LMFDB - Embedded newform 429.2.i.d.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3118758597603.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 $ x^10 - 4x^8 - 16x^6 - 34x^5 + 43x^4 + 155x^3 + 199x^2 + 124*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.1
Root			$-0.359001 - 0.701254i$ of defining polynomial
Character	$\chi$	$=$	429.133
Dual form			429.2.i.d.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18968 - 2.06059i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.83068 + 3.17083i) q^{4} +2.23497 q^{5} +(1.18968 - 2.06059i) q^{6} +(-1.82822 + 3.16657i) q^{7} +3.95297 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.18968 - 2.06059i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.83068 + 3.17083i) q^{4} +2.23497 q^{5} +(1.18968 - 2.06059i) q^{6} +(-1.82822 + 3.16657i) q^{7} +3.95297 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.65890 - 4.60534i) q^{10} +(-0.500000 - 0.866025i) q^{11} -3.66136 q^{12} +(-3.34999 + 1.33326i) q^{13} +8.69998 q^{14} +(1.11748 + 1.93554i) q^{15} +(-1.04141 - 1.80378i) q^{16} +(-3.59151 + 6.22067i) q^{17} +2.37936 q^{18} +(-0.638537 + 1.10598i) q^{19} +(-4.09151 + 7.08670i) q^{20} -3.65643 q^{21} +(-1.18968 + 2.06059i) q^{22} +(-0.817589 - 1.41611i) q^{23} +(1.97648 + 3.42337i) q^{24} -0.00492321 q^{25} +(6.73271 + 5.31679i) q^{26} -1.00000 q^{27} +(-6.69376 - 11.5939i) q^{28} +(4.24560 + 7.35359i) q^{29} +(2.65890 - 4.60534i) q^{30} +0.923965 q^{31} +(1.47507 - 2.55490i) q^{32} +(0.500000 - 0.866025i) q^{33} +17.0910 q^{34} +(-4.08601 + 7.07717i) q^{35} +(-1.83068 - 3.17083i) q^{36} +(-1.07466 - 1.86136i) q^{37} +3.03862 q^{38} +(-2.82963 - 2.23455i) q^{39} +8.83476 q^{40} +(-0.286804 - 0.496760i) q^{41} +(4.34999 + 7.53440i) q^{42} +(2.70418 - 4.68378i) q^{43} +3.66136 q^{44} +(-1.11748 + 1.93554i) q^{45} +(-1.94534 + 3.36942i) q^{46} +10.4084 q^{47} +(1.04141 - 1.80378i) q^{48} +(-3.18476 - 5.51616i) q^{49} +(0.00585704 + 0.0101447i) q^{50} -7.18301 q^{51} +(1.90522 - 13.0630i) q^{52} -2.81140 q^{53} +(1.18968 + 2.06059i) q^{54} +(-1.11748 - 1.93554i) q^{55} +(-7.22689 + 12.5173i) q^{56} -1.27707 q^{57} +(10.1018 - 17.4968i) q^{58} +(6.50549 - 11.2678i) q^{59} -8.18301 q^{60} +(-0.809625 + 1.40231i) q^{61} +(-1.09922 - 1.90391i) q^{62} +(-1.82822 - 3.16657i) q^{63} -11.1851 q^{64} +(-7.48711 + 2.97979i) q^{65} -2.37936 q^{66} +(6.58108 + 11.3988i) q^{67} +(-13.1498 - 22.7761i) q^{68} +(0.817589 - 1.41611i) q^{69} +19.4442 q^{70} +(2.51649 - 4.35868i) q^{71} +(-1.97648 + 3.42337i) q^{72} -3.92720 q^{73} +(-2.55700 + 4.42885i) q^{74} +(-0.00246160 - 0.00426362i) q^{75} +(-2.33791 - 4.04938i) q^{76} +3.65643 q^{77} +(-1.23812 + 8.48909i) q^{78} +6.94126 q^{79} +(-2.32752 - 4.03139i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.682411 + 1.18197i) q^{82} +5.33443 q^{83} +(6.69376 - 11.5939i) q^{84} +(-8.02690 + 13.9030i) q^{85} -12.8685 q^{86} +(-4.24560 + 7.35359i) q^{87} +(-1.97648 - 3.42337i) q^{88} +(9.21505 + 15.9609i) q^{89} +5.31779 q^{90} +(1.90266 - 13.0454i) q^{91} +5.98697 q^{92} +(0.461983 + 0.800177i) q^{93} +(-12.3826 - 21.4473i) q^{94} +(-1.42711 + 2.47183i) q^{95} +2.95015 q^{96} +(-6.42114 + 11.1217i) q^{97} +(-7.57769 + 13.1249i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} - 5 q^{11} - 20 q^{12} + 9 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} - 8 q^{20} - 14 q^{21} - 11 q^{23} + 3 q^{24} - 6 q^{25} - 4 q^{26} - 10 q^{27} - 5 q^{28} + 2 q^{29} + 7 q^{30} + 20 q^{31} + 9 q^{32} + 5 q^{33} + 58 q^{34} + 14 q^{35} - 10 q^{36} - 15 q^{37} - 38 q^{38} - 6 q^{39} + 30 q^{40} + 2 q^{41} + q^{42} - 7 q^{43} + 20 q^{44} + 2 q^{45} - 20 q^{46} + 36 q^{47} + 4 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 30 q^{53} + 2 q^{55} - 3 q^{56} - 14 q^{57} - 5 q^{58} + 4 q^{59} - 16 q^{60} + 14 q^{61} - 46 q^{62} - 7 q^{63} - 74 q^{64} - 44 q^{65} + 5 q^{67} + 24 q^{68} + 11 q^{69} + 80 q^{70} + 13 q^{71} - 3 q^{72} + 56 q^{73} - 15 q^{74} - 3 q^{75} - 2 q^{76} + 14 q^{77} - 23 q^{78} + 32 q^{79} + 22 q^{80} - 5 q^{81} - 4 q^{82} + 24 q^{83} + 5 q^{84} - 13 q^{85} + 4 q^{86} - 2 q^{87} - 3 q^{88} + 6 q^{89} + 14 q^{90} - 29 q^{91} - 4 q^{92} + 10 q^{93} + 2 q^{94} + 21 q^{95} + 18 q^{96} - 9 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 - 5 * q^11 - 20 * q^12 + 9 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 - 8 * q^20 - 14 * q^21 - 11 * q^23 + 3 * q^24 - 6 * q^25 - 4 * q^26 - 10 * q^27 - 5 * q^28 + 2 * q^29 + 7 * q^30 + 20 * q^31 + 9 * q^32 + 5 * q^33 + 58 * q^34 + 14 * q^35 - 10 * q^36 - 15 * q^37 - 38 * q^38 - 6 * q^39 + 30 * q^40 + 2 * q^41 + q^42 - 7 * q^43 + 20 * q^44 + 2 * q^45 - 20 * q^46 + 36 * q^47 + 4 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 30 * q^53 + 2 * q^55 - 3 * q^56 - 14 * q^57 - 5 * q^58 + 4 * q^59 - 16 * q^60 + 14 * q^61 - 46 * q^62 - 7 * q^63 - 74 * q^64 - 44 * q^65 + 5 * q^67 + 24 * q^68 + 11 * q^69 + 80 * q^70 + 13 * q^71 - 3 * q^72 + 56 * q^73 - 15 * q^74 - 3 * q^75 - 2 * q^76 + 14 * q^77 - 23 * q^78 + 32 * q^79 + 22 * q^80 - 5 * q^81 - 4 * q^82 + 24 * q^83 + 5 * q^84 - 13 * q^85 + 4 * q^86 - 2 * q^87 - 3 * q^88 + 6 * q^89 + 14 * q^90 - 29 * q^91 - 4 * q^92 + 10 * q^93 + 2 * q^94 + 21 * q^95 + 18 * q^96 - 9 * q^97 - 16 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.18968	−	2.06059i	−0.841231	−	1.45705i	−0.888854	−	0.458190i	$-0.848498\pi$
$2$	−1.18968	−	2.06059i	−0.841231	−	1.45705i	0.0476234	−	0.998865i	$-0.484835\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.83068	+	3.17083i	−0.915339	+	1.58541i
$5$	2.23497			0.999508			0.499754	−	0.866168i	$-0.333424\pi$
$5$	2.23497			0.999508			0.499754	+	0.866168i	$0.333424\pi$
$6$	1.18968	−	2.06059i	0.485685	−	0.841231i
$7$	−1.82822	+	3.16657i	−0.691001	+	1.19685i	0.280509	+	0.959851i	$0.409497\pi$
$7$	−1.82822	+	3.16657i	−0.691001	+	1.19685i	−0.971510	+	0.236998i	$0.923837\pi$
$8$	3.95297			1.39759
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−2.65890	−	4.60534i	−0.840817	−	1.45634i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−3.66136			−1.05694
$13$	−3.34999	+	1.33326i	−0.929120	+	0.369779i
$13$	−3.34999	+	1.33326i	−0.929120	+	0.369779i
$14$	8.69998			2.32517
$15$	1.11748	+	1.93554i	0.288533	+	0.499754i
$16$	−1.04141	−	1.80378i	−0.260353	−	0.450945i
$17$	−3.59151	+	6.22067i	−0.871068	+	1.50873i	−0.0101755	+	0.999948i	$0.503239\pi$
$17$	−3.59151	+	6.22067i	−0.871068	+	1.50873i	−0.860893	+	0.508786i	$0.830094\pi$
$18$	2.37936			0.560821
$19$	−0.638537	+	1.10598i	−0.146490	+	0.253729i	−0.929928	−	0.367742i	$-0.880131\pi$
$19$	−0.638537	+	1.10598i	−0.146490	+	0.253729i	0.783438	+	0.621470i	$0.213464\pi$
$20$	−4.09151	+	7.08670i	−0.914889	+	1.58463i
$21$	−3.65643			−0.797899
$22$	−1.18968	+	2.06059i	−0.253641	+	0.439319i
$23$	−0.817589	−	1.41611i	−0.170479	−	0.295278i	0.768108	−	0.640320i	$-0.221198\pi$
$23$	−0.817589	−	1.41611i	−0.170479	−	0.295278i	−0.938587	+	0.345041i	$0.887865\pi$
$24$	1.97648	+	3.42337i	0.403448	+	0.698793i
$25$	−0.00492321			−0.000984641
$26$	6.73271	+	5.31679i	1.32039	+	1.04271i
$27$	−1.00000			−0.192450
$28$	−6.69376	−	11.5939i	−1.26500	−	2.19105i
$29$	4.24560	+	7.35359i	0.788387	+	1.36553i	0.926954	+	0.375174i	$0.122417\pi$
$29$	4.24560	+	7.35359i	0.788387	+	1.36553i	−0.138567	+	0.990353i	$0.544250\pi$
$30$	2.65890	−	4.60534i	0.485446	−	0.840817i
$31$	0.923965			0.165949			0.0829745	−	0.996552i	$-0.473558\pi$
$31$	0.923965			0.165949			0.0829745	+	0.996552i	$0.473558\pi$
$32$	1.47507	−	2.55490i	0.260759	−	0.451647i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	17.0910			2.93108
$35$	−4.08601	+	7.07717i	−0.690661	+	1.19626i
$36$	−1.83068	−	3.17083i	−0.305113	−	0.528471i
$37$	−1.07466	−	1.86136i	−0.176673	−	0.306006i	0.764066	−	0.645138i	$-0.223200\pi$
$37$	−1.07466	−	1.86136i	−0.176673	−	0.306006i	−0.940739	+	0.339132i	$0.889867\pi$
$38$	3.03862			0.492929
$39$	−2.82963	−	2.23455i	−0.453103	−	0.357814i
$40$	8.83476			1.39690
$41$	−0.286804	−	0.496760i	−0.0447913	−	0.0775809i	0.842761	−	0.538289i	$-0.180929\pi$
$41$	−0.286804	−	0.496760i	−0.0447913	−	0.0775809i	−0.887552	+	0.460708i	$0.847596\pi$
$42$	4.34999	+	7.53440i	0.671218	+	1.16258i
$43$	2.70418	−	4.68378i	0.412384	−	0.714270i	−0.582766	−	0.812640i	$-0.698030\pi$
$43$	2.70418	−	4.68378i	0.412384	−	0.714270i	0.995150	+	0.0983700i	$0.0313629\pi$
$44$	3.66136			0.551970
$45$	−1.11748	+	1.93554i	−0.166585	+	0.288533i
$46$	−1.94534	+	3.36942i	−0.286824	+	0.496795i
$47$	10.4084			1.51822			0.759108	−	0.650965i	$-0.225635\pi$
$47$	10.4084			1.51822			0.759108	+	0.650965i	$0.225635\pi$
$48$	1.04141	−	1.80378i	0.150315	−	0.260353i
$49$	−3.18476	−	5.51616i	−0.454965	−	0.788023i
$50$	0.00585704	+	0.0101447i	0.000828311	+	0.00143468i
$51$	−7.18301			−1.00582
$52$	1.90522	−	13.0630i	0.264207	−	1.81151i
$53$	−2.81140			−0.386175			−0.193088	−	0.981181i	$-0.561850\pi$
