LMFDB - Embedded newform 570.2.u.g.481.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			481.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	570.481
Dual form			570.2.u.g.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(-0.766044 - 0.642788i) q^{10} +(1.67365 + 2.89884i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-5.19846 + 1.89209i) q^{13} +(-0.0923963 - 0.524005i) q^{14} +(-0.173648 + 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.50387 - 2.94010i) q^{17} -1.00000 q^{18} +(-0.0320889 + 4.35878i) q^{19} +1.00000 q^{20} +(-0.407604 + 0.342020i) q^{21} +(-3.14543 - 1.14484i) q^{22} +(0.0923963 - 0.524005i) q^{23} +(0.173648 + 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(2.76604 - 4.79093i) q^{26} +(0.500000 + 0.866025i) q^{27} +(0.407604 + 0.342020i) q^{28} +(6.36824 + 5.34359i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-3.93242 + 6.81115i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.581252 + 3.29644i) q^{33} +(-0.794263 + 4.50449i) q^{34} +(-0.500000 - 0.181985i) q^{35} +(0.766044 - 0.642788i) q^{36} +5.02229 q^{37} +(-2.77719 - 3.35965i) q^{38} -5.53209 q^{39} +(-0.766044 + 0.642788i) q^{40} +(-10.2233 - 3.72097i) q^{41} +(0.0923963 - 0.524005i) q^{42} +(-1.66250 - 9.42853i) q^{43} +(3.14543 - 1.14484i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(0.266044 + 0.460802i) q^{46} +(4.28699 + 3.59721i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(3.35844 + 5.81699i) q^{49} +(0.500000 - 0.866025i) q^{50} +(4.29813 - 1.56439i) q^{51} +(0.960637 + 5.44804i) q^{52} +(-0.961981 + 5.45567i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(-2.56418 + 2.15160i) q^{55} -0.532089 q^{56} +(-1.52094 + 4.08494i) q^{57} -8.31315 q^{58} +(9.57192 - 8.03179i) q^{59} +(0.939693 + 0.342020i) q^{60} +(-0.432419 + 2.45237i) q^{61} +(-1.36571 - 7.74535i) q^{62} +(-0.500000 + 0.181985i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.76604 - 4.79093i) q^{65} +(-2.56418 - 2.15160i) q^{66} +(-3.75490 - 3.15074i) q^{67} +(-2.28699 - 3.96118i) q^{68} +(0.266044 - 0.460802i) q^{69} +(0.500000 - 0.181985i) q^{70} +(0.936289 + 5.30996i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(-14.1493 - 5.14992i) q^{73} +(-3.84730 + 3.22826i) q^{74} -1.00000 q^{75} +(4.28699 + 0.788496i) q^{76} -1.78106 q^{77} +(4.23783 - 3.55596i) q^{78} +(7.90420 + 2.87689i) q^{79} +(0.173648 - 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(10.2233 - 3.72097i) q^{82} +(1.66637 - 2.88624i) q^{83} +(0.266044 + 0.460802i) q^{84} +(3.50387 + 2.94010i) q^{85} +(7.33409 + 6.15403i) q^{86} +(4.15657 + 7.19940i) q^{87} +(-1.67365 + 2.89884i) q^{88} +(-9.13816 + 3.32602i) q^{89} +(-0.173648 - 0.984808i) q^{90} +(0.511144 - 2.89884i) q^{91} +(-0.500000 - 0.181985i) q^{92} +(-6.02481 + 5.05542i) q^{93} -5.59627 q^{94} +(-4.29813 + 0.725293i) q^{95} +1.00000 q^{96} +(-5.52481 + 4.63587i) q^{97} +(-6.31180 - 2.29731i) q^{98} +(-0.581252 + 3.29644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^7 + 3 * q^8	$ 6 q + 3 q^{7} + 3 q^{8} + 9 q^{11} + 3 q^{12} - 3 q^{13} + 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} + 12 q^{26} + 3 q^{27} + 6 q^{28} + 33 q^{29} - 3 q^{30} + 6 q^{33} - 15 q^{34} - 3 q^{35} + 18 q^{37} - 6 q^{38} - 24 q^{39} - 6 q^{41} - 3 q^{42} - 15 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 18 q^{47} + 12 q^{49} + 3 q^{50} + 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} + 6 q^{56} - 6 q^{57} - 6 q^{58} - 9 q^{59} + 21 q^{61} - 18 q^{62} - 3 q^{63} - 3 q^{64} - 12 q^{65} + 3 q^{66} - 24 q^{67} - 6 q^{68} - 3 q^{69} + 3 q^{70} - 42 q^{71} - 45 q^{73} - 21 q^{74} - 6 q^{75} + 18 q^{76} + 24 q^{77} + 6 q^{78} + 9 q^{79} + 6 q^{82} - 9 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} + 3 q^{87} - 9 q^{88} - 21 q^{89} - 3 q^{91} - 3 q^{92} - 9 q^{93} - 6 q^{94} - 12 q^{95} + 6 q^{96} - 6 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^7 + 3 * q^8 + 9 * q^11 + 3 * q^12 - 3 * q^13 + 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 + 12 * q^26 + 3 * q^27 + 6 * q^28 + 33 * q^29 - 3 * q^30 + 6 * q^33 - 15 * q^34 - 3 * q^35 + 18 * q^37 - 6 * q^38 - 24 * q^39 - 6 * q^41 - 3 * q^42 - 15 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 18 * q^47 + 12 * q^49 + 3 * q^50 + 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 + 6 * q^56 - 6 * q^57 - 6 * q^58 - 9 * q^59 + 21 * q^61 - 18 * q^62 - 3 * q^63 - 3 * q^64 - 12 * q^65 + 3 * q^66 - 24 * q^67 - 6 * q^68 - 3 * q^69 + 3 * q^70 - 42 * q^71 - 45 * q^73 - 21 * q^74 - 6 * q^75 + 18 * q^76 + 24 * q^77 + 6 * q^78 + 9 * q^79 + 6 * q^82 - 9 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 + 3 * q^87 - 9 * q^88 - 21 * q^89 - 3 * q^91 - 3 * q^92 - 9 * q^93 - 6 * q^94 - 12 * q^95 + 6 * q^96 - 6 * q^97 - 3 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	−0.911914	−	0.410382i	$-0.865395\pi$
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	0.811358	+	0.584549i	$0.198729\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	−0.766044	−	0.642788i	−0.242245	−	0.203267i
$11$	1.67365	+	2.89884i	0.504624	+	0.874034i	0.999986	+	0.00534749i	$0.00170217\pi$
$11$	1.67365	+	2.89884i	0.504624	+	0.874034i	−0.495362	+	0.868687i	$0.664964\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−5.19846	+	1.89209i	−1.44179	+	0.524770i	−0.940287	−	0.340383i	$-0.889443\pi$
$13$	−5.19846	+	1.89209i	−1.44179	+	0.524770i	−0.501507	+	0.865153i	$0.667221\pi$
$14$	−0.0923963	−	0.524005i	−0.0246939	−	0.140046i
$15$	−0.173648	+	0.984808i	−0.0448358	+	0.254276i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.50387	−	2.94010i	0.849813	−	0.713078i	−0.109935	−	0.993939i	$-0.535064\pi$
$17$	3.50387	−	2.94010i	0.849813	−	0.713078i	0.959749	+	0.280861i	$0.0906199\pi$
$18$	−1.00000			−0.235702
$19$	−0.0320889	+	4.35878i	−0.00736170	+	0.999973i
$19$	−0.0320889	+	4.35878i	−0.00736170	+	0.999973i
$20$	1.00000			0.223607
$21$	−0.407604	+	0.342020i	−0.0889464	+	0.0746349i
$22$	−3.14543	−	1.14484i	−0.670608	−	0.244081i
$23$	0.0923963	−	0.524005i	0.0192660	−	0.109263i	−0.973658	−	0.228012i	$-0.926777\pi$
$23$	0.0923963	−	0.524005i	0.0192660	−	0.109263i	0.992924	+	0.118749i	$0.0378885\pi$
$24$	0.173648	+	0.984808i	0.0354458	+	0.201023i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	2.76604	−	4.79093i	0.542466	−	0.939579i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	0.407604	+	0.342020i	0.0770299	+	0.0646357i
$29$	6.36824	+	5.34359i	1.18255	+	0.992279i	0.999959	+	0.00909108i	$0.00289382\pi$
$29$	6.36824	+	5.34359i	1.18255	+	0.992279i	0.182594	+	0.983188i	$0.441551\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−3.93242	+	6.81115i	−0.706283	+	1.22332i	0.259943	+	0.965624i	$0.416296\pi$
$31$	−3.93242	+	6.81115i	−0.706283	+	1.22332i	−0.966226	+	0.257695i	$0.917037\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.581252	+	3.29644i	0.101183	+	0.573837i
$34$	−0.794263	+	4.50449i	−0.136215	+	0.772513i
$35$	−0.500000	−	0.181985i	−0.0845154	−	0.0307611i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	5.02229			0.825659			0.412830	−	0.910808i	$-0.364541\pi$
$37$	5.02229			0.825659			0.412830	+	0.910808i	$0.364541\pi$
$38$	−2.77719	−	3.35965i	−0.450520	−	0.545007i
$39$	−5.53209			−0.885843
$40$	−0.766044	+	0.642788i	−0.121122	+	0.101634i
$41$	−10.2233	−	3.72097i	−1.59661	−	0.581118i	−0.617878	−	0.786274i	$-0.712008\pi$
$41$	−10.2233	−	3.72097i	−1.59661	−	0.581118i	−0.978729	+	0.205156i	$0.934230\pi$
$42$	0.0923963	−	0.524005i	0.0142571	−	0.0808558i
$43$	−1.66250	−	9.42853i	−0.253529	−	1.43784i	−0.799819	−	0.600241i	$-0.795071\pi$
$43$	−1.66250	−	9.42853i	−0.253529	−	1.43784i	0.546290	−	0.837596i	$-0.316040\pi$
$44$	3.14543	−	1.14484i	0.474191	−	0.172592i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	0.266044	+	0.460802i	0.0392261	+	0.0679416i
$47$	4.28699	+	3.59721i	0.625322	+	0.524707i	0.899471	−	0.436980i	$-0.143952\pi$
$47$	4.28699	+	3.59721i	0.625322	+	0.524707i	−0.274150	+	0.961687i	$0.588396\pi$
$48$	−0.766044	−	0.642788i	−0.110569	−	0.0927784i
$49$	3.35844	+	5.81699i	0.479777	+	0.830999i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	4.29813	−	1.56439i	0.601859	−	0.219059i
$52$	0.960637	+	5.44804i	0.133216	+	0.755508i
$53$	−0.961981	+	5.45567i	−0.132138	+	0.749394i	0.844672	+	0.535285i	$0.179796\pi$
$53$	−0.961981	+	5.45567i	−0.132138	+	0.749394i	−0.976810	+	0.214109i	$0.931315\pi$
$54$	−0.939693	−	0.342020i	−0.127876	−	0.0465430i
$55$	−2.56418	+	2.15160i	−0.345754	+	0.290122i
$56$	−0.532089			−0.0711034
$57$	−1.52094	+	4.08494i	−0.201454	+	0.541063i
$58$	−8.31315			−1.09157
$59$	9.57192	−	8.03179i	1.24616	−	1.04565i	0.249141	−	0.968467i	$-0.419852\pi$
$59$	9.57192	−	8.03179i	1.24616	−	1.04565i	0.997017	−	0.0771831i	$-0.0245926\pi$
$60$	0.939693	+	0.342020i	0.121314	+	0.0441546i
$61$	−0.432419	+	2.45237i	−0.0553655	+	0.313994i	−0.999896	−	0.0144306i	$-0.995406\pi$
$61$	−0.432419	+	2.45237i	−0.0553655	+	0.313994i	0.944530	+	0.328424i	$0.106518\pi$
$62$	−1.36571	−	7.74535i	−0.173446	−	0.983661i
$63$	−0.500000	+	0.181985i	−0.0629941	+	0.0229280i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.76604	−	4.79093i	−0.343086	−	0.594242i
$66$	−2.56418	−	2.15160i	−0.315628	−	0.264844i
$67$	−3.75490	−	3.15074i	−0.458734	−	0.384924i	0.383931	−	0.923362i	$-0.374570\pi$
$67$	−3.75490	−	3.15074i	−0.458734	−	0.384924i	−0.842665	+	0.538438i	$0.819015\pi$
$68$	−2.28699	−	3.96118i	−0.277338	−	0.480364i
