LMFDB - Embedded newform 349.2.e.a.123.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(123,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("349.123");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.e (of order $6$, 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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			123.8
Character	$\chi$	$=$	349.123
Dual form			349.2.e.a.227.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33595 + 0.771310i) q^{2} +(-0.677977 + 1.17429i) q^{3} +(0.189837 - 0.328808i) q^{4} +(1.91694 - 3.32023i) q^{5} -2.09172i q^{6} +(-1.98739 + 1.14742i) q^{7} -2.49955i q^{8} +(0.580694 + 1.00579i) q^{9} +O(q^{10})$	\(q+(-1.33595 + 0.771310i) q^{2} +(-0.677977 + 1.17429i) q^{3} +(0.189837 - 0.328808i) q^{4} +(1.91694 - 3.32023i) q^{5} -2.09172i q^{6} +(-1.98739 + 1.14742i) q^{7} -2.49955i q^{8} +(0.580694 + 1.00579i) q^{9} +5.91420i q^{10} +4.42226i q^{11} +(0.257411 + 0.445849i) q^{12} +(-2.49246 + 1.43902i) q^{13} +(1.77003 - 3.06579i) q^{14} +(2.59928 + 4.50208i) q^{15} +(2.30760 + 3.99688i) q^{16} +0.781534 q^{17} +(-1.55155 - 0.895789i) q^{18} +(-2.88981 + 5.00531i) q^{19} +(-0.727812 - 1.26061i) q^{20} -3.11170i q^{21} +(-3.41093 - 5.90791i) q^{22} +(0.260901 + 0.451894i) q^{23} +(2.93519 + 1.69463i) q^{24} +(-4.84928 - 8.39921i) q^{25} +(2.21987 - 3.84492i) q^{26} -5.64265 q^{27} +0.871293i q^{28} +(-2.06205 + 3.57157i) q^{29} +(-6.94500 - 4.00970i) q^{30} -1.72475 q^{31} +(-1.83632 - 1.06020i) q^{32} +(-5.19302 - 2.99819i) q^{33} +(-1.04409 + 0.602805i) q^{34} +8.79813i q^{35} +0.440949 q^{36} +8.24916 q^{37} -8.91577i q^{38} -3.90250i q^{39} +(-8.29906 - 4.79147i) q^{40} -7.75381 q^{41} +(2.40009 + 4.15707i) q^{42} +(-4.29240 - 2.47822i) q^{43} +(1.45407 + 0.839510i) q^{44} +4.45261 q^{45} +(-0.697100 - 0.402471i) q^{46} +2.64810i q^{47} -6.25800 q^{48} +(-0.866851 + 1.50143i) q^{49} +(12.9568 + 7.48060i) q^{50} +(-0.529863 + 0.917749i) q^{51} +1.09272i q^{52} +9.61126i q^{53} +(7.53829 - 4.35223i) q^{54} +(14.6829 + 8.47719i) q^{55} +(2.86803 + 4.96757i) q^{56} +(-3.91846 - 6.78697i) q^{57} -6.36191i q^{58} +(11.3861 + 6.57378i) q^{59} +1.97376 q^{60} -3.56819i q^{61} +(2.30417 - 1.33031i) q^{62} +(-2.30813 - 1.33260i) q^{63} -5.95942 q^{64} +11.0341i q^{65} +9.25014 q^{66} +5.40753 q^{67} +(0.148364 - 0.256975i) q^{68} -0.707540 q^{69} +(-6.78608 - 11.7538i) q^{70} +(-2.50000 + 1.44337i) q^{71} +(2.51402 - 1.45147i) q^{72} +(7.13145 - 12.3520i) q^{73} +(-11.0204 + 6.36266i) q^{74} +13.1508 q^{75} +(1.09719 + 1.90039i) q^{76} +(-5.07419 - 8.78876i) q^{77} +(3.01004 + 5.21354i) q^{78} +5.67907i q^{79} +17.6941 q^{80} +(2.08351 - 3.60874i) q^{81} +(10.3587 - 5.98059i) q^{82} +(-6.74336 - 11.6798i) q^{83} +(-1.02315 - 0.590717i) q^{84} +(1.49815 - 2.59487i) q^{85} +7.64589 q^{86} +(-2.79604 - 4.84289i) q^{87} +11.0536 q^{88} +(1.77824 + 1.02667i) q^{89} +(-5.94845 + 3.43434i) q^{90} +(3.30233 - 5.71981i) q^{91} +0.198115 q^{92} +(1.16934 - 2.02536i) q^{93} +(-2.04251 - 3.53773i) q^{94} +(11.0792 + 19.1897i) q^{95} +(2.48997 - 1.43758i) q^{96} +(-12.1182 + 6.99642i) q^{97} -2.67444i q^{98} +(-4.44787 + 2.56798i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.33595	+	0.771310i	−0.944658	+	0.545398i	−0.891417	−	0.453183i	$-0.850288\pi$
$2$	−1.33595	+	0.771310i	−0.944658	+	0.545398i	−0.0532403	+	0.998582i	$0.516955\pi$
$3$	−0.677977	+	1.17429i	−0.391430	+	0.677977i	−0.992638	−	0.121115i	$-0.961353\pi$
$3$	−0.677977	+	1.17429i	−0.391430	+	0.677977i	0.601208	+	0.799092i	$0.294686\pi$
$4$	0.189837	−	0.328808i	0.0949187	−	0.164404i
$5$	1.91694	−	3.32023i	0.857280	−	1.48485i	−0.0172343	−	0.999851i	$-0.505486\pi$
$5$	1.91694	−	3.32023i	0.857280	−	1.48485i	0.874514	−	0.485000i	$-0.161181\pi$
$6$		−	2.09172i		−	0.853942i
$7$	−1.98739	+	1.14742i	−0.751163	+	0.433684i	−0.826114	−	0.563503i	$-0.809453\pi$
$7$	−1.98739	+	1.14742i	−0.751163	+	0.433684i	0.0749508	+	0.997187i	$0.476120\pi$
$8$		−	2.49955i		−	0.883723i
$9$	0.580694	+	1.00579i	0.193565	+	0.335264i
$10$			5.91420i			1.87024i
$11$			4.42226i			1.33336i	0.745344	+	0.666681i	$0.232285\pi$
$11$			4.42226i			1.33336i	−0.745344	+	0.666681i	$0.767715\pi$
$12$	0.257411	+	0.445849i	0.0743081	+	0.128705i
$13$	−2.49246	+	1.43902i	−0.691285	+	0.399114i	−0.804093	−	0.594503i	$-0.797349\pi$
$13$	−2.49246	+	1.43902i	−0.691285	+	0.399114i	0.112808	+	0.993617i	$0.464015\pi$
$14$	1.77003	−	3.06579i	0.473061	−	0.819366i
$15$	2.59928	+	4.50208i	0.671131	+	1.16243i
$16$	2.30760	+	3.99688i	0.576900	+	0.999219i
$17$	0.781534			0.189550			0.0947750	−	0.995499i	$-0.469787\pi$
$17$	0.781534			0.189550			0.0947750	+	0.995499i	$0.469787\pi$
$18$	−1.55155	−	0.895789i	−0.365704	−	0.211140i
$19$	−2.88981	+	5.00531i	−0.662969	+	1.14830i	0.316863	+	0.948471i	$0.397371\pi$
$19$	−2.88981	+	5.00531i	−0.662969	+	1.14830i	−0.979832	+	0.199824i	$0.935963\pi$
$20$	−0.727812	−	1.26061i	−0.162744	−	0.281880i
$21$		−	3.11170i		−	0.679029i
$22$	−3.41093	−	5.90791i	−0.727213	−	1.25957i
$23$	0.260901	+	0.451894i	0.0544016	+	0.0942264i	0.891944	−	0.452146i	$-0.149342\pi$
$23$	0.260901	+	0.451894i	0.0544016	+	0.0942264i	−0.837542	+	0.546373i	$0.816008\pi$
$24$	2.93519	+	1.69463i	0.599144	+	0.345916i
$25$	−4.84928	−	8.39921i	−0.969857	−	1.67984i
$26$	2.21987	−	3.84492i	0.435352	−	0.754052i
$27$	−5.64265			−1.08593
$28$			0.871293i			0.164659i
$29$	−2.06205	+	3.57157i	−0.382913	+	0.663225i	−0.991477	−	0.130280i	$-0.958412\pi$
$29$	−2.06205	+	3.57157i	−0.382913	+	0.663225i	0.608564	+	0.793505i	$0.291746\pi$
$30$	−6.94500	−	4.00970i	−1.26798	−	0.732067i
$31$	−1.72475			−0.309774			−0.154887	−	0.987932i	$-0.549501\pi$
$31$	−1.72475			−0.309774			−0.154887	+	0.987932i	$0.549501\pi$
$32$	−1.83632	−	1.06020i	−0.324619	−	0.187419i
$33$	−5.19302	−	2.99819i	−0.903989	−	0.521918i
$34$	−1.04409	+	0.602805i	−0.179060	+	0.103380i
$35$			8.79813i			1.48715i
$36$	0.440949			0.0734916
$37$	8.24916			1.35615			0.678077	−	0.734991i	$-0.262814\pi$
$37$	8.24916			1.35615			0.678077	+	0.734991i	$0.262814\pi$
$38$		−	8.91577i		−	1.44633i
$39$		−	3.90250i		−	0.624901i
$40$	−8.29906	−	4.79147i	−1.31220	−	0.757597i
$41$	−7.75381			−1.21094			−0.605471	−	0.795867i	$-0.707015\pi$
$41$	−7.75381			−1.21094			−0.605471	+	0.795867i	$0.707015\pi$
$42$	2.40009	+	4.15707i	0.370341	+	0.641450i
$43$	−4.29240	−	2.47822i	−0.654584	−	0.377924i	0.135626	−	0.990760i	$-0.456695\pi$
$43$	−4.29240	−	2.47822i	−0.654584	−	0.377924i	−0.790210	+	0.612836i	$0.790029\pi$
$44$	1.45407	+	0.839510i	0.219210	+	0.126561i
$45$	4.45261			0.663756
$46$	−0.697100	−	0.402471i	−0.102782	−	0.0593411i
$47$			2.64810i			0.386266i	0.981173	+	0.193133i	$0.0618648\pi$
$47$			2.64810i			0.386266i	−0.981173	+	0.193133i	$0.938135\pi$
$48$	−6.25800			−0.903264
$49$	−0.866851	+	1.50143i	−0.123836	+	0.214490i
$50$	12.9568	+	7.48060i	1.83237	+	1.05792i
$51$	−0.529863	+	0.917749i	−0.0741956	+	0.128511i
$52$			1.09272i			0.151533i
$53$			9.61126i			1.32021i	0.751174	+	0.660104i	$0.229488\pi$
$53$			9.61126i			1.32021i	−0.751174	+	0.660104i	$0.770512\pi$
$54$	7.53829	−	4.35223i	1.02583	−	0.592264i
$55$	14.6829	+	8.47719i	1.97984	+	1.14306i
$56$	2.86803	+	4.96757i	0.383257	+	0.663820i
$57$	−3.91846	−	6.78697i	−0.519012	−	0.898956i
$58$		−	6.36191i		−	0.835360i
$59$	11.3861	+	6.57378i	1.48235	+	0.855833i	0.999799	−	0.0200374i	$-0.00637853\pi$
$59$	11.3861	+	6.57378i	1.48235	+	0.855833i	0.482547	+	0.875870i	$0.339712\pi$
$60$	1.97376			0.254811
$61$		−	3.56819i		−	0.456860i	−0.973560	−	0.228430i	$-0.926641\pi$
$61$		−	3.56819i		−	0.456860i	0.973560	−	0.228430i	$-0.0733592\pi$
$62$	2.30417	−	1.33031i	0.292630	−	0.168950i
$63$	−2.30813	−	1.33260i	−0.290797	−	0.167892i
$64$	−5.95942			−0.744928
$65$			11.0341i			1.36861i
$66$	9.25014			1.13861
$67$	5.40753			0.660634			0.330317	−	0.943870i	$-0.392844\pi$
$67$	5.40753			0.660634			0.330317	+	0.943870i	$0.392844\pi$
$68$	0.148364	−	0.256975i	0.0179918	−	0.0311628i
$69$	−0.707540			−0.0851778
$70$	−6.78608	−	11.7538i	−0.811092	−	1.40485i
$71$	−2.50000	+	1.44337i	−0.296695	+	0.171297i	−0.640957	−	0.767577i	$-0.721462\pi$
$71$	−2.50000	+	1.44337i	−0.296695	+	0.171297i	0.344262	+	0.938874i	$0.388129\pi$
$72$	2.51402	−	1.45147i	0.296280	−	0.171057i
$73$	7.13145	−	12.3520i	0.834674	−	1.44570i	−0.0596224	−	0.998221i	$-0.518990\pi$
