LMFDB - Embedded newform 570.2.u.g.301.1

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			301.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	570.301
Dual form			570.2.u.g.481.1

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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	0.811358	−	0.584549i	$-0.198729\pi$
$7$	−0.266044	−	0.460802i	−0.100555	−	0.174167i	−0.911914	+	0.410382i	$0.865395\pi$
$8$	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	−0.495362	−	0.868687i	$-0.664964\pi$
$11$	1.67365	−	2.89884i	0.504624	−	0.874034i	0.999986	−	0.00534749i	$-0.00170217\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−5.19846	−	1.89209i	−1.44179	−	0.524770i	−0.501507	−	0.865153i	$-0.667221\pi$
$13$	−5.19846	−	1.89209i	−1.44179	−	0.524770i	−0.940287	+	0.340383i	$0.889443\pi$
$14$	−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	0.959749	−	0.280861i	$-0.0906199\pi$
$17$	3.50387	+	2.94010i	0.849813	+	0.713078i	−0.109935	+	0.993939i	$0.535064\pi$
$18$	−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	0.992924	−	0.118749i	$-0.0378885\pi$
$23$	0.0923963	+	0.524005i	0.0192660	+	0.109263i	−0.973658	+	0.228012i	$0.926777\pi$
$24$	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	0.182594	−	0.983188i	$-0.441551\pi$
$29$	6.36824	−	5.34359i	1.18255	−	0.992279i	0.999959	−	0.00909108i	$-0.00289382\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−3.93242	−	6.81115i	−0.706283	−	1.22332i	−0.966226	−	0.257695i	$-0.917037\pi$
$31$	−3.93242	−	6.81115i	−0.706283	−	1.22332i	0.259943	−	0.965624i	$-0.416296\pi$
$32$	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	−0.978729	−	0.205156i	$-0.934230\pi$
$41$	−10.2233	+	3.72097i	−1.59661	+	0.581118i	−0.617878	+	0.786274i	$0.712008\pi$
$42$	0.0923963	+	0.524005i	0.0142571	+	0.0808558i
$43$	−1.66250	+	9.42853i	−0.253529	+	1.43784i	0.546290	+	0.837596i	$0.316040\pi$
$43$	−1.66250	+	9.42853i	−0.253529	+	1.43784i	−0.799819	+	0.600241i	$0.795071\pi$
$44$	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	−0.274150	−	0.961687i	$-0.588396\pi$
$47$	4.28699	−	3.59721i	0.625322	−	0.524707i	0.899471	+	0.436980i	$0.143952\pi$
$48$	−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	−0.976810	−	0.214109i	$-0.931315\pi$
$53$	−0.961981	−	5.45567i	−0.132138	−	0.749394i	0.844672	−	0.535285i	$-0.179796\pi$
$54$	−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	0.997017	+	0.0771831i	$0.0245926\pi$
$59$	9.57192	+	8.03179i	1.24616	+	1.04565i	0.249141	+	0.968467i	$0.419852\pi$
$60$	0.939693	−	0.342020i	0.121314	−	0.0441546i
$61$	−0.432419	−	2.45237i	−0.0553655	−	0.313994i	0.944530	−	0.328424i	$-0.106518\pi$
$61$	−0.432419	−	2.45237i	−0.0553655	−	0.313994i	−0.999896	+	0.0144306i	$0.995406\pi$
$62$	−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	−0.842665	−	0.538438i	$-0.819015\pi$
$67$	−3.75490	+	3.15074i	−0.458734	+	0.384924i	0.383931	+	0.923362i	$0.374570\pi$
$68$	−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	−0.877483	−	0.479608i	$-0.840779\pi$
$71$	0.936289	−	5.30996i	0.111117	−	0.630176i	0.988600	−	0.150568i	$-0.0481102\pi$
$72$	−0.173648	−	0.984808i	−0.0204646	−	0.116061i
$73$	−14.1493	+	5.14992i	−1.65605	+	0.602753i	−0.989735	−	0.142917i	$-0.954352\pi$
$73$	−14.1493	+	5.14992i	−1.65605	+	0.602753i	−0.666316	+	0.745670i	$0.732130\pi$
$74$	−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	0.143338	−	0.989674i	$-0.454216\pi$
$79$	7.90420	−	2.87689i	0.889292	−	0.323676i	0.745954	+	0.665998i	$0.231994\pi$
