LMFDB - Embedded newform 87.2.g.b.52.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			52.2
Root			$0.0185039 + 0.0810709i$ of defining polynomial
Character	$\chi$	$=$	87.52
Dual form			87.2.g.b.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0518468 + 0.0650138i) q^{2} +(0.222521 - 0.974928i) q^{3} +(0.443503 + 1.94311i) q^{4} +(1.20357 - 1.50923i) q^{5} +(0.0518468 + 0.0650138i) q^{6} +(-0.0765305 + 0.335302i) q^{7} +(-0.299165 - 0.144070i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})$	\(q+(-0.0518468 + 0.0650138i) q^{2} +(0.222521 - 0.974928i) q^{3} +(0.443503 + 1.94311i) q^{4} +(1.20357 - 1.50923i) q^{5} +(0.0518468 + 0.0650138i) q^{6} +(-0.0765305 + 0.335302i) q^{7} +(-0.299165 - 0.144070i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(0.0357195 + 0.156498i) q^{10} +(2.18408 - 1.05180i) q^{11} +1.99309 q^{12} +(-3.27160 + 1.57552i) q^{13} +(-0.0178314 - 0.0223599i) q^{14} +(-1.20357 - 1.50923i) q^{15} +(-3.56654 + 1.71755i) q^{16} -6.15354 q^{17} +(0.0749208 - 0.0360799i) q^{18} +(0.300553 + 1.31681i) q^{19} +(3.46640 + 1.66933i) q^{20} +(0.309866 + 0.149223i) q^{21} +(-0.0448561 + 0.196528i) q^{22} +(-2.16114 - 2.70998i) q^{23} +(-0.207029 + 0.259606i) q^{24} +(0.283411 + 1.24171i) q^{25} +(0.0671914 - 0.294385i) q^{26} +(-0.623490 + 0.781831i) q^{27} -0.685471 q^{28} +(-4.26305 + 3.29035i) q^{29} +0.160522 q^{30} +(6.85222 - 8.59242i) q^{31} +(0.221024 - 0.968370i) q^{32} +(-0.539423 - 2.36337i) q^{33} +(0.319041 - 0.400065i) q^{34} +(0.413938 + 0.519062i) q^{35} +(0.443503 - 1.94311i) q^{36} +(2.78149 + 1.33950i) q^{37} +(-0.101193 - 0.0487322i) q^{38} +(0.808018 + 3.54016i) q^{39} +(-0.577502 + 0.278110i) q^{40} +5.28313 q^{41} +(-0.0257671 + 0.0124088i) q^{42} +(-0.00526324 - 0.00659989i) q^{43} +(3.01241 + 3.77744i) q^{44} +(-1.73921 + 0.837560i) q^{45} +0.288234 q^{46} +(5.22270 - 2.51512i) q^{47} +(0.880862 + 3.85931i) q^{48} +(6.20021 + 2.98586i) q^{49} +(-0.0954221 - 0.0459528i) q^{50} +(-1.36929 + 5.99926i) q^{51} +(-4.51238 - 5.65834i) q^{52} +(-2.58271 + 3.23861i) q^{53} +(-0.0185039 - 0.0810709i) q^{54} +(1.04129 - 4.56219i) q^{55} +(0.0712023 - 0.0892849i) q^{56} +1.35067 q^{57} +(0.00710697 - 0.447751i) q^{58} +5.76819 q^{59} +(2.39882 - 3.00802i) q^{60} +(1.38805 - 6.08144i) q^{61} +(0.203360 + 0.890979i) q^{62} +(0.214434 - 0.268891i) q^{63} +(-4.88474 - 6.12527i) q^{64} +(-1.55978 + 6.83384i) q^{65} +(0.181619 + 0.0874630i) q^{66} +(-9.92346 - 4.77889i) q^{67} +(-2.72912 - 11.9570i) q^{68} +(-3.12293 + 1.50393i) q^{69} -0.0552076 q^{70} +(-11.5818 + 5.57748i) q^{71} +(0.207029 + 0.259606i) q^{72} +(0.286311 + 0.359022i) q^{73} +(-0.231297 + 0.111387i) q^{74} +1.27364 q^{75} +(-2.42541 + 1.16802i) q^{76} +(0.185521 + 0.812820i) q^{77} +(-0.272052 - 0.131013i) q^{78} +(11.2434 + 5.41452i) q^{79} +(-1.70040 + 7.44993i) q^{80} +(0.623490 + 0.781831i) q^{81} +(-0.273913 + 0.343476i) q^{82} +(-0.640518 - 2.80629i) q^{83} +(-0.152532 + 0.668285i) q^{84} +(-7.40623 + 9.28712i) q^{85} +0.000701966 q^{86} +(2.25924 + 4.88834i) q^{87} -0.804933 q^{88} +(-7.62150 + 9.55706i) q^{89} +(0.0357195 - 0.156498i) q^{90} +(-0.277897 - 1.21755i) q^{91} +(4.30733 - 5.40122i) q^{92} +(-6.85222 - 8.59242i) q^{93} +(-0.107263 + 0.469948i) q^{94} +(2.34911 + 1.13127i) q^{95} +(-0.894908 - 0.430965i) q^{96} +(0.606191 + 2.65590i) q^{97} +(-0.515584 + 0.248292i) q^{98} -2.42414 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20} + 4 q^{21} + 20 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 3 q^{26} + 3 q^{27} - 48 q^{28} - 10 q^{29} + 8 q^{30} + 8 q^{31} + 55 q^{32} - 8 q^{33} + 6 q^{34} + 31 q^{35} - 6 q^{36} + 20 q^{37} - 20 q^{38} - 10 q^{39} - 59 q^{40} - 68 q^{41} - 19 q^{42} - 3 q^{43} - 10 q^{44} + 14 q^{45} - 12 q^{46} + 19 q^{47} + 24 q^{48} + 17 q^{49} + 23 q^{50} + 11 q^{51} - 4 q^{52} - q^{53} - 5 q^{54} + 3 q^{55} + 7 q^{56} - 2 q^{57} - 30 q^{58} + 20 q^{59} + 47 q^{60} + 24 q^{61} + 79 q^{62} + 3 q^{63} - 23 q^{64} + 6 q^{65} + 50 q^{66} - 14 q^{67} - 8 q^{68} - 8 q^{69} + 28 q^{70} - 28 q^{71} + 4 q^{72} + 43 q^{73} - 47 q^{74} - 18 q^{75} + 19 q^{76} + 26 q^{77} - 11 q^{78} + 9 q^{79} - 74 q^{80} - 3 q^{81} - 17 q^{82} + 8 q^{83} - 15 q^{84} - 21 q^{85} - 140 q^{86} - 11 q^{87} - 58 q^{88} - 6 q^{89} + 6 q^{90} - 15 q^{91} + 11 q^{92} - 8 q^{93} + 6 q^{94} - 16 q^{95} + 36 q^{96} - 81 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{5}{7}\right)$	$1$

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 $

$2$	−0.0518468	+	0.0650138i	−0.0366612	+	0.0459717i	−0.799824	−	0.600234i	$-0.795074\pi$
$2$	−0.0518468	+	0.0650138i	−0.0366612	+	0.0459717i	0.763163	+	0.646206i	$0.223645\pi$
$3$	0.222521	−	0.974928i	0.128473	−	0.562875i
$3$	0.222521	−	0.974928i	0.128473	−	0.562875i
$4$	0.443503	+	1.94311i	0.221752	+	0.971557i
$5$	1.20357	−	1.50923i	0.538253	−	0.674948i	−0.436119	−	0.899889i	$-0.643647\pi$
$5$	1.20357	−	1.50923i	0.538253	−	0.674948i	0.974372	+	0.224941i	$0.0722188\pi$
$6$	0.0518468	+	0.0650138i	0.0211664	+	0.0265418i
$7$	−0.0765305	+	0.335302i	−0.0289258	+	0.126732i	−0.987329	−	0.158684i	$-0.949275\pi$
$7$	−0.0765305	+	0.335302i	−0.0289258	+	0.126732i	0.958404	+	0.285417i	$0.0921319\pi$
$8$	−0.299165	−	0.144070i	−0.105771	−	0.0509365i
$9$	−0.900969	−	0.433884i	−0.300323	−	0.144628i
$10$	0.0357195	+	0.156498i	0.0112955	+	0.0494889i
$11$	2.18408	−	1.05180i	0.658525	−	0.317129i	−0.0746095	−	0.997213i	$-0.523771\pi$
$11$	2.18408	−	1.05180i	0.658525	−	0.317129i	0.733134	+	0.680084i	$0.238057\pi$
$12$	1.99309			0.575354
$13$	−3.27160	+	1.57552i	−0.907378	+	0.436970i	−0.828548	−	0.559918i	$-0.810833\pi$
$13$	−3.27160	+	1.57552i	−0.907378	+	0.436970i	−0.0788298	+	0.996888i	$0.525118\pi$
$14$	−0.0178314	−	0.0223599i	−0.00476564	−	0.00597593i
$15$	−1.20357	−	1.50923i	−0.310761	−	0.389682i
$16$	−3.56654	+	1.71755i	−0.891634	+	0.429389i
$17$	−6.15354			−1.49245			−0.746227	−	0.665692i	$-0.768137\pi$
$17$	−6.15354			−1.49245			−0.746227	+	0.665692i	$0.768137\pi$
$18$	0.0749208	−	0.0360799i	0.0176590	−	0.00850413i
$19$	0.300553	+	1.31681i	0.0689516	+	0.302097i	0.997631	−	0.0687856i	$-0.0219125\pi$
$19$	0.300553	+	1.31681i	0.0689516	+	0.302097i	−0.928680	+	0.370882i	$0.879055\pi$
$20$	3.46640	+	1.66933i	0.775110	+	0.373273i
$21$	0.309866	+	0.149223i	0.0676182	+	0.0325632i
$22$	−0.0448561	+	0.196528i	−0.00956336	+	0.0418998i
$23$	−2.16114	−	2.70998i	−0.450628	−	0.565070i	0.503681	−	0.863889i	$-0.331979\pi$
$23$	−2.16114	−	2.70998i	−0.450628	−	0.565070i	−0.954310	+	0.298820i	$0.903407\pi$
$24$	−0.207029	+	0.259606i	−0.0422595	+	0.0529918i
$25$	0.283411	+	1.24171i	0.0566823	+	0.248341i
$26$	0.0671914	−	0.294385i	0.0131773	−	0.0577336i
$27$	−0.623490	+	0.781831i	−0.119991	+	0.150464i
$28$	−0.685471			−0.129542
$29$	−4.26305	+	3.29035i	−0.791628	+	0.611003i
$29$	−4.26305	+	3.29035i	−0.791628	+	0.611003i
$30$	0.160522			0.0293072
$31$	6.85222	−	8.59242i	1.23070	−	1.54324i	0.489411	−	0.872053i	$-0.337212\pi$
$31$	6.85222	−	8.59242i	1.23070	−	1.54324i	0.741285	−	0.671190i	$-0.234217\pi$
$32$	0.221024	−	0.968370i	0.0390719	−	0.171185i
$33$	−0.539423	−	2.36337i	−0.0939015	−	0.411409i
$34$	0.319041	−	0.400065i	0.0547152	−	0.0686106i
$35$	0.413938	+	0.519062i	0.0699683	+	0.0877375i
$36$	0.443503	−	1.94311i	0.0739172	−	0.323852i
$37$	2.78149	+	1.33950i	0.457275	+	0.220212i	0.648318	−	0.761370i	$-0.275473\pi$
$37$	2.78149	+	1.33950i	0.457275	+	0.220212i	−0.191043	+	0.981582i	$0.561187\pi$
$38$	−0.101193	−	0.0487322i	−0.0164158	−	0.00790541i
