LMFDB - Embedded newform 722.2.e.l.389.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not 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:	$5.76519902594$
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:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			389.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	722.389
Dual form			722.2.e.l.245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(1.43969 - 1.20805i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.87939 - 0.684040i) q^{5} +(-1.43969 - 1.20805i) q^{6} +(-2.53209 + 4.38571i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.0923963 - 0.524005i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(1.43969 - 1.20805i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.87939 - 0.684040i) q^{5} +(-1.43969 - 1.20805i) q^{6} +(-2.53209 + 4.38571i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.0923963 - 0.524005i) q^{9} +(-0.347296 + 1.96962i) q^{10} +(0.705737 + 1.22237i) q^{11} +(-0.939693 + 1.62760i) q^{12} +(1.00000 + 0.839100i) q^{13} +(4.75877 + 1.73205i) q^{14} +(-3.53209 + 1.28558i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.414878 + 2.35289i) q^{17} -0.532089 q^{18} +2.00000 q^{20} +(1.65270 + 9.37295i) q^{21} +(1.08125 - 0.907278i) q^{22} +(2.87939 - 1.04801i) q^{23} +(1.76604 + 0.642788i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(0.652704 - 1.13052i) q^{26} +(2.31908 + 4.01676i) q^{27} +(0.879385 - 4.98724i) q^{28} +(-1.46791 + 8.32494i) q^{29} +(1.87939 + 3.25519i) q^{30} +(0.184793 - 0.320070i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(2.49273 + 0.907278i) q^{33} +(2.24510 - 0.817150i) q^{34} +(7.75877 - 6.51038i) q^{35} +(0.0923963 + 0.524005i) q^{36} -4.82295 q^{37} +2.45336 q^{39} +(-0.347296 - 1.96962i) q^{40} +(1.17365 - 0.984808i) q^{41} +(8.94356 - 3.25519i) q^{42} +(0.713011 + 0.259515i) q^{43} +(-1.08125 - 0.907278i) q^{44} +(-0.532089 + 0.921605i) q^{45} +(-1.53209 - 2.65366i) q^{46} +(-1.77332 + 10.0570i) q^{47} +(0.326352 - 1.85083i) q^{48} +(-9.32295 - 16.1478i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.43969 + 2.88624i) q^{51} +(-1.22668 - 0.446476i) q^{52} +(1.57398 - 0.572881i) q^{53} +(3.55303 - 2.98135i) q^{54} +(-0.490200 - 2.78006i) q^{55} -5.06418 q^{56} +8.45336 q^{58} +(-0.124485 - 0.705990i) q^{59} +(2.87939 - 2.41609i) q^{60} +(-9.17024 + 3.33770i) q^{61} +(-0.347296 - 0.126406i) q^{62} +(2.06418 + 1.73205i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.30541 - 2.26103i) q^{65} +(0.460637 - 2.61240i) q^{66} +(0.243756 - 1.38241i) q^{67} +(-1.19459 - 2.06910i) q^{68} +(2.87939 - 4.98724i) q^{69} +(-7.75877 - 6.51038i) q^{70} +(-5.98545 - 2.17853i) q^{71} +(0.500000 - 0.181985i) q^{72} +(-3.49273 + 2.93075i) q^{73} +(0.837496 + 4.74968i) q^{74} -1.87939 q^{75} -7.14796 q^{77} +(-0.426022 - 2.41609i) q^{78} +(1.71688 - 1.44063i) q^{79} +(-1.87939 + 0.684040i) q^{80} +(9.69119 + 3.52730i) q^{81} +(-1.17365 - 0.984808i) q^{82} +(1.99273 - 3.45150i) q^{83} +(-4.75877 - 8.24243i) q^{84} +(0.829755 - 4.70578i) q^{85} +(0.131759 - 0.747243i) q^{86} +(7.94356 + 13.7587i) q^{87} +(-0.705737 + 1.22237i) q^{88} +(8.15523 + 6.84305i) q^{89} +(1.00000 + 0.363970i) q^{90} +(-6.21213 + 2.26103i) q^{91} +(-2.34730 + 1.96962i) q^{92} +(-0.120615 - 0.684040i) q^{93} +10.2121 q^{94} -1.87939 q^{96} +(0.266044 + 1.50881i) q^{97} +(-14.2836 + 11.9854i) q^{98} +(0.705737 - 0.256867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 3 q^{6} - 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 3 * q^6 - 6 * q^7 + 3 * q^8 - 3 * q^9	$ 6 q + 3 q^{3} - 3 q^{6} - 6 q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{11} + 6 q^{13} + 6 q^{14} - 12 q^{15} + 24 q^{17} + 6 q^{18} + 12 q^{20} + 12 q^{21} + 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} - 6 q^{28} - 18 q^{29} - 6 q^{31} - 3 q^{33} + 12 q^{34} + 24 q^{35} - 3 q^{36} + 12 q^{37} - 12 q^{39} + 6 q^{41} + 24 q^{42} + 12 q^{43} - 9 q^{44} + 6 q^{45} - 24 q^{47} + 3 q^{48} - 15 q^{49} - 3 q^{50} + 15 q^{51} + 6 q^{52} - 6 q^{53} + 9 q^{54} - 12 q^{56} + 24 q^{58} + 12 q^{59} + 6 q^{60} - 12 q^{61} - 6 q^{63} - 3 q^{64} - 12 q^{65} - 6 q^{66} + 9 q^{67} - 3 q^{68} + 6 q^{69} - 24 q^{70} + 3 q^{72} - 3 q^{73} - 12 q^{77} - 18 q^{78} - 6 q^{79} + 12 q^{81} - 6 q^{82} - 6 q^{83} - 6 q^{84} + 48 q^{85} + 6 q^{86} + 18 q^{87} + 6 q^{88} + 36 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 12 q^{93} + 12 q^{94} - 3 q^{97} - 36 q^{98} - 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 - 3 * q^6 - 6 * q^7 + 3 * q^8 - 3 * q^9 - 6 * q^11 + 6 * q^13 + 6 * q^14 - 12 * q^15 + 24 * q^17 + 6 * q^18 + 12 * q^20 + 12 * q^21 + 9 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 - 6 * q^28 - 18 * q^29 - 6 * q^31 - 3 * q^33 + 12 * q^34 + 24 * q^35 - 3 * q^36 + 12 * q^37 - 12 * q^39 + 6 * q^41 + 24 * q^42 + 12 * q^43 - 9 * q^44 + 6 * q^45 - 24 * q^47 + 3 * q^48 - 15 * q^49 - 3 * q^50 + 15 * q^51 + 6 * q^52 - 6 * q^53 + 9 * q^54 - 12 * q^56 + 24 * q^58 + 12 * q^59 + 6 * q^60 - 12 * q^61 - 6 * q^63 - 3 * q^64 - 12 * q^65 - 6 * q^66 + 9 * q^67 - 3 * q^68 + 6 * q^69 - 24 * q^70 + 3 * q^72 - 3 * q^73 - 12 * q^77 - 18 * q^78 - 6 * q^79 + 12 * q^81 - 6 * q^82 - 6 * q^83 - 6 * q^84 + 48 * q^85 + 6 * q^86 + 18 * q^87 + 6 * q^88 + 36 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 12 * q^93 + 12 * q^94 - 3 * q^97 - 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	1.43969	−	1.20805i	0.831207	−	0.697465i	−0.124361	−	0.992237i	$-0.539688\pi$
$3$	1.43969	−	1.20805i	0.831207	−	0.697465i	0.955568	+	0.294772i	$0.0952436\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−1.87939	−	0.684040i	−0.840487	−	0.305912i	−0.114331	−	0.993443i	$-0.536473\pi$
$5$	−1.87939	−	0.684040i	−0.840487	−	0.305912i	−0.726155	+	0.687531i	$0.758695\pi$
$6$	−1.43969	−	1.20805i	−0.587752	−	0.493183i
$7$	−2.53209	+	4.38571i	−0.957040	+	1.65764i	−0.227410	+	0.973799i	$0.573026\pi$
$7$	−2.53209	+	4.38571i	−0.957040	+	1.65764i	−0.729630	+	0.683842i	$0.760308\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.0923963	−	0.524005i	0.0307988	−	0.174668i
$10$	−0.347296	+	1.96962i	−0.109825	+	0.622847i
$11$	0.705737	+	1.22237i	0.212788	+	0.368559i	0.952586	−	0.304270i	$-0.0984124\pi$
$11$	0.705737	+	1.22237i	0.212788	+	0.368559i	−0.739798	+	0.672829i	$0.765079\pi$
$12$	−0.939693	+	1.62760i	−0.271266	+	0.469846i
$13$	1.00000	+	0.839100i	0.277350	+	0.232724i	0.770843	−	0.637026i	$-0.219836\pi$
$13$	1.00000	+	0.839100i	0.277350	+	0.232724i	−0.493492	+	0.869750i	$0.664280\pi$
$14$	4.75877	+	1.73205i	1.27183	+	0.462910i
$15$	−3.53209	+	1.28558i	−0.911981	+	0.331934i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.414878	+	2.35289i	0.100623	+	0.570659i	0.992879	+	0.119130i	$0.0380104\pi$
$17$	0.414878	+	2.35289i	0.100623	+	0.570659i	−0.892256	+	0.451530i	$0.850879\pi$
$18$	−0.532089			−0.125415
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	1.65270	+	9.37295i	0.360650	+	2.04534i
$22$	1.08125	−	0.907278i	0.230524	−	0.193432i
$23$	2.87939	−	1.04801i	0.600393	−	0.218525i	−0.0239012	−	0.999714i	$-0.507609\pi$
$23$	2.87939	−	1.04801i	0.600393	−	0.218525i	0.624295	+	0.781189i	$0.285387\pi$
$24$	1.76604	+	0.642788i	0.360492	+	0.131208i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	0.652704	−	1.13052i	0.128006	−	0.221712i
$27$	2.31908	+	4.01676i	0.446307	+	0.773026i
$28$	0.879385	−	4.98724i	0.166188	−	0.942500i
$29$	−1.46791	+	8.32494i	−0.272584	+	1.54590i	0.473948	+	0.880553i	$0.342828\pi$
$29$	−1.46791	+	8.32494i	−0.272584	+	1.54590i	−0.746532	+	0.665349i	$0.768283\pi$
$30$	1.87939	+	3.25519i	0.343127	+	0.594314i
$31$	0.184793	−	0.320070i	0.0331897	−	0.0574863i	−0.848953	−	0.528468i	$-0.822767\pi$
$31$	0.184793	−	0.320070i	0.0331897	−	0.0574863i	0.882143	+	0.470981i	$0.156100\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	2.49273	+	0.907278i	0.433928	+	0.157937i
$34$	2.24510	−	0.817150i	0.385031	−	0.140140i
$35$	7.75877	−	6.51038i	1.31147	−	1.10046i
$36$	0.0923963	+	0.524005i	0.0153994	+	0.0873342i
$37$	−4.82295			−0.792888			−0.396444	−	0.918059i	$-0.629756\pi$
$37$	−4.82295			−0.792888			−0.396444	+	0.918059i	$0.629756\pi$
$38$		0			0
$39$	2.45336			0.392853
$40$	−0.347296	−	1.96962i	−0.0549124	−	0.311424i
$41$	1.17365	−	0.984808i	0.183293	−	0.153801i	−0.546524	−	0.837443i	$-0.684049\pi$
$41$	1.17365	−	0.984808i	0.183293	−	0.153801i	0.729818	+	0.683642i	$0.239605\pi$
$42$	8.94356	−	3.25519i	1.38002	−	0.502287i
$43$	0.713011	+	0.259515i	0.108733	+	0.0395756i	0.395814	−	0.918331i	$-0.370463\pi$
$43$	0.713011	+	0.259515i	0.108733	+	0.0395756i	−0.287081	+	0.957906i	$0.592685\pi$
$44$	−1.08125	−	0.907278i	−0.163005	−	0.136777i
$45$	−0.532089	+	0.921605i	−0.0793191	+	0.137385i
$46$	−1.53209	−	2.65366i	−0.225894	−	0.391260i
$47$	−1.77332	+	10.0570i	−0.258665	+	1.46696i	0.527822	+	0.849355i	$0.323009\pi$
$47$	−1.77332	+	10.0570i	−0.258665	+	1.46696i	−0.786487	+	0.617607i	$0.788102\pi$
$48$	0.326352	−	1.85083i	0.0471048	−	0.267145i
$49$	−9.32295	−	16.1478i	−1.33185	−	2.30683i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	3.43969	+	2.88624i	0.481653	+	0.404155i
$52$	−1.22668	−	0.446476i	−0.170110	−	0.0619150i
$53$	1.57398	−	0.572881i	0.216202	−	0.0786913i	−0.231648	−	0.972800i	$-0.574412\pi$
$53$	1.57398	−	0.572881i	0.216202	−	0.0786913i	0.447851	+	0.894108i	$0.352190\pi$
$54$	3.55303	−	2.98135i	0.483507	−	0.405710i
$55$	−0.490200	−	2.78006i	−0.0660985	−	0.374863i
$56$	−5.06418			−0.676729
$57$		0			0
$58$	8.45336			1.10998
$59$	−0.124485	−	0.705990i	−0.0162066	−	0.0919121i	0.975632	−	0.219415i	$-0.0704149\pi$