$53$	−2.81140			−0.386175			−0.193088	+	0.981181i	$0.561850\pi$
$54$	1.18968	+	2.06059i	0.161895	+	0.280410i
$55$	−1.11748	−	1.93554i	−0.150681	−	0.260988i
$56$	−7.22689	+	12.5173i	−0.965734	+	1.67270i
$57$	−1.27707			−0.169153
$58$	10.1018	−	17.4968i	1.32643	−	2.29745i
$59$	6.50549	−	11.2678i	0.846943	−	1.46695i	−0.0369809	−	0.999316i	$-0.511774\pi$
$59$	6.50549	−	11.2678i	0.846943	−	1.46695i	0.883923	−	0.467632i	$-0.154893\pi$
$60$	−8.18301			−1.05642
$61$	−0.809625	+	1.40231i	−0.103662	+	0.179548i	−0.913191	−	0.407532i	$-0.866389\pi$
$61$	−0.809625	+	1.40231i	−0.103662	+	0.179548i	0.809529	+	0.587080i	$0.199723\pi$
$62$	−1.09922	−	1.90391i	−0.139601	−	0.241797i
$63$	−1.82822	−	3.16657i	−0.230334	−	0.398950i
$64$	−11.1851			−1.39814
$65$	−7.48711	+	2.97979i	−0.928662	+	0.369597i
$66$	−2.37936			−0.292879
$67$	6.58108	+	11.3988i	0.804007	+	1.39258i	0.916959	+	0.398981i	$0.130636\pi$
$67$	6.58108	+	11.3988i	0.804007	+	1.39258i	−0.112952	+	0.993600i	$0.536031\pi$
$68$	−13.1498	−	22.7761i	−1.59465	−	2.76201i
$69$	0.817589	−	1.41611i	0.0984261	−	0.170479i
$70$	19.4442			2.32402
$71$	2.51649	−	4.35868i	0.298652	−	0.517280i	−0.677176	−	0.735821i	$-0.736796\pi$
$71$	2.51649	−	4.35868i	0.298652	−	0.517280i	0.975828	+	0.218541i	$0.0701297\pi$
$72$	−1.97648	+	3.42337i	−0.232931	+	0.403448i
$73$	−3.92720			−0.459644			−0.229822	−	0.973233i	$-0.573814\pi$
$73$	−3.92720			−0.459644			−0.229822	+	0.973233i	$0.573814\pi$
$74$	−2.55700	+	4.42885i	−0.297245	+	0.514844i
$75$	−0.00246160	−	0.00426362i	−0.000284241	−	0.000492321i
$76$	−2.33791	−	4.04938i	−0.268177	−	0.464496i
$77$	3.65643			0.416689
$78$	−1.23812	+	8.48909i	−0.140190	+	0.961201i
$79$	6.94126			0.780952			0.390476	−	0.920613i	$-0.372310\pi$
$79$	6.94126			0.780952			0.390476	+	0.920613i	$0.372310\pi$
$80$	−2.32752	−	4.03139i	−0.260225	−	0.450723i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.682411	+	1.18197i	−0.0753597	+	0.130527i
$83$	5.33443			0.585530			0.292765	−	0.956184i	$-0.405425\pi$
$83$	5.33443			0.585530			0.292765	+	0.956184i	$0.405425\pi$
$84$	6.69376	−	11.5939i	0.730349	−	1.26500i
$85$	−8.02690	+	13.9030i	−0.870639	+	1.50799i
$86$	−12.8685			−1.38764
$87$	−4.24560	+	7.35359i	−0.455176	+	0.788387i
$88$	−1.97648	−	3.42337i	−0.210694	−	0.364933i
$89$	9.21505	+	15.9609i	0.976793	+	1.69186i	0.673885	+	0.738836i	$0.264624\pi$
$89$	9.21505	+	15.9609i	0.976793	+	1.69186i	0.302908	+	0.953020i	$0.402042\pi$
$90$	5.31779			0.560545
$91$	1.90266	−	13.0454i	0.199453	−	1.36753i
$92$	5.98697			0.624185
$93$	0.461983	+	0.800177i	0.0479054	+	0.0829745i
$94$	−12.3826	−	21.4473i	−1.27717	−	2.21212i
$95$	−1.42711	+	2.47183i	−0.146418	+	0.253604i
$96$	2.95015			0.301098
$97$	−6.42114	+	11.1217i	−0.651968	+	1.12924i	0.330677	+	0.943744i	$0.392723\pi$
$97$	−6.42114	+	11.1217i	−0.651968	+	1.12924i	−0.982645	+	0.185497i	$0.940610\pi$
$98$	−7.57769	+	13.1249i	−0.765462	+	1.32582i
$99$	1.00000			0.100504
$100$	0.00901281	−	0.0156106i	0.000901281	−	0.00156106i
$101$	−5.93188	−	10.2743i	−0.590244	−	1.02233i	−0.994199	−	0.107554i	$-0.965698\pi$
$101$	−5.93188	−	10.2743i	−0.590244	−	1.02233i	0.403955	−	0.914779i	$-0.367635\pi$
$102$	8.54549	+	14.8012i	0.846130	+	1.46554i
$103$	−13.5485			−1.33498			−0.667489	−	0.744620i	$-0.732631\pi$
$103$	−13.5485			−1.33498			−0.667489	+	0.744620i	$0.732631\pi$
$104$	−13.2424	+	5.27033i	−1.29852	+	0.516798i
$105$	−8.17201			−0.797507
$106$	3.34467	+	5.79313i	0.324863	+	0.562679i
$107$	−6.35370	−	11.0049i	−0.614236	−	1.06389i	−0.990518	−	0.137382i	$-0.956131\pi$
$107$	−6.35370	−	11.0049i	−0.614236	−	1.06389i	0.376282	−	0.926505i	$-0.377202\pi$
$108$	1.83068	−	3.17083i	0.176157	−	0.305113i
$109$	−1.32693			−0.127097			−0.0635483	−	0.997979i	$-0.520242\pi$
$109$	−1.32693			−0.127097			−0.0635483	+	0.997979i	$0.520242\pi$
$110$	−2.65890	+	4.60534i	−0.253516	+	0.439102i
$111$	1.07466	−	1.86136i	0.102002	−	0.176673i
$112$	7.61572			0.719618
$113$	−9.30526	+	16.1172i	−0.875365	+	1.51618i	−0.0189923	+	0.999820i	$0.506046\pi$
$113$	−9.30526	+	16.1172i	−0.875365	+	1.51618i	−0.856373	+	0.516358i	$0.827288\pi$
$114$	1.51931	+	2.63152i	0.142296	+	0.246465i
$115$	−1.82728	−	3.16495i	−0.170395	−	0.295133i
$116$	−31.0893			−2.88657
$117$	0.520359	−	3.56780i	0.0481072	−	0.329844i
$118$	−30.9578			−2.84990
$119$	−13.1321	−	22.7455i	−1.20382	−	2.08507i
$120$	4.41738	+	7.65112i	0.403250	+	0.698449i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	3.85278			0.348814
$123$	0.286804	−	0.496760i	0.0258603	−	0.0447913i
$124$	−1.69148	+	2.92974i	−0.151900	+	0.263098i
$125$	−11.1858			−1.00049
$126$	−4.34999	+	7.53440i	−0.387528	+	0.671218i
$127$	9.32752	+	16.1557i	0.827684	+	1.43359i	0.899851	+	0.436198i	$0.143675\pi$
$127$	9.32752	+	16.1557i	0.827684	+	1.43359i	−0.0721669	+	0.997393i	$0.522991\pi$
$128$	10.3566	+	17.9381i	0.915400	+	1.58552i
$129$	5.40837			0.476180
$130$	15.0474	+	11.8829i	1.31974	+	1.04220i
$131$	15.1816			1.32642			0.663212	−	0.748431i	$-0.269193\pi$
$131$	15.1816			1.32642			0.663212	+	0.748431i	$0.269193\pi$
$132$	1.83068	+	3.17083i	0.159340	+	0.275985i
$133$	−2.33477	−	4.04394i	−0.202450	−	0.350654i
$134$	15.6588	−	27.1218i	1.35271	−	2.34297i
$135$	−2.23497			−0.192355
$136$	−14.1971	+	24.5901i	−1.21739	+	2.10859i
$137$	4.99951	−	8.65940i	0.427137	−	0.739823i	−0.569480	−	0.822005i	$-0.692856\pi$
$137$	4.99951	−	8.65940i	0.427137	−	0.739823i	0.996617	+	0.0821820i	$0.0261889\pi$
$138$	−3.89068			−0.331196
$139$	−1.13151	+	1.95983i	−0.0959732	+	0.166230i	−0.910014	−	0.414577i	$-0.863930\pi$
$139$	−1.13151	+	1.95983i	−0.0959732	+	0.166230i	0.814041	+	0.580807i	$0.197263\pi$
$140$	−14.9603	−	25.9120i	−1.26438	−	2.18997i
$141$	5.20418	+	9.01391i	0.438271	+	0.759108i
$142$	−11.9753			−1.00494
$143$	2.82963	+	2.23455i	0.236625	+	0.186862i
$144$	2.08283			0.173569
$145$	9.48877	+	16.4350i	0.787999	+	1.36485i
$146$	4.67211	+	8.09233i	0.386667	+	0.669726i
$147$	3.18476	−	5.51616i	0.262674	−	0.454965i
$148$	7.86942			0.646862
$149$	7.69271	−	13.3242i	0.630211	−	1.09156i	−0.357297	−	0.933991i	$-0.616302\pi$
$149$	7.69271	−	13.3242i	0.630211	−	1.09156i	0.987508	−	0.157567i	$-0.0503650\pi$
$150$	−0.00585704	+	0.0101447i	−0.000478226	+	0.000828311i
$151$	4.50994			0.367014			0.183507	−	0.983018i	$-0.441255\pi$
$151$	4.50994			0.367014			0.183507	+	0.983018i	$0.441255\pi$
$152$	−2.52412	+	4.37190i	−0.204733	+	0.354608i
$153$	−3.59151	−	6.22067i	−0.290356	−	0.502912i
$154$	−4.34999	−	7.53440i	−0.350532	−	0.607139i
$155$	2.06503			0.165867
$156$	12.2655	−	4.88153i	0.982027	−	0.390835i
$157$	−1.90197			−0.151794			−0.0758970	−	0.997116i	$-0.524182\pi$
$157$	−1.90197			−0.151794			−0.0758970	+	0.997116i	$0.524182\pi$
$158$	−8.25788	−	14.3031i	−0.656961	−	1.13789i
$159$	−1.40570	−	2.43474i	−0.111479	−	0.193088i
$160$	3.29674	−	5.71012i	0.260630	−	0.451425i
$161$	5.97892			0.471205
$162$	−1.18968	+	2.06059i	−0.0934701	+	0.161895i
$163$	2.44008	−	4.22635i	0.191122	−	0.331033i	−0.754500	−	0.656300i	$-0.772121\pi$
$163$	2.44008	−	4.22635i	0.191122	−	0.331033i	0.945622	+	0.325267i	$0.105454\pi$
$164$	2.10019			0.163997
$165$	1.11748	−	1.93554i	0.0869960	−	0.150681i
$166$	−6.34627	−	10.9921i	−0.492566	−	0.853149i
$167$	−1.20313	−	2.08389i	−0.0931012	−	0.161256i	0.815713	−	0.578456i	$-0.196345\pi$
$167$	−1.20313	−	2.08389i	−0.0931012	−	0.161256i	−0.908815	+	0.417200i	$0.863011\pi$
$168$	−14.4538			−1.11513
$169$	9.44485	−	8.93280i	0.726527	−	0.687138i
$170$	38.1978			2.92964
$171$	−0.638537	−	1.10598i	−0.0488301	−	0.0845763i
$172$	9.90098	+	17.1490i	0.754943	+	1.30760i
$173$	11.0068	−	19.0643i	0.836830	−	1.44943i	−0.0557019	−	0.998447i	$-0.517740\pi$
$173$	11.0068	−	19.0643i	0.836830	−	1.44943i	0.892532	−	0.450984i	$-0.148927\pi$
$174$	20.2036			1.53163
$175$	0.00900069	−	0.0155897i	0.000680388	−	0.00117847i
$176$	−1.04141	+	1.80378i	−0.0784994	+	0.135965i
$177$	13.0110			0.977965
$178$	21.9259	−	37.9768i	1.64342	−	2.84648i
$179$	−2.88230	−	4.99229i	−0.215433	−	0.373141i	0.737973	−	0.674830i	$-0.235783\pi$
$179$	−2.88230	−	4.99229i	−0.215433	−	0.373141i	−0.953407	+	0.301689i	$0.902450\pi$
$180$	−4.09151	−	7.08670i	−0.304963	−	0.528211i
$181$	−10.2279			−0.760237			−0.380119	−	0.924938i	$-0.624117\pi$
$181$	−10.2279			−0.760237			−0.380119	+	0.924938i	$0.624117\pi$
$182$	−29.1448	+	11.5993i	−2.16036	+	0.859798i
$183$	−1.61925			−0.119698
$184$	−3.23190	−	5.59782i	−0.238259	−	0.412677i
$185$	−2.40183	−	4.16009i	−0.176586	−	0.305856i
$186$	1.09922	−	1.90391i	0.0805990	−	0.139601i
$187$	7.18301			0.525274
$188$	−19.0544	+	33.0031i	−1.38968	+	2.40700i
$189$	1.82822	−	3.16657i	0.132983	−	0.230334i
$190$	6.79121			0.492686
$191$	1.79064	−	3.10148i	0.129566	−	0.224415i	−0.793942	−	0.607993i	$-0.791975\pi$
$191$	1.79064	−	3.10148i	0.129566	−	0.224415i	0.923509	+	0.383578i	$0.125308\pi$
$192$	−5.59256	−	9.68659i	−0.403608	−	0.699070i
