LMFDB - Embedded newform 693.2.k.c.331.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(67,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4, 0]))

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

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

chi := DirichletCharacter("693.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.35
Character	$\chi$	$=$	693.331
Dual form			693.2.k.c.67.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05826 + 1.83296i) q^{2} +(0.638324 + 1.61014i) q^{3} +(-1.23983 + 2.14745i) q^{4} +2.56660 q^{5} +(-2.27581 + 2.87397i) q^{6} +(1.99855 - 1.73373i) q^{7} -1.01522 q^{8} +(-2.18509 + 2.05558i) q^{9} +O(q^{10})$	\(q+(1.05826 + 1.83296i) q^{2} +(0.638324 + 1.61014i) q^{3} +(-1.23983 + 2.14745i) q^{4} +2.56660 q^{5} +(-2.27581 + 2.87397i) q^{6} +(1.99855 - 1.73373i) q^{7} -1.01522 q^{8} +(-2.18509 + 2.05558i) q^{9} +(2.71613 + 4.70448i) q^{10} -1.00000 q^{11} +(-4.24911 - 0.625531i) q^{12} +(-0.929012 - 1.60910i) q^{13} +(5.29284 + 1.82852i) q^{14} +(1.63832 + 4.13258i) q^{15} +(1.40529 + 2.43404i) q^{16} +(-1.06686 - 1.84786i) q^{17} +(-6.08019 - 1.82984i) q^{18} +(-1.15601 + 2.00227i) q^{19} +(-3.18216 + 5.51166i) q^{20} +(4.06726 + 2.11125i) q^{21} +(-1.05826 - 1.83296i) q^{22} -1.77038 q^{23} +(-0.648041 - 1.63465i) q^{24} +1.58744 q^{25} +(1.96627 - 3.40569i) q^{26} +(-4.70456 - 2.20616i) q^{27} +(1.24524 + 6.44132i) q^{28} +(2.80170 - 4.85268i) q^{29} +(-5.84109 + 7.37633i) q^{30} +(-0.889754 + 1.54110i) q^{31} +(-3.98956 + 6.91012i) q^{32} +(-0.638324 - 1.61014i) q^{33} +(2.25803 - 3.91103i) q^{34} +(5.12947 - 4.44979i) q^{35} +(-1.70512 - 7.24094i) q^{36} +(-1.80917 + 3.13358i) q^{37} -4.89344 q^{38} +(1.99786 - 2.52296i) q^{39} -2.60567 q^{40} +(-4.82423 - 8.35581i) q^{41} +(0.434375 + 9.68939i) q^{42} +(2.55974 - 4.43359i) q^{43} +(1.23983 - 2.14745i) q^{44} +(-5.60824 + 5.27585i) q^{45} +(-1.87352 - 3.24504i) q^{46} +(1.33353 + 2.30974i) q^{47} +(-3.02211 + 3.81642i) q^{48} +(0.988373 - 6.92987i) q^{49} +(1.67992 + 2.90971i) q^{50} +(2.29430 - 2.89732i) q^{51} +4.60728 q^{52} +(-2.96849 - 5.14158i) q^{53} +(-0.934834 - 10.9580i) q^{54} -2.56660 q^{55} +(-2.02897 + 1.76012i) q^{56} +(-3.96183 - 0.583239i) q^{57} +11.8597 q^{58} +(3.89667 - 6.74923i) q^{59} +(-10.9058 - 1.60549i) q^{60} +(1.70010 + 2.94466i) q^{61} -3.76637 q^{62} +(-0.803180 + 7.89651i) q^{63} -11.2668 q^{64} +(-2.38440 - 4.12991i) q^{65} +(2.27581 - 2.87397i) q^{66} +(-1.53909 + 2.66579i) q^{67} +5.29092 q^{68} +(-1.13007 - 2.85055i) q^{69} +(13.5846 + 4.69308i) q^{70} -13.1025 q^{71} +(2.21835 - 2.08687i) q^{72} +(5.55336 + 9.61870i) q^{73} -7.65831 q^{74} +(1.01330 + 2.55599i) q^{75} +(-2.86652 - 4.96495i) q^{76} +(-1.99855 + 1.73373i) q^{77} +(6.73875 + 0.992041i) q^{78} +(-2.43640 - 4.21997i) q^{79} +(3.60683 + 6.24721i) q^{80} +(0.549197 - 8.98323i) q^{81} +(10.2106 - 17.6853i) q^{82} +(1.63826 - 2.83756i) q^{83} +(-9.57654 + 6.11665i) q^{84} +(-2.73821 - 4.74271i) q^{85} +10.8355 q^{86} +(9.60188 + 1.41354i) q^{87} +1.01522 q^{88} +(-6.01619 + 10.4203i) q^{89} +(-15.6054 - 4.69647i) q^{90} +(-4.64641 - 1.60520i) q^{91} +(2.19497 - 3.80181i) q^{92} +(-3.04933 - 0.448906i) q^{93} +(-2.82244 + 4.88861i) q^{94} +(-2.96701 + 5.13902i) q^{95} +(-13.6729 - 2.01285i) q^{96} +(7.02007 - 12.1591i) q^{97} +(13.7481 - 5.52196i) q^{98} +(2.18509 - 2.05558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 40 q^{4} + 8 q^{5} + 6 q^{6} - q^{7} + 2 q^{9}+O(q^{10}) $ 80 * q - 40 * q^4 + 8 * q^5 + 6 * q^6 - q^7 + 2 * q^9	\( 80 q - 40 q^{4} + 8 q^{5} + 6 q^{6} - q^{7} + 2 q^{9} + 12 q^{10} - 80 q^{11} - 10 q^{12} + 21 q^{13} - 8 q^{14} - 5 q^{15} - 40 q^{16} - 3 q^{17} + 32 q^{18} + 18 q^{19} - 12 q^{20} + 18 q^{21} - 8 q^{23} - 14 q^{24} + 80 q^{25} - 12 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} + 20 q^{30} + 32 q^{31} + 35 q^{32} + 28 q^{34} - 18 q^{35} - 16 q^{36} - 7 q^{37} + 46 q^{38} - 48 q^{39} - 102 q^{40} - 2 q^{41} - 14 q^{42} + 9 q^{43} + 40 q^{44} - 5 q^{45} - 6 q^{46} - 26 q^{47} - 28 q^{48} - 19 q^{49} + 2 q^{50} + 22 q^{51} - 88 q^{52} + 4 q^{53} + 19 q^{54} - 8 q^{55} + 18 q^{56} + 16 q^{57} + 32 q^{58} - 24 q^{59} - 10 q^{60} + 69 q^{61} + 12 q^{62} + 20 q^{63} + 44 q^{64} - 7 q^{65} - 6 q^{66} + 7 q^{67} + 34 q^{68} + 15 q^{69} - 22 q^{70} + 34 q^{71} - 70 q^{72} + 26 q^{73} + 8 q^{74} - 64 q^{75} + 52 q^{76} + q^{77} - 60 q^{78} - 5 q^{79} - 47 q^{80} + 46 q^{81} + 60 q^{82} + 4 q^{83} + 29 q^{84} + 13 q^{85} - 38 q^{87} - 38 q^{89} - 43 q^{90} + 13 q^{91} - 21 q^{92} + 35 q^{93} + 56 q^{94} - 20 q^{95} + 15 q^{96} + 49 q^{97} - 84 q^{98} - 2 q^{99}+O(q^{100}) \) 80 * q - 40 * q^4 + 8 * q^5 + 6 * q^6 - q^7 + 2 * q^9 + 12 * q^10 - 80 * q^11 - 10 * q^12 + 21 * q^13 - 8 * q^14 - 5 * q^15 - 40 * q^16 - 3 * q^17 + 32 * q^18 + 18 * q^19 - 12 * q^20 + 18 * q^21 - 8 * q^23 - 14 * q^24 + 80 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 + 20 * q^30 + 32 * q^31 + 35 * q^32 + 28 * q^34 - 18 * q^35 - 16 * q^36 - 7 * q^37 + 46 * q^38 - 48 * q^39 - 102 * q^40 - 2 * q^41 - 14 * q^42 + 9 * q^43 + 40 * q^44 - 5 * q^45 - 6 * q^46 - 26 * q^47 - 28 * q^48 - 19 * q^49 + 2 * q^50 + 22 * q^51 - 88 * q^52 + 4 * q^53 + 19 * q^54 - 8 * q^55 + 18 * q^56 + 16 * q^57 + 32 * q^58 - 24 * q^59 - 10 * q^60 + 69 * q^61 + 12 * q^62 + 20 * q^63 + 44 * q^64 - 7 * q^65 - 6 * q^66 + 7 * q^67 + 34 * q^68 + 15 * q^69 - 22 * q^70 + 34 * q^71 - 70 * q^72 + 26 * q^73 + 8 * q^74 - 64 * q^75 + 52 * q^76 + q^77 - 60 * q^78 - 5 * q^79 - 47 * q^80 + 46 * q^81 + 60 * q^82 + 4 * q^83 + 29 * q^84 + 13 * q^85 - 38 * q^87 - 38 * q^89 - 43 * q^90 + 13 * q^91 - 21 * q^92 + 35 * q^93 + 56 * q^94 - 20 * q^95 + 15 * q^96 + 49 * q^97 - 84 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.05826	+	1.83296i	0.748304	+	1.29610i	0.948635	+	0.316372i	$0.102465\pi$
$2$	1.05826	+	1.83296i	0.748304	+	1.29610i	−0.200332	+	0.979728i	$0.564202\pi$
$3$	0.638324	+	1.61014i	0.368536	+	0.929613i
$3$	0.638324	+	1.61014i	0.368536	+	0.929613i
$4$	−1.23983	+	2.14745i	−0.619916	+	1.07373i
$5$	2.56660			1.14782			0.573909	−	0.818919i	$-0.305426\pi$
$5$	2.56660			1.14782			0.573909	+	0.818919i	$0.305426\pi$
$6$	−2.27581	+	2.87397i	−0.929095	+	1.17329i
$7$	1.99855	−	1.73373i	0.755379	−	0.655288i
$7$	1.99855	−	1.73373i	0.755379	−	0.655288i
$8$	−1.01522			−0.358936
$9$	−2.18509	+	2.05558i	−0.728362	+	0.685193i
$10$	2.71613	+	4.70448i	0.858917	+	1.48769i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	−4.24911	−	0.625531i	−1.22661	−	0.180575i
$13$	−0.929012	−	1.60910i	−0.257662	−	0.446283i	0.707953	−	0.706259i	$-0.249619\pi$
$13$	−0.929012	−	1.60910i	−0.257662	−	0.446283i	−0.965615	+	0.259976i	$0.916285\pi$
$14$	5.29284	+	1.82852i	1.41457	+	0.488693i
$15$	1.63832	+	4.13258i	0.423013	+	1.06703i
$16$	1.40529	+	2.43404i	0.351324	+	0.608510i
$17$	−1.06686	−	1.84786i	−0.258752	−	0.448171i	0.707156	−	0.707058i	$-0.249978\pi$
$17$	−1.06686	−	1.84786i	−0.258752	−	0.448171i	−0.965908	+	0.258886i	$0.916644\pi$
$18$	−6.08019	−	1.82984i	−1.43311	−	0.431297i
$19$	−1.15601	+	2.00227i	−0.265207	+	0.459351i	−0.967618	−	0.252420i	$-0.918773\pi$
$19$	−1.15601	+	2.00227i	−0.265207	+	0.459351i	0.702411	+	0.711771i	$0.252107\pi$
$20$	−3.18216	+	5.51166i	−0.711552	+	1.23244i
$21$	4.06726	+	2.11125i	0.887549	+	0.460713i
$22$	−1.05826	−	1.83296i	−0.225622	−	0.390789i
$23$	−1.77038			−0.369149			−0.184575	−	0.982818i	$-0.559091\pi$
$23$	−1.77038			−0.369149			−0.184575	+	0.982818i	$0.559091\pi$
$24$	−0.648041	−	1.63465i	−0.132281	−	0.333671i
$25$	1.58744			0.317487
$26$	1.96627	−	3.40569i	0.385618	−	0.667910i
$27$	−4.70456	−	2.20616i	−0.905392	−	0.424576i
$28$	1.24524	+	6.44132i	0.235328	+	1.21729i
$29$	2.80170	−	4.85268i	0.520262	−	0.901120i	−0.479460	−	0.877564i	$-0.659168\pi$
$29$	2.80170	−	4.85268i	0.520262	−	0.901120i	0.999722	−	0.0235569i	$-0.00749909\pi$
$30$	−5.84109	+	7.37633i	−1.06643	+	1.34673i
$31$	−0.889754	+	1.54110i	−0.159805	+	0.276790i	−0.934798	−	0.355180i	$-0.884420\pi$
$31$	−0.889754	+	1.54110i	−0.159805	+	0.276790i	0.774994	+	0.631969i	$0.217753\pi$
$32$	−3.98956	+	6.91012i	−0.705261	+	1.22155i
$33$	−0.638324	−	1.61014i	−0.111118	−	0.280289i
$34$	2.25803	−	3.91103i	0.387250	−	0.670736i
$35$	5.12947	−	4.44979i	0.867038	−	0.752151i
$36$	−1.70512	−	7.24094i	−0.284186	−	1.20682i
$37$	−1.80917	+	3.13358i	−0.297426	+	0.515157i	−0.975546	−	0.219794i	$-0.929462\pi$
$37$	−1.80917	+	3.13358i	−0.297426	+	0.515157i	0.678120	+	0.734951i	$0.262795\pi$
$38$	−4.89344			−0.793820
$39$	1.99786	−	2.52296i	0.319913	−	0.403997i
$40$	−2.60567			−0.411993
$41$	−4.82423	−	8.35581i	−0.753418	−	1.30496i	−0.946157	−	0.323708i	$-0.895070\pi$
$41$	−4.82423	−	8.35581i	−0.753418	−	1.30496i	0.192739	−	0.981250i	$-0.438263\pi$
$42$	0.434375	+	9.68939i	0.0670256	+	1.49511i
$43$	2.55974	−	4.43359i	0.390356	−	0.676117i	−0.602140	−	0.798390i	$-0.705685\pi$
$43$	2.55974	−	4.43359i	0.390356	−	0.676117i	0.992496	+	0.122274i	$0.0390186\pi$
$44$	1.23983	−	2.14745i	0.186912	−	0.323741i
$45$	−5.60824	+	5.27585i	−0.836027	+	0.786477i
$46$	−1.87352	−	3.24504i	−0.276236	−	0.478455i
$47$	1.33353	+	2.30974i	0.194515	+	0.336910i	0.946741	−	0.321995i	$-0.104353\pi$
$47$	1.33353	+	2.30974i	0.194515	+	0.336910i	−0.752226	+	0.658905i	$0.771020\pi$