$80$	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	0.942870	−	0.333162i	$-0.108116\pi$
$83$	1.66637	+	2.88624i	0.182908	+	0.316807i	−0.759961	+	0.649968i	$0.774782\pi$
$84$	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	−0.191228	−	0.981546i	$-0.561247\pi$
$89$	−9.13816	−	3.32602i	−0.968643	−	0.352557i	−0.777415	+	0.628989i	$0.783469\pi$
$90$	−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	0.317672	−	0.948201i	$-0.397099\pi$
$97$	−5.52481	−	4.63587i	−0.560960	−	0.470701i	−0.878632	+	0.477499i	$0.841543\pi$
$98$	−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	0.962588	−	0.270968i	$-0.0873437\pi$
$101$	15.3341	+	5.58115i	1.52580	+	0.555346i	0.563211	+	0.826313i	$0.309566\pi$
$102$	−2.28699	−	3.96118i	−0.226446	−	0.392215i
$103$	−2.25490	+	3.90560i	−0.222182	+	0.384830i	−0.955470	−	0.295087i	$-0.904651\pi$
$103$	−2.25490	+	3.90560i	−0.222182	+	0.384830i	0.733288	+	0.679918i	$0.237985\pi$
$104$	−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	0.977296	−	0.211877i	$-0.0679575\pi$
$107$	3.15657	+	5.46735i	0.305158	+	0.528548i	−0.672139	+	0.740425i	$0.734624\pi$
$108$	0.939693	+	0.342020i	0.0904220	+	0.0329109i
$109$	−3.11081	+	17.6423i	−0.297962	+	1.68983i	0.356952	+	0.934123i	$0.383816\pi$
$109$	−3.11081	+	17.6423i	−0.297962	+	1.68983i	−0.654914	+	0.755704i	$0.727295\pi$
$110$	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	0.916639	−	0.399715i	$-0.130891\pi$
$127$	15.3478	+	5.58613i	1.36189	+	0.495689i	0.445254	+	0.895404i	$0.353113\pi$
$128$	−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	0.959939	−	0.280208i	$-0.0904034\pi$
$131$	9.73648	+	8.16988i	0.850680	+	0.713806i	−0.109259	+	0.994013i	$0.534848\pi$
$132$	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	0.511166	+	0.859482i	$0.329214\pi$
$137$	3.80154	+	21.5596i	0.324787	+	1.84196i	−0.186379	+	0.982478i	$0.559675\pi$
$138$	0.0923963	−	0.524005i	0.00786529	−	0.0446063i
$139$	18.4868	+	6.72864i	1.56803	+	0.570716i	0.972558	−	0.232660i	$-0.0747430\pi$
$139$	18.4868	+	6.72864i	1.56803	+	0.570716i	0.595472	+	0.803376i	$0.296965\pi$
$140$	−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	−0.131771	−	0.991280i	$-0.542066\pi$
$149$	4.93717	−	1.79698i	0.404468	−	0.147214i	0.536240	+	0.844066i	$0.319844\pi$
$150$	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	−0.959232	−	0.282621i	$-0.908796\pi$
$157$	0.486329	−	2.75811i	0.0388133	−	0.220121i	0.998045	+	0.0624997i	$0.0199073\pi$
$158$	−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	−0.954051	−	0.299644i	$-0.903132\pi$
$163$	−2.77719	+	4.81023i	−0.217526	+	0.376766i	0.736525	+	0.676410i	$0.236465\pi$
$164$	−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	−0.991251	−	0.131992i	$-0.957863\pi$
$167$	−1.35591	−	7.68977i	−0.104924	−	0.595053i	0.886327	−	0.463060i	$-0.153249\pi$
$168$	−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	0.650206	−	0.759758i	$-0.274683\pi$
$173$	0.195937	+	0.164411i	0.0148968	+	0.0124999i	−0.635309	+	0.772258i	$0.719127\pi$
$174$	−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	−0.775457	−	0.631401i	$-0.782480\pi$
$179$	2.12836	−	3.68642i	0.159081	−	0.275536i	0.934537	+	0.355865i	$0.115814\pi$
$180$	0.766044	−	0.642788i	0.0570976	−	0.0479106i
$181$	−14.4422	+	12.1185i	−1.07348	+	0.900758i	−0.995363	−	0.0961860i	$-0.969336\pi$
$181$	−14.4422	+	12.1185i	−1.07348	+	0.900758i	−0.0781183	+	0.996944i	$0.524891\pi$
$182$	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	−0.933508	−	0.358556i	$-0.883269\pi$
$193$	−19.7015	+	7.17074i	−1.41814	+	0.516161i	−0.484634	+	0.874717i	$0.661047\pi$
