LMFDB - Embedded newform 722.2.c.l.429.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(429,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("722.429");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.c (of order $3$, degree $2$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			429.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	722.429
Dual form			722.2.c.l.653.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.939693 + 1.62760i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.939693 + 1.62760i) q^{6} +5.06418 q^{7} -1.00000 q^{8} +(-0.266044 - 0.460802i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.939693 + 1.62760i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.939693 + 1.62760i) q^{6} +5.06418 q^{7} -1.00000 q^{8} +(-0.266044 - 0.460802i) q^{9} +(1.00000 + 1.73205i) q^{10} -1.41147 q^{11} +1.87939 q^{12} +(-0.652704 - 1.13052i) q^{13} +(2.53209 - 4.38571i) q^{14} +(-1.87939 - 3.25519i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.19459 + 2.06910i) q^{17} -0.532089 q^{18} +2.00000 q^{20} +(-4.75877 + 8.24243i) q^{21} +(-0.705737 + 1.22237i) q^{22} +(1.53209 + 2.65366i) q^{23} +(0.939693 - 1.62760i) q^{24} +(0.500000 + 0.866025i) q^{25} -1.30541 q^{26} -4.63816 q^{27} +(-2.53209 - 4.38571i) q^{28} +(4.22668 + 7.32083i) q^{29} -3.75877 q^{30} -0.369585 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.32635 - 2.29731i) q^{33} +(1.19459 + 2.06910i) q^{34} +(-5.06418 + 8.77141i) q^{35} +(-0.266044 + 0.460802i) q^{36} -4.82295 q^{37} +2.45336 q^{39} +(1.00000 - 1.73205i) q^{40} +(-0.766044 + 1.32683i) q^{41} +(4.75877 + 8.24243i) q^{42} +(0.379385 - 0.657115i) q^{43} +(0.705737 + 1.22237i) q^{44} +1.06418 q^{45} +3.06418 q^{46} +(5.10607 + 8.84397i) q^{47} +(-0.939693 - 1.62760i) q^{48} +18.6459 q^{49} +1.00000 q^{50} +(-2.24510 - 3.88863i) q^{51} +(-0.652704 + 1.13052i) q^{52} +(0.837496 + 1.45059i) q^{53} +(-2.31908 + 4.01676i) q^{54} +(1.41147 - 2.44474i) q^{55} -5.06418 q^{56} +8.45336 q^{58} +(0.358441 - 0.620838i) q^{59} +(-1.87939 + 3.25519i) q^{60} +(-4.87939 - 8.45134i) q^{61} +(-0.184793 + 0.320070i) q^{62} +(-1.34730 - 2.33359i) q^{63} +1.00000 q^{64} +2.61081 q^{65} +(-1.32635 - 2.29731i) q^{66} +(-0.701867 - 1.21567i) q^{67} +2.38919 q^{68} -5.75877 q^{69} +(5.06418 + 8.77141i) q^{70} +(-3.18479 + 5.51622i) q^{71} +(0.266044 + 0.460802i) q^{72} +(2.27972 - 3.94858i) q^{73} +(-2.41147 + 4.17680i) q^{74} -1.87939 q^{75} -7.14796 q^{77} +(1.22668 - 2.12467i) q^{78} +(-1.12061 + 1.94096i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(5.15657 - 8.93145i) q^{81} +(0.766044 + 1.32683i) q^{82} -3.98545 q^{83} +9.51754 q^{84} +(-2.38919 - 4.13819i) q^{85} +(-0.379385 - 0.657115i) q^{86} -15.8871 q^{87} +1.41147 q^{88} +(-5.32295 - 9.21962i) q^{89} +(0.532089 - 0.921605i) q^{90} +(-3.30541 - 5.72513i) q^{91} +(1.53209 - 2.65366i) q^{92} +(0.347296 - 0.601535i) q^{93} +10.2121 q^{94} -1.87939 q^{96} +(-0.766044 + 1.32683i) q^{97} +(9.32295 - 16.1478i) q^{98} +(0.375515 + 0.650411i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 + 3 * q^9	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} + 3 q^{9} + 6 q^{10} + 12 q^{11} - 6 q^{13} + 6 q^{14} - 3 q^{16} - 3 q^{17} + 6 q^{18} + 12 q^{20} - 6 q^{21} + 6 q^{22} + 3 q^{25} - 12 q^{26} + 6 q^{27} - 6 q^{28} + 12 q^{29} + 12 q^{31} + 3 q^{32} + 9 q^{33} + 3 q^{34} - 12 q^{35} + 3 q^{36} + 12 q^{37} - 12 q^{39} + 6 q^{40} + 6 q^{42} - 9 q^{43} - 6 q^{44} - 12 q^{45} + 6 q^{47} + 30 q^{49} + 6 q^{50} - 12 q^{51} - 6 q^{52} + 3 q^{54} - 12 q^{55} - 12 q^{56} + 24 q^{58} - 6 q^{59} - 18 q^{61} + 6 q^{62} - 6 q^{63} + 6 q^{64} + 24 q^{65} - 9 q^{66} - 18 q^{67} + 6 q^{68} - 12 q^{69} + 12 q^{70} - 12 q^{71} - 3 q^{72} - 12 q^{73} + 6 q^{74} - 12 q^{77} - 6 q^{78} - 18 q^{79} - 6 q^{80} + 9 q^{81} + 12 q^{83} + 12 q^{84} - 6 q^{85} + 9 q^{86} - 36 q^{87} - 12 q^{88} + 9 q^{89} - 6 q^{90} - 24 q^{91} + 12 q^{94} + 15 q^{98} + 15 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 + 3 * q^9 + 6 * q^10 + 12 * q^11 - 6 * q^13 + 6 * q^14 - 3 * q^16 - 3 * q^17 + 6 * q^18 + 12 * q^20 - 6 * q^21 + 6 * q^22 + 3 * q^25 - 12 * q^26 + 6 * q^27 - 6 * q^28 + 12 * q^29 + 12 * q^31 + 3 * q^32 + 9 * q^33 + 3 * q^34 - 12 * q^35 + 3 * q^36 + 12 * q^37 - 12 * q^39 + 6 * q^40 + 6 * q^42 - 9 * q^43 - 6 * q^44 - 12 * q^45 + 6 * q^47 + 30 * q^49 + 6 * q^50 - 12 * q^51 - 6 * q^52 + 3 * q^54 - 12 * q^55 - 12 * q^56 + 24 * q^58 - 6 * q^59 - 18 * q^61 + 6 * q^62 - 6 * q^63 + 6 * q^64 + 24 * q^65 - 9 * q^66 - 18 * q^67 + 6 * q^68 - 12 * q^69 + 12 * q^70 - 12 * q^71 - 3 * q^72 - 12 * q^73 + 6 * q^74 - 12 * q^77 - 6 * q^78 - 18 * q^79 - 6 * q^80 + 9 * q^81 + 12 * q^83 + 12 * q^84 - 6 * q^85 + 9 * q^86 - 36 * q^87 - 12 * q^88 + 9 * q^89 - 6 * q^90 - 24 * q^91 + 12 * q^94 + 15 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.939693	+	1.62760i	−0.542532	+	0.939693i	0.456226	+	0.889864i	$0.349201\pi$
$3$	−0.939693	+	1.62760i	−0.542532	+	0.939693i	−0.998758	+	0.0498287i	$0.984132\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$	0.939693	+	1.62760i	0.383628	+	0.664463i
$7$	5.06418			1.91408			0.957040	−	0.289957i	$-0.0936410\pi$
$7$	5.06418			1.91408			0.957040	+	0.289957i	$0.0936410\pi$
$8$	−1.00000			−0.353553
$9$	−0.266044	−	0.460802i	−0.0886815	−	0.153601i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	−1.41147			−0.425575			−0.212788	−	0.977098i	$-0.568254\pi$
$11$	−1.41147			−0.425575			−0.212788	+	0.977098i	$0.568254\pi$
$12$	1.87939			0.542532
$13$	−0.652704	−	1.13052i	−0.181027	−	0.313549i	0.761203	−	0.648513i	$-0.224609\pi$
$13$	−0.652704	−	1.13052i	−0.181027	−	0.313549i	−0.942231	+	0.334965i	$0.891276\pi$
$14$	2.53209	−	4.38571i	0.676729	−	1.17213i
$15$	−1.87939	−	3.25519i	−0.485255	−	0.840487i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.19459	+	2.06910i	−0.289731	+	0.501829i	−0.973746	−	0.227639i	$-0.926899\pi$
$17$	−1.19459	+	2.06910i	−0.289731	+	0.501829i	0.684014	+	0.729469i	$0.260233\pi$
$18$	−0.532089			−0.125415
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	−4.75877	+	8.24243i	−1.03845	+	1.79865i
$22$	−0.705737	+	1.22237i	−0.150464	+	0.260611i
$23$	1.53209	+	2.65366i	0.319463	+	0.553325i	0.980376	−	0.197137i	$-0.0631643\pi$
$23$	1.53209	+	2.65366i	0.319463	+	0.553325i	−0.660913	+	0.750462i	$0.729831\pi$
$24$	0.939693	−	1.62760i	0.191814	−	0.332232i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−1.30541			−0.256011
$27$	−4.63816			−0.892613
$28$	−2.53209	−	4.38571i	−0.478520	−	0.828821i
$29$	4.22668	+	7.32083i	0.784875	+	1.35944i	0.929074	+	0.369895i	$0.120606\pi$
$29$	4.22668	+	7.32083i	0.784875	+	1.35944i	−0.144199	+	0.989549i	$0.546060\pi$
$30$	−3.75877			−0.686254
$31$	−0.369585			−0.0663794			−0.0331897	−	0.999449i	$-0.510567\pi$
$31$	−0.369585			−0.0663794			−0.0331897	+	0.999449i	$0.510567\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.32635	−	2.29731i	0.230888	−	0.399910i
$34$	1.19459	+	2.06910i	0.204871	+	0.354847i
$35$	−5.06418	+	8.77141i	−0.856002	+	1.48264i
$36$	−0.266044	+	0.460802i	−0.0443407	+	0.0768004i
$37$	−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
$40$	1.00000	−	1.73205i	0.158114	−	0.273861i
$41$	−0.766044	+	1.32683i	−0.119636	+	0.207216i	−0.919623	−	0.392801i	$-0.871506\pi$
$41$	−0.766044	+	1.32683i	−0.119636	+	0.207216i	0.799987	+	0.600017i	$0.204839\pi$
$42$	4.75877	+	8.24243i	0.734294	+	1.27183i
$43$	0.379385	−	0.657115i	0.0578557	−	0.100209i	−0.835647	−	0.549267i	$-0.814907\pi$
$43$	0.379385	−	0.657115i	0.0578557	−	0.100209i	0.893503	+	0.449058i	$0.148240\pi$
$44$	0.705737	+	1.22237i	0.106394	+	0.184280i
$45$	1.06418			0.158638
$46$	3.06418			0.451788
$47$	5.10607	+	8.84397i	0.744796	+	1.29003i	0.950290	+	0.311367i	$0.100787\pi$
$47$	5.10607	+	8.84397i	0.744796	+	1.29003i	−0.205493	+	0.978658i	$0.565880\pi$
$48$	−0.939693	−	1.62760i	−0.135633	−	0.234923i
$49$	18.6459			2.66370
$50$	1.00000			0.141421
$51$	−2.24510	−	3.88863i	−0.314377	−	0.544517i
$52$	−0.652704	+	1.13052i	−0.0905137	+	0.156774i
$53$	0.837496	+	1.45059i	0.115039	+	0.199253i	0.917795	−	0.397054i	$-0.129967\pi$
$53$	0.837496	+	1.45059i	0.115039	+	0.199253i	−0.802756	+	0.596307i	$0.796634\pi$
$54$	−2.31908	+	4.01676i	−0.315587	+	0.546612i
$55$	1.41147	−	2.44474i	0.190323	−	0.329649i
$56$	−5.06418			−0.676729
$57$		0			0
$58$	8.45336			1.10998
