LMFDB - Embedded newform 693.2.l.c.529.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(529,693)]

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([4, 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("693.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.53363286007$
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			529.6
Character	$\chi$	$=$	693.529
Dual form			693.2.l.c.562.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.11652 q^{2} +(1.07526 - 1.35787i) q^{3} +2.47967 q^{4} +(-1.28330 + 2.22274i) q^{5} +(-2.27581 + 2.87397i) q^{6} +(0.502180 - 2.59766i) q^{7} -1.01522 q^{8} +(-0.687640 - 2.92013i) q^{9} +O(q^{10})$	\(q-2.11652 q^{2} +(1.07526 - 1.35787i) q^{3} +2.47967 q^{4} +(-1.28330 + 2.22274i) q^{5} +(-2.27581 + 2.87397i) q^{6} +(0.502180 - 2.59766i) q^{7} -1.01522 q^{8} +(-0.687640 - 2.92013i) q^{9} +(2.71613 - 4.70448i) q^{10} +(0.500000 + 0.866025i) q^{11} +(2.66628 - 3.36707i) q^{12} +(-0.929012 - 1.60910i) q^{13} +(-1.06287 + 5.49800i) q^{14} +(1.63832 + 4.13258i) q^{15} -2.81059 q^{16} +(-1.06686 + 1.84786i) q^{17} +(1.45541 + 6.18052i) q^{18} +(-1.15601 - 2.00227i) q^{19} +(-3.18216 + 5.51166i) q^{20} +(-2.98731 - 3.47505i) q^{21} +(-1.05826 - 1.83296i) q^{22} +(0.885189 - 1.53319i) q^{23} +(-1.09163 + 1.37855i) q^{24} +(-0.793718 - 1.37476i) 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} +(-3.46754 - 8.74670i) q^{30} +1.77951 q^{31} +7.97912 q^{32} +(1.71358 + 0.252264i) 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} +(2.44672 + 4.23784i) q^{38} +(-3.18388 - 0.468713i) q^{39} +(1.30284 - 2.25658i) q^{40} +(-4.82423 - 8.35581i) q^{41} +(6.32272 + 7.35501i) q^{42} +(2.55974 - 4.43359i) q^{43} +(1.23983 + 2.14745i) q^{44} +(7.37314 + 2.21896i) q^{45} +(-1.87352 + 3.24504i) q^{46} -2.66705 q^{47} +(-3.02211 + 3.81642i) q^{48} +(-6.49563 - 2.60898i) q^{49} +(1.67992 + 2.90971i) q^{50} +(1.36201 + 3.43559i) q^{51} +(-2.30364 - 3.99002i) q^{52} +(-2.96849 + 5.14158i) q^{53} +(9.95730 + 4.66939i) q^{54} -2.56660 q^{55} +(-0.509825 + 2.63720i) q^{56} +(-3.96183 - 0.583239i) q^{57} +(-5.92985 + 10.2708i) q^{58} -7.79334 q^{59} +(4.06249 + 10.2474i) q^{60} -3.40020 q^{61} -3.76637 q^{62} +(-7.93081 + 0.319823i) q^{63} -11.2668 q^{64} +4.76881 q^{65} +(-3.62683 - 0.533923i) q^{66} +3.07818 q^{67} +(-2.64546 + 4.58207i) q^{68} +(-1.13007 - 2.85055i) q^{69} +(-10.8566 - 9.41807i) q^{70} -13.1025 q^{71} +(0.698109 + 2.96458i) q^{72} +(5.55336 - 9.61870i) q^{73} +(3.82915 + 6.63229i) q^{74} +(-2.72020 - 0.400453i) q^{75} +(-2.86652 - 4.96495i) q^{76} +(2.50073 - 0.863928i) q^{77} +(6.73875 + 0.992041i) q^{78} +4.87281 q^{79} +(3.60683 - 6.24721i) q^{80} +(-8.05430 + 4.01600i) q^{81} +(10.2106 + 17.6853i) q^{82} +(1.63826 - 2.83756i) q^{83} +(-7.40754 - 8.61696i) q^{84} +(-2.73821 - 4.74271i) q^{85} +(-5.41774 + 9.38380i) q^{86} +(-3.57678 - 9.02224i) q^{87} +(-0.507612 - 0.879209i) 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} +(1.91343 - 2.41635i) q^{93} +5.64488 q^{94} +5.93403 q^{95} +(8.57961 - 10.8346i) 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 + 80 q^{4} - 4 q^{5} + 6 q^{6} - q^{7} - 4 q^{9}+O(q^{10}) $ 80 * q + 80 * q^4 - 4 * q^5 + 6 * q^6 - q^7 - 4 * q^9	\( 80 q + 80 q^{4} - 4 q^{5} + 6 q^{6} - q^{7} - 4 q^{9} + 12 q^{10} + 40 q^{11} + 5 q^{12} + 21 q^{13} + 7 q^{14} - 5 q^{15} + 80 q^{16} - 3 q^{17} - 10 q^{18} + 18 q^{19} - 12 q^{20} - 33 q^{21} + 4 q^{23} - 2 q^{24} - 40 q^{25} - 12 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} + 14 q^{30} - 64 q^{31} - 70 q^{32} + 28 q^{34} - 18 q^{35} - 16 q^{36} - 7 q^{37} - 23 q^{38} + 42 q^{39} + 51 q^{40} - 2 q^{41} + 25 q^{42} + 9 q^{43} + 40 q^{44} - 14 q^{45} - 6 q^{46} + 52 q^{47} - 28 q^{48} - q^{49} + 2 q^{50} - 20 q^{51} + 44 q^{52} + 4 q^{53} - 2 q^{54} - 8 q^{55} + 6 q^{56} + 16 q^{57} - 16 q^{58} + 48 q^{59} - 70 q^{60} - 138 q^{61} + 12 q^{62} + 95 q^{63} + 44 q^{64} + 14 q^{65} + 3 q^{66} - 14 q^{67} - 17 q^{68} + 15 q^{69} - 40 q^{70} + 34 q^{71} - 19 q^{72} + 26 q^{73} - 4 q^{74} + 14 q^{75} + 52 q^{76} - 2 q^{77} - 60 q^{78} + 10 q^{79} - 47 q^{80} - 44 q^{81} + 60 q^{82} + 4 q^{83} - 205 q^{84} + 13 q^{85} + 82 q^{87} - 38 q^{89} - 43 q^{90} + 13 q^{91} - 21 q^{92} + 44 q^{93} - 112 q^{94} + 40 q^{95} - 78 q^{96} + 49 q^{97} - 84 q^{98} - 2 q^{99}+O(q^{100}) \) 80 * q + 80 * q^4 - 4 * q^5 + 6 * q^6 - q^7 - 4 * q^9 + 12 * q^10 + 40 * q^11 + 5 * q^12 + 21 * q^13 + 7 * q^14 - 5 * q^15 + 80 * q^16 - 3 * q^17 - 10 * q^18 + 18 * q^19 - 12 * q^20 - 33 * q^21 + 4 * q^23 - 2 * q^24 - 40 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 + 14 * q^30 - 64 * q^31 - 70 * q^32 + 28 * q^34 - 18 * q^35 - 16 * q^36 - 7 * q^37 - 23 * q^38 + 42 * q^39 + 51 * q^40 - 2 * q^41 + 25 * q^42 + 9 * q^43 + 40 * q^44 - 14 * q^45 - 6 * q^46 + 52 * q^47 - 28 * q^48 - q^49 + 2 * q^50 - 20 * q^51 + 44 * q^52 + 4 * q^53 - 2 * q^54 - 8 * q^55 + 6 * q^56 + 16 * q^57 - 16 * q^58 + 48 * q^59 - 70 * q^60 - 138 * q^61 + 12 * q^62 + 95 * q^63 + 44 * q^64 + 14 * q^65 + 3 * q^66 - 14 * q^67 - 17 * q^68 + 15 * q^69 - 40 * q^70 + 34 * q^71 - 19 * q^72 + 26 * q^73 - 4 * q^74 + 14 * q^75 + 52 * q^76 - 2 * q^77 - 60 * q^78 + 10 * q^79 - 47 * q^80 - 44 * q^81 + 60 * q^82 + 4 * q^83 - 205 * q^84 + 13 * q^85 + 82 * q^87 - 38 * q^89 - 43 * q^90 + 13 * q^91 - 21 * q^92 + 44 * q^93 - 112 * q^94 + 40 * q^95 - 78 * 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 $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.11652			−1.49661			−0.748304	−	0.663356i	$-0.769131\pi$
$2$	−2.11652			−1.49661			−0.748304	+	0.663356i	$0.769131\pi$
$3$	1.07526	−	1.35787i	0.620801	−	0.783969i
$3$	1.07526	−	1.35787i	0.620801	−	0.783969i
$4$	2.47967			1.23983
$5$	−1.28330	+	2.22274i	−0.573909	+	0.994040i	0.422250	+	0.906479i	$0.361240\pi$
$5$	−1.28330	+	2.22274i	−0.573909	+	0.994040i	−0.996159	+	0.0875606i	$0.972093\pi$
$6$	−2.27581	+	2.87397i	−0.929095	+	1.17329i
$7$	0.502180	−	2.59766i	0.189806	−	0.981822i
$7$	0.502180	−	2.59766i	0.189806	−	0.981822i
$8$	−1.01522			−0.358936
$9$	−0.687640	−	2.92013i	−0.229213	−	0.973376i
$10$	2.71613	−	4.70448i	0.858917	−	1.48769i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	2.66628	−	3.36707i	0.769689	−	0.971990i
$13$	−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	$0.916285\pi$
$14$	−1.06287	+	5.49800i	−0.284065	+	1.46940i
$15$	1.63832	+	4.13258i	0.423013	+	1.06703i
