LMFDB - Embedded newform 63.2.s.b.59.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(47,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("63.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.4
Root			$-1.04536 - 1.81062i$ of defining polynomial
Character	$\chi$	$=$	63.59
Dual form			63.2.s.b.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30778 + 0.755047i) q^{2} +(-0.919842 + 1.46761i) q^{3} +(0.140193 + 0.242822i) q^{4} -0.775876 q^{5} +(-2.31107 + 1.22479i) q^{6} +(2.05881 - 1.66171i) q^{7} -2.59678i q^{8} +(-1.30778 - 2.69995i) q^{9} +O(q^{10})$	\(q+(1.30778 + 0.755047i) q^{2} +(-0.919842 + 1.46761i) q^{3} +(0.140193 + 0.242822i) q^{4} -0.775876 q^{5} +(-2.31107 + 1.22479i) q^{6} +(2.05881 - 1.66171i) q^{7} -2.59678i q^{8} +(-1.30778 - 2.69995i) q^{9} +(-1.01468 - 0.585823i) q^{10} +3.84319i q^{11} +(-0.485324 - 0.0176082i) q^{12} +(-2.54198 - 1.46761i) q^{13} +(3.94715 - 0.618650i) q^{14} +(0.713684 - 1.13869i) q^{15} +(2.24108 - 3.88166i) q^{16} +(-2.69901 + 4.67482i) q^{17} +(0.328298 - 4.51837i) q^{18} +(-0.376551 + 0.217402i) q^{19} +(-0.108773 - 0.188400i) q^{20} +(0.544964 + 4.55006i) q^{21} +(-2.90179 + 5.02605i) q^{22} -0.0557186i q^{23} +(3.81107 + 2.38863i) q^{24} -4.39802 q^{25} +(-2.21624 - 3.83863i) q^{26} +(5.16543 + 0.564208i) q^{27} +(0.692131 + 0.266964i) q^{28} +(-0.187994 + 0.108538i) q^{29} +(1.79310 - 0.950287i) q^{30} +(5.67806 - 3.27823i) q^{31} +(1.36392 - 0.787461i) q^{32} +(-5.64031 - 3.53513i) q^{33} +(-7.05942 + 4.07576i) q^{34} +(-1.59739 + 1.28928i) q^{35} +(0.472264 - 0.696071i) q^{36} +(3.14698 + 5.45073i) q^{37} -0.656595 q^{38} +(4.49211 - 2.38067i) q^{39} +2.01478i q^{40} +(3.78757 - 6.56026i) q^{41} +(-2.72281 + 6.36195i) q^{42} +(6.42703 + 11.1319i) q^{43} +(-0.933209 + 0.538789i) q^{44} +(1.01468 + 2.09482i) q^{45} +(0.0420702 - 0.0728677i) q^{46} +(0.482772 - 0.836186i) q^{47} +(3.63534 + 6.85955i) q^{48} +(1.47744 - 6.84231i) q^{49} +(-5.75164 - 3.32071i) q^{50} +(-4.37817 - 8.26120i) q^{51} -0.822998i q^{52} +(-6.46438 - 3.73221i) q^{53} +(6.32924 + 4.63800i) q^{54} -2.98184i q^{55} +(-4.31510 - 5.34629i) q^{56} +(0.0273056 - 0.752608i) q^{57} -0.327806 q^{58} +(-1.56219 - 2.70580i) q^{59} +(0.376551 + 0.0136618i) q^{60} +(-3.01744 - 1.74212i) q^{61} +9.90087 q^{62} +(-7.17901 - 3.38554i) q^{63} -6.58603 q^{64} +(1.97226 + 1.13869i) q^{65} +(-4.70711 - 8.88187i) q^{66} +(2.10088 + 3.63884i) q^{67} -1.51353 q^{68} +(0.0817733 + 0.0512523i) q^{69} +(-3.06250 + 0.479996i) q^{70} -3.50812i q^{71} +(-7.01117 + 3.39602i) q^{72} +(-7.05942 - 4.07576i) q^{73} +9.50448i q^{74} +(4.04548 - 6.45459i) q^{75} +(-0.105580 - 0.0609566i) q^{76} +(6.38626 + 7.91241i) q^{77} +(7.67222 + 0.278359i) q^{78} +(2.48110 - 4.29739i) q^{79} +(-1.73880 + 3.01169i) q^{80} +(-5.57942 + 7.06187i) q^{81} +(9.90662 - 5.71959i) q^{82} +(-4.31033 - 7.46571i) q^{83} +(-1.02845 + 0.770216i) q^{84} +(2.09410 - 3.62708i) q^{85} +19.4108i q^{86} +(0.0136324 - 0.375740i) q^{87} +9.97991 q^{88} +(7.82041 + 13.5453i) q^{89} +(-0.254718 + 3.50570i) q^{90} +(-7.67222 + 1.20249i) q^{91} +(0.0135297 - 0.00781136i) q^{92} +(-0.411745 + 11.3487i) q^{93} +(1.26272 - 0.729031i) q^{94} +(0.292157 - 0.168677i) q^{95} +(-0.0989048 + 2.72605i) q^{96} +(1.24162 - 0.716849i) q^{97} +(7.09843 - 7.83270i) q^{98} +(10.3764 - 5.02605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7}+O(q^{10}) $ 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7	$ 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7} - 15 q^{10} + 6 q^{13} - 6 q^{14} - 3 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} + 3 q^{19} - 3 q^{20} + 18 q^{21} + 5 q^{22} + 27 q^{24} - 14 q^{25} + 3 q^{26} + 27 q^{27} + 2 q^{28} - 15 q^{29} - 9 q^{31} + 48 q^{32} - 9 q^{33} + 3 q^{34} - 15 q^{35} - 18 q^{36} + 6 q^{37} + 36 q^{38} + 12 q^{39} - 9 q^{41} - 6 q^{42} + 3 q^{43} + 24 q^{44} + 15 q^{45} - 13 q^{46} + 15 q^{47} - 15 q^{48} - 23 q^{49} + 3 q^{50} - 24 q^{51} - 9 q^{53} + 27 q^{54} - 51 q^{56} - 36 q^{57} - 16 q^{58} - 18 q^{59} - 3 q^{60} + 12 q^{61} + 12 q^{62} + 9 q^{63} + 6 q^{64} - 3 q^{65} - 33 q^{66} - 10 q^{67} - 54 q^{68} - 3 q^{69} + 9 q^{70} + 18 q^{72} + 3 q^{73} - 21 q^{75} + 9 q^{76} + 45 q^{77} + 24 q^{78} + 20 q^{79} - 30 q^{80} - 48 q^{81} + 9 q^{82} - 15 q^{83} + 60 q^{84} + 18 q^{85} + 30 q^{87} + 16 q^{88} + 24 q^{89} + 24 q^{90} - 24 q^{91} + 39 q^{92} + 6 q^{93} - 3 q^{94} + 3 q^{96} + 6 q^{97} + 45 q^{98} + 21 q^{99}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7 - 15 * q^10 + 6 * q^13 - 6 * q^14 - 3 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 + 3 * q^19 - 3 * q^20 + 18 * q^21 + 5 * q^22 + 27 * q^24 - 14 * q^25 + 3 * q^26 + 27 * q^27 + 2 * q^28 - 15 * q^29 - 9 * q^31 + 48 * q^32 - 9 * q^33 + 3 * q^34 - 15 * q^35 - 18 * q^36 + 6 * q^37 + 36 * q^38 + 12 * q^39 - 9 * q^41 - 6 * q^42 + 3 * q^43 + 24 * q^44 + 15 * q^45 - 13 * q^46 + 15 * q^47 - 15 * q^48 - 23 * q^49 + 3 * q^50 - 24 * q^51 - 9 * q^53 + 27 * q^54 - 51 * q^56 - 36 * q^57 - 16 * q^58 - 18 * q^59 - 3 * q^60 + 12 * q^61 + 12 * q^62 + 9 * q^63 + 6 * q^64 - 3 * q^65 - 33 * q^66 - 10 * q^67 - 54 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^72 + 3 * q^73 - 21 * q^75 + 9 * q^76 + 45 * q^77 + 24 * q^78 + 20 * q^79 - 30 * q^80 - 48 * q^81 + 9 * q^82 - 15 * q^83 + 60 * q^84 + 18 * q^85 + 30 * q^87 + 16 * q^88 + 24 * q^89 + 24 * q^90 - 24 * q^91 + 39 * q^92 + 6 * q^93 - 3 * q^94 + 3 * q^96 + 6 * q^97 + 45 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.30778	+	0.755047i	0.924740	+	0.533899i	0.885144	−	0.465317i	$-0.154060\pi$
$2$	1.30778	+	0.755047i	0.924740	+	0.533899i	0.0395961	+	0.999216i	$0.487393\pi$
$3$	−0.919842	+	1.46761i	−0.531071	+	0.847327i
$3$	−0.919842	+	1.46761i	−0.531071	+	0.847327i
$4$	0.140193	+	0.242822i	0.0700966	+	0.121411i
$5$	−0.775876			−0.346982			−0.173491	−	0.984835i	$-0.555505\pi$
$5$	−0.775876			−0.346982			−0.173491	+	0.984835i	$0.555505\pi$
$6$	−2.31107	+	1.22479i	−0.943490	+	0.500019i
$7$	2.05881	−	1.66171i	0.778159	−	0.628068i
$7$	2.05881	−	1.66171i	0.778159	−	0.628068i
$8$		−	2.59678i		−	0.918100i
$9$	−1.30778	−	2.69995i	−0.435927	−	0.899982i
$10$	−1.01468	−	0.585823i	−0.320869	−	0.185254i
$11$			3.84319i			1.15876i	0.815056	+	0.579382i	$0.196706\pi$
$11$			3.84319i			1.15876i	−0.815056	+	0.579382i	$0.803294\pi$
$12$	−0.485324	−	0.0176082i	−0.140101	−	0.00508306i
$13$	−2.54198	−	1.46761i	−0.705019	−	0.407043i	0.104195	−	0.994557i	$-0.466773\pi$
$13$	−2.54198	−	1.46761i	−0.705019	−	0.407043i	−0.809214	+	0.587514i	$0.800107\pi$
$14$	3.94715	−	0.618650i	1.05492	−	0.165341i
$15$	0.713684	−	1.13869i	0.184272	−	0.294008i
$16$	2.24108	−	3.88166i	0.560270	−	0.970415i
$17$	−2.69901	+	4.67482i	−0.654606	+	1.13381i	0.327387	+	0.944890i	$0.393832\pi$
$17$	−2.69901	+	4.67482i	−0.654606	+	1.13381i	−0.981993	+	0.188920i	$0.939501\pi$
$18$	0.328298	−	4.51837i	0.0773805	−	1.06499i
$19$	−0.376551	+	0.217402i	−0.0863868	+	0.0498755i	−0.542571	−	0.840010i	$-0.682549\pi$
$19$	−0.376551	+	0.217402i	−0.0863868	+	0.0498755i	0.456184	+	0.889885i	$0.349216\pi$
$20$	−0.108773	−	0.188400i	−0.0243223	−	0.0421274i
$21$	0.544964	+	4.55006i	0.118921	+	0.992904i
$22$	−2.90179	+	5.02605i	−0.618663	+	1.07156i
$23$		−	0.0557186i		−	0.0116181i	−0.999983	−	0.00580906i	$-0.998151\pi$
$23$		−	0.0557186i		−	0.0116181i	0.999983	−	0.00580906i	$-0.00184909\pi$
$24$	3.81107	+	2.38863i	0.777931	+	0.487577i
$25$	−4.39802			−0.879603
$26$	−2.21624	−	3.83863i	−0.434640	−	0.752818i
$27$	5.16543	+	0.564208i	0.994088	+	0.108582i
$28$	0.692131	+	0.266964i	0.130800	+	0.0504515i
$29$	−0.187994	+	0.108538i	−0.0349096	+	0.0201551i	−0.517353	−	0.855772i	$-0.673083\pi$
$29$	−0.187994	+	0.108538i	−0.0349096	+	0.0201551i	0.482444	+	0.875927i	$0.339749\pi$
$30$	1.79310	−	0.950287i	0.327375	−	0.173498i
$31$	5.67806	−	3.27823i	1.01981	−	0.588787i	0.105761	−	0.994392i	$-0.466272\pi$
$31$	5.67806	−	3.27823i	1.01981	−	0.588787i	0.914049	+	0.405604i	$0.132939\pi$
$32$	1.36392	−	0.787461i	0.241110	−	0.139205i
$33$	−5.64031	−	3.53513i	−0.981853	−	0.615386i
$34$	−7.05942	+	4.07576i	−1.21068	+	0.698987i
$35$	−1.59739	+	1.28928i	−0.270007	+	0.217928i
$36$	0.472264	−	0.696071i	0.0787106	−	0.116012i
$37$	3.14698	+	5.45073i	0.517361	+	0.896095i	0.999797	+	0.0201636i	$0.00641872\pi$
$37$	3.14698	+	5.45073i	0.517361	+	0.896095i	−0.482436	+	0.875931i	$0.660248\pi$
$38$	−0.656595			−0.106514
$39$	4.49211	−	2.38067i	0.719314	−	0.381213i
$40$			2.01478i			0.318565i
$41$	3.78757	−	6.56026i	0.591519	−	1.02454i	−0.402509	−	0.915416i	$-0.631862\pi$
$41$	3.78757	−	6.56026i	0.591519	−	1.02454i	0.994028	−	0.109125i	$-0.0348049\pi$
$42$	−2.72281	+	6.36195i	−0.420139	+	0.981670i
$43$	6.42703	+	11.1319i	0.980112	+	1.69760i	0.661914	+	0.749580i	$0.269745\pi$
$43$	6.42703	+	11.1319i	0.980112	+	1.69760i	0.318198	+	0.948024i	$0.396922\pi$
$44$	−0.933209	+	0.538789i	−0.140687	+	0.0812254i
$45$	1.01468	+	2.09482i	0.151259	+	0.312278i
$46$	0.0420702	−	0.0728677i	0.00620291	−	0.0107437i
$47$	0.482772	−	0.836186i	0.0704195	−	0.121970i	−0.828666	−	0.559744i	$-0.810900\pi$
$47$	0.482772	−	0.836186i	0.0704195	−	0.121970i	0.899085	+	0.437774i	$0.144233\pi$
$48$	3.63534	+	6.85955i	0.524716	+	0.990091i
$49$	1.47744	−	6.84231i	0.211062	−	0.977473i
$50$	−5.75164	−	3.32071i	−0.813405	−	0.469619i
$51$	−4.37817	−	8.26120i	−0.613066	−	1.15680i
$52$		−	0.822998i		−	0.114129i
$53$	−6.46438	−	3.73221i	−0.887950	−	0.512658i	−0.0146788	−	0.999892i	$-0.504673\pi$
$53$	−6.46438	−	3.73221i	−0.887950	−	0.512658i	−0.873272	+	0.487234i	$0.838006\pi$
$54$	6.32924	+	4.63800i	0.861301	+	0.631153i
$55$		−	2.98184i		−	0.402071i
