LMFDB - Embedded newform 273.2.l.c.16.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.9
Root			$1.14017 + 1.97483i$ of defining polynomial
Character	$\chi$	$=$	273.16
Dual form			273.2.l.c.256.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.28034 q^{2} +(-0.500000 + 0.866025i) q^{3} +3.19995 q^{4} +(-1.46862 + 2.54373i) q^{5} +(-1.14017 + 1.97483i) q^{6} +(0.102378 + 2.64377i) q^{7} +2.73629 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+2.28034 q^{2} +(-0.500000 + 0.866025i) q^{3} +3.19995 q^{4} +(-1.46862 + 2.54373i) q^{5} +(-1.14017 + 1.97483i) q^{6} +(0.102378 + 2.64377i) q^{7} +2.73629 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.34896 + 5.80057i) q^{10} +(2.58477 - 4.47696i) q^{11} +(-1.59997 + 2.77124i) q^{12} +(-0.364757 - 3.58705i) q^{13} +(0.233457 + 6.02869i) q^{14} +(-1.46862 - 2.54373i) q^{15} -0.160234 q^{16} +5.05291 q^{17} +(-1.14017 - 1.97483i) q^{18} +(-1.12929 - 1.95599i) q^{19} +(-4.69952 + 8.13980i) q^{20} +(-2.34076 - 1.23322i) q^{21} +(5.89416 - 10.2090i) q^{22} +5.23204 q^{23} +(-1.36814 + 2.36969i) q^{24} +(-1.81371 - 3.14143i) q^{25} +(-0.831769 - 8.17970i) q^{26} +1.00000 q^{27} +(0.327604 + 8.45992i) q^{28} +(0.216901 + 0.375683i) q^{29} +(-3.34896 - 5.80057i) q^{30} +(-1.34122 - 2.32306i) q^{31} -5.83796 q^{32} +(2.58477 + 4.47696i) q^{33} +11.5224 q^{34} +(-6.87539 - 3.62228i) q^{35} +(-1.59997 - 2.77124i) q^{36} -4.24772 q^{37} +(-2.57517 - 4.46033i) q^{38} +(3.28886 + 1.47764i) q^{39} +(-4.01857 + 6.96037i) q^{40} +(0.269622 + 0.466999i) q^{41} +(-5.33773 - 2.81217i) q^{42} +(-4.66348 + 8.07739i) q^{43} +(8.27113 - 14.3260i) q^{44} +2.93725 q^{45} +11.9308 q^{46} +(-4.87054 + 8.43603i) q^{47} +(0.0801172 - 0.138767i) q^{48} +(-6.97904 + 0.541328i) q^{49} +(-4.13587 - 7.16354i) q^{50} +(-2.52646 + 4.37595i) q^{51} +(-1.16720 - 11.4784i) q^{52} +(0.377571 + 0.653972i) q^{53} +2.28034 q^{54} +(7.59211 + 13.1499i) q^{55} +(0.280135 + 7.23411i) q^{56} +2.25859 q^{57} +(0.494607 + 0.856685i) q^{58} -3.64771 q^{59} +(-4.69952 - 8.13980i) q^{60} +(-3.47734 - 6.02293i) q^{61} +(-3.05843 - 5.29736i) q^{62} +(2.23838 - 1.41055i) q^{63} -12.9921 q^{64} +(9.66019 + 4.34019i) q^{65} +(5.89416 + 10.2090i) q^{66} +(6.68012 - 11.5703i) q^{67} +16.1691 q^{68} +(-2.61602 + 4.53108i) q^{69} +(-15.6782 - 8.26003i) q^{70} +(3.90487 - 6.76343i) q^{71} +(-1.36814 - 2.36969i) q^{72} +(-7.94401 - 13.7594i) q^{73} -9.68624 q^{74} +3.62742 q^{75} +(-3.61368 - 6.25908i) q^{76} +(12.1007 + 6.37520i) q^{77} +(7.49971 + 3.36952i) q^{78} +(-7.79235 + 13.4967i) q^{79} +(0.235324 - 0.407593i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.614830 + 1.06492i) q^{82} +13.2349 q^{83} +(-7.49031 - 3.94625i) q^{84} +(-7.42083 + 12.8532i) q^{85} +(-10.6343 + 18.4192i) q^{86} -0.433801 q^{87} +(7.07267 - 12.2502i) q^{88} -4.00286 q^{89} +6.69792 q^{90} +(9.44600 - 1.33157i) q^{91} +16.7423 q^{92} +2.68244 q^{93} +(-11.1065 + 19.2370i) q^{94} +6.63403 q^{95} +(2.91898 - 5.05582i) q^{96} +(2.69653 - 4.67053i) q^{97} +(-15.9146 + 1.23441i) q^{98} -5.16954 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.28034			1.61244			0.806222	−	0.591614i	$-0.201509\pi$
$2$	2.28034			1.61244			0.806222	+	0.591614i	$0.201509\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	3.19995			1.59997
$5$	−1.46862	+	2.54373i	−0.656788	+	1.13759i	0.324654	+	0.945833i	$0.394752\pi$
$5$	−1.46862	+	2.54373i	−0.656788	+	1.13759i	−0.981442	+	0.191758i	$0.938581\pi$
$6$	−1.14017	+	1.97483i	−0.465472	+	0.806222i
$7$	0.102378	+	2.64377i	0.0386952	+	0.999251i
$7$	0.102378	+	2.64377i	0.0386952	+	0.999251i
$8$	2.73629			0.967423
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−3.34896	+	5.80057i	−1.05903	+	1.83430i
$11$	2.58477	−	4.47696i	0.779338	−	1.34985i	−0.152986	−	0.988228i	$-0.548889\pi$
$11$	2.58477	−	4.47696i	0.779338	−	1.34985i	0.932324	−	0.361624i	$-0.117778\pi$
$12$	−1.59997	+	2.77124i	−0.461873	+	0.799987i
$13$	−0.364757	−	3.58705i	−0.101165	−	0.994870i
$13$	−0.364757	−	3.58705i	−0.101165	−	0.994870i
$14$	0.233457	+	6.02869i	0.0623939	+	1.61124i
$15$	−1.46862	−	2.54373i	−0.379197	−	0.656788i
$16$	−0.160234			−0.0400586
$17$	5.05291			1.22551			0.612756	−	0.790272i	$-0.290061\pi$
$17$	5.05291			1.22551			0.612756	+	0.790272i	$0.290061\pi$
$18$	−1.14017	−	1.97483i	−0.268741	−	0.465472i
$19$	−1.12929	−	1.95599i	−0.259078	−	0.448736i	0.706917	−	0.707296i	$-0.250085\pi$
$19$	−1.12929	−	1.95599i	−0.259078	−	0.448736i	−0.965995	+	0.258560i	$0.916752\pi$
$20$	−4.69952	+	8.13980i	−1.05084	+	1.82011i
$21$	−2.34076	−	1.23322i	−0.510796	−	0.269111i
$22$	5.89416	−	10.2090i	1.25664	−	2.17656i
$23$	5.23204			1.09096			0.545478	−	0.838125i	$-0.316348\pi$
$23$	5.23204			1.09096			0.545478	+	0.838125i	$0.316348\pi$
$24$	−1.36814	+	2.36969i	−0.279271	+	0.483712i
$25$	−1.81371	−	3.14143i	−0.362742	−	0.628287i
$26$	−0.831769	−	8.17970i	−0.163123	−	1.60417i
$27$	1.00000			0.192450
$28$	0.327604	+	8.45992i	0.0619114	+	1.59878i
$29$	0.216901	+	0.375683i	0.0402775	+	0.0697626i	0.885461	−	0.464713i	$-0.153842\pi$
$29$	0.216901	+	0.375683i	0.0402775	+	0.0697626i	−0.845184	+	0.534476i	$0.820509\pi$
$30$	−3.34896	−	5.80057i	−0.611433	−	1.05903i
$31$	−1.34122	−	2.32306i	−0.240890	−	0.417234i	0.720078	−	0.693893i	$-0.244106\pi$
$31$	−1.34122	−	2.32306i	−0.240890	−	0.417234i	−0.960968	+	0.276659i	$0.910773\pi$
$32$	−5.83796			−1.03202
$33$	2.58477	+	4.47696i	0.449951	+	0.779338i
$34$	11.5224			1.97607
$35$	−6.87539	−	3.62228i	−1.16215	−	0.612277i
$36$	−1.59997	−	2.77124i	−0.266662	−	0.461873i
$37$	−4.24772			−0.698321			−0.349160	−	0.937063i	$-0.613533\pi$
$37$	−4.24772			−0.698321			−0.349160	+	0.937063i	$0.613533\pi$
$38$	−2.57517	−	4.46033i	−0.417748	−	0.723561i
$39$	3.28886	+	1.47764i	0.526639	+	0.236611i
$40$	−4.01857	+	6.96037i	−0.635392	+	1.10053i
$41$	0.269622	+	0.466999i	0.0421079	+	0.0729330i	0.886311	−	0.463090i	$-0.153259\pi$
$41$	0.269622	+	0.466999i	0.0421079	+	0.0729330i	−0.844203	+	0.536023i	$0.819926\pi$
$42$	−5.33773	−	2.81217i	−0.823629	−	0.433927i
$43$	−4.66348	+	8.07739i	−0.711175	+	1.23179i	0.253242	+	0.967403i	$0.418503\pi$
$43$	−4.66348	+	8.07739i	−0.711175	+	1.23179i	−0.964416	+	0.264388i	$0.914830\pi$
$44$	8.27113	−	14.3260i	1.24692	−	2.15973i
$45$	2.93725			0.437859
$46$	11.9308			1.75910
$47$	−4.87054	+	8.43603i	−0.710442	+	1.23052i	0.254250	+	0.967139i	$0.418172\pi$
$47$	−4.87054	+	8.43603i	−0.710442	+	1.23052i	−0.964691	+	0.263383i	$0.915162\pi$
$48$	0.0801172	−	0.138767i	0.0115639	−	0.0200293i
$49$	−6.97904	+	0.541328i	−0.997005	+	0.0773325i
$50$	−4.13587	−	7.16354i	−0.584900	−	1.01308i
$51$	−2.52646	+	4.37595i	−0.353775	+	0.612756i
$52$	−1.16720	−	11.4784i	−0.161862	−	1.59176i
$53$	0.377571	+	0.653972i	0.0518634	+	0.0898300i	0.890792	−	0.454412i	$-0.150151\pi$
$53$	0.377571	+	0.653972i	0.0518634	+	0.0898300i	−0.838928	+	0.544242i	$0.816817\pi$
$54$	2.28034			0.310315
$55$	7.59211	+	13.1499i	1.02372	+	1.77313i
$56$	0.280135	+	7.23411i	0.0374347	+	0.966698i
$57$	2.25859			0.299157
$58$	0.494607	+	0.856685i	0.0649451	+	0.112488i
$59$	−3.64771			−0.474891			−0.237445	−	0.971401i	$-0.576310\pi$
$59$	−3.64771			−0.474891			−0.237445	+	0.971401i	$0.576310\pi$
$60$	−4.69952	−	8.13980i	−0.606705	−	1.05084i
$61$	−3.47734	−	6.02293i	−0.445228	−	0.771157i	0.552841	−	0.833287i	$-0.313544\pi$
$61$	−3.47734	−	6.02293i	−0.445228	−	0.771157i	−0.998068	+	0.0621304i	$0.980211\pi$
$62$	−3.05843	−	5.29736i	−0.388422	−	0.672766i
$63$	2.23838	−	1.41055i	0.282010	−	0.177712i
$64$	−12.9921			−1.62401
$65$	9.66019	+	4.34019i	1.19820	+	0.538334i
$66$	5.89416	+	10.2090i	0.725520	+	1.25664i
$67$	6.68012	−	11.5703i	0.816107	−	1.41354i	−0.0924236	−	0.995720i	$-0.529461\pi$
$67$	6.68012	−	11.5703i	0.816107	−	1.41354i	0.908530	−	0.417819i	$-0.137205\pi$
$68$	16.1691			1.96079
$69$	−2.61602	+	4.53108i	−0.314932	+	0.545478i
$70$	−15.6782	−	8.26003i	−1.87391	−	0.987262i
$71$	3.90487	−	6.76343i	0.463423	−	0.802672i	−0.535706	−	0.844404i	$-0.679955\pi$
$71$	3.90487	−	6.76343i	0.463423	−	0.802672i	0.999129	+	0.0417329i	$0.0132879\pi$
$72$	−1.36814	−	2.36969i	−0.161237	−	0.279271i
$73$	−7.94401	−	13.7594i	−0.929776	−	1.61042i	−0.783694	−	0.621147i	$-0.786667\pi$
$73$	−7.94401	−	13.7594i	−0.929776	−	1.61042i	−0.146083	−	0.989272i	$-0.546667\pi$
$74$	−9.68624			−1.12600
$75$	3.62742			0.418858
$76$	−3.61368	−	6.25908i	−0.414517	−	0.717965i
$77$	12.1007	+	6.37520i	1.37900	+	0.726521i
$78$	7.49971	+	3.36952i	0.849175	+	0.381523i