$73$	7.13145	−	12.3520i	0.834674	−	1.44570i	0.894296	−	0.447476i	$-0.147677\pi$
$74$	−11.0204	+	6.36266i	−1.28110	+	0.739644i
$75$	13.1508			1.51853
$76$	1.09719	+	1.90039i	0.125856	+	0.217989i
$77$	−5.07419	−	8.78876i	−0.578258	−	1.00157i
$78$	3.01004	+	5.21354i	0.340820	+	0.590317i
$79$			5.67907i			0.638946i	0.947595	+	0.319473i	$0.103506\pi$
$79$			5.67907i			0.638946i	−0.947595	+	0.319473i	$0.896494\pi$
$80$	17.6941			1.97826
$81$	2.08351	−	3.60874i	0.231501	−	0.400971i
$82$	10.3587	−	5.98059i	1.14393	−	0.660446i
$83$	−6.74336	−	11.6798i	−0.740180	−	1.28203i	−0.952413	−	0.304811i	$-0.901407\pi$
$83$	−6.74336	−	11.6798i	−0.740180	−	1.28203i	0.212233	−	0.977219i	$-0.431926\pi$
$84$	−1.02315	−	0.590717i	−0.111635	−	0.0644525i
$85$	1.49815	−	2.59487i	0.162497	−	0.281454i
$86$	7.64589			0.824477
$87$	−2.79604	−	4.84289i	−0.299767	−	0.519212i
$88$	11.0536			1.17832
$89$	1.77824	+	1.02667i	0.188493	+	0.108827i	0.591277	−	0.806469i	$-0.298624\pi$
$89$	1.77824	+	1.02667i	0.188493	+	0.108827i	−0.402784	+	0.915295i	$0.631957\pi$
$90$	−5.94845	+	3.43434i	−0.627022	+	0.362011i
$91$	3.30233	−	5.71981i	0.346179	−	0.599599i
$92$	0.198115			0.0206549
$93$	1.16934	−	2.02536i	0.121255	−	0.210020i
$94$	−2.04251	−	3.53773i	−0.210669	−	0.364889i
$95$	11.0792	+	19.1897i	1.13670	+	1.96882i
$96$	2.48997	−	1.43758i	0.254131	−	0.146723i
$97$	−12.1182	+	6.99642i	−1.23041	+	0.710379i	−0.967116	−	0.254337i	$-0.918143\pi$
$97$	−12.1182	+	6.99642i	−1.23041	+	0.710379i	−0.263296	+	0.964715i	$0.584810\pi$
$98$		−	2.67444i		−	0.270159i
$99$	−4.44787	+	2.56798i	−0.447028	+	0.258092i
$100$	−3.68230			−0.368230
$101$			7.47096i			0.743388i	0.928355	+	0.371694i	$0.121223\pi$
$101$			7.47096i			0.743388i	−0.928355	+	0.371694i	$0.878777\pi$
$102$		−	1.63475i		−	0.161865i
$103$			11.4122i			1.12448i	0.826975	+	0.562239i	$0.190060\pi$
$103$			11.4122i			1.12448i	−0.826975	+	0.562239i	$0.809940\pi$
$104$	3.59691	+	6.23003i	0.352706	+	0.610904i
$105$	−10.3316	−	5.96493i	−1.00826	−	0.582118i
$106$	−7.41326	−	12.8401i	−0.720039	−	1.24714i
$107$	9.18045	−	5.30034i	0.887508	−	0.512403i	0.0143812	−	0.999897i	$-0.495422\pi$
$107$	9.18045	−	5.30034i	0.887508	−	0.512403i	0.873126	+	0.487494i	$0.162089\pi$
$108$	−1.07119	+	1.85535i	−0.103075	+	0.178531i
$109$	0.0964781	−	0.167105i	0.00924093	−	0.0160058i	−0.861368	−	0.507982i	$-0.830392\pi$
$109$	0.0964781	−	0.167105i	0.00924093	−	0.0160058i	0.870609	+	0.491976i	$0.163725\pi$
$110$	−26.1541			−2.49370
$111$	−5.59274	+	9.68692i	−0.530840	+	0.919442i
$112$	−9.17220	−	5.29557i	−0.866692	−	0.500385i
$113$	17.7587	−	10.2530i	1.67060	−	0.964521i	0.703296	−	0.710897i	$-0.251711\pi$
$113$	17.7587	−	10.2530i	1.67060	−	0.964521i	0.967303	−	0.253623i	$-0.0816223\pi$
$114$	10.4697	+	6.04469i	0.980578	+	0.566137i
$115$	2.00052			0.186550
$116$	0.782908	+	1.35604i	0.0726912	+	0.125905i
$117$	−2.89472	−	1.67127i	−0.267617	−	0.154509i
$118$	−20.2817			−1.86708
$119$	−1.55321	+	0.896749i	−0.142383	+	0.0822048i
$120$	11.2532	−	6.49701i	1.02727	−	0.593093i
$121$	−8.55637			−0.777852
$122$	2.75218	+	4.76691i	0.249171	+	0.431576i
$123$	5.25691	−	9.10523i	0.473999	−	0.820991i
$124$	−0.327422	+	0.567111i	−0.0294033	+	0.0509280i
$125$	−18.0137			−1.61119
$126$	4.11139			0.366272
$127$		−	5.43341i		−	0.482137i	−0.970508	−	0.241069i	$-0.922502\pi$
$127$		−	5.43341i		−	0.482137i	0.970508	−	0.241069i	$-0.0774979\pi$
$128$	11.6341	−	6.71696i	1.02832	−	0.593701i
$129$	5.82029	−	3.36035i	0.512448	−	0.295862i
$130$	−8.51069	−	14.7409i	−0.746437	−	1.29287i
$131$			0.253860i			0.0221798i	0.999939	+	0.0110899i	$0.00353010\pi$
$131$			0.253860i			0.0221798i	−0.999939	+	0.0110899i	$0.996470\pi$
$132$	−1.97166	+	1.13834i	−0.171611	+	0.0990795i
$133$		−	13.2633i		−	1.15008i
$134$	−7.22417	+	4.17088i	−0.624073	+	0.360309i
$135$	−10.8166	+	18.7349i	−0.930945	+	1.61244i
$136$		−	1.95348i		−	0.167510i
$137$	16.0333	+	9.25685i	1.36982	+	0.790866i	0.990905	−	0.134565i	$-0.0429636\pi$
$137$	16.0333	+	9.25685i	1.36982	+	0.790866i	0.378916	+	0.925431i	$0.376297\pi$
$138$	0.945236	−	0.545732i	0.0804638	−	0.0464558i
$139$	−6.90134			−0.585364			−0.292682	−	0.956210i	$-0.594548\pi$
$139$	−6.90134			−0.585364			−0.292682	+	0.956210i	$0.594548\pi$
$140$	2.89289	+	1.67021i	0.244494	+	0.141159i
$141$	−3.10964	−	1.79535i	−0.261879	−	0.151196i
$142$	2.22658	−	3.85655i	0.186850	−	0.323634i
$143$	−6.36374	−	11.0223i	−0.532163	−	0.921733i
$144$	−2.68002	+	4.64192i	−0.223335	+	0.386827i
$145$	7.90563	+	13.6930i	0.656527	+	1.13714i
$146$			22.0022i			1.82092i
$147$	−1.17541	−	2.03587i	−0.0969462	−	0.167916i
$148$	1.56600	−	2.71239i	0.128724	−	0.222957i
$149$	19.3998	−	11.2005i	1.58930	−	0.917580i	0.595873	−	0.803079i	$-0.296806\pi$
$149$	19.3998	−	11.2005i	1.58930	−	0.917580i	0.993423	−	0.114502i	$-0.0365271\pi$
$150$	−17.5688	+	10.1434i	−1.43449	+	0.828201i
$151$	3.33112	−	5.76967i	0.271083	−	0.469529i	−0.698056	−	0.716043i	$-0.745952\pi$
$151$	3.33112	−	5.76967i	0.271083	−	0.469529i	0.969139	+	0.246513i	$0.0792849\pi$
$152$	12.5110	+	7.22322i	1.01478	+	0.585881i
$153$	0.453832	+	0.786060i	0.0366902	+	0.0635492i
$154$	13.5577	+	7.82755i	1.09251	+	0.630762i
$155$	−3.30623	+	5.72656i	−0.265563	+	0.459968i
$156$	−1.28317	−	0.740841i	−0.102736	−	0.0593148i
$157$	−0.922836	+	1.59840i	−0.0736504	+	0.127566i	−0.900499	−	0.434859i	$-0.856798\pi$
$157$	−0.922836	+	1.59840i	−0.0736504	+	0.127566i	0.826848	+	0.562425i	$0.190132\pi$
$158$	−4.38032	−	7.58694i	−0.348480	−	0.603585i
$159$	−11.2864	−	6.51621i	−0.895071	−	0.516769i
$160$	−7.04022	+	4.06467i	−0.556578	+	0.321341i
$161$	−1.03702	−	0.598726i	−0.0817290	−	0.0471863i
$162$			6.42812i			0.505041i
$163$		−	15.4113i		−	1.20711i	−0.797321	−	0.603555i	$-0.793750\pi$
$163$		−	15.4113i		−	1.20711i	0.797321	−	0.603555i	$-0.206250\pi$
$164$	−1.47196	+	2.54951i	−0.114941	+	0.199084i
$165$	−19.9094	+	11.4947i	−1.54994	+	0.894859i
$166$	18.0176	+	10.4024i	1.39843	+	0.807386i
$167$			10.4829i			0.811191i	0.914053	+	0.405596i	$0.132936\pi$
$167$			10.4829i			0.811191i	−0.914053	+	0.405596i	$0.867064\pi$
$168$	−7.77784			−0.600073
$169$	−2.35841	+	4.08489i	−0.181417	+	0.314223i
$170$			4.62215i			0.354503i
$171$	−6.71239			−0.513309
$172$	−1.62971	+	0.940916i	−0.124265	+	0.0717442i
$173$	−19.6822	+	11.3635i	−1.49641	+	0.863955i	−0.999991	−	0.00412680i	$-0.998686\pi$
$173$	−19.6822	+	11.3635i	−1.49641	+	0.863955i	−0.496422	+	0.868081i	$0.665353\pi$
$174$	7.47074	+	4.31323i	0.566355	+	0.326985i
$175$	19.2748	+	11.1283i	1.45704	+	0.841223i
$176$	−17.6752	+	10.2048i	−1.33232	+	0.769216i
$177$	−15.4391	+	8.91374i	−1.16047	+	0.669998i
$178$	−3.16752			−0.237415
$179$		−	6.09622i		−	0.455653i	−0.973702	−	0.227826i	$-0.926838\pi$
$179$		−	6.09622i		−	0.455653i	0.973702	−	0.227826i	$-0.0731619\pi$
$180$	0.845272	−	1.46405i	0.0630028	−	0.109124i
$181$	−3.35715			−0.249535			−0.124768	−	0.992186i	$-0.539819\pi$
$181$	−3.35715			−0.249535			−0.124768	+	0.992186i	$0.539819\pi$
$182$			10.1885i			0.755221i
$183$	4.19009	+	2.41915i	0.309741	+	0.178829i
$184$	1.12953	−	0.652134i	0.0832700	−	0.0480759i
$185$	15.8131	−	27.3891i	1.16260	−	2.01369i
$186$			3.60769i			0.264529i
$187$			3.45615i			0.252739i
$188$	0.870717	+	0.502709i	0.0635036	+	0.0366638i
$189$	11.2142	−	6.47450i	0.815710	−	0.470950i
$190$	−29.6024	−	17.0910i	−2.14758	−	1.23991i
$191$	−2.39705	−	4.15182i	−0.173445	−	0.300415i	0.766177	−	0.642629i	$-0.222156\pi$
$191$	−2.39705	−	4.15182i	−0.173445	−	0.300415i	−0.939622	+	0.342214i	$0.888823\pi$
$192$	4.04035	−	6.99809i	0.291587	−	0.505044i
$193$	−20.8141	−	12.0170i	−1.49823	−	0.865003i	−0.498231	−	0.867045i	$-0.666017\pi$
$193$	−20.8141	−	12.0170i	−1.49823	−	0.865003i	−0.999998	+	0.00204195i	$0.999350\pi$
$194$	10.7928	−	18.6937i	0.774879	−	1.34213i
$195$	−12.9572	−	7.48085i	−0.927885	−	0.535715i
$196$	0.329121	+	0.570055i	0.0235087	+	0.0407182i
$197$	12.3743	+	7.14429i	0.881631	+	0.509010i	0.871196	−	0.490936i	$-0.163345\pi$
$197$	12.3743	+	7.14429i	0.881631	+	0.509010i	0.0104350	+	0.999946i	$0.496678\pi$
$198$	3.96141	−	6.86137i	0.281525	−	0.487616i
$199$	9.33402	−	5.38900i	0.661671	−	0.382016i	−0.131242	−	0.991350i	$-0.541897\pi$
$199$	9.33402	−	5.38900i	0.661671	−	0.382016i	0.792913	+	0.609334i	$0.208563\pi$
$200$	−20.9942	+	12.1210i	−1.48451	+	0.857084i
$201$	−3.66618	+	6.35001i	−0.258592	+	0.447895i
$202$	−5.76242	−	9.98081i	−0.405443	−	0.702247i