$56$	−4.31510	−	5.34629i	−0.576629	−	0.714428i
$57$	0.0273056	−	0.752608i	0.00361672	−	0.0996853i
$58$	−0.327806			−0.0430431
$59$	−1.56219	−	2.70580i	−0.203380	−	0.352265i	0.746235	−	0.665682i	$-0.231859\pi$
$59$	−1.56219	−	2.70580i	−0.203380	−	0.352265i	−0.949615	+	0.313418i	$0.898526\pi$
$60$	0.376551	+	0.0136618i	0.0486126	+	0.00176373i
$61$	−3.01744	−	1.74212i	−0.386343	−	0.223055i	0.294231	−	0.955734i	$-0.404936\pi$
$61$	−3.01744	−	1.74212i	−0.386343	−	0.223055i	−0.680575	+	0.732679i	$0.738270\pi$
$62$	9.90087			1.25741
$63$	−7.17901	−	3.38554i	−0.904470	−	0.426538i
$64$	−6.58603			−0.823254
$65$	1.97226	+	1.13869i	0.244629	+	0.141237i
$66$	−4.70711	−	8.88187i	−0.579405	−	1.09328i
$67$	2.10088	+	3.63884i	0.256664	+	0.444555i	0.965346	−	0.260973i	$-0.0840433\pi$
$67$	2.10088	+	3.63884i	0.256664	+	0.444555i	−0.708682	+	0.705528i	$0.750710\pi$
$68$	−1.51353			−0.183542
$69$	0.0817733	+	0.0512523i	0.00984435	+	0.00617005i
$70$	−3.06250	+	0.479996i	−0.366039	+	0.0573705i
$71$		−	3.50812i		−	0.416337i	−0.978093	−	0.208169i	$-0.933250\pi$
$71$		−	3.50812i		−	0.416337i	0.978093	−	0.208169i	$-0.0667503\pi$
$72$	−7.01117	+	3.39602i	−0.826274	+	0.400225i
$73$	−7.05942	−	4.07576i	−0.826243	−	0.477031i	0.0263219	−	0.999654i	$-0.491621\pi$
$73$	−7.05942	−	4.07576i	−0.826243	−	0.477031i	−0.852564	+	0.522622i	$0.824954\pi$
$74$			9.50448i			1.10487i
$75$	4.04548	−	6.45459i	0.467132	−	0.745312i
$76$	−0.105580	−	0.0609566i	−0.0121108	−	0.00699220i
$77$	6.38626	+	7.91241i	0.727782	+	0.901703i
$78$	7.67222	+	0.278359i	0.868708	+	0.0315179i
$79$	2.48110	−	4.29739i	0.279145	−	0.483494i	−0.692027	−	0.721871i	$-0.743282\pi$
$79$	2.48110	−	4.29739i	0.279145	−	0.483494i	0.971173	+	0.238377i	$0.0766155\pi$
$80$	−1.73880	+	3.01169i	−0.194404	+	0.336717i
$81$	−5.57942	+	7.06187i	−0.619936	+	0.784653i
$82$	9.90662	−	5.71959i	1.09400	−	0.631623i
$83$	−4.31033	−	7.46571i	−0.473120	−	0.819469i	0.526406	−	0.850233i	$-0.323539\pi$
$83$	−4.31033	−	7.46571i	−0.473120	−	0.819469i	−0.999527	+	0.0307645i	$0.990206\pi$
$84$	−1.02845	+	0.770216i	−0.112213	+	0.0840374i
$85$	2.09410	−	3.62708i	0.227137	−	0.393412i
$86$			19.4108i			2.09312i
$87$	0.0136324	−	0.375740i	0.00146154	−	0.0402836i
$88$	9.97991			1.06386
$89$	7.82041	+	13.5453i	0.828962	+	1.43580i	0.898853	+	0.438249i	$0.144401\pi$
$89$	7.82041	+	13.5453i	0.828962	+	1.43580i	−0.0698916	+	0.997555i	$0.522265\pi$
$90$	−0.254718	+	3.50570i	−0.0268497	+	0.369533i
$91$	−7.67222	+	1.20249i	−0.804267	+	0.126055i
$92$	0.0135297	−	0.00781136i	0.00141057	−	0.000814391i
$93$	−0.411745	+	11.3487i	−0.0426959	+	1.17680i
$94$	1.26272	−	0.729031i	0.130240	−	0.0751938i
$95$	0.292157	−	0.168677i	0.0299747	−	0.0173059i
$96$	−0.0989048	+	2.72605i	−0.0100944	+	0.278226i
$97$	1.24162	−	0.716849i	0.126067	−	0.0727850i	−0.435640	−	0.900121i	$-0.643478\pi$
$97$	1.24162	−	0.716849i	0.126067	−	0.0727850i	0.561708	+	0.827336i	$0.310145\pi$
$98$	7.09843	−	7.83270i	0.717050	−	0.791222i
$99$	10.3764	−	5.02605i	1.04287	−	0.505137i
$100$	−0.616572	−	1.06793i	−0.0616572	−	0.106793i
$101$	16.0219			1.59424			0.797120	−	0.603821i	$-0.206356\pi$
$101$	16.0219			1.59424			0.797120	+	0.603821i	$0.206356\pi$
$102$	0.511914	−	14.1096i	0.0506870	−	1.39705i
$103$			16.8660i			1.66186i	0.556381	+	0.830928i	$0.312190\pi$
$103$			16.8660i			1.66186i	−0.556381	+	0.830928i	$0.687810\pi$
$104$	−3.81107	+	6.60097i	−0.373706	+	0.647278i
$105$	−0.422825	−	3.53028i	−0.0412635	−	0.344520i
$106$	−5.63599	−	9.76182i	−0.547416	−	0.948152i
$107$	−3.36444	+	1.94246i	−0.325253	+	0.187785i	−0.653731	−	0.756727i	$-0.726797\pi$
$107$	−3.36444	+	1.94246i	−0.325253	+	0.187785i	0.328479	+	0.944511i	$0.393464\pi$
$108$	0.587156	+	1.33338i	0.0564991	+	0.128304i
$109$	1.28254	−	2.22143i	0.122845	−	0.212774i	−0.798043	−	0.602600i	$-0.794131\pi$
$109$	1.28254	−	2.22143i	0.122845	−	0.212774i	0.920889	+	0.389826i	$0.127465\pi$
$110$	2.25143	−	3.89959i	0.214665	−	0.371811i
$111$	−10.8943	−	0.395260i	−1.03404	−	0.0375164i
$112$	−1.83623	−	11.7156i	−0.173508	−	1.10702i
$113$	−9.79043	−	5.65251i	−0.921006	−	0.531743i	−0.0370501	−	0.999313i	$-0.511796\pi$
$113$	−9.79043	−	5.65251i	−0.921006	−	0.531743i	−0.883956	+	0.467570i	$0.845129\pi$
$114$	0.603964	−	0.963629i	0.0565664	−	0.0902521i
$115$			0.0432307i			0.00403129i
$116$	−0.0527109	−	0.0304327i	−0.00489408	−	0.00282560i
$117$	−0.638125	+	8.78253i	−0.0589946	+	0.811945i
$118$		−	4.71812i		−	0.434338i
$119$	2.21144	+	14.1096i	0.202722	+	1.29342i
$120$	−2.95692	−	1.85328i	−0.269929	−	0.169181i
$121$	−3.77009			−0.342735
$122$	−2.63076	−	4.55662i	−0.238178	−	0.412537i
$123$	6.14397	+	11.5931i	0.553983	+	1.04531i
$124$	1.59205	+	0.919171i	0.142970	+	0.0825440i
$125$	7.29170			0.652189
$126$	−6.83232	−	9.84803i	−0.608672	−	0.877332i
$127$	2.65660			0.235735			0.117867	−	0.993029i	$-0.462394\pi$
$127$	2.65660			0.235735			0.117867	+	0.993029i	$0.462394\pi$
$128$	−11.3409	−	6.54769i	−1.00241	−	0.578739i
$129$	−22.2492	−	0.807233i	−1.95894	−	0.0710729i
$130$	1.71953	+	2.97830i	0.150812	+	0.261215i
$131$	−8.23623			−0.719602			−0.359801	−	0.933029i	$-0.617155\pi$
$131$	−8.23623			−0.719602			−0.359801	+	0.933029i	$0.617155\pi$
$132$	0.0676717	−	1.86519i	0.00589006	−	0.162344i
$133$	−0.413990	+	1.07331i	−0.0358975	+	0.0930678i
$134$			6.34507i			0.548131i
$135$	−4.00774	−	0.437756i	−0.344931	−	0.0376760i
$136$	12.1395	+	7.00873i	1.04095	+	0.600994i
$137$		−	17.3272i		−	1.48036i	−0.672408	−	0.740180i	$-0.734740\pi$
$137$		−	17.3272i		−	1.48036i	0.672408	−	0.740180i	$-0.265260\pi$
$138$	0.0682437	+	0.128769i	0.00580929	+	0.0109616i
$139$	−5.47677	−	3.16201i	−0.464533	−	0.268198i	0.249415	−	0.968397i	$-0.419762\pi$
$139$	−5.47677	−	3.16201i	−0.464533	−	0.268198i	−0.713949	+	0.700198i	$0.753095\pi$
$140$	−0.537008	−	0.207131i	−0.0453855	−	0.0175058i
$141$	0.783123	+	1.47768i	0.0659509	+	0.124443i
$142$	2.64880	−	4.58785i	0.222282	−	0.385004i
$143$	5.64031	−	9.76931i	0.471667	−	0.816951i
$144$	−13.4111	−	0.974430i	−1.11759	−	0.0812025i
$145$	0.145860	−	0.0842123i	0.0121130	−	0.00699345i
$146$	−6.15478	−	10.6604i	−0.509373	−	0.882260i
$147$	8.68286	+	8.46215i	0.716150	+	0.697946i
$148$	−0.882370	+	1.52831i	−0.0725304	+	0.125626i
$149$		−	12.8242i		−	1.05060i	−0.850917	−	0.525300i	$-0.823953\pi$
$149$		−	12.8242i		−	1.05060i	0.850917	−	0.525300i	$-0.176047\pi$
$150$	10.1641	−	5.38666i	0.829897	−	0.439819i
$151$	5.25517			0.427660			0.213830	−	0.976871i	$-0.431406\pi$
$151$	5.25517			0.427660			0.213830	+	0.976871i	$0.431406\pi$
$152$	0.564545	+	0.977821i	0.0457907	+	0.0793118i
$153$	16.1515	+	1.17354i	1.30577	+	0.0948751i
$154$	2.37759	+	15.1696i	0.191591	+	1.22240i
$155$	−4.40547	+	2.54350i	−0.353856	+	0.204299i
$156$	1.20784	+	0.757028i	0.0967048	+	0.0606107i
$157$	−6.91794	+	3.99407i	−0.552111	+	0.318762i	−0.749973	−	0.661468i	$-0.769934\pi$
$157$	−6.91794	+	3.99407i	−0.552111	+	0.318762i	0.197862	+	0.980230i	$0.436600\pi$
$158$	6.48946	−	3.74669i	0.516274	−	0.298071i
$159$	11.4236	−	6.05416i	0.905954	−	0.480126i
$160$	−1.05823	+	0.610972i	−0.0836608	+	0.0483016i
$161$	−0.0925881	−	0.114714i	−0.00729697	−	0.00904075i
$162$	−12.6287	+	5.02265i	−0.992205	+	0.394617i
$163$	5.75231	+	9.96329i	0.450556	+	0.780385i	0.998421	−	0.0561817i	$-0.0178926\pi$
$163$	5.75231	+	9.96329i	0.450556	+	0.780385i	−0.547865	+	0.836567i	$0.684559\pi$
$164$	2.12397			0.165854
$165$	4.37619	+	2.74282i	0.340686	+	0.213528i
$166$		−	13.0180i		−	1.01039i
$167$	−8.38240	+	14.5187i	−0.648650	+	1.12349i	0.334796	+	0.942291i	$0.391333\pi$
$167$	−8.38240	+	14.5187i	−0.648650	+	1.12349i	−0.983446	+	0.181204i	$0.942001\pi$
$168$	11.8155	−	1.41515i	0.911585	−	0.109181i
$169$	−2.19222	−	3.79704i	−0.168632	−	0.292080i
$170$	5.47724	−	3.16228i	0.420085	−	0.242536i
$171$	1.07942	+	0.732354i	0.0825454	+	0.0560045i
$172$	−1.80205	+	3.12124i	−0.137405	+	0.237992i
$173$	0.856396	−	1.48332i	0.0651106	−	0.112775i	−0.831632	−	0.555326i	$-0.812593\pi$
$173$	0.856396	−	1.48332i	0.0651106	−	0.112775i	0.896743	+	0.442552i	$0.145927\pi$
$174$	0.301530	−	0.481093i	0.0228589	−	0.0364716i
$175$	−9.05470	+	7.30823i	−0.684471	+	0.552450i
$176$	14.9180	+	8.61288i	1.12448	+	0.649220i
$177$	5.40804	+	0.196211i	0.406493	+	0.0147481i
$178$			23.6191i			1.77033i
$179$	−12.4141	−	7.16731i	−0.927877	−	0.535710i	−0.0417372	−	0.999129i	$-0.513289\pi$
$179$	−12.4141	−	7.16731i	−0.927877	−	0.535710i	−0.886139	+	0.463419i	$0.846623\pi$
$180$	−0.366418	+	0.540065i	−0.0273112	+	0.0402541i
$181$			4.83147i			0.359121i	0.983747	+	0.179560i	$0.0574675\pi$
$181$			4.83147i			0.359121i	−0.983747	+	0.179560i	$0.942532\pi$
$182$	−10.9415	−	4.22029i	−0.811039	−	0.312829i
$183$	5.33232	−	2.82596i	0.394177	−	0.208901i
$184$	−0.144689			−0.0106666
$185$	−2.44167	−	4.22909i	−0.179515	−	0.310929i
$186$	−9.10724	+	14.5307i	−0.667775	+	1.06544i
$187$	−17.9662	−	10.3728i	−1.31382	−	0.758534i
$188$	0.270725			0.0197447
$189$	11.5722	−	7.42185i	0.841755	−	0.539860i
$190$	0.509437			0.0369584
$191$	−2.72114	−	1.57105i	−0.196895	−	0.113677i	0.398311	−	0.917250i	$-0.369596\pi$
$191$	−2.72114	−	1.57105i	−0.196895	−	0.113677i	−0.595206	+	0.803573i	$0.702930\pi$
$192$	6.05811	−	9.66575i	0.437206	−	0.697566i
$193$	−3.00508	−	5.20496i	−0.216311	−	0.374661i	0.737367	−	0.675493i	$-0.236069\pi$
$193$	−3.00508	−	5.20496i	−0.216311	−	0.374661i	−0.953677	+	0.300832i	$0.902736\pi$
$194$	2.16502			0.155439
$195$	−3.48532	+	1.84711i	−0.249589	+	0.132274i
$196$	1.86859	−	0.600491i	0.133471	−	0.0428922i
$197$			14.0902i			1.00388i	0.864901	+	0.501942i	$0.167381\pi$
$197$			14.0902i			1.00388i	−0.864901	+	0.501942i	$0.832619\pi$
