LMFDB - Embedded newform 201.2.e.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.e (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:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 49x^{6} - 39x^{5} + 128x^{4} - 14x^{3} + 119x^{2} - 49x + 49 $ x^10 - 2x^9 + 10x^8 - 8x^7 + 49x^6 - 39x^5 + 128x^4 - 14x^3 + 119x^2 - 49*x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Root			$0.330147 + 0.571831i$ of defining polynomial
Character	$\chi$	$=$	201.37
Dual form			201.2.e.b.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.330147 - 0.571831i) q^{2} -1.00000 q^{3} +(0.782006 - 1.35447i) q^{4} +3.22431 q^{5} +(0.330147 + 0.571831i) q^{6} +(-1.02143 + 1.76916i) q^{7} -2.35330 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.330147 - 0.571831i) q^{2} -1.00000 q^{3} +(0.782006 - 1.35447i) q^{4} +3.22431 q^{5} +(0.330147 + 0.571831i) q^{6} +(-1.02143 + 1.76916i) q^{7} -2.35330 q^{8} +1.00000 q^{9} +(-1.06450 - 1.84376i) q^{10} +(2.63358 - 4.56149i) q^{11} +(-0.782006 + 1.35447i) q^{12} +(0.956931 + 1.65745i) q^{13} +1.34888 q^{14} -3.22431 q^{15} +(-0.787078 - 1.36326i) q^{16} +(-1.83694 - 3.18168i) q^{17} +(-0.330147 - 0.571831i) q^{18} +(0.564495 + 0.977734i) q^{19} +(2.52143 - 4.36724i) q^{20} +(1.02143 - 1.76916i) q^{21} -3.47787 q^{22} +(0.160294 + 0.277638i) q^{23} +2.35330 q^{24} +5.39615 q^{25} +(0.631856 - 1.09441i) q^{26} -1.00000 q^{27} +(1.59752 + 2.76699i) q^{28} +(3.24114 - 5.61382i) q^{29} +(1.06450 + 1.84376i) q^{30} +(-3.63358 + 6.29354i) q^{31} +(-2.87300 + 4.97618i) q^{32} +(-2.63358 + 4.56149i) q^{33} +(-1.21292 + 2.10084i) q^{34} +(-3.29339 + 5.70432i) q^{35} +(0.782006 - 1.35447i) q^{36} +(4.40651 + 7.63230i) q^{37} +(0.372733 - 0.645592i) q^{38} +(-0.956931 - 1.65745i) q^{39} -7.58775 q^{40} +(-3.86065 + 6.68684i) q^{41} -1.34888 q^{42} -11.1699 q^{43} +(-4.11895 - 7.13423i) q^{44} +3.22431 q^{45} +(0.105841 - 0.183322i) q^{46} +(-4.74622 + 8.22069i) q^{47} +(0.787078 + 1.36326i) q^{48} +(1.41338 + 2.44804i) q^{49} +(-1.78152 - 3.08569i) q^{50} +(1.83694 + 3.18168i) q^{51} +2.99330 q^{52} +12.0691 q^{53} +(0.330147 + 0.571831i) q^{54} +(8.49146 - 14.7076i) q^{55} +(2.40372 - 4.16336i) q^{56} +(-0.564495 - 0.977734i) q^{57} -4.28022 q^{58} -1.27730 q^{59} +(-2.52143 + 4.36724i) q^{60} +(2.99216 + 5.18258i) q^{61} +4.79846 q^{62} +(-1.02143 + 1.76916i) q^{63} +0.645737 q^{64} +(3.08544 + 5.34413i) q^{65} +3.47787 q^{66} +(1.12164 - 8.10814i) q^{67} -5.74600 q^{68} +(-0.160294 - 0.277638i) q^{69} +4.34921 q^{70} +(-1.02116 + 1.76870i) q^{71} -2.35330 q^{72} +(-6.23309 - 10.7960i) q^{73} +(2.90959 - 5.03956i) q^{74} -5.39615 q^{75} +1.76575 q^{76} +(5.38001 + 9.31845i) q^{77} +(-0.631856 + 1.09441i) q^{78} +(1.61722 - 2.80112i) q^{79} +(-2.53778 - 4.39556i) q^{80} +1.00000 q^{81} +5.09833 q^{82} +(-0.0476578 - 0.0825457i) q^{83} +(-1.59752 - 2.76699i) q^{84} +(-5.92286 - 10.2587i) q^{85} +(3.68771 + 6.38731i) q^{86} +(-3.24114 + 5.61382i) q^{87} +(-6.19759 + 10.7345i) q^{88} -6.17088 q^{89} +(-1.06450 - 1.84376i) q^{90} -3.90974 q^{91} +0.501404 q^{92} +(3.63358 - 6.29354i) q^{93} +6.26780 q^{94} +(1.82010 + 3.15251i) q^{95} +(2.87300 - 4.97618i) q^{96} +(5.80974 + 10.0628i) q^{97} +(0.933245 - 1.61643i) q^{98} +(2.63358 - 4.56149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 10 * q^3 - 6 * q^4 + 2 * q^5 + 2 * q^6 - q^7 + 12 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} + 6 q^{12} + 3 q^{13} - 22 q^{14} - 2 q^{15} + 2 q^{17} - 2 q^{18} + 3 q^{19} + 16 q^{20} + q^{21} + 6 q^{22} - q^{23} - 12 q^{24} + 7 q^{26} - 10 q^{27} - 9 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 9 q^{32} - 2 q^{33} - 20 q^{34} + 19 q^{35} - 6 q^{36} + 27 q^{37} - 16 q^{38} - 3 q^{39} - 22 q^{40} - 7 q^{41} + 22 q^{42} + 12 q^{43} - 7 q^{44} + 2 q^{45} + 30 q^{46} - 33 q^{47} - 24 q^{49} + 21 q^{50} - 2 q^{51} - 32 q^{52} - 24 q^{53} + 2 q^{54} + 6 q^{55} - q^{56} - 3 q^{57} + 44 q^{58} + 24 q^{59} - 16 q^{60} + q^{61} + 2 q^{62} - q^{63} - 8 q^{64} - 6 q^{65} - 6 q^{66} + 2 q^{67} - 18 q^{68} + q^{69} + 42 q^{70} - q^{71} + 12 q^{72} + 12 q^{73} + 43 q^{74} + 2 q^{76} + 40 q^{77} - 7 q^{78} + 7 q^{79} - q^{80} + 10 q^{81} - 74 q^{82} + 12 q^{83} + 9 q^{84} - 27 q^{85} - 27 q^{86} - 12 q^{87} - 10 q^{88} + 12 q^{89} - 8 q^{90} - 80 q^{91} - 28 q^{92} + 12 q^{93} + 30 q^{94} - 12 q^{95} + 9 q^{96} - 9 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 10 * q^3 - 6 * q^4 + 2 * q^5 + 2 * q^6 - q^7 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 2 * q^11 + 6 * q^12 + 3 * q^13 - 22 * q^14 - 2 * q^15 + 2 * q^17 - 2 * q^18 + 3 * q^19 + 16 * q^20 + q^21 + 6 * q^22 - q^23 - 12 * q^24 + 7 * q^26 - 10 * q^27 - 9 * q^28 + 12 * q^29 + 8 * q^30 - 12 * q^31 - 9 * q^32 - 2 * q^33 - 20 * q^34 + 19 * q^35 - 6 * q^36 + 27 * q^37 - 16 * q^38 - 3 * q^39 - 22 * q^40 - 7 * q^41 + 22 * q^42 + 12 * q^43 - 7 * q^44 + 2 * q^45 + 30 * q^46 - 33 * q^47 - 24 * q^49 + 21 * q^50 - 2 * q^51 - 32 * q^52 - 24 * q^53 + 2 * q^54 + 6 * q^55 - q^56 - 3 * q^57 + 44 * q^58 + 24 * q^59 - 16 * q^60 + q^61 + 2 * q^62 - q^63 - 8 * q^64 - 6 * q^65 - 6 * q^66 + 2 * q^67 - 18 * q^68 + q^69 + 42 * q^70 - q^71 + 12 * q^72 + 12 * q^73 + 43 * q^74 + 2 * q^76 + 40 * q^77 - 7 * q^78 + 7 * q^79 - q^80 + 10 * q^81 - 74 * q^82 + 12 * q^83 + 9 * q^84 - 27 * q^85 - 27 * q^86 - 12 * q^87 - 10 * q^88 + 12 * q^89 - 8 * q^90 - 80 * q^91 - 28 * q^92 + 12 * q^93 + 30 * q^94 - 12 * q^95 + 9 * q^96 - 9 * q^97 + 4 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.330147	−	0.571831i	−0.233449	−	0.404346i	0.725372	−	0.688357i	$-0.241668\pi$
$2$	−0.330147	−	0.571831i	−0.233449	−	0.404346i	−0.958821	+	0.284012i	$0.908335\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.782006	−	1.35447i	0.391003	−	0.677237i
$5$	3.22431			1.44195			0.720977	−	0.692959i	$-0.243693\pi$
$5$	3.22431			1.44195			0.720977	+	0.692959i	$0.243693\pi$
$6$	0.330147	+	0.571831i	0.134782	+	0.233449i
$7$	−1.02143	+	1.76916i	−0.386063	+	0.668680i	−0.991916	−	0.126896i	$-0.959499\pi$
$7$	−1.02143	+	1.76916i	−0.386063	+	0.668680i	0.605853	+	0.795576i	$0.292832\pi$
$8$	−2.35330			−0.832016
$9$	1.00000			0.333333
$10$	−1.06450	−	1.84376i	−0.336623	−	0.583048i
$11$	2.63358	−	4.56149i	0.794054	−	1.37534i	−0.129384	−	0.991595i	$-0.541300\pi$
$11$	2.63358	−	4.56149i	0.794054	−	1.37534i	0.923438	−	0.383747i	$-0.125367\pi$
$12$	−0.782006	+	1.35447i	−0.225746	+	0.391003i
$13$	0.956931	+	1.65745i	0.265405	+	0.459695i	0.967670	−	0.252221i	$-0.0811611\pi$
$13$	0.956931	+	1.65745i	0.265405	+	0.459695i	−0.702265	+	0.711916i	$0.747828\pi$
$14$	1.34888			0.360504
$15$	−3.22431			−0.832512
$16$	−0.787078	−	1.36326i	−0.196769	−	0.340815i
$17$	−1.83694	−	3.18168i	−0.445524	−	0.771670i	0.552565	−	0.833470i	$-0.313649\pi$
$17$	−1.83694	−	3.18168i	−0.445524	−	0.771670i	−0.998089	+	0.0618000i	$0.980316\pi$
$18$	−0.330147	−	0.571831i	−0.0778164	−	0.134782i
$19$	0.564495	+	0.977734i	0.129504	+	0.224308i	0.923485	−	0.383636i	$-0.125328\pi$
$19$	0.564495	+	0.977734i	0.129504	+	0.224308i	−0.793980	+	0.607943i	$0.791995\pi$
$20$	2.52143	−	4.36724i	0.563808	−	0.976544i
$21$	1.02143	−	1.76916i	0.222893	−	0.386063i
$22$	−3.47787			−0.741485
$23$	0.160294	+	0.277638i	0.0334236	+	0.0578914i	0.882253	−	0.470775i	$-0.156026\pi$
$23$	0.160294	+	0.277638i	0.0334236	+	0.0578914i	−0.848830	+	0.528666i	$0.822692\pi$
$24$	2.35330			0.480365
$25$	5.39615			1.07923
$26$	0.631856	−	1.09441i	0.123917	−	0.214631i
$27$	−1.00000			−0.192450
$28$	1.59752	+	2.76699i	0.301903	+	0.522912i
$29$	3.24114	−	5.61382i	0.601865	−	1.04246i	−0.390673	−	0.920529i	$-0.627758\pi$
$29$	3.24114	−	5.61382i	0.601865	−	1.04246i	0.992538	−	0.121932i	$-0.0389089\pi$
$30$	1.06450	+	1.84376i	0.194349	+	0.336623i
$31$	−3.63358	+	6.29354i	−0.652610	+	1.13035i	0.329877	+	0.944024i	$0.392993\pi$
$31$	−3.63358	+	6.29354i	−0.652610	+	1.13035i	−0.982487	+	0.186330i	$0.940341\pi$
$32$	−2.87300	+	4.97618i	−0.507879	+	0.879673i
$33$	−2.63358	+	4.56149i	−0.458447	+	0.794054i
$34$	−1.21292	+	2.10084i	−0.208014	+	0.360292i
$35$	−3.29339	+	5.70432i	−0.556684	+	0.964206i
$36$	0.782006	−	1.35447i	0.130334	−	0.225746i
$37$	4.40651	+	7.63230i	0.724426	+	1.25474i	0.959210	+	0.282695i	$0.0912283\pi$
$37$	4.40651	+	7.63230i	0.724426	+	1.25474i	−0.234784	+	0.972047i	$0.575438\pi$
$38$	0.372733	−	0.645592i	0.0604652	−	0.104729i
$39$	−0.956931	−	1.65745i	−0.153232	−	0.265405i
$40$	−7.58775			−1.19973
$41$	−3.86065	+	6.68684i	−0.602932	+	1.04431i	0.389443	+	0.921051i	$0.372668\pi$
$41$	−3.86065	+	6.68684i	−0.602932	+	1.04431i	−0.992375	+	0.123258i	$0.960666\pi$
$42$	−1.34888			−0.208137
$43$	−11.1699			−1.70340			−0.851698	−	0.524034i	$-0.824427\pi$
$43$	−11.1699			−1.70340			−0.851698	+	0.524034i	$0.824427\pi$
$44$	−4.11895	−	7.13423i	−0.620955	−	1.07553i
$45$	3.22431			0.480651
$46$	0.105841	−	0.183322i	0.0156054	−	0.0270294i