$203$		−	9.46415i		−	0.664253i
$204$	0.201175	+	0.348446i	0.0140851	+	0.0243961i
$205$	−14.8636	+	25.7444i	−1.03812	+	1.79807i
$206$	−8.80235	−	15.2461i	−0.613289	−	1.06225i
$207$	−0.303007	+	0.524824i	−0.0210605	+	0.0364778i
$208$	−11.5032	−	6.64138i	−0.797604	−	0.460497i
$209$	−22.1348	−	12.7795i	−1.53109	−	0.883977i
$210$	18.4032			1.26994
$211$	18.3047	−	10.5682i	1.26015	−	0.727547i	0.287045	−	0.957917i	$-0.407327\pi$
$211$	18.3047	−	10.5682i	1.26015	−	0.727547i	0.973103	+	0.230370i	$0.0739938\pi$
$212$	3.16026	+	1.82458i	0.217047	+	0.125312i
$213$		−	3.91430i		−	0.268204i
$214$	−8.17640	+	14.1619i	−0.558927	+	0.968090i
$215$	−16.4565	+	9.50116i	−1.12232	+	0.647974i
$216$			14.1041i			0.959660i
$217$	3.42775	−	1.97901i	0.232691	−	0.134344i
$218$			0.297658i			0.0201599i
$219$	9.66993	+	16.7488i	0.653433	+	1.13178i
$220$	5.57473	−	3.21857i	0.375848	−	0.216996i
$221$	−1.94795	+	1.12465i	−0.131033	+	0.0756520i
$222$		−	17.2550i		−	1.15808i
$223$	−7.59130			−0.508351			−0.254175	−	0.967158i	$-0.581804\pi$
$223$	−7.59130			−0.508351			−0.254175	+	0.967158i	$0.581804\pi$
$224$	4.86599			0.325122
$225$	5.63190	−	9.75473i	0.375460	−	0.650315i
$226$	−15.8165	+	27.3949i	−1.05210	+	1.82228i
$227$	−8.43537	−	14.6105i	−0.559875	−	0.969733i	−0.997506	−	0.0705780i	$-0.977516\pi$
$227$	−8.43537	−	14.6105i	−0.559875	−	0.969733i	0.437631	−	0.899155i	$-0.355818\pi$
$228$	−2.97548			−0.197056
$229$	12.9545	−	7.47927i	0.856056	−	0.494244i	−0.00663360	−	0.999978i	$-0.502112\pi$
$229$	12.9545	−	7.47927i	0.856056	−	0.494244i	0.862690	+	0.505734i	$0.168778\pi$
$230$	−2.67259	+	1.54302i	−0.176225	+	0.101744i
$231$	13.7607			0.905391
$232$	8.92731	+	5.15419i	0.586107	+	0.338389i
$233$	4.01704	+	6.95773i	0.263165	+	0.455816i	0.967081	−	0.254467i	$-0.0819002\pi$
$233$	4.01704	+	6.95773i	0.263165	+	0.455816i	−0.703916	+	0.710283i	$0.748567\pi$
$234$	5.15625			0.337075
$235$	8.79231	+	5.07624i	0.573547	+	0.331138i
$236$	4.32302	−	2.49590i	0.281405	−	0.162469i
$237$	−6.66888	−	3.85028i	−0.433191	−	0.250103i
$238$	1.38334	−	2.39602i	0.0896688	−	0.155311i
$239$	14.9655			0.968036			0.484018	−	0.875058i	$-0.339177\pi$
$239$	14.9655			0.968036			0.484018	+	0.875058i	$0.339177\pi$
$240$	−11.9962	+	20.7780i	−0.774350	+	1.34121i
$241$	−5.78054	+	10.0122i	−0.372358	+	0.644942i	−0.989928	−	0.141573i	$-0.954784\pi$
$241$	−5.78054	+	10.0122i	−0.372358	+	0.644942i	0.617570	+	0.786516i	$0.288117\pi$
$242$	11.4309	−	6.59962i	0.734804	−	0.424239i
$243$	−5.63884	−	9.76675i	−0.361731	−	0.626537i
$244$	−1.17325	−	0.677376i	−0.0751096	−	0.0433645i
$245$	3.32339	+	5.75629i	0.212324	+	0.367756i
$246$			16.2188i			1.03407i
$247$		−	16.6341i		−	1.05840i
$248$			4.31108i			0.273754i
$249$	18.2874			1.15892
$250$	24.0654	−	13.8941i	1.52203	−	0.878743i
$251$		−	26.6180i		−	1.68011i	−0.542498	−	0.840057i	$-0.682522\pi$
$251$		−	26.6180i		−	1.68011i	0.542498	−	0.840057i	$-0.317478\pi$
$252$	−0.876339	+	0.505955i	−0.0552042	+	0.0318721i
$253$	−1.99839	+	1.15377i	−0.125638	+	0.0725370i
$254$	4.19084	+	7.25875i	0.262957	+	0.455455i
$255$	2.03142	+	3.51853i	0.127213	+	0.220339i
$256$	−4.40229	+	7.62499i	−0.275143	+	0.476562i
$257$	−5.52057			−0.344364			−0.172182	−	0.985065i	$-0.555082\pi$
$257$	−5.52057			−0.344364			−0.172182	+	0.985065i	$0.555082\pi$
$258$	−5.18374	+	8.97850i	−0.322725	+	0.558977i
$259$	−16.3943	+	9.46526i	−1.01869	+	0.588143i
$260$	3.62809	+	2.09468i	0.225005	+	0.129906i
$261$	−4.78968			−0.296473
$262$	−0.195804	−	0.339143i	−0.0120968	−	0.0209523i
$263$	−0.998393			−0.0615636			−0.0307818	−	0.999526i	$-0.509800\pi$
$263$	−0.998393			−0.0615636			−0.0307818	+	0.999526i	$0.509800\pi$
$264$	−7.49411	+	12.9802i	−0.461231	+	0.798875i
$265$	31.9116	+	18.4242i	1.96031	+	1.13179i
$266$	10.2301	+	17.7191i	0.627250	+	1.08643i
$267$	−2.41121	+	1.39212i	−0.147564	+	0.0851961i
$268$	1.02655	−	1.77804i	0.0627065	−	0.108611i
$269$	32.1548			1.96051			0.980256	−	0.197731i	$-0.0633573\pi$
$269$	32.1548			1.96051			0.980256	+	0.197731i	$0.0633573\pi$
$270$		−	33.3718i		−	2.03094i
$271$	14.8165	+	25.6630i	0.900039	+	1.55891i	0.827441	+	0.561552i	$0.189796\pi$
$271$	14.8165	+	25.6630i	0.900039	+	1.55891i	0.0725978	+	0.997361i	$0.476871\pi$
$272$	1.80347	+	3.12370i	0.109351	+	0.189402i
$273$	4.47781	+	7.75580i	0.271010	+	0.469403i
$274$	−28.5596			−1.72535
$275$	37.1435	−	21.4448i	2.23984	−	1.29317i
$276$	−0.134317	+	0.232645i	−0.00808496	+	0.0140036i
$277$	5.38762	−	3.11054i	0.323711	−	0.186894i	−0.329335	−	0.944213i	$-0.606824\pi$
$277$	5.38762	−	3.11054i	0.323711	−	0.186894i	0.653045	+	0.757319i	$0.273491\pi$
$278$	9.21983	−	5.32307i	0.552968	−	0.319256i
$279$	−1.00155	−	1.73474i	−0.0599612	−	0.103856i
$280$	21.9913			1.31423
$281$	9.04824	−	15.6720i	0.539772	−	0.934913i	−0.459143	−	0.888362i	$-0.651844\pi$
$281$	9.04824	−	15.6720i	0.539772	−	0.934913i	0.998916	−	0.0465512i	$-0.0148231\pi$
$282$	5.53909			0.329848
$283$	−23.7171			−1.40984			−0.704918	−	0.709289i	$-0.749016\pi$
$283$	−23.7171			−1.40984			−0.704918	+	0.709289i	$0.749016\pi$
$284$			1.09603i			0.0650372i
$285$	−30.0457			−1.77975
$286$	17.0032	+	9.81683i	1.00542	+	0.580481i
$287$	15.4099	−	8.89689i	0.909615	−	0.525167i
$288$		−	2.46261i		−	0.145111i
$289$	−16.3892			−0.964071
$290$	−21.1230	−	12.1954i	−1.24039	−	0.716137i
$291$		−	18.9736i		−	1.11225i
$292$	−2.70763	−	4.68976i	−0.158452	−	0.274447i
$293$	−0.191321	−	0.331377i	−0.0111771	−	0.0193593i	0.860383	−	0.509648i	$-0.170225\pi$
$293$	−0.191321	−	0.331377i	−0.0111771	−	0.0193593i	−0.871560	+	0.490289i	$0.836891\pi$
$294$	3.14057	+	1.81321i	0.183162	+	0.105749i
$295$	43.6529	−	25.2030i	2.54157	−	1.46738i
$296$		−	20.6192i		−	1.19846i
$297$		−	24.9533i		−	1.44794i
$298$	−17.2781	+	29.9266i	−1.00089	+	1.73360i
$299$	−1.30057	−	0.750886i	−0.0752141	−	0.0434249i
$300$	2.49652	−	4.32409i	0.144136	−	0.249652i
$301$	11.3742			0.655600
$302$			10.2773i			0.591393i
$303$	−8.77308	−	5.06514i	−0.504000	−	0.290985i
$304$	−26.6741			−1.52987
$305$	−11.8472	−	6.83999i	−0.678369	−	0.391657i
$306$	−1.21259	−	0.700090i	−0.0693193	−	0.0400215i
$307$	15.5113	+	26.8664i	0.885278	+	1.53335i	0.845395	+	0.534142i	$0.179365\pi$
$307$	15.5113	+	26.8664i	0.885278	+	1.53335i	0.0398828	+	0.999204i	$0.487302\pi$
$308$	−3.85308			−0.219550
$309$	−13.4013	−	7.73722i	−0.762371	−	0.440155i
$310$		−	10.2005i		−	0.579350i
$311$		−	6.62025i		−	0.375400i	−0.982226	−	0.187700i	$-0.939897\pi$
$311$		−	6.62025i		−	0.375400i	0.982226	−	0.187700i	$-0.0601033\pi$
$312$	−9.75449			−0.552239
$313$	−5.28869			−0.298935			−0.149467	−	0.988767i	$-0.547756\pi$
$313$	−5.28869			−0.298935			−0.149467	+	0.988767i	$0.547756\pi$
$314$		−	2.84717i		−	0.160675i
$315$	−8.84908	+	5.10902i	−0.498589	+	0.287861i
$316$	1.86732	+	1.07810i	0.105045	+	0.0606479i
$317$	10.8180	+	6.24578i	0.607600	+	0.350798i	0.772026	−	0.635591i	$-0.219244\pi$
$317$	10.8180	+	6.24578i	0.607600	+	0.350798i	−0.164426	+	0.986389i	$0.552577\pi$
$318$	20.1041			1.12738
$319$	−15.7944	−	9.11892i	−0.884318	−	0.510561i
$320$	−11.4238	+	19.7866i	−0.638611	+	1.10611i
$321$			14.3740i			0.802280i
$322$	1.84721			0.102941
$323$	−2.25849	+	3.91182i	−0.125666	+	0.217659i
$324$	−0.791055	−	1.37015i	−0.0439475	−	0.0761193i
$325$	24.1733	+	13.9565i	1.34090	+	0.774166i
$326$	11.8869	+	20.5888i	0.658356	+	1.14031i
$327$	0.130820	+	0.226587i	0.00723436	+	0.0125303i
$328$			19.3810i			1.07014i
$329$	−3.03849	−	5.26282i	−0.167517	−	0.290148i
$330$	17.7319	−	30.7126i	0.976110	−	1.69067i
$331$	10.0495	+	5.80207i	0.552369	+	0.318910i	0.750077	−	0.661351i	$-0.230016\pi$
$331$	10.0495	+	5.80207i	0.552369	+	0.318910i	−0.197708	+	0.980261i	$0.563350\pi$
$332$	−5.12057			−0.281028
$333$	4.79024	+	8.29693i	0.262503	+	0.454669i
$334$	−8.08556	−	14.0046i	−0.442422	−	0.766298i
$335$	10.3659	−	17.9542i	0.566348	−	0.980944i
$336$	12.4371	−	7.18056i	0.678499	−	0.391731i
$337$	5.10214	+	8.83717i	0.277931	+	0.481391i	0.970870	−	0.239605i	$-0.0770179\pi$
$337$	5.10214	+	8.83717i	0.277931	+	0.481391i	−0.692939	+	0.720996i	$0.743685\pi$
$338$		−	7.27627i		−	0.395777i
$339$			27.8052i			1.51017i
$340$	−0.568810	−	0.985208i	−0.0308481	−	0.0534304i
$341$		−	7.62728i		−	0.413040i
$342$	8.96740	−	5.17733i	0.484901	−	0.279958i
$343$		−	20.0425i		−	1.08219i
$344$	−6.19441	+	10.7290i	−0.333980	+	0.578471i
$345$	−1.35631	+	2.34919i	−0.0730212	+	0.126476i