$198$	17.3650	+	1.26171i	1.23407	+	0.0896658i
$199$	−6.84234	−	3.95043i	−0.485041	−	0.280038i	0.237474	−	0.971394i	$-0.423681\pi$
$199$	−6.84234	−	3.95043i	−0.485041	−	0.280038i	−0.722515	+	0.691355i	$0.757014\pi$
$200$			11.4207i			0.807564i
$201$	−7.27289	−	0.263871i	−0.512990	−	0.0186120i
$202$	20.9531	+	12.0973i	1.47426	+	0.851163i
$203$	−0.206685	+	0.535852i	−0.0145065	+	0.0376094i
$204$	1.39221	−	2.22128i	0.0974741	−	0.155520i
$205$	−2.93869	+	5.08995i	−0.205247	+	0.355498i
$206$	−12.7346	+	22.0570i	−0.887263	+	1.53678i
$207$	−0.150437	+	0.0728677i	−0.0104561	+	0.00506465i
$208$	−11.3936	+	6.57807i	−0.790001	+	0.456107i
$209$	−0.835517	−	1.44716i	−0.0577939	−	0.100102i
$210$	2.11257	−	4.93609i	0.145781	−	0.340622i
$211$	2.57821	−	4.46559i	0.177491	−	0.307424i	−0.763529	−	0.645773i	$-0.776535\pi$
$211$	2.57821	−	4.46559i	0.177491	−	0.307424i	0.941021	+	0.338349i	$0.109868\pi$
$212$		−	2.09292i		−	0.143742i
$213$	5.14856	+	3.22692i	0.352774	+	0.221105i
$214$	−5.86660			−0.401032
$215$	−4.98658	−	8.63701i	−0.340082	−	0.589039i
$216$	1.46512	−	13.4135i	0.0996891	−	0.912672i
$217$	6.24261	−	16.1846i	0.423776	−	1.09868i
$218$	3.35457	−	1.93676i	0.227200	−	0.131174i
$219$	12.4752	−	6.61145i	0.842995	−	0.446760i
$220$	0.724055	−	0.418033i	0.0488158	−	0.0281838i
$221$	13.7217	−	7.92220i	0.923019	−	0.532905i
$222$	−13.9489	−	8.74262i	−0.936189	−	0.586766i
$223$	3.79823	−	2.19291i	0.254348	−	0.146848i	−0.367405	−	0.930061i	$-0.619754\pi$
$223$	3.79823	−	2.19291i	0.254348	−	0.146848i	0.621754	+	0.783213i	$0.286420\pi$
$224$	1.49953	−	3.88768i	0.100192	−	0.259756i
$225$	5.75164	+	11.8744i	0.383443	+	0.791627i
$226$	−8.53582	−	14.7845i	−0.567794	−	0.983449i
$227$	9.67394			0.642082			0.321041	−	0.947065i	$-0.395967\pi$
$227$	9.67394			0.642082			0.321041	+	0.947065i	$0.395967\pi$
$228$	0.186578	−	0.0988800i	0.0123564	−	0.00654849i
$229$		−	8.85314i		−	0.585032i	−0.956261	−	0.292516i	$-0.905508\pi$
$229$		−	8.85314i		−	0.585032i	0.956261	−	0.292516i	$-0.0944925\pi$
$230$	−0.0326412	+	0.0565363i	−0.00215230	+	0.00372789i
$231$	−17.4867	+	2.09440i	−1.15054	+	0.137801i
$232$	0.281850	+	0.488179i	0.0185044	+	0.0320505i
$233$	11.1612	−	6.44391i	0.731194	−	0.422155i	−0.0876651	−	0.996150i	$-0.527941\pi$
$233$	11.1612	−	6.44391i	0.731194	−	0.422155i	0.818859	+	0.573995i	$0.194607\pi$
$234$	−7.46575	+	11.0038i	−0.488052	+	0.719341i
$235$	−0.374571	+	0.648777i	−0.0244343	+	0.0423215i
$236$	0.438017	−	0.758668i	0.0285125	−	0.0493851i
$237$	4.02469	+	7.59421i	0.261432	+	0.493297i
$238$	−7.76131	+	20.1219i	−0.503091	+	1.30431i
$239$	4.18421	+	2.41575i	0.270654	+	0.156262i	0.629185	−	0.777256i	$-0.283389\pi$
$239$	4.18421	+	2.41575i	0.270654	+	0.156262i	−0.358531	+	0.933518i	$0.616722\pi$
$240$	−2.82058	−	5.32217i	−0.182067	−	0.343544i
$241$		−	10.0336i		−	0.646323i	−0.946344	−	0.323161i	$-0.895254\pi$
$241$		−	10.0336i		−	0.646323i	0.946344	−	0.323161i	$-0.104746\pi$
$242$	−4.93045	−	2.84659i	−0.316941	−	0.182986i
$243$	−5.23192	−	14.6842i	−0.335628	−	0.941995i
$244$		−	0.976932i		−	0.0625417i
$245$	−1.14631	+	5.30879i	−0.0732349	+	0.339166i
$246$	−0.718379	+	19.8002i	−0.0458022	+	1.26242i
$247$	1.27625			0.0812058
$248$	−8.51284	−	14.7447i	−0.540566	−	0.936288i
$249$	14.9216	+	0.541377i	0.945619	+	0.0343083i
$250$	9.53594	+	5.50558i	0.603106	+	0.348203i
$251$	−7.98203			−0.503821			−0.251911	−	0.967751i	$-0.581059\pi$
$251$	−7.98203			−0.503821			−0.251911	+	0.967751i	$0.581059\pi$
$252$	−0.184366	−	2.21785i	−0.0116140	−	0.139711i
$253$	0.214137			0.0134627
$254$	3.47424	+	2.00586i	0.217993	+	0.125859i
$255$	3.39692	+	6.40967i	0.212723	+	0.401389i
$256$	−3.30160	−	5.71853i	−0.206350	−	0.357408i
$257$	−2.68230			−0.167317			−0.0836585	−	0.996494i	$-0.526660\pi$
$257$	−2.68230			−0.167317			−0.0836585	+	0.996494i	$0.526660\pi$
$258$	−28.4876	−	17.8549i	−1.77356	−	1.11160i
$259$	15.5366	+	5.99267i	0.965397	+	0.372367i
$260$			0.638544i			0.0396008i
$261$	0.538902	+	0.365629i	0.0333572	+	0.0226319i
$262$	−10.7712	−	6.21874i	−0.665445	−	0.384195i
$263$			23.4359i			1.44512i	0.691309	+	0.722560i	$0.257034\pi$
$263$			23.4359i			1.44512i	−0.691309	+	0.722560i	$0.742966\pi$
$264$	−9.17994	+	14.6467i	−0.564986	+	0.901439i
$265$	5.01556	+	2.89573i	0.308103	+	0.177883i
$266$	−1.35181	+	1.09107i	−0.0828847	+	0.0668979i
$267$	−27.0729	−	0.982241i	−1.65683	−	0.0601122i
$268$	−0.589059	+	1.02028i	−0.0359825	+	0.0623236i
$269$	−1.98955	+	3.44600i	−0.121305	+	0.210106i	−0.920283	−	0.391254i	$-0.872041\pi$
$269$	−1.98955	+	3.44600i	−0.121305	+	0.210106i	0.798978	+	0.601361i	$0.205375\pi$
$270$	−4.91071	−	3.59852i	−0.298856	−	0.218999i
$271$	10.8303	−	6.25288i	0.657895	−	0.379836i	−0.133580	−	0.991038i	$-0.542647\pi$
$271$	10.8303	−	6.25288i	0.657895	−	0.379836i	0.791474	+	0.611202i	$0.209314\pi$
$272$	12.0974	+	20.9533i	0.733511	+	1.27048i
$273$	5.29244	−	12.3660i	0.320313	−	0.748422i
$274$	13.0828	−	22.6601i	0.790363	−	1.36895i
$275$		−	16.9024i		−	1.01925i
$276$	−0.000981105		0.0270416i	−5.90556e−5		0.00162771i
$277$	−19.6909			−1.18311			−0.591557	−	0.806263i	$-0.701487\pi$
$277$	−19.6909			−1.18311			−0.591557	+	0.806263i	$0.701487\pi$
$278$	−4.77494	−	8.27044i	−0.286382	−	0.496028i
$279$	−16.2767	−	11.0433i	−0.974460	−	0.661142i
$280$	3.34798	+	4.14806i	0.200080	+	0.247894i
$281$	7.03456	−	4.06141i	0.419647	−	0.242283i	−0.275279	−	0.961364i	$-0.588770\pi$
$281$	7.03456	−	4.06141i	0.419647	−	0.242283i	0.694926	+	0.719081i	$0.255437\pi$
$282$	−0.0915661	+	2.52378i	−0.00545268	+	0.150289i
$283$	1.16390	−	0.671978i	0.0691867	−	0.0399450i	−0.465008	−	0.885307i	$-0.653948\pi$
$283$	1.16390	−	0.671978i	0.0691867	−	0.0399450i	0.534194	+	0.845362i	$0.320615\pi$
$284$	0.851847	−	0.491814i	0.0505478	−	0.0291838i
$285$	−0.0211858	+	0.583931i	−0.00125494	+	0.0345891i
$286$	14.7526	−	8.51741i	0.872339	−	0.503645i
$287$	−3.10335	−	19.8002i	−0.183185	−	1.16877i
$288$	−3.90981	−	2.65269i	−0.230388	−	0.156311i
$289$	−6.06929	−	10.5123i	−0.357017	−	0.618371i
$290$	0.254337			0.0149352
$291$	−0.0900361	+	2.48161i	−0.00527801	+	0.145474i
$292$		−	2.28557i		−	0.133753i
$293$	−10.6300	+	18.4117i	−0.621012	+	1.07562i	0.368285	+	0.929713i	$0.379945\pi$
$293$	−10.6300	+	18.4117i	−0.621012	+	1.07562i	−0.989298	+	0.145912i	$0.953388\pi$
$294$	4.96595	+	17.6226i	0.289620	+	1.02777i
$295$	1.21207	+	2.09936i	0.0705693	+	0.122230i
$296$	14.1543	−	8.17202i	0.822705	−	0.474989i
$297$	−2.16836	+	19.8517i	−0.125821	+	1.15191i
$298$	9.68289	−	16.7713i	0.560915	−	0.971533i
$299$	−0.0817733	+	0.141636i	−0.00472907	+	0.00819100i
$300$	2.13446	+	0.0774412i	0.123233	+	0.00447107i
$301$	31.7301	+	12.2387i	1.82889	+	0.705429i
$302$	6.87261	+	3.96790i	0.395474	+	0.228327i
$303$	−14.7376	+	23.5140i	−0.846655	+	1.35084i
$304$			1.94886i			0.111775i
$305$	2.34116	+	1.35167i	0.134054	+	0.0773963i
$306$	20.2365	+	13.7299i	1.15684	+	0.784884i
$307$			13.2098i			0.753925i	0.926229	+	0.376962i	$0.123031\pi$
$307$			13.2098i			0.753925i	−0.926229	+	0.376962i	$0.876969\pi$
$308$	−1.02599	+	2.65999i	−0.0584614	+	0.151567i
$309$	−24.7528	−	15.5140i	−1.40814	−	0.882563i
$310$	−7.68185			−0.436300
$311$	10.2687	+	17.7859i	0.582283	+	1.00854i	0.995208	+	0.0977785i	$0.0311737\pi$
$311$	10.2687	+	17.7859i	0.582283	+	1.00854i	−0.412925	+	0.910765i	$0.635493\pi$
$312$	−6.18209	−	11.6650i	−0.349992	−	0.660402i
$313$	14.2976	+	8.25471i	0.808147	+	0.466584i	0.846312	−	0.532688i	$-0.178818\pi$
$313$	14.2976	+	8.25471i	0.808147	+	0.466584i	−0.0381649	+	0.999271i	$0.512151\pi$
$314$	−12.0629			−0.680746
$315$	5.57002	+	2.62676i	0.313835	+	0.148001i
$316$	1.39133			0.0782685
$317$	8.11112	+	4.68296i	0.455566	+	0.263021i	0.710178	−	0.704022i	$-0.248614\pi$
$317$	8.11112	+	4.68296i	0.455566	+	0.263021i	−0.254612	+	0.967043i	$0.581948\pi$
$318$	19.5108	+	0.707879i	1.09411	+	0.0396959i
$319$	−0.417133	−	0.722496i	−0.0233550	−	0.0404520i
$320$	5.10995			0.285655
$321$	0.243972	−	6.72445i	0.0136172	−	0.375322i
$322$	−0.0344703	−	0.219929i	−0.00192095	−	0.0122562i
$323$		−	2.34708i		−	0.130595i
$324$	−2.49697	−	0.364778i	−0.138721	−	0.0202654i
$325$	11.1797	+	6.45459i	0.620137	+	0.358036i
$326$			17.3731i			0.962205i
$327$	2.08046	+	3.92564i	0.115050	+	0.217089i
$328$	−17.0356	−	9.83548i	−0.940631	−	0.543074i
$329$	−0.395560	−	2.52378i	−0.0218079	−	0.139140i
$330$	3.65213	+	6.89124i	0.201043	+	0.379350i
$331$	−14.4220	+	24.9796i	−0.792702	+	1.37300i	0.131586	+	0.991305i	$0.457993\pi$
$331$	−14.4220	+	24.9796i	−0.792702	+	1.37300i	−0.924288	+	0.381696i	$0.875340\pi$
$332$	1.20856	−	2.09328i	0.0663282	−	0.114884i
$333$	10.6011	−	15.6250i	0.580938	−	0.856247i
$334$	−21.9247	+	12.6582i	−1.19967	+	0.692627i
$335$	−1.63003	−	2.82329i	−0.0890579	−	0.154253i
$336$	18.8831	+	8.08166i	1.03016	+	0.440891i
$337$	−6.26205	+	10.8462i	−0.341116	+	0.590829i	−0.984640	−	0.174596i	$-0.944138\pi$
$337$	−6.26205	+	10.8462i	−0.341116	+	0.590829i	0.643525	+	0.765425i	$0.277471\pi$
$338$		−	6.62092i		−	0.360130i
$339$	17.3013	−	9.16915i	0.939680	−	0.498000i
$340$	1.17431			0.0636860
$341$	12.5988	+	21.8218i	0.682266	+	1.18172i
$342$	0.858683	+	1.77277i	0.0464322	+	0.0958606i
$343$	−8.32817	−	16.5421i	−0.449679	−	0.893190i
$344$	28.9072	−	16.6896i	1.55857	−	0.899841i
$345$	−0.0634460	−	0.0397654i	−0.00341582	−	0.00214090i
$346$	2.23996	−	1.29324i	0.120421	−	0.0695250i
$347$	24.8740	−	14.3610i	1.33531	−	0.770939i	0.349199	−	0.937049i	$-0.386454\pi$
$347$	24.8740	−	14.3610i	1.33531	−	0.770939i	0.986107	+	0.166109i	$0.0531204\pi$
$348$	0.0931491	−	0.0493660i	0.00499332	−	0.00264630i
$349$	11.0854	−	6.40017i	0.593389	−	0.342593i	−0.173048	−	0.984913i	$-0.555361\pi$