$47$	−4.74622	+	8.22069i	−0.692307	+	1.19911i	0.278774	+	0.960357i	$0.410072\pi$
$47$	−4.74622	+	8.22069i	−0.692307	+	1.19911i	−0.971080	+	0.238753i	$0.923261\pi$
$48$	0.787078	+	1.36326i	0.113605	+	0.196769i
$49$	1.41338	+	2.44804i	0.201911	+	0.349720i
$50$	−1.78152	−	3.08569i	−0.251945	−	0.436382i
$51$	1.83694	+	3.18168i	0.257223	+	0.445524i
$52$	2.99330			0.415096
$53$	12.0691			1.65781			0.828907	−	0.559387i	$-0.188963\pi$
$53$	12.0691			1.65781			0.828907	+	0.559387i	$0.188963\pi$
$54$	0.330147	+	0.571831i	0.0449273	+	0.0778164i
$55$	8.49146	−	14.7076i	1.14499	−	1.98318i
$56$	2.40372	−	4.16336i	0.321210	−	0.556352i
$57$	−0.564495	−	0.977734i	−0.0747692	−	0.129504i
$58$	−4.28022			−0.562020
$59$	−1.27730			−0.166291			−0.0831453	−	0.996537i	$-0.526497\pi$
$59$	−1.27730			−0.166291			−0.0831453	+	0.996537i	$0.526497\pi$
$60$	−2.52143	+	4.36724i	−0.325515	+	0.563808i
$61$	2.99216	+	5.18258i	0.383107	+	0.663561i	0.991505	−	0.130071i	$-0.0415206\pi$
$61$	2.99216	+	5.18258i	0.383107	+	0.663561i	−0.608397	+	0.793633i	$0.708187\pi$
$62$	4.79846			0.609405
$63$	−1.02143	+	1.76916i	−0.128688	+	0.222893i
$64$	0.645737			0.0807171
$65$	3.08544	+	5.34413i	0.382701	+	0.662858i
$66$	3.47787			0.428097
$67$	1.12164	−	8.10814i	0.137030	−	0.990567i
$67$	1.12164	−	8.10814i	0.137030	−	0.990567i
$68$	−5.74600			−0.696805
$69$	−0.160294	−	0.277638i	−0.0192971	−	0.0334236i
$70$	4.34921			0.519830
$71$	−1.02116	+	1.76870i	−0.121189	+	0.209906i	−0.920237	−	0.391362i	$-0.872004\pi$
$71$	−1.02116	+	1.76870i	−0.121189	+	0.209906i	0.799048	+	0.601268i	$0.205337\pi$
$72$	−2.35330			−0.277339
$73$	−6.23309	−	10.7960i	−0.729528	−	1.26358i	−0.957083	−	0.289814i	$-0.906406\pi$
$73$	−6.23309	−	10.7960i	−0.729528	−	1.26358i	0.227555	−	0.973765i	$-0.426927\pi$
$74$	2.90959	−	5.03956i	0.338233	−	0.585837i
$75$	−5.39615			−0.623093
$76$	1.76575			0.202546
$77$	5.38001	+	9.31845i	0.613109	+	1.06194i
$78$	−0.631856	+	1.09441i	−0.0715436	+	0.123917i
$79$	1.61722	−	2.80112i	0.181952	−	0.315150i	−0.760593	−	0.649229i	$-0.775092\pi$
$79$	1.61722	−	2.80112i	0.181952	−	0.315150i	0.942545	+	0.334079i	$0.108425\pi$
$80$	−2.53778	−	4.39556i	−0.283732	−	0.491439i
$81$	1.00000			0.111111
$82$	5.09833			0.563016
$83$	−0.0476578	−	0.0825457i	−0.00523112	−	0.00906057i	0.863398	−	0.504523i	$-0.168332\pi$
$83$	−0.0476578	−	0.0825457i	−0.00523112	−	0.00906057i	−0.868629	+	0.495463i	$0.834998\pi$
$84$	−1.59752	−	2.76699i	−0.174304	−	0.301903i
$85$	−5.92286	−	10.2587i	−0.642425	−	1.11271i
$86$	3.68771	+	6.38731i	0.397656	+	0.688761i
$87$	−3.24114	+	5.61382i	−0.347487	+	0.601865i
$88$	−6.19759	+	10.7345i	−0.660665	+	1.14431i
$89$	−6.17088			−0.654111			−0.327056	−	0.945005i	$-0.606056\pi$
$89$	−6.17088			−0.654111			−0.327056	+	0.945005i	$0.606056\pi$
$90$	−1.06450	−	1.84376i	−0.112208	−	0.194349i
$91$	−3.90974			−0.409852
$92$	0.501404			0.0522750
$93$	3.63358	−	6.29354i	0.376785	−	0.652610i
$94$	6.26780			0.646474
$95$	1.82010	+	3.15251i	0.186739	+	0.323441i
$96$	2.87300	−	4.97618i	0.293224	−	0.507879i
$97$	5.80974	+	10.0628i	0.589890	+	1.02172i	0.994246	+	0.107118i	$0.0341623\pi$
$97$	5.80974	+	10.0628i	0.589890	+	1.02172i	−0.404356	+	0.914602i	$0.632504\pi$
$98$	0.933245	−	1.61643i	0.0942720	−	0.163284i
$99$	2.63358	−	4.56149i	0.264685	−	0.458447i
$100$	4.21982	−	7.30894i	0.421982	−	0.730894i
$101$	−0.258373	+	0.447516i	−0.0257091	+	0.0445295i	−0.878594	−	0.477570i	$-0.841518\pi$
$101$	−0.258373	+	0.447516i	−0.0257091	+	0.0445295i	0.852885	+	0.522099i	$0.174851\pi$
$102$	1.21292	−	2.10084i	0.120097	−	0.208014i
$103$	−1.10939	+	1.92152i	−0.109311	+	0.189333i	−0.915491	−	0.402337i	$-0.868198\pi$
$103$	−1.10939	+	1.92152i	−0.109311	+	0.189333i	0.806180	+	0.591670i	$0.201531\pi$
$104$	−2.25194	−	3.90048i	−0.220821	−	0.382473i
$105$	3.29339	−	5.70432i	0.321402	−	0.556684i
$106$	−3.98457	−	6.90147i	−0.387015	−	0.670330i
$107$	3.56799			0.344931			0.172465	−	0.985016i	$-0.444827\pi$
$107$	3.56799			0.344931			0.172465	+	0.985016i	$0.444827\pi$
$108$	−0.782006	+	1.35447i	−0.0752485	+	0.130334i
$109$	−9.74392			−0.933298			−0.466649	−	0.884443i	$-0.654539\pi$
$109$	−9.74392			−0.933298			−0.466649	+	0.884443i	$0.654539\pi$
$110$	−11.2137			−1.06919
$111$	−4.40651	−	7.63230i	−0.418247	−	0.724426i
$112$	3.21577			0.303861
$113$	4.86317	−	8.42326i	0.457489	−	0.792394i	−0.541339	−	0.840805i	$-0.682082\pi$
$113$	4.86317	−	8.42326i	0.457489	−	0.792394i	0.998828	+	0.0484106i	$0.0154156\pi$
$114$	−0.372733	+	0.645592i	−0.0349096	+	0.0604652i
$115$	0.516837	+	0.895188i	0.0481953	+	0.0834768i
$116$	−5.06919	−	8.78009i	−0.470662	−	0.815211i
$117$	0.956931	+	1.65745i	0.0884683	+	0.153232i
$118$	0.421697	+	0.730401i	0.0388204	+	0.0672389i
$119$	7.50520			0.688001
$120$	7.58775			0.692663
$121$	−8.37147	−	14.4998i	−0.761043	−	1.31817i
$122$	1.97571	−	3.42203i	0.178872	−	0.309816i
$123$	3.86065	−	6.68684i	0.348103	−	0.602932i
$124$	5.68296	+	9.84317i	0.510345	+	0.883943i
$125$	1.27730			0.114245
$126$	1.34888			0.120168
$127$	−6.28123	+	10.8794i	−0.557369	+	0.965392i	0.440346	+	0.897828i	$0.354856\pi$
$127$	−6.28123	+	10.8794i	−0.557369	+	0.965392i	−0.997715	+	0.0675634i	$0.978477\pi$
$128$	5.53281	+	9.58311i	0.489036	+	0.847035i
$129$	11.1699			0.983456
$130$	2.03730	−	3.52870i	0.178683	−	0.309488i
$131$	−11.0520			−0.965620			−0.482810	−	0.875725i	$-0.660384\pi$
$131$	−11.0520			−0.965620			−0.482810	+	0.875725i	$0.660384\pi$
$132$	4.11895	+	7.13423i	0.358508	+	0.620955i
$133$	−2.30636			−0.199987
$134$	−5.00680	+	2.03549i	−0.432521	+	0.175840i
$135$	−3.22431			−0.277504
$136$	4.32287	+	7.48743i	0.370683	+	0.642042i
$137$	−15.0156			−1.28287			−0.641436	−	0.767176i	$-0.721661\pi$
$137$	−15.0156			−1.28287			−0.641436	+	0.767176i	$0.721661\pi$
$138$	−0.105841	+	0.183322i	−0.00900981	+	0.0156054i
$139$	14.3906			1.22059			0.610296	−	0.792174i	$-0.291051\pi$
$139$	14.3906			1.22059			0.610296	+	0.792174i	$0.291051\pi$
$140$	5.15090	+	8.92162i	0.435330	+	0.754014i
$141$	4.74622	−	8.22069i	0.399703	−	0.692307i
$142$	1.34853			0.113166
$143$	10.0806			0.842983
$144$	−0.787078	−	1.36326i	−0.0655898	−	0.113605i
$145$	10.4504	−	18.1007i	0.867862	−	1.50318i
$146$	−4.11567	+	7.12855i	−0.340615	+	0.589963i
$147$	−1.41338	−	2.44804i	−0.116573	−	0.201911i
$148$	13.7837			1.13301
$149$	−17.0700			−1.39843			−0.699216	−	0.714911i	$-0.746467\pi$
$149$	−17.0700			−1.39843			−0.699216	+	0.714911i	$0.746467\pi$
$150$	1.78152	+	3.08569i	0.145461	+	0.251945i
$151$	0.134062	+	0.232203i	0.0109098	+	0.0188964i	0.871429	−	0.490522i	$-0.163194\pi$
$151$	0.134062	+	0.232203i	0.0109098	+	0.0188964i	−0.860519	+	0.509418i	$0.829861\pi$
$152$	−1.32842	−	2.30090i	−0.107749	−	0.186627i
$153$	−1.83694	−	3.18168i	−0.148508	−	0.257223i
$154$	3.55239	−	6.15292i	0.286260	−	0.495816i
$155$	−11.7158	+	20.2923i	−0.941033	+	1.62992i
$156$	−2.99330			−0.239656
$157$	5.96776	+	10.3365i	0.476279	+	0.824939i	0.999631	−	0.0271775i	$-0.00865194\pi$
$157$	5.96776	+	10.3365i	0.476279	+	0.824939i	−0.523352	+	0.852117i	$0.675319\pi$
$158$	−2.13569			−0.169906
$159$	−12.0691			−0.957139
$160$	−9.26343	+	16.0447i	−0.732338	+	1.26845i
$161$	−0.654914			−0.0516145
$162$	−0.330147	−	0.571831i	−0.0259388	−	0.0449273i
$163$	9.68534	−	16.7755i	0.758615	−	1.31396i	−0.184943	−	0.982749i	$-0.559210\pi$
$163$	9.68534	−	16.7755i	0.758615	−	1.31396i	0.943557	−	0.331210i	$-0.107457\pi$
$164$	6.03810	+	10.4583i	0.471496	+	0.816656i
$165$	−8.49146	+	14.7076i	−0.661060	+	1.14499i
$166$	−0.0314682	+	0.0545045i	−0.00244240	+	0.00423037i
$167$	4.17665	−	7.23417i	0.323199	−	0.559797i	−0.657947	−	0.753064i	$-0.728575\pi$
$167$	4.17665	−	7.23417i	0.323199	−	0.559797i	0.981146	+	0.193267i	$0.0619084\pi$
$168$	−2.40372	+	4.16336i	−0.185451	+	0.321210i
$169$	4.66857	−	8.08619i	0.359121	−	0.622015i
$170$	−3.91083	+	6.77376i	−0.299947	+	0.519524i
$171$	0.564495	+	0.977734i	0.0431680	+	0.0747692i
$172$	−8.73493	+	15.1293i	−0.666032	+	1.15360i
$173$	−9.26388	−	16.0455i	−0.704320	−	1.21992i	−0.966936	−	0.255018i	$-0.917919\pi$
$173$	−9.26388	−	16.0455i	−0.704320	−	1.21992i	0.262616	−	0.964900i	$-0.415415\pi$
$174$	4.28022			0.324482
$175$	−5.51177	+	9.54666i	−0.416650	+	0.721659i
$176$	−8.29133			−0.624982
$177$	1.27730			0.0960079
$178$	2.03730	+	3.52870i	0.152702	+	0.264487i
$179$	11.2810			0.843178			0.421589	−	0.906787i	$-0.361473\pi$
$179$	11.2810			0.843178			0.421589	+	0.906787i	$0.361473\pi$
$180$	2.52143	−	4.36724i	0.187936	−	0.325515i
$181$	5.82959	−	10.0971i	0.433310	−	0.750515i	−0.563846	−	0.825880i	$-0.690679\pi$
$181$	5.82959	−	10.0971i	0.433310	−	0.750515i	0.997156	+	0.0753650i	$0.0240122\pi$
$182$	1.29079	+	2.23571i	0.0956796	+	0.165722i
$183$	−2.99216	−	5.18258i	−0.221187	−	0.383107i
$184$	−0.377220	−	0.653363i	−0.0278090	−	0.0481666i
$185$	14.2079	+	24.6089i	1.04459	+	1.80928i
$186$	−4.79846			−0.351840
$187$	−19.3509			−1.41508
$188$	7.42314	+	12.8572i	0.541388	+	0.937711i
