LMFDB - Embedded newform 570.2.i.j.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(121,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("570.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.i (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29654208.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 14x^{4} + 49x^{2} + 12 $ x^6 + 14x^4 + 49x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$-0.514306i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.2.i.j.391.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +3.84469 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +3.84469 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +5.73549 q^{11} +1.00000 q^{12} +(-2.36774 + 4.10105i) q^{13} +(-1.92234 - 3.32960i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.31315 + 5.73854i) q^{17} +1.00000 q^{18} +(-4.29009 + 0.771459i) q^{19} +1.00000 q^{20} +(-1.92234 - 3.32960i) q^{21} +(-2.86774 - 4.96708i) q^{22} +(2.86774 - 4.96708i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +4.73549 q^{26} +1.00000 q^{27} +(-1.92234 + 3.32960i) q^{28} +(5.15783 - 8.93363i) q^{29} +1.00000 q^{30} +4.73549 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.86774 - 4.96708i) q^{33} +(3.31315 - 5.73854i) q^{34} +(-1.92234 - 3.32960i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.00000 q^{37} +(2.81315 + 3.32960i) q^{38} +4.73549 q^{39} +(-0.500000 - 0.866025i) q^{40} +(-4.39928 - 7.61978i) q^{41} +(-1.92234 + 3.32960i) q^{42} +(-0.523059 - 0.905965i) q^{43} +(-2.86774 + 4.96708i) q^{44} +1.00000 q^{45} -5.73549 q^{46} +(-0.890804 + 1.54292i) q^{47} +(-0.500000 + 0.866025i) q^{48} +7.78161 q^{49} +1.00000 q^{50} +(3.31315 - 5.73854i) q^{51} +(-2.36774 - 4.10105i) q^{52} +(-2.55460 + 4.42469i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.86774 - 4.96708i) q^{55} +3.84469 q^{56} +(2.81315 + 3.32960i) q^{57} -10.3157 q^{58} +(-3.00000 - 5.19615i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(0.0545981 - 0.0945666i) q^{61} +(-2.36774 - 4.10105i) q^{62} +(-1.92234 + 3.32960i) q^{63} +1.00000 q^{64} +4.73549 q^{65} +(-2.86774 + 4.96708i) q^{66} +(-2.94540 + 5.10159i) q^{67} -6.62629 q^{68} -5.73549 q^{69} +(-1.92234 + 3.32960i) q^{70} +(3.31315 + 5.73854i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.05460 + 5.29072i) q^{73} +(0.500000 + 0.866025i) q^{74} +1.00000 q^{75} +(1.47694 - 4.10105i) q^{76} +22.0512 q^{77} +(-2.36774 - 4.10105i) q^{78} +(3.36774 + 5.83311i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.39928 + 7.61978i) q^{82} -16.9420 q^{83} +3.84469 q^{84} +(3.31315 - 5.73854i) q^{85} +(-0.523059 + 0.905965i) q^{86} -10.3157 q^{87} +5.73549 q^{88} +(2.55460 - 4.42469i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-9.10323 + 15.7673i) q^{91} +(2.86774 + 4.96708i) q^{92} +(-2.36774 - 4.10105i) q^{93} +1.78161 q^{94} +(2.81315 + 3.32960i) q^{95} +1.00000 q^{96} +(-4.57766 - 7.92873i) q^{97} +(-3.89080 - 6.73907i) q^{98} +(-2.86774 + 4.96708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} + 6 q^{12} - q^{13} - q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} + 6 q^{18} - 2 q^{19} + 6 q^{20} - q^{21} - 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} + 6 q^{27} - q^{28} - 6 q^{29} + 6 q^{30} + 2 q^{31} - 3 q^{32} - 4 q^{33} + 4 q^{34} - q^{35} - 3 q^{36} - 6 q^{37} + q^{38} + 2 q^{39} - 3 q^{40} - 8 q^{41} - q^{42} - 11 q^{43} - 4 q^{44} + 6 q^{45} - 8 q^{46} - 3 q^{48} + 36 q^{49} + 6 q^{50} + 4 q^{51} - q^{52} - 18 q^{53} - 3 q^{54} - 4 q^{55} + 2 q^{56} + q^{57} + 12 q^{58} - 18 q^{59} - 3 q^{60} + 3 q^{61} - q^{62} - q^{63} + 6 q^{64} + 2 q^{65} - 4 q^{66} - 15 q^{67} - 8 q^{68} - 8 q^{69} - q^{70} + 4 q^{71} - 3 q^{72} + 21 q^{73} + 3 q^{74} + 6 q^{75} + q^{76} + 32 q^{77} - q^{78} + 7 q^{79} - 3 q^{80} - 3 q^{81} - 8 q^{82} + 4 q^{83} + 2 q^{84} + 4 q^{85} - 11 q^{86} + 12 q^{87} + 8 q^{88} + 18 q^{89} - 3 q^{90} - 15 q^{91} + 4 q^{92} - q^{93} + q^{95} + 6 q^{96} - 38 q^{97} - 18 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 + 6 * q^12 - q^13 - q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 + 6 * q^18 - 2 * q^19 + 6 * q^20 - q^21 - 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 + 6 * q^27 - q^28 - 6 * q^29 + 6 * q^30 + 2 * q^31 - 3 * q^32 - 4 * q^33 + 4 * q^34 - q^35 - 3 * q^36 - 6 * q^37 + q^38 + 2 * q^39 - 3 * q^40 - 8 * q^41 - q^42 - 11 * q^43 - 4 * q^44 + 6 * q^45 - 8 * q^46 - 3 * q^48 + 36 * q^49 + 6 * q^50 + 4 * q^51 - q^52 - 18 * q^53 - 3 * q^54 - 4 * q^55 + 2 * q^56 + q^57 + 12 * q^58 - 18 * q^59 - 3 * q^60 + 3 * q^61 - q^62 - q^63 + 6 * q^64 + 2 * q^65 - 4 * q^66 - 15 * q^67 - 8 * q^68 - 8 * q^69 - q^70 + 4 * q^71 - 3 * q^72 + 21 * q^73 + 3 * q^74 + 6 * q^75 + q^76 + 32 * q^77 - q^78 + 7 * q^79 - 3 * q^80 - 3 * q^81 - 8 * q^82 + 4 * q^83 + 2 * q^84 + 4 * q^85 - 11 * q^86 + 12 * q^87 + 8 * q^88 + 18 * q^89 - 3 * q^90 - 15 * q^91 + 4 * q^92 - q^93 + q^95 + 6 * q^96 - 38 * q^97 - 18 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	3.84469			1.45315			0.726577	−	0.687085i	$-0.241110\pi$
$7$	3.84469			1.45315			0.726577	+	0.687085i	$0.241110\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	5.73549			1.72932			0.864658	−	0.502362i	$-0.167535\pi$
$11$	5.73549			1.72932			0.864658	+	0.502362i	$0.167535\pi$
$12$	1.00000			0.288675
$13$	−2.36774	+	4.10105i	−0.656694	+	1.13743i	0.324772	+	0.945792i	$0.394712\pi$
$13$	−2.36774	+	4.10105i	−0.656694	+	1.13743i	−0.981466	+	0.191635i	$0.938621\pi$
$14$	−1.92234	−	3.32960i	−0.513768	−	0.889872i
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.31315	+	5.73854i	0.803556	+	1.39180i	0.917262	+	0.398285i	$0.130395\pi$
$17$	3.31315	+	5.73854i	0.803556	+	1.39180i	−0.113705	+	0.993515i	$0.536272\pi$
$18$	1.00000			0.235702
$19$	−4.29009	+	0.771459i	−0.984214	+	0.176985i
$19$	−4.29009	+	0.771459i	−0.984214	+	0.176985i
$20$	1.00000			0.223607
$21$	−1.92234	−	3.32960i	−0.419490	−	0.726577i
$22$	−2.86774	−	4.96708i	−0.611405	−	1.05898i
$23$	2.86774	−	4.96708i	0.597966	−	1.03571i	−0.395155	−	0.918615i	$-0.629309\pi$
$23$	2.86774	−	4.96708i	0.597966	−	1.03571i	0.993121	−	0.117093i	$-0.0373576\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	4.73549			0.928706
$27$	1.00000			0.192450
$28$	−1.92234	+	3.32960i	−0.363289	+	0.629234i
$29$	5.15783	−	8.93363i	0.957785	−	1.65893i	0.229924	−	0.973209i	$-0.426152\pi$
$29$	5.15783	−	8.93363i	0.957785	−	1.65893i	0.727861	−	0.685724i	$-0.240514\pi$
$30$	1.00000			0.182574
$31$	4.73549			0.850519			0.425260	−	0.905071i	$-0.360183\pi$
$31$	4.73549			0.850519			0.425260	+	0.905071i	$0.360183\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.86774	−	4.96708i	−0.499210	−	0.864658i
$34$	3.31315	−	5.73854i	0.568200	−	0.984151i
$35$	−1.92234	−	3.32960i	−0.324935	−	0.562804i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	2.81315	+	3.32960i	0.456353	+	0.540132i
$39$	4.73549			0.758285
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−4.39928	−	7.61978i	−0.687053	−	1.19001i	−0.972787	−	0.231701i	$-0.925571\pi$
$41$	−4.39928	−	7.61978i	−0.687053	−	1.19001i	0.285734	−	0.958309i	$-0.407763\pi$
$42$	−1.92234	+	3.32960i	−0.296624	+	0.513768i
$43$	−0.523059	−	0.905965i	−0.0797658	−	0.138158i	0.823383	−	0.567486i	$-0.192084\pi$
$43$	−0.523059	−	0.905965i	−0.0797658	−	0.138158i	−0.903149	+	0.429328i	$0.858751\pi$
$44$	−2.86774	+	4.96708i	−0.432329	+	0.748815i
$45$	1.00000			0.149071
$46$	−5.73549			−0.845652
$47$	−0.890804	+	1.54292i	−0.129937	+	0.225058i	−0.923652	−	0.383232i	$-0.874811\pi$
$47$	−0.890804	+	1.54292i	−0.129937	+	0.225058i	0.793715	+	0.608290i	$0.208144\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	7.78161			1.11166
$50$	1.00000			0.141421
$51$	3.31315	−	5.73854i	0.463933	−	0.803556i
$52$	−2.36774	−	4.10105i	−0.328347	−	0.568714i
$53$	−2.55460	+	4.42469i	−0.350901	+	0.607778i	−0.986408	−	0.164317i	$-0.947458\pi$
$53$	−2.55460	+	4.42469i	−0.350901	+	0.607778i	0.635507	+	0.772095i	$0.280791\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−2.86774	−	4.96708i	−0.386687	−	0.669761i
$56$	3.84469			0.513768
$57$	2.81315	+	3.32960i	0.372610	+	0.441016i
$58$	−10.3157			−1.35451
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	0.0545981	−	0.0945666i	0.00699057	−	0.0121080i	−0.862509	−	0.506042i	$-0.831108\pi$
$61$	0.0545981	−	0.0945666i	0.00699057	−	0.0121080i	0.869500	+	0.493934i	$0.164441\pi$
$62$	−2.36774	−	4.10105i	−0.300704	−	0.520834i
$63$	−1.92234	+	3.32960i	−0.242192	+	0.419490i
$64$	1.00000			0.125000
$65$	4.73549			0.587365
$66$	−2.86774	+	4.96708i	−0.352995	+	0.611405i