$349$	11.0854	−	6.40017i	0.593389	−	0.342593i	0.766436	+	0.642320i	$0.222028\pi$
$350$	−17.3596	+	2.72083i	−0.927911	+	0.145435i
$351$	−12.3024	−	9.01506i	−0.656653	−	0.481188i
$352$	3.02636	+	5.24181i	0.161305	+	0.279389i
$353$	−26.9982			−1.43697			−0.718485	−	0.695542i	$-0.755164\pi$
$353$	−26.9982			−1.43697			−0.718485	+	0.695542i	$0.755164\pi$
$354$	6.92437	+	4.33992i	0.368026	+	0.230664i
$355$			2.72187i			0.144462i
$356$	−2.19274	+	3.79793i	−0.116215	+	0.201290i
$357$	−22.7416	−	9.73303i	−1.20361	−	0.515126i
$358$	−10.8233	−	18.7465i	−0.572030	−	0.990785i
$359$	−24.2669	+	14.0105i	−1.28076	+	0.739445i	−0.976987	−	0.213300i	$-0.931579\pi$
$359$	−24.2669	+	14.0105i	−1.28076	+	0.739445i	−0.303770	+	0.952745i	$0.598245\pi$
$360$	5.43980	−	2.63489i	0.286703	−	0.138871i
$361$	−9.40547	+	16.2908i	−0.495025	+	0.857408i
$362$	−3.64799	+	6.31851i	−0.191734	+	0.332093i
$363$	3.46789	−	5.53303i	0.182017	−	0.290409i
$364$	−1.36758	−	1.69440i	−0.0716809	−	0.0888107i
$365$	5.47724	+	3.16228i	0.286692	+	0.165522i
$366$	9.10724	+	0.330423i	0.476043	+	0.0172715i
$367$		−	33.4382i		−	1.74546i	−0.488202	−	0.872731i	$-0.662347\pi$
$367$		−	33.4382i		−	1.74546i	0.488202	−	0.872731i	$-0.337653\pi$
$368$	−0.216281	−	0.124870i	−0.0112744	−	0.00650928i
$369$	−22.6657	−	1.64685i	−1.17993	−	0.0857316i
$370$		−	7.37430i		−	0.383372i
$371$	−19.5108	+	3.05799i	−1.01295	+	0.158763i
$372$	−2.81342	+	1.49102i	−0.145869	+	0.0773059i
$373$	−7.96805			−0.412570			−0.206285	−	0.978492i	$-0.566137\pi$
$373$	−7.96805			−0.412570			−0.206285	+	0.978492i	$0.566137\pi$
$374$	−15.6639	−	27.1307i	−0.809961	−	1.40289i
$375$	−6.70721	+	10.7014i	−0.346359	+	0.552618i
$376$	−2.17139	−	1.25365i	−0.111981	−	0.0646522i
$377$	0.637169			0.0328159
$378$	20.7378	−	0.968580i	1.06664	−	0.0498184i
$379$	3.88714			0.199669			0.0998345	−	0.995004i	$-0.468169\pi$
$379$	3.88714			0.199669			0.0998345	+	0.995004i	$0.468169\pi$
$380$	0.0819169	+	0.0472948i	0.00420225	+	0.00242617i
$381$	−2.44365	+	3.89886i	−0.125192	+	0.199744i
$382$	−2.37244	−	4.10918i	−0.121384	−	0.210244i
$383$	12.6830			0.648071			0.324036	−	0.946045i	$-0.394960\pi$
$383$	12.6830			0.648071			0.324036	+	0.946045i	$0.394960\pi$
$384$	20.0413	−	10.6213i	1.02273	−	0.542014i
$385$	−4.95495	−	6.13905i	−0.252528	−	0.312875i
$386$		−	9.07592i		−	0.461952i
$387$	21.6505	−	31.9108i	1.10056	−	1.62211i
$388$	0.348133	+	0.200995i	0.0176738	+	0.0102040i
$389$		−	20.5614i		−	1.04250i	−0.853403	−	0.521252i	$-0.825465\pi$
$389$		−	20.5614i		−	1.04250i	0.853403	−	0.521252i	$-0.174535\pi$
$390$	−5.95269	−	0.215972i	−0.301426	−	0.0109362i
$391$	0.260474	+	0.150385i	0.0131727	+	0.00760529i
$392$	−17.7680	−	3.83658i	−0.897418	−	0.193776i
$393$	7.57603	−	12.0876i	0.382160	−	0.609739i
$394$	−10.6388	+	18.4269i	−0.535973	+	0.928332i
$395$	−1.92503	+	3.33424i	−0.0968586	+	0.167764i
$396$	2.67513	+	1.81500i	0.134430	+	0.0912070i
$397$	12.9646	−	7.48513i	0.650676	−	0.375668i	−0.138039	−	0.990427i	$-0.544080\pi$
$397$	12.9646	−	7.48513i	0.650676	−	0.375668i	0.788715	+	0.614759i	$0.210747\pi$
$398$	−5.96552	−	10.3326i	−0.299025	−	0.517926i
$399$	−1.19440	−	1.59485i	−0.0597947	−	0.0798426i
$400$	−9.85630	+	17.0716i	−0.492815	+	0.853580i
$401$			10.3164i			0.515178i	0.966255	+	0.257589i	$0.0829280\pi$
$401$			10.3164i			0.515178i	−0.966255	+	0.257589i	$0.917072\pi$
$402$	−9.31211	−	5.83646i	−0.464446	−	0.291096i
$403$	−19.2447			−0.958647
$404$	2.24616	+	3.89047i	0.111751	+	0.193558i
$405$	4.32894	−	5.47914i	0.215107	−	0.272261i
$406$	−0.674892	+	0.544719i	−0.0334943	+	0.0270340i
$407$	−20.9482	+	12.0944i	−1.03836	+	0.599499i
$408$	−21.4525	+	11.3691i	−1.06206	+	0.562856i
$409$	−16.0387	+	9.25995i	−0.793063	+	0.457875i	−0.841040	−	0.540973i	$-0.818056\pi$
$409$	−16.0387	+	9.25995i	−0.793063	+	0.457875i	0.0479769	+	0.998848i	$0.484723\pi$
$410$	−7.68631	+	4.43769i	−0.379600	+	0.219162i
$411$	25.4296	+	15.9383i	1.25435	+	0.786177i
$412$	−4.09543	+	2.36450i	−0.201767	+	0.116490i
$413$	−7.71252	−	2.97482i	−0.379508	−	0.146381i
$414$	−0.251757	−	0.0182923i	−0.0123732	−	0.000899017i
$415$	3.34429	+	5.79247i	0.164165	+	0.284341i
$416$	−4.62275			−0.226649
$417$	9.67838	−	5.12923i	0.473952	−	0.251179i
$418$		−	2.52342i		−	0.123424i
$419$	6.37677	−	11.0449i	0.311526	−	0.539578i	−0.667167	−	0.744908i	$-0.732493\pi$
$419$	6.37677	−	11.0449i	0.311526	−	0.539578i	0.978693	+	0.205330i	$0.0658267\pi$
$420$	0.797952	−	0.597592i	0.0389361	−	0.0291595i
$421$	6.78793	+	11.7570i	0.330824	+	0.573003i	0.982674	−	0.185345i	$-0.0593402\pi$
$421$	6.78793	+	11.7570i	0.330824	+	0.573003i	−0.651850	+	0.758348i	$0.726007\pi$
$422$	6.74347	−	3.89334i	0.328267	−	0.189525i
$423$	−2.88902	−	0.209911i	−0.140469	−	0.0102062i
$424$	−9.69173	+	16.7866i	−0.470672	+	0.815227i
$425$	11.8703	−	20.5599i	0.575793	−	0.997303i
$426$	4.29672	+	8.10751i	0.208177	+	0.392810i
$427$	−9.10724	+	1.42741i	−0.440730	+	0.0690772i
$428$	−0.943342	−	0.544639i	−0.0455982	−	0.0263261i
$429$	9.14938	+	17.2640i	0.441736	+	0.833515i
$430$		−	15.0604i		−	0.726277i
$431$	31.3069	+	18.0750i	1.50800	+	0.870643i	0.999957	+	0.00931038i	$0.00296363\pi$
$431$	31.3069	+	18.0750i	1.50800	+	0.870643i	0.508041	+	0.861333i	$0.330370\pi$
$432$	13.7662	−	18.7860i	0.662326	−	0.903843i
$433$			33.0085i			1.58629i	0.609034	+	0.793144i	$0.291557\pi$
$433$			33.0085i			1.58629i	−0.609034	+	0.793144i	$0.708443\pi$
$434$	20.3841	−	16.4524i	0.978466	−	0.789740i
$435$	−0.0105770	+	0.291528i	−0.000507130	+	0.0139777i
$436$	0.719215			0.0344442
$437$	0.0121133	+	0.0209809i	0.000579459	+	0.00100365i
$438$	21.3068	+	0.773039i	1.01808	+	0.0369372i
$439$	26.4673	+	15.2809i	1.26321	+	0.729317i	0.973695	−	0.227856i	$-0.0731714\pi$
$439$	26.4673	+	15.2809i	1.26321	+	0.729317i	0.289519	+	0.957172i	$0.406505\pi$
$440$	−7.74318			−0.369141
$441$	−20.4060	+	4.95924i	−0.971716	+	0.236154i
$442$	23.9266			1.13807
$443$	−17.9290	−	10.3513i	−0.851833	−	0.491806i	0.00943615	−	0.999955i	$-0.496996\pi$
$443$	−17.9290	−	10.3513i	−0.851833	−	0.491806i	−0.861269	+	0.508150i	$0.830330\pi$
$444$	−1.43133	−	2.70078i	−0.0679278	−	0.128174i
$445$	−6.06767	−	10.5095i	−0.287635	−	0.498199i
$446$	6.62300			0.313608
$447$	18.8210	+	11.7963i	0.890203	+	0.557944i
$448$	−13.5594	+	10.9441i	−0.640622	+	0.517059i
$449$		−	6.40243i		−	0.302150i	−0.988522	−	0.151075i	$-0.951727\pi$
$449$		−	6.40243i		−	0.302150i	0.988522	−	0.151075i	$-0.0482734\pi$
$450$	−1.44386	+	19.8719i	−0.0680641	+	0.936769i
$451$	25.2123	+	14.5563i	1.18720	+	0.685431i
$452$		−	3.16977i		−	0.149093i
$453$	−4.83393	+	7.71256i	−0.227118	+	0.362368i
$454$	12.6514	+	7.30428i	0.593759	+	0.342807i
$455$	5.95269	−	0.932986i	0.279067	−	0.0437390i
$456$	−1.95436	−	0.0709067i	−0.0915211	−	0.00332051i
$457$	1.57340	−	2.72521i	0.0736007	−	0.127480i	−0.826876	−	0.562384i	$-0.809884\pi$
$457$	1.57340	−	2.72521i	0.0736007	−	0.127480i	0.900477	+	0.434904i	$0.143218\pi$
$458$	6.68454	−	11.5780i	0.312348	−	0.541003i
$459$	−16.5791	+	22.6246i	−0.773846	+	1.05603i
$460$	−0.0104974	+	0.00606065i	−0.000489442	+	0.000282579i
$461$	7.44225	+	12.8904i	0.346620	+	0.600364i	0.985647	−	0.168821i	$-0.0539959\pi$
$461$	7.44225	+	12.8904i	0.346620	+	0.600364i	−0.639026	+	0.769185i	$0.720663\pi$
$462$	−24.4502	−	10.4643i	−1.13752	−	0.486843i
$463$	13.3616	−	23.1429i	0.620964	−	1.07554i	−0.368342	−	0.929690i	$-0.620075\pi$
$463$	13.3616	−	23.1429i	0.620964	−	1.07554i	0.989307	−	0.145851i	$-0.0465921\pi$
$464$			0.972971i			0.0451691i
$465$	0.319463	−	8.80515i	0.0148147	−	0.408329i
$466$	19.4618			0.901552
$467$	−12.3967	−	21.4717i	−0.573650	−	0.993591i	−0.996187	−	0.0872454i	$-0.972194\pi$
$467$	−12.3967	−	21.4717i	−0.573650	−	0.993591i	0.422537	−	0.906346i	$-0.361140\pi$
$468$	−2.22205	+	1.07630i	−0.102714	+	0.0497520i
$469$	10.3720	+	4.00063i	0.478936	+	0.184732i
$470$	−0.979714	+	0.565638i	−0.0451908	+	0.0260909i
$471$	0.501654	−	13.8268i	0.0231150	−	0.637104i
$472$	−7.02636	+	4.05667i	−0.323414	+	0.186723i
$473$	−42.7821	+	24.7003i	−1.96712	+	1.13572i
$474$	−0.470584	+	12.9704i	−0.0216146	+	0.595750i
$475$	1.65608	−	0.956138i	0.0759861	−	0.0438706i
$476$	−3.11608	+	2.51505i	−0.142825	+	0.115277i
$477$	−1.62278	+	22.3344i	−0.0743020	+	1.02262i
$478$	3.64801	+	6.31855i	0.166856	+	0.289004i
$479$	12.5271			0.572377			0.286189	−	0.958173i	$-0.407612\pi$
$479$	12.5271			0.572377			0.286189	+	0.958173i	$0.407612\pi$
$480$	0.0767379	−	2.11508i	0.00350259	−	0.0965397i
$481$		−	18.4742i		−	0.842352i
$482$	7.57587	−	13.1218i	0.345071	−	0.597681i
$483$	0.253523	−	0.0303646i	0.0115357	−	0.00138164i
$484$	−0.528540	−	0.915459i	−0.0240246	−	0.0416118i
$485$	−0.963343	+	0.556187i	−0.0437432	+	0.0252551i
$486$	4.24510	−	23.1541i	0.192562	−	1.05029i
$487$	1.69748	−	2.94012i	0.0769202	−	0.133230i	−0.824999	−	0.565133i	$-0.808825\pi$
$487$	1.69748	−	2.94012i	0.0769202	−	0.133230i	0.901920	+	0.431904i	$0.142158\pi$
$488$	−4.52390	+	7.83562i	−0.204787	+	0.354702i
$489$	−19.9135	−	0.722488i	−0.900519	−	0.0326720i
$490$	−5.50750	+	6.07721i	−0.248804	+	0.274540i
$491$	0.780171	+	0.450432i	0.0352086	+	0.0203277i	0.517501	−	0.855683i	$-0.326862\pi$
$491$	0.780171	+	0.450432i	0.0352086	+	0.0203277i	−0.482292	+	0.876010i	$0.660196\pi$
$492$	−1.95371	+	3.11716i	−0.0880802	+	0.140532i
$493$		−	1.17178i		−	0.0527745i
$494$	1.66905	+	0.963629i	0.0750943	+	0.0433557i
$495$	−8.05080	+	3.89959i	−0.361857	+	0.175274i
$496$		−	29.3871i		−	1.31952i
$497$	−5.82948	−	7.22257i	−0.261488	−	0.323976i
$498$	19.1054	+	11.9745i	0.856135	+	0.536591i
$499$	21.8688			0.978984			0.489492	−	0.872008i	$-0.337182\pi$
$499$	21.8688			0.978984			0.489492	+	0.872008i	$0.337182\pi$