$346$	17.5296	−	30.3622i	0.942399	−	1.63228i
$347$	−25.0292	+	14.4506i	−1.34364	+	0.775748i	−0.987339	−	0.158625i	$-0.949294\pi$
$347$	−25.0292	+	14.4506i	−1.34364	+	0.775748i	−0.356296	+	0.934373i	$0.615961\pi$
$348$	−2.12317			−0.113814
$349$	−13.7967	+	12.5956i	−0.738522	+	0.674230i
$349$	−13.7967	+	12.5956i	−0.738522	+	0.674230i
$350$	−34.3336			−1.83521
$351$	14.0641	−	8.11992i	0.750687	−	0.433409i
$352$	4.68848	−	8.12069i	0.249897	−	0.432834i
$353$	−8.81937	+	15.2756i	−0.469408	+	0.813038i	−0.999388	−	0.0349720i	$-0.988866\pi$
$353$	−8.81937	+	15.2756i	−0.469408	+	0.813038i	0.529981	+	0.848010i	$0.322199\pi$
$354$	13.7505	−	23.8166i	0.730831	−	1.26584i
$355$			11.0674i			0.587398i
$356$	0.675153	−	0.389800i	0.0357830	−	0.0206594i
$357$		−	2.43190i		−	0.128710i
$358$	4.70207	+	8.14423i	0.248512	+	0.430436i
$359$			14.6783i			0.774693i	0.921934	+	0.387346i	$0.126608\pi$
$359$			14.6783i			0.774693i	−0.921934	+	0.387346i	$0.873392\pi$
$360$		−	11.1295i		−	0.586576i
$361$	−7.20206	−	12.4743i	−0.379056	−	0.656544i
$362$	4.48498	−	2.58941i	0.235725	−	0.136096i
$363$	5.80103	−	10.0477i	0.304475	−	0.527366i
$364$	−1.25381	−	2.17167i	−0.0657176	−	0.113826i
$365$	−27.3411	−	47.3561i	−1.43110	−	2.47873i
$366$	−7.46366			−0.390132
$367$	23.6274	+	13.6413i	1.23334	+	0.712070i	0.967725	−	0.252009i	$-0.0810912\pi$
$367$	23.6274	+	13.6413i	1.23334	+	0.712070i	0.265617	+	0.964079i	$0.414424\pi$
$368$	−1.20411	+	2.08558i	−0.0627685	+	0.108718i
$369$	−4.50259	−	7.79871i	−0.234395	−	0.405985i
$370$			48.7872i			2.53633i
$371$	−11.0282	−	19.1013i	−0.572553	−	0.991692i
$372$	−0.443969	−	0.768976i	−0.0230187	−	0.0398696i
$373$	10.0904	+	5.82570i	0.522461	+	0.301643i	0.737941	−	0.674865i	$-0.235798\pi$
$373$	10.0904	+	5.82570i	0.522461	+	0.301643i	−0.215480	+	0.976508i	$0.569132\pi$
$374$	−2.66576	−	4.61723i	−0.137843	−	0.238751i
$375$	12.2129	−	21.1533i	0.630670	−	1.09235i
$376$	6.61905			0.341352
$377$		−	11.8694i		−	0.611303i
$378$	−9.98768	+	17.2992i	−0.513711	+	0.889774i
$379$	29.6002	+	17.0897i	1.52046	+	0.877838i	0.999709	+	0.0241293i	$0.00768135\pi$
$379$	29.6002	+	17.0897i	1.52046	+	0.877838i	0.520751	+	0.853709i	$0.325652\pi$
$380$	8.41297			0.431576
$381$	6.38041	+	3.68373i	0.326878	+	0.188723i
$382$	6.40467	+	3.69774i	0.327692	+	0.189193i
$383$	−31.4641	+	18.1658i	−1.60774	+	0.928230i	−0.617867	+	0.786283i	$0.712003\pi$
$383$	−31.4641	+	18.1658i	−1.60774	+	0.928230i	−0.989874	+	0.141947i	$0.954664\pi$
$384$			18.2158i			0.929570i
$385$	−38.9076			−1.98291
$386$	37.0753			1.88708
$387$		−	5.75634i		−	0.292611i
$388$			5.31273i			0.269713i
$389$	1.50664	+	0.869856i	0.0763894	+	0.0441035i	0.537708	−	0.843131i	$-0.319290\pi$
$389$	1.50664	+	0.869856i	0.0763894	+	0.0441035i	−0.461319	+	0.887234i	$0.652624\pi$
$390$	23.0802			1.16871
$391$	0.203903	+	0.353171i	0.0103118	+	0.0178606i
$392$	3.75289	+	2.16673i	0.189550	+	0.109437i
$393$	−0.298105	−	0.172111i	−0.0150374	−	0.00868185i
$394$	−22.0418			−1.11045
$395$	18.8558	+	10.8864i	0.948740	+	0.547755i
$396$			1.94999i			0.0979908i
$397$	−21.9355			−1.10091			−0.550455	−	0.834865i	$-0.685546\pi$
$397$	−21.9355			−1.10091			−0.550455	+	0.834865i	$0.685546\pi$
$398$	−8.31317	+	14.3988i	−0.416702	+	0.721749i
$399$	15.5750	+	8.99224i	0.779726	+	0.450175i
$400$	22.3804	−	38.7640i	1.11902	−	1.93820i
$401$			36.1062i			1.80306i	0.432721	+	0.901528i	$0.357554\pi$
$401$			36.1062i			1.80306i	−0.432721	+	0.901528i	$0.642446\pi$
$402$		−	11.3110i		−	0.564143i
$403$	4.29887	−	2.48195i	0.214142	−	0.123635i
$404$	2.45651	+	1.41827i	0.122216	+	0.0705614i
$405$	−7.98790	−	13.8355i	−0.396922	−	0.687489i
$406$	7.29979	+	12.6436i	0.362283	+	0.627492i
$407$			36.4799i			1.80824i
$408$	2.29395	+	1.32442i	0.113568	+	0.0655683i
$409$	−20.9532			−1.03607			−0.518034	−	0.855360i	$-0.673336\pi$
$409$	−20.9532			−1.03607			−0.518034	+	0.855360i	$0.673336\pi$
$410$		−	45.8576i		−	2.26475i
$411$	−21.7405	+	12.5519i	−1.07238	+	0.619138i
$412$	3.75242	+	2.16646i	0.184869	+	0.106734i
$413$	−30.1716			−1.48465
$414$		−	0.934849i		−	0.0459453i
$415$	−51.7064			−2.53817
$416$	6.10262			0.299206
$417$	4.67895	−	8.10418i	0.229129	−	0.396863i
$418$	39.4278			1.92848
$419$	−4.19287	−	7.26227i	−0.204835	−	0.354785i	0.745245	−	0.666791i	$-0.232333\pi$
$419$	−4.19287	−	7.26227i	−0.204835	−	0.354785i	−0.950080	+	0.312006i	$0.898999\pi$
$420$	−3.92263	+	2.26473i	−0.191405	+	0.110508i
$421$	−6.06534	+	3.50182i	−0.295607	+	0.170668i	−0.640468	−	0.767985i	$-0.721259\pi$
$421$	−6.06534	+	3.50182i	−0.295607	+	0.170668i	0.344861	+	0.938654i	$0.387926\pi$
$422$	−16.3028	+	28.2372i	−0.793606	+	1.37457i
$423$	−2.66344	+	1.53774i	−0.129501	+	0.0747673i
$424$	24.0238			1.16670
$425$	−3.78988	−	6.56427i	−0.183836	−	0.318414i
$426$	3.01914	+	5.22930i	0.146278	+	0.253360i
$427$	4.09422	+	7.09139i	0.198133	+	0.343176i
$428$		−	4.02481i		−	0.194546i
$429$	17.2579			0.833219
$430$	14.6567	−	25.3861i	0.706808	−	1.22423i
$431$	−3.86176	+	2.22959i	−0.186015	+	0.107396i	−0.590115	−	0.807319i	$-0.700918\pi$
$431$	−3.86176	+	2.22959i	−0.186015	+	0.107396i	0.404101	+	0.914714i	$0.367584\pi$
$432$	−13.0210	−	22.5530i	−0.626472	−	1.08508i
$433$	−27.8176	−	16.0605i	−1.33683	−	0.771818i	−0.350492	−	0.936566i	$-0.613986\pi$
$433$	−27.8176	−	16.0605i	−1.33683	−	0.771818i	−0.986336	+	0.164748i	$0.947319\pi$
$434$	−3.05286	+	5.28771i	−0.146542	+	0.253818i
$435$	−21.4393			−1.02794
$436$	−0.0366303	−	0.0634455i	−0.00175427	−	0.00303849i
$437$	−3.01582			−0.144266
$438$	−25.8370	−	14.9170i	−1.23454	−	0.712763i
$439$	−14.6823	+	8.47684i	−0.700749	+	0.404578i	−0.807626	−	0.589695i	$-0.799248\pi$
$439$	−14.6823	+	8.47684i	−0.700749	+	0.404578i	0.106877	+	0.994272i	$0.465915\pi$
$440$	21.1891	−	36.7006i	1.01015	−	1.74963i
$441$	−2.01350			−0.0958809
$442$	1.73490	−	3.00494i	0.0825209	−	0.142930i
$443$	−13.6129	−	23.5782i	−0.646767	−	1.12023i	−0.983890	−	0.178773i	$-0.942787\pi$
$443$	−13.6129	−	23.5782i	−0.646767	−	1.12023i	0.337123	−	0.941460i	$-0.390546\pi$
$444$	2.12342	+	3.67788i	0.100773	+	0.174544i
$445$	6.81755	−	3.93611i	0.323183	−	0.186590i
$446$	10.1416	−	5.85524i	0.480218	−	0.277254i
$447$			30.3747i			1.43668i
$448$	11.8437	−	6.83796i	0.559562	−	0.323063i
$449$	0.221195			0.0104388			0.00521942	−	0.999986i	$-0.498339\pi$
$449$	0.221195			0.0104388			0.00521942	+	0.999986i	$0.498339\pi$
$450$			17.3757i			0.819101i
$451$		−	34.2894i		−	1.61462i
$452$		−	7.78561i		−	0.366204i
$453$	4.51685	+	7.82342i	0.212220	+	0.367576i
$454$	22.5384	+	13.0126i	1.05778	+	0.610710i
$455$	−12.6607	−	21.9290i	−0.593544	−	1.02805i
$456$	−16.9643	+	9.79436i	−0.794428	+	0.458663i
$457$	5.43113	−	9.40700i	0.254058	−	0.440041i	−0.710582	−	0.703615i	$-0.751568\pi$
$457$	5.43113	−	9.40700i	0.254058	−	0.440041i	0.964639	+	0.263574i	$0.0849014\pi$
$458$	−11.5377	+	19.9838i	−0.539120	+	0.933783i
$459$	−4.40993			−0.205838
$460$	0.379774	−	0.657787i	0.0177070	−	0.0306695i
$461$	9.21706	+	5.32147i	0.429281	+	0.247846i	0.699040	−	0.715082i	$-0.253611\pi$
$461$	9.21706	+	5.32147i	0.429281	+	0.247846i	−0.269759	+	0.962928i	$0.586944\pi$
$462$	−18.3836	+	10.6138i	−0.855284	+	0.493799i
$463$	−6.31638	−	3.64676i	−0.293547	−	0.169479i	0.345993	−	0.938237i	$-0.387542\pi$
$463$	−6.31638	−	3.64676i	−0.293547	−	0.169479i	−0.639540	+	0.768758i	$0.720875\pi$
$464$	−19.0335			−0.883609
$465$	−4.48310	−	7.76495i	−0.207899	−	0.360091i
$466$	−10.7331	−	6.19677i	−0.497202	−	0.287060i
$467$	14.0560			0.650434			0.325217	−	0.945639i	$-0.394563\pi$
$467$	14.0560			0.650434			0.325217	+	0.945639i	$0.394563\pi$
$468$	−1.09905	+	0.634537i	−0.0508036	+	0.0293315i
$469$	−10.7469	+	6.20471i	−0.496244	+	0.286507i
$470$	−15.6614			−0.722408
$471$	−1.25132	−	2.16736i	−0.0576580	−	0.0998665i
$472$	16.4315	−	28.4601i	0.756319	−	1.30998i
$473$	10.9593	−	18.9821i	0.503910	−	0.872797i
$474$	11.8790			0.545622
$475$	56.0541			2.57194
$476$			0.680946i			0.0312111i
$477$	−9.66692	+	5.58120i	−0.442618	+	0.255545i
$478$	−19.9931	+	11.5430i	−0.914463	+	0.527965i
$479$	14.8364	+	25.6973i	0.677891	+	1.17414i	0.975615	+	0.219490i	$0.0704392\pi$
$479$	14.8364	+	25.6973i	0.677891	+	1.17414i	−0.297724	+	0.954652i	$0.596227\pi$
$480$		−	11.0230i		−	0.503130i
$481$	−20.5607	+	11.8708i	−0.937489	+	0.541260i
$482$		−	17.8344i		−	0.812333i
$483$	1.40616	−	0.811846i	0.0639824	−	0.0369403i