$67$	−2.94540	+	5.10159i	−0.359838	+	0.623258i	−0.987934	−	0.154878i	$-0.950501\pi$
$67$	−2.94540	+	5.10159i	−0.359838	+	0.623258i	0.628095	+	0.778136i	$0.283835\pi$
$68$	−6.62629			−0.803556
$69$	−5.73549			−0.690472
$70$	−1.92234	+	3.32960i	−0.229764	+	0.397963i
$71$	3.31315	+	5.73854i	0.393198	+	0.681039i	0.992869	−	0.119207i	$-0.0380353\pi$
$71$	3.31315	+	5.73854i	0.393198	+	0.681039i	−0.599671	+	0.800246i	$0.704702\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	3.05460	+	5.29072i	0.357514	+	0.619232i	0.987545	−	0.157338i	$-0.0502912\pi$
$73$	3.05460	+	5.29072i	0.357514	+	0.619232i	−0.630031	+	0.776570i	$0.716958\pi$
$74$	0.500000	+	0.866025i	0.0581238	+	0.100673i
$75$	1.00000			0.115470
$76$	1.47694	−	4.10105i	0.169417	−	0.470423i
$77$	22.0512			2.51296
$78$	−2.36774	−	4.10105i	−0.268094	−	0.464353i
$79$	3.36774	+	5.83311i	0.378901	+	0.656276i	0.990903	−	0.134581i	$-0.0429688\pi$
$79$	3.36774	+	5.83311i	0.378901	+	0.656276i	−0.612002	+	0.790856i	$0.709635\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.39928	+	7.61978i	−0.485820	+	0.841464i
$83$	−16.9420			−1.85962			−0.929811	−	0.368038i	$-0.880030\pi$
$83$	−16.9420			−1.85962			−0.929811	+	0.368038i	$0.880030\pi$
$84$	3.84469			0.419490
$85$	3.31315	−	5.73854i	0.359361	−	0.622432i
$86$	−0.523059	+	0.905965i	−0.0564029	+	0.0976927i
$87$	−10.3157			−1.10596
$88$	5.73549			0.611405
$89$	2.55460	−	4.42469i	0.270787	−	0.469017i	−0.698277	−	0.715828i	$-0.746049\pi$
$89$	2.55460	−	4.42469i	0.270787	−	0.469017i	0.969064	+	0.246811i	$0.0793828\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	−9.10323	+	15.7673i	−0.954278	+	1.65286i
$92$	2.86774	+	4.96708i	0.298983	+	0.517854i
$93$	−2.36774	−	4.10105i	−0.245524	−	0.425260i
$94$	1.78161			0.183759
$95$	2.81315	+	3.32960i	0.288623	+	0.341609i
$96$	1.00000			0.102062
$97$	−4.57766	−	7.92873i	−0.464791	−	0.805041i	0.534401	−	0.845231i	$-0.320537\pi$
$97$	−4.57766	−	7.92873i	−0.464791	−	0.805041i	−0.999192	+	0.0401898i	$0.987204\pi$
$98$	−3.89080	−	6.73907i	−0.393031	−	0.680749i
$99$	−2.86774	+	4.96708i	−0.288219	+	0.499210i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	1.84469	−	3.19509i	0.183553	−	0.317923i	−0.759535	−	0.650467i	$-0.774573\pi$
$101$	1.84469	−	3.19509i	0.183553	−	0.317923i	0.943088	+	0.332543i	$0.107907\pi$
$102$	−6.62629			−0.656101
$103$	2.06308			0.203281			0.101641	−	0.994821i	$-0.467591\pi$
$103$	2.06308			0.203281			0.101641	+	0.994821i	$0.467591\pi$
$104$	−2.36774	+	4.10105i	−0.232176	+	0.402141i
$105$	−1.92234	+	3.32960i	−0.187601	+	0.324935i
$106$	5.10920			0.496249
$107$	14.5341			1.40506			0.702530	−	0.711654i	$-0.252054\pi$
$107$	14.5341			1.40506			0.702530	+	0.711654i	$0.252054\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−4.31315	−	7.47059i	−0.413125	−	0.715553i	0.582105	−	0.813114i	$-0.302229\pi$
$109$	−4.31315	−	7.47059i	−0.413125	−	0.715553i	−0.995230	+	0.0975609i	$0.968896\pi$
$110$	−2.86774	+	4.96708i	−0.273429	+	0.473592i
$111$	0.500000	+	0.866025i	0.0474579	+	0.0821995i
$112$	−1.92234	−	3.32960i	−0.181644	−	0.314617i
$113$	−8.53406			−0.802817			−0.401408	−	0.915899i	$-0.631479\pi$
$113$	−8.53406			−0.802817			−0.401408	+	0.915899i	$0.631479\pi$
$114$	1.47694	−	4.10105i	0.138328	−	0.384099i
$115$	−5.73549			−0.534837
$116$	5.15783	+	8.93363i	0.478893	+	0.829467i
$117$	−2.36774	−	4.10105i	−0.218898	−	0.379143i
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$	12.7380	+	22.0629i	1.16769	+	2.02250i
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	21.8958			1.99053
$122$	−0.109196			−0.00988615
$123$	−4.39928	+	7.61978i	−0.396670	+	0.687053i
$124$	−2.36774	+	4.10105i	−0.212630	+	0.368286i
$125$	1.00000			0.0894427
$126$	3.84469			0.342512
$127$	−2.33621	+	4.04643i	−0.207305	+	0.359062i	−0.950865	−	0.309607i	$-0.899802\pi$
$127$	−2.33621	+	4.04643i	−0.207305	+	0.359062i	0.743560	+	0.668669i	$0.233136\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.523059	+	0.905965i	−0.0460528	+	0.0797658i
$130$	−2.36774	−	4.10105i	−0.207665	−	0.359686i
$131$	6.82163	+	11.8154i	0.596008	+	1.03232i	0.993404	+	0.114669i	$0.0365808\pi$
$131$	6.82163	+	11.8154i	0.596008	+	1.03232i	−0.397395	+	0.917647i	$0.630086\pi$
$132$	5.73549			0.499210
$133$	−16.4940	+	2.96602i	−1.43021	+	0.257186i
$134$	5.89080			0.508888
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	3.31315	+	5.73854i	0.284100	+	0.492076i
$137$	6.95388	−	12.0445i	0.594110	−	1.02903i	−0.399562	−	0.916706i	$-0.630838\pi$
$137$	6.95388	−	12.0445i	0.594110	−	1.02903i	0.993672	−	0.112323i	$-0.0358290\pi$
$138$	2.86774	+	4.96708i	0.244119	+	0.422826i
$139$	0.367745	−	0.636953i	0.0311917	−	0.0540256i	−0.850008	−	0.526770i	$-0.823403\pi$
$139$	0.367745	−	0.636953i	0.0311917	−	0.0540256i	0.881200	+	0.472744i	$0.156736\pi$
$140$	3.84469			0.324935
$141$	1.78161			0.150038
$142$	3.31315	−	5.73854i	0.278033	−	0.481567i
$143$	−13.5802	+	23.5216i	−1.13563	+	1.96697i
$144$	1.00000			0.0833333
$145$	−10.3157			−0.856669
$146$	3.05460	−	5.29072i	0.252800	−	0.437863i
$147$	−3.89080	−	6.73907i	−0.320908	−	0.555829i
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	5.42234	+	9.39177i	0.444216	+	0.769404i	0.997997	−	0.0632579i	$-0.0201491\pi$
$149$	5.42234	+	9.39177i	0.444216	+	0.769404i	−0.553782	+	0.832662i	$0.686816\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−0.936922			−0.0762456			−0.0381228	−	0.999273i	$-0.512138\pi$
$151$	−0.936922			−0.0762456			−0.0381228	+	0.999273i	$0.512138\pi$
$152$	−4.29009	+	0.771459i	−0.347972	+	0.0625736i
$153$	−6.62629			−0.535704
$154$	−11.0256	−	19.0969i	−0.888466	−	1.53887i
$155$	−2.36774	−	4.10105i	−0.190182	−	0.329405i
$156$	−2.36774	+	4.10105i	−0.189571	+	0.328347i
$157$	−4.34469	−	7.52522i	−0.346744	−	0.600578i	0.638925	−	0.769269i	$-0.279379\pi$
$157$	−4.34469	−	7.52522i	−0.346744	−	0.600578i	−0.985669	+	0.168691i	$0.946046\pi$
$158$	3.36774	−	5.83311i	0.267923	−	0.464057i
$159$	5.10920			0.405186
$160$	1.00000			0.0790569
$161$	11.0256	−	19.0969i	0.868937	−	1.50504i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−0.206468			−0.0161719			−0.00808593	−	0.999967i	$-0.502574\pi$
$163$	−0.206468			−0.0161719			−0.00808593	+	0.999967i	$0.502574\pi$
$164$	8.79857			0.687053
$165$	−2.86774	+	4.96708i	−0.223254	+	0.386687i
$166$	8.47098	+	14.6722i	0.657475	+	1.13878i
$167$	−8.86774	+	15.3594i	−0.686207	+	1.18854i	0.286849	+	0.957976i	$0.407392\pi$
$167$	−8.86774	+	15.3594i	−0.686207	+	1.18854i	−0.973056	+	0.230569i	$0.925941\pi$
$168$	−1.92234	−	3.32960i	−0.148312	−	0.256884i
$169$	−4.71243	−	8.16217i	−0.362495	−	0.627859i
$170$	−6.62629			−0.508214
$171$	1.47694	−	4.10105i	0.112944	−	0.313615i
$172$	1.04612			0.0797658
$173$	−0.709912	−	1.22960i	−0.0539736	−	0.0934851i	0.837776	−	0.546014i	$-0.183855\pi$
$173$	−0.709912	−	1.22960i	−0.0539736	−	0.0934851i	−0.891750	+	0.452529i	$0.850522\pi$
$174$	5.15783	+	8.93363i	0.391014	+	0.677257i
$175$	−1.92234	+	3.32960i	−0.145315	+	0.251694i
$176$	−2.86774	−	4.96708i	−0.216164	−	0.374408i
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	−5.10920			−0.382950
$179$	−17.2065			−1.28607			−0.643036	−	0.765836i	$-0.722325\pi$
$179$	−17.2065			−1.28607			−0.643036	+	0.765836i	$0.722325\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−8.26703	+	14.3189i	−0.614483	+	1.06432i	0.375992	+	0.926623i	$0.377302\pi$
$181$	−8.26703	+	14.3189i	−0.614483	+	1.06432i	−0.990475	+	0.137693i	$0.956031\pi$
$182$	18.2065			1.34955
$183$	−0.109196			−0.00807201
$184$	2.86774	−	4.96708i	0.211413	−	0.366178i
$185$	0.500000	+	0.866025i	0.0367607	+	0.0636715i
$186$	−2.36774	+	4.10105i	−0.173611	+	0.300704i
$187$	19.0025	+	32.9133i	1.38960	+	2.40686i
$188$	−0.890804	−	1.54292i	−0.0649685	−	0.112529i
$189$	3.84469			0.279660
$190$	1.47694	−	4.10105i	0.107149	−	0.297522i
$191$	−22.4129			−1.62174			−0.810872	−	0.585224i	$-0.801007\pi$
$191$	−22.4129			−1.62174			−0.810872	+	0.585224i	$0.801007\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	11.5256	+	19.9629i	0.829629	+	1.43696i	0.898329	+	0.439323i	$0.144781\pi$
$193$	11.5256	+	19.9629i	0.829629	+	1.43696i	−0.0687002	+	0.997637i	$0.521885\pi$
$194$	−4.57766	+	7.92873i	−0.328657	+	0.569250i
$195$	−2.36774	−	4.10105i	−0.169558	−	0.293683i
$196$	−3.89080	+	6.73907i	−0.277915	+	0.481362i
$197$	2.67241			0.190401			0.0952007	−	0.995458i	$-0.469651\pi$
$197$	2.67241			0.190401			0.0952007	+	0.995458i	$0.469651\pi$
$198$	5.73549			0.407603
$199$	5.79009	−	10.0287i	0.410448	−	0.710918i	−0.584490	−	0.811401i	$-0.698706\pi$
$199$	5.79009	−	10.0287i	0.410448	−	0.710918i	0.994939	+	0.100483i	$0.0320388\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	5.89080			0.415505