$500$	1.02225	+	1.77058i	0.0457162	+	0.0791829i
$501$	−13.5974	−	25.6571i	−0.607488	−	1.14627i
$502$	−10.4387	−	6.02681i	−0.465904	−	0.268990i
$503$	42.9876			1.91672			0.958362	−	0.285557i	$-0.0921785\pi$
$503$	42.9876			1.91672			0.958362	+	0.285557i	$0.0921785\pi$
$504$	−8.79149	+	18.6423i	−0.391604	+	0.830394i
$505$	−12.4310			−0.553173
$506$	0.280044	+	0.161684i	0.0124495	+	0.00718771i
$507$	7.58908	+	0.275342i	0.337043	+	0.0122284i
$508$	0.372436	+	0.645079i	0.0165242	+	0.0286207i
$509$	−30.0832			−1.33342			−0.666708	−	0.745319i	$-0.732297\pi$
$509$	−30.0832			−1.33342			−0.666708	+	0.745319i	$0.732297\pi$
$510$	−0.397182	+	10.9473i	−0.0175875	+	0.484753i
$511$	−21.3068	+	3.33948i	−0.942556	+	0.147730i
$512$			16.2193i			0.716799i
$513$	−2.06771	+	0.910522i	−0.0912916	+	0.0402005i
$514$	−3.50785	−	2.02526i	−0.154725	−	0.0893304i
$515$		−	13.0859i		−	0.576635i
$516$	−2.92318	−	5.51576i	−0.128686	−	0.242818i
$517$	3.21362	+	1.85538i	0.141335	+	0.0815997i
$518$	15.7937	+	19.5680i	0.693935	+	0.859767i
$519$	1.38919	+	2.62128i	0.0609789	+	0.115061i
$520$	2.95692	−	5.12153i	0.129669	−	0.224594i
$521$	6.00837	−	10.4068i	0.263231	−	0.455930i	−0.703867	−	0.710331i	$-0.748545\pi$
$521$	6.00837	−	10.4068i	0.263231	−	0.455930i	0.967099	+	0.254401i	$0.0818784\pi$
$522$	0.428699	+	0.885059i	0.0187636	+	0.0387380i
$523$	−16.1185	+	9.30602i	−0.704813	+	0.406924i	−0.809137	−	0.587620i	$-0.800065\pi$
$523$	−16.1185	+	9.30602i	−0.704813	+	0.406924i	0.104325	+	0.994543i	$0.466732\pi$
$524$	−1.15466	−	1.99993i	−0.0504417	−	0.0873675i
$525$	−2.39676	−	20.0112i	−0.104603	−	0.873361i
$526$	−17.6952	+	30.6490i	−0.771548	+	1.33636i
$527$			35.3919i			1.54169i
$528$	−26.3625	+	13.9713i	−1.14728	+	0.608023i
$529$	22.9969			0.999865
$530$	4.37283	+	7.57397i	0.189944	+	0.328992i
$531$	−5.26250	+	7.75642i	−0.228373	+	0.336600i
$532$	−0.318662	+	0.0499449i	−0.0138157	+	0.00216539i
$533$	−19.2559	+	11.1174i	−0.834064	+	0.481547i
$534$	−34.6637	−	21.7259i	−1.50005	−	0.940170i
$535$	2.61039	−	1.50711i	0.112857	−	0.0651580i
$536$	9.44926	−	5.45554i	0.408146	−	0.235643i
$537$	21.9379	−	11.6264i	0.946690	−	0.501715i
$538$	−5.20379	+	3.00441i	−0.224351	+	0.129529i
$539$	26.2963	+	5.67806i	1.13266	+	0.244572i
$540$	−0.455560	−	1.03454i	−0.0196042	−	0.0445193i
$541$	−21.1242	−	36.5882i	−0.908201	−	1.57305i	−0.816562	−	0.577258i	$-0.804123\pi$
$541$	−21.1242	−	36.5882i	−0.908201	−	1.57305i	−0.0916391	−	0.995792i	$-0.529211\pi$
$542$	18.8849			0.811176
$543$	−7.09074	−	4.44419i	−0.304293	−	0.190719i
$544$			8.50145i			0.364497i
$545$	−0.995095	+	1.72356i	−0.0426252	+	0.0738290i
$546$	16.2582	−	12.1759i	0.695788	−	0.521081i
$547$	−6.92349	−	11.9918i	−0.296027	−	0.512734i	0.679196	−	0.733957i	$-0.262329\pi$
$547$	−6.92349	−	11.9918i	−0.296027	−	0.512734i	−0.975223	+	0.221223i	$0.928995\pi$
$548$	4.20741	−	2.42915i	0.179732	−	0.103768i
$549$	−0.757480	+	10.4252i	−0.0323285	+	0.444938i
$550$	12.7621	−	22.1046i	0.544178	−	0.942544i
$551$	0.0471929	−	0.0817405i	0.00201049	−	0.00348226i
$552$	0.133091	−	0.212347i	0.00566473	−	0.00903810i
$553$	−2.03289	−	12.9704i	−0.0864474	−	0.551557i
$554$	−25.7514	−	14.8676i	−1.09407	−	0.631664i
$555$	8.45263	+	0.306673i	0.358794	+	0.0130175i
$556$		−	1.77317i		−	0.0751992i
$557$	−27.2305	−	15.7215i	−1.15379	−	0.666143i	−0.203985	−	0.978974i	$-0.565389\pi$
$557$	−27.2305	−	15.7215i	−1.15379	−	0.666143i	−0.949809	+	0.312831i	$0.898723\pi$
$558$	−12.9482	−	26.7318i	−0.548140	−	1.13165i
$559$		−	37.7296i		−	1.59579i
$560$	1.42469	+	9.08989i	0.0602041	+	0.384118i
$561$	31.7493	−	16.8261i	1.34046	−	0.710399i
$562$	12.2662			0.517419
$563$	17.0829	+	29.5884i	0.719956	+	1.24700i	0.961017	+	0.276491i	$0.0891716\pi$
$563$	17.0829	+	29.5884i	0.719956	+	1.24700i	−0.241060	+	0.970510i	$0.577495\pi$
$564$	−0.249025	+	0.397320i	−0.0104858	+	0.0167302i
$565$	7.59616	+	4.38565i	0.319573	+	0.184506i
$566$	2.02950			0.0853063
$567$	0.247797	+	23.8105i	0.0104065	+	0.999946i
$568$	−9.10981			−0.382239
$569$	19.6652	+	11.3537i	0.824407	+	0.475972i	0.851934	−	0.523649i	$-0.175430\pi$
$569$	19.6652	+	11.3537i	0.824407	+	0.475972i	−0.0275266	+	0.999621i	$0.508763\pi$
$570$	−0.468602	+	0.747657i	−0.0196276	+	0.0313159i
$571$	5.29931	+	9.17867i	0.221769	+	0.384116i	0.955345	−	0.295492i	$-0.0954835\pi$
$571$	5.29931	+	9.17867i	0.221769	+	0.384116i	−0.733576	+	0.679607i	$0.762150\pi$
$572$	3.16293			0.132249
$573$	4.80872	−	2.54846i	0.200887	−	0.106464i
$574$	10.8916	−	28.2375i	0.454606	−	1.17861i
$575$			0.245051i			0.0102193i
$576$	8.61308	+	17.7819i	0.358878	+	0.740914i
$577$	−12.6222	−	7.28745i	−0.525471	−	0.303381i	0.213699	−	0.976899i	$-0.431449\pi$
$577$	−12.6222	−	7.28745i	−0.525471	−	0.303381i	−0.739170	+	0.673519i	$0.764782\pi$
$578$		−	18.3304i		−	0.762444i
$579$	10.4031	+	0.377438i	0.432337	+	0.0156858i
$580$	0.0408971	+	0.0236120i	0.00169816	+	0.000980434i
$581$	−21.2800	−	8.20800i	−0.882845	−	0.340525i
$582$	−1.99148	+	3.17741i	−0.0825494	+	0.131708i
$583$	14.3436	−	24.8438i	0.594050	−	1.02893i
$584$	−10.5838	+	18.3318i	−0.437963	+	0.758574i
$585$	0.495106	−	6.81416i	0.0204701	−	0.281731i
$586$	−27.8035	+	16.0523i	−1.14855	+	0.663116i
$587$	−15.0927	−	26.1414i	−0.622944	−	1.07897i	−0.988935	−	0.148352i	$-0.952603\pi$
$587$	−15.0927	−	26.1414i	−0.622944	−	1.07897i	0.365991	−	0.930619i	$-0.380730\pi$
$588$	−0.837516	+	3.29472i	−0.0345386	+	0.135872i
$589$	−1.42539	+	2.46884i	−0.0587321	+	0.101727i
$590$			3.66068i			0.150708i
$591$	−20.6789	−	12.9607i	−0.850618	−	0.533134i
$592$	28.2105			1.15945
$593$	15.2911	+	26.4850i	0.627930	+	1.08761i	0.987966	+	0.154669i	$0.0494310\pi$
$593$	15.2911	+	26.4850i	0.627930	+	1.08761i	−0.360036	+	0.932938i	$0.617236\pi$
$594$	−17.8247	+	24.3245i	−0.731357	+	0.998045i
$595$	−1.71580	−	10.9473i	−0.0703411	−	0.448794i
$596$	3.11400	−	1.79787i	0.127554	−	0.0736435i
$597$	12.0916	−	6.40815i	0.494875	−	0.262268i
$598$	−0.213883	+	0.123485i	−0.00874633	+	0.00504970i
$599$	2.33872	−	1.35026i	0.0955573	−	0.0551701i	−0.451460	−	0.892291i	$-0.649097\pi$
$599$	2.33872	−	1.35026i	0.0955573	−	0.0551701i	0.547017	+	0.837121i	$0.315763\pi$
$600$	−16.7611	−	10.5052i	−0.684271	−	0.428874i
$601$	−21.0197	+	12.1357i	−0.857411	+	0.495026i	−0.863144	−	0.504957i	$-0.831508\pi$
$601$	−21.0197	+	12.1357i	−0.857411	+	0.495026i	0.00573343	+	0.999984i	$0.498175\pi$
$602$	32.2552	+	39.9633i	1.31462	+	1.62878i
$603$	7.07717	−	10.4311i	0.288205	−	0.424786i
$604$	0.736739	+	1.27607i	0.0299775	+	0.0519225i
$605$	2.92512			0.118923
$606$	−37.0278	+	19.6235i	−1.50415	+	0.797151i
$607$		−	21.4181i		−	0.869334i	−0.900591	−	0.434667i	$-0.856866\pi$
$607$		−	21.4181i		−	0.869334i	0.900591	−	0.434667i	$-0.143134\pi$
$608$	−0.342391	+	0.593039i	−0.0138858	+	0.0240509i
$609$	−0.596305	−	0.796233i	−0.0241635	−	0.0322650i
$610$	2.04115	+	3.53537i	0.0826437	+	0.143143i
$611$	−2.45439	+	1.41705i	−0.0992942	+	0.0573275i
$612$	1.97936	+	4.08645i	0.0800111	+	0.165185i
$613$	−2.95306	+	5.11485i	−0.119273	+	0.206587i	−0.919480	−	0.393137i	$-0.871390\pi$
$613$	−2.95306	+	5.11485i	−0.119273	+	0.206587i	0.800207	+	0.599724i	$0.204723\pi$
$614$	−9.97404	+	17.2756i	−0.402520	+	0.697185i
$615$	−4.76696	−	8.99481i	−0.192222	−	0.362706i
$616$	20.5468	−	16.5837i	0.827854	−	0.668177i
$617$	−1.19246	−	0.688465i	−0.0480065	−	0.0277166i	0.475805	−	0.879551i	$-0.342157\pi$
$617$	−1.19246	−	0.688465i	−0.0480065	−	0.0277166i	−0.523811	+	0.851834i	$0.675490\pi$
$618$	−20.6573	−	38.9785i	−0.830960	−	1.56794i
$619$			33.8233i			1.35947i	0.733457	+	0.679736i	$0.237906\pi$
$619$			33.8233i			1.35947i	−0.733457	+	0.679736i	$0.762094\pi$
$620$	−1.23523	−	0.713163i	−0.0496082	−	0.0286413i
$621$	0.0314369	−	0.287810i	0.00126152	−	0.0115494i
$622$			31.0133i			1.24352i
$623$	38.6092	+	14.8921i	1.54685	+	0.596640i
$624$	0.826204	−	22.7721i	0.0330746	−	0.911615i
$625$	16.3326			0.653305
$626$	12.4654	+	21.5907i	0.498218	+	0.862938i
$627$	2.89241	+	0.104941i	0.115512	+	0.00419093i
$628$	−1.93969	−	1.11988i	−0.0774022	−	0.0446882i
$629$	−33.9749			−1.35467
$630$	5.30104	+	7.64085i	0.211198	+	0.304419i
$631$	−25.0205			−0.996049			−0.498024	−	0.867163i	$-0.665941\pi$
$631$	−25.0205			−0.996049			−0.498024	+	0.867163i	$0.665941\pi$
$632$	−11.1594	−	6.44287i	−0.443896	−	0.256283i
$633$	4.18222	+	7.89146i	0.166228	+	0.313657i
$634$	7.07171	+	12.2486i	0.280853	+	0.486452i
$635$	−2.06119			−0.0817958
$636$	3.07160	+	1.92516i	0.121797	+	0.0763374i
$637$	−13.7975	+	15.2247i	−0.546676	+	0.603225i
$638$		−	1.25982i		−	0.0498768i
$639$	−9.47173	+	4.58785i	−0.374696	+	0.181493i
$640$	8.79916	+	5.08020i	0.347817	+	0.200812i
$641$		−	10.6830i		−	0.421952i	−0.977491	−	0.210976i	$-0.932336\pi$
$641$		−	10.6830i		−	0.421952i	0.977491	−	0.210976i	$-0.0676642\pi$
$642$	5.39634	−	8.60990i	0.212977	−	0.339805i
$643$	−38.1128	−	22.0044i	−1.50302	−	0.867771i	−0.999994	−	0.00350106i	$-0.998886\pi$
$643$	−38.1128	−	22.0044i	−1.50302	−	0.867771i	−0.503029	−	0.864270i	$-0.667781\pi$
$644$	0.0148749	−	0.0385646i	0.000586152	−	0.00151966i
$645$	17.2627	+	0.626313i	0.679716	+	0.0246610i
$646$	1.77216	−	3.06946i	0.0697246	−	0.120766i
$647$	23.5043	−	40.7107i	0.924050	−	1.60050i	0.130968	−	0.991387i	$-0.458192\pi$
$647$	23.5043	−	40.7107i	0.924050	−	1.60050i	0.793082	−	0.609115i	$-0.208475\pi$
$648$	18.3381	+	14.4885i	0.720390	+	0.569163i
$649$	10.3989	−	6.00380i	0.408192	−	0.235670i
$650$	9.74704	+	16.8824i	0.382310	+	0.662181i
$651$	18.0105	+	24.0490i	0.705886	+	0.942554i
$652$	−1.61287	+	2.79357i	−0.0631648	+	0.109405i
$653$		−	33.9388i		−	1.32813i	−0.747677	−	0.664063i	$-0.768831\pi$