$69$	0.266044	−	0.460802i	0.0320280	−	0.0554741i
$70$	0.500000	−	0.181985i	0.0597614	−	0.0217514i
$71$	0.936289	+	5.30996i	0.111117	+	0.630176i	0.988600	+	0.150568i	$0.0481102\pi$
$71$	0.936289	+	5.30996i	0.111117	+	0.630176i	−0.877483	+	0.479608i	$0.840779\pi$
$72$	−0.173648	+	0.984808i	−0.0204646	+	0.116061i
$73$	−14.1493	−	5.14992i	−1.65605	−	0.602753i	−0.666316	−	0.745670i	$-0.732130\pi$
$73$	−14.1493	−	5.14992i	−1.65605	−	0.602753i	−0.989735	+	0.142917i	$0.954352\pi$
$74$	−3.84730	+	3.22826i	−0.447239	+	0.375278i
$75$	−1.00000			−0.115470
$76$	4.28699	+	0.788496i	0.491751	+	0.0904467i
$77$	−1.78106			−0.202971
$78$	4.23783	−	3.55596i	0.479839	−	0.402633i
$79$	7.90420	+	2.87689i	0.889292	+	0.323676i	0.745954	−	0.665998i	$-0.231994\pi$
$79$	7.90420	+	2.87689i	0.889292	+	0.323676i	0.143338	+	0.989674i	$0.454216\pi$
$80$	0.173648	−	0.984808i	0.0194145	−	0.110105i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	10.2233	−	3.72097i	1.12897	−	0.410912i
$83$	1.66637	−	2.88624i	0.182908	−	0.316807i	−0.759961	−	0.649968i	$-0.774782\pi$
$83$	1.66637	−	2.88624i	0.182908	−	0.316807i	0.942870	+	0.333162i	$0.108116\pi$
$84$	0.266044	+	0.460802i	0.0290278	+	0.0502777i
$85$	3.50387	+	2.94010i	0.380048	+	0.318898i
$86$	7.33409	+	6.15403i	0.790856	+	0.663607i
$87$	4.15657	+	7.19940i	0.445632	+	0.771856i
$88$	−1.67365	+	2.89884i	−0.178411	+	0.309018i
$89$	−9.13816	+	3.32602i	−0.968643	+	0.352557i	−0.777415	−	0.628989i	$-0.783469\pi$
$89$	−9.13816	+	3.32602i	−0.968643	+	0.352557i	−0.191228	+	0.981546i	$0.561247\pi$
$90$	−0.173648	−	0.984808i	−0.0183041	−	0.103808i
$91$	0.511144	−	2.89884i	0.0535825	−	0.303881i
$92$	−0.500000	−	0.181985i	−0.0521286	−	0.0189733i
$93$	−6.02481	+	5.05542i	−0.624744	+	0.524223i
$94$	−5.59627			−0.577211
$95$	−4.29813	+	0.725293i	−0.440979	+	0.0744135i
$96$	1.00000			0.102062
$97$	−5.52481	+	4.63587i	−0.560960	+	0.470701i	−0.878632	−	0.477499i	$-0.841543\pi$
$97$	−5.52481	+	4.63587i	−0.560960	+	0.470701i	0.317672	+	0.948201i	$0.397099\pi$
$98$	−6.31180	−	2.29731i	−0.637588	−	0.232063i
$99$	−0.581252	+	3.29644i	−0.0584180	+	0.331305i
$100$	0.173648	+	0.984808i	0.0173648	+	0.0984808i
$101$	15.3341	−	5.58115i	1.52580	−	0.555346i	0.563211	−	0.826313i	$-0.309566\pi$
$101$	15.3341	−	5.58115i	1.52580	−	0.555346i	0.962588	+	0.270968i	$0.0873437\pi$
$102$	−2.28699	+	3.96118i	−0.226446	+	0.392215i
$103$	−2.25490	−	3.90560i	−0.222182	−	0.384830i	0.733288	−	0.679918i	$-0.237985\pi$
$103$	−2.25490	−	3.90560i	−0.222182	−	0.384830i	−0.955470	+	0.295087i	$0.904651\pi$
$104$	−4.23783	−	3.55596i	−0.415553	−	0.348690i
$105$	−0.407604	−	0.342020i	−0.0397781	−	0.0333777i
$106$	−2.76991	−	4.79763i	−0.269038	−	0.465987i
$107$	3.15657	−	5.46735i	0.305158	−	0.528548i	−0.672139	−	0.740425i	$-0.734624\pi$
$107$	3.15657	−	5.46735i	0.305158	−	0.528548i	0.977296	+	0.211877i	$0.0679575\pi$
$108$	0.939693	−	0.342020i	0.0904220	−	0.0329109i
$109$	−3.11081	−	17.6423i	−0.297962	−	1.68983i	−0.654914	−	0.755704i	$-0.727295\pi$
$109$	−3.11081	−	17.6423i	−0.297962	−	1.68983i	0.356952	−	0.934123i	$-0.383816\pi$
$110$	0.581252	−	3.29644i	0.0554202	−	0.314304i
$111$	4.71941	+	1.71772i	0.447946	+	0.163039i
$112$	0.407604	−	0.342020i	0.0385149	−	0.0323179i
$113$	12.5817			1.18359			0.591794	−	0.806089i	$-0.298420\pi$
$113$	12.5817			1.18359			0.591794	+	0.806089i	$0.298420\pi$
$114$	−1.46064	−	4.10689i	−0.136801	−	0.384645i
$115$	0.532089			0.0496175
$116$	6.36824	−	5.34359i	0.591276	−	0.496140i
$117$	−5.19846	−	1.89209i	−0.480598	−	0.174923i
$118$	−2.16978	+	12.3054i	−0.199744	+	1.13281i
$119$	0.422618	+	2.39679i	0.0387414	+	0.219713i
$120$	−0.939693	+	0.342020i	−0.0857818	+	0.0312220i
$121$	−0.102196	+	0.177009i	−0.00929059	+	0.0160918i
$122$	−1.24510	−	2.15658i	−0.112726	−	0.195247i
$123$	−8.33409	−	6.99313i	−0.751460	−	0.630550i
$124$	6.02481	+	5.05542i	0.541044	+	0.453990i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	0.266044	−	0.460802i	0.0237011	−	0.0410515i
$127$	15.3478	−	5.58613i	1.36189	−	0.495689i	0.445254	−	0.895404i	$-0.353113\pi$
$127$	15.3478	−	5.58613i	1.36189	−	0.495689i	0.916639	+	0.399715i	$0.130891\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	1.66250	−	9.42853i	0.146375	−	0.830136i
$130$	5.19846	+	1.89209i	0.455935	+	0.165947i
$131$	9.73648	−	8.16988i	0.850680	−	0.713806i	−0.109259	−	0.994013i	$-0.534848\pi$
$131$	9.73648	−	8.16988i	0.850680	−	0.713806i	0.959939	+	0.280208i	$0.0904034\pi$
$132$	3.34730			0.291345
$133$	−2.00000	−	1.17442i	−0.173422	−	0.101835i
$134$	4.90167			0.423440
$135$	−0.766044	+	0.642788i	−0.0659306	+	0.0553223i
$136$	4.29813	+	1.56439i	0.368562	+	0.134146i
$137$	3.80154	−	21.5596i	0.324787	−	1.84196i	−0.186379	−	0.982478i	$-0.559675\pi$
$137$	3.80154	−	21.5596i	0.324787	−	1.84196i	0.511166	−	0.859482i	$-0.329214\pi$
$138$	0.0923963	+	0.524005i	0.00786529	+	0.0446063i
$139$	18.4868	−	6.72864i	1.56803	−	0.570716i	0.595472	−	0.803376i	$-0.296965\pi$
$139$	18.4868	−	6.72864i	1.56803	−	0.570716i	0.972558	+	0.232660i	$0.0747430\pi$
$140$	−0.266044	+	0.460802i	−0.0224849	+	0.0389449i
$141$	2.79813	+	4.84651i	0.235645	+	0.408150i
$142$	−4.13041	−	3.46583i	−0.346617	−	0.290846i
$143$	−14.1853	−	11.9028i	−1.18623	−	0.995366i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.15657	+	7.19940i	−0.345185	+	0.597877i
$146$	14.1493	−	5.14992i	1.17100	−	0.426211i
$147$	1.16637	+	6.61484i	0.0962009	+	0.545583i
$148$	0.872111	−	4.94599i	0.0716871	−	0.406558i
$149$	4.93717	+	1.79698i	0.404468	+	0.147214i	0.536240	−	0.844066i	$-0.319844\pi$
$149$	4.93717	+	1.79698i	0.404468	+	0.147214i	−0.131771	+	0.991280i	$0.542066\pi$
$150$	0.766044	−	0.642788i	0.0625473	−	0.0524834i
$151$	9.36278			0.761932			0.380966	−	0.924589i	$-0.375591\pi$
$151$	9.36278			0.761932			0.380966	+	0.924589i	$0.375591\pi$
$152$	−3.79086	+	2.15160i	−0.307479	+	0.174518i
$153$	4.57398			0.369784
$154$	1.36437	−	1.14484i	0.109944	−	0.0922541i
$155$	−7.39053	−	2.68993i	−0.593622	−	0.216061i
$156$	−0.960637	+	5.44804i	−0.0769125	+	0.436193i
$157$	0.486329	+	2.75811i	0.0388133	+	0.220121i	0.998045	−	0.0624997i	$-0.0199073\pi$
$157$	0.486329	+	2.75811i	0.0388133	+	0.220121i	−0.959232	+	0.282621i	$0.908796\pi$
$158$	−7.90420	+	2.87689i	−0.628824	+	0.228873i
$159$	−2.76991	+	4.79763i	−0.219669	+	0.380477i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	0.216881	+	0.181985i	0.0170927	+	0.0143424i
$162$	−0.766044	−	0.642788i	−0.0601861	−	0.0505022i
$163$	−2.77719	−	4.81023i	−0.217526	−	0.376766i	0.736525	−	0.676410i	$-0.236465\pi$
$163$	−2.77719	−	4.81023i	−0.217526	−	0.376766i	−0.954051	+	0.299644i	$0.903132\pi$
$164$	−5.43969	+	9.42182i	−0.424769	+	0.735721i
$165$	−3.14543	+	1.14484i	−0.244871	+	0.0891259i
$166$	0.578726	+	3.28212i	0.0449178	+	0.254742i
$167$	−1.35591	+	7.68977i	−0.104924	+	0.595053i	0.886327	+	0.463060i	$0.153249\pi$
$167$	−1.35591	+	7.68977i	−0.104924	+	0.595053i	−0.991251	+	0.131992i	$0.957863\pi$
$168$	−0.500000	−	0.181985i	−0.0385758	−	0.0140405i
$169$	13.4855	−	11.3156i	1.03734	−	0.870434i
$170$	−4.57398			−0.350808
$171$	−2.82635	+	3.31839i	−0.216137	+	0.253764i
$172$	−9.57398			−0.730009
$173$	0.195937	−	0.164411i	0.0148968	−	0.0124999i	−0.635309	−	0.772258i	$-0.719127\pi$
$173$	0.195937	−	0.164411i	0.0148968	−	0.0124999i	0.650206	+	0.759758i	$0.274683\pi$
$174$	−7.81180	−	2.84326i	−0.592211	−	0.215547i
$175$	0.0923963	−	0.524005i	0.00698450	−	0.0396111i
$176$	−0.581252	−	3.29644i	−0.0438135	−	0.248479i
$177$	11.7417	−	4.27363i	0.882560	−	0.321226i
$178$	4.86231	−	8.42177i	0.364446	−	0.631238i
$179$	2.12836	+	3.68642i	0.159081	+	0.275536i	0.934537	−	0.355865i	$-0.115814\pi$
$179$	2.12836	+	3.68642i	0.159081	+	0.275536i	−0.775457	+	0.631401i	$0.782480\pi$
$180$	0.766044	+	0.642788i	0.0570976	+	0.0479106i
$181$	−14.4422	−	12.1185i	−1.07348	−	0.900758i	−0.0781183	−	0.996944i	$-0.524891\pi$
$181$	−14.4422	−	12.1185i	−1.07348	−	0.900758i	−0.995363	+	0.0961860i	$0.969336\pi$
$182$	1.47178	+	2.54920i	0.109096	+	0.188959i
$183$	−1.24510	+	2.15658i	−0.0920404	+	0.159419i
$184$	0.500000	−	0.181985i	0.0368605	−	0.0134161i
$185$	0.872111	+	4.94599i	0.0641189	+	0.363636i
$186$	1.36571	−	7.74535i	0.100139	−	0.567917i
$187$	14.3871	+	5.23649i	1.05209	+	0.382930i
$188$	4.28699	−	3.59721i	0.312661	−	0.262354i
$189$	−0.532089			−0.0387038
$190$	2.82635	−	3.31839i	0.205045	−	0.240742i
$191$	2.14796			0.155421			0.0777103	−	0.996976i	$-0.475239\pi$
$191$	2.14796			0.155421			0.0777103	+	0.996976i	$0.475239\pi$
$192$	−0.766044	+	0.642788i	−0.0552845	+	0.0463892i
$193$	−19.7015	−	7.17074i	−1.41814	−	0.516161i	−0.484634	−	0.874717i	$-0.661047\pi$
$193$	−19.7015	−	7.17074i	−1.41814	−	0.516161i	−0.933508	+	0.358556i	$0.883269\pi$
$194$	1.25237	−	7.10257i	0.0899152	−	0.509934i
$195$	−0.960637	−	5.44804i	−0.0687927	−	0.390143i
$196$	6.31180	−	2.29731i	0.450843	−	0.164093i
$197$	−5.37346	+	9.30710i	−0.382843	+	0.663103i	−0.991467	−	0.130355i	$-0.958388\pi$
$197$	−5.37346	+	9.30710i	−0.382843	+	0.663103i	0.608625	+	0.793458i	$0.291722\pi$
$198$	−1.67365	−	2.89884i	−0.118941	−	0.206012i
$199$	7.91013	+	6.63739i	0.560734	+	0.470512i	0.878557	−	0.477638i	$-0.158507\pi$
$199$	7.91013	+	6.63739i	0.560734	+	0.470512i	−0.317822	+	0.948150i	$0.602952\pi$
$200$	−0.766044	−	0.642788i	−0.0541675	−	0.0454519i
$201$	−2.45084	−	4.24497i	−0.172869	−	0.299417i
$202$	−8.15910	+	14.1320i	−0.574072	+	0.994322i
$203$	−4.15657	+	1.51287i	−0.291734	+	0.106183i