$194$	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	0.608625	−	0.793458i	$-0.291722\pi$
$197$	−5.37346	−	9.30710i	−0.382843	−	0.663103i	−0.991467	+	0.130355i	$0.958388\pi$
$198$	−1.67365	+	2.89884i	−0.118941	+	0.206012i
$199$	7.91013	−	6.63739i	0.560734	−	0.470512i	−0.317822	−	0.948150i	$-0.602952\pi$
$199$	7.91013	−	6.63739i	0.560734	−	0.470512i	0.878557	+	0.477638i	$0.158507\pi$
$200$	−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	0.790027	−	0.613072i	$-0.210066\pi$
$211$	4.69846	+	3.94248i	0.323456	+	0.271411i	−0.466571	+	0.884484i	$0.654511\pi$
$212$	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	−0.917053	−	0.398765i	$-0.869439\pi$
$223$	1.21079	−	6.86673i	0.0810805	−	0.459830i	0.998134	−	0.0610655i	$-0.0194499\pi$
$224$	−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	−0.919604	−	0.392846i	$-0.871490\pi$
$233$	1.20439	−	6.83045i	0.0789024	−	0.447478i	0.998507	−	0.0546315i	$-0.0173984\pi$
$234$	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	0.235175	+	0.971953i	$0.424434\pi$
$239$	−11.1951	+	19.3904i	−0.724148	+	1.25426i	−0.959324	+	0.282309i	$0.908900\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−1.05778	−	0.385001i	−0.0681377	−	0.0248001i	0.307726	−	0.951475i	$-0.400432\pi$
$241$	−1.05778	−	0.385001i	−0.0681377	−	0.0248001i	−0.375864	+	0.926675i	$0.622654\pi$
$242$	−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	−0.812734	−	0.582635i	$-0.802022\pi$
$251$	−3.93360	−	22.3086i	−0.248287	−	1.40810i	0.564447	−	0.825469i	$-0.309089\pi$
$252$	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	−0.430524	−	0.902579i	$-0.641671\pi$
$257$	6.14930	−	5.15988i	0.383583	−	0.321864i	0.814107	+	0.580715i	$0.197227\pi$
$258$	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	0.210367	−	0.977622i	$-0.432534\pi$
$263$	16.2160	−	5.90214i	0.999922	−	0.363942i	0.789554	+	0.613681i	$0.210312\pi$
$264$	−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	−0.830763	−	0.556626i	$-0.812096\pi$
$269$	−18.1951	+	6.62246i	−1.10937	+	0.403779i	−0.278609	+	0.960405i	$0.589873\pi$
$270$	0.173648	+	0.984808i	0.0105679	+	0.0599335i
$271$	−1.94444	+	11.0275i	−0.118116	+	0.669871i	0.867044	+	0.498232i	$0.166017\pi$
$271$	−1.94444	+	11.0275i	−0.118116	+	0.669871i	−0.985160	+	0.171639i	$0.945094\pi$
$272$	−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	−0.943769	−	0.330606i	$-0.892747\pi$
$277$	−3.08853	+	5.34948i	−0.185572	+	0.321419i	0.758197	+	0.652025i	$0.226080\pi$
$278$	−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	−0.882718	−	0.469903i	$-0.844289\pi$
$281$	−3.58647	−	20.3399i	−0.213951	−	1.21337i	0.668767	−	0.743472i	$-0.266822\pi$
$282$	−5.25877	+	1.91404i	−0.313155	+	0.113979i
$283$	1.79813	+	1.50881i	0.106888	+	0.0896896i	0.694665	−	0.719333i	$-0.255552\pi$
$283$	1.79813	+	1.50881i	0.106888	+	0.0896896i	−0.587777	+	0.809023i	$0.699997\pi$
$284$	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	−0.693368	−	0.720583i	$-0.743874\pi$
$293$	4.74763	−	8.22313i	0.277359	−	0.480400i	0.970728	+	0.240183i	$0.0772074\pi$
$294$	−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	−0.236371	−	0.971663i	$-0.575958\pi$
$307$	3.62923	−	1.32093i	0.207131	−	0.0753896i	0.443502	+	0.896273i	$0.353736\pi$
$308$	−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	0.977844	−	0.209336i	$-0.0671302\pi$
$311$	5.42514	+	9.39663i	0.307632	+	0.532834i	−0.670212	+	0.742170i	$0.733797\pi$
$312$	−2.76604	+	4.79093i	−0.156596	+	0.271233i
$313$	−10.6591	+	8.94405i	−0.602488	+	0.505547i	−0.892244	−	0.451553i	$-0.850870\pi$