$39$	0.808018	+	3.54016i	0.129386	+	0.566879i
$40$	−0.577502	+	0.278110i	−0.0913111	+	0.0439731i
$41$	5.28313			0.825086			0.412543	−	0.910938i	$-0.364641\pi$
$41$	5.28313			0.825086			0.412543	+	0.910938i	$0.364641\pi$
$42$	−0.0257671	+	0.0124088i	−0.00397595	+	0.00191472i
$43$	−0.00526324	−	0.00659989i	−0.000802636	−	0.00100647i	0.781430	−	0.623993i	$-0.214491\pi$
$43$	−0.00526324	−	0.00659989i	−0.000802636	−	0.00100647i	−0.782233	+	0.622986i	$0.785919\pi$
$44$	3.01241	+	3.77744i	0.454138	+	0.569470i
$45$	−1.73921	+	0.837560i	−0.259266	+	0.124856i
$46$	0.288234			0.0424978
$47$	5.22270	−	2.51512i	0.761809	−	0.366868i	−0.0122968	−	0.999924i	$-0.503914\pi$
$47$	5.22270	−	2.51512i	0.761809	−	0.366868i	0.774105	+	0.633057i	$0.218200\pi$
$48$	0.880862	+	3.85931i	0.127141	+	0.557043i
$49$	6.20021	+	2.98586i	0.885745	+	0.426552i
$50$	−0.0954221	−	0.0459528i	−0.0134947	−	0.00649871i
$51$	−1.36929	+	5.99926i	−0.191739	+	0.840065i
$52$	−4.51238	−	5.65834i	−0.625754	−	0.784671i
$53$	−2.58271	+	3.23861i	−0.354762	+	0.444857i	−0.926905	−	0.375297i	$-0.877541\pi$
$53$	−2.58271	+	3.23861i	−0.354762	+	0.444857i	0.572143	+	0.820154i	$0.306112\pi$
$54$	−0.0185039	−	0.0810709i	−0.00251806	−	0.0110324i
$55$	1.04129	−	4.56219i	0.140408	−	0.615166i
$56$	0.0712023	−	0.0892849i	0.00951481	−	0.0119312i
$57$	1.35067			0.178901
$58$	0.00710697	−	0.447751i	0.000933191	−	0.0587926i
$59$	5.76819			0.750955			0.375477	−	0.926832i	$-0.377479\pi$
$59$	5.76819			0.750955			0.375477	+	0.926832i	$0.377479\pi$
$60$	2.39882	−	3.00802i	0.309686	−	0.388334i
$61$	1.38805	−	6.08144i	0.177722	−	0.778649i	−0.804957	−	0.593333i	$-0.797812\pi$
$61$	1.38805	−	6.08144i	0.177722	−	0.778649i	0.982679	−	0.185316i	$-0.0593310\pi$
$62$	0.203360	+	0.890979i	0.0258268	+	0.113154i
$63$	0.214434	−	0.268891i	0.0270161	−	0.0338771i
$64$	−4.88474	−	6.12527i	−0.610593	−	0.765659i
$65$	−1.55978	+	6.83384i	−0.193467	+	0.847634i
$66$	0.181619	+	0.0874630i	0.0223557	+	0.0107660i
$67$	−9.92346	−	4.77889i	−1.21234	−	0.583834i	−0.285174	−	0.958476i	$-0.592051\pi$
$67$	−9.92346	−	4.77889i	−1.21234	−	0.583834i	−0.927170	+	0.374642i	$0.877766\pi$
$68$	−2.72912	−	11.9570i	−0.330954	−	1.45000i
$69$	−3.12293	+	1.50393i	−0.375957	+	0.181051i
$70$	−0.0552076			−0.00659856
$71$	−11.5818	+	5.57748i	−1.37450	+	0.661925i	−0.967820	−	0.251645i	$-0.919029\pi$
$71$	−11.5818	+	5.57748i	−1.37450	+	0.661925i	−0.406682	+	0.913570i	$0.633314\pi$
$72$	0.207029	+	0.259606i	0.0243986	+	0.0305948i
$73$	0.286311	+	0.359022i	0.0335102	+	0.0420204i	0.798304	−	0.602254i	$-0.205731\pi$
$73$	0.286311	+	0.359022i	0.0335102	+	0.0420204i	−0.764794	+	0.644275i	$0.777159\pi$
$74$	−0.231297	+	0.111387i	−0.0268878	+	0.0129485i
$75$	1.27364			0.147067
$76$	−2.42541	+	1.16802i	−0.278214	+	0.133981i
$77$	0.185521	+	0.812820i	0.0211421	+	0.0926295i
$78$	−0.272052	−	0.131013i	−0.0308039	−	0.0148344i
$79$	11.2434	+	5.41452i	1.26498	+	0.609181i	0.941487	−	0.337050i	$-0.109429\pi$
$79$	11.2434	+	5.41452i	1.26498	+	0.609181i	0.323491	+	0.946231i	$0.395143\pi$
$80$	−1.70040	+	7.44993i	−0.190110	+	0.832927i
$81$	0.623490	+	0.781831i	0.0692766	+	0.0868702i
$82$	−0.273913	+	0.343476i	−0.0302487	+	0.0379306i
$83$	−0.640518	−	2.80629i	−0.0703060	−	0.308031i	0.927533	−	0.373742i	$-0.121925\pi$
$83$	−0.640518	−	2.80629i	−0.0703060	−	0.308031i	−0.997839	+	0.0657114i	$0.979068\pi$
$84$	−0.152532	+	0.668285i	−0.0166426	+	0.0729159i
$85$	−7.40623	+	9.28712i	−0.803318	+	1.00733i
$86$	0.000701966	0		7.56950e−5	0
$87$	2.25924	+	4.88834i	0.242216	+	0.524085i
$88$	−0.804933			−0.0858061
$89$	−7.62150	+	9.55706i	−0.807878	+	1.01305i	0.191624	+	0.981468i	$0.438625\pi$
$89$	−7.62150	+	9.55706i	−0.807878	+	1.01305i	−0.999501	+	0.0315781i	$0.989947\pi$
$90$	0.0357195	−	0.156498i	0.00376517	−	0.0164963i
$91$	−0.277897	−	1.21755i	−0.0291316	−	0.127634i
$92$	4.30733	−	5.40122i	0.449070	−	0.563116i
$93$	−6.85222	−	8.59242i	−0.710543	−	0.890992i
$94$	−0.107263	+	0.469948i	−0.0110633	+	0.0484715i
$95$	2.34911	+	1.13127i	0.241013	+	0.116066i
$96$	−0.894908	−	0.430965i	−0.0913362	−	0.0439852i
$97$	0.606191	+	2.65590i	0.0615494	+	0.269666i	0.996334	−	0.0855498i	$-0.0272647\pi$
$97$	0.606191	+	2.65590i	0.0615494	+	0.269666i	−0.934784	+	0.355215i	$0.884408\pi$
$98$	−0.515584	+	0.248292i	−0.0520818	+	0.0250813i
$99$	−2.42414			−0.243636
$100$	−2.28708	+	1.10140i	−0.228708	+	0.110140i
$101$	−11.3909	−	14.2838i	−1.13344	−	1.42129i	−0.892673	−	0.450704i	$-0.851173\pi$
$101$	−11.3909	−	14.2838i	−1.13344	−	1.42129i	−0.240765	−	0.970583i	$-0.577398\pi$
$102$	−0.319041	−	0.400065i	−0.0315898	−	0.0396124i
$103$	14.4782	−	6.97235i	1.42658	−	0.687006i	0.448224	−	0.893921i	$-0.352057\pi$
$103$	14.4782	−	6.97235i	1.42658	−	0.687006i	0.978359	+	0.206916i	$0.0663425\pi$
$104$	1.20573			0.118232
$105$	0.598158	−	0.288058i	0.0583742	−	0.0281115i
$106$	−0.0766494	−	0.335823i	−0.00744485	−	0.0326180i
$107$	14.5741	+	7.01851i	1.40893	+	0.678505i	0.974951	−	0.222419i	$-0.0713953\pi$
$107$	14.5741	+	7.01851i	1.40893	+	0.678505i	0.433978	+	0.900923i	$0.357110\pi$
$108$	−1.79571	−	0.864767i	−0.172792	−	0.0832123i
$109$	−2.04709	+	8.96888i	−0.196075	+	0.859063i	0.777169	+	0.629292i	$0.216655\pi$
$109$	−2.04709	+	8.96888i	−0.196075	+	0.859063i	−0.973245	+	0.229771i	$0.926202\pi$
$110$	0.242618	+	0.304233i	0.0231327	+	0.0290075i
$111$	1.92485	−	2.41369i	0.182699	−	0.229097i
$112$	−0.302950	−	1.32731i	−0.0286261	−	0.125419i
$113$	4.50744	−	19.7484i	0.424024	−	1.85777i	−0.0840533	−	0.996461i	$-0.526787\pi$
$113$	4.50744	−	19.7484i	0.424024	−	1.85777i	0.508078	−	0.861311i	$-0.330356\pi$
$114$	−0.0700281	+	0.0878124i	−0.00655873	+	0.00822439i
$115$	−6.69107			−0.623945
$116$	−8.28421	−	6.82431i	−0.769169	−	0.633621i
$117$	3.63120			0.335704
$118$	−0.299062	+	0.375012i	−0.0275309	+	0.0345227i
$119$	0.470934	−	2.06329i	0.0431704	−	0.189142i
$120$	0.142631	+	0.624908i	0.0130204	+	0.0570460i
$121$	−3.19446	+	4.00573i	−0.290406	+	0.364157i
$122$	0.323412	+	0.405546i	0.0292803	+	0.0367164i
$123$	1.17561	−	5.15067i	0.106001	−	0.464420i
$124$	19.7350	+	9.50389i	1.77226	+	0.853475i
$125$	10.9112	+	5.25455i	0.975926	+	0.469981i
$126$	0.00636395	+	0.0278823i	0.000566946	+	0.00248395i
$127$	−8.61739	+	4.14992i	−0.764670	+	0.368246i	−0.775214	−	0.631699i	$-0.782358\pi$
$127$	−8.61739	+	4.14992i	−0.764670	+	0.368246i	0.0105441	+	0.999944i	$0.496644\pi$
$128$	2.63803			0.233171
$129$	−0.00760560	+	0.00366266i	−0.000669636	+	0.000322480i
$130$	−0.363425	−	0.455720i	−0.0318745	−	0.0399693i
$131$	10.4762	+	13.1367i	0.915307	+	1.14776i	0.988618	+	0.150449i	$0.0480721\pi$
$131$	10.4762	+	13.1367i	0.915307	+	1.14776i	−0.0733108	+	0.997309i	$0.523356\pi$
$132$	4.35306	−	2.09632i	0.378885	−	0.182461i
$133$	−0.464530			−0.0402799
$134$	0.825193	−	0.397392i	0.0712859	−	0.0343295i
$135$	0.429550	+	1.88198i	0.0369697	+	0.161975i
$136$	1.84093	+	0.886543i	0.157858	+	0.0760204i
$137$	5.18170	+	2.49538i	0.442703	+	0.213194i	0.641937	−	0.766757i	$-0.278131\pi$
$137$	5.18170	+	2.49538i	0.442703	+	0.213194i	−0.199234	+	0.979952i	$0.563845\pi$
$138$	0.0641381	−	0.281008i	0.00545980	−	0.0239209i
$139$	0.976909	+	1.22501i	0.0828603	+	0.103904i	0.821534	−	0.570160i	$-0.193119\pi$
$139$	0.976909	+	1.22501i	0.0828603	+	0.103904i	−0.738673	+	0.674064i	$0.764547\pi$
$140$	−0.825014	+	1.03453i	−0.0697264	+	0.0874341i
$141$	−1.28990	−	5.65142i	−0.108629	−	0.475935i
$142$	0.237864	−	1.04215i	0.0199611	−	0.0874552i
$143$	−5.48830	+	6.88211i	−0.458955	+	0.575511i
$144$	3.95856			0.329880