$193$	−4.61947	−	8.00115i	−0.332517	−	0.575935i	0.650488	−	0.759516i	$-0.274564\pi$
$193$	−4.61947	−	8.00115i	−0.332517	−	0.575935i	−0.983005	+	0.183581i	$0.941231\pi$
$194$	30.5564			2.19382
$195$	−6.32413	−	4.99414i	−0.452880	−	0.357638i
$196$	23.3211			1.66579
$197$	−0.282568	−	0.489423i	−0.0201322	−	0.0348699i	0.855784	−	0.517334i	$-0.173075\pi$
$197$	−0.282568	−	0.489423i	−0.0201322	−	0.0348699i	−0.875916	+	0.482464i	$0.839742\pi$
$198$	−1.18968	−	2.06059i	−0.0845469	−	0.146440i
$199$	−10.0729	+	17.4468i	−0.714050	+	1.23677i	0.249275	+	0.968433i	$0.419808\pi$
$199$	−10.0729	+	17.4468i	−0.714050	+	1.23677i	−0.963325	+	0.268338i	$0.913526\pi$
$200$	−0.0194613			−0.00137612
$201$	−6.58108	+	11.3988i	−0.464194	+	0.804007i
$202$	−14.1141	+	24.4463i	−0.993063	+	1.72004i
$203$	−31.0475			−2.17911
$204$	13.1498	−	22.7761i	0.920670	−	1.59465i
$205$	−0.640999	−	1.11024i	−0.0447693	−	0.0775427i
$206$	16.1184	+	27.9180i	1.12302	+	1.94514i
$207$	1.63518			0.113653
$208$	5.89362	+	4.65417i	0.408649	+	0.322709i
$209$	1.27707			0.0883370
$210$	9.72208	+	16.8391i	0.670887	+	1.16201i
$211$	−4.84987	−	8.40021i	−0.333879	−	0.578295i	0.649390	−	0.760455i	$-0.275024\pi$
$211$	−4.84987	−	8.40021i	−0.333879	−	0.578295i	−0.983269	+	0.182161i	$0.941691\pi$
$212$	5.14677	−	8.91447i	0.353482	−	0.612248i
$213$	5.03297			0.344854
$214$	−15.1178	+	26.1847i	−1.03343	+	1.78995i
$215$	6.04376	−	10.4681i	0.412181	−	0.713918i
$216$	−3.95297			−0.268966
$217$	−1.68921	+	2.92580i	−0.114671	+	0.198616i
$218$	1.57862	+	2.73425i	0.106918	+	0.185187i
$219$	−1.96360	−	3.40105i	−0.132688	−	0.229822i
$220$	8.18301			0.551699
$221$	3.73775	−	25.6276i	0.251428	−	1.72390i
$222$	−5.11400			−0.343229
$223$	1.95672	+	3.38914i	0.131032	+	0.226954i	0.924075	−	0.382212i	$-0.124838\pi$
$223$	1.95672	+	3.38914i	0.131032	+	0.226954i	−0.793043	+	0.609166i	$0.791504\pi$
$224$	5.39351	+	9.34183i	0.360369	+	0.624177i
$225$	0.00246160	−	0.00426362i	0.000164107	−	0.000284241i
$226$	44.2811			2.94554
$227$	−2.40687	+	4.16881i	−0.159749	+	0.276694i	−0.934778	−	0.355232i	$-0.884402\pi$
$227$	−2.40687	+	4.16881i	−0.159749	+	0.276694i	0.775029	+	0.631926i	$0.217735\pi$
$228$	2.33791	−	4.04938i	0.154832	−	0.268177i
$229$	23.6091			1.56014			0.780068	−	0.625694i	$-0.215184\pi$
$229$	23.6091			1.56014			0.780068	+	0.625694i	$0.215184\pi$
$230$	−4.34777	+	7.53055i	−0.286683	+	0.496550i
$231$	1.82822	+	3.16657i	0.120288	+	0.208345i
$232$	16.7827	+	29.0685i	1.10184	+	1.90844i
$233$	−8.86419			−0.580713			−0.290356	−	0.956919i	$-0.593774\pi$
$233$	−8.86419			−0.580713			−0.290356	+	0.956919i	$0.593774\pi$
$234$	−7.97083	+	3.17230i	−0.521070	+	0.207380i
$235$	23.2624			1.51747
$236$	23.8189	+	41.2556i	1.55048	+	2.68551i
$237$	3.47063	+	6.01130i	0.225442	+	0.390476i
$238$	−31.2460	+	54.1197i	−2.02538	+	3.50806i
$239$	7.01633			0.453849			0.226924	−	0.973912i	$-0.427133\pi$
$239$	7.01633			0.453849			0.226924	+	0.973912i	$0.427133\pi$
$240$	2.32752	−	4.03139i	0.150241	−	0.260225i
$241$	3.64941	−	6.32096i	0.235079	−	0.407169i	−0.724217	−	0.689572i	$-0.757798\pi$
$241$	3.64941	−	6.32096i	0.235079	−	0.407169i	0.959296	+	0.282404i	$0.0911318\pi$
$242$	2.37936			0.152951
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.96433	−	5.13437i	−0.189772	−	0.328694i
$245$	−7.11783	−	12.3284i	−0.454741	−	0.787635i
$246$	−1.36482			−0.0870179
$247$	0.664537	−	4.55635i	0.0422835	−	0.289914i
$248$	3.65241			0.231928
$249$	2.66721	+	4.61975i	0.169028	+	0.292765i
$250$	13.3076	+	23.0494i	0.841645	+	1.45777i
$251$	−9.56342	+	16.5643i	−0.603638	+	1.04553i	0.388627	+	0.921395i	$0.372949\pi$
$251$	−9.56342	+	16.5643i	−0.603638	+	1.04553i	−0.992265	+	0.124137i	$0.960384\pi$
$252$	13.3875			0.843334
$253$	−0.817589	+	1.41611i	−0.0514014	+	0.0890298i
$254$	22.1935	−	38.4403i	1.39255	−	2.41196i
$255$	−16.0538			−1.00533
$256$	13.4569	−	23.3080i	0.841056	−	1.45675i
$257$	6.35374	+	11.0050i	0.396335	+	0.686473i	0.993271	−	0.115816i	$-0.0369484\pi$
$257$	6.35374	+	11.0050i	0.396335	+	0.686473i	−0.596935	+	0.802289i	$0.703615\pi$
$258$	−6.43423	−	11.1444i	−0.400577	−	0.693820i
$259$	7.85884			0.488324
$260$	4.25811	−	29.1954i	0.264077	−	1.81062i
$261$	−8.49119			−0.525592
$262$	−18.0613	−	31.2831i	−1.11583	−	1.93267i
$263$	7.11115	+	12.3169i	0.438492	+	0.759491i	0.997573	−	0.0696221i	$-0.0221794\pi$
$263$	7.11115	+	12.3169i	0.438492	+	0.759491i	−0.559081	+	0.829113i	$0.688846\pi$
$264$	1.97648	−	3.42337i	0.121644	−	0.210694i
$265$	−6.28339			−0.385985
$266$	−5.55526	+	9.62199i	−0.340615	+	0.589962i
$267$	−9.21505	+	15.9609i	−0.563952	+	0.976793i
$268$	−48.1914			−2.94376
$269$	−5.39551	+	9.34531i	−0.328970	+	0.569793i	−0.982308	−	0.187273i	$-0.940035\pi$
$269$	−5.39551	+	9.34531i	−0.328970	+	0.569793i	0.653337	+	0.757067i	$0.273368\pi$
$270$	2.65890	+	4.60534i	0.161815	+	0.280272i
$271$	−13.1700	−	22.8111i	−0.800021	−	1.38568i	−0.919602	−	0.392852i	$-0.871488\pi$
$271$	−13.1700	−	22.8111i	−0.800021	−	1.38568i	0.119581	−	0.992824i	$-0.461845\pi$
$272$	14.9610			0.907142
$273$	12.2490	−	4.87497i	0.741344	−	0.295047i
$274$	−23.7913			−1.43728
$275$	0.00246160	+	0.00426362i	0.000148440	+	0.000257106i
$276$	2.99348	+	5.18487i	0.180187	+	0.312092i
$277$	−13.1343	+	22.7493i	−0.789163	+	1.36687i	0.137317	+	0.990527i	$0.456152\pi$
$277$	−13.1343	+	22.7493i	−0.789163	+	1.36687i	−0.926480	+	0.376344i	$0.877181\pi$
$278$	5.38453			0.322943
$279$	−0.461983	+	0.800177i	−0.0276582	+	0.0479054i
$280$	−16.1519	+	27.9758i	−0.965258	+	1.67188i
$281$	9.29179			0.554302			0.277151	−	0.960826i	$-0.410610\pi$
$281$	9.29179			0.554302			0.277151	+	0.960826i	$0.410610\pi$
$282$	12.3826	−	21.4473i	0.737375	−	1.27717i
$283$	15.1644	+	26.2655i	0.901429	+	1.56132i	0.825640	+	0.564197i	$0.190814\pi$
$283$	15.1644	+	26.2655i	0.901429	+	1.56132i	0.0757891	+	0.997124i	$0.475852\pi$
$284$	9.21375	+	15.9587i	0.546736	+	0.946974i
$285$	−2.85422			−0.169069
$286$	1.23812	−	8.48909i	0.0732117	−	0.501971i
$287$	2.09736			0.123803
$288$	1.47507	+	2.55490i	0.0869195	+	0.150549i
$289$	−17.2978	−	29.9607i	−1.01752	−	1.76240i
$290$	22.5772	−	39.1049i	1.32578	−	2.29632i
$291$	−12.8423			−0.752827
$292$	7.18944	−	12.4525i	0.420730	−	0.728726i
$293$	−4.46906	+	7.74065i	−0.261086	+	0.452213i	−0.966531	−	0.256551i	$-0.917414\pi$
$293$	−4.46906	+	7.74065i	−0.261086	+	0.452213i	0.705445	+	0.708765i	$0.250747\pi$
$294$	−15.1554			−0.883879
$295$	14.5396	−	25.1832i	0.846526	−	1.46623i
$296$	−4.24809	−	7.35791i	−0.246915	−	0.427670i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	−36.6075			−2.12061
$299$	4.62695	+	3.65388i	0.267583	+	0.211309i
$300$	0.0180256			0.00104071
$301$	9.88767	+	17.1259i	0.569916	+	0.987123i
$302$	−5.36539	−	9.29313i	−0.308743	−	0.534759i
$303$	5.93188	−	10.2743i	0.340778	−	0.590244i
$304$	2.65992			0.152557
$305$	−1.80949	+	3.13412i	−0.103611	+	0.179459i
$306$	−8.54549	+	14.8012i	−0.488513	+	0.846130i
$307$	−9.17737			−0.523780			−0.261890	−	0.965098i	$-0.584346\pi$
$307$	−9.17737			−0.523780			−0.261890	+	0.965098i	$0.584346\pi$
$308$	−6.69376	+	11.5939i	−0.381412	+	0.660625i
$309$	−6.77427	−	11.7334i	−0.385375	−	0.667489i
$310$	−2.45673	−	4.25518i	−0.139533	−	0.241678i
$311$	−5.91879			−0.335624			−0.167812	−	0.985819i	$-0.553670\pi$
$311$	−5.91879			−0.335624			−0.167812	+	0.985819i	$0.553670\pi$
$312$	−11.1854	−	8.83309i	−0.633251	−	0.500076i
$313$	26.0730			1.47373			0.736865	−	0.676040i	$-0.236305\pi$
$313$	26.0730			1.47373			0.736865	+	0.676040i	$0.236305\pi$
$314$	2.26274	+	3.91918i	0.127694	+	0.221172i
$315$	−4.08601	−	7.07717i	−0.230220	−	0.398753i
$316$	−12.7072	+	22.0095i	−0.714836	+	1.23813i
$317$	−6.35960			−0.357191			−0.178595	−	0.983923i	$-0.557155\pi$
$317$	−6.35960			−0.357191			−0.178595	+	0.983923i	$0.557155\pi$
$318$	−3.34467	+	5.79313i	−0.187560	+	0.324863i
$319$	4.24560	−	7.35359i	0.237708	−	0.411722i
$320$	−24.9984			−1.39745
$321$	6.35370	−	11.0049i	0.354629	−	0.614236i
$322$	−7.11300	−	12.3201i	−0.396392	−	0.686571i
$323$	−4.58662	−	7.94426i	−0.255206	−	0.442030i
$324$	3.66136			0.203409
$325$	0.0164927	−	0.00656390i	0.000914850	−	0.000364100i
$326$	−11.6117			−0.643111
$327$	−0.663464	−	1.14915i	−0.0366896	−	0.0635483i
$328$	−1.13373	−	1.96368i	−0.0625997	−	0.108426i
$329$	−19.0288	+	32.9588i	−1.04909	+	1.81708i
$330$	−5.31779			−0.292735
$331$	5.34938	−	9.26540i	0.294029	−	0.509273i	−0.680730	−	0.732535i	$-0.738337\pi$
$331$	5.34938	−	9.26540i	0.294029	−	0.509273i	0.974758	+	0.223262i	$0.0716706\pi$
$332$	−9.76563	+	16.9146i	−0.535958	+	0.928307i
$333$	2.14932			0.117782
$334$	−2.86269	+	4.95832i	−0.156639	+	0.271307i
$335$	14.7085	+	25.4759i	0.803611	+	1.39190i
$336$	3.80786	+	6.59540i	0.207736	+	0.359809i
$337$	21.0237			1.14524			0.572618	−	0.819823i	$-0.305928\pi$
$337$	21.0237			1.14524			0.572618	+	0.819823i	$0.305928\pi$
$338$	−29.6432	−	8.83476i	−1.61237	−	0.480547i
$339$	−18.6105			−1.01078
