LMFDB - Embedded newform 731.2.f.c.259.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (of order $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.9
Character	$\chi$	$=$	731.259
Dual form			731.2.f.c.302.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.52916i q^{2} +(-0.854970 + 0.854970i) q^{3} -0.338329 q^{4} +(-2.11844 + 2.11844i) q^{5} +(1.30739 + 1.30739i) q^{6} +(0.0998235 + 0.0998235i) q^{7} -2.54096i q^{8} +1.53805i q^{9} +O(q^{10})$	\(q-1.52916i q^{2} +(-0.854970 + 0.854970i) q^{3} -0.338329 q^{4} +(-2.11844 + 2.11844i) q^{5} +(1.30739 + 1.30739i) q^{6} +(0.0998235 + 0.0998235i) q^{7} -2.54096i q^{8} +1.53805i q^{9} +(3.23944 + 3.23944i) q^{10} +(-0.566977 - 0.566977i) q^{11} +(0.289261 - 0.289261i) q^{12} -0.931997 q^{13} +(0.152646 - 0.152646i) q^{14} -3.62241i q^{15} -4.56219 q^{16} +(-2.87088 - 2.95940i) q^{17} +2.35193 q^{18} -6.07890i q^{19} +(0.716732 - 0.716732i) q^{20} -0.170692 q^{21} +(-0.866998 + 0.866998i) q^{22} +(-2.28941 - 2.28941i) q^{23} +(2.17244 + 2.17244i) q^{24} -3.97561i q^{25} +1.42517i q^{26} +(-3.87990 - 3.87990i) q^{27} +(-0.0337732 - 0.0337732i) q^{28} +(0.337969 - 0.337969i) q^{29} -5.53925 q^{30} +(-0.280005 + 0.280005i) q^{31} +1.89440i q^{32} +0.969496 q^{33} +(-4.52539 + 4.39004i) q^{34} -0.422941 q^{35} -0.520369i q^{36} +(-2.76514 + 2.76514i) q^{37} -9.29561 q^{38} +(0.796830 - 0.796830i) q^{39} +(5.38288 + 5.38288i) q^{40} +(-3.07080 - 3.07080i) q^{41} +0.261016i q^{42} +1.00000i q^{43} +(0.191825 + 0.191825i) q^{44} +(-3.25828 - 3.25828i) q^{45} +(-3.50088 + 3.50088i) q^{46} -12.2227 q^{47} +(3.90054 - 3.90054i) q^{48} -6.98007i q^{49} -6.07935 q^{50} +(4.98471 + 0.0756774i) q^{51} +0.315322 q^{52} +6.97443i q^{53} +(-5.93298 + 5.93298i) q^{54} +2.40222 q^{55} +(0.253648 - 0.253648i) q^{56} +(5.19728 + 5.19728i) q^{57} +(-0.516809 - 0.516809i) q^{58} -9.08346i q^{59} +1.22557i q^{60} +(7.50304 + 7.50304i) q^{61} +(0.428173 + 0.428173i) q^{62} +(-0.153534 + 0.153534i) q^{63} -6.22754 q^{64} +(1.97438 - 1.97438i) q^{65} -1.48251i q^{66} -3.09261 q^{67} +(0.971304 + 1.00125i) q^{68} +3.91476 q^{69} +0.646744i q^{70} +(1.56208 - 1.56208i) q^{71} +3.90813 q^{72} +(-2.17057 + 2.17057i) q^{73} +(4.22835 + 4.22835i) q^{74} +(3.39903 + 3.39903i) q^{75} +2.05667i q^{76} -0.113195i q^{77} +(-1.21848 - 1.21848i) q^{78} +(9.00586 + 9.00586i) q^{79} +(9.66475 - 9.66475i) q^{80} +2.02023 q^{81} +(-4.69574 + 4.69574i) q^{82} -5.68480i q^{83} +0.0577502 q^{84} +(12.3511 + 0.187513i) q^{85} +1.52916 q^{86} +0.577907i q^{87} +(-1.44066 + 1.44066i) q^{88} -13.3813 q^{89} +(-4.98243 + 4.98243i) q^{90} +(-0.0930353 - 0.0930353i) q^{91} +(0.774576 + 0.774576i) q^{92} -0.478792i q^{93} +18.6904i q^{94} +(12.8778 + 12.8778i) q^{95} +(-1.61966 - 1.61966i) q^{96} +(-4.34329 + 4.34329i) q^{97} -10.6736 q^{98} +(0.872040 - 0.872040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		−	1.52916i		−	1.08128i	−0.841254	−	0.540640i	$-0.818182\pi$
$2$		−	1.52916i		−	1.08128i	0.841254	−	0.540640i	$-0.181818\pi$
$3$	−0.854970	+	0.854970i	−0.493617	+	0.493617i	−0.909444	−	0.415827i	$-0.863492\pi$
$3$	−0.854970	+	0.854970i	−0.493617	+	0.493617i	0.415827	+	0.909444i	$0.363492\pi$
$4$	−0.338329			−0.169165
$5$	−2.11844	+	2.11844i	−0.947397	+	0.947397i	−0.998684	−	0.0512869i	$-0.983668\pi$
$5$	−2.11844	+	2.11844i	−0.947397	+	0.947397i	0.0512869	+	0.998684i	$0.483668\pi$
$6$	1.30739	+	1.30739i	0.533738	+	0.533738i
$7$	0.0998235	+	0.0998235i	0.0377297	+	0.0377297i	0.725720	−	0.687990i	$-0.241507\pi$
$7$	0.0998235	+	0.0998235i	0.0377297	+	0.0377297i	−0.687990	+	0.725720i	$0.741507\pi$
$8$		−	2.54096i		−	0.898365i
$9$			1.53805i			0.512684i
$10$	3.23944	+	3.23944i	1.02440	+	1.02440i
$11$	−0.566977	−	0.566977i	−0.170950	−	0.170950i	0.616447	−	0.787397i	$-0.288572\pi$
$11$	−0.566977	−	0.566977i	−0.170950	−	0.170950i	−0.787397	+	0.616447i	$0.788572\pi$
$12$	0.289261	−	0.289261i	0.0835026	−	0.0835026i
$13$	−0.931997			−0.258490			−0.129245	−	0.991613i	$-0.541255\pi$
$13$	−0.931997			−0.258490			−0.129245	+	0.991613i	$0.541255\pi$
$14$	0.152646	−	0.152646i	0.0407964	−	0.0407964i
$15$		−	3.62241i		−	0.935303i
$16$	−4.56219			−1.14055
$17$	−2.87088	−	2.95940i	−0.696291	−	0.717759i
$17$	−2.87088	−	2.95940i	−0.696291	−	0.717759i
$18$	2.35193			0.554355
$19$		−	6.07890i		−	1.39460i	−0.716781	−	0.697298i	$-0.754385\pi$
$19$		−	6.07890i		−	1.39460i	0.716781	−	0.697298i	$-0.245615\pi$
$20$	0.716732	−	0.716732i	0.160266	−	0.160266i
$21$	−0.170692			−0.0372481
$22$	−0.866998	+	0.866998i	−0.184845	+	0.184845i
$23$	−2.28941	−	2.28941i	−0.477376	−	0.477376i	0.426916	−	0.904291i	$-0.359600\pi$
$23$	−2.28941	−	2.28941i	−0.477376	−	0.477376i	−0.904291	+	0.426916i	$0.859600\pi$
$24$	2.17244	+	2.17244i	0.443448	+	0.443448i
$25$		−	3.97561i		−	0.795122i
$26$			1.42517i			0.279499i
$27$	−3.87990	−	3.87990i	−0.746687	−	0.746687i
$28$	−0.0337732	−	0.0337732i	−0.00638254	−	0.00638254i
$29$	0.337969	−	0.337969i	0.0627593	−	0.0627593i	−0.675031	−	0.737790i	$-0.735870\pi$
$29$	0.337969	−	0.337969i	0.0627593	−	0.0627593i	0.737790	+	0.675031i	$0.235870\pi$
$30$	−5.53925			−1.01132
$31$	−0.280005	+	0.280005i	−0.0502904	+	0.0502904i	−0.731805	−	0.681514i	$-0.761322\pi$
$31$	−0.280005	+	0.280005i	−0.0502904	+	0.0502904i	0.681514	+	0.731805i	$0.261322\pi$
$32$			1.89440i			0.334886i
$33$	0.969496			0.168768
$34$	−4.52539	+	4.39004i	−0.776098	+	0.752885i
$35$	−0.422941			−0.0714901
$36$		−	0.520369i		−	0.0867281i
$37$	−2.76514	+	2.76514i	−0.454587	+	0.454587i	−0.896874	−	0.442287i	$-0.854167\pi$
$37$	−2.76514	+	2.76514i	−0.454587	+	0.454587i	0.442287	+	0.896874i	$0.354167\pi$
$38$	−9.29561			−1.50795
$39$	0.796830	−	0.796830i	0.127595	−	0.127595i
$40$	5.38288	+	5.38288i	0.851108	+	0.851108i
$41$	−3.07080	−	3.07080i	−0.479578	−	0.479578i	0.425419	−	0.904997i	$-0.360127\pi$
$41$	−3.07080	−	3.07080i	−0.479578	−	0.479578i	−0.904997	+	0.425419i	$0.860127\pi$
$42$			0.261016i			0.0402756i
$43$			1.00000i			0.152499i
$43$			1.00000i			0.152499i
$44$	0.191825	+	0.191825i	0.0289187	+	0.0289187i
$45$	−3.25828	−	3.25828i	−0.485716	−	0.485716i
$46$	−3.50088	+	3.50088i	−0.516177	+	0.516177i
$47$	−12.2227			−1.78286			−0.891430	−	0.453159i	$-0.850297\pi$
$47$	−12.2227			−1.78286			−0.891430	+	0.453159i	$0.850297\pi$
$48$	3.90054	−	3.90054i	0.562994	−	0.562994i
$49$		−	6.98007i		−	0.997153i
$50$	−6.07935			−0.859749
$51$	4.98471	+	0.0756774i	0.697999	+	0.0105970i
$52$	0.315322			0.0437273
$53$			6.97443i			0.958012i	0.877812	+	0.479006i	$0.159003\pi$
$53$			6.97443i			0.958012i	−0.877812	+	0.479006i	$0.840997\pi$
$54$	−5.93298	+	5.93298i	−0.807377	+	0.807377i
$55$	2.40222			0.323915
$56$	0.253648	−	0.253648i	0.0338951	−	0.0338951i
$57$	5.19728	+	5.19728i	0.688396	+	0.688396i
$58$	−0.516809	−	0.516809i	−0.0678603	−	0.0678603i
$59$		−	9.08346i		−	1.18257i	−0.806464	−	0.591283i	$-0.798622\pi$
$59$		−	9.08346i		−	1.18257i	0.806464	−	0.591283i	$-0.201378\pi$
$60$			1.22557i			0.158220i
$61$	7.50304	+	7.50304i	0.960666	+	0.960666i	0.999255	−	0.0385896i	$-0.0122865\pi$
$61$	7.50304	+	7.50304i	0.960666	+	0.960666i	−0.0385896	+	0.999255i	$0.512286\pi$
$62$	0.428173	+	0.428173i	0.0543780	+	0.0543780i
$63$	−0.153534	+	0.153534i	−0.0193435	+	0.0193435i
$64$	−6.22754			−0.778443
$65$	1.97438	−	1.97438i	0.244892	−	0.244892i
$66$		−	1.48251i		−	0.182485i
$67$	−3.09261			−0.377822			−0.188911	−	0.981994i	$-0.560496\pi$
$67$	−3.09261			−0.377822			−0.188911	+	0.981994i	$0.560496\pi$
$68$	0.971304	+	1.00125i	0.117788	+	0.121420i
$69$	3.91476			0.471282
$70$			0.646744i			0.0773007i
$71$	1.56208	−	1.56208i	0.185385	−	0.185385i	−0.608312	−	0.793698i	$-0.708153\pi$
$71$	1.56208	−	1.56208i	0.185385	−	0.185385i	0.793698	+	0.608312i	$0.208153\pi$
$72$	3.90813			0.460578
$73$	−2.17057	+	2.17057i	−0.254046	+	0.254046i	−0.822627	−	0.568581i	$-0.807493\pi$
$73$	−2.17057	+	2.17057i	−0.254046	+	0.254046i	0.568581	+	0.822627i	$0.307493\pi$
$74$	4.22835	+	4.22835i	0.491535	+	0.491535i