$204$	−0.794263	−	4.50449i	−0.0556095	−	0.315377i
$205$	1.88919	−	10.7141i	0.131946	−	0.748305i
$206$	4.23783	+	1.54244i	0.295263	+	0.107467i
$207$	0.407604	−	0.342020i	0.0283304	−	0.0237720i
$208$	5.53209			0.383581
$209$	−12.6891	+	7.20204i	−0.877725	+	0.498176i
$210$	0.532089			0.0367176
$211$	4.69846	−	3.94248i	0.323456	−	0.271411i	−0.466571	−	0.884484i	$-0.654511\pi$
$211$	4.69846	−	3.94248i	0.323456	−	0.271411i	0.790027	+	0.613072i	$0.210066\pi$
$212$	5.20574	+	1.89473i	0.357531	+	0.130131i
$213$	−0.936289	+	5.30996i	−0.0641535	+	0.363832i
$214$	1.09627	+	6.21724i	0.0749392	+	0.425002i
$215$	8.99660	−	3.27449i	0.613563	−	0.223319i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−2.09240	−	3.62414i	−0.142041	−	0.246022i
$218$	13.7233	+	11.5152i	0.929458	+	0.779908i
$219$	−11.5346	−	9.67869i	−0.779437	−	0.654025i
$220$	1.67365	+	2.89884i	0.112837	+	0.195440i
$221$	−12.6518	+	21.9136i	−0.851054	+	1.47407i
$222$	−4.71941	+	1.71772i	−0.316746	+	0.115286i
$223$	1.21079	+	6.86673i	0.0810805	+	0.459830i	0.998134	+	0.0610655i	$0.0194499\pi$
$223$	1.21079	+	6.86673i	0.0810805	+	0.459830i	−0.917053	+	0.398765i	$0.869439\pi$
$224$	−0.0923963	+	0.524005i	−0.00617349	+	0.0350116i
$225$	−0.939693	−	0.342020i	−0.0626462	−	0.0228013i
$226$	−9.63816	+	8.08737i	−0.641121	+	0.537964i
$227$	−2.02229			−0.134224			−0.0671120	−	0.997745i	$-0.521378\pi$
$227$	−2.02229			−0.134224			−0.0671120	+	0.997745i	$0.521378\pi$
$228$	3.75877	+	2.20718i	0.248931	+	0.146174i
$229$	−18.4270			−1.21769			−0.608844	−	0.793290i	$-0.708366\pi$
$229$	−18.4270			−1.21769			−0.608844	+	0.793290i	$0.708366\pi$
$230$	−0.407604	+	0.342020i	−0.0268766	+	0.0225521i
$231$	−1.67365	−	0.609158i	−0.110118	−	0.0400797i
$232$	−1.44356	+	8.18685i	−0.0947746	+	0.537493i
$233$	1.20439	+	6.83045i	0.0789024	+	0.447478i	0.998507	+	0.0546315i	$0.0173984\pi$
$233$	1.20439	+	6.83045i	0.0789024	+	0.447478i	−0.919604	+	0.392846i	$0.871490\pi$
$234$	5.19846	−	1.89209i	0.339834	−	0.123690i
$235$	−2.79813	+	4.84651i	−0.182530	+	0.316151i
$236$	−6.24763	−	10.8212i	−0.406686	−	0.704401i
$237$	6.44356	+	5.40679i	0.418554	+	0.351209i
$238$	−1.86437	−	1.56439i	−0.120849	−	0.101405i
$239$	−11.1951	−	19.3904i	−0.724148	−	1.25426i	−0.959324	−	0.282309i	$-0.908900\pi$
$239$	−11.1951	−	19.3904i	−0.724148	−	1.25426i	0.235175	−	0.971953i	$-0.424434\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−1.05778	+	0.385001i	−0.0681377	+	0.0248001i	−0.375864	−	0.926675i	$-0.622654\pi$
$241$	−1.05778	+	0.385001i	−0.0681377	+	0.0248001i	0.307726	+	0.951475i	$0.400432\pi$
$242$	−0.0354925	−	0.201288i	−0.00228154	−	0.0129393i
$243$	−0.173648	+	0.984808i	−0.0111395	+	0.0631754i
$244$	2.34002	+	0.851698i	0.149805	+	0.0545244i
$245$	−5.14543	+	4.31753i	−0.328729	+	0.275837i
$246$	10.8794			0.693644
$247$	−8.08037	−	22.7197i	−0.514142	−	1.44562i
$248$	−7.86484			−0.499418
$249$	2.55303	−	2.14225i	0.161792	−	0.135760i
$250$	0.939693	+	0.342020i	0.0594314	+	0.0216313i
$251$	−3.93360	+	22.3086i	−0.248287	+	1.40810i	0.564447	+	0.825469i	$0.309089\pi$
$251$	−3.93360	+	22.3086i	−0.248287	+	1.40810i	−0.812734	+	0.582635i	$0.802022\pi$
$252$	0.0923963	+	0.524005i	0.00582042	+	0.0330092i
$253$	1.67365	−	0.609158i	0.105221	−	0.0382974i
$254$	−8.16637	+	14.1446i	−0.512404	+	0.887510i
$255$	2.28699	+	3.96118i	0.143217	+	0.248059i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	6.14930	+	5.15988i	0.383583	+	0.321864i	0.814107	−	0.580715i	$-0.197227\pi$
$257$	6.14930	+	5.15988i	0.383583	+	0.321864i	−0.430524	+	0.902579i	$0.641671\pi$
$258$	4.78699	+	8.29131i	0.298025	+	0.516194i
$259$	−1.33615	+	2.31428i	−0.0830244	+	0.143803i
$260$	−5.19846	+	1.89209i	−0.322395	+	0.117342i
$261$	1.44356	+	8.18685i	0.0893543	+	0.506753i
$262$	−2.20708	+	12.5170i	−0.136354	+	0.773302i
$263$	16.2160	+	5.90214i	0.999922	+	0.363942i	0.789554	−	0.613681i	$-0.210312\pi$
$263$	16.2160	+	5.90214i	0.999922	+	0.363942i	0.210367	+	0.977622i	$0.432534\pi$
$264$	−2.56418	+	2.15160i	−0.157814	+	0.132422i
$265$	−5.53983			−0.340309
$266$	2.28699	−	0.385920i	0.140224	−	0.0236623i
$267$	−9.72462			−0.595137
$268$	−3.75490	+	3.15074i	−0.229367	+	0.192462i
$269$	−18.1951	−	6.62246i	−1.10937	−	0.403779i	−0.278609	−	0.960405i	$-0.589873\pi$
$269$	−18.1951	−	6.62246i	−1.10937	−	0.403779i	−0.830763	+	0.556626i	$0.812096\pi$
$270$	0.173648	−	0.984808i	0.0105679	−	0.0599335i
$271$	−1.94444	−	11.0275i	−0.118116	−	0.669871i	−0.985160	−	0.171639i	$-0.945094\pi$
$271$	−1.94444	−	11.0275i	−0.118116	−	0.669871i	0.867044	−	0.498232i	$-0.166017\pi$
$272$	−4.29813	+	1.56439i	−0.260613	+	0.0948552i
$273$	1.47178	−	2.54920i	0.0890763	−	0.154285i
$274$	10.9461	+	18.9592i	0.661277	+	1.14537i
$275$	−2.56418	−	2.15160i	−0.154626	−	0.129746i
$276$	−0.407604	−	0.342020i	−0.0245349	−	0.0205872i
$277$	−3.08853	−	5.34948i	−0.185572	−	0.321419i	0.758197	−	0.652025i	$-0.226080\pi$
$277$	−3.08853	−	5.34948i	−0.185572	−	0.321419i	−0.943769	+	0.330606i	$0.892747\pi$
$278$	−9.83662	+	17.0375i	−0.589961	+	1.02184i
$279$	−7.39053	+	2.68993i	−0.442459	+	0.161042i
$280$	−0.0923963	−	0.524005i	−0.00552173	−	0.0313153i
$281$	−3.58647	+	20.3399i	−0.213951	+	1.21337i	0.668767	+	0.743472i	$0.266822\pi$
$281$	−3.58647	+	20.3399i	−0.213951	+	1.21337i	−0.882718	+	0.469903i	$0.844289\pi$
$282$	−5.25877	−	1.91404i	−0.313155	−	0.113979i
$283$	1.79813	−	1.50881i	0.106888	−	0.0896896i	−0.587777	−	0.809023i	$-0.699997\pi$
$283$	1.79813	−	1.50881i	0.106888	−	0.0896896i	0.694665	+	0.719333i	$0.255552\pi$
$284$	5.39187			0.319949
$285$	−4.28699	−	0.788496i	−0.253939	−	0.0467065i
$286$	18.5175			1.09497
$287$	4.43448	−	3.72097i	0.261759	−	0.219642i
$288$	0.939693	+	0.342020i	0.0553719	+	0.0201537i
$289$	0.680922	−	3.86170i	0.0400542	−	0.227159i
$290$	−1.44356	−	8.18685i	−0.0847689	−	0.480749i
$291$	−6.77719	+	2.46669i	−0.397286	+	0.144600i
$292$	−7.52869	+	13.0401i	−0.440583	+	0.763112i
$293$	4.74763	+	8.22313i	0.277359	+	0.480400i	0.970728	−	0.240183i	$-0.0772074\pi$
$293$	4.74763	+	8.22313i	0.277359	+	0.480400i	−0.693368	+	0.720583i	$0.743874\pi$
$294$	−5.14543	−	4.31753i	−0.300088	−	0.251803i
$295$	9.57192	+	8.03179i	0.557299	+	0.467629i
$296$	2.51114	+	4.34943i	0.145957	+	0.252805i
$297$	−1.67365	+	2.89884i	−0.0971149	+	0.168208i
$298$	−4.93717	+	1.79698i	−0.286002	+	0.104096i
$299$	0.511144	+	2.89884i	0.0295602	+	0.167644i
$300$	−0.173648	+	0.984808i	−0.0100256	+	0.0568579i
$301$	4.78699	+	1.74232i	0.275917	+	0.100426i
$302$	−7.17230	+	6.01828i	−0.412720	+	0.346313i
$303$	16.3182			0.937456
$304$	1.52094	−	4.08494i	0.0872322	−	0.234287i
$305$	−2.49020			−0.142588
$306$	−3.50387	+	2.94010i	−0.200303	+	0.168074i
$307$	3.62923	+	1.32093i	0.207131	+	0.0753896i	0.443502	−	0.896273i	$-0.353736\pi$
$307$	3.62923	+	1.32093i	0.207131	+	0.0753896i	−0.236371	+	0.971663i	$0.575958\pi$
$308$	−0.309278	+	1.75400i	−0.0176227	+	0.0999435i
$309$	−0.783119	−	4.44129i	−0.0445501	−	0.252656i
$310$	7.39053	−	2.68993i	0.419754	−	0.152778i
$311$	5.42514	−	9.39663i	0.307632	−	0.532834i	−0.670212	−	0.742170i	$-0.733797\pi$
$311$	5.42514	−	9.39663i	0.307632	−	0.532834i	0.977844	+	0.209336i	$0.0671302\pi$
$312$	−2.76604	−	4.79093i	−0.156596	−	0.271233i
$313$	−10.6591	−	8.94405i	−0.602488	−	0.505547i	0.289756	−	0.957100i	$-0.406426\pi$
$313$	−10.6591	−	8.94405i	−0.602488	−	0.505547i	−0.892244	+	0.451553i	$0.850870\pi$
$314$	−2.14543	−	1.80023i	−0.121074	−	0.101593i
$315$	−0.266044	−	0.460802i	−0.0149899	−	0.0259633i
$316$	4.20574	−	7.28455i	0.236591	−	0.409788i
$317$	−5.28611	+	1.92399i	−0.296898	+	0.108062i	−0.486174	−	0.873862i	$-0.661608\pi$
$317$	−5.28611	+	1.92399i	−0.296898	+	0.108062i	0.189277	+	0.981924i	$0.439386\pi$
$318$	−0.961981	−	5.45567i	−0.0539452	−	0.305939i
$319$	−4.83203	+	27.4038i	−0.270542	+	1.53432i
$320$	−0.939693	−	0.342020i	−0.0525304	−	0.0191195i
$321$	4.83615	−	4.05801i	0.269928	−	0.226496i
$322$	−0.283119			−0.0157776
$323$	12.7028	+	15.3669i	0.706803	+	0.855040i
$324$	1.00000			0.0555556
$325$	4.23783	−	3.55596i	0.235072	−	0.197249i
$326$	5.21941	+	1.89971i	0.289076	+	0.105215i
$327$	3.11081	−	17.6423i	0.172028	−	0.975622i
$328$	−1.88919	−	10.7141i	−0.104313	−	0.591587i
$329$	−2.79813	+	1.01844i	−0.154266	+	0.0561483i
$330$	1.67365	−	2.89884i	0.0921313	−	0.159576i
$331$	14.8687	+	25.7534i	0.817258	+	1.41553i	0.907695	+	0.419630i	$0.137840\pi$
$331$	14.8687	+	25.7534i	0.817258	+	1.41553i	−0.0904370	+	0.995902i	$0.528826\pi$
$332$	−2.55303	−	2.14225i	−0.140116	−	0.117571i
$333$	3.84730	+	3.22826i	0.210831	+	0.176908i
$334$	−3.90420	−	6.76227i	−0.213628	−	0.370015i
$335$	2.45084	−	4.24497i	0.133904	−	0.231928i
$336$	0.500000	−	0.181985i	0.0272772	−	0.00992810i
$337$	3.20439	+	18.1730i	0.174554	+	0.989947i	0.938657	+	0.344852i	$0.112071\pi$
$337$	3.20439	+	18.1730i	0.174554	+	0.989947i	−0.764103	+	0.645095i	$0.776818\pi$
$338$	−3.05690	+	17.3366i	−0.166274	+	0.942985i
$339$	11.8229	+	4.30320i	0.642134	+	0.233718i
$340$	3.50387	−	2.94010i	0.190024	−	0.159449i
$341$	−26.3259			−1.42563
$342$	0.0320889	−	4.35878i	0.00173517	−	0.235696i
$343$	−7.29860			−0.394087
$344$	7.33409	−	6.15403i	0.395428	−	0.331803i
$345$	0.500000	+	0.181985i	0.0269191	+	0.00979775i
$346$	−0.0444153	+	0.251892i	−0.00238778	+	0.0135418i
$347$	−2.98767	−	16.9439i	−0.160387	−	0.909598i	−0.953694	−	0.300777i	$-0.902754\pi$
$347$	−2.98767	−	16.9439i	−0.160387	−	0.909598i	0.793308	−	0.608821i	$-0.208357\pi$