$48$	−3.02211	+	3.81642i	−0.436204	+	0.550853i
$49$	0.988373	−	6.92987i	0.141196	−	0.989982i
$50$	1.67992	+	2.90971i	0.237577	+	0.411495i
$51$	2.29430	−	2.89732i	0.321266	−	0.405707i
$52$	4.60728			0.638915
$53$	−2.96849	−	5.14158i	−0.407754	−	0.706250i	0.586884	−	0.809671i	$-0.300355\pi$
$53$	−2.96849	−	5.14158i	−0.407754	−	0.706250i	−0.994638	+	0.103421i	$0.967021\pi$
$54$	−0.934834	−	10.9580i	−0.127215	−	1.49119i
$55$	−2.56660			−0.346080
$56$	−2.02897	+	1.76012i	−0.271133	+	0.235206i
$57$	−3.96183	−	0.583239i	−0.524757	−	0.0772519i
$58$	11.8597			1.55726
$59$	3.89667	−	6.74923i	0.507303	−	0.878675i	−0.492661	−	0.870221i	$-0.663976\pi$
$59$	3.89667	−	6.74923i	0.507303	−	0.878675i	0.999964	−	0.00845359i	$-0.00269089\pi$
$60$	−10.9058	−	1.60549i	−1.40793	−	0.207268i
$61$	1.70010	+	2.94466i	0.217675	+	0.377025i	0.954097	−	0.299498i	$-0.0968193\pi$
$61$	1.70010	+	2.94466i	0.217675	+	0.377025i	−0.736422	+	0.676523i	$0.763486\pi$
$62$	−3.76637			−0.478329
$63$	−0.803180	+	7.89651i	−0.101191	+	0.994867i
$64$	−11.2668			−1.40835
$65$	−2.38440	−	4.12991i	−0.295749	−	0.512252i
$66$	2.27581	−	2.87397i	0.280133	−	0.353761i
$67$	−1.53909	+	2.66579i	−0.188030	+	0.325678i	−0.944593	−	0.328243i	$-0.893544\pi$
$67$	−1.53909	+	2.66579i	−0.188030	+	0.325678i	0.756563	+	0.653920i	$0.226877\pi$
$68$	5.29092			0.641618
$69$	−1.13007	−	2.85055i	−0.136045	−	0.343166i
$70$	13.5846	+	4.69308i	1.62367	+	0.560931i
$71$	−13.1025			−1.55498			−0.777492	−	0.628893i	$-0.783508\pi$
$71$	−13.1025			−1.55498			−0.777492	+	0.628893i	$0.783508\pi$
$72$	2.21835	−	2.08687i	0.261435	−	0.245940i
$73$	5.55336	+	9.61870i	0.649972	+	1.12578i	0.983129	+	0.182913i	$0.0585526\pi$
$73$	5.55336	+	9.61870i	0.649972	+	1.12578i	−0.333158	+	0.942871i	$0.608114\pi$
$74$	−7.65831			−0.890260
$75$	1.01330	+	2.55599i	0.117006	+	0.295140i
$76$	−2.86652	−	4.96495i	−0.328812	−	0.569519i
$77$	−1.99855	+	1.73373i	−0.227755	+	0.197577i
$78$	6.73875	+	0.992041i	0.763013	+	0.112327i
$79$	−2.43640	−	4.21997i	−0.274117	−	0.474784i	0.695795	−	0.718240i	$-0.255052\pi$
$79$	−2.43640	−	4.21997i	−0.274117	−	0.474784i	−0.969912	+	0.243456i	$0.921719\pi$
$80$	3.60683	+	6.24721i	0.403256	+	0.698459i
$81$	0.549197	−	8.98323i	0.0610219	−	0.998136i
$82$	10.2106	−	17.6853i	1.12757	−	1.95301i
$83$	1.63826	−	2.83756i	0.179823	−	0.311462i	−0.761997	−	0.647581i	$-0.775781\pi$
$83$	1.63826	−	2.83756i	0.179823	−	0.311462i	0.941820	+	0.336118i	$0.109114\pi$
$84$	−9.57654	+	6.11665i	−1.04489	+	0.667381i
$85$	−2.73821	−	4.74271i	−0.297000	−	0.514419i
$86$	10.8355			1.16842
$87$	9.60188	+	1.41354i	1.02943	+	0.151547i
$88$	1.01522			0.108223
$89$	−6.01619	+	10.4203i	−0.637715	+	1.10455i	0.348218	+	0.937413i	$0.386787\pi$
$89$	−6.01619	+	10.4203i	−0.637715	+	1.10455i	−0.985933	+	0.167141i	$0.946547\pi$
$90$	−15.6054	−	4.69647i	−1.64495	−	0.495051i
$91$	−4.64641	−	1.60520i	−0.487076	−	0.168271i
$92$	2.19497	−	3.80181i	0.228842	−	0.396366i
$93$	−3.04933	−	0.448906i	−0.316201	−	0.0465494i
$94$	−2.82244	+	4.88861i	−0.291112	+	0.504221i
$95$	−2.96701	+	5.13902i	−0.304409	+	0.527252i
$96$	−13.6729	−	2.01285i	−1.39548	−	0.205435i
$97$	7.02007	−	12.1591i	0.712780	−	1.23457i	−0.251030	−	0.967979i	$-0.580769\pi$
$97$	7.02007	−	12.1591i	0.712780	−	1.23457i	0.963810	−	0.266592i	$-0.0858975\pi$
$98$	13.7481	−	5.52196i	1.38877	−	0.557803i
$99$	2.18509	−	2.05558i	0.219609	−	0.206593i
$100$	−1.96816	+	3.40895i	−0.196816	+	0.340895i
$101$	12.7900			1.27266			0.636328	−	0.771419i	$-0.280453\pi$
$101$	12.7900			1.27266			0.636328	+	0.771419i	$0.280453\pi$
$102$	7.73865	+	1.13924i	0.766241	+	0.112802i
$103$	14.8648			1.46467			0.732336	−	0.680943i	$-0.238430\pi$
$103$	14.8648			1.46467			0.732336	+	0.680943i	$0.238430\pi$
$104$	0.943155	+	1.63359i	0.0924840	+	0.160187i
$105$	10.4390	+	5.41874i	1.01875	+	0.528815i
$106$	6.28288	−	10.8823i	0.610247	−	1.05698i
$107$	−6.72103	+	11.6412i	−0.649747	+	1.12539i	0.333437	+	0.942772i	$0.391792\pi$
$107$	−6.72103	+	11.6412i	−0.649747	+	1.12539i	−0.983183	+	0.182622i	$0.941542\pi$
$108$	10.5705	−	7.36754i	1.01715	−	0.708942i
$109$	3.63203	+	6.29086i	0.347885	+	0.602555i	0.985874	−	0.167491i	$-0.0535665\pi$
$109$	3.63203	+	6.29086i	0.347885	+	0.602555i	−0.637988	+	0.770046i	$0.720233\pi$
$110$	−2.71613	−	4.70448i	−0.258973	−	0.448555i
$111$	−6.20033	−	0.912779i	−0.588509	−	0.0866371i
$112$	7.02851	+	2.42814i	0.664132	+	0.229438i
$113$	8.33506	+	14.4367i	0.784096	+	1.35809i	0.929537	+	0.368728i	$0.120207\pi$
$113$	8.33506	+	14.4367i	0.784096	+	1.35809i	−0.145441	+	0.989367i	$0.546460\pi$
$114$	−3.12360	−	7.87911i	−0.292552	−	0.737946i
$115$	−4.54385			−0.423717
$116$	6.94727	+	12.0330i	0.645038	+	1.11724i
$117$	5.33759	+	1.60636i	0.493461	+	0.148508i
$118$	16.4948			1.51847
$119$	−5.33585	−	1.84338i	−0.489137	−	0.168982i
$120$	−1.66326	−	4.19549i	−0.151834	−	0.382994i
$121$	1.00000			0.0909091
$122$	−3.59830	+	6.23243i	−0.325774	+	0.564258i
$123$	10.3746	−	13.1014i	0.935444	−	1.18131i
$124$	−2.20629	−	3.82141i	−0.198131	−	0.343173i
$125$	−8.75869			−0.783401
$126$	−15.3240	+	6.88437i	−1.36517	+	0.613309i
$127$	−4.66388			−0.413852			−0.206926	−	0.978357i	$-0.566346\pi$
$127$	−4.66388			−0.413852			−0.206926	+	0.978357i	$0.566346\pi$
$128$	−3.94410	−	6.83139i	−0.348613	−	0.603815i
$129$	8.77264	+	1.29146i	0.772387	+	0.113707i
$130$	5.04664	−	8.74104i	0.442620	−	0.766640i
$131$	9.63639			0.841935			0.420968	−	0.907076i	$-0.361691\pi$
$131$	9.63639			0.841935			0.420968	+	0.907076i	$0.361691\pi$
$132$	4.24911	+	0.625531i	0.369838	+	0.0544455i
$133$	1.16105	+	6.00583i	0.100676	+	0.520771i
$134$	−6.51504			−0.562814
$135$	−12.0747	−	5.66234i	−1.03923	−	0.487337i
$136$	1.08310	+	1.87599i	0.0928753	+	0.160865i
$137$	−19.0302			−1.62586			−0.812932	−	0.582359i	$-0.802130\pi$
$137$	−19.0302			−1.62586			−0.812932	+	0.582359i	$0.802130\pi$
$138$	4.02904	−	5.08801i	0.342975	−	0.433120i
$139$	7.51250	+	13.0120i	0.637202	+	1.10367i	0.986044	+	0.166485i	$0.0532416\pi$
$139$	7.51250	+	13.0120i	0.637202	+	1.10367i	−0.348842	+	0.937182i	$0.613425\pi$
$140$	3.19603	+	16.5323i	0.270114	+	1.39723i
$141$	−2.86777	+	3.62152i	−0.241510	+	0.304987i
$142$	−13.8659	−	24.0164i	−1.16360	−	2.01541i
$143$	0.929012	+	1.60910i	0.0776879	+	0.134559i
$144$	−8.07405	−	2.42990i	−0.672838	−	0.202491i
$145$	7.19084	−	12.4549i	0.597166	−	1.03432i
$146$	−11.7538	+	20.3582i	−0.972752	+	1.68486i
$147$	11.7889	−	2.83209i	0.972336	−	0.233587i
$148$	−4.48614	−	7.77023i	−0.368759	−	0.638709i
$149$	−15.5615			−1.27485			−0.637424	−	0.770513i	$-0.720000\pi$
$149$	−15.5615			−1.27485			−0.637424	+	0.770513i	$0.720000\pi$
$150$	−3.61270	+	4.56224i	−0.294976	+	0.372506i
$151$	0.573149			0.0466422			0.0233211	−	0.999728i	$-0.492576\pi$
$151$	0.573149			0.0466422			0.0233211	+	0.999728i	$0.492576\pi$
$152$	1.17361	−	2.03275i	0.0951921	−	0.164878i
$153$	6.12960	+	1.84471i	0.495549	+	0.149136i
$154$	−5.29284	−	1.82852i	−0.426509	−	0.147346i
$155$	−2.28364	+	3.95539i	−0.183427	+	0.317704i
$156$	2.94094	+	7.41835i	0.235463	+	0.593944i
$157$	−3.57344	+	6.18938i	−0.285192	+	0.493966i	−0.972656	−	0.232252i	$-0.925391\pi$
$157$	−3.57344	+	6.18938i	−0.285192	+	0.493966i	0.687464	+	0.726218i	$0.258724\pi$
$158$	5.15670	−	8.93167i	0.410245	−	0.710565i
$159$	6.38379	−	8.06167i	0.506268	−	0.639332i
$160$	−10.2396	+	17.7355i	−0.809512	+	1.40212i
$161$	−3.53818	+	3.06936i	−0.278848	+	0.241899i
$162$	17.0471	−	8.49994i	1.33935	−	0.667819i
$163$	2.32523	−	4.02742i	0.182126	−	0.315452i	−0.760478	−	0.649363i	$-0.775035\pi$
$163$	2.32523	−	4.02742i	0.182126	−	0.315452i	0.942604	+	0.333912i	$0.108369\pi$
$164$	23.9249			1.86822
$165$	−1.63832	−	4.13258i	−0.127543	−	0.321721i
$166$	6.93485			0.538249
$167$	10.1331	+	17.5511i	0.784124	+	1.35814i	0.929521	+	0.368769i	$0.120221\pi$
$167$	10.1331	+	17.5511i	0.784124	+	1.35814i	−0.145397	+	0.989373i	$0.546446\pi$
$168$	−4.12918	−	2.14339i	−0.318573	−	0.165367i
$169$	4.77387	−	8.26859i	0.367221	−	0.636045i
$170$	5.79547	−	10.0381i	0.444492	−	0.769884i
$171$	−1.58984	−	6.75139i	−0.121578	−	0.516292i
$172$	6.34729	+	10.9938i	0.483976	+	0.838272i
$173$	−7.83696	−	13.5740i	−0.595833	−	1.03201i	−0.993429	−	0.114453i	$-0.963489\pi$
$173$	−7.83696	−	13.5740i	−0.595833	−	1.03201i	0.397595	−	0.917561i	$-0.369845\pi$
$174$	7.57033	+	19.0958i	0.573906	+	1.44765i
$175$	3.17257	−	2.75218i	0.239823	−	0.208046i
$176$	−1.40529	−	2.43404i	−0.105928	−	0.183473i
$177$	13.3545	+	1.96598i	1.00379	+	0.147772i
$178$	−25.4668			−1.90882
$179$	10.6006	+	18.3608i	0.792328	+	1.37235i	0.924522	+	0.381128i	$0.124464\pi$
$179$	10.6006	+	18.3608i	0.792328	+	1.37235i	−0.132194	+	0.991224i	$0.542202\pi$
$180$	−4.37636	−	18.5846i	−0.326194	−	1.38521i
$181$	19.2753			1.43272			0.716359	−	0.697731i	$-0.245807\pi$
$181$	19.2753			1.43272			0.716359	+	0.697731i	$0.245807\pi$
$182$	−1.97485	−	10.2154i	−0.146385	−	0.757217i
$183$	−3.65609	+	4.61704i	−0.270266	+	0.341301i
$184$	1.79733			0.132501
$185$	−4.64342	+	8.04265i	−0.341391	+	0.591307i
$186$	−2.40416	−	6.06437i	−0.176282	−	0.444661i
$187$	1.06686	+	1.84786i	0.0780166	+	0.135129i
$188$	−6.61340			−0.482332
$189$	−13.2272	+	3.74730i	−0.962134	+	0.272576i
$190$	−12.5595			−0.911162