$75$	3.39903	+	3.39903i	0.392486	+	0.392486i
$76$			2.05667i			0.235916i
$77$		−	0.113195i		−	0.0128998i
$78$	−1.21848	−	1.21848i	−0.137966	−	0.137966i
$79$	9.00586	+	9.00586i	1.01324	+	1.01324i	0.999911	+	0.0133267i	$0.00424214\pi$
$79$	9.00586	+	9.00586i	1.01324	+	1.01324i	0.0133267	+	0.999911i	$0.495758\pi$
$80$	9.66475	−	9.66475i	1.08055	−	1.08055i
$81$	2.02023			0.224470
$82$	−4.69574	+	4.69574i	−0.518557	+	0.518557i
$83$		−	5.68480i		−	0.623987i	−0.950084	−	0.311994i	$-0.899003\pi$
$83$		−	5.68480i		−	0.623987i	0.950084	−	0.311994i	$-0.100997\pi$
$84$	0.0577502			0.00630106
$85$	12.3511	+	0.187513i	1.33967	+	0.0203387i
$86$	1.52916			0.164894
$87$			0.577907i			0.0619581i
$88$	−1.44066	+	1.44066i	−0.153575	+	0.153575i
$89$	−13.3813			−1.41841			−0.709207	−	0.705000i	$-0.750947\pi$
$89$	−13.3813			−1.41841			−0.709207	+	0.705000i	$0.750947\pi$
$90$	−4.98243	+	4.98243i	−0.525194	+	0.525194i
$91$	−0.0930353	−	0.0930353i	−0.00975275	−	0.00975275i
$92$	0.774576	+	0.774576i	0.0807552	+	0.0807552i
$93$		−	0.478792i		−	0.0496484i
$94$			18.6904i			1.92777i
$95$	12.8778	+	12.8778i	1.32124	+	1.32124i
$96$	−1.61966	−	1.61966i	−0.165305	−	0.165305i
$97$	−4.34329	+	4.34329i	−0.440994	+	0.440994i	−0.892346	−	0.451352i	$-0.850942\pi$
$97$	−4.34329	+	4.34329i	−0.440994	+	0.440994i	0.451352	+	0.892346i	$0.350942\pi$
$98$	−10.6736			−1.07820
$99$	0.872040	−	0.872040i	0.0876434	−	0.0876434i
$100$			1.34507i			0.134507i
$101$	3.33671			0.332016			0.166008	−	0.986124i	$-0.446912\pi$
$101$	3.33671			0.332016			0.166008	+	0.986124i	$0.446912\pi$
$102$	0.115723	−	7.62242i	0.0114583	−	0.754732i
$103$	3.61598			0.356293			0.178147	−	0.984004i	$-0.442990\pi$
$103$	3.61598			0.356293			0.178147	+	0.984004i	$0.442990\pi$
$104$			2.36817i			0.232218i
$105$	0.361602	−	0.361602i	0.0352887	−	0.0352887i
$106$	10.6650			1.03588
$107$	−7.18887	+	7.18887i	−0.694974	+	0.694974i	−0.963322	−	0.268348i	$-0.913522\pi$
$107$	−7.18887	+	7.18887i	−0.694974	+	0.694974i	0.268348	+	0.963322i	$0.413522\pi$
$108$	1.31268	+	1.31268i	0.126313	+	0.126313i
$109$	7.61409	+	7.61409i	0.729298	+	0.729298i	0.970480	−	0.241182i	$-0.0775351\pi$
$109$	7.61409	+	7.61409i	0.729298	+	0.729298i	−0.241182	+	0.970480i	$0.577535\pi$
$110$		−	3.67337i		−	0.350242i
$111$		−	4.72823i		−	0.448784i
$112$	−0.455414	−	0.455414i	−0.0430326	−	0.0430326i
$113$	2.86135	+	2.86135i	0.269174	+	0.269174i	0.828767	−	0.559594i	$-0.189043\pi$
$113$	2.86135	+	2.86135i	0.269174	+	0.269174i	−0.559594	+	0.828767i	$0.689043\pi$
$114$	7.94747	−	7.94747i	0.744349	−	0.744349i
$115$	9.69999			0.904529
$116$	−0.114345	+	0.114345i	−0.0106167	+	0.0106167i
$117$		−	1.43346i		−	0.132524i
$118$	−13.8901			−1.27868
$119$	0.00883585	−	0.581999i	0.000809981	−	0.0533518i
$120$	−9.20440			−0.840243
$121$		−	10.3571i		−	0.941552i
$122$	11.4733	−	11.4733i	1.03875	−	1.03875i
$123$	5.25088			0.473456
$124$	0.0947340	−	0.0947340i	0.00850736	−	0.00850736i
$125$	−2.17011	−	2.17011i	−0.194100	−	0.194100i
$126$	0.234778	+	0.234778i	0.0209157	+	0.0209157i
$127$		−	21.3493i		−	1.89444i	−0.320580	−	0.947221i	$-0.603878\pi$
$127$		−	21.3493i		−	1.89444i	0.320580	−	0.947221i	$-0.396122\pi$
$128$			13.3117i			1.17660i
$129$	−0.854970	−	0.854970i	−0.0752759	−	0.0752759i
$130$	−3.01915	−	3.01915i	−0.264797	−	0.264797i
$131$	−0.165998	+	0.165998i	−0.0145033	+	0.0145033i	−0.714321	−	0.699818i	$-0.753264\pi$
$131$	−0.165998	+	0.165998i	−0.0145033	+	0.0145033i	0.699818	+	0.714321i	$0.253264\pi$
$132$	−0.328009			−0.0285495
$133$	0.606817	−	0.606817i	0.0526177	−	0.0526177i
$134$			4.72909i			0.408531i
$135$	16.4387			1.41482
$136$	−7.51971	+	7.29480i	−0.644810	+	0.625524i
$137$	−3.20160			−0.273531			−0.136766	−	0.990603i	$-0.543671\pi$
$137$	−3.20160			−0.273531			−0.136766	+	0.990603i	$0.543671\pi$
$138$		−	5.98629i		−	0.509587i
$139$	0.754177	−	0.754177i	0.0639685	−	0.0639685i	−0.674399	−	0.738367i	$-0.735597\pi$
$139$	0.754177	−	0.754177i	0.0639685	−	0.0639685i	0.738367	+	0.674399i	$0.235597\pi$
$140$	0.143093			0.0120936
$141$	10.4500	−	10.4500i	0.880050	−	0.880050i
$142$	−2.38868	−	2.38868i	−0.200453	−	0.200453i
$143$	0.528421	+	0.528421i	0.0441888	+	0.0441888i
$144$		−	7.01690i		−	0.584741i
$145$			1.43194i			0.118916i
$146$	3.31915	+	3.31915i	0.274695	+	0.274695i
$147$	5.96775	+	5.96775i	0.492212	+	0.492212i
$148$	0.935530	−	0.935530i	0.0769001	−	0.0769001i
$149$	11.6094			0.951081			0.475540	−	0.879694i	$-0.342253\pi$
$149$	11.6094			0.951081			0.475540	+	0.879694i	$0.342253\pi$
$150$	5.19766	−	5.19766i	0.424387	−	0.424387i
$151$		−	9.09492i		−	0.740134i	−0.929005	−	0.370067i	$-0.879335\pi$
$151$		−	9.09492i		−	0.740134i	0.929005	−	0.370067i	$-0.120665\pi$
$152$	−15.4462			−1.25286
$153$	4.55171	−	4.41557i	0.367984	−	0.356978i
$154$	−0.173094			−0.0139483
$155$		−	1.18635i		−	0.0952900i
$156$	−0.269591	+	0.269591i	−0.0215845	+	0.0215845i
$157$	−1.30034			−0.103779			−0.0518894	−	0.998653i	$-0.516524\pi$
$157$	−1.30034			−0.103779			−0.0518894	+	0.998653i	$0.516524\pi$
$158$	13.7714	−	13.7714i	1.09559	−	1.09559i
$159$	−5.96293	−	5.96293i	−0.472891	−	0.472891i
$160$	−4.01318	−	4.01318i	−0.317270	−	0.317270i
$161$		−	0.457075i		−	0.0360225i
$162$		−	3.08926i		−	0.242715i
$163$	12.3407	+	12.3407i	0.966600	+	0.966600i	0.999460	−	0.0328596i	$-0.0104614\pi$
$163$	12.3407	+	12.3407i	0.966600	+	0.966600i	−0.0328596	+	0.999460i	$0.510461\pi$
$164$	1.03894	+	1.03894i	0.0811276	+	0.0811276i
$165$	−2.05382	+	2.05382i	−0.159890	+	0.159890i
$166$	−8.69296			−0.674705
$167$	0.140916	−	0.140916i	0.0109044	−	0.0109044i	−0.701634	−	0.712538i	$-0.747546\pi$
$167$	0.140916	−	0.140916i	0.0109044	−	0.0109044i	0.712538	+	0.701634i	$0.247546\pi$
$168$			0.433722i			0.0334624i
$169$	−12.1314			−0.933183
$170$	0.286738	−	18.8868i	0.0219918	−	1.44855i
$171$	9.34968			0.714988
$172$		−	0.338329i		−	0.0257974i
$173$	−0.870004	+	0.870004i	−0.0661452	+	0.0661452i	−0.739406	−	0.673260i	$-0.764893\pi$
$173$	−0.870004	+	0.870004i	−0.0661452	+	0.0661452i	0.673260	+	0.739406i	$0.264893\pi$
$174$	0.883712			0.0669940
$175$	0.396860	−	0.396860i	0.0299998	−	0.0299998i
$176$	2.58666	+	2.58666i	0.194977	+	0.194977i
$177$	7.76609	+	7.76609i	0.583735	+	0.583735i
$178$			20.4621i			1.53370i
$179$			21.0328i			1.57206i	0.618187	+	0.786031i	$0.287867\pi$
$179$			21.0328i			1.57206i	−0.618187	+	0.786031i	$0.712133\pi$
$180$	1.10237	+	1.10237i	0.0821660	+	0.0821660i
$181$	−15.8346	−	15.8346i	−1.17698	−	1.17698i	−0.980511	−	0.196466i	$-0.937053\pi$
$181$	−15.8346	−	15.8346i	−1.17698	−	1.17698i	−0.196466	−	0.980511i	$-0.562947\pi$
$182$	−0.142266	+	0.142266i	−0.0105454	+	0.0105454i
$183$	−12.8297			−0.948402
$184$	−5.81731	+	5.81731i	−0.428858	+	0.428858i
$185$		−	11.7156i		−	0.861348i
$186$	−0.732149			−0.0536838
$187$	−0.0501858	+	3.30563i	−0.00366995	+	0.241732i
$188$	4.13529			0.301597
$189$		−	0.774610i		−	0.0563446i
$190$	19.6922	−	19.6922i	1.42863	−	1.42863i
$191$	2.02961			0.146858			0.0734288	−	0.997300i	$-0.476606\pi$
$191$	2.02961			0.146858			0.0734288	+	0.997300i	$0.476606\pi$
$192$	5.32436	−	5.32436i	0.384253	−	0.384253i
$193$	−0.980619	−	0.980619i	−0.0705865	−	0.0705865i	0.670932	−	0.741519i	$-0.265894\pi$
$193$	−0.980619	−	0.980619i	−0.0705865	−	0.0705865i	−0.741519	+	0.670932i	$0.765894\pi$
$194$	6.64158	+	6.64158i	0.476838	+	0.476838i
$195$			3.37608i			0.241766i
$196$			2.36156i			0.168683i
$197$	−15.0802	−	15.0802i	−1.07442	−	1.07442i	−0.996999	−	0.0774208i	$-0.975332\pi$
$197$	−15.0802	−	15.0802i	−1.07442	−	1.07442i	−0.0774208	−	0.996999i	$-0.524668\pi$
$198$	−1.33349	−	1.33349i	−0.0947669	−	0.0947669i
$199$	−5.69985	+	5.69985i	−0.404051	+	0.404051i	−0.879658	−	0.475607i	$-0.842229\pi$
$199$	−5.69985	+	5.69985i	−0.404051	+	0.404051i	0.475607	+	0.879658i	$0.342229\pi$
$200$	−10.1019			−0.714310
$201$	2.64409	−	2.64409i	0.186499	−	0.186499i
$202$		−	5.10237i		−	0.359001i
$203$	0.0674745			0.00473578
$204$	−1.68648	−	0.0256039i	−0.118077	−	0.00179263i
$205$	13.0106			0.908701
$206$		−	5.52942i		−	0.385253i