$16$	−2.81059			−0.702647
$17$	−1.06686	+	1.84786i	−0.258752	+	0.448171i	−0.965908	−	0.258886i	$-0.916644\pi$
$17$	−1.06686	+	1.84786i	−0.258752	+	0.448171i	0.707156	+	0.707058i	$0.249978\pi$
$18$	1.45541	+	6.18052i	0.343042	+	1.45676i
$19$	−1.15601	−	2.00227i	−0.265207	−	0.459351i	0.702411	−	0.711771i	$-0.252107\pi$
$19$	−1.15601	−	2.00227i	−0.265207	−	0.459351i	−0.967618	+	0.252420i	$0.918773\pi$
$20$	−3.18216	+	5.51166i	−0.711552	+	1.23244i
$21$	−2.98731	−	3.47505i	−0.651886	−	0.758317i
$22$	−1.05826	−	1.83296i	−0.225622	−	0.390789i
$23$	0.885189	−	1.53319i	0.184575	−	0.319693i	−0.758858	−	0.651256i	$-0.774243\pi$
$23$	0.885189	−	1.53319i	0.184575	−	0.319693i	0.943433	+	0.331563i	$0.107576\pi$
$24$	−1.09163	+	1.37855i	−0.222828	+	0.281394i
$25$	−0.793718	−	1.37476i	−0.158744	−	0.274952i
$26$	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	$-0.00749909\pi$
$30$	−3.46754	−	8.74670i	−0.633084	−	1.59692i
$31$	1.77951			0.319609			0.159805	−	0.987149i	$-0.448914\pi$
$31$	1.77951			0.319609			0.159805	+	0.987149i	$0.448914\pi$
$32$	7.97912			1.41052
$33$	1.71358	+	0.252264i	0.298296	+	0.0439135i
$34$	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	0.678120	−	0.734951i	$-0.262795\pi$
$37$	−1.80917	−	3.13358i	−0.297426	−	0.515157i	−0.975546	+	0.219794i	$0.929462\pi$
$38$	2.44672	+	4.23784i	0.396910	+	0.687468i
$39$	−3.18388	−	0.468713i	−0.509828	−	0.0750541i
$40$	1.30284	−	2.25658i	0.205997	−	0.356797i
$41$	−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	$-0.438263\pi$
$42$	6.32272	+	7.35501i	0.975617	+	1.13490i
$43$	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
$45$	7.37314	+	2.21896i	1.09912	+	0.330782i
$46$	−1.87352	+	3.24504i	−0.276236	+	0.478455i
$47$	−2.66705			−0.389030			−0.194515	−	0.980900i	$-0.562313\pi$
$47$	−2.66705			−0.389030			−0.194515	+	0.980900i	$0.562313\pi$
$48$	−3.02211	+	3.81642i	−0.436204	+	0.550853i
$49$	−6.49563	−	2.60898i	−0.927947	−	0.372711i
$50$	1.67992	+	2.90971i	0.237577	+	0.411495i
$51$	1.36201	+	3.43559i	0.190719	+	0.481078i
$52$	−2.30364	−	3.99002i	−0.319457	−	0.553316i
$53$	−2.96849	+	5.14158i	−0.407754	+	0.706250i	−0.994638	−	0.103421i	$-0.967021\pi$
$53$	−2.96849	+	5.14158i	−0.407754	+	0.706250i	0.586884	+	0.809671i	$0.300355\pi$
$54$	9.95730	+	4.66939i	1.35502	+	0.635424i
$55$	−2.56660			−0.346080
$56$	−0.509825	+	2.63720i	−0.0681282	+	0.352411i
$57$	−3.96183	−	0.583239i	−0.524757	−	0.0772519i
$58$	−5.92985	+	10.2708i	−0.778628	+	1.34862i
$59$	−7.79334			−1.01461			−0.507303	−	0.861768i	$-0.669358\pi$
$59$	−7.79334			−1.01461			−0.507303	+	0.861768i	$0.669358\pi$
$60$	4.06249	+	10.2474i	0.524465	+	1.32294i
$61$	−3.40020			−0.435351			−0.217675	−	0.976021i	$-0.569847\pi$
$61$	−3.40020			−0.435351			−0.217675	+	0.976021i	$0.569847\pi$
$62$	−3.76637			−0.478329
$63$	−7.93081	+	0.319823i	−0.999188	+	0.0402940i
$64$	−11.2668			−1.40835
$65$	4.76881			0.591498
$66$	−3.62683	−	0.533923i	−0.446432	−	0.0657213i
$67$	3.07818			0.376060			0.188030	−	0.982163i	$-0.439790\pi$
$67$	3.07818			0.376060			0.188030	+	0.982163i	$0.439790\pi$
$68$	−2.64546	+	4.58207i	−0.320809	+	0.555657i
$69$	−1.13007	−	2.85055i	−0.136045	−	0.343166i
$70$	−10.8566	−	9.41807i	−1.29762	−	1.12568i
$71$	−13.1025			−1.55498			−0.777492	−	0.628893i	$-0.783508\pi$
$71$	−13.1025			−1.55498			−0.777492	+	0.628893i	$0.783508\pi$
$72$	0.698109	+	2.96458i	0.0822729	+	0.349380i
$73$	5.55336	−	9.61870i	0.649972	−	1.12578i	−0.333158	−	0.942871i	$-0.608114\pi$
$73$	5.55336	−	9.61870i	0.649972	−	1.12578i	0.983129	−	0.182913i	$-0.0585526\pi$
$74$	3.82915	+	6.63229i	0.445130	+	0.770988i
$75$	−2.72020	−	0.400453i	−0.314102	−	0.0462404i
$76$	−2.86652	−	4.96495i	−0.328812	−	0.569519i
$77$	2.50073	−	0.863928i	0.284984	−	0.0984537i
$78$	6.73875	+	0.992041i	0.763013	+	0.112327i
$79$	4.87281			0.548233			0.274117	−	0.961696i	$-0.411615\pi$
$79$	4.87281			0.548233			0.274117	+	0.961696i	$0.411615\pi$
$80$	3.60683	−	6.24721i	0.403256	−	0.698459i
$81$	−8.05430	+	4.01600i	−0.894922	+	0.446222i
$82$	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	$0.109114\pi$
$84$	−7.40754	−	8.61696i	−0.808229	−	0.940187i
$85$	−2.73821	−	4.74271i	−0.297000	−	0.514419i
$86$	−5.41774	+	9.38380i	−0.584210	+	1.01188i
$87$	−3.57678	−	9.02224i	−0.383471	−	0.967285i
$88$	−0.507612	−	0.879209i	−0.0541116	−	0.0937240i
$89$	−6.01619	−	10.4203i	−0.637715	−	1.10455i	−0.985933	−	0.167141i	$-0.946547\pi$
$89$	−6.01619	−	10.4203i	−0.637715	−	1.10455i	0.348218	−	0.937413i	$-0.386787\pi$
$90$	−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
$93$	1.91343	−	2.41635i	0.198413	−	0.250563i
$94$	5.64488			0.582225
$95$	5.93403			0.608818
$96$	8.57961	−	10.8346i	0.875653	−	1.10581i
$97$	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
$101$	−6.39501	−	11.0765i	−0.636328	−	1.10215i	−0.986232	−	0.165366i	$-0.947119\pi$
$101$	−6.39501	−	11.0765i	−0.636328	−	1.10215i	0.349905	−	0.936785i	$-0.386214\pi$
$102$	−2.88271	−	7.27149i	−0.285431	−	0.719985i
$103$	−7.43240	+	12.8733i	−0.732336	+	1.26844i	0.223546	+	0.974693i	$0.428237\pi$
$103$	−7.43240	+	12.8733i	−0.732336	+	1.26844i	−0.955882	+	0.293750i	$0.905097\pi$
$104$	0.943155	+	1.63359i	0.0924840	+	0.160187i
$105$	11.5578	−	2.18050i	1.12792	−	0.212795i
$106$	6.28288	−	10.8823i	0.610247	−	1.05698i
$107$	−6.72103	−	11.6412i	−0.649747	−	1.12539i	−0.983183	−	0.182622i	$-0.941542\pi$
$107$	−6.72103	−	11.6412i	−0.649747	−	1.12539i	0.333437	−	0.942772i	$-0.391792\pi$
$108$	−11.6657	−	5.47055i	−1.12254	−	0.526404i
$109$	3.63203	−	6.29086i	0.347885	−	0.602555i	−0.637988	−	0.770046i	$-0.720233\pi$
$109$	3.63203	−	6.29086i	0.347885	−	0.602555i	0.985874	+	0.167491i	$0.0535665\pi$
$110$	5.43227			0.517946
$111$	−6.20033	−	0.912779i	−0.588509	−	0.0866371i
$112$	−1.41142	+	7.30094i	−0.133367	+	0.689874i
$113$	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	$0.546460\pi$
$114$	8.38530	+	1.23444i	0.785356	+	0.115616i
$115$	2.27193	+	3.93509i	0.211858	+	0.366949i
$116$	6.94727	−	12.0330i	0.645038	−	1.11724i
$117$	−4.05994	+	3.81931i	−0.375342	+	0.353096i
$118$	16.4948			1.51847
$119$	4.26434	+	3.69929i	0.390912	+	0.339114i
$120$	−1.66326	−	4.19549i	−0.151834	−	0.382994i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	7.19659			0.651549
$123$	−16.5334	−	2.43396i	−1.49077	−	0.219463i
$124$	4.41259			0.396262
$125$	−8.75869			−0.783401