$59$	0.358441	−	0.620838i	0.0466650	−	0.0808262i	−0.841749	−	0.539868i	$-0.818474\pi$
$59$	0.358441	−	0.620838i	0.0466650	−	0.0808262i	0.888414	+	0.459042i	$0.151807\pi$
$60$	−1.87939	+	3.25519i	−0.242628	+	0.420243i
$61$	−4.87939	−	8.45134i	−0.624741	−	1.08208i	−0.988591	−	0.150626i	$-0.951871\pi$
$61$	−4.87939	−	8.45134i	−0.624741	−	1.08208i	0.363850	−	0.931458i	$-0.381462\pi$
$62$	−0.184793	+	0.320070i	−0.0234687	+	0.0406489i
$63$	−1.34730	−	2.33359i	−0.169743	−	0.294004i
$64$	1.00000			0.125000
$65$	2.61081			0.323832
$66$	−1.32635	−	2.29731i	−0.163263	−	0.282779i
$67$	−0.701867	−	1.21567i	−0.0857467	−	0.148518i	0.819962	−	0.572417i	$-0.193994\pi$
$67$	−0.701867	−	1.21567i	−0.0857467	−	0.148518i	−0.905709	+	0.423900i	$0.860661\pi$
$68$	2.38919			0.289731
$69$	−5.75877			−0.693274
$70$	5.06418	+	8.77141i	0.605285	+	1.04838i
$71$	−3.18479	+	5.51622i	−0.377965	+	0.654655i	−0.990766	−	0.135582i	$-0.956709\pi$
$71$	−3.18479	+	5.51622i	−0.377965	+	0.654655i	0.612801	+	0.790237i	$0.290043\pi$
$72$	0.266044	+	0.460802i	0.0313536	+	0.0543061i
$73$	2.27972	−	3.94858i	0.266820	−	0.462147i	−0.701219	−	0.712946i	$-0.747360\pi$
$73$	2.27972	−	3.94858i	0.266820	−	0.462147i	0.968039	+	0.250800i	$0.0806936\pi$
$74$	−2.41147	+	4.17680i	−0.280328	+	0.485543i
$75$	−1.87939			−0.217013
$76$		0			0
$77$	−7.14796			−0.814585
$78$	1.22668	−	2.12467i	0.138894	−	0.240572i
$79$	−1.12061	+	1.94096i	−0.126079	+	0.218375i	−0.922154	−	0.386822i	$-0.873573\pi$
$79$	−1.12061	+	1.94096i	−0.126079	+	0.218375i	0.796075	+	0.605198i	$0.206906\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$	5.15657	−	8.93145i	0.572953	−	0.992383i
$82$	0.766044	+	1.32683i	0.0845955	+	0.146524i
$83$	−3.98545			−0.437460			−0.218730	−	0.975785i	$-0.570191\pi$
$83$	−3.98545			−0.437460			−0.218730	+	0.975785i	$0.570191\pi$
$84$	9.51754			1.03845
$85$	−2.38919	−	4.13819i	−0.259144	−	0.448850i
$86$	−0.379385	−	0.657115i	−0.0409102	−	0.0708585i
$87$	−15.8871			−1.70328
$88$	1.41147			0.150464
$89$	−5.32295	−	9.21962i	−0.564231	−	0.977277i	−0.997121	−	0.0758304i	$-0.975839\pi$
$89$	−5.32295	−	9.21962i	−0.564231	−	0.977277i	0.432889	−	0.901447i	$-0.357494\pi$
$90$	0.532089	−	0.921605i	0.0560871	−	0.0971457i
$91$	−3.30541	−	5.72513i	−0.346501	−	0.600157i
$92$	1.53209	−	2.65366i	0.159731	−	0.276663i
$93$	0.347296	−	0.601535i	0.0360130	−	0.0623763i
$94$	10.2121			1.05330
$95$		0			0
$96$	−1.87939			−0.191814
$97$	−0.766044	+	1.32683i	−0.0777800	+	0.134719i	−0.902292	−	0.431126i	$-0.858117\pi$
$97$	−0.766044	+	1.32683i	−0.0777800	+	0.134719i	0.824512	+	0.565845i	$0.191450\pi$
$98$	9.32295	−	16.1478i	0.941760	−	1.63118i
$99$	0.375515	+	0.650411i	0.0377407	+	0.0653687i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−4.41147	−	7.64090i	−0.438958	−	0.760298i	0.558651	−	0.829403i	$-0.311319\pi$
$101$	−4.41147	−	7.64090i	−0.438958	−	0.760298i	−0.997609	+	0.0691049i	$0.977986\pi$
$102$	−4.49020			−0.444596
$103$	7.14796			0.704309			0.352155	−	0.935942i	$-0.385449\pi$
$103$	7.14796			0.704309			0.352155	+	0.935942i	$0.385449\pi$
$104$	0.652704	+	1.13052i	0.0640029	+	0.110856i
$105$	−9.51754	−	16.4849i	−0.928817	−	1.60876i
$106$	1.67499			0.162690
$107$	9.36959			0.905792			0.452896	−	0.891563i	$-0.350391\pi$
$107$	9.36959			0.905792			0.452896	+	0.891563i	$0.350391\pi$
$108$	2.31908	+	4.01676i	0.223153	+	0.386513i
$109$	5.53209	−	9.58186i	0.529878	−	0.917776i	−0.469515	−	0.882925i	$-0.655571\pi$
$109$	5.53209	−	9.58186i	0.529878	−	0.917776i	0.999393	−	0.0348509i	$-0.0110956\pi$
$110$	−1.41147	−	2.44474i	−0.134579	−	0.233097i
$111$	4.53209	−	7.84981i	0.430167	−	0.745071i
$112$	−2.53209	+	4.38571i	−0.239260	+	0.414410i
$113$	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
$116$	4.22668	−	7.32083i	0.392438	−	0.679722i
$117$	−0.347296	+	0.601535i	−0.0321076	+	0.0556119i
$118$	−0.358441	−	0.620838i	−0.0329971	−	0.0571527i
$119$	−6.04963	+	10.4783i	−0.554569	+	0.960541i
$120$	1.87939	+	3.25519i	0.171564	+	0.297157i
$121$	−9.00774			−0.818886
$122$	−9.75877			−0.883518
$123$	−1.43969	−	2.49362i	−0.129813	−	0.224842i
$124$	0.184793	+	0.320070i	0.0165949	+	0.0287431i
$125$	−12.0000			−1.07331
$126$	−2.69459			−0.240053
$127$	−2.85710	−	4.94864i	−0.253526	−	0.439120i	0.710968	−	0.703224i	$-0.248257\pi$
$127$	−2.85710	−	4.94864i	−0.253526	−	0.439120i	−0.964494	+	0.264104i	$0.914924\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.713011	+	1.23497i	0.0627771	+	0.108733i
$130$	1.30541	−	2.26103i	0.114492	−	0.198306i
$131$	4.93969	−	8.55580i	0.431583	−	0.747524i	−0.565427	−	0.824798i	$-0.691289\pi$
$131$	4.93969	−	8.55580i	0.431583	−	0.747524i	0.997010	+	0.0772748i	$0.0246219\pi$
$132$	−2.65270			−0.230888
$133$		0			0
$134$	−1.40373			−0.121264
$135$	4.63816	−	8.03352i	0.399189	−	0.691415i
$136$	1.19459	−	2.06910i	0.102435	−	0.177423i
$137$	−2.69846	−	4.67388i	−0.230545	−	0.399316i	0.727423	−	0.686189i	$-0.240718\pi$
$137$	−2.69846	−	4.67388i	−0.230545	−	0.399316i	−0.957969	+	0.286873i	$0.907384\pi$
$138$	−2.87939	+	4.98724i	−0.245110	+	0.424542i
$139$	1.16978	+	2.02611i	0.0992193	+	0.171853i	0.911362	−	0.411606i	$-0.135032\pi$
$139$	1.16978	+	2.02611i	0.0992193	+	0.171853i	−0.812142	+	0.583459i	$0.801699\pi$
$140$	10.1284			0.856002
$141$	−19.1925			−1.61630
$142$	3.18479	+	5.51622i	0.267262	+	0.462911i
$143$	0.921274	+	1.59569i	0.0770408	+	0.133439i
$144$	0.532089			0.0443407
$145$	−16.9067			−1.40403
$146$	−2.27972	−	3.94858i	−0.188671	−	0.326787i
$147$	−17.5214	+	30.3480i	−1.44514	+	2.50306i
$148$	2.41147	+	4.17680i	0.198222	+	0.343330i
$149$	7.18479	−	12.4444i	0.588601	−	1.01949i	−0.405815	−	0.913955i	$-0.633012\pi$
$149$	7.18479	−	12.4444i	0.588601	−	1.01949i	0.994416	−	0.105532i	$-0.0336545\pi$
$150$	−0.939693	+	1.62760i	−0.0767256	+	0.132893i
$151$	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
$154$	−3.57398	+	6.19031i	−0.287999	+	0.498830i
$155$	0.369585	−	0.640140i	0.0296858	−	0.0514173i
$156$	−1.22668	−	2.12467i	−0.0982131	−	0.170110i
$157$	−3.18479	+	5.51622i	−0.254174	+	0.440242i	−0.964671	−	0.263458i	$-0.915137\pi$
$157$	−3.18479	+	5.51622i	−0.254174	+	0.440242i	0.710497	+	0.703700i	$0.248470\pi$
$158$	1.12061	+	1.94096i	0.0891513	+	0.154415i
$159$	−3.14796			−0.249649
$160$	−2.00000			−0.158114
$161$	7.75877	+	13.4386i	0.611477	+	1.05911i
$162$	−5.15657	−	8.93145i	−0.405139	−	0.701721i
$163$	4.73143			0.370594			0.185297	−	0.982683i	$-0.440675\pi$
$163$	4.73143			0.370594			0.185297	+	0.982683i	$0.440675\pi$
$164$	1.53209			0.119636
$165$	2.65270	+	4.59462i	0.206513	+	0.357690i
$166$	−1.99273	+	3.45150i	−0.154666	+	0.267889i
$167$	8.63816	+	14.9617i	0.668441	+	1.15777i	0.978340	+	0.207004i	$0.0663712\pi$
$167$	8.63816	+	14.9617i	0.668441	+	1.15777i	−0.309900	+	0.950769i	$0.600295\pi$
$168$	4.75877	−	8.24243i	0.367147	−	0.635917i
$169$	5.64796	−	9.78255i	0.434458	−	0.752504i
$170$	−4.77837			−0.366484
$171$		0			0
$172$	−0.758770			−0.0578557
$173$	9.41147	−	16.3012i	0.715541	−	1.23935i	−0.247209	−	0.968962i	$-0.579514\pi$
$173$	9.41147	−	16.3012i	0.715541	−	1.23935i	0.962750	−	0.270391i	$-0.0871531\pi$
$174$	−7.94356	+	13.7587i	−0.602200	+	1.04304i
$175$	2.53209	+	4.38571i	0.191408	+	0.331528i
$176$	0.705737	−	1.22237i	0.0531969	−	0.0921398i
$177$	0.673648	+	1.16679i	0.0506345	+	0.0877015i
$178$	−10.6459			−0.797944
$179$	13.8280			1.03355			0.516777	−	0.856120i	$-0.327132\pi$
$179$	13.8280			1.03355			0.516777	+	0.856120i	$0.327132\pi$
$180$	−0.532089	−	0.921605i	−0.0396596	−	0.0686924i
$181$	6.12836	+	10.6146i	0.455517	+	0.788979i	0.998718	−	0.0506242i	$-0.0161211\pi$
$181$	6.12836	+	10.6146i	0.455517	+	0.788979i	−0.543201	+	0.839603i	$0.682788\pi$
$182$	−6.61081			−0.490026
$183$	18.3405			1.35577
$184$	−1.53209	−	2.65366i	−0.112947	−	0.195630i
$185$	4.82295	−	8.35359i	0.354590	−	0.614168i
$186$	−0.347296	−	0.601535i	−0.0254650	−	0.0441067i
$187$	1.68614	−	2.92047i	0.123303	−	0.213566i
$188$	5.10607	−	8.84397i	0.372398	−	0.645013i
$189$	−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	$0.759163\pi$
$192$	−0.939693	+	1.62760i	−0.0678165	+	0.117462i
$193$	8.34255	−	14.4497i	0.600510	−	1.04011i	−0.392234	−	0.919865i	$-0.628298\pi$
$193$	8.34255	−	14.4497i	0.600510	−	1.04011i	0.992744	−	0.120248i	$-0.0383690\pi$
$194$	0.766044	+	1.32683i	0.0549988	+	0.0952607i
$195$	−2.45336	+	4.24935i	−0.175689	+	0.304302i
$196$	−9.32295	−	16.1478i	−0.665925	−	1.15342i