$191$	−8.15778	−	14.1297i	−0.590276	−	1.02239i	−0.994195	−	0.107593i	$-0.965686\pi$
$191$	−8.15778	−	14.1297i	−0.590276	−	1.02239i	0.403919	−	0.914795i	$-0.367648\pi$
$192$	−7.19187	−	18.1411i	−0.519029	−	1.30922i
$193$	1.46546	−	2.53826i	0.105486	−	0.182708i	−0.808450	−	0.588564i	$-0.799693\pi$
$193$	1.46546	−	2.53826i	0.105486	−	0.182708i	0.913937	+	0.405857i	$0.133027\pi$
$194$	29.7163			2.13350
$195$	5.12770	−	6.47543i	0.367202	−	0.463715i
$196$	13.6562	+	10.7144i	0.975440	+	0.765312i
$197$	−21.1419			−1.50630			−0.753150	−	0.657849i	$-0.771466\pi$
$197$	−21.1419			−1.50630			−0.753150	+	0.657849i	$0.771466\pi$
$198$	6.08019	+	1.82984i	0.432100	+	0.130041i
$199$	3.21454	+	5.56775i	0.227873	+	0.394687i	0.957177	−	0.289502i	$-0.0934897\pi$
$199$	3.21454	+	5.56775i	0.227873	+	0.394687i	−0.729305	+	0.684189i	$0.760156\pi$
$200$	−1.61160			−0.113958
$201$	−5.27472	−	0.776515i	−0.372050	−	0.0547712i
$202$	13.5352	+	23.4436i	0.952332	+	1.64949i
$203$	−2.81391	−	14.5557i	−0.197498	−	1.02161i
$204$	3.37732	+	8.51910i	0.236460	+	0.596457i
$205$	−12.3819	−	21.4460i	−0.864787	−	1.49785i
$206$	15.7308	+	27.2466i	1.09602	+	1.89836i
$207$	3.86843	−	3.63915i	0.268874	−	0.252939i
$208$	2.61107	−	4.52251i	0.181045	−	0.313579i
$209$	1.15601	−	2.00227i	0.0799628	−	0.138500i
$210$	1.11487	+	24.8688i	0.0769332	+	1.71611i
$211$	1.23860	+	2.14531i	0.0852685	+	0.147689i	0.905506	−	0.424334i	$-0.139492\pi$
$211$	1.23860	+	2.14531i	0.0852685	+	0.147689i	−0.820237	+	0.572024i	$0.806159\pi$
$212$	14.7217			1.01109
$213$	−8.36366	−	21.0969i	−0.573068	−	1.44553i
$214$	−28.4504			−1.94483
$215$	6.56982	−	11.3793i	0.448058	−	0.776059i
$216$	4.77618	+	2.23975i	0.324978	+	0.152396i
$217$	0.893633	+	4.62255i	0.0606637	+	0.313799i
$218$	−7.68727	+	13.3147i	−0.520648	+	0.901788i
$219$	−11.9426	+	15.0815i	−0.807005	+	1.01911i
$220$	3.18216	−	5.51166i	0.214541	−	0.371596i
$221$	−1.98225	+	3.43336i	−0.133341	+	0.230953i
$222$	−4.88848	−	12.3309i	−0.328093	−	0.827598i
$223$	−11.8656	+	20.5519i	−0.794581	+	1.37626i	0.128523	+	0.991706i	$0.458976\pi$
$223$	−11.8656	+	20.5519i	−0.794581	+	1.37626i	−0.923105	+	0.384549i	$0.874357\pi$
$224$	4.00695	+	20.7270i	0.267726	+	1.38488i
$225$	−3.46869	+	3.26310i	−0.231246	+	0.217540i
$226$	−17.6413	+	30.5557i	−1.17348	+	2.03253i
$227$	22.0629			1.46436			0.732182	−	0.681109i	$-0.238502\pi$
$227$	22.0629			1.46436			0.732182	+	0.681109i	$0.238502\pi$
$228$	6.16449	−	7.78473i	0.408253	−	0.515556i
$229$	−14.0765			−0.930199			−0.465100	−	0.885258i	$-0.653982\pi$
$229$	−14.0765			−0.930199			−0.465100	+	0.885258i	$0.653982\pi$
$230$	−4.80858	−	8.32871i	−0.317069	−	0.549179i
$231$	−4.06726	−	2.11125i	−0.267606	−	0.138910i
$232$	−2.84435	+	4.92656i	−0.186741	+	0.323444i
$233$	11.9299	−	20.6633i	0.781557	−	1.35370i	−0.149477	−	0.988765i	$-0.547759\pi$
$233$	11.9299	−	20.6633i	0.781557	−	1.35370i	0.931034	−	0.364931i	$-0.118908\pi$
$234$	2.70418	+	11.4836i	0.176778	+	0.750703i
$235$	3.42263	+	5.92817i	0.223268	+	0.386711i
$236$	9.66244	+	16.7358i	0.628971	+	1.08941i
$237$	5.23952	−	6.61665i	0.340344	−	0.429798i
$238$	−2.26788	−	11.7312i	−0.147005	−	0.760420i
$239$	2.99808	+	5.19283i	0.193930	+	0.335896i	0.946549	−	0.322560i	$-0.104543\pi$
$239$	2.99808	+	5.19283i	0.193930	+	0.335896i	−0.752619	+	0.658456i	$0.771210\pi$
$240$	−7.75654	+	9.79523i	−0.500683	+	0.632280i
$241$	−15.3912			−0.991432			−0.495716	−	0.868485i	$-0.665094\pi$
$241$	−15.3912			−0.991432			−0.495716	+	0.868485i	$0.665094\pi$
$242$	1.05826	+	1.83296i	0.0680276	+	0.117827i
$243$	14.8148	−	4.84993i	0.950370	−	0.311123i
$244$	−8.43135			−0.539762
$245$	2.53676	−	17.7862i	0.162067	−	1.13632i
$246$	34.9933	+	5.15153i	2.23109	+	0.328449i
$247$	4.29579			0.273334
$248$	0.903299	−	1.56456i	0.0573596	−	0.0993497i
$249$	5.61460	+	0.826551i	0.355811	+	0.0523805i
$250$	−9.26898	−	16.0543i	−0.586221	−	1.01537i
$251$	9.85982			0.622346			0.311173	−	0.950353i	$-0.399278\pi$
$251$	9.85982			0.622346			0.311173	+	0.950353i	$0.399278\pi$
$252$	−15.9616	−	11.5151i	−1.00549	−	0.725386i
$253$	1.77038			0.111303
$254$	−4.93560	−	8.54871i	−0.309687	−	0.536394i
$255$	5.88856	−	7.43627i	0.368756	−	0.465677i
$256$	−2.91903	+	5.05590i	−0.182439	+	0.315994i
$257$	−18.3119			−1.14226			−0.571132	−	0.820858i	$-0.693496\pi$
$257$	−18.3119			−1.14226			−0.571132	+	0.820858i	$0.693496\pi$
$258$	6.91654	+	17.4466i	0.430605	+	1.08618i
$259$	1.81706	+	9.39922i	0.112907	+	0.584039i
$260$	11.8250			0.733358
$261$	3.85312	+	16.3626i	0.238502	+	1.01282i
$262$	10.1978	+	17.6631i	0.630023	+	1.09123i
$263$	−0.386445			−0.0238292			−0.0119146	−	0.999929i	$-0.503793\pi$
$263$	−0.386445			−0.0238292			−0.0119146	+	0.999929i	$0.503793\pi$
$264$	0.648041	+	1.63465i	0.0398842	+	0.100606i
$265$	−7.61893	−	13.1964i	−0.468027	−	0.810647i
$266$	−9.77976	+	8.48389i	−0.599635	+	0.520181i
$267$	−20.6185	−	3.03534i	−1.26183	−	0.185760i
$268$	−3.81643	−	6.61026i	−0.233126	−	0.403786i
$269$	−12.5045	−	21.6584i	−0.762413	−	1.32054i	−0.941603	−	0.336724i	$-0.890681\pi$
$269$	−12.5045	−	21.6584i	−0.762413	−	1.32054i	0.179190	−	0.983815i	$-0.442652\pi$
$270$	−2.39935	−	28.1247i	−0.146020	−	1.71162i
$271$	2.91056	−	5.04124i	0.176804	−	0.306233i	−0.763980	−	0.645240i	$-0.776758\pi$
$271$	2.91056	−	5.04124i	0.176804	−	0.306233i	0.940784	+	0.339006i	$0.110091\pi$
$272$	2.99851	−	5.19357i	0.181811	−	0.314906i
$273$	−0.381324	−	8.50599i	−0.0230788	−	0.514806i
$274$	−20.1390	−	34.8817i	−1.21664	−	2.10728i
$275$	−1.58744			−0.0957260
$276$	7.52253	+	1.10743i	0.452803	+	0.0666592i
$277$	−13.4360			−0.807293			−0.403646	−	0.914915i	$-0.632257\pi$
$277$	−13.4360			−0.807293			−0.403646	+	0.914915i	$0.632257\pi$
$278$	−15.9004	+	27.5403i	−0.953641	+	1.65175i
$279$	−1.22366	−	5.19639i	−0.0732587	−	0.311100i
$280$	−5.20756	+	4.51753i	−0.311211	+	0.269974i
$281$	8.10418	−	14.0368i	0.483455	−	0.837368i	−0.516365	−	0.856369i	$-0.672715\pi$
$281$	8.10418	−	14.0368i	0.483455	−	0.837368i	0.999819	+	0.0190006i	$0.00604846\pi$
$282$	−9.67296	−	1.42400i	−0.576016	−	0.0847980i
$283$	10.1814	−	17.6348i	0.605224	−	1.04828i	−0.386792	−	0.922167i	$-0.626417\pi$
$283$	10.1814	−	17.6348i	0.605224	−	1.04828i	0.992016	−	0.126112i	$-0.0402497\pi$
$284$	16.2449	−	28.1371i	0.963960	−	1.66963i
$285$	−10.1684	−	1.49694i	−0.602326	−	0.0886712i
$286$	−1.96627	+	3.40569i	−0.116268	+	0.201383i
$287$	−24.1281	−	8.33557i	−1.42424	−	0.492033i
$288$	−5.48676	−	23.3001i	−0.323311	−	1.37297i
$289$	6.22362	−	10.7796i	0.366095	−	0.634095i
$290$	30.4391			1.78745
$291$	24.0589	+	3.54182i	1.41036	+	0.207625i
$292$	−27.5410			−1.61171
$293$	−4.41771	−	7.65170i	−0.258085	−	0.447017i	0.707644	−	0.706569i	$-0.249758\pi$
$293$	−4.41771	−	7.65170i	−0.258085	−	0.447017i	−0.965729	+	0.259553i	$0.916425\pi$
$294$	17.6669	+	18.6116i	1.03035	+	1.08545i
$295$	10.0012	−	17.3226i	0.582292	−	1.00856i
$296$	1.83672	−	3.18128i	0.106757	−	0.184908i
$297$	4.70456	+	2.20616i	0.272986	+	0.128015i
$298$	−16.4681	−	28.5236i	−0.953973	−	1.65233i
$299$	1.64470	+	2.84871i	0.0951156	+	0.164745i
$300$	−6.74520	−	0.992991i	−0.389434	−	0.0573303i
$301$	−2.57090	−	13.2986i	−0.148184	−	0.766520i
$302$	0.606541	+	1.05056i	0.0349025	+	0.0604529i
$303$	8.16418	+	20.5937i	0.469020	+	1.18308i
$304$	−6.49813			−0.372693
$305$	4.36347	+	7.55776i	0.249852	+	0.432756i
$306$	3.10543	+	13.1875i	0.177526	+	0.753879i
$307$	28.2303			1.61119			0.805593	−	0.592469i	$-0.201847\pi$
$307$	28.2303			1.61119			0.805593	+	0.592469i	$0.201847\pi$
$308$	−1.24524	−	6.44132i	−0.0709540	−	0.367028i
$309$	9.48856	+	23.9344i	0.539785	+	1.36158i
$310$	−9.66676			−0.549035
$311$	−1.72190	+	2.98242i	−0.0976400	+	0.169117i	−0.910707	−	0.413052i	$-0.864463\pi$
$311$	−1.72190	+	2.98242i	−0.0976400	+	0.169117i	0.813067	+	0.582170i	$0.197796\pi$
$312$	−2.02827	+	2.56137i	−0.114828	+	0.145009i
$313$	3.63277	+	6.29213i	0.205336	+	0.355652i	0.950240	−	0.311520i	$-0.100838\pi$
$313$	3.63277	+	6.29213i	0.205336	+	0.355652i	−0.744904	+	0.667172i	$0.767505\pi$
$314$	−15.1265			−0.853639
$315$	−2.06144	+	20.2672i	−0.116149	+	1.14193i
$316$	12.0829			0.679718
$317$	−12.6092	−	21.8398i	−0.708203	−	1.22664i	−0.965523	−	0.260318i	$-0.916173\pi$
$317$	−12.6092	−	21.8398i	−0.708203	−	1.22664i	0.257320	−	0.966326i	$-0.417161\pi$
$318$	21.5325	+	3.16989i	1.20748	+	0.177759i
$319$	−2.80170	+	4.85268i	−0.156865	+	0.271698i
$320$	−28.9174			−1.61653
$321$	−23.0341	−	3.39095i	−1.28564	−	0.189264i
$322$	−9.37033	−	3.23718i	−0.522188	−	0.180401i
$323$	4.93320			0.274491
$324$	18.6102	+	12.3171i	1.03390	+	0.684282i
$325$	−1.47475	−	2.55434i	−0.0818043	−	0.141689i
$326$	9.84281			0.545143
$327$	−7.81074	+	9.86368i	−0.431935	+	0.545462i
$328$	4.89767	+	8.48301i	0.270429	+	0.468396i
$329$	6.66957	+	2.30414i	0.367705	+	0.127031i
$330$	5.84109	−	7.37633i	0.321541	−	0.406054i
$331$	3.71091	+	6.42748i	0.203970	+	0.353286i	0.949804	−	0.312845i	$-0.101282\pi$
$331$	3.71091	+	6.42748i	0.203970	+	0.353286i	−0.745834	+	0.666132i	$0.767949\pi$
$332$	4.06235	+	7.03620i	0.222950	+	0.386161i
$333$	−2.48812	−	10.5660i	−0.136348	−	0.579015i
$334$	−21.4470	+	37.1472i	−1.17353	+	2.03261i
$335$	−3.95023	+	6.84201i	−0.215824	+	0.373819i
$336$	0.576819	+	12.8668i	0.0314681	+	0.701942i
