LMFDB - Embedded newform 87.2.g.b.82.2

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			82.2
Root			$0.0185039 - 0.0810709i$ of defining polynomial
Character	$\chi$	$=$	87.82
Dual form			87.2.g.b.52.2

$q$-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 $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

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	0.763163	−	0.646206i	$-0.223645\pi$
$2$	−0.0518468	−	0.0650138i	−0.0366612	−	0.0459717i	−0.799824	+	0.600234i	$0.795074\pi$
$3$	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	0.974372	−	0.224941i	$-0.0722188\pi$
$5$	1.20357	+	1.50923i	0.538253	+	0.674948i	−0.436119	+	0.899889i	$0.643647\pi$
$6$	0.0518468	−	0.0650138i	0.0211664	−	0.0265418i
$7$	−0.0765305	−	0.335302i	−0.0289258	−	0.126732i	0.958404	−	0.285417i	$-0.0921319\pi$
$7$	−0.0765305	−	0.335302i	−0.0289258	−	0.126732i	−0.987329	+	0.158684i	$0.949275\pi$
$8$	−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	0.733134	−	0.680084i	$-0.238057\pi$
$11$	2.18408	+	1.05180i	0.658525	+	0.317129i	−0.0746095	+	0.997213i	$0.523771\pi$
$12$	1.99309			0.575354
$13$	−3.27160	−	1.57552i	−0.907378	−	0.436970i	−0.0788298	−	0.996888i	$-0.525118\pi$
$13$	−3.27160	−	1.57552i	−0.907378	−	0.436970i	−0.828548	+	0.559918i	$0.810833\pi$
$14$	−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	−0.928680	−	0.370882i	$-0.879055\pi$
$19$	0.300553	−	1.31681i	0.0689516	−	0.302097i	0.997631	+	0.0687856i	$0.0219125\pi$
$20$	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	−0.954310	−	0.298820i	$-0.903407\pi$
$23$	−2.16114	+	2.70998i	−0.450628	+	0.565070i	0.503681	+	0.863889i	$0.331979\pi$
$24$	−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	0.741285	+	0.671190i	$0.234217\pi$
$31$	6.85222	+	8.59242i	1.23070	+	1.54324i	0.489411	+	0.872053i	$0.337212\pi$
$32$	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	−0.191043	−	0.981582i	$-0.561187\pi$
$37$	2.78149	−	1.33950i	0.457275	−	0.220212i	0.648318	+	0.761370i	$0.275473\pi$
$38$	−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	−0.782233	−	0.622986i	$-0.785919\pi$
$43$	−0.00526324	+	0.00659989i	−0.000802636	+	0.00100647i	0.781430	+	0.623993i	$0.214491\pi$
$44$	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	0.774105	−	0.633057i	$-0.218200\pi$
$47$	5.22270	+	2.51512i	0.761809	+	0.366868i	−0.0122968	+	0.999924i	$0.503914\pi$
$48$	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	0.572143	−	0.820154i	$-0.306112\pi$
$53$	−2.58271	−	3.23861i	−0.354762	−	0.444857i	−0.926905	+	0.375297i	$0.877541\pi$
$54$	−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	0.982679	+	0.185316i	$0.0593310\pi$
$61$	1.38805	+	6.08144i	0.177722	+	0.778649i	−0.804957	+	0.593333i	$0.797812\pi$
$62$	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	−0.927170	−	0.374642i	$-0.877766\pi$
$67$	−9.92346	+	4.77889i	−1.21234	+	0.583834i	−0.285174	+	0.958476i	$0.592051\pi$
$68$	−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	−0.406682	−	0.913570i	$-0.633314\pi$
$71$	−11.5818	−	5.57748i	−1.37450	−	0.661925i	−0.967820	+	0.251645i	$0.919029\pi$
$72$	0.207029	−	0.259606i	0.0243986	−	0.0305948i
$73$	0.286311	−	0.359022i	0.0335102	−	0.0420204i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	0.286311	−	0.359022i	0.0335102	−	0.0420204i	0.798304	+	0.602254i	$0.205731\pi$
$74$	−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	0.323491	−	0.946231i	$-0.395143\pi$
$79$	11.2434	−	5.41452i	1.26498	−	0.609181i	0.941487	+	0.337050i	$0.109429\pi$
$80$	−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	−0.997839	−	0.0657114i	$-0.979068\pi$
$83$	−0.640518	+	2.80629i	−0.0703060	+	0.308031i	0.927533	+	0.373742i	$0.121925\pi$
$84$	−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	−0.999501	−	0.0315781i	$-0.989947\pi$
$89$	−7.62150	−	9.55706i	−0.807878	−	1.01305i	0.191624	−	0.981468i	$-0.438625\pi$
$90$	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	−0.934784	−	0.355215i	$-0.884408\pi$
$97$	0.606191	−	2.65590i	0.0615494	−	0.269666i	0.996334	+	0.0855498i	$0.0272647\pi$
$98$	−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	−0.240765	+	0.970583i	$0.577398\pi$
$101$	−11.3909	+	14.2838i	−1.13344	+	1.42129i	−0.892673	+	0.450704i	$0.851173\pi$
$102$	−0.319041	+	0.400065i	−0.0315898	+	0.0396124i
$103$	14.4782	+	6.97235i	1.42658	+	0.687006i	0.978359	−	0.206916i	$-0.0663425\pi$
$103$	14.4782	+	6.97235i	1.42658	+	0.687006i	0.448224	+	0.893921i	$0.352057\pi$
$104$	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	0.433978	−	0.900923i	$-0.357110\pi$
$107$	14.5741	−	7.01851i	1.40893	−	0.678505i	0.974951	+	0.222419i	$0.0713953\pi$
$108$	−1.79571	+	0.864767i	−0.172792	+	0.0832123i
$109$	−2.04709	−	8.96888i	−0.196075	−	0.859063i	−0.973245	−	0.229771i	$-0.926202\pi$