$197$	12.9905			0.925535			0.462768	−	0.886480i	$-0.346856\pi$
$197$	12.9905			0.925535			0.462768	+	0.886480i	$0.346856\pi$
$198$	0.751030			0.0533734
$199$	−8.59627	−	14.8892i	−0.609373	−	1.05547i	−0.991344	−	0.131291i	$-0.958088\pi$
$199$	−8.59627	−	14.8892i	−0.609373	−	1.05547i	0.381971	−	0.924174i	$-0.375246\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	2.63816			0.186081
$202$	−8.82295			−0.620780
$203$	21.4047	+	37.0740i	1.50231	+	2.60208i
$204$	−2.24510	+	3.88863i	−0.157188	+	0.272258i
$205$	−1.53209	−	2.65366i	−0.107006	−	0.185339i
$206$	3.57398	−	6.19031i	0.249011	−	0.431299i
$207$	0.815207	−	1.41198i	0.0566608	−	0.0981394i
$208$	1.30541			0.0905137
$209$		0			0
$210$	−19.0351			−1.31355
$211$	−8.05438	+	13.9506i	−0.554486	+	0.960398i	0.443457	+	0.896296i	$0.353752\pi$
$211$	−8.05438	+	13.9506i	−0.554486	+	0.960398i	−0.997943	+	0.0641027i	$0.979581\pi$
$212$	0.837496	−	1.45059i	0.0575195	−	0.0996267i
$213$	−5.98545	−	10.3671i	−0.410116	−	0.710342i
$214$	4.68479	−	8.11430i	0.320246	−	0.554682i
$215$	0.758770	+	1.31423i	0.0517477	+	0.0896297i
$216$	4.63816			0.315587
$217$	−1.87164			−0.127056
$218$	−5.53209	−	9.58186i	−0.374680	−	0.648965i
$219$	4.28446	+	7.42091i	0.289517	+	0.501458i
$220$	−2.82295			−0.190323
$221$	3.11886			0.209797
$222$	−4.53209	−	7.84981i	−0.304174	−	0.526845i
$223$	2.04189	−	3.53666i	0.136735	−	0.236832i	−0.789524	−	0.613720i	$-0.789672\pi$
$223$	2.04189	−	3.53666i	0.136735	−	0.236832i	0.926259	+	0.376888i	$0.123006\pi$
$224$	2.53209	+	4.38571i	0.169182	+	0.293032i
$225$	0.266044	−	0.460802i	0.0177363	−	0.0307202i
$226$	6.64930	−	11.5169i	0.442305	−	0.766094i
$227$	−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	$0.555193\pi$
$230$	−3.06418	+	5.30731i	−0.202046	+	0.349954i
$231$	6.71688	−	11.6340i	0.441938	−	0.765460i
$232$	−4.22668	−	7.32083i	−0.277495	−	0.480636i
$233$	13.5214	−	23.4198i	0.885817	−	1.53428i	0.0410429	−	0.999157i	$-0.486932\pi$
$233$	13.5214	−	23.4198i	0.885817	−	1.53428i	0.844774	−	0.535123i	$-0.179735\pi$
$234$	0.347296	+	0.601535i	0.0227035	+	0.0393236i
$235$	−20.4243			−1.33233
$236$	−0.716881			−0.0466650
$237$	−2.10607	−	3.64781i	−0.136804	−	0.236951i
$238$	6.04963	+	10.4783i	0.392139	+	0.679205i
$239$	−0.285807			−0.0184873			−0.00924366	−	0.999957i	$-0.502942\pi$
$239$	−0.285807			−0.0184873			−0.00924366	+	0.999957i	$0.502942\pi$
$240$	3.75877			0.242628
$241$	1.55051	+	2.68556i	0.0998769	+	0.172992i	0.911634	−	0.411004i	$-0.134822\pi$
$241$	1.55051	+	2.68556i	0.0998769	+	0.172992i	−0.811757	+	0.583996i	$0.801488\pi$
$242$	−4.50387	+	7.80093i	−0.289520	+	0.501463i
$243$	2.73396	+	4.73535i	0.175383	+	0.303773i
$244$	−4.87939	+	8.45134i	−0.312371	+	0.541042i
$245$	−18.6459	+	32.2956i	−1.19124	+	2.06329i
$246$	−2.87939			−0.183583
$247$		0			0
$248$	0.369585			0.0234687
$249$	3.74510	−	6.48670i	0.237336	−	0.411078i
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	6.32888	+	10.9619i	0.399475	+	0.691911i	0.993661	−	0.112416i	$-0.0358590\pi$
$251$	6.32888	+	10.9619i	0.399475	+	0.691911i	−0.594186	+	0.804328i	$0.702526\pi$
$252$	−1.34730	+	2.33359i	−0.0848717	+	0.147002i
$253$	−2.16250	−	3.74557i	−0.135955	−	0.235482i
$254$	−5.71419			−0.358540
$255$	8.98040			0.562374
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.1964	−	26.3209i	−0.947926	−	1.64186i	−0.749785	−	0.661682i	$-0.769843\pi$
$257$	−15.1964	−	26.3209i	−0.947926	−	1.64186i	−0.198141	−	0.980174i	$-0.563490\pi$
$258$	1.42602			0.0887803
$259$	−24.4243			−1.51765
$260$	−1.30541	−	2.26103i	−0.0809579	−	0.140223i
$261$	2.24897	−	3.89533i	0.139208	−	0.241115i
$262$	−4.93969	−	8.55580i	−0.305175	−	0.528579i
$263$	−10.9513	+	18.9682i	−0.675286	+	1.16963i	0.301099	+	0.953593i	$0.402647\pi$
$263$	−10.9513	+	18.9682i	−0.675286	+	1.16963i	−0.976385	+	0.216037i	$0.930687\pi$
$264$	−1.32635	+	2.29731i	−0.0816313	+	0.141390i
$265$	−3.34998			−0.205788
$266$		0			0
$267$	20.0077			1.22445
$268$	−0.701867	+	1.21567i	−0.0428733	+	0.0742588i
$269$	−0.716881	+	1.24168i	−0.0437090	+	0.0757063i	−0.887052	−	0.461669i	$-0.847251\pi$
$269$	−0.716881	+	1.24168i	−0.0437090	+	0.0757063i	0.843343	+	0.537375i	$0.180584\pi$
$270$	−4.63816	−	8.03352i	−0.282269	−	0.488905i
$271$	−8.08647	+	14.0062i	−0.491218	+	0.850814i	−0.999949	−	0.0101112i	$-0.996781\pi$
$271$	−8.08647	+	14.0062i	−0.491218	+	0.850814i	0.508731	+	0.860926i	$0.330115\pi$
$272$	−1.19459	−	2.06910i	−0.0724328	−	0.125457i
$273$	12.4243			0.751951
$274$	−5.39693			−0.326040
$275$	−0.705737	−	1.22237i	−0.0425575	−	0.0737118i
$276$	2.87939	+	4.98724i	0.173319	+	0.300197i
$277$	11.1088			0.667460			0.333730	−	0.942669i	$-0.391693\pi$
$277$	11.1088			0.667460			0.333730	+	0.942669i	$0.391693\pi$
$278$	2.33956			0.140317
$279$	0.0983261	+	0.170306i	0.00588663	+	0.0101959i
$280$	5.06418	−	8.77141i	0.302643	−	0.524192i
$281$	2.12449	+	3.67972i	0.126736	+	0.219513i	0.922410	−	0.386211i	$-0.126217\pi$
$281$	2.12449	+	3.67972i	0.126736	+	0.219513i	−0.795674	+	0.605725i	$0.792883\pi$
$282$	−9.59627	+	16.6212i	−0.571449	+	0.989779i
$283$	2.72803	−	4.72508i	0.162164	−	0.280877i	−0.773480	−	0.633820i	$-0.781486\pi$
$283$	2.72803	−	4.72508i	0.162164	−	0.280877i	0.935645	+	0.352943i	$0.114819\pi$
$284$	6.36959			0.377965
$285$		0			0
$286$	1.84255			0.108952
$287$	−3.87939	+	6.71929i	−0.228993	+	0.396627i
$288$	0.266044	−	0.460802i	0.0156768	−	0.0271530i
$289$	5.64590	+	9.77898i	0.332112	+	0.575234i
$290$	−8.45336	+	14.6417i	−0.496399	+	0.859788i
$291$	−1.43969	−	2.49362i	−0.0843963	−	0.146179i
$292$	−4.55943			−0.266820
$293$	−17.8135			−1.04067			−0.520337	−	0.853961i	$-0.674193\pi$
$293$	−17.8135			−1.04067			−0.520337	+	0.853961i	$0.674193\pi$
$294$	17.5214	+	30.3480i	1.02187	+	1.76993i
$295$	0.716881	+	1.24168i	0.0417384	+	0.0722931i
$296$	4.82295			0.280328
$297$	6.54664			0.379874
$298$	−7.18479	−	12.4444i	−0.416204	−	0.720886i
$299$	2.00000	−	3.46410i	0.115663	−	0.200334i
$300$	0.939693	+	1.62760i	0.0542532	+	0.0939693i
$301$	1.92127	−	3.32774i	0.110740	−	0.191808i
$302$	10.4192	−	18.0466i	0.599558	−	1.03847i
$303$	16.5817			0.952595
$304$		0			0
$305$	19.5175			1.11757
$306$	0.635630	−	1.10094i	0.0363365	−	0.0629367i
$307$	−14.3293	+	24.8192i	−0.817819	+	1.41650i	0.0894671	+	0.995990i	$0.471484\pi$
$307$	−14.3293	+	24.8192i	−0.817819	+	1.41650i	−0.907286	+	0.420514i	$0.861850\pi$
$308$	3.57398	+	6.19031i	0.203646	+	0.352726i
$309$	−6.71688	+	11.6340i	−0.382110	+	0.661834i
$310$	−0.369585	−	0.640140i	−0.0209910	−	0.0363575i
$311$	15.8135			0.896699			0.448349	−	0.893858i	$-0.352012\pi$
$311$	15.8135			0.896699			0.448349	+	0.893858i	$0.352012\pi$
$312$	−2.45336			−0.138894
$313$	−6.57011	−	11.3798i	−0.371364	−	0.643222i	0.618411	−	0.785855i	$-0.287777\pi$
$313$	−6.57011	−	11.3798i	−0.371364	−	0.643222i	−0.989776	+	0.142633i	$0.954443\pi$
$314$	3.18479	+	5.51622i	0.179728	+	0.311298i
$315$	5.38919			0.303646
$316$	2.24123			0.126079
$317$	−10.7023	−	18.5370i	−0.601103	−	1.04114i	−0.992654	−	0.120985i	$-0.961395\pi$
$317$	−10.7023	−	18.5370i	−0.601103	−	1.04114i	0.391551	−	0.920156i	$-0.371939\pi$
$318$	−1.57398	+	2.72621i	−0.0882643	+	0.152878i
$319$	−5.96585	−	10.3332i	−0.334024	−	0.578546i
$320$	−1.00000	+	1.73205i	−0.0559017	+	0.0968246i
$321$	−8.80453	+	15.2499i	−0.491421	+	0.851166i
$322$	15.5175			0.864759
$323$		0			0
$324$	−10.3131			−0.572953
$325$	0.652704	−	1.13052i	0.0362055	−	0.0627097i
$326$	2.36571	−	4.09754i	0.131025	−	0.226942i
$327$	10.3969	+	18.0080i	0.574951	+	0.995845i
$328$	0.766044	−	1.32683i	0.0422977	−	0.0732618i
$329$	25.8580	+	44.7874i	1.42560	+	2.46921i
$330$	5.30541			0.292053
$331$	25.3979			1.39599			0.697996	−	0.716101i	$-0.254075\pi$
$331$	25.3979			1.39599			0.697996	+	0.716101i	$0.254075\pi$
$332$	1.99273	+	3.45150i	0.109365	+	0.189426i
$333$	1.28312	+	2.22243i	0.0703145	+	0.121788i
$334$	17.2763			0.945318
$335$	2.80747			0.153388
$336$	−4.75877	−	8.24243i	−0.259612	−	0.449662i
$337$	13.1887	−	22.8434i	0.718432	−	1.24436i	−0.243188	−	0.969979i	$-0.578193\pi$
$337$	13.1887	−	22.8434i	0.718432	−	1.24436i	0.961621	−	0.274382i	$-0.0884733\pi$
$338$	−5.64796	−	9.78255i	−0.307208	−	0.532100i
$339$	−12.4966	+	21.6447i	−0.678722	+	1.17558i
$340$	−2.38919	+	4.13819i	−0.129572	+	0.224425i
$341$	0.521660			0.0282495
$342$		0			0
$343$	58.9769			3.18445
$344$	−0.379385	+	0.657115i	−0.0204551	+	0.0354292i
$345$	5.75877	−	9.97448i	0.310042	−	0.537008i