$59$	−0.124485	−	0.705990i	−0.0162066	−	0.0919121i	−0.991838	+	0.127503i	$0.959304\pi$
$60$	2.87939	−	2.41609i	0.371727	−	0.311916i
$61$	−9.17024	+	3.33770i	−1.17413	+	0.427348i	−0.854125	−	0.520068i	$-0.825907\pi$
$61$	−9.17024	+	3.33770i	−1.17413	+	0.427348i	−0.320005	+	0.947416i	$0.603684\pi$
$62$	−0.347296	−	0.126406i	−0.0441067	−	0.0160535i
$63$	2.06418	+	1.73205i	0.260062	+	0.218218i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.30541	−	2.26103i	−0.161916	−	0.280446i
$66$	0.460637	−	2.61240i	0.0567005	−	0.321565i
$67$	0.243756	−	1.38241i	0.0297795	−	0.168888i	−0.966291	−	0.257453i	$-0.917117\pi$
$67$	0.243756	−	1.38241i	0.0297795	−	0.168888i	0.996070	+	0.0885646i	$0.0282280\pi$
$68$	−1.19459	−	2.06910i	−0.144866	−	0.250915i
$69$	2.87939	−	4.98724i	0.346637	−	0.600393i
$70$	−7.75877	−	6.51038i	−0.927350	−	0.778139i
$71$	−5.98545	−	2.17853i	−0.710342	−	0.258544i	−0.0385222	−	0.999258i	$-0.512265\pi$
$71$	−5.98545	−	2.17853i	−0.710342	−	0.258544i	−0.671820	+	0.740714i	$0.734487\pi$
$72$	0.500000	−	0.181985i	0.0589256	−	0.0214472i
$73$	−3.49273	+	2.93075i	−0.408793	+	0.343018i	−0.823880	−	0.566764i	$-0.808195\pi$
$73$	−3.49273	+	2.93075i	−0.408793	+	0.343018i	0.415088	+	0.909781i	$0.363751\pi$
$74$	0.837496	+	4.74968i	0.0973570	+	0.552139i
$75$	−1.87939			−0.217013
$76$		0			0
$77$	−7.14796			−0.814585
$78$	−0.426022	−	2.41609i	−0.0482375	−	0.273568i
$79$	1.71688	−	1.44063i	0.193164	−	0.162084i	−0.541076	−	0.840974i	$-0.681983\pi$
$79$	1.71688	−	1.44063i	0.193164	−	0.162084i	0.734240	+	0.678890i	$0.237538\pi$
$80$	−1.87939	+	0.684040i	−0.210122	+	0.0764780i
$81$	9.69119	+	3.52730i	1.07680	+	0.391923i
$82$	−1.17365	−	0.984808i	−0.129608	−	0.108754i
$83$	1.99273	−	3.45150i	0.218730	−	0.378852i	−0.735690	−	0.677319i	$-0.763142\pi$
$83$	1.99273	−	3.45150i	0.218730	−	0.378852i	0.954420	+	0.298467i	$0.0964752\pi$
$84$	−4.75877	−	8.24243i	−0.519224	−	0.899323i
$85$	0.829755	−	4.70578i	0.0899996	−	0.510413i
$86$	0.131759	−	0.747243i	0.0142080	−	0.0805773i
$87$	7.94356	+	13.7587i	0.851639	+	1.47508i
$88$	−0.705737	+	1.22237i	−0.0752318	+	0.130305i
$89$	8.15523	+	6.84305i	0.864453	+	0.725362i	0.962923	−	0.269778i	$-0.0869504\pi$
$89$	8.15523	+	6.84305i	0.864453	+	0.725362i	−0.0984699	+	0.995140i	$0.531395\pi$
$90$	1.00000	+	0.363970i	0.105409	+	0.0383658i
$91$	−6.21213	+	2.26103i	−0.651209	+	0.237021i
$92$	−2.34730	+	1.96962i	−0.244723	+	0.205347i
$93$	−0.120615	−	0.684040i	−0.0125072	−	0.0709317i
$94$	10.2121			1.05330
$95$		0			0
$96$	−1.87939			−0.191814
$97$	0.266044	+	1.50881i	0.0270127	+	0.153197i	0.995331	−	0.0965237i	$-0.0307724\pi$
$97$	0.266044	+	1.50881i	0.0270127	+	0.153197i	−0.968318	+	0.249720i	$0.919661\pi$
$98$	−14.2836	+	11.9854i	−1.44286	+	1.21070i
$99$	0.705737	−	0.256867i	0.0709292	−	0.0258161i
$100$	0.939693	+	0.342020i	0.0939693	+	0.0342020i
$101$	6.75877	+	5.67128i	0.672523	+	0.564314i	0.913811	−	0.406140i	$-0.133125\pi$
$101$	6.75877	+	5.67128i	0.672523	+	0.564314i	−0.241288	+	0.970454i	$0.577570\pi$
$102$	2.24510	−	3.88863i	0.222298	−	0.385031i
$103$	−3.57398	−	6.19031i	−0.352155	−	0.609950i	0.634472	−	0.772946i	$-0.281218\pi$
$103$	−3.57398	−	6.19031i	−0.352155	−	0.609950i	−0.986627	+	0.162996i	$0.947884\pi$
$104$	−0.226682	+	1.28558i	−0.0222280	+	0.126061i
$105$	3.30541	−	18.7459i	0.322575	−	1.82941i
$106$	−0.837496	−	1.45059i	−0.0813448	−	0.140893i
$107$	−4.68479	+	8.11430i	−0.452896	+	0.784439i	−0.998565	−	0.0535622i	$-0.982942\pi$
$107$	−4.68479	+	8.11430i	−0.452896	+	0.784439i	0.545669	+	0.838001i	$0.316276\pi$
$108$	−3.55303	−	2.98135i	−0.341891	−	0.286880i
$109$	10.3969	+	3.78417i	0.995845	+	0.362458i	0.787981	−	0.615700i	$-0.211127\pi$
$109$	10.3969	+	3.78417i	0.995845	+	0.362458i	0.207864	+	0.978158i	$0.433349\pi$
$110$	−2.65270	+	0.965505i	−0.252925	+	0.0920573i
$111$	−6.94356	+	5.82634i	−0.659054	+	0.553012i
$112$	0.879385	+	4.98724i	0.0830941	+	0.471250i
$113$	13.2986			1.25103			0.625514	−	0.780213i	$-0.284890\pi$
$113$	13.2986			1.25103			0.625514	+	0.780213i	$0.284890\pi$
$114$		0			0
$115$	−6.12836			−0.571472
$116$	−1.46791	−	8.32494i	−0.136292	−	0.772951i
$117$	0.532089	−	0.446476i	0.0491916	−	0.0412767i
$118$	−0.673648	+	0.245188i	−0.0620143	+	0.0225714i
$119$	−11.3696	−	4.13819i	−1.04225	−	0.379347i
$120$	−2.87939	−	2.41609i	−0.262851	−	0.220558i
$121$	4.50387	−	7.80093i	0.409443	−	0.709176i
$122$	4.87939	+	8.45134i	0.441759	+	0.765149i
$123$	0.500000	−	2.83564i	0.0450835	−	0.255681i
$124$	−0.0641778	+	0.363970i	−0.00576333	+	0.0326855i
$125$	6.00000	+	10.3923i	0.536656	+	0.929516i
$126$	1.34730	−	2.33359i	0.120027	−	0.207892i
$127$	4.37733	+	3.67301i	0.388425	+	0.325927i	0.815999	−	0.578053i	$-0.196187\pi$
$127$	4.37733	+	3.67301i	0.388425	+	0.325927i	−0.427574	+	0.903980i	$0.640632\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	1.34002	−	0.487728i	0.117982	−	0.0429421i
$130$	−2.00000	+	1.67820i	−0.175412	+	0.147188i
$131$	−1.71554	−	9.72930i	−0.149887	−	0.850052i	−0.963312	−	0.268383i	$-0.913511\pi$
$131$	−1.71554	−	9.72930i	−0.149887	−	0.850052i	0.813425	−	0.581670i	$-0.197600\pi$
$132$	−2.65270			−0.230888
$133$		0			0
$134$	−1.40373			−0.121264
$135$	−1.61081	−	9.13538i	−0.138637	−	0.786249i
$136$	−1.83022	+	1.53574i	−0.156940	+	0.131689i
$137$	−5.07145	+	1.84586i	−0.433283	+	0.157702i	−0.549448	−	0.835528i	$-0.685162\pi$
$137$	−5.07145	+	1.84586i	−0.433283	+	0.157702i	0.116165	+	0.993230i	$0.462940\pi$
$138$	−5.41147	−	1.96962i	−0.460655	−	0.167665i
$139$	−1.79220	−	1.50384i	−0.152013	−	0.127554i	0.563609	−	0.826041i	$-0.309412\pi$
$139$	−1.79220	−	1.50384i	−0.152013	−	0.127554i	−0.715622	+	0.698488i	$0.753857\pi$
$140$	−5.06418	+	8.77141i	−0.428001	+	0.741320i
$141$	9.59627	+	16.6212i	0.808151	+	1.39976i
$142$	−1.10607	+	6.27282i	−0.0928191	+	0.526403i
$143$	−0.319955	+	1.81456i	−0.0267560	+	0.151741i
$144$	−0.266044	−	0.460802i	−0.0221704	−	0.0384002i
$145$	8.45336	−	14.6417i	0.702014	−	1.21592i
$146$	3.49273	+	2.93075i	0.289060	+	0.242550i
$147$	−32.9295	−	11.9854i	−2.71598	−	0.988535i
$148$	4.53209	−	1.64955i	0.372535	−	0.135592i
$149$	−11.0077	+	9.23659i	−0.901789	+	0.756691i	−0.970539	−	0.240943i	$-0.922543\pi$
$149$	−11.0077	+	9.23659i	−0.901789	+	0.756691i	0.0687500	+	0.997634i	$0.478099\pi$
$150$	0.326352	+	1.85083i	0.0266465	+	0.151120i
$151$	20.8384			1.69581			0.847904	−	0.530150i	$-0.177865\pi$
$151$	20.8384			1.69581			0.847904	+	0.530150i	$0.177865\pi$
$152$		0			0
$153$	1.27126			0.102775
$154$	1.24123	+	7.03936i	0.100021	+	0.567248i
$155$	−0.566237	+	0.475129i	−0.0454813	+	0.0381633i
$156$	−2.30541	+	0.839100i	−0.184580	+	0.0671817i
$157$	−5.98545	−	2.17853i	−0.477691	−	0.173865i	0.0919421	−	0.995764i	$-0.470693\pi$
$157$	−5.98545	−	2.17853i	−0.477691	−	0.173865i	−0.569633	+	0.821899i	$0.692915\pi$
$158$	−1.71688	−	1.44063i	−0.136588	−	0.114611i
$159$	1.57398	−	2.72621i	0.124825	−	0.216202i
$160$	1.00000	+	1.73205i	0.0790569	+	0.136931i
$161$	−2.69459	+	15.2818i	−0.212364	+	1.20437i
$162$	1.79086	−	10.1565i	0.140703	−	0.797968i
$163$	−2.36571	−	4.09754i	−0.185297	−	0.320944i	0.758380	−	0.651813i	$-0.225991\pi$
$163$	−2.36571	−	4.09754i	−0.185297	−	0.320944i	−0.943677	+	0.330869i	$0.892658\pi$
$164$	−0.766044	+	1.32683i	−0.0598180	+	0.103608i
$165$	−4.06418	−	3.41025i	−0.316396	−	0.265488i
$166$	−3.74510	−	1.36310i	−0.290676	−	0.105797i
$167$	16.2344	−	5.90885i	1.25626	−	0.457240i	0.373746	−	0.927531i	$-0.378073\pi$
$167$	16.2344	−	5.90885i	1.25626	−	0.457240i	0.882511	+	0.470291i	$0.155851\pi$
$168$	−7.29086	+	6.11776i	−0.562502	+	0.471995i
$169$	−1.96151	−	11.1243i	−0.150886	−	0.855716i
$170$	−4.77837			−0.366484
$171$		0			0
$172$	−0.758770			−0.0578557
$173$	−3.26857	−	18.5370i	−0.248505	−	1.40934i	−0.812210	−	0.583365i	$-0.801736\pi$
$173$	−3.26857	−	18.5370i	−0.248505	−	1.40934i	0.563705	−	0.825976i	$-0.309375\pi$
$174$	12.1702	−	10.2120i	0.922624	−	0.774173i
$175$	4.75877	−	1.73205i	0.359729	−	0.130931i
$176$	1.32635	+	0.482753i	0.0999775	+	0.0363888i
$177$	−1.03209	−	0.866025i	−0.0775766	−	0.0650945i
$178$	5.32295	−	9.21962i	0.398972	−	0.691039i
$179$	−6.91400	−	11.9754i	−0.516777	−	0.895083i	−0.999810	−	0.0194816i	$-0.993798\pi$
$179$	−6.91400	−	11.9754i	−0.516777	−	0.895083i	0.483034	−	0.875602i	$-0.339535\pi$
$180$	0.184793	−	1.04801i	0.0137736	−	0.0781141i
$181$	−2.12836	+	12.0705i	−0.158199	+	0.897194i	0.797603	+	0.603183i	$0.206101\pi$
$181$	−2.12836	+	12.0705i	−0.158199	+	0.897194i	−0.955802	+	0.294010i	$0.905010\pi$
$182$	3.30541	+	5.72513i	0.245013	+	0.424375i
$183$	−9.17024	+	15.8833i	−0.677884	+	1.17413i
$184$	2.34730	+	1.96962i	0.173045	+	0.145202i
$185$	9.06418	+	3.29909i	0.666412	+	0.242554i
$186$	−0.652704	+	0.237565i	−0.0478586	+	0.0174191i
$187$	−2.58331	+	2.16766i	−0.188910	+	0.158515i
$188$	−1.77332	−	10.0570i	−0.129333	−	0.733481i
$189$	−23.4884			−1.70853
$190$		0			0
$191$	−20.0993			−1.45433			−0.727166	−	0.686462i	$-0.759163\pi$
$191$	−20.0993			−1.45433			−0.727166	+	0.686462i	$0.759163\pi$
$192$	0.326352	+	1.85083i	0.0235524	+	0.133572i
$193$	−12.7815	+	10.7250i	−0.920034	+	0.772001i	−0.974001	−	0.226542i	$-0.927258\pi$
$193$	−12.7815	+	10.7250i	−0.920034	+	0.772001i	0.0539670	+	0.998543i	$0.482813\pi$
$194$	1.43969	−	0.524005i	0.103364	−	0.0376214i
$195$	−4.61081	−	1.67820i	−0.330187	−	0.120178i
$196$	14.2836	+	11.9854i	1.02026	+	0.856097i
$197$	−6.49525	+	11.2501i	−0.462768	+	0.801537i	−0.999098	−	0.0424714i	$-0.986477\pi$
$197$	−6.49525	+	11.2501i	−0.462768	+	0.801537i	0.536330	+	0.844008i	$0.319810\pi$