$484$	−1.62432	+	2.81340i	−0.0738327	+	0.127882i
$485$			53.6467i			2.43597i
$486$	15.0664	+	8.69858i	0.683425	+	0.394575i
$487$	−35.5837	+	20.5443i	−1.61245	+	0.930950i	−0.623653	+	0.781701i	$0.714352\pi$
$487$	−35.5837	+	20.5443i	−1.61245	+	0.930950i	−0.988800	+	0.149249i	$0.952315\pi$
$488$	−8.91885			−0.403737
$489$	18.0974	+	10.4485i	0.818393	+	0.472499i
$490$	−8.87976	−	5.12673i	−0.401147	−	0.231602i
$491$	1.02974	−	1.78356i	0.0464715	−	0.0804910i	−0.841854	−	0.539705i	$-0.818536\pi$
$491$	1.02974	−	1.78356i	0.0464715	−	0.0804910i	0.888326	+	0.459214i	$0.151869\pi$
$492$	−1.99591	−	3.45703i	−0.0899828	−	0.155855i
$493$	−1.61156	+	2.79131i	−0.0725811	+	0.125714i
$494$	12.8300	+	22.2222i	0.577250	+	0.999826i
$495$			19.6906i			0.885026i
$496$	−3.98002	−	6.89361i	−0.178708	−	0.309532i
$497$	3.31232	−	5.73710i	0.148578	−	0.257344i
$498$	−24.4310	+	14.1052i	−1.09478	+	0.632071i
$499$	−9.71012	+	5.60614i	−0.434685	+	0.250965i	−0.701340	−	0.712827i	$-0.747415\pi$
$499$	−9.71012	+	5.60614i	−0.434685	+	0.250965i	0.266656	+	0.963792i	$0.414081\pi$
$500$	−3.41967	+	5.92305i	−0.152932	+	0.264887i
$501$	−12.3100	−	7.10717i	−0.549969	−	0.317525i
$502$	20.5307	+	35.5603i	0.916331	+	1.58713i
$503$	−3.43061	−	1.98067i	−0.152964	−	0.0883135i	0.421565	−	0.906798i	$-0.361481\pi$
$503$	−3.43061	−	1.98067i	−0.152964	−	0.0883135i	−0.574528	+	0.818485i	$0.694814\pi$
$504$	−3.33089	+	5.76928i	−0.148370	+	0.256984i
$505$	24.8053	+	14.3213i	1.10382	+	0.637291i
$506$	1.77983	−	3.08276i	0.0791231	−	0.137045i
$507$	−3.19790	−	5.53893i	−0.142024	−	0.245993i
$508$	−1.78655	−	1.03146i	−0.0792653	−	0.0457638i
$509$	31.1846	−	18.0044i	1.38223	−	0.798032i	0.389808	−	0.920896i	$-0.372541\pi$
$509$	31.1846	−	18.0044i	1.38223	−	0.798032i	0.992423	+	0.122864i	$0.0392080\pi$
$510$	−5.42775	−	3.13372i	−0.240345	−	0.138763i
$511$			32.7311i			1.44794i
$512$			13.2857i			0.587151i
$513$	16.3062	−	28.2432i	0.719937	−	1.24697i
$514$	7.37519	−	4.25807i	0.325306	−	0.187815i
$515$	37.8912	+	21.8765i	1.66968	+	0.963992i
$516$		−	2.55168i		−	0.112331i
$517$	−11.7106			−0.515032
$518$	14.6013	−	25.2902i	0.641544	−	1.11119i
$519$		−	30.8169i		−	1.35271i
$520$	27.5802			1.20947
$521$	−12.5660	+	7.25496i	−0.550525	+	0.317846i	−0.749334	−	0.662193i	$-0.769626\pi$
$521$	−12.5660	+	7.25496i	−0.550525	+	0.317846i	0.198809	+	0.980038i	$0.436293\pi$
$522$	6.39876	−	3.69432i	0.280066	−	0.161696i
$523$	11.0735	+	6.39327i	0.484209	+	0.279558i	0.722169	−	0.691717i	$-0.243145\pi$
$523$	11.0735	+	6.39327i	0.484209	+	0.279558i	−0.237960	+	0.971275i	$0.576479\pi$
$524$	0.0834711	+	0.0481920i	0.00364645	+	0.00210528i
$525$	−26.1358	+	15.0895i	−1.14066	+	0.658561i
$526$	1.33380	−	0.770070i	0.0581565	−	0.0335767i
$527$	−1.34795			−0.0587176
$528$		−	27.6745i		−	1.20438i
$529$	11.3639	−	19.6828i	0.494081	−	0.855773i
$530$	−56.8429			−2.46910
$531$			15.2694i			0.662636i
$532$	−4.36109	−	2.51788i	−0.189077	−	0.109164i
$533$	19.3261	−	11.1579i	0.837106	−	0.483304i
$534$	2.14750	−	3.71959i	0.0929316	−	0.160962i
$535$		−	40.6416i		−	1.75709i
$536$		−	13.5164i		−	0.583818i
$537$	7.15874	+	4.13310i	0.308922	+	0.178356i
$538$	−42.9571	+	24.8013i	−1.85201	+	1.06926i
$539$	−6.63971	−	3.83344i	−0.285993	−	0.165118i
$540$	4.10679	+	7.11317i	0.176728	+	0.306102i
$541$	5.60681	−	9.71128i	0.241056	−	0.417521i	−0.719960	−	0.694016i	$-0.755840\pi$
$541$	5.60681	−	9.71128i	0.241056	−	0.417521i	0.961015	+	0.276495i	$0.0891731\pi$
$542$	−39.5882	−	22.8562i	−1.70046	−	0.981760i
$543$	2.27607	−	3.94228i	0.0976757	−	0.169179i
$544$	−1.43515	−	0.828583i	−0.0615315	−	0.0355252i
$545$	−0.369885	−	0.640659i	−0.0158441	−	0.0274428i
$546$	−11.9643	−	6.90756i	−0.512023	−	0.295616i
$547$	−15.8710	+	27.4894i	−0.678594	+	1.17536i	0.296810	+	0.954937i	$0.404077\pi$
$547$	−15.8710	+	27.4894i	−0.678594	+	1.17536i	−0.975404	+	0.220424i	$0.929256\pi$
$548$	6.08745	−	3.51459i	0.260043	−	0.150136i
$549$	3.58885	−	2.07203i	0.153169	−	0.0884319i
$550$	−33.0811	+	57.2982i	−1.41058	+	2.44320i
$551$	−11.9179	−	20.6424i	−0.507719	−	0.879395i
$552$			1.76853i			0.0752735i
$553$	−6.51629	−	11.2865i	−0.277101	−	0.479952i
$554$	−4.79839	+	8.31105i	−0.203864	+	0.353103i
$555$	21.4419	+	37.1384i	0.910156	+	1.57644i
$556$	−1.31013	+	2.26921i	−0.0555620	+	0.0962361i
$557$	33.8817	+	19.5616i	1.43561	+	0.828852i	0.997541	−	0.0700877i	$-0.0223279\pi$
$557$	33.8817	+	19.5616i	1.43561	+	0.828852i	0.438073	+	0.898940i	$0.355661\pi$
$558$	2.67604	+	1.54501i	0.113286	+	0.0654055i
$559$	14.2649			0.603339
$560$	−35.1650	+	20.3025i	−1.48599	+	0.857939i
$561$	−4.05852	−	2.34319i	−0.171351	−	0.0989295i
$562$			27.9160i			1.17756i
$563$	1.88462	−	3.26426i	0.0794274	−	0.137572i	−0.823576	−	0.567206i	$-0.808024\pi$
$563$	1.88462	−	3.26426i	0.0794274	−	0.137572i	0.903003	+	0.429634i	$0.141357\pi$
$564$	−1.18065	+	0.681650i	−0.0497145	+	0.0287027i
$565$		−	78.6173i		−	3.30746i
$566$	31.6848	−	18.2932i	1.33181	−	0.768922i
$567$			9.56264i			0.401593i
$568$	3.60778	+	6.24886i	0.151379	+	0.262196i
$569$	−2.63250	+	1.51988i	−0.110360	+	0.0637166i	−0.554164	−	0.832407i	$-0.686962\pi$
$569$	−2.63250	+	1.51988i	−0.110360	+	0.0637166i	0.443804	+	0.896124i	$0.353629\pi$
$570$	40.1395	−	23.1746i	1.68126	−	0.970675i
$571$		−	11.2026i		−	0.468814i	−0.972139	−	0.234407i	$-0.924685\pi$
$571$		−	11.2026i		−	0.468814i	0.972139	−	0.234407i	$-0.0753149\pi$
$572$	−4.83230			−0.202049
$573$	6.50059			0.271566
$574$	−13.7245	+	23.7715i	−0.572850	+	0.992205i
$575$	2.53037	−	4.38272i	0.105524	−	0.182772i
$576$	−3.46060	−	5.99393i	−0.144192	−	0.249747i
$577$	−20.1057			−0.837010			−0.418505	−	0.908215i	$-0.637446\pi$
$577$	−20.1057			−0.837010			−0.418505	+	0.908215i	$0.637446\pi$
$578$	21.8951	−	12.6412i	0.910717	−	0.525803i
$579$	28.2229	−	16.2945i	1.17290	−	0.677177i
$580$	6.00314			0.249267
$581$	26.8034	+	15.4749i	1.11199	+	0.642009i
$582$	14.6346	+	25.3478i	0.606622	+	1.05070i
$583$	−42.5035			−1.76031
$584$	−30.8745	−	17.8254i	−1.27760	−	0.737620i
$585$	−11.0980	+	6.40742i	−0.458845	+	0.264914i
$586$	0.511189	+	0.295135i	0.0211170	+	0.0121919i
$587$	9.39689	−	16.2759i	0.387851	−	0.671778i	−0.604309	−	0.796750i	$-0.706551\pi$
$587$	9.39689	−	16.2759i	0.387851	−	0.671778i	0.992160	+	0.124972i	$0.0398841\pi$
$588$	−0.892547			−0.0368080
$589$	4.98420	−	8.63289i	0.205370	−	0.355712i
$590$	−38.8787	+	67.3398i	−1.60061	+	2.77234i
$591$	−16.7790	+	9.68734i	−0.690194	+	0.398484i
$592$	19.0358	+	32.9709i	0.782365	+	1.35510i
$593$	24.5941	+	14.1994i	1.00996	+	0.583099i	0.911179	−	0.412010i	$-0.135173\pi$
$593$	24.5941	+	14.1994i	1.00996	+	0.583099i	0.0987782	+	0.995109i	$0.468507\pi$
$594$	19.2467	+	33.3363i	0.789702	+	1.36780i
$595$			6.87604i			0.281890i
$596$		−	8.50509i		−	0.348382i
$597$			14.6145i			0.598131i
$598$	2.31666			0.0947354
$599$	9.52376	−	5.49854i	0.389130	−	0.224664i	−0.292653	−	0.956219i	$-0.594538\pi$
$599$	9.52376	−	5.49854i	0.389130	−	0.224664i	0.681783	+	0.731554i	$0.261205\pi$
$600$		−	32.8711i		−	1.34196i
$601$	8.58109	−	4.95430i	0.350030	−	0.202090i	−0.314668	−	0.949202i	$-0.601893\pi$
$601$	8.58109	−	4.95430i	0.350030	−	0.202090i	0.664699	+	0.747112i	$0.268560\pi$
$602$	−15.1954	+	8.77305i	−0.619317	+	0.357563i
$603$	3.14012	+	5.43884i	0.127875	+	0.221487i
$604$	−1.26474	−	2.19060i	−0.0514617	−	0.0891342i
$605$	−16.4020	+	28.4091i	−0.666837	+	1.15500i
$606$	15.6272			0.634810
$607$	4.22926	−	7.32529i	0.171660	−	0.297324i	−0.767340	−	0.641240i	$-0.778420\pi$
$607$	4.22926	−	7.32529i	0.171660	−	0.297324i	0.939000	+	0.343916i	$0.111754\pi$
$608$	10.6133	−	6.12757i	0.430424	−	0.248506i
$609$	11.1137	+	6.41648i	0.450349	+	0.260009i
$610$	21.1030			0.854436
$611$	−3.81069	−	6.60030i	−0.154164	−	0.267020i
$612$	0.344617			0.0139303
$613$	18.0523	−	31.2675i	0.729125	−	1.26288i	−0.228128	−	0.973631i	$-0.573260\pi$
$613$	18.0523	−	31.2675i	0.729125	−	1.26288i	0.957253	−	0.289251i	$-0.0934063\pi$
$614$	−41.4446	−	23.9281i	−1.67257	−	0.965658i
$615$	−20.1543	−	34.9083i	−0.812700	−	1.40764i
$616$	−21.9679	+	12.6832i	−0.885112	+	0.511020i
$617$	−13.3566	+	23.1344i	−0.537718	+	0.931355i	0.461308	+	0.887240i	$0.347380\pi$
$617$	−13.3566	+	23.1344i	−0.537718	+	0.931355i	−0.999026	+	0.0441153i	$0.985953\pi$
$618$	23.8712			0.960239
$619$		−	39.6504i		−	1.59368i	−0.604187	−	0.796842i	$-0.706502\pi$