$346$	−9.41147	−	16.3012i	−0.505964	−	0.876355i
$347$	12.8157	−	22.1974i	0.687981	−	1.19162i	−0.284508	−	0.958674i	$-0.591830\pi$
$347$	12.8157	−	22.1974i	0.687981	−	1.19162i	0.972490	−	0.232945i	$-0.0748363\pi$
$348$	7.94356	+	13.7587i	0.425820	+	0.737541i
$349$	−5.84255			−0.312744			−0.156372	−	0.987698i	$-0.549980\pi$
$349$	−5.84255			−0.312744			−0.156372	+	0.987698i	$0.549980\pi$
$350$	5.06418			0.270692
$351$	3.02734	+	5.24351i	0.161588	+	0.279878i
$352$	−0.705737	−	1.22237i	−0.0376159	−	0.0651527i
$353$	−22.4097			−1.19275			−0.596375	−	0.802706i	$-0.703393\pi$
$353$	−22.4097			−1.19275			−0.596375	+	0.802706i	$0.703393\pi$
$354$	1.34730			0.0716080
$355$	−6.36959	−	11.0324i	−0.338062	−	0.585541i
$356$	−5.32295	+	9.21962i	−0.282116	+	0.488639i
$357$	−11.3696	−	19.6927i	−0.601742	−	1.04225i
$358$	6.91400	−	11.9754i	0.365416	−	0.632920i
$359$	−4.80840	+	8.32839i	−0.253778	+	0.439556i	−0.964563	−	0.263853i	$-0.915006\pi$
$359$	−4.80840	+	8.32839i	−0.253778	+	0.439556i	0.710785	+	0.703409i	$0.248340\pi$
$360$	−1.06418			−0.0560871
$361$		0			0
$362$	12.2567			0.644198
$363$	8.46451	−	14.6610i	0.444271	−	0.769501i
$364$	−3.30541	+	5.72513i	−0.173250	+	0.300079i
$365$	4.55943	+	7.89716i	0.238651	+	0.413356i
$366$	9.17024	−	15.8833i	0.479336	−	0.830235i
$367$	−11.6800	−	20.2304i	−0.609693	−	1.05602i	−0.991291	−	0.131691i	$-0.957959\pi$
$367$	−11.6800	−	20.2304i	−0.609693	−	1.05602i	0.381597	−	0.924329i	$-0.375374\pi$
$368$	−3.06418			−0.159731
$369$	0.815207			0.0424380
$370$	−4.82295	−	8.35359i	−0.250733	−	0.434283i
$371$	4.24123	+	7.34603i	0.220194	+	0.381387i
$372$	−0.694593			−0.0360130
$373$	25.9418			1.34322			0.671608	−	0.740907i	$-0.265604\pi$
$373$	25.9418			1.34322			0.671608	+	0.740907i	$0.265604\pi$
$374$	−1.68614	−	2.92047i	−0.0871881	−	0.151014i
$375$	11.2763	−	19.5311i	0.582306	−	1.00858i
$376$	−5.10607	−	8.84397i	−0.263325	−	0.456093i
$377$	5.51754	−	9.55666i	0.284168	−	0.492193i
$378$	−11.7442	+	20.3416i	−0.604058	+	1.04626i
$379$	−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
$382$	−10.0496	+	17.4065i	−0.514184	+	0.890592i
$383$	−6.74422	+	11.6813i	−0.344614	+	0.596888i	−0.985284	−	0.170928i	$-0.945323\pi$
$383$	−6.74422	+	11.6813i	−0.344614	+	0.596888i	0.640670	+	0.767816i	$0.278657\pi$
$384$	0.939693	+	1.62760i	0.0479535	+	0.0830579i
$385$	7.14796	−	12.3806i	0.364294	−	0.630975i
$386$	−8.34255	−	14.4497i	−0.424625	−	0.735471i
$387$	−0.403733			−0.0205229
$388$	1.53209			0.0777800
$389$	12.5740	+	21.7788i	0.637526	+	1.10423i	0.985974	+	0.166899i	$0.0533755\pi$
$389$	12.5740	+	21.7788i	0.637526	+	1.10423i	−0.348448	+	0.937328i	$0.613291\pi$
$390$	2.45336	+	4.24935i	0.124231	+	0.215174i
$391$	−7.32089			−0.370233
$392$	−18.6459			−0.941760
$393$	9.28359	+	16.0796i	0.468295	+	0.811111i
$394$	6.49525	−	11.2501i	0.327226	−	0.566772i
$395$	−2.24123	−	3.88192i	−0.112768	−	0.195321i
$396$	0.375515	−	0.650411i	0.0188703	−	0.0326844i
$397$	−3.28312	+	5.68653i	−0.164775	+	0.285399i	−0.936575	−	0.350466i	$-0.886023\pi$
$397$	−3.28312	+	5.68653i	−0.164775	+	0.285399i	0.771800	+	0.635865i	$0.219356\pi$
$398$	−17.1925			−0.861784
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−14.7554	+	25.5570i	−0.736848	+	1.27626i	0.217060	+	0.976158i	$0.430353\pi$
$401$	−14.7554	+	25.5570i	−0.736848	+	1.27626i	−0.953908	+	0.300100i	$0.902980\pi$
$402$	1.31908	−	2.28471i	0.0657896	−	0.113951i
$403$	0.241230	+	0.417822i	0.0120165	+	0.0208132i
$404$	−4.41147	+	7.64090i	−0.219479	+	0.380149i
$405$	10.3131	+	17.8629i	0.512464	+	0.887614i
$406$	42.8093			2.12459
$407$	6.80747			0.337434
$408$	2.24510	+	3.88863i	0.111149	+	0.192516i
$409$	10.5655	+	18.3000i	0.522431	+	0.904878i	0.999659	+	0.0260982i	$0.00830827\pi$
$409$	10.5655	+	18.3000i	0.522431	+	0.904878i	−0.477228	+	0.878780i	$0.658358\pi$
$410$	−3.06418			−0.151329
$411$	10.1429			0.500313
$412$	−3.57398	−	6.19031i	−0.176077	−	0.304975i
$413$	1.81521	−	3.14403i	0.0893205	−	0.154708i
$414$	−0.815207	−	1.41198i	−0.0400653	−	0.0693951i
$415$	3.98545	−	6.90301i	0.195638	−	0.338855i
$416$	0.652704	−	1.13052i	0.0320014	−	0.0554281i
$417$	−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	$0.738492\pi$
$420$	−9.51754	+	16.4849i	−0.464408	+	0.804379i
$421$	−0.0222887	+	0.0386052i	−0.00108629	+	0.00188150i	−0.866568	−	0.499059i	$-0.833679\pi$
$421$	−0.0222887	+	0.0386052i	−0.00108629	+	0.00188150i	0.865482	+	0.500940i	$0.167012\pi$
$422$	8.05438	+	13.9506i	0.392081	+	0.679104i
$423$	2.71688	−	4.70578i	0.132099	−	0.228803i
$424$	−0.837496	−	1.45059i	−0.0406724	−	0.0704467i
$425$	−2.38919			−0.115893
$426$	−11.9709			−0.579992
$427$	−24.7101	−	42.7991i	−1.19580	−	2.07119i
$428$	−4.68479	−	8.11430i	−0.226448	−	0.392219i
$429$	−3.46286			−0.167188
$430$	1.51754			0.0731823
$431$	−5.89393	−	10.2086i	−0.283901	−	0.491731i	0.688441	−	0.725292i	$-0.258295\pi$
$431$	−5.89393	−	10.2086i	−0.283901	−	0.491731i	−0.972342	+	0.233562i	$0.924962\pi$
$432$	2.31908	−	4.01676i	0.111577	−	0.193256i
$433$	13.8229	+	23.9420i	0.664289	+	1.15058i	0.979478	+	0.201553i	$0.0645987\pi$
$433$	13.8229	+	23.9420i	0.664289	+	1.15058i	−0.315189	+	0.949029i	$0.602068\pi$
$434$	−0.935822	+	1.62089i	−0.0449209	+	0.0778053i
$435$	15.8871	−	27.5173i	0.761729	−	1.31935i
$436$	−11.0642			−0.529878
$437$		0			0
$438$	8.56893			0.409439
$439$	18.7246	−	32.4320i	0.893677	−	1.54789i	0.0582445	−	0.998302i	$-0.481450\pi$
$439$	18.7246	−	32.4320i	0.893677	−	1.54789i	0.835433	−	0.549592i	$-0.185217\pi$
$440$	−1.41147	+	2.44474i	−0.0672894	+	0.116549i
$441$	−4.96064	−	8.59208i	−0.236221	−	0.409146i
$442$	1.55943	−	2.70101i	0.0741745	−	0.128474i
$443$	−10.4941	−	18.1763i	−0.498588	−	0.863580i	0.501410	−	0.865210i	$-0.332815\pi$
$443$	−10.4941	−	18.1763i	−0.498588	−	0.863580i	−0.999999	+	0.00162930i	$0.999481\pi$
$444$	−9.06418			−0.430167
$445$	21.2918			1.00933
$446$	−2.04189	−	3.53666i	−0.0966862	−	0.167465i
$447$	13.5030	+	23.3879i	0.638670	+	1.10621i
$448$	5.06418			0.239260
$449$	21.8949			1.03328			0.516641	−	0.856202i	$-0.327182\pi$
$449$	21.8949			1.03328			0.516641	+	0.856202i	$0.327182\pi$
$450$	−0.266044	−	0.460802i	−0.0125415	−	0.0217224i
$451$	1.08125	−	1.87278i	0.0509142	−	0.0881859i
$452$	−6.64930	−	11.5169i	−0.312757	−	0.541711i
$453$	−19.5817	+	33.9165i	−0.920029	+	1.59354i
$454$	−6.83022	+	11.8303i	−0.320558	+	0.555223i
$455$	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	$0.598729\pi$
$458$	−2.61081	+	4.52206i	−0.121995	+	0.211302i
$459$	5.54071	−	9.59679i	0.258618	−	0.447940i
$460$	3.06418	+	5.30731i	0.142868	+	0.247455i
$461$	−2.20439	+	3.81812i	−0.102669	+	0.177828i	−0.912783	−	0.408444i	$-0.866072\pi$
$461$	−2.20439	+	3.81812i	−0.102669	+	0.177828i	0.810115	+	0.586272i	$0.199405\pi$
$462$	−6.71688	−	11.6340i	−0.312498	−	0.541262i
$463$	26.6655			1.23925			0.619625	−	0.784898i	$-0.287285\pi$
$463$	26.6655			1.23925			0.619625	+	0.784898i	$0.287285\pi$
$464$	−8.45336			−0.392438
$465$	0.694593	+	1.20307i	0.0322110	+	0.0557910i
$466$	−13.5214	−	23.4198i	−0.626367	−	1.08490i
$467$	30.1138			1.39350			0.696750	−	0.717314i	$-0.254629\pi$
$467$	30.1138			1.39350			0.696750	+	0.717314i	$0.254629\pi$
$468$	0.694593			0.0321076
$469$	−3.55438	−	6.15636i	−0.164126	−	0.284274i
$470$	−10.2121	+	17.6879i	−0.471051	+	0.815884i
$471$	−5.98545	−	10.3671i	−0.275795	−	0.477691i
$472$	−0.358441	+	0.620838i	−0.0164986	+	0.0285764i
$473$	−0.535492	+	0.927500i	−0.0246220	+	0.0426465i
$474$	−4.21213			−0.193470
$475$		0			0
$476$	12.0993			0.554569
$477$	0.445622	−	0.771841i	0.0204036	−	0.0353402i
$478$	−0.142903	+	0.247516i	−0.00653625	+	0.0113211i
$479$	−4.08378	−	7.07331i	−0.186593	−	0.323188i	0.757519	−	0.652813i	$-0.226411\pi$
$479$	−4.08378	−	7.07331i	−0.186593	−	0.323188i	−0.944112	+	0.329625i	$0.893078\pi$
$480$	1.87939	−	3.25519i	0.0857818	−	0.148578i
$481$	3.14796	+	5.45242i	0.143534	+	0.248609i
$482$	3.10101			0.141247
$483$	−29.1634			−1.32698
$484$	4.50387	+	7.80093i	0.204721	+	0.354588i
$485$	−1.53209	−	2.65366i	−0.0695686	−	0.120496i
$486$	5.46791			0.248029
$487$	−26.5871			−1.20478			−0.602388	−	0.798203i	$-0.705784\pi$
$487$	−26.5871			−1.20478			−0.602388	+	0.798203i	$0.705784\pi$
$488$	4.87939	+	8.45134i	0.220879	+	0.382574i
$489$	−4.44609	+	7.70085i	−0.201059	+	0.348245i
$490$	18.6459	+	32.2956i	0.842336	+	1.45897i
$491$	−19.4145	+	33.6268i	−0.876163	+	1.51756i	−0.0206436	+	0.999787i	$0.506572\pi$