$202$	−3.68937			−0.259583
$203$	19.8302	−	34.3470i	1.39181	−	2.41069i
$204$	3.31315	+	5.73854i	0.231967	+	0.401778i
$205$	−4.39928	+	7.61978i	−0.307259	+	0.532189i
$206$	−1.03154	−	1.78668i	−0.0718707	−	0.124484i
$207$	2.86774	+	4.96708i	0.199322	+	0.345236i
$208$	4.73549			0.328347
$209$	−24.6058	+	4.42469i	−1.70202	+	0.306062i
$210$	3.84469			0.265309
$211$	−11.6117	−	20.1121i	−0.799383	−	1.38457i	−0.920018	−	0.391876i	$-0.871826\pi$
$211$	−11.6117	−	20.1121i	−0.799383	−	1.38457i	0.120635	−	0.992697i	$-0.461507\pi$
$212$	−2.55460	−	4.42469i	−0.175451	−	0.303889i
$213$	3.31315	−	5.73854i	0.227013	−	0.393198i
$214$	−7.26703	−	12.5869i	−0.496764	−	0.860420i
$215$	−0.523059	+	0.905965i	−0.0356723	+	0.0617863i
$216$	1.00000			0.0680414
$217$	18.2065			1.23594
$218$	−4.31315	+	7.47059i	−0.292123	+	0.505972i
$219$	3.05460	−	5.29072i	0.206411	−	0.357514i
$220$	5.73549			0.386687
$221$	−31.3787			−2.11076
$222$	0.500000	−	0.866025i	0.0335578	−	0.0581238i
$223$	7.50252	+	12.9947i	0.502406	+	0.870192i	0.999996	+	0.00278017i	$0.000884956\pi$
$223$	7.50252	+	12.9947i	0.502406	+	0.870192i	−0.497590	+	0.867412i	$0.665782\pi$
$224$	−1.92234	+	3.32960i	−0.128442	+	0.222468i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	4.26703	+	7.39071i	0.283839	+	0.491623i
$227$	−20.5341			−1.36289			−0.681447	−	0.731868i	$-0.738649\pi$
$227$	−20.5341			−1.36289			−0.681447	+	0.731868i	$0.738649\pi$
$228$	−4.29009	+	0.771459i	−0.284118	+	0.0510911i
$229$	−13.2645			−0.876544			−0.438272	−	0.898843i	$-0.644409\pi$
$229$	−13.2645			−0.876544			−0.438272	+	0.898843i	$0.644409\pi$
$230$	2.86774	+	4.96708i	0.189093	+	0.327520i
$231$	−11.0256	−	19.0969i	−0.725430	−	1.25648i
$232$	5.15783	−	8.93363i	0.338628	−	0.586521i
$233$	−9.42486	−	16.3243i	−0.617443	−	1.06944i	−0.989951	−	0.141414i	$-0.954835\pi$
$233$	−9.42486	−	16.3243i	−0.617443	−	1.06944i	0.372507	−	0.928029i	$-0.378498\pi$
$234$	−2.36774	+	4.10105i	−0.154784	+	0.268094i
$235$	1.78161			0.116219
$236$	6.00000			0.390567
$237$	3.36774	−	5.83311i	0.218759	−	0.378901i
$238$	12.7380	−	22.0629i	0.825682	−	1.43012i
$239$	13.9078			0.899618			0.449809	−	0.893125i	$-0.351492\pi$
$239$	13.9078			0.899618			0.449809	+	0.893125i	$0.351492\pi$
$240$	1.00000			0.0645497
$241$	15.1032	−	26.1596i	0.972885	−	1.68509i	0.286139	−	0.958188i	$-0.407628\pi$
$241$	15.1032	−	26.1596i	0.972885	−	1.68509i	0.686745	−	0.726898i	$-0.259039\pi$
$242$	−10.9479	−	18.9624i	−0.703759	−	1.21895i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.0545981	+	0.0945666i	0.00349528	+	0.00605401i
$245$	−3.89080	−	6.73907i	−0.248574	−	0.430543i
$246$	8.79857			0.560976
$247$	6.99404	−	19.4205i	0.445020	−	1.23570i
$248$	4.73549			0.300704
$249$	8.47098	+	14.6722i	0.536826	+	0.929811i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	10.5171	−	18.2161i	0.663833	−	1.14979i	−0.315767	−	0.948837i	$-0.602262\pi$
$251$	10.5171	−	18.2161i	0.663833	−	1.14979i	0.979600	−	0.200956i	$-0.0644049\pi$
$252$	−1.92234	−	3.32960i	−0.121096	−	0.209745i
$253$	16.4479	−	28.4886i	1.03407	−	1.79107i
$254$	4.67241			0.293173
$255$	−6.62629			−0.414955
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	1.04612			0.0651285
$259$	−3.84469			−0.238897
$260$	−2.36774	+	4.10105i	−0.146841	+	0.254337i
$261$	5.15783	+	8.93363i	0.319262	+	0.552978i
$262$	6.82163	−	11.8154i	0.421441	−	0.729958i
$263$	3.39677	+	5.88337i	0.209454	+	0.362784i	0.951543	−	0.307517i	$-0.0994982\pi$
$263$	3.39677	+	5.88337i	0.209454	+	0.362784i	−0.742089	+	0.670301i	$0.766165\pi$
$264$	−2.86774	−	4.96708i	−0.176497	−	0.305703i
$265$	5.10920			0.313855
$266$	10.8157	+	12.8012i	0.663151	+	0.784895i
$267$	−5.10920			−0.312678
$268$	−2.94540	−	5.10159i	−0.179919	−	0.311629i
$269$	−6.04864	−	10.4765i	−0.368792	−	0.638766i	0.620585	−	0.784139i	$-0.286895\pi$
$269$	−6.04864	−	10.4765i	−0.368792	−	0.638766i	−0.989377	+	0.145373i	$0.953562\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	0.580175	+	1.00489i	0.0352431	+	0.0610429i	0.883109	−	0.469168i	$-0.155446\pi$
$271$	0.580175	+	1.00489i	0.0352431	+	0.0610429i	−0.847866	+	0.530211i	$0.822113\pi$
$272$	3.31315	−	5.73854i	0.200889	−	0.347950i
$273$	18.2065			1.10191
$274$	−13.9078			−0.840199
$275$	−2.86774	+	4.96708i	−0.172932	+	0.299526i
$276$	2.86774	−	4.96708i	0.172618	−	0.298983i
$277$	4.83965			0.290786			0.145393	−	0.989374i	$-0.453555\pi$
$277$	4.83965			0.290786			0.145393	+	0.989374i	$0.453555\pi$
$278$	−0.735489			−0.0441117
$279$	−2.36774	+	4.10105i	−0.141753	+	0.245524i
$280$	−1.92234	−	3.32960i	−0.114882	−	0.198981i
$281$	−4.66379	+	8.07793i	−0.278219	+	0.481889i	−0.970942	−	0.239314i	$-0.923077\pi$
$281$	−4.66379	+	8.07793i	−0.278219	+	0.481889i	0.692723	+	0.721203i	$0.256411\pi$
$282$	−0.890804	−	1.54292i	−0.0530466	−	0.0918794i
$283$	4.67241	+	8.09285i	0.277746	+	0.481070i	0.970824	−	0.239792i	$-0.0770793\pi$
$283$	4.67241	+	8.09285i	0.277746	+	0.481070i	−0.693078	+	0.720862i	$0.743746\pi$
$284$	−6.62629			−0.393198
$285$	1.47694	−	4.10105i	0.0874864	−	0.242925i
$286$	27.1604			1.60603
$287$	−16.9139	−	29.2957i	−0.998394	−	1.72927i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−13.4539	+	23.3028i	−0.791405	+	1.37075i
$290$	5.15783	+	8.93363i	0.302878	+	0.524601i
$291$	−4.57766	+	7.92873i	−0.268347	+	0.464791i
$292$	−6.10920			−0.357514
$293$	3.20143			0.187030			0.0935148	−	0.995618i	$-0.470190\pi$
$293$	3.20143			0.187030			0.0935148	+	0.995618i	$0.470190\pi$
$294$	−3.89080	+	6.73907i	−0.226916	+	0.393031i
$295$	−3.00000	+	5.19615i	−0.174667	+	0.302532i
$296$	−1.00000			−0.0581238
$297$	5.73549			0.332807
$298$	5.42234	−	9.39177i	0.314108	−	0.544051i
$299$	13.5802	+	23.5216i	0.785362	+	1.36029i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−2.01100	−	3.48315i	−0.115912	−	0.200765i
$302$	0.468461	+	0.811398i	0.0269569	+	0.0466907i
$303$	−3.68937			−0.211949
$304$	2.81315	+	3.32960i	0.161345	+	0.190965i
$305$	−0.109196			−0.00625255
$306$	3.31315	+	5.73854i	0.189400	+	0.328050i
$307$	14.1117	+	24.4422i	0.805398	+	1.39499i	0.916022	+	0.401128i	$0.131382\pi$
$307$	14.1117	+	24.4422i	0.805398	+	1.39499i	−0.110624	+	0.993862i	$0.535285\pi$
$308$	−11.0256	+	19.0969i	−0.628241	+	1.08814i
$309$	−1.03154	−	1.78668i	−0.0586822	−	0.101641i
$310$	−2.36774	+	4.10105i	−0.134479	+	0.232924i
$311$	−12.8497			−0.728641			−0.364320	−	0.931274i	$-0.618699\pi$
$311$	−12.8497			−0.728641			−0.364320	+	0.931274i	$0.618699\pi$
$312$	4.73549			0.268094
$313$	−14.5171	+	25.1443i	−0.820555	+	1.42124i	0.0847148	+	0.996405i	$0.473002\pi$
$313$	−14.5171	+	25.1443i	−0.820555	+	1.42124i	−0.905270	+	0.424837i	$0.860331\pi$
$314$	−4.34469	+	7.52522i	−0.245185	+	0.424673i
$315$	3.84469			0.216623
$316$	−6.73549			−0.378901
$317$	−2.22701	+	3.85729i	−0.125081	+	0.216647i	−0.921765	−	0.387750i	$-0.873253\pi$
$317$	−2.22701	+	3.85729i	−0.125081	+	0.216647i	0.796683	+	0.604397i	$0.206586\pi$
$318$	−2.55460	−	4.42469i	−0.143255	−	0.248124i
$319$	29.5827	−	51.2387i	1.65631	−	2.86882i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−7.26703	−	12.5869i	−0.405606	−	0.702530i
$322$	−22.0512			−1.22886
$323$	−18.6407	−	22.0629i	−1.03720	−	1.22761i
$324$	1.00000			0.0555556
$325$	−2.36774	−	4.10105i	−0.131339	−	0.227486i
$326$	0.103234	+	0.178807i	0.00571762	+	0.00990320i
$327$	−4.31315	+	7.47059i	−0.238518	+	0.413125i
$328$	−4.39928	−	7.61978i	−0.242910	−	0.420732i
$329$	−3.42486	+	5.93203i	−0.188819	+	0.327044i
$330$	5.73549			0.315728
$331$	−11.8447			−0.651043			−0.325521	−	0.945535i	$-0.605540\pi$
$331$	−11.8447			−0.651043			−0.325521	+	0.945535i	$0.605540\pi$
$332$	8.47098	−	14.6722i	0.464905	−	0.805240i
$333$	0.500000	−	0.866025i	0.0273998	−	0.0474579i
$334$	17.7355			0.970443
$335$	5.89080			0.321849
$336$	−1.92234	+	3.32960i	−0.104872	+	0.181644i
$337$	−3.58614	−	6.21137i	−0.195349	−	0.338355i	0.751666	−	0.659544i	$-0.229251\pi$
$337$	−3.58614	−	6.21137i	−0.195349	−	0.338355i	−0.947015	+	0.321189i	$0.895917\pi$
$338$	−4.71243	+	8.16217i	−0.256322	+	0.443963i
$339$	4.26703	+	7.39071i	0.231753	+	0.401408i
$340$	3.31315	+	5.73854i	0.179681	+	0.311216i
$341$	27.1604			1.47082
$342$	−4.29009	+	0.771459i	−0.231981	+	0.0417157i
$343$	3.00504			0.162257
$344$	−0.523059	−	0.905965i	−0.0282015	−	0.0488464i
$345$	2.86774	+	4.96708i	0.154394	+	0.267419i
$346$	−0.709912	+	1.22960i	−0.0381651	+	0.0661039i
$347$	−11.2065	−	19.4102i	−0.601595	−	1.04199i	−0.992580	−	0.121596i	$-0.961199\pi$
$347$	−11.2065	−	19.4102i	−0.601595	−	1.04199i	0.390985	−	0.920397i	$-0.372134\pi$
$348$	5.15783	−	8.93363i	0.276489	−	0.478893i