$340$	−29.3893	−	50.9038i	−1.59386	−	2.76065i
$341$	−0.461983	−	0.800177i	−0.0250178	−	0.0433320i
$342$	−1.51931	+	2.63152i	−0.0821549	+	0.142296i
$343$	−2.30533			−0.124476
$344$	10.6896	−	18.5148i	0.576342	−	0.998254i
$345$	1.82728	−	3.16495i	0.0983776	−	0.170395i
$346$	−52.3782			−2.81587
$347$	15.1474	−	26.2361i	0.813156	−	1.40843i	−0.0974881	−	0.995237i	$-0.531081\pi$
$347$	15.1474	−	26.2361i	0.813156	−	1.40843i	0.910644	−	0.413191i	$-0.135586\pi$
$348$	−15.5446	−	26.9241i	−0.833280	−	1.44328i
$349$	13.7927	+	23.8897i	0.738308	+	1.27879i	0.953257	+	0.302162i	$0.0977084\pi$
$349$	13.7927	+	23.8897i	0.738308	+	1.27879i	−0.214948	+	0.976625i	$0.568958\pi$
$350$	−0.0428318			−0.00228946
$351$	3.34999	−	1.33326i	0.178809	−	0.0711640i
$352$	−2.95015			−0.157243
$353$	9.96888	+	17.2666i	0.530590	+	0.919009i	0.999363	+	0.0356903i	$0.0113630\pi$
$353$	9.96888	+	17.2666i	0.530590	+	0.919009i	−0.468773	+	0.883319i	$0.655304\pi$
$354$	−15.4789	−	26.8103i	−0.822695	−	1.42495i
$355$	5.62426	−	9.74151i	0.298505	−	0.517026i
$356$	−67.4792			−3.57639
$357$	13.1321	−	22.7455i	0.695025	−	1.20382i
$358$	−6.85803	+	11.8785i	−0.362458	+	0.627796i
$359$	13.5729			0.716349			0.358175	−	0.933655i	$-0.383399\pi$
$359$	13.5729			0.716349			0.358175	+	0.933655i	$0.383399\pi$
$360$	−4.41738	+	7.65112i	−0.232816	+	0.403250i
$361$	8.68454	+	15.0421i	0.457081	+	0.791688i
$362$	12.1680	+	21.0756i	0.639535	+	1.10771i
$363$	−1.00000			−0.0524864
$364$	37.8817	+	29.9150i	1.98554	+	1.56797i
$365$	−8.77716			−0.459417
$366$	1.92639	+	3.33661i	0.100694	+	0.174407i
$367$	−10.4223	−	18.0520i	−0.544041	−	0.942307i	−0.998667	−	0.0516244i	$-0.983560\pi$
$367$	−10.4223	−	18.0520i	−0.544041	−	0.942307i	0.454625	−	0.890683i	$-0.349773\pi$
$368$	−1.70289	+	2.94950i	−0.0887695	+	0.153753i
$369$	0.573609			0.0298609
$370$	−5.71481	+	9.89834i	−0.297099	+	0.514590i
$371$	5.13985	−	8.90248i	0.266848	−	0.462194i
$372$	−3.38297			−0.175399
$373$	1.08367	−	1.87697i	0.0561104	−	0.0971860i	−0.836606	−	0.547805i	$-0.815463\pi$
$373$	1.08367	−	1.87697i	0.0561104	−	0.0971860i	0.892716	+	0.450619i	$0.148797\pi$
$374$	−8.54549	−	14.8012i	−0.441877	−	0.765353i
$375$	−5.59292	−	9.68722i	−0.288817	−	0.500246i
$376$	41.1440			2.12184
$377$	−24.0269	−	18.9740i	−1.23745	−	0.977209i
$378$	−8.69998			−0.447479
$379$	−0.435882	−	0.754970i	−0.0223898	−	0.0387802i	0.854613	−	0.519265i	$-0.173794\pi$
$379$	−0.435882	−	0.754970i	−0.0223898	−	0.0387802i	−0.877003	+	0.480485i	$0.840461\pi$
$380$	−5.22516	−	9.05024i	−0.268045	−	0.464267i
$381$	−9.32752	+	16.1557i	−0.477863	+	0.827684i
$382$	−8.52117			−0.435981
$383$	−16.0014	+	27.7152i	−0.817632	+	1.41618i	0.0897912	+	0.995961i	$0.471380\pi$
$383$	−16.0014	+	27.7152i	−0.817632	+	1.41618i	−0.907423	+	0.420219i	$0.861953\pi$
$384$	−10.3566	+	17.9381i	−0.528506	+	0.915400i
$385$	8.17201			0.416484
$386$	−10.9914	+	19.0376i	−0.559446	+	0.968990i
$387$	2.70418	+	4.68378i	0.137461	+	0.238090i
$388$	−23.5101	−	40.7206i	−1.19354	−	2.06728i
$389$	24.5314			1.24379			0.621895	−	0.783101i	$-0.286363\pi$
$389$	24.5314			1.24379			0.621895	+	0.783101i	$0.286363\pi$
$390$	−2.76716	+	18.9728i	−0.140121	+	0.960727i
$391$	11.7455			0.593995
$392$	−12.5892	−	21.8052i	−0.635853	−	1.10133i
$393$	7.59081	+	13.1477i	0.382906	+	0.663212i
$394$	−0.672332	+	1.16451i	−0.0338716	+	0.0586674i
$395$	15.5135			0.780568
$396$	−1.83068	+	3.17083i	−0.0919951	+	0.159340i
$397$	9.86331	−	17.0838i	0.495025	−	0.857409i	−0.504958	−	0.863144i	$-0.668492\pi$
$397$	9.86331	−	17.0838i	0.495025	−	0.857409i	0.999984	+	0.00573465i	$0.00182541\pi$
$398$	47.9342			2.40272
$399$	2.33477	−	4.04394i	0.116885	−	0.202450i
$400$	0.00512709	+	0.00888038i	0.000256355	+	0.000444019i
$401$	0.0969081	+	0.167850i	0.00483936	+	0.00838202i	0.868435	−	0.495803i	$-0.165126\pi$
$401$	0.0969081	+	0.167850i	0.00483936	+	0.00838202i	−0.863596	+	0.504185i	$0.831793\pi$
$402$	31.3175			1.56198
$403$	−3.09527	+	1.23188i	−0.154187	+	0.0613645i
$404$	43.4375			2.16110
$405$	−1.11748	−	1.93554i	−0.0555282	−	0.0961777i
$406$	36.9366	+	63.9760i	1.83313	+	3.17508i
$407$	−1.07466	+	1.86136i	−0.0532688	+	0.0922644i
$408$	−28.3942			−1.40572
$409$	−14.2571	+	24.6941i	−0.704970	+	1.22104i	0.261732	+	0.965141i	$0.415706\pi$
$409$	−14.2571	+	24.6941i	−0.704970	+	1.22104i	−0.966702	+	0.255904i	$0.917627\pi$
$410$	−1.52517	+	2.64167i	−0.0753226	+	0.130463i
$411$	9.99902			0.493215
$412$	24.8030	−	42.9601i	1.22196	−	2.11649i
$413$	23.7869	+	41.2001i	1.17048	+	2.02733i
$414$	−1.94534	−	3.36942i	−0.0956082	−	0.165598i
$415$	11.9223			0.585241
$416$	−1.53514	+	10.5255i	−0.0752662	+	0.516057i
$417$	−2.26302			−0.110820
$418$	−1.51931	−	2.63152i	−0.0743119	−	0.128712i
$419$	16.3057	+	28.2424i	0.796588	+	1.37973i	0.921826	+	0.387604i	$0.126697\pi$
$419$	16.3057	+	28.2424i	0.796588	+	1.37973i	−0.125238	+	0.992127i	$0.539969\pi$
$420$	14.9603	−	25.9120i	0.729989	−	1.26438i
$421$	−31.2446			−1.52277			−0.761385	−	0.648300i	$-0.775480\pi$
$421$	−31.2446			−1.52277			−0.761385	+	0.648300i	$0.775480\pi$
$422$	−11.5396	+	19.9871i	−0.561738	+	0.972959i
$423$	−5.20418	+	9.01391i	−0.253036	+	0.438271i
$424$	−11.1134			−0.539713
$425$	0.0176817	−	0.0306257i	0.000857690	−	0.00148556i
$426$	−5.98763	−	10.3709i	−0.290102	−	0.502471i
$427$	−2.96034	−	5.12746i	−0.143261	−	0.248135i
$428$	46.5264			2.24894
$429$	−0.520359	+	3.56780i	−0.0251232	+	0.172255i
$430$	−28.7606			−1.38696
$431$	−16.9327	−	29.3283i	−0.815619	−	1.41269i	−0.908883	−	0.417052i	$-0.863063\pi$
$431$	−16.9327	−	29.3283i	−0.815619	−	1.41269i	0.0932639	−	0.995641i	$-0.470270\pi$
$432$	1.04141	+	1.80378i	0.0501050	+	0.0867844i
$433$	2.97703	−	5.15636i	0.143067	−	0.247799i	−0.785583	−	0.618756i	$-0.787637\pi$
$433$	2.97703	−	5.15636i	0.143067	−	0.247799i	0.928650	+	0.370957i	$0.120970\pi$
$434$	8.03848			0.385859
$435$	−9.48877	+	16.4350i	−0.454951	+	0.787999i
$436$	2.42918	−	4.20746i	0.116337	−	0.201501i
$437$	2.08824			0.0998942
$438$	−4.67211	+	8.09233i	−0.223242	+	0.386667i
$439$	8.17340	+	14.1567i	0.390095	+	0.675664i	0.992462	−	0.122555i	$-0.0391088\pi$
$439$	8.17340	+	14.1567i	0.390095	+	0.675664i	−0.602367	+	0.798220i	$0.705775\pi$
$440$	−4.41738	−	7.65112i	−0.210590	−	0.364753i
$441$	6.36951			0.303310
$442$	−57.2546	+	22.7867i	−2.72332	+	1.08385i
$443$	5.58072			0.265148			0.132574	−	0.991173i	$-0.457676\pi$
$443$	5.58072			0.265148			0.132574	+	0.991173i	$0.457676\pi$
$444$	3.93471	+	6.81512i	0.186733	+	0.323431i
$445$	20.5953	+	35.6722i	0.976312	+	1.69102i
$446$	4.65574	−	8.06399i	0.220456	−	0.381841i
$447$	15.3854			0.727705
$448$	20.4488	−	35.4184i	0.966116	−	1.67336i
$449$	7.65620	−	13.2609i	0.361318	−	0.625822i	−0.626860	−	0.779132i	$-0.715660\pi$
$449$	7.65620	−	13.2609i	0.361318	−	0.625822i	0.988178	+	0.153311i	$0.0489935\pi$
$450$	−0.0117141			−0.000552207
$451$	−0.286804	+	0.496760i	−0.0135051	+	0.0233915i
$452$	−34.0699	−	59.0108i	−1.60251	−	2.77563i
$453$	2.25497	+	3.90572i	0.105948	+	0.183507i
$454$	11.4536			0.537544
$455$	4.25238	−	29.1561i	0.199355	−	1.36686i
$456$	−5.04823			−0.236405
$457$	−3.24942	−	5.62816i	−0.152001	−	0.263274i	0.779962	−	0.625827i	$-0.215238\pi$
$457$	−3.24942	−	5.62816i	−0.152001	−	0.263274i	−0.931963	+	0.362553i	$0.881905\pi$
$458$	−28.0873	−	48.6487i	−1.31244	−	2.27320i
$459$	3.59151	−	6.22067i	0.167637	−	0.290356i
$460$	13.3807			0.623877
$461$	14.4575	−	25.0412i	0.673354	−	1.16628i	−0.303593	−	0.952802i	$-0.598186\pi$
$461$	14.4575	−	25.0412i	0.673354	−	1.16628i	0.976947	−	0.213481i	$-0.0684802\pi$
$462$	4.34999	−	7.53440i	0.202380	−	0.350532i
$463$	3.57061			0.165940			0.0829701	−	0.996552i	$-0.473559\pi$
$463$	3.57061			0.165940			0.0829701	+	0.996552i	$0.473559\pi$
$464$	8.84284	−	15.3162i	0.410518	−	0.711039i
$465$	1.03252	+	1.78837i	0.0478818	+	0.0829337i
$466$	10.5456	+	18.2654i	0.488513	+	0.846130i
$467$	−28.8673			−1.33582			−0.667909	−	0.744243i	$-0.732810\pi$
$467$	−28.8673			−1.33582			−0.667909	+	0.744243i	$0.732810\pi$
$468$	10.3603	+	8.18147i	0.478904	+	0.378189i
$469$	−48.1266			−2.22228
$470$	−27.6748	−	47.9341i	−1.27654	−	2.21104i
$471$	−0.950986	−	1.64716i	−0.0438191	−	0.0758970i
$472$	25.7160	−	44.5414i	1.18368	−	2.05019i
$473$	−5.40837			−0.248677
$474$	8.25788	−	14.3031i	0.379297	−	0.656961i
$475$	0.00314365	−	0.00544496i	0.000144241	−	0.000249832i
$476$	96.1627			4.40761
$477$	1.40570	−	2.43474i	0.0643626	−	0.111479i
$478$	−8.34720	−	14.4578i	−0.381792	−	0.661283i
$479$	−10.9444	−	18.9563i	−0.500064	−	0.866136i	−1.00000		7.39087e-5i	$-0.999976\pi$
$479$	−10.9444	−	18.9563i	−0.500064	−	0.866136i	0.499936	−	0.866062i	$-0.333357\pi$
$480$	6.59348			0.300950
$481$	6.08177	+	4.80275i	0.277305	+	0.218987i
$482$	−17.3665			−0.791023
$483$	2.98946	+	5.17790i	0.136025	+	0.235602i
$484$	−1.83068	−	3.17083i	−0.0832127	−	0.144129i
$485$	−14.3510	+	24.8567i	−0.651647	+	1.12868i