$198$	−0.375515	−	0.650411i	−0.0266867	−	0.0462227i
$199$	2.98545	−	16.9313i	0.211633	−	1.20023i	−0.675021	−	0.737798i	$-0.735866\pi$
$199$	2.98545	−	16.9313i	0.211633	−	1.20023i	0.886654	−	0.462433i	$-0.153023\pi$
$200$	0.173648	−	0.984808i	0.0122788	−	0.0696364i
$201$	−1.31908	−	2.28471i	−0.0930406	−	0.161151i
$202$	4.41147	−	7.64090i	0.310390	−	0.537612i
$203$	−32.7939	−	27.5173i	−2.30168	−	1.93134i
$204$	−4.21941	−	1.53574i	−0.295418	−	0.107523i
$205$	−2.87939	+	1.04801i	−0.201105	+	0.0731962i
$206$	−5.47565	+	4.59462i	−0.381507	+	0.320122i
$207$	−0.283119	−	1.60565i	−0.0196781	−	0.111600i
$208$	1.30541			0.0905137
$209$		0			0
$210$	−19.0351			−1.31355
$211$	2.79726	+	15.8640i	0.192571	+	1.09212i	0.915836	+	0.401554i	$0.131530\pi$
$211$	2.79726	+	15.8640i	0.192571	+	1.09212i	−0.723265	+	0.690571i	$0.757359\pi$
$212$	−1.28312	+	1.07666i	−0.0881249	+	0.0739456i
$213$	−11.2490	+	4.09429i	−0.770767	+	0.280536i
$214$	8.80453	+	3.20459i	0.601865	+	0.219061i
$215$	−1.16250	−	0.975457i	−0.0792821	−	0.0665256i
$216$	−2.31908	+	4.01676i	−0.157793	+	0.273306i
$217$	0.935822	+	1.62089i	0.0635278	+	0.110033i
$218$	1.92127	−	10.8961i	0.130125	−	0.737976i
$219$	−1.48798	+	8.43874i	−0.100548	+	0.570237i
$220$	1.41147	+	2.44474i	0.0951616	+	0.164825i
$221$	−1.55943	+	2.70101i	−0.104899	+	0.181690i
$222$	6.94356	+	5.82634i	0.466021	+	0.391038i
$223$	3.83750	+	1.39673i	0.256978	+	0.0935323i	0.467297	−	0.884101i	$-0.345228\pi$
$223$	3.83750	+	1.39673i	0.256978	+	0.0935323i	−0.210319	+	0.977633i	$0.567450\pi$
$224$	4.75877	−	1.73205i	0.317959	−	0.115728i
$225$	−0.407604	+	0.342020i	−0.0271736	+	0.0228013i
$226$	−2.30928	−	13.0966i	−0.153611	−	0.871171i
$227$	−13.6604			−0.906676			−0.453338	−	0.891339i	$-0.649767\pi$
$227$	−13.6604			−0.906676			−0.453338	+	0.891339i	$0.649767\pi$
$228$		0			0
$229$	−5.22163			−0.345055			−0.172527	−	0.985005i	$-0.555193\pi$
$229$	−5.22163			−0.345055			−0.172527	+	0.985005i	$0.555193\pi$
$230$	1.06418	+	6.03525i	0.0701698	+	0.397953i
$231$	−10.2909	+	8.63506i	−0.677089	+	0.568145i
$232$	−7.94356	+	2.89122i	−0.521520	+	0.189818i
$233$	25.4119	+	9.24919i	1.66479	+	0.605935i	0.991105	−	0.133083i	$-0.0424875\pi$
$233$	25.4119	+	9.24919i	1.66479	+	0.605935i	0.673687	+	0.739017i	$0.264710\pi$
$234$	−0.532089	−	0.446476i	−0.0347837	−	0.0291870i
$235$	10.2121	−	17.6879i	0.666166	−	1.15383i
$236$	0.358441	+	0.620838i	0.0233325	+	0.0404131i
$237$	0.731429	−	4.14814i	0.0475114	−	0.269451i
$238$	−2.10101	+	11.9154i	−0.136189	+	0.772364i
$239$	0.142903	+	0.247516i	0.00924366	+	0.0160105i	0.870610	−	0.491973i	$-0.163724\pi$
$239$	0.142903	+	0.247516i	0.00924366	+	0.0160105i	−0.861367	+	0.507984i	$0.830391\pi$
$240$	−1.87939	+	3.25519i	−0.121314	+	0.210122i
$241$	−2.37551	−	1.99329i	−0.153020	−	0.128399i	0.563063	−	0.826414i	$-0.309623\pi$
$241$	−2.37551	−	1.99329i	−0.153020	−	0.128399i	−0.716084	+	0.698014i	$0.754067\pi$
$242$	−8.46451	−	3.08083i	−0.544119	−	0.198043i
$243$	5.13816	−	1.87014i	0.329613	−	0.119969i
$244$	7.47565	−	6.27282i	0.478580	−	0.401576i
$245$	6.47565	+	36.7252i	0.413714	+	2.34629i
$246$	−2.87939			−0.183583
$247$		0			0
$248$	0.369585			0.0234687
$249$	−1.30066	−	7.37641i	−0.0824259	−	0.467461i
$250$	9.19253	−	7.71345i	0.581387	−	0.487841i
$251$	11.8944	−	4.32921i	0.750768	−	0.273257i	0.0618390	−	0.998086i	$-0.480303\pi$
$251$	11.8944	−	4.32921i	0.750768	−	0.273257i	0.688929	+	0.724829i	$0.258081\pi$
$252$	−2.53209	−	0.921605i	−0.159507	−	0.0580557i
$253$	3.31315	+	2.78006i	0.208296	+	0.174781i
$254$	2.85710	−	4.94864i	0.179270	−	0.310505i
$255$	−4.49020	−	7.77725i	−0.281187	−	0.487031i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	5.27766	−	29.9311i	0.329211	−	1.86705i	−0.149048	−	0.988830i	$-0.547621\pi$
$257$	5.27766	−	29.9311i	0.329211	−	1.86705i	0.478259	−	0.878219i	$-0.341268\pi$
$258$	−0.713011	−	1.23497i	−0.0443901	−	0.0768860i
$259$	12.2121	−	21.1520i	0.758825	−	1.31432i
$260$	2.00000	+	1.67820i	0.124035	+	0.104078i
$261$	4.22668	+	1.53839i	0.261625	+	0.0952237i
$262$	−9.28359	+	3.37895i	−0.573542	+	0.208752i
$263$	16.7784	−	14.0787i	1.03460	−	0.868131i	0.0432077	−	0.999066i	$-0.486242\pi$
$263$	16.7784	−	14.0787i	1.03460	−	0.868131i	0.991391	+	0.130935i	$0.0417978\pi$
$264$	0.460637	+	2.61240i	0.0283503	+	0.160782i
$265$	−3.34998			−0.205788
$266$		0			0
$267$	20.0077			1.22445
$268$	0.243756	+	1.38241i	0.0148898	+	0.0844440i
$269$	1.09833	−	0.921605i	0.0669661	−	0.0561912i	−0.608690	−	0.793408i	$-0.708305\pi$
$269$	1.09833	−	0.921605i	0.0669661	−	0.0561912i	0.675656	+	0.737217i	$0.263860\pi$
$270$	−8.71688	+	3.17269i	−0.530493	+	0.193083i
$271$	−15.1976	−	5.53147i	−0.923188	−	0.336013i	−0.163682	−	0.986513i	$-0.552337\pi$
$271$	−15.1976	−	5.53147i	−0.923188	−	0.336013i	−0.759506	+	0.650500i	$0.774559\pi$
$272$	1.83022	+	1.53574i	0.110974	+	0.0931178i
$273$	−6.21213	+	10.7597i	−0.375975	+	0.651209i
$274$	2.69846	+	4.67388i	0.163020	+	0.282359i
$275$	0.245100	−	1.39003i	0.0147801	−	0.0838220i
$276$	−1.00000	+	5.67128i	−0.0601929	+	0.341371i
$277$	−5.55438	−	9.62046i	−0.333730	−	0.578038i	0.649510	−	0.760353i	$-0.274974\pi$
$277$	−5.55438	−	9.62046i	−0.333730	−	0.578038i	−0.983240	+	0.182315i	$0.941641\pi$
$278$	−1.16978	+	2.02611i	−0.0701586	+	0.121518i
$279$	−0.150644	−	0.126406i	−0.00901884	−	0.00756770i
$280$	9.51754	+	3.46410i	0.568782	+	0.207020i
$281$	3.99273	−	1.45323i	0.238186	−	0.0866926i	−0.220169	−	0.975462i	$-0.570661\pi$
$281$	3.99273	−	1.45323i	0.238186	−	0.0866926i	0.458355	+	0.888769i	$0.348439\pi$
$282$	14.7023	−	12.3367i	0.875511	−	0.734641i
$283$	−0.947433	−	5.37316i	−0.0563191	−	0.319401i	0.943613	−	0.331050i	$-0.107403\pi$
$283$	−0.947433	−	5.37316i	−0.0563191	−	0.319401i	−0.999932	+	0.0116491i	$0.996292\pi$
$284$	6.36959			0.377965
$285$		0			0
$286$	1.84255			0.108952
$287$	1.34730	+	7.64090i	0.0795284	+	0.451028i
$288$	−0.407604	+	0.342020i	−0.0240183	+	0.0201537i
$289$	10.6108	−	3.86202i	0.624166	−	0.227178i
$290$	−15.8871	−	5.78244i	−0.932924	−	0.339557i
$291$	2.20574	+	1.85083i	0.129303	+	0.108498i
$292$	2.27972	−	3.94858i	0.133410	−	0.231073i
$293$	8.90673	+	15.4269i	0.520337	+	0.901249i	0.999720	+	0.0236440i	$0.00752682\pi$
$293$	8.90673	+	15.4269i	0.520337	+	0.901249i	−0.479384	+	0.877605i	$0.659140\pi$
$294$	−6.08512	+	34.5104i	−0.354892	+	2.01269i
$295$	−0.248970	+	1.41198i	−0.0144956	+	0.0822087i
$296$	−2.41147	−	4.17680i	−0.140164	−	0.242771i
$297$	−3.27332	+	5.66955i	−0.189937	+	0.328981i
$298$	11.0077	+	9.23659i	0.637661	+	0.535061i
$299$	3.75877	+	1.36808i	0.217375	+	0.0791181i
$300$	1.76604	−	0.642788i	0.101963	−	0.0371114i
$301$	−2.94356	+	2.46994i	−0.169664	+	0.142365i
$302$	−3.61856	−	20.5218i	−0.208224	−	1.18090i
$303$	16.5817			0.952595
$304$		0			0
$305$	19.5175			1.11757
$306$	−0.220752	−	1.25195i	−0.0126195	−	0.0715690i
$307$	21.9538	−	18.4215i	1.25297	−	1.05137i	0.256577	−	0.966524i	$-0.417405\pi$
$307$	21.9538	−	18.4215i	1.25297	−	1.05137i	0.996394	−	0.0848439i	$-0.0270392\pi$
$308$	6.71688	−	2.44474i	0.382730	−	0.139302i
$309$	−12.6236	−	4.59462i	−0.718132	−	0.261379i
$310$	0.566237	+	0.475129i	0.0321601	+	0.0269855i
$311$	−7.90673	+	13.6949i	−0.448349	+	0.776564i	−0.998279	−	0.0586473i	$-0.981321\pi$
$311$	−7.90673	+	13.6949i	−0.448349	+	0.776564i	0.549929	+	0.835211i	$0.314655\pi$
$312$	1.22668	+	2.12467i	0.0694472	+	0.120286i
$313$	2.28177	−	12.9406i	0.128974	−	0.731445i	−0.849895	−	0.526953i	$-0.823334\pi$
$313$	2.28177	−	12.9406i	0.128974	−	0.731445i	0.978868	−	0.204492i	$-0.0655544\pi$
$314$	−1.10607	+	6.27282i	−0.0624190	+	0.353996i
$315$	−2.69459	−	4.66717i	−0.151823	−	0.262965i
$316$	−1.12061	+	1.94096i	−0.0630395	+	0.109188i
$317$	16.3969	+	13.7587i	0.920943	+	0.772763i	0.974169	−	0.225819i	$-0.0725059\pi$
$317$	16.3969	+	13.7587i	0.920943	+	0.772763i	−0.0532260	+	0.998582i	$0.516950\pi$
$318$	−2.95811	−	1.07666i	−0.165883	−	0.0603763i
$319$	−11.2121	+	4.08088i	−0.627759	+	0.228486i
$320$	1.53209	−	1.28558i	0.0856464	−	0.0718658i
$321$	3.05778	+	17.3415i	0.170669	+	0.967910i
$322$	15.5175			0.864759
$323$		0			0
$324$	−10.3131			−0.572953
$325$	−0.226682	−	1.28558i	−0.0125740	−	0.0713109i
$326$	−3.62449	+	3.04130i	−0.200742	+	0.168442i
$327$	19.5398	−	7.11192i	1.08056	−	0.393290i
$328$	1.43969	+	0.524005i	0.0794937	+	0.0289334i
$329$	−39.6168	−	33.2424i	−2.18414	−	1.83272i
$330$	−2.65270	+	4.59462i	−0.146027	+	0.252925i
$331$	−12.6989	−	21.9952i	−0.697996	−	1.20897i	−0.969160	−	0.246432i	$-0.920742\pi$
$331$	−12.6989	−	21.9952i	−0.697996	−	1.20897i	0.271164	−	0.962533i	$-0.412591\pi$
$332$	−0.692066	+	3.92490i	−0.0379821	+	0.215407i
$333$	−0.445622	+	2.52725i	−0.0244200	+	0.138492i
$334$	−8.63816	−	14.9617i	−0.472659	−	0.818669i
$335$	−1.40373	+	2.43134i	−0.0766941	+	0.132838i
$336$	7.29086	+	6.11776i	0.397749	+	0.333751i
$337$	24.7866	+	9.02158i	1.35021	+	0.491437i	0.913014	−	0.407929i	$-0.133749\pi$
$337$	24.7866	+	9.02158i	1.35021	+	0.491437i	0.437197	+	0.899366i	$0.355971\pi$
$338$	−10.6147	+	3.86343i	−0.577363	+	0.210143i
$339$	19.1459	−	16.0653i	1.03986	−	0.872548i
$340$	0.829755	+	4.70578i	0.0449998	+	0.255207i
$341$	0.521660			0.0282495
$342$		0			0
$343$	58.9769			3.18445
$344$	0.131759	+	0.747243i	0.00710398	+	0.0402886i
$345$	−8.82295	+	7.40333i	−0.475012	+	0.398582i
$346$	−17.6878	+	6.43783i	−0.950901	+	0.346100i
$347$	24.0856	+	8.76644i	1.29298	+	0.470607i	0.894705	−	0.446658i	$-0.147386\pi$
$347$	24.0856	+	8.76644i	1.29298	+	0.470607i	0.398277	+	0.917265i	$0.369608\pi$
$348$	−12.1702	−	10.2120i	−0.652394	−	0.547423i