$109$	−2.04709	−	8.96888i	−0.196075	−	0.859063i	0.777169	−	0.629292i	$-0.216655\pi$
$110$	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	0.508078	+	0.861311i	$0.330356\pi$
$113$	4.50744	+	19.7484i	0.424024	+	1.85777i	−0.0840533	+	0.996461i	$0.526787\pi$
$114$	−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	0.0105441	−	0.999944i	$-0.496644\pi$
$127$	−8.61739	−	4.14992i	−0.764670	−	0.368246i	−0.775214	+	0.631699i	$0.782358\pi$
$128$	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	−0.0733108	−	0.997309i	$-0.523356\pi$
$131$	10.4762	−	13.1367i	0.915307	−	1.14776i	0.988618	−	0.150449i	$-0.0480721\pi$
$132$	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	−0.199234	−	0.979952i	$-0.563845\pi$
$137$	5.18170	−	2.49538i	0.442703	−	0.213194i	0.641937	+	0.766757i	$0.278131\pi$
$138$	0.0641381	+	0.281008i	0.00545980	+	0.0239209i
$139$	0.976909	−	1.22501i	0.0828603	−	0.103904i	−0.738673	−	0.674064i	$-0.764547\pi$
$139$	0.976909	−	1.22501i	0.0828603	−	0.103904i	0.821534	+	0.570160i	$0.193119\pi$
$140$	−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	0.719151	+	0.694854i	$0.244531\pi$
$149$	−2.81077	+	12.3148i	−0.230267	+	1.00887i	−0.949418	+	0.314014i	$0.898326\pi$
$150$	−0.0660341	−	0.0828042i	−0.00539166	−	0.00676093i
$151$	−6.40179	+	8.02760i	−0.520971	+	0.653277i	−0.970815	−	0.239831i	$-0.922908\pi$
$151$	−6.40179	+	8.02760i	−0.520971	+	0.653277i	0.449844	+	0.893107i	$0.351480\pi$
$152$	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	0.635991	−	0.771696i	$-0.280591\pi$
$163$	5.47952	+	2.63880i	0.429189	+	0.206687i	−0.206802	+	0.978383i	$0.566306\pi$
$164$	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	0.997028	+	0.0770460i	$0.0245488\pi$
$167$	1.70796	+	7.48305i	0.132166	+	0.579056i	−0.864862	+	0.502010i	$0.832594\pi$
$168$	−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	0.250225	−	0.968188i	$-0.419495\pi$
$179$	−10.0259	−	12.5720i	−0.749369	−	0.939679i	−0.999594	+	0.0285091i	$0.990924\pi$
$180$	−2.39882	+	3.00802i	−0.178797	+	0.224205i
$181$	1.26245	+	5.53117i	0.0938375	+	0.411129i	0.999929	−	0.0119539i	$-0.00380512\pi$
$181$	1.26245	+	5.53117i	0.0938375	+	0.411129i	−0.906091	+	0.423083i	$0.860948\pi$
$182$	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	−0.799135	−	0.601152i	$-0.794709\pi$
$193$	2.52413	−	11.0589i	0.181691	−	0.796039i	0.980826	−	0.194887i	$-0.0624341\pi$
$194$	−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	−0.999665	−	0.0258911i	$-0.991758\pi$
$197$	−10.5545	+	13.2349i	−0.751976	+	0.942949i	0.247688	+	0.968840i	$0.420329\pi$
$198$	0.125684	+	0.157603i	0.00893198	+	0.0112004i
$199$	−1.93102	+	8.46037i	−0.136887	+	0.599740i	0.859222	+	0.511603i	$0.170948\pi$
$199$	−1.93102	+	8.46037i	−0.136887	+	0.599740i	−0.996108	+	0.0881362i	$0.971909\pi$
$200$	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	−0.785313	−	0.619099i	$-0.787498\pi$
$211$	−11.4887	+	5.53267i	−0.790916	+	0.380885i	−0.00560320	+	0.999984i	$0.501784\pi$
$212$	−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	−0.910447	−	0.413626i	$-0.864262\pi$
$223$	−17.2436	+	8.30407i	−1.15472	+	0.556082i	−0.244268	+	0.969708i	$0.578548\pi$
$224$	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	−0.958060	−	0.286569i	$-0.907485\pi$
$227$	−15.4320	−	19.3511i	−1.02426	−	1.28438i	−0.0661958	−	0.997807i	$-0.521086\pi$
$228$	0.599028	−	2.62451i	0.0396716	−	0.173813i
$229$	4.32439	+	18.9464i	0.285764	+	1.25201i	0.890277	+	0.455419i	$0.150510\pi$
$229$	4.32439	+	18.9464i	0.285764	+	1.25201i	−0.604514	+	0.796595i	$0.706632\pi$
$230$	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	−0.999040	−	0.0437983i	$-0.986054\pi$
$239$	−1.82330	−	7.98840i	−0.117939	−	0.516727i	0.881101	−	0.472928i	$-0.156803\pi$
$240$	6.88477	−	3.31553i	0.444410	−	0.214017i
$241$	6.43502	−	3.09894i	0.414516	−	0.199620i	−0.214989	−	0.976616i	$-0.568972\pi$
$241$	6.43502	−	3.09894i	0.414516	−	0.199620i	0.629506	+	0.776996i	$0.283257\pi$
$242$	−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	−0.988612	−	0.150486i	$-0.951916\pi$
$251$	−0.516642	+	2.26356i	−0.0326102	+	0.142874i	0.956002	+	0.293360i	$0.0947735\pi$
$252$	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	−0.527884	−	0.849316i	$-0.677015\pi$
$257$	5.06951	−	22.2110i	0.316228	−	1.38548i	0.844112	−	0.536167i	$-0.180128\pi$
$258$	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	0.763126	−	0.646250i	$-0.223664\pi$
$263$	−0.595714	−	0.747002i	−0.0367333	−	0.0460621i	−0.799859	+	0.600188i	$0.795092\pi$
$264$	−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	−0.800879	−	0.598826i	$-0.795634\pi$
$269$	−13.6464	+	6.57178i	−0.832038	+	0.400688i	−0.0311589	+	0.999514i	$0.509920\pi$
$270$	−0.144625	+	0.0696480i	−0.00880163	+	0.00423864i