$145$	−0.164981	+	10.3941i	−0.0137009	+	0.863183i
$146$	−0.0381857			−0.00316027
$147$	4.29068	−	5.38034i	0.353889	−	0.443763i
$148$	−1.36919	+	5.99883i	−0.112547	+	0.493101i
$149$	−2.81077	−	12.3148i	−0.230267	−	1.00887i	−0.949418	−	0.314014i	$-0.898326\pi$
$149$	−2.81077	−	12.3148i	−0.230267	−	1.00887i	0.719151	−	0.694854i	$-0.244531\pi$
$150$	−0.0660341	+	0.0828042i	−0.00539166	+	0.00676093i
$151$	−6.40179	−	8.02760i	−0.520971	−	0.653277i	0.449844	−	0.893107i	$-0.351480\pi$
$151$	−6.40179	−	8.02760i	−0.520971	−	0.653277i	−0.970815	+	0.239831i	$0.922908\pi$
$152$	0.0997981	−	0.437244i	0.00809469	−	0.0354652i
$153$	5.54415	+	2.66992i	0.448218	+	0.215850i
$154$	−0.0624632	−	0.0300807i	−0.00503343	−	0.00242397i
$155$	−4.72080	−	20.6832i	−0.379184	−	1.66131i
$156$	−6.52057	+	3.14014i	−0.522064	+	0.251413i
$157$	−3.78665			−0.302207			−0.151104	−	0.988518i	$-0.548283\pi$
$157$	−3.78665			−0.302207			−0.151104	+	0.988518i	$0.548283\pi$
$158$	−0.934952	+	0.450249i	−0.0743808	+	0.0358199i
$159$	2.58271	+	3.23861i	0.204822	+	0.256839i
$160$	−1.19548	−	1.49908i	−0.0945106	−	0.118513i
$161$	1.07405	−	0.517237i	0.0846473	−	0.0407640i
$162$	−0.0831558			−0.00653334
$163$	5.47952	−	2.63880i	0.429189	−	0.206687i	−0.206802	−	0.978383i	$-0.566306\pi$
$163$	5.47952	−	2.63880i	0.429189	−	0.206687i	0.635991	+	0.771696i	$0.280591\pi$
$164$	2.34308	+	10.2657i	0.182964	+	0.801618i
$165$	−4.21610	−	2.03037i	−0.328223	−	0.158064i
$166$	0.215657	+	0.103855i	0.0167382	+	0.00806069i
$167$	1.70796	−	7.48305i	0.132166	−	0.579056i	−0.864862	−	0.502010i	$-0.832594\pi$
$167$	1.70796	−	7.48305i	0.132166	−	0.579056i	0.997028	−	0.0770460i	$-0.0245488\pi$
$168$	−0.0712023	−	0.0892849i	−0.00549338	−	0.00688848i
$169$	0.115724	−	0.145113i	0.00890183	−	0.0111625i
$170$	−0.219802	−	0.963014i	−0.0168580	−	0.0738598i
$171$	0.300553	−	1.31681i	0.0229839	−	0.100699i
$172$	0.0104901	−	0.0131541i	0.000799861	−	0.00100299i
$173$	−14.9932			−1.13991			−0.569956	−	0.821675i	$-0.693040\pi$
$173$	−14.9932			−1.13991			−0.569956	+	0.821675i	$0.693040\pi$
$174$	−0.434944	−	0.106563i	−0.0329730	−	0.00807851i
$175$	−0.438036			−0.0331124
$176$	−5.98308	+	7.50255i	−0.450992	+	0.565526i
$177$	1.28354	−	5.62357i	0.0964771	−	0.422694i
$178$	−0.226191	−	0.991006i	−0.0169537	−	0.0742790i
$179$	−10.0259	+	12.5720i	−0.749369	+	0.939679i	−0.999594	−	0.0285091i	$-0.990924\pi$
$179$	−10.0259	+	12.5720i	−0.749369	+	0.939679i	0.250225	+	0.968188i	$0.419495\pi$
$180$	−2.39882	−	3.00802i	−0.178797	−	0.224205i
$181$	1.26245	−	5.53117i	0.0938375	−	0.411129i	−0.906091	−	0.423083i	$-0.860948\pi$
$181$	1.26245	−	5.53117i	0.0938375	−	0.411129i	0.999929	+	0.0119539i	$0.00380512\pi$
$182$	0.0935655	+	0.0450588i	0.00693554	+	0.00333998i
$183$	−5.62010	−	2.70650i	−0.415450	−	0.200070i
$184$	0.256109	+	1.12209i	0.0188806	+	0.0827213i
$185$	5.36933	−	2.58573i	0.394761	−	0.190107i
$186$	0.913892			0.0670098
$187$	−13.4398	+	6.47228i	−0.982817	+	0.473300i
$188$	7.20344	+	9.03283i	0.525365	+	0.658787i
$189$	−0.214434	−	0.268891i	−0.0155978	−	0.0195590i
$190$	−0.195342	+	0.0940716i	−0.0141716	+	0.00682467i
$191$	0.636893			0.0460839			0.0230420	−	0.999734i	$-0.492665\pi$
$191$	0.636893			0.0460839			0.0230420	+	0.999734i	$0.492665\pi$
$192$	−7.05866	+	3.39927i	−0.509415	+	0.245321i
$193$	2.52413	+	11.0589i	0.181691	+	0.796039i	0.980826	+	0.194887i	$0.0624341\pi$
$193$	2.52413	+	11.0589i	0.181691	+	0.796039i	−0.799135	+	0.601152i	$0.794709\pi$
$194$	−0.204099	−	0.0982890i	−0.0146535	−	0.00705674i
$195$	6.31542	+	3.04135i	0.452257	+	0.217795i
$196$	−3.05206	+	13.3720i	−0.218004	+	0.955140i
$197$	−10.5545	−	13.2349i	−0.751976	−	0.942949i	0.247688	−	0.968840i	$-0.420329\pi$
$197$	−10.5545	−	13.2349i	−0.751976	−	0.942949i	−0.999665	+	0.0258911i	$0.991758\pi$
$198$	0.125684	−	0.157603i	0.00893198	−	0.0112004i
$199$	−1.93102	−	8.46037i	−0.136887	−	0.599740i	−0.996108	−	0.0881362i	$-0.971909\pi$
$199$	−1.93102	−	8.46037i	−0.136887	−	0.599740i	0.859222	−	0.511603i	$-0.170948\pi$
$200$	0.0941063	−	0.412306i	0.00665432	−	0.0291545i
$201$	−6.86725	+	8.61126i	−0.484378	+	0.607391i
$202$	1.51922			0.106892
$203$	−0.777008	−	1.68122i	−0.0545353	−	0.117999i
$204$	−12.2645			−0.858689
$205$	6.35862	−	7.97346i	0.444105	−	0.556891i
$206$	−0.297351	+	1.30278i	−0.0207174	+	0.0907689i
$207$	0.771301	+	3.37929i	0.0536091	+	0.234877i
$208$	8.96224	−	11.2383i	0.621419	−	0.779235i
$209$	2.04145	+	2.55989i	0.141210	+	0.177072i
$210$	−0.0122848	+	0.0538234i	−0.000847734	+	0.00371417i
$211$	−11.4887	−	5.53267i	−0.790916	−	0.380885i	−0.00560320	−	0.999984i	$-0.501784\pi$
$211$	−11.4887	−	5.53267i	−0.790916	−	0.380885i	−0.785313	+	0.619099i	$0.787498\pi$
$212$	−7.43843	−	3.58216i	−0.510873	−	0.246024i
$213$	2.86046	+	12.5325i	0.195995	+	0.858712i
$214$	−1.21192	+	0.583629i	−0.0828451	+	0.0398961i
$215$	−0.0162954			−0.00111134
$216$	0.299165	−	0.144070i	0.0203556	−	0.00980274i
$217$	2.35665	+	2.95515i	0.159980	+	0.200608i
$218$	−0.476966	−	0.598096i	−0.0323042	−	0.0405082i
$219$	0.413731	−	0.199242i	0.0279574	−	0.0134636i
$220$	9.32667			0.628804
$221$	20.1319	−	9.69502i	1.35422	−	0.652158i
$222$	0.0571257	+	0.250284i	0.00383403	+	0.0167980i
$223$	−17.2436	−	8.30407i	−1.15472	−	0.556082i	−0.244268	−	0.969708i	$-0.578548\pi$
$223$	−17.2436	−	8.30407i	−1.15472	−	0.556082i	−0.910447	+	0.413626i	$0.864262\pi$
$224$	0.307781	+	0.148220i	0.0205645	+	0.00990334i
$225$	0.283411	−	1.24171i	0.0188941	−	0.0827804i
$226$	1.05022	+	1.31694i	0.0698597	+	0.0876013i
$227$	−15.4320	+	19.3511i	−1.02426	+	1.28438i	−0.0661958	+	0.997807i	$0.521086\pi$
$227$	−15.4320	+	19.3511i	−1.02426	+	1.28438i	−0.958060	+	0.286569i	$0.907485\pi$
$228$	0.599028	+	2.62451i	0.0396716	+	0.173813i
$229$	4.32439	−	18.9464i	0.285764	−	1.25201i	−0.604514	−	0.796595i	$-0.706632\pi$
$229$	4.32439	−	18.9464i	0.285764	−	1.25201i	0.890277	−	0.455419i	$-0.150510\pi$
$230$	0.346910	−	0.435012i	0.0228746	−	0.0286838i
$231$	0.833724			0.0548550
$232$	1.74940	−	0.370180i	0.114854	−	0.0243035i
$233$	18.2842			1.19784			0.598918	−	0.800810i	$-0.295598\pi$
$233$	18.2842			1.19784			0.598918	+	0.800810i	$0.295598\pi$
$234$	−0.188266	+	0.236078i	−0.0123073	+	0.0154329i
$235$	2.48999	−	10.9094i	0.162429	−	0.711649i
$236$	2.55821	+	11.2083i	0.166525	+	0.729596i
$237$	7.78066	−	9.75663i	0.505408	−	0.633761i
$238$	0.109726	+	0.137592i	0.00711250	+	0.00891879i
$239$	−1.82330	+	7.98840i	−0.117939	+	0.516727i	0.881101	+	0.472928i	$0.156803\pi$
$239$	−1.82330	+	7.98840i	−0.117939	+	0.516727i	−0.999040	+	0.0437983i	$0.986054\pi$
$240$	6.88477	+	3.31553i	0.444410	+	0.214017i
$241$	6.43502	+	3.09894i	0.414516	+	0.199620i	0.629506	−	0.776996i	$-0.283257\pi$
$241$	6.43502	+	3.09894i	0.414516	+	0.199620i	−0.214989	+	0.976616i	$0.568972\pi$
$242$	−0.0948052	−	0.415369i	−0.00609431	−	0.0267009i
$243$	0.900969	−	0.433884i	0.0577972	−	0.0278337i
$244$	12.4325			0.795912
$245$	11.9688	−	5.76385i	0.764656	−	0.368239i
$246$	0.273913	+	0.343476i	0.0174641	+	0.0218993i
$247$	−3.05795	−	3.83454i	−0.194572	−	0.243986i
$248$	−3.28786	+	1.58335i	−0.208779	+	0.100543i
$249$	−2.87846			−0.182415
$250$	−0.907328	+	0.436946i	−0.0573845	+	0.0276349i
$251$	−0.516642	−	2.26356i	−0.0326102	−	0.142874i	0.956002	−	0.293360i	$-0.0947735\pi$
$251$	−0.516642	−	2.26356i	−0.0326102	−	0.142874i	−0.988612	+	0.150486i	$0.951916\pi$
$252$	0.617588	+	0.297415i	0.0389044	+	0.0187354i
$253$	−7.57044	−	3.64573i	−0.475950	−	0.229205i
$254$	0.176982	−	0.775409i	0.0111048	−	0.0486535i
$255$	7.40623	+	9.28712i	0.463796	+	0.581582i