$79$	−7.79235	+	13.4967i	−0.876708	+	1.51850i	−0.0217756	+	0.999763i	$0.506932\pi$
$79$	−7.79235	+	13.4967i	−0.876708	+	1.51850i	−0.854932	+	0.518740i	$0.826401\pi$
$80$	0.235324	−	0.407593i	0.0263100	−	0.0455703i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.614830	+	1.06492i	0.0678966	+	0.117600i
$83$	13.2349			1.45272			0.726360	−	0.687315i	$-0.241211\pi$
$83$	13.2349			1.45272			0.726360	+	0.687315i	$0.241211\pi$
$84$	−7.49031	−	3.94625i	−0.817260	−	0.430571i
$85$	−7.42083	+	12.8532i	−0.804902	+	1.39413i
$86$	−10.6343	+	18.4192i	−1.14673	+	1.98619i
$87$	−0.433801			−0.0465084
$88$	7.07267	−	12.2502i	0.753949	−	1.30588i
$89$	−4.00286			−0.424303			−0.212151	−	0.977237i	$-0.568047\pi$
$89$	−4.00286			−0.424303			−0.212151	+	0.977237i	$0.568047\pi$
$90$	6.69792			0.706023
$91$	9.44600	−	1.33157i	0.990210	−	0.139586i
$92$	16.7423			1.74550
$93$	2.68244			0.278156
$94$	−11.1065	+	19.2370i	−1.14555	+	1.98415i
$95$	6.63403			0.680637
$96$	2.91898	−	5.05582i	0.297917	−	0.516008i
$97$	2.69653	−	4.67053i	0.273791	−	0.474220i	−0.696038	−	0.718005i	$-0.745056\pi$
$97$	2.69653	−	4.67053i	0.273791	−	0.474220i	0.969829	+	0.243784i	$0.0783889\pi$
$98$	−15.9146	+	1.23441i	−1.60761	+	0.124694i
$99$	−5.16954			−0.519559
$100$	−5.80377	−	10.0524i	−0.580377	−	1.00524i
$101$	1.57620	−	2.73006i	0.156838	−	0.271651i	−0.776889	−	0.629638i	$-0.783203\pi$
$101$	1.57620	−	2.73006i	0.156838	−	0.271651i	0.933727	+	0.357987i	$0.116537\pi$
$102$	−5.76118	+	9.97865i	−0.570442	+	0.988034i
$103$	−6.59727	+	11.4268i	−0.650048	+	1.12592i	0.333062	+	0.942905i	$0.391918\pi$
$103$	−6.59727	+	11.4268i	−0.650048	+	1.12592i	−0.983111	+	0.183012i	$0.941415\pi$
$104$	−0.998078	−	9.81520i	−0.0978696	−	0.962460i
$105$	6.57468	−	4.14312i	0.641623	−	0.404327i
$106$	0.860990	+	1.49128i	0.0836267	+	0.144846i
$107$	5.86701			0.567185			0.283593	−	0.958945i	$-0.408474\pi$
$107$	5.86701			0.567185			0.283593	+	0.958945i	$0.408474\pi$
$108$	3.19995			0.307915
$109$	2.74399	+	4.75273i	0.262826	+	0.455229i	0.966992	−	0.254807i	$-0.0820120\pi$
$109$	2.74399	+	4.75273i	0.262826	+	0.455229i	−0.704166	+	0.710036i	$0.748679\pi$
$110$	17.3126	+	29.9863i	1.65069	+	2.85908i
$111$	2.12386	−	3.67863i	0.201588	−	0.349160i
$112$	−0.0164045	−	0.423623i	−0.00155008	−	0.0400286i
$113$	0.794808	−	1.37665i	0.0747692	−	0.129504i	−0.826217	−	0.563352i	$-0.809511\pi$
$113$	0.794808	−	1.37665i	0.0747692	−	0.129504i	0.900986	+	0.433848i	$0.142845\pi$
$114$	5.15034			0.482374
$115$	−7.68390	+	13.3089i	−0.716527	+	1.24106i
$116$	0.694071	+	1.20217i	0.0644428	+	0.111618i
$117$	−2.92410	+	2.10942i	−0.270333	+	0.195016i
$118$	−8.31800			−0.765734
$119$	0.517307	+	13.3587i	0.0474215	+	1.22459i
$120$	−4.01857	−	6.96037i	−0.366844	−	0.635392i
$121$	−7.86209	−	13.6175i	−0.714735	−	1.23796i
$122$	−7.92951	−	13.7343i	−0.717904	−	1.24345i
$123$	−0.539244			−0.0486220
$124$	−4.29183	−	7.43367i	−0.385418	−	0.667563i
$125$	−4.03162			−0.360599
$126$	5.10427	−	3.21653i	0.454725	−	0.286551i
$127$	0.348278	+	0.603236i	0.0309047	+	0.0535285i	0.881064	−	0.472997i	$-0.156828\pi$
$127$	0.348278	+	0.603236i	0.0309047	+	0.0535285i	−0.850159	+	0.526525i	$0.823494\pi$
$128$	−17.9504			−1.58660
$129$	−4.66348	−	8.07739i	−0.410597	−	0.711175i
$130$	22.0285	+	9.89710i	1.93203	+	0.868033i
$131$	3.35469	−	5.81049i	0.293101	−	0.507665i	−0.681441	−	0.731873i	$-0.738646\pi$
$131$	3.35469	−	5.81049i	0.293101	−	0.507665i	0.974541	+	0.224208i	$0.0719796\pi$
$132$	8.27113	+	14.3260i	0.719910	+	1.24692i
$133$	5.05558	−	3.18584i	0.438375	−	0.276248i
$134$	15.2329	−	26.3842i	1.31593	−	2.27925i
$135$	−1.46862	+	2.54373i	−0.126399	+	0.218929i
$136$	13.8262			1.18559
$137$	12.4993			1.06789			0.533944	−	0.845520i	$-0.320709\pi$
$137$	12.4993			1.06789			0.533944	+	0.845520i	$0.320709\pi$
$138$	−5.96541	+	10.3324i	−0.507810	+	0.879552i
$139$	−0.657614	+	1.13902i	−0.0557781	+	0.0966105i	−0.892566	−	0.450916i	$-0.851097\pi$
$139$	−0.657614	+	1.13902i	−0.0557781	+	0.0966105i	0.836788	+	0.547527i	$0.184431\pi$
$140$	−22.0009	−	11.5911i	−1.85941	−	0.979627i
$141$	−4.87054	−	8.43603i	−0.410174	−	0.710442i
$142$	8.90442	−	15.4229i	0.747243	−	1.29426i
$143$	−17.0019	−	7.63871i	−1.42177	−	0.638781i
$144$	0.0801172	+	0.138767i	0.00667643	+	0.0115639i
$145$	−1.27418			−0.105815
$146$	−18.1150	−	31.3762i	−1.49921	−	2.59671i
$147$	3.02072	−	6.31469i	0.249144	−	0.520827i
$148$	−13.5925			−1.11729
$149$	−10.5964	−	18.3534i	−0.868088	−	1.50357i	−0.863948	−	0.503581i	$-0.832016\pi$
$149$	−10.5964	−	18.3534i	−0.868088	−	1.50357i	−0.00413964	−	0.999991i	$-0.501318\pi$
$150$	8.27174			0.675385
$151$	7.90358	+	13.6894i	0.643185	+	1.11403i	0.984718	+	0.174159i	$0.0557205\pi$
$151$	7.90358	+	13.6894i	0.643185	+	1.11403i	−0.341533	+	0.939870i	$0.610946\pi$
$152$	−3.09007	−	5.35216i	−0.250638	−	0.434117i
$153$	−2.52646	−	4.37595i	−0.204252	−	0.353775i
$154$	27.5936	+	14.5376i	2.22356	+	1.17147i
$155$	7.87898			0.632855
$156$	10.5242	+	4.72836i	0.842608	+	0.378572i
$157$	−2.76205	−	4.78402i	−0.220436	−	0.381806i	0.734505	−	0.678604i	$-0.237415\pi$
$157$	−2.76205	−	4.78402i	−0.220436	−	0.381806i	−0.954940	+	0.296798i	$0.904081\pi$
$158$	−17.7692	+	30.7772i	−1.41364	+	2.44850i
$159$	−0.755142			−0.0598866
$160$	8.57376	−	14.8502i	0.677815	−	1.17401i
$161$	0.535646	+	13.8323i	0.0422148	+	1.09014i
$162$	−1.14017	+	1.97483i	−0.0895802	+	0.155157i
$163$	1.57435	+	2.72685i	0.123313	+	0.213584i	0.921072	−	0.389392i	$-0.127315\pi$
$163$	1.57435	+	2.72685i	0.123313	+	0.213584i	−0.797759	+	0.602976i	$0.793982\pi$
$164$	0.862777	+	1.49437i	0.0673715	+	0.116691i
$165$	−15.1842			−1.18209
$166$	30.1801			2.34243
$167$	6.71152	+	11.6247i	0.519353	+	0.899546i	0.999747	+	0.0224932i	$0.00716043\pi$
$167$	6.71152	+	11.6247i	0.519353	+	0.899546i	−0.480394	+	0.877053i	$0.659506\pi$
$168$	−6.40499	−	3.37445i	−0.494156	−	0.260344i
$169$	−12.7339	+	2.61680i	−0.979531	+	0.201293i
$170$	−16.9220	+	29.3098i	−1.29786	+	2.24796i
$171$	−1.12929	+	1.95599i	−0.0863592	+	0.149579i
$172$	−14.9229	+	25.8472i	−1.13786	+	1.97083i
$173$	6.42442	+	11.1274i	0.488439	+	0.846002i	0.999912	−	0.0132981i	$-0.00423305\pi$
$173$	6.42442	+	11.1274i	0.488439	+	0.846002i	−0.511472	+	0.859300i	$0.670900\pi$
$174$	−0.989214			−0.0749921
$175$	8.11955	−	5.11664i	0.613780	−	0.386782i
$176$	−0.414169	+	0.717362i	−0.0312192	+	0.0540732i
$177$	1.82385	−	3.15901i	0.137089	−	0.237445i
$178$	−9.12788			−0.684164
$179$	−9.33314	+	16.1655i	−0.697591	+	1.20826i	0.271708	+	0.962380i	$0.412412\pi$
$179$	−9.33314	+	16.1655i	−0.697591	+	1.20826i	−0.969299	+	0.245884i	$0.920922\pi$
$180$	9.39903			0.700562
$181$	0.878433			0.0652934			0.0326467	−	0.999467i	$-0.489606\pi$
$181$	0.878433			0.0652934			0.0326467	+	0.999467i	$0.489606\pi$
$182$	21.5401	−	3.03643i	1.59666	−	0.225075i
$183$	6.95468			0.514104
$184$	14.3164			1.05542
$185$	6.23830	−	10.8051i	0.458649	−	0.794403i
$186$	6.11687			0.448511
$187$	13.0606	−	22.6217i	0.955088	−	1.65426i
$188$	−15.5855	+	26.9948i	−1.13669	+	1.96880i
$189$	0.102378	+	2.64377i	0.00744690	+	0.192306i
$190$	15.1278			1.09749
$191$	7.97565	+	13.8142i	0.577097	+	0.999562i	0.995810	+	0.0914434i	$0.0291481\pi$
$191$	7.97565	+	13.8142i	0.577097	+	0.999562i	−0.418713	+	0.908119i	$0.637519\pi$
$192$	6.49603	−	11.2515i	0.468811	−	0.812004i
$193$	−1.97533	+	3.42137i	−0.142187	+	0.246276i	−0.928320	−	0.371782i	$-0.878747\pi$
$193$	−1.97533	+	3.42137i	−0.142187	+	0.246276i	0.786133	+	0.618058i	$0.212080\pi$
$194$	6.14900	−	10.6504i	0.441473	−	0.764653i
$195$	−8.58881	+	6.19587i	−0.615057	+	0.443696i
$196$	−22.3325	+	1.73222i	−1.59518	+	0.123730i
$197$	−6.72353	−	11.6455i	−0.479032	−	0.829708i	0.520679	−	0.853753i	$-0.325679\pi$
$197$	−6.72353	−	11.6455i	−0.479032	−	0.829708i	−0.999711	+	0.0240448i	$0.992346\pi$
$198$	−11.7883			−0.837759
$199$	20.8291			1.47654			0.738268	−	0.674508i	$-0.235644\pi$
$199$	20.8291			1.47654			0.738268	+	0.674508i	$0.235644\pi$
$200$	−4.96282	−	8.59586i	−0.350925	−	0.607819i
$201$	6.68012	+	11.5703i	0.471179	+	0.816107i
$202$	3.59427	−	6.22546i	0.252892	−	0.438022i
$203$	−0.971014	+	0.611897i	−0.0681518	+	0.0429468i
$204$	−8.08453	+	14.0028i	−0.566030	+	0.980393i
$205$	−1.58389			−0.110624
$206$	−15.0440	+	26.0570i	−1.04817	+	1.81548i
$207$	−2.61602	−	4.53108i	−0.181826	−	0.314932i
$208$	0.0584466	+	0.574769i	0.00405254	+	0.0398531i
$209$	−11.6759			−0.807636
$210$	14.9925	−	9.44773i	1.03458	−	0.651955i