$126$	16.7857	−	0.676913i	1.49539	−	0.0603042i
$127$	−4.66388			−0.413852			−0.206926	−	0.978357i	$-0.566346\pi$
$127$	−4.66388			−0.413852			−0.206926	+	0.978357i	$0.566346\pi$
$128$	7.88821			0.697226
$129$	−3.26788	−	8.24305i	−0.287721	−	0.725760i
$130$	−10.0933			−0.885239
$131$	−4.81819	+	8.34536i	−0.420968	+	0.729137i	−0.996034	−	0.0889692i	$-0.971643\pi$
$131$	−4.81819	+	8.34536i	−0.420968	+	0.729137i	0.575067	+	0.818106i	$0.304976\pi$
$132$	4.24911	+	0.625531i	0.369838	+	0.0544455i
$133$	−5.78172	+	1.99742i	−0.501339	+	0.173198i
$134$	−6.51504			−0.562814
$135$	10.9411	−	7.62584i	0.941659	−	0.656328i
$136$	1.08310	−	1.87599i	0.0928753	−	0.160865i
$137$	9.51512	+	16.4807i	0.812932	+	1.40804i	0.910804	+	0.412840i	$0.135463\pi$
$137$	9.51512	+	16.4807i	0.812932	+	1.40804i	−0.0978718	+	0.995199i	$0.531204\pi$
$138$	2.39183	+	6.03326i	0.203606	+	0.513585i
$139$	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	$0.613425\pi$
$140$	12.7194	+	11.0340i	1.07498	+	0.932542i
$141$	−2.86777	+	3.62152i	−0.241510	+	0.304987i
$142$	27.7318			2.32720
$143$	0.929012	−	1.60910i	0.0776879	−	0.134559i
$144$	1.93267	+	8.20728i	0.161056	+	0.683940i
$145$	7.19084	+	12.4549i	0.597166	+	1.03432i
$146$	−11.7538	+	20.3582i	−0.972752	+	1.68486i
$147$	−10.5271	+	6.01492i	−0.868264	+	0.496102i
$148$	−4.48614	−	7.77023i	−0.368759	−	0.638709i
$149$	7.78075	−	13.4767i	0.637424	−	1.10405i	−0.348572	−	0.937282i	$-0.613333\pi$
$149$	7.78075	−	13.4767i	0.637424	−	1.10405i	0.985996	−	0.166769i	$-0.0533333\pi$
$150$	5.75737	+	0.847568i	0.470087	+	0.0692037i
$151$	−0.286574	−	0.496362i	−0.0233211	−	0.0403933i	0.854129	−	0.520061i	$-0.174091\pi$
$151$	−0.286574	−	0.496362i	−0.0233211	−	0.0403933i	−0.877450	+	0.479667i	$0.840757\pi$
$152$	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
$156$	−7.89495	−	1.16225i	−0.632102	−	0.0930546i
$157$	7.14688			0.570383			0.285192	−	0.958471i	$-0.407943\pi$
$157$	7.14688			0.570383			0.285192	+	0.958471i	$0.407943\pi$
$158$	−10.3134			−0.820490
$159$	3.78972	+	9.55936i	0.300544	+	0.758107i
$160$	−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	0.942604	−	0.333912i	$-0.108369\pi$
$163$	2.32523	+	4.02742i	0.182126	+	0.315452i	−0.760478	+	0.649363i	$0.775035\pi$
$164$	−11.9625	−	20.7196i	−0.934112	−	1.61793i
$165$	−2.75976	+	3.48512i	−0.214847	+	0.271316i
$166$	−3.46742	+	6.00575i	−0.269124	+	0.466137i
$167$	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	$0.546446\pi$
$168$	3.03279	+	3.52795i	0.233985	+	0.272187i
$169$	4.77387	−	8.26859i	0.367221	−	0.636045i
$170$	5.79547	+	10.0381i	0.444492	+	0.769884i
$171$	−5.05196	+	4.75253i	−0.386333	+	0.363435i
$172$	6.34729	−	10.9938i	0.483976	−	0.838272i
$173$	15.6739			1.19167			0.595833	−	0.803108i	$-0.296822\pi$
$173$	15.6739			1.19167			0.595833	+	0.803108i	$0.296822\pi$
$174$	7.57033	+	19.0958i	0.573906	+	1.44765i
$175$	−3.96974	+	1.37143i	−0.300084	+	0.103670i
$176$	−1.40529	−	2.43404i	−0.105928	−	0.183473i
$177$	−8.37985	+	10.5824i	−0.629868	+	0.795419i
$178$	12.7334	+	22.0549i	0.954408	+	1.65308i
$179$	10.6006	−	18.3608i	0.792328	−	1.37235i	−0.132194	−	0.991224i	$-0.542202\pi$
$179$	10.6006	−	18.3608i	0.792328	−	1.37235i	0.924522	−	0.381128i	$-0.124464\pi$
$180$	18.2829	+	5.50227i	1.36273	+	0.410115i
$181$	19.2753			1.43272			0.716359	−	0.697731i	$-0.245807\pi$
$181$	19.2753			1.43272			0.716359	+	0.697731i	$0.245807\pi$
$182$	9.83423	−	3.39744i	0.728961	−	0.251835i
$183$	−3.65609	+	4.61704i	−0.270266	+	0.341301i
$184$	−0.898665	+	1.55653i	−0.0662505	+	0.114749i
$185$	9.28685			0.682783
$186$	−4.04982	+	5.11425i	−0.296947	+	0.374995i
$187$	−2.13372			−0.156033
$188$	−6.61340			−0.482332
$189$	−8.09339	+	11.1129i	−0.588707	+	0.808346i
$190$	−12.5595			−0.911162
$191$	16.3156			1.18055			0.590276	−	0.807201i	$-0.299019\pi$
$191$	16.3156			1.18055			0.590276	+	0.807201i	$0.299019\pi$
$192$	−12.1147	+	15.2989i	−0.874305	+	1.10410i
$193$	−2.93093			−0.210973			−0.105486	−	0.994421i	$-0.533640\pi$
$193$	−2.93093			−0.210973			−0.105486	+	0.994421i	$0.533640\pi$
$194$	−14.8581	+	25.7350i	−1.06675	+	1.84767i
$195$	5.12770	−	6.47543i	0.367202	−	0.463715i
$196$	−16.1070	−	6.46940i	−1.15050	−	0.462100i
$197$	−21.1419			−1.50630			−0.753150	−	0.657849i	$-0.771466\pi$
$197$	−21.1419			−1.50630			−0.753150	+	0.657849i	$0.771466\pi$
$198$	−4.62478	+	4.35068i	−0.328669	+	0.309189i
$199$	3.21454	−	5.56775i	0.227873	−	0.394687i	−0.729305	−	0.684189i	$-0.760156\pi$
$199$	3.21454	−	5.56775i	0.227873	−	0.394687i	0.957177	+	0.289502i	$0.0934897\pi$
$200$	0.805802	+	1.39569i	0.0569788	+	0.0986902i
$201$	3.30984	−	4.17978i	0.233458	−	0.294819i
$202$	13.5352	+	23.4436i	0.952332	+	1.64949i
$203$	−11.1986	−	9.71476i	−0.785991	−	0.681843i
$204$	3.37732	+	8.51910i	0.236460	+	0.596457i
$205$	24.7637			1.72957
$206$	15.7308	−	27.2466i	1.09602	−	1.89836i
$207$	−5.08581	−	1.53058i	−0.353488	−	0.106383i
$208$	2.61107	+	4.52251i	0.181045	+	0.313579i
$209$	1.15601	−	2.00227i	0.0799628	−	0.138500i
$210$	−24.4622	+	4.61508i	−1.68805	+	0.318470i
$211$	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	$0.806159\pi$
$212$	−7.36087	+	12.7494i	−0.505547	+	0.875633i
$213$	−14.0886	+	17.7916i	−0.965335	+	1.21906i
$214$	14.2252	+	24.6388i	0.972415	+	1.68427i
$215$	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
$219$	−7.08968	−	17.8833i	−0.479076	−	1.20844i
$220$	−6.36431			−0.429082
$221$	3.96451			0.266682
$222$	13.1231	+	1.93192i	0.880767	+	0.129662i
$223$	−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
$227$	−11.0314	−	19.1070i	−0.732182	−	1.26818i	−0.955949	−	0.293533i	$-0.905169\pi$
$227$	−11.0314	−	19.1070i	−0.732182	−	1.26818i	0.223767	−	0.974643i	$-0.428165\pi$
$228$	−9.82402	−	1.44624i	−0.650612	−	0.0957795i
$229$	7.03824	−	12.1906i	0.465100	−	0.805576i	−0.534106	−	0.845417i	$-0.679352\pi$
$229$	7.03824	−	12.1906i	0.465100	−	0.805576i	0.999206	+	0.0398410i	$0.0126851\pi$
$230$	−4.80858	−	8.32871i	−0.317069	−	0.549179i
$231$	1.51582	−	4.32461i	0.0997337	−	0.284539i
$232$	−2.84435	+	4.92656i	−0.186741	+	0.323444i
$233$	11.9299	+	20.6633i	0.781557	+	1.35370i	0.931034	+	0.364931i	$0.118908\pi$
$233$	11.9299	+	20.6633i	0.781557	+	1.35370i	−0.149477	+	0.988765i	$0.547759\pi$
$234$	8.59296	−	8.08366i	0.561739	−	0.528446i
$235$	3.42263	−	5.92817i	0.223268	−	0.386711i
$236$	−19.3249			−1.25794
$237$	5.23952	−	6.61665i	0.340344	−	0.429798i