$189$	1.02143	−	1.76916i	0.0742978	−	0.128688i
$190$	1.20180	−	2.08159i	0.0871881	−	0.151014i
$191$	−0.200088	−	0.346563i	−0.0144779	−	0.0250764i	0.858696	−	0.512486i	$-0.171275\pi$
$191$	−0.200088	−	0.346563i	−0.0144779	−	0.0250764i	−0.873174	+	0.487409i	$0.837942\pi$
$192$	−0.645737			−0.0466021
$193$	−9.62550			−0.692859			−0.346430	−	0.938076i	$-0.612606\pi$
$193$	−9.62550			−0.692859			−0.346430	+	0.938076i	$0.612606\pi$
$194$	3.83614	−	6.64439i	0.275419	−	0.477039i
$195$	−3.08544	−	5.34413i	−0.220953	−	0.382701i
$196$	4.42108			0.315791
$197$	−4.35281	+	7.53929i	−0.310125	+	0.537152i	−0.978389	−	0.206772i	$-0.933704\pi$
$197$	−4.35281	+	7.53929i	−0.310125	+	0.537152i	0.668264	+	0.743924i	$0.267038\pi$
$198$	−3.47787			−0.247162
$199$	−11.6274	−	20.1392i	−0.824241	−	1.42763i	−0.902498	−	0.430694i	$-0.858269\pi$
$199$	−11.6274	−	20.1392i	−0.824241	−	1.42763i	0.0782569	−	0.996933i	$-0.475065\pi$
$200$	−12.6987			−0.897936
$201$	−1.12164	+	8.10814i	−0.0791142	+	0.571904i
$202$	0.341205			0.0240071
$203$	6.62118	+	11.4682i	0.464715	+	0.804911i
$204$	5.74600			0.402300
$205$	−12.4479	+	21.5604i	−0.869400	+	1.50584i
$206$	1.46505			0.102075
$207$	0.160294	+	0.277638i	0.0111412	+	0.0192971i
$208$	1.50636	−	2.60909i	0.104447	−	0.180908i
$209$	5.94657			0.411333
$210$	−4.34921			−0.300124
$211$	9.40278	+	16.2861i	0.647314	+	1.12118i	0.983762	+	0.179479i	$0.0574411\pi$
$211$	9.40278	+	16.2861i	0.647314	+	1.12118i	−0.336448	+	0.941702i	$0.609226\pi$
$212$	9.43808	−	16.3472i	0.648210	−	1.12273i
$213$	1.02116	−	1.76870i	0.0699687	−	0.121189i
$214$	−1.17796	−	2.04029i	−0.0805238	−	0.139471i
$215$	−36.0152			−2.45622
$216$	2.35330			0.160122
$217$	−7.42286	−	12.8568i	−0.503897	−	0.872775i
$218$	3.21693	+	5.57188i	0.217878	+	0.377375i
$219$	6.23309	+	10.7960i	0.421193	+	0.729528i
$220$	−13.2807	−	23.0029i	−0.895388	−	1.55086i
$221$	3.51565	−	6.08929i	0.236488	−	0.409610i
$222$	−2.90959	+	5.03956i	−0.195279	+	0.338233i
$223$	17.6246			1.18023			0.590116	−	0.807318i	$-0.299082\pi$
$223$	17.6246			1.18023			0.590116	+	0.807318i	$0.299082\pi$
$224$	−5.86911	−	10.1656i	−0.392146	−	0.679218i
$225$	5.39615			0.359743
$226$	−6.42225			−0.427202
$227$	7.78145	−	13.4779i	0.516473	−	0.894557i	−0.483344	−	0.875430i	$-0.660578\pi$
$227$	7.78145	−	13.4779i	0.516473	−	0.894557i	0.999817	−	0.0191269i	$-0.00608864\pi$
$228$	−1.76575			−0.116940
$229$	12.5244	+	21.6929i	0.827635	+	1.43351i	0.899889	+	0.436119i	$0.143647\pi$
$229$	12.5244	+	21.6929i	0.827635	+	1.43351i	−0.0722539	+	0.997386i	$0.523019\pi$
$230$	0.341265	−	0.591088i	0.0225023	−	0.0389752i
$231$	−5.38001	−	9.31845i	−0.353979	−	0.613109i
$232$	−7.62737	+	13.2110i	−0.500761	+	0.867344i
$233$	9.14598	−	15.8413i	0.599173	−	1.03780i	−0.393770	−	0.919209i	$-0.628829\pi$
$233$	9.14598	−	15.8413i	0.599173	−	1.03780i	0.992943	−	0.118590i	$-0.0378373\pi$
$234$	0.631856	−	1.09441i	0.0413057	−	0.0715436i
$235$	−15.3032	+	26.5060i	−0.998274	+	1.72906i
$236$	−0.998857	+	1.73007i	−0.0650201	+	0.112618i
$237$	−1.61722	+	2.80112i	−0.105050	+	0.181952i
$238$	−2.47782	−	4.29171i	−0.160613	−	0.278190i
$239$	12.7400	−	22.0663i	0.824081	−	1.42735i	−0.0785382	−	0.996911i	$-0.525025\pi$
$239$	12.7400	−	22.0663i	0.824081	−	1.42735i	0.902619	−	0.430439i	$-0.141641\pi$
$240$	2.53778	+	4.39556i	0.163813	+	0.283732i
$241$	−11.6873			−0.752843			−0.376422	−	0.926448i	$-0.622846\pi$
$241$	−11.6873			−0.752843			−0.376422	+	0.926448i	$0.622846\pi$
$242$	−5.52764	+	9.57415i	−0.355330	+	0.615449i
$243$	−1.00000			−0.0641500
$244$	9.35956			0.599184
$245$	4.55716	+	7.89324i	0.291146	+	0.504281i
$246$	−5.09833			−0.325057
$247$	−1.08037	+	1.87125i	−0.0687420	+	0.119065i
$248$	8.55089	−	14.8106i	0.542982	−	0.940472i
$249$	0.0476578	+	0.0825457i	0.00302019	+	0.00523112i
$250$	−0.421697	−	0.730401i	−0.0266705	−	0.0461946i
$251$	−1.05596	−	1.82897i	−0.0666515	−	0.115444i	0.830774	−	0.556610i	$-0.187898\pi$
$251$	−1.05596	−	1.82897i	−0.0666515	−	0.115444i	−0.897425	+	0.441166i	$0.854565\pi$
$252$	1.59752	+	2.76699i	0.100634	+	0.174304i
$253$	1.68859			0.106161
$254$	8.29492			0.520470
$255$	5.92286	+	10.2587i	0.370904	+	0.642425i
$256$	4.29902	−	7.44612i	0.268689	−	0.465382i
$257$	−3.03781	+	5.26164i	−0.189493	+	0.328212i	−0.945081	−	0.326835i	$-0.894018\pi$
$257$	−3.03781	+	5.26164i	−0.189493	+	0.328212i	0.755588	+	0.655047i	$0.227351\pi$
$258$	−3.68771	−	6.38731i	−0.229587	−	0.397656i
$259$	−18.0037			−1.11869
$260$	9.65132			0.598549
$261$	3.24114	−	5.61382i	0.200622	−	0.347487i
$262$	3.64879	+	6.31990i	0.225423	+	0.390445i
$263$	9.04785			0.557914			0.278957	−	0.960304i	$-0.410011\pi$
$263$	9.04785			0.557914			0.278957	+	0.960304i	$0.410011\pi$
$264$	6.19759	−	10.7345i	0.381435	−	0.660665i
$265$	38.9144			2.39049
$266$	0.761438	+	1.31885i	0.0466868	+	0.0808638i
$267$	6.17088			0.377651
$268$	−10.1051	−	7.85984i	−0.617269	−	0.480116i
$269$	−5.57862			−0.340135			−0.170067	−	0.985432i	$-0.554399\pi$
$269$	−5.57862			−0.340135			−0.170067	+	0.985432i	$0.554399\pi$
$270$	1.06450	+	1.84376i	0.0647831	+	0.112208i
$271$	28.0141			1.70174			0.850869	−	0.525378i	$-0.176076\pi$
$271$	28.0141			1.70174			0.850869	+	0.525378i	$0.176076\pi$
$272$	−2.89163	+	5.00846i	−0.175331	+	0.303682i
$273$	3.90974			0.236628
$274$	4.95737	+	8.58641i	0.299486	+	0.518724i
$275$	14.2112	−	24.6145i	0.856966	−	1.48431i
$276$	−0.501404			−0.0301810
$277$	−16.0511			−0.964415			−0.482207	−	0.876057i	$-0.660165\pi$
$277$	−16.0511			−0.964415			−0.482207	+	0.876057i	$0.660165\pi$
$278$	−4.75100	−	8.22898i	−0.284946	−	0.493541i
$279$	−3.63358	+	6.29354i	−0.217537	+	0.376785i
$280$	7.75032	−	13.4239i	0.463170	−	0.802234i
$281$	6.22591	+	10.7836i	0.371407	+	0.643296i	0.989782	−	0.142587i	$-0.0455422\pi$
$281$	6.22591	+	10.7836i	0.371407	+	0.643296i	−0.618375	+	0.785883i	$0.712209\pi$
$282$	−6.26780			−0.373242
$283$	−15.5545			−0.924619			−0.462310	−	0.886719i	$-0.652979\pi$
$283$	−15.5545			−0.924619			−0.462310	+	0.886719i	$0.652979\pi$
$284$	1.59711	+	2.76627i	0.0947708	+	0.164148i
$285$	−1.82010	−	3.15251i	−0.107814	−	0.186739i
$286$	−3.32808	−	5.76441i	−0.196794	−	0.340857i
$287$	−7.88673	−	13.6602i	−0.465539	−	0.806337i
$288$	−2.87300	+	4.97618i	−0.169293	+	0.293224i
$289$	1.75129	−	3.03332i	0.103017	−	0.178430i
$290$	−13.8007			−0.810406
$291$	−5.80974	−	10.0628i	−0.340573	−	0.589890i
$292$	−19.4973			−1.14099
$293$	−5.69650			−0.332793			−0.166397	−	0.986059i	$-0.553213\pi$
$293$	−5.69650			−0.332793			−0.166397	+	0.986059i	$0.553213\pi$
$294$	−0.933245	+	1.61643i	−0.0544280	+	0.0942720i
$295$	−4.11841			−0.239783
$296$	−10.3698	−	17.9611i	−0.602734	−	1.04397i
$297$	−2.63358	+	4.56149i	−0.152816	+	0.264685i
$298$	5.63562	+	9.76118i	0.326463	+	0.565450i
$299$	−0.306781	+	0.531360i	−0.0177416	+	0.0307293i
$300$	−4.21982	+	7.30894i	−0.243631	+	0.421982i
$301$	11.4092	−	19.7614i	0.657617	−	1.13903i
$302$	0.0885205	−	0.153322i	0.00509378	−	0.00882269i
$303$	0.258373	−	0.447516i	0.0148432	−	0.0257091i
$304$	0.888603	−	1.53911i	0.0509649	−	0.0882738i
$305$	9.64765	+	16.7102i	0.552423	+	0.956825i
$306$	−1.21292	+	2.10084i	−0.0693381	+	0.120097i
$307$	−7.19048	−	12.4543i	−0.410382	−	0.710803i	0.584549	−	0.811358i	$-0.301271\pi$
$307$	−7.19048	−	12.4543i	−0.410382	−	0.710803i	−0.994931	+	0.100555i	$0.967938\pi$
$308$	16.8288			0.958910
$309$	1.10939	−	1.92152i	0.0631109	−	0.109311i
$310$	15.4717			0.878734
$311$	26.8484			1.52243			0.761217	−	0.648497i	$-0.224602\pi$
$311$	26.8484			1.52243			0.761217	+	0.648497i	$0.224602\pi$
$312$	2.25194	+	3.90048i	0.127491	+	0.220821i
$313$	17.3971			0.983343			0.491672	−	0.870781i	$-0.336386\pi$
$313$	17.3971			0.983343			0.491672	+	0.870781i	$0.336386\pi$
$314$	3.94048	−	6.82510i	0.222374	−	0.385163i
$315$	−3.29339	+	5.70432i	−0.185561	+	0.321402i
$316$	−2.52936	−	4.38098i	−0.142288	−	0.246449i
$317$	−3.65522	−	6.33103i	−0.205298	−	0.355586i	0.744930	−	0.667143i	$-0.232483\pi$
$317$	−3.65522	−	6.33103i	−0.205298	−	0.355586i	−0.950228	+	0.311557i	$0.899150\pi$
$318$	3.98457	+	6.90147i	0.223443	+	0.387015i
$319$	−17.0716	−	29.5689i	−0.955827	−	1.65554i
$320$	2.08205			0.116390
$321$	−3.56799			−0.199146
$322$	0.216218	+	0.374501i	0.0120494	+	0.0208701i
$323$	2.07389	−	3.59208i	0.115394	−	0.199869i
$324$	0.782006	−	1.35447i	0.0434448	−	0.0752485i
$325$	5.16374	+	8.94386i	0.286433	+	0.496116i
$326$	−12.7903			−0.708392
$327$	9.74392			0.538840
$328$	9.08525	−	15.7361i	0.501649	−	0.868881i
$329$	−9.69581	−	16.7936i	−0.534548	−	0.925864i
$330$	11.2137			0.617295
$331$	−13.1276	+	22.7376i	−0.721556	+	1.24977i	0.238819	+	0.971064i	$0.423240\pi$
$331$	−13.1276	+	22.7376i	−0.721556	+	1.24977i	−0.960376	+	0.278708i	$0.910094\pi$
$332$	−0.149075			−0.00818154
$333$	4.40651	+	7.63230i	0.241475	+	0.418247i
$334$	−5.51563			−0.301802
$335$	3.61650	−	26.1431i	0.197591	−	1.42835i
$336$	−3.21577			−0.175434