$486$	−2.37936			−0.107930
$487$	−12.2160	+	21.1588i	−0.553561	+	0.958797i	0.444452	+	0.895802i	$0.353398\pi$
$487$	−12.2160	+	21.1588i	−0.553561	+	0.958797i	−0.998014	+	0.0629941i	$0.979935\pi$
$488$	−3.20042	+	5.54330i	−0.144876	+	0.250933i
$489$	4.88017			0.220689
$490$	−16.9359	+	29.3338i	−0.765085	+	1.32517i
$491$	−0.603068	−	1.04454i	−0.0272161	−	0.0471396i	0.852097	−	0.523385i	$-0.175331\pi$
$491$	−0.603068	−	1.04454i	−0.0272161	−	0.0471396i	−0.879313	+	0.476245i	$0.841998\pi$
$492$	1.05009	+	1.81882i	0.0473419	+	0.0819986i
$493$	−60.9923			−2.74696
$494$	−10.1793	+	4.05126i	−0.457990	+	0.182275i
$495$	2.23497			0.100454
$496$	−0.962229	−	1.66663i	−0.0432054	−	0.0748339i
$497$	9.20137	+	15.9372i	0.412738	+	0.714883i
$498$	6.34627	−	10.9921i	0.284383	−	0.492566i
$499$	23.3819			1.04672			0.523358	−	0.852113i	$-0.324679\pi$
$499$	23.3819			1.04672			0.523358	+	0.852113i	$0.324679\pi$
$500$	20.4777	−	35.4684i	0.915790	−	1.58619i
$501$	1.20313	−	2.08389i	0.0537520	−	0.0931012i
$502$	45.5097			2.03120
$503$	11.7711	−	20.3882i	0.524849	−	0.909064i	−0.474733	−	0.880130i	$-0.657455\pi$
$503$	11.7711	−	20.3882i	0.524849	−	0.909064i	0.999581	−	0.0289343i	$-0.00921136\pi$
$504$	−7.22689	−	12.5173i	−0.321911	−	0.557567i
$505$	−13.2576	−	22.9628i	−0.589954	−	1.02183i
$506$	3.89068			0.172962
$507$	12.4585	+	3.71308i	0.553299	+	0.164904i
$508$	−68.3028			−3.03045
$509$	12.5251	+	21.6942i	0.555167	+	0.961577i	0.997891	+	0.0649189i	$0.0206789\pi$
$509$	12.5251	+	21.6942i	0.555167	+	0.961577i	−0.442724	+	0.896658i	$0.645988\pi$
$510$	19.0989	+	33.0802i	0.845713	+	1.46482i
$511$	7.17977	−	12.4357i	0.317614	−	0.550124i
$512$	−22.6113			−0.999289
$513$	0.638537	−	1.10598i	0.0281921	−	0.0488301i
$514$	15.1178	−	26.1849i	0.666819	−	1.15496i
$515$	−30.2806			−1.33432
$516$	−9.90098	+	17.1490i	−0.435866	+	0.754943i
$517$	−5.20418	−	9.01391i	−0.228880	−	0.396431i
$518$	−9.34951	−	16.1938i	−0.410794	−	0.711516i
$519$	22.0136			0.966288
$520$	−29.5963	+	11.7790i	−1.29789	+	0.516544i
$521$	16.6826			0.730879			0.365439	−	0.930835i	$-0.380919\pi$
$521$	16.6826			0.730879			0.365439	+	0.930835i	$0.380919\pi$
$522$	10.1018	+	17.4968i	0.442144	+	0.765816i
$523$	9.00452	+	15.5963i	0.393740	+	0.681978i	0.992940	−	0.118622i	$-0.0378476\pi$
$523$	9.00452	+	15.5963i	0.393740	+	0.681978i	−0.599199	+	0.800600i	$0.704514\pi$
$524$	−27.7927	+	48.1383i	−1.21413	+	2.10293i
$525$	0.0180014			0.000785645
$526$	16.9200	−	29.3063i	0.737747	−	1.27781i
$527$	−3.31843	+	5.74768i	−0.144553	+	0.250373i
$528$	−2.08283			−0.0906434
$529$	10.1631	−	17.6030i	0.441874	−	0.765348i
$530$	7.47522	+	12.9475i	0.324703	+	0.562402i
$531$	6.50549	+	11.2678i	0.282314	+	0.488983i
$532$	17.0968			0.741242
$533$	1.62310	+	1.28176i	0.0703043	+	0.0555190i
$534$	43.8519			1.89766
$535$	−14.2003	−	24.5957i	−0.613933	−	1.06336i
$536$	26.0148	+	45.0590i	1.12367	+	1.94625i
$537$	2.88230	−	4.99229i	0.124380	−	0.215433i
$538$	25.6758			1.10696
$539$	−3.18476	+	5.51616i	−0.137177	+	0.237598i
$540$	4.09151	−	7.08670i	0.176070	−	0.304963i
$541$	4.66401			0.200521			0.100261	−	0.994961i	$-0.468032\pi$
$541$	4.66401			0.200521			0.100261	+	0.994961i	$0.468032\pi$
$542$	−31.3362	+	54.2759i	−1.34600	+	2.33135i
$543$	−5.11397	−	8.85766i	−0.219462	−	0.380119i
$544$	10.5955	+	18.3519i	0.454277	+	0.786831i
$545$	−2.96564			−0.127034
$546$	−24.6177	−	19.4405i	−1.05354	−	0.831977i
$547$	22.0014			0.940713			0.470357	−	0.882476i	$-0.344125\pi$
$547$	22.0014			0.940713			0.470357	+	0.882476i	$0.344125\pi$
$548$	18.3050	+	31.7052i	0.781951	+	1.35438i
$549$	−0.809625	−	1.40231i	−0.0345540	−	0.0598492i
$550$	0.00585704	−	0.0101447i	0.000249745	−	0.000432571i
$551$	−10.8439			−0.461965
$552$	3.23190	−	5.59782i	0.137559	−	0.238259i
$553$	−12.6901	+	21.9799i	−0.539639	+	0.934682i
$554$	62.5025			2.65547
$555$	2.40183	−	4.16009i	0.101952	−	0.176586i
$556$	−4.14285	−	7.17563i	−0.175696	−	0.304315i
$557$	−16.0907	−	27.8700i	−0.681787	−	1.18089i	−0.974435	−	0.224669i	$-0.927870\pi$
$557$	−16.0907	−	27.8700i	−0.681787	−	1.18089i	0.292648	−	0.956220i	$-0.405464\pi$
$558$	2.19845			0.0930677
$559$	−2.81429	+	19.2960i	−0.119032	+	0.816133i
$560$	17.0209			0.719263
$561$	3.59151	+	6.22067i	0.151634	+	0.262637i
$562$	−11.0543	−	19.1465i	−0.466296	−	0.807648i
$563$	5.45167	−	9.44258i	0.229761	−	0.397957i	−0.727976	−	0.685602i	$-0.759539\pi$
$563$	5.45167	−	9.44258i	0.229761	−	0.397957i	0.957737	+	0.287645i	$0.0928723\pi$
$564$	−38.1088			−1.60467
$565$	−20.7970	+	36.0214i	−0.874934	+	1.51543i
$566$	36.0815	−	62.4951i	1.51662	−	2.62686i
$567$	3.65643			0.153556
$568$	9.94759	−	17.2297i	0.417392	−	0.722944i
$569$	13.6577	+	23.6558i	0.572559	+	0.991702i	0.996302	+	0.0859191i	$0.0273827\pi$
$569$	13.6577	+	23.6558i	0.572559	+	0.991702i	−0.423743	+	0.905782i	$0.639284\pi$
$570$	3.39561	+	5.88136i	0.142226	+	0.246343i
$571$	15.0890			0.631454			0.315727	−	0.948850i	$-0.397752\pi$
$571$	15.0890			0.631454			0.315727	+	0.948850i	$0.397752\pi$
$572$	−12.2655	+	4.88153i	−0.512847	+	0.204107i
$573$	3.58128			0.149610
$574$	−2.49519	−	4.32180i	−0.104147	−	0.180388i
$575$	0.00402516	+	0.00697178i	0.000167861	+	0.000290743i
$576$	5.59256	−	9.68659i	0.233023	−	0.403608i
$577$	40.5659			1.68878			0.844389	−	0.535730i	$-0.179964\pi$
$577$	40.5659			1.68878			0.844389	+	0.535730i	$0.179964\pi$
$578$	−41.1578	+	71.2874i	−1.71194	+	2.96517i
$579$	4.61947	−	8.00115i	0.191978	−	0.332517i
$580$	−69.4835			−2.88515
$581$	−9.75250	+	16.8918i	−0.404602	+	0.700791i
$582$	15.2782	+	26.4626i	0.633302	+	1.09691i
$583$	1.40570	+	2.43474i	0.0582181	+	0.100837i
$584$	−15.5241			−0.642391
$585$	1.16299	−	7.97392i	0.0480835	−	0.329681i
$586$	21.2670			0.878533
$587$	−12.0261	−	20.8298i	−0.496370	−	0.859737i	0.503622	−	0.863924i	$-0.332001\pi$
$587$	−12.0261	−	20.8298i	−0.496370	−	0.859737i	−0.999991	+	0.00418707i	$0.998667\pi$
$588$	11.6605	+	20.1966i	0.480872	+	0.832895i
$589$	−0.589986	+	1.02189i	−0.0243099	+	0.0421061i
$590$	−69.1897			−2.84849
$591$	0.282568	−	0.489423i	0.0116233	−	0.0201322i
$592$	−2.23833	+	3.87690i	−0.0919947	+	0.159339i
$593$	−34.7667			−1.42770			−0.713848	−	0.700300i	$-0.753049\pi$
$593$	−34.7667			−1.42770			−0.713848	+	0.700300i	$0.753049\pi$
$594$	1.18968	−	2.06059i	0.0488132	−	0.0845469i
$595$	−29.3498	−	50.8354i	−1.20323	−	2.08405i
$596$	28.1658	+	48.7845i	1.15371	+	1.99829i
$597$	−20.1458			−0.824514
$598$	2.02455	−	13.8812i	0.0827900	−	0.567643i
$599$	−20.2237			−0.826319			−0.413159	−	0.910659i	$-0.635575\pi$
$599$	−20.2237			−0.826319			−0.413159	+	0.910659i	$0.635575\pi$
$600$	−0.00973064	−	0.0168540i	−0.000397252	−	0.000688060i
$601$	1.54148	+	2.66993i	0.0628785	+	0.108909i	0.895751	−	0.444556i	$-0.146639\pi$
$601$	1.54148	+	2.66993i	0.0628785	+	0.108909i	−0.832872	+	0.553465i	$0.813305\pi$
$602$	23.5263	−	40.7488i	0.958862	−	1.66080i
$603$	−13.1622			−0.536005
$604$	−8.25625	+	14.3003i	−0.335942	+	0.581869i
$605$	−1.11748	+	1.93554i	−0.0454322	+	0.0786908i
$606$	−28.2282			−1.14669
$607$	3.67413	−	6.36378i	0.149128	−	0.258298i	−0.781777	−	0.623558i	$-0.785687\pi$
$607$	3.67413	−	6.36378i	0.149128	−	0.258298i	0.930906	+	0.365260i	$0.119020\pi$
$608$	1.88378	+	3.26280i	0.0763972	+	0.132324i
$609$	−15.5237	−	26.8879i	−0.629054	−	1.08955i
$610$	8.61084			0.348643
$611$	−34.8679	+	13.8770i	−1.41060	+	0.561405i
$612$	26.2996			1.06310
$613$	15.7461	+	27.2730i	0.635979	+	1.10155i	0.986307	+	0.164921i	$0.0527368\pi$
$613$	15.7461	+	27.2730i	0.635979	+	1.10155i	−0.350328	+	0.936627i	$0.613930\pi$
$614$	10.9181	+	18.9108i	0.440620	+	0.763176i
$615$	0.640999	−	1.11024i	0.0258476	−	0.0447693i
$616$	14.4538			0.582359
$617$	−3.54892	+	6.14691i	−0.142874	+	0.247465i	−0.928578	−	0.371138i	$-0.878968\pi$
$617$	−3.54892	+	6.14691i	−0.142874	+	0.247465i	0.785704	+	0.618603i	$0.212301\pi$
$618$	−16.1184	+	27.9180i	−0.648379	+	1.12302i
$619$	13.2229			0.531472			0.265736	−	0.964046i	$-0.414385\pi$
$619$	13.2229			0.531472			0.265736	+	0.964046i	$0.414385\pi$
$620$	−3.78041	+	6.54786i	−0.151825	+	0.262968i
$621$	0.817589	+	1.41611i	0.0328087	+	0.0568263i
$622$	7.04146	+	12.1962i	0.282337	+	0.489022i
$623$	−67.3885			−2.69986
$624$	−1.08382	+	7.43111i	−0.0433874	+	0.297483i
$625$	−24.9754			−0.999014
$626$	−31.0185	−	53.7256i	−1.23975	−	2.14731i
$627$	0.638537	+	1.10598i	0.0255007	+	0.0441685i
$628$	3.48190	−	6.03083i	0.138943	−	0.240656i
$629$	15.4386			0.615576
$630$	−9.72208	+	16.8391i	−0.387337	+	0.670887i
$631$	15.7893	−	27.3478i	0.628561	−	1.08870i	−0.359280	−	0.933230i	$-0.616978\pi$
$631$	15.7893	−	27.3478i	0.628561	−	1.08870i	0.987841	−	0.155469i	$-0.0496889\pi$
$632$	27.4386			1.09145
$633$	4.84987	−	8.40021i	0.192765	−	0.333879i
$634$	7.56589	+	13.1045i	0.300480	+	0.520446i
$635$	20.8467	+	36.1076i	0.827276	+	1.43288i
$636$	10.2935			0.408165
$637$	18.0234	+	14.2330i	0.714112	+	0.563931i
$638$	−20.2036			−0.799868