$653$		−	33.9388i		−	1.32813i	0.747677	−	0.664063i	$-0.231169\pi$
$654$	−0.243257	+	6.70473i	−0.00951209	+	0.262176i
$655$	6.39029			0.249689
$656$	−16.9765	−	29.4041i	−0.662820	−	1.14804i
$657$	−1.77216	+	24.3903i	−0.0691384	+	0.951554i
$658$	1.38827	−	3.59921i	0.0541203	−	0.140312i
$659$	−1.36652	+	0.788962i	−0.0532322	+	0.0307336i	−0.526380	−	0.850249i	$-0.676451\pi$
$659$	−1.36652	+	0.788962i	−0.0532322	+	0.0307336i	0.473148	+	0.880983i	$0.343118\pi$
$660$	−0.0525049	+	1.44716i	−0.00204375	+	0.0563305i
$661$	2.08470	−	1.20360i	0.0810854	−	0.0468147i	−0.458909	−	0.888483i	$-0.651760\pi$
$661$	2.08470	−	1.20360i	0.0810854	−	0.0468147i	0.539994	+	0.841669i	$0.318426\pi$
$662$	−37.7215	+	21.7785i	−1.46609	+	0.846446i
$663$	−0.995026	+	27.4253i	−0.0386436	+	1.06511i
$664$	−19.3868	+	11.1930i	−0.752354	+	0.434372i
$665$	0.321205	−	0.832756i	0.0124558	−	0.0322929i
$666$	25.6616	−	12.4298i	0.994366	−	0.481644i
$667$	0.00604760	+	0.0104747i	0.000234164	+	0.000405584i
$668$	−4.70062			−0.181873
$669$	−0.275429	+	7.59146i	−0.0106487	+	0.293503i
$670$		−	4.92299i		−	0.190192i
$671$	6.69529	−	11.5966i	0.258469	−	0.447681i
$672$	4.32628	+	5.77678i	0.166890	+	0.222844i
$673$	12.1767	+	21.0906i	0.469377	+	0.812984i	0.999387	−	0.0350069i	$-0.0111453\pi$
$673$	12.1767	+	21.0906i	0.469377	+	0.812984i	−0.530010	+	0.847991i	$0.677812\pi$
$674$	−16.3788	+	9.45629i	−0.630887	+	0.364243i
$675$	−22.7176	−	2.48140i	−0.874403	−	0.0955090i
$676$	0.614668	−	1.06464i	0.0236411	−	0.0409476i
$677$	−4.83847	+	8.38048i	−0.185958	+	0.322088i	−0.943899	−	0.330235i	$-0.892872\pi$
$677$	−4.83847	+	8.38048i	−0.185958	+	0.322088i	0.757941	+	0.652323i	$0.226205\pi$
$678$	29.5495	+	1.07210i	1.13484	+	0.0411736i
$679$	1.36507	−	3.53907i	0.0523865	−	0.135817i
$680$	−9.41873	−	5.43791i	−0.361192	−	0.208534i
$681$	−8.89850	+	14.1976i	−0.340991	+	0.544053i
$682$			38.0509i			1.45704i
$683$	18.6341	+	10.7584i	0.713012	+	0.411658i	0.812175	−	0.583413i	$-0.198283\pi$
$683$	18.6341	+	10.7584i	0.713012	+	0.411658i	−0.0991632	+	0.995071i	$0.531617\pi$
$684$	−0.0265042	+	0.364778i	−0.00101341	+	0.0139476i
$685$			13.4437i			0.513659i
$686$	1.59867	−	27.9216i	0.0610374	−	1.06605i
$687$	12.9930	+	8.14349i	0.495714	+	0.310694i
$688$	57.6139			2.19651
$689$	10.9549	+	18.9744i	0.417348	+	0.722868i
$690$	−0.0529487	−	0.0999092i	−0.00201572	−	0.00380348i
$691$	−25.4980	−	14.7213i	−0.969989	−	0.560023i	−0.0707559	−	0.997494i	$-0.522541\pi$
$691$	−25.4980	−	14.7213i	−0.969989	−	0.560023i	−0.899233	+	0.437470i	$0.855874\pi$
$692$	0.480244			0.0182561
$693$	13.0113	−	27.5903i	0.494257	−	1.04807i
$694$	43.3730			1.64642
$695$	4.24929	+	2.45333i	0.161185	+	0.0930602i
$696$	−0.975715	−	0.0354003i	−0.0369844	−	0.00134184i
$697$	20.4454	+	35.4124i	0.774423	+	1.34134i
$698$	19.3297			0.731641
$699$	−0.809354	+	22.3077i	−0.0306126	+	0.843754i
$700$	−3.04400	−	1.17411i	−0.115053	−	0.0443773i
$701$		−	40.4325i		−	1.52712i	−0.645740	−	0.763558i	$-0.723451\pi$
$701$		−	40.4325i		−	1.52712i	0.645740	−	0.763558i	$-0.276549\pi$
$702$	−9.28202	−	21.0786i	−0.350327	−	0.795561i
$703$	−2.37000	−	1.36832i	−0.0893863	−	0.0516072i
$704$		−	25.3114i		−	0.953958i
$705$	−0.607607	−	1.14650i	−0.0228838	−	0.0431796i
$706$	−35.3077	−	20.3849i	−1.32882	−	0.767197i
$707$	32.9861	−	26.6238i	1.24057	−	1.00129i
$708$	0.710525	+	1.34070i	0.0267032	+	0.0503864i
$709$	7.95114	−	13.7718i	0.298611	−	0.517210i	−0.677207	−	0.735792i	$-0.736810\pi$
$709$	7.95114	−	13.7718i	0.298611	−	0.517210i	0.975818	+	0.218582i	$0.0701433\pi$
$710$	−2.05514	+	3.55960i	−0.0771280	+	0.133590i
$711$	−14.8474	−	1.07879i	−0.556823	−	0.0404579i
$712$	35.1743	−	20.3079i	1.31821	−	0.761070i
$713$	−0.182658	−	0.316373i	−0.00684061	−	0.0118483i
$714$	−22.3921	−	29.8996i	−0.838002	−	1.11896i
$715$	−4.37619	+	7.57978i	−0.163660	+	0.283468i
$716$		−	4.01923i		−	0.150206i
$717$	−7.39420	+	3.91869i	−0.276141	+	0.146346i
$718$	−42.3143			−1.57916
$719$	−13.0488	−	22.6012i	−0.486638	−	0.842883i	0.513244	−	0.858243i	$-0.328444\pi$
$719$	−13.0488	−	22.6012i	−0.486638	−	0.842883i	−0.999882	+	0.0153605i	$0.995110\pi$
$720$	10.4054	+	0.756037i	0.387785	+	0.0281758i
$721$	28.0264	+	34.7239i	1.04376	+	1.29319i
$722$	−24.6006	+	14.2032i	−0.915539	+	0.528587i
$723$	14.7255	+	9.22936i	0.547647	+	0.343243i
$724$	−1.17319	+	0.677340i	−0.0436011	+	0.0251731i
$725$	0.826800	−	0.477353i	0.0307066	−	0.0177285i
$726$	8.71294	−	4.61757i	0.323367	−	0.171374i
$727$	3.74533	−	2.16237i	0.138907	−	0.0801977i	−0.428936	−	0.903335i	$-0.641111\pi$
$727$	3.74533	−	2.16237i	0.138907	−	0.0801977i	0.567843	+	0.823137i	$0.307778\pi$
$728$	3.12261	+	19.9231i	0.115732	+	0.738398i
$729$	26.3633	+	5.82876i	0.976420	+	0.215880i
$730$	4.77535	+	8.27115i	0.176744	+	0.306129i
$731$	−69.3864			−2.56635
$732$	1.43376	+	0.898624i	0.0529933	+	0.0332141i
$733$			42.3174i			1.56303i	0.623886	+	0.781515i	$0.285553\pi$
$733$			42.3174i			1.56303i	−0.623886	+	0.781515i	$0.714447\pi$
$734$	25.2475	−	43.7299i	0.931901	−	1.61410i
$735$	−6.73682	−	6.56558i	−0.248492	−	0.242175i
$736$	−0.0438762	−	0.0759958i	−0.00161730	−	0.00280124i
$737$	−13.9847	+	8.07409i	−0.515135	+	0.297413i
$738$	−28.3983	−	19.2674i	−1.04535	−	0.709242i
$739$	1.62120	−	2.80801i	0.0596369	−	0.103294i	−0.834666	−	0.550757i	$-0.814339\pi$
$739$	1.62120	−	2.80801i	0.0596369	−	0.103294i	0.894302	+	0.447463i	$0.147672\pi$
$740$	0.684610	−	1.18578i	0.0251668	−	0.0435901i
$741$	−1.17395	+	1.87304i	−0.0431261	+	0.0688079i
$742$	−27.8248	−	10.7324i	−1.02148	−	0.393999i
$743$	5.41770	+	3.12791i	0.198756	+	0.114752i	0.596075	−	0.802929i	$-0.296726\pi$
$743$	5.41770	+	3.12791i	0.198756	+	0.114752i	−0.397319	+	0.917681i	$0.630059\pi$
$744$	29.4700	+	1.06921i	1.08042	+	0.0391992i
$745$			9.95001i			0.364540i
$746$	−10.4205	−	6.01626i	−0.381520	−	0.220271i
$747$	−14.5201	+	21.4012i	−0.531261	+	0.783028i
$748$		−	5.81678i		−	0.212682i
$749$	−3.69895	+	9.58989i	−0.135157	+	0.350407i
$750$	−16.8516	+	8.93082i	−0.615334	+	0.326107i
$751$	−18.9063			−0.689900			−0.344950	−	0.938621i	$-0.612104\pi$
$751$	−18.9063			−0.689900			−0.344950	+	0.938621i	$0.612104\pi$
$752$	−2.16386	−	3.74791i	−0.0789078	−	0.136672i
$753$	7.34220	−	11.7145i	0.267565	−	0.426901i
$754$	0.833277	+	0.481093i	0.0303462	+	0.0175204i
$755$	−4.07736			−0.148390
$756$	3.42453	+	1.76949i	0.124549	+	0.0643558i
$757$	−40.7873			−1.48244			−0.741220	−	0.671262i	$-0.765752\pi$
$757$	−40.7873			−1.48244			−0.741220	+	0.671262i	$0.765752\pi$
$758$	5.08353	+	2.93498i	0.184642	+	0.106603i
$759$	−0.196972	+	0.314270i	−0.00714964	+	0.0114073i
$760$	−0.438017	−	0.758668i	−0.0158886	−	0.0275198i
$761$	−42.6212			−1.54502			−0.772508	−	0.635005i	$-0.780998\pi$
$761$	−42.6212			−1.54502			−0.772508	+	0.635005i	$0.780998\pi$
$762$	−6.13958	+	3.25378i	−0.222413	+	0.117872i
$763$	−1.05085	−	6.70473i	−0.0380435	−	0.242728i
$764$		−	0.881003i		−	0.0318736i
$765$	−12.5315	−	0.910522i	−0.453079	−	0.0329200i
$766$	16.5866	+	9.57627i	0.599298	+	0.346005i
$767$			9.17078i			0.331138i
$768$	11.4295	+	0.414680i	0.412428	+	0.0149635i
$769$	−0.932209	−	0.538211i	−0.0336163	−	0.0194084i	0.483098	−	0.875566i	$-0.339512\pi$
$769$	−0.932209	−	0.538211i	−0.0336163	−	0.0194084i	−0.516714	+	0.856158i	$0.672845\pi$
$770$	−1.84471	−	11.7698i	−0.0664789	−	0.424153i
$771$	2.46729	−	3.93658i	0.0888573	−	0.141772i
$772$	0.842584	−	1.45940i	0.0303253	−	0.0525249i
$773$	2.96855	−	5.14169i	0.106771	−	0.184934i	−0.807689	−	0.589609i	$-0.799282\pi$
$773$	2.96855	−	5.14169i	0.106771	−	0.184934i	0.914461	+	0.404675i	$0.132615\pi$
$774$	52.4082	−	25.3851i	1.88377	−	0.912449i
$775$	−24.9722	+	14.4177i	−0.897028	+	0.517899i
$776$	−1.86150	−	3.22421i	−0.0668240	−	0.115742i
$777$	−23.0861	+	17.2894i	−0.828211	+	0.620254i
$778$	15.5248	−	26.8898i	0.556592	−	0.964046i
$779$			3.29370i			0.118009i
$780$	−0.937137	−	0.587360i	−0.0335549	−	0.0210309i
$781$	13.4824			0.482437
$782$	0.227095	+	0.393341i	0.00812091	+	0.0140658i
$783$	−1.03231	+	0.454579i	−0.0368917	+	0.0162453i
$784$	−23.2485	−	21.0691i	−0.830303	−	0.752466i
$785$	5.36746	−	3.09891i	0.191573	−	0.110605i
$786$	19.0345	−	10.0877i	0.678938	−	0.359815i
$787$	−7.65434	+	4.41923i	−0.272848	+	0.157529i	−0.630181	−	0.776448i	$-0.717019\pi$
$787$	−7.65434	+	4.41923i	−0.272848	+	0.157529i	0.357333	+	0.933977i	$0.383686\pi$
$788$	−3.42140	+	1.97535i	−0.121882	+	0.0703688i
$789$	−34.3948	−	21.5573i	−1.22449	−	0.767461i
$790$	−5.03502	+	2.90697i	−0.179138	+	0.103425i
$791$	−29.5495	+	4.63139i	−1.05066	+	0.164673i
$792$	−13.0515	−	26.9452i	−0.463766	−	0.957457i
$793$	5.11351	+	8.85687i	0.181586	+	0.314517i
$794$	22.6065			0.802275
$795$	−8.86334	+	4.69728i	−0.314350	+	0.166595i
$796$		−	2.21529i		−	0.0785190i
$797$	19.0123	−	32.9303i	0.673450	−	1.16645i	−0.303469	−	0.952841i	$-0.598145\pi$
$797$	19.0123	−	32.9303i	0.673450	−	1.16645i	0.976919	−	0.213609i	$-0.0685218\pi$
$798$	−0.357821	−	2.98755i	−0.0126667	−	0.105758i
$799$	2.60601	+	4.51374i	0.0921940	+	0.159685i
$800$	−5.99855	+	3.46326i	−0.212081	+	0.122445i
$801$	26.3443	−	38.8290i	0.930831	−	1.37196i
$802$	−7.78939	+	13.4916i	−0.275053	+	0.476406i
$803$	15.6639	−	27.1307i	0.552767	−	0.957421i
$804$	−0.955536	−	1.80301i	−0.0336992	−	0.0635872i
$805$	0.0718369	+	0.0890041i	0.00253192	+	0.00313698i
$806$	−25.1678	−	14.5307i	−0.886499	−	0.511821i
$807$	−3.22733	−	6.08967i	−0.113607	−	0.214366i
$808$		−	41.6054i		−	1.46367i
$809$	14.6570	+	8.46222i	0.515312	+	0.297516i	0.735015	−	0.678051i	$-0.237175\pi$
$809$	14.6570	+	8.46222i	0.515312	+	0.297516i	−0.219702	+	0.975567i	$0.570509\pi$
$810$	9.79832	−	3.89696i	0.344278	−	0.136925i