$271$	1.83597	−	8.04392i	0.111527	−	0.488633i	−0.888055	−	0.459737i	$-0.847944\pi$
$271$	1.83597	−	8.04392i	0.111527	−	0.488633i	0.999582	−	0.0288962i	$-0.00919922\pi$
$272$	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	−0.0778412	−	0.996966i	$-0.524803\pi$
$277$	−15.0761	−	7.26026i	−0.905834	−	0.436227i	−0.827992	+	0.560739i	$0.810517\pi$
$278$	−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	0.269313	−	0.963053i	$-0.413203\pi$
$281$	19.9509	−	9.60786i	1.19017	−	0.573157i	0.920859	+	0.389896i	$0.127489\pi$
$282$	0.434298	−	0.209147i	0.0258620	−	0.0124545i
$283$	3.92964	+	17.2169i	0.233593	+	1.02344i	0.946633	+	0.322314i	$0.104461\pi$
$283$	3.92964	+	17.2169i	0.233593	+	1.02344i	−0.713040	+	0.701123i	$0.752682\pi$
$284$	−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	−0.868808	−	0.495150i	$-0.835113\pi$
$293$	−5.15017	−	22.5644i	−0.300876	−	1.31823i	0.567931	−	0.823076i	$-0.307744\pi$
$294$	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	−0.535210	−	0.844719i	$-0.679768\pi$
$311$	−3.67659	+	1.77055i	−0.208480	+	0.100399i	0.326730	+	0.945118i	$0.394053\pi$
$312$	0.268301	+	1.17550i	0.0151895	+	0.0665497i
$313$	17.9270	−	22.4797i	1.01329	−	1.27063i	0.0509742	−	0.998700i	$-0.483767\pi$
$313$	17.9270	−	22.4797i	1.01329	−	1.27063i	0.962318	−	0.271928i	$-0.0876612\pi$
$314$	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	0.941594	−	0.336751i	$-0.109328\pi$
$317$	7.18877	+	9.01443i	0.403762	+	0.506301i	−0.537832	+	0.843052i	$0.680757\pi$
$318$	−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	−0.510640	−	0.859794i	$-0.670592\pi$
$337$	−27.5590	−	13.2717i	−1.50123	−	0.722956i	−0.990593	+	0.136838i	$0.956306\pi$
$338$	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	0.479020	−	0.877804i	$-0.340992\pi$
$353$	−9.08165	−	11.3880i	−0.483368	−	0.606124i	−0.962388	+	0.271680i	$0.912421\pi$
$354$	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	0.342569	−	0.939493i	$-0.388703\pi$
$359$	−3.37960	−	1.62753i	−0.178368	−	0.0858976i	−0.520937	+	0.853595i	$0.674417\pi$
$360$	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	0.827013	+	0.562182i	$0.190038\pi$
$367$	−3.10389	+	13.5990i	−0.162022	+	0.709864i	−0.989035	+	0.147681i	$0.952819\pi$
$368$	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	−0.911436	−	0.411441i	$-0.865026\pi$
$373$	1.70453	−	7.46802i	0.0882571	−	0.386679i	0.999693	+	0.0247617i	$0.00788271\pi$
$374$	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	0.538681	−	0.842510i	$-0.318923\pi$
$379$	−7.83725	−	9.82760i	−0.402573	−	0.504810i	−0.941254	+	0.337700i	$0.890351\pi$
$380$	−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	−0.249315	−	0.968422i	$-0.580206\pi$
$383$	14.6837	−	18.4128i	0.750305	−	0.940852i	0.999620	+	0.0275703i	$0.00877700\pi$
$384$	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	−0.736171	−	0.676796i	$-0.763368\pi$
$397$	−13.2705	+	6.39072i	−0.666026	+	0.320741i	0.0701450	+	0.997537i	$0.477654\pi$
$398$	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	0.545323	−	0.838226i	$-0.316407\pi$
$401$	−7.87447	−	9.87428i	−0.393233	−	0.493098i	−0.938556	+	0.345128i	$0.887836\pi$
$402$	−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	0.722766	+	0.691093i	$0.242871\pi$
$409$	7.51172	+	32.9110i	0.371430	+	1.62734i	−0.351335	+	0.936250i	$0.614272\pi$
$410$	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	0.888787	−	0.458321i	$-0.151549\pi$
$419$	22.2013	+	10.6916i	1.08461	+	0.522319i	0.195819	+	0.980640i	$0.437263\pi$
$420$	0.825014	−	1.03453i	0.0402565	−	0.0504801i
$421$	7.64133	−	9.58193i	0.372416	−	0.466995i	−0.559942	−	0.828532i	$-0.689177\pi$
$421$	7.64133	−	9.58193i	0.372416	−	0.466995i	0.932358	+	0.361537i	$0.117748\pi$
$422$	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	−0.909797	−	0.415053i	$-0.863763\pi$
$431$	1.86817	−	8.18500i	0.0899867	−	0.394257i	0.999784	+	0.0207960i	$0.00662003\pi$
$432$	0.880862	+	3.85931i	0.0423805	+	0.185681i
$433$	5.76203	+	7.22535i	0.276905	+	0.347228i	0.900764	−	0.434309i	$-0.143007\pi$
$433$	5.76203	+	7.22535i	0.276905	+	0.347228i	−0.623859	+	0.781537i	$0.714436\pi$
$434$	−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	0.794146	+	0.607727i	$0.207919\pi$
$439$	−3.87697	+	16.9861i	−0.185038	+	0.810704i	−0.979184	+	0.202976i	$0.934939\pi$
$440$	−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	−0.935156	−	0.354235i	$-0.884741\pi$
$443$	−26.1256	+	12.5814i	−1.24127	+	0.597762i	−0.306109	+	0.951997i	$0.599027\pi$
$444$	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	−0.943244	−	0.332100i	$-0.892243\pi$
$449$	−8.67883	+	10.8829i	−0.409579	+	0.513596i	0.533665	+	0.845696i	$0.320814\pi$
$450$	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	0.979863	−	0.199672i	$-0.0639875\pi$