$211$	7.17814	+	12.4329i	0.494164	+	0.855917i	0.999977	−	0.00672604i	$-0.00214098\pi$
$211$	7.17814	+	12.4329i	0.494164	+	0.855917i	−0.505814	+	0.862643i	$0.668808\pi$
$212$	1.20821	+	2.09268i	0.0829800	+	0.143726i
$213$	3.90487	+	6.76343i	0.267557	+	0.463423i
$214$	13.3788			0.914554
$215$	−13.6978	−	23.7253i	−0.934182	−	1.61805i
$216$	2.73629			0.186181
$217$	6.00432	−	3.78370i	0.407600	−	0.256855i
$218$	6.25722	+	10.8378i	0.423793	+	0.734030i
$219$	15.8880			1.07361
$220$	24.2943	+	42.0790i	1.63792	+	2.83697i
$221$	−1.84308	−	18.1251i	−0.123979	−	1.21922i
$222$	4.84312	−	8.38853i	0.325049	−	0.563001i
$223$	0.596931	+	1.03392i	0.0399735	+	0.0692361i	0.885320	−	0.464982i	$-0.153939\pi$
$223$	0.596931	+	1.03392i	0.0399735	+	0.0692361i	−0.845346	+	0.534218i	$0.820606\pi$
$224$	−0.597679	−	15.4342i	−0.0399341	−	1.03124i
$225$	−1.81371	+	3.14143i	−0.120914	+	0.209429i
$226$	1.81243	−	3.13922i	0.120561	−	0.208818i
$227$	−15.8887			−1.05457			−0.527286	−	0.849688i	$-0.676790\pi$
$227$	−15.8887			−1.05457			−0.527286	+	0.849688i	$0.676790\pi$
$228$	7.22736			0.478643
$229$	−4.39323	+	7.60931i	−0.290313	+	0.502837i	−0.973884	−	0.227047i	$-0.927093\pi$
$229$	−4.39323	+	7.60931i	−0.290313	+	0.502837i	0.683571	+	0.729884i	$0.260426\pi$
$230$	−17.5219	+	30.3488i	−1.15536	+	2.00114i
$231$	−11.5714	+	7.29188i	−0.761343	+	0.479771i
$232$	0.593502	+	1.02798i	0.0389653	+	0.0674899i
$233$	2.86714	−	4.96604i	0.187833	−	0.325336i	−0.756695	−	0.653769i	$-0.773187\pi$
$233$	2.86714	−	4.96604i	0.187833	−	0.325336i	0.944527	+	0.328432i	$0.106520\pi$
$234$	−6.66794	+	4.81018i	−0.435897	+	0.314451i
$235$	−14.3060	−	24.7787i	−0.933220	−	1.61638i
$236$	−11.6725			−0.759813
$237$	−7.79235	−	13.4967i	−0.506168	−	0.876708i
$238$	1.17964	+	30.4625i	0.0764644	+	1.97459i
$239$	−11.5411			−0.746532			−0.373266	−	0.927724i	$-0.621762\pi$
$239$	−11.5411			−0.746532			−0.373266	+	0.927724i	$0.621762\pi$
$240$	0.235324	+	0.407593i	0.0151901	+	0.0263100i
$241$	−5.66060			−0.364631			−0.182316	−	0.983240i	$-0.558359\pi$
$241$	−5.66060			−0.364631			−0.182316	+	0.983240i	$0.558359\pi$
$242$	−17.9282	−	31.0526i	−1.15247	−	1.99614i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−11.1273	−	19.2730i	−0.712352	−	1.23383i
$245$	8.87258	−	18.5478i	0.566849	−	1.18498i
$246$	−1.22966			−0.0784003
$247$	−6.60434	+	4.76430i	−0.420224	+	0.303145i
$248$	−3.66996	−	6.35655i	−0.233043	−	0.403642i
$249$	−6.61745	+	11.4618i	−0.419364	+	0.726360i
$250$	−9.19346			−0.581445
$251$	12.1872	−	21.1088i	0.769249	−	1.33238i	−0.168721	−	0.985664i	$-0.553964\pi$
$251$	12.1872	−	21.1088i	0.769249	−	1.33238i	0.937971	−	0.346715i	$-0.112703\pi$
$252$	7.16271	−	4.51367i	0.451208	−	0.284335i
$253$	13.5236	−	23.4236i	0.850223	−	1.47263i
$254$	0.794193	+	1.37558i	0.0498321	+	0.0863117i
$255$	−7.42083	−	12.8532i	−0.464710	−	0.804902i
$256$	−14.9488			−0.934303
$257$	4.60536			0.287275			0.143637	−	0.989630i	$-0.454120\pi$
$257$	4.60536			0.287275			0.143637	+	0.989630i	$0.454120\pi$
$258$	−10.6343	−	18.4192i	−0.662064	−	1.14673i
$259$	−0.434873	−	11.2300i	−0.0270217	−	0.697798i
$260$	30.9121	+	13.8884i	1.91709	+	0.861320i
$261$	0.216901	−	0.375683i	0.0134258	−	0.0232542i
$262$	7.64983	−	13.2499i	0.472608	−	0.818581i
$263$	−11.4912	+	19.9033i	−0.708576	+	1.22729i	0.256809	+	0.966462i	$0.417329\pi$
$263$	−11.4912	+	19.9033i	−0.708576	+	1.22729i	−0.965385	+	0.260828i	$0.916004\pi$
$264$	7.07267	+	12.2502i	0.435293	+	0.753949i
$265$	−2.21804			−0.136253
$266$	11.5284	−	7.26480i	0.706854	−	0.445434i
$267$	2.00143	−	3.46658i	0.122486	−	0.212151i
$268$	21.3760	−	37.0244i	1.30575	−	2.26162i
$269$	14.0049			0.853896			0.426948	−	0.904276i	$-0.359589\pi$
$269$	14.0049			0.853896			0.426948	+	0.904276i	$0.359589\pi$
$270$	−3.34896	+	5.80057i	−0.203811	+	0.353011i
$271$	−19.1060			−1.16061			−0.580303	−	0.814401i	$-0.697066\pi$
$271$	−19.1060			−1.16061			−0.580303	+	0.814401i	$0.697066\pi$
$272$	−0.809651			−0.0490923
$273$	−3.56983	+	8.84626i	−0.216056	+	0.535400i
$274$	28.5027			1.72191
$275$	−18.7521			−1.13079
$276$	−8.37113	+	14.4992i	−0.503883	+	0.872750i
$277$	12.9200			0.776285			0.388142	−	0.921599i	$-0.373117\pi$
$277$	12.9200			0.776285			0.388142	+	0.921599i	$0.373117\pi$
$278$	−1.49958	+	2.59735i	−0.0899390	+	0.155779i
$279$	−1.34122	+	2.32306i	−0.0802967	+	0.139078i
$280$	−18.8130	−	9.91159i	−1.12429	−	0.592331i
$281$	−19.6264			−1.17082			−0.585408	−	0.810739i	$-0.699066\pi$
$281$	−19.6264			−1.17082			−0.585408	+	0.810739i	$0.699066\pi$
$282$	−11.1065	−	19.2370i	−0.661382	−	1.14555i
$283$	−1.63363	+	2.82954i	−0.0971095	+	0.168199i	−0.910487	−	0.413538i	$-0.864293\pi$
$283$	−1.63363	+	2.82954i	−0.0971095	+	0.168199i	0.813378	+	0.581736i	$0.197626\pi$
$284$	12.4954	−	21.6426i	0.741464	−	1.28425i
$285$	−3.31701	+	5.74523i	−0.196483	+	0.340318i
$286$	−38.7701	−	17.4189i	−2.29252	−	1.03000i
$287$	−1.20704	+	0.760629i	−0.0712490	+	0.0448985i
$288$	2.91898	+	5.05582i	0.172003	+	0.297917i
$289$	8.53194			0.501879
$290$	−2.90557			−0.170621
$291$	2.69653	+	4.67053i	0.158073	+	0.273791i
$292$	−25.4204	−	44.0295i	−1.48762	−	2.57663i
$293$	9.50947	−	16.4709i	0.555549	−	0.962239i	−0.442311	−	0.896862i	$-0.645841\pi$
$293$	9.50947	−	16.4709i	0.555549	−	0.962239i	0.997861	−	0.0653778i	$-0.0208252\pi$
$294$	6.88826	−	14.3996i	0.401731	−	0.839803i
$295$	5.35710	−	9.27878i	0.311903	−	0.540231i
$296$	−11.6230			−0.675572
$297$	2.58477	−	4.47696i	0.149984	−	0.259779i
$298$	−24.1633	−	41.8521i	−1.39974	−	2.42442i
$299$	−1.90842	−	18.7676i	−0.110367	−	1.08536i
$300$	11.6075			0.670162
$301$	−21.8322	−	11.5022i	−1.25839	−	0.662978i
$302$	18.0229	+	31.2165i	1.03710	+	1.79631i
$303$	1.57620	+	2.73006i	0.0905504	+	0.156838i
$304$	0.180952	+	0.313418i	0.0103783	+	0.0179757i
$305$	20.4276			1.16968
$306$	−5.76118	−	9.97865i	−0.329345	−	0.570442i
$307$	−8.30660			−0.474083			−0.237041	−	0.971500i	$-0.576178\pi$
$307$	−8.30660			−0.474083			−0.237041	+	0.971500i	$0.576178\pi$
$308$	38.7215	+	20.4003i	2.20636	+	1.16241i
$309$	−6.59727	−	11.4268i	−0.375306	−	0.650048i
$310$	17.9668			1.02044
$311$	5.42853	+	9.40250i	0.307824	+	0.533167i	0.977886	−	0.209138i	$-0.0670659\pi$
$311$	5.42853	+	9.40250i	0.307824	+	0.533167i	−0.670062	+	0.742305i	$0.733733\pi$
$312$	8.99925	+	4.04324i	0.509482	+	0.228903i
$313$	0.566928	−	0.981949i	0.0320447	−	0.0555030i	−0.849558	−	0.527495i	$-0.823131\pi$
$313$	0.566928	−	0.981949i	0.0320447	−	0.0555030i	0.881603	+	0.471992i	$0.156465\pi$
$314$	−6.29842	−	10.9092i	−0.355440	−	0.615641i
$315$	0.300709	+	7.76540i	0.0169431	+	0.437531i
$316$	−24.9351	+	43.1889i	−1.40271	+	2.42956i
$317$	−4.98712	+	8.63795i	−0.280105	+	0.485155i	−0.971410	−	0.237407i	$-0.923702\pi$
$317$	−4.98712	+	8.63795i	−0.280105	+	0.485155i	0.691306	+	0.722562i	$0.257036\pi$
$318$	−1.72198			−0.0965638
$319$	2.24256			0.125559
$320$	19.0804	−	33.0483i	1.06663	−	1.84746i
$321$	−2.93351	+	5.08098i	−0.163732	+	0.283593i
$322$	1.22145	+	31.5424i	0.0680690	+	1.75779i
$323$	−5.70622	−	9.88347i	−0.317503	−	0.549931i
$324$	−1.59997	+	2.77124i	−0.0888874	+	0.153958i
$325$	−10.6069	+	7.65173i	−0.588367	+	0.424441i
$326$	3.59005	+	6.21815i	0.198835	+	0.344392i
$327$	−5.48797			−0.303486
$328$	0.737763	+	1.27784i	0.0407362	+	0.0705571i
$329$	−22.8016	−	12.0129i	−1.25709	−	0.662294i
$330$	−34.6252			−1.90605
$331$	0.827569	+	1.43339i	0.0454873	+	0.0787863i	0.887873	−	0.460089i	$-0.152183\pi$
$331$	0.827569	+	1.43339i	0.0454873	+	0.0787863i	−0.842385	+	0.538876i	$0.818849\pi$
$332$	42.3510			2.32431
$333$	2.12386	+	3.67863i	0.116387	+	0.201588i
$334$	15.3045	+	26.5083i	0.837428	+	1.45047i
$335$	19.6212	+	33.9849i	1.07202	+	1.85679i
$336$	0.375070	+	0.197605i	0.0204618	+	0.0107802i
$337$	−12.4081			−0.675913			−0.337956	−	0.941162i	$-0.609736\pi$
$337$	−12.4081			−0.675913			−0.337956	+	0.941162i	$0.609736\pi$
$338$	−29.0376	+	5.96720i	−1.57944	+	0.324573i
$339$	0.794808	+	1.37665i	0.0431680	+	0.0747692i
$340$	−23.7463	+	41.1297i	−1.28782	+	2.23057i
$341$	−13.8670			−0.750939
$342$	−2.57517	+	4.46033i	−0.139249	+	0.241187i
$343$	−2.14565	−	18.3955i	−0.115854	−	0.993266i
$344$	−12.7606	+	22.1021i	−0.688007	+	1.19166i
$345$	−7.68390	−	13.3089i	−0.413687	−	0.716527i
$346$	14.6498	+	25.3743i	0.787581	+	1.36413i
$347$	13.2452			0.711041			0.355521	−	0.934668i	$-0.384304\pi$
$347$	13.2452			0.711041			0.355521	+	0.934668i	$0.384304\pi$
$348$	−1.38814			−0.0744122
$349$	17.5068	+	30.3227i	0.937119	+	1.62314i	0.770812	+	0.637063i	$0.219851\pi$
