\pi$
$163$	−13.6305	+	1.79450i	−1.06763	+	0.140556i	−0.423822	+	0.905746i	$0.639312\pi$
$164$	−1.12441	−	12.1431i	−0.0878020	−	0.948218i
$165$	0.0744520	−	0.565519i	0.00579608	−	0.0440256i
$166$	1.16314	−	1.27582i	0.0902772	−	0.0990228i
$167$	−0.443775	+	0.443775i	−0.0343403	+	0.0343403i	−0.724068	−	0.689728i	$-0.757730\pi$
$167$	−0.443775	+	0.443775i	−0.0343403	+	0.0343403i	0.689728	+	0.724068i	$0.257730\pi$
$168$	−0.0800562	−	9.32781i	−0.00617647	−	0.719656i
$169$	1.16507	+	1.16507i	0.0896206	+	0.0896206i
$170$	−2.19652	+	0.101478i	−0.168466	+	0.00778305i
$171$	−5.08204	−	0.669063i	−0.388633	−	0.0511645i
$172$	−6.42791	+	20.7528i	−0.490123	+	1.58239i
$173$	0.535394	+	4.06672i	0.0407052	+	0.309187i	0.999671	+	0.0256639i	$0.00816996\pi$
$173$	0.535394	+	4.06672i	0.0407052	+	0.309187i	−0.958965	+	0.283523i	$0.908497\pi$
$174$	0.999101	−	11.7629i	0.0757417	−	0.891747i
$175$	10.3896	−	7.98844i	0.785380	−	0.603869i
$176$	0.456075	+	8.47419i	0.0343779	+	0.638766i
$177$	8.19404	−	4.73083i	0.615902	−	0.355591i
$178$	13.4270	−	19.2796i	1.00640	−	1.44506i
$179$	20.0529	−	15.3871i	1.49882	−	1.15009i	0.549625	−	0.835411i	$-0.314770\pi$
$179$	20.0529	−	15.3871i	1.49882	−	1.15009i	0.949199	−	0.314677i	$-0.101896\pi$
$180$	−0.623357	−	0.0240524i	−0.0464623	−	0.00179276i
$181$	−1.08379	−	2.61651i	−0.0805578	−	0.194484i	0.878469	−	0.477800i	$-0.158566\pi$
$181$	−1.08379	−	2.61651i	−0.0805578	−	0.194484i	−0.959027	+	0.283316i	$0.908566\pi$
$182$	−13.4737	−	4.85045i	−0.998736	−	0.359539i
$183$	0.726759	+	0.726759i	0.0537236	+	0.0537236i
$184$	3.91509	+	14.1793i	0.288624	+	1.04532i
$185$	−0.145352	−	0.542460i	−0.0106865	−	0.0398825i
$186$	−1.86102	+	8.49632i	−0.136456	+	0.622980i
$187$	12.1341	+	9.31079i	0.887330	+	0.680872i
$188$	−10.7237	−	1.83489i	−0.782104	−	0.133823i
$189$	−10.3788	−	10.3585i	−0.754948	−	0.753467i
$190$	0.697029	+	0.826426i	0.0505678	+	0.0599552i
$191$	−6.61571	−	11.4587i	−0.478696	−	0.829125i	0.521006	−	0.853553i	$-0.325557\pi$
$191$	−6.61571	−	11.4587i	−0.478696	−	0.829125i	−0.999702	+	0.0244277i	$0.992224\pi$
$192$	−9.86597	+	1.45177i	−0.712015	+	0.104773i
$193$	−1.04305	+	1.80661i	−0.0750803	+	0.130043i	−0.901121	−	0.433567i	$-0.857255\pi$
$193$	−1.04305	+	1.80661i	−0.0750803	+	0.130043i	0.826041	+	0.563610i	$0.190588\pi$
$194$	−4.99313	+	13.8274i	−0.358486	+	0.992750i
$195$	0.393764	−	0.950631i	0.0281980	−	0.0680761i
$196$	13.9378	−	1.31820i	0.995557	−	0.0941572i
$197$	−17.8938	+	7.41186i	−1.27488	+	0.528073i	−0.914445	−	0.404710i	$-0.867372\pi$
$197$	−17.8938	+	7.41186i	−1.27488	+	0.528073i	−0.360437	+	0.932784i	$0.617372\pi$
$198$	3.20654	+	2.92335i	0.227879	+	0.207753i
$199$	−4.53719	−	16.9330i	−0.321633	−	1.20035i	−0.917654	−	0.397381i	$-0.869919\pi$
$199$	−4.53719	−	16.9330i	−0.321633	−	1.20035i	0.596021	−	0.802969i	$-0.296748\pi$
$200$	−9.98198	−	9.83138i	−0.705832	−	0.695184i
$201$	−1.44636	+	5.39787i	−0.102018	+	0.380737i
$202$	−0.238952	−	0.123622i	−0.0168126	−	0.00869803i
$203$	17.7178	−	0.0173934i	1.24354	−	0.00122078i
$204$	−9.57961	+	15.2065i	−0.670707	+	1.06467i
$205$	0.171657	+	1.30387i	0.0119891	+	0.0910661i
$206$	−0.174769	+	0.250947i	−0.0121767	+	0.0174843i
$207$	6.51352	+	3.76058i	0.452721	+	0.261378i
$208$	−3.16182	+	14.9788i	−0.219233	+	1.03860i
$209$		−	7.51997i		−	0.520167i
$210$	0.0474114	+	1.00483i	0.00327170	+	0.0693400i
$211$	−19.7231	−	8.16958i	−1.35779	−	0.562417i	−0.419343	−	0.907828i	$-0.637740\pi$
$211$	−19.7231	−	8.16958i	−1.35779	−	0.562417i	−0.938452	+	0.345411i	$0.887740\pi$
$212$	−8.50423	−	9.18684i	−0.584073	−	0.630955i
$213$	4.43479	+	0.583852i	0.303867	+	0.0400049i
$214$	1.46020	+	2.27929i	0.0998171	+	0.155809i
$215$	0.606382	−	2.26305i	0.0413549	−	0.154339i
$216$	−9.44809	+	12.5087i	−0.642861	+	0.851110i
$217$	−12.9438	−	1.69116i	−0.878686	−	0.114804i
$218$	−8.03140	−	25.2491i	−0.543955	−	1.71009i
$219$	11.9820	+	9.19413i	0.809670	+	0.621282i
$220$	−0.0843818	−	0.911282i	−0.00568902	−	0.0614386i
$221$	16.7959	+	21.8889i	1.12982	+	1.47241i
$222$	−4.31733	−	1.55900i	−0.289760	−	0.104633i
$223$	−10.3561			−0.693498			−0.346749	−	0.937958i	$-0.612714\pi$
$223$	−10.3561			−0.693498			−0.346749	+	0.937958i	$0.612714\pi$
$224$	−3.43851	−	14.5663i	−0.229745	−	0.973251i
$225$	−7.16358			−0.477572
$226$	−1.94830	−	0.703540i	−0.129599	−	0.0467988i
$227$	10.8095	+	14.0872i	0.717450	+	0.934999i	0.999704	−	0.0243408i	$-0.00774869\pi$
$227$	10.8095	+	14.0872i	0.717450	+	0.934999i	−0.282254	+	0.959340i	$0.591082\pi$
$228$	8.79889	−	0.814749i	0.582721	−	0.0539581i
$229$	−9.61260	−	7.37601i	−0.635219	−	0.487420i	0.240240	−	0.970714i	$-0.422774\pi$
$229$	−9.61260	−	7.37601i	−0.635219	−	0.487420i	−0.875459	+	0.483293i	$0.839441\pi$
$230$	−0.480847	−	1.51169i	−0.0317061	−	0.0996777i
$231$	4.25410	−	5.55534i	0.279899	−	0.365514i
$232$	−2.61497	−	18.7597i	−0.171681	−	1.23164i
$233$	3.86660	−	14.4304i	0.253310	−	0.945364i	−0.715713	−	0.698394i	$-0.753898\pi$
$233$	3.86660	−	14.4304i	0.253310	−	0.945364i	0.969023	−	0.246970i	$-0.0794350\pi$
$234$	4.22238	+	6.59090i	0.276026	+	0.430861i
$235$	1.16321	+	0.153140i	0.0758796	+	0.00998973i
$236$	11.1404	−	10.3126i	0.725177	−	0.671294i
$237$	2.69277	+	1.11538i	0.174914	+	0.0724519i
$238$	−23.9694	−	12.3708i	−1.55371	−	0.801879i
$239$			25.1348i			1.62584i	0.582379	+	0.812918i	$0.302122\pi$
$239$			25.1348i			1.62584i	−0.582379	+	0.812918i	$0.697878\pi$
$240$	1.05712	−	0.197465i	0.0682369	−	0.0127463i
$241$	11.2112	+	6.47277i	0.722175	+	0.416948i	0.815553	−	0.578683i	$-0.196433\pi$
$241$	11.2112	+	6.47277i	0.722175	+	0.416948i	−0.0933776	+	0.995631i	$0.529766\pi$
$242$	5.25244	−	7.54186i	0.337640	−	0.484809i
$243$	1.75207	+	13.3083i	0.112395	+	0.853728i
$244$	1.39527	+	0.878976i	0.0893228	+	0.0562706i
$245$	−1.49646	+	0.200002i	−0.0956051	+	0.0127777i
$246$	9.54709	+	4.93920i	0.608700	+	0.314912i
$247$	3.51100	−	13.1032i	0.223399	−	0.833738i
$248$	0.106067	+	13.9548i	0.00673526	+	0.886128i
$249$	0.393854	+	1.46988i	0.0249595	+	0.0931501i
$250$	2.24356	+	2.04541i	0.141895	+	0.129363i
$251$	−2.13451	+	0.884142i	−0.134729	+	0.0558065i	−0.449029	−	0.893517i	$-0.648230\pi$
$251$	−2.13451	+	0.884142i	−0.134729	+	0.0558065i	0.314300	+	0.949324i	$0.398230\pi$
$252$	−6.47873	−	4.07253i	−0.408122	−	0.256545i
$253$	−4.22251	+	10.1941i	−0.265467	+	0.640895i
$254$	−10.4750	+	29.0084i	−0.657261	+	1.82015i
$255$	0.969071	−	1.67848i	0.0606856	−	0.105110i
$256$	−14.9211	+	5.77591i	−0.932568	+	0.360995i
$257$	−7.31441	−	12.6689i	−0.456261	−	0.790267i	0.542499	−	0.840056i	$-0.317478\pi$
$257$	−7.31441	−	12.6689i	−0.456261	−	0.790267i	−0.998760	+	0.0497898i	$0.984145\pi$
$258$	−12.3462	−	14.6381i	−0.768638	−	0.911328i
$259$	1.77650	−	6.65611i	0.110386	−	0.413590i
$260$	0.278436	−	1.62727i	0.0172679	−	0.100919i
$261$	−7.68328	−	5.89559i	−0.475583	−	0.364928i
$262$	1.80059	−	8.22045i	0.111241	−	0.507861i
$263$	−3.08270	−	11.5048i	−0.190087	−	0.709415i	−0.993484	−	0.113971i	$-0.963643\pi$
$263$	−3.08270	−	11.5048i	−0.190087	−	0.709415i	0.803397	−	0.595444i	$-0.203024\pi$
$264$	−6.50628	−	3.69075i	−0.400434	−	0.227150i
$265$	0.954614	+	0.954614i	0.0586415	+	0.0586415i
$266$	2.34885	+	13.0525i	0.144017	+	0.800300i
$267$	7.92484	+	19.1323i	0.484992	+	1.17088i
$268$	−0.345705	+	8.95951i	−0.0211173	+	0.547289i
$269$	−22.3885	+	17.1793i	−1.36505	+	1.04744i	−0.372192	+	0.928156i	$0.621394\pi$
$269$	−22.3885	+	17.1793i	−1.36505	+	1.04744i	−0.992860	+	0.119285i	$0.961940\pi$