$349$	2.92127	−	5.05980i	0.156372	−	0.270845i	−0.777186	−	0.629271i	$-0.783353\pi$
$349$	2.92127	−	5.05980i	0.156372	−	0.270845i	0.933558	+	0.358427i	$0.116687\pi$
$350$	−2.53209	−	4.38571i	−0.135346	−	0.234426i
$351$	−1.05138	+	5.96270i	−0.0561188	+	0.318265i
$352$	0.245100	−	1.39003i	0.0130639	−	0.0740889i
$353$	11.2049	+	19.4074i	0.596375	+	1.03295i	0.993351	+	0.115122i	$0.0367260\pi$
$353$	11.2049	+	19.4074i	0.596375	+	1.03295i	−0.396977	+	0.917829i	$0.629941\pi$
$354$	−0.673648	+	1.16679i	−0.0358040	+	0.0620143i
$355$	9.75877	+	8.18858i	0.517942	+	0.434605i
$356$	−10.0039	−	3.64111i	−0.530204	−	0.192978i
$357$	−21.3678	+	7.77725i	−1.13091	+	0.411616i
$358$	−10.5929	+	8.88847i	−0.559850	+	0.469770i
$359$	1.66994	+	9.47070i	0.0881361	+	0.499844i	0.996636	+	0.0819588i	$0.0261176\pi$
$359$	1.66994	+	9.47070i	0.0881361	+	0.499844i	−0.908500	+	0.417886i	$0.862771\pi$
$360$	−1.06418			−0.0560871
$361$		0			0
$362$	12.2567			0.644198
$363$	−2.93969	−	16.6718i	−0.154294	−	0.875044i
$364$	5.06418	−	4.24935i	0.265435	−	0.222726i
$365$	8.56893	−	3.11883i	0.448518	−	0.163247i
$366$	17.2344	+	6.27282i	0.900858	+	0.327885i
$367$	17.8949	+	15.0156i	0.934104	+	0.783807i	0.976550	−	0.215292i	$-0.0690704\pi$
$367$	17.8949	+	15.0156i	0.934104	+	0.783807i	−0.0424453	+	0.999099i	$0.513515\pi$
$368$	1.53209	−	2.65366i	0.0798657	−	0.138331i
$369$	−0.407604	−	0.705990i	−0.0212190	−	0.0367524i
$370$	1.67499	−	9.49935i	0.0870787	−	0.493848i
$371$	−1.47296	+	8.35359i	−0.0764725	+	0.433697i
$372$	0.347296	+	0.601535i	0.0180065	+	0.0311881i
$373$	−12.9709	+	22.4663i	−0.671608	+	1.16326i	0.305840	+	0.952083i	$0.401063\pi$
$373$	−12.9709	+	22.4663i	−0.671608	+	1.16326i	−0.977448	+	0.211176i	$0.932271\pi$
$374$	2.58331	+	2.16766i	0.133580	+	0.112087i
$375$	21.1925	+	7.71345i	1.09438	+	0.398321i
$376$	−9.59627	+	3.49276i	−0.494890	+	0.180125i
$377$	−8.45336	+	7.09321i	−0.435370	+	0.365319i
$378$	4.07873	+	23.1316i	0.209787	+	1.18976i
$379$	−9.47834			−0.486870			−0.243435	−	0.969917i	$-0.578274\pi$
$379$	−9.47834			−0.486870			−0.243435	+	0.969917i	$0.578274\pi$
$380$		0			0
$381$	10.7392			0.550184
$382$	3.49020	+	19.7939i	0.178574	+	1.01274i
$383$	10.3327	−	8.67021i	0.527979	−	0.443027i	−0.339424	−	0.940633i	$-0.610232\pi$
$383$	10.3327	−	8.67021i	0.527979	−	0.443027i	0.867403	+	0.497607i	$0.165788\pi$
$384$	1.76604	−	0.642788i	0.0901231	−	0.0328021i
$385$	13.4338	+	4.88949i	0.684648	+	0.249191i
$386$	12.7815	+	10.7250i	0.650563	+	0.545887i
$387$	0.201867	−	0.349643i	0.0102615	−	0.0177734i
$388$	−0.766044	−	1.32683i	−0.0388900	−	0.0673595i
$389$	−4.36690	+	24.7659i	−0.221410	+	1.25568i	0.648019	+	0.761624i	$0.275598\pi$
$389$	−4.36690	+	24.7659i	−0.221410	+	1.25568i	−0.869430	+	0.494057i	$0.835513\pi$
$390$	−0.852044	+	4.83218i	−0.0431449	+	0.244687i
$391$	3.66044	+	6.34008i	0.185117	+	0.320631i
$392$	9.32295	−	16.1478i	0.470880	−	0.815588i
$393$	−14.2233	−	11.9347i	−0.717469	−	0.602028i
$394$	12.2071	+	4.44301i	0.614984	+	0.223836i
$395$	−4.21213	+	1.53309i	−0.211935	+	0.0771382i
$396$	−0.575322	+	0.482753i	−0.0289110	+	0.0242592i
$397$	1.14022	+	6.46648i	0.0572258	+	0.324543i	0.999959	−	0.00900292i	$-0.00286576\pi$
$397$	1.14022	+	6.46648i	0.0572258	+	0.324543i	−0.942734	+	0.333546i	$0.891755\pi$
$398$	−17.1925			−0.861784
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	5.12449	+	29.0624i	0.255905	+	1.45131i	0.793740	+	0.608257i	$0.208131\pi$
$401$	5.12449	+	29.0624i	0.255905	+	1.45131i	−0.537835	+	0.843050i	$0.680758\pi$
$402$	−2.02094	+	1.69577i	−0.100796	+	0.0845775i
$403$	0.453363	−	0.165011i	0.0225836	−	0.00821977i
$404$	−8.29086	−	3.01763i	−0.412486	−	0.150133i
$405$	−15.8007	−	13.2583i	−0.785141	−	0.658812i
$406$	−21.4047	+	37.0740i	−1.06230	+	1.83995i
$407$	−3.40373	−	5.89544i	−0.168717	−	0.292226i
$408$	−0.779715	+	4.42198i	−0.0386016	+	0.218921i
$409$	−3.66937	+	20.8100i	−0.181439	+	1.02899i	0.749008	+	0.662561i	$0.230530\pi$
$409$	−3.66937	+	20.8100i	−0.181439	+	1.02899i	−0.930446	+	0.366428i	$0.880581\pi$
$410$	1.53209	+	2.65366i	0.0756645	+	0.131055i
$411$	−5.07145	+	8.78401i	−0.250156	+	0.433283i
$412$	5.47565	+	4.59462i	0.269766	+	0.226361i
$413$	3.41147	+	1.24168i	0.167868	+	0.0610988i
$414$	−1.53209	+	0.557635i	−0.0752981	+	0.0274063i
$415$	−6.10607	+	5.12360i	−0.299735	+	0.251508i
$416$	−0.226682	−	1.28558i	−0.0111140	−	0.0630305i
$417$	−4.39693			−0.215318
$418$		0			0
$419$	−27.8830			−1.36217			−0.681087	−	0.732202i	$-0.738492\pi$
$419$	−27.8830			−1.36217			−0.681087	+	0.732202i	$0.738492\pi$
$420$	3.30541	+	18.7459i	0.161287	+	0.914706i
$421$	0.0341483	−	0.0286538i	0.00166429	−	0.00139650i	−0.641955	−	0.766742i	$-0.721876\pi$
$421$	0.0341483	−	0.0286538i	0.00166429	−	0.00139650i	0.643619	+	0.765346i	$0.277432\pi$
$422$	15.1373	−	5.50952i	0.736871	−	0.268199i
$423$	5.10607	+	1.85846i	0.248265	+	0.0903612i
$424$	1.28312	+	1.07666i	0.0623137	+	0.0522874i
$425$	1.19459	−	2.06910i	0.0579463	−	0.100366i
$426$	5.98545	+	10.3671i	0.289996	+	0.502288i
$427$	8.58172	−	48.6693i	0.415298	−	2.35527i
$428$	1.62701	−	9.22724i	0.0786446	−	0.446015i
$429$	1.73143	+	2.99892i	0.0835942	+	0.144789i
$430$	−0.758770	+	1.31423i	−0.0365912	+	0.0633778i
$431$	9.03003	+	7.57709i	0.434961	+	0.364976i	0.833820	−	0.552037i	$-0.186149\pi$
$431$	9.03003	+	7.57709i	0.434961	+	0.364976i	−0.398859	+	0.917012i	$0.630594\pi$
$432$	4.35844	+	1.58634i	0.209696	+	0.0763229i
$433$	25.9786	−	9.45545i	1.24845	−	0.454400i	0.368575	−	0.929598i	$-0.379846\pi$
$433$	25.9786	−	9.45545i	1.24845	−	0.454400i	0.879879	+	0.475198i	$0.157624\pi$
$434$	1.43376	−	1.20307i	0.0688228	−	0.0577492i
$435$	−5.51754	−	31.2915i	−0.264546	−	1.50031i
$436$	−11.0642			−0.529878
$437$		0			0
$438$	8.56893			0.409439
$439$	−6.50299	−	36.8803i	−0.310371	−	1.76020i	−0.597078	−	0.802183i	$-0.703672\pi$
$439$	−6.50299	−	36.8803i	−0.310371	−	1.76020i	0.286708	−	0.958018i	$-0.407439\pi$
$440$	2.16250	−	1.81456i	0.103093	−	0.0865056i
$441$	−9.32295	+	3.39328i	−0.443950	+	0.161585i
$442$	2.93077	+	1.06671i	0.139403	+	0.0507384i
$443$	16.0778	+	13.4909i	0.763882	+	0.640973i	0.939134	−	0.343551i	$-0.111630\pi$
$443$	16.0778	+	13.4909i	0.763882	+	0.640973i	−0.175252	+	0.984524i	$0.556074\pi$
$444$	4.53209	−	7.84981i	0.215083	−	0.372535i
$445$	−10.6459	−	18.4392i	−0.504664	−	0.874104i
$446$	0.709141	−	4.02174i	0.0335788	−	0.190435i
$447$	−4.68954	+	26.5957i	−0.221808	+	1.25793i
$448$	−2.53209	−	4.38571i	−0.119630	−	0.207205i
$449$	−10.9474	+	18.9615i	−0.516641	+	0.894849i	0.483172	+	0.875525i	$0.339485\pi$
$449$	−10.9474	+	18.9615i	−0.516641	+	0.894849i	−0.999813	+	0.0193235i	$0.993849\pi$
$450$	0.407604	+	0.342020i	0.0192146	+	0.0161230i
$451$	2.03209	+	0.739620i	0.0956873	+	0.0348273i
$452$	−12.4966	+	4.54839i	−0.587790	+	0.213938i
$453$	30.0009	−	25.1738i	1.40957	−	1.18277i
$454$	2.37211	+	13.4529i	0.111329	+	0.631376i
$455$	13.2216			0.619840
$456$		0			0
$457$	−13.0496			−0.610436			−0.305218	−	0.952283i	$-0.598729\pi$
$457$	−13.0496			−0.610436			−0.305218	+	0.952283i	$0.598729\pi$
$458$	0.906726	+	5.14230i	0.0423685	+	0.240284i
$459$	−8.48886	+	7.12300i	−0.396226	+	0.332473i
$460$	5.75877	−	2.09602i	0.268504	−	0.0977275i
$461$	−4.14290	−	1.50789i	−0.192954	−	0.0702296i	0.243736	−	0.969842i	$-0.421627\pi$
$461$	−4.14290	−	1.50789i	−0.192954	−	0.0702296i	−0.436690	+	0.899612i	$0.643849\pi$
$462$	10.2909	+	8.63506i	0.478774	+	0.401739i
$463$	−13.3327	+	23.0930i	−0.619625	+	1.07322i	0.369929	+	0.929060i	$0.379382\pi$
$463$	−13.3327	+	23.0930i	−0.619625	+	1.07322i	−0.989554	+	0.144162i	$0.953951\pi$
$464$	4.22668	+	7.32083i	0.196219	+	0.339861i
$465$	−0.241230	+	1.36808i	−0.0111868	+	0.0634432i
$466$	4.69594	−	26.6320i	0.217535	−	1.23370i
$467$	−15.0569	−	26.0793i	−0.696750	−	1.20681i	−0.969587	−	0.244747i	$-0.921295\pi$
$467$	−15.0569	−	26.0793i	−0.696750	−	1.20681i	0.272837	−	0.962060i	$-0.412038\pi$
$468$	−0.347296	+	0.601535i	−0.0160538	+	0.0278060i
$469$	5.44562	+	4.56942i	0.251455	+	0.210996i
$470$	−19.1925	−	6.98551i	−0.885286	−	0.322218i
$471$	−11.2490	+	4.09429i	−0.518325	+	0.188655i
$472$	0.549163	−	0.460802i	0.0252773	−	0.0212102i
$473$	0.185975	+	1.05471i	0.00855112	+	0.0484958i
$474$	−4.21213			−0.193470
$475$		0			0
$476$	12.0993			0.554569
$477$	−0.154763	−	0.877705i	−0.00708611	−	0.0401873i
$478$	0.218941	−	0.183713i	0.0100141	−	0.00840284i
$479$	−7.67499	+	2.79347i	−0.350679	+	0.127637i	−0.511353	−	0.859371i	$-0.670856\pi$
$479$	−7.67499	+	2.79347i	−0.350679	+	0.127637i	0.160674	+	0.987008i	$0.448633\pi$
$480$	3.53209	+	1.28558i	0.161217	+	0.0586782i
$481$	−4.82295	−	4.04693i	−0.219908	−	0.184524i
$482$	−1.55051	+	2.68556i	−0.0706237	+	0.122324i
$483$	14.5817	+	25.2563i	0.663491	+	1.14920i
$484$	−1.56418	+	8.87089i	−0.0710990	+	0.403222i
$485$	0.532089	−	3.01763i	0.0241609	−	0.137023i
$486$	−2.73396	−	4.73535i	−0.124015	−	0.214800i
$487$	13.2935	−	23.0251i	0.602388	−	1.04337i	−0.390070	−	0.920785i	$-0.627549\pi$
$487$	13.2935	−	23.0251i	0.602388	−	1.04337i	0.992458	−	0.122582i	$-0.0391174\pi$
$488$	−7.47565	−	6.27282i	−0.338407	−	0.283957i
$489$	−8.35591	−	3.04130i	−0.377868	−	0.137533i
$490$	35.0428	−	12.7545i	1.58307	−	0.576192i
$491$	29.7447	−	24.9588i	1.34236	−	1.12637i	0.361346	−	0.932432i	$-0.382317\pi$
$491$	29.7447	−	24.9588i	1.34236	−	1.12637i	0.981013	−	0.193941i	$-0.0621271\pi$
$492$	0.500000	+	2.83564i	0.0225417	+	0.127841i
$493$	−20.1967			−0.909611
$494$		0			0
$495$	−1.50206			−0.0675125
$496$	−0.0641778	−	0.363970i	−0.00288167	−	0.0163427i
$497$	24.7101	−	20.7342i	1.10840	−	0.930057i
$498$	−7.03849	+	2.56180i	−0.315402	+	0.114797i