$491$	−19.4145	+	33.6268i	−0.876163	+	1.51756i	−0.855519	+	0.517771i	$0.826762\pi$
$492$	−1.43969	+	2.49362i	−0.0649064	+	0.112421i
$493$	−20.1967			−0.909611
$494$		0			0
$495$	−1.50206			−0.0675125
$496$	0.184793	−	0.320070i	0.00829743	−	0.0143716i
$497$	−16.1284	+	27.9351i	−0.723456	+	1.25306i
$498$	−3.74510	−	6.48670i	−0.167822	−	0.290676i
$499$	−10.3293	+	17.8910i	−0.462405	+	0.800909i	−0.999080	−	0.0428800i	$-0.986347\pi$
$499$	−10.3293	+	17.8910i	−0.462405	+	0.800909i	0.536675	+	0.843789i	$0.319680\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$	−32.4688			−1.45060
$502$	12.6578			0.564943
$503$	−0.0368366	−	0.0638029i	−0.00164246	−	0.00284483i	0.865203	−	0.501422i	$-0.167189\pi$
$503$	−0.0368366	−	0.0638029i	−0.00164246	−	0.00284483i	−0.866845	+	0.498577i	$0.833856\pi$
$504$	1.34730	+	2.33359i	0.0600133	+	0.103946i
$505$	17.6459			0.785232
$506$	−4.32501			−0.192270
$507$	10.6147	+	18.3852i	0.471415	+	0.816514i
$508$	−2.85710	+	4.94864i	−0.126763	+	0.219560i
$509$	7.50980	+	13.0074i	0.332866	+	0.576541i	0.983073	−	0.183217i	$-0.0586510\pi$
$509$	7.50980	+	13.0074i	0.332866	+	0.576541i	−0.650207	+	0.759758i	$0.725318\pi$
$510$	4.49020	−	7.77725i	0.198829	−	0.344383i
$511$	11.5449	−	19.9963i	0.510716	−	0.884585i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−30.3928			−1.34057
$515$	−7.14796	+	12.3806i	−0.314977	+	0.545555i
$516$	0.713011	−	1.23497i	0.0313886	−	0.0543666i
$517$	−7.20708	−	12.4830i	−0.316967	−	0.549003i
$518$	−12.2121	+	21.1520i	−0.536570	+	0.929367i
$519$	17.6878	+	30.6361i	0.776408	+	1.34478i
$520$	−2.61081			−0.114492
$521$	−45.1712			−1.97899			−0.989493	−	0.144583i	$-0.953816\pi$
$521$	−45.1712			−1.97899			−0.989493	+	0.144583i	$0.953816\pi$
$522$	−2.24897	−	3.89533i	−0.0984348	−	0.170494i
$523$	0.0837781	+	0.145108i	0.00366336	+	0.00634513i	0.867851	−	0.496824i	$-0.165501\pi$
$523$	0.0837781	+	0.145108i	0.00366336	+	0.00634513i	−0.864188	+	0.503169i	$0.832167\pi$
$524$	−9.87939			−0.431583
$525$	−9.51754			−0.415380
$526$	10.9513	+	18.9682i	0.477500	+	0.827053i
$527$	0.441504	−	0.764707i	0.0192322	−	0.0333111i
$528$	1.32635	+	2.29731i	0.0577221	+	0.0999775i
$529$	6.80541	−	11.7873i	0.295887	−	0.512492i
$530$	−1.67499	+	2.90117i	−0.0727570	+	0.126019i
$531$	−0.381445			−0.0165533
$532$		0			0
$533$	2.00000			0.0866296
$534$	10.0039	−	17.3272i	0.432910	−	0.749822i
$535$	−9.36959	+	16.2286i	−0.405082	+	0.701623i
$536$	0.701867	+	1.21567i	0.0303160	+	0.0525089i
$537$	−12.9941	+	22.5064i	−0.560736	+	0.971222i
$538$	0.716881	+	1.24168i	0.0309070	+	0.0535324i
$539$	−26.3182			−1.13361
$540$	−9.27631			−0.399189
$541$	0.490200	+	0.849051i	0.0210753	+	0.0365036i	0.876371	−	0.481637i	$-0.159958\pi$
$541$	0.490200	+	0.849051i	0.0210753	+	0.0365036i	−0.855295	+	0.518141i	$0.826624\pi$
$542$	8.08647	+	14.0062i	0.347343	+	0.601617i
$543$	−23.0351			−0.988530
$544$	−2.38919			−0.102435
$545$	11.0642	+	19.1637i	0.473937	+	0.820883i
$546$	6.21213	−	10.7597i	0.265855	−	0.460474i
$547$	14.2023	+	24.5992i	0.607248	+	1.05178i	0.991692	+	0.128636i	$0.0410599\pi$
$547$	14.2023	+	24.5992i	0.607248	+	1.05178i	−0.384444	+	0.923148i	$0.625607\pi$
$548$	−2.69846	+	4.67388i	−0.115273	+	0.199658i
$549$	−2.59627	+	4.49687i	−0.110806	+	0.191922i
$550$	−1.41147			−0.0601855
$551$		0			0
$552$	5.75877			0.245110
$553$	−5.67499	+	9.82938i	−0.241325	+	0.417988i
$554$	5.55438	−	9.62046i	0.235983	−	0.408734i
$555$	9.06418	+	15.6996i	0.384753	+	0.666412i
$556$	1.16978	−	2.02611i	0.0496096	−	0.0859264i
$557$	−17.8161	−	30.8585i	−0.754894	−	1.30751i	−0.945427	−	0.325834i	$-0.894355\pi$
$557$	−17.8161	−	30.8585i	−0.754894	−	1.30751i	0.190533	−	0.981681i	$-0.438978\pi$
$558$	0.196652			0.00832495
$559$	−0.990505			−0.0418939
$560$	−5.06418	−	8.77141i	−0.214001	−	0.370660i
$561$	3.16890	+	5.48870i	0.133791	+	0.231733i
$562$	4.24897			0.179232
$563$	−8.62773			−0.363615			−0.181808	−	0.983334i	$-0.558195\pi$
$563$	−8.62773			−0.363615			−0.181808	+	0.983334i	$0.558195\pi$
$564$	9.59627	+	16.6212i	0.404076	+	0.699880i
$565$	−13.2986	+	23.0339i	−0.559476	+	0.969041i
$566$	−2.72803	−	4.72508i	−0.114667	−	0.198610i
$567$	26.1138	−	45.2304i	1.09668	−	1.89950i
$568$	3.18479	−	5.51622i	0.133631	−	0.231456i
$569$	−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	$0.564137\pi$
$572$	0.921274	−	1.59569i	0.0385204	−	0.0667193i
$573$	18.8871	−	32.7135i	0.789021	−	1.36662i
$574$	3.87939	+	6.71929i	0.161922	+	0.280458i
$575$	−1.53209	+	2.65366i	−0.0638925	+	0.110665i
$576$	−0.266044	−	0.460802i	−0.0110852	−	0.0192001i
$577$	22.4757			0.935674			0.467837	−	0.883815i	$-0.345033\pi$
$577$	22.4757			0.935674			0.467837	+	0.883815i	$0.345033\pi$
$578$	11.2918			0.469677
$579$	15.6789	+	27.1566i	0.651591	+	1.12859i
$580$	8.45336	+	14.6417i	0.351007	+	0.607962i
$581$	−20.1830			−0.837334
$582$	−2.87939			−0.119354
$583$	−1.18210	−	2.04746i	−0.0489578	−	0.0847973i
$584$	−2.27972	+	3.94858i	−0.0943353	+	0.163393i
$585$	−0.694593	−	1.20307i	−0.0287179	−	0.0497408i
$586$	−8.90673	+	15.4269i	−0.367933	+	0.637279i
$587$	−2.07398	+	3.59224i	−0.0856022	+	0.148267i	−0.905648	−	0.424031i	$-0.860615\pi$
$587$	−2.07398	+	3.59224i	−0.0856022	+	0.148267i	0.820045	+	0.572298i	$0.193948\pi$
$588$	35.0428			1.44514
$589$		0			0
$590$	1.43376			0.0590271
$591$	−12.2071	+	21.1433i	−0.502132	+	0.869719i
$592$	2.41147	−	4.17680i	0.0991110	−	0.171665i
$593$	−5.20873	−	9.02179i	−0.213897	−	0.370480i	0.739034	−	0.673668i	$-0.235282\pi$
$593$	−5.20873	−	9.02179i	−0.213897	−	0.370480i	−0.952931	+	0.303188i	$0.901949\pi$
$594$	3.27332	−	5.66955i	0.134306	−	0.232625i
$595$	−12.0993	−	20.9565i	−0.496021	−	0.859134i
$596$	−14.3696			−0.588601
$597$	32.3114			1.32242
$598$	−2.00000	−	3.46410i	−0.0817861	−	0.141658i
$599$	−19.8280	−	34.3431i	−0.810150	−	1.40322i	−0.912759	−	0.408499i	$-0.866052\pi$
$599$	−19.8280	−	34.3431i	−0.810150	−	1.40322i	0.102608	−	0.994722i	$-0.467281\pi$
$600$	1.87939			0.0767256
$601$	−23.8648			−0.973467			−0.486734	−	0.873551i	$-0.661812\pi$
$601$	−23.8648			−0.973467			−0.486734	+	0.873551i	$0.661812\pi$
$602$	−1.92127	−	3.32774i	−0.0783053	−	0.135629i
$603$	−0.373455	+	0.646844i	−0.0152083	+	0.0263415i
$604$	−10.4192	−	18.0466i	−0.423952	−	0.734306i
$605$	9.00774	−	15.6019i	0.366217	−	0.634306i
$606$	8.29086	−	14.3602i	0.336793	−	0.583343i
$607$	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
$610$	9.75877	−	16.9027i	0.395121	−	0.684370i
$611$	6.66550	−	11.5450i	0.269657	−	0.467060i
$612$	−0.635630	−	1.10094i	−0.0256938	−	0.0445030i
$613$	17.7888	−	30.8111i	0.718483	−	1.24445i	−0.243118	−	0.969997i	$-0.578170\pi$
$613$	17.7888	−	30.8111i	0.718483	−	1.24445i	0.961601	−	0.274452i	$-0.0884965\pi$
$614$	14.3293	+	24.8192i	0.578285	+	1.00162i
$615$	5.75877			0.232216
$616$	7.14796			0.287999
$617$	−6.01620	−	10.4204i	−0.242203	−	0.419508i	0.719139	−	0.694867i	$-0.244537\pi$
$617$	−6.01620	−	10.4204i	−0.242203	−	0.419508i	−0.961342	+	0.275359i	$0.911203\pi$
$618$	6.71688	+	11.6340i	0.270193	+	0.467987i
$619$	−17.1129			−0.687824			−0.343912	−	0.939002i	$-0.611752\pi$
$619$	−17.1129			−0.687824			−0.343912	+	0.939002i	$0.611752\pi$
$620$	−0.739170			−0.0296858
$621$	−7.10607	−	12.3081i	−0.285157	−	0.493906i
$622$	7.90673	−	13.6949i	0.317031	−	0.549114i
$623$	−26.9564	−	46.6898i	−1.07998	−	1.87059i
$624$	−1.22668	+	2.12467i	−0.0491066	+	0.0850551i
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−13.1402			−0.525189
$627$		0			0
$628$	6.36959			0.254174
$629$	5.76146	−	9.97914i	0.229724	−	0.397894i
$630$	2.69459	−	4.66717i	0.107355	−	0.185945i
$631$	−9.17024	−	15.8833i	−0.365062	−	0.632305i	0.623724	−	0.781644i	$-0.285619\pi$
$631$	−9.17024	−	15.8833i	−0.365062	−	0.632305i	−0.988786	+	0.149339i	$0.952285\pi$
$632$	1.12061	−	1.94096i	0.0445757	−	0.0772073i
$633$	−15.1373	−	26.2185i	−0.601653	−	1.04209i
$634$	−21.4047			−0.850088
$635$	11.4284			0.453522
$636$	1.57398	+	2.72621i	0.0624123	+	0.108101i
$637$	−12.1702	−	21.0795i	−0.482203	−	0.835199i
$638$	−11.9317			−0.472381
$639$	3.38919			0.134074
$640$	1.00000	+	1.73205i	0.0395285	+	0.0684653i
$641$	−15.5890	+	27.0009i	−0.615728	+	1.06647i	0.374528	+	0.927216i	$0.377805\pi$
$641$	−15.5890	+	27.0009i	−0.615728	+	1.06647i	−0.990256	+	0.139257i	$0.955529\pi$
$642$	8.80453	+	15.2499i	0.347487	+	0.601865i