$270$	0.966116	−	1.38722i	0.0587959	−	0.0844237i
$271$	23.1368	−	13.3580i	1.40546	−	0.811443i	0.410514	−	0.911854i	$-0.365349\pi$
$271$	23.1368	−	13.3580i	1.40546	−	0.811443i	0.994946	+	0.100412i	$0.0320160\pi$
$272$	−9.58734	+	27.1954i	−0.581318	+	1.64896i
$273$	10.0063	−	7.69373i	0.605609	−	0.465646i
$274$	0.285423	−	3.36044i	0.0172430	−	0.203012i
$275$	−1.37175	−	10.4195i	−0.0827195	−	0.628317i
$276$	−12.3852	−	3.83616i	−0.745504	−	0.230910i
$277$	−3.03152	−	0.399107i	−0.182146	−	0.0239800i	0.0389012	−	0.999243i	$-0.487614\pi$
$277$	−3.03152	−	0.399107i	−0.182146	−	0.0239800i	−0.221048	+	0.975263i	$0.570948\pi$
$278$	3.68511	−	0.170251i	0.221018	−	0.0102110i
$279$	5.04539	+	5.04539i	0.302059	+	0.302059i
$280$	0.431099	+	1.55537i	0.0257631	+	0.0929509i
$281$	7.10678	−	7.10678i	0.423955	−	0.423955i	−0.462608	−	0.886563i	$-0.653086\pi$
$281$	7.10678	−	7.10678i	0.423955	−	0.423955i	0.886563	+	0.462608i	$0.153086\pi$
$282$	6.46064	−	7.08652i	0.384726	−	0.421996i
$283$	3.54274	−	26.9098i	0.210594	−	1.59962i	−0.480591	−	0.876945i	$-0.659578\pi$
$283$	3.54274	−	26.9098i	0.210594	−	1.59962i	0.691185	−	0.722678i	$-0.257089\pi$
$284$	7.14627	−	0.661722i	0.424053	−	0.0392660i
$285$	−0.944781	+	0.124383i	−0.0559640	+	0.00736780i
$286$	−8.77796	+	7.40356i	−0.519052	+	0.437782i
$287$	−6.15903	+	14.9106i	−0.363556	+	0.880145i
$288$	−3.36315	+	7.45750i	−0.198175	+	0.439437i
$289$	17.4846	+	30.2842i	1.02851	+	1.78143i
$290$	0.359791	+	2.01068i	0.0211277	+	0.118071i
$291$	−7.88841	−	10.2804i	−0.462427	−	0.602647i
$292$	22.0134	+	10.1295i	1.28824	+	0.592786i
$293$	12.9251	−	5.35374i	0.755091	−	0.312769i	0.0282738	−	0.999600i	$-0.490999\pi$
$293$	12.9251	−	5.35374i	0.755091	−	0.312769i	0.726817	+	0.686831i	$0.240999\pi$
$294$	−5.64869	+	10.9712i	−0.329438	+	0.639854i
$295$	−1.15761	+	1.15761i	−0.0673985	+	0.0673985i
$296$	−7.30885	−	0.905769i	−0.424818	−	0.0526467i
$297$	−11.3579	+	3.04334i	−0.659052	+	0.176592i
$298$	11.2096	+	17.4976i	0.649356	+	1.01361i
$299$	−12.1170	+	15.7912i	−0.700747	+	0.913231i
$300$	12.0429	−	2.73393i	0.695296	−	0.157844i
$301$	20.3024	−	20.3423i	1.17021	−	1.17251i
$302$	−0.223965	+	2.63686i	−0.0128877	+	0.151734i
$303$	0.205366	−	0.118568i	0.0117980	−	0.00681156i
$304$	13.4777	−	4.40017i	0.773002	−	0.252367i
$305$	−0.154009	−	0.0889170i	−0.00881851	−	0.00509137i
$306$	6.26481	+	13.3465i	0.358135	+	0.762971i
$307$	5.63314	+	2.33332i	0.321500	+	0.133170i	0.537596	−	0.843202i	$-0.319332\pi$
$307$	5.63314	+	2.33332i	0.321500	+	0.133170i	−0.216096	+	0.976372i	$0.569332\pi$
$308$	4.68290	−	10.2032i	0.266833	−	0.581381i
$309$	−0.103151	−	0.249030i	−0.00586808	−	0.0141668i
$310$	−0.0694530	−	1.50332i	−0.00394466	−	0.0853831i
$311$	−19.0790	+	5.11219i	−1.08187	+	0.289886i	−0.755361	−	0.655309i	$-0.772539\pi$
$311$	−19.0790	+	5.11219i	−1.08187	+	0.289886i	−0.326508	+	0.945195i	$0.605872\pi$
$312$	−9.61372	−	9.46868i	−0.544270	−	0.536059i
$313$	12.4518	+	3.33645i	0.703817	+	0.188587i	0.592939	−	0.805247i	$-0.297967\pi$
$313$	12.4518	+	3.33645i	0.703817	+	0.188587i	0.110877	+	0.993834i	$0.464634\pi$
$314$	2.43113	−	0.773311i	0.137197	−	0.0436405i
$315$	0.715082	+	0.411917i	0.0402903	+	0.0232089i
$316$	4.60942	+	0.788704i	0.259300	+	0.0443681i
$317$	−13.6866	+	1.80188i	−0.768718	+	0.101204i	−0.504677	−	0.863308i	$-0.668389\pi$
$317$	−13.6866	+	1.80188i	−0.768718	+	0.101204i	−0.264040	+	0.964512i	$0.585055\pi$
$318$	10.8619	−	1.94363i	0.609104	−	0.108993i
$319$	7.10389	−	12.3043i	0.397742	−	0.688909i
$320$	1.58388	−	0.684454i	0.0885416	−	0.0382621i
$321$	−2.38594			−0.133170
$322$	4.14498	−	19.0128i	0.230990	−	1.05954i
$323$	9.77829	−	23.6069i	0.544079	−	1.31352i
$324$	−1.78249	−	4.82120i	−0.0990272	−	0.267844i
$325$	2.47453	−	18.7959i	0.137262	−	1.04261i
$326$	4.16010	−	18.9926i	0.230406	−	1.05190i
$327$	22.5583	+	6.04447i	1.24747	+	0.334260i
$328$	16.6922	+	4.33696i	0.921674	+	0.239469i
$329$	11.4267	+	8.75023i	0.629976	+	0.482416i
$330$	0.716462	+	0.370663i	0.0394400	+	0.0204043i
$331$	7.25779	−	9.45854i	0.398924	−	0.519888i	−0.550097	−	0.835101i	$-0.685409\pi$
$331$	7.25779	−	9.45854i	0.398924	−	0.519888i	0.949021	+	0.315213i	$0.102076\pi$
$332$	1.13835	+	2.15995i	0.0624749	+	0.118543i
$333$	−2.98744	+	2.29235i	−0.163711	+	0.125620i
$334$	−0.377131	−	0.803440i	−0.0206357	−	0.0439623i
$335$		−	0.966914i		−	0.0528282i
$336$	12.4458	+	4.37386i	0.678975	+	0.238613i
$337$		−	6.88603i		−	0.375106i	−0.982254	−	0.187553i	$-0.939944\pi$
$337$		−	6.88603i		−	0.375106i	0.982254	−	0.187553i	$-0.0600556\pi$
$338$	−2.10932	+	0.990106i	−0.114732	+	0.0538546i
$339$	1.44852	−	1.11149i	0.0786730	−	0.0603679i
$340$	0.920055	−	2.97044i	0.0498970	−	0.161095i
$341$	−6.37240	+	8.30468i	−0.345085	+	0.449723i
$342$	3.33096	−	6.43850i	0.180118	−	0.348154i
$343$	−17.1313	−	7.03697i	−0.925003	−	0.379961i
$344$	−24.5168	−	18.5181i	−1.32186	−	0.998428i
$345$	1.35058	+	0.361888i	0.0727130	+	0.0194834i
$346$	−5.66650	−	1.24118i	−0.304633	−	0.0667262i
$347$	−2.49415	+	18.9449i	−0.133893	+	1.01702i	0.784160	+	0.620559i	$0.213094\pi$
$347$	−2.49415	+	18.9449i	−0.133893	+	1.01702i	−0.918053	+	0.396458i	$0.870239\pi$
$348$	15.1666	+	6.97894i	0.813013	+	0.374111i
$349$	−6.87406	+	16.5955i	−0.367960	+	0.888334i	0.626124	+	0.779723i	$0.284640\pi$
$349$	−6.87406	+	16.5955i	−0.367960	+	0.888334i	−0.994084	+	0.108611i	$0.965360\pi$
$350$	5.63545	+	17.6567i	0.301228	+	0.943791i
$351$	−21.2115			−1.13219
$352$	−11.4910	−	3.46368i	−0.612471	−	0.184615i
$353$	8.34381	−	14.4519i	0.444096	−	0.769197i	−0.553893	−	0.832588i	$-0.686858\pi$
$353$	8.34381	−	14.4519i	0.444096	−	0.769197i	0.997989	+	0.0633910i	$0.0201915\pi$
$354$	2.35693	+	13.1716i	0.125270	+	0.700062i
$355$	−0.767330	+	0.101021i	−0.0407257	+	0.00536164i
$356$	19.1954	+	27.1203i	1.01735	+	1.43737i
$357$	20.5782	−	11.9078i	1.08912	−	0.630227i
$358$	10.8353	+	34.0641i	0.572664	+	1.80034i
$359$	−6.90872	−	1.85119i	−0.364628	−	0.0977019i	0.0718529	−	0.997415i	$-0.477109\pi$
$359$	−6.90872	−	1.85119i	−0.364628	−	0.0977019i	−0.436481	+	0.899713i	$0.643775\pi$
$360$	0.331405	−	0.817604i	0.0174666	−	0.0430915i
$361$	6.21748	−	1.66597i	0.327236	−	0.0876825i
$362$	4.00091	−	0.184841i	0.210283	−	0.00971501i
$363$	3.10007	+	7.48424i	0.162712	+	0.392821i
$364$	12.9235	−	15.5922i	0.677376	−	0.817254i
$365$	−2.41428	−	1.00003i	−0.126369	−	0.0523439i
$366$	−1.31577	+	0.617619i	−0.0687767	+	0.0322835i
$367$	−6.59509	−	3.80767i	−0.344261	−	0.198759i	0.317894	−	0.948126i	$-0.397024\pi$
$367$	−6.59509	−	3.80767i	−0.344261	−	0.198759i	−0.662155	+	0.749367i	$0.730358\pi$
$368$	−20.7411	−	1.60299i	−1.08121	−	0.0835617i
$369$	7.63668	−	4.40904i	0.397549	−	0.229525i
$370$	0.791368	+	0.0672158i	0.0411412	+	0.00349438i
$371$	4.30195	+	15.9923i	0.223346	+	0.830278i
$372$	−10.4075	−	6.55639i	−0.539602	−	0.339933i
$373$	−19.8436	+	25.8606i	−1.02746	+	1.33901i	−0.0880897	+	0.996113i	$0.528076\pi$
$373$	−19.8436	+	25.8606i	−1.02746	+	1.33901i	−0.939372	+	0.342901i	$0.888590\pi$
$374$	−18.2130	+	11.6679i	−0.941770	+	0.603333i
$375$	−2.58483	+	0.692602i	−0.133480	+	0.0357658i
$376$	7.59148	−	13.3827i	0.391501	−	0.690161i
$377$	18.1230	−	18.1230i	0.933381	−	0.933381i
$378$	18.7634	−	8.82997i	0.965087	−	0.454164i
$379$	12.9076	−	5.34651i	0.663020	−	0.274632i	−0.0256886	−	0.999670i	$-0.508178\pi$
$379$	12.9076	−	5.34651i	0.663020	−	0.274632i	0.688709	+	0.725038i	$0.258178\pi$
$380$	−1.43407	+	0.530202i	−0.0735660	+	0.0271988i