$499$	−19.4128	−	7.06569i	−0.869037	−	0.316304i	−0.131260	−	0.991348i	$-0.541902\pi$
$499$	−19.4128	−	7.06569i	−0.869037	−	0.316304i	−0.737777	+	0.675044i	$0.764124\pi$
$500$	−9.19253	−	7.71345i	−0.411103	−	0.344956i
$501$	16.2344	−	28.1188i	0.725301	−	1.25626i
$502$	−6.32888	−	10.9619i	−0.282472	−	0.489255i
$503$	0.0127932	−	0.0725540i	0.000570422	−	0.00323502i	−0.984521	−	0.175265i	$-0.943922\pi$
$503$	0.0127932	−	0.0725540i	0.000570422	−	0.00323502i	0.985092	+	0.172030i	$0.0550327\pi$
$504$	−0.467911	+	2.65366i	−0.0208424	+	0.118203i
$505$	−8.82295	−	15.2818i	−0.392616	−	0.680031i
$506$	2.16250	−	3.74557i	0.0961350	−	0.166511i
$507$	−16.2626	−	13.6460i	−0.722249	−	0.606039i
$508$	−5.36959	−	1.95437i	−0.238237	−	0.0867111i
$509$	14.1138	−	5.13701i	0.625584	−	0.227694i	−0.00972438	−	0.999953i	$-0.503095\pi$
$509$	14.1138	−	5.13701i	0.625584	−	0.227694i	0.635308	+	0.772259i	$0.280873\pi$
$510$	−6.87939	+	5.77249i	−0.304624	+	0.255610i
$511$	−4.00950	−	22.7390i	−0.177370	−	1.00591i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−30.3928			−1.34057
$515$	2.48246	+	14.0787i	0.109390	+	0.620383i
$516$	−1.09240	+	0.916629i	−0.0480901	+	0.0403524i
$517$	−13.5449	+	4.92993i	−0.595703	+	0.216818i
$518$	−22.9513	−	8.35359i	−1.00842	−	0.367036i
$519$	−27.0993	−	22.7390i	−1.18953	−	0.998130i
$520$	1.30541	−	2.26103i	0.0572459	−	0.0991528i
$521$	22.5856	+	39.1194i	0.989493	+	1.71385i	0.619959	+	0.784634i	$0.287149\pi$
$521$	22.5856	+	39.1194i	0.989493	+	1.71385i	0.369533	+	0.929217i	$0.379518\pi$
$522$	0.781059	−	4.42961i	0.0341860	−	0.193879i
$523$	−0.0290958	+	0.165011i	−0.00127227	+	0.00721541i	−0.985437	−	0.170039i	$-0.945611\pi$
$523$	−0.0290958	+	0.165011i	−0.00127227	+	0.00721541i	0.984165	+	0.177255i	$0.0567216\pi$
$524$	4.93969	+	8.55580i	0.215791	+	0.373762i
$525$	4.75877	−	8.24243i	0.207690	−	0.359729i
$526$	−16.7784	−	14.0787i	−0.731572	−	0.613862i
$527$	0.829755	+	0.302006i	0.0361447	+	0.0131556i
$528$	2.49273	−	0.907278i	0.108482	−	0.0394842i
$529$	−10.4265	+	8.74886i	−0.453326	+	0.380385i
$530$	0.581719	+	3.29909i	0.0252682	+	0.143303i
$531$	−0.381445			−0.0165533
$532$		0			0
$533$	2.00000			0.0866296
$534$	−3.47431	−	19.7038i	−0.150348	−	0.852666i
$535$	14.3550	−	12.0453i	0.620622	−	0.520764i
$536$	1.31908	−	0.480105i	0.0569755	−	0.0207374i
$537$	−24.4209	−	8.88847i	−1.05384	−	0.383566i
$538$	−1.09833	−	0.921605i	−0.0473522	−	0.0397332i
$539$	13.1591	−	22.7922i	0.566803	−	0.981731i
$540$	4.63816	+	8.03352i	0.199594	+	0.345708i
$541$	−0.170245	+	0.965505i	−0.00731939	+	0.0415103i	−0.988249	−	0.152854i	$-0.951153\pi$
$541$	−0.170245	+	0.965505i	−0.00731939	+	0.0415103i	0.980929	+	0.194365i	$0.0622645\pi$
$542$	−2.80840	+	15.9272i	−0.120631	+	0.684133i
$543$	11.5175	+	19.9490i	0.494265	+	0.856092i
$544$	1.19459	−	2.06910i	0.0512177	−	0.0887117i
$545$	−16.9513	−	14.2238i	−0.726114	−	0.609282i
$546$	11.6750	+	4.24935i	0.499644	+	0.181855i
$547$	26.6917	−	9.71497i	1.14125	−	0.415382i	0.298887	−	0.954288i	$-0.403385\pi$
$547$	26.6917	−	9.71497i	1.14125	−	0.415382i	0.842366	+	0.538906i	$0.181162\pi$
$548$	4.13429	−	3.46908i	0.176608	−	0.148192i
$549$	0.901674	+	5.11365i	0.0384825	+	0.218245i
$550$	−1.41147			−0.0601855
$551$		0			0
$552$	5.75877			0.245110
$553$	1.97090	+	11.1776i	0.0838114	+	0.475318i
$554$	−8.50980	+	7.14057i	−0.361547	+	0.303374i
$555$	17.0351	−	6.20026i	0.723099	−	0.263186i
$556$	2.19846	+	0.800175i	0.0932356	+	0.0339350i
$557$	27.2959	+	22.9040i	1.15656	+	0.970473i	0.999853	−	0.0171711i	$-0.00546600\pi$
$557$	27.2959	+	22.9040i	1.15656	+	0.970473i	0.156712	+	0.987644i	$0.449910\pi$
$558$	−0.0983261	+	0.170306i	−0.00416247	+	0.00720962i
$559$	0.495252	+	0.857802i	0.0209469	+	0.0362812i
$560$	1.75877	−	9.97448i	0.0743216	−	0.421499i
$561$	−1.10055	+	6.24152i	−0.0464652	+	0.263517i
$562$	−2.12449	−	3.67972i	−0.0896160	−	0.155219i
$563$	4.31386	−	7.47183i	0.181808	−	0.314900i	−0.760688	−	0.649117i	$-0.775139\pi$
$563$	4.31386	−	7.47183i	0.181808	−	0.314900i	0.942496	+	0.334217i	$0.108472\pi$
$564$	−14.7023	−	12.3367i	−0.619080	−	0.519470i
$565$	−24.9932	−	9.09678i	−1.05147	−	0.382704i
$566$	−5.12701	+	1.86608i	−0.215504	+	0.0784372i
$567$	−40.0087	+	33.5713i	−1.68021	+	1.40986i
$568$	−1.10607	−	6.27282i	−0.0464095	−	0.263202i
$569$	−22.3310			−0.936164			−0.468082	−	0.883685i	$-0.655055\pi$
$569$	−22.3310			−0.936164			−0.468082	+	0.883685i	$0.655055\pi$
$570$		0			0
$571$	−9.56448			−0.400261			−0.200131	−	0.979769i	$-0.564137\pi$
$571$	−9.56448			−0.400261			−0.200131	+	0.979769i	$0.564137\pi$
$572$	−0.319955	−	1.81456i	−0.0133780	−	0.0758704i
$573$	−28.9368	+	24.2808i	−1.20885	+	1.01435i
$574$	7.29086	−	2.65366i	0.304315	−	0.110761i
$575$	−2.87939	−	1.04801i	−0.120079	−	0.0437051i
$576$	0.407604	+	0.342020i	0.0169835	+	0.0142508i
$577$	−11.2378	+	19.4645i	−0.467837	+	0.810317i	−0.999325	−	0.0367489i	$-0.988300\pi$
$577$	−11.2378	+	19.4645i	−0.467837	+	0.810317i	0.531488	+	0.847066i	$0.321633\pi$
$578$	−5.64590	−	9.77898i	−0.234838	−	0.406752i
$579$	−5.44521	+	30.8813i	−0.226295	+	1.28338i
$580$	−2.93582	+	16.6499i	−0.121903	+	0.691348i
$581$	10.0915	+	17.4790i	0.418667	+	0.725152i
$582$	1.43969	−	2.49362i	0.0596772	−	0.103364i
$583$	1.81109	+	1.51968i	0.0750076	+	0.0629389i
$584$	−4.28446	−	1.55942i	−0.177292	−	0.0645291i
$585$	−1.30541	+	0.475129i	−0.0539719	+	0.0196442i
$586$	13.6459	−	11.4503i	0.563707	−	0.473006i
$587$	0.720285	+	4.08494i	0.0297293	+	0.168603i	0.996058	−	0.0887090i	$-0.0282741\pi$
$587$	0.720285	+	4.08494i	0.0297293	+	0.168603i	−0.966328	+	0.257313i	$0.917163\pi$
$588$	35.0428			1.44514
$589$		0			0
$590$	1.43376			0.0590271
$591$	4.23947	+	24.0433i	0.174389	+	0.989007i
$592$	−3.69459	+	3.10013i	−0.151847	+	0.127415i
$593$	−9.78921	+	3.56298i	−0.401995	+	0.146314i	−0.535102	−	0.844788i	$-0.679727\pi$
$593$	−9.78921	+	3.56298i	−0.401995	+	0.146314i	0.133107	+	0.991102i	$0.457505\pi$
$594$	6.15183	+	2.23908i	0.252412	+	0.0918706i
$595$	18.5371	+	15.5545i	0.759949	+	0.637673i
$596$	7.18479	−	12.4444i	0.294301	−	0.509744i
$597$	−16.1557	−	27.9825i	−0.661209	−	1.14525i
$598$	0.694593	−	3.93923i	0.0284040	−	0.161087i
$599$	6.88619	−	39.0535i	0.281362	−	1.59568i	−0.436635	−	0.899639i	$-0.643830\pi$
$599$	6.88619	−	39.0535i	0.281362	−	1.59568i	0.717997	−	0.696046i	$-0.245059\pi$
$600$	−0.939693	−	1.62760i	−0.0383628	−	0.0664463i
$601$	11.9324	−	20.6676i	0.486734	−	0.843047i	−0.513150	−	0.858299i	$-0.671522\pi$
$601$	11.9324	−	20.6676i	0.486734	−	0.843047i	0.999884	+	0.0152517i	$0.00485495\pi$
$602$	2.94356	+	2.46994i	0.119971	+	0.100667i
$603$	−0.701867	−	0.255459i	−0.0285822	−	0.0104031i
$604$	−19.5817	+	7.12716i	−0.796769	+	0.290000i
$605$	−13.8007	+	11.5801i	−0.561077	+	0.470799i
$606$	−2.87939	−	16.3298i	−0.116967	−	0.663353i
$607$	29.9317			1.21489			0.607445	−	0.794362i	$-0.292194\pi$
$607$	29.9317			1.21489			0.607445	+	0.794362i	$0.292194\pi$
$608$		0			0
$609$	−80.4552			−3.26021
$610$	−3.38919	−	19.2210i	−0.137224	−	0.778237i
$611$	−10.2121	+	8.56900i	−0.413139	+	0.346665i
$612$	−1.19459	+	0.434796i	−0.0482885	+	0.0175756i
$613$	33.4320	+	12.1683i	1.35031	+	0.491471i	0.913043	−	0.407863i	$-0.133726\pi$
$613$	33.4320	+	12.1683i	1.35031	+	0.491471i	0.437263	+	0.899334i	$0.355948\pi$
$614$	−21.9538	−	18.4215i	−0.885984	−	0.743429i
$615$	−2.87939	+	4.98724i	−0.116108	+	0.201105i
$616$	−3.57398	−	6.19031i	−0.144000	−	0.249415i
$617$	2.08940	−	11.8496i	0.0841162	−	0.477047i	−0.913428	−	0.407001i	$-0.866574\pi$
$617$	2.08940	−	11.8496i	0.0841162	−	0.477047i	0.997544	−	0.0700454i	$-0.0223144\pi$
$618$	−2.33275	+	13.2297i	−0.0938369	+	0.532176i
$619$	8.55644	+	14.8202i	0.343912	+	0.595673i	0.985156	−	0.171664i	$-0.0549144\pi$
$619$	8.55644	+	14.8202i	0.343912	+	0.595673i	−0.641243	+	0.767338i	$0.721581\pi$
$620$	0.369585	−	0.640140i	0.0148429	−	0.0257086i
$621$	10.8871	+	9.13538i	0.436885	+	0.366590i
$622$	14.8598	+	5.40852i	0.595823	+	0.216862i
$623$	−50.6614	+	18.4392i	−2.02971	+	0.738752i
$624$	1.87939	−	1.57699i	0.0752356	−	0.0631302i
$625$	−3.29932	−	18.7113i	−0.131973	−	0.748454i
$626$	−13.1402			−0.525189
$627$		0			0
$628$	6.36959			0.254174
$629$	−2.00093	−	11.3479i	−0.0797824	−	0.452469i
$630$	−4.12836	+	3.46410i	−0.164478	+	0.138013i
$631$	−17.2344	+	6.27282i	−0.686092	+	0.249717i	−0.661461	−	0.749980i	$-0.730063\pi$
$631$	−17.2344	+	6.27282i	−0.686092	+	0.249717i	−0.0246307	+	0.999697i	$0.507841\pi$
$632$	2.10607	+	0.766546i	0.0837748	+	0.0304915i
$633$	23.1917	+	19.4601i	0.921786	+	0.773470i
$634$	10.7023	−	18.5370i	0.425044	−	0.736198i
$635$	−5.71419	−	9.89727i	−0.226761	−	0.392761i
$636$	−0.546637	+	3.10013i	−0.0216756	+	0.122928i
$637$	4.22668	−	23.9707i	0.167467	−	0.949754i
$638$	5.96585	+	10.3332i	0.236190	+	0.409094i
$639$	−1.69459	+	2.93512i	−0.0670371	+	0.116112i
$640$	−1.53209	−	1.28558i	−0.0605611	−	0.0508168i
$641$	−29.2977	−	10.6635i	−1.15719	−	0.421183i	−0.309098	−	0.951030i	$-0.600027\pi$
$641$	−29.2977	−	10.6635i	−1.15719	−	0.421183i	−0.848093	+	0.529847i	$0.822249\pi$
$642$	16.5471	−	6.02265i	0.653062	−	0.237695i
$643$	−24.4748	+	20.5368i	−0.965191	+	0.809891i	−0.981790	−	0.189971i	$-0.939161\pi$
$643$	−24.4748	+	20.5368i	−0.965191	+	0.809891i	0.0165988	+	0.999862i	$0.494716\pi$
$644$	−2.69459	−	15.2818i	−0.106182	−	0.602187i
$645$	−2.85204			−0.112299
$646$		0			0
$647$	2.99588			0.117780			0.0588901	−	0.998264i	$-0.481244\pi$
$647$	2.99588			0.117780			0.0588901	+	0.998264i	$0.481244\pi$
$648$	1.79086	+	10.1565i	0.0703516	+	0.398984i
$649$	0.775129	−	0.650411i	0.0304265	−	0.0255309i