$349$	−24.3037			−1.30095			−0.650475	−	0.759528i	$-0.725430\pi$
$349$	−24.3037			−1.30095			−0.650475	+	0.759528i	$0.725430\pi$
$350$	3.84469			0.205507
$351$	−2.36774	+	4.10105i	−0.126381	+	0.218898i
$352$	−2.86774	+	4.96708i	−0.152851	+	0.264746i
$353$	32.7286			1.74197			0.870984	−	0.491312i	$-0.163482\pi$
$353$	32.7286			1.74197			0.870984	+	0.491312i	$0.163482\pi$
$354$	6.00000			0.318896
$355$	3.31315	−	5.73854i	0.175844	−	0.304570i
$356$	2.55460	+	4.42469i	0.135393	+	0.234508i
$357$	12.7380	−	22.0629i	0.674167	−	1.16769i
$358$	8.60323	+	14.9012i	0.454695	+	0.787555i
$359$	0.577657	+	1.00053i	0.0304876	+	0.0528060i	0.880867	−	0.473365i	$-0.156961\pi$
$359$	0.577657	+	1.00053i	0.0304876	+	0.0528060i	−0.850379	+	0.526171i	$0.823627\pi$
$360$	1.00000			0.0527046
$361$	17.8097	−	6.61925i	0.937353	−	0.348382i
$362$	16.5341			0.869011
$363$	−10.9479	−	18.9624i	−0.574617	−	0.995265i
$364$	−9.10323	−	15.7673i	−0.477139	−	0.826429i
$365$	3.05460	−	5.29072i	0.159885	−	0.276929i
$366$	0.0545981	+	0.0945666i	0.00285389	+	0.00494308i
$367$	−13.8387	+	23.9694i	−0.722375	+	1.25119i	0.237670	+	0.971346i	$0.423616\pi$
$367$	−13.8387	+	23.9694i	−0.722375	+	1.25119i	−0.960045	+	0.279845i	$0.909717\pi$
$368$	−5.73549			−0.298983
$369$	8.79857			0.458035
$370$	0.500000	−	0.866025i	0.0259938	−	0.0450225i
$371$	−9.82163	+	17.0116i	−0.509913	+	0.883196i
$372$	4.73549			0.245524
$373$	−23.5171			−1.21767			−0.608835	−	0.793297i	$-0.708363\pi$
$373$	−23.5171			−1.21767			−0.608835	+	0.793297i	$0.708363\pi$
$374$	19.0025	−	32.9133i	0.982597	−	1.70191i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	−0.890804	+	1.54292i	−0.0459397	+	0.0795699i
$377$	24.4249	+	42.3051i	1.25794	+	2.17882i
$378$	−1.92234	−	3.32960i	−0.0988746	−	0.171256i
$379$	8.29870			0.426276			0.213138	−	0.977022i	$-0.431632\pi$
$379$	8.29870			0.426276			0.213138	+	0.977022i	$0.431632\pi$
$380$	−4.29009	+	0.771459i	−0.220077	+	0.0395750i
$381$	4.67241			0.239375
$382$	11.2065	+	19.4102i	0.573373	+	0.993111i
$383$	−6.89080	−	11.9352i	−0.352104	−	0.609861i	0.634514	−	0.772911i	$-0.281200\pi$
$383$	−6.89080	−	11.9352i	−0.352104	−	0.609861i	−0.986618	+	0.163050i	$0.947867\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−11.0256	−	19.0969i	−0.561915	−	0.973266i
$386$	11.5256	−	19.9629i	0.586636	−	1.01608i
$387$	1.04612			0.0531772
$388$	9.15531			0.464791
$389$	0.842168	−	1.45868i	0.0426996	−	0.0739579i	−0.843886	−	0.536523i	$-0.819737\pi$
$389$	0.842168	−	1.45868i	0.0426996	−	0.0739579i	0.886585	+	0.462565i	$0.153071\pi$
$390$	−2.36774	+	4.10105i	−0.119895	+	0.207665i
$391$	38.0050			1.92200
$392$	7.78161			0.393031
$393$	6.82163	−	11.8154i	0.344106	−	0.596008i
$394$	−1.33621	−	2.31438i	−0.0673171	−	0.116597i
$395$	3.36774	−	5.83311i	0.169450	−	0.293495i
$396$	−2.86774	−	4.96708i	−0.144110	−	0.249605i
$397$	−7.28161	−	12.6121i	−0.365453	−	0.632984i	0.623395	−	0.781907i	$-0.285753\pi$
$397$	−7.28161	−	12.6121i	−0.365453	−	0.632984i	−0.988849	+	0.148923i	$0.952419\pi$
$398$	−11.5802			−0.580462
$399$	10.8157	+	12.8012i	0.541460	+	0.640864i
$400$	1.00000			0.0500000
$401$	−10.7816	−	18.6743i	−0.538408	−	0.932550i	−0.998990	−	0.0449326i	$-0.985693\pi$
$401$	−10.7816	−	18.6743i	−0.538408	−	0.932550i	0.460582	−	0.887617i	$-0.347641\pi$
$402$	−2.94540	−	5.10159i	−0.146903	−	0.254444i
$403$	−11.2124	+	19.4205i	−0.558531	+	0.967404i
$404$	1.84469	+	3.19509i	0.0917765	+	0.158962i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	−39.6605			−1.96832
$407$	−5.73549			−0.284298
$408$	3.31315	−	5.73854i	0.164025	−	0.284100i
$409$	6.64935	−	11.5170i	0.328789	−	0.569480i	−0.653483	−	0.756942i	$-0.726693\pi$
$409$	6.64935	−	11.5170i	0.328789	−	0.569480i	0.982272	+	0.187462i	$0.0600261\pi$
$410$	8.79857			0.434530
$411$	−13.9078			−0.686019
$412$	−1.03154	+	1.78668i	−0.0508203	+	0.0880233i
$413$	−11.5341	−	19.9776i	−0.567554	−	0.983032i
$414$	2.86774	−	4.96708i	0.140942	−	0.244119i
$415$	8.47098	+	14.6722i	0.415824	+	0.720228i
$416$	−2.36774	−	4.10105i	−0.116088	−	0.201071i
$417$	−0.735489			−0.0360171
$418$	16.1348	+	19.0969i	0.789178	+	0.934058i
$419$	−36.9881			−1.80699			−0.903493	−	0.428603i	$-0.859006\pi$
$419$	−36.9881			−1.80699			−0.903493	+	0.428603i	$0.859006\pi$
$420$	−1.92234	−	3.32960i	−0.0938007	−	0.162468i
$421$	1.68685	+	2.92172i	0.0822122	+	0.142396i	0.904200	−	0.427110i	$-0.140468\pi$
$421$	1.68685	+	2.92172i	0.0822122	+	0.142396i	−0.821988	+	0.569505i	$0.807135\pi$
$422$	−11.6117	+	20.1121i	−0.565249	+	0.979041i
$423$	−0.890804	−	1.54292i	−0.0433124	−	0.0750192i
$424$	−2.55460	+	4.42469i	−0.124062	+	0.214882i
$425$	−6.62629			−0.321422
$426$	−6.62629			−0.321045
$427$	0.209912	−	0.363579i	0.0101584	−	0.0175948i
$428$	−7.26703	+	12.5869i	−0.351265	+	0.608409i
$429$	27.1604			1.31131
$430$	1.04612			0.0504483
$431$	−11.5827	+	20.0618i	−0.557919	+	0.966344i	0.439751	+	0.898120i	$0.355067\pi$
$431$	−11.5827	+	20.0618i	−0.557919	+	0.966344i	−0.997670	+	0.0682240i	$0.978267\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−0.836206	+	1.44835i	−0.0401855	+	0.0696033i	−0.885419	−	0.464794i	$-0.846128\pi$
$433$	−0.836206	+	1.44835i	−0.0401855	+	0.0696033i	0.845233	+	0.534398i	$0.179462\pi$
$434$	−9.10323	−	15.7673i	−0.436969	−	0.756853i
$435$	5.15783	+	8.93363i	0.247299	+	0.428335i
$436$	8.62629			0.413125
$437$	−8.47098	+	23.5216i	−0.405222	+	1.12519i
$438$	−6.10920			−0.291909
$439$	13.3703	+	23.1580i	0.638128	+	1.10527i	0.985843	+	0.167670i	$0.0536242\pi$
$439$	13.3703	+	23.1580i	0.638128	+	1.10527i	−0.347715	+	0.937600i	$0.613042\pi$
$440$	−2.86774	−	4.96708i	−0.136714	−	0.236796i
$441$	−3.89080	+	6.73907i	−0.185276	+	0.320908i
$442$	15.6894	+	27.1748i	0.746267	+	1.29257i
$443$	−3.04864	+	5.28039i	−0.144845	+	0.250879i	−0.929315	−	0.369288i	$-0.879602\pi$
$443$	−3.04864	+	5.28039i	−0.144845	+	0.250879i	0.784470	+	0.620167i	$0.212935\pi$
$444$	−1.00000			−0.0474579
$445$	−5.10920			−0.242199
$446$	7.50252	−	12.9947i	0.355255	−	0.615319i
$447$	5.42234	−	9.39177i	0.256468	−	0.444216i
$448$	3.84469			0.181644
$449$	−5.10920			−0.241118			−0.120559	−	0.992706i	$-0.538469\pi$
$449$	−5.10920			−0.241118			−0.120559	+	0.992706i	$0.538469\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	−25.2320	−	43.7032i	−1.18813	−	2.05790i
$452$	4.26703	−	7.39071i	0.200704	−	0.347630i
$453$	0.468461	+	0.811398i	0.0220102	+	0.0381228i
$454$	10.2670	+	17.7830i	0.481856	+	0.834598i
$455$	18.2065			0.853532
$456$	2.81315	+	3.32960i	0.131738	+	0.155923i
$457$	−34.3960			−1.60898			−0.804488	−	0.593969i	$-0.797560\pi$
$457$	−34.3960			−1.60898			−0.804488	+	0.593969i	$0.797560\pi$
$458$	6.63226	+	11.4874i	0.309905	+	0.536771i
$459$	3.31315	+	5.73854i	0.154644	+	0.267852i
$460$	2.86774	−	4.96708i	0.133709	−	0.231591i
$461$	5.73549	+	9.93416i	0.267128	+	0.462680i	0.968119	−	0.250491i	$-0.0805919\pi$
$461$	5.73549	+	9.93416i	0.267128	+	0.462680i	−0.700991	+	0.713170i	$0.747259\pi$
$462$	−11.0256	+	19.0969i	−0.512956	+	0.888466i
$463$	1.93692			0.0900164			0.0450082	−	0.998987i	$-0.485669\pi$
$463$	1.93692			0.0900164			0.0450082	+	0.998987i	$0.485669\pi$
$464$	−10.3157			−0.478893
$465$	−2.36774	+	4.10105i	−0.109802	+	0.190182i
$466$	−9.42486	+	16.3243i	−0.436598	+	0.756210i
$467$	−9.78664			−0.452872			−0.226436	−	0.974026i	$-0.572707\pi$
$467$	−9.78664			−0.452872			−0.226436	+	0.974026i	$0.572707\pi$
$468$	4.73549			0.218898
$469$	−11.3241	+	19.6140i	−0.522900	+	0.905690i
$470$	−0.890804	−	1.54292i	−0.0410897	−	0.0711695i
$471$	−4.34469	+	7.52522i	−0.200193	+	0.346744i
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	−3.00000	−	5.19615i	−0.137940	−	0.238919i
$474$	−6.73549			−0.309371
$475$	1.47694	−	4.10105i	0.0677667	−	0.188169i
$476$	−25.4760			−1.16769
$477$	−2.55460	−	4.42469i	−0.116967	−	0.202593i
$478$	−6.95388	−	12.0445i	−0.318063	−	0.550902i
$479$	−13.2040	+	22.8699i	−0.603304	+	1.04495i	0.389013	+	0.921232i	$0.372816\pi$
$479$	−13.2040	+	22.8699i	−0.603304	+	1.04495i	−0.992317	+	0.123721i	$0.960517\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	2.36774	−	4.10105i	0.107960	−	0.186992i
$482$	−30.2065			−1.37587
$483$	−22.0512			−1.00336
$484$	−10.9479	+	18.9624i	−0.497633	+	0.861925i
$485$	−4.57766	+	7.92873i	−0.207861	+	0.360025i
$486$	1.00000			0.0453609
$487$	39.3377			1.78256			0.891280	−	0.453454i	$-0.149808\pi$
$487$	39.3377			1.78256			0.891280	+	0.453454i	$0.149808\pi$
$488$	0.0545981	−	0.0945666i	0.00247154	−	0.00428083i
$489$	0.103234	+	0.178807i	0.00466841	+	0.00808593i
$490$	−3.89080	+	6.73907i	−0.175769	+	0.304440i
$491$	−5.33872	−	9.24694i	−0.240933	−	0.417309i	0.720047	−	0.693925i	$-0.244120\pi$