$313$	−10.6591	+	8.94405i	−0.602488	+	0.505547i	0.289756	+	0.957100i	$0.406426\pi$
$314$	−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	0.189277	−	0.981924i	$-0.439386\pi$
$317$	−5.28611	−	1.92399i	−0.296898	−	0.108062i	−0.486174	+	0.873862i	$0.661608\pi$
$318$	−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	−0.0904370	−	0.995902i	$-0.528826\pi$
$331$	14.8687	−	25.7534i	0.817258	−	1.41553i	0.907695	−	0.419630i	$-0.137840\pi$
$332$	−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	−0.764103	−	0.645095i	$-0.776818\pi$
$337$	3.20439	−	18.1730i	0.174554	−	0.989947i	0.938657	−	0.344852i	$-0.112071\pi$
$338$	−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	0.793308	+	0.608821i	$0.208357\pi$
$347$	−2.98767	+	16.9439i	−0.160387	+	0.909598i	−0.953694	+	0.300777i	$0.902754\pi$
$348$	7.81180	+	2.84326i	0.418757	+	0.152415i
$349$	−4.00134	−	6.93053i	−0.214187	−	0.370983i	0.738834	−	0.673888i	$-0.235377\pi$
$349$	−4.00134	−	6.93053i	−0.214187	−	0.370983i	−0.953021	+	0.302905i	$0.902044\pi$
$350$	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	−0.445777	−	0.895144i	$-0.647072\pi$
$353$	10.3773	−	17.9741i	0.552329	−	0.956662i	0.998106	−	0.0615182i	$-0.0195942\pi$
$354$	−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	0.103104	−	0.994671i	$-0.467123\pi$
$359$	−16.2672	−	13.6498i	−0.858551	−	0.720410i	−0.961655	+	0.274260i	$0.911567\pi$
$360$	−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	0.759496	−	0.650512i	$-0.225446\pi$
$367$	17.6853	+	6.43691i	0.923163	+	0.336004i	0.163667	+	0.986516i	$0.447668\pi$
$368$	−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	−0.966362	−	0.257187i	$-0.917204\pi$
$373$	−13.6334	−	23.6138i	−0.705911	−	1.22267i	0.260451	−	0.965487i	$-0.416129\pi$
$374$	−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	−0.685102	−	0.728448i	$-0.740242\pi$
$383$	−14.5150	+	5.28303i	−0.741683	+	0.269950i	−0.0565811	+	0.998398i	$0.518020\pi$
$384$	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	−0.474909	−	0.880035i	$-0.657519\pi$
$389$	6.10014	−	5.11862i	0.309289	−	0.259524i	0.784198	+	0.620510i	$0.213075\pi$
$390$	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	0.974309	−	0.225213i	$-0.0723079\pi$
$397$	18.3648	+	15.4099i	0.921705	+	0.773402i	−0.0526047	+	0.998615i	$0.516752\pi$
$398$	−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	0.607018	−	0.794688i	$-0.292366\pi$
$401$	−1.40554	−	1.17939i	−0.0701895	−	0.0588960i	−0.677207	+	0.735792i	$0.736810\pi$
$402$	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	−0.895694	−	0.444672i	$-0.853320\pi$
$409$	−12.4035	+	10.4078i	−0.613313	+	0.514631i	0.282381	+	0.959302i	$0.408876\pi$
$410$	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	−0.760418	−	0.649434i	$-0.775006\pi$
$421$	−18.9893	+	6.91155i	−0.925483	+	0.336848i	−0.165065	+	0.986283i	$0.552783\pi$
$422$	−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	0.0497785	−	0.998760i	$-0.484148\pi$
$431$	−11.5030	−	4.18675i	−0.554080	−	0.201669i	−0.603858	+	0.797092i	$0.706371\pi$
$432$	−0.173648	+	0.984808i	−0.00835465	+	0.0473816i
$433$	−4.05350	−	22.9885i	−0.194799	−	1.10476i	−0.912705	−	0.408619i	$-0.866010\pi$
$433$	−4.05350	−	22.9885i	−0.194799	−	1.10476i	0.717906	−	0.696140i	$-0.245101\pi$
$434$	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	0.989635	−	0.143607i	$-0.0458702\pi$
$439$	21.3726	+	17.9337i	1.02006	+	0.855930i	0.0304227	+	0.999537i	$0.490315\pi$
$440$	−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	0.320604	−	0.947213i	$-0.396114\pi$