$650$	−1.22668	+	0.446476i	−0.0481144	+	0.0175122i
$651$	3.30541	+	1.20307i	0.129549	+	0.0471520i
$652$	3.62449	+	3.04130i	0.141946	+	0.119107i
$653$	−0.467911	+	0.810446i	−0.0183108	+	0.0317152i	−0.875036	−	0.484059i	$-0.839162\pi$
$653$	−0.467911	+	0.810446i	−0.0183108	+	0.0317152i	0.856725	+	0.515774i	$0.172495\pi$
$654$	−10.3969	−	18.0080i	−0.406552	−	0.704169i
$655$	−3.43107	+	19.4586i	−0.134063	+	0.760310i
$656$	0.266044	−	1.50881i	0.0103873	−	0.0589093i
$657$	1.21301	+	2.10100i	0.0473241	+	0.0819677i
$658$	−25.8580	+	44.7874i	−1.00805	+	1.74600i
$659$	9.37417	+	7.86586i	0.365166	+	0.306411i	0.806846	−	0.590762i	$-0.201173\pi$
$659$	9.37417	+	7.86586i	0.365166	+	0.306411i	−0.441680	+	0.897173i	$0.645617\pi$
$660$	4.98545	+	1.81456i	0.194058	+	0.0706315i
$661$	−11.2344	+	4.08900i	−0.436968	+	0.159043i	−0.551131	−	0.834419i	$-0.685804\pi$
$661$	−11.2344	+	4.08900i	−0.436968	+	0.159043i	0.114163	+	0.993462i	$0.463581\pi$
$662$	−19.4559	+	16.3254i	−0.756175	+	0.634506i
$663$	1.01785	+	5.77249i	0.0395299	+	0.224185i
$664$	3.98545			0.154666
$665$		0			0
$666$	2.56624			0.0994397
$667$	4.49794	+	25.5091i	0.174161	+	0.987716i
$668$	−13.2344	+	11.1050i	−0.512055	+	0.429665i
$669$	7.21213	−	2.62500i	0.278837	−	0.101488i
$670$	2.63816	+	0.960210i	0.101921	+	0.0370962i
$671$	−10.5517	−	8.85392i	−0.407343	−	0.341802i
$672$	4.75877	−	8.24243i	0.183574	−	0.317959i
$673$	22.4317	+	38.8529i	0.864679	+	1.49767i	0.867366	+	0.497671i	$0.165811\pi$
$673$	22.4317	+	38.8529i	0.864679	+	1.49767i	−0.00268731	+	0.999996i	$0.500855\pi$
$674$	4.58037	−	25.9766i	0.176429	−	1.00058i
$675$	0.805407	−	4.56769i	0.0310001	−	0.175811i
$676$	5.64796	+	9.78255i	0.217229	+	0.376252i
$677$	0.472964	−	0.819197i	0.0181775	−	0.0314843i	−0.856794	−	0.515660i	$-0.827547\pi$
$677$	0.472964	−	0.819197i	0.0181775	−	0.0314843i	0.874971	+	0.484175i	$0.160880\pi$
$678$	−19.1459	−	16.0653i	−0.735294	−	0.616985i
$679$	−7.29086	−	2.65366i	−0.279798	−	0.101838i
$680$	4.49020	−	1.63430i	0.172191	−	0.0626725i
$681$	−19.6668	+	16.5024i	−0.753635	+	0.632375i
$682$	−0.0905853	−	0.513735i	−0.00346869	−	0.0196719i
$683$	5.92221			0.226607			0.113303	−	0.993560i	$-0.463857\pi$
$683$	5.92221			0.226607			0.113303	+	0.993560i	$0.463857\pi$
$684$		0			0
$685$	10.7939			0.412412
$686$	−10.2412	−	58.0809i	−0.391012	−	2.21754i
$687$	−7.51754	+	6.30797i	−0.286812	+	0.240664i
$688$	0.713011	−	0.259515i	0.0271833	−	0.00989391i
$689$	2.05468	+	0.747843i	0.0782772	+	0.0284906i
$690$	8.82295	+	7.40333i	0.335884	+	0.281840i
$691$	−0.103074	+	0.178529i	−0.00392111	+	0.00679156i	−0.867979	−	0.496600i	$-0.834581\pi$
$691$	−0.103074	+	0.178529i	−0.00392111	+	0.00679156i	0.864058	+	0.503392i	$0.167915\pi$
$692$	9.41147	+	16.3012i	0.357771	+	0.619677i
$693$	−0.660444	+	3.74557i	−0.0250882	+	0.142282i
$694$	4.45084	−	25.2420i	0.168951	−	0.958171i
$695$	2.33956	+	4.05223i	0.0887444	+	0.153710i
$696$	−7.94356	+	13.7587i	−0.301100	+	0.521520i
$697$	2.80406	+	2.35289i	0.106211	+	0.0891220i
$698$	−5.49020	−	1.99827i	−0.207807	−	0.0756356i
$699$	47.7588	−	17.3828i	1.80640	−	0.657478i
$700$	−3.87939	+	3.25519i	−0.146627	+	0.123035i
$701$	0.758770	+	4.30320i	0.0286584	+	0.162530i	0.995778	−	0.0917911i	$-0.0292592\pi$
$701$	0.758770	+	4.30320i	0.0286584	+	0.162530i	−0.967120	+	0.254321i	$0.918148\pi$
$702$	6.05468			0.228519
$703$		0			0
$704$	−1.41147			−0.0531969
$705$	−6.66550	−	37.8019i	−0.251037	−	1.42370i
$706$	17.1668	−	14.4047i	0.646083	−	0.542128i
$707$	−41.9864	+	15.2818i	−1.57906	+	0.574731i
$708$	1.26604	+	0.460802i	0.0475809	+	0.0173180i
$709$	6.70645	+	5.62738i	0.251866	+	0.211341i	0.759975	−	0.649952i	$-0.225211\pi$
$709$	6.70645	+	5.62738i	0.251866	+	0.211341i	−0.508109	+	0.861293i	$0.669655\pi$
$710$	6.36959	−	11.0324i	0.239046	−	0.414040i
$711$	−0.596267	−	1.03276i	−0.0223617	−	0.0387317i
$712$	−1.84864	+	10.4842i	−0.0692807	+	0.392911i
$713$	0.196652	−	1.11527i	0.00736468	−	0.0417672i
$714$	11.3696	+	19.6927i	0.425496	+	0.736981i
$715$	1.84255	−	3.19139i	0.0689074	−	0.119351i
$716$	10.5929	+	8.88847i	0.395874	+	0.332178i
$717$	0.504748	+	0.183713i	0.0188501	+	0.00686089i
$718$	9.03684	−	3.28914i	0.337252	−	0.122750i
$719$	−21.1480	+	17.7452i	−0.788686	+	0.661786i	−0.945420	−	0.325855i	$-0.894348\pi$
$719$	−21.1480	+	17.7452i	−0.788686	+	0.661786i	0.156734	+	0.987641i	$0.449903\pi$
$720$	0.184793	+	1.04801i	0.00688681	+	0.0390570i
$721$	36.1985			1.34810
$722$		0			0
$723$	−5.82800			−0.216746
$724$	−2.12836	−	12.0705i	−0.0790997	−	0.448597i
$725$	6.47565	−	5.43372i	0.240500	−	0.201803i
$726$	−15.9081	+	5.79006i	−0.590404	+	0.214889i
$727$	−26.9094	−	9.79423i	−0.998015	−	0.363248i	−0.209196	−	0.977874i	$-0.567085\pi$
$727$	−26.9094	−	9.79423i	−0.998015	−	0.363248i	−0.788819	+	0.614626i	$0.789307\pi$
$728$	−5.06418	−	4.24935i	−0.187691	−	0.157491i
$729$	−10.3316	+	17.8948i	−0.382651	+	0.662770i
$730$	−4.55943	−	7.89716i	−0.168752	−	0.292287i
$731$	−0.314797	+	1.78530i	−0.0116432	+	0.0660318i
$732$	3.18479	−	18.0619i	0.117713	−	0.667585i
$733$	−18.4807	−	32.0095i	−0.682600	−	1.18230i	−0.974184	−	0.225753i	$-0.927516\pi$
$733$	−18.4807	−	32.0095i	−0.682600	−	1.18230i	0.291584	−	0.956545i	$-0.405818\pi$
$734$	11.6800	−	20.2304i	0.431118	−	0.746719i
$735$	53.6887	+	45.0502i	1.98034	+	1.66170i
$736$	−2.87939	−	1.04801i	−0.106136	−	0.0386302i
$737$	1.86184	−	0.677656i	0.0685819	−	0.0249618i
$738$	−0.624485	+	0.524005i	−0.0229876	+	0.0192889i
$739$	7.99242	+	45.3273i	0.294006	+	1.66739i	0.671215	+	0.741263i	$0.265773\pi$
$739$	7.99242	+	45.3273i	0.294006	+	1.66739i	−0.377209	+	0.926128i	$0.623116\pi$
$740$	−9.64590			−0.354590
$741$		0			0
$742$	8.48246			0.311401
$743$	−4.58616	−	26.0094i	−0.168250	−	0.954193i	−0.945650	−	0.325186i	$-0.894573\pi$
$743$	−4.58616	−	26.0094i	−0.168250	−	0.954193i	0.777400	−	0.629007i	$-0.216538\pi$
$744$	0.532089	−	0.446476i	0.0195073	−	0.0163686i
$745$	27.0060	−	9.82938i	0.989423	−	0.360120i
$746$	24.3773	+	8.87262i	0.892517	+	0.324850i
$747$	−1.62449	−	1.36310i	−0.0594368	−	0.0498734i
$748$	1.68614	−	2.92047i	0.0616513	−	0.106783i
$749$	−23.7246	−	41.0923i	−0.866879	−	1.50148i
$750$	3.91622	−	22.2100i	0.143000	−	0.810994i
$751$	4.71925	−	26.7642i	0.172208	−	0.976638i	−0.769110	−	0.639117i	$-0.779300\pi$
$751$	4.71925	−	26.7642i	0.172208	−	0.976638i	0.941318	−	0.337522i	$-0.109589\pi$
$752$	5.10607	+	8.84397i	0.186199	+	0.322506i
$753$	11.8944	−	20.6017i	0.433456	−	0.750768i
$754$	8.45336	+	7.09321i	0.307853	+	0.258320i
$755$	−39.1634	−	14.2543i	−1.42530	−	0.518768i
$756$	22.0719	−	8.03352i	0.802748	−	0.292176i
$757$	14.8648	−	12.4731i	0.540272	−	0.453342i	−0.331359	−	0.943505i	$-0.607507\pi$
$757$	14.8648	−	12.4731i	0.540272	−	0.453342i	0.871631	+	0.490163i	$0.163063\pi$
$758$	1.64590	+	9.33434i	0.0597817	+	0.339039i
$759$	8.12836			0.295041
$760$		0			0
$761$	40.2645			1.45959			0.729793	−	0.683669i	$-0.239617\pi$
$761$	40.2645			1.45959			0.729793	+	0.683669i	$0.239617\pi$
$762$	−1.86484	−	10.5760i	−0.0675559	−	0.383129i
$763$	−42.9222	+	36.0160i	−1.55389	+	1.30387i
$764$	18.8871	−	6.87435i	0.683312	−	0.248705i
$765$	−2.38919	−	0.869592i	−0.0863812	−	0.0314402i
$766$	−10.3327	−	8.67021i	−0.373337	−	0.313267i
$767$	0.467911	−	0.810446i	0.0168953	−	0.0292635i
$768$	−0.939693	−	1.62760i	−0.0339082	−	0.0587308i
$769$	−6.76217	+	38.3502i	−0.243850	+	1.38294i	0.579298	+	0.815116i	$0.303327\pi$
$769$	−6.76217	+	38.3502i	−0.243850	+	1.38294i	−0.823148	+	0.567827i	$0.807784\pi$
$770$	2.48246	−	14.0787i	0.0894616	−	0.507362i
$771$	−28.5599	−	49.4672i	−1.02856	−	1.78152i
$772$	8.34255	−	14.4497i	0.300255	−	0.520057i
$773$	5.18067	+	4.34710i	0.186336	+	0.156354i	0.731184	−	0.682181i	$-0.238968\pi$
$773$	5.18067	+	4.34710i	0.186336	+	0.156354i	−0.544848	+	0.838535i	$0.683413\pi$
$774$	−0.379385	−	0.138085i	−0.0136367	−	0.00496336i
$775$	−0.347296	+	0.126406i	−0.0124753	+	0.00454062i
$776$	−1.17365	+	0.984808i	−0.0421315	+	0.0353525i
$777$	−7.97090	−	45.2052i	−0.285955	−	1.62173i
$778$	25.1480			0.901598
$779$		0			0
$780$	4.90673			0.175689
$781$	−1.56118	−	8.85392i	−0.0558636	−	0.316818i
$782$	5.60813	−	4.70578i	0.200546	−	0.168278i
$783$	−36.8435	+	13.4099i	−1.31668	+	0.479232i
$784$	−17.5214	−	6.37727i	−0.625765	−	0.227760i
$785$	9.75877	+	8.18858i	0.348305	+	0.292263i
$786$	−9.28359	+	16.0796i	−0.331135	+	0.573542i
$787$	2.90239	+	5.02709i	0.103459	+	0.179196i	0.913108	−	0.407719i	$-0.133676\pi$
$787$	2.90239	+	5.02709i	0.103459	+	0.179196i	−0.809649	+	0.586915i	$0.800342\pi$
$788$	2.25578	−	12.7931i	0.0803587	−	0.455737i
$789$	7.14796	−	40.5381i	0.254474	−	1.44319i
$790$	2.24123	+	3.88192i	0.0797394	+	0.138113i
$791$	−33.6732	+	58.3238i	−1.19728	+	2.07375i
$792$	0.575322	+	0.482753i	0.0204432	+	0.0171539i
$793$	−11.9709	−	4.35705i	−0.425099	−	0.154723i
$794$	6.17024	−	2.24579i	0.218974	−	0.0796999i
$795$	−4.82295	+	4.04693i	−0.171052	+	0.143530i
$796$	2.98545	+	16.9313i	0.105817	+	0.600115i
$797$	39.2181			1.38918			0.694589	−	0.719407i	$-0.255586\pi$
$797$	39.2181			1.38918			0.694589	+	0.719407i	$0.255586\pi$
$798$		0			0
$799$	−24.3987			−0.863163
$800$	0.173648	+	0.984808i	0.00613939	+	0.0348182i
$801$	4.33931	−	3.64111i	0.153322	−	0.128652i
$802$	27.7310	−	10.0933i	0.979216	−	0.356406i
$803$	−6.04741	−	2.20108i	−0.213408	−	0.0776743i
$804$	2.02094	+	1.69577i	0.0712732	+	0.0598053i
$805$	15.5175	−	26.8772i	0.546921	−	0.947296i
$806$	−0.241230	−	0.417822i	−0.00849695	−	0.0147171i
$807$	0.467911	−	2.65366i	0.0164713	−	0.0934131i
$808$	−1.53209	+	8.68891i	−0.0538987	+	0.305675i