$238$	−9.02557	−	7.82964i	−0.585041	−	0.507520i
$239$	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	$0.771210\pi$
$240$	−4.60465	−	11.6150i	−0.297229	−	0.749744i
$241$	7.69558	+	13.3291i	0.495716	+	0.858605i	0.999988	−	0.00493960i	$-0.00157233\pi$
$241$	7.69558	+	13.3291i	0.495716	+	0.858605i	−0.504272	+	0.863545i	$0.668239\pi$
$242$	1.05826	−	1.83296i	0.0680276	−	0.117827i
$243$	−3.20724	+	15.2550i	−0.205745	+	0.978606i
$244$	−8.43135			−0.539762
$245$	14.1349	−	11.0900i	0.903048	−	0.708514i
$246$	34.9933	+	5.15153i	2.23109	+	0.328449i
$247$	−2.14789	+	3.72026i	−0.136667	+	0.236714i
$248$	−1.80660			−0.114719
$249$	−2.09149	−	5.27566i	−0.132543	−	0.334332i
$250$	18.5380			1.17244
$251$	9.85982			0.622346			0.311173	−	0.950353i	$-0.399278\pi$
$251$	9.85982			0.622346			0.311173	+	0.950353i	$0.399278\pi$
$252$	−19.6658	+	0.793055i	−1.23883	+	0.0499578i
$253$	1.77038			0.111303
$254$	9.87120			0.619374
$255$	−9.38428	−	1.38150i	−0.587666	−	0.0865130i
$256$	5.83805			0.364878
$257$	9.15595	−	15.8586i	0.571132	−	0.989230i	−0.425318	−	0.905044i	$-0.639838\pi$
$257$	9.15595	−	15.8586i	0.571132	−	0.989230i	0.996450	−	0.0841862i	$-0.0268291\pi$
$258$	6.91654	+	17.4466i	0.430605	+	1.08618i
$259$	−9.04849	+	3.12599i	−0.562246	+	0.194239i
$260$	11.8250			0.733358
$261$	−16.0970	−	4.84442i	−0.996380	−	0.299862i
$262$	10.1978	−	17.6631i	0.630023	−	1.09123i
$263$	0.193223	+	0.334672i	0.0119146	+	0.0206367i	0.871921	−	0.489646i	$-0.162874\pi$
$263$	0.193223	+	0.334672i	0.0119146	+	0.0206367i	−0.860007	+	0.510283i	$0.829541\pi$
$264$	−1.73967	−	0.256104i	−0.107069	−	0.0157621i
$265$	−7.61893	−	13.1964i	−0.468027	−	0.810647i
$266$	12.2371	−	4.22757i	0.750307	−	0.259209i
$267$	−20.6185	−	3.03534i	−1.26183	−	0.185760i
$268$	7.63287			0.466252
$269$	−12.5045	+	21.6584i	−0.762413	+	1.32054i	0.179190	+	0.983815i	$0.442652\pi$
$269$	−12.5045	+	21.6584i	−0.762413	+	1.32054i	−0.941603	+	0.336724i	$0.890681\pi$
$270$	−23.1571	+	16.1403i	−1.40929	+	0.982265i
$271$	2.91056	+	5.04124i	0.176804	+	0.306233i	0.940784	−	0.339006i	$-0.110091\pi$
$271$	2.91056	+	5.04124i	0.176804	+	0.306233i	−0.763980	+	0.645240i	$0.776758\pi$
$272$	2.99851	−	5.19357i	0.181811	−	0.314906i
$273$	−2.81643	+	8.03524i	−0.170458	+	0.486315i
$274$	−20.1390	−	34.8817i	−1.21664	−	2.10728i
$275$	0.793718	−	1.37476i	0.0478630	−	0.0829012i
$276$	−2.80221	−	7.06842i	−0.168673	−	0.425469i
$277$	6.71801	+	11.6359i	0.403646	+	0.699136i	0.994163	−	0.107890i	$-0.0344093\pi$
$277$	6.71801	+	11.6359i	0.403646	+	0.699136i	−0.590517	+	0.807026i	$0.701076\pi$
$278$	−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	$0.00604846\pi$
$282$	6.06970	−	7.66503i	0.361445	−	0.456446i
$283$	−20.3629			−1.21045			−0.605224	−	0.796055i	$-0.706916\pi$
$283$	−20.3629			−1.21045			−0.605224	+	0.796055i	$0.706916\pi$
$284$	−32.4899			−1.92792
$285$	6.38061	−	8.05765i	0.377955	−	0.477294i
$286$	−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
$290$	−15.2196	−	26.3611i	−0.893724	−	1.54797i
$291$	−8.96215	−	22.6065i	−0.525371	−	1.32522i
$292$	13.7705	−	23.8512i	0.805856	−	1.39578i
$293$	−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	$0.916425\pi$
$294$	22.2809	−	12.7307i	1.29945	−	0.742470i
$295$	10.0012	−	17.3226i	0.582292	−	1.00856i
$296$	1.83672	+	3.18128i	0.106757	+	0.184908i
$297$	−0.441684	−	5.17735i	−0.0256291	−	0.300420i
$298$	−16.4681	+	28.5236i	−0.953973	+	1.65233i
$299$	−3.28941			−0.190231
$300$	−6.74520	−	0.992991i	−0.389434	−	0.0573303i
$301$	−10.2315	−	8.87577i	−0.589734	−	0.511591i
$302$	0.606541	+	1.05056i	0.0349025	+	0.0604529i
$303$	−21.9168	−	3.22646i	−1.25908	−	0.185356i
$304$	3.24907	+	5.62755i	0.186347	+	0.322762i
$305$	4.36347	−	7.55776i	0.249852	−	0.432756i
$306$	−12.9734	−	3.90437i	−0.741642	−	0.223198i
$307$	28.2303			1.61119			0.805593	−	0.592469i	$-0.201847\pi$
$307$	28.2303			1.61119			0.805593	+	0.592469i	$0.201847\pi$
$308$	6.20096	−	2.14225i	0.353333	−	0.122066i
$309$	9.48856	+	23.9344i	0.539785	+	1.36158i
$310$	4.83338	−	8.37166i	0.274518	−	0.475478i
$311$	3.44380			0.195280			0.0976400	−	0.995222i	$-0.468871\pi$
$311$	3.44380			0.195280			0.0976400	+	0.995222i	$0.468871\pi$
$312$	3.23235	+	0.475848i	0.182996	+	0.0269396i
$313$	−7.26553			−0.410672			−0.205336	−	0.978692i	$-0.565829\pi$
$313$	−7.26553			−0.410672			−0.205336	+	0.978692i	$0.565829\pi$
$314$	−15.1265			−0.853639
$315$	9.46672	−	18.0386i	0.533389	−	1.01636i
$316$	12.0829			0.679718
$317$	25.2184			1.41641			0.708203	−	0.706009i	$-0.249506\pi$
$317$	25.2184			1.41641			0.708203	+	0.706009i	$0.249506\pi$
$318$	−8.02102	−	20.2326i	−0.449797	−	1.13459i
$319$	5.60339			0.313730
$320$	14.4587	−	25.0432i	0.808266	−	1.39996i
$321$	−23.0341	−	3.39095i	−1.28564	−	0.189264i
$322$	7.48864	+	6.49636i	0.417326	+	0.362028i
$323$	4.93320			0.274491
$324$	−19.9720	+	9.95833i	−1.10955	+	0.553240i
$325$	−1.47475	+	2.55434i	−0.0818043	+	0.141689i
$326$	−4.92140	−	8.52412i	−0.272571	−	0.472107i
$327$	−4.63682	−	11.6961i	−0.256417	−	0.646798i
$328$	4.89767	+	8.48301i	0.270429	+	0.468396i
$329$	−1.33934	+	6.92809i	−0.0738402	+	0.381958i
$330$	5.84109	−	7.37633i	0.321541	−	0.406054i
$331$	−7.42181			−0.407940			−0.203970	−	0.978977i	$-0.565384\pi$
$331$	−7.42181			−0.407940			−0.203970	+	0.978977i	$0.565384\pi$
$332$	4.06235	−	7.03620i	0.222950	−	0.386161i
$333$	−7.90639	+	7.43779i	−0.433268	+	0.407589i
$334$	−21.4470	−	37.1472i	−1.17353	−	2.03261i
$335$	−3.95023	+	6.84201i	−0.215824	+	0.373819i
$336$	8.39611	+	9.76693i	0.458046	+	0.532830i
$337$	−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	$0.908033\pi$
$338$	−10.1040	+	17.5007i	−0.549586	+	0.951910i
$339$	28.5656	+	4.20527i	1.55147	+	0.228399i
$340$	−6.78983	−	11.7603i	−0.368231	−	0.637794i
$341$	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
$345$	7.78627	+	1.14625i	0.419198	+	0.0617121i
$346$	−33.1742			−1.78346
$347$	34.4715			1.85053			0.925265	−	0.379322i	$-0.123843\pi$
$347$	34.4715			1.85053			0.925265	+	0.379322i	$0.123843\pi$
$348$	−8.86922	−	22.3721i	−0.475440	−	1.19927i
$349$	−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
$353$	−4.54056	−	7.86447i	−0.241669	−	0.418584i	0.719521	−	0.694471i	$-0.244362\pi$
$353$	−4.54056	−	7.86447i	−0.241669	−	0.418584i	−0.961190	+	0.275887i	$0.911028\pi$
$354$	17.7361	−	22.3978i	0.942665	−	1.19043i
$355$	16.8145	−	29.1235i	0.892420	−	1.54572i