$337$	−4.26866	−	7.39353i	−0.232529	−	0.402751i	0.726023	−	0.687670i	$-0.241367\pi$
$337$	−4.26866	−	7.39353i	−0.232529	−	0.402751i	−0.958552	+	0.284919i	$0.908033\pi$
$338$	20.2080			1.09917
$339$	−17.9247	+	22.6359i	−0.973535	+	1.22941i
$340$	13.5797			0.736461
$341$	0.889754	−	1.54110i	0.0481829	−	0.0834552i
$342$	10.6926	−	10.0588i	0.578188	−	0.543920i
$343$	−10.0392	−	15.5632i	−0.542066	−	0.840336i
$344$	−2.59870	+	4.50109i	−0.140113	+	0.242682i
$345$	−2.90045	−	7.31623i	−0.156155	−	0.393893i
$346$	16.5871	−	28.7297i	0.891728	−	1.54452i
$347$	−17.2358	+	29.8532i	−0.925265	+	1.60261i	−0.134130	+	0.990964i	$0.542824\pi$
$347$	−17.2358	+	29.8532i	−0.925265	+	1.60261i	−0.791135	+	0.611642i	$0.790509\pi$
$348$	−14.9402	+	18.8670i	−0.800880	+	1.01138i
$349$	−12.0505	+	20.8721i	−0.645050	+	1.11726i	0.339240	+	0.940700i	$0.389830\pi$
$349$	−12.0505	+	20.8721i	−0.645050	+	1.11726i	−0.984290	+	0.176560i	$0.943503\pi$
$350$	8.40205	+	2.90266i	0.449109	+	0.155154i
$351$	0.820660	+	9.61964i	0.0438036	+	0.513458i
$352$	3.98956	−	6.91012i	0.212644	−	0.368311i
$353$	9.08111			0.483339			0.241669	−	0.970359i	$-0.422305\pi$
$353$	9.08111			0.483339			0.241669	+	0.970359i	$0.422305\pi$
$354$	10.5290	+	26.5589i	0.559610	+	1.41159i
$355$	−33.6290			−1.78484
$356$	−14.9181	−	25.8390i	−0.790660	−	1.36946i
$357$	−0.437905	−	9.76813i	−0.0231764	−	0.516984i
$358$	−22.4365	+	38.8611i	−1.18580	+	2.05387i
$359$	−3.73295	+	6.46566i	−0.197018	+	0.341244i	−0.947560	−	0.319578i	$-0.896459\pi$
$359$	−3.73295	+	6.46566i	−0.197018	+	0.341244i	0.750542	+	0.660822i	$0.229792\pi$
$360$	5.69362	−	5.35617i	0.300080	−	0.282295i
$361$	6.82729	+	11.8252i	0.359331	+	0.622379i
$362$	20.3983	+	35.3308i	1.07211	+	1.85695i
$363$	0.638324	+	1.61014i	0.0335033	+	0.0845103i
$364$	9.20786	−	7.98777i	0.482623	−	0.418673i
$365$	14.2533	+	24.6874i	0.746049	+	1.29220i
$366$	−12.3320	−	1.81544i	−0.644601	−	0.0948947i
$367$	−24.3051			−1.26872			−0.634358	−	0.773039i	$-0.718735\pi$
$367$	−24.3051			−1.26872			−0.634358	+	0.773039i	$0.718735\pi$
$368$	−2.48790	−	4.30917i	−0.129691	−	0.224631i
$369$	27.7174	+	8.34158i	1.44291	+	0.434245i
$370$	−19.6558			−1.02186
$371$	−14.8468	−	5.12913i	−0.770806	−	0.266291i
$372$	4.74467	−	5.99173i	0.246000	−	0.310657i
$373$	25.5290			1.32184			0.660920	−	0.750456i	$-0.270166\pi$
$373$	25.5290			1.32184			0.660920	+	0.750456i	$0.270166\pi$
$374$	−2.25803	+	3.91103i	−0.116760	+	0.202235i
$375$	−5.59088	−	14.1027i	−0.288712	−	0.728260i
$376$	−1.35383	−	2.34490i	−0.0698184	−	0.120929i
$377$	−10.4112			−0.536206
$378$	−20.8664	−	20.2793i	−1.07325	−	1.04305i
$379$	−24.3496			−1.25075			−0.625376	−	0.780323i	$-0.715055\pi$
$379$	−24.3496			−1.25075			−0.625376	+	0.780323i	$0.715055\pi$
$380$	−7.35720	−	12.7430i	−0.377416	−	0.653704i
$381$	−2.97706	−	7.50948i	−0.152520	−	0.384722i
$382$	17.2661	−	29.9058i	0.883411	−	1.53011i
$383$	10.4407			0.533492			0.266746	−	0.963767i	$-0.414051\pi$
$383$	10.4407			0.533492			0.266746	+	0.963767i	$0.414051\pi$
$384$	8.48186	−	10.7112i	0.432838	−	0.546603i
$385$	−5.12947	+	4.44979i	−0.261422	+	0.226782i
$386$	6.20337			0.315743
$387$	3.52036	+	14.9495i	0.178950	+	0.759927i
$388$	17.4074	+	30.1505i	0.883728	+	1.53066i
$389$	−7.66041			−0.388398			−0.194199	−	0.980962i	$-0.562211\pi$
$389$	−7.66041			−0.388398			−0.194199	+	0.980962i	$0.562211\pi$
$390$	17.2957	+	2.54617i	0.875800	+	0.128930i
$391$	1.88875	+	3.27141i	0.0955181	+	0.165442i
$392$	−1.00342	+	7.03537i	−0.0506803	+	0.355340i
$393$	6.15114	+	15.5159i	0.310284	+	0.782674i
$394$	−22.3737	−	38.7523i	−1.12717	−	1.95231i
$395$	−6.25327	−	10.8310i	−0.314636	−	0.544966i
$396$	1.70512	+	7.24094i	0.0856854	+	0.363871i
$397$	0.725935	−	1.25736i	0.0364337	−	0.0631049i	−0.847234	−	0.531221i	$-0.821734\pi$
$397$	0.725935	−	1.25736i	0.0364337	−	0.0631049i	0.883667	+	0.468116i	$0.155067\pi$
$398$	−6.80364	+	11.7843i	−0.341036	+	0.590691i
$399$	−8.92908	+	5.70311i	−0.447013	+	0.285513i
$400$	2.23082	+	3.86389i	0.111541	+	0.193194i
$401$	−4.28115			−0.213790			−0.106895	−	0.994270i	$-0.534091\pi$
$401$	−4.28115			−0.213790			−0.106895	+	0.994270i	$0.534091\pi$
$402$	−4.15871	−	10.4901i	−0.207418	−	0.523200i
$403$	3.30637			0.164702
$404$	−15.8575	+	27.4660i	−0.788940	+	1.36648i
$405$	1.40957	−	23.0564i	0.0700420	−	1.14568i
$406$	23.7022	−	20.5615i	1.17632	−	1.02045i
$407$	1.80917	−	3.13358i	0.0896774	−	0.155326i
$408$	−2.32923	+	2.94143i	−0.115314	+	0.145623i
$409$	2.57805	−	4.46532i	0.127476	−	0.220796i	−0.795222	−	0.606319i	$-0.792646\pi$
$409$	2.57805	−	4.46532i	0.127476	−	0.220796i	0.922698	+	0.385523i	$0.125979\pi$
$410$	26.2065	−	45.3910i	1.29425	−	2.24170i
$411$	−12.1475	−	30.6413i	−0.599190	−	1.51142i
$412$	−18.4299	+	31.9215i	−0.907975	+	1.57266i
$413$	−3.91366	−	20.2444i	−0.192578	−	0.996162i
$414$	10.7642	+	3.23951i	0.529033	+	0.159213i
$415$	4.20477	−	7.28288i	0.206404	−	0.357502i
$416$	14.8254			0.726875
$417$	−16.1558	+	20.4021i	−0.791151	+	0.999093i
$418$	4.89344			0.239346
$419$	−14.2813	−	24.7360i	−0.697689	−	1.20843i	−0.969266	−	0.246016i	$-0.920879\pi$
$419$	−14.2813	−	24.7360i	−0.697689	−	1.20843i	0.271577	−	0.962417i	$-0.412455\pi$
$420$	−24.5792	+	15.6990i	−1.19934	+	0.766033i
$421$	6.01232	−	10.4136i	0.293022	−	0.507530i	−0.681500	−	0.731818i	$-0.738672\pi$
$421$	6.01232	−	10.4136i	0.293022	−	0.507530i	0.974523	+	0.224288i	$0.0720056\pi$
$422$	−2.62152	+	4.54060i	−0.127613	+	0.221033i
$423$	−7.66171	−	2.30580i	−0.372525	−	0.112112i
$424$	3.01368	+	5.21985i	0.146357	+	0.253499i
$425$	−1.69357	−	2.93336i	−0.0821504	−	0.142289i
$426$	29.8188	−	37.6563i	1.44473	−	1.82445i
$427$	8.50296	+	2.93752i	0.411487	+	0.142157i
$428$	−16.6659	−	28.8662i	−0.805577	−	1.39530i
$429$	−1.99786	+	2.52296i	−0.0964574	+	0.121810i
$430$	27.8103			1.34113
$431$	8.25079	+	14.2908i	0.397427	+	0.688363i	0.993408	−	0.114635i	$-0.0365700\pi$
$431$	8.25079	+	14.2908i	0.397427	+	0.688363i	−0.595981	+	0.802999i	$0.703237\pi$
$432$	−1.24139	−	14.5514i	−0.0597265	−	0.700104i
$433$	−31.9072			−1.53336			−0.766682	−	0.642027i	$-0.778094\pi$
$433$	−31.9072			−1.53336			−0.766682	+	0.642027i	$0.778094\pi$
$434$	−7.52726	+	6.52986i	−0.361320	+	0.313443i
$435$	24.6442	+	3.62798i	1.18160	+	0.173948i
$436$	−18.0124			−0.862640
$437$	2.04657	−	3.54477i	0.0979009	−	0.169569i
$438$	−40.2822	−	5.93013i	−1.92476	−	0.283352i
$439$	17.8736	+	30.9579i	0.853058	+	1.47754i	0.878435	+	0.477862i	$0.158588\pi$
$439$	17.8736	+	30.9579i	0.853058	+	1.47754i	−0.0253769	+	0.999678i	$0.508079\pi$
$440$	2.60567			0.124221
$441$	12.0852	+	17.1740i	0.575486	+	0.817811i
$442$	−8.39097			−0.399118
$443$	−19.8900	−	34.4505i	−0.945002	−	1.63679i	−0.755748	−	0.654863i	$-0.772726\pi$
$443$	−19.8900	−	34.4505i	−0.945002	−	1.63679i	−0.189254	−	0.981928i	$-0.560607\pi$
$444$	9.64753	−	12.1832i	0.457851	−	0.578191i
$445$	−15.4412	+	26.7449i	−0.731981	+	1.26783i
$446$	−50.2277			−2.37835
$447$	−9.93328	−	25.0562i	−0.469828	−	1.18512i
$448$	−22.5172	+	19.5336i	−1.06384	+	0.922875i
$449$	−29.0017			−1.36868			−0.684338	−	0.729165i	$-0.739909\pi$
$449$	−29.0017			−1.36868			−0.684338	+	0.729165i	$0.739909\pi$
$450$	−9.65191	−	2.90476i	−0.454996	−	0.136931i
$451$	4.82423	+	8.35581i	0.227164	+	0.393460i
$452$	−41.3363			−1.94430
$453$	0.365855	+	0.922849i	0.0171893	+	0.0433592i
$454$	23.3483	+	40.4404i	1.09579	+	1.89796i
$455$	−11.9255	−	4.11990i	−0.559075	−	0.193144i
$456$	4.02214	+	0.592118i	0.188354	+	0.0277285i
$457$	18.9562	+	32.8330i	0.886732	+	1.53586i	0.843716	+	0.536790i	$0.180363\pi$
$457$	18.9562	+	32.8330i	0.886732	+	1.53586i	0.0430155	+	0.999074i	$0.486304\pi$
$458$	−14.8966	−	25.8016i	−0.696072	−	1.20563i
$459$	0.942431	+	11.0470i	0.0439889	+	0.515631i
$460$	5.63362	−	9.75772i	0.262669	−	0.454956i
$461$	3.70303	−	6.41384i	0.172467	−	0.298722i	−0.766815	−	0.641869i	$-0.778159\pi$
$461$	3.70303	−	6.41384i	0.172467	−	0.298722i	0.939282	+	0.343147i	$0.111493\pi$
$462$	−0.434375	−	9.68939i	−0.0202090	−	0.450791i
$463$	20.9557	+	36.2963i	0.973892	+	1.68683i	0.683542	+	0.729911i	$0.260438\pi$
$463$	20.9557	+	36.2963i	0.973892	+	1.68683i	0.290350	+	0.956921i	$0.406228\pi$
$464$	15.7488			0.731121
$465$	−7.82642	−	1.15216i	−0.362941	−	0.0534302i
$466$	50.5000			2.33937
$467$	−20.9977	+	36.3691i	−0.971657	+	1.68296i	−0.281104	+	0.959677i	$0.590701\pi$
$467$	−20.9977	+	36.3691i	−0.971657	+	1.68296i	−0.690553	+	0.723282i	$0.742633\pi$
$468$	−10.0673	+	9.47062i	−0.465361	+	0.437780i
$469$	1.54580	+	7.99606i	0.0713785	+	0.369224i
$470$	−7.24407	+	12.5471i	−0.334144	+	0.578755i
$471$	−12.2468	−	1.80290i	−0.564301	−	0.0830733i
$472$	−3.95599	+	6.85198i	−0.182089	+	0.315388i
$473$	−2.55974	+	4.43359i	−0.117697	+	0.203857i
$474$	17.6729	+	2.60170i	0.811741	+	0.119500i
$475$	−1.83509	+	3.17847i	−0.0841998	+	0.145838i
$476$	10.5741	−	9.17301i	0.484665	−	0.420444i
$477$	17.0553	+	5.13282i	0.780910	+	0.235016i
$478$	−6.34550	+	10.9907i	−0.290236	+	0.502704i
$479$	17.2609			0.788670			0.394335	−	0.918967i	$-0.370975\pi$
$479$	17.2609			0.788670			0.394335	+	0.918967i	$0.370975\pi$
$480$	−35.0928	−	5.16617i	−1.60176	−	0.235802i
$481$	6.72297			0.306541
$482$	−16.2879	−	28.2114i	−0.741892	−	1.28500i
$483$	−7.20059	−	3.73772i	−0.327638	−	0.170072i
$484$	−1.23983	+	2.14745i	−0.0563560	+	0.0976115i