$349$	17.5068	+	30.3227i	0.937119	+	1.62314i	0.166307	+	0.986074i	$0.446816\pi$
$350$	18.5153	−	11.6677i	0.989685	−	0.623663i
$351$	−0.364757	−	3.58705i	−0.0194693	−	0.191463i
$352$	−15.0898	+	26.1363i	−0.804289	+	1.39307i
$353$	−11.5541	+	20.0123i	−0.614964	+	1.06515i	0.375427	+	0.926852i	$0.377496\pi$
$353$	−11.5541	+	20.0123i	−0.614964	+	1.06515i	−0.990391	+	0.138297i	$0.955837\pi$
$354$	4.15900	−	7.20360i	0.221048	−	0.382867i
$355$	11.4696	+	19.8659i	0.608741	+	1.05437i
$356$	−12.8089			−0.678873
$357$	−11.8277	−	6.23137i	−0.625986	−	0.329799i
$358$	−21.2827	+	36.8628i	−1.12483	+	1.94826i
$359$	−6.44458	+	11.1623i	−0.340132	+	0.589126i	−0.984457	−	0.175626i	$-0.943805\pi$
$359$	−6.44458	+	11.1623i	−0.340132	+	0.589126i	0.644325	+	0.764752i	$0.277138\pi$
$360$	8.03714			0.423595
$361$	6.94939	−	12.0367i	0.365758	−	0.633511i
$362$	2.00312			0.105282
$363$	15.7242			0.825305
$364$	30.2267	−	4.26095i	1.58431	−	0.223334i
$365$	46.6670			2.44266
$366$	15.8590			0.828964
$367$	13.2465	−	22.9436i	0.691460	−	1.19764i	−0.279900	−	0.960029i	$-0.590301\pi$
$367$	13.2465	−	22.9436i	0.691460	−	1.19764i	0.971360	−	0.237614i	$-0.0763655\pi$
$368$	−0.838353			−0.0437022
$369$	0.269622	−	0.466999i	0.0140360	−	0.0243110i
$370$	14.2254	−	24.6392i	0.739545	−	1.28093i
$371$	−1.69030	+	1.06516i	−0.0877558	+	0.0553005i
$372$	8.58366			0.445042
$373$	6.18549	+	10.7136i	0.320273	+	0.554729i	0.980544	−	0.196298i	$-0.0628921\pi$
$373$	6.18549	+	10.7136i	0.320273	+	0.554729i	−0.660271	+	0.751027i	$0.729559\pi$
$374$	29.7827	−	51.5851i	1.54002	−	2.66740i
$375$	2.01581	−	3.49148i	0.104096	−	0.180299i
$376$	−13.3272	+	23.0834i	−0.687298	+	1.19043i
$377$	1.26848	−	0.915067i	0.0653300	−	0.0471284i
$378$	0.233457	+	6.02869i	0.0120077	+	0.310082i
$379$	−14.0179	−	24.2797i	−0.720050	−	1.24716i	−0.960979	−	0.276621i	$-0.910785\pi$
$379$	−14.0179	−	24.2797i	−0.720050	−	1.24716i	0.240929	−	0.970543i	$-0.422548\pi$
$380$	21.2285			1.08900
$381$	−0.696557			−0.0356857
$382$	18.1872	+	31.5011i	0.930537	+	1.61174i
$383$	13.1452	+	22.7681i	0.671687	+	1.16340i	0.977426	+	0.211280i	$0.0677632\pi$
$383$	13.1452	+	22.7681i	0.671687	+	1.16340i	−0.305739	+	0.952115i	$0.598903\pi$
$384$	8.97519	−	15.5455i	0.458013	−	0.793302i
$385$	−33.9881	+	21.4181i	−1.73219	+	1.09157i
$386$	−4.50442	+	7.80188i	−0.229269	+	0.397105i
$387$	9.32697			0.474116
$388$	8.62875	−	14.9454i	0.438059	−	0.758740i
$389$	−13.4205	−	23.2449i	−0.680445	−	1.17856i	−0.974845	−	0.222883i	$-0.928453\pi$
$389$	−13.4205	−	23.2449i	−0.680445	−	1.17856i	0.294400	−	0.955682i	$-0.404880\pi$
$390$	−19.5854	+	14.1287i	−0.991745	+	0.715434i
$391$	26.4371			1.33698
$392$	−19.0966	+	1.48123i	−0.964526	+	0.0748133i
$393$	3.35469	+	5.81049i	0.169222	+	0.293101i
$394$	−15.3319	−	26.5557i	−0.772412	−	1.33786i
$395$	−22.8881	−	39.6433i	−1.15162	−	1.99467i
$396$	−16.5423			−0.831280
$397$	−12.2621	−	21.2386i	−0.615419	−	1.06594i	−0.990311	−	0.138868i	$-0.955654\pi$
$397$	−12.2621	−	21.2386i	−0.615419	−	1.06594i	0.374892	−	0.927068i	$-0.377680\pi$
$398$	47.4974			2.38083
$399$	0.231230	+	5.97118i	0.0115760	+	0.298933i
$400$	0.290618	+	0.503366i	0.0145309	+	0.0251683i
$401$	3.16570			0.158088			0.0790438	−	0.996871i	$-0.474813\pi$
$401$	3.16570			0.158088			0.0790438	+	0.996871i	$0.474813\pi$
$402$	15.2329	+	26.3842i	0.759750	+	1.31593i
$403$	−7.84372	+	5.65838i	−0.390724	+	0.281864i
$404$	5.04376	−	8.73605i	0.250936	−	0.434635i
$405$	−1.46862	−	2.54373i	−0.0729765	−	0.126399i
$406$	−2.21424	+	1.39533i	−0.109891	+	0.0692492i
$407$	−10.9794	+	19.0169i	−0.544228	+	0.942630i
$408$	−6.91311	+	11.9739i	−0.342250	+	0.592794i
$409$	19.0685			0.942876			0.471438	−	0.881899i	$-0.343735\pi$
$409$	19.0685			0.942876			0.471438	+	0.881899i	$0.343735\pi$
$410$	−3.61181			−0.178375
$411$	−6.24965	+	10.8247i	−0.308273	+	0.533944i
$412$	−21.1109	+	36.5652i	−1.04006	+	1.80144i
$413$	−0.373445	−	9.64369i	−0.0183760	−	0.474535i
$414$	−5.96541	−	10.3324i	−0.293184	−	0.507810i
$415$	−19.4371	+	33.6660i	−0.954129	+	1.65260i
$416$	2.12943	+	20.9411i	0.104404	+	1.02672i
$417$	−0.657614	−	1.13902i	−0.0322035	−	0.0557781i
$418$	−26.6249			−1.30227
$419$	7.80534	+	13.5192i	0.381316	+	0.660458i	0.991251	−	0.131993i	$-0.0421377\pi$
$419$	7.80534	+	13.5192i	0.381316	+	0.660458i	−0.609935	+	0.792452i	$0.708804\pi$
$420$	21.0386	−	13.2578i	1.02658	−	0.646913i
$421$	−18.0525			−0.879827			−0.439913	−	0.898040i	$-0.644991\pi$
$421$	−18.0525			−0.879827			−0.439913	+	0.898040i	$0.644991\pi$
$422$	16.3686	+	28.3512i	0.796811	+	1.38012i
$423$	9.74109			0.473628
$424$	1.03314	+	1.78945i	0.0501738	+	0.0869036i
$425$	−9.16451	−	15.8734i	−0.444544	−	0.769973i
$426$	8.90442	+	15.4229i	0.431421	+	0.747243i
$427$	15.5672	−	9.80990i	0.753351	−	0.474734i
$428$	18.7741			0.907481
$429$	15.1163	−	10.9047i	0.729820	−	0.526484i
$430$	−31.2356	−	54.1017i	−1.50632	−	2.60902i
$431$	8.75826	−	15.1698i	0.421871	−	0.730701i	−0.574252	−	0.818679i	$-0.694707\pi$
$431$	8.75826	−	15.1698i	0.421871	−	0.730701i	0.996122	+	0.0879774i	$0.0280403\pi$
$432$	−0.160234			−0.00770928
$433$	−3.02961	+	5.24744i	−0.145594	+	0.252176i	−0.929594	−	0.368584i	$-0.879843\pi$
$433$	−3.02961	+	5.24744i	−0.145594	+	0.252176i	0.784001	+	0.620760i	$0.213176\pi$
$434$	13.6919	−	8.62813i	0.657232	−	0.414163i
$435$	0.637091	−	1.10347i	0.0305462	−	0.0529075i
$436$	8.78061	+	15.2085i	0.420515	+	0.728354i
$437$	−5.90851	−	10.2338i	−0.282642	−	0.489551i
$438$	36.2301			1.73114
$439$	23.3824			1.11598			0.557990	−	0.829848i	$-0.311573\pi$
$439$	23.3824			1.11598			0.557990	+	0.829848i	$0.311573\pi$
$440$	20.7742	+	35.9819i	0.990370	+	1.71537i
$441$	3.95832	+	5.77336i	0.188492	+	0.274922i
$442$	−4.20286	−	41.3313i	−0.199910	−	1.96593i
$443$	4.44712	−	7.70264i	0.211289	−	0.365963i	−0.740829	−	0.671693i	$-0.765567\pi$
$443$	4.44712	−	7.70264i	0.211289	−	0.365963i	0.952118	+	0.305730i	$0.0989005\pi$
$444$	6.79624	−	11.7714i	0.322535	−	0.558647i
$445$	5.87870	−	10.1822i	0.278677	−	0.482683i
$446$	1.36121	+	2.35768i	0.0644550	+	0.111639i
$447$	21.1927			1.00238
$448$	−1.33010	−	34.3480i	−0.0628414	−	1.62279i
$449$	−19.3671	+	33.5448i	−0.913989	+	1.58308i	−0.105614	+	0.994407i	$0.533681\pi$
$449$	−19.3671	+	33.5448i	−0.913989	+	1.58308i	−0.808375	+	0.588668i	$0.799652\pi$
$450$	−4.13587	+	7.16354i	−0.194967	+	0.337692i
$451$	2.78765			0.131265
$452$	2.54334	−	4.40520i	0.119629	−	0.207203i
$453$	−15.8072			−0.742686
$454$	−36.2317			−1.70044
$455$	−10.4855	+	25.9836i	−0.491566	+	1.21813i
$456$	6.18014			0.289411
$457$	22.4003			1.04784			0.523920	−	0.851767i	$-0.324469\pi$
$457$	22.4003			1.04784			0.523920	+	0.851767i	$0.324469\pi$
$458$	−10.0181	+	17.3518i	−0.468113	+	0.810796i
$459$	5.05291			0.235850
$460$	−24.5881	+	42.5878i	−1.14642	+	1.98567i
$461$	−1.40367	+	2.43123i	−0.0653755	+	0.113234i	−0.896860	−	0.442314i	$-0.854158\pi$
$461$	−1.40367	+	2.43123i	−0.0653755	+	0.113234i	0.831485	+	0.555547i	$0.187491\pi$
$462$	−26.3868	+	16.6280i	−1.22762	+	0.773603i
$463$	37.7530			1.75453			0.877266	−	0.480004i	$-0.159365\pi$
$463$	37.7530			1.75453			0.877266	+	0.480004i	$0.159365\pi$
$464$	−0.0347550	−	0.0601974i	−0.00161346	−	0.00279459i
$465$	−3.93949	+	6.82340i	−0.182690	+	0.316428i
$466$	6.53806	−	11.3243i	0.302870	−	0.524586i
$467$	−8.04389	+	13.9324i	−0.372227	+	0.644716i	−0.989908	−	0.141713i	$-0.954739\pi$
$467$	−8.04389	+	13.9324i	−0.372227	+	0.644716i	0.617681	+	0.786429i	$0.288072\pi$
$468$	−9.35697	+	6.75002i	−0.432526	+	0.312020i
$469$	31.2731	+	16.4762i	1.44406	+	0.760798i
$470$	−32.6225	−	56.5038i	−1.50476	−	2.60633i
$471$	5.52411			0.254537
$472$	−9.98116			−0.459420
$473$	24.1081	+	41.7564i	1.10849	+	1.91996i
$474$	−17.7692	−	30.7772i	−0.816166	−	1.41364i
$475$	−4.09642	+	7.09520i	−0.187956	+	0.325550i
$476$	1.65536	+	42.7473i	0.0758731	+	1.95932i
$477$	0.377571	−	0.653972i	0.0172878	−	0.0299433i
$478$	−26.3176			−1.20374
$479$	−4.27425	+	7.40322i	−0.195295	+	0.338262i	−0.946997	−	0.321241i	$-0.895900\pi$
$479$	−4.27425	+	7.40322i	−0.195295	+	0.338262i	0.751702	+	0.659503i	$0.229233\pi$
$480$	8.57376	+	14.8502i	0.391337	+	0.677815i
$481$	1.54938	+	15.2368i	0.0706458	+	0.694738i
$482$	−12.9081			−0.587948
$483$	−12.2470	−	6.45227i	−0.557256	−	0.293589i
$484$	−25.1583	−	43.5754i	−1.14356	−	1.98070i
$485$	7.92037	+	13.7185i	0.359646	+	0.622925i
$486$	−1.14017	−	1.97483i	−0.0517191	−	0.0895802i
$487$	−35.5761			−1.61211			−0.806054	−	0.591842i	$-0.798401\pi$