$356$	−14.9181	−	25.8390i	−0.790660	−	1.36946i
$357$	9.60844	−	1.81274i	0.508533	−	0.0959404i
$358$	−22.4365	+	38.8611i	−1.18580	+	2.05387i
$359$	−3.73295	−	6.46566i	−0.197018	−	0.341244i	0.750542	−	0.660822i	$-0.229792\pi$
$359$	−3.73295	−	6.46566i	−0.197018	−	0.341244i	−0.947560	+	0.319578i	$0.896459\pi$
$360$	−7.48538	−	2.25274i	−0.394514	−	0.118730i
$361$	6.82729	−	11.8252i	0.359331	−	0.622379i
$362$	−40.7965			−2.14422
$363$	0.638324	+	1.61014i	0.0335033	+	0.0845103i
$364$	−11.5215	+	3.98036i	−0.603893	+	0.208627i
$365$	14.2533	+	24.6874i	0.746049	+	1.29220i
$366$	7.73819	−	9.77206i	0.404482	−	0.510794i
$367$	12.1525	+	21.0488i	0.634358	+	1.09874i	0.986651	+	0.162850i	$0.0520688\pi$
$367$	12.1525	+	21.0488i	0.634358	+	1.09874i	−0.352293	+	0.935890i	$0.614598\pi$
$368$	−2.48790	+	4.30917i	−0.129691	+	0.224631i
$369$	−21.0827	+	19.8332i	−1.09752	+	1.03247i
$370$	−19.6558			−1.02186
$371$	11.8653	+	10.2931i	0.616018	+	0.534392i
$372$	4.74467	−	5.99173i	0.246000	−	0.310657i
$373$	−12.7645	+	22.1087i	−0.660920	+	1.14475i	0.319454	+	0.947602i	$0.396501\pi$
$373$	−12.7645	+	22.1087i	−0.660920	+	1.14475i	−0.980374	+	0.197146i	$0.936833\pi$
$374$	4.51607			0.233520
$375$	−9.41785	+	11.8932i	−0.486336	+	0.614161i
$376$	2.70766			0.139637
$377$	−10.4112			−0.536206
$378$	17.1298	−	23.5208i	0.881063	−	1.20978i
$379$	−24.3496			−1.25075			−0.625376	−	0.780323i	$-0.715055\pi$
$379$	−24.3496			−1.25075			−0.625376	+	0.780323i	$0.715055\pi$
$380$	14.7144			0.754833
$381$	−5.01487	+	6.33295i	−0.256920	+	0.324447i
$382$	−34.5322			−1.76682
$383$	−5.22033	+	9.04187i	−0.266746	+	0.462018i	−0.968020	−	0.250874i	$-0.919282\pi$
$383$	−5.22033	+	9.04187i	−0.266746	+	0.462018i	0.701273	+	0.712892i	$0.252615\pi$
$384$	8.48186	−	10.7112i	0.432838	−	0.546603i
$385$	−1.28889	+	6.66714i	−0.0656881	+	0.339789i
$386$	6.20337			0.315743
$387$	−14.7068	−	4.42604i	−0.747591	−	0.224988i
$388$	17.4074	−	30.1505i	0.883728	−	1.53066i
$389$	3.83021	+	6.63411i	0.194199	+	0.336363i	0.946638	−	0.322300i	$-0.104456\pi$
$389$	3.83021	+	6.63411i	0.194199	+	0.336363i	−0.752439	+	0.658662i	$0.771123\pi$
$390$	−10.8529	+	13.7054i	−0.549557	+	0.694000i
$391$	1.88875	+	3.27141i	0.0955181	+	0.165442i
$392$	6.59452	+	2.64870i	0.333073	+	0.133779i
$393$	6.15114	+	15.5159i	0.310284	+	0.782674i
$394$	44.7473			2.25434
$395$	−6.25327	+	10.8310i	−0.314636	+	0.544966i
$396$	5.41828	−	5.09715i	0.272279	−	0.256141i
$397$	0.725935	+	1.25736i	0.0364337	+	0.0631049i	0.883667	−	0.468116i	$-0.155067\pi$
$397$	0.725935	+	1.25736i	0.0364337	+	0.0631049i	−0.847234	+	0.531221i	$0.821734\pi$
$398$	−6.80364	+	11.7843i	−0.341036	+	0.590691i
$399$	−3.50461	+	9.99858i	−0.175450	+	0.500555i
$400$	2.23082	+	3.86389i	0.111541	+	0.193194i
$401$	2.14057	−	3.70758i	0.106895	−	0.185148i	−0.807616	−	0.589709i	$-0.799242\pi$
$401$	2.14057	−	3.70758i	0.106895	−	0.185148i	0.914511	+	0.404561i	$0.132576\pi$
$402$	−7.00535	+	8.84661i	−0.349395	+	0.441229i
$403$	−1.65318	−	2.86340i	−0.0823510	−	0.142636i
$404$	−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
$408$	−1.38274	−	3.48789i	−0.0684558	−	0.172676i
$409$	−5.15610			−0.254953			−0.127476	−	0.991842i	$-0.540688\pi$
$409$	−5.15610			−0.254953			−0.127476	+	0.991842i	$0.540688\pi$
$410$	−52.4130			−2.58849
$411$	32.6099	+	4.80065i	1.60853	+	0.236798i
$412$	−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
$416$	−7.41270	−	12.8392i	−0.363438	−	0.629492i
$417$	25.7466	+	3.79027i	1.26082	+	0.185610i
$418$	−2.44672	+	4.23784i	−0.119673	+	0.207280i
$419$	−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	$-0.412455\pi$
$420$	28.6594	−	5.40691i	1.39843	−	0.263830i
$421$	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
$423$	1.83397	+	7.78814i	0.0891708	+	0.378672i
$424$	3.01368	−	5.21985i	0.146357	−	0.253499i
$425$	3.38715			0.164301
$426$	29.8188	−	37.6563i	1.44473	−	1.82445i
$427$	−1.70751	+	8.83254i	−0.0826322	+	0.427437i
$428$	−16.6659	−	28.8662i	−0.805577	−	1.39530i
$429$	−1.18602	−	2.99167i	−0.0572616	−	0.144439i
$430$	−13.9052	−	24.0845i	−0.670567	−	1.16146i
$431$	8.25079	−	14.2908i	0.397427	−	0.688363i	−0.595981	−	0.802999i	$-0.703237\pi$
$431$	8.25079	−	14.2908i	0.397427	−	0.688363i	0.993408	+	0.114635i	$0.0365700\pi$
$432$	13.2226	+	6.20062i	0.636171	+	0.298327i
$433$	−31.9072			−1.53336			−0.766682	−	0.642027i	$-0.778094\pi$
$433$	−31.9072			−1.53336			−0.766682	+	0.642027i	$0.778094\pi$
$434$	−1.89139	+	9.78373i	−0.0907898	+	0.469634i
$435$	24.6442	+	3.62798i	1.18160	+	0.173948i
$436$	9.00622	−	15.5992i	0.431320	−	0.747068i
$437$	−4.09315			−0.195802
$438$	15.0055	+	37.8505i	0.716989	+	1.80857i
$439$	−35.7471			−1.70612			−0.853058	−	0.521816i	$-0.825255\pi$
$439$	−35.7471			−1.70612			−0.853058	+	0.521816i	$0.825255\pi$
$440$	2.60567			0.124221
$441$	−3.15190	+	20.7621i	−0.150090	+	0.988672i
$442$	−8.39097			−0.399118
$443$	39.7800			1.89000			0.945002	−	0.327066i	$-0.106060\pi$
$443$	39.7800			1.89000			0.945002	+	0.327066i	$0.106060\pi$
$444$	−15.3748	−	2.26339i	−0.729653	−	0.107416i
$445$	30.8823			1.46396
$446$	25.1139	−	43.4985i	1.18918	−	2.05971i
$447$	−9.93328	−	25.0562i	−0.469828	−	1.18512i
$448$	−5.65796	+	29.2673i	−0.267314	+	1.38275i
$449$	−29.0017			−1.36868			−0.684338	−	0.729165i	$-0.739909\pi$
$449$	−29.0017			−1.36868			−0.684338	+	0.729165i	$0.739909\pi$
$450$	7.34155	−	6.90642i	0.346084	−	0.325572i
$451$	4.82423	−	8.35581i	0.227164	−	0.393460i
$452$	20.6682	+	35.7983i	0.972148	+	1.68381i
$453$	−0.982138	−	0.144585i	−0.0461448	−	0.00679319i
$454$	23.3483	+	40.4404i	1.09579	+	1.89796i
$455$	2.39480	−	12.3877i	0.112270	−	0.580745i
$456$	4.02214	+	0.592118i	0.188354	+	0.0277285i
$457$	−37.9123			−1.77346			−0.886732	−	0.462285i	$-0.847030\pi$
$457$	−37.9123			−1.77346			−0.886732	+	0.462285i	$0.847030\pi$
$458$	−14.8966	+	25.8016i	−0.696072	+	1.20563i
$459$	9.09578	−	6.33968i	0.424555	−	0.295911i
$460$	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	$0.111493\pi$
$462$	−3.20827	+	9.15314i	−0.149262	+	0.425843i
$463$	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	$0.406228\pi$
$464$	−7.87442	+	13.6389i	−0.365561	+	0.633170i
$465$	2.91541	+	7.35396i	0.135199	+	0.341032i
$466$	−25.2500	−	43.7343i	−1.16968	−	2.02595i
$467$	−20.9977	−	36.3691i	−0.971657	−	1.68296i	−0.690553	−	0.723282i	$-0.742633\pi$
$467$	−20.9977	−	36.3691i	−0.971657	−	1.68296i	−0.281104	−	0.959677i	$-0.590701\pi$