$457$	0.222385	+	0.974330i	0.0104027	+	0.0455773i	−0.969460	+	0.245249i	$0.921130\pi$
$458$	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	−0.989437	−	0.144966i	$-0.953693\pi$
$461$	−3.45431	−	15.1343i	−0.160883	−	0.704876i	0.828553	−	0.559910i	$-0.189164\pi$
$462$	−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	0.991868	−	0.127273i	$-0.0406225\pi$
$467$	0.929323	+	4.07163i	0.0430039	+	0.188413i	−0.948864	+	0.315686i	$0.897765\pi$
$468$	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	−0.972351	−	0.233523i	$-0.924975\pi$
$479$	−11.5627	+	14.4992i	−0.528315	+	0.662486i	0.444037	+	0.896009i	$0.353546\pi$
$480$	−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	−0.424483	−	0.905436i	$-0.639544\pi$
$487$	12.1972	−	15.2948i	0.552708	−	0.693074i	0.977191	+	0.212362i	$0.0681157\pi$
$488$	−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	0.814343	−	0.580383i	$-0.197097\pi$
$491$	1.49134	+	1.87008i	0.0673030	+	0.0843953i	−0.747040	+	0.664779i	$0.768526\pi$
$492$	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	−0.962859	−	0.270005i	$-0.912974\pi$
$499$	−10.8423	+	13.5958i	−0.485367	+	0.608631i	0.477492	+	0.878636i	$0.341546\pi$
$500$	−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	0.771081	+	0.636737i	$0.219716\pi$
$503$	−4.48348	+	19.6434i	−0.199909	+	0.875857i	−0.970990	+	0.239120i	$0.923141\pi$
$504$	−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	−0.244964	−	0.969532i	$-0.578776\pi$
$509$	−26.0740	−	12.5566i	−1.15571	−	0.556560i	−0.910743	+	0.412973i	$0.864491\pi$
$510$	−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	0.651625	+	0.758542i	$0.274088\pi$
$541$	−6.15415	+	26.9631i	−0.264588	+	1.15923i	−0.916212	+	0.400693i	$0.868769\pi$
$542$	−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	−0.993296	−	0.115602i	$-0.963120\pi$
$547$	−1.12752	+	4.93998i	−0.0482091	+	0.211218i	0.945086	+	0.326821i	$0.105977\pi$
$548$	−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	−0.521051	−	0.853525i	$-0.674460\pi$
$557$	10.0780	−	12.6374i	0.427019	−	0.535465i	0.948070	+	0.318060i	$0.103031\pi$
$558$	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	0.0699080	−	0.997553i	$-0.477729\pi$
$569$	−15.8967	−	7.65544i	−0.666424	−	0.320933i	−0.736332	+	0.676621i	$0.763444\pi$
$570$	0.0482454	−	0.211377i	0.00202078	−	0.00885361i
$571$	−26.3470	+	12.6880i	−1.10259	+	0.530978i	−0.894471	−	0.447126i	$-0.852448\pi$
$571$	−26.3470	+	12.6880i	−1.10259	+	0.530978i	−0.208116	+	0.978104i	$0.566733\pi$
$572$	−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	0.990347	+	0.138614i	$0.0442647\pi$
$577$	3.80051	+	16.6511i	0.158217	+	0.693196i	−0.832129	+	0.554582i	$0.812878\pi$
$578$	−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	0.849794	+	0.527115i	$0.176726\pi$
$587$	7.58007	+	33.2104i	0.312863	+	1.37074i	−0.536931	+	0.843626i	$0.680416\pi$
$588$	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	0.998921	−	0.0464494i	$-0.0147906\pi$
$593$	38.6075	+	18.5924i	1.58542	+	0.763499i	0.586501	+	0.809948i	$0.300505\pi$
$594$	−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	−0.994193	−	0.107613i	$-0.965679\pi$
$599$	−1.26691	+	5.55071i	−0.0517646	+	0.226796i	0.942428	+	0.334408i	$0.108536\pi$
$600$	−0.381028	+	0.183494i	−0.0155554	+	0.00749110i
$601$	8.07342	−	3.88796i	0.329322	−	0.158593i	−0.261915	−	0.965091i	$-0.584354\pi$
$601$	8.07342	−	3.88796i	0.329322	−	0.158593i	0.591237	+	0.806498i	$0.298640\pi$
$602$	−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	0.998141	−	0.0609410i	$-0.0194101\pi$
$607$	17.6557	+	22.1395i	0.716621	+	0.898614i	−0.281520	+	0.959555i	$0.590839\pi$
$608$	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	−0.599945	−	0.800041i	$-0.704811\pi$
$613$	7.12340	−	31.2097i	0.287712	−	1.26055i	0.887657	−	0.460506i	$-0.152332\pi$
$614$	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	−0.319962	−	0.947430i	$-0.603670\pi$
$617$	5.49638	−	2.64692i	0.221276	−	0.106561i	0.541238	+	0.840870i	$0.317956\pi$
$618$	1.20395	−	0.579791i	0.0484299	−	0.0233226i
$619$	−0.158208	+	0.693153i	−0.00635890	+	0.0278602i	−0.978008	−	0.208568i	$-0.933120\pi$
$619$	−0.158208	+	0.693153i	−0.00635890	+	0.0278602i	0.971649	+	0.236428i	$0.0759768\pi$
$620$	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	0.941070	+	0.338212i	$0.109822\pi$
$631$	6.02722	+	26.4070i	0.239940	+	1.05125i	−0.701130	+	0.713033i	$0.747321\pi$
$632$	−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	−0.939709	−	0.341976i	$-0.888904\pi$
$641$	−6.11273	−	26.7816i	−0.241438	−	1.05781i	0.698270	−	0.715834i	$-0.253953\pi$
$642$	0.299319	−	1.31140i	0.0118132	−	0.0517570i
$643$	−16.5799	−	20.7905i	−0.653848	−	0.819899i	0.338810	−	0.940855i	$-0.389976\pi$