$256$	9.63271	−	12.0790i	0.602045	−	0.754940i
$257$	5.06951	+	22.2110i	0.316228	+	1.38548i	0.844112	+	0.536167i	$0.180128\pi$
$257$	5.06951	+	22.2110i	0.316228	+	1.38548i	−0.527884	+	0.849316i	$0.677015\pi$
$258$	0.000156202	0	0.000684367i	9.72472e−6	0	4.26068e-5i
$259$	−0.662005	+	0.830127i	−0.0411350	+	0.0515816i
$260$	−13.9707			−0.866426
$261$	5.26850	−	1.11484i	0.326112	−	0.0690067i
$262$	−1.39722			−0.0863207
$263$	−0.595714	+	0.747002i	−0.0367333	+	0.0460621i	−0.799859	−	0.600188i	$-0.795092\pi$
$263$	−0.595714	+	0.747002i	−0.0367333	+	0.0460621i	0.763126	+	0.646250i	$0.223664\pi$
$264$	−0.179114	+	0.784752i	−0.0110237	+	0.0482981i
$265$	1.77934	+	7.79580i	0.109304	+	0.478892i
$266$	0.0240844	−	0.0302009i	0.00147671	−	0.00185173i
$267$	7.62150	+	9.55706i	0.466428	+	0.584883i
$268$	4.88484	−	21.4019i	0.298389	−	1.30733i
$269$	−13.6464	−	6.57178i	−0.832038	−	0.400688i	−0.0311589	−	0.999514i	$-0.509920\pi$
$269$	−13.6464	−	6.57178i	−0.832038	−	0.400688i	−0.800879	+	0.598826i	$0.795634\pi$
$270$	−0.144625	−	0.0696480i	−0.00880163	−	0.00423864i
$271$	1.83597	+	8.04392i	0.111527	+	0.488633i	0.999582	+	0.0288962i	$0.00919922\pi$
$271$	1.83597	+	8.04392i	0.111527	+	0.488633i	−0.888055	+	0.459737i	$0.847944\pi$
$272$	21.9468	−	10.5690i	1.33072	−	0.640842i
$273$	−1.24886			−0.0755844
$274$	−0.430889	+	0.207505i	−0.0260309	+	0.0125358i
$275$	1.92502	+	2.41389i	0.116083	+	0.145563i
$276$	−4.30733	−	5.40122i	−0.259271	−	0.325115i
$277$	−15.0761	+	7.26026i	−0.905834	+	0.436227i	−0.827992	−	0.560739i	$-0.810517\pi$
$277$	−15.0761	+	7.26026i	−0.905834	+	0.436227i	−0.0778412	+	0.996966i	$0.524803\pi$
$278$	−0.130292			−0.00781439
$279$	−9.90175	+	4.76843i	−0.592802	+	0.285479i
$280$	−0.0490544	−	0.214921i	−0.00293156	−	0.0128440i
$281$	19.9509	+	9.60786i	1.19017	+	0.573157i	0.920859	−	0.389896i	$-0.127489\pi$
$281$	19.9509	+	9.60786i	1.19017	+	0.573157i	0.269313	+	0.963053i	$0.413203\pi$
$282$	0.434298	+	0.209147i	0.0258620	+	0.0124545i
$283$	3.92964	−	17.2169i	0.233593	−	1.02344i	−0.713040	−	0.701123i	$-0.752682\pi$
$283$	3.92964	−	17.2169i	0.233593	−	1.02344i	0.946633	−	0.322314i	$-0.104461\pi$
$284$	−15.9742	−	20.0310i	−0.947896	−	1.18862i
$285$	1.62563	−	2.03848i	0.0962941	−	0.120749i
$286$	−0.162882	−	0.713631i	−0.00963139	−	0.0421979i
$287$	−0.404320	+	1.77144i	−0.0238663	+	0.104565i
$288$	−0.619296	+	0.776572i	−0.0364924	+	0.0457600i
$289$	20.8661			1.22742
$290$	−0.667206	−	0.549627i	−0.0391797	−	0.0322752i
$291$	2.72420			0.159695
$292$	−0.570642	+	0.715562i	−0.0333943	+	0.0418751i
$293$	−5.15017	+	22.5644i	−0.300876	+	1.31823i	0.567931	+	0.823076i	$0.307744\pi$
$293$	−5.15017	+	22.5644i	−0.300876	+	1.31823i	−0.868808	+	0.495150i	$0.835113\pi$
$294$	0.127339	+	0.557907i	0.00742654	+	0.0325378i
$295$	6.94243	−	8.70553i	0.404204	−	0.506856i
$296$	−0.639144	−	0.801461i	−0.0371495	−	0.0465840i
$297$	−0.539423	+	2.36337i	−0.0313005	+	0.137136i
$298$	0.946362	+	0.455744i	0.0548213	+	0.0264005i
$299$	11.3400	+	5.46105i	0.655809	+	0.315821i
$300$	0.564863	+	2.47483i	0.0326124	+	0.142884i
$301$	0.00261575	−	0.00125968i	0.000150770	−	7.26068e-5i
$302$	0.853817			0.0491317
$303$	−16.4604	+	7.92689i	−0.945623	+	0.455388i
$304$	−3.33362	−	4.18023i	−0.191196	−	0.239753i
$305$	−7.50768	−	9.41434i	−0.429889	−	0.539063i
$306$	−0.461028	+	0.222020i	−0.0263552	+	0.0126920i
$307$	−22.9984			−1.31259			−0.656293	−	0.754506i	$-0.727876\pi$
$307$	−22.9984			−1.31259			−0.656293	+	0.754506i	$0.727876\pi$
$308$	−1.49712	+	0.720977i	−0.0853065	+	0.0410815i
$309$	−3.57583	−	15.6667i	−0.203422	−	0.891249i
$310$	1.58945	+	0.765439i	0.0902747	+	0.0434740i
$311$	−3.67659	−	1.77055i	−0.208480	−	0.100399i	0.326730	−	0.945118i	$-0.394053\pi$
$311$	−3.67659	−	1.77055i	−0.208480	−	0.100399i	−0.535210	+	0.844719i	$0.679768\pi$
$312$	0.268301	−	1.17550i	0.0151895	−	0.0665497i
$313$	17.9270	+	22.4797i	1.01329	+	1.27063i	0.962318	+	0.271928i	$0.0876612\pi$
$313$	17.9270	+	22.4797i	1.01329	+	1.27063i	0.0509742	+	0.998700i	$0.483767\pi$
$314$	0.196325	−	0.246184i	0.0110793	−	0.0138930i
$315$	−0.147733	−	0.647260i	−0.00832380	−	0.0364689i
$316$	−5.53457	+	24.2485i	−0.311344	+	1.36409i
$317$	7.18877	−	9.01443i	0.403762	−	0.506301i	−0.537832	−	0.843052i	$-0.680757\pi$
$317$	7.18877	−	9.01443i	0.403762	−	0.506301i	0.941594	+	0.336751i	$0.109328\pi$
$318$	−0.344459			−0.0193163
$319$	−5.85005	+	11.6703i	−0.327540	+	0.653409i
$320$	−15.1236			−0.845434
$321$	10.0856	−	12.6469i	0.562922	−	0.705882i
$322$	−0.0220587	+	0.0966455i	−0.00122928	+	0.00538584i
$323$	−1.84947	−	8.10304i	−0.102907	−	0.450865i
$324$	−1.24267	+	1.55826i	−0.0690371	+	0.0865698i
$325$	−2.88354	−	3.61584i	−0.159950	−	0.200571i
$326$	−0.112537	+	0.493058i	−0.00623286	+	0.0273080i
$327$	8.28849	+	3.99153i	0.458354	+	0.220732i
$328$	−1.58053	−	0.761142i	−0.0872700	−	0.0420270i
$329$	0.443628	+	1.94366i	0.0244580	+	0.107158i
$330$	0.350593	−	0.168837i	0.0192995	−	0.00929416i
$331$	12.3038			0.676277			0.338139	−	0.941096i	$-0.390203\pi$
$331$	12.3038			0.676277			0.338139	+	0.941096i	$0.390203\pi$
$332$	5.16888	−	2.48920i	0.283679	−	0.136613i
$333$	−1.92485	−	2.41369i	−0.105481	−	0.132269i
$334$	0.397950	+	0.499013i	0.0217748	+	0.0273048i
$335$	−19.1560	+	9.22506i	−1.04661	+	0.504019i
$336$	−1.36145			−0.0742730
$337$	−27.5590	+	13.2717i	−1.50123	+	0.722956i	−0.990593	−	0.136838i	$-0.956306\pi$
$337$	−27.5590	+	13.2717i	−1.50123	+	0.722956i	−0.510640	+	0.859794i	$0.670592\pi$
$338$	0.00343445	+	0.0150473i	0.000186809	+	0.000818465i
$339$	−18.2503	−	8.78886i	−0.991218	−	0.477345i
$340$	−21.3306	−	10.2723i	−1.15681	−	0.557093i
$341$	5.92832	−	25.9737i	0.321037	−	1.40655i
$342$	0.0700281	+	0.0878124i	0.00378668	+	0.00474835i
$343$	−2.97671	+	3.73267i	−0.160727	+	0.201545i
$344$	0.000623729		0.00273273i	3.36292e−5		0.000147339i
$345$	−1.48890	+	6.52331i	−0.0801598	+	0.351203i
$346$	0.777349	−	0.974765i	0.0417906	−	0.0524037i
$347$	−2.30431			−0.123702			−0.0618508	−	0.998085i	$-0.519700\pi$
$347$	−2.30431			−0.123702			−0.0618508	+	0.998085i	$0.519700\pi$
$348$	−8.49662	+	6.55795i	−0.455467	+	0.351543i
$349$	9.12305			0.488345			0.244173	−	0.969732i	$-0.421484\pi$
$349$	9.12305			0.488345			0.244173	+	0.969732i	$0.421484\pi$
$350$	0.0227108	−	0.0284784i	0.00121394	−	0.00152223i
$351$	0.808018	−	3.54016i	0.0431288	−	0.188960i
$352$	−0.535795	−	2.34747i	−0.0285579	−	0.125121i
$353$	−9.08165	+	11.3880i	−0.483368	+	0.606124i	−0.962388	−	0.271680i	$-0.912421\pi$
$353$	−9.08165	+	11.3880i	−0.483368	+	0.606124i	0.479020	+	0.877804i	$0.340992\pi$
$354$	0.299062	+	0.375012i	0.0158950	+	0.0199317i
$355$	−5.52177	+	24.1924i	−0.293065	+	1.28400i
$356$	−21.9506	−	10.5709i	−1.16338	−	0.560255i
$357$	−1.90677	−	0.918253i	−0.100917	−	0.0485991i
$358$	−0.297547	−	1.30364i	−0.0157259	−	0.0688995i
$359$	−3.37960	+	1.62753i	−0.178368	+	0.0858976i	−0.520937	−	0.853595i	$-0.674417\pi$
$359$	−3.37960	+	1.62753i	−0.178368	+	0.0858976i	0.342569	+	0.939493i	$0.388703\pi$
$360$	0.640979			0.0337825
$361$	15.4748	−	7.45225i	0.814461	−	0.392224i
$362$	0.294148	+	0.368851i	0.0154601	+	0.0193864i
$363$	3.19446	+	4.00573i	0.167666	+	0.210246i
$364$	2.24259	−	1.07997i	0.117543	−	0.0566060i
$365$	0.886443			0.0463986
$366$	0.467344	−	0.225061i	0.0244285	−	0.0117641i
$367$	−3.10389	−	13.5990i	−0.162022	−	0.709864i	−0.989035	−	0.147681i	$-0.952819\pi$
$367$	−3.10389	−	13.5990i	−0.162022	−	0.709864i	0.827013	−	0.562182i	$-0.190038\pi$
$368$	12.3623	+	5.95338i	0.644430	+	0.310341i