$381$	−16.5490	−	21.5671i	−0.847832	−	1.10492i
$382$	18.4195	−	3.29599i	0.942422	−	0.168638i
$383$	9.79069	+	16.9580i	0.500281	+	0.866512i	1.00000		0.000324324i	$0.000103235\pi$
$383$	9.79069	+	16.9580i	0.500281	+	0.866512i	−0.499719	+	0.866188i	$0.666563\pi$
$384$	2.80776	−	13.8205i	0.143283	−	0.705275i
$385$	−0.462205	+	1.11897i	−0.0235562	+	0.0570279i
$386$	−1.90206	−	2.25516i	−0.0968125	−	0.114785i
$387$	−15.5750	+	2.05049i	−0.791721	+	0.104232i
$388$	−15.9942	−	13.2832i	−0.811981	−	0.674352i
$389$	−2.92635	+	22.2278i	−0.148372	+	1.12700i	0.741555	+	0.670892i	$0.234089\pi$
$389$	−2.92635	+	22.2278i	−0.148372	+	1.12700i	−0.889927	+	0.456104i	$0.849245\pi$
$390$	1.07535	+	0.980372i	0.0544522	+	0.0496431i
$391$	−26.5108	+	26.5108i	−1.34071	+	1.34071i
$392$	−4.94122	+	19.1725i	−0.249569	+	0.968357i
$393$	5.24497	+	5.24497i	0.264574	+	0.264574i
$394$	−1.26409	−	27.3615i	−0.0636839	−	1.37845i
$395$	−0.499991	−	0.0658250i	−0.0251573	−	0.00331202i
$396$	−5.42865	+	2.86103i	−0.272800	+	0.143772i
$397$	4.35424	+	33.0737i	0.218533	+	1.65992i	0.651601	+	0.758562i	$0.274098\pi$
$397$	4.35424	+	33.0737i	0.218533	+	1.65992i	−0.433068	+	0.901361i	$0.642569\pi$
$398$	24.7027	+	2.09816i	1.23824	+	0.105171i
$399$	−10.8042	−	4.46282i	−0.540886	−	0.223421i
$400$	17.8717	−	8.55528i	0.893587	−	0.427764i
$401$	−9.46637	+	5.46541i	−0.472728	+	0.272930i	−0.717381	−	0.696681i	$-0.754659\pi$
$401$	−9.46637	+	5.46541i	−0.472728	+	0.272930i	0.244653	+	0.969611i	$0.421326\pi$
$402$	−6.48525	−	4.51658i	−0.323455	−	0.225267i
$403$	−14.9810	+	11.4953i	−0.746257	+	0.572623i
$404$	0.279210	−	0.258463i	0.0138912	−	0.0128590i
$405$	0.212127	+	0.512121i	0.0105407	+	0.0254475i
$406$	−8.48709	+	23.5756i	−0.421207	+	1.17004i
$407$	−3.90629	−	3.90629i	−0.193628	−	0.193628i
$408$	−15.6255	−	20.0463i	−0.773580	−	0.992438i
$409$	6.72708	+	25.1058i	0.332632	+	1.24140i	0.906413	+	0.422392i	$0.138810\pi$
$409$	6.72708	+	25.1058i	0.332632	+	1.24140i	−0.573781	+	0.819009i	$0.694524\pi$
$410$	−1.81679	−	0.397945i	−0.0897247	−	0.0196531i
$411$	2.35836	+	1.80963i	0.116329	+	0.0892626i
$412$	−0.249851	−	0.353004i	−0.0123093	−	0.0173912i
$413$	−19.3930	+	5.21674i	−0.954265	+	0.256699i
$414$	−8.13071	+	6.85765i	−0.399602	+	0.337035i
$415$	−0.131649	−	0.228023i	−0.00646240	−	0.0111932i
$416$	−18.4054	−	11.4003i	−0.902397	−	0.558947i
$417$	−1.62581	+	2.81599i	−0.0796163	+	0.137900i
$418$	10.0027	+	3.61200i	0.489247	+	0.176669i
$419$	−10.8125	+	26.1038i	−0.528227	+	1.27525i	0.404456	+	0.914558i	$0.367461\pi$
$419$	−10.8125	+	26.1038i	−0.528227	+	1.27525i	−0.932683	+	0.360696i	$0.882539\pi$
$420$	−1.35935	−	0.419578i	−0.0663294	−	0.0204733i
$421$	−34.0793	+	14.1161i	−1.66092	+	0.687977i	−0.998147	−	0.0608405i	$-0.980622\pi$
$421$	−34.0793	+	14.1161i	−1.66092	+	0.687977i	−0.662776	+	0.748818i	$0.730622\pi$
$422$	20.3402	−	22.3106i	0.990144	−	1.08606i
$423$	−2.03608	−	7.59876i	−0.0989977	−	0.369464i
$424$	16.3046	−	6.89924i	0.791822	−	0.335057i
$425$	9.24230	−	34.4927i	0.448317	−	1.67314i
$426$	−2.90673	+	5.61849i	−0.140832	+	0.272217i
$427$	−1.09260	−	1.88815i	−0.0528745	−	0.0913741i
$428$	−3.73315	+	0.847488i	−0.180449	+	0.0409649i
$429$	−1.32114	−	10.0351i	−0.0637853	−	0.484498i
$430$	2.71893	+	1.89357i	0.131118	+	0.0913160i
$431$	−15.8972	−	9.17826i	−0.765742	−	0.442101i	0.0656118	−	0.997845i	$-0.479100\pi$
$431$	−15.8972	−	9.17826i	−0.765742	−	0.442101i	−0.831353	+	0.555744i	$0.812433\pi$
$432$	−12.1003	−	18.5755i	−0.582176	−	0.893716i
$433$		−	10.6987i		−	0.514148i	−0.966392	−	0.257074i	$-0.917242\pi$
$433$		−	10.6987i		−	0.514148i	0.966392	−	0.257074i	$-0.0827584\pi$
$434$	8.46670	−	16.4049i	0.406415	−	0.787462i
$435$	−1.66337	−	0.688989i	−0.0797523	−	0.0330345i
$436$	37.4427	+	1.44474i	1.79318	+	0.0691903i
$437$	18.2761	+	2.40610i	0.874265	+	0.115099i
$438$	−17.9848	+	11.5217i	−0.859345	+	0.550529i
$439$	9.65259	−	36.0240i	0.460693	−	1.71933i	−0.210096	−	0.977681i	$-0.567377\pi$
$439$	9.65259	−	36.0240i	0.460693	−	1.71933i	0.670788	−	0.741649i	$-0.265956\pi$
$440$	1.25267	+	0.325468i	0.0597187	+	0.0155161i
$441$	5.07880	+	8.75699i	0.241848	+	0.416999i
$442$	−37.1829	+	11.8274i	−1.76861	+	0.562571i
$443$	−5.06309	−	3.88505i	−0.240555	−	0.184584i	0.481447	−	0.876475i	$-0.340111\pi$
$443$	−5.06309	−	3.88505i	−0.240555	−	0.184584i	−0.722002	+	0.691891i	$0.756778\pi$
$444$	4.14741	−	4.99386i	0.196827	−	0.236998i
$445$	−2.18126	−	2.84267i	−0.103402	−	0.134755i
$446$	4.97427	−	13.7752i	0.235539	−	0.652274i
$447$	−18.3163			−0.866334
$448$	21.0269	+	2.42277i	0.993427	+	0.114465i
$449$	20.8650			0.984680			0.492340	−	0.870403i	$-0.336142\pi$
$449$	20.8650			0.984680			0.492340	+	0.870403i	$0.336142\pi$
$450$	3.44082	−	9.52861i	0.162202	−	0.449183i
$451$	7.87531	+	10.2633i	0.370834	+	0.483280i
$452$	1.87162	−	2.25361i	0.0880338	−	0.106001i
$453$	−1.85055	−	1.41998i	−0.0869465	−	0.0667164i
$454$	−23.9300	+	7.61182i	−1.12309	+	0.357240i
$455$	−1.32781	+	1.73395i	−0.0622485	+	0.0812889i
$456$	−3.14256	+	12.0952i	−0.147164	+	0.566408i
$457$	−0.617791	+	2.30563i	−0.0288990	+	0.107853i	−0.978869	−	0.204489i	$-0.934447\pi$
$457$	−0.617791	+	2.30563i	−0.0288990	+	0.107853i	0.949970	+	0.312342i	$0.101113\pi$
$458$	14.4283	−	9.24332i	0.674191	−	0.431912i
$459$	−39.6122	−	5.21505i	−1.84894	−	0.243418i
$460$	2.24173	+	0.0864977i	0.104521	+	0.00403298i
$461$	−14.7405	−	6.10571i	−0.686533	−	0.284371i	0.0120219	−	0.999928i	$-0.496173\pi$
$461$	−14.7405	−	6.10571i	−0.686533	−	0.284371i	−0.698555	+	0.715556i	$0.746173\pi$
$462$	5.34608	+	8.32693i	0.248722	+	0.387404i
$463$			2.04572i			0.0950725i	0.998870	+	0.0475362i	$0.0151370\pi$
$463$			2.04572i			0.0950725i	−0.998870	+	0.0475362i	$0.984863\pi$
$464$	26.2092	+	5.53240i	1.21673	+	0.256835i
$465$	1.14877	+	0.663242i	0.0532729	+	0.0307571i
$466$	17.3373	+	12.0744i	0.803135	+	0.559334i
$467$	3.47990	+	26.4325i	0.161031	+	1.22315i	0.860861	+	0.508840i	$0.169925\pi$
$467$	3.47990	+	26.4325i	0.161031	+	1.22315i	−0.699831	+	0.714309i	$0.746741\pi$
$468$	−10.7950	+	2.45064i	−0.498998	+	0.113281i
$469$	5.92048	−	10.2779i	0.273382	−	0.474588i
$470$	−0.762413	+	1.47369i	−0.0351675	+	0.0679761i
$471$	−0.581997	+	2.17204i	−0.0268170	+	0.100082i
$472$	8.36633	+	19.7717i	0.385091	+	0.910066i
$473$	−5.96488	−	22.2612i	−0.274266	−	1.02357i
$474$	−2.77702	+	3.04604i	−0.127553	+	0.139909i
$475$	−16.2209	+	6.71893i	−0.744268	+	0.308286i
$476$	27.9680	−	25.9409i	1.28191	−	1.18900i
$477$	3.46411	−	8.36309i	0.158611	−	0.382920i
$478$	−33.4330	−	12.0728i	−1.52919	−	0.552196i
$479$	3.11186	−	5.38989i	0.142184	−	0.246270i	−0.786135	−	0.618055i	$-0.787921\pi$
$479$	3.11186	−	5.38989i	0.142184	−	0.246270i	0.928319	+	0.371785i	$0.121254\pi$
$480$	−0.245100	+	1.50097i	−0.0111872	+	0.0685097i
$481$	−4.98273	−	8.63035i	−0.227193	−	0.393510i
$482$	−13.9947	+	11.8035i	−0.637441	+	0.537635i
$483$	12.1402	+	12.1164i	0.552400	+	0.551316i
$484$	7.50892	+	10.6090i	0.341315	+	0.482229i
$485$	1.77876	+	1.36489i	0.0807695	+	0.0619766i
$486$	−18.5436	−	4.06175i	−0.841153	−	0.184245i
$487$	7.22721	+	26.9723i	0.327496	+	1.22223i	0.911778	+	0.410682i	$0.134709\pi$
$487$	7.22721	+	26.9723i	0.327496	+	1.22223i	−0.584282	+	0.811551i	$0.698624\pi$
$488$	−1.83934	+	1.43372i	−0.0832631	+	0.0649014i
$489$	12.1180	+	12.1180i	0.547995	+	0.547995i
$490$	0.452747	−	2.08657i	0.0204530	−	0.0942618i
$491$	−6.95705	−	16.7958i	−0.313967	−	0.757984i	−0.999550	−	0.0299894i	$-0.990453\pi$