$443$	−0.897804	−	0.326774i	−0.0426559	−	0.0155255i	−0.363260	+	0.931688i	$0.618336\pi$
$444$	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	0.926617	+	0.376008i	$0.122703\pi$
$449$	16.7173	+	28.9553i	0.788940	+	1.36648i	−0.137676	+	0.990477i	$0.543963\pi$
$450$	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	0.807384	+	0.590026i	$0.200882\pi$
$461$	−3.28740	+	18.6438i	−0.153109	+	0.868327i	−0.960494	+	0.278301i	$0.910229\pi$
$462$	1.67365	+	0.609158i	0.0778652	+	0.0283406i
$463$	−4.25624	−	7.37203i	−0.197804	−	0.342607i	0.750012	−	0.661424i	$-0.230048\pi$
$463$	−4.25624	−	7.37203i	−0.197804	−	0.342607i	−0.947816	+	0.318817i	$0.896714\pi$
$464$	−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	0.475058	+	0.879954i	$0.342427\pi$
$467$	−11.3353	+	19.6333i	−0.524534	+	0.908519i	−0.999592	+	0.0285650i	$0.990906\pi$
$468$	−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	0.960646	−	0.277776i	$-0.0895973\pi$
$479$	−0.811337	−	4.60132i	−0.0370709	−	0.210240i	−0.997717	+	0.0675362i	$0.978486\pi$
$480$	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	−0.989266	−	0.146125i	$-0.953320\pi$
$487$	−13.7083	−	23.7434i	−0.621181	−	1.07592i	0.368085	−	0.929792i	$-0.380013\pi$
$488$	−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	−0.944696	−	0.327946i	$-0.893643\pi$
$491$	−32.2977	+	11.7554i	−1.45758	+	0.530514i	−0.512879	+	0.858461i	$0.671421\pi$
$492$	−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	−0.993712	−	0.111969i	$-0.964284\pi$
$499$	−0.483231	+	2.74054i	−0.0216324	+	0.122683i	0.972079	+	0.234653i	$0.0753953\pi$
$500$	−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	−0.113732	−	0.993512i	$-0.536280\pi$
$503$	18.9500	−	15.9009i	0.844937	−	0.708986i	0.958669	+	0.284525i	$0.0918360\pi$
$504$	−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	−0.915981	−	0.401223i	$-0.868585\pi$
$509$	−4.34224	−	24.6261i	−0.192467	−	1.09153i	0.723514	−	0.690310i	$-0.242526\pi$
$510$	−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	−0.346598	−	0.938014i	$-0.612663\pi$
$521$	14.5865	−	25.2645i	0.639045	−	1.10686i	0.985643	−	0.168844i	$-0.0540035\pi$
$522$	−6.36824	+	5.34359i	−0.278730	+	0.233883i
$523$	−29.7015	+	24.9225i	−1.29875	+	1.08978i	−0.308395	+	0.951258i	$0.599792\pi$
$523$	−29.7015	+	24.9225i	−1.29875	+	1.08978i	−0.990359	+	0.138526i	$0.955764\pi$
$524$	−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	−0.163660	−	0.986517i	$-0.552330\pi$
$541$	18.1295	−	15.2125i	0.779450	−	0.654036i	0.943110	+	0.332481i	$0.107886\pi$
$542$	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	0.973751	+	0.227615i	$0.0730928\pi$
$547$	3.19418	+	18.1151i	0.136573	+	0.774546i	−0.837178	+	0.546931i	$0.815796\pi$
$548$	−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	0.983711	−	0.179757i	$-0.0575311\pi$
$557$	38.2743	+	13.9307i	1.62173	+	0.590262i	0.638021	+	0.770019i	$0.279753\pi$
$558$	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	0.978818	−	0.204731i	$-0.0656321\pi$
$563$	7.40554	+	12.8268i	0.312106	+	0.540584i	−0.666712	+	0.745316i	$0.732299\pi$
$564$	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	0.893662	−	0.448740i	$-0.148127\pi$
$577$	1.39827	+	2.42188i	0.0582108	+	0.100824i	−0.835452	+	0.549564i	$0.814794\pi$
$578$	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	0.999921	−	0.0125859i	$-0.00400633\pi$
$587$	28.1327	+	23.6061i	1.16116	+	0.974329i	0.161240	+	0.986915i	$0.448451\pi$
$588$	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	0.957208	+	0.289401i	$0.0934563\pi$