$639$	2.51649	+	4.35868i	0.0995506	+	0.172427i
$640$	23.1466	+	40.0910i	0.914949	+	1.58474i
$641$	15.4523	−	26.7641i	0.610328	−	1.05712i	−0.380857	−	0.924634i	$-0.624371\pi$
$641$	15.4523	−	26.7641i	0.610328	−	1.05712i	0.991185	−	0.132485i	$-0.0422956\pi$
$642$	−30.2355			−1.19330
$643$	14.7141	−	25.4855i	0.580267	−	1.00505i	−0.415181	−	0.909739i	$-0.636282\pi$
$643$	14.7141	−	25.4855i	0.580267	−	1.00505i	0.995447	−	0.0953125i	$-0.0303850\pi$
$644$	−10.9455	+	18.9581i	−0.431312	+	0.747055i
$645$	12.0875			0.475946
$646$	−10.9132	+	18.9023i	−0.429375	+	0.743699i
$647$	6.55195	+	11.3483i	0.257584	+	0.446148i	0.965594	−	0.260054i	$-0.0837403\pi$
$647$	6.55195	+	11.3483i	0.257584	+	0.446148i	−0.708010	+	0.706202i	$0.750407\pi$
$648$	−1.97648	−	3.42337i	−0.0776437	−	0.134483i
$649$	−13.0110			−0.510726
$650$	−0.0331465	−	0.0261757i	−0.00130011	−	0.00102669i
$651$	−3.37842			−0.132411
$652$	8.93402	+	15.4742i	0.349883	+	0.606015i
$653$	−12.4894	−	21.6323i	−0.488749	−	0.846538i	0.511167	−	0.859481i	$-0.329213\pi$
$653$	−12.4894	−	21.6323i	−0.488749	−	0.846538i	−0.999916	+	0.0129433i	$0.995880\pi$
$654$	−1.57862	+	2.73425i	−0.0617289	+	0.106918i
$655$	33.9304			1.32577
$656$	−0.597364	+	1.03466i	−0.0233231	+	0.0403969i
$657$	1.96360	−	3.40105i	0.0766073	−	0.132688i
$658$	90.5525			3.53011
$659$	−16.1276	+	27.9338i	−0.628241	+	1.08814i	0.359664	+	0.933082i	$0.382891\pi$
$659$	−16.1276	+	27.9338i	−0.628241	+	1.08814i	−0.987905	+	0.155063i	$0.950442\pi$
$660$	4.09151	+	7.08670i	0.159262	+	0.275849i
$661$	9.03796	+	15.6542i	0.351536	+	0.608878i	0.986519	−	0.163648i	$-0.0523262\pi$
$661$	9.03796	+	15.6542i	0.351536	+	0.608878i	−0.634983	+	0.772526i	$0.718993\pi$
$662$	−25.4562			−0.989384
$663$	24.0630	−	9.57681i	0.934530	−	0.371932i
$664$	21.0868			0.818328
$665$	−5.21813	−	9.03807i	−0.202350	−	0.350481i
$666$	−2.55700	−	4.42885i	−0.0990818	−	0.171615i
$667$	6.94230	−	12.0244i	0.268807	−	0.465587i
$668$	8.81020			0.340877
$669$	−1.95672	+	3.38914i	−0.0756512	+	0.131032i
$670$	34.9968	−	60.6163i	1.35205	−	2.34181i
$671$	1.61925			0.0625105
$672$	−5.39351	+	9.34183i	−0.208059	+	0.360369i
$673$	13.1859	+	22.8386i	0.508279	+	0.880365i	0.999954	+	0.00958617i	$0.00305142\pi$
$673$	13.1859	+	22.8386i	0.508279	+	0.880365i	−0.491675	+	0.870779i	$0.663615\pi$
$674$	−25.0115	−	43.3212i	−0.963407	−	1.66867i
$675$	0.00492321			0.000189494
$676$	11.0339	+	46.3011i	0.424380	+	1.78081i
$677$	−19.2610			−0.740261			−0.370131	−	0.928980i	$-0.620687\pi$
$677$	−19.2610			−0.740261			−0.370131	+	0.928980i	$0.620687\pi$
$678$	22.1406	+	38.3486i	0.850304	+	1.47277i
$679$	−23.4785	−	40.6659i	−0.901021	−	1.56061i
$680$	−31.7301	+	54.9581i	−1.21679	+	2.10755i
$681$	−4.81373			−0.184463
$682$	−1.09922	+	1.90391i	−0.0420914	+	0.0729045i
$683$	13.4492	−	23.2947i	0.514619	−	0.891347i	−0.485237	−	0.874383i	$-0.661267\pi$
$683$	13.4492	−	23.2947i	0.514619	−	0.891347i	0.999856	−	0.0169641i	$-0.00540009\pi$
$684$	4.67582			0.178785
$685$	11.1737	−	19.3535i	0.426927	−	0.739459i
$686$	2.74261	+	4.75033i	0.104713	+	0.181369i
$687$	11.8046	+	20.4461i	0.450373	+	0.780068i
$688$	−11.2647			−0.429462
$689$	9.41816	−	3.74832i	0.358803	−	0.142800i
$690$	−8.69553			−0.331033
$691$	5.23026	+	9.05908i	0.198968	+	0.344623i	0.948194	−	0.317691i	$-0.102908\pi$
$691$	5.23026	+	9.05908i	0.198968	+	0.344623i	−0.749226	+	0.662315i	$0.769574\pi$
$692$	40.2998	+	69.8012i	1.53197	+	2.65344i
$693$	−1.82822	+	3.16657i	−0.0694482	+	0.120288i
$694$	−72.0824			−2.73621
$695$	−2.52888	+	4.38015i	−0.0959260	+	0.166149i
$696$	−16.7827	+	29.0685i	−0.636147	+	1.10184i
$697$	4.12024			0.156065
$698$	32.8179	−	56.8423i	1.24218	−	2.15151i
$699$	−4.43210	−	7.67662i	−0.167637	−	0.290356i
$700$	0.0329548	+	0.0570793i	0.00124557	+	0.00215740i
$701$	−44.0438			−1.66351			−0.831756	−	0.555142i	$-0.812664\pi$
$701$	−44.0438			−1.66351			−0.831756	+	0.555142i	$0.812664\pi$
$702$	−6.73271	−	5.31679i	−0.254110	−	0.200669i
$703$	2.74484			0.103523
$704$	5.59256	+	9.68659i	0.210777	+	0.365077i
$705$	11.6312	+	20.1458i	0.438055	+	0.758734i
$706$	23.7196	−	41.0835i	0.892698	−	1.54620i
$707$	43.3791			1.63144
$708$	−23.8189	+	41.2556i	−0.895170	+	1.55048i
$709$	−9.85545	+	17.0701i	−0.370129	+	0.641083i	−0.989585	−	0.143949i	$-0.954020\pi$
$709$	−9.85545	+	17.0701i	−0.370129	+	0.641083i	0.619456	+	0.785032i	$0.287353\pi$
$710$	−26.7643			−1.00445
$711$	−3.47063	+	6.01130i	−0.130159	+	0.225442i
$712$	36.4268	+	63.0931i	1.36515	+	2.36451i
$713$	−0.755423	−	1.30843i	−0.0282908	−	0.0490012i
$714$	−62.4921			−2.33871
$715$	6.32413	+	4.99414i	0.236509	+	0.186770i
$716$	21.1063			0.788778
$717$	3.50817	+	6.07632i	0.131015	+	0.226924i
$718$	−16.1474	−	27.9681i	−0.602615	−	1.04376i
$719$	−7.75162	+	13.4262i	−0.289087	+	0.500713i	−0.973592	−	0.228295i	$-0.926685\pi$
$719$	−7.75162	+	13.4262i	−0.289087	+	0.500713i	0.684505	+	0.729008i	$0.260018\pi$
$720$	4.65505			0.173483
$721$	24.7697	−	42.9024i	0.922471	−	1.59777i
$722$	20.6637	−	35.7905i	0.769022	−	1.33198i
$723$	7.29881			0.271446
$724$	18.7241	−	32.4311i	0.695875	−	1.20529i
$725$	−0.0209019	−	0.0362032i	−0.000776279	−	0.00134455i
$726$	1.18968	+	2.06059i	0.0441532	+	0.0764756i
$727$	−29.7007			−1.10154			−0.550769	−	0.834658i	$-0.685665\pi$
$727$	−29.7007			−1.10154			−0.550769	+	0.834658i	$0.685665\pi$
$728$	7.52116	−	51.5682i	0.278753	−	1.91125i
$729$	1.00000			0.0370370
$730$	10.4420	+	18.0861i	0.386476	+	0.669396i
$731$	19.4242	+	33.6437i	0.718429	+	1.24436i
$732$	2.96433	−	5.13437i	0.109565	−	0.189772i
$733$	−35.4792			−1.31045			−0.655227	−	0.755432i	$-0.727427\pi$
$733$	−35.4792			−1.31045			−0.655227	+	0.755432i	$0.727427\pi$
$734$	−24.7985	+	42.9522i	−0.915329	+	1.58540i
$735$	7.11783	−	12.3284i	0.262545	−	0.454741i
$736$	−4.82401			−0.177815
$737$	6.58108	−	11.3988i	0.242417	−	0.419879i
$738$	−0.682411	−	1.18197i	−0.0251199	−	0.0435090i
$739$	−16.4147	−	28.4311i	−0.603824	−	1.04585i	−0.992236	−	0.124368i	$-0.960310\pi$
$739$	−16.4147	−	28.4311i	−0.603824	−	1.04585i	0.388413	−	0.921486i	$-0.373024\pi$
$740$	17.5879			0.646544
$741$	4.27818	−	1.70267i	0.157163	−	0.0625491i
$742$	−24.4591			−0.897922
$743$	−14.0038	−	24.2554i	−0.513751	−	0.889843i	−0.999873	−	0.0159517i	$-0.994922\pi$
$743$	−14.0038	−	24.2554i	−0.513751	−	0.889843i	0.486122	−	0.873891i	$-0.338411\pi$
$744$	1.82620	+	3.16308i	0.0669519	+	0.115964i
$745$	17.1929	−	29.7791i	0.629901	−	1.09102i
$746$	−5.15689			−0.188807
$747$	−2.66721	+	4.61975i	−0.0975883	+	0.169028i
$748$	−13.1498	+	22.7761i	−0.480804	+	0.832777i
$749$	46.4638			1.69775
$750$	−13.3076	+	23.0494i	−0.485924	+	0.841645i
$751$	−3.36812	−	5.83376i	−0.122905	−	0.212877i	0.798007	−	0.602648i	$-0.205888\pi$
$751$	−3.36812	−	5.83376i	−0.122905	−	0.212877i	−0.920912	+	0.389771i	$0.872554\pi$
$752$	−10.8394	−	18.7744i	−0.395272	−	0.684632i
$753$	−19.1268			−0.697021
$754$	−10.5131	+	72.0825i	−0.382866	+	2.62509i
$755$	10.0796			0.366833
$756$	6.69376	+	11.5939i	0.243450	+	0.421667i
$757$	16.1033	+	27.8917i	0.585284	+	1.01374i	0.994840	+	0.101457i	$0.0323503\pi$
$757$	16.1033	+	27.8917i	0.585284	+	1.01374i	−0.409556	+	0.912285i	$0.634316\pi$
$758$	−1.03712	+	1.79635i	−0.0376699	+	0.0652462i
$759$	−1.63518			−0.0593532
$760$	−5.64132	+	9.77105i	−0.204632	+	0.354433i
$761$	−13.8524	+	23.9930i	−0.502148	+	0.869745i	0.497849	+	0.867264i	$0.334123\pi$
$761$	−13.8524	+	23.9930i	−0.502148	+	0.869745i	−0.999997	+	0.00248160i	$0.999210\pi$
$762$	44.3871			1.60797
$763$	2.42591	−	4.20180i	0.0878239	−	0.152116i
$764$	6.55618	+	11.3556i	0.237194	+	0.410833i
$765$	−8.02690	−	13.9030i	−0.290213	−	0.502664i
$766$	76.1460			2.75127
$767$	−6.77038	+	46.4206i	−0.244464	+	1.67615i
$768$	26.9138			0.971167
$769$	−3.47736	−	6.02297i	−0.125397	−	0.217194i	0.796491	−	0.604650i	$-0.206687\pi$
$769$	−3.47736	−	6.02297i	−0.125397	−	0.217194i	−0.921888	+	0.387456i	$0.873354\pi$
$770$	−9.72208	−	16.8391i	−0.350359	−	0.606840i
$771$	−6.35374	+	11.0050i	−0.228824	+	0.396335i
$772$	33.8270			1.21746
$773$	14.0463	−	24.3290i	0.505211	−	0.875052i	−0.494770	−	0.869024i	$-0.664748\pi$
$773$	14.0463	−	24.3290i	0.505211	−	0.875052i	0.999982	−	0.00602810i	$-0.00191882\pi$
$774$	6.43423	−	11.1444i	0.231273	−	0.400577i
$775$	−0.00454887			−0.000163400
$776$	−25.3826	+	43.9639i	−0.911181	+	1.57821i
$777$	3.92942	+	6.80595i	0.140967	+	0.244162i
$778$	−29.1845	−	50.5490i	−1.04631	−	1.81227i
$779$	0.732541			0.0262460
$780$	27.4130	−	10.9101i	0.981543	−	0.390643i
$781$	−5.03297			−0.180094
$782$	−13.9734	−	24.2026i	−0.499687	−	0.865484i
$783$	−4.24560	−	7.35359i	−0.151725	−	0.262796i
$784$	−6.63329	+	11.4892i	−0.236903	+	0.410329i
$785$	−4.25085			−0.151719
$786$	18.0613	−	31.2831i	0.644225	−	1.11583i
$787$	−9.37818	+	16.2435i	−0.334296	+	0.579017i	−0.983349	−	0.181725i	$-0.941832\pi$
$787$	−9.37818	+	16.2435i	−0.334296	+	0.579017i	0.649053	+	0.760743i	$0.275165\pi$