$485$	18.0177	−	31.2076i	0.818142	−	1.41706i
$486$	24.5677	+	22.0225i	1.11441	+	0.998960i
$487$	8.83490	+	15.3025i	0.400347	+	0.693422i	0.993768	−	0.111471i	$-0.0355561\pi$
$487$	8.83490	+	15.3025i	0.400347	+	0.693422i	−0.593420	+	0.804893i	$0.702223\pi$
$488$	−1.72598	−	2.98949i	−0.0781315	−	0.135328i
$489$	7.96895	+	1.17314i	0.360368	+	0.0530514i
$490$	35.2860	−	14.1727i	1.59406	−	0.640256i
$491$	2.15787	+	3.73755i	0.0973835	+	0.168673i	0.910601	−	0.413287i	$-0.135619\pi$
$491$	2.15787	+	3.73755i	0.0973835	+	0.168673i	−0.813217	+	0.581960i	$0.802286\pi$
$492$	15.2719	+	38.5225i	0.688509	+	1.73673i
$493$	−11.9561			−0.538475
$494$	4.54606	+	7.87401i	0.204537	+	0.354268i
$495$	5.60824	−	5.27585i	0.252072	−	0.237132i
$496$	−5.00146			−0.224572
$497$	−26.1860	+	22.7162i	−1.17460	+	1.01896i
$498$	4.42668	+	11.1661i	0.198364	+	0.500363i
$499$	−15.4549			−0.691857			−0.345929	−	0.938261i	$-0.612436\pi$
$499$	−15.4549			−0.691857			−0.345929	+	0.938261i	$0.612436\pi$
$500$	10.8593	−	18.8089i	0.485643	−	0.841158i
$501$	−21.7914	+	27.5190i	−0.973569	+	1.22946i
$502$	10.4343	+	18.0727i	0.465704	+	0.806623i
$503$	10.2318			0.456215			0.228107	−	0.973636i	$-0.426746\pi$
$503$	10.2318			0.456215			0.228107	+	0.973636i	$0.426746\pi$
$504$	0.815407	−	8.01673i	0.0363211	−	0.357093i
$505$	32.8269			1.46078
$506$	1.87352	+	3.24504i	0.0832882	+	0.144259i
$507$	16.3608	+	2.40855i	0.726611	+	0.106968i
$508$	5.78243	−	10.0155i	0.256554	−	0.444364i
$509$	13.3448			0.591500			0.295750	−	0.955265i	$-0.404430\pi$
$509$	13.3448			0.591500			0.295750	+	0.955265i	$0.404430\pi$
$510$	19.8620	+	2.92398i	0.879506	+	0.129476i
$511$	27.7749	+	9.59540i	1.22869	+	0.424476i
$512$	−28.1328			−1.24330
$513$	9.85583	−	6.86943i	0.435146	−	0.303293i
$514$	−19.3788	−	33.5650i	−0.854761	−	1.48049i
$515$	38.1520			1.68118
$516$	−13.6500	+	17.2376i	−0.600906	+	0.758845i
$517$	−1.33353	−	2.30974i	−0.0586484	−	0.101582i
$518$	−15.3055	+	13.2774i	−0.672484	+	0.583377i
$519$	16.8535	−	21.2832i	0.739787	−	0.934229i
$520$	2.42070	+	4.19278i	0.106155	+	0.183866i
$521$	−5.22825	−	9.05559i	−0.229054	−	0.396733i	0.728474	−	0.685073i	$-0.240230\pi$
$521$	−5.22825	−	9.05559i	−0.229054	−	0.396733i	−0.957528	+	0.288341i	$0.906896\pi$
$522$	−25.9145	+	24.3786i	−1.13425	+	1.06702i
$523$	−8.33846	+	14.4426i	−0.364615	+	0.631533i	−0.988714	−	0.149813i	$-0.952133\pi$
$523$	−8.33846	+	14.4426i	−0.364615	+	0.631533i	0.624099	+	0.781345i	$0.285466\pi$
$524$	−11.9475	+	20.6937i	−0.521930	+	0.904008i
$525$	6.45652	+	3.35148i	0.281786	+	0.146271i
$526$	−0.408960	−	0.708340i	−0.0178315	−	0.0308851i
$527$	3.79697			0.165399
$528$	3.02211	−	3.81642i	0.131520	−	0.166089i
$529$	−19.8658			−0.863729
$530$	16.1256	−	27.9304i	0.700453	−	1.21322i
$531$	5.35901	+	22.7576i	0.232561	+	0.987594i
$532$	−14.3367	−	4.95292i	−0.621576	−	0.214736i
$533$	−8.96353	+	15.5253i	−0.388254	+	0.672475i
$534$	−16.2561	−	41.0050i	−0.703469	−	1.77446i
$535$	−17.2502	+	29.8782i	−0.745791	+	1.29175i
$536$	1.56252	−	2.70637i	0.0674907	−	0.116897i
$537$	−22.7968	+	28.7886i	−0.983755	+	1.24232i
$538$	26.4661	−	45.8406i	1.14103	−	1.97633i
$539$	−0.988373	+	6.92987i	−0.0425722	+	0.298491i
$540$	27.1302	−	18.9095i	1.16750	−	0.813737i
$541$	−0.849669	+	1.47167i	−0.0365301	+	0.0632720i	−0.883712	−	0.468030i	$-0.844964\pi$
$541$	−0.849669	+	1.47167i	−0.0365301	+	0.0632720i	0.847182	+	0.531302i	$0.178297\pi$
$542$	12.3205			0.529212
$543$	12.3039	+	31.0358i	0.528009	+	1.33187i
$544$	17.0252			0.729950
$545$	9.32197	+	16.1461i	0.399309	+	0.691624i
$546$	15.1876	−	9.70051i	0.649970	−	0.415144i
$547$	13.5504	−	23.4700i	0.579373	−	1.00350i	−0.416178	−	0.909283i	$-0.636631\pi$
$547$	13.5504	−	23.4700i	0.579373	−	1.00350i	0.995551	−	0.0942211i	$-0.0300360\pi$
$548$	23.5943	−	40.8666i	1.00790	−	1.74573i
$549$	−9.76783	−	2.93964i	−0.416881	−	0.125461i
$550$	−1.67992	−	2.90971i	−0.0716321	−	0.124071i
$551$	6.47757	+	11.2195i	0.275954	+	0.477966i
$552$	1.14728	+	2.89395i	0.0488314	+	0.123175i
$553$	−12.1855	−	4.20975i	−0.518182	−	0.179017i
$554$	−14.2188	−	24.6277i	−0.604100	−	1.04633i
$555$	−15.9138	−	2.34274i	−0.675502	−	0.0994437i
$556$	−37.2570			−1.58005
$557$	−4.30101	−	7.44957i	−0.182240	−	0.315648i	0.760403	−	0.649451i	$-0.225001\pi$
$557$	−4.30101	−	7.44957i	−0.182240	−	0.315648i	−0.942643	+	0.333803i	$0.891668\pi$
$558$	8.22984	−	7.74206i	0.348397	−	0.327748i
$559$	−9.51210			−0.402319
$560$	18.0394	+	6.23208i	0.762303	+	0.263353i
$561$	−2.29430	+	2.89732i	−0.0968655	+	0.122325i
$562$	34.3053			1.44708
$563$	7.90771	−	13.6966i	0.333270	−	0.577241i	−0.649881	−	0.760036i	$-0.725181\pi$
$563$	7.90771	−	13.6966i	0.333270	−	0.577241i	0.983151	+	0.182795i	$0.0585145\pi$
$564$	−4.22149	−	10.6485i	−0.177757	−	0.448382i
$565$	21.3928	+	37.0534i	0.900000	+	1.55885i
$566$	43.0985			1.81156
$567$	−14.4769	−	18.9056i	−0.607972	−	0.793959i
$568$	13.3020			0.558139
$569$	−3.17014	−	5.49085i	−0.132899	−	0.230188i	0.791894	−	0.610659i	$-0.209095\pi$
$569$	−3.17014	−	5.49085i	−0.132899	−	0.230188i	−0.924793	+	0.380471i	$0.875762\pi$
$570$	−8.01702	−	20.2225i	−0.335796	−	0.847028i
$571$	0.0809891	−	0.140277i	0.00338929	−	0.00587042i	−0.864326	−	0.502932i	$-0.832254\pi$
$571$	0.0809891	−	0.140277i	0.00338929	−	0.00587042i	0.867715	+	0.497062i	$0.165588\pi$
$572$	−4.60728			−0.192640
$573$	17.5434	−	22.1545i	0.732887	−	0.925516i
$574$	−10.2551	−	53.0472i	−0.428039	−	2.21415i
$575$	−2.81036			−0.117200
$576$	24.6189	−	23.1598i	1.02579	−	0.964992i
$577$	20.5912	+	35.6650i	0.857224	+	1.48476i	0.874566	+	0.484906i	$0.161146\pi$
$577$	20.5912	+	35.6650i	0.857224	+	1.48476i	−0.0173425	+	0.999850i	$0.505521\pi$
$578$	26.3448			1.09580
$579$	5.02238	+	0.739367i	0.208723	+	0.0307271i
$580$	17.8309	+	30.8840i	0.740387	+	1.28239i
$581$	−1.64541	−	8.51130i	−0.0682630	−	0.353108i
$582$	18.9686	+	47.8473i	0.786273	+	1.98333i
$583$	2.96849	+	5.14158i	0.122942	+	0.212942i
$584$	−5.63790	−	9.76513i	−0.233298	−	0.404084i
$585$	13.6995	+	4.12287i	0.566403	+	0.170460i
$586$	9.35018	−	16.1950i	0.386252	−	0.669009i
$587$	11.3628	−	19.6809i	0.468992	−	0.812318i	−0.530380	−	0.847760i	$-0.677951\pi$
$587$	11.3628	−	19.6809i	0.468992	−	0.812318i	0.999372	+	0.0354423i	$0.0112840\pi$
$588$	−8.53455	+	28.8275i	−0.351959	+	1.18883i
$589$	−2.05713	−	3.56305i	−0.0847624	−	0.146813i
$590$	42.3355			1.74292
$591$	−13.4954	−	34.0414i	−0.555126	−	1.40028i
$592$	−10.1697			−0.417971
$593$	21.1695	−	36.6666i	0.869327	−	1.50572i	0.00664168	−	0.999978i	$-0.497886\pi$
$593$	21.1695	−	36.6666i	0.869327	−	1.50572i	0.862685	−	0.505741i	$-0.168781\pi$
$594$	0.934834	+	10.9580i	0.0383567	+	0.449611i
$595$	−13.6950	−	4.73122i	−0.561440	−	0.193961i
$596$	19.2937	−	33.4176i	0.790299	−	1.36884i
$597$	−6.91292	+	8.72988i	−0.282927	+	0.357290i
$598$	−3.48105	+	6.02936i	−0.142351	+	0.246559i
$599$	−12.9555	+	22.4395i	−0.529346	+	0.916854i	0.470068	+	0.882630i	$0.344229\pi$
$599$	−12.9555	+	22.4395i	−0.529346	+	0.916854i	−0.999414	+	0.0342239i	$0.989104\pi$
$600$	−1.02872	−	2.59490i	−0.0419975	−	0.105936i
$601$	−0.0851273	+	0.147445i	−0.00347242	+	0.00601440i	−0.867756	−	0.496990i	$-0.834439\pi$
$601$	−0.0851273	+	0.147445i	−0.00347242	+	0.00601440i	0.864284	+	0.503004i	$0.167772\pi$
$602$	21.6552	−	18.7858i	0.882600	−	0.765651i
$603$	−2.11668	−	8.98869i	−0.0861980	−	0.366048i
$604$	−0.710609	+	1.23081i	−0.0289143	+	0.0500810i
$605$	2.56660			0.104347
$606$	−29.1076	+	36.7581i	−1.18242	+	1.49320i
$607$	5.81274			0.235932			0.117966	−	0.993018i	$-0.462363\pi$
$607$	5.81274			0.235932			0.117966	+	0.993018i	$0.462363\pi$
$608$	−9.22393	−	15.9763i	−0.374080	−	0.647925i
$609$	21.6405	−	13.8220i	0.876916	−	0.560097i
$610$	−9.23539	+	15.9962i	−0.373930	+	0.647666i
$611$	2.47773	−	4.29155i	0.100238	−	0.173617i
$612$	−11.5611	+	10.8759i	−0.467330	+	0.439632i
$613$	−14.8034	−	25.6402i	−0.597904	−	1.03560i	−0.993130	−	0.117016i	$-0.962667\pi$
$613$	−14.8034	−	25.6402i	−0.597904	−	1.03560i	0.395226	−	0.918584i	$-0.370666\pi$
$614$	29.8750	+	51.7450i	1.20566	+	2.08826i
$615$	26.6274	−	33.6260i	1.07372	−	1.35593i
$616$	2.02897	−	1.76012i	0.0817496	−	0.0709173i
$617$	13.6833	+	23.7002i	0.550869	+	0.954132i	0.998212	+	0.0597703i	$0.0190368\pi$
$617$	13.6833	+	23.7002i	0.550869	+	0.954132i	−0.447344	+	0.894362i	$0.647630\pi$
$618$	−33.8294	+	42.7210i	−1.36082	+	1.71849i
$619$	22.0770			0.887349			0.443674	−	0.896188i	$-0.353675\pi$
$619$	22.0770			0.887349			0.443674	+	0.896188i	$0.353675\pi$
$620$	−5.66267	−	9.80803i	−0.227418	−	0.393900i
$621$	8.32884	+	3.90574i	0.334225	+	0.156732i
$622$	−7.28888			−0.292257
$623$	6.04242	+	31.2560i	0.242084	+	1.25224i
$624$	8.94857	+	1.31736i	0.358229	+	0.0527366i
$625$	−30.4172			−1.21669
$626$	−7.68883	+	13.3174i	−0.307307	+	0.532272i
$627$	3.96183	+	0.583239i	0.158220	+	0.0232923i
$628$	−8.86094	−	15.3476i	−0.353590	−	0.612436i
$629$	7.72054			0.307838
$630$	−39.3305	+	17.6694i	−1.56697	+	0.703967i
$631$	40.1182			1.59708			0.798540	−	0.601941i	$-0.205606\pi$
$631$	40.1182			1.59708			0.798540	+	0.601941i	$0.205606\pi$
$632$	2.47349	+	4.28422i	0.0983903	+	0.170417i
$633$	−2.66362	+	3.36371i	−0.105869	+	0.133696i
$634$	26.6876	−	46.2244i	1.05990	−	1.83580i
$635$	−11.9703			−0.475027