$207$	3.52124	−	3.52124i	0.244743	−	0.244743i
$208$	4.25195			0.294820
$209$	−3.44660	+	3.44660i	−0.238406	+	0.238406i
$210$	−0.552947	−	0.552947i	−0.0381570	−	0.0381570i
$211$	14.4067	+	14.4067i	0.991801	+	0.991801i	0.999967	−	0.00816548i	$-0.00259918\pi$
$211$	14.4067	+	14.4067i	0.991801	+	0.991801i	−0.00816548	+	0.999967i	$0.502599\pi$
$212$		−	2.35966i		−	0.162062i
$213$			2.67107i			0.183019i
$214$	10.9929	+	10.9929i	0.751461	+	0.751461i
$215$	−2.11844	−	2.11844i	−0.144477	−	0.144477i
$216$	−9.85867	+	9.85867i	−0.670797	+	0.670797i
$217$	−0.0559022			−0.00379489
$218$	11.6432	−	11.6432i	0.788575	−	0.788575i
$219$		−	3.71155i		−	0.250803i
$220$	−0.812741			−0.0547950
$221$	2.67566	+	2.75815i	0.179984	+	0.185533i
$222$	−7.23022			−0.485260
$223$			14.8701i			0.995778i	0.867241	+	0.497889i	$0.165891\pi$
$223$			14.8701i			0.995778i	−0.867241	+	0.497889i	$0.834109\pi$
$224$	−0.189106	+	0.189106i	−0.0126352	+	0.0126352i
$225$	6.11470			0.407647
$226$	4.37547	−	4.37547i	0.291052	−	0.291052i
$227$	−5.97611	−	5.97611i	−0.396648	−	0.396648i	0.480401	−	0.877049i	$-0.340491\pi$
$227$	−5.97611	−	5.97611i	−0.396648	−	0.396648i	−0.877049	+	0.480401i	$0.840491\pi$
$228$	−1.75839	−	1.75839i	−0.116452	−	0.116452i
$229$			14.7646i			0.975673i	0.872935	+	0.487837i	$0.162214\pi$
$229$			14.7646i			0.975673i	−0.872935	+	0.487837i	$0.837786\pi$
$230$		−	14.8328i		−	0.978049i
$231$	0.0967785	+	0.0967785i	0.00636756	+	0.00636756i
$232$	−0.858766	−	0.858766i	−0.0563808	−	0.0563808i
$233$	−14.3442	+	14.3442i	−0.939718	+	0.939718i	−0.998284	−	0.0585654i	$-0.981347\pi$
$233$	−14.3442	+	14.3442i	−0.939718	+	0.939718i	0.0585654	+	0.998284i	$0.481347\pi$
$234$	−2.19199			−0.143295
$235$	25.8930	−	25.8930i	1.68908	−	1.68908i
$236$			3.07320i			0.200048i
$237$	−15.3995			−1.00030
$238$	−0.889969	−	0.0135114i	−0.0576882	−	0.000875815i
$239$	4.58068			0.296300			0.148150	−	0.988965i	$-0.452668\pi$
$239$	4.58068			0.296300			0.148150	+	0.988965i	$0.452668\pi$
$240$			16.5261i			1.06676i
$241$	2.26439	−	2.26439i	0.145862	−	0.145862i	−0.630404	−	0.776267i	$-0.717111\pi$
$241$	2.26439	−	2.26439i	0.145862	−	0.145862i	0.776267	+	0.630404i	$0.217111\pi$
$242$	−15.8376			−1.01808
$243$	9.91246	−	9.91246i	0.635885	−	0.635885i
$244$	−2.53850	−	2.53850i	−0.162511	−	0.162511i
$245$	14.7869	+	14.7869i	0.944700	+	0.944700i
$246$		−	8.02943i		−	0.511938i
$247$			5.66552i			0.360489i
$248$	0.711482	+	0.711482i	0.0451791	+	0.0451791i
$249$	4.86033	+	4.86033i	0.308011	+	0.308011i
$250$	−3.31844	+	3.31844i	−0.209877	+	0.209877i
$251$	16.4059			1.03553			0.517765	−	0.855523i	$-0.326764\pi$
$251$	16.4059			1.03553			0.517765	+	0.855523i	$0.326764\pi$
$252$	0.0519450	−	0.0519450i	0.00327223	−	0.00327223i
$253$			2.59609i			0.163215i
$254$	−32.6465			−2.04842
$255$	−10.7202	+	10.3995i	−0.671322	+	0.651243i
$256$	7.90064			0.493790
$257$		−	8.83612i		−	0.551182i	−0.961275	−	0.275591i	$-0.911126\pi$
$257$		−	8.83612i		−	0.551182i	0.961275	−	0.275591i	$-0.0888736\pi$
$258$	−1.30739	+	1.30739i	−0.0813943	+	0.0813943i
$259$	−0.552053			−0.0343029
$260$	−0.667992	+	0.667992i	−0.0414271	+	0.0414271i
$261$	0.519815	+	0.519815i	0.0321757	+	0.0321757i
$262$	0.253838	+	0.253838i	0.0156822	+	0.0156822i
$263$		−	13.1974i		−	0.813787i	−0.913476	−	0.406894i	$-0.866612\pi$
$263$		−	13.1974i		−	0.813787i	0.913476	−	0.406894i	$-0.133388\pi$
$264$		−	2.46345i		−	0.151615i
$265$	−14.7749	−	14.7749i	−0.907618	−	0.907618i
$266$	−0.927921	−	0.927921i	−0.0568945	−	0.0568945i
$267$	11.4406	−	11.4406i	0.700153	−	0.700153i
$268$	1.04632			0.0639142
$269$	−6.16117	+	6.16117i	−0.375653	+	0.375653i	−0.869531	−	0.493878i	$-0.835579\pi$
$269$	−6.16117	+	6.16117i	−0.375653	+	0.375653i	0.493878	+	0.869531i	$0.335579\pi$
$270$		−	25.1374i		−	1.52981i
$271$	14.0895			0.855873			0.427937	−	0.903809i	$-0.359241\pi$
$271$	14.0895			0.855873			0.427937	+	0.903809i	$0.359241\pi$
$272$	13.0975	+	13.5013i	0.794154	+	0.818639i
$273$	0.159085			0.00962824
$274$			4.89576i			0.295764i
$275$	−2.25408	+	2.25408i	−0.135926	+	0.135926i
$276$	−1.32448			−0.0797242
$277$	21.8271	−	21.8271i	1.31147	−	1.31147i	0.391130	−	0.920335i	$-0.372084\pi$
$277$	21.8271	−	21.8271i	1.31147	−	1.31147i	0.920335	−	0.391130i	$-0.127916\pi$
$278$	−1.15326	−	1.15326i	−0.0691678	−	0.0691678i
$279$	−0.430663	−	0.430663i	−0.0257831	−	0.0257831i
$280$			1.07468i			0.0642242i
$281$			3.48415i			0.207847i	0.994585	+	0.103924i	$0.0331397\pi$
$281$			3.48415i			0.207847i	−0.994585	+	0.103924i	$0.966860\pi$
$282$	−15.9797	−	15.9797i	−0.951579	−	0.951579i
$283$	−18.9196	−	18.9196i	−1.12465	−	1.12465i	−0.991033	−	0.133621i	$-0.957340\pi$
$283$	−18.9196	−	18.9196i	−1.12465	−	1.12465i	−0.133621	−	0.991033i	$-0.542660\pi$
$284$	−0.528499	+	0.528499i	−0.0313607	+	0.0313607i
$285$	−22.0203			−1.30437
$286$	0.808040	−	0.808040i	0.0477804	−	0.0477804i
$287$		−	0.613075i		−	0.0361887i
$288$	−2.91369			−0.171691
$289$	−0.516065	+	16.9922i	−0.0303568	+	0.999539i
$290$	2.18966			0.128581
$291$		−	7.42676i		−	0.435364i
$292$	0.734369	−	0.734369i	0.0429757	−	0.0429757i
$293$	−25.9702			−1.51720			−0.758598	−	0.651559i	$-0.774115\pi$
$293$	−25.9702			−1.51720			−0.758598	+	0.651559i	$0.774115\pi$
$294$	9.12564	−	9.12564i	0.532218	−	0.532218i
$295$	19.2428	+	19.2428i	1.12036	+	1.12036i
$296$	7.02612	+	7.02612i	0.408385	+	0.408385i
$297$			4.39962i			0.255292i
$298$		−	17.7527i		−	1.02838i
$299$	2.13373	+	2.13373i	0.123397	+	0.123397i
$300$	−1.14999	−	1.14999i	−0.0663948	−	0.0663948i
$301$	−0.0998235	+	0.0998235i	−0.00575373	+	0.00575373i
$302$	−13.9076			−0.800292
$303$	−2.85279	+	2.85279i	−0.163889	+	0.163889i
$304$			27.7331i			1.59060i
$305$	−31.7895			−1.82026
$306$	−6.75211	−	6.96029i	−0.385993	−	0.397894i
$307$	16.4454			0.938591			0.469295	−	0.883041i	$-0.344508\pi$
$307$	16.4454			0.938591			0.469295	+	0.883041i	$0.344508\pi$
$308$			0.0382973i			0.00218219i
$309$	−3.09156	+	3.09156i	−0.175872	+	0.175872i
$310$	−1.81412			−0.103035
$311$	−12.3625	+	12.3625i	−0.701012	+	0.701012i	−0.964628	−	0.263615i	$-0.915085\pi$
$311$	−12.3625	+	12.3625i	−0.701012	+	0.701012i	0.263615	+	0.964628i	$0.415085\pi$
$312$	−2.02471	−	2.02471i	−0.114627	−	0.114627i
$313$	14.8313	+	14.8313i	0.838314	+	0.838314i	0.988637	−	0.150323i	$-0.0480314\pi$
$313$	14.8313	+	14.8313i	0.838314	+	0.838314i	−0.150323	+	0.988637i	$0.548031\pi$
$314$			1.98843i			0.112214i
$315$		−	0.650506i		−	0.0366519i
$316$	−3.04695	−	3.04695i	−0.171404	−	0.171404i
$317$	4.30600	+	4.30600i	0.241849	+	0.241849i	0.817615	−	0.575766i	$-0.195296\pi$
$317$	4.30600	+	4.30600i	0.241849	+	0.241849i	−0.575766	+	0.817615i	$0.695296\pi$
$318$	−9.11827	+	9.11827i	−0.511327	+	0.511327i
$319$	−0.383241			−0.0214574
$320$	13.1927	−	13.1927i	0.737494	−	0.737494i
$321$		−	12.2925i		−	0.686102i
$322$	−0.698940			−0.0389504
$323$	−17.9899	+	17.4518i	−1.00098	+	0.971045i
$324$	−0.683504			−0.0379724
$325$			3.70526i			0.205531i
$326$	18.8709	−	18.8709i	1.04516	−	1.04516i
$327$	−13.0196			−0.719988
$328$	−7.80277	+	7.80277i	−0.430836	+	0.430836i
$329$	−1.22011	−	1.22011i	−0.0672668	−	0.0672668i
$330$	3.14062	+	3.14062i	0.172886	+	0.172886i
$331$			11.9564i			0.657181i	0.944472	+	0.328591i	$0.106574\pi$
$331$			11.9564i			0.657181i	−0.944472	+	0.328591i	$0.893426\pi$
$332$			1.92333i			0.105557i
$333$	−4.25294	−	4.25294i	−0.233060	−	0.233060i
$334$	−0.215483	−	0.215483i	−0.0117907	−	0.0117907i
$335$	6.55152	−	6.55152i	0.357948	−	0.357948i
$336$	0.778730			0.0424832
$337$	−15.9527	+	15.9527i	−0.868998	+	0.868998i	−0.992362	−	0.123364i	$-0.960632\pi$
$337$	−15.9527	+	15.9527i	−0.868998	+	0.868998i	0.123364	+	0.992362i	$0.460632\pi$
$338$			18.5508i			1.00903i
$339$	−4.89274			−0.265737
$340$	−4.17875	−	0.0634413i	−0.226624	−	0.00344059i
$341$	0.317513			0.0171943
$342$		−	14.2971i		−	0.773101i
$343$	1.39554	−	1.39554i	0.0753521	−	0.0753521i
$344$	2.54096			0.136999
$345$	−8.29320	+	8.29320i	−0.446491	+	0.446491i
$346$	1.33037	+	1.33037i	0.0715214	+	0.0715214i