$788$	2.06917			0.0737111
$789$	−7.11115	+	12.3169i	−0.253164	+	0.438492i
$790$	−18.4561	−	31.9669i	−0.656638	−	1.13733i
$791$	−34.0241	−	58.9314i	−1.20976	−	2.09536i
$792$	3.95297			0.140463
$793$	0.842592	−	5.77717i	0.0299213	−	0.205153i
$794$	−46.9368			−1.66572
$795$	−3.14169	−	5.44157i	−0.111424	−	0.192993i
$796$	−36.8805	−	63.8790i	−1.30720	−	2.26413i
$797$	14.3023	−	24.7723i	0.506614	−	0.877481i	−0.493357	−	0.869827i	$-0.664230\pi$
$797$	14.3023	−	24.7723i	0.506614	−	0.877481i	0.999971	−	0.00765416i	$-0.00243642\pi$
$798$	−11.1105			−0.393308
$799$	−37.3817	+	64.7470i	−1.32247	+	2.29059i
$800$	−0.00726209	+	0.0125783i	−0.000256754	+	0.000444710i
$801$	−18.4301			−0.651196
$802$	0.230579	−	0.399375i	0.00814204	−	0.0141024i
$803$	1.96360	+	3.40105i	0.0692939	+	0.120021i
$804$	−24.0957	−	41.7350i	−0.849790	−	1.47188i
$805$	13.3627			0.470973
$806$	6.22079	+	4.91253i	0.219118	+	0.173037i
$807$	−10.7910			−0.379862
$808$	−23.4485	−	40.6141i	−0.824917	−	1.42880i
$809$	1.39912	+	2.42334i	0.0491904	+	0.0852002i	0.889572	−	0.456795i	$-0.151003\pi$
$809$	1.39912	+	2.42334i	0.0491904	+	0.0852002i	−0.840382	+	0.541995i	$0.817669\pi$
$810$	−2.65890	+	4.60534i	−0.0934241	+	0.161815i
$811$	−2.03472			−0.0714488			−0.0357244	−	0.999362i	$-0.511374\pi$
$811$	−2.03472			−0.0714488			−0.0357244	+	0.999362i	$0.511374\pi$
$812$	56.8380	−	98.4463i	1.99462	−	3.45479i
$813$	13.1700	−	22.8111i	0.461892	−	0.800021i
$814$	5.11400			0.179246
$815$	5.45351	−	9.44575i	0.191028	−	0.330870i
$816$	7.48048	+	12.9566i	0.261869	+	0.453571i
$817$	3.45344	+	5.98154i	0.120821	+	0.209267i
$818$	67.8458			2.37217
$819$	10.3464	+	8.17047i	0.361531	+	0.285499i
$820$	4.69385			0.163916
$821$	8.84612	+	15.3219i	0.308732	+	0.534739i	0.978085	−	0.208205i	$-0.0667622\pi$
$821$	8.84612	+	15.3219i	0.308732	+	0.534739i	−0.669354	+	0.742944i	$0.733429\pi$
$822$	−11.8956	−	20.6038i	−0.414908	−	0.718642i
$823$	6.73124	−	11.6588i	0.234636	−	0.406402i	−0.724531	−	0.689243i	$-0.757943\pi$
$823$	6.73124	−	11.6588i	0.234636	−	0.406402i	0.959167	+	0.282841i	$0.0912768\pi$
$824$	−53.5570			−1.86575
$825$	−0.00246160	+	0.00426362i	−8.57020e−5	+	0.000148440i
$826$	56.5976	−	98.0299i	1.96928	−	3.41090i
$827$	8.40974			0.292435			0.146218	−	0.989252i	$-0.453290\pi$
$827$	8.40974			0.292435			0.146218	+	0.989252i	$0.453290\pi$
$828$	−2.99348	+	5.18487i	−0.104031	+	0.180187i
$829$	−7.89152	−	13.6685i	−0.274084	−	0.474727i	0.695820	−	0.718217i	$-0.255041\pi$
$829$	−7.89152	−	13.6685i	−0.274084	−	0.474727i	−0.969904	+	0.243489i	$0.921708\pi$
$830$	−14.1837	−	24.5669i	−0.492323	−	0.852729i
$831$	−26.2686			−0.911247
$832$	37.4700	−	14.9126i	1.29904	−	0.517003i
$833$	45.7523			1.58522
$834$	2.69226	+	4.66314i	0.0932255	+	0.161471i
$835$	−2.68896	−	4.65742i	−0.0930554	−	0.161177i
$836$	−2.33791	+	4.04938i	−0.0808584	+	0.140051i
$837$	−0.923965			−0.0319369
$838$	38.7973	−	67.1988i	1.34023	−	2.32134i
$839$	−13.3050	+	23.0449i	−0.459338	+	0.795597i	−0.998926	−	0.0463322i	$-0.985247\pi$
$839$	−13.3050	+	23.0449i	−0.459338	+	0.795597i	0.539588	+	0.841929i	$0.318580\pi$
$840$	−32.3037			−1.11458
$841$	−21.5502	+	37.3260i	−0.743109	+	1.28710i
$842$	37.1711	+	64.3823i	1.28100	+	2.21876i
$843$	4.64589	+	8.04692i	0.160013	+	0.277151i
$844$	35.5142			1.22245
$845$	21.1089	−	19.9645i	0.726169	−	0.686800i
$846$	24.7653			0.851447
$847$	−1.82822	−	3.16657i	−0.0628183	−	0.108804i
$848$	2.92783	+	5.07115i	0.100542	+	0.174144i
$849$	−15.1644	+	26.2655i	−0.520440	+	0.901429i
$850$	−0.0841424			−0.00288606
$851$	−1.75726	+	3.04366i	−0.0602380	+	0.104335i
$852$	−9.21375	+	15.9587i	−0.315658	+	0.546736i
$853$	25.4897			0.872752			0.436376	−	0.899764i	$-0.356262\pi$
$853$	25.4897			0.872752			0.436376	+	0.899764i	$0.356262\pi$
$854$	−7.04372	+	12.2001i	−0.241031	+	0.417478i
$855$	−1.42711	−	2.47183i	−0.0488061	−	0.0845346i
$856$	−25.1160	−	43.5022i	−0.858447	−	1.48687i
$857$	8.18020			0.279430			0.139715	−	0.990192i	$-0.455381\pi$
$857$	8.18020			0.279430			0.139715	+	0.990192i	$0.455381\pi$
$858$	7.97083	−	3.17230i	0.272120	−	0.108301i
$859$	0.956777			0.0326448			0.0163224	−	0.999867i	$-0.494804\pi$
$859$	0.956777			0.0326448			0.0163224	+	0.999867i	$0.494804\pi$
$860$	22.1284	+	38.3274i	0.754571	+	1.30696i
$861$	1.04868	+	1.81637i	0.0357390	+	0.0619017i
$862$	−40.2890	+	69.7825i	−1.37225	+	2.37680i
$863$	−21.7277			−0.739618			−0.369809	−	0.929108i	$-0.620577\pi$
$863$	−21.7277			−0.739618			−0.369809	+	0.929108i	$0.620577\pi$
$864$	−1.47507	+	2.55490i	−0.0501830	+	0.0869195i
$865$	24.5998	−	42.6081i	0.836418	−	1.44872i
$866$	−14.1668			−0.481409
$867$	17.2978	−	29.9607i	0.587465	−	1.01752i
$868$	−6.18480	−	10.7124i	−0.209926	−	0.363602i
$869$	−3.47063	−	6.01130i	−0.117733	−	0.203920i
$870$	45.1544			1.53088
$871$	−37.2440	−	29.4115i	−1.26197	−	0.996570i
$872$	−5.24531			−0.177628
$873$	−6.42114	−	11.1217i	−0.217323	−	0.376414i
$874$	−2.48434	−	4.30300i	−0.0840341	−	0.145551i
$875$	20.4501	−	35.4207i	0.691341	−	1.19744i
$876$	14.3789			0.485817
$877$	1.27603	−	2.21015i	0.0430885	−	0.0746314i	−0.843677	−	0.536851i	$-0.819614\pi$
$877$	1.27603	−	2.21015i	0.0430885	−	0.0746314i	0.886765	+	0.462220i	$0.152947\pi$
$878$	19.4475	−	33.6840i	0.656320	−	1.13678i
$879$	−8.93813			−0.301476
$880$	−2.32752	+	4.03139i	−0.0784608	+	0.135898i
$881$	10.5394	+	18.2548i	0.355081	+	0.615018i	0.987132	−	0.159909i	$-0.0511199\pi$
$881$	10.5394	+	18.2548i	0.355081	+	0.615018i	−0.632051	+	0.774927i	$0.717787\pi$
$882$	−7.57769	−	13.1249i	−0.255154	−	0.441940i
$883$	38.1947			1.28535			0.642677	−	0.766137i	$-0.277824\pi$
$883$	38.1947			1.28535			0.642677	+	0.766137i	$0.277824\pi$
$884$	74.4181	+	58.7676i	2.50295	+	1.97657i
$885$	29.0791			0.977483
$886$	−6.63927	−	11.4996i	−0.223051	−	0.386335i
$887$	−7.18062	−	12.4372i	−0.241101	−	0.417600i	0.719927	−	0.694050i	$-0.244175\pi$
$887$	−7.18062	−	12.4372i	−0.241101	−	0.417600i	−0.961028	+	0.276450i	$0.910842\pi$
$888$	4.24809	−	7.35791i	0.142557	−	0.246915i
$889$	−68.2110			−2.28772
$890$	49.0037	−	84.8769i	1.64261	−	2.84508i
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	−14.3285			−0.479754
$893$	−6.64613	+	11.5114i	−0.222404	+	0.385215i
$894$	−18.3037	−	31.7030i	−0.612168	−	1.06031i
$895$	−6.44185	−	11.1576i	−0.215327	−	0.372958i
$896$	−75.7362			−2.53017
$897$	−0.850880	+	5.83399i	−0.0284100	+	0.194791i
$898$	−36.4337			−1.21581
$899$	3.92278	+	6.79446i	0.130832	+	0.226608i
$900$	0.00901281	+	0.0156106i	0.000300427	+	0.000520355i
$901$	10.0972	−	17.4888i	0.336385	−	0.582636i
$902$	1.36482			0.0454436
$903$	−9.88767	+	17.1259i	−0.329041	+	0.569916i
$904$	−36.7834	+	63.7107i	−1.22340	+	2.11899i
$905$	−22.8591			−0.759863
$906$	5.36539	−	9.29313i	0.178253	−	0.308743i
$907$	21.6948	+	37.5765i	0.720365	+	1.24771i	0.960854	+	0.277057i	$0.0893590\pi$
$907$	21.6948	+	37.5765i	0.720365	+	1.24771i	−0.240489	+	0.970652i	$0.577308\pi$
$908$	−8.81240	−	15.2635i	−0.292450	−	0.506538i
$909$	11.8638			0.393496
$910$	−65.1377	+	25.9241i	−2.15929	+	0.859375i
$911$	39.0367			1.29334			0.646671	−	0.762769i	$-0.276161\pi$
$911$	39.0367			1.29334			0.646671	+	0.762769i	$0.276161\pi$
$912$	1.32996	+	2.30356i	0.0440394	+	0.0762785i
$913$	−2.66721	−	4.61975i	−0.0882719	−	0.152891i
$914$	−7.73154	+	13.3914i	−0.255736	+	0.442949i
$915$	−3.61897			−0.119640
$916$	−43.2208	+	74.8606i	−1.42805	+	2.47346i
$917$	−27.7553	+	48.0736i	−0.916561	+	1.58753i
$918$	−17.0910			−0.564086
$919$	−11.7272	+	20.3120i	−0.386843	+	0.670032i	−0.992023	−	0.126056i	$-0.959768\pi$
$919$	−11.7272	+	20.3120i	−0.386843	+	0.670032i	0.605180	+	0.796089i	$0.293101\pi$
$920$	−7.22320	−	12.5109i	−0.238142	−	0.412474i
$921$	−4.58868	−	7.94783i	−0.151202	−	0.261890i
$922$	−68.7993			−2.26578
$923$	−2.61895	+	17.9567i	−0.0862039	+	0.591051i
$924$	−13.3875			−0.440417
$925$	0.00529077	+	0.00916388i	0.000173959	+	0.000301306i
$926$	−4.24788	−	7.35755i	−0.139594	−	0.241784i
$927$	6.77427	−	11.7334i	0.222496	−	0.385375i
$928$	25.0503			0.822315
$929$	17.5993	−	30.4829i	0.577415	−	1.00011i	−0.418360	−	0.908281i	$-0.637395\pi$
$929$	17.5993	−	30.4829i	0.577415	−	1.00011i	0.995775	−	0.0918303i	$-0.0292717\pi$
$930$	2.45673	−	4.25518i	0.0805593	−	0.139533i
$931$	8.13434			0.266592
$932$	16.2275	−	28.1068i	0.531549	−	0.920670i
$933$	−2.95939	−	5.12582i	−0.0968862	−	0.167812i
$934$	34.3428	+	59.4835i	1.12373	+	1.94636i
$935$	16.0538			0.525015
$936$	2.05696	−	14.1034i	0.0672340	−	0.460985i
$937$	−48.1360			−1.57254			−0.786268	−	0.617886i	$-0.787989\pi$
$937$	−48.1360			−1.57254			−0.786268	+	0.617886i	$0.787989\pi$
$938$	57.2553	+	99.1690i	1.86945	+	3.23798i
$939$	13.0365	+	22.5798i	0.425429	+	0.736865i
$940$	−42.5859	+	73.7609i	−1.38900	+	2.40582i
$941$	−24.0365			−0.783569			−0.391784	−	0.920057i	$-0.628142\pi$
$941$	−24.0365			−0.783569			−0.391784	+	0.920057i	$0.628142\pi$