$593$	3.81608	+	21.6421i	0.156708	+	0.888734i	−0.800500	+	0.599333i	$0.795433\pi$
$594$	−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	−0.881464	−	0.472252i	$-0.843441\pi$
$599$	−13.9370	+	11.6945i	−0.569451	+	0.477826i	0.312013	+	0.950078i	$0.398997\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	2.40420	+	4.16420i	0.0980694	+	0.169861i	0.910885	−	0.412659i	$-0.135400\pi$
$601$	2.40420	+	4.16420i	0.0980694	+	0.169861i	−0.812816	+	0.582520i	$0.802067\pi$
$602$	−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	−0.991580	−	0.129499i	$-0.958663\pi$
$613$	−0.383971	+	2.17761i	−0.0155084	+	0.0879527i	0.976071	+	0.217451i	$0.0697743\pi$
$614$	−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	−0.485241	−	0.874380i	$-0.661268\pi$
$617$	7.24304	−	6.07763i	0.291594	−	0.244676i	0.776835	+	0.629704i	$0.216824\pi$
$618$	3.45471	−	2.89884i	0.138969	−	0.116609i
$619$	20.0253	−	34.6848i	0.804884	−	1.39410i	−0.111485	−	0.993766i	$-0.535561\pi$
$619$	20.0253	−	34.6848i	0.804884	−	1.39410i	0.916369	−	0.400334i	$-0.131106\pi$
$620$	−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	0.999237	−	0.0390522i	$-0.0124339\pi$
$631$	1.17823	+	6.68210i	0.0469047	+	0.266010i	−0.952332	+	0.305062i	$0.901323\pi$
$632$	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	−0.994882	−	0.101043i	$-0.967782\pi$
$641$	−0.644086	+	3.65279i	−0.0254398	+	0.144277i	0.969442	+	0.245320i	$0.0788930\pi$
$642$	−1.09627	−	6.21724i	−0.0432662	−	0.245375i
$643$	12.8623	−	4.68150i	0.507240	−	0.184620i	−0.0757075	−	0.997130i	$-0.524122\pi$
$643$	12.8623	−	4.68150i	0.507240	−	0.184620i	0.582948	+	0.812510i	$0.301899\pi$
$644$	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	−0.998087	−	0.0618212i	$-0.980309\pi$
$653$	−14.1206	−	24.4576i	−0.552582	−	0.957101i	0.445505	−	0.895280i	$-0.353024\pi$
$654$	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	0.518845	−	0.854869i	$-0.326362\pi$
$659$	9.41622	+	3.42722i	0.366804	+	0.133506i	−0.152041	+	0.988374i	$0.548585\pi$
$660$	0.581252	−	3.29644i	0.0226252	−	0.128314i
$661$	7.10906	+	40.3175i	0.276510	+	1.56817i	0.734123	+	0.679017i	$0.237594\pi$
$661$	7.10906	+	40.3175i	0.276510	+	1.56817i	−0.457613	+	0.889152i	$0.651295\pi$
$662$	−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	−0.161851	−	0.986815i	$-0.551746\pi$
$673$	20.0710	−	34.7641i	0.773682	−	1.34006i	0.935532	−	0.353241i	$-0.114920\pi$
$674$	−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	0.625102	−	0.780543i	$-0.285057\pi$
$677$	−9.45589	−	16.3781i	−0.363419	−	0.629461i	−0.988521	+	0.151082i	$0.951724\pi$
$678$	−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	0.773306	−	0.634033i	$-0.218602\pi$
$691$	−4.26991	−	7.39571i	−0.162435	−	0.281346i	−0.935742	+	0.352687i	$0.885268\pi$
$692$	−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	0.519298	−	0.854593i	$-0.326193\pi$
$701$	−6.14614	−	5.15723i	−0.232137	−	0.194786i	−0.751435	+	0.659807i	$0.770638\pi$
$702$	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	−0.297158	−	0.954828i	$-0.596039\pi$
$709$	−30.3161	−	11.0342i	−1.13855	−	0.414397i	−0.841388	+	0.540431i	$0.818261\pi$
$710$	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	−0.381110	−	0.924530i	$-0.624458\pi$
$719$	−2.11246	+	0.768874i	−0.0787816	+	0.0286742i	0.302329	+	0.953204i	$0.402236\pi$
$720$	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	−0.522167	−	0.852843i	$-0.674876\pi$
$727$	7.01573	−	39.7882i	0.260199	−	1.47566i	0.782366	−	0.622819i	$-0.214013\pi$