$643$	15.9748	−	27.6691i	0.629984	−	1.09116i	−0.357571	−	0.933886i	$-0.616395\pi$
$643$	15.9748	−	27.6691i	0.629984	−	1.09116i	0.987554	−	0.157278i	$-0.0502717\pi$
$644$	7.75877	−	13.4386i	0.305738	−	0.529554i
$645$	−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	$0.481244\pi$
$648$	−5.15657	+	8.93145i	−0.202569	+	0.350860i
$649$	−0.505930	+	0.876296i	−0.0198595	+	0.0343976i
$650$	−0.652704	−	1.13052i	−0.0256011	−	0.0443425i
$651$	1.75877	−	3.04628i	0.0689316	−	0.119393i
$652$	−2.36571	−	4.09754i	−0.0926485	−	0.160472i
$653$	0.935822			0.0366216			0.0183108	−	0.999832i	$-0.494171\pi$
$653$	0.935822			0.0366216			0.0183108	+	0.999832i	$0.494171\pi$
$654$	20.7939			0.813104
$655$	9.87939	+	17.1116i	0.386020	+	0.668605i
$656$	−0.766044	−	1.32683i	−0.0299090	−	0.0518039i
$657$	−2.42602			−0.0946481
$658$	51.7161			2.01610
$659$	−6.11856	−	10.5976i	−0.238345	−	0.412826i	0.721894	−	0.692003i	$-0.243272\pi$
$659$	−6.11856	−	10.5976i	−0.238345	−	0.412826i	−0.960240	+	0.279177i	$0.909938\pi$
$660$	2.65270	−	4.59462i	0.103256	−	0.178845i
$661$	−5.97771	−	10.3537i	−0.232506	−	0.402712i	0.726039	−	0.687654i	$-0.241359\pi$
$661$	−5.97771	−	10.3537i	−0.232506	−	0.402712i	−0.958545	+	0.284941i	$0.908026\pi$
$662$	12.6989	−	21.9952i	0.493558	−	0.854867i
$663$	−2.93077	+	5.07624i	−0.113822	+	0.197145i
$664$	3.98545			0.154666
$665$		0			0
$666$	2.56624			0.0994397
$667$	−12.9513	+	22.4323i	−0.501476	+	0.868583i
$668$	8.63816	−	14.9617i	0.334220	−	0.578887i
$669$	3.83750	+	6.64674i	0.148366	+	0.256978i
$670$	1.40373	−	2.43134i	0.0542310	−	0.0939308i
$671$	6.88713	+	11.9289i	0.265875	+	0.460508i
$672$	−9.51754			−0.367147
$673$	−44.8634			−1.72936			−0.864679	−	0.502325i	$-0.832478\pi$
$673$	−44.8634			−1.72936			−0.864679	+	0.502325i	$0.832478\pi$
$674$	−13.1887	−	22.8434i	−0.508008	−	0.879896i
$675$	−2.31908	−	4.01676i	−0.0892613	−	0.154605i
$676$	−11.2959			−0.434458
$677$	−0.945927			−0.0363549			−0.0181775	−	0.999835i	$-0.505786\pi$
$677$	−0.945927			−0.0363549			−0.0181775	+	0.999835i	$0.505786\pi$
$678$	12.4966	+	21.6447i	0.479929	+	0.831261i
$679$	−3.87939	+	6.71929i	−0.148877	+	0.257863i
$680$	2.38919	+	4.13819i	0.0916211	+	0.158692i
$681$	12.8366	−	22.2337i	0.491900	−	0.851996i
$682$	0.260830	−	0.451771i	0.00998769	−	0.0172992i
$683$	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
$686$	29.4884	−	51.0755i	1.12587	−	1.95007i
$687$	4.90673	−	8.49870i	0.187203	−	0.324246i
$688$	0.379385	+	0.657115i	0.0144639	+	0.0250523i
$689$	1.09327	−	1.89361i	0.0416504	−	0.0721406i
$690$	−5.75877	−	9.97448i	−0.219233	−	0.379722i
$691$	0.206148			0.00784222			0.00392111	−	0.999992i	$-0.498752\pi$
$691$	0.206148			0.00784222			0.00392111	+	0.999992i	$0.498752\pi$
$692$	−18.8229			−0.715541
$693$	1.90167	+	3.29380i	0.0722386	+	0.125121i
$694$	−12.8157	−	22.1974i	−0.486476	−	0.842602i
$695$	−4.67911			−0.177489
$696$	15.8871			0.602200
$697$	−1.83022	−	3.17004i	−0.0693246	−	0.120074i
$698$	−2.92127	+	5.05980i	−0.110572	+	0.191516i
$699$	25.4119	+	44.0148i	0.961168	+	1.66479i
$700$	2.53209	−	4.38571i	0.0957040	−	0.165764i
$701$	−2.18479	+	3.78417i	−0.0825185	+	0.142926i	−0.904331	−	0.426832i	$-0.859630\pi$
$701$	−2.18479	+	3.78417i	−0.0825185	+	0.142926i	0.821813	+	0.569758i	$0.192963\pi$
$702$	6.05468			0.228519
$703$		0			0
$704$	−1.41147			−0.0531969
$705$	19.1925	−	33.2424i	0.722833	−	1.25198i
$706$	−11.2049	+	19.4074i	−0.421700	+	0.730407i
$707$	−22.3405	−	38.6949i	−0.840201	−	1.45527i
$708$	0.673648	−	1.16679i	0.0253172	−	0.0438508i
$709$	−4.37733	−	7.58175i	−0.164394	−	0.284739i	0.772046	−	0.635567i	$-0.219233\pi$
$709$	−4.37733	−	7.58175i	−0.164394	−	0.284739i	−0.936440	+	0.350828i	$0.885900\pi$
$710$	−12.7392			−0.478093
$711$	1.19253			0.0447235
$712$	5.32295	+	9.21962i	0.199486	+	0.345520i
$713$	−0.566237	−	0.980752i	−0.0212057	−	0.0367294i
$714$	−22.7392			−0.850992
$715$	−3.68510			−0.137815
$716$	−6.91400	−	11.9754i	−0.258388	−	0.447542i
$717$	0.268571	−	0.465178i	0.0100300	−	0.0173724i
$718$	4.80840	+	8.32839i	0.179448	+	0.310813i
$719$	13.8033	−	23.9081i	0.514778	−	0.891622i	−0.485075	−	0.874473i	$-0.661208\pi$
$719$	13.8033	−	23.9081i	0.514778	−	0.891622i	0.999853	−	0.0171491i	$-0.00545899\pi$
$720$	−0.532089	+	0.921605i	−0.0198298	+	0.0343462i
$721$	36.1985			1.34810
$722$		0			0
$723$	−5.82800			−0.216746
$724$	6.12836	−	10.6146i	0.227759	−	0.394489i
$725$	−4.22668	+	7.32083i	−0.156975	+	0.271889i
$726$	−8.46451	−	14.6610i	−0.314147	−	0.544119i
$727$	−14.3182	+	24.7999i	−0.531033	+	0.919776i	0.468311	+	0.883563i	$0.344863\pi$
$727$	−14.3182	+	24.7999i	−0.531033	+	0.919776i	−0.999344	+	0.0362121i	$0.988471\pi$
$728$	3.30541	+	5.72513i	0.122507	+	0.212188i
$729$	20.6631			0.765301
$730$	9.11886			0.337504
$731$	0.906422	+	1.56997i	0.0335252	+	0.0580674i
$732$	−9.17024	−	15.8833i	−0.338942	−	0.587065i
$733$	36.9614			1.36520			0.682600	−	0.730792i	$-0.260849\pi$
$733$	36.9614			1.36520			0.682600	+	0.730792i	$0.260849\pi$
$734$	−23.3601			−0.862237
$735$	−35.0428	−	60.6959i	−1.29257	−	2.23880i
$736$	−1.53209	+	2.65366i	−0.0564735	+	0.0978151i
$737$	0.990667	+	1.71588i	0.0364917	+	0.0632054i
$738$	0.407604	−	0.705990i	0.0150041	−	0.0259879i
$739$	−23.0133	+	39.8601i	−0.846556	+	1.46628i	0.0377062	+	0.999289i	$0.487995\pi$
$739$	−23.0133	+	39.8601i	−0.846556	+	1.46628i	−0.884263	+	0.466990i	$0.845338\pi$
$740$	−9.64590			−0.354590
$741$		0			0
$742$	8.48246			0.311401
$743$	13.2053	−	22.8723i	0.484456	−	0.839103i	−0.515384	−	0.856959i	$-0.672351\pi$
$743$	13.2053	−	22.8723i	0.484456	−	0.839103i	0.999841	+	0.0178561i	$0.00568408\pi$
$744$	−0.347296	+	0.601535i	−0.0127325	+	0.0220533i
$745$	14.3696	+	24.8889i	0.526461	+	0.911857i
$746$	12.9709	−	22.4663i	0.474899	−	0.822548i
$747$	1.06031	+	1.83651i	0.0387946	+	0.0671942i
$748$	−3.37227			−0.123303
$749$	47.4492			1.73376
$750$	−11.2763	−	19.5311i	−0.411753	−	0.713177i
$751$	−13.5885	−	23.5360i	−0.495852	−	0.858841i	0.504136	−	0.863624i	$-0.331811\pi$
$751$	−13.5885	−	23.5360i	−0.495852	−	0.858841i	−0.999989	+	0.00478269i	$0.998478\pi$
$752$	−10.2121			−0.372398
$753$	−23.7888			−0.866912
$754$	−5.51754	−	9.55666i	−0.200937	−	0.348033i
$755$	−20.8384	+	36.0932i	−0.758388	+	1.31357i
$756$	11.7442	+	20.3416i	0.427133	+	0.739816i
$757$	−9.70233	+	16.8049i	−0.352637	+	0.610786i	−0.986711	−	0.162487i	$-0.948048\pi$
$757$	−9.70233	+	16.8049i	−0.352637	+	0.610786i	0.634073	+	0.773273i	$0.281382\pi$
$758$	−4.73917	+	8.20848i	−0.172134	+	0.298146i
$759$	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	$0.239617\pi$
$762$	5.36959	−	9.30039i	0.194520	−	0.336918i
$763$	28.0155	−	48.5242i	1.01423	−	1.75670i
$764$	10.0496	+	17.4065i	0.363583	+	0.629744i
$765$	−1.27126	+	2.20189i	−0.0459625	+	0.0796093i
$766$	6.74422	+	11.6813i	0.243679	+	0.422064i
$767$	−0.935822			−0.0337906
$768$	1.87939			0.0678165
$769$	19.4709	+	33.7246i	0.702139	+	1.21614i	0.967714	+	0.252050i	$0.0811047\pi$
$769$	19.4709	+	33.7246i	0.702139	+	1.21614i	−0.265575	+	0.964090i	$0.585562\pi$
$770$	−7.14796	−	12.3806i	−0.257594	−	0.446167i
$771$	57.1198			2.05712
$772$	−16.6851			−0.600510
$773$	−3.38144	−	5.85683i	−0.121622	−	0.210656i	0.798785	−	0.601616i	$-0.205476\pi$
$773$	−3.38144	−	5.85683i	−0.121622	−	0.210656i	−0.920407	+	0.390960i	$0.872143\pi$
$774$	−0.201867	+	0.349643i	−0.00725595	+	0.0125677i
$775$	−0.184793	−	0.320070i	−0.00663794	−	0.0114973i
$776$	0.766044	−	1.32683i	0.0274994	−	0.0476303i
$777$	22.9513	−	39.7528i	0.823373	−	1.42612i
$778$	25.1480			0.901598
$779$		0			0
$780$	4.90673			0.175689
$781$	4.49525	−	7.78601i	0.160853	−	0.278605i
$782$	−3.66044	+	6.34008i	−0.130897	+	0.226721i
$783$	−19.6040	−	33.9551i	−0.700590	−	1.21346i
$784$	−9.32295	+	16.1478i	−0.332962	+	0.576708i
$785$	−6.36959	−	11.0324i	−0.227340	−	0.393765i
$786$	18.5672			0.662269
$787$	−5.80478			−0.206918			−0.103459	−	0.994634i	$-0.532991\pi$
$787$	−5.80478			−0.206918			−0.103459	+	0.994634i	$0.532991\pi$
$788$	−6.49525	−	11.2501i	−0.231384	−	0.400768i
$789$	−20.5817	−	35.6486i	−0.732729	−	1.26912i
$790$	−4.48246			−0.159479
$791$	67.3465			2.39456
$792$	−0.375515	−	0.650411i	−0.0133433	−	0.0231113i
$793$	−6.36959	+	11.0324i	−0.226191	+	0.391774i
$794$	3.28312	+	5.68653i	0.116514	+	0.201807i
$795$	3.14796	−	5.45242i	0.111646	−	0.193377i
$796$	−8.59627	+	14.8892i	−0.304687	+	0.527733i
$797$	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