$811$			26.9840i			0.947536i	0.880650	+	0.473768i	$0.157106\pi$
$811$			26.9840i			0.947536i	−0.880650	+	0.473768i	$0.842894\pi$
$812$	−0.159092	+	0.0249351i	−0.00558304	+	0.000875049i
$813$	−0.785360	+	21.6464i	−0.0275438	+	0.759172i
$814$	−36.5275			−1.28029
$815$	−4.46308	−	7.73028i	−0.156335	−	0.270780i
$816$	−41.8790	−	1.51943i	−1.46606	−	0.0531906i
$817$	−4.84021	−	2.79450i	−0.169338	−	0.0977671i
$818$	−27.9668			−0.977836
$819$	13.2802	+	19.1420i	0.464049	+	0.668875i
$820$	−1.64793			−0.0575484
$821$	27.7572	+	16.0256i	0.968732	+	0.559297i	0.898849	−	0.438258i	$-0.144404\pi$
$821$	27.7572	+	16.0256i	0.968732	+	0.559297i	0.0698823	+	0.997555i	$0.477738\pi$
$822$	21.2222	+	40.0443i	0.740209	+	1.39671i
$823$	−10.3974	−	18.0089i	−0.362431	−	0.627749i	0.625929	−	0.779880i	$-0.284720\pi$
$823$	−10.3974	−	18.0089i	−0.362431	−	0.627749i	−0.988360	+	0.152131i	$0.951387\pi$
$824$	43.7973			1.52575
$825$	24.8062	+	15.5475i	0.863641	+	0.541296i
$826$	−7.84015	−	9.71373i	−0.272794	−	0.337984i
$827$			34.0792i			1.18505i	0.805552	+	0.592525i	$0.201869\pi$
$827$			34.0792i			1.18505i	−0.805552	+	0.592525i	$0.798131\pi$
$828$	−0.0387841	−	0.0263139i	−0.00134784	−	0.000914470i
$829$	−29.3229	−	16.9296i	−1.01843	−	0.587988i	−0.104778	−	0.994496i	$-0.533413\pi$
$829$	−29.3229	−	16.9296i	−1.01843	−	0.587988i	−0.913648	+	0.406507i	$0.866747\pi$
$830$			10.1004i			0.350589i
$831$	18.1126	−	28.8987i	0.628318	−	1.00248i
$832$	16.7416	+	9.66575i	0.580410	+	0.335100i
$833$	27.9989	+	25.3742i	0.970106	+	0.879164i
$834$	16.5300	+	0.599731i	0.572387	+	0.0207670i
$835$	6.50371	−	11.2648i	0.225070	−	0.389833i
$836$	0.234267	−	0.405763i	0.00810231	−	0.0140336i
$837$	31.1792	−	13.7299i	1.07771	−	0.474573i
$838$	16.6788	−	9.62953i	0.576161	−	0.332647i
$839$	11.7633	+	20.3747i	0.406115	+	0.703412i	0.994451	−	0.105205i	$-0.0335498\pi$
$839$	11.7633	+	20.3747i	0.406115	+	0.703412i	−0.588335	+	0.808617i	$0.700216\pi$
$840$	−9.16736	+	1.09798i	−0.316304	+	0.0378840i
$841$	−14.4764	+	25.0739i	−0.499188	+	0.864618i
$842$			20.5008i			0.706506i
$843$	−0.510112	+	14.0599i	−0.0175692	+	0.484248i
$844$	1.44579			0.0497661
$845$	1.70089	+	2.94603i	0.0585124	+	0.101347i
$846$	−3.61971	−	2.45586i	−0.124448	−	0.0844343i
$847$	−7.76191	+	6.26479i	−0.266702	+	0.215261i
$848$	−28.9743	+	16.7283i	−0.994983	+	0.574454i
$849$	−0.0844003	+	2.32627i	−0.00289661	+	0.0798374i
$850$	31.0474	−	17.9252i	1.06492	−	0.614831i
$851$	0.303707	−	0.175345i	0.0104109	−	0.00601076i
$852$	−0.0617717	+	1.70257i	−0.00211627	+	0.0583292i
$853$	39.7270	−	22.9364i	1.36023	−	0.785328i	0.370574	−	0.928803i	$-0.379161\pi$
$853$	39.7270	−	22.9364i	1.36023	−	0.785328i	0.989654	+	0.143475i	$0.0458277\pi$
$854$	−12.9880	−	5.00966i	−0.444441	−	0.171427i
$855$	−0.837497	−	0.568217i	−0.0286418	−	0.0194326i
$856$	5.04414	+	8.73670i	0.172405	+	0.298614i
$857$	18.2455			0.623253			0.311627	−	0.950205i	$-0.399126\pi$
$857$	18.2455			0.623253			0.311627	+	0.950205i	$0.399126\pi$
$858$	−1.06978	+	29.4858i	−0.0365218	+	1.00663i
$859$			5.81666i			0.198462i	0.995064	+	0.0992309i	$0.0316382\pi$
$859$			5.81666i			0.198462i	−0.995064	+	0.0992309i	$0.968362\pi$
$860$	1.39817	−	2.42170i	0.0476771	−	0.0825792i
$861$	31.9137	+	13.6585i	1.08761	+	0.465482i
$862$	27.2950	+	47.2763i	0.929671	+	1.61024i
$863$	−27.7060	+	15.9961i	−0.943123	+	0.544513i	−0.890938	−	0.454125i	$-0.849952\pi$
$863$	−27.7060	+	15.9961i	−0.943123	+	0.544513i	−0.0521854	+	0.998637i	$0.516619\pi$
$864$	7.48953	−	3.29804i	0.254799	−	0.112202i
$865$	−0.664458	+	1.15087i	−0.0225922	+	0.0391309i
$866$	−24.9230	+	43.1679i	−0.846918	+	1.46690i
$867$	21.0108	+	0.762301i	0.713564	+	0.0258891i
$868$	4.80513	−	0.753125i	0.163097	−	0.0255627i
$869$	16.5157	+	9.53533i	0.560256	+	0.323464i
$870$	−0.233950	+	0.373269i	−0.00793165	+	0.0126550i
$871$		−	12.3332i		−	0.417893i
$872$	−5.76857	−	3.33048i	−0.195348	−	0.112784i
$873$	−3.55922	−	2.41482i	−0.120461	−	0.0817294i
$874$			0.0365846i			0.00123749i
$875$	15.0123	−	12.1167i	0.507507	−	0.409619i
$876$	3.35434	+	2.10237i	0.113333	+	0.0710324i
$877$	−48.3898			−1.63401			−0.817004	−	0.576632i	$-0.804367\pi$
$877$	−48.3898			−1.63401			−0.817004	+	0.576632i	$0.804367\pi$
$878$	23.0756	+	39.9681i	0.778763	+	1.34886i
$879$	−17.2434	−	32.5366i	−0.581604	−	1.09743i
$880$	−11.5745	−	6.68253i	−0.390176	−	0.225268i
$881$	26.6822			0.898946			0.449473	−	0.893294i	$-0.351612\pi$
$881$	26.6822			0.898946			0.449473	+	0.893294i	$0.351612\pi$
$882$	−30.4311	−	8.92192i	−1.02467	−	0.300417i
$883$	35.0484			1.17947			0.589737	−	0.807595i	$-0.299231\pi$
$883$	35.0484			1.17947			0.589737	+	0.807595i	$0.299231\pi$
$884$	3.84736	+	2.22128i	0.129401	+	0.0747096i
$885$	−4.19597	−	0.152235i	−0.141046	−	0.00511734i
$886$	−15.6315	−	27.0745i	−0.525149	−	0.909585i
$887$	12.9676			0.435410			0.217705	−	0.976015i	$-0.430143\pi$
$887$	12.9676			0.435410			0.217705	+	0.976015i	$0.430143\pi$
$888$	−1.02640	+	28.2901i	−0.0344438	+	0.949353i
$889$	5.46944	−	4.41449i	0.183439	−	0.148057i
$890$		−	18.3255i		−	0.614273i
$891$	−27.1401	−	21.4428i	−0.909228	−	0.718359i
$892$	1.06497	+	0.614862i	0.0356579	+	0.0205871i
$893$			0.419822i			0.0140488i
$894$	15.7070	+	29.6377i	0.525321	+	0.991231i
$895$	9.63184	+	5.56095i	0.321957	+	0.185882i
$896$	−34.2292	+	5.36486i	−1.14352	+	0.179227i
$897$	−0.132648	−	0.250294i	−0.00442898	−	0.00835708i
$898$	4.83414	−	8.37298i	0.161317	−	0.279410i
$899$	−0.711627	+	1.23257i	−0.0237341	+	0.0411086i
$900$	−2.07702	+	3.06133i	−0.0692341	+	0.102044i
$901$	34.8948	−	20.1465i	1.16251	−	0.671178i
$902$	21.9815	+	38.0730i	0.731902	+	1.26769i
$903$	−47.1484	+	35.3098i	−1.56900	+	1.17504i
$904$	−14.6783	+	25.4236i	−0.488193	+	0.845576i
$905$		−	3.74863i		−	0.124609i
$906$	−12.1451	+	6.43649i	−0.403493	+	0.213838i
$907$	−9.12613			−0.303028			−0.151514	−	0.988455i	$-0.548415\pi$
$907$	−9.12613			−0.303028			−0.151514	+	0.988455i	$0.548415\pi$
$908$	1.35622	+	2.34904i	0.0450077	+	0.0779557i
$909$	−20.9531	−	43.2583i	−0.694972	−	1.43479i
$910$	8.48926	+	3.27443i	0.281416	+	0.108546i
$911$	41.5720	−	24.0016i	1.37734	−	0.795209i	0.385503	−	0.922707i	$-0.374028\pi$
$911$	41.5720	−	24.0016i	1.37734	−	0.795209i	0.991839	+	0.127498i	$0.0406947\pi$
$912$	−2.86017	−	1.79264i	−0.0947098	−	0.0593604i
$913$	28.6921	−	16.5654i	0.949571	−	0.548235i
$914$	4.11533	−	2.37599i	0.136123	−	0.0785906i
$915$	−4.13722	+	2.19260i	−0.136772	+	0.0724850i
$916$	2.14973	−	1.24115i	0.0710292	−	0.0410087i
$917$	−16.9569	+	13.6862i	−0.559965	+	0.451959i
$918$	−38.7645	+	17.0701i	−1.27942	+	0.563396i
$919$	19.8096	+	34.3113i	0.653459	+	1.13182i	0.982278	+	0.187432i	$0.0600163\pi$
$919$	19.8096	+	34.3113i	0.653459	+	1.13182i	−0.328818	+	0.944393i	$0.606650\pi$
$920$	0.112261			0.00370112
$921$	−19.3869	−	12.1510i	−0.638821	−	0.400388i
$922$			22.4770i			0.740241i
$923$	−5.14856	+	8.91757i	−0.169467	+	0.293526i
$924$	−2.96008	−	3.95253i	−0.0973796	−	0.130029i
$925$	−13.8405	−	23.9724i	−0.455072	−	0.788208i
$926$	34.9480	−	20.1772i	1.14846	−	0.663065i
$927$	45.5373	−	22.0570i	1.49564	−	0.724447i
$928$	−0.170939	+	0.296076i	−0.00561136	+	0.00971915i
$929$	−11.7897	+	20.4204i	−0.386809	+	0.669973i	−0.992018	−	0.126093i	$-0.959756\pi$
$929$	−11.7897	+	20.4204i	−0.386809	+	0.669973i	0.605209	+	0.796066i	$0.293089\pi$
$930$	7.06609	−	11.2740i	0.231706	−	0.369689i
$931$	0.931201	+	2.89768i	0.0305189	+	0.0949676i
$932$	3.12944	+	1.80679i	0.102508	+	0.0591832i
$933$	−35.5483	−	1.28974i	−1.16380	−	0.0422243i
$934$		−	37.4403i		−	1.22509i
$935$	13.9396	+	8.04801i	0.455872	+	0.263198i
$936$	22.8063	+	1.65707i	0.745447	+	0.0541630i
$937$		−	52.5144i		−	1.71557i	−0.514007	−	0.857786i	$-0.671840\pi$
$937$		−	52.5144i		−	1.71557i	0.514007	−	0.857786i	$-0.328160\pi$
$938$	10.5437	+	13.0633i	0.344263	+	0.426533i
$939$	−25.2662	+	13.3903i	−0.824533	+	0.436976i
$940$	−0.210049			−0.00685105
$941$	−24.5713	−	42.5587i	−0.801000	−	1.38737i	−0.918958	−	0.394354i	$-0.870968\pi$
$941$	−24.5713	−	42.5587i	−0.801000	−	1.38737i	0.117958	−	0.993019i	$-0.462365\pi$
$942$	11.0959	−	17.7036i	0.361525	−	0.576815i
$943$	−0.365528	−	0.211038i	−0.0119032	−	0.00687234i
$944$	−14.0040			−0.455791
$945$	−8.97861	+	5.75844i	−0.292074	+	0.187322i
$946$	−74.5995			−2.42544
$947$	8.04907	+	4.64713i	0.261560	+	0.151012i	0.625046	−	0.780588i	$-0.285080\pi$
$947$	8.04907	+	4.64713i	0.261560	+	0.151012i	−0.363486	+	0.931600i	$0.618414\pi$
$948$	−1.27981	+	2.04194i	−0.0415662	+	0.0663191i
$949$	11.9633	+	20.7210i	0.388344	+	0.672632i
$950$	2.88772			0.0936899
$951$	−14.3337	+	7.59641i	−0.464803	+	0.246330i
$952$	36.6394	−	5.74262i	1.18749	−	0.186119i
$953$		−	40.3761i		−	1.30791i	−0.756534	−	0.653955i	$-0.773109\pi$
$953$		−	40.3761i		−	1.30791i	0.756534	−	0.653955i	$-0.226891\pi$
$954$	−18.9858	+	27.9832i	−0.614686	+	0.905989i
$955$	2.11127	+	1.21894i	0.0683191	+	0.0394440i
$956$			1.35469i			0.0438137i
$957$	1.44404	+	0.0523918i	0.0466792	+	0.00169359i
$958$	16.3827	+	9.45854i	0.529300	+	0.305592i
$959$	−28.7928	−	35.6734i	−0.929766	−	1.15196i
$960$	−4.70034	+	7.49943i	−0.151703	+	0.242043i
$961$	5.99358	−	10.3812i	0.193341	−	0.334877i
$962$	13.9489	−	24.1602i	0.449731	−	0.778957i
$963$	9.64448	+	6.54349i	0.310789	+	0.210861i
$964$	2.43638	−	1.40665i	0.0784706	−	0.0453050i
$965$	2.33157	+	4.03840i	0.0750560	+	0.130001i
$966$	0.354479	+	0.151711i	0.0114052	+	0.00488123i
$967$	8.78620	−	15.2181i	0.282545	−	0.489383i	−0.689466	−	0.724318i	$-0.742155\pi$
$967$	8.78620	−	15.2181i	0.282545	−	0.489383i	0.972011	+	0.234936i	$0.0754879\pi$
$968$			9.79009i			0.314665i
$969$	3.44461	+	2.15894i	0.110657	+	0.0693552i