$487$	−35.5761			−1.61211			−0.806054	+	0.591842i	$0.798401\pi$
$488$	−9.51499	−	16.4804i	−0.430723	−	0.746035i
$489$	−3.14870			−0.142389
$490$	20.2325	−	42.2953i	0.914011	−	1.91071i
$491$	15.6990	+	27.1914i	0.708485	+	1.22713i	0.965419	+	0.260703i	$0.0839544\pi$
$491$	15.6990	+	27.1914i	0.708485	+	1.22713i	−0.256934	+	0.966429i	$0.582712\pi$
$492$	−1.72555			−0.0777940
$493$	1.09598	+	1.89829i	0.0493605	+	0.0854949i
$494$	−15.0601	+	10.8642i	−0.677587	+	0.488804i
$495$	7.59211	−	13.1499i	0.341240	−	0.591045i
$496$	0.214909	+	0.372234i	0.00964972	+	0.0167138i
$497$	18.2807	+	9.63115i	0.820003	+	0.432016i
$498$	−15.0900	+	26.1367i	−0.676200	+	1.17121i
$499$	2.14606	−	3.71708i	0.0960708	−	0.166399i	−0.813984	−	0.580887i	$-0.802706\pi$
$499$	2.14606	−	3.71708i	0.0960708	−	0.166399i	0.910055	+	0.414488i	$0.136039\pi$
$500$	−12.9010			−0.576949
$501$	−13.4230			−0.599697
$502$	27.7909	−	48.1353i	1.24037	−	2.14839i
$503$	7.83439	−	13.5696i	0.349318	−	0.605037i	−0.636810	−	0.771021i	$-0.719747\pi$
$503$	7.83439	−	13.5696i	0.349318	−	0.605037i	0.986129	+	0.165984i	$0.0530799\pi$
$504$	6.12485	−	3.85966i	0.272823	−	0.171923i
$505$	4.62969	+	8.01886i	0.206019	+	0.356835i
$506$	30.8385	−	53.4138i	1.37094	−	2.37453i
$507$	4.10073	−	12.3363i	0.182120	−	0.547874i
$508$	1.11447	+	1.93032i	0.0494467	+	0.0856442i
$509$	1.70373			0.0755165			0.0377583	−	0.999287i	$-0.487978\pi$
$509$	1.70373			0.0755165			0.0377583	+	0.999287i	$0.487978\pi$
$510$	−16.9220	−	29.3098i	−0.749319	−	1.29786i
$511$	35.5635	−	22.4108i	1.57324	−	0.991396i
$512$	1.81234			0.0800947
$513$	−1.12929	−	1.95599i	−0.0498595	−	0.0863592i
$514$	10.5018			0.463214
$515$	−19.3778	−	33.5633i	−0.853888	−	1.47898i
$516$	−14.9229	−	25.8472i	−0.656944	−	1.13786i
$517$	25.1785	+	43.6104i	1.10735	+	1.91798i
$518$	−0.991658	−	25.6082i	−0.0435710	−	1.12516i
$519$	−12.8488			−0.564001
$520$	26.4330	+	11.8760i	1.15916	+	0.520797i
$521$	8.39696	+	14.5440i	0.367878	+	0.637183i	0.989234	−	0.146346i	$-0.0467512\pi$
$521$	8.39696	+	14.5440i	0.367878	+	0.637183i	−0.621356	+	0.783528i	$0.713418\pi$
$522$	0.494607	−	0.856685i	0.0216484	−	0.0374961i
$523$	−7.49051			−0.327537			−0.163769	−	0.986499i	$-0.552365\pi$
$523$	−7.49051			−0.327537			−0.163769	+	0.986499i	$0.552365\pi$
$524$	10.7348	−	18.5933i	0.468953	−	0.812251i
$525$	0.371368	+	9.59005i	0.0162078	+	0.418544i
$526$	−26.2038	+	45.3863i	−1.14254	+	1.97894i
$527$	−6.77706	−	11.7382i	−0.295214	−	0.511325i
$528$	−0.414169	−	0.717362i	−0.0180244	−	0.0312192i
$529$	4.37426			0.190185
$530$	−5.05788			−0.219700
$531$	1.82385	+	3.15901i	0.0791485	+	0.137089i
$532$	16.1776	−	10.1945i	0.701388	−	0.441989i
$533$	1.57681	−	1.13749i	0.0682990	−	0.0492702i
$534$	4.56394	−	7.90498i	0.197501	−	0.342082i
$535$	−8.61643	+	14.9241i	−0.372521	+	0.645225i
$536$	18.2787	−	31.6597i	0.789521	−	1.36749i
$537$	−9.33314	−	16.1655i	−0.402755	−	0.697591i
$538$	31.9360			1.37686
$539$	−15.6157	+	32.6440i	−0.672617	+	1.40608i
$540$	−4.69952	+	8.13980i	−0.202235	+	0.350281i
$541$	4.78963	−	8.29588i	0.205922	−	0.356668i	−0.744504	−	0.667618i	$-0.767314\pi$
$541$	4.78963	−	8.29588i	0.205922	−	0.356668i	0.950426	+	0.310950i	$0.100647\pi$
$542$	−43.5681			−1.87141
$543$	−0.439216	+	0.760745i	−0.0188486	+	0.0326467i
$544$	−29.4987			−1.26475
$545$	−16.1195			−0.690485
$546$	−8.14042	+	20.1725i	−0.348378	+	0.863302i
$547$	−30.1843			−1.29059			−0.645293	−	0.763935i	$-0.723265\pi$
$547$	−30.1843			−1.29059			−0.645293	+	0.763935i	$0.723265\pi$
$548$	39.9971			1.70859
$549$	−3.47734	+	6.02293i	−0.148409	+	0.257052i
$550$	−42.7611			−1.82334
$551$	0.489889	−	0.848513i	0.0208700	−	0.0361479i
$552$	−7.15818	+	12.3983i	−0.304672	+	0.527708i
$553$	−36.4801	−	19.2194i	−1.55129	−	0.817292i
$554$	29.4619			1.25172
$555$	6.23830	+	10.8051i	0.264801	+	0.458649i
$556$	−2.10433	+	3.64480i	−0.0892434	+	0.154574i
$557$	2.33571	−	4.04557i	0.0989673	−	0.171416i	−0.812290	−	0.583254i	$-0.801779\pi$
$557$	2.33571	−	4.04557i	0.0989673	−	0.171416i	0.911257	+	0.411837i	$0.135113\pi$
$558$	−3.05843	+	5.29736i	−0.129474	+	0.224255i
$559$	30.6751	+	13.7819i	1.29742	+	0.582912i
$560$	1.10167	+	0.580414i	0.0465542	+	0.0245270i
$561$	13.0606	+	22.6217i	0.551420	+	0.955088i
$562$	−44.7550			−1.88787
$563$	−14.3818			−0.606120			−0.303060	−	0.952971i	$-0.598008\pi$
$563$	−14.3818			−0.606120			−0.303060	+	0.952971i	$0.598008\pi$
$564$	−15.5855	−	26.9948i	−0.656267	−	1.13669i
$565$	2.33455	+	4.04355i	0.0982151	+	0.170114i
$566$	−3.72524	+	6.45231i	−0.156584	+	0.271211i
$567$	−2.34076	−	1.23322i	−0.0983027	−	0.0517905i
$568$	10.6848	−	18.5067i	0.448326	−	0.776523i
$569$	−14.5756			−0.611040			−0.305520	−	0.952186i	$-0.598830\pi$
$569$	−14.5756			−0.611040			−0.305520	+	0.952186i	$0.598830\pi$
$570$	−7.56391	+	13.1011i	−0.316818	+	0.548744i
$571$	−12.9575	−	22.4430i	−0.542254	−	0.939211i	−0.998774	−	0.0494981i	$-0.984238\pi$
$571$	−12.9575	−	22.4430i	−0.542254	−	0.939211i	0.456520	−	0.889713i	$-0.349096\pi$
$572$	−54.4051	−	24.4435i	−2.27479	−	1.02203i
$573$	−15.9513			−0.666375
$574$	−2.75245	+	1.73449i	−0.114885	+	0.0723963i
$575$	−9.48940	−	16.4361i	−0.395735	−	0.685433i
$576$	6.49603	+	11.2515i	0.270668	+	0.468811i
$577$	11.7875	+	20.4165i	0.490719	+	0.849950i	0.999943	−	0.0106839i	$-0.00340085\pi$
$577$	11.7875	+	20.4165i	0.490719	+	0.849950i	−0.509224	+	0.860634i	$0.670068\pi$
$578$	19.4557			0.809251
$579$	−1.97533	−	3.42137i	−0.0820919	−	0.142187i
$580$	−4.07731			−0.169301
$581$	1.35496	+	34.9900i	0.0562133	+	1.45163i
$582$	6.14900	+	10.6504i	0.254884	+	0.441473i
$583$	3.90374			0.161676
$584$	−21.7371	−	37.6497i	−0.899487	−	1.55796i
$585$	−1.07138	−	10.5361i	−0.0442961	−	0.435612i
$586$	21.6848	−	37.5592i	0.895791	−	1.55156i
$587$	−23.7561	−	41.1468i	−0.980521	−	1.69831i	−0.660361	−	0.750948i	$-0.729597\pi$
$587$	−23.7561	−	41.1468i	−0.980521	−	1.69831i	−0.320160	−	0.947364i	$-0.603737\pi$
$588$	9.66613	−	20.2067i	0.398624	−	0.833309i
$589$	−3.02926	+	5.24683i	−0.124818	+	0.216192i
$590$	12.2160	−	21.1588i	0.502925	−	0.871092i
$591$	13.4471			0.553139
$592$	0.680631			0.0279738
$593$	−2.36887	+	4.10300i	−0.0972779	+	0.168490i	−0.910557	−	0.413384i	$-0.864347\pi$
$593$	−2.36887	+	4.10300i	−0.0972779	+	0.168490i	0.813279	+	0.581874i	$0.197680\pi$
$594$	5.89416	−	10.2090i	0.241840	−	0.418879i
$595$	−34.7408	−	18.3031i	−1.42423	−	0.750353i
$596$	−33.9078	−	58.7300i	−1.38892	−	2.40568i
$597$	−10.4145	+	18.0385i	−0.426239	+	0.738268i
$598$	−4.35185	−	42.7965i	−0.177960	−	1.75008i
$599$	1.07453	+	1.86114i	0.0439041	+	0.0760441i	0.887142	−	0.461496i	$-0.152687\pi$
$599$	1.07453	+	1.86114i	0.0439041	+	0.0760441i	−0.843238	+	0.537540i	$0.819354\pi$
$600$	9.92565			0.405213
$601$	0.736182	+	1.27511i	0.0300295	+	0.0520126i	0.880650	−	0.473768i	$-0.157107\pi$
$601$	0.736182	+	1.27511i	0.0300295	+	0.0520126i	−0.850620	+	0.525781i	$0.823773\pi$
$602$	−49.7848	−	26.2290i	−2.02908	−	1.06901i
$603$	−13.3602			−0.544071
$604$	25.2910	+	43.8054i	1.02908	+	1.78242i
$605$	46.1858			1.87772
$606$	3.59427	+	6.22546i	0.146007	+	0.252892i
$607$	6.49295	+	11.2461i	0.263541	+	0.456466i	0.967180	−	0.254091i	$-0.0817763\pi$
$607$	6.49295	+	11.2461i	0.263541	+	0.456466i	−0.703640	+	0.710557i	$0.748443\pi$
$608$	6.59277	+	11.4190i	0.267372	+	0.463102i
$609$	−0.0444117	−	1.14687i	−0.00179965	−	0.0464736i
$610$	46.5818			1.88604
$611$	32.0371	+	14.3938i	1.29608	+	0.582311i
$612$	−8.08453	−	14.0028i	−0.326798	−	0.566030i
$613$	20.0546	−	34.7356i	0.809997	−	1.40296i	−0.102868	−	0.994695i	$-0.532802\pi$
$613$	20.0546	−	34.7356i	0.809997	−	1.40296i	0.912865	−	0.408262i	$-0.133865\pi$
$614$	−18.9419			−0.764432
$615$	0.791947	−	1.37169i	0.0319344	−	0.0553120i
$616$	33.1109	+	17.4444i	1.33407	+	0.702853i
$617$	8.82052	−	15.2776i	0.355101	−	0.615052i	−0.632035	−	0.774940i	$-0.717780\pi$
$617$	8.82052	−	15.2776i	0.355101	−	0.615052i	0.987135	+	0.159888i	$0.0511133\pi$
$618$	−15.0440	−	26.0570i	−0.605159	−	1.04817i
$619$	13.3825	+	23.1792i	0.537890	+	0.931652i	0.999017	+	0.0443184i	$0.0141116\pi$
$619$	13.3825	+	23.1792i	0.537890	+	0.931652i	−0.461128	+	0.887334i	$0.652555\pi$
$620$	25.2123			1.01255
$621$	5.23204			0.209955
$622$	12.3789	+	21.4409i	0.496349	+	0.859701i
$623$	−0.409805	−	10.5826i	−0.0164185	−	0.423985i
$624$	−0.526988	−	0.236769i	−0.0210964	−	0.00947833i
$625$	14.9895	−	25.9625i	0.599579	−	1.03850i
$626$	1.29279	−	2.23918i	0.0516702	−	0.0894955i