$348$	7.81180	−	2.84326i	0.418757	−	0.152415i
$349$	−4.00134	+	6.93053i	−0.214187	+	0.370983i	−0.953021	−	0.302905i	$-0.902044\pi$
$349$	−4.00134	+	6.93053i	−0.214187	+	0.370983i	0.738834	+	0.673888i	$0.235377\pi$
$350$	0.266044	+	0.460802i	0.0142207	+	0.0246309i
$351$	−4.23783	−	3.55596i	−0.226198	−	0.189803i
$352$	2.56418	+	2.15160i	0.136671	+	0.114681i
$353$	10.3773	+	17.9741i	0.552329	+	0.956662i	0.998106	+	0.0615182i	$0.0195942\pi$
$353$	10.3773	+	17.9741i	0.552329	+	0.956662i	−0.445777	+	0.895144i	$0.647072\pi$
$354$	−6.24763	+	10.8212i	−0.332058	+	0.575141i
$355$	−5.06670	+	1.84413i	−0.268913	+	0.0978762i
$356$	1.68866	+	9.57688i	0.0894990	+	0.507574i
$357$	−0.422618	+	2.39679i	−0.0223673	+	0.126851i
$358$	−4.00000	−	1.45588i	−0.211407	−	0.0769457i
$359$	−16.2672	+	13.6498i	−0.858551	+	0.720410i	−0.961655	−	0.274260i	$-0.911567\pi$
$359$	−16.2672	+	13.6498i	−0.858551	+	0.720410i	0.103104	+	0.994671i	$0.467123\pi$
$360$	−1.00000			−0.0527046
$361$	−18.9979	−	0.279737i	−0.999892	−	0.0147230i
$362$	18.8530			0.990891
$363$	−0.156574	+	0.131381i	−0.00821801	+	0.00689573i
$364$	−2.76604	−	1.00676i	−0.144980	−	0.0527684i
$365$	2.61468	−	14.8286i	0.136859	−	0.776165i
$366$	−0.432419	−	2.45237i	−0.0226029	−	0.128187i
$367$	17.6853	−	6.43691i	0.923163	−	0.336004i	0.163667	−	0.986516i	$-0.447668\pi$
$367$	17.6853	−	6.43691i	0.923163	−	0.336004i	0.759496	+	0.650512i	$0.225446\pi$
$368$	−0.266044	+	0.460802i	−0.0138685	+	0.0240210i
$369$	−5.43969	−	9.42182i	−0.283179	−	0.490481i
$370$	−3.84730	−	3.22826i	−0.200011	−	0.167830i
$371$	−2.25806	−	1.89473i	−0.117232	−	0.0983697i
$372$	3.93242	+	6.81115i	0.203886	+	0.353142i
$373$	−13.6334	+	23.6138i	−0.705911	+	1.22267i	0.260451	+	0.965487i	$0.416129\pi$
$373$	−13.6334	+	23.6138i	−0.705911	+	1.22267i	−0.966362	+	0.257187i	$0.917204\pi$
$374$	−14.3871	+	5.23649i	−0.743941	+	0.270772i
$375$	−0.173648	−	0.984808i	−0.00896715	−	0.0508553i
$376$	−0.971782	+	5.51125i	−0.0501158	+	0.284221i
$377$	−43.2156	−	15.7292i	−2.22572	−	0.810094i
$378$	0.407604	−	0.342020i	0.0209649	−	0.0175916i
$379$	35.0925			1.80258			0.901289	−	0.433218i	$-0.142622\pi$
$379$	35.0925			1.80258			0.901289	+	0.433218i	$0.142622\pi$
$380$	−0.0320889	+	4.35878i	−0.00164613	+	0.223601i
$381$	16.3327			0.836752
$382$	−1.64543	+	1.38068i	−0.0841875	+	0.0706417i
$383$	−14.5150	−	5.28303i	−0.741683	−	0.269950i	−0.0565811	−	0.998398i	$-0.518020\pi$
$383$	−14.5150	−	5.28303i	−0.741683	−	0.269950i	−0.685102	+	0.728448i	$0.740242\pi$
$384$	0.173648	−	0.984808i	0.00886145	−	0.0502558i
$385$	−0.309278	−	1.75400i	−0.0157623	−	0.0893922i
$386$	19.7015	−	7.17074i	1.00278	−	0.364981i
$387$	4.78699	−	8.29131i	0.243336	−	0.421471i
$388$	3.60607	+	6.24589i	0.183070	+	0.317087i
$389$	6.10014	+	5.11862i	0.309289	+	0.259524i	0.784198	−	0.620510i	$-0.213075\pi$
$389$	6.10014	+	5.11862i	0.309289	+	0.259524i	−0.474909	+	0.880035i	$0.657519\pi$
$390$	4.23783	+	3.55596i	0.214591	+	0.180063i
$391$	−1.21688	−	2.10770i	−0.0615403	−	0.106591i
$392$	−3.35844	+	5.81699i	−0.169627	+	0.293802i
$393$	11.9436	−	4.34710i	0.602473	−	0.219282i
$394$	−1.86618	−	10.5836i	−0.0940169	−	0.533196i
$395$	−1.46064	+	8.28368i	−0.0734926	+	0.416797i
$396$	3.14543	+	1.14484i	0.158064	+	0.0575305i
$397$	18.3648	−	15.4099i	0.921705	−	0.773402i	−0.0526047	−	0.998615i	$-0.516752\pi$
$397$	18.3648	−	15.4099i	0.921705	−	0.773402i	0.974309	+	0.225213i	$0.0723079\pi$
$398$	−10.3259			−0.517593
$399$	−1.47771	−	1.78763i	−0.0739781	−	0.0894935i
$400$	1.00000			0.0500000
$401$	−1.40554	+	1.17939i	−0.0701895	+	0.0588960i	−0.677207	−	0.735792i	$-0.736810\pi$
$401$	−1.40554	+	1.17939i	−0.0701895	+	0.0588960i	0.607018	+	0.794688i	$0.292366\pi$
$402$	4.60607	+	1.67647i	0.229730	+	0.0836148i
$403$	7.55525	−	42.8480i	0.376354	−	2.13441i
$404$	−2.83363	−	16.0703i	−0.140978	−	0.799527i
$405$	−0.939693	+	0.342020i	−0.0466937	+	0.0169951i
$406$	2.21167	−	3.83072i	0.109763	−	0.190115i
$407$	8.40554	+	14.5588i	0.416647	+	0.721654i
$408$	3.50387	+	2.94010i	0.173467	+	0.145556i
$409$	−12.4035	−	10.4078i	−0.613313	−	0.514631i	0.282381	−	0.959302i	$-0.408876\pi$
$409$	−12.4035	−	10.4078i	−0.613313	−	0.514631i	−0.895694	+	0.444672i	$0.853320\pi$
$410$	5.43969	+	9.42182i	0.268647	+	0.465311i
$411$	10.9461	−	18.9592i	0.539931	−	0.935188i
$412$	−4.23783	+	1.54244i	−0.208783	+	0.0759907i
$413$	1.15451	+	6.54758i	0.0568100	+	0.322185i
$414$	−0.0923963	+	0.524005i	−0.00454103	+	0.0257535i
$415$	3.13176	+	1.13987i	0.153732	+	0.0559539i
$416$	−4.23783	+	3.55596i	−0.207777	+	0.174345i
$417$	19.6732			0.963403
$418$	5.09105	−	13.6735i	0.249011	−	0.668793i
$419$	11.3004			0.552058			0.276029	−	0.961149i	$-0.410981\pi$
$419$	11.3004			0.552058			0.276029	+	0.961149i	$0.410981\pi$
$420$	−0.407604	+	0.342020i	−0.0198890	+	0.0166889i
$421$	−18.9893	−	6.91155i	−0.925483	−	0.336848i	−0.165065	−	0.986283i	$-0.552783\pi$
$421$	−18.9893	−	6.91155i	−0.925483	−	0.336848i	−0.760418	+	0.649434i	$0.775006\pi$
$422$	−1.06506	+	6.04023i	−0.0518461	+	0.294034i
$423$	0.971782	+	5.51125i	0.0472496	+	0.267966i
$424$	−5.20574	+	1.89473i	−0.252813	+	0.0920164i
$425$	−2.28699	+	3.96118i	−0.110935	+	0.192146i
$426$	−2.69594	−	4.66950i	−0.130619	−	0.226238i
$427$	−1.01501	−	0.851698i	−0.0491200	−	0.0412166i
$428$	−4.83615	−	4.05801i	−0.233764	−	0.196151i
$429$	−9.25877	−	16.0367i	−0.447018	−	0.774257i
$430$	−4.78699	+	8.29131i	−0.230849	+	0.399842i
$431$	−11.5030	+	4.18675i	−0.554080	+	0.201669i	−0.603858	−	0.797092i	$-0.706371\pi$
$431$	−11.5030	+	4.18675i	−0.554080	+	0.201669i	0.0497785	+	0.998760i	$0.484148\pi$
$432$	−0.173648	−	0.984808i	−0.00835465	−	0.0473816i
$433$	−4.05350	+	22.9885i	−0.194799	+	1.10476i	0.717906	+	0.696140i	$0.245101\pi$
$433$	−4.05350	+	22.9885i	−0.194799	+	1.10476i	−0.912705	+	0.408619i	$0.866010\pi$
$434$	3.93242	+	1.43128i	0.188762	+	0.0687038i
$435$	−6.36824	+	5.34359i	−0.305334	+	0.256205i
$436$	−17.9145			−0.857947
$437$	2.28106	+	0.419550i	0.109118	+	0.0200698i
$438$	15.0574			0.719469
$439$	21.3726	−	17.9337i	1.02006	−	0.855930i	0.0304227	−	0.999537i	$-0.490315\pi$
$439$	21.3726	−	17.9337i	1.02006	−	0.855930i	0.989635	+	0.143607i	$0.0458702\pi$
$440$	−3.14543	−	1.14484i	−0.149952	−	0.0545782i
$441$	−1.16637	+	6.61484i	−0.0555416	+	0.314992i
$442$	−4.39393	−	24.9192i	−0.208998	−	1.18529i
$443$	−0.897804	+	0.326774i	−0.0426559	+	0.0155255i	−0.363260	−	0.931688i	$-0.618336\pi$
$443$	−0.897804	+	0.326774i	−0.0426559	+	0.0155255i	0.320604	+	0.947213i	$0.396114\pi$
$444$	2.51114	−	4.34943i	0.119174	−	0.206415i
$445$	−4.86231	−	8.42177i	−0.230496	−	0.399230i
$446$	−5.34137	−	4.48194i	−0.252921	−	0.212226i
$447$	4.02481	+	3.37722i	0.190367	+	0.159737i
$448$	−0.266044	−	0.460802i	−0.0125694	−	0.0217709i
$449$	16.7173	−	28.9553i	0.788940	−	1.36648i	−0.137676	−	0.990477i	$-0.543963\pi$
$449$	16.7173	−	28.9553i	0.788940	−	1.36648i	0.926617	−	0.376008i	$-0.122703\pi$
$450$	0.939693	−	0.342020i	0.0442975	−	0.0161230i
$451$	−6.32366	−	35.8633i	−0.297770	−	1.68874i
$452$	2.18479	−	12.3906i	0.102764	−	0.582804i
$453$	8.79813	+	3.20226i	0.413372	+	0.150455i
$454$	1.54916	−	1.29990i	0.0727058	−	0.0610074i
$455$	2.94356			0.137996
$456$	−4.29813	+	0.725293i	−0.201279	+	0.0339650i
$457$	−1.37227			−0.0641922			−0.0320961	−	0.999485i	$-0.510218\pi$
$457$	−1.37227			−0.0641922			−0.0320961	+	0.999485i	$0.510218\pi$
$458$	14.1159	−	11.8446i	0.659591	−	0.553463i
$459$	4.29813	+	1.56439i	0.200620	+	0.0730196i
$460$	0.0923963	−	0.524005i	0.00430800	−	0.0244319i
$461$	−3.28740	−	18.6438i	−0.153109	−	0.868327i	−0.960494	−	0.278301i	$-0.910229\pi$
$461$	−3.28740	−	18.6438i	−0.153109	−	0.868327i	0.807384	−	0.590026i	$-0.200882\pi$
$462$	1.67365	−	0.609158i	0.0778652	−	0.0283406i
$463$	−4.25624	+	7.37203i	−0.197804	+	0.342607i	−0.947816	−	0.318817i	$-0.896714\pi$
$463$	−4.25624	+	7.37203i	−0.197804	+	0.342607i	0.750012	+	0.661424i	$0.230048\pi$
$464$	−4.15657	−	7.19940i	−0.192964	−	0.334224i
$465$	−6.02481	−	5.05542i	−0.279394	−	0.234439i
$466$	−5.31315	−	4.45826i	−0.246127	−	0.206525i
$467$	−11.3353	−	19.6333i	−0.524534	−	0.908519i	−0.999592	−	0.0285650i	$-0.990906\pi$
$467$	−11.3353	−	19.6333i	−0.524534	−	0.908519i	0.475058	−	0.879954i	$-0.342427\pi$
$468$	−2.76604	+	4.79093i	−0.127860	+	0.221461i
$469$	2.45084	−	0.892032i	0.113169	−	0.0411902i
$470$	−0.971782	−	5.51125i	−0.0448249	−	0.254215i
$471$	−0.486329	+	2.75811i	−0.0224089	+	0.127087i
$472$	11.7417	+	4.27363i	0.540455	+	0.196710i
$473$	24.5494	−	20.5994i	1.12878	−	0.947160i
$474$	−8.41147			−0.386352
$475$	−1.46064	−	4.10689i	−0.0670186	−	0.188437i
$476$	2.43376			0.111551
$477$	−4.24376	+	3.56093i	−0.194308	+	0.163044i
$478$	21.0398	+	7.65787i	0.962339	+	0.350263i
$479$	−0.811337	+	4.60132i	−0.0370709	+	0.210240i	−0.997717	−	0.0675362i	$-0.978486\pi$
$479$	−0.811337	+	4.60132i	−0.0370709	+	0.210240i	0.960646	+	0.277776i	$0.0895973\pi$
$480$	0.173648	+	0.984808i	0.00792592	+	0.0449501i
$481$	−26.1082	+	9.50260i	−1.19043	+	0.433281i
$482$	0.562834	−	0.974856i	0.0256364	−	0.0444035i
$483$	0.141559	+	0.245188i	0.00644117	+	0.0111564i
$484$	0.156574	+	0.131381i	0.00711700	+	0.00597187i
$485$	−5.52481	−	4.63587i	−0.250869	−	0.210504i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−13.7083	+	23.7434i	−0.621181	+	1.07592i	0.368085	+	0.929792i	$0.380013\pi$
$487$	−13.7083	+	23.7434i	−0.621181	+	1.07592i	−0.989266	+	0.146125i	$0.953320\pi$