$636$	9.39724	+	23.7040i	0.372625	+	0.939926i
$637$	−12.0690	+	4.84755i	−0.478193	+	0.192067i
$638$	−11.8597			−0.469530
$639$	28.6301	−	26.9333i	1.13259	−	1.06546i
$640$	−10.1229	−	17.5334i	−0.400144	−	0.693070i
$641$	22.2973			0.880692			0.440346	−	0.897828i	$-0.354856\pi$
$641$	22.2973			0.880692			0.440346	+	0.897828i	$0.354856\pi$
$642$	−18.1606	−	45.8091i	−0.716741	−	1.80794i
$643$	1.71771	+	2.97516i	0.0677399	+	0.117329i	0.897906	−	0.440187i	$-0.145088\pi$
$643$	1.71771	+	2.97516i	0.0677399	+	0.117329i	−0.830166	+	0.557516i	$0.811755\pi$
$644$	−2.20454	−	11.4036i	−0.0868711	−	0.449364i
$645$	22.5158	+	3.31466i	0.886561	+	0.130515i
$646$	5.22062	+	9.04237i	0.205402	+	0.355767i
$647$	−23.2216	−	40.2211i	−0.912937	−	1.58125i	−0.809894	−	0.586577i	$-0.800475\pi$
$647$	−23.2216	−	40.2211i	−0.912937	−	1.58125i	−0.103043	−	0.994677i	$-0.532858\pi$
$648$	−0.557557	+	9.11999i	−0.0219029	+	0.358267i
$649$	−3.89667	+	6.74923i	−0.152958	+	0.264930i
$650$	3.12134	−	5.40631i	0.122429	−	0.212053i
$651$	−6.87251	+	4.38955i	−0.269355	+	0.172040i
$652$	5.76580	+	9.98665i	0.225806	+	0.391108i
$653$	0.929311			0.0363668			0.0181834	−	0.999835i	$-0.494212\pi$
$653$	0.929311			0.0363668			0.0181834	+	0.999835i	$0.494212\pi$
$654$	−26.3455	−	3.87845i	−1.03019	−	0.151659i
$655$	24.7328			0.966389
$656$	13.5589	−	23.4847i	0.529387	−	0.916925i
$657$	−31.9066	−	9.60232i	−1.24479	−	0.374622i
$658$	2.83474	+	14.6635i	0.110510	+	0.571641i
$659$	−4.28567	+	7.42301i	−0.166946	+	0.289159i	−0.937345	−	0.348403i	$-0.886724\pi$
$659$	−4.28567	+	7.42301i	−0.166946	+	0.289159i	0.770399	+	0.637563i	$0.220057\pi$
$660$	10.9058	+	1.60549i	0.424506	+	0.0624935i
$661$	−19.5529	+	33.8666i	−0.760518	+	1.31726i	0.182065	+	0.983286i	$0.441722\pi$
$661$	−19.5529	+	33.8666i	−0.760518	+	1.31726i	−0.942584	+	0.333970i	$0.891612\pi$
$662$	−7.85422	+	13.6039i	−0.305263	+	0.528731i
$663$	−6.79351	−	1.00010i	−0.263838	−	0.0388408i
$664$	−1.66321	+	2.88076i	−0.0645449	+	0.111795i
$665$	2.97995	+	15.4146i	0.115557	+	0.597751i
$666$	16.7341	−	15.7423i	0.648432	−	0.610000i
$667$	−4.96006	+	8.59108i	−0.192054	+	0.332648i
$668$	−50.2535			−1.94437
$669$	−40.6655	−	5.98655i	−1.57222	−	0.231453i
$670$	−16.7215			−0.646009
$671$	−1.70010	−	2.94466i	−0.0656316	−	0.113677i
$672$	−30.8156	+	19.6823i	−1.18874	+	0.759261i
$673$	25.1966	−	43.6418i	0.971258	−	1.68227i	0.279490	−	0.960149i	$-0.409835\pi$
$673$	25.1966	−	43.6418i	0.971258	−	1.68227i	0.691768	−	0.722120i	$-0.256832\pi$
$674$	9.03471	−	15.6486i	0.348004	−	0.602761i
$675$	−7.46819	−	3.50215i	−0.287451	−	0.134798i
$676$	11.8376	+	20.5033i	0.455293	+	0.788590i
$677$	−2.96406	−	5.13391i	−0.113918	−	0.197312i	0.803429	−	0.595401i	$-0.203007\pi$
$677$	−2.96406	−	5.13391i	−0.113918	−	0.197312i	−0.917347	+	0.398089i	$0.869674\pi$
$678$	−60.4597	−	8.90055i	−2.32194	−	0.341824i
$679$	−7.05067	−	36.4714i	−0.270580	−	1.39965i
$680$	2.77989	+	4.81491i	0.106604	+	0.184643i
$681$	14.0833	+	35.5242i	0.539671	+	1.36129i
$682$	3.76637			0.144222
$683$	2.69080	+	4.66059i	0.102960	+	0.178333i	0.912903	−	0.408176i	$-0.133835\pi$
$683$	2.69080	+	4.66059i	0.102960	+	0.178333i	−0.809943	+	0.586509i	$0.800502\pi$
$684$	16.4694	+	4.95649i	0.629724	+	0.189516i
$685$	−48.8430			−1.86620
$686$	17.9027	−	34.8714i	0.683529	−	1.33140i
$687$	−8.98535	−	22.6651i	−0.342812	−	0.864726i
$688$	14.3887			0.548565
$689$	−5.51553	+	9.55318i	−0.210125	+	0.363947i
$690$	10.3409	−	13.0589i	0.393673	−	0.497144i
$691$	−1.32759	−	2.29946i	−0.0505040	−	0.0874755i	0.839668	−	0.543100i	$-0.182749\pi$
$691$	−1.32759	−	2.29946i	−0.0505040	−	0.0874755i	−0.890172	+	0.455624i	$0.849416\pi$
$692$	38.8661			1.47747
$693$	0.803180	−	7.89651i	0.0305103	−	0.299964i
$694$	−72.9598			−2.76952
$695$	19.2816	+	33.3967i	0.731392	+	1.26681i
$696$	−9.74805	−	1.43505i	−0.369499	−	0.0543956i
$697$	−10.2936	+	17.8290i	−0.389896	+	0.675320i
$698$	−51.0104			−1.93077
$699$	40.8859	+	6.01900i	1.54645	+	0.227659i
$700$	1.97674	+	10.2252i	0.0747136	+	0.386476i
$701$	4.47309			0.168946			0.0844731	−	0.996426i	$-0.473079\pi$
$701$	4.47309			0.168946			0.0844731	+	0.996426i	$0.473079\pi$
$702$	−16.7640	+	11.6843i	−0.632715	+	0.440996i
$703$	−4.18284	−	7.24489i	−0.157759	−	0.273246i
$704$	11.2668			0.424634
$705$	−7.36042	+	9.29500i	−0.277210	+	0.350070i
$706$	9.61019	+	16.6453i	0.361684	+	0.626455i
$707$	25.5615	−	22.1744i	0.961338	−	0.833955i
$708$	−20.7792	+	26.2407i	−0.780931	+	0.986187i
$709$	−10.5936	−	18.3486i	−0.397851	−	0.689098i	0.595610	−	0.803274i	$-0.296910\pi$
$709$	−10.5936	−	18.3486i	−0.397851	−	0.689098i	−0.993461	+	0.114176i	$0.963577\pi$
$710$	−35.5882	−	61.6406i	−1.33560	−	2.31333i
$711$	13.9982	+	4.21279i	0.524975	+	0.157992i
$712$	6.10778	−	10.5790i	0.228899	−	0.396464i
$713$	1.57520	−	2.72833i	0.0589917	−	0.102177i
$714$	17.4412	−	11.1399i	0.652720	−	0.416900i
$715$	2.38440	+	4.12991i	0.0891716	+	0.154450i
$716$	−52.5720			−1.96471
$717$	−6.44742	+	8.14202i	−0.240783	+	0.304069i
$718$	−15.8017			−0.589716
$719$	7.49753	−	12.9861i	0.279611	−	0.484300i	−0.691677	−	0.722207i	$-0.743128\pi$
$719$	7.49753	−	12.9861i	0.279611	−	0.484300i	0.971288	+	0.237907i	$0.0764612\pi$
$720$	−20.7229	−	6.23657i	−0.772295	−	0.232423i
$721$	29.7080	−	25.7715i	1.10638	−	0.959782i
$722$	−14.4501	+	25.0283i	−0.537777	+	0.931457i
$723$	−9.82455	−	24.7819i	−0.365379	−	0.921649i
$724$	−23.8981	+	41.3927i	−0.888166	+	1.53835i
$725$	4.44752	−	7.70333i	0.165177	−	0.286094i
$726$	−2.27581	+	2.87397i	−0.0844631	+	0.106663i
$727$	12.7155	−	22.0240i	0.471593	−	0.816824i	−0.527879	−	0.849320i	$-0.677012\pi$
$727$	12.7155	−	22.0240i	0.471593	−	0.816824i	0.999472	+	0.0324963i	$0.0103457\pi$
$728$	4.71714	+	1.62964i	0.174829	+	0.0603983i
$729$	17.2657	+	20.7580i	0.639470	+	0.768816i
$730$	−30.1673	+	52.2513i	−1.11654	+	1.93391i
$731$	−10.9235			−0.404021
$732$	−5.38193	−	13.5756i	−0.198922	−	0.501770i
$733$	−25.3527			−0.936422			−0.468211	−	0.883617i	$-0.655101\pi$
$733$	−25.3527			−0.936422			−0.468211	+	0.883617i	$0.655101\pi$
$734$	−25.7211	−	44.5503i	−0.949385	−	1.64438i
$735$	30.2575	−	7.26883i	1.11607	−	0.268115i
$736$	7.06303	−	12.2335i	0.260347	−	0.450934i
$737$	1.53909	−	2.66579i	0.0566932	−	0.0981955i
$738$	14.0424	+	59.6324i	0.516909	+	2.19510i
$739$	10.2114	+	17.6866i	0.375631	+	0.650612i	0.990421	−	0.138078i	$-0.0440926\pi$
$739$	10.2114	+	17.6866i	0.375631	+	0.650612i	−0.614790	+	0.788691i	$0.710759\pi$
$740$	−11.5141	−	19.9431i	−0.423268	−	0.733122i
$741$	2.74210	+	6.91680i	0.100734	+	0.254095i
$742$	−6.31027	−	32.6415i	−0.231657	−	1.19831i
$743$	−7.29649	−	12.6379i	−0.267682	−	0.463639i	0.700581	−	0.713573i	$-0.252924\pi$
$743$	−7.29649	−	12.6379i	−0.267682	−	0.463639i	−0.968263	+	0.249934i	$0.919591\pi$
$744$	3.09575	+	0.455740i	0.113496	+	0.0167082i
$745$	−39.9402			−1.46329
$746$	27.0163	+	46.7937i	0.989138	+	1.71324i
$747$	2.25307	+	9.56789i	0.0824357	+	0.350071i
$748$	−5.29092			−0.193455
$749$	6.75033	+	34.9178i	0.246652	+	1.27587i
$750$	19.9331	−	25.1722i	0.727853	−	0.919158i
$751$	14.8029			0.540167			0.270083	−	0.962837i	$-0.412949\pi$
$751$	14.8029			0.540167			0.270083	+	0.962837i	$0.412949\pi$
$752$	−3.74800	+	6.49172i	−0.136675	+	0.236729i
$753$	6.29376	+	15.8757i	0.229357	+	0.578541i
$754$	−11.0178	−	19.0834i	−0.401245	−	0.694977i
$755$	1.47104			0.0535368
$756$	8.35231	−	33.0507i	0.303771	−	1.20204i
$757$	30.1009			1.09403			0.547017	−	0.837121i	$-0.315763\pi$
$757$	30.1009			1.09403			0.547017	+	0.837121i	$0.315763\pi$
$758$	−25.7682	−	44.6318i	−0.935943	−	1.62110i
$759$	1.13007	+	2.85055i	0.0410191	+	0.103469i
$760$	3.01218	−	5.21725i	0.109263	−	0.189250i
$761$	11.1545			0.404349			0.202175	−	0.979350i	$-0.435199\pi$
$761$	11.1545			0.404349			0.202175	+	0.979350i	$0.435199\pi$
$762$	10.6141	−	13.4038i	0.384508	−	0.485570i
$763$	18.1654	+	6.27562i	0.657633	+	0.227193i
$764$	40.4571			1.46369
$765$	15.7322	+	4.73463i	0.568800	+	0.171181i
$766$	11.0489	+	19.1373i	0.399214	+	0.691459i
$767$	−14.4802			−0.522850
$768$	−10.0040	−	1.47273i	−0.360987	−	0.0531426i
$769$	−19.7817	−	34.2630i	−0.713348	−	1.23555i	−0.963593	−	0.267372i	$-0.913845\pi$
$769$	−19.7817	−	34.2630i	−0.713348	−	1.23555i	0.250246	−	0.968182i	$-0.419489\pi$
$770$	−13.5846	−	4.69308i	−0.489555	−	0.169127i
$771$	−11.6889	−	29.4847i	−0.420966	−	1.06186i
$772$	3.63386	+	6.29403i	0.130785	+	0.226527i
$773$	−14.6510	−	25.3764i	−0.526961	−	0.912724i	−0.999506	−	0.0314174i	$-0.989998\pi$
$773$	−14.6510	−	25.3764i	−0.526961	−	0.912724i	0.472545	−	0.881307i	$-0.343335\pi$
$774$	−23.6764	+	22.2732i	−0.851032	+	0.800593i
$775$	−1.41243	+	2.44640i	−0.0507359	+	0.0878772i
$776$	−7.12694	+	12.3442i	−0.255842	+	0.443132i
$777$	−13.9742	+	8.92546i	−0.501320	+	0.320199i
$778$	−8.10671	−	14.0412i	−0.290640	−	0.503403i
$779$	22.3074			0.799246
$780$	7.54821	+	19.0399i	0.270269	+	0.681740i
$781$	13.1025			0.468845
$782$	−3.99758	+	6.92400i	−0.142953	+	0.247602i
$783$	−23.8865	+	16.6487i	−0.853636	+	0.594976i
$784$	18.2565	−	7.33277i	0.652020	−	0.261885i
$785$	−9.17159	+	15.8857i	−0.327348	+	0.566984i
$786$	−21.9306	+	27.6947i	−0.782237	+	0.987837i
$787$	14.0841	−	24.3943i	0.502043	−	0.869563i	−0.497955	−	0.867203i	$-0.665915\pi$