$369$	−4.75993	−	2.29226i	−0.247792	−	0.119330i
$370$	−0.110274	+	0.483143i	−0.00573288	+	0.0251174i
$371$	−0.888257	−	1.11384i	−0.0461160	−	0.0578276i
$372$	13.6571	−	17.1254i	0.708086	−	0.887912i
$373$	1.70453	+	7.46802i	0.0882571	+	0.386679i	0.999693	−	0.0247617i	$-0.00788271\pi$
$373$	1.70453	+	7.46802i	0.0882571	+	0.386679i	−0.911436	+	0.411441i	$0.865026\pi$
$374$	0.276024	−	1.20934i	0.0142729	−	0.0625335i
$375$	7.55077	−	9.46837i	0.389920	−	0.488944i
$376$	−1.92480			−0.0992641
$377$	8.76297	−	17.4812i	0.451316	−	0.900329i
$378$	0.0285993			0.00147099
$379$	−7.83725	+	9.82760i	−0.402573	+	0.504810i	−0.941254	−	0.337700i	$-0.890351\pi$
$379$	−7.83725	+	9.82760i	−0.402573	+	0.504810i	0.538681	+	0.842510i	$0.318923\pi$
$380$	−1.15635	+	5.06630i	−0.0593195	+	0.259896i
$381$	2.12832	+	9.32478i	0.109037	+	0.477723i
$382$	−0.0330208	+	0.0414068i	−0.00168949	+	0.00211856i
$383$	14.6837	+	18.4128i	0.750305	+	0.940852i	0.999620	−	0.0275703i	$-0.00877700\pi$
$383$	14.6837	+	18.4128i	0.750305	+	0.940852i	−0.249315	+	0.968422i	$0.580206\pi$
$384$	0.587018	−	2.57189i	0.0299561	−	0.131246i
$385$	1.45002	+	0.698293i	0.0738999	+	0.0355883i
$386$	−0.849851	−	0.409267i	−0.0432563	−	0.0208311i
$387$	0.00187843	+	0.00822993i	9.54859e−5	+	0.000418351i
$388$	−4.89187	+	2.35580i	−0.248347	+	0.119598i
$389$	−21.2485			−1.07734			−0.538671	−	0.842516i	$-0.681073\pi$
$389$	−21.2485			−1.07734			−0.538671	+	0.842516i	$0.681073\pi$
$390$	−0.525164	+	0.252906i	−0.0265927	+	0.0128064i
$391$	13.2986	+	16.6760i	0.672542	+	0.843340i
$392$	−1.42471	−	1.78653i	−0.0719588	−	0.0902335i
$393$	15.1385	−	7.29032i	0.763636	−	0.367748i
$394$	1.40767			0.0709173
$395$	21.7040	−	10.4521i	1.09204	−	0.525901i
$396$	−1.07512	−	4.71039i	−0.0540266	−	0.236706i
$397$	−13.2705	−	6.39072i	−0.666026	−	0.320741i	0.0701450	−	0.997537i	$-0.477654\pi$
$397$	−13.2705	−	6.39072i	−0.666026	−	0.320741i	−0.736171	+	0.676796i	$0.763368\pi$
$398$	0.650158	+	0.313100i	0.0325895	+	0.0156943i
$399$	−0.103368	+	0.452883i	−0.00517486	+	0.0226725i
$400$	−3.14350	−	3.94182i	−0.157175	−	0.197091i
$401$	−7.87447	+	9.87428i	−0.393233	+	0.493098i	−0.938556	−	0.345128i	$-0.887836\pi$
$401$	−7.87447	+	9.87428i	−0.393233	+	0.493098i	0.545323	+	0.838226i	$0.316407\pi$
$402$	−0.203806	−	0.892932i	−0.0101649	−	0.0445354i
$403$	−8.88021	+	38.9067i	−0.442355	+	1.93808i
$404$	22.7031	−	28.4688i	1.12952	−	1.41637i
$405$	1.93038			0.0959213
$406$	0.149588	+	0.0366496i	0.00742393	+	0.00181889i
$407$	7.48388			0.370962
$408$	1.27396	−	1.59750i	0.0630704	−	0.0790878i
$409$	7.51172	−	32.9110i	0.371430	−	1.62734i	−0.351335	−	0.936250i	$-0.614272\pi$
$409$	7.51172	−	32.9110i	0.371430	−	1.62734i	0.722766	−	0.691093i	$-0.242871\pi$
$410$	0.188711	+	0.826797i	0.00931977	+	0.0408326i
$411$	3.58585	−	4.49651i	0.176877	−	0.221797i
$412$	19.9692	+	25.0406i	0.983812	+	1.23366i
$413$	−0.441443	+	1.93409i	−0.0217220	+	0.0951702i
$414$	−0.259690	−	0.125060i	−0.0127631	−	0.00614637i
$415$	−5.00625	−	2.41088i	−0.245747	−	0.118346i
$416$	0.802583	+	3.51634i	0.0393499	+	0.172403i
$417$	1.41167	−	0.679827i	0.0691300	−	0.0332912i
$418$	−0.272271			−0.0133172
$419$	22.2013	−	10.6916i	1.08461	−	0.522319i	0.195819	−	0.980640i	$-0.437263\pi$
$419$	22.2013	−	10.6916i	1.08461	−	0.522319i	0.888787	+	0.458321i	$0.151549\pi$
$420$	0.825014	+	1.03453i	0.0402565	+	0.0504801i
$421$	7.64133	+	9.58193i	0.372416	+	0.466995i	0.932358	−	0.361537i	$-0.117748\pi$
$421$	7.64133	+	9.58193i	0.372416	+	0.466995i	−0.559942	+	0.828532i	$0.689177\pi$
$422$	0.955354	−	0.460074i	0.0465059	−	0.0223961i
$423$	−5.79676			−0.281848
$424$	1.23924	−	0.596788i	0.0601830	−	0.0289826i
$425$	−1.74398	−	7.64090i	−0.0845957	−	0.370638i
$426$	−0.963090	−	0.463800i	−0.0466619	−	0.0224712i
$427$	1.93289	+	0.930832i	0.0935392	+	0.0450461i
$428$	−7.17411	+	31.4318i	−0.346774	+	1.51931i
$429$	5.48830	+	6.88211i	0.264978	+	0.332272i
$430$	0.000844866	−	0.00105943i	4.07431e−5	−	5.10902e-5i
$431$	1.86817	+	8.18500i	0.0899867	+	0.394257i	0.999784	−	0.0207960i	$-0.00662003\pi$
$431$	1.86817	+	8.18500i	0.0899867	+	0.394257i	−0.909797	+	0.415053i	$0.863763\pi$
$432$	0.880862	−	3.85931i	0.0423805	−	0.185681i
$433$	5.76203	−	7.22535i	0.276905	−	0.347228i	−0.623859	−	0.781537i	$-0.714436\pi$
$433$	5.76203	−	7.22535i	0.276905	−	0.347228i	0.900764	+	0.434309i	$0.143007\pi$
$434$	−0.314310			−0.0150874
$435$	10.0968	+	2.47375i	0.484104	+	0.118607i
$436$	−18.3354			−0.878108
$437$	2.91899	−	3.66030i	0.139634	−	0.175096i
$438$	−0.00849712	+	0.0372283i	−0.000406008	+	0.00177884i
$439$	−3.87697	−	16.9861i	−0.185038	−	0.810704i	−0.979184	−	0.202976i	$-0.934939\pi$
$439$	−3.87697	−	16.9861i	−0.185038	−	0.810704i	0.794146	−	0.607727i	$-0.207919\pi$
$440$	−0.968794	+	1.21483i	−0.0461854	+	0.0579147i
$441$	−4.29068	−	5.38034i	−0.204318	−	0.256207i
$442$	−0.413465	+	1.81151i	−0.0196665	+	0.0861647i
$443$	−26.1256	−	12.5814i	−1.24127	−	0.597762i	−0.306109	−	0.951997i	$-0.599027\pi$
$443$	−26.1256	−	12.5814i	−1.24127	−	0.597762i	−0.935156	+	0.354235i	$0.884741\pi$
$444$	5.54375	+	2.66973i	0.263095	+	0.126700i
$445$	5.25079	+	23.0052i	0.248911	+	1.09055i
$446$	1.43390	−	0.690532i	0.0678973	−	0.0326976i
$447$	−12.6315			−0.597449
$448$	2.42765	−	1.16909i	0.114696	−	0.0552345i
$449$	−8.67883	−	10.8829i	−0.409579	−	0.513596i	0.533665	−	0.845696i	$-0.320814\pi$
$449$	−8.67883	−	10.8829i	−0.409579	−	0.513596i	−0.943244	+	0.332100i	$0.892243\pi$
$450$	0.0660341	+	0.0828042i	0.00311288	+	0.00390343i
$451$	11.5388	−	5.55678i	0.543339	−	0.261658i
$452$	40.3724			1.89896
$453$	−9.25086	+	4.45498i	−0.434643	+	0.209313i
$454$	−0.457989	−	2.00658i	−0.0214945	−	0.0941736i
$455$	−2.17203	−	1.04599i	−0.101826	−	0.0490370i
$456$	−0.404074	−	0.194592i	−0.0189225	−	0.00911260i
$457$	0.222385	−	0.974330i	0.0104027	−	0.0455773i	−0.969460	−	0.245249i	$-0.921130\pi$
$457$	0.222385	−	0.974330i	0.0104027	−	0.0455773i	0.979863	+	0.199672i	$0.0639875\pi$
$458$	1.00757	+	1.26346i	0.0470807	+	0.0590374i
$459$	3.83667	−	4.81103i	0.179080	−	0.224560i
$460$	−2.96751	−	13.0015i	−0.138361	−	0.606198i
$461$	−3.45431	+	15.1343i	−0.160883	+	0.704876i	0.828553	+	0.559910i	$0.189164\pi$
$461$	−3.45431	+	15.1343i	−0.160883	+	0.704876i	−0.989437	+	0.144966i	$0.953693\pi$
$462$	−0.0432259	+	0.0542036i	−0.00201105	+	0.00252178i
$463$	35.8295			1.66514			0.832568	−	0.553923i	$-0.186870\pi$
$463$	35.8295			1.66514			0.832568	+	0.553923i	$0.186870\pi$
$464$	9.55296	−	19.0572i	0.443485	−	0.884708i
$465$	−21.2151			−0.983826
$466$	−0.947976	+	1.18872i	−0.0439141	+	0.0550666i
$467$	0.929323	−	4.07163i	0.0430039	−	0.188413i	−0.948864	−	0.315686i	$-0.897765\pi$
$467$	0.929323	−	4.07163i	0.0430039	−	0.188413i	0.991868	+	0.127273i	$0.0406225\pi$
$468$	1.61045	+	7.05583i	0.0744430	+	0.326156i
$469$	2.36182	−	2.96163i	0.109059	−	0.136755i
$470$	0.580162	+	0.727500i	0.0267609	+	0.0335571i
$471$	−0.842608	+	3.69171i	−0.0388253	+	0.170105i
$472$	−1.72564	−	0.831026i	−0.0794291	−	0.0382510i
$473$	−0.0184371	−	0.00887883i	−0.000847738	−	0.000408249i
$474$	0.230914	+	1.01170i	0.0106062	+	0.0464689i
$475$	−1.54991	+	0.746397i	−0.0711148	+	0.0342471i
$476$	4.21808			0.193335
$477$	3.73212	−	1.79729i	0.170882	−	0.0822924i
$478$	−0.424824	−	0.532713i	−0.0194310	−	0.0243657i
$479$	−11.5627	−	14.4992i	−0.528315	−	0.662486i	0.444037	−	0.896009i	$-0.353546\pi$
$479$	−11.5627	−	14.4992i	−0.528315	−	0.662486i	−0.972351	+	0.233523i	$0.924975\pi$
$480$	−1.72751	+	0.831926i	−0.0788498	+	0.0379720i
$481$	−11.2103			−0.511147