$347$	10.6483	+	10.6483i	0.571631	+	0.571631i	0.932584	−	0.360953i	$-0.117548\pi$
$347$	10.6483	+	10.6483i	0.571631	+	0.571631i	−0.360953	+	0.932584i	$0.617548\pi$
$348$		−	0.195523i		−	0.0104811i
$349$			30.5085i			1.63308i	0.577288	+	0.816540i	$0.304111\pi$
$349$			30.5085i			1.63308i	−0.577288	+	0.816540i	$0.695889\pi$
$350$	−0.606862	−	0.606862i	−0.0324381	−	0.0324381i
$351$	3.61606	+	3.61606i	0.193011	+	0.193011i
$352$	1.07408	−	1.07408i	0.0572487	−	0.0572487i
$353$	−9.02349			−0.480272			−0.240136	−	0.970739i	$-0.577192\pi$
$353$	−9.02349			−0.480272			−0.240136	+	0.970739i	$0.577192\pi$
$354$	11.8756	−	11.8756i	0.631180	−	0.631180i
$355$			6.61838i			0.351267i
$356$	4.52729			0.239946
$357$	0.490037	+	0.505146i	0.0259355	+	0.0267352i
$358$	32.1624			1.69984
$359$			3.06682i			0.161860i	0.996720	+	0.0809302i	$0.0257891\pi$
$359$			3.06682i			0.161860i	−0.996720	+	0.0809302i	$0.974211\pi$
$360$	−8.27916	+	8.27916i	−0.436350	+	0.436350i
$361$	−17.9531			−0.944898
$362$	−24.2136	+	24.2136i	−1.27264	+	1.27264i
$363$	8.85499	+	8.85499i	0.464766	+	0.464766i
$364$	0.0314766	+	0.0314766i	0.00164982	+	0.00164982i
$365$		−	9.19648i		−	0.481366i
$366$			19.6187i			1.02549i
$367$	−13.8205	−	13.8205i	−0.721424	−	0.721424i	0.247471	−	0.968895i	$-0.420400\pi$
$367$	−13.8205	−	13.8205i	−0.721424	−	0.721424i	−0.968895	+	0.247471i	$0.920400\pi$
$368$	10.4447	+	10.4447i	0.544470	+	0.544470i
$369$	4.72305	−	4.72305i	0.245872	−	0.245872i
$370$	−17.9150			−0.931358
$371$	−0.696212	+	0.696212i	−0.0361456	+	0.0361456i
$372$			0.161989i			0.00839876i
$373$	10.1293			0.524475			0.262238	−	0.965003i	$-0.415540\pi$
$373$	10.1293			0.524475			0.262238	+	0.965003i	$0.415540\pi$
$374$	5.05484	+	0.0767420i	0.261380	+	0.00396824i
$375$	3.71075			0.191622
$376$			31.0573i			1.60166i
$377$	−0.314986	+	0.314986i	−0.0162226	+	0.0162226i
$378$	−1.18450			−0.0609242
$379$	−18.1820	+	18.1820i	−0.933947	+	0.933947i	−0.997950	−	0.0640025i	$-0.979613\pi$
$379$	−18.1820	+	18.1820i	−0.933947	+	0.933947i	0.0640025	+	0.997950i	$0.479613\pi$
$380$	−4.35694	−	4.35694i	−0.223507	−	0.223507i
$381$	18.2530	+	18.2530i	0.935129	+	0.935129i
$382$		−	3.10360i		−	0.158794i
$383$		−	0.512819i		−	0.0262038i	−0.999914	−	0.0131019i	$-0.995829\pi$
$383$		−	0.512819i		−	0.0262038i	0.999914	−	0.0131019i	$-0.00417059\pi$
$384$	−11.3811	−	11.3811i	−0.580790	−	0.580790i
$385$	0.239798	+	0.239798i	0.0122212	+	0.0122212i
$386$	−1.49952	+	1.49952i	−0.0763237	+	0.0763237i
$387$	−1.53805			−0.0781837
$388$	1.46946	−	1.46946i	0.0746006	−	0.0746006i
$389$		−	6.98905i		−	0.354359i	−0.984179	−	0.177179i	$-0.943303\pi$
$389$		−	6.98905i		−	0.354359i	0.984179	−	0.177179i	$-0.0566973\pi$
$390$	5.16256			0.261417
$391$	−0.202647	+	13.3479i	−0.0102483	+	0.675034i
$392$	−17.7361			−0.895807
$393$		−	0.283847i		−	0.0143182i
$394$	−23.0600	+	23.0600i	−1.16175	+	1.16175i
$395$	−38.1568			−1.91988
$396$	−0.295037	+	0.295037i	−0.0148262	+	0.0148262i
$397$	−18.9876	−	18.9876i	−0.952960	−	0.952960i	0.0459819	−	0.998942i	$-0.485358\pi$
$397$	−18.9876	−	18.9876i	−0.952960	−	0.952960i	−0.998942	+	0.0459819i	$0.985358\pi$
$398$	8.71597	+	8.71597i	0.436892	+	0.436892i
$399$			1.03762i			0.0519460i
$400$			18.1375i			0.906875i
$401$	−10.6554	−	10.6554i	−0.532107	−	0.532107i	0.389092	−	0.921199i	$-0.372789\pi$
$401$	−10.6554	−	10.6554i	−0.532107	−	0.532107i	−0.921199	+	0.389092i	$0.872789\pi$
$402$	−4.04323	−	4.04323i	−0.201658	−	0.201658i
$403$	0.260964	−	0.260964i	0.0129995	−	0.0129995i
$404$	−1.12891			−0.0561653
$405$	−4.27975	+	4.27975i	−0.212662	+	0.212662i
$406$		−	0.103179i		−	0.00512070i
$407$	3.13554			0.155423
$408$	0.192293	−	12.6660i	0.00951993	−	0.627058i
$409$	−21.6002			−1.06806			−0.534030	−	0.845466i	$-0.679323\pi$
$409$	−21.6002			−1.06806			−0.534030	+	0.845466i	$0.679323\pi$
$410$		−	19.8953i		−	0.982560i
$411$	2.73727	−	2.73727i	0.135020	−	0.135020i
$412$	−1.22339			−0.0602723
$413$	0.906743	−	0.906743i	0.0446179	−	0.0446179i
$414$	−5.38454	−	5.38454i	−0.264636	−	0.264636i
$415$	12.0429	+	12.0429i	0.591164	+	0.591164i
$416$		−	1.76558i		−	0.0865645i
$417$			1.28960i			0.0631519i
$418$	5.27040	+	5.27040i	0.257783	+	0.257783i
$419$	24.2929	+	24.2929i	1.18678	+	1.18678i	0.977951	+	0.208833i	$0.0669665\pi$
$419$	24.2929	+	24.2929i	1.18678	+	1.18678i	0.208833	+	0.977951i	$0.433034\pi$
$420$	−0.122341	+	0.122341i	−0.00596961	+	0.00596961i
$421$	25.1604			1.22624			0.613122	−	0.789988i	$-0.289913\pi$
$421$	25.1604			1.22624			0.613122	+	0.789988i	$0.289913\pi$
$422$	22.0302	−	22.0302i	1.07241	−	1.07241i
$423$		−	18.7991i		−	0.914044i
$424$	17.7218			0.860645
$425$	−11.7654	+	11.4135i	−0.570707	+	0.553637i
$426$	4.08449			0.197894
$427$			1.49796i			0.0724913i
$428$	2.43221	−	2.43221i	0.117565	−	0.117565i
$429$	−0.903568			−0.0436247
$430$	−3.23944	+	3.23944i	−0.156220	+	0.156220i
$431$	−12.2449	−	12.2449i	−0.589815	−	0.589815i	0.347766	−	0.937581i	$-0.386940\pi$
$431$	−12.2449	−	12.2449i	−0.589815	−	0.589815i	−0.937581	+	0.347766i	$0.886940\pi$
$432$	17.7008	+	17.7008i	0.851632	+	0.851632i
$433$		−	9.98997i		−	0.480087i	−0.970762	−	0.240044i	$-0.922838\pi$
$433$		−	9.98997i		−	0.480087i	0.970762	−	0.240044i	$-0.0771617\pi$
$434$			0.0854834i			0.00410333i
$435$	−1.22426	−	1.22426i	−0.0586989	−	0.0586989i
$436$	−2.57607	−	2.57607i	−0.123371	−	0.123371i
$437$	−13.9171	+	13.9171i	−0.665746	+	0.665746i
$438$	−5.67555			−0.271188
$439$	−0.813540	+	0.813540i	−0.0388282	+	0.0388282i	−0.726254	−	0.687426i	$-0.758741\pi$
$439$	−0.813540	+	0.813540i	−0.0388282	+	0.0388282i	0.687426	+	0.726254i	$0.258741\pi$
$440$		−	6.10394i		−	0.290994i
$441$	10.7357			0.511225
$442$	4.21765	−	4.09150i	0.200613	−	0.194613i
$443$	24.9516			1.18549			0.592743	−	0.805391i	$-0.298045\pi$
$443$	24.9516			1.18549			0.592743	+	0.805391i	$0.298045\pi$
$444$			1.59970i			0.0759183i
$445$	28.3475	−	28.3475i	1.34380	−	1.34380i
$446$	22.7388			1.07671
$447$	−9.92570	+	9.92570i	−0.469470	+	0.469470i
$448$	−0.621655	−	0.621655i	−0.0293704	−	0.0293704i
$449$	−27.2739	−	27.2739i	−1.28714	−	1.28714i	−0.936518	−	0.350618i	$-0.885971\pi$
$449$	−27.2739	−	27.2739i	−1.28714	−	1.28714i	−0.350618	−	0.936518i	$-0.614029\pi$
$450$		−	9.35036i		−	0.440780i
$451$			3.48214i			0.163968i
$452$	−0.968080	−	0.968080i	−0.0455347	−	0.0455347i
$453$	7.77588	+	7.77588i	0.365343	+	0.365343i
$454$	−9.13842	+	9.13842i	−0.428887	+	0.428887i
$455$	0.394180			0.0184794
$456$	13.2061	−	13.2061i	0.618431	−	0.618431i
$457$			0.727156i			0.0340149i	0.999855	+	0.0170075i	$0.00541390\pi$
$457$			0.727156i			0.0340149i	−0.999855	+	0.0170075i	$0.994586\pi$
$458$	22.5774			1.05497
$459$	−0.343428	+	22.6209i	−0.0160298	+	1.05585i
$460$	−3.28179			−0.153014
$461$		−	22.4821i		−	1.04710i	−0.851996	−	0.523549i	$-0.824608\pi$
$461$		−	22.4821i		−	1.04710i	0.851996	−	0.523549i	$-0.175392\pi$
$462$	0.147990	−	0.147990i	0.00688511	−	0.00688511i
$463$	20.8739			0.970093			0.485046	−	0.874488i	$-0.338803\pi$
$463$	20.8739			0.970093			0.485046	+	0.874488i	$0.338803\pi$
$464$	−1.54188	+	1.54188i	−0.0715800	+	0.0715800i
$465$	1.01429	+	1.01429i	0.0470367	+	0.0470367i
$466$	21.9345	+	21.9345i	1.01610	+	1.01610i
$467$			18.1283i			0.838879i	0.907783	+	0.419440i	$0.137773\pi$
$467$			18.1283i			0.838879i	−0.907783	+	0.419440i	$0.862227\pi$
$468$			0.484982i			0.0224183i
$469$	−0.308715	−	0.308715i	−0.0142551	−	0.0142551i
$470$	−39.5946	−	39.5946i	−1.82636	−	1.82636i
$471$	1.11175	−	1.11175i	0.0512270	−	0.0512270i
$472$	−23.0807			−1.06238
$473$	0.566977	−	0.566977i	0.0260696	−	0.0260696i
$474$			23.5482i			1.08161i
$475$	−24.1674			−1.10887
$476$	−0.00298943	+	0.196907i	−0.000137020	+	0.00902524i
$477$	−10.7271			−0.491158
$478$		−	7.00460i		−	0.320383i
$479$	23.1907	−	23.1907i	1.05961	−	1.05961i	0.0615025	−	0.998107i	$-0.480411\pi$
$479$	23.1907	−	23.1907i	1.05961	−	1.05961i	0.998107	−	0.0615025i	$-0.0195892\pi$
$480$	6.86230			0.313220
$481$	2.57711	−	2.57711i	0.117506	−	0.117506i