$491$	−5.33872	−	9.24694i	−0.240933	−	0.417309i	−0.960980	+	0.276617i	$0.910787\pi$
$492$	−4.39928	−	7.61978i	−0.198335	−	0.343526i
$493$	68.3546			3.07854
$494$	−20.3157	+	3.65323i	−0.914045	+	0.164367i
$495$	5.73549			0.257791
$496$	−2.36774	−	4.10105i	−0.106315	−	0.184143i
$497$	12.7380	+	22.0629i	0.571378	+	0.989655i
$498$	8.47098	−	14.6722i	0.379594	−	0.657475i
$499$	−12.7670	−	22.1131i	−0.571531	−	0.989920i	−0.996409	−	0.0846697i	$-0.973016\pi$
$499$	−12.7670	−	22.1131i	−0.571531	−	0.989920i	0.424878	−	0.905250i	$-0.360317\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	17.7355			0.792363
$502$	−21.0342			−0.938802
$503$	11.3387	−	19.6392i	0.505569	−	0.875671i	−0.494411	−	0.869229i	$-0.664616\pi$
$503$	11.3387	−	19.6392i	0.505569	−	0.875671i	0.999979	−	0.00644217i	$-0.00205062\pi$
$504$	−1.92234	+	3.32960i	−0.0856280	+	0.148312i
$505$	−3.68937			−0.164175
$506$	−32.8958			−1.46240
$507$	−4.71243	+	8.16217i	−0.209286	+	0.362495i
$508$	−2.33621	−	4.04643i	−0.103652	−	0.179531i
$509$	−12.3618	+	21.4112i	−0.547926	+	0.949036i	0.450490	+	0.892781i	$0.351249\pi$
$509$	−12.3618	+	21.4112i	−0.547926	+	0.949036i	−0.998416	+	0.0562549i	$0.982084\pi$
$510$	3.31315	+	5.73854i	0.146709	+	0.254107i
$511$	11.7440	+	20.3412i	0.519523	+	0.899840i
$512$	1.00000			0.0441942
$513$	−4.29009	+	0.771459i	−0.189412	+	0.0340607i
$514$	6.00000			0.264649
$515$	−1.03154	−	1.78668i	−0.0454550	−	0.0787304i
$516$	−0.523059	−	0.905965i	−0.0230264	−	0.0398829i
$517$	−5.10920	+	8.84939i	−0.224702	+	0.389196i
$518$	1.92234	+	3.32960i	0.0844629	+	0.146294i
$519$	−0.709912	+	1.22960i	−0.0311617	+	0.0539736i
$520$	4.73549			0.207665
$521$	21.1604			0.927052			0.463526	−	0.886083i	$-0.346584\pi$
$521$	21.1604			0.927052			0.463526	+	0.886083i	$0.346584\pi$
$522$	5.15783	−	8.93363i	0.225752	−	0.391014i
$523$	3.11768	−	5.39997i	0.136326	−	0.236124i	−0.789777	−	0.613394i	$-0.789804\pi$
$523$	3.11768	−	5.39997i	0.136326	−	0.236124i	0.926103	+	0.377270i	$0.123137\pi$
$524$	−13.6433			−0.596008
$525$	3.84469			0.167796
$526$	3.39677	−	5.88337i	0.148106	−	0.256527i
$527$	15.6894	+	27.1748i	0.683440	+	1.18375i
$528$	−2.86774	+	4.96708i	−0.124803	+	0.216164i
$529$	−4.94792	−	8.57005i	−0.215127	−	0.372611i
$530$	−2.55460	−	4.42469i	−0.110965	−	0.192196i
$531$	6.00000			0.260378
$532$	5.67837	−	15.7673i	0.246189	−	0.683598i
$533$	41.6655			1.80473
$534$	2.55460	+	4.42469i	0.110548	+	0.191475i
$535$	−7.26703	−	12.5869i	−0.314181	−	0.544178i
$536$	−2.94540	+	5.10159i	−0.127222	+	0.220355i
$537$	8.60323	+	14.9012i	0.371257	+	0.643036i
$538$	−6.04864	+	10.4765i	−0.260775	+	0.451676i
$539$	44.6313			1.92241
$540$	1.00000			0.0430331
$541$	−20.2636	+	35.0976i	−0.871200	+	1.50896i	−0.0104427	+	0.999945i	$0.503324\pi$
$541$	−20.2636	+	35.0976i	−0.871200	+	1.50896i	−0.860757	+	0.509016i	$0.830009\pi$
$542$	0.580175	−	1.00489i	0.0249207	−	0.0431638i
$543$	16.5341			0.709544
$544$	−6.62629			−0.284100
$545$	−4.31315	+	7.47059i	−0.184755	+	0.320005i
$546$	−9.10323	−	15.7673i	−0.389582	−	0.674777i
$547$	0.632255	−	1.09510i	0.0270333	−	0.0468230i	−0.852192	−	0.523229i	$-0.824727\pi$
$547$	0.632255	−	1.09510i	0.0270333	−	0.0468230i	0.879226	+	0.476406i	$0.158061\pi$
$548$	6.95388	+	12.0445i	0.297055	+	0.514515i
$549$	0.0545981	+	0.0945666i	0.00233019	+	0.00403601i
$550$	5.73549			0.244562
$551$	−15.2356	+	42.3051i	−0.649060	+	1.80226i
$552$	−5.73549			−0.244119
$553$	12.9479	+	22.4265i	0.550602	+	0.953670i
$554$	−2.41982	−	4.19126i	−0.102809	−	0.178070i
$555$	0.500000	−	0.866025i	0.0212238	−	0.0367607i
$556$	0.367745	+	0.636953i	0.0155959	+	0.0270128i
$557$	10.3362	−	17.9028i	0.437959	−	0.758567i	−0.559573	−	0.828781i	$-0.689035\pi$
$557$	10.3362	−	17.9028i	0.437959	−	0.758567i	0.997532	+	0.0702137i	$0.0223681\pi$
$558$	4.73549			0.200469
$559$	4.95388			0.209527
$560$	−1.92234	+	3.32960i	−0.0812338	+	0.140701i
$561$	19.0025	−	32.9133i	0.802287	−	1.38960i
$562$	9.32759			0.393461
$563$	9.03419			0.380746			0.190373	−	0.981712i	$-0.439030\pi$
$563$	9.03419			0.380746			0.190373	+	0.981712i	$0.439030\pi$
$564$	−0.890804	+	1.54292i	−0.0375096	+	0.0649685i
$565$	4.26703	+	7.39071i	0.179515	+	0.310930i
$566$	4.67241	−	8.09285i	0.196396	−	0.340168i
$567$	−1.92234	−	3.32960i	−0.0807308	−	0.139830i
$568$	3.31315	+	5.73854i	0.139017	+	0.240784i
$569$	25.7405			1.07910			0.539549	−	0.841954i	$-0.318595\pi$
$569$	25.7405			1.07910			0.539549	+	0.841954i	$0.318595\pi$
$570$	−4.29009	+	0.771459i	−0.179692	+	0.0323129i
$571$	15.5513			0.650801			0.325401	−	0.945576i	$-0.394501\pi$
$571$	15.5513			0.650801			0.325401	+	0.945576i	$0.394501\pi$
$572$	−13.5802	−	23.5216i	−0.567816	−	0.983486i
$573$	11.2065	+	19.4102i	0.468157	+	0.810872i
$574$	−16.9139	+	29.2957i	−0.705971	+	1.22278i
$575$	2.86774	+	4.96708i	0.119593	+	0.207142i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−38.3157			−1.59510			−0.797551	−	0.603252i	$-0.793872\pi$
$577$	−38.3157			−1.59510			−0.797551	+	0.603252i	$0.793872\pi$
$578$	26.9078			1.11922
$579$	11.5256	−	19.9629i	0.478987	−	0.829629i
$580$	5.15783	−	8.93363i	0.214167	−	0.370949i
$581$	−65.1365			−2.70232
$582$	9.15531			0.379500
$583$	−14.6519	+	25.3778i	−0.606818	+	1.05104i
$584$	3.05460	+	5.29072i	0.126400	+	0.218932i
$585$	−2.36774	+	4.10105i	−0.0978942	+	0.169558i
$586$	−1.60072	−	2.77252i	−0.0661250	−	0.114532i
$587$	−15.3618	−	26.6074i	−0.634049	−	1.09820i	−0.986716	−	0.162456i	$-0.948059\pi$
$587$	−15.3618	−	26.6074i	−0.634049	−	1.09820i	0.352667	−	0.935749i	$-0.385275\pi$
$588$	7.78161			0.320908
$589$	−20.3157	+	3.65323i	−0.837092	+	0.150529i
$590$	6.00000			0.247016
$591$	−1.33621	−	2.31438i	−0.0549642	−	0.0952007i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	−5.98556	+	10.3673i	−0.245797	+	0.425734i	−0.962356	−	0.271794i	$-0.912383\pi$
$593$	−5.98556	+	10.3673i	−0.245797	+	0.425734i	0.716558	+	0.697527i	$0.245716\pi$
$594$	−2.86774	−	4.96708i	−0.117665	−	0.203802i
$595$	12.7380	−	22.0629i	0.522207	−	0.904490i
$596$	−10.8447			−0.444216
$597$	−11.5802			−0.473945
$598$	13.5802	−	23.5216i	0.555335	−	0.961868i
$599$	4.33011	−	7.49996i	0.176923	−	0.306440i	−0.763902	−	0.645332i	$-0.776719\pi$
$599$	4.33011	−	7.49996i	0.176923	−	0.306440i	0.940825	+	0.338892i	$0.110052\pi$
$600$	1.00000			0.0408248
$601$	−44.3787			−1.81025			−0.905123	−	0.425149i	$-0.860222\pi$
$601$	−44.3787			−1.81025			−0.905123	+	0.425149i	$0.860222\pi$
$602$	−2.01100	+	3.48315i	−0.0819622	+	0.141963i
$603$	−2.94540	−	5.10159i	−0.119946	−	0.207753i
$604$	0.468461	−	0.811398i	0.0190614	−	0.0330153i
$605$	−10.9479	−	18.9624i	−0.445096	−	0.770929i
$606$	1.84469	+	3.19509i	0.0749352	+	0.129792i
$607$	−24.6944			−1.00232			−0.501158	−	0.865356i	$-0.667092\pi$
$607$	−24.6944			−1.00232			−0.501158	+	0.865356i	$0.667092\pi$
$608$	1.47694	−	4.10105i	0.0598979	−	0.166320i
$609$	−39.6605			−1.60712
$610$	0.0545981	+	0.0945666i	0.00221061	+	0.00382889i
$611$	−4.21839	−	7.30647i	−0.170658	−	0.295588i
$612$	3.31315	−	5.73854i	0.133926	−	0.231967i
$613$	9.18341	+	15.9061i	0.370914	+	0.642443i	0.989706	−	0.143112i	$-0.0457110\pi$
$613$	9.18341	+	15.9061i	0.370914	+	0.642443i	−0.618792	+	0.785555i	$0.712378\pi$
$614$	14.1117	−	24.4422i	0.569502	−	0.986407i
$615$	8.79857			0.354792
$616$	22.0512			0.888466
$617$	6.00000	−	10.3923i	0.241551	−	0.418378i	−0.719605	−	0.694383i	$-0.755677\pi$
$617$	6.00000	−	10.3923i	0.241551	−	0.418378i	0.961156	+	0.276005i	$0.0890106\pi$
$618$	−1.03154	+	1.78668i	−0.0414946	+	0.0718707i
$619$	8.46594			0.340275			0.170137	−	0.985420i	$-0.445579\pi$
$619$	8.46594			0.340275			0.170137	+	0.985420i	$0.445579\pi$
$620$	4.73549			0.190182
$621$	2.86774	−	4.96708i	0.115079	−	0.199322i
$622$	6.42486	+	11.1282i	0.257613	+	0.446200i
$623$	9.82163	−	17.0116i	0.393495	−	0.681554i
$624$	−2.36774	−	4.10105i	−0.0947856	−	0.164174i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	29.0342			1.16044
$627$	16.1348	+	19.0969i	0.644361	+	0.762655i
$628$	8.68937			0.346744
$629$	−3.31315	−	5.73854i	−0.132104	−	0.228811i
$630$	−1.92234	−	3.32960i	−0.0765880	−	0.132654i
$631$	−10.2611	+	17.7727i	−0.408487	+	0.707520i	−0.994720	−	0.102622i	$-0.967277\pi$
$631$	−10.2611	+	17.7727i	−0.408487	+	0.707520i	0.586234	+	0.810142i	$0.300610\pi$
$632$	3.36774	+	5.83311i	0.133962	+	0.232028i
$633$	−11.6117	+	20.1121i	−0.461524	+	0.799383i
$634$	4.45402			0.176892
$635$	4.67241			0.185419
$636$	−2.55460	+	4.42469i	−0.101296	+	0.175451i
$637$	−18.4249	+	31.9128i	−0.730020	+	1.26443i
$638$	−59.1654			−2.34238
$639$	−6.62629			−0.262132