$482$	−0.535109	+	0.257695i	−0.0243736	+	0.0117377i
$483$	−0.265269	−	1.16222i	−0.0120702	−	0.0528829i
$484$	−9.20035	−	4.43065i	−0.418198	−	0.201393i
$485$	4.73796	+	2.28168i	0.215140	+	0.103606i
$486$	−0.0185039	+	0.0810709i	−0.000839354	+	0.00367745i
$487$	12.1972	+	15.2948i	0.552708	+	0.693074i	0.977191	−	0.212362i	$-0.0681157\pi$
$487$	12.1972	+	15.2948i	0.552708	+	0.693074i	−0.424483	+	0.905436i	$0.639544\pi$
$488$	−1.29141	+	1.61938i	−0.0584595	+	0.0733058i
$489$	−1.35333	−	5.92933i	−0.0611997	−	0.268133i
$490$	−0.245812	+	1.07697i	−0.0111046	+	0.0486526i
$491$	1.49134	−	1.87008i	0.0673030	−	0.0843953i	−0.747040	−	0.664779i	$-0.768526\pi$
$491$	1.49134	−	1.87008i	0.0673030	−	0.0843953i	0.814343	+	0.580383i	$0.197097\pi$
$492$	10.5297			0.474717
$493$	26.2329	−	20.2473i	1.18147	−	0.911894i
$494$	0.407843			0.0183497
$495$	−2.91763	+	3.65859i	−0.131138	+	0.164442i
$496$	−9.68078	+	42.4142i	−0.434680	+	1.90446i
$497$	−0.983782	−	4.31023i	−0.0441287	−	0.193340i
$498$	0.149239	−	0.187140i	0.00668756	−	0.00838594i
$499$	−10.8423	−	13.5958i	−0.485367	−	0.608631i	0.477492	−	0.878636i	$-0.341546\pi$
$499$	−10.8423	−	13.5958i	−0.485367	−	0.608631i	−0.962859	+	0.270005i	$0.912974\pi$
$500$	−5.37104	+	23.5321i	−0.240200	+	1.05239i
$501$	−6.91538	−	3.33027i	−0.308957	−	0.148786i
$502$	0.173949	+	0.0837693i	0.00776371	+	0.00373881i
$503$	−4.48348	−	19.6434i	−0.199909	−	0.875857i	−0.970990	−	0.239120i	$-0.923141\pi$
$503$	−4.48348	−	19.6434i	−0.199909	−	0.875857i	0.771081	−	0.636737i	$-0.219716\pi$
$504$	−0.102890	+	0.0495494i	−0.00458310	+	0.00220710i
$505$	−35.2673			−1.56937
$506$	0.629526	−	0.303164i	0.0279858	−	0.0134773i
$507$	−0.115724	−	0.145113i	−0.00513947	−	0.00644470i
$508$	−11.8856	−	14.9041i	−0.527338	−	0.661261i
$509$	−26.0740	+	12.5566i	−1.15571	+	0.556560i	−0.910743	−	0.412973i	$-0.864491\pi$
$509$	−26.0740	+	12.5566i	−1.15571	+	0.556560i	−0.244964	+	0.969532i	$0.578776\pi$
$510$	−0.987780			−0.0437396
$511$	−0.142292	+	0.0685244i	−0.00629465	+	0.00303134i
$512$	1.45991	+	6.39630i	0.0645197	+	0.282679i
$513$	−1.21691	−	0.586035i	−0.0537281	−	0.0258741i
$514$	−1.70686	−	0.821980i	−0.0752863	−	0.0362560i
$515$	6.90270	−	30.2427i	0.304169	−	1.33265i
$516$	−0.0104901	−	0.0131541i	−0.000461800	−	0.000579079i
$517$	8.76139	−	10.9864i	0.385325	−	0.483183i
$518$	−0.0196469	−	0.0860789i	−0.000863237	−	0.00378209i
$519$	−3.33630	+	14.6173i	−0.146447	+	0.641628i
$520$	1.45119	−	1.81973i	0.0636387	−	0.0798004i
$521$	−3.28970			−0.144125			−0.0720623	−	0.997400i	$-0.522958\pi$
$521$	−3.28970			−0.144125			−0.0720623	+	0.997400i	$0.522958\pi$
$522$	−0.200675	+	0.400326i	−0.00878331	+	0.0175218i
$523$	−0.291341			−0.0127395			−0.00636974	−	0.999980i	$-0.502028\pi$
$523$	−0.291341			−0.0127395			−0.00636974	+	0.999980i	$0.502028\pi$
$524$	−20.8799	+	26.1826i	−0.912142	+	1.14379i
$525$	−0.0974722	+	0.427054i	−0.00425404	+	0.0186382i
$526$	−0.0176796	−	0.0774593i	−0.000770867	−	0.00337739i
$527$	−42.1655	+	52.8738i	−1.83676	+	2.30322i
$528$	5.98308	+	7.50255i	0.260380	+	0.326506i
$529$	2.44450	−	10.7101i	0.106283	−	0.465655i
$530$	−0.599088	−	0.288505i	−0.0260227	−	0.0125319i
$531$	−5.19696	−	2.50273i	−0.225529	−	0.108609i
$532$	−0.206021	−	0.902635i	−0.00893212	−	0.0391342i
$533$	−17.2843	+	8.32367i	−0.748665	+	0.360538i
$534$	−1.01649			−0.0439879
$535$	28.1335	−	13.5484i	1.21632	−	0.585747i
$536$	2.28026	+	2.85935i	0.0984921	+	0.123505i
$537$	10.0259	+	12.5720i	0.432648	+	0.542524i
$538$	1.13478	−	0.546482i	0.0489239	−	0.0235605i
$539$	16.6823			0.718556
$540$	−3.46640	+	1.66933i	−0.149170	+	0.0718364i
$541$	−6.15415	−	26.9631i	−0.264588	−	1.15923i	−0.916212	−	0.400693i	$-0.868769\pi$
$541$	−6.15415	−	26.9631i	−0.264588	−	1.15923i	0.651625	−	0.758542i	$-0.274088\pi$
$542$	−0.618155	−	0.297688i	−0.0265520	−	0.0127868i
$543$	−5.11157	−	2.46160i	−0.219359	−	0.105638i
$544$	−1.36008	+	5.95891i	−0.0583130	+	0.255486i
$545$	11.0723	+	13.8842i	0.474285	+	0.594734i
$546$	0.0647494	−	0.0811931i	0.00277102	−	0.00347475i
$547$	−1.12752	−	4.93998i	−0.0482091	−	0.211218i	0.945086	−	0.326821i	$-0.105977\pi$
$547$	−1.12752	−	4.93998i	−0.0482091	−	0.211218i	−0.993296	+	0.115602i	$0.963120\pi$
$548$	−2.55070	+	11.1754i	−0.108961	+	0.477387i
$549$	−3.88923	+	4.87694i	−0.165988	+	0.208143i
$550$	−0.256742			−0.0109475
$551$	−5.61404	−	4.62469i	−0.239166	−	0.197019i
$552$	1.15094			0.0489874
$553$	−2.67596	+	3.35555i	−0.113793	+	0.142692i
$554$	0.309629	−	1.35657i	0.0131549	−	0.0576353i
$555$	−1.32612	−	5.81009i	−0.0562905	−	0.246625i
$556$	−1.94706	+	2.44154i	−0.0825739	+	0.103544i
$557$	10.0780	+	12.6374i	0.427019	+	0.535465i	0.948070	−	0.318060i	$-0.103031\pi$
$557$	10.0780	+	12.6374i	0.427019	+	0.535465i	−0.521051	+	0.853525i	$0.674460\pi$
$558$	0.203360	−	0.890979i	0.00860892	−	0.0377181i
$559$	0.0276175	+	0.0132999i	0.00116809	+	0.000562524i
$560$	−2.36784	−	1.14029i	−0.100060	−	0.0481862i
$561$	3.31936	+	14.5431i	0.140144	+	0.614009i
$562$	−1.65904	+	0.798949i	−0.0699822	+	0.0337016i
$563$	7.45712			0.314280			0.157140	−	0.987576i	$-0.449773\pi$
$563$	7.45712			0.314280			0.157140	+	0.987576i	$0.449773\pi$
$564$	10.4093	−	5.01284i	0.438310	−	0.211079i
$565$	−24.3799	−	30.5714i	−1.02567	−	1.28615i
$566$	0.915595	+	1.14812i	0.0384853	+	0.0482591i
$567$	−0.309866	+	0.149223i	−0.0130131	+	0.00626679i
$568$	4.26841			0.179098
$569$	−15.8967	+	7.65544i	−0.666424	+	0.320933i	−0.736332	−	0.676621i	$-0.763444\pi$
$569$	−15.8967	+	7.65544i	−0.666424	+	0.320933i	0.0699080	+	0.997553i	$0.477729\pi$
$570$	0.0482454	+	0.211377i	0.00202078	+	0.00885361i
$571$	−26.3470	−	12.6880i	−1.10259	−	0.530978i	−0.208116	−	0.978104i	$-0.566733\pi$
$571$	−26.3470	−	12.6880i	−1.10259	−	0.530978i	−0.894471	+	0.447126i	$0.852448\pi$
$572$	−15.8068	−	7.61216i	−0.660916	−	0.318280i
$573$	0.141722	−	0.620924i	0.00592052	−	0.0259395i
$574$	−0.0942056	−	0.118130i	−0.00393206	−	0.00493065i
$575$	2.75251	−	3.45154i	0.114788	−	0.143939i
$576$	1.74334	+	7.63809i	0.0726394	+	0.318254i
$577$	3.80051	−	16.6511i	0.158217	−	0.693196i	−0.832129	−	0.554582i	$-0.812878\pi$
$577$	3.80051	−	16.6511i	0.158217	−	0.693196i	0.990347	−	0.138614i	$-0.0442647\pi$
$578$	−1.08184	+	1.35658i	−0.0449986	+	0.0564265i
$579$	11.3433			0.471412
$580$	−20.2701	+	4.28924i	−0.841670	+	0.178101i
$581$	0.989975			0.0410711
$582$	−0.141241	+	0.177111i	−0.00585463	+	0.00734147i
$583$	−2.23447	+	9.78986i	−0.0925424	+	0.405455i
$584$	−0.0339297	−	0.148656i	−0.00140402	−	0.00615142i
$585$	4.37041	−	5.48032i	0.180694	−	0.226583i
$586$	−1.19998	−	1.50472i	−0.0495706	−	0.0621596i
$587$	7.58007	−	33.2104i	0.312863	−	1.37074i	−0.536931	−	0.843626i	$-0.680416\pi$
$587$	7.58007	−	33.2104i	0.312863	−	1.37074i	0.849794	−	0.527115i	$-0.176726\pi$
$588$	12.3575	+	5.95108i	0.509617	+	0.245418i
$589$	13.3740	+	6.44059i	0.551067	+	0.265380i
$590$	0.206037	+	0.902708i	0.00848242	+	0.0371639i
$591$	−15.2517	+	7.34482i	−0.627370	+	0.302126i
$592$	−12.2210			−0.502278
$593$	38.6075	−	18.5924i	1.58542	−	0.763499i	0.586501	−	0.809948i	$-0.300505\pi$
$593$	38.6075	−	18.5924i	1.58542	−	0.763499i	0.998921	+	0.0464494i	$0.0147906\pi$
$594$	−0.125684	−	0.157603i	−0.00515688	−	0.00646653i
$595$	−2.54719	−	3.19407i	−0.104424	−	0.130944i
$596$	22.6825	−	10.9233i	0.929110	−	0.447436i
$597$	−8.67794			−0.355164
$598$	−0.942986	+	0.454118i	−0.0385616	+	0.0185703i
$599$	−1.26691	−	5.55071i	−0.0517646	−	0.226796i	0.942428	−	0.334408i	$-0.108536\pi$
$599$	−1.26691	−	5.55071i	−0.0517646	−	0.226796i	−0.994193	+	0.107613i	$0.965679\pi$