$728$	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	−0.963391	−	0.268099i	$-0.913605\pi$
$733$	−6.75537	+	11.7006i	−0.249515	+	0.432173i	0.713876	+	0.700272i	$0.246938\pi$
$734$	−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	0.150117	−	0.988668i	$-0.452035\pi$
$739$	−21.6787	−	18.1906i	−0.797464	−	0.669152i	−0.947581	+	0.319517i	$0.896479\pi$
$740$	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	0.999542	+	0.0302468i	$0.00962932\pi$
$743$	32.7886	+	27.5129i	1.20290	+	1.00935i	0.203356	+	0.979105i	$0.434815\pi$
$744$	−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	−0.129979	−	0.991517i	$-0.541491\pi$
$751$	22.5786	−	18.9457i	0.823903	−	0.691337i	0.953883	+	0.300180i	$0.0970466\pi$
$752$	−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	0.278792	−	0.960352i	$-0.410066\pi$
$757$	30.5308	−	11.1123i	1.10966	−	0.403884i	0.830869	+	0.556468i	$0.187844\pi$
$758$	−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	−0.980875	−	0.194638i	$-0.937647\pi$
$769$	−26.6083	+	22.3271i	−0.959521	+	0.805134i	0.0213537	+	0.999772i	$0.493202\pi$
$770$	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	0.310492	−	0.950576i	$-0.399506\pi$
$773$	−1.74257	−	0.634245i	−0.0626760	−	0.0228122i	−0.373168	+	0.927764i	$0.621728\pi$
$774$	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	−0.979546	−	0.201221i	$-0.935509\pi$
$787$	−8.85117	+	15.3307i	−0.315510	+	0.546479i	0.664036	+	0.747701i	$0.268842\pi$
$788$	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	−0.997705	−	0.0677111i	$-0.978430\pi$
$809$	−12.5209	+	21.6869i	−0.440213	+	0.762471i	0.557492	+	0.830182i	$0.311764\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	−8.75150	−	3.18528i	−0.307307	−	0.111850i	0.183764	−	0.982970i	$-0.441172\pi$
$811$	−8.75150	−	3.18528i	−0.307307	−	0.111850i	−0.491070	+	0.871120i	$0.663394\pi$
$812$	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	0.855511	+	0.517784i	$0.173243\pi$
$821$	6.55257	+	37.1615i	0.228686	+	1.29694i	−0.626825	+	0.779160i	$0.715646\pi$
$822$	3.80154	−	21.5596i	0.132594	−	0.751977i
$823$	−4.24288	−	1.54428i	−0.147897	−	0.0538303i	0.267011	−	0.963694i	$-0.413964\pi$
$823$	−4.24288	−	1.54428i	−0.147897	−	0.0538303i	−0.414908	+	0.909863i	$0.636186\pi$
$824$	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	−0.262855	−	0.964835i	$-0.584664\pi$
$827$	18.4531	−	15.4840i	0.641678	−	0.538431i	0.904533	+	0.426404i	$0.140220\pi$
$828$	−0.266044	+	0.460802i	−0.00924568	+	0.0160140i
$829$	−3.24392	−	5.61863i	−0.112666	−	0.195143i	0.804178	−	0.594388i	$-0.202606\pi$
$829$	−3.24392	−	5.61863i	−0.112666	−	0.195143i	−0.916844	+	0.399245i	$0.869272\pi$
$830$	−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	0.0535057	−	0.998568i	$-0.482960\pi$
$839$	21.3290	−	7.76314i	0.736360	−	0.268013i	0.682855	+	0.730554i	$0.260738\pi$
$840$	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	0.266852	−	0.963738i	$-0.414017\pi$
$853$	−18.5724	−	15.5841i	−0.635906	−	0.533589i	−0.902758	+	0.430149i	$0.858461\pi$
$854$	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	0.288405	−	0.957509i	$-0.406875\pi$
$857$	−17.6958	−	14.8485i	−0.604476	−	0.507216i	−0.892881	+	0.450293i	$0.851320\pi$
$858$	17.4008	−	6.33337i	0.594053	−	0.216218i
$859$	−5.51296	−	31.2655i	−0.188100	−	1.06677i	−0.921908	−	0.387409i	$-0.873370\pi$
$859$	−5.51296	−	31.2655i	−0.188100	−	1.06677i	0.733808	−	0.679357i	$-0.237741\pi$
$860$	−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	0.395425	+	0.918498i	$0.370597\pi$