$488$	−2.34002	+	0.851698i	−0.105928	+	0.0385546i
$489$	−0.964508	−	5.46999i	−0.0436165	−	0.247362i
$490$	1.16637	−	6.61484i	0.0526914	−	0.298828i
$491$	−32.2977	−	11.7554i	−1.45758	−	0.530514i	−0.512879	−	0.858461i	$-0.671421\pi$
$491$	−32.2977	−	11.7554i	−1.45758	−	0.530514i	−0.944696	+	0.327946i	$0.893643\pi$
$492$	−8.33409	+	6.99313i	−0.375730	+	0.315275i
$493$	38.0242			1.71252
$494$	20.7939	+	12.2103i	0.935560	+	0.549368i
$495$	−3.34730			−0.150450
$496$	6.02481	−	5.05542i	0.270522	−	0.226995i
$497$	−2.69594	−	0.981241i	−0.120929	−	0.0440147i
$498$	−0.578726	+	3.28212i	−0.0259333	+	0.147075i
$499$	−0.483231	−	2.74054i	−0.0216324	−	0.122683i	0.972079	−	0.234653i	$-0.0753953\pi$
$499$	−0.483231	−	2.74054i	−0.0216324	−	0.122683i	−0.993712	+	0.111969i	$0.964284\pi$
$500$	−0.939693	+	0.342020i	−0.0420243	+	0.0152956i
$501$	−3.90420	+	6.76227i	−0.174427	+	0.302116i
$502$	−11.3264	−	19.6178i	−0.505520	−	0.875586i
$503$	18.9500	+	15.9009i	0.844937	+	0.708986i	0.958669	−	0.284525i	$-0.0918360\pi$
$503$	18.9500	+	15.9009i	0.844937	+	0.708986i	−0.113732	+	0.993512i	$0.536280\pi$
$504$	−0.407604	−	0.342020i	−0.0181561	−	0.0152348i
$505$	8.15910	+	14.1320i	0.363075	+	0.628865i
$506$	−0.890530	+	1.54244i	−0.0395889	+	0.0685699i
$507$	16.5424	−	6.02093i	0.734672	−	0.267399i
$508$	−2.83615	−	16.0846i	−0.125834	−	0.713639i
$509$	−4.34224	+	24.6261i	−0.192467	+	1.09153i	0.723514	+	0.690310i	$0.242526\pi$
$509$	−4.34224	+	24.6261i	−0.192467	+	1.09153i	−0.915981	+	0.401223i	$0.868585\pi$
$510$	−4.29813	−	1.56439i	−0.190325	−	0.0692725i
$511$	6.13744	−	5.14992i	0.271504	−	0.227819i
$512$	−1.00000			−0.0441942
$513$	−3.79086	+	2.15160i	−0.167371	+	0.0949955i
$514$	−8.02734			−0.354071
$515$	3.45471	−	2.89884i	0.152233	−	0.127738i
$516$	−8.99660	−	3.27449i	−0.396053	−	0.144152i
$517$	−3.25284	+	18.4478i	−0.143060	+	0.811332i
$518$	−0.464041	−	2.63171i	−0.0203888	−	0.115631i
$519$	0.240352	−	0.0874810i	0.0105503	−	0.00383999i
$520$	2.76604	−	4.79093i	0.121299	−	0.210096i
$521$	14.5865	+	25.2645i	0.639045	+	1.10686i	0.985643	+	0.168844i	$0.0540035\pi$
$521$	14.5865	+	25.2645i	0.639045	+	1.10686i	−0.346598	+	0.938014i	$0.612663\pi$
$522$	−6.36824	−	5.34359i	−0.278730	−	0.233883i
$523$	−29.7015	−	24.9225i	−1.29875	−	1.08978i	−0.990359	−	0.138526i	$-0.955764\pi$
$523$	−29.7015	−	24.9225i	−1.29875	−	1.08978i	−0.308395	−	0.951258i	$-0.599792\pi$
$524$	−6.35504	−	11.0072i	−0.277621	−	0.480854i
$525$	0.266044	−	0.460802i	0.0116111	−	0.0201111i
$526$	−16.2160	+	5.90214i	−0.707051	+	0.257346i
$527$	6.24675	+	35.4271i	0.272113	+	1.54323i
$528$	0.581252	−	3.29644i	0.0252957	−	0.143459i
$529$	21.3469	+	7.76963i	0.928125	+	0.337810i
$530$	4.24376	−	3.56093i	0.184337	−	0.154677i
$531$	12.4953			0.542248
$532$	−1.50387	+	1.76568i	−0.0652011	+	0.0765519i
$533$	60.1857			2.60693
$534$	7.44949	−	6.25087i	0.322371	−	0.270501i
$535$	5.93242	+	2.15922i	0.256481	+	0.0933514i
$536$	0.851167	−	4.82721i	0.0367648	−	0.208504i
$537$	0.739170	+	4.19204i	0.0318975	+	0.180900i
$538$	18.1951	−	6.62246i	0.784445	−	0.285515i
$539$	−11.2417	+	19.4712i	−0.484214	+	0.838683i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	18.1295	+	15.2125i	0.779450	+	0.654036i	0.943110	−	0.332481i	$-0.107886\pi$
$541$	18.1295	+	15.2125i	0.779450	+	0.654036i	−0.163660	+	0.986517i	$0.552330\pi$
$542$	8.57785	+	7.19767i	0.368450	+	0.309166i
$543$	−9.42649	−	16.3272i	−0.404529	−	0.700665i
$544$	2.28699	−	3.96118i	0.0980538	−	0.169834i
$545$	16.8341	−	6.12711i	0.721093	−	0.262456i
$546$	0.511144	+	2.89884i	0.0218750	+	0.124059i
$547$	3.19418	−	18.1151i	0.136573	−	0.774546i	−0.837178	−	0.546931i	$-0.815796\pi$
$547$	3.19418	−	18.1151i	0.136573	−	0.774546i	0.973751	−	0.227615i	$-0.0730928\pi$
$548$	−20.5719	−	7.48757i	−0.878789	−	0.319853i
$549$	−1.90760	+	1.60067i	−0.0814145	+	0.0683149i
$550$	3.34730			0.142729
$551$	−23.4959	+	27.5863i	−1.00096	+	1.17522i
$552$	0.532089			0.0226472
$553$	−3.42855	+	2.87689i	−0.145797	+	0.122338i
$554$	5.80453	+	2.11268i	0.246611	+	0.0897590i
$555$	−0.872111	+	4.94599i	−0.0370191	+	0.209946i
$556$	−3.41622	−	19.3744i	−0.144880	−	0.821656i
$557$	38.2743	−	13.9307i	1.62173	−	0.590262i	0.638021	−	0.770019i	$-0.279753\pi$
$557$	38.2743	−	13.9307i	1.62173	−	0.590262i	0.983711	+	0.179757i	$0.0575311\pi$
$558$	3.93242	−	6.81115i	0.166473	−	0.288339i
$559$	26.4820	+	45.8683i	1.12007	+	1.94002i
$560$	0.407604	+	0.342020i	0.0172244	+	0.0144530i
$561$	11.7285	+	9.84137i	0.495177	+	0.415503i
$562$	−10.3268	−	17.8866i	−0.435611	−	0.754500i
$563$	7.40554	−	12.8268i	0.312106	−	0.540584i	−0.666712	−	0.745316i	$-0.732299\pi$
$563$	7.40554	−	12.8268i	0.312106	−	0.540584i	0.978818	+	0.204731i	$0.0656321\pi$
$564$	5.25877	−	1.91404i	0.221434	−	0.0805955i
$565$	2.18479	+	12.3906i	0.0919149	+	0.521275i
$566$	−0.407604	+	2.31164i	−0.0171329	+	0.0971653i
$567$	−0.500000	−	0.181985i	−0.0209980	−	0.00764266i
$568$	−4.13041	+	3.46583i	−0.173308	+	0.145423i
$569$	−26.2935			−1.10228			−0.551141	−	0.834412i	$-0.685808\pi$
$569$	−26.2935			−1.10228			−0.551141	+	0.834412i	$0.685808\pi$
$570$	3.79086	−	2.15160i	0.158782	−	0.0901206i
$571$	−33.6682			−1.40897			−0.704485	−	0.709719i	$-0.748822\pi$
$571$	−33.6682			−1.40897			−0.704485	+	0.709719i	$0.748822\pi$
$572$	−14.1853	+	11.9028i	−0.593115	+	0.497683i
$573$	2.01842	+	0.734644i	0.0843206	+	0.0306902i
$574$	−1.00521	+	5.70086i	−0.0419568	+	0.237949i
$575$	0.0923963	+	0.524005i	0.00385319	+	0.0218525i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	1.39827	−	2.42188i	0.0582108	−	0.100824i	−0.835452	−	0.549564i	$-0.814794\pi$
$577$	1.39827	−	2.42188i	0.0582108	−	0.100824i	0.893662	+	0.448740i	$0.148127\pi$
$578$	1.96064	+	3.39592i	0.0815518	+	0.141252i
$579$	−16.0608	−	13.4766i	−0.667463	−	0.560068i
$580$	6.36824	+	5.34359i	0.264427	+	0.221880i
$581$	0.886659	+	1.53574i	0.0367848	+	0.0637132i
$582$	3.60607	−	6.24589i	0.149476	−	0.258901i
$583$	−17.4251	+	6.34223i	−0.721676	+	0.262668i
$584$	−2.61468	−	14.8286i	−0.108196	−	0.613612i
$585$	0.960637	−	5.44804i	0.0397175	−	0.225249i
$586$	−8.92262	−	3.24757i	−0.368590	−	0.134156i
$587$	28.1327	−	23.6061i	1.16116	−	0.974329i	0.161240	−	0.986915i	$-0.448451\pi$
$587$	28.1327	−	23.6061i	1.16116	−	0.974329i	0.999921	+	0.0125859i	$0.00400633\pi$
$588$	6.71688			0.277000
$589$	−29.5621	−	17.3591i	−1.21809	−	0.715270i
$590$	−12.4953			−0.514421
$591$	−8.23261	+	6.90798i	−0.338644	+	0.284156i
$592$	−4.71941	−	1.71772i	−0.193966	−	0.0705980i
$593$	3.81608	−	21.6421i	0.156708	−	0.888734i	−0.800500	−	0.599333i	$-0.795433\pi$
$593$	3.81608	−	21.6421i	0.156708	−	0.888734i	0.957208	−	0.289401i	$-0.0934563\pi$
$594$	−0.581252	−	3.29644i	−0.0238491	−	0.135255i
$595$	−2.28699	+	0.832396i	−0.0937574	+	0.0341249i
$596$	2.62701	−	4.55012i	0.107607	−	0.186380i
$597$	5.16297	+	8.94253i	0.211306	+	0.365993i
$598$	−2.25490	−	1.89209i	−0.0922097	−	0.0773731i
$599$	−13.9370	−	11.6945i	−0.569451	−	0.477826i	0.312013	−	0.950078i	$-0.398997\pi$
$599$	−13.9370	−	11.6945i	−0.569451	−	0.477826i	−0.881464	+	0.472252i	$0.843441\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	2.40420	−	4.16420i	0.0980694	−	0.169861i	−0.812816	−	0.582520i	$-0.802067\pi$
$601$	2.40420	−	4.16420i	0.0980694	−	0.169861i	0.910885	+	0.412659i	$0.135400\pi$
$602$	−4.78699	+	1.74232i	−0.195103	+	0.0710117i
$603$	−0.851167	−	4.82721i	−0.0346622	−	0.196579i
$604$	1.62583	−	9.22054i	0.0661541	−	0.375178i
$605$	−0.192066	−	0.0699065i	−0.00780861	−	0.00284210i
$606$	−12.5005	+	10.4891i	−0.507797	+	0.426092i
$607$	−16.5107			−0.670150			−0.335075	−	0.942191i	$-0.608762\pi$
$607$	−16.5107			−0.670150			−0.335075	+	0.942191i	$0.608762\pi$
$608$	1.46064	+	4.10689i	0.0592367	+	0.166556i
$609$	−4.42333			−0.179243
$610$	1.90760	−	1.60067i	0.0772366	−	0.0648092i
$611$	−29.0920	−	10.5886i	−1.17694	−	0.428370i
$612$	0.794263	−	4.50449i	0.0321062	−	0.182083i
$613$	−0.383971	−	2.17761i	−0.0155084	−	0.0879527i	0.976071	−	0.217451i	$-0.0697743\pi$
$613$	−0.383971	−	2.17761i	−0.0155084	−	0.0879527i	−0.991580	+	0.129499i	$0.958663\pi$
$614$	−3.62923	+	1.32093i	−0.146464	+	0.0533085i
$615$	5.43969	−	9.42182i	0.219350	−	0.379925i
$616$	−0.890530	−	1.54244i	−0.0358805	−	0.0621468i
$617$	7.24304	+	6.07763i	0.291594	+	0.244676i	0.776835	−	0.629704i	$-0.216824\pi$
$617$	7.24304	+	6.07763i	0.291594	+	0.244676i	−0.485241	+	0.874380i	$0.661268\pi$
$618$	3.45471	+	2.89884i	0.138969	+	0.116609i
$619$	20.0253	+	34.6848i	0.804884	+	1.39410i	0.916369	+	0.400334i	$0.131106\pi$
$619$	20.0253	+	34.6848i	0.804884	+	1.39410i	−0.111485	+	0.993766i	$0.535561\pi$
$620$	−3.93242	+	6.81115i	−0.157930	+	0.273542i
$621$	0.500000	−	0.181985i	0.0200643	−	0.00730281i
$622$	1.88413	+	10.6854i	0.0755468	+	0.428447i
$623$	0.898519	−	5.09575i	0.0359984	−	0.204157i
$624$	5.19846	+	1.89209i	0.208105	+	0.0757441i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	13.9145			0.556134
$627$	−14.3871	+	2.42777i	−0.574566	+	0.0969558i
$628$	2.80066			0.111758
$629$	17.5974	−	14.7660i	0.701656	−	0.588759i
$630$	0.500000	+	0.181985i	0.0199205	+	0.00725046i
$631$	1.17823	−	6.68210i	0.0469047	−	0.266010i	−0.952332	−	0.305062i	$-0.901323\pi$
$631$	1.17823	−	6.68210i	0.0469047	−	0.266010i	0.999237	+	0.0390522i	$0.0124339\pi$
$632$	1.46064	+	8.28368i	0.0581010	+	0.329507i
$633$	5.76352	−	2.09775i	0.229079	−	0.0833780i
$634$	2.81268	−	4.87171i	0.111706	−	0.193480i
$635$	8.16637	+	14.1446i	0.324073	+	0.561310i