$468$	−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
$471$	7.68474	−	9.70456i	0.354094	−	0.447162i
$472$	7.91198			0.364178
$473$	5.11947			0.235394
$474$	−11.0896	+	14.0043i	−0.509361	+	0.643238i
$475$	−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
$479$	−8.63044	−	14.9484i	−0.394335	−	0.683008i	0.598681	−	0.800988i	$-0.295692\pi$
$479$	−8.63044	−	14.9484i	−0.394335	−	0.683008i	−0.993016	+	0.117979i	$0.962358\pi$
$480$	13.0724	+	32.9743i	0.596669	+	1.50507i
$481$	−3.36149	+	5.82227i	−0.153271	+	0.265473i
$482$	−16.2879	−	28.2114i	−0.741892	−	1.28500i
$483$	−7.97226	+	1.50406i	−0.362750	+	0.0684369i
$484$	−1.23983	+	2.14745i	−0.0563560	+	0.0976115i
$485$	18.0177	+	31.2076i	0.818142	+	1.41706i
$486$	6.78819	−	32.2874i	0.307919	−	1.46459i
$487$	8.83490	−	15.3025i	0.400347	−	0.693422i	−0.593420	−	0.804893i	$-0.702223\pi$
$487$	8.83490	−	15.3025i	0.400347	−	0.693422i	0.993768	+	0.111471i	$0.0355561\pi$
$488$	3.45196			0.156263
$489$	7.96895	+	1.17314i	0.360368	+	0.0530514i
$490$	−29.9169	+	23.4722i	−1.35151	+	1.06037i
$491$	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	$0.802286\pi$
$492$	−40.9974	−	6.03541i	−1.84830	−	0.272097i
$493$	5.97804	+	10.3543i	0.269237	+	0.466333i
$494$	4.54606	−	7.87401i	0.204537	−	0.354268i
$495$	1.76490	+	7.49480i	0.0793262	+	0.336866i
$496$	−5.00146			−0.224572
$497$	−6.57982	+	34.0359i	−0.295145	+	1.52672i
$498$	4.42668	+	11.1661i	0.198364	+	0.500363i
$499$	7.72746	−	13.3843i	0.345929	−	0.599166i	−0.639593	−	0.768713i	$-0.720897\pi$
$499$	7.72746	−	13.3843i	0.345929	−	0.599166i	0.985522	+	0.169548i	$0.0542306\pi$
$500$	−21.7186			−0.971286
$501$	34.7278	+	5.11244i	1.55153	+	0.228407i
$502$	−20.8685			−0.931408
$503$	10.2318			0.456215			0.228107	−	0.973636i	$-0.426746\pi$
$503$	10.2318			0.456215			0.228107	+	0.973636i	$0.426746\pi$
$504$	8.05154	−	0.324692i	0.358644	−	0.0144629i
$505$	32.8269			1.46078
$506$	−3.74705			−0.166576
$507$	−6.09455	−	15.3732i	−0.270669	−	0.682747i
$508$	−11.5649			−0.513107
$509$	−6.67242	+	11.5570i	−0.295750	+	0.512254i	−0.975159	−	0.221506i	$-0.928903\pi$
$509$	−6.67242	+	11.5570i	−0.295750	+	0.512254i	0.679409	+	0.733760i	$0.262236\pi$
$510$	19.8620	+	2.92398i	0.879506	+	0.129476i
$511$	−22.1973	−	19.2560i	−0.981950	−	0.851837i
$512$	−28.1328			−1.24330
$513$	1.02118	+	11.9701i	0.0450863	+	0.528494i
$514$	−19.3788	+	33.5650i	−0.854761	+	1.48049i
$515$	−19.0760	−	33.0406i	−0.840589	−	1.45594i
$516$	−8.10325	−	20.4400i	−0.356726	−	0.899822i
$517$	−1.33353	−	2.30974i	−0.0586484	−	0.101582i
$518$	19.1513	−	6.61622i	0.841461	−	0.290700i
$519$	16.8535	−	21.2832i	0.739787	−	0.934229i
$520$	−4.84140			−0.212310
$521$	−5.22825	+	9.05559i	−0.229054	+	0.396733i	−0.957528	−	0.288341i	$-0.906896\pi$
$521$	−5.22825	+	9.05559i	−0.229054	+	0.396733i	0.728474	+	0.685073i	$0.240230\pi$
$522$	34.0697	+	10.2533i	1.49119	+	0.448775i
$523$	−8.33846	−	14.4426i	−0.364615	−	0.631533i	0.624099	−	0.781345i	$-0.285466\pi$
$523$	−8.33846	−	14.4426i	−0.364615	−	0.631533i	−0.988714	+	0.149813i	$0.952133\pi$
$524$	−11.9475	+	20.6937i	−0.521930	+	0.904008i
$525$	−2.40627	+	6.86505i	−0.105018	+	0.299615i
$526$	−0.408960	−	0.708340i	−0.0178315	−	0.0308851i
$527$	−1.89849	+	3.28828i	−0.0826994	+	0.143240i
$528$	−4.81617	−	0.709011i	−0.209597	−	0.0308557i
$529$	9.93288	+	17.2043i	0.431864	+	0.748011i
$530$	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
$534$	43.6394	+	6.42436i	1.88846	+	0.278009i
$535$	34.5004			1.49158
$536$	−3.12505			−0.134981
$537$	−13.5333	−	34.1369i	−0.584003	−	1.47312i
$538$	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	0.847182	−	0.531302i	$-0.178297\pi$
$541$	−0.849669	−	1.47167i	−0.0365301	−	0.0632720i	−0.883712	+	0.468030i	$0.844964\pi$
$542$	−6.16026	−	10.6699i	−0.264606	−	0.458311i
$543$	20.7259	−	26.1734i	0.889433	−	1.12321i
$544$	−8.51261	+	14.7443i	−0.364975	+	0.632156i
$545$	9.32197	+	16.1461i	0.399309	+	0.691624i
$546$	5.96104	−	17.0068i	0.255109	−	0.727822i
$547$	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
$549$	2.33811	+	9.92901i	0.0997882	+	0.423760i
$550$	−1.67992	+	2.90971i	−0.0716321	+	0.124071i
$551$	−12.9551			−0.551908
$552$	1.14728	+	2.89395i	0.0488314	+	0.123175i
$553$	2.44702	−	12.6579i	0.104058	−	0.538267i
$554$	−14.2188	−	24.6277i	−0.604100	−	1.04633i
$555$	9.98576	−	12.6104i	0.423872	−	0.535280i
$556$	18.6285	+	32.2655i	0.790024	+	1.36836i
$557$	−4.30101	+	7.44957i	−0.182240	+	0.315648i	−0.942643	−	0.333803i	$-0.891668\pi$
$557$	−4.30101	+	7.44957i	−0.182240	+	0.315648i	0.760403	+	0.649451i	$0.225001\pi$
$558$	2.58991	+	10.9983i	0.109639	+	0.465594i
$559$	−9.51210			−0.402319
$560$	−14.4168	−	12.5065i	−0.609222	−	0.528497i
$561$	−2.29430	+	2.89732i	−0.0968655	+	0.122325i
$562$	−17.1527	+	29.7093i	−0.723542	+	1.25321i
$563$	−15.8154			−0.666541			−0.333270	−	0.942831i	$-0.608152\pi$
$563$	−15.8154			−0.666541			−0.333270	+	0.942831i	$0.608152\pi$
$564$	−7.11111	+	8.98016i	−0.299432	+	0.378133i
$565$	−42.7855			−1.80000
$566$	43.0985			1.81156
$567$	6.38747	+	22.9391i	0.268248	+	0.963350i
$568$	13.3020			0.558139
$569$	6.34028			0.265798			0.132899	−	0.991130i	$-0.457571\pi$
$569$	6.34028			0.265798			0.132899	+	0.991130i	$0.457571\pi$
$570$	−13.5047	+	17.0542i	−0.565650	+	0.714322i
$571$	−0.161978			−0.00677857			−0.00338929	−	0.999994i	$-0.501079\pi$
$571$	−0.161978			−0.00677857			−0.00338929	+	0.999994i	$0.501079\pi$
$572$	2.30364	−	3.99002i	0.0963200	−	0.166831i
$573$	17.5434	−	22.1545i	0.732887	−	0.925516i
$574$	51.0677	−	17.6424i	2.13153	−	0.736380i
$575$	−2.81036			−0.117200
$576$	7.74751	+	32.9005i	0.322813	+	1.37086i
$577$	20.5912	−	35.6650i	0.857224	−	1.48476i	−0.0173425	−	0.999850i	$-0.505521\pi$
$577$	20.5912	−	35.6650i	0.857224	−	1.48476i	0.874566	−	0.484906i	$-0.161146\pi$
$578$	−13.1724	−	22.8153i	−0.547900	−	0.948991i
$579$	−3.15150	+	3.97983i	−0.130972	+	0.165396i
$580$	17.8309	+	30.8840i	0.740387	+	1.28239i
$581$	−6.54830	−	5.68061i	−0.271669	−	0.235672i
$582$	18.9686	+	47.8473i	0.786273	+	1.98333i
$583$	−5.93699			−0.245885
$584$	−5.63790	+	9.76513i	−0.233298	+	0.404084i
$585$	−3.27922	−	13.9255i	−0.135579	−	0.575750i
$586$	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	$0.0112840\pi$
$588$	−26.1038	+	14.9150i	−1.07650	+	0.615084i
$589$	−2.05713	−	3.56305i	−0.0847624	−	0.146813i
$590$	−21.1677	+	36.6636i	−0.871462	+	1.50942i