$787$	14.0841	−	24.3943i	0.502043	−	0.869563i	0.999997	−	0.00236027i	$-0.000751298\pi$
$788$	26.2125	−	45.4013i	0.933780	−	1.61735i
$789$	−0.246677	−	0.622230i	−0.00878195	−	0.0221520i
$790$	13.2352	−	22.9240i	0.470887	−	0.815600i
$791$	41.6874	+	14.4018i	1.48223	+	0.512068i
$792$	−2.21835	+	2.08687i	−0.0788256	+	0.0741538i
$793$	3.15882	−	5.47125i	0.112173	−	0.194290i
$794$	3.07292			0.109054
$795$	16.3846	−	20.6911i	0.581103	−	0.733838i
$796$	−15.9420			−0.565048
$797$	−6.18443	−	10.7117i	−0.219064	−	0.379430i	0.735458	−	0.677570i	$-0.236967\pi$
$797$	−6.18443	−	10.7117i	−0.219064	−	0.379430i	−0.954522	+	0.298140i	$0.903634\pi$
$798$	−19.9029	−	10.3313i	−0.704554	−	0.365724i
$799$	2.84538	−	4.92833i	0.100662	−	0.174352i
$800$	−6.33318	+	10.9694i	−0.223912	+	0.387826i
$801$	−8.27395	−	35.1361i	−0.292346	−	1.24147i
$802$	−4.53057	−	7.84718i	−0.159980	−	0.277094i
$803$	−5.55336	−	9.61870i	−0.195974	−	0.339437i
$804$	8.20730	−	10.3645i	0.289449	−	0.365527i
$805$	−9.08110	+	7.87781i	−0.320067	+	0.277656i
$806$	3.49900	+	6.06045i	0.123247	+	0.213470i
$807$	26.8912	−	33.9591i	0.946613	−	1.19542i
$808$	−12.9847			−0.456801
$809$	26.4921	+	45.8856i	0.931411	+	1.61325i	0.780912	+	0.624641i	$0.214755\pi$
$809$	26.4921	+	45.8856i	0.931411	+	1.61325i	0.150499	+	0.988610i	$0.451912\pi$
$810$	43.7531	−	21.8160i	1.53733	−	0.766535i
$811$	−42.1161			−1.47890			−0.739449	−	0.673213i	$-0.764914\pi$
$811$	−42.1161			−1.47890			−0.739449	+	0.673213i	$0.764914\pi$
$812$	34.7465	+	12.0039i	1.21936	+	0.421254i
$813$	9.97496	+	1.46846i	0.349837	+	0.0515011i
$814$	7.65831			0.268424
$815$	5.96794	−	10.3368i	0.209048	−	0.362081i
$816$	10.2764	+	1.51283i	0.359745	+	0.0529597i
$817$	5.91816	+	10.2505i	0.207050	+	0.358621i
$818$	10.9130			0.381564
$819$	13.4524	−	6.04356i	0.470065	−	0.211179i
$820$	61.4058			2.14438
$821$	21.4164	+	37.0944i	0.747439	+	1.29460i	0.949047	+	0.315136i	$0.102050\pi$
$821$	21.4164	+	37.0944i	0.747439	+	1.29460i	−0.201608	+	0.979466i	$0.564617\pi$
$822$	43.3092	−	54.6923i	1.51058	−	1.90761i
$823$	−5.13618	+	8.89613i	−0.179036	+	0.310100i	−0.941551	−	0.336872i	$-0.890631\pi$
$823$	−5.13618	+	8.89613i	−0.179036	+	0.310100i	0.762515	+	0.646971i	$0.223965\pi$
$824$	−15.0911			−0.525723
$825$	−1.01330	−	2.55599i	−0.0352785	−	0.0889882i
$826$	32.9656	−	28.5975i	1.14702	−	0.995033i
$827$	−33.5144			−1.16541			−0.582705	−	0.812684i	$-0.698006\pi$
$827$	−33.5144			−1.16541			−0.582705	+	0.812684i	$0.698006\pi$
$828$	3.01870	+	12.8192i	0.104907	+	0.445498i
$829$	10.6212	+	18.3964i	0.368889	+	0.638935i	0.989392	−	0.145269i	$-0.0464048\pi$
$829$	10.6212	+	18.3964i	0.368889	+	0.638935i	−0.620503	+	0.784204i	$0.713072\pi$
$830$	17.7990			0.617812
$831$	−8.57654	−	21.6339i	−0.297517	−	0.750470i
$832$	10.4670	+	18.1294i	0.362878	+	0.628523i
$833$	−13.8599	+	5.56684i	−0.480216	+	0.192879i
$834$	−54.4932	−	8.02219i	−1.88694	−	0.277786i
$835$	26.0077	+	45.0466i	0.900032	+	1.55890i
$836$	2.86652	+	4.96495i	0.0991405	+	0.171716i
$837$	7.58581	−	5.28724i	0.262204	−	0.182754i
$838$	30.2268	−	52.3543i	1.04417	−	1.80855i
$839$	−12.3794	+	21.4418i	−0.427386	+	0.740254i	−0.996640	−	0.0819078i	$-0.973899\pi$
$839$	−12.3794	+	21.4418i	−0.427386	+	0.740254i	0.569254	+	0.822162i	$0.307232\pi$
$840$	−10.5980	−	5.50124i	−0.365664	−	0.189811i
$841$	−1.19901	−	2.07675i	−0.0413453	−	0.0716122i
$842$	25.4504			0.877079
$843$	27.7743	+	4.08879i	0.956599	+	0.140825i
$844$	−6.14261			−0.211437
$845$	12.2526	−	21.2222i	0.421503	−	0.730065i
$846$	−3.88165	−	16.4838i	−0.133454	−	0.566724i
$847$	1.99855	−	1.73373i	0.0686709	−	0.0595716i
$848$	8.34321	−	14.4509i	0.286507	−	0.496245i
$849$	34.8935	+	5.13682i	1.19754	+	0.176295i
$850$	3.58449	−	6.20851i	0.122947	−	0.212950i
$851$	3.20292	−	5.54762i	0.109795	−	0.190170i
$852$	55.6741	+	8.19604i	1.90736	+	0.280792i
$853$	−0.328688	+	0.569305i	−0.0112541	+	0.0194926i	−0.871598	−	0.490222i	$-0.836916\pi$
$853$	−0.328688	+	0.569305i	−0.0112541	+	0.0194926i	0.860344	+	0.509715i	$0.170249\pi$
$854$	3.61398	+	18.6943i	0.123668	+	0.639705i
$855$	−4.08047	−	17.3281i	−0.139549	−	0.592609i
$856$	6.82335	−	11.8184i	0.233217	−	0.403944i
$857$	−39.0815			−1.33500			−0.667500	−	0.744610i	$-0.732635\pi$
$857$	−39.0815			−1.33500			−0.667500	+	0.744610i	$0.732635\pi$
$858$	−6.73875	−	0.992041i	−0.230057	−	0.0338677i
$859$	17.6371			0.601770			0.300885	−	0.953660i	$-0.402718\pi$
$859$	17.6371			0.601770			0.300885	+	0.953660i	$0.402718\pi$
$860$	16.2910	+	28.2168i	0.555517	+	0.962184i
$861$	−1.98016	−	44.1704i	−0.0674836	−	1.50532i
$862$	−17.4630	+	30.2468i	−0.594792	+	1.03021i
$863$	0.850995	−	1.47397i	0.0289682	−	0.0501744i	−0.851178	−	0.524877i	$-0.824111\pi$
$863$	0.850995	−	1.47397i	0.0289682	−	0.0501744i	0.880146	+	0.474703i	$0.157445\pi$
$864$	34.0140	−	23.7074i	1.15718	−	0.806543i
$865$	−20.1144	−	34.8391i	−0.683909	−	1.18456i
$866$	−33.7662	−	58.4848i	−1.14742	−	1.98739i
$867$	21.3293	+	3.13999i	0.724383	+	0.106640i
$868$	−11.0347	−	3.81215i	−0.374541	−	0.129393i
$869$	2.43640	+	4.21997i	0.0826493	+	0.143153i
$870$	19.4300	+	49.0112i	0.658739	+	1.66163i
$871$	5.71934			0.193792
$872$	−3.68732	−	6.38663i	−0.124869	−	0.216279i
$873$	9.65456	+	40.9990i	0.326757	+	1.38761i
$874$	8.66323			0.293038
$875$	−17.5046	+	15.1852i	−0.591765	+	0.513353i
$876$	−17.5800	−	44.3447i	−0.593975	−	1.49827i
$877$	−41.6362			−1.40595			−0.702977	−	0.711213i	$-0.748146\pi$
$877$	−41.6362			−1.40595			−0.702977	+	0.711213i	$0.748146\pi$
$878$	−37.8298	+	65.5231i	−1.27669	+	2.21130i
$879$	9.50035	−	11.9974i	0.320439	−	0.404662i
$880$	−3.60683	−	6.24721i	−0.121586	−	0.210593i
$881$	21.7833			0.733896			0.366948	−	0.930241i	$-0.380403\pi$
$881$	21.7833			0.733896			0.366948	+	0.930241i	$0.380403\pi$
$882$	−18.6900	+	40.3264i	−0.629327	+	1.35786i
$883$	−31.8967			−1.07341			−0.536704	−	0.843770i	$-0.680331\pi$
$883$	−31.8967			−1.07341			−0.536704	+	0.843770i	$0.680331\pi$
$884$	−4.91533	−	8.51360i	−0.165320	−	0.286343i
$885$	34.2757	+	5.04588i	1.15217	+	0.169616i
$886$	42.0976	−	72.9152i	1.41430	−	2.44963i
$887$	6.23191			0.209247			0.104623	−	0.994512i	$-0.466636\pi$
$887$	6.23191			0.209247			0.104623	+	0.994512i	$0.466636\pi$
$888$	6.29472	+	0.926675i	0.211237	+	0.0310972i
$889$	−9.32097	+	8.08589i	−0.312615	+	0.271192i
$890$	−65.3631			−2.19098
$891$	−0.549197	+	8.98323i	−0.0183988	+	0.300949i
$892$	−29.4228	−	50.9618i	−0.985148	−	1.70633i
$893$	−6.16628			−0.206347
$894$	35.4150	−	44.7233i	1.18445	−	1.49577i
$895$	27.2076	+	47.1249i	0.909449	+	1.57521i
$896$	−19.7262	−	6.81484i	−0.659007	−	0.227668i
$897$	−3.53696	+	4.46660i	−0.118096	+	0.149135i
$898$	−30.6914	−	53.1591i	−1.02419	−	1.77394i
$899$	4.98564	+	8.63539i	0.166280	+	0.288006i
$900$	−2.70677	−	11.4945i	−0.0902256	−	0.383151i
$901$	−6.33394	+	10.9707i	−0.211014	+	0.365487i
$902$	−10.2106	+	17.6853i	−0.339975	+	0.588854i
$903$	19.7716	−	12.6283i	0.657956	−	0.420244i
$904$	−8.46195	−	14.6565i	−0.281440	−	0.487469i
$905$	49.4719			1.64450
$906$	−1.30438	+	1.64721i	−0.0433350	+	0.0547250i
$907$	−33.9075			−1.12588			−0.562940	−	0.826498i	$-0.690330\pi$
$907$	−33.9075			−1.12588			−0.562940	+	0.826498i	$0.690330\pi$
$908$	−27.3543	+	47.3790i	−0.907783	+	1.57233i
$909$	−27.9473	+	26.2909i	−0.926953	+	0.872014i
$910$	−5.06864	−	26.2189i	−0.168024	−	0.869147i
$911$	−7.39888	+	12.8152i	−0.245136	+	0.424588i	−0.962170	−	0.272450i	$-0.912166\pi$
$911$	−7.39888	+	12.8152i	−0.245136	+	0.424588i	0.717034	+	0.697038i	$0.245499\pi$
$912$	−4.14791	−	10.4629i	−0.137351	−	0.346461i
$913$	−1.63826	+	2.83756i	−0.0542187	+	0.0939095i
$914$	−40.1211	+	69.4918i	−1.32709	+	2.29859i
$915$	−9.38372	+	11.8501i	−0.310216	+	0.391752i
$916$	17.4525	−	30.2286i	0.576646	−	0.998780i
$917$	19.2588	−	16.7069i	0.635981	−	0.551710i
$918$	−19.2514	+	13.4181i	−0.635392	+	0.442862i
$919$	2.02331	−	3.50447i	0.0667427	−	0.115602i	−0.830723	−	0.556686i	$-0.812073\pi$
$919$	2.02331	−	3.50447i	0.0667427	−	0.115602i	0.897466	+	0.441084i	$0.145406\pi$
$920$	4.61303			0.152087
$921$	18.0201	+	45.4546i	0.593781	+	1.49778i
$922$	15.6751			0.516232
$923$	12.1724	+	21.0832i	0.400660	+	0.693963i
$924$	9.57654	−	6.11665i	0.315045	−	0.201223i
$925$	−2.87195	+	4.97436i	−0.0944291	+	0.163556i
$926$	−44.3531	+	76.8219i	−1.45753	+	2.52452i
$927$	−32.4809	+	30.5558i	−1.06681	+	1.00358i
$928$	22.3551	+	38.7201i	0.733841	+	1.27105i
$929$	17.5601	+	30.4149i	0.576127	+	0.997881i	0.995918	+	0.0902600i	$0.0287698\pi$
$929$	17.5601	+	30.4149i	0.576127	+	0.997881i	−0.419792	+	0.907621i	$0.637897\pi$
$930$	−6.17052	−	15.5648i	−0.202339	−	0.510390i
$931$	12.7329	+	9.98998i	0.417303	+	0.327408i
$932$	29.5823	+	51.2380i	0.969000	+	1.67836i
$933$	−5.90123	−	0.868747i	−0.193198	−	0.0284415i
$934$	−88.8841			−2.90838
$935$	2.73821	+	4.74271i	0.0895489	+	0.155103i
$936$	−5.41885	−	1.63081i	−0.177121	−	0.0533047i
$937$	6.91061			0.225760			0.112880	−	0.993609i	$-0.463992\pi$
$937$	6.91061			0.225760			0.112880	+	0.993609i	$0.463992\pi$
$938$	−13.0206	+	11.2953i	−0.425138	+	0.368805i
$939$	−7.81232	+	9.86567i	−0.254945	+	0.321954i
$940$	−16.9740			−0.553630
$941$	14.3510	−	24.8566i	0.467829	−	0.810303i	−0.531495	−	0.847061i	$-0.678370\pi$
$941$	14.3510	−	24.8566i	0.467829	−	0.810303i	0.999324	+	0.0367578i	$0.0117030\pi$