$600$	−0.381028	−	0.183494i	−0.0155554	−	0.00749110i
$601$	8.07342	+	3.88796i	0.329322	+	0.158593i	0.591237	−	0.806498i	$-0.298640\pi$
$601$	8.07342	+	3.88796i	0.329322	+	0.158593i	−0.261915	+	0.965091i	$0.584354\pi$
$602$	−5.37218e−5	0	0.000235371i	−2.18954e−6	0	9.59299e-6i
$603$	6.86725	+	8.61126i	0.279656	+	0.350678i
$604$	12.7593	−	15.9997i	0.519169	−	0.651018i
$605$	2.20081	+	9.64236i	0.0894755	+	0.392018i
$606$	0.338059	−	1.48113i	0.0137327	−	0.0601670i
$607$	17.6557	−	22.1395i	0.716621	−	0.898614i	−0.281520	−	0.959555i	$-0.590839\pi$
$607$	17.6557	−	22.1395i	0.716621	−	0.898614i	0.998141	+	0.0609410i	$0.0194101\pi$
$608$	1.34159			0.0544086
$609$	−1.81197	+	0.383420i	−0.0734247	+	0.0155370i
$610$	1.00131			0.0405419
$611$	−13.1239	+	16.4569i	−0.530938	+	0.665775i
$612$	−2.72912	+	11.9570i	−0.110318	+	0.483335i
$613$	7.12340	+	31.2097i	0.287712	+	1.26055i	0.887657	+	0.460506i	$0.152332\pi$
$613$	7.12340	+	31.2097i	0.287712	+	1.26055i	−0.599945	+	0.800041i	$0.704811\pi$
$614$	1.19239	−	1.49521i	0.0481210	−	0.0603418i
$615$	−6.35862	−	7.97346i	−0.256404	−	0.321521i
$616$	0.0616019	−	0.269896i	0.00248201	−	0.0108744i
$617$	5.49638	+	2.64692i	0.221276	+	0.106561i	0.541238	−	0.840870i	$-0.317956\pi$
$617$	5.49638	+	2.64692i	0.221276	+	0.106561i	−0.319962	+	0.947430i	$0.603670\pi$
$618$	1.20395	+	0.579791i	0.0484299	+	0.0233226i
$619$	−0.158208	−	0.693153i	−0.00635890	−	0.0278602i	0.971649	−	0.236428i	$-0.0759768\pi$
$619$	−0.158208	−	0.693153i	−0.00635890	−	0.0278602i	−0.978008	+	0.208568i	$0.933120\pi$
$620$	38.0961	−	18.3461i	1.52998	−	0.736797i
$621$	3.46619			0.139094
$622$	0.305730	−	0.147232i	0.0122587	−	0.00590346i
$623$	−2.62122	−	3.28691i	−0.105017	−	0.131687i
$624$	−8.96224	−	11.2383i	−0.358777	−	0.449892i
$625$	15.3252	−	7.38021i	0.613006	−	0.295208i
$626$	−2.39095			−0.0955615
$627$	2.94998	−	1.42063i	0.117811	−	0.0567347i
$628$	−1.67939	−	7.35788i	−0.0670149	−	0.293612i
$629$	−17.1160	−	8.24265i	−0.682461	−	0.328656i
$630$	0.0497403	+	0.0239537i	0.00198170	+	0.000954337i
$631$	6.02722	−	26.4070i	0.239940	−	1.05125i	−0.701130	−	0.713033i	$-0.747321\pi$
$631$	6.02722	−	26.4070i	0.239940	−	1.05125i	0.941070	−	0.338212i	$-0.109822\pi$
$632$	−2.58355	−	3.23967i	−0.102768	−	0.128867i
$633$	−7.95044	+	9.96954i	−0.316002	+	0.396253i
$634$	0.213348	+	0.934739i	0.00847313	+	0.0371232i
$635$	−4.10846	+	18.0003i	−0.163039	+	0.714322i
$636$	−5.14755	+	6.45483i	−0.204114	+	0.255951i
$637$	−24.9889			−0.990095
$638$	−0.455421	−	0.985399i	−0.0180303	−	0.0390123i
$639$	12.8548			0.508527
$640$	3.17506	−	3.98140i	0.125505	−	0.157379i
$641$	−6.11273	+	26.7816i	−0.241438	+	1.05781i	0.698270	+	0.715834i	$0.253953\pi$
$641$	−6.11273	+	26.7816i	−0.241438	+	1.05781i	−0.939709	+	0.341976i	$0.888904\pi$
$642$	0.299319	+	1.31140i	0.0118132	+	0.0517570i
$643$	−16.5799	+	20.7905i	−0.653848	+	0.819899i	−0.992658	−	0.120956i	$-0.961404\pi$
$643$	−16.5799	+	20.7905i	−0.653848	+	0.819899i	0.338810	+	0.940855i	$0.389976\pi$
$644$	1.48140	+	1.85761i	0.0583752	+	0.0732002i
$645$	−0.00362608	+	0.0158869i	−0.000142777	+	0.000625545i
$646$	0.622699	+	0.299876i	0.0244997	+	0.0117985i
$647$	21.9390	+	10.5653i	0.862510	+	0.415363i	0.812206	−	0.583371i	$-0.198267\pi$
$647$	21.9390	+	10.5653i	0.862510	+	0.415363i	0.0503045	+	0.998734i	$0.483981\pi$
$648$	−0.0738877	−	0.323723i	−0.00290258	−	0.0127170i
$649$	12.5982	−	6.06697i	0.494522	−	0.238149i
$650$	0.384582			0.0150846
$651$	3.40546	−	1.63998i	0.133470	−	0.0642760i
$652$	7.55767	+	9.47702i	0.295981	+	0.371149i
$653$	12.9368	+	16.2223i	0.506257	+	0.634826i	0.967628	−	0.252381i	$-0.0812137\pi$
$653$	12.9368	+	16.2223i	0.506257	+	0.634826i	−0.461371	+	0.887207i	$0.652642\pi$
$654$	−0.689236	+	0.331918i	−0.0269513	+	0.0129790i
$655$	32.4351			1.26734
$656$	−18.8425	+	9.07406i	−0.735675	+	0.354283i
$657$	−0.102183	−	0.447694i	−0.00398654	−	0.0174662i
$658$	−0.149366	−	0.0719307i	−0.00582288	−	0.00280415i
$659$	12.0386	+	5.79749i	0.468958	+	0.225838i	0.653411	−	0.757003i	$-0.273337\pi$
$659$	12.0386	+	5.79749i	0.468958	+	0.225838i	−0.184454	+	0.982841i	$0.559052\pi$
$660$	2.07538	−	9.09284i	0.0807841	−	0.353938i
$661$	21.5768	+	27.0564i	0.839240	+	1.05237i	0.997883	+	0.0650374i	$0.0207167\pi$
$661$	21.5768	+	27.0564i	0.839240	+	1.05237i	−0.158643	+	0.987336i	$0.550712\pi$
$662$	−0.637912	+	0.799916i	−0.0247932	+	0.0310896i
$663$	−4.97217	−	21.7845i	−0.193103	−	0.846040i
$664$	−0.212683	+	0.931825i	−0.00825370	+	0.0361618i
$665$	−0.559095	+	0.701083i	−0.0216808	+	0.0271868i
$666$	0.256721			0.00994772
$667$	18.1298	+	4.44187i	0.701989	+	0.171990i
$668$	15.2979			0.591894
$669$	−11.9329	+	14.9634i	−0.461354	+	0.578519i
$670$	0.393423	−	1.72370i	0.0151992	−	0.0665922i
$671$	−3.36483	−	14.7423i	−0.129898	−	0.569120i
$672$	0.212991	−	0.267083i	0.00821632	−	0.0103029i
$673$	23.0254	+	28.8729i	0.887562	+	1.11297i	0.992950	+	0.118537i	$0.0378204\pi$
$673$	23.0254	+	28.8729i	0.887562	+	1.11297i	−0.105387	+	0.994431i	$0.533608\pi$
$674$	0.566001	−	2.47981i	0.0218015	−	0.0955187i
$675$	−1.14751	−	0.552611i	−0.0441677	−	0.0212700i
$676$	0.333295	+	0.160506i	0.0128190	+	0.00617332i
$677$	0.875640	+	3.83643i	0.0336536	+	0.147446i	0.988963	−	0.148161i	$-0.0473353\pi$
$677$	0.875640	+	3.83643i	0.0336536	+	0.147446i	−0.955310	+	0.295607i	$0.904478\pi$
$678$	1.51761	−	0.730845i	0.0582836	−	0.0280679i
$679$	−0.936920			−0.0359557
$680$	3.55368	−	1.71136i	0.136277	−	0.0656278i
$681$	15.4320	+	19.3511i	0.591354	+	0.741535i
$682$	1.38128	+	1.73207i	0.0528921	+	0.0663245i
$683$	−3.50044	+	1.68572i	−0.133941	+	0.0645024i	−0.499654	−	0.866225i	$-0.666539\pi$
$683$	−3.50044	+	1.68572i	−0.133941	+	0.0645024i	0.365713	+	0.930728i	$0.380825\pi$
$684$	2.69201			0.102931
$685$	10.0026	−	4.81702i	0.382182	−	0.184049i
$686$	−0.0883426	−	0.387054i	−0.00337294	−	0.0147778i
$687$	−17.5091	−	8.43194i	−0.668014	−	0.321699i
$688$	0.0301072	+	0.0144989i	0.00114783	+	0.000552764i
$689$	3.34708	−	14.6645i	0.127514	−	0.558674i
$690$	−0.346910	−	0.435012i	−0.0132066	−	0.0165606i
$691$	4.78202	−	5.99646i	0.181917	−	0.228116i	−0.682509	−	0.730877i	$-0.739111\pi$
$691$	4.78202	−	5.99646i	0.181917	−	0.228116i	0.864425	+	0.502761i	$0.167683\pi$
$692$	−6.64953	−	29.1335i	−0.252777	−	1.10749i
$693$	0.185521	−	0.812820i	0.00704736	−	0.0308765i
$694$	0.119471	−	0.149812i	0.00453505	−	0.00568678i
$695$	3.02459			0.114729
$696$	0.0283787	−	1.78791i	0.00107569	−	0.0677705i
$697$	−32.5100			−1.23140
$698$	−0.473001	+	0.593124i	−0.0179033	+	0.0224501i
$699$	4.06861	−	17.8257i	0.153889	−	0.674232i
$700$	−0.194270	−	0.851154i	−0.00734273	−	0.0321706i
$701$	24.5309	−	30.7608i	0.926520	−	1.16182i	−0.0600034	−	0.998198i	$-0.519111\pi$
$701$	24.5309	−	30.7608i	0.926520	−	1.16182i	0.986523	−	0.163621i	$-0.0523174\pi$
$702$	0.188266	+	0.236078i	0.00710564	+	0.00891019i
$703$	−0.927874	+	4.06528i	−0.0349954	+	0.153325i
$704$	−17.1112	−	8.24033i	−0.644903	−	0.310569i
$705$	−10.0818	−	4.85513i	−0.379702	−	0.182855i
$706$	−0.269525	−	1.18087i	−0.0101437	−	0.0444425i
$707$	5.66113	−	2.72625i	0.212909	−	0.102531i
$708$	11.4965			0.432065
$709$	−33.8628	+	16.3075i	−1.27175	+	0.612440i	−0.943256	−	0.332067i	$-0.892254\pi$
$709$	−33.8628	+	16.3075i	−1.27175	+	0.612440i	−0.328490	+	0.944508i	$0.606540\pi$
$710$	−1.28656	−	1.61329i	−0.0482836	−	0.0605457i
$711$	−7.78066	−	9.75663i	−0.291797	−	0.365902i
$712$	3.65698	−	1.76111i	0.137051	−	0.0660003i
$713$	−38.0939			−1.42663
$714$	0.158559	−	0.0763580i	0.00593392	−	0.00285763i