$591$	−22.7330	+	28.7081i	−0.935112	+	1.18089i
$592$	5.08484	+	8.80720i	0.208986	+	0.361974i
$593$	21.1695	+	36.6666i	0.869327	+	1.50572i	0.862685	+	0.505741i	$0.168781\pi$
$593$	21.1695	+	36.6666i	0.869327	+	1.50572i	0.00664168	+	0.999978i	$0.497886\pi$
$594$	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
$597$	−4.10383	−	10.3517i	−0.167959	−	0.423667i
$598$	6.96210			0.284701
$599$	25.9109			1.05869			0.529346	−	0.848406i	$-0.322437\pi$
$599$	25.9109			1.05869			0.529346	+	0.848406i	$0.322437\pi$
$600$	2.76161	+	0.406550i	0.112742	+	0.0165973i
$601$	−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
$605$	−1.28330	−	2.22274i	−0.0521736	−	0.0903673i
$606$	46.3873	+	6.82888i	1.88436	+	0.277404i
$607$	−2.90637	+	5.03398i	−0.117966	+	0.204323i	−0.918961	−	0.394347i	$-0.870971\pi$
$607$	−2.90637	+	5.03398i	−0.117966	+	0.204323i	0.800996	+	0.598670i	$0.204304\pi$
$608$	−9.22393	−	15.9763i	−0.374080	−	0.647925i
$609$	−25.2328	+	4.76046i	−1.02249	+	0.192904i
$610$	−9.23539	+	15.9962i	−0.373930	+	0.647666i
$611$	2.47773	+	4.29155i	0.100238	+	0.173617i
$612$	15.1994	+	4.57426i	0.614397	+	0.184904i
$613$	−14.8034	+	25.6402i	−0.597904	+	1.03560i	0.395226	+	0.918584i	$0.370666\pi$
$613$	−14.8034	+	25.6402i	−0.597904	+	1.03560i	−0.993130	+	0.117016i	$0.962667\pi$
$614$	−59.7500			−2.41131
$615$	26.6274	−	33.6260i	1.07372	−	1.35593i
$616$	−2.53880	+	0.877080i	−0.102291	+	0.0353385i
$617$	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	$0.647630\pi$
$618$	−20.0827	−	50.6576i	−0.807846	−	2.03775i
$619$	−11.0385	−	19.1192i	−0.443674	−	0.768466i	0.554285	−	0.832327i	$-0.312992\pi$
$619$	−11.0385	−	19.1192i	−0.443674	−	0.768466i	−0.997959	+	0.0638609i	$0.979659\pi$
$620$	−5.66267	+	9.80803i	−0.227418	+	0.393900i
$621$	−7.54690	+	5.26012i	−0.302846	+	0.211081i
$622$	−7.28888			−0.292257
$623$	−30.0897	+	10.3951i	−1.20552	+	0.416471i
$624$	8.94857	+	1.31736i	0.358229	+	0.0527366i
$625$	15.2086	−	26.3421i	0.608345	−	1.05368i
$626$	15.3777			0.614615
$627$	−1.47582	−	3.72267i	−0.0589384	−	0.148669i
$628$	17.7219			0.707180
$629$	7.72054			0.307838
$630$	−20.0365	+	38.1790i	−0.798274	+	1.52109i
$631$	40.1182			1.59708			0.798540	−	0.601941i	$-0.205606\pi$
$631$	40.1182			1.59708			0.798540	+	0.601941i	$0.205606\pi$
$632$	−4.94699			−0.196781
$633$	4.24487	+	0.624907i	0.168719	+	0.0248378i
$634$	−53.3753			−2.11980
$635$	5.98515	−	10.3666i	0.237514	−	0.411386i
$636$	9.39724	+	23.7040i	0.372625	+	0.939926i
$637$	1.83642	+	12.8759i	0.0727616	+	0.510161i
$638$	−11.8597			−0.469530
$639$	9.00983	+	38.2611i	0.356423	+	1.51358i
$640$	−10.1229	+	17.5334i	−0.400144	+	0.693070i
$641$	−11.1487	−	19.3101i	−0.440346	−	0.762702i	0.557369	−	0.830265i	$-0.311811\pi$
$641$	−11.1487	−	19.3101i	−0.440346	−	0.762702i	−0.997715	+	0.0675631i	$0.978478\pi$
$642$	48.7521	+	7.17702i	1.92409	+	0.283254i
$643$	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	$0.811755\pi$
$644$	−8.77351	−	7.61098i	−0.345725	−	0.299914i
$645$	22.5158	+	3.31466i	0.886561	+	0.130515i
$646$	−10.4412			−0.410805
$647$	−23.2216	+	40.2211i	−0.912937	+	1.58125i	−0.103043	+	0.994677i	$0.532858\pi$
$647$	−23.2216	+	40.2211i	−0.912937	+	1.58125i	−0.809894	+	0.586577i	$0.800475\pi$
$648$	8.17692	−	4.07713i	0.321220	−	0.160165i
$649$	−3.89667	−	6.74923i	−0.152958	−	0.264930i
$650$	3.12134	−	5.40631i	0.122429	−	0.212053i
$651$	−5.31595	−	6.18387i	−0.208349	−	0.242365i
$652$	5.76580	+	9.98665i	0.225806	+	0.391108i
$653$	−0.464656	+	0.804807i	−0.0181834	+	0.0314945i	−0.874974	−	0.484170i	$-0.839122\pi$
$653$	−0.464656	+	0.804807i	−0.0181834	+	0.0314945i	0.856791	+	0.515665i	$0.172455\pi$
$654$	9.81394	+	24.7551i	0.383755	+	0.968002i
$655$	−12.3664	−	21.4192i	−0.483194	−	0.836917i
$656$	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	$0.220057\pi$
$660$	−6.84328	+	8.64193i	−0.266374	+	0.336387i
$661$	39.1057			1.52104			0.760518	−	0.649316i	$-0.224945\pi$
$661$	39.1057			1.52104			0.760518	+	0.649316i	$0.224945\pi$
$662$	15.7084			0.610526
$663$	4.26287	−	5.38330i	0.165556	−	0.209070i
$664$	−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
$668$	25.1267	+	43.5208i	0.972183	+	1.68387i
$669$	15.1482	+	38.2106i	0.585664	+	1.47731i
$670$	8.36076	−	14.4813i	0.323004	−	0.559460i
$671$	−1.70010	−	2.94466i	−0.0656316	−	0.113677i
$672$	−23.8361	−	27.7278i	−0.919499	−	1.06962i
$673$	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
$675$	0.701146	+	8.21871i	0.0269871	+	0.316338i
$676$	11.8376	−	20.5033i	0.455293	−	0.788590i
$677$	5.92813			0.227836			0.113918	−	0.993490i	$-0.463660\pi$
$677$	5.92813			0.227836			0.113918	+	0.993490i	$0.463660\pi$
$678$	−60.4597	−	8.90055i	−2.32194	−	0.341824i
$679$	−28.0599	−	24.3418i	−1.07684	−	0.934152i
$680$	2.77989	+	4.81491i	0.106604	+	0.184643i
$681$	−37.8065	−	5.56567i	−1.44875	−	0.213277i
$682$	−1.88318	−	3.26177i	−0.0721108	−	0.124900i
$683$	2.69080	−	4.66059i	0.102960	−	0.178333i	−0.809943	−	0.586509i	$-0.800502\pi$
$683$	2.69080	−	4.66059i	0.102960	−	0.178333i	0.912903	+	0.408176i	$0.133835\pi$
$684$	−12.5272	+	11.7847i	−0.478988	+	0.450599i
$685$	−48.8430			−1.86620
$686$	21.2482	−	32.9399i	0.811260	−	1.25765i
$687$	−8.98535	−	22.6651i	−0.342812	−	0.864726i
$688$	−7.19437	+	12.4610i	−0.274283	+	0.475071i
$689$	11.0311			0.420250
$690$	−16.4798	−	2.42607i	−0.627375	−	0.0923588i
$691$	2.65519			0.101008			0.0505040	−	0.998724i	$-0.483917\pi$
$691$	2.65519			0.101008			0.0505040	+	0.998724i	$0.483917\pi$
$692$	38.8661			1.47747
$693$	−4.24238	−	6.70837i	−0.161155	−	0.254830i
$694$	−72.9598			−2.76952
$695$	−38.5632			−1.46278
$696$	3.63123	+	9.15959i	0.137641	+	0.347193i
$697$	20.5871			0.779793
$698$	25.5052	−	44.1763i	0.965387	−	1.67210i
$699$	40.8859	+	6.01900i	1.54645	+	0.227659i
$700$	−9.84364	+	3.40069i	−0.372055	+	0.128534i
$701$	4.47309			0.168946			0.0844731	−	0.996426i	$-0.473079\pi$
$701$	4.47309			0.168946			0.0844731	+	0.996426i	$0.473079\pi$
$702$	−1.73694	−	20.3602i	−0.0655568	−	0.768445i
$703$	−4.18284	+	7.24489i	−0.157759	+	0.273246i
$704$	−5.63340	−	9.75734i	−0.212317	−	0.367744i
$705$	−4.36949	−	11.0218i	−0.164565	−	0.415105i
$706$	9.61019	+	16.6453i	0.361684	+	0.626455i
$707$	−31.9843	+	11.0497i	−1.20290	+	0.415565i
$708$	−20.7792	+	26.2407i	−0.780931	+	0.986187i
$709$	21.1872			0.795701			0.397851	−	0.917450i	$-0.369756\pi$
$709$	21.1872			0.795701			0.397851	+	0.917450i	$0.369756\pi$