$627$	5.83793	−	10.1116i	0.233144	−	0.403818i
$628$	−8.83842	−	15.3086i	−0.352691	−	0.610880i
$629$	−21.4634			−0.855800
$630$	0.685719	+	17.7078i	0.0273197	+	0.705494i
$631$	10.1224	−	17.5324i	0.402964	−	0.697955i	−0.591118	−	0.806585i	$-0.701313\pi$
$631$	10.1224	−	17.5324i	0.402964	−	0.697955i	0.994082	+	0.108630i	$0.0346465\pi$
$632$	−21.3221	+	36.9309i	−0.848147	+	1.46903i
$633$	−14.3563			−0.570611
$634$	−11.3723	+	19.6974i	−0.451653	+	0.782286i
$635$	−2.04596			−0.0811914
$636$	−2.41641			−0.0958170
$637$	4.48742	+	24.8367i	0.177798	+	0.984067i
$638$	5.11379			0.202457
$639$	−7.80974			−0.308948
$640$	26.3623	−	45.6609i	1.04206	−	1.80491i
$641$	−14.7765			−0.583637			−0.291819	−	0.956474i	$-0.594260\pi$
$641$	−14.7765			−0.583637			−0.291819	+	0.956474i	$0.594260\pi$
$642$	−6.68939	+	11.5864i	−0.264009	+	0.457277i
$643$	4.74073	−	8.21118i	0.186956	−	0.323817i	−0.757278	−	0.653093i	$-0.773471\pi$
$643$	4.74073	−	8.21118i	0.186956	−	0.323817i	0.944234	+	0.329276i	$0.106804\pi$
$644$	1.71404	+	44.2627i	0.0675426	+	1.74419i
$645$	27.3956			1.07870
$646$	−13.0121	−	22.5377i	−0.511955	−	0.886732i
$647$	24.9513	−	43.2169i	0.980937	−	1.69903i	0.322177	−	0.946680i	$-0.395586\pi$
$647$	24.9513	−	43.2169i	0.980937	−	1.69903i	0.658760	−	0.752353i	$-0.271081\pi$
$648$	−1.36814	+	2.36969i	−0.0537457	+	0.0930903i
$649$	−9.42848	+	16.3306i	−0.370100	+	0.641033i
$650$	−24.1874	+	17.4485i	−0.948708	+	0.684388i
$651$	0.274623	+	7.09175i	0.0107633	+	0.277948i
$652$	5.03784	+	8.72579i	0.197297	+	0.341728i
$653$	41.4038			1.62026			0.810128	−	0.586252i	$-0.199397\pi$
$653$	41.4038			1.62026			0.810128	+	0.586252i	$0.199397\pi$
$654$	−12.5144			−0.489353
$655$	9.85355	+	17.0668i	0.385010	+	0.666857i
$656$	−0.0432028	−	0.0748294i	−0.00168678	−	0.00292160i
$657$	−7.94401	+	13.7594i	−0.309925	+	0.536807i
$658$	−51.9953	−	27.3936i	−2.02699	−	1.06791i
$659$	1.08993	−	1.88781i	0.0424576	−	0.0735387i	−0.844016	−	0.536318i	$-0.819815\pi$
$659$	1.08993	−	1.88781i	0.0424576	−	0.0735387i	0.886473	+	0.462780i	$0.153148\pi$
$660$	−48.5887			−1.89131
$661$	−16.4283	+	28.4546i	−0.638986	+	1.10676i	0.346669	+	0.937987i	$0.387313\pi$
$661$	−16.4283	+	28.4546i	−0.638986	+	1.10676i	−0.985656	+	0.168769i	$0.946021\pi$
$662$	1.88714	+	3.26862i	0.0733457	+	0.127038i
$663$	16.6183	+	7.46638i	0.645402	+	0.289970i
$664$	36.2145			1.40539
$665$	0.679178	+	17.5388i	0.0263374	+	0.680127i
$666$	4.84312	+	8.38853i	0.187667	+	0.325049i
$667$	1.13483	+	1.96559i	0.0439409	+	0.0761079i
$668$	21.4765	+	37.1984i	0.830951	+	1.43925i
$669$	−1.19386			−0.0461574
$670$	44.7429	+	77.4970i	1.72857	+	2.99397i
$671$	−35.9525			−1.38793
$672$	13.6653	+	7.19951i	0.527149	+	0.277727i
$673$	−5.61199	−	9.72024i	−0.216326	−	0.374688i	0.737356	−	0.675505i	$-0.236074\pi$
$673$	−5.61199	−	9.72024i	−0.216326	−	0.374688i	−0.953682	+	0.300817i	$0.902741\pi$
$674$	−28.2947			−1.08987
$675$	−1.81371	−	3.14143i	−0.0698097	−	0.120914i
$676$	−40.7478	+	8.37363i	−1.56722	+	0.322063i
$677$	10.0207	−	17.3564i	0.385127	−	0.667059i	−0.606660	−	0.794961i	$-0.707491\pi$
$677$	10.0207	−	17.3564i	0.385127	−	0.667059i	0.991787	+	0.127902i	$0.0408244\pi$
$678$	1.81243	+	3.13922i	0.0696060	+	0.120561i
$679$	12.6239	+	6.65085i	0.484460	+	0.255236i
$680$	−20.3055	+	35.1702i	−0.778680	+	1.34871i
$681$	7.94437	−	13.7600i	0.304429	−	0.527286i
$682$	−31.6214			−1.21085
$683$	14.6601			0.560953			0.280476	−	0.959861i	$-0.409508\pi$
$683$	14.6601			0.560953			0.280476	+	0.959861i	$0.409508\pi$
$684$	−3.61368	+	6.25908i	−0.138172	+	0.239322i
$685$	−18.3568	+	31.7949i	−0.701376	+	1.21482i
$686$	−4.89280	−	41.9481i	−0.186808	−	1.60159i
$687$	−4.39323	−	7.60931i	−0.167612	−	0.290313i
$688$	0.747251	−	1.29428i	0.0284887	−	0.0493438i
$689$	2.20811	−	1.59291i	0.0841223	−	0.0606850i
$690$	−17.5219	−	30.3488i	−0.667047	−	1.15536i
$691$	28.9453			1.10113			0.550565	−	0.834792i	$-0.314412\pi$
$691$	28.9453			1.10113			0.550565	+	0.834792i	$0.314412\pi$
$692$	20.5578	+	35.6071i	0.781490	+	1.35358i
$693$	−0.529247	−	13.6671i	−0.0201044	−	0.519169i
$694$	30.2036			1.14651
$695$	−1.93157	−	3.34558i	−0.0732688	−	0.126905i
$696$	−1.18700			−0.0449933
$697$	1.36238	+	2.35971i	0.0516037	+	0.0893803i
$698$	39.9215	+	69.1460i	1.51105	+	2.61722i
$699$	2.86714	+	4.96604i	0.108445	+	0.187833i
$700$	25.9821	−	16.3730i	0.982032	−	0.618840i
$701$	−37.6521			−1.42210			−0.711051	−	0.703141i	$-0.751780\pi$
$701$	−37.6521			−1.42210			−0.711051	+	0.703141i	$0.751780\pi$
$702$	−0.831769	−	8.17970i	−0.0313931	−	0.308723i
$703$	4.79692	+	8.30851i	0.180919	+	0.313362i
$704$	−33.5815	+	58.1649i	−1.26565	+	2.19217i
$705$	28.6120			1.07759
$706$	−26.3473	+	45.6349i	−0.991595	+	1.71749i
$707$	7.37902	+	3.88761i	0.277517	+	0.146209i
$708$	5.83623	−	10.1086i	0.219339	−	0.379906i
$709$	−11.2107	−	19.4175i	−0.421026	−	0.729239i	0.575014	−	0.818144i	$-0.304997\pi$
$709$	−11.2107	−	19.4175i	−0.421026	−	0.729239i	−0.996040	+	0.0889046i	$0.971663\pi$
$710$	26.1545	+	45.3009i	0.981560	+	1.70011i
$711$	15.5847			0.584472
$712$	−10.9530			−0.410480
$713$	−7.01731	−	12.1543i	−0.262800	−	0.455184i
$714$	−26.9711	−	14.2096i	−1.00937	−	0.531782i
$715$	44.4002	−	32.0298i	1.66047	−	1.19785i
$716$	−29.8655	+	51.7286i	−1.11613	+	1.93319i
$717$	5.77055	−	9.99489i	0.215505	−	0.373266i
$718$	−14.6958	+	25.4539i	−0.548444	+	0.949932i
$719$	−4.18609	−	7.25051i	−0.156115	−	0.270399i	0.777350	−	0.629069i	$-0.216564\pi$
$719$	−4.18609	−	7.25051i	−0.156115	−	0.270399i	−0.933464	+	0.358670i	$0.883230\pi$
$720$	−0.470648			−0.0175400
$721$	−30.8853	−	16.2718i	−1.15023	−	0.605994i
$722$	15.8470	−	27.4478i	0.589763	−	1.02150i
$723$	2.83030	−	4.90223i	0.105260	−	0.182316i
$724$	2.81094			0.104468
$725$	0.786789	−	1.36276i	0.0292206	−	0.0506116i
$726$	35.8564			1.33076
$727$	20.0990			0.745432			0.372716	−	0.927945i	$-0.378427\pi$
$727$	20.0990			0.745432			0.372716	+	0.927945i	$0.378427\pi$
$728$	25.8470	−	3.64355i	0.957952	−	0.135039i
$729$	1.00000			0.0370370
$730$	106.417			3.93866
$731$	−23.5642	+	40.8144i	−0.871553	+	1.50957i
$732$	22.2546			0.822553
$733$	5.77804	−	10.0079i	0.213417	−	0.369649i	−0.739365	−	0.673305i	$-0.764874\pi$
$733$	5.77804	−	10.0079i	0.213417	−	0.369649i	0.952782	+	0.303656i	$0.0982074\pi$
$734$	30.2064	−	52.3191i	1.11494	−	1.93113i
$735$	11.6266	+	16.9578i	0.428852	+	0.625497i
$736$	−30.5444			−1.12588
$737$	−34.5332	−	59.8132i	−1.27205	−	2.20325i
$738$	0.614830	−	1.06492i	0.0226322	−	0.0392001i
$739$	−12.1325	+	21.0141i	−0.446300	+	0.773015i	−0.998142	−	0.0609342i	$-0.980592\pi$
$739$	−12.1325	+	21.0141i	−0.446300	+	0.773015i	0.551841	+	0.833949i	$0.313925\pi$
$740$	19.9622	−	34.5756i	0.733826	−	1.27102i
$741$	−0.823835	−	8.10167i	−0.0302643	−	0.297622i
$742$	−3.85445	+	2.42893i	−0.141501	+	0.0891689i
$743$	0.777681	+	1.34698i	0.0285303	+	0.0494160i	0.879938	−	0.475088i	$-0.157584\pi$
$743$	0.777681	+	1.34698i	0.0285303	+	0.0494160i	−0.851408	+	0.524504i	$0.824251\pi$
$744$	7.33992			0.269094
$745$	62.2483			2.28060
$746$	14.1050	+	24.4306i	0.516422	+	0.894468i
$747$	−6.61745	−	11.4618i	−0.242120	−	0.419364i
$748$	41.7933	−	72.3881i	1.52811	−	2.64677i
$749$	0.600653	+	15.5110i	0.0219474	+	0.566761i
$750$	4.59673	−	7.96177i	0.167849	−	0.290723i
$751$	−35.3585			−1.29025			−0.645125	−	0.764077i	$-0.723195\pi$
$751$	−35.3585			−1.29025			−0.645125	+	0.764077i	$0.723195\pi$
$752$	0.780429	−	1.35174i	0.0284593	−	0.0492930i
$753$	12.1872	+	21.1088i	0.444126	+	0.769249i
$754$	2.89256	−	2.08666i	0.105341	−	0.0759918i
$755$	−46.4295			−1.68974
$756$	0.327604	+	8.45992i	0.0119148	+	0.307684i
$757$	9.73684	+	16.8647i	0.353891	+	0.612958i	0.986928	−	0.161164i	$-0.0515249\pi$
$757$	9.73684	+	16.8647i	0.353891	+	0.612958i	−0.633036	+	0.774122i	$0.718192\pi$
$758$	−31.9655	−	55.3659i	−1.16104	−	2.01098i
$759$	13.5236	+	23.4236i	0.490877	+	0.850223i
$760$	18.1526			0.658464
$761$	−8.81978	−	15.2763i	−0.319717	−	0.553766i	0.660712	−	0.750640i	$-0.270254\pi$
$761$	−8.81978	−	15.2763i	−0.319717	−	0.553766i	−0.980429	+	0.196874i	$0.936921\pi$
$762$	−1.58839			−0.0575411
$763$	−12.2842	+	7.74105i	−0.444717	+	0.280245i
$764$	25.5216	+	44.2048i	0.923341	+	1.59927i
$765$	14.8417			0.536601
$766$	29.9754	+	51.9190i	1.08306	+	1.87591i
$767$	1.33052	+	13.0845i	0.0480425	+	0.472454i
$768$	7.47442	−	12.9461i	0.269710	−	0.467151i
$769$	−2.32077	−	4.01969i	−0.0836890	−	0.144954i	0.821143	−	0.570723i	$-0.193337\pi$
$769$	−2.32077	−	4.01969i	−0.0836890	−	0.144954i	−0.904832	+	0.425769i	$0.860004\pi$