$491$	−6.95705	−	16.7958i	−0.313967	−	0.757984i	0.685583	−	0.727994i	$-0.259547\pi$
$492$	−11.1555	+	10.3266i	−0.502930	+	0.465560i
$493$	38.3001	−	29.3887i	1.72495	−	1.32360i
$494$	15.7428	+	10.9639i	0.708302	+	0.493289i
$495$	0.573095	−	0.330877i	0.0257587	−	0.0148718i
$496$	−18.6128	−	6.56168i	−0.835741	−	0.294628i
$497$	−8.77493	−	3.62461i	−0.393610	−	0.162586i
$498$	−2.14434	−	0.182132i	−0.0960901	−	0.00816154i
$499$	0.575382	+	4.37046i	0.0257576	+	0.195649i	0.999486	−	0.0320650i	$-0.0102084\pi$
$499$	0.575382	+	4.37046i	0.0257576	+	0.195649i	−0.973728	+	0.227714i	$0.926875\pi$
$500$	−3.79832	+	2.00181i	−0.169866	+	0.0895236i
$501$	0.775618	+	0.102112i	0.0346520	+	0.00456203i
$502$	−0.150790	−	3.26388i	−0.00673009	−	0.145674i
$503$	−2.85777	−	2.85777i	−0.127422	−	0.127422i	0.640520	−	0.767942i	$-0.278719\pi$
$503$	−2.85777	−	2.85777i	−0.127422	−	0.127422i	−0.767942	+	0.640520i	$0.778719\pi$
$504$	8.52893	−	6.66155i	0.379909	−	0.296729i
$505$	−0.0290129	+	0.0290129i	−0.00129106	+	0.00129106i
$506$	−11.5314	−	10.5130i	−0.512635	−	0.467359i
$507$	0.268081	−	2.03628i	0.0119059	−	0.0904342i
$508$	−33.5540	−	27.8666i	−1.48872	−	1.23638i
$509$	31.9382	−	4.20474i	1.41563	−	0.186372i	0.616420	−	0.787418i	$-0.288583\pi$
$509$	31.9382	−	4.20474i	1.41563	−	0.186372i	0.799214	+	0.601046i	$0.205249\pi$
$510$	1.76716	+	2.09522i	0.0782512	+	0.0927777i
$511$	−19.5395	−	25.4127i	−0.864376	−	1.12419i
$512$	−0.515903	−	22.6215i	−0.0227999	−	0.999740i
$513$	9.82218	+	17.0125i	0.433660	+	0.751121i
$514$	20.3648	−	3.64409i	0.898254	−	0.160734i
$515$	0.0283917	+	0.0370008i	0.00125109	+	0.00163045i
$516$	25.4009	−	9.39122i	1.11821	−	0.413425i
$517$	10.6625	−	4.41657i	0.468938	−	0.194241i
$518$	8.00032	+	5.56007i	0.351514	+	0.244296i
$519$	3.61545	−	3.61545i	0.158701	−	0.158701i
$520$	2.03076	+	1.15197i	0.0890549	+	0.0505173i
$521$	−34.4633	+	9.23441i	−1.50986	+	0.404567i	−0.916390	−	0.400286i	$-0.868911\pi$
$521$	−34.4633	+	9.23441i	−1.50986	+	0.404567i	−0.593474	+	0.804853i	$0.702244\pi$
$522$	11.5324	−	7.38812i	0.504761	−	0.323369i
$523$	−11.1560	+	14.5387i	−0.487816	+	0.635734i	−0.970799	−	0.239896i	$-0.922887\pi$
$523$	−11.1560	+	14.5387i	−0.487816	+	0.635734i	0.482983	+	0.875630i	$0.339553\pi$
$524$	10.0695	+	6.34350i	0.439890	+	0.277117i
$525$	−15.7841	−	4.21273i	−0.688873	−	0.183858i
$526$	16.7837	+	1.42555i	0.731806	+	0.0621569i
$527$	−30.8030	+	17.7841i	−1.34180	+	0.774690i
$528$	8.03435	−	6.88156i	0.349650	−	0.299481i
$529$	−3.50544	−	2.02387i	−0.152410	−	0.0879941i
$530$	−1.72830	+	0.811256i	−0.0750725	+	0.0352387i
$531$	10.1415	+	4.20073i	0.440102	+	0.182296i
$532$	−18.4899	−	3.14508i	−0.801641	−	0.136356i
$533$	8.93055	+	21.5602i	0.386825	+	0.933878i
$534$	−29.2552	+	1.35158i	−1.26600	+	0.0584885i
$535$	0.398761	−	0.106848i	0.0172399	−	0.00461943i
$536$	−11.7514	−	4.76328i	−0.507584	−	0.205742i
$537$	−30.4338	−	8.15471i	−1.31331	−	0.351902i
$538$	−12.0973	−	38.0316i	−0.521553	−	1.63966i
$539$	−11.7645	+	9.06401i	−0.506735	+	0.390414i
$540$	1.38117	+	1.95139i	0.0594359	+	0.0839744i
$541$	20.9757	−	2.76150i	0.901816	−	0.118726i	0.334662	−	0.942338i	$-0.391378\pi$
$541$	20.9757	−	2.76150i	0.901816	−	0.118726i	0.567154	+	0.823612i	$0.308044\pi$
$542$	6.65506	+	37.1915i	0.285859	+	1.59751i
$543$	−1.76514	+	3.05731i	−0.0757493	+	0.131202i
$544$	−31.5689	−	25.8151i	−1.35351	−	1.10681i
$545$	−4.04083			−0.173090
$546$	5.42755	+	17.0053i	0.232278	+	0.727761i
$547$	2.99246	−	7.22444i	0.127948	−	0.308895i	−0.846904	−	0.531746i	$-0.821536\pi$
$547$	2.99246	−	7.22444i	0.127948	−	0.308895i	0.974853	+	0.222851i	$0.0715363\pi$
$548$	4.33278	+	1.99374i	0.185087	+	0.0851685i
$549$	−0.155640	+	1.18220i	−0.00664255	+	0.0504552i
$550$	14.5183	+	3.18006i	0.619062	+	0.135598i
$551$	−22.9274	−	6.14337i	−0.976739	−	0.261716i
$552$	11.0516	−	14.6316i	0.470385	−	0.622762i
$553$	−4.91163	−	3.76117i	−0.208864	−	0.159941i
$554$	1.98697	−	3.84067i	0.0844184	−	0.163174i
$555$	−0.426160	+	0.555383i	−0.0180895	+	0.0235747i
$556$	−1.54358	+	4.98351i	−0.0654623	+	0.211348i
$557$	19.8290	−	15.2153i	0.840183	−	0.644695i	−0.0963219	−	0.995350i	$-0.530708\pi$
$557$	19.8290	−	15.2153i	0.840183	−	0.644695i	0.936505	+	0.350655i	$0.114041\pi$
$558$	−9.13451	+	4.28770i	−0.386695	+	0.181513i
$559$		−	41.5742i		−	1.75840i
$560$	−2.27593	−	0.173649i	−0.0961757	−	0.00733802i
$561$		−	19.0652i		−	0.804933i
$562$	6.03953	+	12.8666i	0.254762	+	0.542745i
$563$	4.74152	−	3.63829i	0.199831	−	0.153336i	−0.503999	−	0.863704i	$-0.668138\pi$
$563$	4.74152	−	3.63829i	0.199831	−	0.153336i	0.703830	+	0.710369i	$0.251472\pi$
$564$	6.32293	+	11.9974i	0.266243	+	0.505182i
$565$	−0.192316	+	0.250631i	−0.00809079	+	0.0105441i
$566$	34.0924	+	17.6377i	1.43301	+	0.741369i
$567$	−0.880932	+	6.74249i	−0.0369957	+	0.283158i
$568$	−2.55232	+	9.82343i	−0.107093	+	0.412182i
$569$	39.8176	+	10.6691i	1.66924	+	0.447272i	0.964906	−	0.262596i	$-0.0845788\pi$
$569$	39.8176	+	10.6691i	1.66924	+	0.447272i	0.704335	+	0.709868i	$0.251245\pi$
$570$	0.288351	−	1.31644i	0.0120777	−	0.0551396i
$571$	1.82643	−	13.8731i	0.0764339	−	0.580573i	−0.909779	−	0.415093i	$-0.863749\pi$
$571$	1.82643	−	13.8731i	0.0764339	−	0.580573i	0.986213	−	0.165480i	$-0.0529175\pi$
$572$	−5.63159	−	15.2321i	−0.235468	−	0.636885i
$573$	−6.31172	+	15.2378i	−0.263676	+	0.636570i
$574$	−16.8750	−	15.3543i	−0.704348	−	0.640876i
$575$	25.7618			1.07434
$576$	−8.30418	−	8.05548i	−0.346008	−	0.335645i
$577$	22.6075	−	39.1574i	0.941164	−	1.63014i	0.177908	−	0.984047i	$-0.443067\pi$
$577$	22.6075	−	39.1574i	0.941164	−	1.63014i	0.763256	−	0.646096i	$-0.223600\pi$
$578$	−48.6807	+	8.71095i	−2.02485	+	0.362328i
$579$	2.57813	−	0.339417i	0.107143	−	0.0141057i
$580$	−2.84731	−	0.487195i	−0.118228	−	0.0202297i
$581$	−0.00317075	−	3.22988i	−0.000131545	−	0.133998i
$582$	17.4634	−	5.55487i	0.723881	−	0.230257i
$583$	12.8275	+	3.43712i	0.531261	+	0.142351i
$584$	−24.0473	+	24.4156i	−0.995083	+	1.01033i
$585$	1.15308	−	0.308966i	0.0476738	−	0.0127742i
$586$	0.913078	+	19.7638i	0.0377189	+	0.816433i
$587$	−12.3455	−	29.8048i	−0.509555	−	1.23017i	−0.944140	−	0.329544i	$-0.893105\pi$
$587$	−12.3455	−	29.8048i	−0.509555	−	1.23017i	0.434585	−	0.900631i	$-0.356895\pi$
$588$	−11.8801	−	12.7833i	−0.489929	−	0.527174i
$589$	16.1568	+	6.69237i	0.665729	+	0.275754i
$590$	−0.983765	−	2.09581i	−0.0405010	−	0.0862832i
$591$	20.9084	+	12.0714i	0.860055	+	0.496553i
$592$	4.71540	−	9.28678i	0.193802	−	0.381685i
$593$	−22.6591	+	13.0822i	−0.930498	+	0.537223i	−0.886969	−	0.461829i	$-0.847193\pi$
$593$	−22.6591	+	13.0822i	−0.930498	+	0.537223i	−0.0435290	+	0.999052i	$0.513860\pi$
$594$	1.40735	−	16.5694i	0.0577442	−	0.679853i
$595$	−2.90597	+	2.91168i	−0.119133	+	0.119367i
$596$	−28.6586	+	6.50598i	−1.17390	+	0.266495i
$597$	−13.3027	+	17.3364i	−0.544443	+	0.709532i
$598$	−15.1846	−	23.7023i	−0.620944	−	0.969260i
$599$	34.3016	−	9.19109i	1.40153	−	0.375538i	0.522633	−	0.852558i	$-0.324950\pi$
$599$	34.3016	−	9.19109i	1.40153	−	0.375538i	0.878893	+	0.477020i	$0.158283\pi$
$600$	−2.14791	+	17.3320i	−0.0876881	+	0.707574i
$601$	−2.58840	+	2.58840i	−0.105583	+	0.105583i	−0.757925	−	0.652342i	$-0.773787\pi$
$601$	−2.58840	+	2.58840i	−0.105583	+	0.105583i	0.652342	+	0.757925i	$0.273787\pi$
$602$	17.3066	+	36.7760i	0.705363	+	1.49888i
$603$	−5.98980	+	2.48106i	−0.243923	+	0.101036i
$604$	−3.39983	−	1.56445i	−0.138337	−	0.0636564i
$605$	−0.853273	−	1.11201i	−0.0346905	−	0.0452095i