$643$	−16.5799	−	20.7905i	−0.653848	−	0.819899i	−0.992658	+	0.120956i	$0.961404\pi$
$644$	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	0.0503045	−	0.998734i	$-0.483981\pi$
$647$	21.9390	−	10.5653i	0.862510	−	0.415363i	0.812206	+	0.583371i	$0.198267\pi$
$648$	−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	−0.461371	−	0.887207i	$-0.652642\pi$
$653$	12.9368	−	16.2223i	0.506257	−	0.634826i	0.967628	+	0.252381i	$0.0812137\pi$
$654$	−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	−0.184454	−	0.982841i	$-0.559052\pi$
$659$	12.0386	−	5.79749i	0.468958	−	0.225838i	0.653411	+	0.757003i	$0.273337\pi$
$660$	2.07538	+	9.09284i	0.0807841	+	0.353938i
$661$	21.5768	−	27.0564i	0.839240	−	1.05237i	−0.158643	−	0.987336i	$-0.550712\pi$
$661$	21.5768	−	27.0564i	0.839240	−	1.05237i	0.997883	−	0.0650374i	$-0.0207167\pi$
$662$	−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	−0.105387	−	0.994431i	$-0.533608\pi$
$673$	23.0254	−	28.8729i	0.887562	−	1.11297i	0.992950	−	0.118537i	$-0.0378204\pi$
$674$	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	−0.955310	−	0.295607i	$-0.904478\pi$
$677$	0.875640	−	3.83643i	0.0336536	−	0.147446i	0.988963	+	0.148161i	$0.0473353\pi$
$678$	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	0.365713	−	0.930728i	$-0.380825\pi$
$683$	−3.50044	−	1.68572i	−0.133941	−	0.0645024i	−0.499654	+	0.866225i	$0.666539\pi$
$684$	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	0.864425	−	0.502761i	$-0.167683\pi$
$691$	4.78202	+	5.99646i	0.181917	+	0.228116i	−0.682509	+	0.730877i	$0.739111\pi$
$692$	−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	0.986523	+	0.163621i	$0.0523174\pi$
$701$	24.5309	+	30.7608i	0.926520	+	1.16182i	−0.0600034	+	0.998198i	$0.519111\pi$
$702$	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	−0.328490	−	0.944508i	$-0.606540\pi$
$709$	−33.8628	−	16.3075i	−1.27175	−	0.612440i	−0.943256	+	0.332067i	$0.892254\pi$
$710$	−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	−0.725045	−	0.688702i	$-0.758181\pi$
$719$	2.88863	−	3.62223i	0.107728	−	0.135086i	0.832772	+	0.553616i	$0.186752\pi$
$720$	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	0.841485	−	0.540280i	$-0.181682\pi$
$727$	3.43787	+	4.31095i	0.127503	+	0.159884i	−0.713982	+	0.700164i	$0.753110\pi$
$728$	−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	−0.981837	−	0.189727i	$-0.939240\pi$
$733$	−39.1400	+	18.8488i	−1.44567	+	0.696197i	−0.463831	+	0.885924i	$0.653525\pi$
$734$	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	0.0542802	−	0.998526i	$-0.482714\pi$
$739$	27.6111	−	34.6233i	1.01569	−	1.27364i	0.961412	−	0.275112i	$-0.0887150\pi$
$740$	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	0.915041	−	0.403362i	$-0.132158\pi$
$743$	31.8973	+	15.3609i	1.17020	+	0.563538i	0.255157	+	0.966900i	$0.417873\pi$
$744$	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	0.987309	−	0.158809i	$-0.0507654\pi$
$751$	0.791159	+	3.46629i	0.0288698	+	0.126487i	−0.958440	+	0.285296i	$0.907908\pi$
$752$	−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	−0.984005	−	0.178139i	$-0.942992\pi$
$757$	−4.80769	−	21.0639i	−0.174739	−	0.765580i	0.809267	−	0.587441i	$-0.199865\pi$
$758$	−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	−0.996809	−	0.0798205i	$-0.974565\pi$
$761$	−3.67857	−	16.1169i	−0.133348	−	0.584236i	0.863461	−	0.504415i	$-0.168292\pi$
$762$	−0.716586	+	0.345090i	−0.0259592	+	0.0125013i
$763$	−2.85062	+	1.37278i	−0.103199	+	0.0496981i
$764$	0.282464	−	1.23755i	0.0102192	−	0.0447732i
$765$	10.7023	+	5.15396i	0.386943	+	0.186342i
$766$	−1.95839			−0.0707597
$767$	−18.8712	−	9.08789i	−0.681400	−	0.328145i
$768$	−9.63271	+	12.0790i	−0.347591	+	0.435865i
$769$	−0.126258	+	0.158322i	−0.00455298	+	0.00570925i	−0.784103	−	0.620631i	$-0.786877\pi$
$769$	−0.126258	+	0.158322i	−0.00455298	+	0.00570925i	0.779550	+	0.626340i	$0.215448\pi$
$770$	−0.120578	−	0.0580671i	−0.00434532	−	0.00209259i
$771$	22.7822			0.820480
$772$	−20.3693	−	9.80933i	−0.733107	−	0.353046i
$773$	3.23009	−	14.1519i	0.116178	−	0.509010i	−0.883033	−	0.469310i	$-0.844503\pi$
$773$	3.23009	−	14.1519i	0.116178	−	0.509010i	0.999212	−	0.0397000i	$-0.0126402\pi$
$774$	−0.000632450	0	0.000304572i	−2.27329e−5	0	1.09476e-5i
$775$	12.6113	−	6.07326i	0.453010	−	0.218158i
$776$	0.201285	+	0.881886i	0.00722570	+	0.0316579i
$777$	0.662005	−	0.830127i	0.0237493	−	0.0297807i
$778$	1.10167	+	1.38145i	0.0394967	+	0.0495272i
$779$	1.58786	−	6.95687i	0.0568910	−	0.249256i
$780$	−3.10877	−	13.6204i	−0.111312	−	0.487690i
$781$	−19.4291	−	24.3633i	−0.695228	−	0.871788i
$782$	−1.77366			−0.0634260
$783$	0.0854657	+	5.38449i	0.00305430	+	0.192426i
$784$	−27.2417			−0.972917
$785$	−4.55750	−	5.71492i	−0.162664	−	0.203974i