$482$	−3.46262	−	3.46262i	−0.157718	−	0.157718i
$483$	0.390785	+	0.390785i	0.0177813	+	0.0177813i
$484$			3.50410i			0.159277i
$485$		−	18.4020i		−	0.835593i
$486$	−15.1577	−	15.1577i	−0.687569	−	0.687569i
$487$	−27.9159	−	27.9159i	−1.26499	−	1.26499i	−0.948644	−	0.316347i	$-0.897544\pi$
$487$	−27.9159	−	27.9159i	−1.26499	−	1.26499i	−0.316347	−	0.948644i	$-0.602456\pi$
$488$	19.0649	−	19.0649i	0.863028	−	0.863028i
$489$	−21.1019			−0.954261
$490$	22.6115	−	22.6115i	1.02148	−	1.02148i
$491$		−	26.3768i		−	1.19037i	−0.803589	−	0.595185i	$-0.797079\pi$
$491$		−	26.3768i		−	1.19037i	0.803589	−	0.595185i	$-0.202921\pi$
$492$	−1.77653			−0.0800920
$493$	−1.97045	−	0.0299152i	−0.0887448	−	0.00134731i
$494$	8.66349			0.389789
$495$			3.69474i			0.166066i
$496$	1.27744	−	1.27744i	0.0573586	−	0.0573586i
$497$	0.311866			0.0139891
$498$	7.43222	−	7.43222i	0.333046	−	0.333046i
$499$	−11.3878	−	11.3878i	−0.509786	−	0.509786i	0.404675	−	0.914461i	$-0.367385\pi$
$499$	−11.3878	−	11.3878i	−0.509786	−	0.509786i	−0.914461	+	0.404675i	$0.867385\pi$
$500$	0.734211	+	0.734211i	0.0328349	+	0.0328349i
$501$			0.240957i			0.0107652i
$502$		−	25.0872i		−	1.11970i
$503$	2.59410	+	2.59410i	0.115665	+	0.115665i	0.762570	−	0.646905i	$-0.223937\pi$
$503$	2.59410	+	2.59410i	0.115665	+	0.115665i	−0.646905	+	0.762570i	$0.723937\pi$
$504$	0.390123	+	0.390123i	0.0173775	+	0.0173775i
$505$	−7.06864	+	7.06864i	−0.314551	+	0.314551i
$506$	3.96984			0.176481
$507$	10.3720	−	10.3720i	0.460635	−	0.460635i
$508$			7.22309i			0.320473i
$509$	8.22742			0.364674			0.182337	−	0.983236i	$-0.441634\pi$
$509$	8.22742			0.364674			0.182337	+	0.983236i	$0.441634\pi$
$510$	15.9025	+	16.3928i	0.704176	+	0.725887i
$511$	−0.433349			−0.0191702
$512$			14.5421i			0.642675i
$513$	−23.5855	+	23.5855i	−1.04133	+	1.04133i
$514$	−13.5118			−0.595982
$515$	−7.66026	+	7.66026i	−0.337551	+	0.337551i
$516$	0.289261	+	0.289261i	0.0127340	+	0.0127340i
$517$	6.92997	+	6.92997i	0.304780	+	0.304780i
$518$			0.844177i			0.0370910i
$519$		−	1.48765i		−	0.0653008i
$520$	−5.01683	−	5.01683i	−0.220003	−	0.220003i
$521$	3.18354	+	3.18354i	0.139473	+	0.139473i	0.773396	−	0.633923i	$-0.218556\pi$
$521$	3.18354	+	3.18354i	0.139473	+	0.139473i	−0.633923	+	0.773396i	$0.718556\pi$
$522$	0.794880	−	0.794880i	0.0347909	−	0.0347909i
$523$	−8.29215			−0.362590			−0.181295	−	0.983429i	$-0.558029\pi$
$523$	−8.29215			−0.362590			−0.181295	+	0.983429i	$0.558029\pi$
$524$	0.0561621	−	0.0561621i	0.00245345	−	0.00245345i
$525$			0.678606i			0.0296168i
$526$	−20.1810			−0.879931
$527$	1.63251	+	0.0247846i	0.0711132	+	0.00107963i
$528$	−4.42303			−0.192488
$529$		−	12.5172i		−	0.544224i
$530$	−22.5933	+	22.5933i	−0.981388	+	0.981388i
$531$	13.9709			0.606283
$532$	−0.205304	+	0.205304i	−0.00890106	+	0.00890106i
$533$	2.86197	+	2.86197i	0.123966	+	0.123966i
$534$	−17.4945	−	17.4945i	−0.757061	−	0.757061i
$535$		−	30.4584i		−	1.31683i
$536$			7.85819i			0.339422i
$537$	−17.9824	−	17.9824i	−0.775996	−	0.775996i
$538$	9.42141	+	9.42141i	0.406186	+	0.406186i
$539$	−3.95754	+	3.95754i	−0.170463	+	0.170463i
$540$	−5.56170			−0.239337
$541$	−23.1320	+	23.1320i	−0.994523	+	0.994523i	−0.999985	−	0.00546218i	$-0.998261\pi$
$541$	−23.1320	+	23.1320i	−0.994523	+	0.994523i	0.00546218	+	0.999985i	$0.498261\pi$
$542$		−	21.5450i		−	0.925438i
$543$	27.0762			1.16195
$544$	5.60629	−	5.43860i	0.240367	−	0.233178i
$545$	−32.2601			−1.38187
$546$		−	0.243266i		−	0.0104108i
$547$	22.3964	−	22.3964i	0.957600	−	0.957600i	−0.0415367	−	0.999137i	$-0.513225\pi$
$547$	22.3964	−	22.3964i	0.957600	−	0.957600i	0.999137	+	0.0415367i	$0.0132253\pi$
$548$	1.08320			0.0462719
$549$	−11.5401	+	11.5401i	−0.492518	+	0.492518i
$550$	3.44685	+	3.44685i	0.146974	+	0.146974i
$551$	−2.05448	−	2.05448i	−0.0875239	−	0.0875239i
$552$		−	9.94725i		−	0.423383i
$553$			1.79799i			0.0764584i
$554$	−33.3772	−	33.3772i	−1.41806	−	1.41806i
$555$	10.0165	+	10.0165i	0.425176	+	0.425176i
$556$	−0.255160	+	0.255160i	−0.0108212	+	0.0108212i
$557$	35.1673			1.49009			0.745044	−	0.667015i	$-0.232428\pi$
$557$	35.1673			1.49009			0.745044	+	0.667015i	$0.232428\pi$
$558$	−0.658552	+	0.658552i	−0.0278787	+	0.0278787i
$559$		−	0.931997i		−	0.0394193i
$560$	1.92954			0.0815379
$561$	−2.78331	−	2.86912i	−0.117511	−	0.121134i
$562$	5.32782			0.224741
$563$		−	1.78628i		−	0.0752826i	−0.999291	−	0.0376413i	$-0.988016\pi$
$563$		−	1.78628i		−	0.0752826i	0.999291	−	0.0376413i	$-0.0119844\pi$
$564$	−3.53555	+	3.53555i	−0.148873	+	0.148873i
$565$	−12.1232			−0.510028
$566$	−28.9311	+	28.9311i	−1.21606	+	1.21606i
$567$	0.201667	+	0.201667i	0.00846920	+	0.00846920i
$568$	−3.96919	−	3.96919i	−0.166544	−	0.166544i
$569$		−	15.6702i		−	0.656931i	−0.944516	−	0.328466i	$-0.893469\pi$
$569$		−	15.6702i		−	0.656931i	0.944516	−	0.328466i	$-0.106531\pi$
$570$			33.6725i			1.41039i
$571$	−20.6071	−	20.6071i	−0.862381	−	0.862381i	0.129233	−	0.991614i	$-0.458748\pi$
$571$	−20.6071	−	20.6071i	−0.862381	−	0.862381i	−0.991614	+	0.129233i	$0.958748\pi$
$572$	−0.178780	−	0.178780i	−0.00747518	−	0.00747518i
$573$	−1.73526	+	1.73526i	−0.0724914	+	0.0724914i
$574$	−0.937490			−0.0391301
$575$	−9.10182	+	9.10182i	−0.379572	+	0.379572i
$576$		−	9.57829i		−	0.399096i
$577$	−31.8457			−1.32575			−0.662876	−	0.748729i	$-0.730664\pi$
$577$	−31.8457			−1.32575			−0.662876	+	0.748729i	$0.730664\pi$
$578$	25.9837	+	0.789146i	1.08078	+	0.0328242i
$579$	1.67680			0.0696854
$580$		−	0.484467i		−	0.0201164i
$581$	0.567476	−	0.567476i	0.0235429	−	0.0235429i
$582$	−11.3567			−0.470750
$583$	3.95434	−	3.95434i	0.163772	−	0.163772i
$584$	5.51534	+	5.51534i	0.228226	+	0.228226i
$585$	3.03671	+	3.03671i	0.125552	+	0.125552i
$586$			39.7126i			1.64051i
$587$			10.1518i			0.419009i	0.977808	+	0.209504i	$0.0671850\pi$
$587$			10.1518i			0.419009i	−0.977808	+	0.209504i	$0.932815\pi$
$588$	−2.01907	−	2.01907i	−0.0832648	−	0.0832648i
$589$	1.70212	+	1.70212i	0.0701348	+	0.0701348i
$590$	29.4253	−	29.4253i	1.21142	−	1.21142i
$591$	25.7862			1.06070
$592$	12.6151	−	12.6151i	0.518478	−	0.518478i
$593$		−	14.1675i		−	0.581788i	−0.956755	−	0.290894i	$-0.906047\pi$
$593$		−	14.1675i		−	0.581788i	0.956755	−	0.290894i	$-0.0939527\pi$
$594$	6.72773			0.276042
$595$	1.21421	+	1.25165i	0.0497779	+	0.0513127i
$596$	−3.92781			−0.160889
$597$		−	9.74639i		−	0.398893i
$598$	3.26281	−	3.26281i	0.133426	−	0.133426i
$599$	20.4313			0.834801			0.417401	−	0.908723i	$-0.362941\pi$
$599$	20.4313			0.834801			0.417401	+	0.908723i	$0.362941\pi$
$600$	8.63679	−	8.63679i	0.352596	−	0.352596i
$601$	−6.62247	−	6.62247i	−0.270136	−	0.270136i	0.559019	−	0.829155i	$-0.311178\pi$
$601$	−6.62247	−	6.62247i	−0.270136	−	0.270136i	−0.829155	+	0.559019i	$0.811178\pi$
$602$	0.152646	+	0.152646i	0.00622139	+	0.00622139i
$603$		−	4.75660i		−	0.193704i
$604$			3.07708i			0.125205i
$605$	21.9409	+	21.9409i	0.892024	+	0.892024i
$606$	4.36237	+	4.36237i	0.177209	+	0.177209i
$607$	−2.11609	+	2.11609i	−0.0858896	+	0.0858896i	−0.748746	−	0.662857i	$-0.769344\pi$
$607$	−2.11609	+	2.11609i	−0.0858896	+	0.0858896i	0.662857	+	0.748746i	$0.269344\pi$
$608$	11.5159			0.467031
$609$	−0.0576887	+	0.0576887i	−0.00233766	+	0.00233766i
$610$			48.6113i			1.96821i
$611$	11.3915			0.460851
$612$	−1.53998	+	1.49392i	−0.0622499	+	0.0603880i
$613$	−31.2673			−1.26287			−0.631437	−	0.775427i	$-0.717535\pi$
$613$	−31.2673			−1.26287			−0.631437	+	0.775427i	$0.717535\pi$
$614$		−	25.1477i		−	1.01488i
$615$	−11.1237	+	11.1237i	−0.448550	+	0.448550i
$616$	−0.287624			−0.0115887
$617$	−8.12658	+	8.12658i	−0.327164	+	0.327164i	−0.851507	−	0.524343i	$-0.824311\pi$
$617$	−8.12658	+	8.12658i	−0.327164	+	0.327164i	0.524343	+	0.851507i	$0.324311\pi$
$618$	4.72748	+	4.72748i	0.190167	+	0.190167i
$619$	−15.9570	−	15.9570i	−0.641365	−	0.641365i	0.309526	−	0.950891i	$-0.399830\pi$
$619$	−15.9570	−	15.9570i	−0.641365	−	0.641365i	−0.950891	+	0.309526i	$0.899830\pi$
$620$			0.401377i			0.0161197i
$621$			17.7654i			0.712901i