$606$	0.0590714	+	0.330118i	0.00239961	+	0.0134101i
$607$	1.10527	+	1.91438i	0.0448614	+	0.0777021i	0.887584	−	0.460646i	$-0.152382\pi$
$607$	1.10527	+	1.91438i	0.0448614	+	0.0777021i	−0.842723	+	0.538348i	$0.819049\pi$
$608$	−0.620775	+	20.0409i	−0.0251757	+	0.812765i
$609$	−13.4621	−	17.5086i	−0.545512	−	0.709482i
$610$	0.192246	−	0.162146i	0.00778382	−	0.00656508i
$611$	20.6411	−	2.71745i	0.835048	−	0.109936i
$612$	−20.7620	+	1.92249i	−0.839253	+	0.0777122i
$613$	−2.20556	+	16.7529i	−0.0890817	+	0.676642i	0.887394	+	0.461013i	$0.152514\pi$
$613$	−2.20556	+	16.7529i	−0.0890817	+	0.676642i	−0.976475	+	0.215630i	$0.930820\pi$
$614$	−5.80938	+	6.37216i	−0.234447	+	0.257159i
$615$	1.15918	−	1.15918i	0.0467427	−	0.0467427i
$616$	11.3225	+	11.1298i	0.456195	+	0.448431i
$617$	6.83969	+	6.83969i	0.275356	+	0.275356i	0.831252	−	0.555896i	$-0.187625\pi$
$617$	6.83969	+	6.83969i	0.275356	+	0.275356i	−0.555896	+	0.831252i	$0.687625\pi$
$618$	0.380792	−	0.0175924i	0.0153177	−	0.000707671i
$619$	44.1940	+	5.81825i	1.77631	+	0.233855i	0.946162	−	0.323695i	$-0.104925\pi$
$619$	44.1940	+	5.81825i	1.77631	+	0.233855i	0.830144	+	0.557550i	$0.188258\pi$
$620$	2.03300	+	0.629696i	0.0816473	+	0.0252892i
$621$	−3.76228	−	28.5773i	−0.150975	−	1.14677i
$622$	2.36406	−	27.8333i	0.0947901	−	1.11601i
$623$	−5.77992	−	43.5723i	−0.231568	−	1.74569i
$624$	17.2124	−	8.23966i	0.689048	−	0.329850i
$625$	−21.0482	+	12.1522i	−0.841929	+	0.486088i
$626$	−10.4188	+	14.9601i	−0.416420	+	0.597928i
$627$	−7.43677	+	5.70644i	−0.296996	+	0.227893i
$628$	−0.139108	+	3.60520i	−0.00555101	+	0.143863i
$629$	−7.18334	−	17.3421i	−0.286418	−	0.691475i
$630$	−0.891379	+	0.753311i	−0.0355134	+	0.0300126i
$631$	5.38193	+	5.38193i	0.214251	+	0.214251i	0.806071	−	0.591819i	$-0.201590\pi$
$631$	5.38193	+	5.38193i	0.214251	+	0.214251i	−0.591819	+	0.806071i	$0.701590\pi$
$632$	−3.26310	+	5.75238i	−0.129799	+	0.228817i
$633$	6.88744	+	25.7043i	0.273751	+	1.02165i
$634$	4.17721	−	19.0707i	0.165898	−	0.757395i
$635$	3.73165	+	2.86339i	0.148086	+	0.113630i
$636$	−2.63188	+	15.3815i	−0.104361	+	0.609915i
$637$	−24.7311	+	10.3009i	−0.979881	+	0.408136i
$638$	12.9544	+	15.3592i	0.512869	+	0.608078i
$639$	2.59473	+	4.49421i	0.102646	+	0.177788i
$640$	0.149653	+	2.43555i	0.00591555	+	0.0962736i
$641$	1.28693	−	2.22903i	0.0508308	−	0.0880415i	−0.839490	−	0.543374i	$-0.817146\pi$
$641$	1.28693	−	2.22903i	0.0508308	−	0.0880415i	0.890321	+	0.455333i	$0.150480\pi$
$642$	1.14602	−	3.17365i	0.0452297	−	0.125254i
$643$	11.0924	−	26.7793i	0.437440	−	1.05607i	−0.539390	−	0.842056i	$-0.681345\pi$
$643$	11.0924	−	26.7793i	0.437440	−	1.05607i	0.976830	−	0.214018i	$-0.0686550\pi$
$644$	23.2989	+	14.6457i	0.918107	+	0.577121i
$645$	−2.69816	+	1.11761i	−0.106240	+	0.0440060i
$646$	26.7039	+	24.3454i	1.05065	+	0.957859i
$647$	−2.89861	−	10.8178i	−0.113956	−	0.425291i	0.885250	−	0.465115i	$-0.153987\pi$
$647$	−2.89861	−	10.8178i	−0.113956	−	0.425291i	−0.999207	+	0.0398241i	$0.987320\pi$
$648$	7.26907	−	0.0552506i	0.285556	−	0.00217045i
$649$	−4.16800	+	15.5552i	−0.163608	+	0.610595i
$650$	23.8128	+	12.3196i	0.934013	+	0.483213i
$651$	8.14982	+	14.0840i	0.319417	+	0.551994i
$652$	23.2647	+	14.6561i	0.911117	+	0.573976i
$653$	2.21171	+	16.7996i	0.0865510	+	0.657420i	0.978643	+	0.205566i	$0.0659037\pi$
$653$	2.21171	+	16.7996i	0.0865510	+	0.657420i	−0.892092	+	0.451853i	$0.850763\pi$
$654$	−18.8752	+	27.1025i	−0.738080	+	1.05979i
$655$	−1.11147	−	0.641707i	−0.0434287	−	0.0250736i
$656$	−13.7864	+	20.1200i	−0.538269	+	0.785553i
$657$			17.5219i			0.683595i
$658$	−17.1276	+	10.9963i	−0.667703	+	0.428681i
$659$	−1.75225	−	0.725805i	−0.0682579	−	0.0282734i	0.348293	−	0.937386i	$-0.386761\pi$
$659$	−1.75225	−	0.725805i	−0.0682579	−	0.0282734i	−0.416551	+	0.909112i	$0.636761\pi$
$660$	−0.837168	+	0.774963i	−0.0325867	+	0.0301654i
$661$	−4.89944	−	0.645023i	−0.190566	−	0.0250885i	0.0346390	−	0.999400i	$-0.488972\pi$
$661$	−4.89944	−	0.645023i	−0.190566	−	0.0250885i	−0.225205	+	0.974311i	$0.572305\pi$
$662$	9.09518	+	14.1971i	0.353494	+	0.551785i
$663$	8.90133	−	33.2202i	0.345699	−	1.29017i
$664$	−3.41982	+	0.476699i	−0.132715	+	0.0184995i
$665$	2.00555	+	0.262033i	0.0777720	+	0.0101612i
$666$	−1.61423	−	5.07480i	−0.0625500	−	0.196645i
$667$	27.6307	+	21.2018i	1.06987	+	0.820937i
$668$	1.24984	−	0.115731i	0.0483577	−	0.00447777i
$669$	7.85863	+	10.2416i	0.303832	+	0.395962i
$670$	1.28614	+	0.464429i	0.0496879	+	0.0179425i
$671$	−1.74932			−0.0675319
$672$	−11.7959	+	14.4539i	−0.455035	+	0.557572i
$673$	16.2083			0.624784			0.312392	−	0.949953i	$-0.398870\pi$
$673$	16.2083			0.624784			0.312392	+	0.949953i	$0.398870\pi$
$674$	9.15943	+	3.30751i	0.352808	+	0.127400i
$675$	16.7127	+	21.7804i	0.643270	+	0.838326i
$676$	−0.303836	−	3.28127i	−0.0116860	−	0.126203i
$677$	28.3311	+	21.7392i	1.08885	+	0.835506i	0.987228	−	0.159317i	$-0.0509291\pi$
$677$	28.3311	+	21.7392i	1.08885	+	0.835506i	0.101625	+	0.994823i	$0.467596\pi$
$678$	0.782691	+	2.46062i	0.0300590	+	0.0944996i
$679$	10.5501	+	25.3997i	0.404876	+	0.974751i
$680$	3.50920	+	2.65057i	0.134572	+	0.101645i
$681$	5.72869	−	21.3798i	0.219524	−	0.819274i
$682$	−7.98564	−	12.4651i	−0.305786	−	0.477315i
$683$	19.0099	+	2.50270i	0.727393	+	0.0957631i	0.485123	−	0.874446i	$-0.338775\pi$
$683$	19.0099	+	2.50270i	0.727393	+	0.0957631i	0.242270	+	0.970209i	$0.422108\pi$
$684$	6.96422	+	7.52322i	0.266283	+	0.287657i
$685$	−0.475191	−	0.196830i	−0.0181561	−	0.00752050i
$686$	17.5887	−	19.4071i	0.671541	−	0.740968i
$687$			15.1034i			0.576232i
$688$	36.4077	−	23.7164i	1.38803	−	0.904178i
$689$	20.7466	+	11.9781i	0.790382	+	0.456328i
$690$	−1.13008	+	1.62265i	−0.0430213	+	0.0617733i
$691$	−1.06265	−	8.07165i	−0.0404252	−	0.307060i	−0.999698	−	0.0245784i	$-0.992176\pi$
$691$	−1.06265	−	8.07165i	−0.0404252	−	0.307060i	0.959273	−	0.282482i	$-0.0911577\pi$
$692$	4.37269	−	6.94111i	0.166225	−	0.263862i
$693$	8.11773	−	0.00796911i	0.308367	−	0.000302722i
$694$	−24.0015	−	12.4172i	−0.911086	−	0.471351i
$695$	0.145615	−	0.543442i	0.00552348	−	0.0206139i
$696$	−16.5678	+	16.8216i	−0.628002	+	0.637622i
$697$	11.3769	+	42.4591i	0.430931	+	1.60825i
$698$	−18.7726	−	17.1147i	−0.710555	−	0.647800i
$699$	−17.2048	+	7.12648i	−0.650747	+	0.269548i
$700$	−26.1929	−	0.984908i	−0.989997	−	0.0372260i
$701$	6.09108	−	14.7052i	0.230057	−	0.555407i	−0.766126	−	0.642690i	$-0.777818\pi$
$701$	6.09108	−	14.7052i	0.230057	−	0.555407i	0.996184	+	0.0872829i	$0.0278184\pi$
$702$	10.1883	−	28.2144i	0.384534	−	1.06489i
$703$	−4.61460	+	7.99271i	−0.174043	+	0.301451i
$704$	10.1266	−	13.6210i	0.381659	−	0.513361i
$705$	−0.731243	−	1.26655i	−0.0275402	−	0.0477011i
$706$	15.2155	+	18.0400i	0.572641	+	0.678946i
$707$	−0.486043	+	0.130746i	−0.0182795	+	0.00491722i
$708$	−18.6522	−	3.19153i	−0.700994	−	0.119945i
$709$	−6.40415	−	4.91408i	−0.240513	−	0.184552i	0.481471	−	0.876462i	$-0.340103\pi$
$709$	−6.40415	−	4.91408i	−0.240513	−	0.184552i	−0.721984	+	0.691910i	$0.756769\pi$
$710$	0.234192	−	1.06918i	0.00878908	−	0.0401258i
$711$	0.875182	+	3.26622i	0.0328219	+	0.122493i
$712$	−45.2939	+	12.5062i	−1.69746	+	0.468690i
$713$	−18.1443	−	18.1443i	−0.679510	−	0.679510i
$714$	5.95497	+	33.0916i	0.222859	+	1.23842i
$715$	0.670194	+	1.61799i	0.0250638	+	0.0605094i
$716$	−50.5147	−	1.94912i	−1.88782	−	0.0728421i
$717$	24.8567	−	19.0732i	0.928291	−	0.712303i
$718$	5.78075	−	8.30045i	0.215736	−	0.309770i