$636$	4.24376	+	3.56093i	0.168276	+	0.141200i
$637$	−28.4650	−	23.8849i	−1.12782	−	0.946356i
$638$	−13.9133	−	24.0985i	−0.550832	−	0.954069i
$639$	−2.69594	+	4.66950i	−0.106650	+	0.184723i
$640$	0.939693	−	0.342020i	0.0371446	−	0.0135195i
$641$	−0.644086	−	3.65279i	−0.0254398	−	0.144277i	0.969442	−	0.245320i	$-0.0788930\pi$
$641$	−0.644086	−	3.65279i	−0.0254398	−	0.144277i	−0.994882	+	0.101043i	$0.967782\pi$
$642$	−1.09627	+	6.21724i	−0.0432662	+	0.245375i
$643$	12.8623	+	4.68150i	0.507240	+	0.184620i	0.582948	−	0.812510i	$-0.301899\pi$
$643$	12.8623	+	4.68150i	0.507240	+	0.184620i	−0.0757075	+	0.997130i	$0.524122\pi$
$644$	0.216881	−	0.181985i	0.00854633	−	0.00717122i
$645$	9.57398			0.376975
$646$	−19.6086	−	3.60656i	−0.771490	−	0.141898i
$647$	−16.9685			−0.667102			−0.333551	−	0.942732i	$-0.608247\pi$
$647$	−16.9685			−0.667102			−0.333551	+	0.942732i	$0.608247\pi$
$648$	−0.766044	+	0.642788i	−0.0300931	+	0.0252511i
$649$	39.3029	+	14.3051i	1.54278	+	0.561524i
$650$	−0.960637	+	5.44804i	−0.0376793	+	0.213690i
$651$	−0.726682	−	4.12122i	−0.0284809	−	0.161523i
$652$	−5.21941	+	1.89971i	−0.204408	+	0.0743983i
$653$	−14.1206	+	24.4576i	−0.552582	+	0.957101i	0.445505	+	0.895280i	$0.353024\pi$
$653$	−14.1206	+	24.4576i	−0.552582	+	0.957101i	−0.998087	+	0.0618212i	$0.980309\pi$
$654$	8.95723	+	15.5144i	0.350256	+	0.606660i
$655$	9.73648	+	8.16988i	0.380436	+	0.319224i
$656$	8.33409	+	6.99313i	0.325392	+	0.273036i
$657$	−7.52869	−	13.0401i	−0.293722	−	0.508741i
$658$	1.48886	−	2.57877i	0.0580416	−	0.100531i
$659$	9.41622	−	3.42722i	0.366804	−	0.133506i	−0.152041	−	0.988374i	$-0.548585\pi$
$659$	9.41622	−	3.42722i	0.366804	−	0.133506i	0.518845	+	0.854869i	$0.326362\pi$
$660$	0.581252	+	3.29644i	0.0226252	+	0.128314i
$661$	7.10906	−	40.3175i	0.276510	−	1.56817i	−0.457613	−	0.889152i	$-0.651295\pi$
$661$	7.10906	−	40.3175i	0.276510	−	1.56817i	0.734123	−	0.679017i	$-0.237594\pi$
$662$	−27.9440	−	10.1708i	−1.08608	−	0.395299i
$663$	−19.3837	+	16.2649i	−0.752801	+	0.631675i
$664$	3.33275			0.129336
$665$	0.809278	−	2.17355i	0.0313824	−	0.0842867i
$666$	−5.02229			−0.194610
$667$	3.38847	−	2.84326i	0.131202	−	0.110092i
$668$	7.33750	+	2.67063i	0.283896	+	0.103330i
$669$	−1.21079	+	6.86673i	−0.0468118	+	0.265483i
$670$	0.851167	+	4.82721i	0.0328834	+	0.186491i
$671$	−7.83275	+	2.85089i	−0.302380	+	0.110057i
$672$	−0.266044	+	0.460802i	−0.0102629	+	0.0177758i
$673$	20.0710	+	34.7641i	0.773682	+	1.34006i	0.935532	+	0.353241i	$0.114920\pi$
$673$	20.0710	+	34.7641i	0.773682	+	1.34006i	−0.161851	+	0.986815i	$0.551746\pi$
$674$	−14.1361	−	11.8616i	−0.544502	−	0.456891i
$675$	−0.766044	−	0.642788i	−0.0294851	−	0.0247409i
$676$	−8.80200	−	15.2455i	−0.338539	−	0.586366i
$677$	−9.45589	+	16.3781i	−0.363419	+	0.629461i	−0.988521	−	0.151082i	$-0.951724\pi$
$677$	−9.45589	+	16.3781i	−0.363419	+	0.629461i	0.625102	+	0.780543i	$0.285057\pi$
$678$	−11.8229	+	4.30320i	−0.454058	+	0.165263i
$679$	−0.666374	−	3.77920i	−0.0255731	−	0.145032i
$680$	−0.794263	+	4.50449i	−0.0304586	+	0.172739i
$681$	−1.90033	−	0.691663i	−0.0728208	−	0.0265046i
$682$	20.1668	−	16.9220i	0.772228	−	0.647976i
$683$	16.4442			0.629220			0.314610	−	0.949221i	$-0.398126\pi$
$683$	16.4442			0.629220			0.314610	+	0.949221i	$0.398126\pi$
$684$	2.77719	+	3.35965i	0.106188	+	0.128459i
$685$	21.8922			0.836457
$686$	5.59105	−	4.69145i	0.213467	−	0.179120i
$687$	−17.3157	−	6.30239i	−0.660634	−	0.240451i
$688$	−1.66250	+	9.42853i	−0.0633824	+	0.359459i
$689$	−5.32177	−	30.1812i	−0.202743	−	1.14981i
$690$	−0.500000	+	0.181985i	−0.0190347	+	0.00692806i
$691$	−4.26991	+	7.39571i	−0.162435	+	0.281346i	−0.935742	−	0.352687i	$-0.885268\pi$
$691$	−4.26991	+	7.39571i	−0.162435	+	0.281346i	0.773306	+	0.634033i	$0.218602\pi$
$692$	−0.127889	−	0.221510i	−0.00486160	−	0.00842054i
$693$	−1.36437	−	1.14484i	−0.0518281	−	0.0434890i
$694$	13.1800	+	11.0594i	0.500308	+	0.419808i
$695$	9.83662	+	17.0375i	0.373124	+	0.646270i
$696$	−4.15657	+	7.19940i	−0.157555	+	0.272892i
$697$	−46.7610	+	17.0196i	−1.77120	+	0.644664i
$698$	−1.38965	−	7.88111i	−0.0525991	−	0.298304i
$699$	−1.20439	+	6.83045i	−0.0455543	+	0.258351i
$700$	−0.500000	−	0.181985i	−0.0188982	−	0.00687839i
$701$	−6.14614	+	5.15723i	−0.232137	+	0.194786i	−0.751435	−	0.659807i	$-0.770638\pi$
$701$	−6.14614	+	5.15723i	−0.232137	+	0.194786i	0.519298	+	0.854593i	$0.326193\pi$
$702$	5.53209			0.208795
$703$	−0.161160	+	21.8911i	−0.00607825	+	0.825637i
$704$	−3.34730			−0.126156
$705$	−4.28699	+	3.59721i	−0.161457	+	0.135479i
$706$	−19.5030	−	7.09851i	−0.734005	−	0.267156i
$707$	−1.50774	+	8.55082i	−0.0567044	+	0.321587i
$708$	−2.16978	−	12.3054i	−0.0815452	−	0.462466i
$709$	−30.3161	+	11.0342i	−1.13855	+	0.414397i	−0.841388	−	0.540431i	$-0.818261\pi$
$709$	−30.3161	+	11.0342i	−1.13855	+	0.414397i	−0.297158	+	0.954828i	$0.596039\pi$
$710$	2.69594	−	4.66950i	0.101177	−	0.175243i
$711$	4.20574	+	7.28455i	0.157727	+	0.273192i
$712$	−7.44949	−	6.25087i	−0.279182	−	0.234261i
$713$	3.20574	+	2.68993i	0.120056	+	0.100739i
$714$	−1.21688	−	2.10770i	−0.0455406	−	0.0788787i
$715$	9.25877	−	16.0367i	0.346258	−	0.599737i
$716$	4.00000	−	1.45588i	0.149487	−	0.0544088i
$717$	−3.88800	−	22.0500i	−0.145200	−	0.823471i
$718$	3.68748	−	20.9127i	0.137616	−	0.780457i
$719$	−2.11246	−	0.768874i	−0.0787816	−	0.0286742i	0.302329	−	0.953204i	$-0.402236\pi$
$719$	−2.11246	−	0.768874i	−0.0787816	−	0.0286742i	−0.381110	+	0.924530i	$0.624458\pi$
$720$	0.766044	−	0.642788i	0.0285488	−	0.0239553i
$721$	2.39961			0.0893663
$722$	14.7331	−	11.9973i	0.548308	−	0.446495i
$723$	−1.12567			−0.0418640
$724$	−14.4422	+	12.1185i	−0.536741	+	0.450379i
$725$	−7.81180	−	2.84326i	−0.290123	−	0.105596i
$726$	0.0354925	−	0.201288i	0.00131725	−	0.00747049i
$727$	7.01573	+	39.7882i	0.260199	+	1.47566i	0.782366	+	0.622819i	$0.214013\pi$
$727$	7.01573	+	39.7882i	0.260199	+	1.47566i	−0.522167	+	0.852843i	$0.674876\pi$
$728$	2.76604	−	1.00676i	0.102516	−	0.0373129i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	7.52869	+	13.0401i	0.278649	+	0.482634i
$731$	−33.5460	−	28.1484i	−1.24074	−	1.04111i
$732$	1.90760	+	1.60067i	0.0705071	+	0.0591625i
$733$	−6.75537	−	11.7006i	−0.249515	−	0.432173i	0.713876	−	0.700272i	$-0.246938\pi$
$733$	−6.75537	−	11.7006i	−0.249515	−	0.432173i	−0.963391	+	0.268099i	$0.913605\pi$
$734$	−9.41013	+	16.2988i	−0.347334	+	0.601601i
$735$	−6.31180	+	2.29731i	−0.232814	+	0.0847375i
$736$	−0.0923963	−	0.524005i	−0.00340577	−	0.0193151i
$737$	2.84911	−	16.1581i	0.104948	−	0.595191i
$738$	10.2233	+	3.72097i	0.376324	+	0.136971i
$739$	−21.6787	+	18.1906i	−0.797464	+	0.669152i	−0.947581	−	0.319517i	$-0.896479\pi$
$739$	−21.6787	+	18.1906i	−0.797464	+	0.669152i	0.150117	+	0.988668i	$0.452035\pi$
$740$	5.02229			0.184623
$741$	0.177519	−	24.1132i	0.00652131	−	0.885819i
$742$	2.94768			0.108213
$743$	32.7886	−	27.5129i	1.20290	−	1.00935i	0.203356	−	0.979105i	$-0.434815\pi$
$743$	32.7886	−	27.5129i	1.20290	−	1.00935i	0.999542	−	0.0302468i	$-0.00962932\pi$
$744$	−7.39053	−	2.68993i	−0.270950	−	0.0986177i
$745$	−0.912351	+	5.17420i	−0.0334260	+	0.189568i
$746$	−4.73483	−	26.8526i	−0.173355	−	0.983143i
$747$	3.13176	−	1.13987i	0.114585	−	0.0417056i
$748$	7.65523	−	13.2592i	0.279903	−	0.484806i
$749$	1.67958	+	2.90911i	0.0613704	+	0.106297i
$750$	0.766044	+	0.642788i	0.0279720	+	0.0234713i
$751$	22.5786	+	18.9457i	0.823903	+	0.691337i	0.953883	−	0.300180i	$-0.0970466\pi$
$751$	22.5786	+	18.9457i	0.823903	+	0.691337i	−0.129979	+	0.991517i	$0.541491\pi$
$752$	−2.79813	−	4.84651i	−0.102037	−	0.176734i
$753$	−11.3264	+	19.6178i	−0.412755	+	0.714913i
$754$	43.2156	−	15.7292i	1.57382	−	0.572823i
$755$	1.62583	+	9.22054i	0.0591700	+	0.335570i
$756$	−0.0923963	+	0.524005i	−0.00336042	+	0.0190579i
$757$	30.5308	+	11.1123i	1.10966	+	0.403884i	0.830869	−	0.556468i	$-0.187844\pi$
$757$	30.5308	+	11.1123i	1.10966	+	0.403884i	0.278792	+	0.960352i	$0.410066\pi$
$758$	−26.8824	+	22.5570i	−0.976412	+	0.819307i
$759$	1.78106			0.0646484
$760$	−2.77719	−	3.35965i	−0.100739	−	0.121867i
$761$	35.0692			1.27126			0.635629	−	0.771994i	$-0.280741\pi$
$761$	35.0692			1.27126			0.635629	+	0.771994i	$0.280741\pi$
$762$	−12.5116	+	10.4985i	−0.453248	+	0.380320i
$763$	8.95723	+	3.26017i	0.324274	+	0.118026i
$764$	0.372989	−	2.11532i	0.0134943	−	0.0765297i
$765$	0.794263	+	4.50449i	0.0287166	+	0.162860i
$766$	14.5150	−	5.28303i	0.524449	−	0.190884i
$767$	−34.5624	+	59.8639i	−1.24798	+	2.16156i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−26.6083	−	22.3271i	−0.959521	−	0.805134i	0.0213537	−	0.999772i	$-0.493202\pi$
$769$	−26.6083	−	22.3271i	−0.959521	−	0.805134i	−0.980875	+	0.194638i	$0.937647\pi$
$770$	1.36437	+	1.14484i	0.0491685	+	0.0412573i
$771$	4.01367	+	6.95188i	0.144549	+	0.250366i
$772$	−10.4829	+	18.1570i	−0.377289	+	0.653483i
$773$	−1.74257	+	0.634245i	−0.0626760	+	0.0228122i	−0.373168	−	0.927764i	$-0.621728\pi$
$773$	−1.74257	+	0.634245i	−0.0626760	+	0.0228122i	0.310492	+	0.950576i	$0.399506\pi$
$774$	1.66250	+	9.42853i	0.0597575	+	0.338901i
$775$	1.36571	−	7.74535i	0.0490579	−	0.278221i
$776$	−6.77719	−	2.46669i	−0.243287	−	0.0885492i
$777$	−2.04710	+	1.71772i	−0.0734394	+	0.0616230i
$778$	−7.96316			−0.285493
$779$	16.5469	−	44.4416i	0.592856	−	1.59229i
$780$	−5.53209			−0.198081
$781$	−13.8257	+	11.6012i	−0.494723	+	0.415122i
$782$	2.28699	+	0.832396i	0.0817826	+	0.0297664i