$619$		−	39.6504i		−	1.59368i	0.604187	−	0.796842i	$-0.293498\pi$
$620$	1.25529	+	2.17423i	0.0504137	+	0.0873192i
$621$	−1.47217	−	2.54988i	−0.0590763	−	0.102323i
$622$	5.10626	+	8.84431i	0.204743	+	0.354624i
$623$	−4.71208			−0.188786
$624$	15.5978	−	9.00541i	0.624413	−	0.360505i
$625$	−10.2847	+	17.8136i	−0.411387	+	0.712544i
$626$	7.06542	−	4.07922i	0.282391	−	0.163038i
$627$	30.0137	−	17.3284i	1.19863	−	0.692031i
$628$	0.350378	+	0.606872i	0.0139816	+	0.0242168i
$629$	6.44700			0.257059
$630$	7.88127	−	13.6508i	0.313997	−	0.543859i
$631$	5.44631			0.216814			0.108407	−	0.994107i	$-0.465425\pi$
$631$	5.44631			0.216814			0.108407	+	0.994107i	$0.465425\pi$
$632$	14.1951			0.564651
$633$			28.6601i			1.13914i
$634$	−19.2697			−0.765299
$635$	−18.0402	−	10.4155i	−0.715903	−	0.413327i
$636$	−4.28517	+	2.47404i	−0.169918	+	0.0981021i
$637$		−	4.98968i		−	0.197698i
$638$	28.1340			1.11384
$639$	−2.90347	−	1.67632i	−0.114859	−	0.0663141i
$640$		−	51.5039i		−	2.03587i
$641$	10.3694	+	17.9603i	0.409567	+	0.709390i	0.994841	−	0.101445i	$-0.0323466\pi$
$641$	10.3694	+	17.9603i	0.409567	+	0.709390i	−0.585274	+	0.810835i	$0.699013\pi$
$642$	−11.0868	−	19.2029i	−0.437562	−	0.757880i
$643$	30.0638	+	17.3573i	1.18560	+	0.684506i	0.957303	−	0.289085i	$-0.0933511\pi$
$643$	30.0638	+	17.3573i	1.18560	+	0.684506i	0.228297	+	0.973592i	$0.426684\pi$
$644$	−0.393732	+	0.227321i	−0.0155152	+	0.00895771i
$645$		−	25.7663i		−	1.01455i
$646$		−	6.96798i		−	0.274151i
$647$	−19.6993	+	34.1203i	−0.774461	+	1.34141i	0.160636	+	0.987014i	$0.448646\pi$
$647$	−19.6993	+	34.1203i	−0.774461	+	1.34141i	−0.935097	+	0.354392i	$0.884688\pi$
$648$	−9.02022	−	5.20782i	−0.354348	−	0.204583i
$649$	−29.0709	+	50.3524i	−1.14113	+	1.97650i
$650$	−43.0591			−1.68892
$651$			5.36690i			0.210345i
$652$	−5.06737	−	2.92565i	−0.198454	−	0.114577i
$653$	−4.02509			−0.157514			−0.0787570	−	0.996894i	$-0.525095\pi$
$653$	−4.02509			−0.157514			−0.0787570	+	0.996894i	$0.525095\pi$
$654$	−0.349537	−	0.201805i	−0.0136680	−	0.00789122i
$655$	0.842872	+	0.486633i	0.0329337	+	0.0190143i
$656$	−17.8927	−	30.9910i	−0.698592	−	1.21000i
$657$	16.5648			0.646253
$658$	8.11852	+	4.68723i	0.316493	+	0.182727i
$659$			39.6989i			1.54645i	0.634132	+	0.773225i	$0.281358\pi$
$659$			39.6989i			1.54645i	−0.634132	+	0.773225i	$0.718642\pi$
$660$			8.72848i			0.339755i
$661$	−6.32135			−0.245872			−0.122936	−	0.992415i	$-0.539231\pi$
$661$	−6.32135			−0.245872			−0.122936	+	0.992415i	$0.539231\pi$
$662$	−17.9008			−0.695733
$663$		−	3.04994i		−	0.118450i
$664$	−29.1943	+	16.8553i	−1.13296	+	0.654114i
$665$	−44.0373	−	25.4250i	−1.70769	−	0.985938i
$666$	−12.7990	−	7.38951i	−0.495952	−	0.286338i
$667$	−2.15196			−0.0833243
$668$	3.44686	+	1.99005i	0.133363	+	0.0769972i
$669$	5.14673	−	8.91439i	0.198984	−	0.344650i
$670$			31.9812i			1.23554i
$671$	15.7795			0.609159
$672$	−3.29903	+	5.71408i	−0.127263	+	0.220426i
$673$	−0.158321	−	0.274221i	−0.00610284	−	0.0105704i	0.862958	−	0.505276i	$-0.168609\pi$
$673$	−0.158321	−	0.274221i	−0.00610284	−	0.0105704i	−0.869061	+	0.494705i	$0.835276\pi$
$674$	−13.6324	−	7.87066i	−0.525100	−	0.303167i
$675$	27.3628	+	47.3938i	1.05320	+	1.82419i
$676$	0.895430	+	1.55093i	0.0344396	+	0.0596512i
$677$		−	0.0901525i		−	0.00346484i	−0.999998	−	0.00173242i	$-0.999449\pi$
$677$		−	0.0901525i		−	0.00346484i	0.999998	−	0.00173242i	$-0.000551447\pi$
$678$	−21.4464	−	37.1463i	−0.823645	−	1.42659i
$679$	16.0557	−	27.8092i	0.616160	−	1.06722i
$680$	−6.48600	−	3.74470i	−0.248727	−	0.143603i
$681$	22.8760			0.876609
$682$	5.88300	+	10.1896i	0.225272	+	0.390182i
$683$	−7.91333	−	13.7063i	−0.302795	−	0.524456i	0.673973	−	0.738756i	$-0.264586\pi$
$683$	−7.91333	−	13.7063i	−0.302795	−	0.524456i	−0.976768	+	0.214300i	$0.931253\pi$
$684$	−1.27426	+	2.20709i	−0.0487226	+	0.0843901i
$685$	61.4698	−	35.4896i	2.34864	−	1.35599i
$686$	15.4589	+	26.7757i	0.590225	+	1.02230i
$687$			20.2831i			0.773849i
$688$		−	22.8749i		−	0.872098i
$689$	−13.8308	−	23.9557i	−0.526913	−	0.912640i
$690$		−	4.18453i		−	0.159302i
$691$	12.0784	−	6.97347i	0.459484	−	0.265283i	−0.252343	−	0.967638i	$-0.581201\pi$
$691$	12.0784	−	6.97347i	0.459484	−	0.265283i	0.711827	+	0.702355i	$0.247868\pi$
$692$			8.62890i			0.328022i
$693$	5.89310	−	10.2072i	0.223860	−	0.387738i
$694$	22.2918	−	38.6105i	0.846184	−	1.46563i
$695$	−13.2294	+	22.9140i	−0.501821	+	0.869179i
$696$	−12.1050	+	6.98884i	−0.458840	+	0.264911i
$697$	−6.05987			−0.229534
$698$	8.71655	−	27.4687i	0.329926	−	1.03970i
$699$	−10.8939			−0.412044
$700$	7.31817	−	4.22515i	0.276601	−	0.159696i
$701$	17.3651	−	30.0772i	0.655869	−	1.13600i	−0.325806	−	0.945437i	$-0.605636\pi$
$701$	17.3651	−	30.0772i	0.655869	−	1.13600i	0.981675	−	0.190562i	$-0.0610310\pi$
$702$	−12.5259	+	21.6956i	−0.472761	+	0.818846i
$703$	−23.8386	+	41.2896i	−0.899088	+	1.55727i
$704$		−	26.3541i		−	0.993258i
$705$	−11.9220	+	6.88315i	−0.449007	+	0.259235i
$706$		−	27.2099i		−	1.02406i
$707$	−8.57233	−	14.8477i	−0.322396	−	0.558406i
$708$			6.76864i			0.254381i
$709$			33.5970i			1.26176i	0.775880	+	0.630881i	$0.217306\pi$
$709$			33.5970i			1.26176i	−0.775880	+	0.630881i	$0.782694\pi$
$710$	−8.53641	−	14.7855i	−0.320366	−	0.554890i
$711$	−5.71196	+	3.29780i	−0.214215	+	0.123677i
$712$	2.56620	−	4.44479i	0.0961725	−	0.166576i
$713$	−0.449988	−	0.779403i	−0.0168522	−	0.0291889i
$714$	1.87575	+	3.24889i	0.0701981	+	0.121587i
$715$	−48.7955			−1.82485
$716$	−2.00449	−	1.15729i	−0.0749111	−	0.0432500i
$717$	−10.1463	+	17.5738i	−0.378919	+	0.656306i
$718$	−11.3215	−	19.6095i	−0.422516	−	0.731820i
$719$		−	32.4770i		−	1.21119i	−0.795774	−	0.605593i	$-0.792936\pi$
$719$		−	32.4770i		−	1.21119i	0.795774	−	0.605593i	$-0.207064\pi$
$720$	10.2748	+	17.7965i	0.382920	+	0.663238i
$721$	−13.0946	−	22.6805i	−0.487669	−	0.844667i
$722$	19.2431	+	11.1100i	0.716156	+	0.413473i
$723$	−7.83816	−	13.5761i	−0.291504	−	0.504900i
$724$	−0.637313	+	1.10386i	−0.0236856	+	0.0410246i
$725$	39.9978			1.48548
$726$			17.8976i			0.664241i
$727$	19.9239	−	34.5092i	0.738937	−	1.27988i	−0.214037	−	0.976826i	$-0.568661\pi$
$727$	19.9239	−	34.5092i	0.738937	−	1.27988i	0.952974	−	0.303051i	$-0.0980053\pi$
$728$	−14.2969	−	8.25433i	−0.529879	−	0.305926i
$729$	27.7931			1.02937
$730$	73.0525	+	42.1769i	2.70379	+	1.56104i
$731$	−3.35466	−	1.93681i	−0.124076	−	0.0716355i
$732$	1.59087	−	0.918491i	0.0588003	−	0.0339484i
$733$			15.1347i			0.559013i	0.960144	+	0.279507i	$0.0901709\pi$
$733$			15.1347i			0.559013i	−0.960144	+	0.279507i	$0.909829\pi$
$734$	−42.0867			−1.55345
$735$	−9.01274			−0.332440
$736$		−	1.10643i		−	0.0407835i
$737$			23.9135i			0.880864i
$738$	12.0304	+	6.94578i	0.442847	+	0.255678i
$739$	−18.8494			−0.693388			−0.346694	−	0.937978i	$-0.612696\pi$
$739$	−18.8494			−0.693388			−0.346694	+	0.937978i	$0.612696\pi$
$740$	−6.00384	−	10.3990i	−0.220706	−	0.382273i
$741$	19.5332	+	11.2775i	0.717571	+	0.414290i
$742$	29.4661	+	17.0123i	1.08173	+	0.624539i
$743$	−23.9464			−0.878508			−0.439254	−	0.898363i	$-0.644757\pi$
$743$	−23.9464			−0.878508			−0.439254	+	0.898363i	$0.644757\pi$
$744$	−5.06247	−	2.92282i	−0.185599	−	0.107156i
$745$		−	85.8825i		−	3.14649i
$746$	−17.9737			−0.658062
$747$	7.83166	−	13.5648i	0.286545	−	0.496311i
$748$	1.13641	+	0.656106i	0.0415512	+	0.0239896i
$749$	−12.1634	+	21.0677i	−0.444442	+	0.769796i
$750$			37.6797i			1.37587i
$751$			19.9244i			0.727053i	0.931584	+	0.363526i	$0.118427\pi$
$751$			19.9244i			0.727053i	−0.931584	+	0.363526i	$0.881573\pi$
$752$	−10.5841	+	6.11076i	−0.385964	+	0.222836i
$753$	31.2573	+	18.0464i	1.13908	+	0.657647i
$754$	9.15495	+	15.8568i	0.333404	+	0.577472i
$755$	−12.7711	−	22.1202i	−0.464788	−	0.805036i
$756$		−	4.91640i		−	0.178808i
$757$	−26.3405	−	15.2077i	−0.957361	−	0.552733i	−0.0620011	−	0.998076i	$-0.519748\pi$
$757$	−26.3405	−	15.2077i	−0.957361	−	0.552733i	−0.895360	+	0.445344i	$0.853082\pi$
$758$	−52.7257			−1.91509
$759$		−	3.12892i		−	0.113573i
$760$	47.9655	−	27.6929i	1.73989	−	1.00453i
$761$	19.9378	+	11.5111i	0.722744	+	0.417276i	0.815762	−	0.578388i	$-0.196318\pi$
$761$	19.9378	+	11.5111i	0.722744	+	0.417276i	−0.0930181	+	0.995664i	$0.529651\pi$
$762$	−11.3652			−0.411717
$763$			0.442804i			0.0160306i
$764$	−1.82020			−0.0658525
$765$	3.47987			0.125815
$766$	28.0229	−	48.5372i	1.01251	−	1.75372i
$767$	−37.8393			−1.36630