$622$	18.9042	+	18.9042i	0.757990	+	0.757990i
$623$	−1.33577	−	1.33577i	−0.0535164	−	0.0535164i
$624$	−3.63529	+	3.63529i	−0.145528	+	0.145528i
$625$	29.0726			1.16290
$626$	22.6794	−	22.6794i	0.906451	−	0.906451i
$627$		−	5.89347i		−	0.235363i
$628$	0.439945			0.0175557
$629$	16.1216	+	0.244756i	0.642809	+	0.00975905i
$630$	−0.994728			−0.0396309
$631$		−	41.0584i		−	1.63451i	−0.576278	−	0.817254i	$-0.695496\pi$
$631$		−	41.0584i		−	1.63451i	0.576278	−	0.817254i	$-0.304504\pi$
$632$	22.8835	−	22.8835i	0.910257	−	0.910257i
$633$	−24.6347			−0.979140
$634$	6.58456	−	6.58456i	0.261506	−	0.261506i
$635$	45.2273	+	45.2273i	1.79479	+	1.79479i
$636$	2.01743	+	2.01743i	0.0799965	+	0.0799965i
$637$			6.50541i			0.257754i
$638$			0.586037i			0.0232014i
$639$	2.40257	+	2.40257i	0.0950442	+	0.0950442i
$640$	−28.2001	−	28.2001i	−1.11471	−	1.11471i
$641$	20.8773	−	20.8773i	0.824603	−	0.824603i	−0.162161	−	0.986764i	$-0.551846\pi$
$641$	20.8773	−	20.8773i	0.824603	−	0.824603i	0.986764	+	0.162161i	$0.0518464\pi$
$642$	−18.7972			−0.741868
$643$	29.2210	−	29.2210i	1.15236	−	1.15236i	0.166284	−	0.986078i	$-0.446823\pi$
$643$	29.2210	−	29.2210i	1.15236	−	1.15236i	0.986078	−	0.166284i	$-0.0531769\pi$
$644$			0.154642i			0.00609374i
$645$	3.62241			0.142632
$646$	26.6866	+	27.5094i	1.04997	+	1.08234i
$647$	−1.56796			−0.0616430			−0.0308215	−	0.999525i	$-0.509812\pi$
$647$	−1.56796			−0.0616430			−0.0308215	+	0.999525i	$0.509812\pi$
$648$		−	5.13333i		−	0.201656i
$649$	−5.15011	+	5.15011i	−0.202160	+	0.202160i
$650$	5.66594			0.222236
$651$	0.0477947	−	0.0477947i	0.00187322	−	0.00187322i
$652$	−4.17523	−	4.17523i	−0.163515	−	0.163515i
$653$	−12.4340	−	12.4340i	−0.486582	−	0.486582i	0.420644	−	0.907226i	$-0.361804\pi$
$653$	−12.4340	−	12.4340i	−0.486582	−	0.486582i	−0.907226	+	0.420644i	$0.861804\pi$
$654$			19.9091i			0.778508i
$655$		−	0.703316i		−	0.0274808i
$656$	14.0096	+	14.0096i	0.546981	+	0.546981i
$657$	−3.33846	−	3.33846i	−0.130246	−	0.130246i
$658$	−1.86574	+	1.86574i	−0.0727342	+	0.0727342i
$659$	23.3519			0.909659			0.454830	−	0.890578i	$-0.349700\pi$
$659$	23.3519			0.909659			0.454830	+	0.890578i	$0.349700\pi$
$660$	0.694869	−	0.694869i	0.0270477	−	0.0270477i
$661$		−	17.9523i		−	0.698264i	−0.937073	−	0.349132i	$-0.886476\pi$
$661$		−	17.9523i		−	0.698264i	0.937073	−	0.349132i	$-0.113524\pi$
$662$	18.2832			0.710597
$663$	−4.64574	−	0.0705311i	−0.180426	−	0.00273920i
$664$	−14.4448			−0.560568
$665$			2.57102i			0.0996998i
$666$	−6.50342	+	6.50342i	−0.252003	+	0.252003i
$667$	−1.54750			−0.0599196
$668$	−0.0476759	+	0.0476759i	−0.00184464	+	0.00184464i
$669$	−12.7135	−	12.7135i	−0.491533	−	0.491533i
$670$	−10.0183	−	10.0183i	−0.387041	−	0.387041i
$671$		−	8.50809i		−	0.328451i
$672$		−	0.323359i		−	0.0124739i
$673$	−36.4293	−	36.4293i	−1.40425	−	1.40425i	−0.785926	−	0.618320i	$-0.787814\pi$
$673$	−36.4293	−	36.4293i	−1.40425	−	1.40425i	−0.618320	−	0.785926i	$-0.712186\pi$
$674$	24.3942	+	24.3942i	0.939629	+	0.939629i
$675$	−15.4250	+	15.4250i	−0.593707	+	0.593707i
$676$	4.10440			0.157862
$677$	13.8564	−	13.8564i	0.532545	−	0.532545i	−0.388784	−	0.921329i	$-0.627105\pi$
$677$	13.8564	−	13.8564i	0.532545	−	0.532545i	0.921329	+	0.388784i	$0.127105\pi$
$678$			7.48178i			0.287336i
$679$	−0.867124			−0.0332772
$680$	0.476464	−	31.3837i	0.0182716	−	1.20351i
$681$	10.2188			0.391584
$682$		−	0.485528i		−	0.0185918i
$683$	−5.68782	+	5.68782i	−0.217638	+	0.217638i	−0.807502	−	0.589864i	$-0.799181\pi$
$683$	−5.68782	+	5.68782i	−0.217638	+	0.217638i	0.589864	+	0.807502i	$0.299181\pi$
$684$	−3.16327			−0.120951
$685$	6.78242	−	6.78242i	0.259143	−	0.259143i
$686$	−2.13400	−	2.13400i	−0.0814766	−	0.0814766i
$687$	−12.6233	−	12.6233i	−0.481609	−	0.481609i
$688$		−	4.56219i		−	0.173932i
$689$		−	6.50015i		−	0.247636i
$690$	12.6816	+	12.6816i	0.482781	+	0.482781i
$691$	−5.23494	−	5.23494i	−0.199147	−	0.199147i	0.600488	−	0.799634i	$-0.294973\pi$
$691$	−5.23494	−	5.23494i	−0.199147	−	0.199147i	−0.799634	+	0.600488i	$0.794973\pi$
$692$	0.294348	−	0.294348i	0.0111894	−	0.0111894i
$693$	0.174100			0.00661352
$694$	16.2830	−	16.2830i	0.618093	−	0.618093i
$695$			3.19537i			0.121207i
$696$	1.46844			0.0556610
$697$	−0.271811	+	17.9036i	−0.0102956	+	0.678147i
$698$	46.6523			1.76582
$699$		−	24.5277i		−	0.927722i
$700$	−0.134269	+	0.134269i	−0.00507490	+	0.00507490i
$701$	43.4002			1.63920			0.819601	−	0.572934i	$-0.194195\pi$
$701$	43.4002			1.63920			0.819601	+	0.572934i	$0.194195\pi$
$702$	5.52953	−	5.52953i	0.208699	−	0.208699i
$703$	16.8090	+	16.8090i	0.633965	+	0.633965i
$704$	3.53087	+	3.53087i	0.133075	+	0.133075i
$705$			44.2755i			1.66751i
$706$			13.7984i			0.519308i
$707$	0.333083	+	0.333083i	0.0125269	+	0.0125269i
$708$	−2.62750	−	2.62750i	−0.0987473	−	0.0987473i
$709$	5.40307	−	5.40307i	0.202917	−	0.202917i	−0.598332	−	0.801248i	$-0.704170\pi$
$709$	5.40307	−	5.40307i	0.202917	−	0.202917i	0.801248	+	0.598332i	$0.204170\pi$
$710$	10.1206			0.379818
$711$	−13.8515	+	13.8515i	−0.519471	+	0.519471i
$712$			34.0013i			1.27425i
$713$	1.28210			0.0480149
$714$	0.772449	−	0.749345i	0.0289082	−	0.0280435i
$715$	−2.23886			−0.0837286
$716$		−	7.11600i		−	0.265937i
$717$	−3.91635	+	3.91635i	−0.146259	+	0.146259i
$718$	4.68966			0.175016
$719$	−3.27028	+	3.27028i	−0.121961	+	0.121961i	−0.765453	−	0.643492i	$-0.777485\pi$
$719$	−3.27028	+	3.27028i	−0.121961	+	0.121961i	0.643492	+	0.765453i	$0.277485\pi$
$720$	14.8649	+	14.8649i	0.553982	+	0.553982i
$721$	0.360960	+	0.360960i	0.0134429	+	0.0134429i
$722$			27.4531i			1.02170i
$723$			3.87198i			0.144000i
$724$	5.35731	+	5.35731i	0.199103	+	0.199103i
$725$	−1.34363	−	1.34363i	−0.0499013	−	0.0499013i
$726$	13.5407	−	13.5407i	0.502542	−	0.502542i
$727$	11.7244			0.434833			0.217417	−	0.976079i	$-0.430237\pi$
$727$	11.7244			0.434833			0.217417	+	0.976079i	$0.430237\pi$
$728$	−0.236399	+	0.236399i	−0.00876152	+	0.00876152i
$729$			23.0104i			0.852237i
$730$	−14.0629			−0.520491
$731$	2.95940	−	2.87088i	0.109457	−	0.106183i
$732$	4.34068			0.160436
$733$			8.15726i			0.301295i	0.988588	+	0.150648i	$0.0481359\pi$
$733$			8.15726i			0.301295i	−0.988588	+	0.150648i	$0.951864\pi$
$734$	−21.1338	+	21.1338i	−0.780061	+	0.780061i
$735$	−25.2847			−0.932640
$736$	4.33707	−	4.33707i	0.159866	−	0.159866i
$737$	1.75344	+	1.75344i	0.0645887	+	0.0645887i
$738$	−7.22230	−	7.22230i	−0.265856	−	0.265856i
$739$			22.4333i			0.825221i	0.910908	+	0.412610i	$0.135383\pi$
$739$			22.4333i			0.825221i	−0.910908	+	0.412610i	$0.864617\pi$
$740$			3.96373i			0.145710i
$741$	−4.84385	−	4.84385i	−0.177943	−	0.177943i
$742$	1.06462	+	1.06462i	0.0390834	+	0.0390834i
$743$	−3.93740	+	3.93740i	−0.144449	+	0.144449i	−0.775633	−	0.631184i	$-0.782569\pi$
$743$	−3.93740	+	3.93740i	−0.144449	+	0.144449i	0.631184	+	0.775633i	$0.282569\pi$
$744$	−1.21659			−0.0446024
$745$	−24.5939	+	24.5939i	−0.901051	+	0.901051i
$746$		−	15.4893i		−	0.567104i
$747$	8.74352			0.319909
$748$	0.0169793	−	1.11839i	0.000620825	−	0.0408925i
$749$	−1.43524			−0.0524424
$750$		−	5.67433i		−	0.207197i
$751$	18.0128	−	18.0128i	0.657297	−	0.657297i	−0.297442	−	0.954740i	$-0.596134\pi$
$751$	18.0128	−	18.0128i	0.657297	−	0.657297i	0.954740	+	0.297442i	$0.0961336\pi$
$752$	55.7622			2.03344
$753$	−14.0265	+	14.0265i	−0.511156	+	0.511156i
$754$	0.481665	+	0.481665i	0.0175412	+	0.0175412i
$755$	19.2671	+	19.2671i	0.701201	+	0.701201i
$756$			0.262073i			0.00953152i
$757$			10.8038i			0.392670i	0.980537	+	0.196335i	$0.0629040\pi$
$757$			10.8038i			0.392670i	−0.980537	+	0.196335i	$0.937096\pi$
$758$	27.8032	+	27.8032i	1.00986	+	1.00986i
$759$	−2.21958	−	2.21958i	−0.0805656	−	0.0805656i
$760$	32.7220	−	32.7220i	1.18695	−	1.18695i
$761$	13.3910			0.485422			0.242711	−	0.970099i	$-0.421963\pi$
$761$	13.3910			0.485422			0.242711	+	0.970099i	$0.421963\pi$
$762$	27.9117	−	27.9117i	1.01114	−	1.01114i
$763$			1.52013i			0.0550324i
$764$	−0.686677			−0.0248431
$765$	−0.288406	+	18.9967i	−0.0104273	+	0.686827i