$783$	−1.44356	+	8.18685i	−0.0515887	+	0.292574i
$784$	−1.16637	−	6.61484i	−0.0416562	−	0.236244i
$785$	−2.63176	+	0.957882i	−0.0939315	+	0.0341883i
$786$	−6.35504	+	11.0072i	−0.226677	+	0.392616i
$787$	−8.85117	−	15.3307i	−0.315510	−	0.546479i	0.664036	−	0.747701i	$-0.268842\pi$
$787$	−8.85117	−	15.3307i	−0.315510	−	0.546479i	−0.979546	+	0.201221i	$0.935509\pi$
$788$	8.23261	+	6.90798i	0.293275	+	0.246087i
$789$	13.2194	+	11.0924i	0.470623	+	0.394900i
$790$	−4.20574	−	7.28455i	−0.149633	−	0.259173i
$791$	−3.34730	+	5.79769i	−0.119016	+	0.206142i
$792$	−3.14543	+	1.14484i	−0.111768	+	0.0406802i
$793$	−2.39218	−	13.5667i	−0.0849487	−	0.481768i
$794$	−4.16297	+	23.6094i	−0.147738	+	0.837866i
$795$	−5.20574	−	1.89473i	−0.184628	−	0.0671993i
$796$	7.91013	−	6.63739i	0.280367	−	0.235256i
$797$	31.8443			1.12798			0.563992	−	0.825781i	$-0.309265\pi$
$797$	31.8443			1.12798			0.563992	+	0.825781i	$0.309265\pi$
$798$	2.28106	+	0.419550i	0.0807486	+	0.0148519i
$799$	25.5972			0.905564
$800$	−0.766044	+	0.642788i	−0.0270838	+	0.0227260i
$801$	−9.13816	−	3.32602i	−0.322881	−	0.117519i
$802$	0.318611	−	1.80693i	0.0112505	−	0.0638050i
$803$	−8.75213	−	49.6358i	−0.308856	−	1.75161i
$804$	−4.60607	+	1.67647i	−0.162443	+	0.0591246i
$805$	−0.141559	+	0.245188i	−0.00498931	+	0.00864174i
$806$	21.7545	+	37.6799i	0.766269	+	1.32722i
$807$	−14.8327	−	12.4462i	−0.522137	−	0.438125i
$808$	12.5005	+	10.4891i	0.439765	+	0.369007i
$809$	−12.5209	−	21.6869i	−0.440213	−	0.762471i	0.557492	−	0.830182i	$-0.311764\pi$
$809$	−12.5209	−	21.6869i	−0.440213	−	0.762471i	−0.997705	+	0.0677111i	$0.978430\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−8.75150	+	3.18528i	−0.307307	+	0.111850i	−0.491070	−	0.871120i	$-0.663394\pi$
$811$	−8.75150	+	3.18528i	−0.307307	+	0.111850i	0.183764	+	0.982970i	$0.441172\pi$
$812$	0.768104	+	4.35613i	0.0269552	+	0.152870i
$813$	1.94444	−	11.0275i	0.0681945	−	0.386750i
$814$	−15.7973	−	5.74973i	−0.553694	−	0.201528i
$815$	4.25490	−	3.57029i	0.149043	−	0.125062i
$816$	−4.57398			−0.160121
$817$	41.1502	−	6.94394i	1.43966	−	0.242938i
$818$	16.1916			0.566126
$819$	2.25490	−	1.89209i	0.0787926	−	0.0661148i
$820$	−10.2233	−	3.72097i	−0.357012	−	0.129942i
$821$	6.55257	−	37.1615i	0.228686	−	1.29694i	−0.626825	−	0.779160i	$-0.715646\pi$
$821$	6.55257	−	37.1615i	0.228686	−	1.29694i	0.855511	−	0.517784i	$-0.173243\pi$
$822$	3.80154	+	21.5596i	0.132594	+	0.751977i
$823$	−4.24288	+	1.54428i	−0.147897	+	0.0538303i	−0.414908	−	0.909863i	$-0.636186\pi$
$823$	−4.24288	+	1.54428i	−0.147897	+	0.0538303i	0.267011	+	0.963694i	$0.413964\pi$
$824$	2.25490	−	3.90560i	0.0785532	−	0.136058i
$825$	−1.67365	−	2.89884i	−0.0582690	−	0.100925i
$826$	−5.09311	−	4.27363i	−0.177212	−	0.148699i
$827$	18.4531	+	15.4840i	0.641678	+	0.538431i	0.904533	−	0.426404i	$-0.140220\pi$
$827$	18.4531	+	15.4840i	0.641678	+	0.538431i	−0.262855	+	0.964835i	$0.584664\pi$
$828$	−0.266044	−	0.460802i	−0.00924568	−	0.0160140i
$829$	−3.24392	+	5.61863i	−0.112666	+	0.195143i	−0.916844	−	0.399245i	$-0.869272\pi$
$829$	−3.24392	+	5.61863i	−0.112666	+	0.195143i	0.804178	+	0.594388i	$0.202606\pi$
$830$	−3.13176	+	1.13987i	−0.108705	+	0.0395654i
$831$	−1.07263	−	6.08321i	−0.0372093	−	0.211024i
$832$	0.960637	−	5.44804i	0.0333041	−	0.188877i
$833$	28.8701	+	10.5078i	1.00029	+	0.364075i
$834$	−15.0706	+	12.6457i	−0.521851	+	0.437885i
$835$	−7.80840			−0.270221
$836$	4.88919	+	13.7470i	0.169096	+	0.475449i
$837$	−7.86484			−0.271849
$838$	−8.65657	+	7.26373i	−0.299036	+	0.250921i
$839$	21.3290	+	7.76314i	0.736360	+	0.268013i	0.682855	−	0.730554i	$-0.260738\pi$
$839$	21.3290	+	7.76314i	0.736360	+	0.268013i	0.0535057	+	0.998568i	$0.482960\pi$
$840$	0.0923963	−	0.524005i	0.00318797	−	0.0180799i
$841$	6.96476	+	39.4991i	0.240164	+	1.36204i
$842$	18.9893	−	6.91155i	0.654415	−	0.238188i
$843$	−10.3268	+	17.8866i	−0.355675	+	0.616046i
$844$	−3.06670	−	5.31169i	−0.105560	−	0.182836i
$845$	13.4855	+	11.3156i	0.463914	+	0.389270i
$846$	−4.28699	−	3.59721i	−0.147390	−	0.123675i
$847$	−0.0543776	−	0.0941848i	−0.00186844	−	0.00323623i
$848$	2.76991	−	4.79763i	0.0951193	−	0.164751i
$849$	2.20574	−	0.802823i	0.0757007	−	0.0275528i
$850$	−0.794263	−	4.50449i	−0.0272430	−	0.154503i
$851$	0.464041	−	2.63171i	0.0159071	−	0.0902137i
$852$	5.06670	+	1.84413i	0.173582	+	0.0631788i
$853$	−18.5724	+	15.5841i	−0.635906	+	0.533589i	−0.902758	−	0.430149i	$-0.858461\pi$
$853$	−18.5724	+	15.5841i	−0.635906	+	0.533589i	0.266852	+	0.963738i	$0.414017\pi$
$854$	1.32501			0.0453408
$855$	−3.75877	−	2.20718i	−0.128547	−	0.0754840i
$856$	6.31315			0.215779
$857$	−17.6958	+	14.8485i	−0.604476	+	0.507216i	−0.892881	−	0.450293i	$-0.851320\pi$
$857$	−17.6958	+	14.8485i	−0.604476	+	0.507216i	0.288405	+	0.957509i	$0.406875\pi$
$858$	17.4008	+	6.33337i	0.594053	+	0.216218i
$859$	−5.51296	+	31.2655i	−0.188100	+	1.06677i	0.733808	+	0.679357i	$0.237741\pi$
$859$	−5.51296	+	31.2655i	−0.188100	+	1.06677i	−0.921908	+	0.387409i	$0.873370\pi$
$860$	−1.66250	−	9.42853i	−0.0566909	−	0.321510i
$861$	5.43969	−	1.97989i	0.185384	−	0.0674743i
$862$	6.12061	−	10.6012i	0.208469	−	0.361079i
$863$	−17.5594	−	30.4138i	−0.597730	−	1.03530i	−0.993155	−	0.116801i	$-0.962736\pi$
$863$	−17.5594	−	30.4138i	−0.597730	−	1.03530i	0.395425	−	0.918498i	$-0.370597\pi$
$864$	0.766044	+	0.642788i	0.0260614	+	0.0218681i
$865$	0.195937	+	0.164411i	0.00666205	+	0.00559013i
$866$	−11.6716	−	20.2158i	−0.396617	−	0.686960i
$867$	1.96064	−	3.39592i	0.0665867	−	0.115332i
$868$	−3.93242	+	1.43128i	−0.133475	+	0.0485809i
$869$	4.88919	+	27.7279i	0.165854	+	0.940606i
$870$	1.44356	−	8.18685i	0.0489414	−	0.277560i
$871$	25.4812	+	9.27439i	0.863397	+	0.314251i
$872$	13.7233	−	11.5152i	0.464729	−	0.389954i
$873$	−7.21213			−0.244094
$874$	−2.01707	+	1.14484i	−0.0682286	+	0.0387249i
$875$	0.532089			0.0179879
$876$	−11.5346	+	9.67869i	−0.389719	+	0.327013i
$877$	−49.0176	−	17.8409i	−1.65521	−	0.602446i	−0.665608	−	0.746302i	$-0.731828\pi$
$877$	−49.0176	−	17.8409i	−1.65521	−	0.602446i	−0.989599	+	0.143856i	$0.954050\pi$
$878$	−4.84477	+	27.4761i	−0.163503	+	0.927272i
$879$	1.64883	+	9.35100i	0.0556138	+	0.315401i
$880$	3.14543	−	1.14484i	0.106032	−	0.0385926i
$881$	19.6557	−	34.0447i	0.662217	−	1.14699i	−0.317815	−	0.948153i	$-0.602949\pi$
$881$	19.6557	−	34.0447i	0.662217	−	1.14699i	0.980032	−	0.198841i	$-0.0637177\pi$
$882$	−3.35844	−	5.81699i	−0.113085	−	0.195868i
$883$	18.5503	+	15.5656i	0.624269	+	0.523824i	0.899142	−	0.437657i	$-0.144191\pi$
$883$	18.5503	+	15.5656i	0.624269	+	0.523824i	−0.274873	+	0.961480i	$0.588636\pi$
$884$	19.3837	+	16.2649i	0.651945	+	0.547047i
$885$	6.24763	+	10.8212i	0.210012	+	0.363751i
$886$	0.477711	−	0.827420i	0.0160490	−	0.0277977i
$887$	−40.3315	+	14.6795i	−1.35420	+	0.492888i	−0.914255	−	0.405138i	$-0.867223\pi$
$887$	−40.3315	+	14.6795i	−1.35420	+	0.492888i	−0.439942	+	0.898026i	$0.645001\pi$
$888$	0.872111	+	4.94599i	0.0292661	+	0.165977i
$889$	−1.50908	+	8.55845i	−0.0506131	+	0.287041i
$890$	9.13816	+	3.32602i	0.306312	+	0.111488i
$891$	−2.56418	+	2.15160i	−0.0859032	+	0.0720813i
$892$	6.97266			0.233462
$893$	−15.8170	+	18.5706i	−0.529296	+	0.621442i
$894$	−5.25402			−0.175721
$895$	−3.26083	+	2.73616i	−0.108998	+	0.0914598i
$896$	0.500000	+	0.181985i	0.0167038	+	0.00607970i
$897$	−0.511144	+	2.89884i	−0.0170666	+	0.0967896i
$898$	5.80587	+	32.9267i	0.193745	+	1.09878i
$899$	−61.4386	+	22.3618i	−2.04909	+	0.745808i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	12.6695	+	21.9443i	0.422083	+	0.731070i
$902$	27.8967	+	23.4081i	0.928858	+	0.779404i
$903$	3.90239	+	3.27449i	0.129863	+	0.108968i
$904$	6.29086	+	10.8961i	0.209231	+	0.362398i
$905$	9.42649	−	16.3272i	0.313347	−	0.542733i
$906$	−8.79813	+	3.20226i	−0.292298	+	0.106388i
$907$	2.15776	+	12.2372i	0.0716471	+	0.406331i	0.999447	+	0.0332527i	$0.0105866\pi$
$907$	2.15776	+	12.2372i	0.0716471	+	0.406331i	−0.927800	+	0.373078i	$0.878302\pi$
$908$	−0.351167	+	1.99157i	−0.0116539	+	0.0660924i
$909$	15.3341	+	5.58115i	0.508600	+	0.185115i
$910$	−2.25490	+	1.89209i	−0.0747492	+	0.0627220i
$911$	−0.0472658			−0.00156598			−0.000782992	−	1.00000i	$-0.500249\pi$
$911$	−0.0472658			−0.00156598			−0.000782992		1.00000i	$0.500249\pi$
$912$	2.82635	−	3.31839i	0.0935899	−	0.109883i
$913$	11.1557			0.369200
$914$	1.05122	−	0.882080i	0.0347713	−	0.0291766i
$915$	−2.34002	−	0.851698i	−0.0773588	−	0.0281563i
$916$	−3.19981	+	18.1470i	−0.105725	+	0.599594i
$917$	1.17436	+	6.66015i	0.0387809	+	0.219937i
$918$	−4.29813	+	1.56439i	−0.141860	+	0.0516326i
$919$	−12.5346	+	21.7106i	−0.413479	+	0.716166i	−0.995267	−	0.0971737i	$-0.969020\pi$
$919$	−12.5346	+	21.7106i	−0.413479	+	0.716166i	0.581789	+	0.813340i	$0.302353\pi$
$920$	0.266044	+	0.460802i	0.00877123	+	0.0151922i
$921$	2.95858	+	2.48254i	0.0974885	+	0.0818025i
$922$	14.5023	+	12.1689i	0.477607	+	0.400760i
$923$	−14.9142	−	25.8321i	−0.490906	−	0.850274i
$924$	−0.890530	+	1.54244i	−0.0292963	+	0.0507426i
$925$	−4.71941	+	1.71772i	−0.155173	+	0.0564784i
$926$	−1.47818	−	8.38316i	−0.0485759	−	0.275488i
$927$	0.783119	−	4.44129i	0.0257210	−	0.145871i
$928$	7.81180	+	2.84326i	0.256435	+	0.0933347i
$929$	22.5815	−	18.9481i	0.740874	−	0.621667i	−0.192198	−	0.981356i	$-0.561562\pi$
$929$	22.5815	−	18.9481i	0.740874	−	0.621667i	0.933072	+	0.359689i	$0.117117\pi$
$930$	7.86484			0.257898