$337$	9.41981	+	16.3156i	0.513129	+	0.888766i	0.999884	+	0.0152276i	$0.00484727\pi$
$337$	9.41981	+	16.3156i	0.513129	+	0.888766i	−0.486755	+	0.873539i	$0.661819\pi$
$338$	−6.16525			−0.335346
$339$	−4.86317	+	8.42326i	−0.264131	+	0.457489i
$340$	−18.5269			−1.00476
$341$	19.1386	+	33.1491i	1.03642	+	1.79512i
$342$	0.372733	−	0.645592i	0.0201551	−	0.0349096i
$343$	−20.0746			−1.08393
$344$	26.2861			1.41725
$345$	−0.516837	−	0.895188i	−0.0278256	−	0.0481953i
$346$	−6.11689	+	10.5948i	−0.328846	+	0.569578i
$347$	−8.06401	+	13.9673i	−0.432899	+	0.749803i	−0.997122	−	0.0758199i	$-0.975843\pi$
$347$	−8.06401	+	13.9673i	−0.432899	+	0.749803i	0.564223	+	0.825623i	$0.309176\pi$
$348$	5.06919	+	8.78009i	0.271737	+	0.470662i
$349$	1.07056			0.0573060			0.0286530	−	0.999589i	$-0.490878\pi$
$349$	1.07056			0.0573060			0.0286530	+	0.999589i	$0.490878\pi$
$350$	7.27877			0.389067
$351$	−0.956931	−	1.65745i	−0.0510772	−	0.0884683i
$352$	15.1325	+	26.2103i	0.806567	+	1.39702i
$353$	−9.61194	−	16.6484i	−0.511592	−	0.886103i	−0.999910	−	0.0134371i	$-0.995723\pi$
$353$	−9.61194	−	16.6484i	−0.511592	−	0.886103i	0.488318	−	0.872666i	$-0.337611\pi$
$354$	−0.421697	−	0.730401i	−0.0224130	−	0.0388204i
$355$	−3.29253	+	5.70283i	−0.174749	+	0.302675i
$356$	−4.82566	+	8.35829i	−0.255759	+	0.442988i
$357$	−7.50520			−0.397217
$358$	−3.72437	−	6.45080i	−0.196839	−	0.340936i
$359$	−15.0350			−0.793519			−0.396760	−	0.917923i	$-0.629865\pi$
$359$	−15.0350			−0.793519			−0.396760	+	0.917923i	$0.629865\pi$
$360$	−7.58775			−0.399909
$361$	8.86269	−	15.3506i	0.466457	−	0.807928i
$362$	−7.69849			−0.404624
$363$	8.37147	+	14.4998i	0.439388	+	0.761043i
$364$	−3.05744	+	5.29563i	−0.160253	+	0.277567i
$365$	−20.0974	−	34.8097i	−1.05195	−	1.82202i
$366$	−1.97571	+	3.42203i	−0.103272	+	0.178872i
$367$	−5.93223	+	10.2749i	−0.309660	+	0.536347i	−0.978288	−	0.207250i	$-0.933549\pi$
$367$	−5.93223	+	10.2749i	−0.309660	+	0.536347i	0.668628	+	0.743597i	$0.266882\pi$
$368$	0.252328	−	0.437045i	0.0131535	−	0.0227825i
$369$	−3.86065	+	6.68684i	−0.200977	+	0.348103i
$370$	9.38142	−	16.2491i	0.487717	−	0.844750i
$371$	−12.3277	+	21.3521i	−0.640020	+	1.10855i
$372$	−5.68296	−	9.84317i	−0.294648	−	0.510345i
$373$	−8.06860	+	13.9752i	−0.417776	+	0.723610i	−0.995715	−	0.0924701i	$-0.970524\pi$
$373$	−8.06860	+	13.9752i	−0.417776	+	0.723610i	0.577939	+	0.816080i	$0.303857\pi$
$374$	6.38865	+	11.0655i	0.330349	+	0.572182i
$375$	−1.27730			−0.0659596
$376$	11.1692	−	19.3457i	0.576010	−	0.997679i
$377$	12.4062			0.638952
$378$	−1.34888			−0.0693791
$379$	−1.07233	−	1.85733i	−0.0550819	−	0.0954047i	0.837170	−	0.546943i	$-0.184209\pi$
$379$	−1.07233	−	1.85733i	−0.0550819	−	0.0954047i	−0.892252	+	0.451539i	$0.850875\pi$
$380$	5.69333			0.292062
$381$	6.28123	−	10.8794i	0.321797	−	0.557369i
$382$	−0.132117	+	0.228833i	−0.00675969	+	0.0117081i
$383$	8.60611	+	14.9062i	0.439752	+	0.761673i	0.997670	−	0.0682234i	$-0.0217330\pi$
$383$	8.60611	+	14.9062i	0.439752	+	0.761673i	−0.557918	+	0.829896i	$0.688400\pi$
$384$	−5.53281	−	9.58311i	−0.282345	−	0.489036i
$385$	17.3468	+	30.0455i	0.884075	+	1.53126i
$386$	3.17783	+	5.50417i	0.161747	+	0.280155i
$387$	−11.1699			−0.567798
$388$	18.1730			0.922595
$389$	−18.5702	−	32.1645i	−0.941547	−	1.63081i	−0.762522	−	0.646963i	$-0.776039\pi$
$389$	−18.5702	−	32.1645i	−0.941547	−	1.63081i	−0.179025	−	0.983844i	$-0.557294\pi$
$390$	−2.03730	+	3.52870i	−0.103163	+	0.178683i
$391$	0.588902	−	1.02001i	0.0297821	−	0.0515840i
$392$	−3.32610	−	5.76097i	−0.167993	−	0.290973i
$393$	11.0520			0.557501
$394$	5.74827			0.289594
$395$	5.21443	−	9.03165i	0.262366	−	0.454432i
$396$	−4.11895	−	7.13423i	−0.206985	−	0.358508i
$397$	−8.24328			−0.413718			−0.206859	−	0.978371i	$-0.566324\pi$
$397$	−8.24328			−0.413718			−0.206859	+	0.978371i	$0.566324\pi$
$398$	−7.67747	+	13.2978i	−0.384837	+	0.666557i
$399$	2.30636			0.115462
$400$	−4.24719	−	7.35635i	−0.212359	−	0.367817i
$401$	−31.7184			−1.58394			−0.791971	−	0.610559i	$-0.790945\pi$
$401$	−31.7184			−1.58394			−0.791971	+	0.610559i	$0.790945\pi$
$402$	5.00680	−	2.03549i	0.249716	−	0.101521i
$403$	−13.9083			−0.692823
$404$	0.404099	+	0.699920i	0.0201047	+	0.0348223i
$405$	3.22431			0.160217
$406$	4.37192	−	7.57239i	0.216975	−	0.375812i
$407$	46.4196			2.30093
$408$	−4.32287	−	7.48743i	−0.214014	−	0.370683i
$409$	14.1297	−	24.4734i	0.698670	−	1.21013i	−0.270258	−	0.962788i	$-0.587109\pi$
$409$	14.1297	−	24.4734i	0.698670	−	1.21013i	0.968928	−	0.247344i	$-0.0795576\pi$
$410$	16.4386			0.811843
$411$	15.0156			0.740667
$412$	1.73510	+	3.00528i	0.0854821	+	0.148059i
$413$	1.30467	−	2.25975i	0.0641986	−	0.111195i
$414$	0.105841	−	0.183322i	0.00520181	−	0.00900981i
$415$	−0.153663	−	0.266153i	−0.00754303	−	0.0130649i
$416$	−10.9970			−0.539174
$417$	−14.3906			−0.704709
$418$	−1.96324	−	3.40044i	−0.0960253	−	0.166321i
$419$	6.39790	+	11.0815i	0.312558	+	0.541366i	0.978915	−	0.204267i	$-0.0654809\pi$
$419$	6.39790	+	11.0815i	0.312558	+	0.541366i	−0.666358	+	0.745632i	$0.732148\pi$
$420$	−5.15090	−	8.92162i	−0.251338	−	0.435330i
$421$	−1.48916	−	2.57929i	−0.0725770	−	0.125707i	0.827453	−	0.561535i	$-0.189789\pi$
$421$	−1.48916	−	2.57929i	−0.0725770	−	0.125707i	−0.900030	+	0.435828i	$0.856456\pi$
$422$	6.20860	−	10.7536i	0.302230	−	0.523478i
$423$	−4.74622	+	8.22069i	−0.230769	+	0.399703i
$424$	−28.4021			−1.37933
$425$	−9.91241	−	17.1688i	−0.480823	−	0.832809i
$426$	−1.34853			−0.0653366
$427$	−12.2251			−0.591614
$428$	2.79019	−	4.83275i	0.134869	−	0.233600i
$429$	−10.0806			−0.486696
$430$	11.8903	+	20.5946i	0.573402	+	0.993161i
$431$	−8.22062	+	14.2385i	−0.395974	+	0.685846i	−0.993225	−	0.116208i	$-0.962926\pi$
$431$	−8.22062	+	14.2385i	−0.395974	+	0.685846i	0.597251	+	0.802054i	$0.296259\pi$
$432$	0.787078	+	1.36326i	0.0378683	+	0.0655898i
$433$	17.7607	−	30.7624i	0.853523	−	1.47835i	−0.0244855	−	0.999700i	$-0.507795\pi$
$433$	17.7607	−	30.7624i	0.853523	−	1.47835i	0.878009	−	0.478645i	$-0.158872\pi$
$434$	−4.90127	+	8.48925i	−0.235269	+	0.407497i
$435$	−10.4504	+	18.1007i	−0.501060	+	0.867862i
$436$	−7.61980	+	13.1979i	−0.364922	+	0.632064i
$437$	−0.180971	+	0.313450i	−0.00865699	+	0.0149944i
$438$	4.11567	−	7.12855i	0.196654	−	0.340615i
$439$	18.3086	+	31.7114i	0.873821	+	1.51350i	0.858013	+	0.513628i	$0.171699\pi$
$439$	18.3086	+	31.7114i	0.873821	+	1.51350i	0.0158080	+	0.999875i	$0.494968\pi$
$440$	−19.9829	+	34.6114i	−0.952649	+	1.65004i
$441$	1.41338	+	2.44804i	0.0673037	+	0.116573i
$442$	−4.64273			−0.220832
$443$	0.231994	−	0.401825i	0.0110224	−	0.0190913i	−0.860462	−	0.509515i	$-0.829825\pi$
$443$	0.231994	−	0.401825i	0.0110224	−	0.0190913i	0.871484	+	0.490424i	$0.163158\pi$
$444$	−13.7837			−0.654144
$445$	−19.8968			−0.943198
$446$	−5.81872	−	10.0783i	−0.275524	−	0.477222i
$447$	17.0700			0.807385
$448$	−0.659573	+	1.14241i	−0.0311619	+	0.0539740i
$449$	−10.6278	+	18.4080i	−0.501559	+	0.868726i	0.498439	+	0.866925i	$0.333907\pi$
$449$	−10.6278	+	18.4080i	−0.501559	+	0.868726i	−0.999998	+	0.00180127i	$0.999427\pi$
$450$	−1.78152	−	3.08569i	−0.0839818	−	0.145461i
$451$	20.3346	+	35.2206i	0.957521	+	1.65847i
$452$	−7.60606	−	13.1741i	−0.357759	−	0.619657i
$453$	−0.134062	−	0.232203i	−0.00629879	−	0.0109098i
$454$	−10.2761			−0.482281
$455$	−12.6062			−0.590987
$456$	1.32842	+	2.30090i	0.0622092	+	0.107749i
$457$	−12.5122	+	21.6718i	−0.585297	+	1.01376i	0.409542	+	0.912291i	$0.365689\pi$
$457$	−12.5122	+	21.6718i	−0.585297	+	1.01376i	−0.994838	+	0.101472i	$0.967645\pi$
$458$	8.26978	−	14.3237i	0.386421	−	0.669302i
$459$	1.83694	+	3.18168i	0.0857411	+	0.148508i
$460$	1.61668			0.0753781
$461$	9.45463			0.440346			0.220173	−	0.975461i	$-0.429338\pi$
$461$	9.45463			0.440346			0.220173	+	0.975461i	$0.429338\pi$
$462$	−3.55239	+	6.15292i	−0.165272	+	0.286260i
$463$	−3.01407	−	5.22053i	−0.140076	−	0.242619i	0.787449	−	0.616380i	$-0.211401\pi$
$463$	−3.01407	−	5.22053i	−0.140076	−	0.242619i	−0.927525	+	0.373761i	$0.878068\pi$
$464$	−10.2041			−0.473715
$465$	11.7158	−	20.2923i	0.543306	−	0.941033i
$466$	−12.0781			−0.559506
$467$	2.87800	+	4.98484i	0.133178	+	0.230671i	0.924900	−	0.380211i	$-0.124149\pi$
$467$	2.87800	+	4.98484i	0.133178	+	0.230671i	−0.791722	+	0.610881i	$0.790815\pi$
$468$	2.99330			0.138365
$469$	13.1989	+	10.2662i	0.609470	+	0.474050i
$470$	20.2093			0.932185
$471$	−5.96776	−	10.3365i	−0.274980	−	0.476279i
$472$	3.00587			0.138356
$473$	−29.4168	+	50.9515i	−1.35259	+	2.34275i
$474$	2.13569			0.0980954
$475$	3.04610	+	5.27600i	0.139765	+	0.242079i
$476$	5.86911	−	10.1656i	0.269010	−	0.465939i
$477$	12.0691			0.552605
$478$	−16.8243			−0.769525
$479$	12.0233	+	20.8249i	0.549356	+	0.951513i	0.998319	+	0.0579625i	$0.0184604\pi$
$479$	12.0233	+	20.8249i	0.549356	+	0.951513i	−0.448962	+	0.893551i	$0.648206\pi$
$480$	9.26343	−	16.0447i	0.422816	−	0.732338i
$481$	−8.43345	+	14.6072i	−0.384532	+	0.666029i
$482$	3.85852	+	6.68315i	0.175751	+	0.304409i