$766$	−0.784183			−0.0283337
$767$			8.46577i			0.305681i
$768$	−6.75481	+	6.75481i	−0.243743	+	0.243743i
$769$	−13.2974			−0.479517			−0.239759	−	0.970833i	$-0.577068\pi$
$769$	−13.2974			−0.479517			−0.239759	+	0.970833i	$0.577068\pi$
$770$	0.366689	−	0.366689i	0.0132146	−	0.0132146i
$771$	7.55462	+	7.55462i	0.272073	+	0.272073i
$772$	0.331772	+	0.331772i	0.0119407	+	0.0119407i
$773$		−	45.6159i		−	1.64069i	−0.571868	−	0.820346i	$-0.693781\pi$
$773$		−	45.6159i		−	1.64069i	0.571868	−	0.820346i	$-0.306219\pi$
$774$			2.35193i			0.0845384i
$775$	1.11319	+	1.11319i	0.0399870	+	0.0399870i
$776$	11.0361	+	11.0361i	0.396173	+	0.396173i
$777$	0.471988	−	0.471988i	0.0169325	−	0.0169325i
$778$	−10.6874			−0.383161
$779$	−18.6671	+	18.6671i	−0.668817	+	0.668817i
$780$		−	1.14223i		−	0.0408983i
$781$	−1.77133			−0.0633832
$782$	20.4111	+	0.309879i	0.729900	+	0.0110813i
$783$	−2.62257			−0.0937231
$784$			31.8444i			1.13730i
$785$	2.75471	−	2.75471i	0.0983197	−	0.0983197i
$786$	−0.434047			−0.0154820
$787$	5.45204	−	5.45204i	0.194344	−	0.194344i	−0.603226	−	0.797570i	$-0.706118\pi$
$787$	5.45204	−	5.45204i	0.194344	−	0.194344i	0.797570	+	0.603226i	$0.206118\pi$
$788$	5.10207	+	5.10207i	0.181754	+	0.181754i
$789$	11.2834	+	11.2834i	0.401699	+	0.401699i
$790$			58.3478i			2.07592i
$791$			0.571261i			0.0203117i
$792$	−2.21582	−	2.21582i	−0.0787357	−	0.0787357i
$793$	−6.99281	−	6.99281i	−0.248322	−	0.248322i
$794$	−29.0351	+	29.0351i	−1.03042	+	1.03042i
$795$	25.2643			0.896031
$796$	1.92843	−	1.92843i	0.0683512	−	0.0683512i
$797$			7.70883i			0.273061i	0.990636	+	0.136530i	$0.0435951\pi$
$797$			7.70883i			0.273061i	−0.990636	+	0.136530i	$0.956405\pi$
$798$	1.58669			0.0561682
$799$	35.0898	+	36.1717i	1.24139	+	1.27966i
$800$	7.53140			0.266275
$801$		−	20.5811i		−	0.727199i
$802$	−16.2939	+	16.2939i	−0.575357	+	0.575357i
$803$	2.46133			0.0868584
$804$	−0.894572	+	0.894572i	−0.0315491	+	0.0315491i
$805$	0.968287	+	0.968287i	0.0341276	+	0.0341276i
$806$	−0.399056	−	0.399056i	−0.0140561	−	0.0140561i
$807$		−	10.5352i		−	0.370857i
$808$		−	8.47846i		−	0.298271i
$809$	−15.8170	−	15.8170i	−0.556096	−	0.556096i	0.372098	−	0.928194i	$-0.378639\pi$
$809$	−15.8170	−	15.8170i	−0.556096	−	0.556096i	−0.928194	+	0.372098i	$0.878639\pi$
$810$	6.54442	+	6.54442i	0.229947	+	0.229947i
$811$	12.8316	−	12.8316i	0.450578	−	0.450578i	−0.444968	−	0.895546i	$-0.646785\pi$
$811$	12.8316	−	12.8316i	0.450578	−	0.450578i	0.895546	+	0.444968i	$0.146785\pi$
$812$	−0.0228286			−0.000801128
$813$	−12.0461	+	12.0461i	−0.422474	+	0.422474i
$814$		−	4.79475i		−	0.168056i
$815$	−52.2863			−1.83151
$816$	−22.7412	−	0.345255i	−0.796102	−	0.0120863i
$817$	6.07890			0.212674
$818$			33.0301i			1.15487i
$819$	0.143093	−	0.143093i	0.00500008	−	0.00500008i
$820$	−4.40188			−0.153720
$821$	−13.8952	+	13.8952i	−0.484946	+	0.484946i	−0.906707	−	0.421761i	$-0.861412\pi$
$821$	−13.8952	+	13.8952i	−0.484946	+	0.484946i	0.421761	+	0.906707i	$0.361412\pi$
$822$	−4.18573	−	4.18573i	−0.145994	−	0.145994i
$823$	18.9754	+	18.9754i	0.661442	+	0.661442i	0.955720	−	0.294278i	$-0.0950791\pi$
$823$	18.9754	+	18.9754i	0.661442	+	0.661442i	−0.294278	+	0.955720i	$0.595079\pi$
$824$		−	9.18807i		−	0.320081i
$825$		−	3.85434i		−	0.134191i
$826$	−1.38656	−	1.38656i	−0.0482444	−	0.0482444i
$827$	6.28076	+	6.28076i	0.218403	+	0.218403i	0.807825	−	0.589422i	$-0.200644\pi$
$827$	6.28076	+	6.28076i	0.218403	+	0.218403i	−0.589422	+	0.807825i	$0.700644\pi$
$828$	−1.19134	+	1.19134i	−0.0414019	+	0.0414019i
$829$	−13.4164			−0.465971			−0.232986	−	0.972480i	$-0.574849\pi$
$829$	−13.4164			−0.465971			−0.232986	+	0.972480i	$0.574849\pi$
$830$	18.4156	−	18.4156i	0.639213	−	0.639213i
$831$			37.3231i			1.29472i
$832$	5.80405			0.201219
$833$	−20.6568	+	20.0390i	−0.715716	+	0.694309i
$834$	1.97200			0.0682848
$835$			0.597044i			0.0206616i
$836$	1.16608	−	1.16608i	0.0403299	−	0.0403299i
$837$	2.17278			0.0751024
$838$	37.1477	−	37.1477i	1.28325	−	1.28325i
$839$	−4.57953	−	4.57953i	−0.158103	−	0.158103i	0.623623	−	0.781726i	$-0.285660\pi$
$839$	−4.57953	−	4.57953i	−0.158103	−	0.158103i	−0.781726	+	0.623623i	$0.785660\pi$
$840$	−0.918816	−	0.918816i	−0.0317022	−	0.0317022i
$841$			28.7716i			0.992123i
$842$		−	38.4743i		−	1.32591i
$843$	−2.97884	−	2.97884i	−0.102597	−	0.102597i
$844$	−4.87423	−	4.87423i	−0.167778	−	0.167778i
$845$	25.6997	−	25.6997i	0.884095	−	0.884095i
$846$	−28.7468			−0.988337
$847$	1.03388	−	1.03388i	0.0355245	−	0.0355245i
$848$		−	31.8187i		−	1.09266i
$849$	32.3514			1.11030
$850$	17.4531	+	17.9912i	0.598636	+	0.617093i
$851$	12.6611			0.434018
$852$		−	0.903702i		−	0.0309603i
$853$	−3.60112	+	3.60112i	−0.123300	+	0.123300i	−0.766064	−	0.642764i	$-0.777788\pi$
$853$	−3.60112	+	3.60112i	−0.123300	+	0.123300i	0.642764	+	0.766064i	$0.277788\pi$
$854$	2.29062			0.0783834
$855$	−19.8068	+	19.8068i	−0.677377	+	0.677377i
$856$	18.2666	+	18.2666i	0.624340	+	0.624340i
$857$	−24.9031	−	24.9031i	−0.850674	−	0.850674i	0.139542	−	0.990216i	$-0.455437\pi$
$857$	−24.9031	−	24.9031i	−0.850674	−	0.850674i	−0.990216	+	0.139542i	$0.955437\pi$
$858$			1.38170i			0.0471704i
$859$		−	43.4360i		−	1.48202i	−0.671496	−	0.741008i	$-0.734348\pi$
$859$		−	43.4360i		−	1.48202i	0.671496	−	0.741008i	$-0.265652\pi$
$860$	0.716732	+	0.716732i	0.0244404	+	0.0244404i
$861$	0.524161	+	0.524161i	0.0178634	+	0.0178634i
$862$	−18.7244	+	18.7244i	−0.637754	+	0.637754i
$863$	−29.2829			−0.996802			−0.498401	−	0.866947i	$-0.666079\pi$
$863$	−29.2829			−0.996802			−0.498401	+	0.866947i	$0.666079\pi$
$864$	7.35008	−	7.35008i	0.250055	−	0.250055i
$865$		−	3.68611i		−	0.125331i
$866$	−15.2763			−0.519108
$867$	−14.0866	−	14.9690i	−0.478405	−	0.508374i
$868$	0.0189134			0.000641961
$869$		−	10.2122i		−	0.346426i
$870$	−1.87209	+	1.87209i	−0.0634699	+	0.0634699i
$871$	2.88230			0.0976631
$872$	19.3471	−	19.3471i	0.655176	−	0.655176i
$873$	−6.68021	−	6.68021i	−0.226091	−	0.226091i
$874$	21.2815	+	21.2815i	0.719858	+	0.719858i
$875$		−	0.433256i		−	0.0146467i
$876$			1.25573i			0.0424271i
$877$	−11.0768	−	11.0768i	−0.374038	−	0.374038i	0.494908	−	0.868945i	$-0.335202\pi$
$877$	−11.0768	−	11.0768i	−0.374038	−	0.374038i	−0.868945	+	0.494908i	$0.835202\pi$
$878$	1.24403	+	1.24403i	0.0419841	+	0.0419841i
$879$	22.2037	−	22.2037i	0.748914	−	0.748914i
$880$	−10.9594			−0.369440
$881$	−20.2034	+	20.2034i	−0.680669	+	0.680669i	−0.960151	−	0.279482i	$-0.909837\pi$
$881$	−20.2034	+	20.2034i	−0.680669	+	0.680669i	0.279482	+	0.960151i	$0.409837\pi$
$882$		−	16.4166i		−	0.552777i
$883$	−54.1423			−1.82203			−0.911017	−	0.412369i	$-0.864702\pi$
$883$	−54.1423			−1.82203			−0.911017	+	0.412369i	$0.864702\pi$
$884$	−0.905253	−	0.933164i	−0.0304470	−	0.0313857i
$885$	−32.9040			−1.10606
$886$		−	38.1550i		−	1.28184i
$887$	−26.7659	+	26.7659i	−0.898713	+	0.898713i	−0.995322	−	0.0966097i	$-0.969200\pi$
$887$	−26.7659	+	26.7659i	−0.898713	+	0.898713i	0.0966097	+	0.995322i	$0.469200\pi$
$888$	−12.0142			−0.403171
$889$	2.13116	−	2.13116i	0.0714768	−	0.0714768i
$890$	−43.3479	−	43.3479i	−1.45302	−	1.45302i
$891$	−1.14542	−	1.14542i	−0.0383731	−	0.0383731i
$892$		−	5.03100i		−	0.168450i
$893$			74.3004i			2.48637i
$894$	15.1780	+	15.1780i	0.507628	+	0.507628i
$895$	−44.5567	−	44.5567i	−1.48937	−	1.48937i
$896$	−1.32882	+	1.32882i	−0.0443928	+	0.0443928i
$897$	−3.64855			−0.121821
$898$	−41.7062	+	41.7062i	−1.39175	+	1.39175i
$899$			0.189266i			0.00631238i
$900$	−2.06878			−0.0689595
$901$	20.6401	−	20.0228i	0.687622	−	0.667056i
$902$	5.32475			0.177295
$903$		−	0.170692i		−	0.00568028i
$904$	7.27059	−	7.27059i	0.241816	−	0.241816i
$905$	67.0895			2.23013
$906$	11.8906	−	11.8906i	0.395038	−	0.395038i
$907$	15.2684	+	15.2684i	0.506979	+	0.506979i	0.913598	−	0.406619i	$-0.133292\pi$
$907$	15.2684	+	15.2684i	0.506979	+	0.506979i	−0.406619	+	0.913598i	$0.633292\pi$
$908$	2.02189	+	2.02189i	0.0670989	+	0.0670989i
$909$			5.13205i			0.170219i
$910$		−	0.602764i		−	0.0199814i