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−2.83228	+	4.90566i	−0.100074	+	0.173333i
$802$	14.7554	+	25.5570i	0.521030	+	0.902451i
$803$	−3.21776	+	5.57332i	−0.113552	+	0.196678i
$804$	−1.31908	−	2.28471i	−0.0465203	−	0.0805755i
$805$	−31.0351			−1.09384
$806$	0.482459			0.0169939
$807$	−1.34730	−	2.33359i	−0.0474271	−	0.0821461i
$808$	4.41147	+	7.64090i	0.155195	+	0.268806i
$809$	7.00269			0.246201			0.123101	−	0.992394i	$-0.460716\pi$
$809$	7.00269			0.246201			0.123101	+	0.992394i	$0.460716\pi$
$810$	20.6263			0.724734
$811$	21.8425	+	37.8324i	0.766996	+	1.32848i	0.939185	+	0.343412i	$0.111583\pi$
$811$	21.8425	+	37.8324i	0.766996	+	1.32848i	−0.172189	+	0.985064i	$0.555084\pi$
$812$	21.4047	−	37.0740i	0.751157	−	1.30104i
$813$	−15.1976	−	26.3230i	−0.533003	−	0.923188i
$814$	3.40373	−	5.89544i	0.119301	−	0.206635i
$815$	−4.73143	+	8.19508i	−0.165735	+	0.287061i
$816$	4.49020			0.157188
$817$		0			0
$818$	21.1310			0.738830
$819$	−1.75877	+	3.04628i	−0.0614564	+	0.106446i
$820$	−1.53209	+	2.65366i	−0.0535029	+	0.0926697i
$821$	−6.19253	−	10.7258i	−0.216121	−	0.374332i	0.737498	−	0.675349i	$-0.236007\pi$
$821$	−6.19253	−	10.7258i	−0.216121	−	0.374332i	−0.953619	+	0.301017i	$0.902674\pi$
$822$	5.07145	−	8.78401i	0.176887	−	0.306378i
$823$	6.41416	+	11.1097i	0.223584	+	0.387258i	0.955894	−	0.293713i	$-0.0948911\pi$
$823$	6.41416	+	11.1097i	0.223584	+	0.387258i	−0.732310	+	0.680971i	$0.761558\pi$
$824$	−7.14796			−0.249011
$825$	2.65270			0.0923553
$826$	−1.81521	−	3.14403i	−0.0631591	−	0.109395i
$827$	12.5483	+	21.7343i	0.436347	+	0.755775i	0.997404	−	0.0720020i	$-0.0229388\pi$
$827$	12.5483	+	21.7343i	0.436347	+	0.755775i	−0.561058	+	0.827777i	$0.689605\pi$
$828$	−1.63041			−0.0566608
$829$	−28.3269			−0.983833			−0.491917	−	0.870642i	$-0.663703\pi$
$829$	−28.3269			−0.983833			−0.491917	+	0.870642i	$0.663703\pi$
$830$	−3.98545	−	6.90301i	−0.138337	−	0.239607i
$831$	−10.4388	+	18.0806i	−0.362118	+	0.627208i
$832$	−0.652704	−	1.13052i	−0.0226284	−	0.0391936i
$833$	−22.2743	+	38.5801i	−0.771757	+	1.33672i
$834$	−2.19846	+	3.80785i	−0.0761266	+	0.131855i
$835$	−34.5526			−1.19574
$836$		0			0
$837$	1.71419			0.0592512
$838$	−13.9415	+	24.1474i	−0.481601	+	0.834158i
$839$	−15.1652	+	26.2669i	−0.523561	+	0.906834i	0.476063	+	0.879411i	$0.342063\pi$
$839$	−15.1652	+	26.2669i	−0.523561	+	0.906834i	−0.999624	+	0.0274225i	$0.991270\pi$
$840$	9.51754	+	16.4849i	0.328386	+	0.568782i
$841$	−21.2297	+	36.7709i	−0.732058	+	1.26796i
$842$	0.0222887	+	0.0386052i	0.000768120	+	0.00133042i
$843$	−7.98545			−0.275034
$844$	16.1088			0.554486
$845$	11.2959	+	19.5651i	0.388591	+	0.673060i
$846$	−2.71688	−	4.70578i	−0.0934083	−	0.161788i
$847$	−45.6168			−1.56741
$848$	−1.67499			−0.0575195
$849$	5.12701	+	8.88024i	0.175959	+	0.304769i
$850$	−1.19459	+	2.06910i	−0.0409742	+	0.0709694i
$851$	−7.38919	−	12.7984i	−0.253298	−	0.438725i
$852$	−5.98545	+	10.3671i	−0.205058	+	0.355171i
$853$	21.8161	−	37.7867i	0.746970	−	1.29379i	−0.202298	−	0.979324i	$-0.564841\pi$
$853$	21.8161	−	37.7867i	0.746970	−	1.29379i	0.949268	−	0.314467i	$-0.101826\pi$
$854$	−49.4201			−1.69112
$855$		0			0
$856$	−9.36959			−0.320246
$857$	−15.7549	+	27.2883i	−0.538177	+	0.932150i	0.460825	+	0.887491i	$0.347554\pi$
$857$	−15.7549	+	27.2883i	−0.538177	+	0.932150i	−0.999002	+	0.0446592i	$0.985780\pi$
$858$	−1.73143	+	2.99892i	−0.0591100	+	0.102382i
$859$	9.34895	+	16.1928i	0.318982	+	0.552493i	0.980276	−	0.197634i	$-0.0633257\pi$
$859$	9.34895	+	16.1928i	0.318982	+	0.552493i	−0.661294	+	0.750127i	$0.729992\pi$
$860$	0.758770	−	1.31423i	0.0258739	−	0.0448148i
$861$	−7.29086	−	12.6281i	−0.248472	−	0.430366i
$862$	−11.7879			−0.401496
$863$	−10.6263			−0.361723			−0.180862	−	0.983509i	$-0.557889\pi$
$863$	−10.6263			−0.361723			−0.180862	+	0.983509i	$0.557889\pi$
$864$	−2.31908	−	4.01676i	−0.0788966	−	0.136653i
$865$	18.8229	+	32.6023i	0.639999	+	1.10851i
$866$	27.6459			0.939446
$867$	−21.2216			−0.720724
$868$	0.935822	+	1.62089i	0.0317639	+	0.0550166i
$869$	1.58172	−	2.73962i	0.0536561	−	0.0929351i
$870$	−15.8871	−	27.5173i	−0.538624	−	0.932924i
$871$	−0.916222	+	1.58694i	−0.0310450	+	0.0537715i
$872$	−5.53209	+	9.58186i	−0.187340	+	0.324483i
$873$	0.815207			0.0275906
$874$		0			0
$875$	−60.7701			−2.05441
$876$	4.28446	−	7.42091i	0.144759	−	0.250729i
$877$	22.4492	−	38.8832i	0.758057	−	1.31299i	−0.185783	−	0.982591i	$-0.559482\pi$
$877$	22.4492	−	38.8832i	0.758057	−	1.31299i	0.943840	−	0.330403i	$-0.107185\pi$
$878$	−18.7246	−	32.4320i	−0.631925	−	1.09453i
$879$	16.7392	−	28.9931i	0.564598	−	0.977913i
$880$	1.41147	+	2.44474i	0.0475808	+	0.0824123i
$881$	−18.0164			−0.606988			−0.303494	−	0.952833i	$-0.598153\pi$
$881$	−18.0164			−0.606988			−0.303494	+	0.952833i	$0.598153\pi$
$882$	−9.92127			−0.334067
$883$	23.2991	+	40.3552i	0.784076	+	1.35806i	0.929549	+	0.368697i	$0.120196\pi$
$883$	23.2991	+	40.3552i	0.784076	+	1.35806i	−0.145473	+	0.989362i	$0.546471\pi$
$884$	−1.55943	−	2.70101i	−0.0524493	−	0.0908449i
$885$	−2.69459			−0.0905777
$886$	−20.9881			−0.705110
$887$	3.53983	+	6.13116i	0.118856	+	0.205864i	0.919315	−	0.393524i	$-0.128744\pi$
$887$	3.53983	+	6.13116i	0.118856	+	0.205864i	−0.800459	+	0.599388i	$0.795411\pi$
$888$	−4.53209	+	7.84981i	−0.152087	+	0.263422i
$889$	−14.4688	−	25.0608i	−0.485269	−	0.840511i
$890$	10.6459	−	18.4392i	0.356851	−	0.618085i
$891$	−7.27837	+	12.6065i	−0.243835	+	0.422334i
$892$	−4.08378			−0.136735
$893$		0			0
$894$	27.0060			0.903215
$895$	−13.8280	+	23.9508i	−0.462219	+	0.800587i
$896$	2.53209	−	4.38571i	0.0845912	−	0.146516i
$897$	3.75877	+	6.51038i	0.125502	+	0.217375i
$898$	10.9474	−	18.9615i	0.365321	−	0.632754i
$899$	−1.56212	−	2.70567i	−0.0520996	−	0.0902391i
$900$	−0.532089			−0.0177363
$901$	−4.00187			−0.133322
$902$	−1.08125	−	1.87278i	−0.0360018	−	0.0623569i
$903$	3.61081	+	6.25411i	0.120160	+	0.208124i
$904$	−13.2986			−0.442305
$905$	−24.5134			−0.814854
$906$	19.5817	+	33.9165i	0.650559	+	1.12680i
$907$	7.55778	−	13.0905i	0.250952	−	0.434662i	−0.712836	−	0.701331i	$-0.752590\pi$
$907$	7.55778	−	13.0905i	0.250952	−	0.434662i	0.963788	+	0.266669i	$0.0859230\pi$
$908$	6.83022	+	11.8303i	0.226669	+	0.392602i
$909$	−2.34730	+	4.06564i	−0.0778549	+	0.134849i
$910$	6.61081	−	11.4503i	0.219146	−	0.379573i
$911$	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
$914$	−6.52481	+	11.3013i	−0.215822	+	0.373814i
$915$	−18.3405	+	31.7667i	−0.606318	+	1.05017i
$916$	2.61081	+	4.52206i	0.0862637	+	0.149413i
$917$	25.0155	−	43.3281i	0.826084	−	1.43082i
$918$	−5.54071	−	9.59679i	−0.182871	−	0.316741i
$919$	−20.6791			−0.682141			−0.341070	−	0.940038i	$-0.610789\pi$
$919$	−20.6791			−0.682141			−0.341070	+	0.940038i	$0.610789\pi$
$920$	6.12836			0.202046
$921$	−26.9304	−	46.6448i	−0.887386	−	1.53700i
$922$	2.20439	+	3.81812i	0.0725978	+	0.125743i
$923$	8.31490			0.273688
$924$	−13.4338			−0.441938
$925$	−2.41147	−	4.17680i	−0.0792888	−	0.137332i
$926$	13.3327	−	23.0930i	0.438141	−	0.758883i
$927$	−1.90167	−	3.29380i	−0.0624592	−	0.108182i
$928$	−4.22668	+	7.32083i	−0.138748	+	0.240318i
$929$	9.12495	−	15.8049i	0.299380	−	0.518541i	−0.676614	−	0.736338i	$-0.736554\pi$
$929$	9.12495	−	15.8049i	0.299380	−	0.518541i	0.975994	+	0.217796i	$0.0698869\pi$
$930$	1.38919			0.0455532
$931$		0			0
$932$	−27.0428			−0.885817
$933$	−14.8598	+	25.7379i	−0.486488	+	0.842621i
$934$	15.0569	−	26.0793i	0.492677	−	0.853341i
$935$	3.37227	+	5.84095i	0.110285	+	0.191019i
$936$	0.347296	−	0.601535i	0.0113517	−	0.0196618i
$937$	2.37346	+	4.11095i	0.0775374	+	0.134299i	0.902187	−	0.431345i	$-0.141961\pi$
$937$	2.37346	+	4.11095i	0.0775374	+	0.134299i	−0.824649	+	0.565644i	$0.808628\pi$
$938$	−7.10876			−0.232109
$939$	24.6955			0.805908
$940$	10.2121	+	17.6879i	0.333083	+	0.576917i
$941$	23.5107	+	40.7218i	0.766428	+	1.32749i	0.939488	+	0.342581i	$0.111301\pi$
$941$	23.5107	+	40.7218i	0.766428	+	1.32749i	−0.173060	+	0.984911i	$0.555366\pi$
$942$	−11.9709			−0.390033
$943$	−4.69459			−0.152877
$944$	0.358441	+	0.620838i	0.0116663	+	0.0202065i
$945$	23.4884	−	40.6832i	0.764079	−	1.32342i
$946$	0.535492	+	0.927500i	0.0174104	+	0.0301556i
$947$	−18.4979	+	32.0394i	−0.601102	+	1.04114i	0.391552	+	0.920156i	$0.371938\pi$
$947$	−18.4979	+	32.0394i	−0.601102	+	1.04114i	−0.992654	+	0.120984i	$0.961395\pi$
$948$	−2.10607	+	3.64781i	−0.0684019	+	0.118476i