$719$	−23.7592	+	13.7174i	−0.886069	+	0.511572i	−0.872655	−	0.488338i	$-0.837603\pi$
$719$	−23.7592	+	13.7174i	−0.886069	+	0.511572i	−0.0134141	+	0.999910i	$0.504270\pi$
$720$	0.928353	+	0.833530i	0.0345977	+	0.0310638i
$721$	0.0752327	+	0.567146i	0.00280181	+	0.0211216i
$722$	−0.770403	+	9.07036i	−0.0286714	+	0.337564i
$723$	−2.10630	−	15.9989i	−0.0783341	−	0.595006i
$724$	−1.67586	+	5.41059i	−0.0622828	+	0.201083i
$725$	−32.8882	−	4.32981i	−1.22144	−	0.160805i
$726$	−11.4442	+	0.528716i	−0.424733	+	0.0196225i
$727$	37.3364	+	37.3364i	1.38473	+	1.38473i	0.835996	+	0.548736i	$0.184891\pi$
$727$	37.3364	+	37.3364i	1.38473	+	1.38473i	0.548736	+	0.835996i	$0.315109\pi$
$728$	14.5325	+	24.6794i	0.538611	+	0.914681i
$729$	17.2835	−	17.2835i	0.640129	−	0.640129i
$730$	2.48981	−	2.73102i	0.0921522	−	0.101079i
$731$	10.2214	−	77.6392i	0.378052	−	2.87159i
$732$	−0.189530	−	2.04683i	−0.00700523	−	0.0756530i
$733$	25.2186	−	3.32009i	0.931471	−	0.122630i	0.350507	−	0.936560i	$-0.386009\pi$
$733$	25.2186	−	3.32009i	0.931471	−	0.122630i	0.580964	+	0.813930i	$0.302676\pi$
$734$	8.23253	−	6.94353i	0.303868	−	0.256290i
$735$	1.33336	+	1.32813i	0.0491816	+	0.0489889i
$736$	12.0946	−	26.8188i	0.445813	−	0.988554i
$737$	−4.75569	−	8.23710i	−0.175178	−	0.303417i
$738$	2.19661	+	12.2757i	0.0808584	+	0.451873i
$739$	−7.05694	−	9.19679i	−0.259594	−	0.338309i	0.645313	−	0.763918i	$-0.276727\pi$
$739$	−7.05694	−	9.19679i	−0.259594	−	0.338309i	−0.904907	+	0.425608i	$0.860060\pi$
$740$	−0.469518	+	1.02035i	−0.0172598	+	0.0375088i
$741$	−15.6225	+	6.47106i	−0.573908	+	0.237720i
$742$	−23.3384	−	1.95920i	−0.856780	−	0.0719246i
$743$	1.78374	−	1.78374i	0.0654392	−	0.0654392i	−0.673630	−	0.739069i	$-0.735266\pi$
$743$	1.78374	−	1.78374i	0.0654392	−	0.0654392i	0.739069	+	0.673630i	$0.235266\pi$
$744$	13.7199	−	10.6943i	0.502995	−	0.392072i
$745$	3.06120	−	0.820246i	0.112154	−	0.0300515i
$746$	−24.8672	−	38.8163i	−0.910452	−	1.42117i
$747$	−1.07474	+	1.40063i	−0.0393227	+	0.0512464i
$748$	−6.77197	−	29.8303i	−0.247608	−	1.09070i
$749$	4.89288	+	1.30590i	0.178782	+	0.0477164i
$750$	0.320284	−	3.77087i	0.0116951	−	0.137693i
$751$	−21.1263	+	12.1973i	−0.770911	+	0.445085i	−0.833199	−	0.552973i	$-0.813493\pi$
$751$	−21.1263	+	12.1973i	−0.770911	+	0.445085i	0.0622888	+	0.998058i	$0.480160\pi$
$752$	14.1546	+	16.5258i	0.516166	+	0.602634i
$753$	2.49410	+	1.43997i	0.0908902	+	0.0524755i
$754$	15.4014	+	32.8111i	0.560885	+	1.19491i
$755$	0.372871	+	0.154448i	0.0135702	+	0.00562095i
$756$	2.73268	+	29.1994i	0.0993866	+	1.06197i
$757$	−7.21820	−	17.4263i	−0.262350	−	0.633369i	0.736733	−	0.676184i	$-0.236367\pi$
$757$	−7.21820	−	17.4263i	−0.262350	−	0.633369i	−0.999083	+	0.0428149i	$0.986367\pi$
$758$	0.911845	+	19.7371i	0.0331197	+	0.716883i
$759$	13.2855	−	3.55983i	0.482232	−	0.129214i
$760$	−0.0164343	−	2.16219i	−0.000596134	−	0.0784307i
$761$	−25.3520	−	6.79304i	−0.919008	−	0.246247i	−0.231847	−	0.972752i	$-0.574477\pi$
$761$	−25.3520	−	6.79304i	−0.919008	−	0.246247i	−0.687161	+	0.726505i	$0.741143\pi$
$762$	36.6363	−	11.6535i	1.32719	−	0.422162i
$763$	−42.9522	−	24.7423i	−1.55497	−	0.895731i
$764$	−4.46311	+	26.0837i	−0.161470	+	0.943677i
$765$	2.22932	−	0.293495i	0.0806011	−	0.0106113i
$766$	−27.2593	+	4.87779i	−0.984918	+	0.176242i
$767$	−14.5251	+	25.1582i	−0.524472	+	0.908412i
$768$	17.0347	+	10.3730i	0.614686	+	0.374304i
$769$	−22.9189			−0.826475			−0.413238	−	0.910623i	$-0.635602\pi$
$769$	−22.9189			−0.826475			−0.413238	+	0.910623i	$0.635602\pi$
$770$	−1.26638	−	1.15226i	−0.0456373	−	0.0415247i
$771$	−6.97832	+	16.8472i	−0.251318	+	0.606736i
$772$	3.91330	−	1.44682i	0.140843	−	0.0520723i
$773$	−6.73646	+	51.1685i	−0.242294	+	1.84040i	0.247895	+	0.968787i	$0.420261\pi$
$773$	−6.73646	+	51.1685i	−0.242294	+	1.84040i	−0.490189	+	0.871616i	$0.663072\pi$
$774$	4.75355	−	21.7019i	0.170863	−	0.780059i
$775$	23.6072	+	6.32553i	0.847995	+	0.227220i
$776$	25.3509	−	14.8944i	0.910045	−	0.534678i
$777$	−7.93054	+	3.29406i	−0.284507	+	0.118174i
$778$	−28.1607	−	14.5690i	−1.00961	−	0.522323i
$779$	13.1568	−	17.1463i	0.471393	−	0.614331i
$780$	−1.82055	+	0.959474i	−0.0651862	+	0.0343547i
$781$	−6.03999	+	4.63464i	−0.216128	+	0.165841i
$782$	−22.5296	−	47.9970i	−0.805657	−	1.71637i
$783$			37.1149i			1.32638i
$784$	−23.1289	−	15.7815i	−0.826031	−	0.563625i
$785$		−	0.389075i		−	0.0138867i
$786$	−9.49585	+	4.45731i	−0.338706	+	0.158987i
$787$	−28.9676	+	22.2276i	−1.03258	+	0.792329i	−0.978508	−	0.206207i	$-0.933888\pi$
$787$	−28.9676	+	22.2276i	−1.03258	+	0.792329i	−0.0540755	+	0.998537i	$0.517221\pi$
$788$	37.0020	+	11.4609i	1.31814	+	0.408277i
$789$	−9.03823	+	11.7789i	−0.321770	+	0.419338i
$790$	0.327713	−	0.633444i	0.0116595	−	0.0225369i
$791$	−3.57886	+	1.48653i	−0.127250	+	0.0528549i
$792$	−1.19810	−	8.59512i	−0.0425725	−	0.305414i
$793$	−3.04812	−	0.816741i	−0.108242	−	0.0290033i
$794$	−46.0844	−	10.0942i	−1.63547	−	0.358231i
$795$	0.219656	−	1.66845i	0.00779038	−	0.0591738i
$796$	−14.6561	+	31.8505i	−0.519472	+	1.12891i
$797$	7.73109	−	18.6645i	0.273849	−	0.661130i	−0.725792	−	0.687914i	$-0.758527\pi$
$797$	7.73109	−	18.6645i	0.273849	−	0.661130i	0.999641	+	0.0267837i	$0.00852655\pi$
$798$	11.1257	−	12.2276i	0.393845	−	0.432852i
$799$	39.2150			1.38733
$800$	2.79561	+	27.8813i	0.0988397	+	0.985754i
$801$	−12.0126	+	20.8065i	−0.424446	+	0.735162i
$802$	−2.72290	−	15.2168i	−0.0961491	−	0.537324i
$803$	−25.4857	+	3.35526i	−0.899371	+	0.118404i
$804$	9.12272	−	6.45693i	0.321734	−	0.227718i
$805$	−2.57159	−	1.48134i	−0.0906366	−	0.0522105i
$806$	−8.09478	−	25.4484i	−0.285127	−	0.896381i
$807$	33.9785	+	9.10451i	1.19610	+	0.320494i
$808$	0.209684	+	0.495535i	0.00737666	+	0.0174329i
$809$	44.9160	−	12.0352i	1.57916	−	0.423135i	0.640496	−	0.767962i	$-0.278729\pi$
$809$	44.9160	−	12.0352i	1.57916	−	0.423135i	0.938666	+	0.344827i	$0.112062\pi$
$810$	−0.783086	+	0.0361782i	−0.0275148	+	0.00127117i
$811$	0.761002	+	1.83722i	0.0267224	+	0.0645136i	0.936677	−	0.350193i	$-0.113884\pi$
$811$	0.761002	+	1.83722i	0.0267224	+	0.0645136i	−0.909955	+	0.414707i	$0.863884\pi$
$812$	−27.2825	−	22.6129i	−0.957428	−	0.793558i
$813$	−30.7673	−	12.7442i	−1.07906	−	0.446960i
$814$	7.07222	−	3.31967i	0.247881	−	0.116354i
$815$	−2.56795	−	1.48260i	−0.0899512	−	0.0519334i
$816$	34.1698	−	11.1556i	1.19618	−	0.390525i
$817$	−33.3442	+	19.2513i	−1.16657	+	0.673517i
$818$	−36.6255	−	3.11084i	−1.28058	−	0.108768i
$819$	14.1485	+	3.77620i	0.494389	+	0.131951i
$820$	1.40197	−	2.22545i	0.0489588	−	0.0777162i
$821$	9.75732	−	12.7160i	0.340533	−	0.443791i	−0.591424	−	0.806361i	$-0.701434\pi$
$821$	9.75732	−	12.7160i	0.340533	−	0.443791i	0.931957	+	0.362570i	$0.118101\pi$
$822$	−3.53985	+	2.26776i	−0.123466	+	0.0790973i
$823$	28.3212	−	7.58865i	0.987215	−	0.264524i	0.271135	−	0.962541i	$-0.412601\pi$
$823$	28.3212	−	7.58865i	0.987215	−	0.264524i	0.716080	+	0.698018i	$0.245934\pi$
$824$	0.589556	−	0.162784i	0.0205381	−	0.00567083i
$825$	−9.26325	+	9.26325i	−0.322505	+	0.322505i
$826$	2.37582	−	28.3012i	0.0826653	−	0.984725i
$827$	7.29696	−	3.02250i	0.253740	−	0.105103i	−0.252188	−	0.967678i	$-0.581150\pi$
$827$	7.29696	−	3.02250i	0.253740	−	0.105103i	0.505928	+	0.862576i	$0.331150\pi$
$828$	−5.21633	−	14.1089i	−0.181280	−	0.490318i
$829$	−23.9651	−	31.2319i	−0.832343	−	1.08473i	−0.995179	−	0.0980769i	$-0.968731\pi$
$829$	−23.9651	−	31.2319i	−0.832343	−	1.08473i	0.162836	−	0.986653i	$-0.447936\pi$