$931$	−25.4628	+	14.4520i	−0.834508	+	0.473647i
$932$	6.93582			0.227190
$933$	8.31180	−	6.97443i	0.272116	−	0.228333i
$934$	21.3033	+	7.75378i	0.697067	+	0.253712i
$935$	−2.65863	+	15.0779i	−0.0869466	+	0.493099i
$936$	−0.960637	−	5.44804i	−0.0313994	−	0.178075i
$937$	−32.3987	+	11.7922i	−1.05842	+	0.385234i	−0.811835	−	0.583887i	$-0.801531\pi$
$937$	−32.3987	+	11.7922i	−1.05842	+	0.385234i	−0.246586	+	0.969121i	$0.579309\pi$
$938$	−1.30406	+	2.25870i	−0.0425792	+	0.0737493i
$939$	−6.95723	−	12.0503i	−0.227041	−	0.393246i
$940$	4.28699	+	3.59721i	0.139826	+	0.117328i
$941$	−18.6045	−	15.6110i	−0.606489	−	0.508904i	0.287035	−	0.957920i	$-0.407330\pi$
$941$	−18.6045	−	15.6110i	−0.606489	−	0.508904i	−0.893524	+	0.449016i	$0.851775\pi$
$942$	−1.40033	−	2.42544i	−0.0456252	−	0.0790252i
$943$	−2.89440	+	5.01325i	−0.0942546	+	0.163254i
$944$	−11.7417	+	4.27363i	−0.382160	+	0.139095i
$945$	−0.0923963	−	0.524005i	−0.00300565	−	0.0170459i
$946$	−5.56489	+	31.5601i	−0.180930	+	1.02611i
$947$	−16.5761	−	6.03320i	−0.538651	−	0.196053i	0.0583462	−	0.998296i	$-0.481417\pi$
$947$	−16.5761	−	6.03320i	−0.538651	−	0.196053i	−0.596997	+	0.802244i	$0.703640\pi$
$948$	6.44356	−	5.40679i	0.209277	−	0.175604i
$949$	83.2987			2.70399
$950$	3.75877	+	2.20718i	0.121951	+	0.0716104i
$951$	−5.62536			−0.182415
$952$	−1.86437	+	1.56439i	−0.0604246	+	0.0507023i
$953$	15.7925	+	5.74800i	0.511570	+	0.186196i	0.584890	−	0.811112i	$-0.301138\pi$
$953$	15.7925	+	5.74800i	0.511570	+	0.186196i	−0.0733209	+	0.997308i	$0.523360\pi$
$954$	0.961981	−	5.45567i	0.0311453	−	0.176634i
$955$	0.372989	+	2.11532i	0.0120696	+	0.0684503i
$956$	−21.0398	+	7.65787i	−0.680477	+	0.247673i
$957$	−13.9133	+	24.0985i	−0.449753	+	0.778994i
$958$	−2.33615	−	4.04633i	−0.0754776	−	0.130731i
$959$	8.92333	+	7.48757i	0.288149	+	0.241786i
$960$	−0.766044	−	0.642788i	−0.0247240	−	0.0207459i
$961$	−15.4278	−	26.7218i	−0.497672	−	0.861993i
$962$	13.8919	−	24.0614i	0.447892	−	0.775772i
$963$	5.93242	−	2.15922i	0.191170	−	0.0695800i
$964$	0.195470	+	1.10857i	0.00629567	+	0.0357045i
$965$	3.64068	−	20.6473i	0.117198	−	0.664661i
$966$	−0.266044	−	0.0968323i	−0.00855984	−	0.00311553i
$967$	29.6393	−	24.8704i	0.953137	−	0.799777i	−0.0266862	−	0.999644i	$-0.508495\pi$
$967$	29.6393	−	24.8704i	0.953137	−	0.799777i	0.979823	+	0.199867i	$0.0640510\pi$
$968$	−0.204393			−0.00656944
$969$	6.68092	+	18.7848i	0.214622	+	0.603455i
$970$	7.21213			0.231568
$971$	24.2854	−	20.3779i	0.779355	−	0.653957i	−0.163731	−	0.986505i	$-0.552353\pi$
$971$	24.2854	−	20.3779i	0.779355	−	0.653957i	0.943086	+	0.332548i	$0.107908\pi$
$972$	0.939693	+	0.342020i	0.0301407	+	0.0109703i
$973$	−1.81773	+	10.3089i	−0.0582739	+	0.330488i
$974$	−4.76083	−	27.0000i	−0.152547	−	0.865136i
$975$	5.19846	−	1.89209i	0.166484	−	0.0605952i
$976$	1.24510	−	2.15658i	0.0398547	−	0.0690303i
$977$	−31.1152	−	53.8930i	−0.995462	−	1.72419i	−0.580143	−	0.814515i	$-0.697003\pi$
$977$	−31.1152	−	53.8930i	−0.995462	−	1.72419i	−0.415319	−	0.909676i	$-0.636330\pi$
$978$	4.25490	+	3.57029i	0.136057	+	0.114165i
$979$	−24.9357	−	20.9235i	−0.796947	−	0.668718i
$980$	3.35844	+	5.81699i	0.107281	+	0.185817i
$981$	8.95723	−	15.5144i	0.285982	−	0.495336i
$982$	32.2977	−	11.7554i	1.03066	−	0.375130i
$983$	−1.73958	−	9.86565i	−0.0554840	−	0.314665i	0.944417	−	0.328751i	$-0.106628\pi$
$983$	−1.73958	−	9.86565i	−0.0554840	−	0.314665i	−0.999901	+	0.0140851i	$0.995516\pi$
$984$	1.88919	−	10.7141i	0.0602250	−	0.341553i
$985$	−10.0988	−	3.67566i	−0.321774	−	0.117116i
$986$	−29.1282	+	24.4415i	−0.927631	+	0.778375i
$987$	−2.97771			−0.0947816
$988$	−23.7777	+	4.01239i	−0.756468	+	0.127651i
$989$	−5.09421			−0.161986
$990$	2.56418	−	2.15160i	0.0814949	−	0.0683824i
$991$	2.91905	+	1.06245i	0.0927268	+	0.0337498i	0.387967	−	0.921673i	$-0.373177\pi$
$991$	2.91905	+	1.06245i	0.0927268	+	0.0337498i	−0.295240	+	0.955423i	$0.595400\pi$
$992$	−1.36571	+	7.74535i	−0.0433615	+	0.245915i
$993$	5.16385	+	29.2856i	0.163870	+	0.929352i
$994$	2.69594	−	0.981241i	0.0855099	−	0.0311231i
$995$	−5.16297	+	8.94253i	−0.163677	+	0.283497i
$996$	−1.66637	−	2.88624i	−0.0528011	−	0.0914542i
$997$	20.3286	+	17.0577i	0.643814	+	0.540224i	0.905187	−	0.425014i	$-0.139731\pi$
$997$	20.3286	+	17.0577i	0.643814	+	0.540224i	−0.261373	+	0.965238i	$0.584175\pi$
$998$	2.13176	+	1.78876i	0.0674797	+	0.0566222i
$999$	2.51114	+	4.34943i	0.0794491	+	0.137610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.g.481.1	yes	6
19.16	even	9	inner	570.2.u.g.301.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.g.301.1	✓	6	19.16	even	9	inner
570.2.u.g.481.1	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.939693 + 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.173648 + 0.984808i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(-0.766044 - 0.642788i) q^{10} +(1.67365 + 2.89884i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-5.19846 + 1.89209i) q^{13} +(-0.0923963 - 0.524005i) q^{14} +(-0.173648 + 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.50387 - 2.94010i) q^{17} -1.00000 q^{18} +(-0.0320889 + 4.35878i) q^{19} +1.00000 q^{20} +(-0.407604 + 0.342020i) q^{21} +(-3.14543 - 1.14484i) q^{22} +(0.0923963 - 0.524005i) q^{23} +(0.173648 + 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(2.76604 - 4.79093i) q^{26} +(0.500000 + 0.866025i) q^{27} +(0.407604 + 0.342020i) q^{28} +(6.36824 + 5.34359i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-3.93242 + 6.81115i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.581252 + 3.29644i) q^{33} +(-0.794263 + 4.50449i) q^{34} +(-0.500000 - 0.181985i) q^{35} +(0.766044 - 0.642788i) q^{36} +5.02229 q^{37} +(-2.77719 - 3.35965i) q^{38} -5.53209 q^{39} +(-0.766044 + 0.642788i) q^{40} +(-10.2233 - 3.72097i) q^{41} +(0.0923963 - 0.524005i) q^{42} +(-1.66250 - 9.42853i) q^{43} +(3.14543 - 1.14484i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(0.266044 + 0.460802i) q^{46} +(4.28699 + 3.59721i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(3.35844 + 5.81699i) q^{49} +(0.500000 - 0.866025i) q^{50} +(4.29813 - 1.56439i) q^{51} +(0.960637 + 5.44804i) q^{52} +(-0.961981 + 5.45567i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(-2.56418 + 2.15160i) q^{55} -0.532089 q^{56} +(-1.52094 + 4.08494i) q^{57} -8.31315 q^{58} +(9.57192 - 8.03179i) q^{59} +(0.939693 + 0.342020i) q^{60} +(-0.432419 + 2.45237i) q^{61} +(-1.36571 - 7.74535i) q^{62} +(-0.500000 + 0.181985i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.76604 - 4.79093i) q^{65} +(-2.56418 - 2.15160i) q^{66} +(-3.75490 - 3.15074i) q^{67} +(-2.28699 - 3.96118i) q^{68} +(0.266044 - 0.460802i) q^{69} +(0.500000 - 0.181985i) q^{70} +(0.936289 + 5.30996i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(-14.1493 - 5.14992i) q^{73} +(-3.84730 + 3.22826i) q^{74} -1.00000 q^{75} +(4.28699 + 0.788496i) q^{76} -1.78106 q^{77} +(4.23783 - 3.55596i) q^{78} +(7.90420 + 2.87689i) q^{79} +(0.173648 - 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(10.2233 - 3.72097i) q^{82} +(1.66637 - 2.88624i) q^{83} +(0.266044 + 0.460802i) q^{84} +(3.50387 + 2.94010i) q^{85} +(7.33409 + 6.15403i) q^{86} +(4.15657 + 7.19940i) q^{87} +(-1.67365 + 2.89884i) q^{88} +(-9.13816 + 3.32602i) q^{89} +(-0.173648 - 0.984808i) q^{90} +(0.511144 - 2.89884i) q^{91} +(-0.500000 - 0.181985i) q^{92} +(-6.02481 + 5.05542i) q^{93} -5.59627 q^{94} +(-4.29813 + 0.725293i) q^{95} +1.00000 q^{96} +(-5.52481 + 4.63587i) q^{97} +(-6.31180 - 2.29731i) q^{98} +(-0.581252 + 3.29644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^7 + 3 * q^8	\( 6 q + 3 q^{7} + 3 q^{8} + 9 q^{11} + 3 q^{12} - 3 q^{13} + 3 q^{14} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 6 q^{20} - 6 q^{21} - 3 q^{22} - 3 q^{23} + 12 q^{26} + 3 q^{27} + 6 q^{28} + 33 q^{29} - 3 q^{30} + 6 q^{33} - 15 q^{34} - 3 q^{35} + 18 q^{37} - 6 q^{38} - 24 q^{39} - 6 q^{41} - 3 q^{42} - 15 q^{43} + 3 q^{44} - 3 q^{45} - 3 q^{46} + 18 q^{47} + 12 q^{49} + 3 q^{50} + 12 q^{51} - 3 q^{52} + 12 q^{53} + 3 q^{55} + 6 q^{56} - 6 q^{57} - 6 q^{58} - 9 q^{59} + 21 q^{61} - 18 q^{62} - 3 q^{63} - 3 q^{64} - 12 q^{65} + 3 q^{66} - 24 q^{67} - 6 q^{68} - 3 q^{69} + 3 q^{70} - 42 q^{71} - 45 q^{73} - 21 q^{74} - 6 q^{75} + 18 q^{76} + 24 q^{77} + 6 q^{78} + 9 q^{79} + 6 q^{82} - 9 q^{83} - 3 q^{84} - 3 q^{85} - 3 q^{86} + 3 q^{87} - 9 q^{88} - 21 q^{89} - 3 q^{91} - 3 q^{92} - 9 q^{93} - 6 q^{94} - 12 q^{95} + 6 q^{96} - 6 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^7 + 3 * q^8 + 9 * q^11 + 3 * q^12 - 3 * q^13 + 3 * q^14 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 6 * q^20 - 6 * q^21 - 3 * q^22 - 3 * q^23 + 12 * q^26 + 3 * q^27 + 6 * q^28 + 33 * q^29 - 3 * q^30 + 6 * q^33 - 15 * q^34 - 3 * q^35 + 18 * q^37 - 6 * q^38 - 24 * q^39 - 6 * q^41 - 3 * q^42 - 15 * q^43 + 3 * q^44 - 3 * q^45 - 3 * q^46 + 18 * q^47 + 12 * q^49 + 3 * q^50 + 12 * q^51 - 3 * q^52 + 12 * q^53 + 3 * q^55 + 6 * q^56 - 6 * q^57 - 6 * q^58 - 9 * q^59 + 21 * q^61 - 18 * q^62 - 3 * q^63 - 3 * q^64 - 12 * q^65 + 3 * q^66 - 24 * q^67 - 6 * q^68 - 3 * q^69 + 3 * q^70 - 42 * q^71 - 45 * q^73 - 21 * q^74 - 6 * q^75 + 18 * q^76 + 24 * q^77 + 6 * q^78 + 9 * q^79 + 6 * q^82 - 9 * q^83 - 3 * q^84 - 3 * q^85 - 3 * q^86 + 3 * q^87 - 9 * q^88 - 21 * q^89 - 3 * q^91 - 3 * q^92 - 9 * q^93 - 6 * q^94 - 12 * q^95 + 6 * q^96 - 6 * q^97 - 3 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more