$768$	−5.96931	−	10.3391i	−0.215399	−	0.373082i
$769$	−19.8021	+	11.4327i	−0.714081	+	0.412275i	−0.812570	−	0.582863i	$-0.801932\pi$
$769$	−19.8021	+	11.4327i	−0.714081	+	0.412275i	0.0984893	+	0.995138i	$0.468599\pi$
$770$	51.9785	−	30.0098i	1.87318	−	1.08148i
$771$	3.74282	−	6.48275i	0.134794	−	0.233471i
$772$	−7.90257	+	4.56255i	−0.284420	+	0.164210i
$773$	40.8063			1.46770			0.733851	−	0.679311i	$-0.237721\pi$
$773$	40.8063			1.46770			0.733851	+	0.679311i	$0.237721\pi$
$774$	4.43992	+	7.69017i	0.159590	+	0.276417i
$775$	8.36379	+	14.4865i	0.300436	+	0.520371i
$776$	17.4879	+	30.2899i	0.627778	+	1.08734i
$777$		−	25.6689i		−	0.920868i
$778$	−2.68371			−0.0962158
$779$	22.4071	−	38.8102i	0.802817	−	1.39052i
$780$	−4.91953	+	2.84029i	−0.176147	+	0.101699i
$781$	−6.38298	−	11.0556i	−0.228401	−	0.395602i
$782$	−0.544808	−	0.314545i	−0.0194823	−	0.0112481i
$783$	11.6354	−	20.1531i	0.415816	−	0.720215i
$784$	−8.00137			−0.285763
$785$	3.53804	+	6.12806i	0.126278	+	0.218720i
$786$	0.531004			0.0189403
$787$	0.176313	+	0.101794i	0.00628488	+	0.00362858i	0.503139	−	0.864205i	$-0.332178\pi$
$787$	0.176313	+	0.101794i	0.00628488	+	0.00362858i	−0.496854	+	0.867834i	$0.665512\pi$
$788$	4.69820	−	2.71251i	0.167366	−	0.0966291i
$789$	0.676888	−	1.17240i	0.0240978	−	0.0417387i
$790$	−33.5872			−1.19498
$791$	−23.5290	+	40.7534i	−0.836595	+	1.44902i
$792$	6.41878	+	11.1176i	0.228081	+	0.395048i
$793$	5.13471	+	8.89359i	0.182339	+	0.315820i
$794$	29.3046	−	16.9190i	1.03998	−	0.600434i
$795$	−43.2707	+	24.9823i	−1.53465	+	0.886032i
$796$		−	4.09213i		−	0.145042i
$797$	12.0779	−	6.97316i	0.427820	−	0.247002i	−0.270597	−	0.962693i	$-0.587221\pi$
$797$	12.0779	−	6.97316i	0.427820	−	0.247002i	0.698418	+	0.715691i	$0.253888\pi$
$798$	−27.7432			−0.982099
$799$			2.06958i			0.0732166i
$800$			20.5649i			0.727077i
$801$			2.38472i			0.0842599i
$802$	−27.8490	−	48.2359i	−0.983384	−	1.70327i
$803$	54.6239	+	31.5371i	1.92764	+	1.11292i
$804$	1.39196	+	2.41094i	0.0490905	+	0.0850272i
$805$	−3.97582	+	2.29544i	−0.140129	+	0.0809036i
$806$	−3.82871	+	6.63152i	−0.134861	+	0.233585i
$807$	−21.8002	+	37.7591i	−0.767404	+	1.32918i
$808$	18.6740			0.656949
$809$	8.77295	−	15.1952i	0.308440	−	0.534234i	−0.669581	−	0.742739i	$-0.733526\pi$
$809$	8.77295	−	15.1952i	0.308440	−	0.534234i	0.978021	+	0.208505i	$0.0668597\pi$
$810$	21.3428	+	12.3223i	0.749911	+	0.432961i
$811$	−31.1437	+	17.9808i	−1.09360	+	0.631392i	−0.934533	−	0.355875i	$-0.884183\pi$
$811$	−31.1437	+	17.9808i	−1.09360	+	0.631392i	−0.159070	+	0.987267i	$0.550849\pi$
$812$	−3.11189	−	1.79665i	−0.109206	−	0.0630500i
$813$	−40.1810			−1.40921
$814$	−28.1373	−	48.7353i	−0.986213	−	1.70817i
$815$	−51.1692	−	29.5426i	−1.79238	−	1.03483i
$816$	−4.89084			−0.171214
$817$	24.8085	−	14.3232i	0.867938	−	0.501104i
$818$	27.9923	−	16.1614i	0.978729	−	0.565070i
$819$	7.67058			0.268032
$820$	5.64332	+	9.77451i	0.197073	+	0.341341i
$821$	8.85329	−	15.3343i	0.308982	−	0.535172i	−0.669158	−	0.743120i	$-0.733345\pi$
$821$	8.85329	−	15.3343i	0.308982	−	0.535172i	0.978140	+	0.207948i	$0.0666785\pi$
$822$	19.3628	−	33.5373i	0.675354	−	1.16975i
$823$	27.5666			0.960911			0.480455	−	0.877019i	$-0.340471\pi$
$823$	27.5666			0.960911			0.480455	+	0.877019i	$0.340471\pi$
$824$	28.5253			0.993727
$825$			58.1563i			2.02474i
$826$	40.3076	−	23.2716i	1.40248	−	0.809723i
$827$	33.2019	−	19.1691i	1.15454	−	0.666576i	0.204554	−	0.978855i	$-0.434426\pi$
$827$	33.2019	−	19.1691i	1.15454	−	0.666576i	0.949990	+	0.312279i	$0.101092\pi$
$828$	0.115044	+	0.199262i	0.00399806	+	0.00692484i
$829$			0.469236i			0.0162972i	0.999967	+	0.00814861i	$0.00259381\pi$
$829$			0.469236i			0.0162972i	−0.999967	+	0.00814861i	$0.997406\pi$
$830$	69.0770	−	39.8816i	2.39770	−	1.38431i
$831$			8.43551i			0.292625i
$832$	14.8536	−	8.57575i	0.514957	−	0.297311i
$833$	−0.677474	+	1.17342i	−0.0234731	+	0.0406566i
$834$			14.4357i			0.499867i
$835$	34.8056	+	20.0950i	1.20450	+	0.695418i
$836$	−8.40401	+	4.85206i	−0.290659	+	0.167812i
$837$	9.73215			0.336392
$838$	11.2029	+	6.46801i	0.386998	+	0.223434i
$839$	23.3917	+	13.5052i	0.807570	+	0.466251i	0.846111	−	0.533006i	$-0.178938\pi$
$839$	23.3917	+	13.5052i	0.807570	+	0.466251i	−0.0385415	+	0.999257i	$0.512271\pi$
$840$	−14.9096	+	25.8242i	−0.514431	+	0.891020i
$841$	5.99591	+	10.3852i	0.206755	+	0.358111i
$842$	5.40198	−	9.35651i	0.186165	−	0.322447i
$843$	12.2690	+	21.2505i	0.422567	+	0.731907i
$844$		−	8.02498i		−	0.276231i
$845$	9.04186	+	15.6610i	0.311049	+	0.538753i
$846$	2.37214	−	4.10867i	0.0815559	−	0.141259i
$847$	17.0049	−	9.81776i	0.584294	−	0.337342i
$848$	−38.4150	+	22.1789i	−1.31918	+	0.761627i
$849$	16.0797	−	27.8508i	0.551853	−	0.955837i
$850$	10.1262	+	5.84635i	0.347325	+	0.200528i
$851$	2.15221	+	3.72775i	0.0737770	+	0.127785i
$852$	−1.28705	−	0.743081i	−0.0440937	−	0.0254575i
$853$	8.02747	−	13.9040i	0.274855	−	0.476063i	−0.695243	−	0.718775i	$-0.744703\pi$
$853$	8.02747	−	13.9040i	0.274855	−	0.476063i	0.970099	+	0.242711i	$0.0780367\pi$
$854$	−10.9393	−	6.31582i	−0.374336	−	0.216123i
$855$	−12.8672	+	22.2867i	−0.440050	+	0.762188i
$856$	−13.2484	−	22.9470i	−0.452822	−	0.784311i
$857$	−7.19027	−	4.15131i	−0.245615	−	0.141806i	0.372140	−	0.928177i	$-0.378624\pi$
$857$	−7.19027	−	4.15131i	−0.245615	−	0.141806i	−0.617755	+	0.786371i	$0.711958\pi$
$858$	−23.0556	+	13.3112i	−0.787106	+	0.454436i
$859$	27.3092	+	15.7670i	0.931779	+	0.537963i	0.887374	−	0.461051i	$-0.152527\pi$
$859$	27.3092	+	15.7670i	0.931779	+	0.537963i	0.0444055	+	0.999014i	$0.485861\pi$
$860$			7.21470i			0.246019i
$861$			24.1275i			0.822264i
$862$	3.43941	−	5.95723i	0.117147	−	0.202904i
$863$	−12.6632	+	7.31112i	−0.431061	+	0.248873i	−0.699799	−	0.714340i	$-0.746727\pi$
$863$	−12.6632	+	7.31112i	−0.431061	+	0.248873i	0.268737	+	0.963214i	$0.413394\pi$
$864$	10.3617	+	5.98234i	0.352513	+	0.203523i
$865$			87.1328i			2.96260i
$866$	49.5505			1.68379
$867$	11.1115	−	19.2457i	0.377367	−	0.653618i
$868$		−	1.50276i		−	0.0510070i
$869$	−25.1143			−0.851945
$870$	28.6418	−	16.5364i	0.971050	−	0.560636i
$871$	−13.4781	+	7.78156i	−0.456687	+	0.263668i
$872$	−0.417687	−	0.241151i	−0.0141447	−	0.00816642i
$873$	−14.0739	−	8.12555i	−0.476328	−	0.275008i
$874$	4.02898	−	2.32613i	0.136282	−	0.0786826i
$875$	35.8003	−	20.6693i	1.21027	−	0.698750i
$876$	7.34285			0.248092
$877$			36.4005i			1.22916i	0.788856	+	0.614578i	$0.210674\pi$
$877$			36.4005i			1.22916i	−0.788856	+	0.614578i	$0.789326\pi$
$878$	13.0765	−	22.6492i	0.441312	−	0.764375i
$879$	0.518845			0.0175002
$880$			78.2478i			2.63773i
$881$	−45.4325	−	26.2305i	−1.53066	−	0.883728i	−0.999331	−	0.0365626i	$-0.988359\pi$
$881$	−45.4325	−	26.2305i	−1.53066	−	0.883728i	−0.531330	−	0.847165i	$-0.678308\pi$
$882$	2.68993	−	1.55303i	0.0905746	−	0.0522933i
$883$	0.786501	−	1.36226i	0.0264679	−	0.0458437i	−0.852488	−	0.522747i	$-0.824907\pi$
$883$	0.786501	−	1.36226i	0.0264679	−	0.0458437i	0.878956	+	0.476903i	$0.158241\pi$
$884$			0.854000i			0.0287231i
$885$			68.3483i			2.29750i
$886$	36.3722	+	20.9995i	1.22195	+	0.705491i
$887$	49.6789	−	28.6821i	1.66806	−	0.963052i	0.699370	−	0.714760i	$-0.253464\pi$
$887$	49.6789	−	28.6821i	1.66806	−	0.963052i	0.968685	−	0.248292i	$-0.0798694\pi$
$888$	24.2129	+	13.9793i	0.812531	+	0.469115i
$889$	6.23441	+	10.7983i	0.209095	+	0.362164i
$890$	−6.07192	+	10.5169i	−0.203531	+	0.352527i
$891$	15.9588	+	9.21381i	0.534640	+	0.308674i
$892$	−1.44111	+	2.49608i	−0.0482520	+	0.0835749i
$893$	−13.2546	−	7.65253i	−0.443547	−	0.256082i
$894$	−23.4283	−	40.5790i	−0.783560	−	1.35717i
$895$	−20.2409	−	11.6861i	−0.676577	−	0.390622i
$896$	−15.4144	+	26.6985i	−0.514958	+	0.891933i
$897$	1.76352	−	1.01817i	0.0588821	−	0.0339956i
$898$	−0.295505	+	0.170610i	−0.00986113	+	0.00569332i
$899$	3.55651	−	6.16006i	0.118616	−	0.205450i
$900$	−2.13829	−	3.70362i	−0.0712763	−	0.123454i
$901$			7.51153i			0.250245i
$902$	26.4477	+	45.8088i	0.880613	+	1.52527i
$903$	−7.71147	+	13.3567i	−0.256622	+	0.444482i
$904$	−25.6278	−	44.3887i	−0.852369	−	1.47635i
$905$	−6.43545	+	11.1465i	−0.213922	+	0.370523i
$906$	−12.0686	−	6.96778i	−0.400951	−	0.231489i
$907$	−2.18959	−	1.26416i	−0.0727042	−	0.0419758i	0.463207	−	0.886250i	$-0.346699\pi$
$907$	−2.18959	−	1.26416i	−0.0727042	−	0.0419758i	−0.535911	+	0.844274i	$0.680032\pi$