$942$	−9.65562	−	24.3558i	−0.314597	−	0.793555i
$943$	8.54071	+	14.7929i	0.278124	+	0.481724i
$944$	21.9039			0.712910
$945$	−33.9488	+	9.61783i	−1.10436	+	0.312868i
$946$	−10.8355			−0.352292
$947$	−14.5078	−	25.1283i	−0.471441	−	0.816560i	0.528025	−	0.849229i	$-0.322933\pi$
$947$	−14.5078	−	25.1283i	−0.471441	−	0.816560i	−0.999466	+	0.0326690i	$0.989599\pi$
$948$	7.71282	+	19.4552i	0.250501	+	0.631875i
$949$	10.3183	−	17.8718i	0.334945	−	0.580143i
$950$	−7.76802			−0.252028
$951$	27.1163	−	34.2434i	0.879306	−	1.11042i
$952$	5.41708	+	1.87144i	0.175569	+	0.0606538i
$953$	43.0740			1.39530			0.697651	−	0.716437i	$-0.254228\pi$
$953$	43.0740			1.39530			0.697651	+	0.716437i	$0.254228\pi$
$954$	8.64072	+	36.6936i	0.279754	+	1.18800i
$955$	−20.9378	−	36.2653i	−0.677530	−	1.17352i
$956$	−14.8685			−0.480881
$957$	−9.60188	−	1.41354i	−0.310385	−	0.0456931i
$958$	18.2665	+	31.6386i	0.590165	+	1.02220i
$959$	−38.0328	+	32.9933i	−1.22814	+	1.06541i
$960$	−18.4587	−	46.5610i	−0.595751	−	1.50275i
$961$	13.9167	+	24.1044i	0.448925	+	0.777561i
$962$	7.11466	+	12.3230i	0.229386	+	0.397308i
$963$	−9.24330	−	39.2525i	−0.297861	−	1.26490i
$964$	19.0825	−	33.0518i	0.614605	−	1.06453i
$965$	3.76126	−	6.51469i	0.121079	−	0.209715i
$966$	−0.769009	−	17.1539i	−0.0247424	−	0.551917i
$967$	3.82707	+	6.62867i	0.123070	+	0.213164i	0.920977	−	0.389617i	$-0.127393\pi$
$967$	3.82707	+	6.62867i	0.123070	+	0.213164i	−0.797907	+	0.602781i	$0.794059\pi$
$968$	−1.01522			−0.0326305
$969$	3.14898	+	7.94313i	0.101160	+	0.255170i
$970$	76.2697			2.44887
$971$	−16.0197	+	27.7469i	−0.514096	+	0.890441i	0.485770	+	0.874087i	$0.338539\pi$
$971$	−16.0197	+	27.7469i	−0.514096	+	0.890441i	−0.999866	+	0.0163541i	$0.994794\pi$
$972$	−7.95288	+	37.8272i	−0.255089	+	1.21331i
$973$	37.5734	+	12.9805i	1.20455	+	0.416136i
$974$	−18.6993	+	32.3881i	−0.599163	+	1.03778i
$975$	3.17147	−	4.00504i	0.101568	−	0.128264i
$976$	−4.77828	+	8.27622i	−0.152949	+	0.264915i
$977$	−21.5360	+	37.3014i	−0.688997	+	1.19338i	0.283165	+	0.959071i	$0.408615\pi$
$977$	−21.5360	+	37.3014i	−0.688997	+	1.19338i	−0.972163	+	0.234307i	$0.924718\pi$
$978$	6.28290	+	15.8483i	0.200905	+	0.506772i
$979$	6.01619	−	10.4203i	0.192278	−	0.333036i
$980$	35.0499	+	27.4995i	1.11963	+	0.878439i
$981$	−20.8677	−	6.28015i	−0.666253	−	0.200510i
$982$	−4.56719	+	7.91060i	−0.145745	+	0.252437i
$983$	11.7905			0.376057			0.188029	−	0.982164i	$-0.439790\pi$
$983$	11.7905			0.376057			0.188029	+	0.982164i	$0.439790\pi$
$984$	−10.5325	+	13.3008i	−0.335764	+	0.424015i
$985$	−54.2629			−1.72896
$986$	−12.6527	−	21.9150i	−0.402943	−	0.697917i
$987$	0.547361	+	12.2097i	0.0174227	+	0.388639i
$988$	−5.32606	+	9.22500i	−0.169444	+	0.293486i
$989$	−4.53170	+	7.84914i	−0.144100	+	0.249588i
$990$	15.6054	+	4.69647i	0.495973	+	0.149264i
$991$	−28.5783	−	49.4990i	−0.907819	−	1.57239i	−0.817088	−	0.576512i	$-0.804413\pi$
$991$	−28.5783	−	49.4990i	−0.907819	−	1.57239i	−0.0907302	−	0.995876i	$-0.528920\pi$
$992$	−7.09945	−	12.2966i	−0.225408	−	0.390418i
$993$	−7.98037	+	10.0779i	−0.253249	+	0.319812i
$994$	−69.3496	−	23.9583i	−2.19964	−	0.759910i
$995$	8.25044	+	14.2902i	0.261556	+	0.453029i
$996$	−8.73615	+	11.0323i	−0.276815	+	0.349572i
$997$	3.01322			0.0954297			0.0477149	−	0.998861i	$-0.484806\pi$
$997$	3.01322			0.0954297			0.0477149	+	0.998861i	$0.484806\pi$
$998$	−16.3553	−	28.3283i	−0.517719	−	0.896716i
$999$	15.4245	−	10.7508i	0.488011	−	0.340139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.k.c.331.35	yes	80
7.4	even	3		693.2.l.c.529.6	yes	80
9.4	even	3		693.2.l.c.562.6	yes	80
63.4	even	3	inner	693.2.k.c.67.35	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.k.c.67.35	✓	80	63.4	even	3	inner
693.2.k.c.331.35	yes	80	1.1	even	1	trivial
693.2.l.c.529.6	yes	80	7.4	even	3
693.2.l.c.562.6	yes	80	9.4	even	3

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05826 + 1.83296i) q^{2} +(0.638324 + 1.61014i) q^{3} +(-1.23983 + 2.14745i) q^{4} +2.56660 q^{5} +(-2.27581 + 2.87397i) q^{6} +(1.99855 - 1.73373i) q^{7} -1.01522 q^{8} +(-2.18509 + 2.05558i) q^{9} +O(q^{10})\)	\(q+(1.05826 + 1.83296i) q^{2} +(0.638324 + 1.61014i) q^{3} +(-1.23983 + 2.14745i) q^{4} +2.56660 q^{5} +(-2.27581 + 2.87397i) q^{6} +(1.99855 - 1.73373i) q^{7} -1.01522 q^{8} +(-2.18509 + 2.05558i) q^{9} +(2.71613 + 4.70448i) q^{10} -1.00000 q^{11} +(-4.24911 - 0.625531i) q^{12} +(-0.929012 - 1.60910i) q^{13} +(5.29284 + 1.82852i) q^{14} +(1.63832 + 4.13258i) q^{15} +(1.40529 + 2.43404i) q^{16} +(-1.06686 - 1.84786i) q^{17} +(-6.08019 - 1.82984i) q^{18} +(-1.15601 + 2.00227i) q^{19} +(-3.18216 + 5.51166i) q^{20} +(4.06726 + 2.11125i) q^{21} +(-1.05826 - 1.83296i) q^{22} -1.77038 q^{23} +(-0.648041 - 1.63465i) q^{24} +1.58744 q^{25} +(1.96627 - 3.40569i) q^{26} +(-4.70456 - 2.20616i) q^{27} +(1.24524 + 6.44132i) q^{28} +(2.80170 - 4.85268i) q^{29} +(-5.84109 + 7.37633i) q^{30} +(-0.889754 + 1.54110i) q^{31} +(-3.98956 + 6.91012i) q^{32} +(-0.638324 - 1.61014i) q^{33} +(2.25803 - 3.91103i) q^{34} +(5.12947 - 4.44979i) q^{35} +(-1.70512 - 7.24094i) q^{36} +(-1.80917 + 3.13358i) q^{37} -4.89344 q^{38} +(1.99786 - 2.52296i) q^{39} -2.60567 q^{40} +(-4.82423 - 8.35581i) q^{41} +(0.434375 + 9.68939i) q^{42} +(2.55974 - 4.43359i) q^{43} +(1.23983 - 2.14745i) q^{44} +(-5.60824 + 5.27585i) q^{45} +(-1.87352 - 3.24504i) q^{46} +(1.33353 + 2.30974i) q^{47} +(-3.02211 + 3.81642i) q^{48} +(0.988373 - 6.92987i) q^{49} +(1.67992 + 2.90971i) q^{50} +(2.29430 - 2.89732i) q^{51} +4.60728 q^{52} +(-2.96849 - 5.14158i) q^{53} +(-0.934834 - 10.9580i) q^{54} -2.56660 q^{55} +(-2.02897 + 1.76012i) q^{56} +(-3.96183 - 0.583239i) q^{57} +11.8597 q^{58} +(3.89667 - 6.74923i) q^{59} +(-10.9058 - 1.60549i) q^{60} +(1.70010 + 2.94466i) q^{61} -3.76637 q^{62} +(-0.803180 + 7.89651i) q^{63} -11.2668 q^{64} +(-2.38440 - 4.12991i) q^{65} +(2.27581 - 2.87397i) q^{66} +(-1.53909 + 2.66579i) q^{67} +5.29092 q^{68} +(-1.13007 - 2.85055i) q^{69} +(13.5846 + 4.69308i) q^{70} -13.1025 q^{71} +(2.21835 - 2.08687i) q^{72} +(5.55336 + 9.61870i) q^{73} -7.65831 q^{74} +(1.01330 + 2.55599i) q^{75} +(-2.86652 - 4.96495i) q^{76} +(-1.99855 + 1.73373i) q^{77} +(6.73875 + 0.992041i) q^{78} +(-2.43640 - 4.21997i) q^{79} +(3.60683 + 6.24721i) q^{80} +(0.549197 - 8.98323i) q^{81} +(10.2106 - 17.6853i) q^{82} +(1.63826 - 2.83756i) q^{83} +(-9.57654 + 6.11665i) q^{84} +(-2.73821 - 4.74271i) q^{85} +10.8355 q^{86} +(9.60188 + 1.41354i) q^{87} +1.01522 q^{88} +(-6.01619 + 10.4203i) q^{89} +(-15.6054 - 4.69647i) q^{90} +(-4.64641 - 1.60520i) q^{91} +(2.19497 - 3.80181i) q^{92} +(-3.04933 - 0.448906i) q^{93} +(-2.82244 + 4.88861i) q^{94} +(-2.96701 + 5.13902i) q^{95} +(-13.6729 - 2.01285i) q^{96} +(7.02007 - 12.1591i) q^{97} +(13.7481 - 5.52196i) q^{98} +(2.18509 - 2.05558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 40 q^{4} + 8 q^{5} + 6 q^{6} - q^{7} + 2 q^{9}+O(q^{10}) \) 80 * q - 40 * q^4 + 8 * q^5 + 6 * q^6 - q^7 + 2 * q^9	\( 80 q - 40 q^{4} + 8 q^{5} + 6 q^{6} - q^{7} + 2 q^{9} + 12 q^{10} - 80 q^{11} - 10 q^{12} + 21 q^{13} - 8 q^{14} - 5 q^{15} - 40 q^{16} - 3 q^{17} + 32 q^{18} + 18 q^{19} - 12 q^{20} + 18 q^{21} - 8 q^{23} - 14 q^{24} + 80 q^{25} - 12 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} + 20 q^{30} + 32 q^{31} + 35 q^{32} + 28 q^{34} - 18 q^{35} - 16 q^{36} - 7 q^{37} + 46 q^{38} - 48 q^{39} - 102 q^{40} - 2 q^{41} - 14 q^{42} + 9 q^{43} + 40 q^{44} - 5 q^{45} - 6 q^{46} - 26 q^{47} - 28 q^{48} - 19 q^{49} + 2 q^{50} + 22 q^{51} - 88 q^{52} + 4 q^{53} + 19 q^{54} - 8 q^{55} + 18 q^{56} + 16 q^{57} + 32 q^{58} - 24 q^{59} - 10 q^{60} + 69 q^{61} + 12 q^{62} + 20 q^{63} + 44 q^{64} - 7 q^{65} - 6 q^{66} + 7 q^{67} + 34 q^{68} + 15 q^{69} - 22 q^{70} + 34 q^{71} - 70 q^{72} + 26 q^{73} + 8 q^{74} - 64 q^{75} + 52 q^{76} + q^{77} - 60 q^{78} - 5 q^{79} - 47 q^{80} + 46 q^{81} + 60 q^{82} + 4 q^{83} + 29 q^{84} + 13 q^{85} - 38 q^{87} - 38 q^{89} - 43 q^{90} + 13 q^{91} - 21 q^{92} + 35 q^{93} + 56 q^{94} - 20 q^{95} + 15 q^{96} + 49 q^{97} - 84 q^{98} - 2 q^{99}+O(q^{100}) \) 80 * q - 40 * q^4 + 8 * q^5 + 6 * q^6 - q^7 + 2 * q^9 + 12 * q^10 - 80 * q^11 - 10 * q^12 + 21 * q^13 - 8 * q^14 - 5 * q^15 - 40 * q^16 - 3 * q^17 + 32 * q^18 + 18 * q^19 - 12 * q^20 + 18 * q^21 - 8 * q^23 - 14 * q^24 + 80 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 + 20 * q^30 + 32 * q^31 + 35 * q^32 + 28 * q^34 - 18 * q^35 - 16 * q^36 - 7 * q^37 + 46 * q^38 - 48 * q^39 - 102 * q^40 - 2 * q^41 - 14 * q^42 + 9 * q^43 + 40 * q^44 - 5 * q^45 - 6 * q^46 - 26 * q^47 - 28 * q^48 - 19 * q^49 + 2 * q^50 + 22 * q^51 - 88 * q^52 + 4 * q^53 + 19 * q^54 - 8 * q^55 + 18 * q^56 + 16 * q^57 + 32 * q^58 - 24 * q^59 - 10 * q^60 + 69 * q^61 + 12 * q^62 + 20 * q^63 + 44 * q^64 - 7 * q^65 - 6 * q^66 + 7 * q^67 + 34 * q^68 + 15 * q^69 - 22 * q^70 + 34 * q^71 - 70 * q^72 + 26 * q^73 + 8 * q^74 - 64 * q^75 + 52 * q^76 + q^77 - 60 * q^78 - 5 * q^79 - 47 * q^80 + 46 * q^81 + 60 * q^82 + 4 * q^83 + 29 * q^84 + 13 * q^85 - 38 * q^87 - 38 * q^89 - 43 * q^90 + 13 * q^91 - 21 * q^92 + 35 * q^93 + 56 * q^94 - 20 * q^95 + 15 * q^96 + 49 * q^97 - 84 * q^98 - 2 * q^99

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