$949$	−5.95191			−0.193207
$950$		0			0
$951$	40.2276			1.30447
$952$	6.04963	−	10.4783i	0.196070	−	0.339603i
$953$	−18.8546	+	32.6572i	−0.610761	+	1.05787i	0.380351	+	0.924842i	$0.375803\pi$
$953$	−18.8546	+	32.6572i	−0.610761	+	1.05787i	−0.991112	+	0.133027i	$0.957530\pi$
$954$	−0.445622	−	0.771841i	−0.0144276	−	0.0249893i
$955$	20.0993	−	34.8129i	0.650397	−	1.12652i
$956$	0.142903	+	0.247516i	0.00462183	+	0.00800524i
$957$	22.4243			0.724874
$958$	−8.16756			−0.263882
$959$	−13.6655	−	23.6693i	−0.441282	−	0.764323i
$960$	−1.87939	−	3.25519i	−0.0606569	−	0.105061i
$961$	−30.8634			−0.995594
$962$	6.29591			0.202988
$963$	−2.49273	−	4.31753i	−0.0803270	−	0.139130i
$964$	1.55051	−	2.68556i	0.0499385	−	0.0864960i
$965$	16.6851	+	28.8994i	0.537112	+	0.930306i
$966$	−14.5817	+	25.2563i	−0.469159	+	0.812607i
$967$	−20.2567	+	35.0857i	−0.651412	+	1.12828i	0.331369	+	0.943501i	$0.392490\pi$
$967$	−20.2567	+	35.0857i	−0.651412	+	1.12828i	−0.982780	+	0.184777i	$0.940844\pi$
$968$	9.00774			0.289520
$969$		0			0
$970$	−3.06418			−0.0983848
$971$	−7.03895	+	12.1918i	−0.225891	+	0.391254i	−0.956586	−	0.291449i	$-0.905863\pi$
$971$	−7.03895	+	12.1918i	−0.225891	+	0.391254i	0.730696	+	0.682703i	$0.239196\pi$
$972$	2.73396	−	4.73535i	0.0876917	−	0.151886i
$973$	5.92396	+	10.2606i	0.189914	+	0.328940i
$974$	−13.2935	+	23.0251i	−0.425953	+	0.737772i
$975$	1.22668	+	2.12467i	0.0392853	+	0.0680441i
$976$	9.75877			0.312371
$977$	35.2057			1.12633			0.563164	−	0.826345i	$-0.309584\pi$
$977$	35.2057			1.12633			0.563164	+	0.826345i	$0.309584\pi$
$978$	4.44609	+	7.70085i	0.142170	+	0.246246i
$979$	7.51320	+	13.0133i	0.240123	+	0.415905i
$980$	37.2918			1.19124
$981$	−5.88713			−0.187961
$982$	19.4145	+	33.6268i	0.619541	+	1.07308i
$983$	11.2199	−	19.4334i	0.357858	−	0.619829i	−0.629744	−	0.776802i	$-0.716840\pi$
$983$	11.2199	−	19.4334i	0.357858	−	0.619829i	0.987603	+	0.156973i	$0.0501737\pi$
$984$	1.43969	+	2.49362i	0.0458957	+	0.0794937i
$985$	−12.9905	+	22.5002i	−0.413912	+	0.716916i
$986$	−10.0983	+	17.4908i	−0.321596	+	0.557021i
$987$	−97.1944			−3.09373
$988$		0			0
$989$	2.32501			0.0739309
$990$	−0.751030	+	1.30082i	−0.0238693	+	0.0413428i
$991$	13.5517	−	23.4722i	0.430484	−	0.745619i	−0.566431	−	0.824109i	$-0.691676\pi$
$991$	13.5517	−	23.4722i	0.430484	−	0.745619i	0.996915	+	0.0784895i	$0.0250097\pi$
$992$	−0.184793	−	0.320070i	−0.00586717	−	0.0101622i
$993$	−23.8662	+	41.3374i	−0.757370	+	1.31180i
$994$	16.1284	+	27.9351i	0.511560	+	0.886049i
$995$	34.3851			1.09008
$996$	−7.49020			−0.237336
$997$	−13.9736	−	24.2030i	−0.442548	−	0.766516i	0.555330	−	0.831630i	$-0.312592\pi$
$997$	−13.9736	−	24.2030i	−0.442548	−	0.766516i	−0.997878	+	0.0651145i	$0.979259\pi$
$998$	10.3293	+	17.8910i	0.326970	+	0.566328i
$999$	22.3696			0.707742

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.5.1	✓	6	19.15	odd	18
38.2.e.a.23.1	yes	6	19.3	odd	18
304.2.u.c.81.1		6	76.15	even	18
304.2.u.c.289.1		6	76.3	even	18
342.2.u.c.271.1		6	57.53	even	18
342.2.u.c.289.1		6	57.41	even	18
722.2.a.k.1.3		3	19.11	even	3
722.2.a.l.1.1		3	19.8	odd	6
722.2.c.k.429.3		6	19.18	odd	2
722.2.c.k.653.3		6	19.12	odd	6
722.2.c.l.429.1		6	1.1	even	1	trivial
722.2.c.l.653.1		6	19.7	even	3	inner
722.2.e.a.415.1		6	19.6	even	9
722.2.e.a.595.1		6	19.17	even	9
722.2.e.b.245.1		6	19.10	odd	18
722.2.e.b.389.1		6	19.14	odd	18
722.2.e.k.99.1		6	19.16	even	9
722.2.e.k.423.1		6	19.4	even	9
722.2.e.l.245.1		6	19.9	even	9
722.2.e.l.389.1		6	19.5	even	9
722.2.e.m.415.1		6	19.13	odd	18
722.2.e.m.595.1		6	19.2	odd	18
950.2.l.d.251.1		6	95.79	odd	18
950.2.l.d.651.1		6	95.34	odd	18
950.2.u.b.99.1		12	95.3	even	36
950.2.u.b.99.2		12	95.22	even	36
950.2.u.b.499.1		12	95.72	even	36
950.2.u.b.499.2		12	95.53	even	36
5776.2.a.bn.1.3		3	76.27	even	6
5776.2.a.bo.1.1		3	76.11	odd	6
6498.2.a.bl.1.3		3	57.8	even	6
6498.2.a.bq.1.3		3	57.11	odd	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.939693 + 1.62760i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.939693 + 1.62760i) q^{6} +5.06418 q^{7} -1.00000 q^{8} +(-0.266044 - 0.460802i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.939693 + 1.62760i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.939693 + 1.62760i) q^{6} +5.06418 q^{7} -1.00000 q^{8} +(-0.266044 - 0.460802i) q^{9} +(1.00000 + 1.73205i) q^{10} -1.41147 q^{11} +1.87939 q^{12} +(-0.652704 - 1.13052i) q^{13} +(2.53209 - 4.38571i) q^{14} +(-1.87939 - 3.25519i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.19459 + 2.06910i) q^{17} -0.532089 q^{18} +2.00000 q^{20} +(-4.75877 + 8.24243i) q^{21} +(-0.705737 + 1.22237i) q^{22} +(1.53209 + 2.65366i) q^{23} +(0.939693 - 1.62760i) q^{24} +(0.500000 + 0.866025i) q^{25} -1.30541 q^{26} -4.63816 q^{27} +(-2.53209 - 4.38571i) q^{28} +(4.22668 + 7.32083i) q^{29} -3.75877 q^{30} -0.369585 q^{31} +(0.500000 + 0.866025i) q^{32} +(1.32635 - 2.29731i) q^{33} +(1.19459 + 2.06910i) q^{34} +(-5.06418 + 8.77141i) q^{35} +(-0.266044 + 0.460802i) q^{36} -4.82295 q^{37} +2.45336 q^{39} +(1.00000 - 1.73205i) q^{40} +(-0.766044 + 1.32683i) q^{41} +(4.75877 + 8.24243i) q^{42} +(0.379385 - 0.657115i) q^{43} +(0.705737 + 1.22237i) q^{44} +1.06418 q^{45} +3.06418 q^{46} +(5.10607 + 8.84397i) q^{47} +(-0.939693 - 1.62760i) q^{48} +18.6459 q^{49} +1.00000 q^{50} +(-2.24510 - 3.88863i) q^{51} +(-0.652704 + 1.13052i) q^{52} +(0.837496 + 1.45059i) q^{53} +(-2.31908 + 4.01676i) q^{54} +(1.41147 - 2.44474i) q^{55} -5.06418 q^{56} +8.45336 q^{58} +(0.358441 - 0.620838i) q^{59} +(-1.87939 + 3.25519i) q^{60} +(-4.87939 - 8.45134i) q^{61} +(-0.184793 + 0.320070i) q^{62} +(-1.34730 - 2.33359i) q^{63} +1.00000 q^{64} +2.61081 q^{65} +(-1.32635 - 2.29731i) q^{66} +(-0.701867 - 1.21567i) q^{67} +2.38919 q^{68} -5.75877 q^{69} +(5.06418 + 8.77141i) q^{70} +(-3.18479 + 5.51622i) q^{71} +(0.266044 + 0.460802i) q^{72} +(2.27972 - 3.94858i) q^{73} +(-2.41147 + 4.17680i) q^{74} -1.87939 q^{75} -7.14796 q^{77} +(1.22668 - 2.12467i) q^{78} +(-1.12061 + 1.94096i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(5.15657 - 8.93145i) q^{81} +(0.766044 + 1.32683i) q^{82} -3.98545 q^{83} +9.51754 q^{84} +(-2.38919 - 4.13819i) q^{85} +(-0.379385 - 0.657115i) q^{86} -15.8871 q^{87} +1.41147 q^{88} +(-5.32295 - 9.21962i) q^{89} +(0.532089 - 0.921605i) q^{90} +(-3.30541 - 5.72513i) q^{91} +(1.53209 - 2.65366i) q^{92} +(0.347296 - 0.601535i) q^{93} +10.2121 q^{94} -1.87939 q^{96} +(-0.766044 + 1.32683i) q^{97} +(9.32295 - 16.1478i) q^{98} +(0.375515 + 0.650411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 + 3 * q^9	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{7} - 6 q^{8} + 3 q^{9} + 6 q^{10} + 12 q^{11} - 6 q^{13} + 6 q^{14} - 3 q^{16} - 3 q^{17} + 6 q^{18} + 12 q^{20} - 6 q^{21} + 6 q^{22} + 3 q^{25} - 12 q^{26} + 6 q^{27} - 6 q^{28} + 12 q^{29} + 12 q^{31} + 3 q^{32} + 9 q^{33} + 3 q^{34} - 12 q^{35} + 3 q^{36} + 12 q^{37} - 12 q^{39} + 6 q^{40} + 6 q^{42} - 9 q^{43} - 6 q^{44} - 12 q^{45} + 6 q^{47} + 30 q^{49} + 6 q^{50} - 12 q^{51} - 6 q^{52} + 3 q^{54} - 12 q^{55} - 12 q^{56} + 24 q^{58} - 6 q^{59} - 18 q^{61} + 6 q^{62} - 6 q^{63} + 6 q^{64} + 24 q^{65} - 9 q^{66} - 18 q^{67} + 6 q^{68} - 12 q^{69} + 12 q^{70} - 12 q^{71} - 3 q^{72} - 12 q^{73} + 6 q^{74} - 12 q^{77} - 6 q^{78} - 18 q^{79} - 6 q^{80} + 9 q^{81} + 12 q^{83} + 12 q^{84} - 6 q^{85} + 9 q^{86} - 36 q^{87} - 12 q^{88} + 9 q^{89} - 6 q^{90} - 24 q^{91} + 12 q^{94} + 15 q^{98} + 15 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^7 - 6 * q^8 + 3 * q^9 + 6 * q^10 + 12 * q^11 - 6 * q^13 + 6 * q^14 - 3 * q^16 - 3 * q^17 + 6 * q^18 + 12 * q^20 - 6 * q^21 + 6 * q^22 + 3 * q^25 - 12 * q^26 + 6 * q^27 - 6 * q^28 + 12 * q^29 + 12 * q^31 + 3 * q^32 + 9 * q^33 + 3 * q^34 - 12 * q^35 + 3 * q^36 + 12 * q^37 - 12 * q^39 + 6 * q^40 + 6 * q^42 - 9 * q^43 - 6 * q^44 - 12 * q^45 + 6 * q^47 + 30 * q^49 + 6 * q^50 - 12 * q^51 - 6 * q^52 + 3 * q^54 - 12 * q^55 - 12 * q^56 + 24 * q^58 - 6 * q^59 - 18 * q^61 + 6 * q^62 - 6 * q^63 + 6 * q^64 + 24 * q^65 - 9 * q^66 - 18 * q^67 + 6 * q^68 - 12 * q^69 + 12 * q^70 - 12 * q^71 - 3 * q^72 - 12 * q^73 + 6 * q^74 - 12 * q^77 - 6 * q^78 - 18 * q^79 - 6 * q^80 + 9 * q^81 + 12 * q^83 + 12 * q^84 - 6 * q^85 + 9 * q^86 - 36 * q^87 - 12 * q^88 + 9 * q^89 - 6 * q^90 - 24 * q^91 + 12 * q^94 + 15 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more