$770$	−77.5044	+	48.8404i	−2.79306	+	1.76009i
$771$	−2.30268	+	3.98836i	−0.0829290	+	0.143637i
$772$	−6.32095	+	10.9482i	−0.227496	+	0.394034i
$773$	20.0445			0.720949			0.360475	−	0.932769i	$-0.382615\pi$
$773$	20.0445			0.720949			0.360475	+	0.932769i	$0.382615\pi$
$774$	21.2687			0.764486
$775$	−4.86516	+	8.42670i	−0.174762	+	0.302696i
$776$	7.37848	−	12.7799i	0.264872	−	0.458772i
$777$	9.94290	+	5.23839i	0.356699	+	0.187926i
$778$	−30.6032	−	53.0063i	−1.09718	−	1.90037i
$779$	0.608965	−	1.05476i	0.0218184	−	0.0377906i
$780$	−27.4837	+	19.8265i	−0.984075	+	0.709901i
$781$	−20.1864	−	34.9638i	−0.722326	−	1.25110i
$782$	60.2855			2.15580
$783$	0.216901	+	0.375683i	0.00775140	+	0.0134258i
$784$	1.11828	−	0.0867393i	0.0399386	−	0.00309783i
$785$	16.2257			0.579119
$786$	7.64983	+	13.2499i	0.272860	+	0.472608i
$787$	−10.1166			−0.360620			−0.180310	−	0.983610i	$-0.557710\pi$
$787$	−10.1166			−0.360620			−0.180310	+	0.983610i	$0.557710\pi$
$788$	−21.5150	−	37.2650i	−0.766438	−	1.32751i
$789$	−11.4912	−	19.9033i	−0.409097	−	0.708576i
$790$	−52.1925	−	90.4001i	−1.85693	−	3.21629i
$791$	3.72091	+	1.96035i	0.132300	+	0.0697020i
$792$	−14.1453			−0.502633
$793$	−20.3362	+	14.6703i	−0.722159	+	0.520958i
$794$	−27.9618	−	48.4313i	−0.992328	−	1.71876i
$795$	1.10902	−	1.92088i	0.0393328	−	0.0681265i
$796$	66.6520			2.36242
$797$	−4.44188	+	7.69357i	−0.157340	+	0.272520i	−0.933908	−	0.357512i	$-0.883625\pi$
$797$	−4.44188	+	7.69357i	−0.157340	+	0.272520i	0.776569	+	0.630032i	$0.216958\pi$
$798$	0.527282	+	13.6163i	0.0186656	+	0.482013i
$799$	−24.6104	+	42.6265i	−0.870655	+	1.50802i
$800$	10.5884	+	18.3396i	0.374355	+	0.648402i
$801$	2.00143	+	3.46658i	0.0707171	+	0.122486i
$802$	7.21887			0.254907
$803$	−82.1338			−2.89844
$804$	21.3760	+	37.0244i	0.753875	+	1.30575i
$805$	−35.9723	−	18.9519i	−1.26786	−	0.667967i
$806$	−17.8863	+	12.9030i	−0.630020	+	0.454489i
$807$	−7.00246	+	12.1286i	−0.246498	+	0.426948i
$808$	4.31294	−	7.47022i	0.151729	−	0.262802i
$809$	20.8784	−	36.1625i	0.734047	−	1.27141i	−0.221094	−	0.975253i	$-0.570963\pi$
$809$	20.8784	−	36.1625i	0.734047	−	1.27141i	0.955140	−	0.296153i	$-0.0957039\pi$
$810$	−3.34896	−	5.80057i	−0.117670	−	0.203811i
$811$	−31.3690			−1.10151			−0.550757	−	0.834666i	$-0.685661\pi$
$811$	−31.3690			−1.10151			−0.550757	+	0.834666i	$0.685661\pi$
$812$	−3.10719	+	1.95804i	−0.109041	+	0.0687137i
$813$	9.55299	−	16.5463i	0.335038	−	0.580303i
$814$	−25.0367	+	43.3649i	−0.877537	+	1.51994i
$815$	−9.24851			−0.323961
$816$	0.404825	−	0.701178i	0.0141717	−	0.0245461i
$817$	21.0658			0.736998
$818$	43.4826			1.52033
$819$	−5.87617	−	7.51469i	−0.205330	−	0.262585i
$820$	−5.06838			−0.176995
$821$	30.5508			1.06623			0.533114	−	0.846043i	$-0.321022\pi$
$821$	30.5508			1.06623			0.533114	+	0.846043i	$0.321022\pi$
$822$	−14.2513	+	24.6840i	−0.497072	+	0.860954i
$823$	3.34874			0.116730			0.0583650	−	0.998295i	$-0.481411\pi$
$823$	3.34874			0.116730			0.0583650	+	0.998295i	$0.481411\pi$
$824$	−18.0520	+	31.2670i	−0.628872	+	1.08924i
$825$	9.37604	−	16.2398i	0.326432	−	0.565397i
$826$	−0.851581	−	21.9909i	−0.0296303	−	0.765161i
$827$	−48.2646			−1.67833			−0.839163	−	0.543880i	$-0.816955\pi$
$827$	−48.2646			−1.67833			−0.839163	+	0.543880i	$0.816955\pi$
$828$	−8.37113	−	14.4992i	−0.290917	−	0.503883i
$829$	−24.9146	+	43.1534i	−0.865320	+	1.49878i	0.00140835	+	0.999999i	$0.499552\pi$
$829$	−24.9146	+	43.1534i	−0.865320	+	1.49878i	−0.866729	+	0.498780i	$0.833782\pi$
$830$	−44.3231	+	76.7699i	−1.53848	+	2.66472i
$831$	−6.45998	+	11.1890i	−0.224094	+	0.388142i
$832$	4.73894	+	46.6032i	0.164293	+	1.61568i
$833$	−35.2645	+	2.73528i	−1.22184	+	0.0947719i
$834$	−1.49958	−	2.59735i	−0.0519263	−	0.0899390i
$835$	−39.4268			−1.36442
$836$	−37.3621			−1.29220
$837$	−1.34122	−	2.32306i	−0.0463593	−	0.0802967i
$838$	17.7988	+	30.8285i	0.614850	+	1.06495i
$839$	16.4441	−	28.4819i	0.567712	−	0.983305i	−0.429080	−	0.903266i	$-0.641162\pi$
$839$	16.4441	−	28.4819i	0.567712	−	0.983305i	0.996792	−	0.0800390i	$-0.0255045\pi$
$840$	17.9902	−	11.3368i	0.620721	−	0.391156i
$841$	14.4059	−	24.9518i	0.496755	−	0.860406i
$842$	−41.1659			−1.41867
$843$	9.81322	−	16.9970i	0.337985	−	0.585408i
$844$	22.9697	+	39.7846i	0.790649	+	1.36944i
$845$	12.0449	−	36.2347i	0.414356	−	1.24651i
$846$	22.2130			0.763698
$847$	35.1967	−	22.1797i	1.20937	−	0.762103i
$848$	−0.0604999	−	0.104789i	−0.00207757	−	0.00359846i
$849$	−1.63363	−	2.82954i	−0.0560662	−	0.0971095i
$850$	−20.8982	−	36.1967i	−0.716802	−	1.24154i
$851$	−22.2242			−0.761837
$852$	12.4954	+	21.6426i	0.428084	+	0.741464i
$853$	−17.9823			−0.615701			−0.307850	−	0.951435i	$-0.599610\pi$
$853$	−17.9823			−0.615701			−0.307850	+	0.951435i	$0.599610\pi$
$854$	35.4986	−	22.3699i	1.21474	−	0.765482i
$855$	−3.31701	−	5.74523i	−0.113439	−	0.196483i
$856$	16.0538			0.548708
$857$	23.5502	+	40.7901i	0.804459	+	1.39336i	0.916656	+	0.399678i	$0.130878\pi$
$857$	23.5502	+	40.7901i	0.804459	+	1.39336i	−0.112196	+	0.993686i	$0.535789\pi$
$858$	34.4702	−	24.8664i	1.17679	−	0.848926i
$859$	−13.8486	+	23.9866i	−0.472510	+	0.818411i	−0.999505	−	0.0314573i	$-0.989985\pi$
$859$	−13.8486	+	23.9866i	−0.472510	+	0.818411i	0.526995	+	0.849868i	$0.323319\pi$
$860$	−43.8322	−	75.9197i	−1.49467	−	2.58884i
$861$	−0.0552068	−	1.42564i	−0.00188144	−	0.0485856i
$862$	19.9718	−	34.5922i	0.680242	−	1.17821i
$863$	18.5569	−	32.1414i	0.631683	−	1.09411i	−0.355525	−	0.934667i	$-0.615698\pi$
$863$	18.5569	−	32.1414i	0.631683	−	1.09411i	0.987208	−	0.159440i	$-0.0509689\pi$
$864$	−5.83796			−0.198611
$865$	−37.7402			−1.28320
$866$	−6.90854	+	11.9659i	−0.234762	+	0.406619i
$867$	−4.26597	+	7.38888i	−0.144880	+	0.250939i
$868$	19.2135	−	12.1077i	0.652149	−	0.410961i
$869$	40.2829	+	69.7720i	1.36650	+	2.36685i
$870$	1.45278	−	2.51629i	0.0492540	−	0.0853104i
$871$	−43.9399	−	19.7416i	−1.48885	−	0.668919i
$872$	7.50833	+	13.0048i	0.254264	+	0.440399i
$873$	−5.39306			−0.182527
$874$	−13.4734	−	23.3366i	−0.455745	−	0.789373i
$875$	−0.412749	−	10.6587i	−0.0139535	−	0.360329i
$876$	50.8408			1.71775
$877$	−14.1491	−	24.5069i	−0.477780	−	0.827538i	0.521896	−	0.853009i	$-0.325225\pi$
$877$	−14.1491	−	24.5069i	−0.477780	−	0.827538i	−0.999676	+	0.0254707i	$0.991892\pi$
$878$	53.3198			1.79945
$879$	9.50947	+	16.4709i	0.320746	+	0.555549i
$880$	−1.21652	−	2.10707i	−0.0410088	−	0.0710293i
$881$	−9.74919	−	16.8861i	−0.328458	−	0.568907i	0.653748	−	0.756713i	$-0.273196\pi$
$881$	−9.74919	−	16.8861i	−0.328458	−	0.568907i	−0.982206	+	0.187806i	$0.939862\pi$
$882$	9.02632	+	13.1652i	0.303932	+	0.443296i
$883$	36.8164			1.23897			0.619485	−	0.785009i	$-0.287342\pi$
$883$	36.8164			1.23897			0.619485	+	0.785009i	$0.287342\pi$
$884$	−5.89777	−	57.9993i	−0.198364	−	1.95073i
$885$	5.35710	+	9.27878i	0.180077	+	0.311903i
$886$	10.1409	−	17.5646i	0.340692	−	0.590095i
$887$	−22.1839			−0.744863			−0.372432	−	0.928060i	$-0.621476\pi$
$887$	−22.1839			−0.744863			−0.372432	+	0.928060i	$0.621476\pi$
$888$	5.81149	−	10.0658i	0.195021	−	0.337786i
$889$	−1.55916	+	0.982526i	−0.0522926	+	0.0329529i
$890$	13.4054	−	23.2189i	0.449351	−	0.778298i
$891$	2.58477	+	4.47696i	0.0865931	+	0.149984i
$892$	1.91015	+	3.30847i	0.0639565	+	0.110776i
$893$	22.0011			0.736238
$894$	48.3266			1.61628
$895$	−27.4137	−	47.4820i	−0.916340	−	1.58715i
$896$	−1.83772	−	47.4567i	−0.0613941	−	1.58542i
$897$	17.2074	+	7.73106i	0.574540	+	0.258133i
$898$	−44.1635	+	76.4935i	−1.47376	+	2.55262i
$899$	0.581823	−	1.00775i	0.0194049	−	0.0336102i
$900$	−5.80377	+	10.0524i	−0.193459	+	0.335081i
$901$	1.90783	+	3.30446i	0.0635592	+	0.110088i
$902$	6.35678			0.211658
$903$	20.8773	−	13.1561i	0.694754	−	0.437808i
$904$	2.17482	−	3.76690i	0.0723335	−	0.125285i
$905$	−1.29009	+	2.23450i	−0.0428839	+	0.0742771i
$906$	−36.0457			−1.19754
$907$	23.3042	−	40.3640i	0.773803	−	1.34027i	−0.161662	−	0.986846i	$-0.551685\pi$
$907$	23.3042	−	40.3640i	0.773803	−	1.34027i	0.935465	−	0.353420i	$-0.114981\pi$
$908$	−50.8431			−1.68729
$909$	−3.15240			−0.104559
$910$	−23.9104	+	59.2515i	−0.792623	+	1.96417i
$911$	0.542513			0.0179743			0.00898714	−	0.999960i	$-0.497139\pi$
$911$	0.542513			0.0179743			0.00898714	+	0.999960i	$0.497139\pi$
$912$	−0.361903			−0.0119838
$913$	34.2092	−	59.2521i	1.13216	−	1.96096i
$914$	51.0802			1.68958
$915$	−10.2138	+	17.6908i	−0.337658	+	0.584840i
$916$	−14.0581	+	24.3494i	−0.464493	+	0.804526i