$483$	0.654914			0.0297996
$484$	−26.1862			−1.19028
$485$	18.7324	+	32.4454i	0.850594	+	1.47327i
$486$	0.330147	+	0.571831i	0.0149758	+	0.0259388i
$487$	−12.0393	−	20.8527i	−0.545555	−	0.944928i	−0.998572	−	0.0534264i	$-0.982986\pi$
$487$	−12.0393	−	20.8527i	−0.545555	−	0.944928i	0.453017	−	0.891502i	$-0.350348\pi$
$488$	−7.04145	−	12.1961i	−0.318751	−	0.552094i
$489$	−9.68534	+	16.7755i	−0.437986	+	0.758615i
$490$	3.00907	−	5.21186i	0.135936	−	0.235448i
$491$	12.6417			0.570511			0.285255	−	0.958452i	$-0.407922\pi$
$491$	12.6417			0.570511			0.285255	+	0.958452i	$0.407922\pi$
$492$	−6.03810	−	10.4583i	−0.272219	−	0.471496i
$493$	−23.8152			−1.07258
$494$	1.42672			0.0641911
$495$	8.49146	−	14.7076i	0.381663	−	0.661060i
$496$	11.4396			0.513655
$497$	−2.08608	−	3.61319i	−0.0935734	−	0.162074i
$498$	0.0314682	−	0.0545045i	0.00141012	−	0.00244240i
$499$	−3.23646	−	5.60572i	−0.144884	−	0.250947i	0.784446	−	0.620198i	$-0.212948\pi$
$499$	−3.23646	−	5.60572i	−0.144884	−	0.250947i	−0.929330	+	0.369251i	$0.879614\pi$
$500$	0.998857	−	1.73007i	0.0446703	−	0.0773712i
$501$	−4.17665	+	7.23417i	−0.186599	+	0.323199i
$502$	−0.697243	+	1.20766i	−0.0311195	+	0.0539005i
$503$	17.8451	−	30.9086i	0.795674	−	1.37815i	−0.126736	−	0.991936i	$-0.540450\pi$
$503$	17.8451	−	30.9086i	0.795674	−	1.37815i	0.922410	−	0.386211i	$-0.126216\pi$
$504$	2.40372	−	4.16336i	0.107070	−	0.185451i
$505$	−0.833075	+	1.44293i	−0.0370714	+	0.0642095i
$506$	−0.557483	−	0.965588i	−0.0247831	−	0.0429256i
$507$	−4.66857	+	8.08619i	−0.207338	+	0.359121i
$508$	9.82392	+	17.0155i	0.435866	+	0.754942i
$509$	−26.6705			−1.18215			−0.591076	−	0.806616i	$-0.701297\pi$
$509$	−26.6705			−1.18215			−0.591076	+	0.806616i	$0.701297\pi$
$510$	3.91083	−	6.77376i	0.173175	−	0.299947i
$511$	25.4666			1.12657
$512$	16.4540			0.727171
$513$	−0.564495	−	0.977734i	−0.0249231	−	0.0431680i
$514$	4.01169			0.176948
$515$	−3.57701	+	6.19556i	−0.157622	+	0.273009i
$516$	8.73493	−	15.1293i	0.384534	−	0.666032i
$517$	24.9991	+	43.2996i	1.09946	+	1.90432i
$518$	5.94387	+	10.2951i	0.261158	+	0.452340i
$519$	9.26388	+	16.0455i	0.406639	+	0.704320i
$520$	−7.26095	−	12.5763i	−0.318414	−	0.551509i
$521$	−8.08047			−0.354012			−0.177006	−	0.984210i	$-0.556641\pi$
$521$	−8.08047			−0.354012			−0.177006	+	0.984210i	$0.556641\pi$
$522$	−4.28022			−0.187340
$523$	−8.10686	−	14.0415i	−0.354488	−	0.613992i	0.632542	−	0.774526i	$-0.282012\pi$
$523$	−8.10686	−	14.0415i	−0.354488	−	0.613992i	−0.987030	+	0.160534i	$0.948678\pi$
$524$	−8.64275	+	14.9697i	−0.377560	+	0.653954i
$525$	5.51177	−	9.54666i	0.240553	−	0.416650i
$526$	−2.98712	−	5.17384i	−0.130245	−	0.225590i
$527$	26.6987			1.16301
$528$	8.29133			0.360834
$529$	11.4486	−	19.8296i	0.497766	−	0.862156i
$530$	−12.8475	−	22.2525i	−0.558058	−	0.966585i
$531$	−1.27730			−0.0554302
$532$	−1.80359	+	3.12390i	−0.0781954	+	0.135438i
$533$	−14.7775			−0.640084
$534$	−2.03730	−	3.52870i	−0.0881624	−	0.152702i
$535$	11.5043			0.497374
$536$	−2.63955	+	19.0809i	−0.114011	+	0.824167i
$537$	−11.2810			−0.486809
$538$	1.84177	+	3.19003i	0.0794042	+	0.137532i
$539$	14.8890			0.641313
$540$	−2.52143	+	4.36724i	−0.108505	+	0.187936i
$541$	18.8161			0.808968			0.404484	−	0.914545i	$-0.367451\pi$
$541$	18.8161			0.808968			0.404484	+	0.914545i	$0.367451\pi$
$542$	−9.24878	−	16.0194i	−0.397269	−	0.688091i
$543$	−5.82959	+	10.0971i	−0.250172	+	0.433310i
$544$	21.1101			0.905089
$545$	−31.4174			−1.34577
$546$	−1.29079	−	2.23571i	−0.0552406	−	0.0956796i
$547$	3.97681	−	6.88803i	0.170036	−	0.294511i	−0.768396	−	0.639974i	$-0.778945\pi$
$547$	3.97681	−	6.88803i	0.170036	−	0.294511i	0.938432	+	0.345464i	$0.112278\pi$
$548$	−11.7423	+	20.3383i	−0.501607	+	0.868808i
$549$	2.99216	+	5.18258i	0.127702	+	0.221187i
$550$	−18.7671			−0.800233
$551$	7.31844			0.311776
$552$	0.377220	+	0.653363i	0.0160555	+	0.0278090i
$553$	3.30375	+	5.72226i	0.140490	+	0.243335i
$554$	5.29921	+	9.17850i	0.225142	+	0.389957i
$555$	−14.2079	−	24.6089i	−0.603093	−	1.04459i
$556$	11.2535	−	19.4916i	0.477255	−	0.826630i
$557$	16.6803	−	28.8912i	0.706768	−	1.22416i	−0.259282	−	0.965802i	$-0.583486\pi$
$557$	16.6803	−	28.8912i	0.706768	−	1.22416i	0.966050	−	0.258356i	$-0.0831808\pi$
$558$	4.79846			0.203135
$559$	−10.6888	−	18.5136i	−0.452089	−	0.783042i
$560$	10.3686			0.438154
$561$	19.3509			0.816997
$562$	4.11093	−	7.12035i	0.173409	−	0.300354i
$563$	−42.4288			−1.78816			−0.894081	−	0.447906i	$-0.852170\pi$
$563$	−42.4288			−1.78816			−0.894081	+	0.447906i	$0.852170\pi$
$564$	−7.42314	−	12.8572i	−0.312570	−	0.541388i
$565$	15.6804	−	27.1592i	0.659678	−	1.14260i
$566$	5.13527	+	8.89456i	0.215852	+	0.373866i
$567$	−1.02143	+	1.76916i	−0.0428959	+	0.0742978i
$568$	2.40309	−	4.16228i	0.100831	−	0.174645i
$569$	11.3592	−	19.6747i	0.476202	−	0.824807i	−0.523426	−	0.852071i	$-0.675346\pi$
$569$	11.3592	−	19.6747i	0.476202	−	0.824807i	0.999628	+	0.0272645i	$0.00867964\pi$
$570$	−1.20180	+	2.08159i	−0.0503381	+	0.0871881i
$571$	2.24391	−	3.88656i	0.0939046	−	0.162648i	−0.815246	−	0.579114i	$-0.803398\pi$
$571$	2.24391	−	3.88656i	0.0939046	−	0.162648i	0.909151	+	0.416467i	$0.136732\pi$
$572$	7.88310	−	13.6539i	0.329609	−	0.570899i
$573$	0.200088	+	0.346563i	0.00835880	+	0.0144779i
$574$	−5.20756	+	9.01976i	−0.217359	+	0.376478i
$575$	0.864971	+	1.49817i	0.0360718	+	0.0624782i
$576$	0.645737			0.0269057
$577$	2.96272	−	5.13159i	0.123340	−	0.213631i	−0.797743	−	0.602998i	$-0.793973\pi$
$577$	2.96272	−	5.13159i	0.123340	−	0.213631i	0.921083	+	0.389367i	$0.127306\pi$
$578$	−2.31273			−0.0961969
$579$	9.62550			0.400022
$580$	−16.3446	−	28.3097i	−0.678673	−	1.17550i
$581$	0.194716			0.00807817
$582$	−3.83614	+	6.64439i	−0.159013	+	0.275419i
$583$	31.7848	−	55.0529i	1.31639	−	2.28006i
$584$	14.6683	+	25.4063i	0.606979	+	1.05132i
$585$	3.08544	+	5.34413i	0.127567	+	0.220953i
$586$	1.88068	+	3.25744i	0.0776903	+	0.134564i
$587$	5.99440	+	10.3826i	0.247415	+	0.428536i	0.962808	−	0.270187i	$-0.0870854\pi$
$587$	5.99440	+	10.3826i	0.247415	+	0.428536i	−0.715392	+	0.698723i	$0.753752\pi$
$588$	−4.42108			−0.182322
$589$	−8.20455			−0.338063
$590$	1.35968	+	2.35504i	0.0559772	+	0.0969554i
$591$	4.35281	−	7.53929i	0.179051	−	0.310125i
$592$	6.93653	−	12.0144i	0.285090	−	0.493790i
$593$	7.20177	+	12.4738i	0.295741	+	0.512239i	0.975157	−	0.221515i	$-0.0711000\pi$
$593$	7.20177	+	12.4738i	0.295741	+	0.512239i	−0.679416	+	0.733754i	$0.737767\pi$
$594$	3.47787			0.142699
$595$	24.1991			0.992065
$596$	−13.3489	+	23.1209i	−0.546791	+	0.947069i
$597$	11.6274	+	20.1392i	0.475876	+	0.824241i
$598$	0.405131			0.0165670
$599$	8.59056	−	14.8793i	0.351001	−	0.607951i	−0.635424	−	0.772163i	$-0.719175\pi$
$599$	8.59056	−	14.8793i	0.351001	−	0.607951i	0.986425	+	0.164212i	$0.0525081\pi$
$600$	12.6987			0.518424
$601$	−0.0320328	−	0.0554824i	−0.00130664	−	0.00226317i	0.865371	−	0.501131i	$-0.167083\pi$
$601$	−0.0320328	−	0.0554824i	−0.00130664	−	0.00226317i	−0.866678	+	0.498868i	$0.833749\pi$
$602$	−15.0669			−0.614081
$603$	1.12164	−	8.10814i	0.0456766	−	0.330189i
$604$	0.419350			0.0170631
$605$	−26.9922	−	46.7519i	−1.09739	−	1.90073i
$606$	−0.341205			−0.0138605
$607$	10.2195	−	17.7007i	0.414796	−	0.718448i	−0.580611	−	0.814181i	$-0.697186\pi$
$607$	10.2195	−	17.7007i	0.414796	−	0.718448i	0.995407	+	0.0957334i	$0.0305196\pi$
$608$	−6.48718			−0.263090
$609$	−6.62118	−	11.4682i	−0.268304	−	0.464715i
$610$	6.37029	−	11.0337i	0.257925	−	0.446740i
$611$	−18.1672			−0.734966
$612$	−5.74600			−0.232268
$613$	−10.6264	−	18.4054i	−0.429194	−	0.743387i	0.567607	−	0.823299i	$-0.307869\pi$
$613$	−10.6264	−	18.4054i	−0.429194	−	0.743387i	−0.996802	+	0.0799127i	$0.974536\pi$
$614$	−4.74783	+	8.22348i	−0.191607	+	0.331873i
$615$	12.4479	−	21.5604i	0.501948	−	0.869400i
$616$	−12.6608	−	21.9291i	−0.510117	−	0.883548i
$617$	−38.0615			−1.53230			−0.766150	−	0.642662i	$-0.777830\pi$
$617$	−38.0615			−1.53230			−0.766150	+	0.642662i	$0.777830\pi$
$618$	−1.46505			−0.0589328
$619$	16.4348	+	28.4659i	0.660570	+	1.14414i	0.980466	+	0.196688i	$0.0630186\pi$
$619$	16.4348	+	28.4659i	0.660570	+	1.14414i	−0.319896	+	0.947453i	$0.603648\pi$
$620$	18.3236	+	31.7374i	0.735893	+	1.27460i
$621$	−0.160294	−	0.277638i	−0.00643238	−	0.0111412i
$622$	−8.86392	−	15.3528i	−0.355411	−	0.615590i
$623$	6.30309	−	10.9173i	0.252528	−	0.437391i
$624$	−1.50636	+	2.60909i	−0.0603026	+	0.104447i
$625$	−22.8623			−0.914493
$626$	−5.74361	−	9.94822i	−0.229561	−	0.397611i
$627$	−5.94657			−0.237483
$628$	18.6673			0.744906
$629$	16.1890	−	28.0402i	0.645498	−	1.11804i
$630$	4.34921			0.173277
$631$	−7.05296	−	12.2161i	−0.280774	−	0.486314i	0.690802	−	0.723044i	$-0.257258\pi$
$631$	−7.05296	−	12.2161i	−0.280774	−	0.486314i	−0.971576	+	0.236730i	$0.923924\pi$
$632$	−3.80581	+	6.59185i	−0.151387	+	0.262210i
$633$	−9.40278	−	16.2861i	−0.373727	−	0.647314i