$786$	−0.310911	−	1.36219i	−0.0110898	−	0.0485878i
$787$	7.58479	−	33.2311i	0.270369	−	1.18456i	−0.639211	−	0.769032i	$-0.720739\pi$
$787$	7.58479	−	33.2311i	0.270369	−	1.18456i	0.909579	−	0.415530i	$-0.136404\pi$
$788$	21.0360	+	26.3783i	0.749377	+	0.939688i
$789$	0.595714	−	0.747002i	0.0212080	−	0.0265940i
$790$	−0.445751	−	1.95296i	−0.0158591	−	0.0694834i
$791$	6.27672	−	3.02271i	0.223174	−	0.107475i
$792$	0.725219	−	0.349247i	0.0257696	−	0.0124100i
$793$	5.04029	−	22.0829i	0.178986	−	0.784188i
$794$	1.10352	+	0.531426i	0.0391624	+	0.0188596i
$795$	7.99628			0.283599
$796$	15.5830	+	7.50440i	0.552326	+	0.265986i
$797$	8.95279	−	11.2264i	0.317124	−	0.397661i	−0.597564	−	0.801821i	$-0.703865\pi$
$797$	8.95279	−	11.2264i	0.317124	−	0.397661i	0.914688	+	0.404160i	$0.132436\pi$
$798$	−0.0240844	+	0.0302009i	−0.000852578	+	0.00106910i
$799$	−32.1381	−	15.4769i	−1.13696	−	0.547533i
$800$	1.26507			0.0447271
$801$	11.0134	+	5.30377i	0.389139	+	0.187399i
$802$	−0.233698	+	1.02390i	−0.00825218	+	0.0361551i
$803$	1.00294	−	0.482992i	0.0353931	−	0.0170444i
$804$	−19.7783	+	9.52473i	−0.697527	+	0.335911i
$805$	0.512070	+	2.24353i	0.0180481	+	0.0790739i
$806$	−2.06907	+	2.59453i	−0.0728797	+	0.0913883i
$807$	−9.44363	−	11.8419i	−0.332431	−	0.416856i
$808$	1.34990	−	5.91430i	0.0474893	−	0.208064i
$809$	6.31920	+	27.6862i	0.222171	+	0.973396i	0.955840	+	0.293888i	$0.0949494\pi$
$809$	6.31920	+	27.6862i	0.222171	+	0.973396i	−0.733669	+	0.679508i	$0.762193\pi$
$810$	−0.100084	−	0.125501i	−0.00351659	−	0.00440967i
$811$	−41.4768			−1.45645			−0.728224	−	0.685339i	$-0.759654\pi$
$811$	−41.4768			−1.45645			−0.728224	+	0.685339i	$0.759654\pi$
$812$	2.92220	+	2.25544i	0.102549	+	0.0791505i
$813$	8.25078			0.289368
$814$	−0.388015	−	0.486555i	−0.0135999	−	0.0170538i
$815$	2.61244	+	11.4458i	0.0915098	+	0.400930i
$816$	−5.42042	+	23.7484i	−0.189753	+	0.831361i
$817$	0.00710892	+	0.00891430i	0.000248709	+	0.000311872i
$818$	1.75021	−	2.19469i	0.0611947	−	0.0767357i
$819$	−0.277897	−	1.21755i	−0.00971052	−	0.0425446i
$820$	18.3134	−	8.81927i	0.639532	−	0.307982i
$821$	40.7646	−	19.6312i	1.42269	−	0.685133i	0.445070	−	0.895496i	$-0.353179\pi$
$821$	40.7646	−	19.6312i	1.42269	−	0.685133i	0.977623	+	0.210363i	$0.0674645\pi$
$822$	0.106421	−	0.466260i	0.00371185	−	0.0162627i
$823$	1.62926	+	0.784611i	0.0567925	+	0.0273498i	0.462064	−	0.886846i	$-0.347109\pi$
$823$	1.62926	+	0.784611i	0.0567925	+	0.0273498i	−0.405272	+	0.914196i	$0.632823\pi$
$824$	−5.33589			−0.185885
$825$	2.78173	+	1.33961i	0.0968474	+	0.0466392i
$826$	−0.102855	+	0.128976i	−0.00357878	+	0.00448765i
$827$	−14.2992	+	17.9306i	−0.497231	+	0.623508i	−0.965602	−	0.260024i	$-0.916270\pi$
$827$	−14.2992	+	17.9306i	−0.497231	+	0.623508i	0.468371	+	0.883532i	$0.344841\pi$
$828$	−6.22427	−	2.99745i	−0.216308	−	0.104169i
$829$	−9.99341			−0.347085			−0.173543	−	0.984826i	$-0.555521\pi$
$829$	−9.99341			−0.347085			−0.173543	+	0.984826i	$0.555521\pi$
$830$	0.416299	+	0.200479i	0.0144499	+	0.00695873i
$831$	3.72348	−	16.3136i	0.129166	−	0.565914i
$832$	25.6314	−	12.3434i	0.888609	−	0.427931i
$833$	−38.1533	+	18.3736i	−1.32193	+	0.636609i
$834$	−0.0289927	−	0.127025i	−0.00100393	−	0.00439852i
$835$	−9.23801	+	11.5841i	−0.319694	+	0.400884i
$836$	−4.06878	−	5.10209i	−0.140722	−	0.176459i
$837$	2.44553	−	10.7146i	0.0845299	−	0.370350i
$838$	−0.455966	−	1.99772i	−0.0157511	−	0.0690100i
$839$	15.0625	+	18.8878i	0.520016	+	0.652080i	0.970612	−	0.240648i	$-0.0773599\pi$
$839$	15.0625	+	18.8878i	0.520016	+	0.652080i	−0.450596	+	0.892728i	$0.648789\pi$
$840$	−0.220448			−0.00760619
$841$	7.34716	+	28.0539i	0.253350	+	0.967375i
$842$	−1.01914			−0.0351218
$843$	13.8065	+	17.3128i	0.475520	+	0.596283i
$844$	5.65534	+	24.7777i	0.194665	+	0.852882i
$845$	−0.0797272	+	0.349308i	−0.00274270	+	0.0120165i
$846$	0.300543	+	0.376869i	0.0103329	+	0.0129570i
$847$	−1.09866	+	1.37767i	−0.0377502	+	0.0473373i
$848$	3.64883	+	15.9866i	0.125301	+	0.548981i
$849$	−15.9108	+	7.66223i	−0.546057	+	0.262967i
$850$	0.587184	−	0.282773i	0.0201402	−	0.00969903i
$851$	−2.38118	+	10.4326i	−0.0816257	+	0.357626i
$852$	−23.0834	−	11.1164i	−0.790825	−	0.380841i
$853$	12.9629			0.443842			0.221921	−	0.975065i	$-0.428767\pi$
$853$	12.9629			0.443842			0.221921	+	0.975065i	$0.428767\pi$
$854$	−0.160731	−	0.0774040i	−0.00550011	−	0.00264871i
$855$	−1.62563	+	2.03848i	−0.0555954	+	0.0697145i
$856$	−3.34890	+	4.19938i	−0.114463	+	0.143532i
$857$	19.3854	+	9.33554i	0.662194	+	0.318896i	0.734621	−	0.678478i	$-0.237360\pi$
$857$	19.3854	+	9.33554i	0.662194	+	0.318896i	−0.0724268	+	0.997374i	$0.523074\pi$
$858$	−0.731983			−0.0249895
$859$	4.15015	+	1.99861i	0.141601	+	0.0681915i	0.503343	−	0.864087i	$-0.332103\pi$