$908$	−6.40540			−0.212571
$909$	−7.51422	+	4.33834i	−0.249231	+	0.143894i
$910$	33.8281	+	19.5307i	1.12139	+	0.647436i
$911$		−	28.7989i		−	0.954149i	−0.878863	−	0.477074i	$-0.841697\pi$
$911$		−	28.7989i		−	0.954149i	0.878863	−	0.477074i	$-0.158303\pi$
$912$	18.0844	−	31.3232i	0.598836	−	1.03721i
$913$	51.6513	−	29.8209i	1.70941	−	0.986928i
$914$			16.7563i			0.554250i
$915$	16.0643	−	9.27471i	0.531069	−	0.306613i
$916$		−	5.67938i		−	0.187652i
$917$	−0.291284	−	0.504518i	−0.00961904	−	0.0166607i
$918$	5.89143	−	3.40142i	0.194446	−	0.112264i
$919$	−14.3041	+	8.25848i	−0.471849	+	0.272422i	−0.717013	−	0.697059i	$-0.754491\pi$
$919$	−14.3041	+	8.25848i	−0.471849	+	0.272422i	0.245164	+	0.969482i	$0.421158\pi$
$920$		−	5.00039i		−	0.164858i
$921$	−42.0653			−1.38610
$922$	−16.4180			−0.540698
$923$	4.15410	−	7.19512i	0.136734	−	0.236830i
$924$	2.61230	−	4.52464i	0.0859385	−	0.148850i
$925$	−40.0025	−	69.2864i	−1.31528	−	2.27812i
$926$	11.2511			0.369735
$927$	−11.4783	+	6.62700i	−0.376997	+	0.217659i
$928$	7.57317	−	4.37237i	0.248601	−	0.143530i
$929$	−30.0796			−0.986881			−0.493440	−	0.869780i	$-0.664261\pi$
$929$	−30.0796			−0.986881			−0.493440	+	0.869780i	$0.664261\pi$
$930$	11.9784	+	6.91571i	0.392786	+	0.226775i
$931$	−5.01008	−	8.67771i	−0.164199	−	0.284400i
$932$	3.05034			0.0999172
$933$	7.77410	+	4.48838i	0.254513	+	0.146943i
$934$	−18.7781	+	10.8415i	−0.614437	+	0.354745i
$935$	11.4752	+	6.62521i	0.375279	+	0.216668i
$936$	−4.17740	+	7.23548i	−0.136543	+	0.236499i
$937$	−4.28343			−0.139933			−0.0699667	−	0.997549i	$-0.522289\pi$
$937$	−4.28343			−0.139933			−0.0699667	+	0.997549i	$0.522289\pi$
$938$	9.57150	−	16.5783i	0.312521	−	0.541302i
$939$	3.58561	−	6.21046i	0.117012	−	0.202671i
$940$	3.33822	−	1.92732i	0.108881	−	0.0628623i
$941$	16.7579	+	29.0255i	0.546292	+	0.946205i	0.998524	+	0.0543050i	$0.0172943\pi$
$941$	16.7579	+	29.0255i	0.546292	+	0.946205i	−0.452233	+	0.891900i	$0.649372\pi$
$942$	3.34341	+	1.93032i	0.108934	+	0.0628931i
$943$	−2.02298	−	3.50390i	−0.0658772	−	0.114103i
$944$			60.6785i			1.97492i
$945$		−	49.6448i		−	1.61494i
$946$			33.8121i			1.09933i
$947$	12.0986			0.393153			0.196577	−	0.980488i	$-0.437018\pi$
$947$	12.0986			0.393153			0.196577	+	0.980488i	$0.437018\pi$
$948$	−2.53201	+	1.46185i	−0.0822357	+	0.0474788i
$949$			41.0494i			1.33252i
$950$	−74.8854	+	43.2351i	−2.42960	+	1.40273i
$951$	−14.6687	+	8.46900i	−0.475666	+	0.274626i
$952$	2.24146	+	3.88233i	0.0726463	+	0.125827i
$953$	−12.5999	−	21.8236i	−0.408150	−	0.706937i	0.586532	−	0.809926i	$-0.300493\pi$
$953$	−12.5999	−	21.8236i	−0.408150	−	0.706937i	−0.994683	+	0.102989i	$0.967159\pi$
$954$	8.60966	−	14.9124i	0.278748	−	0.482806i
$955$	−18.3800			−0.594762
$956$	2.84101	−	4.92077i	0.0918847	−	0.159149i
$957$	21.4165	−	12.3648i	0.692298	−	0.399698i
$958$	−39.6412	−	22.8869i	−1.28075	−	0.739441i
$959$	−42.4860			−1.37195
$960$	−15.4902	−	26.8298i	−0.499944	−	0.865928i
$961$	−28.0252			−0.904040
$962$	18.3121	−	31.7174i	0.590404	−	1.02261i
$963$	10.6621	+	6.15574i	0.343580	+	0.198366i
$964$	2.19473	+	3.80138i	0.0706874	+	0.122434i
$965$	−79.7984	+	46.0716i	−2.56880	+	1.48310i
$966$	−1.25237	+	2.16917i	−0.0402943	+	0.0697918i
$967$	−42.2212			−1.35774			−0.678871	−	0.734258i	$-0.737530\pi$
$967$	−42.2212			−1.35774			−0.678871	+	0.734258i	$0.737530\pi$
$968$			21.3870i			0.687406i
$969$	−3.06241	−	5.30425i	−0.0983788	−	0.170397i
$970$	−41.3782	−	71.6692i	−1.32858	−	2.30116i
$971$	10.4147	+	18.0388i	0.334223	+	0.578892i	0.983335	−	0.181801i	$-0.0581927\pi$
$971$	10.4147	+	18.0388i	0.334223	+	0.578892i	−0.649112	+	0.760693i	$0.724859\pi$
$972$	−4.28185			−0.137340
$973$	13.7157	−	7.91874i	0.439704	−	0.253863i
$974$	31.6920	−	54.8922i	1.01548	−	1.75886i
$975$	−32.7779	+	18.9244i	−1.04973	+	0.606064i
$976$	14.2616	−	8.23395i	0.456503	−	0.263562i
$977$	−5.00122	−	8.66237i	−0.160003	−	0.277134i	0.774866	−	0.632125i	$-0.217817\pi$
$977$	−5.00122	−	8.66237i	−0.160003	−	0.277134i	−0.934870	+	0.354991i	$0.884484\pi$
$978$	−32.2362			−1.03080
$979$	−4.54019	+	7.86384i	−0.145105	+	0.251330i
$980$	2.52362			0.0806140
$981$	0.224097			0.00715487
$982$			3.17699i			0.101382i
$983$	26.9288			0.858896			0.429448	−	0.903092i	$-0.358708\pi$
$983$	26.9288			0.858896			0.429448	+	0.903092i	$0.358708\pi$
$984$	−22.7589	−	13.1399i	−0.725528	−	0.418884i
$985$	47.4414	−	27.3903i	1.51161	−	0.872727i
$986$		−	4.97205i		−	0.158342i
$987$	8.24011			0.262285
$988$	−5.46941	−	3.15777i	−0.174005	−	0.100462i
$989$		−	2.58628i		−	0.0822388i
$990$	−15.1875	−	26.3056i	−0.482692	−	0.836047i
$991$	−24.5759	−	42.5667i	−0.780680	−	1.35218i	−0.931546	−	0.363623i	$-0.881540\pi$
$991$	−24.5759	−	42.5667i	−0.780680	−	1.35218i	0.150867	−	0.988554i	$-0.451794\pi$
$992$	3.16719	+	1.82858i	0.100558	+	0.0580574i
$993$	−13.6266	+	7.86734i	−0.432428	+	0.249662i
$994$			10.2193i			0.324136i
$995$		−	41.3215i		−	1.30998i
$996$	3.47163	−	6.01304i	0.110003	−	0.190530i
$997$	−27.5310	−	15.8951i	−0.871917	−	0.503401i	−0.00393196	−	0.999992i	$-0.501252\pi$
$997$	−27.5310	−	15.8951i	−0.871917	−	0.503401i	−0.867985	+	0.496591i	$0.834585\pi$
$998$	8.64814	−	14.9790i	0.273752	−	0.474152i
$999$	−46.5472			−1.47269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.e.a.123.8	✓	58
349.227	even	6	inner	349.2.e.a.227.8	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.8	✓	58	1.1	even	1	trivial
349.2.e.a.227.8	yes	58	349.227	even	6	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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33595 + 0.771310i) q^{2} +(-0.677977 + 1.17429i) q^{3} +(0.189837 - 0.328808i) q^{4} +(1.91694 - 3.32023i) q^{5} -2.09172i q^{6} +(-1.98739 + 1.14742i) q^{7} -2.49955i q^{8} +(0.580694 + 1.00579i) q^{9} +O(q^{10})\)	\(q+(-1.33595 + 0.771310i) q^{2} +(-0.677977 + 1.17429i) q^{3} +(0.189837 - 0.328808i) q^{4} +(1.91694 - 3.32023i) q^{5} -2.09172i q^{6} +(-1.98739 + 1.14742i) q^{7} -2.49955i q^{8} +(0.580694 + 1.00579i) q^{9} +5.91420i q^{10} +4.42226i q^{11} +(0.257411 + 0.445849i) q^{12} +(-2.49246 + 1.43902i) q^{13} +(1.77003 - 3.06579i) q^{14} +(2.59928 + 4.50208i) q^{15} +(2.30760 + 3.99688i) q^{16} +0.781534 q^{17} +(-1.55155 - 0.895789i) q^{18} +(-2.88981 + 5.00531i) q^{19} +(-0.727812 - 1.26061i) q^{20} -3.11170i q^{21} +(-3.41093 - 5.90791i) q^{22} +(0.260901 + 0.451894i) q^{23} +(2.93519 + 1.69463i) q^{24} +(-4.84928 - 8.39921i) q^{25} +(2.21987 - 3.84492i) q^{26} -5.64265 q^{27} +0.871293i q^{28} +(-2.06205 + 3.57157i) q^{29} +(-6.94500 - 4.00970i) q^{30} -1.72475 q^{31} +(-1.83632 - 1.06020i) q^{32} +(-5.19302 - 2.99819i) q^{33} +(-1.04409 + 0.602805i) q^{34} +8.79813i q^{35} +0.440949 q^{36} +8.24916 q^{37} -8.91577i q^{38} -3.90250i q^{39} +(-8.29906 - 4.79147i) q^{40} -7.75381 q^{41} +(2.40009 + 4.15707i) q^{42} +(-4.29240 - 2.47822i) q^{43} +(1.45407 + 0.839510i) q^{44} +4.45261 q^{45} +(-0.697100 - 0.402471i) q^{46} +2.64810i q^{47} -6.25800 q^{48} +(-0.866851 + 1.50143i) q^{49} +(12.9568 + 7.48060i) q^{50} +(-0.529863 + 0.917749i) q^{51} +1.09272i q^{52} +9.61126i q^{53} +(7.53829 - 4.35223i) q^{54} +(14.6829 + 8.47719i) q^{55} +(2.86803 + 4.96757i) q^{56} +(-3.91846 - 6.78697i) q^{57} -6.36191i q^{58} +(11.3861 + 6.57378i) q^{59} +1.97376 q^{60} -3.56819i q^{61} +(2.30417 - 1.33031i) q^{62} +(-2.30813 - 1.33260i) q^{63} -5.95942 q^{64} +11.0341i q^{65} +9.25014 q^{66} +5.40753 q^{67} +(0.148364 - 0.256975i) q^{68} -0.707540 q^{69} +(-6.78608 - 11.7538i) q^{70} +(-2.50000 + 1.44337i) q^{71} +(2.51402 - 1.45147i) q^{72} +(7.13145 - 12.3520i) q^{73} +(-11.0204 + 6.36266i) q^{74} +13.1508 q^{75} +(1.09719 + 1.90039i) q^{76} +(-5.07419 - 8.78876i) q^{77} +(3.01004 + 5.21354i) q^{78} +5.67907i q^{79} +17.6941 q^{80} +(2.08351 - 3.60874i) q^{81} +(10.3587 - 5.98059i) q^{82} +(-6.74336 - 11.6798i) q^{83} +(-1.02315 - 0.590717i) q^{84} +(1.49815 - 2.59487i) q^{85} +7.64589 q^{86} +(-2.79604 - 4.84289i) q^{87} +11.0536 q^{88} +(1.77824 + 1.02667i) q^{89} +(-5.94845 + 3.43434i) q^{90} +(3.30233 - 5.71981i) q^{91} +0.198115 q^{92} +(1.16934 - 2.02536i) q^{93} +(-2.04251 - 3.53773i) q^{94} +(11.0792 + 19.1897i) q^{95} +(2.48997 - 1.43758i) q^{96} +(-12.1182 + 6.99642i) q^{97} -2.67444i q^{98} +(-4.44787 + 2.56798i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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