$809$	−3.50134	−	6.06451i	−0.123101	−	0.213217i	0.797888	−	0.602805i	$-0.205950\pi$
$809$	−3.50134	−	6.06451i	−0.123101	−	0.213217i	−0.920989	+	0.389589i	$0.872617\pi$
$810$	−10.3131	+	17.8629i	−0.362367	+	0.627638i
$811$	−33.4647	−	28.0802i	−1.17511	−	0.986031i	−0.999999	−	0.00148108i	$-0.999529\pi$
$811$	−33.4647	−	28.0802i	−1.17511	−	0.986031i	−0.175107	−	0.984549i	$-0.556027\pi$
$812$	40.2276	+	14.6417i	1.41171	+	0.513821i
$813$	−28.5621	+	10.3958i	−1.00172	+	0.364595i
$814$	−5.21482	+	4.37576i	−0.182779	+	0.153370i
$815$	1.64321	+	9.31910i	0.0575591	+	0.326434i
$816$	4.49020			0.157188
$817$		0			0
$818$	21.1310			0.738830
$819$	0.610815	+	3.46410i	0.0213436	+	0.121046i
$820$	2.34730	−	1.96962i	0.0819711	−	0.0687820i
$821$	−11.6382	+	4.23594i	−0.406174	+	0.147835i	−0.537024	−	0.843567i	$-0.680452\pi$
$821$	−11.6382	+	4.23594i	−0.406174	+	0.147835i	0.130850	+	0.991402i	$0.458229\pi$
$822$	9.53121	+	3.46908i	0.332439	+	0.120998i
$823$	−9.82707	−	8.24589i	−0.342550	−	0.287434i	0.455240	−	0.890369i	$-0.349553\pi$
$823$	−9.82707	−	8.24589i	−0.342550	−	0.287434i	−0.797790	+	0.602935i	$0.793998\pi$
$824$	3.57398	−	6.19031i	0.124505	−	0.215650i
$825$	−1.32635	−	2.29731i	−0.0461776	−	0.0799820i
$826$	0.630415	−	3.57526i	0.0219349	−	0.124399i
$827$	−4.35797	+	24.7153i	−0.151542	+	0.859435i	0.810338	+	0.585962i	$0.199283\pi$
$827$	−4.35797	+	24.7153i	−0.151542	+	0.859435i	−0.961880	+	0.273473i	$0.911828\pi$
$828$	0.815207	+	1.41198i	0.0283304	+	0.0490697i
$829$	14.1634	−	24.5318i	0.491917	−	0.852024i	−0.508040	−	0.861333i	$-0.669630\pi$
$829$	14.1634	−	24.5318i	0.491917	−	0.852024i	0.999957	+	0.00930899i	$0.00296319\pi$
$830$	6.10607	+	5.12360i	0.211945	+	0.177843i
$831$	−19.6186	−	7.14057i	−0.680560	−	0.247704i
$832$	−1.22668	+	0.446476i	−0.0425275	+	0.0154788i
$833$	34.1261	−	28.6352i	1.18240	−	0.992152i
$834$	0.763518	+	4.33013i	0.0264385	+	0.149940i
$835$	−34.5526			−1.19574
$836$		0			0
$837$	1.71419			0.0592512
$838$	4.84183	+	27.4594i	0.167258	+	0.948569i
$839$	23.2344	−	19.4960i	0.802141	−	0.673077i	−0.146577	−	0.989199i	$-0.546826\pi$
$839$	23.2344	−	19.4960i	0.802141	−	0.673077i	0.948718	+	0.316123i	$0.102381\pi$
$840$	17.8871	−	6.51038i	0.617164	−	0.224630i
$841$	−39.8987	−	14.5220i	−1.37582	−	0.500757i
$842$	−0.0341483	−	0.0286538i	−0.00117683	−	0.000987475i
$843$	3.99273	−	6.91560i	0.137517	−	0.238186i
$844$	−8.05438	−	13.9506i	−0.277243	−	0.480199i
$845$	−3.92303	+	22.2486i	−0.134956	+	0.765375i
$846$	0.943563	−	5.35121i	0.0324404	−	0.183978i
$847$	22.8084	+	39.5053i	0.783706	+	1.35742i
$848$	0.837496	−	1.45059i	0.0287597	−	0.0498133i
$849$	−7.85504	−	6.59116i	−0.269584	−	0.226208i
$850$	−2.24510	−	0.817150i	−0.0770063	−	0.0280280i
$851$	−13.8871	+	5.05450i	−0.476045	+	0.173266i
$852$	9.17024	−	7.69475i	0.314167	−	0.263618i
$853$	−7.57667	−	42.9694i	−0.259420	−	1.47124i	−0.784467	−	0.620171i	$-0.787063\pi$
$853$	−7.57667	−	42.9694i	−0.259420	−	1.47124i	0.525047	−	0.851074i	$-0.324048\pi$
$854$	−49.4201			−1.69112
$855$		0			0
$856$	−9.36959			−0.320246
$857$	5.47162	+	31.0311i	0.186907	+	1.06000i	0.923481	+	0.383645i	$0.125331\pi$
$857$	5.47162	+	31.0311i	0.186907	+	1.06000i	−0.736574	+	0.676357i	$0.763558\pi$
$858$	2.65270	−	2.22588i	0.0905618	−	0.0759904i
$859$	17.5703	−	6.39506i	0.599490	−	0.218196i	−0.0244084	−	0.999702i	$-0.507770\pi$
$859$	17.5703	−	6.39506i	0.599490	−	0.218196i	0.623898	+	0.781506i	$0.285548\pi$
$860$	1.42602	+	0.519030i	0.0486269	+	0.0176988i
$861$	11.1702	+	9.37295i	0.380681	+	0.319429i
$862$	5.89393	−	10.2086i	0.200748	−	0.347706i
$863$	5.31315	+	9.20264i	0.180862	+	0.313262i	0.942174	−	0.335123i	$-0.108778\pi$
$863$	5.31315	+	9.20264i	0.180862	+	0.313262i	−0.761313	+	0.648385i	$0.775445\pi$
$864$	0.805407	−	4.56769i	0.0274005	−	0.155396i
$865$	−6.53714	+	37.0740i	−0.222269	+	1.26055i
$866$	−13.8229	−	23.9420i	−0.469723	−	0.813584i
$867$	10.6108	−	18.3785i	0.360362	−	0.624166i
$868$	−1.43376	−	1.20307i	−0.0486651	−	0.0408349i
$869$	2.97266	+	1.08196i	0.100841	+	0.0367030i
$870$	−29.8580	+	10.8674i	−1.01228	+	0.368441i
$871$	1.40373	−	1.17787i	0.0475637	−	0.0399107i
$872$	1.92127	+	10.8961i	0.0650626	+	0.368988i
$873$	0.815207			0.0275906
$874$		0			0
$875$	−60.7701			−2.05441
$876$	−1.48798	−	8.43874i	−0.0502741	−	0.285119i
$877$	−34.3942	+	28.8602i	−1.16141	+	0.974539i	−0.999924	−	0.0123354i	$-0.996073\pi$
$877$	−34.3942	+	28.8602i	−1.16141	+	0.974539i	−0.161487	+	0.986875i	$0.551629\pi$
$878$	−35.1908	+	12.8084i	−1.18763	+	0.432262i
$879$	31.4593	+	11.4503i	1.06110	+	0.386208i
$880$	−2.16250	−	1.81456i	−0.0728980	−	0.0611687i
$881$	9.00821	−	15.6027i	0.303494	−	0.525667i	−0.673431	−	0.739250i	$-0.735180\pi$
$881$	9.00821	−	15.6027i	0.303494	−	0.525667i	0.976925	+	0.213583i	$0.0685134\pi$
$882$	4.96064	+	8.59208i	0.167033	+	0.289310i
$883$	−8.09168	+	45.8902i	−0.272307	+	1.54433i	0.475082	+	0.879941i	$0.342418\pi$
$883$	−8.09168	+	45.8902i	−0.272307	+	1.54433i	−0.747389	+	0.664387i	$0.768693\pi$
$884$	0.541584	−	3.07148i	0.0182155	−	0.103305i
$885$	1.34730	+	2.33359i	0.0452889	+	0.0784426i
$886$	10.4941	−	18.1763i	0.352555	−	0.610643i
$887$	−5.42333	−	4.55072i	−0.182098	−	0.152798i	0.547182	−	0.837013i	$-0.315700\pi$
$887$	−5.42333	−	4.55072i	−0.182098	−	0.152798i	−0.729280	+	0.684215i	$0.760145\pi$
$888$	−8.51754	−	3.10013i	−0.285830	−	0.104034i
$889$	−27.1925	+	9.89727i	−0.912008	+	0.331944i
$890$	−16.3105	+	13.6861i	−0.546728	+	0.458759i
$891$	2.52775	+	14.3356i	0.0846829	+	0.480260i
$892$	−4.08378			−0.136735
$893$		0			0
$894$	27.0060			0.903215
$895$	4.80241	+	27.2358i	0.160527	+	0.910394i
$896$	−3.87939	+	3.25519i	−0.129601	+	0.108748i
$897$	7.06418	−	2.57115i	0.235866	−	0.0858482i
$898$	20.5744	+	7.48849i	0.686578	+	0.249894i
$899$	2.39330	+	2.00822i	0.0798212	+	0.0669779i
$900$	0.266044	−	0.460802i	0.00886815	−	0.0153601i
$901$	2.00093	+	3.46572i	0.0666608	+	0.115460i
$902$	0.375515	−	2.12965i	0.0125033	−	0.0709096i
$903$	−1.25402	+	7.11192i	−0.0417313	+	0.236670i
$904$	6.64930	+	11.5169i	0.221152	+	0.383047i
$905$	12.2567	−	21.2292i	0.407427	−	0.705684i
$906$	−30.0009	−	25.1738i	−0.996714	−	0.836343i
$907$	14.2040	+	5.16983i	0.471635	+	0.171661i	0.566893	−	0.823791i	$-0.308145\pi$
$907$	14.2040	+	5.16983i	0.471635	+	0.171661i	−0.0952576	+	0.995453i	$0.530367\pi$
$908$	12.8366	−	4.67215i	0.425998	−	0.155051i
$909$	3.59627	−	3.01763i	0.119281	−	0.100088i
$910$	−2.29591	−	13.0208i	−0.0761087	−	0.431634i
$911$	12.8366			0.425294			0.212647	−	0.977129i	$-0.431792\pi$
$911$	12.8366			0.425294			0.212647	+	0.977129i	$0.431792\pi$
$912$		0			0
$913$	5.62536			0.186172
$914$	2.26604	+	12.8514i	0.0749541	+	0.425086i
$915$	28.0993	−	23.5781i	0.928933	−	0.779467i
$916$	4.90673	−	1.78590i	0.162123	−	0.0590079i
$917$	47.0137	+	17.1116i	1.55253	+	0.565075i
$918$	8.48886	+	7.12300i	0.280174	+	0.235094i
$919$	10.3396	−	17.9086i	0.341070	−	0.590751i	−0.643561	−	0.765395i	$-0.722544\pi$
$919$	10.3396	−	17.9086i	0.341070	−	0.590751i	0.984632	+	0.174643i	$0.0558772\pi$
$920$	−3.06418	−	5.30731i	−0.101023	−	0.174977i
$921$	9.35282	−	53.0425i	0.308186	−	1.74781i
$922$	−0.765578	+	4.34181i	−0.0252130	+	0.142990i
$923$	−4.15745	−	7.20092i	−0.136844	−	0.237021i
$924$	6.71688	−	11.6340i	0.220969	−	0.382730i
$925$	3.69459	+	3.10013i	0.121477	+	0.101932i
$926$	25.0574	+	9.12014i	0.823436	+	0.299706i
$927$	−3.57398	+	1.30082i	−0.117385	+	0.0427246i
$928$	6.47565	−	5.43372i	0.212574	−	0.178371i
$929$	−3.16906	−	17.9726i	−0.103974	−	0.589663i	−0.991625	−	0.129148i	$-0.958776\pi$
$929$	−3.16906	−	17.9726i	−0.103974	−	0.589663i	0.887652	−	0.460515i	$-0.152335\pi$
$930$	1.38919			0.0455532
$931$		0			0
$932$	−27.0428			−0.885817
$933$	5.16075	+	29.2681i	0.168955	+	0.958193i
$934$	−23.0685	+	19.3568i	−0.754825	+	0.633373i
$935$	6.33780	−	2.30677i	0.207268	−	0.0754395i
$936$	0.652704	+	0.237565i	0.0213343	+	0.00776505i
$937$	−3.63634	−	3.05126i	−0.118794	−	0.0996802i	0.581455	−	0.813578i	$-0.302483\pi$
$937$	−3.63634	−	3.05126i	−0.118794	−	0.0996802i	−0.700250	+	0.713898i	$0.746928\pi$
$938$	3.55438	−	6.15636i	0.116055	−	0.201012i
$939$	−12.3478	−	21.3870i	−0.402954	−	0.697937i
$940$	−3.54664	+	20.1140i	−0.115679	+	0.656046i
$941$	−8.16519	+	46.3071i	−0.266178	+	1.50957i	0.499483	+	0.866324i	$0.333523\pi$
$941$	−8.16519	+	46.3071i	−0.266178	+	1.50957i	−0.765661	+	0.643245i	$0.777588\pi$
$942$	5.98545	+	10.3671i	0.195017	+	0.337779i
$943$	2.34730	−	4.06564i	0.0764385	−	0.132395i
$944$	−0.549163	−	0.460802i	−0.0178737	−	0.0149978i
$945$	44.1438	+	16.0670i	1.43600	+	0.522661i
$946$	1.00640	−	0.366298i	0.0327208	−	0.0119094i
$947$	28.3405	−	23.7805i	0.920942	−	0.772762i	−0.0532268	−	0.998582i	$-0.516951\pi$
$947$	28.3405	−	23.7805i	0.920942	−	0.772762i	0.974169	+	0.225820i	$0.0725062\pi$
$948$	0.731429	+	4.14814i	0.0237557	+	0.134725i
$949$	−5.95191			−0.193207
$950$		0			0
$951$	40.2276			1.30447
$952$	−2.10101	−	11.9154i	−0.0680943	−	0.386182i
$953$	28.8870	−	24.2390i	0.935741	−	0.785180i	−0.0410985	−	0.999155i	$-0.513086\pi$
$953$	28.8870	−	24.2390i	0.935741	−	0.785180i	0.976839	+	0.213976i	$0.0686413\pi$
$954$	−0.837496	+	0.304824i	−0.0271149	+	0.00986903i
$955$	37.7743	+	13.7487i	1.22235	+	0.444898i
$956$	−0.218941	−	0.183713i	−0.00708105	−	0.00594171i
$957$	−11.2121	+	19.4200i	−0.362437	+	0.627759i
$958$	4.08378	+	7.07331i	0.131941	+	0.228528i
$959$	4.74598	−	26.9158i	0.153256	−	0.869156i
$960$	0.652704	−	3.70167i	0.0210659	−	0.119471i
$961$	15.4317	+	26.7285i	0.497797	+	0.862209i
$962$	−3.14796	+	5.45242i	−0.101494	+	0.175793i
$963$	3.81908	+	3.20459i	0.123068	+	0.103266i