$859$	4.15015	+	1.99861i	0.141601	+	0.0681915i	−0.361741	+	0.932278i	$0.617818\pi$
$860$	−0.00722708	+	0.0316639i	−0.000246441	+	0.00107973i
$861$	1.63706	−	0.788366i	0.0557908	−	0.0268675i
$862$	−0.628997	+	0.302909i	−0.0214237	+	0.0103171i
$863$	4.27980	+	18.7510i	0.145686	+	0.638292i	0.994054	+	0.108886i	$0.0347282\pi$
$863$	4.27980	+	18.7510i	0.145686	+	0.638292i	−0.848368	+	0.529407i	$0.822415\pi$
$864$	0.619296	−	0.776572i	0.0210689	−	0.0264195i
$865$	−18.0454	−	22.6282i	−0.613561	−	0.769382i
$866$	0.171005	−	0.749223i	0.00581099	−	0.0254596i
$867$	4.64314	+	20.3429i	0.157689	+	0.690882i
$868$	−4.69700	−	5.88986i	−0.159427	−	0.199915i
$869$	30.2514			1.02621
$870$	−0.684314	−	0.528175i	−0.0232004	−	0.0179068i
$871$	39.9948			1.35517
$872$	1.90457	+	2.38825i	0.0644967	+	0.0808763i
$873$	0.606191	+	2.65590i	0.0205165	+	0.0898885i
$874$	0.0866297	−	0.379549i	0.00293029	−	0.0128384i
$875$	−2.59690	−	3.25641i	−0.0877912	−	0.110087i
$876$	0.570642	−	0.715562i	0.0192802	−	0.0241766i
$877$	6.20282	+	27.1763i	0.209454	+	0.917679i	0.964931	+	0.262504i	$0.0845482\pi$
$877$	6.20282	+	27.1763i	0.209454	+	0.917679i	−0.755477	+	0.655176i	$0.772595\pi$
$878$	1.30534	−	0.628619i	0.0440532	−	0.0212149i
$879$	20.8526	−	10.0421i	0.703342	−	0.338712i
$880$	4.12201	−	18.0597i	0.138953	−	0.608792i
$881$	−25.0177	−	12.0479i	−0.842869	−	0.405904i	−0.0379434	−	0.999280i	$-0.512081\pi$
$881$	−25.0177	−	12.0479i	−0.842869	−	0.405904i	−0.804926	+	0.593375i	$0.797795\pi$
$882$	0.572255			0.0192688
$883$	0.288502	+	0.138935i	0.00970888	+	0.00467555i	0.438732	−	0.898618i	$-0.355428\pi$
$883$	0.288502	+	0.138935i	0.00970888	+	0.00467555i	−0.429023	+	0.903294i	$0.641142\pi$
$884$	27.7671	−	34.8188i	0.933909	−	1.17108i
$885$	−6.94243	+	8.70553i	−0.233367	+	0.292633i
$886$	2.17250	+	1.04622i	0.0729864	+	0.0351484i
$887$	−24.7909			−0.832397			−0.416198	−	0.909274i	$-0.636638\pi$
$887$	−24.7909			−0.832397			−0.416198	+	0.909274i	$0.636638\pi$
$888$	−0.923589	−	0.444777i	−0.0309936	−	0.0149257i
$889$	−0.731982	+	3.20702i	−0.0245499	+	0.107560i
$890$	−1.76789	+	0.851373i	−0.0592599	+	0.0285381i
$891$	2.18408	−	1.05180i	0.0731694	−	0.0352365i
$892$	8.48817	+	37.1891i	0.284205	+	1.24518i
$893$	4.88163	−	6.12137i	0.163357	−	0.204844i
$894$	0.654903	+	0.821222i	0.0219032	+	0.0274658i
$895$	6.90726	−	30.2627i	0.230884	−	1.01157i
$896$	−0.201890	−	0.884537i	−0.00674467	−	0.0295503i
$897$	7.84752	+	9.84048i	0.262021	+	0.328564i
$898$	1.15751			0.0386266
$899$	−0.939278	−	59.1761i	−0.0313267	−	1.97363i
$900$	2.53847			0.0846157
$901$	15.8928	+	19.9289i	0.529466	+	0.663929i
$902$	−0.236981	−	1.03828i	−0.00789060	−	0.0345710i
$903$	−0.000646038		0.00283048i	−2.14988e−5		9.41924e-5i
$904$	−4.19363	−	5.25864i	−0.139478	−	0.174900i
$905$	−6.82836	+	8.56249i	−0.226982	+	0.284627i
$906$	0.189992	+	0.832410i	0.00631207	+	0.0276550i
$907$	39.6611	−	19.0998i	1.31693	−	0.634198i	0.362316	−	0.932055i	$-0.381986\pi$
$907$	39.6611	−	19.0998i	1.31693	−	0.634198i	0.954611	+	0.297857i	$0.0962718\pi$
$908$	−44.4455	+	21.4038i	−1.47497	+	0.710310i
$909$	4.06537	−	17.8116i	0.134840	−	0.590772i
$910$	0.180617	+	0.0869805i	0.00598739	+	0.00288338i
$911$	58.6374			1.94275			0.971373	−	0.237561i	$-0.0763480\pi$
$911$	58.6374			1.94275			0.971373	+	0.237561i	$0.0763480\pi$
$912$	−4.81723	−	2.31985i	−0.159514	−	0.0768181i
$913$	−4.35059	+	5.45547i	−0.143984	+	0.180550i
$914$	0.0518150	−	0.0649740i	0.00171389	−	0.00214915i
$915$	−10.8489	−	5.22456i	−0.358654	−	0.172719i
$916$	38.7329			1.27977
$917$	−5.20651	−	2.50732i	−0.171934	−	0.0827990i
$918$	0.113865	−	0.498873i	0.00375809	−	0.0164653i
$919$	32.7665	−	15.7795i	1.08087	−	0.520519i	0.193274	−	0.981145i	$-0.438089\pi$
$919$	32.7665	−	15.7795i	1.08087	−	0.520519i	0.887594	+	0.460626i	$0.152375\pi$
$920$	2.00173	−	0.963984i	0.0659952	−	0.0317816i
$921$	−5.11762	−	22.4217i	−0.168631	−	0.738822i
$922$	−0.804846	+	1.00924i	−0.0265062	+	0.0332377i
$923$	29.1034	+	36.4945i	0.957951	+	1.20123i
$924$	0.369759	−	1.62002i	0.0121642	−	0.0532948i
$925$	−0.874954	−	3.83343i	−0.0287683	−	0.126042i
$926$	−1.85764	−	2.32941i	−0.0610459	−	0.0765492i
$927$	−16.0696			−0.527796
$928$	2.24404	−	4.85546i	0.0736643	−	0.159388i
$929$	0.895129			0.0293682			0.0146841	−	0.999892i	$-0.495326\pi$
$929$	0.895129			0.0293682			0.0146841	+	0.999892i	$0.495326\pi$
$930$	1.09993	+	1.37927i	0.0360683	+	0.0452282i
$931$	−2.06832	−	9.06191i	−0.0677865	−	0.296992i
$932$	8.10909	−	35.5282i	0.265622	−	1.16377i
$933$	−2.54428	−	3.19043i	−0.0832960	−	0.104450i
$934$	0.216530	−	0.271520i	0.00708507	−	0.00888440i
$935$	−6.40763	−	28.0736i	−0.209552	−	0.918106i
$936$	−1.08633	+	0.523148i	−0.0355077	+	0.0170996i
$937$	−20.9176	+	10.0734i	−0.683349	+	0.329083i	−0.743148	−	0.669127i	$-0.766668\pi$