$830$	0.366538	−	0.0655885i	0.0127227	−	0.00227661i
$831$	1.90574	+	3.30084i	0.0661094	+	0.114505i
$832$	24.0046	−	19.0060i	0.832210	−	0.658915i
$833$	−48.7176	+	13.1564i	−1.68796	+	0.455842i
$834$	−2.96477	−	3.51515i	−0.102661	−	0.121720i
$835$	−0.134201	+	0.0176679i	−0.00464423	+	0.000611424i
$836$	−9.60899	+	11.5701i	−0.332334	+	0.400160i
$837$	3.56924	−	27.1110i	0.123371	−	0.937095i
$838$	−29.5284	−	26.9205i	−1.02004	−	0.929953i
$839$	31.2997	−	31.2997i	1.08059	−	1.08059i	0.0841319	−	0.996455i	$-0.473188\pi$
$839$	31.2997	−	31.2997i	1.08059	−	1.08059i	0.996455	−	0.0841319i	$-0.0268117\pi$
$840$	1.21102	−	1.60660i	0.0417843	−	0.0554330i
$841$	−11.2046	−	11.2046i	−0.386366	−	0.386366i
$842$	−2.40750	−	52.1108i	−0.0829678	−	1.79586i
$843$	−12.4211	−	1.63526i	−0.427804	−	0.0563214i
$844$	19.9066	+	37.7717i	0.685213	+	1.30015i
$845$	0.0463847	+	0.352327i	0.00159568	+	0.0121204i
$846$	11.0854	+	0.941557i	0.381125	+	0.0323714i
$847$	−2.26101	−	17.0448i	−0.0776894	−	0.585666i
$848$	1.34556	+	25.0014i	0.0462066	+	0.858551i
$849$	−29.3005	+	16.9166i	−1.00559	+	0.580577i
$850$	41.4411	+	28.8612i	1.42142	+	0.989931i
$851$	10.7435	−	8.24377i	0.368282	−	0.282593i
$852$	−6.07726	−	6.56506i	−0.208203	−	0.224915i
$853$	−13.0830	−	31.5851i	−0.447953	−	1.08145i	−0.973088	−	0.230435i	$-0.925985\pi$
$853$	−13.0830	−	31.5851i	−0.447953	−	1.08145i	0.525135	−	0.851019i	$-0.324015\pi$
$854$	3.03632	−	0.546397i	0.103901	−	0.0186973i
$855$	−0.781745	−	0.781745i	−0.0267351	−	0.0267351i
$856$	0.665828	−	5.37271i	0.0227575	−	0.183635i
$857$	−6.60584	−	24.6533i	−0.225651	−	0.842142i	−0.982143	−	0.188138i	$-0.939755\pi$
$857$	−6.60584	−	24.6533i	−0.225651	−	0.842142i	0.756491	−	0.654004i	$-0.226912\pi$
$858$	13.9827	+	3.06274i	0.477361	+	0.104560i
$859$	−43.9038	−	33.6885i	−1.49798	−	1.14944i	−0.949708	−	0.313136i	$-0.898620\pi$
$859$	−43.9038	−	33.6885i	−1.49798	−	1.14944i	−0.548269	−	0.836302i	$-0.684713\pi$
$860$	−3.82468	+	2.70706i	−0.130421	+	0.0923099i
$861$	19.4193	−	5.22383i	0.661809	−	0.178028i
$862$	19.8442	−	16.7371i	0.675896	−	0.570069i
$863$	12.3555	+	21.4003i	0.420586	+	0.728476i	0.995997	−	0.0893882i	$-0.0284912\pi$
$863$	12.3555	+	21.4003i	0.420586	+	0.728476i	−0.575411	+	0.817864i	$0.695158\pi$
$864$	30.5202	−	7.17296i	1.03832	−	0.244029i
$865$	−0.442340	+	0.766156i	−0.0150400	+	0.0260501i
$866$	14.2309	+	5.13882i	0.483585	+	0.174624i
$867$	16.6812	−	40.2720i	0.566523	−	1.36771i
$868$	17.7542	+	19.1416i	0.602618	+	0.649708i
$869$	−4.58315	+	1.89840i	−0.155473	+	0.0643989i
$870$	1.71541	−	1.88159i	0.0581578	−	0.0637918i
$871$	−4.44076	−	16.5732i	−0.150470	−	0.561560i
$872$	−19.9062	+	49.1103i	−0.674110	+	1.66309i
$873$	3.89096	−	14.5213i	0.131689	−	0.491470i
$874$	−11.9789	+	23.1542i	−0.405191	+	0.783204i
$875$	5.67982	−	0.00557584i	0.192013	−	0.000188498i
$876$	−6.68712	−	29.4565i	−0.225937	−	0.995243i
$877$	−3.59714	−	27.3230i	−0.121467	−	0.922633i	−0.938315	−	0.345781i	$-0.887614\pi$
$877$	−3.59714	−	27.3230i	−0.121467	−	0.922633i	0.816848	−	0.576852i	$-0.195719\pi$
$878$	43.2808	+	30.1424i	1.46066	+	1.01726i
$879$	−15.1025	−	8.71945i	−0.509396	−	0.294100i
$880$	−1.03460	+	1.50991i	−0.0348765	+	0.0508989i
$881$		−	26.8351i		−	0.904096i	−0.891994	−	0.452048i	$-0.850694\pi$
$881$		−	26.8351i		−	0.904096i	0.891994	−	0.452048i	$-0.149306\pi$
$882$	−14.0875	+	2.54939i	−0.474352	+	0.0858423i
$883$	8.17897	+	3.38784i	0.275244	+	0.114010i	0.516036	−	0.856567i	$-0.327407\pi$
$883$	8.17897	+	3.38784i	0.275244	+	0.114010i	−0.240792	+	0.970577i	$0.577407\pi$
$884$	2.12758	−	55.1397i	0.0715582	−	1.85455i
$885$	2.02324	+	0.266364i	0.0680103	+	0.00895373i
$886$	7.59960	−	4.86859i	0.255313	−	0.163563i
$887$	−6.81164	+	25.4214i	−0.228712	+	0.853566i	0.752171	+	0.658968i	$0.229007\pi$
$887$	−6.81164	+	25.4214i	−0.228712	+	0.853566i	−0.980883	+	0.194598i	$0.937660\pi$
$888$	4.65048	+	7.91532i	0.156060	+	0.265621i
$889$	22.1330	+	53.2857i	0.742316	+	1.78715i
$890$	4.82887	−	1.53600i	0.161864	−	0.0514868i
$891$	4.32593	+	3.31940i	0.144924	+	0.111204i
$892$	15.9338	+	13.2330i	0.533502	+	0.443074i
$893$	−11.7375	−	15.2966i	−0.392781	−	0.511883i
$894$	8.79773	−	24.3634i	0.294240	−	0.814835i
$895$	5.45157			0.182226
$896$	−13.3223	+	26.8052i	−0.445067	+	0.895497i
$897$	24.8114			0.828428
$898$	−10.0219	+	27.7535i	−0.334435	+	0.926147i
$899$	20.1140	+	26.2130i	0.670838	+	0.874253i
$900$	11.0218	+	9.15359i	0.367392	+	0.305120i
$901$	35.7991	+	27.4696i	1.19264	+	0.915145i
$902$	−17.4344	+	5.54564i	−0.580501	+	0.184650i
$903$	−35.5234	−	4.64127i	−1.18215	−	0.154452i
$904$	2.09865	+	3.57199i	0.0698000	+	0.118803i
$905$	0.158093	−	0.590013i	0.00525521	−	0.0196127i
$906$	2.77764	−	1.77946i	0.0922809	−	0.0591186i
$907$	7.61259	+	1.00222i	0.252772	+	0.0332781i	0.255847	−	0.966717i	$-0.417646\pi$
$907$	7.61259	+	1.00222i	0.252772	+	0.0332781i	−0.00307534	+	0.999995i	$0.500979\pi$
$908$	1.36926	−	35.4866i	0.0454405	−	1.17766i
$909$	0.254174	+	0.105282i	0.00843042	+	0.00349199i
$910$	−1.66864	−	2.59903i	−0.0553148	−	0.0861571i
$911$			13.0632i			0.432802i	0.976305	+	0.216401i	$0.0694318\pi$
$911$			13.0632i			0.432802i	−0.976305	+	0.216401i	$0.930568\pi$
$912$	−14.5789	−	9.98962i	−0.482756	−	0.330789i
$913$	−2.24303	−	1.29501i	−0.0742333	−	0.0428586i
$914$	−2.77008	−	1.92919i	−0.0916263	−	0.0638120i
$915$	0.0289344	+	0.219778i	0.000956541	+	0.00726565i
$916$	5.36476	+	23.6315i	0.177257	+	0.780808i
$917$	−7.88521	−	13.6267i	−0.260392	−	0.449992i
$918$	25.9634	−	50.1852i	0.856919	−	1.65636i
$919$	−0.573723	+	2.14116i	−0.0189254	+	0.0706305i	−0.974743	−	0.223331i	$-0.928307\pi$
$919$	−0.573723	+	2.14116i	−0.0189254	+	0.0706305i	0.955817	+	0.293961i	$0.0949737\pi$
$920$	−1.19180	+	2.94028i	−0.0392926	+	0.0969382i
$921$	−1.96713	−	7.34143i	−0.0648191	−	0.241908i
$922$	15.2017	−	16.6743i	0.500640	−	0.549139i
$923$	−12.6883	+	5.25566i	−0.417640	+	0.172992i
$924$	−13.6439	+	3.11148i	−0.448850	+	0.102360i
$925$	−4.93587	+	11.9162i	−0.162290	+	0.391804i
$926$	−2.72110	−	0.982601i	−0.0894210	−	0.0322903i
$927$	0.156359	−	0.270822i	0.00513551	−	0.00889496i
$928$	−19.9478	+	32.2048i	−0.654817	+	1.05717i
$929$	−16.4138	−	28.4296i	−0.538521	−	0.932745i	−0.998984	−	0.0450664i	$-0.985650\pi$
$929$	−16.4138	−	28.4296i	−0.538521	−	0.932745i	0.460463	−	0.887679i	$-0.347683\pi$
$930$	−1.43399	+	1.20946i	−0.0470223	+	0.0396599i
$931$	19.7137	+	15.0654i	0.646090	+	0.493750i
$932$	−24.3881	+	17.2616i	−0.798860	+	0.565422i
$933$	19.5335	+	14.9886i	0.639497	+	0.490703i
$934$	−36.8305	−	8.06729i	−1.20513	−	0.263970i
$935$	0.853780	+	3.18635i	0.0279216	+	0.104205i
$936$	1.92534	−	15.5360i	0.0629317	−	0.507810i
$937$	16.3925	+	16.3925i	0.535520	+	0.535520i	0.922210	−	0.386690i	$-0.126382\pi$
$937$	16.3925	+	16.3925i	0.535520	+	0.535520i	−0.386690	+	0.922210i	$0.626382\pi$
$938$	10.8273	+	12.8118i	0.353525	+	0.418320i
$939$	−6.14935	−	14.8458i	−0.200676	−	0.484476i
$940$	−1.59402	−	1.72196i	−0.0519911	−	0.0561643i
$941$	−6.17173	+	4.73574i	−0.201193	+	0.154381i	−0.704444	−	0.709759i	$-0.748804\pi$
$941$	−6.17173	+	4.73574i	−0.201193	+	0.154381i	0.503251	+	0.864140i	$0.332137\pi$
$942$	−2.60959	−	1.81742i	−0.0850251	−	0.0592147i
$943$	−27.4631	+	15.8559i	−0.894323	+	0.516338i
$944$	−30.3178	+	1.63168i	−0.986760	+	0.0531067i
$945$	−0.415883	−	3.13516i	−0.0135287	−	0.101987i
$946$	32.4758	+	2.75837i	1.05588	+	0.0896825i
$947$	−2.89787	−	22.0115i	−0.0941681	−	0.715278i	−0.971777	−	0.235901i	$-0.924196\pi$