$911$	−25.6313	−	25.6313i	−0.849202	−	0.849202i	0.140832	−	0.990034i	$-0.455022\pi$
$911$	−25.6313	−	25.6313i	−0.849202	−	0.849202i	−0.990034	+	0.140832i	$0.955022\pi$
$912$	−23.7110	−	23.7110i	−0.785149	−	0.785149i
$913$	−3.22315	+	3.22315i	−0.106671	+	0.106671i
$914$	1.11194			0.0367796
$915$	27.1791	−	27.1791i	0.898513	−	0.898513i
$916$		−	4.99530i		−	0.165049i
$917$	−0.0331411			−0.00109441
$918$	34.5910	+	0.525156i	1.14167	+	0.0173327i
$919$	−27.6186			−0.911054			−0.455527	−	0.890222i	$-0.650549\pi$
$919$	−27.6186			−0.911054			−0.455527	+	0.890222i	$0.650549\pi$
$920$		−	24.6473i		−	0.812597i
$921$	−14.0604	+	14.0604i	−0.463304	+	0.463304i
$922$	−34.3788			−1.13221
$923$	−1.45586	+	1.45586i	−0.0479202	+	0.0479202i
$924$	−0.0327430	−	0.0327430i	−0.00107717	−	0.00107717i
$925$	10.9931	+	10.9931i	0.361452	+	0.361452i
$926$		−	31.9195i		−	1.04894i
$927$			5.56158i			0.182666i
$928$	0.640249	+	0.640249i	0.0210172	+	0.0210172i
$929$	25.5448	+	25.5448i	0.838099	+	0.838099i	0.988609	−	0.150510i	$-0.0480914\pi$
$929$	25.5448	+	25.5448i	0.838099	+	0.838099i	−0.150510	+	0.988609i	$0.548091\pi$
$930$	1.55102	−	1.55102i	0.0508599	−	0.0508599i
$931$	−42.4312			−1.39063
$932$	4.85306	−	4.85306i	0.158967	−	0.158967i
$933$		−	21.1391i		−	0.692063i
$934$	27.7211			0.907063
$935$	−6.89648	−	7.10911i	−0.225539	−	0.232493i
$936$	−3.64237			−0.119055
$937$		−	37.6853i		−	1.23113i	−0.788088	−	0.615563i	$-0.788929\pi$
$937$		−	37.6853i		−	1.23113i	0.788088	−	0.615563i	$-0.211071\pi$
$938$	−0.472075	+	0.472075i	−0.0154138	+	0.0154138i
$939$	−25.3606			−0.827612
$940$	−8.76038	+	8.76038i	−0.285732	+	0.285732i
$941$	10.2219	+	10.2219i	0.333224	+	0.333224i	0.853810	−	0.520585i	$-0.174286\pi$
$941$	10.2219	+	10.2219i	0.333224	+	0.333224i	−0.520585	+	0.853810i	$0.674286\pi$
$942$	−1.70005	−	1.70005i	−0.0553906	−	0.0553906i
$943$			14.0607i			0.457878i
$944$			41.4405i			1.34877i
$945$	1.64097	+	1.64097i	0.0533807	+	0.0533807i
$946$	−0.866998	−	0.866998i	−0.0281885	−	0.0281885i
$947$	24.3757	−	24.3757i	0.792104	−	0.792104i	−0.189732	−	0.981836i	$-0.560762\pi$
$947$	24.3757	−	24.3757i	0.792104	−	0.792104i	0.981836	+	0.189732i	$0.0607618\pi$
$948$	5.21009			0.169216
$949$	2.02297	−	2.02297i	0.0656684	−	0.0656684i
$950$			36.9558i			1.19900i
$951$	−7.36300			−0.238762
$952$	−1.47884	−	0.0224515i	−0.0479294	−	0.000727658i
$953$	−7.61474			−0.246666			−0.123333	−	0.992365i	$-0.539358\pi$
$953$	−7.61474			−0.246666			−0.123333	+	0.992365i	$0.539358\pi$
$954$			16.4034i			0.531079i
$955$	−4.29962	+	4.29962i	−0.139132	+	0.139132i
$956$	−1.54978			−0.0501235
$957$	0.327660	−	0.327660i	0.0105917	−	0.0105917i
$958$	−35.4623	−	35.4623i	−1.14573	−	1.14573i
$959$	−0.319595	−	0.319595i	−0.0103203	−	0.0103203i
$960$			22.5587i			0.728080i
$961$			30.8432i			0.994942i
$962$	−3.94081	−	3.94081i	−0.127057	−	0.127057i
$963$	−11.0569	−	11.0569i	−0.356302	−	0.356302i
$964$	−0.766111	+	0.766111i	−0.0246748	+	0.0246748i
$965$	4.15477			0.133747
$966$	0.597573	−	0.597573i	0.0192266	−	0.0192266i
$967$		−	26.0919i		−	0.839058i	−0.907742	−	0.419529i	$-0.862195\pi$
$967$		−	26.0919i		−	0.839058i	0.907742	−	0.419529i	$-0.137805\pi$
$968$	−26.3169			−0.845858
$969$	0.460035	−	30.3016i	0.0147785	−	0.973427i
$970$	−28.1396			−0.903509
$971$		−	33.3576i		−	1.07049i	−0.844695	−	0.535247i	$-0.820218\pi$
$971$		−	33.3576i		−	1.07049i	0.844695	−	0.535247i	$-0.179782\pi$
$972$	−3.35368	+	3.35368i	−0.107569	+	0.107569i
$973$	0.150569			0.00482703
$974$	−42.6879	+	42.6879i	−1.36781	+	1.36781i
$975$	−3.16789	−	3.16789i	−0.101454	−	0.101454i
$976$	−34.2303	−	34.2303i	−1.09569	−	1.09569i
$977$		−	5.43735i		−	0.173956i	−0.996210	−	0.0869782i	$-0.972279\pi$
$977$		−	5.43735i		−	0.173956i	0.996210	−	0.0869782i	$-0.0277210\pi$
$978$			32.2682i			1.03182i
$979$	7.58688	+	7.58688i	0.242478	+	0.242478i
$980$	−5.00284	−	5.00284i	−0.159810	−	0.159810i
$981$	−11.7109	+	11.7109i	−0.373900	+	0.373900i
$982$	−40.3344			−1.28712
$983$	−2.61914	+	2.61914i	−0.0835376	+	0.0835376i	−0.747641	−	0.664103i	$-0.768814\pi$
$983$	−2.61914	+	2.61914i	−0.0835376	+	0.0835376i	0.664103	+	0.747641i	$0.268814\pi$
$984$		−	13.3423i		−	0.425336i
$985$	63.8931			2.03580
$986$	−0.0457452	+	3.01314i	−0.00145682	+	0.0959579i
$987$	2.08631			0.0664081
$988$		−	1.91681i		−	0.0609819i
$989$	2.28941	−	2.28941i	0.0727991	−	0.0727991i
$990$	5.64984			0.179564
$991$	31.0568	−	31.0568i	0.986551	−	0.986551i	−0.0133601	−	0.999911i	$-0.504253\pi$
$991$	31.0568	−	31.0568i	0.986551	−	0.986551i	0.999911	+	0.0133601i	$0.00425277\pi$
$992$	−0.530442	−	0.530442i	−0.0168415	−	0.0168415i
$993$	−10.2223	−	10.2223i	−0.324396	−	0.324396i
$994$		−	0.476892i		−	0.0151261i
$995$		−	24.1496i		−	0.765594i
$996$	−1.64439	−	1.64439i	−0.0521046	−	0.0521046i
$997$	−4.83958	−	4.83958i	−0.153271	−	0.153271i	0.626306	−	0.779577i	$-0.284566\pi$
$997$	−4.83958	−	4.83958i	−0.153271	−	0.153271i	−0.779577	+	0.626306i	$0.784566\pi$
$998$	−17.4137	+	17.4137i	−0.551221	+	0.551221i
$999$	21.4570			0.678868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.c.259.9	✓	56
17.13	even	4	inner	731.2.f.c.302.20	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.c.259.9	✓	56	1.1	even	1	trivial
731.2.f.c.302.20	yes	56	17.13	even	4	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.52916i q^{2} +(-0.854970 + 0.854970i) q^{3} -0.338329 q^{4} +(-2.11844 + 2.11844i) q^{5} +(1.30739 + 1.30739i) q^{6} +(0.0998235 + 0.0998235i) q^{7} -2.54096i q^{8} +1.53805i q^{9} +O(q^{10})\)	\(q-1.52916i q^{2} +(-0.854970 + 0.854970i) q^{3} -0.338329 q^{4} +(-2.11844 + 2.11844i) q^{5} +(1.30739 + 1.30739i) q^{6} +(0.0998235 + 0.0998235i) q^{7} -2.54096i q^{8} +1.53805i q^{9} +(3.23944 + 3.23944i) q^{10} +(-0.566977 - 0.566977i) q^{11} +(0.289261 - 0.289261i) q^{12} -0.931997 q^{13} +(0.152646 - 0.152646i) q^{14} -3.62241i q^{15} -4.56219 q^{16} +(-2.87088 - 2.95940i) q^{17} +2.35193 q^{18} -6.07890i q^{19} +(0.716732 - 0.716732i) q^{20} -0.170692 q^{21} +(-0.866998 + 0.866998i) q^{22} +(-2.28941 - 2.28941i) q^{23} +(2.17244 + 2.17244i) q^{24} -3.97561i q^{25} +1.42517i q^{26} +(-3.87990 - 3.87990i) q^{27} +(-0.0337732 - 0.0337732i) q^{28} +(0.337969 - 0.337969i) q^{29} -5.53925 q^{30} +(-0.280005 + 0.280005i) q^{31} +1.89440i q^{32} +0.969496 q^{33} +(-4.52539 + 4.39004i) q^{34} -0.422941 q^{35} -0.520369i q^{36} +(-2.76514 + 2.76514i) q^{37} -9.29561 q^{38} +(0.796830 - 0.796830i) q^{39} +(5.38288 + 5.38288i) q^{40} +(-3.07080 - 3.07080i) q^{41} +0.261016i q^{42} +1.00000i q^{43} +(0.191825 + 0.191825i) q^{44} +(-3.25828 - 3.25828i) q^{45} +(-3.50088 + 3.50088i) q^{46} -12.2227 q^{47} +(3.90054 - 3.90054i) q^{48} -6.98007i q^{49} -6.07935 q^{50} +(4.98471 + 0.0756774i) q^{51} +0.315322 q^{52} +6.97443i q^{53} +(-5.93298 + 5.93298i) q^{54} +2.40222 q^{55} +(0.253648 - 0.253648i) q^{56} +(5.19728 + 5.19728i) q^{57} +(-0.516809 - 0.516809i) q^{58} -9.08346i q^{59} +1.22557i q^{60} +(7.50304 + 7.50304i) q^{61} +(0.428173 + 0.428173i) q^{62} +(-0.153534 + 0.153534i) q^{63} -6.22754 q^{64} +(1.97438 - 1.97438i) q^{65} -1.48251i q^{66} -3.09261 q^{67} +(0.971304 + 1.00125i) q^{68} +3.91476 q^{69} +0.646744i q^{70} +(1.56208 - 1.56208i) q^{71} +3.90813 q^{72} +(-2.17057 + 2.17057i) q^{73} +(4.22835 + 4.22835i) q^{74} +(3.39903 + 3.39903i) q^{75} +2.05667i q^{76} -0.113195i q^{77} +(-1.21848 - 1.21848i) q^{78} +(9.00586 + 9.00586i) q^{79} +(9.66475 - 9.66475i) q^{80} +2.02023 q^{81} +(-4.69574 + 4.69574i) q^{82} -5.68480i q^{83} +0.0577502 q^{84} +(12.3511 + 0.187513i) q^{85} +1.52916 q^{86} +0.577907i q^{87} +(-1.44066 + 1.44066i) q^{88} -13.3813 q^{89} +(-4.98243 + 4.98243i) q^{90} +(-0.0930353 - 0.0930353i) q^{91} +(0.774576 + 0.774576i) q^{92} -0.478792i q^{93} +18.6904i q^{94} +(12.8778 + 12.8778i) q^{95} +(-1.61966 - 1.61966i) q^{96} +(-4.34329 + 4.34329i) q^{97} -10.6736 q^{98} +(0.872040 - 0.872040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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