$964$	2.91400	+	1.06061i	0.0938536	+	0.0341599i
$965$	31.3577	−	11.4133i	1.00944	−	0.367406i
$966$	22.3405	−	18.7459i	0.718793	−	0.603139i
$967$	7.03508	+	39.8979i	0.226233	+	1.28303i	0.860314	+	0.509764i	$0.170267\pi$
$967$	7.03508	+	39.8979i	0.226233	+	1.28303i	−0.634081	+	0.773267i	$0.718621\pi$
$968$	9.00774			0.289520
$969$		0			0
$970$	−3.06418			−0.0983848
$971$	2.44460	+	13.8640i	0.0784510	+	0.444918i	0.998579	+	0.0532991i	$0.0169737\pi$
$971$	2.44460	+	13.8640i	0.0784510	+	0.444918i	−0.920128	+	0.391619i	$0.871915\pi$
$972$	−4.18866	+	3.51471i	−0.134351	+	0.112734i
$973$	11.1334	−	4.05223i	0.356921	−	0.129909i
$974$	−24.9837	−	9.09332i	−0.800529	−	0.291369i
$975$	−1.87939	−	1.57699i	−0.0601885	−	0.0505041i
$976$	−4.87939	+	8.45134i	−0.156185	+	0.270521i
$977$	−17.6028	−	30.4890i	−0.563164	−	0.975429i	−0.997218	−	0.0745421i	$-0.976250\pi$
$977$	−17.6028	−	30.4890i	−0.563164	−	0.975429i	0.434054	−	0.900887i	$-0.357083\pi$
$978$	−1.54411	+	8.75709i	−0.0493752	+	0.280021i
$979$	−2.60931	+	14.7981i	−0.0833939	+	0.472950i
$980$	−18.6459	−	32.2956i	−0.595621	−	1.03165i
$981$	2.94356	−	5.09840i	0.0939807	−	0.162779i
$982$	−29.7447	−	24.9588i	−0.949191	−	0.796466i
$983$	21.0865	+	7.67485i	0.672554	+	0.244790i	0.655647	−	0.755067i	$-0.272396\pi$
$983$	21.0865	+	7.67485i	0.672554	+	0.244790i	0.0169068	+	0.999857i	$0.494618\pi$
$984$	2.70574	−	0.984808i	0.0862557	−	0.0313945i
$985$	19.9026	−	16.7003i	0.634150	−	0.532115i
$986$	3.50711	+	19.8898i	0.111689	+	0.633421i
$987$	−97.1944			−3.09373
$988$		0			0
$989$	2.32501			0.0739309
$990$	0.260830	+	1.47924i	0.00828972	+	0.0470133i
$991$	−20.7624	+	17.4217i	−0.659539	+	0.553419i	−0.909949	−	0.414721i	$-0.863879\pi$
$991$	−20.7624	+	17.4217i	−0.659539	+	0.553419i	0.250410	+	0.968140i	$0.419435\pi$
$992$	−0.347296	+	0.126406i	−0.0110267	+	0.00401338i
$993$	−44.8537	−	16.3254i	−1.42339	−	0.518072i
$994$	−24.7101	−	20.7342i	−0.783756	−	0.657649i
$995$	−17.1925	+	29.7783i	−0.545040	+	0.944037i
$996$	3.74510	+	6.48670i	0.118668	+	0.205539i
$997$	4.85298	−	27.5226i	0.153695	−	0.871650i	−0.806274	−	0.591543i	$-0.798519\pi$
$997$	4.85298	−	27.5226i	0.153695	−	0.871650i	0.959969	−	0.280107i	$-0.0903699\pi$
$998$	−3.58734	+	20.3448i	−0.113555	+	0.644005i
$999$	−11.1848	−	19.3726i	−0.353871	−	0.612923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.l.389.1		6
19.2	odd	18		722.2.e.b.245.1		6
19.3	odd	18		38.2.e.a.5.1	✓	6
19.4	even	9		722.2.c.l.429.1		6
19.5	even	9		722.2.e.a.415.1		6
19.6	even	9		722.2.a.k.1.3		3
19.7	even	3		722.2.e.k.99.1		6
19.8	odd	6		722.2.e.m.595.1		6
19.9	even	9		722.2.c.l.653.1		6
19.10	odd	18		722.2.c.k.653.3		6
19.11	even	3		722.2.e.a.595.1		6
19.12	odd	6		38.2.e.a.23.1	yes	6
19.13	odd	18		722.2.a.l.1.1		3
19.14	odd	18		722.2.e.m.415.1		6
19.15	odd	18		722.2.c.k.429.3		6
19.16	even	9		722.2.e.k.423.1		6
19.17	even	9	inner	722.2.e.l.245.1		6
19.18	odd	2		722.2.e.b.389.1		6
57.32	even	18		6498.2.a.bl.1.3		3
57.41	even	18		342.2.u.c.271.1		6
57.44	odd	18		6498.2.a.bq.1.3		3
57.50	even	6		342.2.u.c.289.1		6
76.3	even	18		304.2.u.c.81.1		6
76.31	even	6		304.2.u.c.289.1		6
76.51	even	18		5776.2.a.bn.1.3		3
76.63	odd	18		5776.2.a.bo.1.1		3
95.3	even	36		950.2.u.b.499.2		12
95.12	even	12		950.2.u.b.99.2		12
95.22	even	36		950.2.u.b.499.1		12
95.69	odd	6		950.2.l.d.251.1		6
95.79	odd	18		950.2.l.d.651.1		6
95.88	even	12		950.2.u.b.99.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.5.1	✓	6	19.3	odd	18
38.2.e.a.23.1	yes	6	19.12	odd	6
304.2.u.c.81.1		6	76.3	even	18
304.2.u.c.289.1		6	76.31	even	6
342.2.u.c.271.1		6	57.41	even	18
342.2.u.c.289.1		6	57.50	even	6
722.2.a.k.1.3		3	19.6	even	9
722.2.a.l.1.1		3	19.13	odd	18
722.2.c.k.429.3		6	19.15	odd	18
722.2.c.k.653.3		6	19.10	odd	18
722.2.c.l.429.1		6	19.4	even	9
722.2.c.l.653.1		6	19.9	even	9
722.2.e.a.415.1		6	19.5	even	9
722.2.e.a.595.1		6	19.11	even	3
722.2.e.b.245.1		6	19.2	odd	18
722.2.e.b.389.1		6	19.18	odd	2
722.2.e.k.99.1		6	19.7	even	3
722.2.e.k.423.1		6	19.16	even	9
722.2.e.l.245.1		6	19.17	even	9	inner
722.2.e.l.389.1		6	1.1	even	1	trivial
722.2.e.m.415.1		6	19.14	odd	18
722.2.e.m.595.1		6	19.8	odd	6
950.2.l.d.251.1		6	95.69	odd	6
950.2.l.d.651.1		6	95.79	odd	18
950.2.u.b.99.1		12	95.88	even	12
950.2.u.b.99.2		12	95.12	even	12
950.2.u.b.499.1		12	95.22	even	36
950.2.u.b.499.2		12	95.3	even	36
5776.2.a.bn.1.3		3	76.51	even	18
5776.2.a.bo.1.1		3	76.63	odd	18
6498.2.a.bl.1.3		3	57.32	even	18
6498.2.a.bq.1.3		3	57.44	odd	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(1.43969 - 1.20805i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.87939 - 0.684040i) q^{5} +(-1.43969 - 1.20805i) q^{6} +(-2.53209 + 4.38571i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.0923963 - 0.524005i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(1.43969 - 1.20805i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.87939 - 0.684040i) q^{5} +(-1.43969 - 1.20805i) q^{6} +(-2.53209 + 4.38571i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.0923963 - 0.524005i) q^{9} +(-0.347296 + 1.96962i) q^{10} +(0.705737 + 1.22237i) q^{11} +(-0.939693 + 1.62760i) q^{12} +(1.00000 + 0.839100i) q^{13} +(4.75877 + 1.73205i) q^{14} +(-3.53209 + 1.28558i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.414878 + 2.35289i) q^{17} -0.532089 q^{18} +2.00000 q^{20} +(1.65270 + 9.37295i) q^{21} +(1.08125 - 0.907278i) q^{22} +(2.87939 - 1.04801i) q^{23} +(1.76604 + 0.642788i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(0.652704 - 1.13052i) q^{26} +(2.31908 + 4.01676i) q^{27} +(0.879385 - 4.98724i) q^{28} +(-1.46791 + 8.32494i) q^{29} +(1.87939 + 3.25519i) q^{30} +(0.184793 - 0.320070i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(2.49273 + 0.907278i) q^{33} +(2.24510 - 0.817150i) q^{34} +(7.75877 - 6.51038i) q^{35} +(0.0923963 + 0.524005i) q^{36} -4.82295 q^{37} +2.45336 q^{39} +(-0.347296 - 1.96962i) q^{40} +(1.17365 - 0.984808i) q^{41} +(8.94356 - 3.25519i) q^{42} +(0.713011 + 0.259515i) q^{43} +(-1.08125 - 0.907278i) q^{44} +(-0.532089 + 0.921605i) q^{45} +(-1.53209 - 2.65366i) q^{46} +(-1.77332 + 10.0570i) q^{47} +(0.326352 - 1.85083i) q^{48} +(-9.32295 - 16.1478i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(3.43969 + 2.88624i) q^{51} +(-1.22668 - 0.446476i) q^{52} +(1.57398 - 0.572881i) q^{53} +(3.55303 - 2.98135i) q^{54} +(-0.490200 - 2.78006i) q^{55} -5.06418 q^{56} +8.45336 q^{58} +(-0.124485 - 0.705990i) q^{59} +(2.87939 - 2.41609i) q^{60} +(-9.17024 + 3.33770i) q^{61} +(-0.347296 - 0.126406i) q^{62} +(2.06418 + 1.73205i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.30541 - 2.26103i) q^{65} +(0.460637 - 2.61240i) q^{66} +(0.243756 - 1.38241i) q^{67} +(-1.19459 - 2.06910i) q^{68} +(2.87939 - 4.98724i) q^{69} +(-7.75877 - 6.51038i) q^{70} +(-5.98545 - 2.17853i) q^{71} +(0.500000 - 0.181985i) q^{72} +(-3.49273 + 2.93075i) q^{73} +(0.837496 + 4.74968i) q^{74} -1.87939 q^{75} -7.14796 q^{77} +(-0.426022 - 2.41609i) q^{78} +(1.71688 - 1.44063i) q^{79} +(-1.87939 + 0.684040i) q^{80} +(9.69119 + 3.52730i) q^{81} +(-1.17365 - 0.984808i) q^{82} +(1.99273 - 3.45150i) q^{83} +(-4.75877 - 8.24243i) q^{84} +(0.829755 - 4.70578i) q^{85} +(0.131759 - 0.747243i) q^{86} +(7.94356 + 13.7587i) q^{87} +(-0.705737 + 1.22237i) q^{88} +(8.15523 + 6.84305i) q^{89} +(1.00000 + 0.363970i) q^{90} +(-6.21213 + 2.26103i) q^{91} +(-2.34730 + 1.96962i) q^{92} +(-0.120615 - 0.684040i) q^{93} +10.2121 q^{94} -1.87939 q^{96} +(0.266044 + 1.50881i) q^{97} +(-14.2836 + 11.9854i) q^{98} +(0.705737 - 0.256867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 3 q^{6} - 6 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 3 * q^6 - 6 * q^7 + 3 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 3 q^{6} - 6 q^{7} + 3 q^{8} - 3 q^{9} - 6 q^{11} + 6 q^{13} + 6 q^{14} - 12 q^{15} + 24 q^{17} + 6 q^{18} + 12 q^{20} + 12 q^{21} + 9 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} - 6 q^{28} - 18 q^{29} - 6 q^{31} - 3 q^{33} + 12 q^{34} + 24 q^{35} - 3 q^{36} + 12 q^{37} - 12 q^{39} + 6 q^{41} + 24 q^{42} + 12 q^{43} - 9 q^{44} + 6 q^{45} - 24 q^{47} + 3 q^{48} - 15 q^{49} - 3 q^{50} + 15 q^{51} + 6 q^{52} - 6 q^{53} + 9 q^{54} - 12 q^{56} + 24 q^{58} + 12 q^{59} + 6 q^{60} - 12 q^{61} - 6 q^{63} - 3 q^{64} - 12 q^{65} - 6 q^{66} + 9 q^{67} - 3 q^{68} + 6 q^{69} - 24 q^{70} + 3 q^{72} - 3 q^{73} - 12 q^{77} - 18 q^{78} - 6 q^{79} + 12 q^{81} - 6 q^{82} - 6 q^{83} - 6 q^{84} + 48 q^{85} + 6 q^{86} + 18 q^{87} + 6 q^{88} + 36 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 12 q^{93} + 12 q^{94} - 3 q^{97} - 36 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 - 3 * q^6 - 6 * q^7 + 3 * q^8 - 3 * q^9 - 6 * q^11 + 6 * q^13 + 6 * q^14 - 12 * q^15 + 24 * q^17 + 6 * q^18 + 12 * q^20 + 12 * q^21 + 9 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 - 6 * q^28 - 18 * q^29 - 6 * q^31 - 3 * q^33 + 12 * q^34 + 24 * q^35 - 3 * q^36 + 12 * q^37 - 12 * q^39 + 6 * q^41 + 24 * q^42 + 12 * q^43 - 9 * q^44 + 6 * q^45 - 24 * q^47 + 3 * q^48 - 15 * q^49 - 3 * q^50 + 15 * q^51 + 6 * q^52 - 6 * q^53 + 9 * q^54 - 12 * q^56 + 24 * q^58 + 12 * q^59 + 6 * q^60 - 12 * q^61 - 6 * q^63 - 3 * q^64 - 12 * q^65 - 6 * q^66 + 9 * q^67 - 3 * q^68 + 6 * q^69 - 24 * q^70 + 3 * q^72 - 3 * q^73 - 12 * q^77 - 18 * q^78 - 6 * q^79 + 12 * q^81 - 6 * q^82 - 6 * q^83 - 6 * q^84 + 48 * q^85 + 6 * q^86 + 18 * q^87 + 6 * q^88 + 36 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 12 * q^93 + 12 * q^94 - 3 * q^97 - 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more