$947$	−2.89787	−	22.0115i	−0.0941681	−	0.715278i	0.877609	−	0.479377i	$-0.159137\pi$
$948$	−2.71782	−	5.15692i	−0.0882708	−	0.167489i
$949$	−45.9742	−	6.05262i	−1.49239	−	0.196476i
$950$	−1.14591	−	24.8035i	−0.0371783	−	0.804731i
$951$	12.1679	+	12.1679i	0.394570	+	0.394570i
$952$	21.0716	+	49.6615i	0.682934	+	1.60954i
$953$	−9.12055	+	9.12055i	−0.295443	+	0.295443i	−0.839226	−	0.543783i	$-0.816992\pi$
$953$	−9.12055	+	9.12055i	−0.295443	+	0.295443i	0.543783	+	0.839226i	$0.316992\pi$
$954$	9.46026	+	8.62474i	0.306287	+	0.279236i
$955$	0.372490	−	2.82934i	0.0120535	−	0.0915554i
$956$	32.1171	−	38.6720i	1.03874	−	1.25074i
$957$	−17.5589	+	2.31167i	−0.567598	+	0.0747257i
$958$	5.67466	+	6.72811i	0.183340	+	0.217375i
$959$	−3.84586	−	5.00184i	−0.124189	−	0.161518i
$960$	−1.87879	−	1.04697i	−0.0606377	−	0.0337907i
$961$	3.32834	+	5.76485i	0.107366	+	0.185963i
$962$	13.8729	−	2.48243i	0.447282	−	0.0800368i
$963$	−1.68510	−	2.19606i	−0.0543015	−	0.0707670i
$964$	−8.97844	−	24.2845i	−0.289176	−	0.782151i
$965$	−0.415681	+	0.172181i	−0.0133813	+	0.00554270i
$966$	−21.9478	+	10.3285i	−0.706160	+	0.332315i
$967$	−29.1918	+	29.1918i	−0.938746	+	0.938746i	−0.998229	−	0.0594832i	$-0.981055\pi$
$967$	−29.1918	+	29.1918i	−0.938746	+	0.938746i	0.0594832	+	0.998229i	$0.481055\pi$
$968$	−17.7183	+	4.89223i	−0.569487	+	0.157242i
$969$	−30.7658	+	8.24368i	−0.988341	+	0.264825i
$970$	−2.66989	+	1.71043i	−0.0857249	+	0.0549186i
$971$	19.9552	−	26.0062i	0.640394	−	0.834578i	−0.354547	−	0.935038i	$-0.615365\pi$
$971$	19.9552	−	26.0062i	0.640394	−	0.834578i	0.994941	+	0.100460i	$0.0320316\pi$
$972$	14.3096	−	22.7147i	0.458980	−	0.728575i
$973$	4.87535	−	4.88493i	0.156297	−	0.156604i
$974$	−39.3486	−	3.34212i	−1.26081	−	0.107088i
$975$	−20.4657	+	11.8159i	−0.655428	+	0.378411i
$976$	−1.02358	−	3.13524i	−0.0327641	−	0.100357i
$977$	−35.3440	−	20.4059i	−1.13076	−	0.652842i	−0.186631	−	0.982430i	$-0.559757\pi$
$977$	−35.3440	−	20.4059i	−1.13076	−	0.652842i	−0.944125	+	0.329588i	$0.893090\pi$
$978$	−21.9393	+	10.2982i	−0.701541	+	0.329300i
$979$	−32.5635	−	13.4882i	−1.04073	−	0.431086i
$980$	2.55799	+	1.60445i	0.0817118	+	0.0512521i
$981$	10.3686	+	25.0320i	0.331043	+	0.799209i
$982$	25.6825	−	1.18652i	0.819562	−	0.0378634i
$983$	−55.1464	+	14.7764i	−1.75890	+	0.471295i	−0.986488	−	0.163833i	$-0.947614\pi$
$983$	−55.1464	+	14.7764i	−1.75890	+	0.471295i	−0.772408	+	0.635127i	$0.780948\pi$
$984$	−8.37771	−	19.7986i	−0.267071	−	0.631156i
$985$	−4.03499	−	1.08117i	−0.128565	−	0.0344490i
$986$	20.6950	+	65.0608i	0.659062	+	2.07196i
$987$	−0.0176119	−	17.9403i	−0.000560592	−	0.571046i
$988$	−22.1452	+	15.6741i	−0.704532	+	0.498658i
$989$	56.0110	−	7.37399i	1.78105	−	0.234479i
$990$	0.164845	+	0.921228i	0.00523912	+	0.0292786i
$991$	5.91906	−	10.2521i	0.188025	−	0.325669i	−0.756567	−	0.653917i	$-0.773125\pi$
$991$	5.91906	−	10.2521i	0.188025	−	0.325669i	0.944592	+	0.328248i	$0.106458\pi$
$992$	17.6681	−	21.6061i	0.560964	−	0.685994i
$993$	−14.8614			−0.471612
$994$	9.03605	−	9.93098i	0.286606	−	0.314992i
$995$	1.44691	−	3.49315i	0.0458701	−	0.110740i
$996$	1.27223	−	2.76480i	0.0403123	−	0.0876061i
$997$	0.184807	−	1.40375i	0.00585290	−	0.0444572i	−0.988269	−	0.152722i	$-0.951196\pi$
$997$	0.184807	−	1.40375i	0.00585290	−	0.0444572i	0.994122	+	0.108265i	$0.0345294\pi$
$998$	−6.08972	−	1.33388i	−0.192767	−	0.0422232i
$999$	13.9394	+	3.73506i	0.441024	+	0.118172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.11	yes	240
4.3	odd	2		896.2.bh.a.529.21		240
7.2	even	3	inner	224.2.bd.a.205.29	yes	240
28.23	odd	6		896.2.bh.a.401.10		240
32.5	even	8	inner	224.2.bd.a.165.29	yes	240
32.27	odd	8		896.2.bh.a.753.10		240
224.37	even	24	inner	224.2.bd.a.37.11	✓	240
224.219	odd	24		896.2.bh.a.625.21		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.11	✓	240	224.37	even	24	inner
224.2.bd.a.109.11	yes	240	1.1	even	1	trivial
224.2.bd.a.165.29	yes	240	32.5	even	8	inner
224.2.bd.a.205.29	yes	240	7.2	even	3	inner
896.2.bh.a.401.10		240	28.23	odd	6
896.2.bh.a.529.21		240	4.3	odd	2
896.2.bh.a.625.21		240	224.219	odd	24
896.2.bh.a.753.10		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.480321 + 1.33015i) q^{2} +(-0.758838 - 0.988936i) q^{3} +(-1.53858 - 1.27780i) q^{4} +(0.171111 + 0.131298i) q^{5} +(1.67992 - 0.534359i) q^{6} +(1.01488 + 2.44336i) q^{7} +(2.43867 - 1.43279i) q^{8} +(0.374296 - 1.39689i) q^{9} +O(q^{10})\)	\(q+(-0.480321 + 1.33015i) q^{2} +(-0.758838 - 0.988936i) q^{3} +(-1.53858 - 1.27780i) q^{4} +(0.171111 + 0.131298i) q^{5} +(1.67992 - 0.534359i) q^{6} +(1.01488 + 2.44336i) q^{7} +(2.43867 - 1.43279i) q^{8} +(0.374296 - 1.39689i) q^{9} +(-0.256834 + 0.164537i) q^{10} +(2.10346 + 0.276926i) q^{11} +(-0.0961237 + 2.49120i) q^{12} +(3.53590 + 1.46462i) q^{13} +(-3.73750 + 0.176348i) q^{14} -0.268851i q^{15} +(0.734477 + 3.93199i) q^{16} +(6.24315 + 3.60448i) q^{17} +(1.67829 + 1.16883i) q^{18} +(-0.462645 - 3.51414i) q^{19} +(-0.0954963 - 0.420657i) q^{20} +(1.64620 - 2.85777i) q^{21} +(-1.37869 + 2.66490i) q^{22} +(-1.34605 + 5.02353i) q^{23} +(-3.26749 - 1.32443i) q^{24} +(-1.28206 - 4.78470i) q^{25} +(-3.64652 + 3.99978i) q^{26} +(-5.12039 + 2.12094i) q^{27} +(1.56063 - 5.05613i) q^{28} +(2.56271 - 6.18694i) q^{29} +(0.357612 + 0.129135i) q^{30} +(-2.46695 + 4.27288i) q^{31} +(-5.58291 - 0.911655i) q^{32} +(-1.32232 - 2.29033i) q^{33} +(-7.79321 + 6.57300i) q^{34} +(-0.147150 + 0.551337i) q^{35} +(-2.36083 + 1.67096i) q^{36} +(-2.06576 - 1.58511i) q^{37} +(4.89654 + 1.07253i) q^{38} +(-1.23476 - 4.60818i) q^{39} +(0.605405 + 0.0750265i) q^{40} +(4.31161 + 4.31161i) q^{41} +(3.01055 + 3.56233i) q^{42} +(-4.15699 - 10.0359i) q^{43} +(-2.88250 - 3.11387i) q^{44} +(0.247455 - 0.189879i) q^{45} +(-6.03550 - 4.20335i) q^{46} +(4.71097 - 2.71988i) q^{47} +(3.33114 - 3.71009i) q^{48} +(-4.94002 + 4.95946i) q^{49} +(6.98015 + 0.592868i) q^{50} +(-1.17293 - 8.90930i) q^{51} +(-3.56879 - 6.77158i) q^{52} +(6.20584 + 0.817015i) q^{53} +(-0.361725 - 7.82960i) q^{54} +(0.323565 + 0.323565i) q^{55} +(5.97579 + 4.50443i) q^{56} +(-3.12418 + 3.12418i) q^{57} +(6.99861 + 6.38050i) q^{58} +(-0.990748 + 7.52548i) q^{59} +(-0.343537 + 0.413650i) q^{60} +(-0.817471 + 0.107622i) q^{61} +(-4.49863 - 5.33376i) q^{62} +(3.79298 - 0.503144i) q^{63} +(3.89422 - 6.98821i) q^{64} +(0.412729 + 0.714867i) q^{65} +(3.68162 - 0.658791i) q^{66} +(-2.72913 - 3.55667i) q^{67} +(-4.99981 - 13.5233i) q^{68} +(5.98939 - 2.48089i) q^{69} +(-0.662680 - 0.460551i) q^{70} +(-2.53740 + 2.53740i) q^{71} +(-1.08867 - 3.94285i) q^{72} +(-11.7032 + 3.13587i) q^{73} +(3.10066 - 1.98640i) q^{74} +(-3.75889 + 4.89868i) q^{75} +(-3.77853 + 5.99796i) q^{76} +(1.45814 + 5.42056i) q^{77} +(6.72264 + 0.570996i) q^{78} +(-2.02495 + 1.16910i) q^{79} +(-0.390585 + 0.769241i) q^{80} +(2.22575 + 1.28504i) q^{81} +(-7.80603 + 3.66412i) q^{82} +(-1.12785 - 0.467172i) q^{83} +(-6.18445 + 2.29342i) q^{84} +(0.595009 + 1.43648i) q^{85} +(15.3459 - 0.708973i) q^{86} +(-8.06317 + 2.16052i) q^{87} +(5.52643 - 2.33849i) q^{88} +(-16.0470 - 4.29977i) q^{89} +(0.133709 + 0.420355i) q^{90} +(0.00994050 + 10.1259i) q^{91} +(8.49006 - 6.00914i) q^{92} +(6.09762 - 0.802767i) q^{93} +(1.35506 + 7.57270i) q^{94} +(0.382235 - 0.662051i) q^{95} +(3.33495 + 6.21294i) q^{96} +10.3954 q^{97} +(-4.22401 - 8.95308i) q^{98} +(1.17415 - 2.83466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more