$863$	−17.5594	+	30.4138i	−0.597730	+	1.03530i	−0.993155	+	0.116801i	$0.962736\pi$
$864$	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	−0.989599	−	0.143856i	$-0.954050\pi$
$877$	−49.0176	+	17.8409i	−1.65521	+	0.602446i	−0.665608	+	0.746302i	$0.731828\pi$
$878$	−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	0.980032	+	0.198841i	$0.0637177\pi$
$881$	19.6557	+	34.0447i	0.662217	+	1.14699i	−0.317815	+	0.948153i	$0.602949\pi$
$882$	−3.35844	+	5.81699i	−0.113085	+	0.195868i
$883$	18.5503	−	15.5656i	0.624269	−	0.523824i	−0.274873	−	0.961480i	$-0.588636\pi$
$883$	18.5503	−	15.5656i	0.624269	−	0.523824i	0.899142	+	0.437657i	$0.144191\pi$
$884$	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	−0.439942	−	0.898026i	$-0.645001\pi$
$887$	−40.3315	−	14.6795i	−1.35420	−	0.492888i	−0.914255	+	0.405138i	$0.867223\pi$
$888$	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	−0.927800	−	0.373078i	$-0.878302\pi$
$907$	2.15776	−	12.2372i	0.0716471	−	0.406331i	0.999447	−	0.0332527i	$-0.0105866\pi$
$908$	−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	0.581789	−	0.813340i	$-0.302353\pi$
$919$	−12.5346	−	21.7106i	−0.413479	−	0.716166i	−0.995267	+	0.0971737i	$0.969020\pi$
$920$	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	0.933072	−	0.359689i	$-0.117117\pi$
$929$	22.5815	+	18.9481i	0.740874	+	0.621667i	−0.192198	+	0.981356i	$0.561562\pi$
$930$	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	−0.246586	−	0.969121i	$-0.579309\pi$
$937$	−32.3987	−	11.7922i	−1.05842	−	0.385234i	−0.811835	+	0.583887i	$0.801531\pi$
$938$	−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	−0.893524	−	0.449016i	$-0.851775\pi$
$941$	−18.6045	+	15.6110i	−0.606489	+	0.508904i	0.287035	+	0.957920i	$0.407330\pi$
$942$	−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	−0.596997	−	0.802244i	$-0.703640\pi$
$947$	−16.5761	+	6.03320i	−0.538651	+	0.196053i	0.0583462	+	0.998296i	$0.481417\pi$
$948$	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	−0.0733209	−	0.997308i	$-0.523360\pi$
$953$	15.7925	−	5.74800i	0.511570	−	0.186196i	0.584890	+	0.811112i	$0.301138\pi$
$954$	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	0.979823	−	0.199867i	$-0.0640510\pi$
$967$	29.6393	+	24.8704i	0.953137	+	0.799777i	−0.0266862	+	0.999644i	$0.508495\pi$
$968$	−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	0.943086	−	0.332548i	$-0.107908\pi$
$971$	24.2854	+	20.3779i	0.779355	+	0.653957i	−0.163731	+	0.986505i	$0.552353\pi$
$972$	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	−0.415319	+	0.909676i	$0.636330\pi$
$977$	−31.1152	+	53.8930i	−0.995462	+	1.72419i	−0.580143	+	0.814515i	$0.697003\pi$
$978$	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	−0.999901	−	0.0140851i	$-0.995516\pi$
$983$	−1.73958	+	9.86565i	−0.0554840	+	0.314665i	0.944417	+	0.328751i	$0.106628\pi$
$984$	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	−0.295240	−	0.955423i	$-0.595400\pi$
$991$	2.91905	−	1.06245i	0.0927268	−	0.0337498i	0.387967	+	0.921673i	$0.373177\pi$
$992$	−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	−0.261373	−	0.965238i	$-0.584175\pi$
$997$	20.3286	−	17.0577i	0.643814	−	0.540224i	0.905187	+	0.425014i	$0.139731\pi$
$998$	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.301.1	✓	6
19.6	even	9	inner	570.2.u.g.481.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.g.301.1	✓	6	1.1	even	1	trivial
570.2.u.g.481.1	yes	6	19.6	even	9	inner

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

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