$715$	3.78113	+	16.5662i	0.141406	+	0.619542i
$716$	−28.8754	−	13.9057i	−1.07913	−	0.519679i
$717$	7.38239	+	3.55517i	0.275700	+	0.132770i
$718$	0.0694094	−	0.304102i	0.00259034	−	0.0113490i
$719$	2.88863	+	3.62223i	0.107728	+	0.135086i	0.832772	−	0.553616i	$-0.186752\pi$
$719$	2.88863	+	3.62223i	0.107728	+	0.135086i	−0.725045	+	0.688702i	$0.758181\pi$
$720$	4.76441	−	5.97438i	0.177559	−	0.222652i
$721$	1.22982	+	5.38818i	0.0458007	+	0.200666i
$722$	−0.317817	+	1.39245i	−0.0118279	+	0.0518216i
$723$	4.45317	−	5.58410i	0.165615	−	0.207675i
$724$	11.3076			0.420244
$725$	−5.29385	−	4.36093i	−0.196609	−	0.161961i
$726$	−0.426051			−0.0158122
$727$	3.43787	−	4.31095i	0.127503	−	0.159884i	−0.713982	−	0.700164i	$-0.753110\pi$
$727$	3.43787	−	4.31095i	0.127503	−	0.159884i	0.841485	+	0.540280i	$0.181682\pi$
$728$	−0.0922753	+	0.404285i	−0.00341995	+	0.0149838i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	−0.0459592	+	0.0576311i	−0.00170103	+	0.00213302i
$731$	0.0323876	+	0.0406127i	0.00119790	+	0.00150212i
$732$	2.76650	−	12.1208i	0.102253	−	0.447999i
$733$	−39.1400	−	18.8488i	−1.44567	−	0.696197i	−0.463831	−	0.885924i	$-0.653525\pi$
$733$	−39.1400	−	18.8488i	−1.44567	−	0.696197i	−0.981837	+	0.189727i	$0.939240\pi$
$734$	1.04505	+	0.503271i	0.0385736	+	0.0185761i
$735$	−2.95604	−	12.9512i	−0.109035	−	0.477714i
$736$	−3.10193	+	1.49381i	−0.114339	+	0.0550625i
$737$	−26.7000			−0.983509
$738$	0.395816	−	0.190615i	0.0145702	−	0.00701664i
$739$	27.6111	+	34.6233i	1.01569	+	1.27364i	0.961412	+	0.275112i	$0.0887150\pi$
$739$	27.6111	+	34.6233i	1.01569	+	1.27364i	0.0542802	+	0.998526i	$0.482714\pi$
$740$	7.40569	+	9.28645i	0.272239	+	0.341377i
$741$	−4.41886	+	2.12801i	−0.162331	+	0.0781744i
$742$	0.118468			0.00434910
$743$	31.8973	−	15.3609i	1.17020	−	0.563538i	0.255157	−	0.966900i	$-0.417873\pi$
$743$	31.8973	−	15.3609i	1.17020	−	0.563538i	0.915041	+	0.403362i	$0.132158\pi$
$744$	0.812034	+	3.55775i	0.0297706	+	0.130434i
$745$	−21.9688	−	10.5796i	−0.804876	−	0.387608i
$746$	−0.573899	−	0.276375i	−0.0210119	−	0.0101188i
$747$	−0.640518	+	2.80629i	−0.0234353	+	0.102677i
$748$	−18.5370	−	23.2446i	−0.677779	−	0.849908i
$749$	−3.46868	+	4.34959i	−0.126743	+	0.158930i
$750$	0.224092	+	0.981809i	0.00818267	+	0.0358506i
$751$	0.791159	−	3.46629i	0.0288698	−	0.126487i	−0.958440	−	0.285296i	$-0.907908\pi$
$751$	0.791159	−	3.46629i	0.0288698	−	0.126487i	0.987309	+	0.158809i	$0.0507654\pi$
$752$	−14.3071	+	17.9405i	−0.521726	+	0.654224i
$753$	−2.32177			−0.0846100
$754$	0.682189	+	1.47606i	0.0248439	+	0.0537549i
$755$	−19.8205			−0.721342
$756$	0.427384	−	0.535923i	0.0155438	−	0.0194913i
$757$	−4.80769	+	21.0639i	−0.174739	+	0.765580i	0.809267	+	0.587441i	$0.199865\pi$
$757$	−4.80769	+	21.0639i	−0.174739	+	0.765580i	−0.984005	+	0.178139i	$0.942992\pi$
$758$	−0.232594	−	1.01906i	−0.00844818	−	0.0370139i
$759$	−5.23891	+	6.56938i	−0.190160	+	0.238453i
$760$	−0.539788	−	0.676873i	−0.0195802	−	0.0245528i
$761$	−3.67857	+	16.1169i	−0.133348	+	0.584236i	0.863461	+	0.504415i	$0.168292\pi$
$761$	−3.67857	+	16.1169i	−0.133348	+	0.584236i	−0.996809	+	0.0798205i	$0.974565\pi$
$762$	−0.716586	−	0.345090i	−0.0259592	−	0.0125013i
$763$	−2.85062	−	1.37278i	−0.103199	−	0.0496981i
$764$	0.282464	+	1.23755i	0.0102192

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0518468 + 0.0650138i) q^{2} +(0.222521 - 0.974928i) q^{3} +(0.443503 + 1.94311i) q^{4} +(1.20357 - 1.50923i) q^{5} +(0.0518468 + 0.0650138i) q^{6} +(-0.0765305 + 0.335302i) q^{7} +(-0.299165 - 0.144070i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})\)	\(q+(-0.0518468 + 0.0650138i) q^{2} +(0.222521 - 0.974928i) q^{3} +(0.443503 + 1.94311i) q^{4} +(1.20357 - 1.50923i) q^{5} +(0.0518468 + 0.0650138i) q^{6} +(-0.0765305 + 0.335302i) q^{7} +(-0.299165 - 0.144070i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(0.0357195 + 0.156498i) q^{10} +(2.18408 - 1.05180i) q^{11} +1.99309 q^{12} +(-3.27160 + 1.57552i) q^{13} +(-0.0178314 - 0.0223599i) q^{14} +(-1.20357 - 1.50923i) q^{15} +(-3.56654 + 1.71755i) q^{16} -6.15354 q^{17} +(0.0749208 - 0.0360799i) q^{18} +(0.300553 + 1.31681i) q^{19} +(3.46640 + 1.66933i) q^{20} +(0.309866 + 0.149223i) q^{21} +(-0.0448561 + 0.196528i) q^{22} +(-2.16114 - 2.70998i) q^{23} +(-0.207029 + 0.259606i) q^{24} +(0.283411 + 1.24171i) q^{25} +(0.0671914 - 0.294385i) q^{26} +(-0.623490 + 0.781831i) q^{27} -0.685471 q^{28} +(-4.26305 + 3.29035i) q^{29} +0.160522 q^{30} +(6.85222 - 8.59242i) q^{31} +(0.221024 - 0.968370i) q^{32} +(-0.539423 - 2.36337i) q^{33} +(0.319041 - 0.400065i) q^{34} +(0.413938 + 0.519062i) q^{35} +(0.443503 - 1.94311i) q^{36} +(2.78149 + 1.33950i) q^{37} +(-0.101193 - 0.0487322i) q^{38} +(0.808018 + 3.54016i) q^{39} +(-0.577502 + 0.278110i) q^{40} +5.28313 q^{41} +(-0.0257671 + 0.0124088i) q^{42} +(-0.00526324 - 0.00659989i) q^{43} +(3.01241 + 3.77744i) q^{44} +(-1.73921 + 0.837560i) q^{45} +0.288234 q^{46} +(5.22270 - 2.51512i) q^{47} +(0.880862 + 3.85931i) q^{48} +(6.20021 + 2.98586i) q^{49} +(-0.0954221 - 0.0459528i) q^{50} +(-1.36929 + 5.99926i) q^{51} +(-4.51238 - 5.65834i) q^{52} +(-2.58271 + 3.23861i) q^{53} +(-0.0185039 - 0.0810709i) q^{54} +(1.04129 - 4.56219i) q^{55} +(0.0712023 - 0.0892849i) q^{56} +1.35067 q^{57} +(0.00710697 - 0.447751i) q^{58} +5.76819 q^{59} +(2.39882 - 3.00802i) q^{60} +(1.38805 - 6.08144i) q^{61} +(0.203360 + 0.890979i) q^{62} +(0.214434 - 0.268891i) q^{63} +(-4.88474 - 6.12527i) q^{64} +(-1.55978 + 6.83384i) q^{65} +(0.181619 + 0.0874630i) q^{66} +(-9.92346 - 4.77889i) q^{67} +(-2.72912 - 11.9570i) q^{68} +(-3.12293 + 1.50393i) q^{69} -0.0552076 q^{70} +(-11.5818 + 5.57748i) q^{71} +(0.207029 + 0.259606i) q^{72} +(0.286311 + 0.359022i) q^{73} +(-0.231297 + 0.111387i) q^{74} +1.27364 q^{75} +(-2.42541 + 1.16802i) q^{76} +(0.185521 + 0.812820i) q^{77} +(-0.272052 - 0.131013i) q^{78} +(11.2434 + 5.41452i) q^{79} +(-1.70040 + 7.44993i) q^{80} +(0.623490 + 0.781831i) q^{81} +(-0.273913 + 0.343476i) q^{82} +(-0.640518 - 2.80629i) q^{83} +(-0.152532 + 0.668285i) q^{84} +(-7.40623 + 9.28712i) q^{85} +0.000701966 q^{86} +(2.25924 + 4.88834i) q^{87} -0.804933 q^{88} +(-7.62150 + 9.55706i) q^{89} +(0.0357195 - 0.156498i) q^{90} +(-0.277897 - 1.21755i) q^{91} +(4.30733 - 5.40122i) q^{92} +(-6.85222 - 8.59242i) q^{93} +(-0.107263 + 0.469948i) q^{94} +(2.34911 + 1.13127i) q^{95} +(-0.894908 - 0.430965i) q^{96} +(0.606191 + 2.65590i) q^{97} +(-0.515584 + 0.248292i) q^{98} -2.42414 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20} + 4 q^{21} + 20 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 3 q^{26} + 3 q^{27} - 48 q^{28} - 10 q^{29} + 8 q^{30} + 8 q^{31} + 55 q^{32} - 8 q^{33} + 6 q^{34} + 31 q^{35} - 6 q^{36} + 20 q^{37} - 20 q^{38} - 10 q^{39} - 59 q^{40} - 68 q^{41} - 19 q^{42} - 3 q^{43} - 10 q^{44} + 14 q^{45} - 12 q^{46} + 19 q^{47} + 24 q^{48} + 17 q^{49} + 23 q^{50} + 11 q^{51} - 4 q^{52} - q^{53} - 5 q^{54} + 3 q^{55} + 7 q^{56} - 2 q^{57} - 30 q^{58} + 20 q^{59} + 47 q^{60} + 24 q^{61} + 79 q^{62} + 3 q^{63} - 23 q^{64} + 6 q^{65} + 50 q^{66} - 14 q^{67} - 8 q^{68} - 8 q^{69} + 28 q^{70} - 28 q^{71} + 4 q^{72} + 43 q^{73} - 47 q^{74} - 18 q^{75} + 19 q^{76} + 26 q^{77} - 11 q^{78} + 9 q^{79} - 74 q^{80} - 3 q^{81} - 17 q^{82} + 8 q^{83} - 15 q^{84} - 21 q^{85} - 140 q^{86} - 11 q^{87} - 58 q^{88} - 6 q^{89} + 6 q^{90} - 15 q^{91} + 11 q^{92} - 8 q^{93} + 6 q^{94} - 16 q^{95} + 36 q^{96} - 81 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more