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−14.1434	−	24.4971i	−0.558630	−	0.967576i	−0.997611	−	0.0690797i	$-0.977994\pi$
$641$	−14.1434	−	24.4971i	−0.558630	−	0.967576i	0.438981	−	0.898496i	$-0.355340\pi$
$642$	−7.26703	+	12.5869i	−0.286807	+	0.496764i
$643$	15.4795	+	26.8112i	0.610450	+	1.05733i	0.991165	+	0.132638i	$0.0423448\pi$
$643$	15.4795	+	26.8112i	0.610450	+	1.05733i	−0.380714	+	0.924693i	$0.624322\pi$
$644$	11.0256	+	19.0969i	0.434469	+	0.752522i
$645$	1.04612			0.0411909
$646$	−9.78664	+	27.1748i	−0.385050	+	1.06918i
$647$	−33.0220			−1.29823			−0.649114	−	0.760691i	$-0.724860\pi$
$647$	−33.0220			−1.29823			−0.649114	+	0.760691i	$0.724860\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−17.2065	−	29.8025i	−0.675413	−	1.16985i
$650$	−2.36774	+	4.10105i	−0.0928706	+	0.160857i
$651$	−9.10323	−	15.7673i	−0.356784	−	0.617968i
$652$	0.103234	−	0.178807i	0.00404297	−	0.00700262i
$653$	33.1193			1.29606			0.648029	−	0.761616i	$-0.275594\pi$
$653$	33.1193			1.29606			0.648029	+	0.761616i	$0.275594\pi$
$654$	8.62629			0.337315
$655$	6.82163	−	11.8154i	0.266543	−	0.461666i
$656$	−4.39928	+	7.61978i	−0.171763	+	0.297503i
$657$	−6.10920			−0.238342
$658$	6.84972			0.267030
$659$	6.55712	−	11.3573i	0.255429	−	0.442416i	−0.709583	−	0.704622i	$-0.751117\pi$
$659$	6.55712	−	11.3573i	0.255429	−	0.442416i	0.965012	+	0.262206i	$0.0844500\pi$
$660$	−2.86774	−	4.96708i	−0.111627	−	0.193343i
$661$	−3.17227	+	5.49454i	−0.123387	+	0.213713i	−0.921101	−	0.389323i	$-0.872709\pi$
$661$	−3.17227	+	5.49454i	−0.123387	+	0.213713i	0.797714	+	0.603036i	$0.206042\pi$
$662$	5.92234	+	10.2578i	0.230178	+	0.398681i
$663$	15.6894	+	27.1748i	0.609325	+	1.05538i
$664$	−16.9420			−0.657475
$665$	10.8157	+	12.8012i	0.419413	+	0.496411i
$666$	−1.00000			−0.0387492
$667$	−29.5827	−	51.2387i	−1.14545	−	1.98397i
$668$	−8.86774	−	15.3594i	−0.343103	−	0.594272i
$669$	7.50252	−	12.9947i	0.290064	−	0.502406i
$670$	−2.94540	−	5.10159i	−0.113791	−	0.197091i
$671$	0.313147	−	0.542386i	0.0120889	−	0.0209386i
$672$	3.84469			0.148312
$673$	32.2987			1.24502			0.622512	−	0.782610i	$-0.286112\pi$
$673$	32.2987			1.24502			0.622512	+	0.782610i	$0.286112\pi$
$674$	−3.58614	+	6.21137i	−0.138133	+	0.239253i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	9.42486			0.362495
$677$	1.54598			0.0594169			0.0297084	−	0.999559i	$-0.490542\pi$
$677$	1.54598			0.0594169			0.0297084	+	0.999559i	$0.490542\pi$
$678$	4.26703	−	7.39071i	0.163874	−	0.283839i
$679$	−17.5997	−	30.4835i	−0.675413	−	1.16985i
$680$	3.31315	−	5.73854i	0.127053	−	0.220063i
$681$	10.2670	+	17.7830i	0.393433	+	0.681447i
$682$	−13.5802	−	23.5216i	−0.520012	−	0.900687i
$683$	−14.5341			−0.556130			−0.278065	−	0.960562i	$-0.589693\pi$
$683$	−14.5341			−0.556130			−0.278065	+	0.960562i	$0.589693\pi$
$684$	2.81315	+	3.32960i	0.107563	+	0.127310i
$685$	−13.9078			−0.531388
$686$	−1.50252	−	2.60244i	−0.0573664	−	0.0993615i
$687$	6.63226	+	11.4874i	0.253036	+	0.438272i
$688$	−0.523059	+	0.905965i	−0.0199414	+	0.0345396i
$689$	−12.0973	−	20.9531i	−0.460869	−	0.798249i
$690$	2.86774	−	4.96708i	0.109173	−	0.189093i
$691$	8.48794			0.322896			0.161448	−	0.986881i	$-0.448384\pi$
$691$	8.48794			0.322896			0.161448	+	0.986881i	$0.448384\pi$
$692$	1.41982			0.0539736
$693$	−11.0256	+	19.0969i	−0.418827	+	0.725430i
$694$	−11.2065	+	19.4102i	−0.425392	+	0.736800i
$695$	−0.735489			−0.0278987
$696$	−10.3157			−0.391014
$697$	29.1509	−	50.4909i	1.10417	−	1.91248i
$698$	12.1519	+	21.0477i	0.459955	+	0.796666i
$699$	−9.42486	+	16.3243i	−0.356481	+	0.617443i
$700$	−1.92234	−	3.32960i	−0.0726577	−	0.125847i
$701$	9.29870	+	16.1058i	0.351207	+	0.608309i	0.986461	−	0.163994i	$-0.0524379\pi$
$701$	9.29870	+	16.1058i	0.351207	+	0.608309i	−0.635254	+	0.772303i	$0.719105\pi$
$702$	4.73549			0.178730
$703$	4.29009	−	0.771459i	0.161804	−	0.0290961i
$704$	5.73549			0.216164
$705$	−0.890804	−	1.54292i	−0.0335496	−	0.0581096i
$706$	−16.3643	−	28.3438i	−0.615879	−	1.06673i
$707$	7.09224	−	12.2841i	0.266731	−	0.461992i
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	−3.96236	+	6.86301i	−0.148810	+	0.257746i	−0.930788	−	0.365560i	$-0.880877\pi$
$709$	−3.96236	+	6.86301i	−0.148810	+	0.257746i	0.781978	+	0.623306i	$0.214211\pi$
$710$	−6.62629			−0.248680
$711$	−6.73549			−0.252601
$712$	2.55460	−	4.42469i	0.0957376	−	0.165822i
$713$	13.5802	−	23.5216i	0.508582	−	0.880889i
$714$	−25.4760			−0.953416
$715$	27.1604			1.01574
$716$	8.60323	−	14.9012i	0.321518	−	0.556885i
$717$	−6.95388	−	12.0445i	−0.259697	−	0.449809i
$718$	0.577657	−	1.00053i	0.0215580	−	0.0373395i
$719$	14.8328	+	25.6911i	0.553169	+	0.958116i	0.998043	+	0.0625235i	$0.0199148\pi$
$719$	14.8328	+	25.6911i	0.553169	+	0.958116i	−0.444875	+	0.895593i	$0.646752\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	7.93189			0.295399
$722$	−14.6373	−	12.1140i	−0.544744	−	0.450837i
$723$	−30.2065			−1.12339
$724$	−8.26703	−	14.3189i	−0.307242	−	0.532158i
$725$	5.15783	+	8.93363i	0.191557	+	0.331787i
$726$	−10.9479	+	18.9624i	−0.406315	+	0.703759i
$727$	7.25855	+	12.5722i	0.269205	+	0.466276i	0.968657	−	0.248403i	$-0.0799059\pi$
$727$	7.25855	+	12.5722i	0.269205	+	0.466276i	−0.699452	+	0.714680i	$0.746573\pi$
$728$	−9.10323	+	15.7673i	−0.337388	+	0.584374i
$729$	1.00000			0.0370370
$730$	−6.10920			−0.226111
$731$	3.46594	−	6.00319i	0.128193	−	0.222036i
$732$	0.0545981	−	0.0945666i	0.00201800	−	0.00349528i
$733$	25.7355			0.950562			0.475281	−	0.879834i	$-0.342346\pi$
$733$	25.7355			0.950562			0.475281	+	0.879834i	$0.342346\pi$
$734$	27.6774			1.02159
$735$	−3.89080	+	6.73907i	−0.143514	+	0.248574i
$736$	2.86774	+	4.96708i	0.105706	+	0.183089i
$737$	−16.8933	+	29.2601i	−0.622274	+	1.07781i
$738$	−4.39928	−	7.61978i	−0.161940	−	0.280488i
$739$	2.23297	+	3.86762i	0.0821412	+	0.142273i	0.904169	−	0.427174i	$-0.140491\pi$
$739$	2.23297	+	3.86762i	0.0821412	+	0.142273i	−0.822028	+	0.569447i	$0.807157\pi$
$740$	−1.00000			−0.0367607
$741$	−20.3157	+	3.65323i	−0.746315	+	0.134205i
$742$	19.6433			0.721127
$743$	−5.04002	−	8.72957i	−0.184900	−	0.320257i	0.758643	−	0.651507i	$-0.225863\pi$
$743$	−5.04002	−	8.72957i	−0.184900	−	0.320257i	−0.943543	+	0.331250i	$0.892530\pi$
$744$	−2.36774	−	4.10105i	−0.0868057	−	0.150352i
$745$	5.42234	−	9.39177i	0.198659	−	0.344088i
$746$	11.7585	+	20.3664i	0.430511	+	0.745667i
$747$	8.47098	−	14.6722i	0.309937	−	0.536826i
$748$	−38.0050			−1.38960
$749$	55.8789			2.04177
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	1.94792	−	3.37390i	0.0710806	−	0.123115i	−0.828295	−	0.560293i	$-0.810689\pi$
$751$	1.94792	−	3.37390i	0.0710806	−	0.123115i	0.899375	+	0.437178i	$0.144022\pi$
$752$	1.78161			0.0649685
$753$	−21.0342			−0.766529
$754$	24.4249	−	42.3051i	0.889501	−	1.54066i
$755$	0.468461	+	0.811398i	0.0170490	+	0.0295298i
$756$	−1.92234	+	3.32960i	−0.0699149	+	0.121096i
$757$	−18.2866	−	31.6734i	−0.664639	−	1.15119i	−0.979383	−	0.202012i	$-0.935252\pi$
$757$	−18.2866	−	31.6734i	−0.664639	−	1.15119i	0.314744	−	0.949177i	$-0.398081\pi$
$758$	−4.14935	−	7.18689i	−0.150711	−	0.261040i
$759$	−32.8958			−1.19404
$760$	2.81315	+	3.32960i	0.102044	+	0.120777i
$761$	29.9589			1.08601			0.543005	−	0.839729i	$-0.317286\pi$
$761$	29.9589			1.08601			0.543005	+	0.839729i	$0.317286\pi$
$762$	−2.33621	−	4.04643i	−0.0846318	−	0.146587i
$763$	−16.5827	−	28.7221i	−0.600334	−	1.03981i
$764$	11.2065	−	19.4102i	0.405436	−	0.702235i
$765$	3.31315	+	5.73854i	0.119787	+	0.207477i
$766$	−6.89080	+	11.9352i	−0.248975	+	0.431237i
$767$	28.4129			1.02593
$768$	1.00000			0.0360844
$769$	24.9940	−	43.2909i	0.901308	−	1.56111i	0.0755103	−	0.997145i	$-0.475941\pi$
$769$	24.9940	−	43.2909i	0.901308	−	1.56111i	0.825798	−	0.563966i	$-0.190725\pi$
$770$	−11.0256	+	19.0969i	−0.397334	+	0.688203i
$771$	6.00000			0.216085
$772$	−23.0512			−0.829629
$773$	14.3532	−	24.8604i	0.516247	−	0.894167i	−0.483575	−	0.875303i	$-0.660662\pi$
$773$	14.3532	−	24.8604i	0.516247	−	0.894167i	0.999822	−	0.0188637i	$-0.00600486\pi$
$774$	−0.523059	−	0.905965i	−0.0188010	−	0.0325642i
$775$	−2.36774	+	4.10105i	−0.0850519	+	0.147314i
$776$	−4.57766	−	7.92873i	−0.164328	−	0.284625i
$777$	1.92234	+	3.32960i	0.0689637	+	0.119449i
$778$	−1.68434			−0.0603863
$779$	24.7517	+	29.2957i	0.886820	+	1.04963i
$780$	4.73549			0.169558
$781$	19.0025	+	32.9133i	0.679964	+	1.17773i
$782$	−19.0025	−	32.9133i	−0.679529	−	1.17698i
$783$	5.15783	−	8.93363i	0.184326	−	0.319262i
$784$	−3.89080	−	6.73907i	−0.138957	−	0.240681i
$785$	−4.34469	+	7.52522i	−0.155068	+	0.268586i
$786$	−13.6433			−0.486639
$787$	14.3960			0.513161			0.256581	−	0.966523i	$-0.417404\pi$