$917$	15.7051	+	8.27416i	0.518626	+	0.273237i
$918$	11.5224			0.380294
$919$	−16.8311	−	29.1522i	−0.555205	−	0.961644i	−0.997888	−	0.0649652i	$-0.979306\pi$
$919$	−16.8311	−	29.1522i	−0.555205	−	0.961644i	0.442682	−	0.896679i	$-0.354027\pi$
$920$	−21.0253	+	36.4170i	−0.693185	+	1.20063i
$921$	4.15330	−	7.19373i	0.136856	−	0.237041i
$922$	−3.20085	+	5.54403i	−0.105414	+	0.182583i
$923$	−25.6851	−	11.5400i	−0.845436	−	0.379843i
$924$	−37.0279	+	23.3336i	−1.21813	+	0.767620i
$925$	7.70412	+	13.3439i	0.253310	+	0.438746i
$926$	86.0897			2.82908
$927$	13.1945			0.433365
$928$	−1.26626	−	2.19322i	−0.0415669	−	0.0719961i
$929$	21.3392	+	36.9606i	0.700116	+	1.21264i	0.968425	+	0.249304i	$0.0802019\pi$
$929$	21.3392	+	36.9606i	0.700116	+	1.21264i	−0.268309	+	0.963333i	$0.586465\pi$
$930$	−8.98338	+	15.5597i	−0.294576	+	0.510221i
$931$	8.94021	+	13.0396i	0.293004	+	0.427357i
$932$	9.17471	−	15.8911i	0.300528	−	0.520529i
$933$	−10.8571			−0.355444
$934$	−18.3428	+	31.7707i	−0.600195	+	1.03957i
$935$	38.3623	+	66.4454i	1.25458	+	2.17300i
$936$	−8.00118	+	5.77196i	−0.261527	+	0.188662i
$937$	−10.2859			−0.336026			−0.168013	−	0.985785i	$-0.553735\pi$
$937$	−10.2859			−0.336026			−0.168013	+	0.985785i	$0.553735\pi$
$938$	71.3134	+	37.5712i	2.32846	+	1.22674i
$939$	0.566928	+	0.981949i	0.0185010	+	0.0320447i
$940$	−45.7784	−	79.2905i	−1.49313	−	2.58617i
$941$	5.84119	+	10.1172i	0.190417	+	0.329813i	0.945389	−	0.325945i	$-0.105683\pi$
$941$	5.84119	+	10.1172i	0.190417	+	0.329813i	−0.754971	+	0.655758i	$0.772349\pi$
$942$	12.5968			0.410427
$943$	1.41067	+	2.44336i	0.0459379	+	0.0795667i
$944$	0.584488			0.0190235
$945$	−6.87539	−	3.62228i	−0.223656	−	0.117833i
$946$	54.9746	+	95.2188i	1.78738	+	3.09583i
$947$	31.8808			1.03599			0.517993	−	0.855385i	$-0.326679\pi$
$947$	31.8808			1.03599			0.517993	+	0.855385i	$0.326679\pi$
$948$	−24.9351	−	43.1889i	−0.809855	−	1.40271i
$949$	−46.4582	+	33.5144i	−1.50810	+	1.08792i
$950$	−9.34122	+	16.1795i	−0.303069	+	0.524931i
$951$	−4.98712	−	8.63795i	−0.161718	−	0.280105i
$952$	1.41550	+	36.5533i	0.0458766	+	1.18470i
$953$	3.72492	−	6.45175i	0.120662	−	0.208993i	−0.799367	−	0.600843i	$-0.794832\pi$
$953$	3.72492	−	6.45175i	0.120662	−	0.208993i	0.920029	+	0.391850i	$0.128165\pi$
$954$	0.860990	−	1.49128i	0.0278756	−	0.0482819i
$955$	−46.8529			−1.51612
$956$	−36.9309			−1.19443
$957$	−1.12128	+	1.94211i	−0.0362458	+	0.0627795i
$958$	−9.74674	+	16.8818i	−0.314903	+	0.545428i
$959$	1.27965	+	33.0453i	0.0413222	+	1.06709i
$960$	19.0804	+	33.0483i	0.615819	+	1.06663i
$961$	11.9023	−	20.6153i	0.383944	−	0.665010i
$962$	3.53312	+	34.7451i	0.113912	+	1.12023i
$963$	−2.93351	−	5.08098i	−0.0945309	−	0.163732i
$964$	−18.1136			−0.583401
$965$	−5.80203	−	10.0494i	−0.186774	−	0.323502i
$966$	−27.9272	−	14.7134i	−0.898544	−	0.473395i
$967$	−51.0981			−1.64320			−0.821602	−	0.570061i	$-0.806920\pi$
$967$	−51.0981			−1.64320			−0.821602	+	0.570061i	$0.806920\pi$
$968$	−21.5129	−	37.2615i	−0.691451	−	1.19763i
$969$	11.4124			0.366621
$970$	18.0611	+	31.2828i	0.579908	+	1.00443i
$971$	−2.50917	−	4.34602i	−0.0805232	−	0.139470i	0.822952	−	0.568112i	$-0.192326\pi$
$971$	−2.50917	−	4.34602i	−0.0805232	−	0.139470i	−0.903475	+	0.428641i	$0.858992\pi$
$972$	−1.59997	−	2.77124i	−0.0513192	−	0.0888874i
$973$	−3.07863	−	1.62197i	−0.0986964	−	0.0519979i
$974$	−81.1256			−2.59943
$975$	−1.32312	−	13.0117i	−0.0423739	−	0.416709i
$976$	0.557189	+	0.965080i	0.0178352	+	0.0308915i
$977$	13.8306	−	23.9553i	0.442479	−	0.766396i	−0.555394	−	0.831588i	$-0.687432\pi$
$977$	13.8306	−	23.9553i	0.442479	−	0.766396i	0.997873	+	0.0651911i	$0.0207657\pi$
$978$	−7.18011			−0.229594
$979$	−10.3465	+	17.9206i	−0.330675	+	0.572746i
$980$	28.3918	−	59.3519i	0.906943	−	1.89593i
$981$	2.74399	−	4.75273i	0.0876088	−	0.151743i
$982$	35.7990	+	62.0057i	1.14239	+	1.97868i
$983$	2.23464	+	3.87050i	0.0712738	+	0.123450i	0.899460	−	0.437003i	$-0.143960\pi$
$983$	2.23464	+	3.87050i	0.0712738	+	0.123450i	−0.828186	+	0.560453i	$0.810627\pi$
$984$	−1.47553			−0.0470381
$985$	39.4974			1.25849
$986$	2.49921	+	4.32875i	0.0795910	+	0.137856i
$987$	21.8043	−	13.7403i	0.694038	−	0.437357i
$988$	−21.1335	+	15.2455i	−0.672347	+	0.485024i
$989$	−24.3995	+	42.2613i	−0.775860	+	1.34383i
$990$	17.3126	−	29.9863i	0.550230	−	0.953026i
$991$	−5.21216	+	9.02772i	−0.165570	+	0.286775i	−0.936857	−	0.349712i	$-0.886280\pi$
$991$	−5.21216	+	9.02772i	−0.165570	+	0.286775i	0.771288	+	0.636487i	$0.219613\pi$
$992$	7.82998	+	13.5619i	0.248602	+	0.430592i
$993$	−1.65514			−0.0525242
$994$	41.6863	+	21.9623i	1.32221	+	0.696601i
$995$	−30.5901	+	52.9836i	−0.969771	+	1.67969i
$996$	−21.1755	+	36.6770i	−0.670971	+	1.16216i
$997$	−14.5120			−0.459599			−0.229800	−	0.973238i	$-0.573807\pi$
$997$	−14.5120			−0.459599			−0.229800	+	0.973238i	$0.573807\pi$
$998$	4.89374	−	8.47621i	0.154909	−	0.268310i
$999$	−4.24772			−0.134392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.c.16.9	yes	20
3.2	odd	2		819.2.s.f.289.2		20
7.4	even	3		273.2.j.c.172.2	yes	20
13.9	even	3		273.2.j.c.100.2	✓	20
21.11	odd	6		819.2.n.f.172.9		20
39.35	odd	6		819.2.n.f.100.9		20
91.74	even	3	inner	273.2.l.c.256.9	yes	20
273.74	odd	6		819.2.s.f.802.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.2	✓	20	13.9	even	3
273.2.j.c.172.2	yes	20	7.4	even	3
273.2.l.c.16.9	yes	20	1.1	even	1	trivial
273.2.l.c.256.9	yes	20	91.74	even	3	inner
819.2.n.f.100.9		20	39.35	odd	6
819.2.n.f.172.9		20	21.11	odd	6
819.2.s.f.289.2		20	3.2	odd	2
819.2.s.f.802.2		20	273.74	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.28034 q^{2} +(-0.500000 + 0.866025i) q^{3} +3.19995 q^{4} +(-1.46862 + 2.54373i) q^{5} +(-1.14017 + 1.97483i) q^{6} +(0.102378 + 2.64377i) q^{7} +2.73629 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+2.28034 q^{2} +(-0.500000 + 0.866025i) q^{3} +3.19995 q^{4} +(-1.46862 + 2.54373i) q^{5} +(-1.14017 + 1.97483i) q^{6} +(0.102378 + 2.64377i) q^{7} +2.73629 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.34896 + 5.80057i) q^{10} +(2.58477 - 4.47696i) q^{11} +(-1.59997 + 2.77124i) q^{12} +(-0.364757 - 3.58705i) q^{13} +(0.233457 + 6.02869i) q^{14} +(-1.46862 - 2.54373i) q^{15} -0.160234 q^{16} +5.05291 q^{17} +(-1.14017 - 1.97483i) q^{18} +(-1.12929 - 1.95599i) q^{19} +(-4.69952 + 8.13980i) q^{20} +(-2.34076 - 1.23322i) q^{21} +(5.89416 - 10.2090i) q^{22} +5.23204 q^{23} +(-1.36814 + 2.36969i) q^{24} +(-1.81371 - 3.14143i) q^{25} +(-0.831769 - 8.17970i) q^{26} +1.00000 q^{27} +(0.327604 + 8.45992i) q^{28} +(0.216901 + 0.375683i) q^{29} +(-3.34896 - 5.80057i) q^{30} +(-1.34122 - 2.32306i) q^{31} -5.83796 q^{32} +(2.58477 + 4.47696i) q^{33} +11.5224 q^{34} +(-6.87539 - 3.62228i) q^{35} +(-1.59997 - 2.77124i) q^{36} -4.24772 q^{37} +(-2.57517 - 4.46033i) q^{38} +(3.28886 + 1.47764i) q^{39} +(-4.01857 + 6.96037i) q^{40} +(0.269622 + 0.466999i) q^{41} +(-5.33773 - 2.81217i) q^{42} +(-4.66348 + 8.07739i) q^{43} +(8.27113 - 14.3260i) q^{44} +2.93725 q^{45} +11.9308 q^{46} +(-4.87054 + 8.43603i) q^{47} +(0.0801172 - 0.138767i) q^{48} +(-6.97904 + 0.541328i) q^{49} +(-4.13587 - 7.16354i) q^{50} +(-2.52646 + 4.37595i) q^{51} +(-1.16720 - 11.4784i) q^{52} +(0.377571 + 0.653972i) q^{53} +2.28034 q^{54} +(7.59211 + 13.1499i) q^{55} +(0.280135 + 7.23411i) q^{56} +2.25859 q^{57} +(0.494607 + 0.856685i) q^{58} -3.64771 q^{59} +(-4.69952 - 8.13980i) q^{60} +(-3.47734 - 6.02293i) q^{61} +(-3.05843 - 5.29736i) q^{62} +(2.23838 - 1.41055i) q^{63} -12.9921 q^{64} +(9.66019 + 4.34019i) q^{65} +(5.89416 + 10.2090i) q^{66} +(6.68012 - 11.5703i) q^{67} +16.1691 q^{68} +(-2.61602 + 4.53108i) q^{69} +(-15.6782 - 8.26003i) q^{70} +(3.90487 - 6.76343i) q^{71} +(-1.36814 - 2.36969i) q^{72} +(-7.94401 - 13.7594i) q^{73} -9.68624 q^{74} +3.62742 q^{75} +(-3.61368 - 6.25908i) q^{76} +(12.1007 + 6.37520i) q^{77} +(7.49971 + 3.36952i) q^{78} +(-7.79235 + 13.4967i) q^{79} +(0.235324 - 0.407593i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.614830 + 1.06492i) q^{82} +13.2349 q^{83} +(-7.49031 - 3.94625i) q^{84} +(-7.42083 + 12.8532i) q^{85} +(-10.6343 + 18.4192i) q^{86} -0.433801 q^{87} +(7.07267 - 12.2502i) q^{88} -4.00286 q^{89} +6.69792 q^{90} +(9.44600 - 1.33157i) q^{91} +16.7423 q^{92} +2.68244 q^{93} +(-11.1065 + 19.2370i) q^{94} +6.63403 q^{95} +(2.91898 - 5.05582i) q^{96} +(2.69653 - 4.67053i) q^{97} +(-15.9146 + 1.23441i) q^{98} -5.16954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more