$634$	−2.41352	+	4.18034i	−0.0958532	+	0.166023i
$635$	−20.2526	+	35.0785i	−0.803700	+	1.39205i
$636$	−9.43808	+	16.3472i	−0.374244	+	0.648210i
$637$	−2.70501	+	4.68522i	−0.107176	+	0.185635i
$638$	−11.2723	+	19.5242i	−0.446274	+	0.772969i
$639$	−1.02116	+	1.76870i	−0.0403965	+	0.0699687i
$640$	17.8395	+	30.8989i	0.705167	+	1.22139i
$641$	−18.6767	+	32.3489i	−0.737683	+	1.27771i	0.215853	+	0.976426i	$0.430747\pi$
$641$	−18.6767	+	32.3489i	−0.737683	+	1.27771i	−0.953536	+	0.301279i	$0.902586\pi$
$642$	1.17796	+	2.04029i	0.0464904	+	0.0805238i
$643$	−9.31913			−0.367511			−0.183755	−	0.982972i	$-0.558825\pi$
$643$	−9.31913			−0.367511			−0.183755	+	0.982972i	$0.558825\pi$
$644$	−0.512147	+	0.887064i	−0.0201814	+	0.0349552i
$645$	36.0152			1.41810
$646$	−2.73875			−0.107755
$647$	−10.0322	−	17.3763i	−0.394408	−	0.683134i	0.598618	−	0.801035i	$-0.295717\pi$
$647$	−10.0322	−	17.3763i	−0.394408	−	0.683134i	−0.993025	+	0.117901i	$0.962384\pi$
$648$	−2.35330			−0.0924462
$649$	−3.36387	+	5.82640i	−0.132044	+	0.228706i
$650$	3.40959	−	5.90558i	0.133735	−	0.231636i
$651$	7.42286	+	12.8568i	0.290925	+	0.503897i
$652$	−15.1480	−	26.2371i	−0.593241	−	1.02752i
$653$	0.344246	+	0.596251i	0.0134714	+	0.0233331i	0.872683	−	0.488288i	$-0.162378\pi$
$653$	0.344246	+	0.596251i	0.0134714	+	0.0233331i	−0.859211	+	0.511621i	$0.829045\pi$
$654$	−3.21693	−	5.57188i	−0.125792	−	0.217878i
$655$	−35.6351			−1.39238
$656$	12.1545			0.474554
$657$	−6.23309	−	10.7960i	−0.243176	−	0.421193i
$658$	−6.40209	+	11.0887i	−0.249579	+	0.432284i
$659$	10.0102	−	17.3381i	0.389941	−	0.675397i	−0.602500	−	0.798119i	$-0.705829\pi$
$659$	10.0102	−	17.3381i	0.389941	−	0.675397i	0.992441	+	0.122721i	$0.0391622\pi$
$660$	13.2807	+	23.0029i	0.516952	+	0.895388i
$661$	27.6482			1.07539			0.537696	−	0.843139i	$-0.319295\pi$
$661$	27.6482			1.07539			0.537696	+	0.843139i	$0.319295\pi$
$662$	17.3361			0.673787
$663$	−3.51565	+	6.08929i	−0.136537	+	0.236488i
$664$	0.112153	+	0.194255i	0.00435238	+	0.00753854i
$665$	−7.43641			−0.288372
$666$	2.90959	−	5.03956i	0.112744	−	0.195279i
$667$	2.07814			0.0804661
$668$	−6.53233	−	11.3143i	−0.252743	−	0.437764i
$669$	−17.6246			−0.681408
$670$	−16.1434	+	6.56304i	−0.623675	+	0.253553i
$671$	31.5204			1.21683
$672$	5.86911	+	10.1656i	0.226406	+	0.392146i
$673$	22.2550			0.857867			0.428934	−	0.903336i	$-0.358889\pi$
$673$	22.2550			0.857867			0.428934	+	0.903336i	$0.358889\pi$
$674$	6.21984	−	10.7731i	0.239579	−	0.414964i
$675$	−5.39615			−0.207698
$676$	−7.30169	−	12.6469i	−0.280834	−	0.486419i
$677$	−11.1961	+	19.3922i	−0.430301	+	0.745303i	−0.996899	−	0.0786916i	$-0.974926\pi$
$677$	−11.1961	+	19.3922i	−0.430301	+	0.745303i	0.566598	+	0.823994i	$0.308259\pi$
$678$	6.42225			0.246645
$679$	−23.7369			−0.910938
$680$	13.9383	+	24.1418i	0.534507	+	0.925794i
$681$	−7.78145	+	13.4779i	−0.298186	+	0.516473i
$682$	12.6371	−	21.8881i	0.483901	−	0.838140i
$683$	2.67643	+	4.63571i	0.102411	+	0.177381i	0.912677	−	0.408681i	$-0.134011\pi$
$683$	2.67643	+	4.63571i	0.102411	+	0.177381i	−0.810267	+	0.586061i	$0.800678\pi$
$684$	1.76575			0.0675153
$685$	−48.4150			−1.84984
$686$	6.62757	+	11.4793i	0.253042	+	0.438281i
$687$	−12.5244	−	21.6929i	−0.477835	−	0.827635i
$688$	8.79159	+	15.2275i	0.335176	+	0.580542i
$689$	11.5493	+	20.0039i	0.439992	+	0.762088i
$690$	−0.341265	+	0.591088i	−0.0129917	+	0.0225023i
$691$	−4.85468	+	8.40855i	−0.184681	+	0.319876i	−0.943469	−	0.331461i	$-0.892458\pi$
$691$	−4.85468	+	8.40855i	−0.184681	+	0.319876i	0.758788	+	0.651337i	$0.225792\pi$
$692$	−28.9776			−1.10156
$693$	5.38001	+	9.31845i	0.204370	+	0.353979i
$694$	10.6492			0.404240
$695$	46.3996			1.76004
$696$	7.62737	−	13.2110i	0.289115	−	0.500761i
$697$	28.3672			1.07448
$698$	−0.353444	−	0.612182i	−0.0133780	−	0.0231714i
$699$	−9.14598	+	15.8413i	−0.345933	+	0.599173i
$700$	8.62047	+	14.9311i	0.325823	+	0.564342i
$701$	−1.32184	+	2.28950i	−0.0499254	+	0.0864733i	−0.889908	−	0.456140i	$-0.849232\pi$
$701$	−1.32184	+	2.28950i	−0.0499254	+	0.0864733i	0.839983	+	0.542613i	$0.182565\pi$
$702$	−0.631856	+	1.09441i	−0.0238479	+	0.0413057i
$703$	−4.97491	+	8.61679i	−0.187632	+	0.324988i
$704$	1.70060	−	2.94552i	0.0640938	−	0.111014i
$705$	15.3032	−	26.5060i	0.576354	−	0.998274i
$706$	−6.34670	+	10.9928i	−0.238861	+	0.413720i
$707$	−0.527819	−	0.914209i	−0.0198507	−	0.0343824i
$708$	0.998857	−	1.73007i	0.0375394	−	0.0650201i
$709$	19.6209	+	33.9844i	0.736879	+	1.27631i	0.953894	+	0.300144i	$0.0970346\pi$
$709$	19.6209	+	33.9844i	0.736879	+	1.27631i	−0.217015	+	0.976168i	$0.569632\pi$
$710$	4.34808			0.163180
$711$	1.61722	−	2.80112i	0.0606507	−	0.105050i
$712$	14.5219			0.544231
$713$	−2.32977			−0.0872504
$714$	2.47782	+	4.29171i	0.0927301	+	0.160613i
$715$	32.5030			1.21554
$716$	8.82177	−	15.2798i	0.329685	−	0.571031i
$717$	−12.7400	+	22.0663i	−0.475784	+	0.824081i
$718$	4.96377	+	8.59751i	0.185246	+	0.320856i
$719$	−20.2660	−	35.1017i	−0.755794	−	1.30907i	−0.944978	−	0.327133i	$-0.893918\pi$
$719$	−20.2660	−	35.1017i	−0.755794	−	1.30907i	0.189184	−	0.981942i	$-0.439416\pi$
$720$	−2.53778	−	4.39556i	−0.0945775	−	0.163813i
$721$	−2.26632	−	3.92538i	−0.0844021	−	0.146189i
$722$	−11.7040			−0.435576
$723$	11.6873			0.434654
$724$	−9.11755	−	15.7921i	−0.338851	−	0.586907i
$725$	17.4897	−	30.2930i	0.649551	−	1.12505i
$726$	5.52764	−	9.57415i	0.205150	−	0.355330i
$727$	−21.8100	−	37.7761i	−0.808889	−	1.40104i	−0.913634	−	0.406537i	$-0.866736\pi$
$727$	−21.8100	−	37.7761i	−0.808889	−	1.40104i	0.104745	−	0.994499i	$-0.466597\pi$
$728$	9.20077			0.341003
$729$	1.00000			0.0370370
$730$	−13.2702	+	22.9846i	−0.491152	+	0.850700i
$731$	20.5185	+	35.5390i	0.758903	+	1.31446i
$732$	−9.35956			−0.345939
$733$	2.97951	−	5.16067i	0.110051	−	0.190614i	−0.805740	−	0.592270i	$-0.798232\pi$
$733$	2.97951	−	5.16067i	0.110051	−	0.190614i	0.915791	+	0.401656i	$0.131565\pi$
$734$	7.83403			0.289159
$735$	−4.55716	−	7.89324i	−0.168094	−	0.291146i
$736$	−1.84210			−0.0679007
$737$	−34.0313	−	26.4698i	−1.25356	−	0.975026i
$738$	5.09833			0.187672
$739$	18.3262	+	31.7419i	0.674139	+	1.16764i	0.976720	+	0.214520i	$0.0688186\pi$
$739$	18.3262	+	31.7419i	0.674139	+	1.16764i	−0.302580	+	0.953124i	$0.597848\pi$
$740$	44.4427			1.63375
$741$	1.08037	−	1.87125i	0.0396882	−	0.0687420i
$742$	16.2798			0.597649
$743$	4.21190	+	7.29522i	0.154520	+	0.267636i	0.932884	−	0.360177i	$-0.117284\pi$
$743$	4.21190	+	7.29522i	0.154520	+	0.267636i	−0.778364	+	0.627813i	$0.783950\pi$
$744$	−8.55089	+	14.8106i	−0.313491	+	0.542982i
$745$	−55.0390			−2.01647
$746$	10.6553			0.390118
$747$	−0.0476578	−	0.0825457i	−0.00174371	−	0.00302019i
$748$	−15.1325	+	26.2103i	−0.553300	+	0.958344i
$749$	−3.64444	+	6.31235i	−0.133165	+	0.230648i
$750$	0.421697	+	0.730401i	0.0153982	+	0.0266705i
$751$	−35.0401			−1.27863			−0.639316	−	0.768944i	$-0.720783\pi$
$751$	−35.0401			−1.27863			−0.639316	+	0.768944i	$0.720783\pi$
$752$	14.9426			0.544899
$753$	1.05596	+	1.82897i	0.0384813	+	0.0666515i
$754$	−4.09587	−	7.09426i	−0.149163	−	0.258358i
$755$	0.432258	+	0.748692i	0.0157315	+	0.0272477i
$756$	−1.59752	−	2.76699i	−0.0581013	−	0.100634i
$757$	−7.81315	+	13.5328i	−0.283974	+	0.491857i	−0.972360	−	0.233488i	$-0.924986\pi$
$757$	−7.81315	+	13.5328i	−0.283974	+	0.491857i	0.688386	+	0.725344i	$0.258319\pi$
$758$	−0.708054	+	1.22639i	−0.0257177	+	0.0445443i
$759$	−1.68859			−0.0612919
$760$	−4.28325	−	7.41880i	−0.155370	−	0.269108i
$761$	−36.3759			−1.31862			−0.659312	−	0.751869i	$-0.729152\pi$
$761$	−36.3759			−1.31862			−0.659312	+	0.751869i	$0.729152\pi$
$762$	−8.29492			−0.300493
$763$	9.95269	−	17.2386i	0.360312	−	0.624078i
$764$	−0.625880			−0.0226436
$765$	−5.92286	−	10.2587i	−0.214142	−	0.370904i
$766$	5.68257	−	9.84249i	0.205319	−	0.355624i
$767$	−1.22229	−	2.11707i	−0.0441343	−	0.0764429i
$768$	−4.29902	+	7.44612i	−0.155127	+	0.268689i
$769$	−9.31162	+	16.1282i	−0.335785	+	0.581598i	−0.983635	−	0.180170i	$-0.942335\pi$
$769$	−9.31162	+	16.1282i	−0.335785	+	0.581598i	0.647850	+	0.761768i	$0.275668\pi$
$770$	11.4540	−	19.8389i	0.412773	−	0.714944i
$771$	3.03781	−	5.26164i	0.109404	−	0.189493i
$772$	−7.52720	+	13.0375i	−0.270910	+	0.469230i
$773$	−7.62480	+	13.2065i	−0.274245	+	0.475006i	−0.969944	−	0.243327i	$-0.921761\pi$
$773$	−7.62480	+	13.2065i	−0.274245	+	0.475006i	0.695699	+	0.718333i	$0.255095\pi$
$774$	3.68771	+	6.38731i	0.132552	+	0.229587i
$775$	−19.6073	+	33.9609i	−0.704316	+	1.21991i
$776$	−13.6720	−	23.6807i	−0.490798	−	0.850087i
$777$	18.0037			0.645879
$778$	−12.2618	+	21.2381i	−0.439607	+	0.761421i
$779$	−8.71727			−0.312329
$780$	−9.65132			−0.345573
$781$	5.37861	+	9.31603i	0.192462	+	0.333354i
$782$	−0.777697			−0.0278104
$783$	−3.24114	+	5.61382i	−0.115829	+	0.200622i
$784$	2.22488	−	3.85360i	0.0794599	−	0.137629i
$785$	19.2419	+	33.3279i	0.686772	+	1.18952i
$786$	−3.64879	−	6.31990i	−0.130148	−	0.225423i