$970$	−1.67979			−0.0539348
$971$	−20.1321	−	34.8697i	−0.646068	−	1.11902i	−0.984054	−	0.177872i	$-0.943079\pi$
$971$	−20.1321	−	34.8697i	−0.646068	−	1.11902i	0.337985	−	0.941151i	$-0.390255\pi$
$972$	2.83217	−	3.32905i	0.0908420	−	0.106779i
$973$	−16.5300	+	2.59080i	−0.529928	+	0.0830573i
$974$	4.43986	−	2.56336i	0.142262	−	0.0821353i
$975$	−19.7564	+	10.4702i	−0.632711	+	0.335316i
$976$	−13.5246	+	7.80845i	−0.432913	+	0.249942i
$977$	−22.9591	+	13.2555i	−0.734527	+	0.424080i	−0.820076	−	0.572254i	$-0.806069\pi$
$977$	−22.9591	+	13.2555i	−0.734527	+	0.424080i	0.0855487	+	0.996334i	$0.472736\pi$
$978$	−25.4969	−	15.9805i	−0.815302	−	0.510999i
$979$	−52.0573	+	30.0553i	−1.66376	+	0.960572i
$980$	−1.44979	+	0.465907i	−0.0463119	+	0.0148829i
$981$	−7.67503	−	0.557655i	−0.245045	−	0.0178046i
$982$	0.680195	+	1.17813i	0.0217059	+	0.0375957i
$983$	−38.2714			−1.22067			−0.610334	−	0.792144i	$-0.708965\pi$
$983$	−38.2714			−1.22067			−0.610334	+	0.792144i	$0.708965\pi$
$984$	30.1047	−	15.9545i	0.959703	−	0.508612i
$985$		−	10.9322i		−	0.348330i
$986$	0.884752	−	1.53243i	0.0281762	−	0.0488027i
$987$	4.06779	+	1.74095i	0.129479	+	0.0554150i
$988$	0.178921	+	0.309901i	0.00569225	+	0.00985926i
$989$	0.620255	−	0.358105i	0.0197230	−	0.0113871i
$990$	−13.4731	−	0.978931i	−0.428202	−	0.0311125i
$991$	30.4509	−	52.7425i	0.967305	−	1.67542i	0.264016	−	0.964518i	$-0.414953\pi$
$991$	30.4509	−	52.7425i	0.967305	−	1.67542i	0.703289	−	0.710904i	$-0.251714\pi$
$992$	5.16295	−	8.94250i	0.163924	−	0.283925i
$993$	−23.3944	−	44.1431i	−0.742399	−	1.40084i
$994$	−2.17030	−	13.8471i	−0.0688377	−	0.439202i
$995$	5.30881	+	3.06504i	0.168301	+	0.0971684i
$996$	1.96045	+	3.69919i	0.0621192	+	0.117213i
$997$			14.4115i			0.456415i	0.973612	+	0.228208i	$0.0732865\pi$
$997$			14.4115i			0.456415i	−0.973612	+	0.228208i	$0.926713\pi$
$998$	28.5996	+	16.5120i	0.905306	+	0.522679i
$999$	13.1802	+	29.9309i	0.417002	+	0.946973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.s.b.59.4	yes	10
3.2	odd	2		189.2.s.b.17.2		10
4.3	odd	2		1008.2.df.b.689.4		10
7.2	even	3		441.2.i.b.68.2		10
7.3	odd	6		441.2.o.d.293.2		10
7.4	even	3		441.2.o.c.293.2		10
7.5	odd	6		63.2.i.b.5.2	✓	10
7.6	odd	2		441.2.s.b.374.4		10
9.2	odd	6		63.2.i.b.38.4	yes	10
9.4	even	3		567.2.p.c.80.2		10
9.5	odd	6		567.2.p.d.80.4		10
9.7	even	3		189.2.i.b.143.2		10
12.11	even	2		3024.2.df.b.17.3		10
21.2	odd	6		1323.2.i.b.1097.4		10
21.5	even	6		189.2.i.b.152.4		10
21.11	odd	6		1323.2.o.d.881.4		10
21.17	even	6		1323.2.o.c.881.4		10
21.20	even	2		1323.2.s.b.962.2		10
28.19	even	6		1008.2.ca.b.257.2		10
36.7	odd	6		3024.2.ca.b.2033.3		10
36.11	even	6		1008.2.ca.b.353.2		10
63.2	odd	6		441.2.s.b.362.4		10
63.5	even	6		567.2.p.c.404.2		10
63.11	odd	6		441.2.o.d.146.2		10
63.16	even	3		1323.2.s.b.656.2		10
63.20	even	6		441.2.i.b.227.4		10
63.25	even	3		1323.2.o.c.440.4		10
63.34	odd	6		1323.2.i.b.521.2		10
63.38	even	6		441.2.o.c.146.2		10
63.40	odd	6		567.2.p.d.404.4		10
63.47	even	6	inner	63.2.s.b.47.4	yes	10
63.52	odd	6		1323.2.o.d.440.4		10
63.61	odd	6		189.2.s.b.89.2		10
84.47	odd	6		3024.2.ca.b.2609.3		10
252.47	odd	6		1008.2.df.b.929.4		10
252.187	even	6		3024.2.df.b.1601.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.2	✓	10	7.5	odd	6
63.2.i.b.38.4	yes	10	9.2	odd	6
63.2.s.b.47.4	yes	10	63.47	even	6	inner
63.2.s.b.59.4	yes	10	1.1	even	1	trivial
189.2.i.b.143.2		10	9.7	even	3
189.2.i.b.152.4		10	21.5	even	6
189.2.s.b.17.2		10	3.2	odd	2
189.2.s.b.89.2		10	63.61	odd	6
441.2.i.b.68.2		10	7.2	even	3
441.2.i.b.227.4		10	63.20	even	6
441.2.o.c.146.2		10	63.38	even	6
441.2.o.c.293.2		10	7.4	even	3
441.2.o.d.146.2		10	63.11	odd	6
441.2.o.d.293.2		10	7.3	odd	6
441.2.s.b.362.4		10	63.2	odd	6
441.2.s.b.374.4		10	7.6	odd	2
567.2.p.c.80.2		10	9.4	even	3
567.2.p.c.404.2		10	63.5	even	6
567.2.p.d.80.4		10	9.5	odd	6
567.2.p.d.404.4		10	63.40	odd	6
1008.2.ca.b.257.2		10	28.19	even	6
1008.2.ca.b.353.2		10	36.11	even	6
1008.2.df.b.689.4		10	4.3	odd	2
1008.2.df.b.929.4		10	252.47	odd	6
1323.2.i.b.521.2		10	63.34	odd	6
1323.2.i.b.1097.4		10	21.2	odd	6
1323.2.o.c.440.4		10	63.25	even	3
1323.2.o.c.881.4		10	21.17	even	6
1323.2.o.d.440.4		10	63.52	odd	6
1323.2.o.d.881.4		10	21.11	odd	6
1323.2.s.b.656.2		10	63.16	even	3
1323.2.s.b.962.2		10	21.20	even	2
3024.2.ca.b.2033.3		10	36.7	odd	6
3024.2.ca.b.2609.3		10	84.47	odd	6
3024.2.df.b.17.3		10	12.11	even	2
3024.2.df.b.1601.3		10	252.187	even	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30778 + 0.755047i) q^{2} +(-0.919842 + 1.46761i) q^{3} +(0.140193 + 0.242822i) q^{4} -0.775876 q^{5} +(-2.31107 + 1.22479i) q^{6} +(2.05881 - 1.66171i) q^{7} -2.59678i q^{8} +(-1.30778 - 2.69995i) q^{9} +O(q^{10})\)	\(q+(1.30778 + 0.755047i) q^{2} +(-0.919842 + 1.46761i) q^{3} +(0.140193 + 0.242822i) q^{4} -0.775876 q^{5} +(-2.31107 + 1.22479i) q^{6} +(2.05881 - 1.66171i) q^{7} -2.59678i q^{8} +(-1.30778 - 2.69995i) q^{9} +(-1.01468 - 0.585823i) q^{10} +3.84319i q^{11} +(-0.485324 - 0.0176082i) q^{12} +(-2.54198 - 1.46761i) q^{13} +(3.94715 - 0.618650i) q^{14} +(0.713684 - 1.13869i) q^{15} +(2.24108 - 3.88166i) q^{16} +(-2.69901 + 4.67482i) q^{17} +(0.328298 - 4.51837i) q^{18} +(-0.376551 + 0.217402i) q^{19} +(-0.108773 - 0.188400i) q^{20} +(0.544964 + 4.55006i) q^{21} +(-2.90179 + 5.02605i) q^{22} -0.0557186i q^{23} +(3.81107 + 2.38863i) q^{24} -4.39802 q^{25} +(-2.21624 - 3.83863i) q^{26} +(5.16543 + 0.564208i) q^{27} +(0.692131 + 0.266964i) q^{28} +(-0.187994 + 0.108538i) q^{29} +(1.79310 - 0.950287i) q^{30} +(5.67806 - 3.27823i) q^{31} +(1.36392 - 0.787461i) q^{32} +(-5.64031 - 3.53513i) q^{33} +(-7.05942 + 4.07576i) q^{34} +(-1.59739 + 1.28928i) q^{35} +(0.472264 - 0.696071i) q^{36} +(3.14698 + 5.45073i) q^{37} -0.656595 q^{38} +(4.49211 - 2.38067i) q^{39} +2.01478i q^{40} +(3.78757 - 6.56026i) q^{41} +(-2.72281 + 6.36195i) q^{42} +(6.42703 + 11.1319i) q^{43} +(-0.933209 + 0.538789i) q^{44} +(1.01468 + 2.09482i) q^{45} +(0.0420702 - 0.0728677i) q^{46} +(0.482772 - 0.836186i) q^{47} +(3.63534 + 6.85955i) q^{48} +(1.47744 - 6.84231i) q^{49} +(-5.75164 - 3.32071i) q^{50} +(-4.37817 - 8.26120i) q^{51} -0.822998i q^{52} +(-6.46438 - 3.73221i) q^{53} +(6.32924 + 4.63800i) q^{54} -2.98184i q^{55} +(-4.31510 - 5.34629i) q^{56} +(0.0273056 - 0.752608i) q^{57} -0.327806 q^{58} +(-1.56219 - 2.70580i) q^{59} +(0.376551 + 0.0136618i) q^{60} +(-3.01744 - 1.74212i) q^{61} +9.90087 q^{62} +(-7.17901 - 3.38554i) q^{63} -6.58603 q^{64} +(1.97226 + 1.13869i) q^{65} +(-4.70711 - 8.88187i) q^{66} +(2.10088 + 3.63884i) q^{67} -1.51353 q^{68} +(0.0817733 + 0.0512523i) q^{69} +(-3.06250 + 0.479996i) q^{70} -3.50812i q^{71} +(-7.01117 + 3.39602i) q^{72} +(-7.05942 - 4.07576i) q^{73} +9.50448i q^{74} +(4.04548 - 6.45459i) q^{75} +(-0.105580 - 0.0609566i) q^{76} +(6.38626 + 7.91241i) q^{77} +(7.67222 + 0.278359i) q^{78} +(2.48110 - 4.29739i) q^{79} +(-1.73880 + 3.01169i) q^{80} +(-5.57942 + 7.06187i) q^{81} +(9.90662 - 5.71959i) q^{82} +(-4.31033 - 7.46571i) q^{83} +(-1.02845 + 0.770216i) q^{84} +(2.09410 - 3.62708i) q^{85} +19.4108i q^{86} +(0.0136324 - 0.375740i) q^{87} +9.97991 q^{88} +(7.82041 + 13.5453i) q^{89} +(-0.254718 + 3.50570i) q^{90} +(-7.67222 + 1.20249i) q^{91} +(0.0135297 - 0.00781136i) q^{92} +(-0.411745 + 11.3487i) q^{93} +(1.26272 - 0.729031i) q^{94} +(0.292157 - 0.168677i) q^{95} +(-0.0989048 + 2.72605i) q^{96} +(1.24162 - 0.716849i) q^{97} +(7.09843 - 7.83270i) q^{98} +(10.3764 - 5.02605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7}+O(q^{10}) \) 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7	\( 10 q + 4 q^{4} - 12 q^{6} + 3 q^{7} - 15 q^{10} + 6 q^{13} - 6 q^{14} - 3 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} + 3 q^{19} - 3 q^{20} + 18 q^{21} + 5 q^{22} + 27 q^{24} - 14 q^{25} + 3 q^{26} + 27 q^{27} + 2 q^{28} - 15 q^{29} - 9 q^{31} + 48 q^{32} - 9 q^{33} + 3 q^{34} - 15 q^{35} - 18 q^{36} + 6 q^{37} + 36 q^{38} + 12 q^{39} - 9 q^{41} - 6 q^{42} + 3 q^{43} + 24 q^{44} + 15 q^{45} - 13 q^{46} + 15 q^{47} - 15 q^{48} - 23 q^{49} + 3 q^{50} - 24 q^{51} - 9 q^{53} + 27 q^{54} - 51 q^{56} - 36 q^{57} - 16 q^{58} - 18 q^{59} - 3 q^{60} + 12 q^{61} + 12 q^{62} + 9 q^{63} + 6 q^{64} - 3 q^{65} - 33 q^{66} - 10 q^{67} - 54 q^{68} - 3 q^{69} + 9 q^{70} + 18 q^{72} + 3 q^{73} - 21 q^{75} + 9 q^{76} + 45 q^{77} + 24 q^{78} + 20 q^{79} - 30 q^{80} - 48 q^{81} + 9 q^{82} - 15 q^{83} + 60 q^{84} + 18 q^{85} + 30 q^{87} + 16 q^{88} + 24 q^{89} + 24 q^{90} - 24 q^{91} + 39 q^{92} + 6 q^{93} - 3 q^{94} + 3 q^{96} + 6 q^{97} + 45 q^{98} + 21 q^{99}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^6 + 3 * q^7 - 15 * q^10 + 6 * q^13 - 6 * q^14 - 3 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 + 3 * q^19 - 3 * q^20 + 18 * q^21 + 5 * q^22 + 27 * q^24 - 14 * q^25 + 3 * q^26 + 27 * q^27 + 2 * q^28 - 15 * q^29 - 9 * q^31 + 48 * q^32 - 9 * q^33 + 3 * q^34 - 15 * q^35 - 18 * q^36 + 6 * q^37 + 36 * q^38 + 12 * q^39 - 9 * q^41 - 6 * q^42 + 3 * q^43 + 24 * q^44 + 15 * q^45 - 13 * q^46 + 15 * q^47 - 15 * q^48 - 23 * q^49 + 3 * q^50 - 24 * q^51 - 9 * q^53 + 27 * q^54 - 51 * q^56 - 36 * q^57 - 16 * q^58 - 18 * q^59 - 3 * q^60 + 12 * q^61 + 12 * q^62 + 9 * q^63 + 6 * q^64 - 3 * q^65 - 33 * q^66 - 10 * q^67 - 54 * q^68 - 3 * q^69 + 9 * q^70 + 18 * q^72 + 3 * q^73 - 21 * q^75 + 9 * q^76 + 45 * q^77 + 24 * q^78 + 20 * q^79 - 30 * q^80 - 48 * q^81 + 9 * q^82 - 15 * q^83 + 60 * q^84 + 18 * q^85 + 30 * q^87 + 16 * q^88 + 24 * q^89 + 24 * q^90 - 24 * q^91 + 39 * q^92 + 6 * q^93 - 3 * q^94 + 3 * q^96 + 6 * q^97 + 45 * q^98 + 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more