$937$	−20.9176	+	10.0734i	−0.683349	+	0.329083i	0.0597994	+	0.998210i	$0.480954\pi$
$938$	0.0700939	−	0.307102i	0.00228865	−	0.0100272i
$939$	25.9052	+	12.4753i	0.845385	+	0.407116i
$940$	22.3025			0.727427
$941$	−23.7548	−	11.4397i	−0.774383	−	0.372923i	0.00458264	−	0.999989i	$-0.498541\pi$
$941$	−23.7548	−	11.4397i	−0.774383	−	0.372923i	−0.778966	+	0.627066i	$0.784256\pi$
$942$	−0.196325	+	0.246184i	−0.00639663	+	0.00802112i
$943$	−11.4176	+	14.3172i	−0.371807	+	0.466231i
$944$	−20.5725	−	9.90719i	−0.669577	−	0.322451i
$945$	−0.663905			−0.0215968
$946$	0.00153315		0.000738326i	4.98470e−5		2.40051e-5i
$947$	−11.3405	+	49.6860i	−0.368517	+	1.61458i	0.362338	+	0.932047i	$0.381979\pi$
$947$	−11.3405	+	49.6860i	−0.368517	+	1.61458i	−0.730855	+	0.682533i	$0.760878\pi$
$948$	22.4090	−	10.7916i	0.727810	−	0.350495i
$949$	−1.50234	+	0.723489i	−0.0487680	+	0.0234854i
$950$	0.0318317	+	0.139464i	0.00103276	+	0.00452481i
$951$	−7.18877	+	9.01443i	−0.233112	+	0.292313i
$952$	−0.438146	−	0.549418i	−0.0142004	−	0.0178067i
$953$	5.59449	−	24.5111i	0.181223	−	0.793991i	−0.799826	−	0.600232i	$-0.795075\pi$
$953$	5.59449	−	24.5111i	0.181223	−	0.793991i	0.981049	−	0.193759i	$-0.0620680\pi$
$954$	−0.0766494	−	0.335823i	−0.00248162	−	0.0108727i
$955$	0.766545	+	0.961218i	0.0248048	+	0.0311043i
$956$	−16.3310			−0.528183
$957$	10.0759	−	8.30025i	0.325707	−	0.268309i
$958$	1.54214			0.0498243
$959$	−1.23326	−	1.54646i	−0.0398241	−	0.0499379i
$960$	−3.36532	−	14.7444i	−0.108615	−	0.475874i
$961$	−19.9785	+	87.5316i	−0.644468	+	2.82360i
$962$	0.581219	+	0.728826i	0.0187393	+	0.0234983i
$963$	−10.0856	+	12.6469i	−0.325003	+	0.407541i
$964$	−3.16765	−	13.8784i	−0.102023	−	0.446992i
$965$	19.7284	−	9.50071i	0.635081	−	0.305839i
$966$	0.0893138	−	0.0430113i	0.00287363	−	0.00138387i
$967$	−11.1729	+	48.9516i	−0.359296	+	1.57418i	0.395657	+	0.918398i	$0.370517\pi$
$967$	−11.1729	+	48.9516i	−0.359296	+	1.57418i	−0.754953	+	0.655779i	$0.772340\pi$
$968$	1.53278	+	0.738147i	0.0492654	+	0.0237250i
$969$	−8.31143			−0.267001
$970$	−0.393989	−	0.189735i	−0.0126502	−	0.00609202i
$971$	−20.2855	+	25.4372i	−0.650991	+	0.816317i	−0.992329	−	0.123623i	$-0.960549\pi$
$971$	−20.2855	+	25.4372i	−0.650991	+	0.816317i	0.341338	+	0.939941i	$0.389120\pi$
$972$	1.24267	−	1.55826i	0.0398586	−	0.0499811i
$973$	−0.485510	−	0.233809i	−0.0155647	−	0.00749558i
$974$	−1.62676			−0.0521247
$975$	−4.16684	−	2.00664i	−0.133446	−	0.0642640i
$976$	5.49468	−	24.0738i	0.175880	−	0.770582i
$977$	29.4287	−	14.1721i	0.941509	−	0.453407i	0.100807	−	0.994906i	$-0.467857\pi$
$977$	29.4287	−	14.1721i	0.941509	−	0.453407i	0.840701	+	0.541499i	$0.182143\pi$
$978$	0.455654	−	0.219431i	0.0145702	−	0.00701664i
$979$	−6.59387	−	28.8897i	−0.210741	−	0.923317i
$980$	16.5080	−	20.7004i	0.527329	−	0.661249i
$981$	5.73581	+	7.19248i	0.183130	+	0.229638i
$982$	0.0442598	−	0.193915i	0.00141239	−	0.00618807i
$983$	−0.398538	−	1.74611i	−0.0127114	−	0.0556922i	0.968174	−	0.250276i	$-0.0805214\pi$
$983$	−0.398538	−	1.74611i	−0.0127114	−	0.0556922i	−0.980886	+	0.194584i	$0.937664\pi$
$984$	−1.09376	−	1.37153i	−0.0348678	−	0.0437228i
$985$	−32.6776			−1.04120
$986$	−0.0437331	−	2.75526i	−0.00139274	−	0.0877453i
$987$	1.99365			0.0634585
$988$	6.09474	+	7.64257i	0.193900	+	0.243142i
$989$	−0.00651100	−	0.0285265i	−0.000207038	−	0.000907091i
$990$	−0.0865893	+	0.379373i	−0.00275199	+	0.0120573i
$991$	17.8799	+	22.4207i	0.567975	+	0.712218i	0.980010	−	0.198950i	$-0.0637533\pi$
$991$	17.8799	+	22.4207i	0.567975	+	0.712218i	−0.412035	+	0.911168i	$0.635182\pi$
$992$	−6.80613	+	8.53462i	−0.216095	+	0.270974i
$993$	2.73785	+	11.9953i	0.0868831	+	0.380660i
$994$	0.331231	−	0.159512i	0.0105060	−	0.00505942i
$995$	−15.0928	+	7.26829i	−0.478473	+	0.230420i
$996$	−1.27661	+	5.59318i	−0.0404508	+	0.177227i
$997$	31.2342	+	15.0416i	0.989198	+	0.476373i	0.857259	−	0.514885i	$-0.172165\pi$
$997$	31.2342	+	15.0416i	0.989198	+	0.476373i	0.131939	+	0.991258i	$0.457880\pi$
$998$	1.44605			0.0457739
$999$	−2.78149	−	1.33950i	−0.0880025	−	0.0423798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.g.b.82.2	yes	18
3.2	odd	2		261.2.k.b.82.2		18
29.9	even	14		2523.2.a.q.1.5		9
29.20	even	7		2523.2.a.p.1.5		9
29.23	even	7	inner	87.2.g.b.52.2	✓	18
87.20	odd	14		7569.2.a.bl.1.5		9
87.23	odd	14		261.2.k.b.226.2		18
87.38	odd	14		7569.2.a.bk.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.b.52.2	✓	18	29.23	even	7	inner
87.2.g.b.82.2	yes	18	1.1	even	1	trivial
261.2.k.b.82.2		18	3.2	odd	2
261.2.k.b.226.2		18	87.23	odd	14
2523.2.a.p.1.5		9	29.20	even	7
2523.2.a.q.1.5		9	29.9	even	14
7569.2.a.bk.1.5		9	87.38	odd	14
7569.2.a.bl.1.5		9	87.20	odd	14

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