$787$	23.5234	+	40.7438i	0.838520	+	1.45236i	0.891132	+	0.453745i	$0.149912\pi$
$787$	23.5234	+	40.7438i	0.838520	+	1.45236i	−0.0526112	+	0.998615i	$0.516754\pi$
$788$	6.80785	+	11.7915i	0.242520	+	0.420056i
$789$	−9.04785			−0.322112
$790$	−6.88611			−0.244997
$791$	9.93474	+	17.2075i	0.353239	+	0.611828i
$792$	−6.19759	+	10.7345i	−0.220222	+	0.381435i
$793$	−5.72659	+	9.91874i	−0.203357	+	0.352225i
$794$	2.72149	+	4.71376i	0.0965822	+	0.167285i
$795$	−38.9144			−1.38015
$796$	−36.3706			−1.28912
$797$	14.6381	−	25.3539i	0.518507	−	0.898081i	−0.481261	−	0.876577i	$-0.659821\pi$
$797$	14.6381	−	25.3539i	0.518507	−	0.898081i	0.999769	−	0.0215039i	$-0.00684543\pi$
$798$	−0.761438	−	1.31885i	−0.0269546	−	0.0466868i
$799$	34.8741			1.23376
$800$	−15.5031	+	26.8522i	−0.548118	+	0.949369i
$801$	−6.17088			−0.218037
$802$	10.4717	+	18.1376i	0.369770	+	0.640460i
$803$	−65.6613			−2.31714
$804$	10.1051	+	7.85984i	0.356381	+	0.277195i
$805$	−2.11164			−0.0744257
$806$	4.59180	+	7.95322i	0.161739	+	0.280140i
$807$	5.57862			0.196377
$808$	0.608029	−	1.05314i	0.0213904	−	0.0370492i
$809$	−31.1363			−1.09469			−0.547347	−	0.836906i	$-0.684362\pi$
$809$	−31.1363			−1.09469			−0.547347	+	0.836906i	$0.684362\pi$
$810$	−1.06450	−	1.84376i	−0.0374025	−	0.0647831i
$811$	−12.4717	+	21.6016i	−0.437940	+	0.758535i	−0.997530	−	0.0702348i	$-0.977625\pi$
$811$	−12.4717	+	21.6016i	−0.437940	+	0.758535i	0.559590	+	0.828769i	$0.310958\pi$
$812$	20.7112			0.726820
$813$	−28.0141			−0.982499
$814$	−15.3253	−	26.5442i	−0.537151	−	0.930373i
$815$	31.2285	−	54.0894i	1.09389	−	1.89467i
$816$	2.89163	−	5.00846i	0.101227	−	0.175331i
$817$	−6.30536	−	10.9212i	−0.220597	−	0.382084i
$818$	−18.6595			−0.652416
$819$	−3.90974			−0.136617
$820$	19.4687	+	33.7207i	0.679876	+	1.17758i
$821$	15.6193	+	27.0534i	0.545117	+	0.944170i	0.998600	+	0.0529051i	$0.0168481\pi$
$821$	15.6193	+	27.0534i	0.545117	+	0.944170i	−0.453483	+	0.891265i	$0.649819\pi$
$822$	−4.95737	−	8.58641i	−0.172908	−	0.299486i
$823$	25.9121	+	44.8810i	0.903238	+	1.56445i	0.823265	+	0.567657i	$0.192150\pi$
$823$	25.9121	+	44.8810i	0.903238	+	1.56445i	0.0799734	+	0.996797i	$0.474516\pi$
$824$	2.61072	−	4.52190i	0.0909488	−	0.157528i
$825$	−14.2112	+	24.6145i	−0.494770	+	0.856966i
$826$	−1.72293			−0.0599484
$827$	0.636715	+	1.10282i	0.0221407	+	0.0383489i	0.876883	−	0.480703i	$-0.159618\pi$
$827$	0.636715	+	1.10282i	0.0221407	+	0.0383489i	−0.854743	+	0.519052i	$0.826285\pi$
$828$	0.501404			0.0174250
$829$	−27.6332			−0.959740			−0.479870	−	0.877340i	$-0.659316\pi$
$829$	−27.6332			−0.959740			−0.479870	+	0.877340i	$0.659316\pi$
$830$	−0.101463	+	0.175739i	−0.00352183	+	0.00609999i
$831$	16.0511			0.556805
$832$	0.617926	+	1.07028i	0.0214227	+	0.0371052i
$833$	5.19259	−	8.99383i	0.179913	−	0.311618i
$834$	4.75100	+	8.22898i	0.164514	+	0.284946i
$835$	13.4668	−	23.3252i	0.466037	−	0.807201i
$836$	4.65025	−	8.05447i	0.160832	−	0.278570i
$837$	3.63358	−	6.29354i	0.125595	−	0.217537i
$838$	4.22449	−	7.31704i	0.145933	−	0.252763i
$839$	22.9444	−	39.7409i	0.792130	−	1.37201i	−0.132516	−	0.991181i	$-0.542306\pi$
$839$	22.9444	−	39.7409i	0.792130	−	1.37201i	0.924646	−	0.380828i	$-0.124361\pi$
$840$	−7.75032	+	13.4239i	−0.267411	+	0.463170i
$841$	−6.51002	−	11.2757i	−0.224483	−	0.388817i
$842$	−0.983280	+	1.70309i	−0.0338861	+	0.0586924i
$843$	−6.22591	−	10.7836i	−0.214432	−	0.371407i
$844$	29.4121			1.01241
$845$	15.0529	−	26.0724i	0.517835	−	0.896917i
$846$	6.26780			0.215491
$847$	34.2034			1.17524
$848$	−9.49929	−	16.4533i	−0.326207	−	0.565007i
$849$	15.5545			0.533829
$850$	−6.54511	+	11.3365i	−0.224495	+	0.388837i
$851$	−1.41268	+	2.44683i	−0.0484259	+	0.0838761i
$852$	−1.59711	−	2.76627i	−0.0547159	−	0.0947708i
$853$	−9.90339	−	17.1532i	−0.339086	−	0.587314i	0.645175	−	0.764035i	$-0.276784\pi$
$853$	−9.90339	−	17.1532i	−0.339086	−	0.587314i	−0.984261	+	0.176721i	$0.943451\pi$
$854$	4.03608	+	6.99070i	0.138112	+	0.239217i
$855$	1.82010	+	3.15251i	0.0622463	+	0.107814i
$856$	−8.39654			−0.286988
$857$	21.1535			0.722588			0.361294	−	0.932452i	$-0.382335\pi$
$857$	21.1535			0.722588			0.361294	+	0.932452i	$0.382335\pi$
$858$	3.32808	+	5.76441i	0.113619	+	0.196794i
$859$	1.28402	−	2.22399i	0.0438103	−	0.0758817i	−0.843289	−	0.537461i	$-0.819384\pi$
$859$	1.28402	−	2.22399i	0.0438103	−	0.0758817i	0.887099	+	0.461579i	$0.152717\pi$
$860$	−28.1641	+	48.7816i	−0.960388	+	1.66344i
$861$	7.88673	+	13.6602i	0.268779	+	0.465539i
$862$	10.8561			0.369759
$863$	−2.15077			−0.0732130			−0.0366065	−	0.999330i	$-0.511655\pi$
$863$	−2.15077			−0.0732130			−0.0366065	+	0.999330i	$0.511655\pi$
$864$	2.87300	−	4.97618i	0.0977414	−	0.169293i
$865$	−29.8696	−	51.7356i	−1.01560	−	1.75906i
$866$	−23.4545			−0.797017
$867$	−1.75129	+	3.03332i	−0.0594768	+	0.103017i
$868$	−23.2189			−0.788100
$869$	−8.51818	−	14.7539i	−0.288959	−	0.500492i
$870$	13.8007			0.467888
$871$	14.5122	−	5.89987i	0.491727	−	0.199909i
$872$	22.9303			0.776519
$873$	5.80974	+	10.0628i	0.196630	+	0.340573i
$874$	0.238988			0.00808387
$875$	−1.30467	+	2.25975i	−0.0441059	+	0.0763936i
$876$	19.4973			0.658751
$877$	−10.4560	−	18.1103i	−0.353074	−	0.611543i	0.633712	−	0.773569i	$-0.281530\pi$
$877$	−10.4560	−	18.1103i	−0.353074	−	0.611543i	−0.986786	+	0.162026i	$0.948197\pi$
$878$	12.0891	−	20.9389i	0.407986	−	0.706652i
$879$	5.69650			0.192138
$880$	−26.7338			−0.901195
$881$	2.74592	+	4.75607i	0.0925124	+	0.160236i	0.908568	−	0.417738i	$-0.137177\pi$
$881$	2.74592	+	4.75607i	0.0925124	+	0.160236i	−0.816055	+	0.577974i	$0.803844\pi$
$882$	0.933245	−	1.61643i	0.0314240	−	0.0544280i
$883$	−12.9076	+	22.3566i	−0.434376	+	0.752361i	−0.997244	−	0.0741854i	$-0.976364\pi$
$883$	−12.9076	+	22.3566i	−0.434376	+	0.752361i	0.562869	+	0.826546i	$0.309698\pi$
$884$	−5.49852	−	9.52372i	−0.184935	−	0.320317i
$885$	4.11841			0.138439
$886$	−0.306368			−0.0102926
$887$	−0.748130	−	1.29580i	−0.0251198	−	0.0435087i	0.853192	−	0.521597i	$-0.174663\pi$
$887$	−0.748130	−	1.29580i	−0.0251198	−	0.0435087i	−0.878312	+	0.478088i	$0.841330\pi$
$888$	10.3698	+	17.9611i	0.347988	+	0.602734i
$889$	−12.8316	−	22.2250i	−0.430359	−	0.745403i
$890$	6.56887	+	11.3776i	0.220189	+	0.381378i
$891$	2.63358	−	4.56149i	0.0882282	−	0.152816i
$892$	13.7826	−	23.8721i	0.461475	−	0.799297i
$893$	−10.7169			−0.358626
$894$	−5.63562	−	9.76118i	−0.188483	−	0.326463i
$895$	36.3732			1.21582
$896$	−22.6054			−0.755194
$897$	0.306781	−	0.531360i	0.0102431	−	0.0177416i
$898$	14.0350			0.468354
$899$	23.5539	+	40.7965i	0.785566	+	1.36064i
$900$	4.21982	−	7.30894i	0.140661	−	0.243631i
$901$	−22.1702	−	38.3999i	−0.738596	−	1.27929i
$902$	13.4268	−	23.2560i	0.447065	−	0.774339i
$903$	−11.4092	+	19.7614i	−0.379676	+	0.657617i
$904$	−11.4445	+	19.8224i	−0.380638	+	0.659284i
$905$	18.7964	−	32.5563i	0.624813	−	1.08221i
$906$	−0.0885205	+	0.153322i	−0.00294090	+	0.00509378i
$907$	22.7040	−	39.3245i	0.753875	−	1.30575i	−0.192057	−	0.981384i	$-0.561516\pi$
$907$	22.7040	−	39.3245i	0.753875	−	1.30575i	0.945932	−	0.324366i	$-0.105151\pi$
$908$	−12.1703	−	21.0795i	−0.403885	−	0.699549i
$909$	−0.258373	+	0.447516i	−0.00856971	+	0.0148432i
$910$	4.16189	+	7.20861i	0.137965	+	0.238963i
$911$	−46.0178			−1.52464			−0.762319	−	0.647202i	$-0.775939\pi$
$911$	−46.0178			−1.52464			−0.762319	+	0.647202i	$0.775939\pi$
$912$	−0.888603	+	1.53911i	−0.0294246	+	0.0509649i
$913$	−0.502042			−0.0166152
$914$	16.5235			0.546548
$915$	−9.64765	−	16.7102i	−0.318942	−	0.552423i
$916$	39.1766			1.29443
$917$	11.2888	−	19.5528i	0.372790	−	0.645691i
$918$	1.21292	−	2.10084i	0.0400324	−	0.0693381i
$919$	−14.3280	−	24.8168i	−0.472637	−	0.818631i	0.526873	−	0.849944i	$-0.323365\pi$
$919$	−14.3280	−	24.8168i	−0.472637	−	0.818631i	−0.999510	+	0.0313129i	$0.990031\pi$
$920$	−1.21627	−	2.10664i	−0.0400993	−	0.0694540i
$921$	7.19048	+	12.4543i	0.236934	+	0.410382i
$922$	−3.12142	−	5.40646i	−0.102798	−	0.178052i
$923$	−3.90872			−0.128657
$924$	−16.8288			−0.553627
$925$	23.7782	+	41.1850i	0.781822	+	1.35415i
$926$	−1.99018	+	3.44708i	−0.0654012	+	0.113278i
$927$	−1.10939	+	1.92152i	−0.0364371	+	0.0631109i
$928$	18.6236	+	32.2570i	0.611350	+	1.05889i
$929$	−27.9501			−0.917014			−0.458507	−	0.888691i	$-0.651616\pi$
$929$	−27.9501			−0.917014			−0.458507	+	0.888691i	$0.651616\pi$
$930$	−15.4717			−0.507337
$931$	−1.59569	+	2.76382i	−0.0522966	+	0.0905804i
$932$	−14.3044	−	24.7760i	−0.468557	−	0.811565i
$933$	−26.8484			−0.878977
$934$	1.90032	−	3.29146i	0.0621805	−	0.107700i
$935$	−62.3933			−2.04048
$936$	−2.25194	−	3.90048i	−0.0736070	−	0.127491i
$937$	26.2666			0.858094			0.429047	−	0.903282i	$-0.358849\pi$
$937$	26.2666			0.858094			0.429047	+	0.903282i	$0.358849\pi$
$938$	1.51296	−	10.9369i	0.0493998	−	0.357104i
$939$	−17.3971			−0.567733
$940$	23.9345	+	41.4557i	0.780656	+	1.35214i
$941$	32.1373			1.04764			0.523822	−	0.851828i	$-0.324506\pi$