$787$	14.3960			0.513161			0.256581	+	0.966523i	$0.417404\pi$
$788$	−1.33621	+	2.31438i	−0.0476004	+	0.0824462i
$789$	3.39677	−	5.88337i	0.120928	−	0.209454i
$790$	−6.73549			−0.239638
$791$	−32.8108			−1.16662
$792$	−2.86774	+	4.96708i	−0.101901	+	0.176497i
$793$	0.258549	+	0.447819i	0.00918133	+	0.0159025i
$794$	−7.28161	+	12.6121i	−0.258415	+	0.447587i
$795$	−2.55460	−	4.42469i	−0.0906023	−	0.156928i
$796$	5.79009	+	10.0287i	0.205224	+	0.355459i
$797$	−35.8328			−1.26926			−0.634631	−	0.772815i	$-0.718848\pi$
$797$	−35.8328			−1.26926			−0.634631	+	0.772815i	$0.718848\pi$
$798$	5.67837	−	15.7673i	0.201012	−	0.558155i
$799$	−11.8055			−0.417647
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	2.55460	+	4.42469i	0.0902623	+	0.156339i
$802$	−10.7816	+	18.6743i	−0.380712	+	0.659412i
$803$	17.5196	+	30.3449i	0.618254	+	1.07085i
$804$	−2.94540	+	5.10159i	−0.103876	+	0.179919i
$805$	−22.0512			−0.777201
$806$	22.4249			0.789882
$807$	−6.04864	+	10.4765i	−0.212922	+	0.368792i
$808$	1.84469	−	3.19509i	0.0648958	−	0.112403i
$809$	−28.2184			−0.992106			−0.496053	−	0.868292i	$-0.665218\pi$
$809$	−28.2184			−0.992106			−0.496053	+	0.868292i	$0.665218\pi$
$810$	1.00000			0.0351364
$811$	8.24397	−	14.2790i	0.289485	−	0.501403i	−0.684202	−	0.729293i	$-0.739849\pi$
$811$	8.24397	−	14.2790i	0.289485	−	0.501403i	0.973687	+	0.227890i	$0.0731827\pi$
$812$	19.8302	+	34.3470i	0.695905	+	1.20534i
$813$	0.580175	−	1.00489i	0.0203476	−	0.0352431i
$814$	2.86774	+	4.96708i	0.100514	+	0.174096i
$815$	0.103234	+	0.178807i	0.00361614	+	0.00626333i
$816$	−6.62629			−0.231967
$817$	2.94288	+	3.48315i	0.102958	+	0.121860i
$818$	−13.2987			−0.464978
$819$	−9.10323	−	15.7673i	−0.318093	−	0.550953i
$820$	−4.39928	−	7.61978i	−0.153630	−	0.266094i
$821$	26.4710	−	45.8491i	0.923844	−	1.60014i	0.130433	−	0.991457i	$-0.458363\pi$
$821$	26.4710	−	45.8491i	0.923844	−	1.60014i	0.793411	−	0.608687i	$-0.208303\pi$
$822$	6.95388	+	12.0445i	0.242544	+	0.420099i
$823$	−0.916381	+	1.58722i	−0.0319430	+	0.0553270i	−0.881555	−	0.472081i	$-0.843503\pi$
$823$	−0.916381	+	1.58722i	−0.0319430	+	0.0553270i	0.849612	+	0.527408i	$0.176836\pi$
$824$	2.06308			0.0718707
$825$	5.73549			0.199684
$826$	−11.5341	+	19.9776i	−0.401321	+	0.695109i
$827$	3.73801	−	6.47442i	0.129983	−	0.225138i	−0.793687	−	0.608327i	$-0.791841\pi$
$827$	3.73801	−	6.47442i	0.129983	−	0.225138i	0.923670	+	0.383189i	$0.125174\pi$
$828$	−5.73549			−0.199322
$829$	24.7116			0.858271			0.429135	−	0.903240i	$-0.358818\pi$
$829$	24.7116			0.858271			0.429135	+	0.903240i	$0.358818\pi$
$830$	8.47098	−	14.6722i	0.294032	−	0.509278i
$831$	−2.41982	−	4.19126i	−0.0839428	−	0.145393i
$832$	−2.36774	+	4.10105i	−0.0820868	+	0.142178i
$833$	25.7816	+	44.6551i	0.893280	+	1.54721i
$834$	0.367745	+	0.636953i	0.0127340	+	0.0220559i
$835$	17.7355			0.613762
$836$	8.47098	−	23.5216i	0.292975	−	0.813510i
$837$	4.73549			0.163682
$838$	18.4940	+	32.0326i	0.638866	+	1.10655i
$839$	17.8328	+	30.8872i	0.615655	+	1.06635i	0.990269	+	0.139165i	$0.0444420\pi$
$839$	17.8328	+	30.8872i	0.615655	+	1.06635i	−0.374614	+	0.927181i	$0.622225\pi$
$840$	−1.92234	+	3.32960i	−0.0663271	+	0.114882i
$841$	−38.7065	−	67.0416i	−1.33471	−	2.31178i
$842$	1.68685	−	2.92172i	0.0581328	−	0.100689i
$843$	9.32759			0.321259
$844$	23.2234			0.799383
$845$	−4.71243	+	8.16217i	−0.162113	+	0.280787i
$846$	−0.890804	+	1.54292i	−0.0306265	+	0.0530466i
$847$	84.1826			2.89255
$848$	5.10920			0.175451
$849$	4.67241	−	8.09285i	0.160357	−	0.277746i
$850$	3.31315	+	5.73854i	0.113640	+	0.196830i
$851$	−2.86774	+	4.96708i	−0.0983050	+	0.170269i
$852$	3.31315	+	5.73854i	0.113507	+	0.196599i
$853$	−5.99404	−	10.3820i	−0.205232	−	0.355472i	0.744975	−	0.667093i	$-0.232462\pi$
$853$	−5.99404	−	10.3820i	−0.205232	−	0.355472i	−0.950207	+	0.311621i	$0.899128\pi$
$854$	−0.419825			−0.0143661
$855$	−4.29009	+	0.771459i	−0.146718	+	0.0263833i
$856$	14.5341			0.496764
$857$	−16.2184	−	28.0911i	−0.554010	−	0.959573i	−0.997980	−	0.0635314i	$-0.979764\pi$
$857$	−16.2184	−	28.0911i	−0.554010	−	0.959573i	0.443970	−	0.896042i	$-0.353570\pi$
$858$	−13.5802	−	23.5216i	−0.463620	−	0.803013i
$859$	0.548636	−	0.950266i	0.0187192	−	0.0324226i	−0.856514	−	0.516124i	$-0.827374\pi$
$859$	0.548636	−	0.950266i	0.0187192	−	0.0324226i	0.875233	+	0.483701i	$0.160708\pi$
$860$	−0.523059	−	0.905965i	−0.0178362	−	0.0308931i
$861$	−16.9139	+	29.2957i	−0.576423	+	0.998394i
$862$	23.1654			0.789016
$863$	22.8036			0.776244			0.388122	−	0.921608i	$-0.373124\pi$
$863$	22.8036			0.776244			0.388122	+	0.921608i	$0.373124\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−0.709912	+	1.22960i	−0.0241377	+	0.0418078i
$866$	1.67241			0.0568309
$867$	26.9078			0.913836
$868$	−9.10323	+	15.7673i	−0.308984	+	0.535176i
$869$	19.3157	+	33.4557i	0.655239	+	1.13491i
$870$	5.15783	−	8.93363i	0.174867	−	0.302878i
$871$	−13.9479	−	24.1585i	−0.472607	−	0.818580i
$872$	−4.31315	−	7.47059i	−0.146062	−	0.252986i
$873$	9.15531			0.309860
$874$	24.6058	−	4.42469i	0.832302	−	0.149667i
$875$	3.84469			0.129974
$876$	3.05460	+	5.29072i	0.103205	+	0.178757i
$877$	8.54612	+	14.8023i	0.288582	+	0.499839i	0.973471	−	0.228808i	$-0.0734829\pi$
$877$	8.54612	+	14.8023i	0.288582	+	0.499839i	−0.684890	+	0.728647i	$0.740150\pi$
$878$	13.3703	−	23.1580i	0.451225	−	0.781544i
$879$	−1.60072	−	2.77252i	−0.0539908	−	0.0935148i
$880$	−2.86774	+	4.96708i	−0.0966717	+	0.167440i
$881$	41.9589			1.41363			0.706816	−	0.707398i	$-0.250131\pi$
$881$	41.9589			1.41363			0.706816	+	0.707398i	$0.250131\pi$
$882$	7.78161			0.262020
$883$	18.3122	−	31.7177i	0.616255	−	1.06739i	−0.373908	−	0.927466i	$-0.621982\pi$
$883$	18.3122	−	31.7177i	0.616255	−	1.06739i	0.990163	−	0.139920i	$-0.0446844\pi$
$884$	15.6894	−	27.1748i	0.527691	−	0.913987i
$885$	6.00000			0.201688
$886$	6.09727			0.204842
$887$	5.20647	−	9.01787i	0.174816	−	0.302790i	−0.765282	−	0.643696i	$-0.777400\pi$
$887$	5.20647	−	9.01787i	0.174816	−	0.302790i	0.940098	+	0.340905i	$0.110734\pi$
$888$	0.500000	+	0.866025i	0.0167789	+	0.0290619i
$889$	−8.98198	+	15.5572i	−0.301246	+	0.521773i
$890$	2.55460	+	4.42469i	0.0856303	+	0.148316i
$891$	−2.86774	−	4.96708i	−0.0960731	−	0.166403i
$892$	−15.0050			−0.502406
$893$	2.63133	−	7.30647i	0.0880541	−	0.244502i
$894$	−10.8447			−0.362701
$895$	8.60323	+	14.9012i	0.287574	+	0.498093i
$896$	−1.92234	−	3.32960i	−0.0642210	−	0.111234i
$897$	13.5802	−	23.5216i	0.453429	−	0.785362i
$898$	2.55460	+	4.42469i	0.0852480	+	0.147654i
$899$	24.4249	−	42.3051i	0.814615	−	1.41095i
$900$	1.00000			0.0333333
$901$	−33.8550			−1.12787
$902$	−25.2320	+	43.7032i	−0.840135	+	1.45516i
$903$	−2.01100	+	3.48315i	−0.0669218	+	0.115912i
$904$	−8.53406			−0.283839
$905$	16.5341			0.549611
$906$	0.468461	−	0.811398i	0.0155636	−	0.0269569i
$907$	−2.48290	−	4.30051i	−0.0824434	−	0.142796i	0.821856	−	0.569696i	$-0.192939\pi$
$907$	−2.48290	−	4.30051i	−0.0824434	−	0.142796i	−0.904299	+	0.426900i	$0.859606\pi$
$908$	10.2670	−	17.7830i	0.340723	−	0.590150i
$909$	1.84469	+	3.19509i	0.0611844	+	0.105974i
$910$	−9.10323	−	15.7673i	−0.301769	−	0.522680i
$911$	1.18420			0.0392342			0.0196171	−	0.999808i	$-0.493755\pi$
$911$	1.18420			0.0392342			0.0196171	+	0.999808i	$0.493755\pi$
$912$	1.47694	−	4.10105i	0.0489064	−	0.135799i
$913$	−97.1704			−3.21587
$914$	17.1980	+	29.7878i	0.568859	+	0.985293i
$915$	0.0545981	+	0.0945666i	0.00180496	+	0.00312628i
$916$	6.63226	−	11.4874i	0.219136	−	0.379554i
$917$	26.2270	+	45.4265i	0.866092	+	1.50012i
$918$	3.31315	−	5.73854i	0.109350	−	0.189400i
$919$	17.3618			0.572712			0.286356	−	0.958123i	$-0.407556\pi$
$919$	17.3618			0.572712			0.286356	+	0.958123i	$0.407556\pi$
$920$	−5.73549			−0.189093
$921$	14.1117	−	24.4422i	0.464997	−	0.805398i
$922$	5.73549	−	9.93416i	0.188888	−	0.327164i
$923$	−31.3787			−1.03284
$924$	22.0512			0.725430
$925$	0.500000	−	0.866025i	0.0164399	−	0.0284747i
$926$	−0.968461	−	1.67742i	−0.0318256	−	0.0551236i
$927$	−1.03154	+	1.78668i	−0.0338802	+	0.0586822i
$928$	5.15783	+	8.93363i	0.169314	+	0.293261i
$929$	−22.2951	−	38.6163i	−0.731479	−	1.26696i	−0.956251	−	0.292548i	$-0.905497\pi$
$929$	−22.2951	−	38.6163i	−0.731479	−	1.26696i	0.224772	−	0.974411i	$-0.427836\pi$
$930$	4.73549			0.155283
$931$	−33.3838	+	6.00319i	−1.09411	+	0.196747i
$932$	18.8497			0.617443
$933$	6.42486	+	11.1282i	0.210340	+	0.364320i
$934$	4.89332	+	8.47548i	0.160114	+	0.277326i
$935$	19.0025	−	32.9133i	0.621449	−	1.07638i
$936$	−2.36774	−	4.10105i	−0.0773922	−	0.134047i
$937$	−14.0888	+	24.4025i	−0.460261	+	0.797195i	−0.998974	−	0.0452943i	$-0.985577\pi$