$942$	−2.26274	+	3.91918i	−0.0737240	+	0.127694i
$943$	−0.468976	+	0.812291i	−0.0152720	+	0.0264518i
$944$	−27.0996			−0.882017
$945$	4.08601	−	7.07717i	0.132918	−	0.230220i
$946$	6.43423	+	11.1444i	0.209195	+	0.362336i
$947$	−2.35623	−	4.08111i	−0.0765671	−	0.132618i	0.825200	−	0.564841i	$-0.191063\pi$
$947$	−2.35623	−	4.08111i	−0.0765671	−	0.132618i	−0.901767	+	0.432223i	$0.857729\pi$
$948$	−25.4144			−0.825422
$949$	13.1561	−	5.23597i	0.427064	−	0.169967i
$950$	−0.0149598			−0.000485358
$951$	−3.17980	−	5.50757i	−0.103112	−	0.178595i
$952$	−51.9108	−	89.9122i	−1.68244	−	2.91407i
$953$	11.7408	−	20.3356i	0.380321	−	0.658736i	−0.610787	−	0.791795i	$-0.709147\pi$
$953$	11.7408	−	20.3356i	0.380321	−	0.658736i	0.991108	+	0.133059i	$0.0424800\pi$
$954$	−6.68933			−0.216575
$955$	4.00203	−	6.93171i	0.129503	−	0.224305i
$956$	−12.8447	+	22.2476i	−0.415426	+	0.719539i
$957$	8.49119			0.274481
$958$	−26.0408	+	45.1039i	−0.841339	+	1.45724i
$959$	18.2804	+	31.6625i	0.590304	+	1.02244i
$960$	−12.4992	−	21.6492i	−0.403409	−	0.698725i
$961$	−30.1463			−0.972461
$962$	2.66112	−	18.2458i	0.0857979	−	0.588267i
$963$	12.7074			0.409490
$964$	13.3618	+	23.1433i	0.430354	+	0.745395i
$965$	−10.3244	−	17.8823i	−0.332353	−	0.575652i
$966$	7.11300	−	12.3201i	0.228857	−	0.396392i
$967$	45.0501			1.44872			0.724358	−	0.689424i	$-0.242136\pi$
$967$	45.0501			1.44872			0.724358	+	0.689424i	$0.242136\pi$
$968$	−1.97648	+	3.42337i	−0.0635266	+	0.110031i
$969$	4.58662	−	7.94426i	0.147343	−	0.255206i
$970$	68.2925			2.19274
$971$	−6.38651	+	11.0618i	−0.204953	+	0.354989i	−0.950118	−	0.311891i	$-0.899037\pi$
$971$	−6.38651	+	11.0618i	−0.204953	+	0.354989i	0.745165	+	0.666880i	$0.232371\pi$
$972$	1.83068	+	3.17083i	0.0587191	+	0.101704i
$973$	−4.13728	−	7.16599i	−0.132635	−	0.229731i
$974$	58.1327			1.86269
$975$	0.0139309	+	0.0110011i	0.000446144	+	0.000352318i
$976$	3.37262			0.107955
$977$	−6.41143	−	11.1049i	−0.205120	−	0.355278i	0.745051	−	0.667008i	$-0.232425\pi$
$977$	−6.41143	−	11.1049i	−0.205120	−	0.355278i	−0.950171	+	0.311729i	$0.899092\pi$
$978$	−5.80584	−	10.0560i	−0.185650	−	0.321556i
$979$	9.21505	−	15.9609i	0.294514	−	0.510114i
$980$	52.1218			1.66497
$981$	0.663464	−	1.14915i	0.0211828	−	0.0366896i
$982$	−1.43492	+	2.48535i	−0.0457900	+	0.0793107i
$983$	−29.6101			−0.944414			−0.472207	−	0.881488i	$-0.656543\pi$
$983$	−29.6101			−0.944414			−0.472207	+	0.881488i	$0.656543\pi$
$984$	1.13373	−	1.96368i	0.0361420	−	0.0625997i
$985$	−0.631531	−	1.09384i	−0.0201223	−	0.0348528i
$986$	72.5614	+	125.680i	2.31083	+	4.00247i
$987$	−38.0575			−1.21138
$988$	13.2308	+	10.4483i	0.420929	+	0.332406i
$989$	−8.84364			−0.281211
$990$	−2.65890	−	4.60534i	−0.0845053	−	0.146367i
$991$	−17.2640	−	29.9021i	−0.548408	−	0.949871i	−0.998384	−	0.0568302i	$-0.981901\pi$
$991$	−17.2640	−	29.9021i	−0.548408	−	0.949871i	0.449976	−	0.893041i	$-0.351433\pi$
$992$	1.36292	−	2.36064i	0.0432726	−	0.0749504i
$993$	10.6988			0.339515
$994$	21.8934	−	37.9204i	0.694415	−	1.20276i
$995$	−22.5126	+	38.9930i	−0.713698	+	1.23616i
$996$	−19.5313			−0.618872
$997$	−22.7645	+	39.4293i	−0.720960	+	1.24874i	0.239655	+	0.970858i	$0.422966\pi$
$997$	−22.7645	+	39.4293i	−0.720960	+	1.24874i	−0.960615	+	0.277882i	$0.910368\pi$
$998$	−27.8170	−	48.1804i	−0.880531	−	1.52512i
$999$	1.07466	+	1.86136i	0.0340007	+	0.0588909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.d.133.1	yes	10
13.3	even	3		5577.2.a.r.1.5		5
13.9	even	3	inner	429.2.i.d.100.1	✓	10
13.10	even	6		5577.2.a.s.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.d.100.1	✓	10	13.9	even	3	inner
429.2.i.d.133.1	yes	10	1.1	even	1	trivial
5577.2.a.r.1.5		5	13.3	even	3
5577.2.a.s.1.1		5	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18968 - 2.06059i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.83068 + 3.17083i) q^{4} +2.23497 q^{5} +(1.18968 - 2.06059i) q^{6} +(-1.82822 + 3.16657i) q^{7} +3.95297 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.18968 - 2.06059i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.83068 + 3.17083i) q^{4} +2.23497 q^{5} +(1.18968 - 2.06059i) q^{6} +(-1.82822 + 3.16657i) q^{7} +3.95297 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.65890 - 4.60534i) q^{10} +(-0.500000 - 0.866025i) q^{11} -3.66136 q^{12} +(-3.34999 + 1.33326i) q^{13} +8.69998 q^{14} +(1.11748 + 1.93554i) q^{15} +(-1.04141 - 1.80378i) q^{16} +(-3.59151 + 6.22067i) q^{17} +2.37936 q^{18} +(-0.638537 + 1.10598i) q^{19} +(-4.09151 + 7.08670i) q^{20} -3.65643 q^{21} +(-1.18968 + 2.06059i) q^{22} +(-0.817589 - 1.41611i) q^{23} +(1.97648 + 3.42337i) q^{24} -0.00492321 q^{25} +(6.73271 + 5.31679i) q^{26} -1.00000 q^{27} +(-6.69376 - 11.5939i) q^{28} +(4.24560 + 7.35359i) q^{29} +(2.65890 - 4.60534i) q^{30} +0.923965 q^{31} +(1.47507 - 2.55490i) q^{32} +(0.500000 - 0.866025i) q^{33} +17.0910 q^{34} +(-4.08601 + 7.07717i) q^{35} +(-1.83068 - 3.17083i) q^{36} +(-1.07466 - 1.86136i) q^{37} +3.03862 q^{38} +(-2.82963 - 2.23455i) q^{39} +8.83476 q^{40} +(-0.286804 - 0.496760i) q^{41} +(4.34999 + 7.53440i) q^{42} +(2.70418 - 4.68378i) q^{43} +3.66136 q^{44} +(-1.11748 + 1.93554i) q^{45} +(-1.94534 + 3.36942i) q^{46} +10.4084 q^{47} +(1.04141 - 1.80378i) q^{48} +(-3.18476 - 5.51616i) q^{49} +(0.00585704 + 0.0101447i) q^{50} -7.18301 q^{51} +(1.90522 - 13.0630i) q^{52} -2.81140 q^{53} +(1.18968 + 2.06059i) q^{54} +(-1.11748 - 1.93554i) q^{55} +(-7.22689 + 12.5173i) q^{56} -1.27707 q^{57} +(10.1018 - 17.4968i) q^{58} +(6.50549 - 11.2678i) q^{59} -8.18301 q^{60} +(-0.809625 + 1.40231i) q^{61} +(-1.09922 - 1.90391i) q^{62} +(-1.82822 - 3.16657i) q^{63} -11.1851 q^{64} +(-7.48711 + 2.97979i) q^{65} -2.37936 q^{66} +(6.58108 + 11.3988i) q^{67} +(-13.1498 - 22.7761i) q^{68} +(0.817589 - 1.41611i) q^{69} +19.4442 q^{70} +(2.51649 - 4.35868i) q^{71} +(-1.97648 + 3.42337i) q^{72} -3.92720 q^{73} +(-2.55700 + 4.42885i) q^{74} +(-0.00246160 - 0.00426362i) q^{75} +(-2.33791 - 4.04938i) q^{76} +3.65643 q^{77} +(-1.23812 + 8.48909i) q^{78} +6.94126 q^{79} +(-2.32752 - 4.03139i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.682411 + 1.18197i) q^{82} +5.33443 q^{83} +(6.69376 - 11.5939i) q^{84} +(-8.02690 + 13.9030i) q^{85} -12.8685 q^{86} +(-4.24560 + 7.35359i) q^{87} +(-1.97648 - 3.42337i) q^{88} +(9.21505 + 15.9609i) q^{89} +5.31779 q^{90} +(1.90266 - 13.0454i) q^{91} +5.98697 q^{92} +(0.461983 + 0.800177i) q^{93} +(-12.3826 - 21.4473i) q^{94} +(-1.42711 + 2.47183i) q^{95} +2.95015 q^{96} +(-6.42114 + 11.1217i) q^{97} +(-7.57769 + 13.1249i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 10 q^{4} - 4 q^{5} - 7 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} - 5 q^{11} - 20 q^{12} + 9 q^{13} + 2 q^{14} - 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} - 8 q^{20} - 14 q^{21} - 11 q^{23} + 3 q^{24} - 6 q^{25} - 4 q^{26} - 10 q^{27} - 5 q^{28} + 2 q^{29} + 7 q^{30} + 20 q^{31} + 9 q^{32} + 5 q^{33} + 58 q^{34} + 14 q^{35} - 10 q^{36} - 15 q^{37} - 38 q^{38} - 6 q^{39} + 30 q^{40} + 2 q^{41} + q^{42} - 7 q^{43} + 20 q^{44} + 2 q^{45} - 20 q^{46} + 36 q^{47} + 4 q^{48} - 14 q^{49} + 2 q^{50} - 6 q^{51} - 3 q^{52} + 30 q^{53} + 2 q^{55} - 3 q^{56} - 14 q^{57} - 5 q^{58} + 4 q^{59} - 16 q^{60} + 14 q^{61} - 46 q^{62} - 7 q^{63} - 74 q^{64} - 44 q^{65} + 5 q^{67} + 24 q^{68} + 11 q^{69} + 80 q^{70} + 13 q^{71} - 3 q^{72} + 56 q^{73} - 15 q^{74} - 3 q^{75} - 2 q^{76} + 14 q^{77} - 23 q^{78} + 32 q^{79} + 22 q^{80} - 5 q^{81} - 4 q^{82} + 24 q^{83} + 5 q^{84} - 13 q^{85} + 4 q^{86} - 2 q^{87} - 3 q^{88} + 6 q^{89} + 14 q^{90} - 29 q^{91} - 4 q^{92} + 10 q^{93} + 2 q^{94} + 21 q^{95} + 18 q^{96} - 9 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 10 * q^4 - 4 * q^5 - 7 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 - 5 * q^11 - 20 * q^12 + 9 * q^13 + 2 * q^14 - 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 - 8 * q^20 - 14 * q^21 - 11 * q^23 + 3 * q^24 - 6 * q^25 - 4 * q^26 - 10 * q^27 - 5 * q^28 + 2 * q^29 + 7 * q^30 + 20 * q^31 + 9 * q^32 + 5 * q^33 + 58 * q^34 + 14 * q^35 - 10 * q^36 - 15 * q^37 - 38 * q^38 - 6 * q^39 + 30 * q^40 + 2 * q^41 + q^42 - 7 * q^43 + 20 * q^44 + 2 * q^45 - 20 * q^46 + 36 * q^47 + 4 * q^48 - 14 * q^49 + 2 * q^50 - 6 * q^51 - 3 * q^52 + 30 * q^53 + 2 * q^55 - 3 * q^56 - 14 * q^57 - 5 * q^58 + 4 * q^59 - 16 * q^60 + 14 * q^61 - 46 * q^62 - 7 * q^63 - 74 * q^64 - 44 * q^65 + 5 * q^67 + 24 * q^68 + 11 * q^69 + 80 * q^70 + 13 * q^71 - 3 * q^72 + 56 * q^73 - 15 * q^74 - 3 * q^75 - 2 * q^76 + 14 * q^77 - 23 * q^78 + 32 * q^79 + 22 * q^80 - 5 * q^81 - 4 * q^82 + 24 * q^83 + 5 * q^84 - 13 * q^85 + 4 * q^86 - 2 * q^87 - 3 * q^88 + 6 * q^89 + 14 * q^90 - 29 * q^91 - 4 * q^92 + 10 * q^93 + 2 * q^94 + 21 * q^95 + 18 * q^96 - 9 * q^97 - 16 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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