$941$	32.1373			1.04764			0.523822	+	0.851828i	$0.324506\pi$
$942$	−3.94048	+	6.82510i	−0.128388	+	0.222374i
$943$	−2.47536			−0.0806087
$944$	1.00534	+	1.74129i	0.0327209	+	0.0566743i
$945$	3.29339	−	5.70432i	0.107134	−	0.185561i
$946$	38.8475			1.26304
$947$	33.2149			1.07934			0.539669	−	0.841877i	$-0.318549\pi$
$947$	33.2149			1.07934			0.539669	+	0.841877i	$0.318549\pi$
$948$	2.52936	+	4.38098i	0.0821498	+	0.142288i
$949$	11.9293	−	20.6621i	0.387241	−	0.670720i
$950$	2.01132	−	3.48371i	0.0652559	−	0.113027i
$951$	3.65522	+	6.33103i	0.118529	+	0.205298i
$952$	−17.6620			−0.572427
$953$	36.2004			1.17265			0.586323	−	0.810077i	$-0.300575\pi$
$953$	36.2004			1.17265			0.586323	+	0.810077i	$0.300575\pi$
$954$	−3.98457	−	6.90147i	−0.129005	−	0.223443i
$955$	−0.645145	−	1.11742i	−0.0208764	−	0.0361590i
$956$	−19.9255	−	34.5120i	−0.644436	−	1.11620i
$957$	17.0716	+	29.5689i	0.551847	+	0.955827i
$958$	7.93888	−	13.7505i	0.256494	−	0.444260i
$959$	15.3374	−	26.5651i	0.495269	−	0.857831i
$960$	−2.08205			−0.0671980
$961$	−10.9058	−	18.8894i	−0.351800	−	0.609335i
$962$	11.1371			0.359075
$963$	3.56799			0.114977
$964$	−9.13951	+	15.8301i	−0.294364	+	0.509853i
$965$	−31.0356			−0.999070
$966$	−0.216218	−	0.374501i	−0.00695670	−	0.0120494i
$967$	12.3092	−	21.3202i	0.395838	−	0.685612i	−0.597370	−	0.801966i	$-0.703787\pi$
$967$	12.3092	−	21.3202i	0.395838	−	0.685612i	0.993208	+	0.116354i	$0.0371208\pi$
$968$	19.7006	+	34.1224i	0.633200	+	1.09673i
$969$	−2.07389	+	3.59208i	−0.0666229	+	0.115394i
$970$	12.3689	−	21.4235i	0.397141	−	0.687868i
$971$	−10.5997	+	18.3592i	−0.340160	+	0.589175i	−0.984462	−	0.175596i	$-0.943815\pi$
$971$	−10.5997	+	18.3592i	−0.340160	+	0.589175i	0.644302	+	0.764771i	$0.277148\pi$
$972$	−0.782006	+	1.35447i	−0.0250828	+	0.0434448i
$973$	−14.6989	+	25.4592i	−0.471225	+	0.816186i
$974$	−7.94950	+	13.7689i	−0.254719	+	0.441185i
$975$	−5.16374	−	8.94386i	−0.165372	−	0.286433i
$976$	4.71013	−	8.15819i	0.150768	−	0.261137i
$977$	−6.85029	−	11.8651i	−0.219160	−	0.379597i	0.735391	−	0.677643i	$-0.236998\pi$
$977$	−6.85029	−	11.8651i	−0.219160	−	0.379597i	−0.954552	+	0.298046i	$0.903665\pi$
$978$	12.7903			0.408990
$979$	−16.2515	+	28.1484i	−0.519400	+	0.899627i
$980$	14.2549			0.455357
$981$	−9.74392			−0.311099
$982$	−4.17361	−	7.22891i	−0.133185	−	0.230684i
$983$	−14.9488			−0.476793			−0.238397	−	0.971168i	$-0.576622\pi$
$983$	−14.9488			−0.476793			−0.238397	+	0.971168i	$0.576622\pi$
$984$	−9.08525	+	15.7361i	−0.289627	+	0.501649i
$985$	−14.0348	+	24.3090i	−0.447186	+	0.774549i
$986$	7.86251	+	13.6183i	0.250393	+	0.433694i
$987$	9.69581	+	16.7936i	0.308621	+	0.534548i
$988$	1.68970	+	2.92665i	0.0537567	+	0.0931093i
$989$	−1.79047	−	3.10119i	−0.0569337	−	0.0986120i
$990$	−11.2137			−0.356396
$991$	13.7233			0.435936			0.217968	−	0.975956i	$-0.430057\pi$
$991$	13.7233			0.435936			0.217968	+	0.975956i	$0.430057\pi$
$992$	−20.8785	−	36.1627i	−0.662894	−	1.14817i
$993$	13.1276	−	22.7376i	0.416591	−	0.721556i
$994$	−1.37743	+	2.38577i	−0.0436893	+	0.0756720i
$995$	−37.4901	−	64.9348i	−1.18852	−	2.05857i
$996$	0.149075			0.00472361
$997$	−19.4069			−0.614622			−0.307311	−	0.951609i	$-0.599429\pi$
$997$	−19.4069			−0.614622			−0.307311	+	0.951609i	$0.599429\pi$
$998$	−2.13702	+	3.70142i	−0.0676461	+	0.117167i
$999$	−4.40651	−	7.63230i	−0.139416	−	0.241475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.e.b.37.3	✓	10
3.2	odd	2		603.2.g.g.37.3		10
67.29	even	3	inner	201.2.e.b.163.3	yes	10
201.29	odd	6		603.2.g.g.163.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.e.b.37.3	✓	10	1.1	even	1	trivial
201.2.e.b.163.3	yes	10	67.29	even	3	inner
603.2.g.g.37.3		10	3.2	odd	2
603.2.g.g.163.3		10	201.29	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.330147 - 0.571831i) q^{2} -1.00000 q^{3} +(0.782006 - 1.35447i) q^{4} +3.22431 q^{5} +(0.330147 + 0.571831i) q^{6} +(-1.02143 + 1.76916i) q^{7} -2.35330 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.330147 - 0.571831i) q^{2} -1.00000 q^{3} +(0.782006 - 1.35447i) q^{4} +3.22431 q^{5} +(0.330147 + 0.571831i) q^{6} +(-1.02143 + 1.76916i) q^{7} -2.35330 q^{8} +1.00000 q^{9} +(-1.06450 - 1.84376i) q^{10} +(2.63358 - 4.56149i) q^{11} +(-0.782006 + 1.35447i) q^{12} +(0.956931 + 1.65745i) q^{13} +1.34888 q^{14} -3.22431 q^{15} +(-0.787078 - 1.36326i) q^{16} +(-1.83694 - 3.18168i) q^{17} +(-0.330147 - 0.571831i) q^{18} +(0.564495 + 0.977734i) q^{19} +(2.52143 - 4.36724i) q^{20} +(1.02143 - 1.76916i) q^{21} -3.47787 q^{22} +(0.160294 + 0.277638i) q^{23} +2.35330 q^{24} +5.39615 q^{25} +(0.631856 - 1.09441i) q^{26} -1.00000 q^{27} +(1.59752 + 2.76699i) q^{28} +(3.24114 - 5.61382i) q^{29} +(1.06450 + 1.84376i) q^{30} +(-3.63358 + 6.29354i) q^{31} +(-2.87300 + 4.97618i) q^{32} +(-2.63358 + 4.56149i) q^{33} +(-1.21292 + 2.10084i) q^{34} +(-3.29339 + 5.70432i) q^{35} +(0.782006 - 1.35447i) q^{36} +(4.40651 + 7.63230i) q^{37} +(0.372733 - 0.645592i) q^{38} +(-0.956931 - 1.65745i) q^{39} -7.58775 q^{40} +(-3.86065 + 6.68684i) q^{41} -1.34888 q^{42} -11.1699 q^{43} +(-4.11895 - 7.13423i) q^{44} +3.22431 q^{45} +(0.105841 - 0.183322i) q^{46} +(-4.74622 + 8.22069i) q^{47} +(0.787078 + 1.36326i) q^{48} +(1.41338 + 2.44804i) q^{49} +(-1.78152 - 3.08569i) q^{50} +(1.83694 + 3.18168i) q^{51} +2.99330 q^{52} +12.0691 q^{53} +(0.330147 + 0.571831i) q^{54} +(8.49146 - 14.7076i) q^{55} +(2.40372 - 4.16336i) q^{56} +(-0.564495 - 0.977734i) q^{57} -4.28022 q^{58} -1.27730 q^{59} +(-2.52143 + 4.36724i) q^{60} +(2.99216 + 5.18258i) q^{61} +4.79846 q^{62} +(-1.02143 + 1.76916i) q^{63} +0.645737 q^{64} +(3.08544 + 5.34413i) q^{65} +3.47787 q^{66} +(1.12164 - 8.10814i) q^{67} -5.74600 q^{68} +(-0.160294 - 0.277638i) q^{69} +4.34921 q^{70} +(-1.02116 + 1.76870i) q^{71} -2.35330 q^{72} +(-6.23309 - 10.7960i) q^{73} +(2.90959 - 5.03956i) q^{74} -5.39615 q^{75} +1.76575 q^{76} +(5.38001 + 9.31845i) q^{77} +(-0.631856 + 1.09441i) q^{78} +(1.61722 - 2.80112i) q^{79} +(-2.53778 - 4.39556i) q^{80} +1.00000 q^{81} +5.09833 q^{82} +(-0.0476578 - 0.0825457i) q^{83} +(-1.59752 - 2.76699i) q^{84} +(-5.92286 - 10.2587i) q^{85} +(3.68771 + 6.38731i) q^{86} +(-3.24114 + 5.61382i) q^{87} +(-6.19759 + 10.7345i) q^{88} -6.17088 q^{89} +(-1.06450 - 1.84376i) q^{90} -3.90974 q^{91} +0.501404 q^{92} +(3.63358 - 6.29354i) q^{93} +6.26780 q^{94} +(1.82010 + 3.15251i) q^{95} +(2.87300 - 4.97618i) q^{96} +(5.80974 + 10.0628i) q^{97} +(0.933245 - 1.61643i) q^{98} +(2.63358 - 4.56149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 10 * q^3 - 6 * q^4 + 2 * q^5 + 2 * q^6 - q^7 + 12 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} - 10 q^{3} - 6 q^{4} + 2 q^{5} + 2 q^{6} - q^{7} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} + 6 q^{12} + 3 q^{13} - 22 q^{14} - 2 q^{15} + 2 q^{17} - 2 q^{18} + 3 q^{19} + 16 q^{20} + q^{21} + 6 q^{22} - q^{23} - 12 q^{24} + 7 q^{26} - 10 q^{27} - 9 q^{28} + 12 q^{29} + 8 q^{30} - 12 q^{31} - 9 q^{32} - 2 q^{33} - 20 q^{34} + 19 q^{35} - 6 q^{36} + 27 q^{37} - 16 q^{38} - 3 q^{39} - 22 q^{40} - 7 q^{41} + 22 q^{42} + 12 q^{43} - 7 q^{44} + 2 q^{45} + 30 q^{46} - 33 q^{47} - 24 q^{49} + 21 q^{50} - 2 q^{51} - 32 q^{52} - 24 q^{53} + 2 q^{54} + 6 q^{55} - q^{56} - 3 q^{57} + 44 q^{58} + 24 q^{59} - 16 q^{60} + q^{61} + 2 q^{62} - q^{63} - 8 q^{64} - 6 q^{65} - 6 q^{66} + 2 q^{67} - 18 q^{68} + q^{69} + 42 q^{70} - q^{71} + 12 q^{72} + 12 q^{73} + 43 q^{74} + 2 q^{76} + 40 q^{77} - 7 q^{78} + 7 q^{79} - q^{80} + 10 q^{81} - 74 q^{82} + 12 q^{83} + 9 q^{84} - 27 q^{85} - 27 q^{86} - 12 q^{87} - 10 q^{88} + 12 q^{89} - 8 q^{90} - 80 q^{91} - 28 q^{92} + 12 q^{93} + 30 q^{94} - 12 q^{95} + 9 q^{96} - 9 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 10 * q^3 - 6 * q^4 + 2 * q^5 + 2 * q^6 - q^7 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 2 * q^11 + 6 * q^12 + 3 * q^13 - 22 * q^14 - 2 * q^15 + 2 * q^17 - 2 * q^18 + 3 * q^19 + 16 * q^20 + q^21 + 6 * q^22 - q^23 - 12 * q^24 + 7 * q^26 - 10 * q^27 - 9 * q^28 + 12 * q^29 + 8 * q^30 - 12 * q^31 - 9 * q^32 - 2 * q^33 - 20 * q^34 + 19 * q^35 - 6 * q^36 + 27 * q^37 - 16 * q^38 - 3 * q^39 - 22 * q^40 - 7 * q^41 + 22 * q^42 + 12 * q^43 - 7 * q^44 + 2 * q^45 + 30 * q^46 - 33 * q^47 - 24 * q^49 + 21 * q^50 - 2 * q^51 - 32 * q^52 - 24 * q^53 + 2 * q^54 + 6 * q^55 - q^56 - 3 * q^57 + 44 * q^58 + 24 * q^59 - 16 * q^60 + q^61 + 2 * q^62 - q^63 - 8 * q^64 - 6 * q^65 - 6 * q^66 + 2 * q^67 - 18 * q^68 + q^69 + 42 * q^70 - q^71 + 12 * q^72 + 12 * q^73 + 43 * q^74 + 2 * q^76 + 40 * q^77 - 7 * q^78 + 7 * q^79 - q^80 + 10 * q^81 - 74 * q^82 + 12 * q^83 + 9 * q^84 - 27 * q^85 - 27 * q^86 - 12 * q^87 - 10 * q^88 + 12 * q^89 - 8 * q^90 - 80 * q^91 - 28 * q^92 + 12 * q^93 + 30 * q^94 - 12 * q^95 + 9 * q^96 - 9 * q^97 + 4 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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