$937$	−14.0888	+	24.4025i	−0.460261	+	0.797195i	0.538713	+	0.842489i	$0.318911\pi$
$938$	22.6483			0.739493
$939$	29.0342			0.947495
$940$	−0.890804	+	1.54292i	−0.0290548	+	0.0503244i
$941$	−15.2501	+	26.4139i	−0.497138	+	0.861068i	−0.999995	−	0.00330157i	$-0.998949\pi$
$941$	−15.2501	+	26.4139i	−0.497138	+	0.861068i	0.502857	+	0.864370i	$0.332282\pi$
$942$	8.68937			0.283115
$943$	−50.4641			−1.64334
$944$	−3.00000	+	5.19615i	−0.0976417	+	0.169120i
$945$	−1.92234	−	3.32960i	−0.0625338	−	0.108312i
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	7.46846	+	12.9358i	0.242692	+	0.420356i	0.961480	−	0.274874i	$-0.0886361\pi$
$947$	7.46846	+	12.9358i	0.242692	+	0.420356i	−0.718788	+	0.695229i	$0.755303\pi$
$948$	3.36774	+	5.83311i	0.109379	+	0.189450i
$949$	−28.9300			−0.939109
$950$	−4.29009	+	0.771459i	−0.139189	+	0.0250294i
$951$	4.45402			0.144431
$952$	12.7380	+	22.0629i	0.412841	+	0.715062i
$953$	−13.3787	−	23.1727i	−0.433380	−	0.750636i	0.563782	−	0.825924i	$-0.309346\pi$
$953$	−13.3787	−	23.1727i	−0.433380	−	0.750636i	−0.997162	+	0.0752876i	$0.976013\pi$
$954$	−2.55460	+	4.42469i	−0.0827082	+	0.143255i
$955$	11.2065	+	19.4102i	0.362633	+	0.628098i
$956$	−6.95388	+	12.0445i	−0.224905	+	0.389546i
$957$	−59.1654			−1.91255
$958$	26.4079			0.853201
$959$	26.7355	−	46.3072i	0.863334	−	1.49534i
$960$	−0.500000	+	0.866025i	−0.0161374	+	0.0279508i
$961$	−8.57514			−0.276617
$962$	−4.73549			−0.152678
$963$	−7.26703	+	12.5869i	−0.234177	+	0.405606i
$964$	15.1032	+	26.1596i	0.486442	+	0.842543i
$965$	11.5256	−	19.9629i	0.371021	−	0.642628i
$966$	11.0256	+	19.0969i	0.354742	+	0.614431i
$967$	−20.3677	−	35.2780i	−0.654983	−	1.13446i	−0.981898	−	0.189409i	$-0.939343\pi$
$967$	−20.3677	−	35.2780i	−0.654983	−	1.13446i	0.326916	−	0.945054i	$-0.393991\pi$
$968$	21.8958			0.703759
$969$	−9.78664	+	27.1748i	−0.314392	+	0.872980i
$970$	9.15531			0.293959
$971$	2.67241	+	4.62875i	0.0857618	+	0.148544i	0.905716	−	0.423886i	$-0.139334\pi$
$971$	2.67241	+	4.62875i	0.0857618	+	0.148544i	−0.819954	+	0.572430i	$0.806001\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	1.41386	−	2.44888i	0.0453264	−	0.0785076i
$974$	−19.6688	−	34.0674i	−0.630230	−	1.09159i
$975$	−2.36774	+	4.10105i	−0.0758285	+	0.131339i
$976$	−0.109196			−0.00349528
$977$	−42.6947			−1.36592			−0.682962	−	0.730454i	$-0.739309\pi$
$977$	−42.6947			−1.36592			−0.682962	+	0.730454i	$0.739309\pi$
$978$	0.103234	−	0.178807i	0.00330107	−	0.00571762i
$979$	14.6519	−	25.3778i	0.468276	−	0.811077i
$980$	7.78161			0.248574
$981$	8.62629			0.275416
$982$	−5.33872	+	9.24694i	−0.170366	+	0.295082i
$983$	7.28757	+	12.6224i	0.232437	+	0.402593i	0.958525	−	0.285009i	$-0.0919966\pi$
$983$	7.28757	+	12.6224i	0.232437	+	0.402593i	−0.726087	+	0.687602i	$0.758663\pi$
$984$	−4.39928	+	7.61978i	−0.140244	+	0.242910i
$985$	−1.33621	−	2.31438i	−0.0425751	−	0.0737422i
$986$	−34.1773	−	59.1968i	−1.08843	−	1.88521i
$987$	6.84972			0.218029
$988$	13.3216	+	15.7673i	0.423817	+	0.501623i
$989$	−6.00000			−0.190789
$990$	−2.86774	−	4.96708i	−0.0911429	−	0.157864i
$991$	21.5425	+	37.3128i	0.684321	+	1.18528i	0.973650	+	0.228049i	$0.0732347\pi$
$991$	21.5425	+	37.3128i	0.684321	+	1.18528i	−0.289328	+	0.957230i	$0.593432\pi$
$992$	−2.36774	+	4.10105i	−0.0751760	+	0.130209i
$993$	5.92234	+	10.2578i	0.187940	+	0.325521i
$994$	12.7380	−	22.0629i	0.404025	−	0.699792i
$995$	−11.5802			−0.367116
$996$	−16.9420			−0.536826
$997$	20.1144	−	34.8391i	0.637028	−	1.10337i	−0.349053	−	0.937103i	$-0.613497\pi$
$997$	20.1144	−	34.8391i	0.637028	−	1.10337i	0.986081	−	0.166263i	$-0.0531700\pi$
$998$	−12.7670	+	22.1131i	−0.404133	+	0.699979i
$999$	−1.00000			−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.i.j.121.3	✓	6
3.2	odd	2		1710.2.l.q.1261.3		6
19.11	even	3	inner	570.2.i.j.391.3	yes	6
57.11	odd	6		1710.2.l.q.1531.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.j.121.3	✓	6	1.1	even	1	trivial
570.2.i.j.391.3	yes	6	19.11	even	3	inner
1710.2.l.q.1261.3		6	3.2	odd	2
1710.2.l.q.1531.3		6	57.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +3.84469 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +3.84469 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +5.73549 q^{11} +1.00000 q^{12} +(-2.36774 + 4.10105i) q^{13} +(-1.92234 - 3.32960i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.31315 + 5.73854i) q^{17} +1.00000 q^{18} +(-4.29009 + 0.771459i) q^{19} +1.00000 q^{20} +(-1.92234 - 3.32960i) q^{21} +(-2.86774 - 4.96708i) q^{22} +(2.86774 - 4.96708i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +4.73549 q^{26} +1.00000 q^{27} +(-1.92234 + 3.32960i) q^{28} +(5.15783 - 8.93363i) q^{29} +1.00000 q^{30} +4.73549 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.86774 - 4.96708i) q^{33} +(3.31315 - 5.73854i) q^{34} +(-1.92234 - 3.32960i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.00000 q^{37} +(2.81315 + 3.32960i) q^{38} +4.73549 q^{39} +(-0.500000 - 0.866025i) q^{40} +(-4.39928 - 7.61978i) q^{41} +(-1.92234 + 3.32960i) q^{42} +(-0.523059 - 0.905965i) q^{43} +(-2.86774 + 4.96708i) q^{44} +1.00000 q^{45} -5.73549 q^{46} +(-0.890804 + 1.54292i) q^{47} +(-0.500000 + 0.866025i) q^{48} +7.78161 q^{49} +1.00000 q^{50} +(3.31315 - 5.73854i) q^{51} +(-2.36774 - 4.10105i) q^{52} +(-2.55460 + 4.42469i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.86774 - 4.96708i) q^{55} +3.84469 q^{56} +(2.81315 + 3.32960i) q^{57} -10.3157 q^{58} +(-3.00000 - 5.19615i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(0.0545981 - 0.0945666i) q^{61} +(-2.36774 - 4.10105i) q^{62} +(-1.92234 + 3.32960i) q^{63} +1.00000 q^{64} +4.73549 q^{65} +(-2.86774 + 4.96708i) q^{66} +(-2.94540 + 5.10159i) q^{67} -6.62629 q^{68} -5.73549 q^{69} +(-1.92234 + 3.32960i) q^{70} +(3.31315 + 5.73854i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.05460 + 5.29072i) q^{73} +(0.500000 + 0.866025i) q^{74} +1.00000 q^{75} +(1.47694 - 4.10105i) q^{76} +22.0512 q^{77} +(-2.36774 - 4.10105i) q^{78} +(3.36774 + 5.83311i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.39928 + 7.61978i) q^{82} -16.9420 q^{83} +3.84469 q^{84} +(3.31315 - 5.73854i) q^{85} +(-0.523059 + 0.905965i) q^{86} -10.3157 q^{87} +5.73549 q^{88} +(2.55460 - 4.42469i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-9.10323 + 15.7673i) q^{91} +(2.86774 + 4.96708i) q^{92} +(-2.36774 - 4.10105i) q^{93} +1.78161 q^{94} +(2.81315 + 3.32960i) q^{95} +1.00000 q^{96} +(-4.57766 - 7.92873i) q^{97} +(-3.89080 - 6.73907i) q^{98} +(-2.86774 + 4.96708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} + 6 q^{12} - q^{13} - q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} + 6 q^{18} - 2 q^{19} + 6 q^{20} - q^{21} - 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} + 6 q^{27} - q^{28} - 6 q^{29} + 6 q^{30} + 2 q^{31} - 3 q^{32} - 4 q^{33} + 4 q^{34} - q^{35} - 3 q^{36} - 6 q^{37} + q^{38} + 2 q^{39} - 3 q^{40} - 8 q^{41} - q^{42} - 11 q^{43} - 4 q^{44} + 6 q^{45} - 8 q^{46} - 3 q^{48} + 36 q^{49} + 6 q^{50} + 4 q^{51} - q^{52} - 18 q^{53} - 3 q^{54} - 4 q^{55} + 2 q^{56} + q^{57} + 12 q^{58} - 18 q^{59} - 3 q^{60} + 3 q^{61} - q^{62} - q^{63} + 6 q^{64} + 2 q^{65} - 4 q^{66} - 15 q^{67} - 8 q^{68} - 8 q^{69} - q^{70} + 4 q^{71} - 3 q^{72} + 21 q^{73} + 3 q^{74} + 6 q^{75} + q^{76} + 32 q^{77} - q^{78} + 7 q^{79} - 3 q^{80} - 3 q^{81} - 8 q^{82} + 4 q^{83} + 2 q^{84} + 4 q^{85} - 11 q^{86} + 12 q^{87} + 8 q^{88} + 18 q^{89} - 3 q^{90} - 15 q^{91} + 4 q^{92} - q^{93} + q^{95} + 6 q^{96} - 38 q^{97} - 18 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 + 6 * q^12 - q^13 - q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 + 6 * q^18 - 2 * q^19 + 6 * q^20 - q^21 - 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 + 6 * q^27 - q^28 - 6 * q^29 + 6 * q^30 + 2 * q^31 - 3 * q^32 - 4 * q^33 + 4 * q^34 - q^35 - 3 * q^36 - 6 * q^37 + q^38 + 2 * q^39 - 3 * q^40 - 8 * q^41 - q^42 - 11 * q^43 - 4 * q^44 + 6 * q^45 - 8 * q^46 - 3 * q^48 + 36 * q^49 + 6 * q^50 + 4 * q^51 - q^52 - 18 * q^53 - 3 * q^54 - 4 * q^55 + 2 * q^56 + q^57 + 12 * q^58 - 18 * q^59 - 3 * q^60 + 3 * q^61 - q^62 - q^63 + 6 * q^64 + 2 * q^65 - 4 * q^66 - 15 * q^67 - 8 * q^68 - 8 * q^69 - q^70 + 4 * q^71 - 3 * q^72 + 21 * q^73 + 3 * q^74 + 6 * q^75 + q^76 + 32 * q^77 - q^78 + 7 * q^79 - 3 * q^80 - 3 * q^81 - 8 * q^82 + 4 * q^83 + 2 * q^84 + 4 * q^85 - 11 * q^86 + 12 * q^87 + 8 * q^88 + 18 * q^89 - 3 * q^90 - 15 * q^91 + 4 * q^92 - q^93 + q^95 + 6 * q^96 - 38 * q^97 - 18 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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