$710$	−35.5882	+	61.6406i	−1.33560	+	2.31333i
$711$	−3.35074	−	14.2292i	−0.125662	−	0.533637i
$712$	6.10778	+	10.5790i	0.228899	+	0.396464i
$713$	1.57520	−	2.72833i	0.0589917	−	0.102177i
$714$	−20.3365	+	3.83670i	−0.761073	+	0.143585i
$715$	2.38440	+	4.12991i	0.0891716	+	0.154450i
$716$	26.2860	−	45.5287i	0.982354	−	1.70149i
$717$	10.2749	+	1.51262i	0.383723	+	0.0564897i
$718$	7.90087	+	13.6847i	0.294858	+	0.510709i
$719$	7.49753	+	12.9861i	0.279611	+	0.484300i	0.971288	−	0.237907i	$-0.0764612\pi$
$719$	7.49753	+	12.9861i	0.279611	+	0.484300i	−0.691677	+	0.722207i	$0.743128\pi$
$720$	−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
$723$	26.3740	+	3.88264i	0.980860	+	0.144397i
$724$	47.7962			1.77633
$725$	−8.89504			−0.330353
$726$	−1.35103	−	3.40789i	−0.0501413	−	0.126479i
$727$	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
$731$	5.46177	+	9.46005i	0.202011	+	0.349893i
$732$	−9.06588	+	11.4487i	−0.335085	+	0.423157i
$733$	12.6763	−	21.9561i	0.468211	−	0.810965i	−0.531129	−	0.847291i	$-0.678232\pi$
$733$	12.6763	−	21.9561i	0.468211	−	0.810965i	0.999340	+	0.0363257i	$0.0115654\pi$
$734$	−25.7211	−	44.5503i	−0.949385	−	1.64438i
$735$	0.139881	−	31.1181i	0.00515957	−	1.14781i
$736$	7.06303	−	12.2335i	0.260347	−	0.450934i
$737$	1.53909	+	2.66579i	0.0566932	+	0.0981955i
$738$	44.6220	−	41.9773i	1.64256	−	1.54521i
$739$	10.2114	−	17.6866i	0.375631	−	0.650612i	−0.614790	−	0.788691i	$-0.710759\pi$
$739$	10.2114	−	17.6866i	0.375631	−	0.650612i	0.990421	+	0.138078i	$0.0440926\pi$
$740$	23.0283			0.846536
$741$	2.74210	+	6.91680i	0.100734	+	0.254095i
$742$	−25.1133	−	21.7856i	−0.921937	−	0.799775i
$743$	−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	$0.919591\pi$
$744$	−1.94256	+	2.45313i	−0.0712177	+	0.0899362i
$745$	19.9701	+	34.5892i	0.731647	+	1.26725i
$746$	27.0163	−	46.7937i	0.989138	−	1.71324i
$747$	−9.41257	−	2.83273i	−0.344388	−	0.103644i
$748$	−5.29092			−0.193455
$749$	−33.6149	+	11.6130i	−1.22826	+	0.424329i
$750$	19.9331	−	25.1722i	0.727853	−	0.919158i
$751$	−7.40147	+	12.8197i	−0.270083	+	0.467798i	−0.968883	−	0.247519i	$-0.920385\pi$
$751$	−7.40147	+	12.8197i	−0.270083	+	0.467798i	0.698800	+	0.715318i	$0.253718\pi$
$752$	7.49599			0.273351
$753$	10.6019	−	13.3884i	0.386353	−	0.487900i
$754$	22.0356			0.802490
$755$	1.47104			0.0535368
$756$	−20.0689	+	27.5563i	−0.729899	+	1.00221i
$757$	30.1009			1.09403			0.547017	−	0.837121i	$-0.315763\pi$
$757$	30.1009			1.09403			0.547017	+	0.837121i	$0.315763\pi$
$758$	51.5364			1.87189
$759$	1.90361	−	2.40395i	0.0690968	−	0.0872578i
$760$	−6.02436			−0.218527
$761$	−5.57723	+	9.66005i	−0.202175	+	0.350177i	−0.949229	−	0.314586i	$-0.898134\pi$
$761$	−5.57723	+	9.66005i	−0.202175	+	0.350177i	0.747054	+	0.664763i	$0.231468\pi$
$762$	10.6141	−	13.4038i	0.384508	−	0.485570i
$763$	−14.5176	−	12.5939i	−0.525571	−	0.455930i
$764$	40.4571			1.46369
$765$	−11.9664	+	11.2572i	−0.432647	+	0.407005i
$766$	11.0489	−	19.1373i	0.399214	−	0.691459i
$767$	7.24011	+	12.5402i	0.261425	+	0.452802i
$768$	6.27741	−	7.92733i	0.226517	−	0.286053i
$769$	−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	$-0.419489\pi$
$770$	2.72797	−	14.1112i	0.0983093	−	0.508531i
$771$	−11.6889	−	29.4847i	−0.420966	−	1.06186i
$772$	−7.26772			−0.261571
$773$	−14.6510	+	25.3764i	−0.526961	+	0.912724i	0.472545	+	0.881307i	$0.343335\pi$
$773$	−14.6510	+	25.3764i	−0.526961	+	0.912724i	−0.999506	+	0.0314174i	$0.989998\pi$
$774$	31.1274	+	9.36782i	1.11885	+	0.336719i
$775$	−1.41243	−	2.44640i	−0.0507359	−	0.0878772i
$776$	−7.12694	+	12.3442i	−0.255842	+	0.443132i
$777$	−5.48477	+	15.6479i	−0.196765	+	0.561367i
$778$	−8.10671	−	14.0412i	−0.290640	−	0.503403i
$779$	−11.1537	+	19.3188i	−0.399623	+	0.692167i
$780$	12.7150	−	16.0569i	0.455269	−	0.574930i
$781$	−6.55126	−	11.3471i	−0.234423	−	0.406032i
$782$	−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
$786$	−13.0190	−	32.8398i	−0.464373	−	1.17136i
$787$	−28.1681			−1.00409			−0.502043	−	0.864843i	$-0.667418\pi$
$787$	−28.1681			−1.00409			−0.502043	+	0.864843i	$0.667418\pi$
$788$	−52.4249			−1.86756
$789$	0.662206	+	0.0974863i	0.0235752	+	0.00347061i
$790$	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
$794$	−1.53646	−	2.66122i	−0.0545269	−	0.0944433i
$795$	−26.1113	−	3.84397i	−0.926074	−	0.136331i
$796$	7.97098	−	13.8061i	0.282524	−	0.489346i
$797$	−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	$0.903634\pi$
$798$	7.41758	−	21.1622i	0.262579	−	0.749135i
$799$	2.84538	−	4.92833i	0.100662	−	0.174352i
$800$	−6.33318	−	10.9694i	−0.223912	−	0.387826i
$801$	−26.2918	+	24.7335i	−0.928974	+	0.873915i
$802$	−4.53057	+	7.84718i	−0.159980	+	0.277094i
$803$	11.1067			0.391948
$804$	8.20730	−	10.3645i	0.289449	−	0.365527i
$805$	11.3629	−	3.92556i	0.400491	−	0.138358i
$806$	3.49900	+	6.06045i	0.123247	+	0.213470i
$807$	15.9639	+	40.2680i	0.561954	+	1.41750i
$808$	6.49237	+	11.2451i	0.228401	+	0.395602i
$809$	26.4921	−	45.8856i	0.931411	−	1.61325i	0.150499	−	0.988610i	$-0.451912\pi$
$809$	26.4921	−	45.8856i	0.931411	−	1.61325i	0.780912	−	0.624641i	$-0.214755\pi$
$810$	−2.98338	+	48.7993i	−0.104825	+	1.71463i
$811$	−42.1161			−1.47890			−0.739449	−	0.673213i	$-0.764914\pi$
$811$	−42.1161			−1.47890			−0.739449	+	0.673213i	$0.764914\pi$
$812$	−27.7689	−	24.0894i	−0.974497	−	0.845371i
$813$	9.97496	+	1.46846i	0.349837	+	0.0515011i
$814$	−3.82915	+	6.63229i	−0.134212	+	0.232462i
$815$	−11.9359			−0.418096
$816$	−3.82804	−	9.65602i	−0.134008	−	0.338028i
$817$	−11.8363			−0.414100
$818$	10.9130			0.381564
$819$	7.88244	+	12.4643i	0.275435	+	0.435538i
$820$	61.4058			2.14438
$821$	−42.8329			−1.49488			−0.747439	−	0.664331i	$-0.768717\pi$
$821$	−42.8329			−1.49488			−0.747439	+	0.664331i	$0.768717\pi$
$822$	−69.0195	−	10.1607i	−2.40733	−	0.354394i
$823$	10.2724			0.358072			0.179036	−	0.983843i	$-0.442702\pi$
$823$	10.2724			0.358072			0.179036	+	0.983843i	$0.442702\pi$
$824$	7.54555	−	13.0693i	0.262862	−	0.455290i
$825$	−1.01330	−	2.55599i	−0.0352785	−	0.0889882i
$826$	8.28334	−	42.8477i	0.288214	−	1.49086i
$827$	−33.5144			−1.16541			−0.582705	−	0.812684i	$-0.698006\pi$
$827$	−33.5144			−1.16541			−0.582705	+	0.812684i	$0.698006\pi$
$828$	−12.6111	−	3.79533i	−0.438267	−	0.131897i
$829$	10.6212	−	18.3964i	0.368889	−	0.638935i	−0.620503	−	0.784204i	$-0.713072\pi$
$829$	10.6212	−	18.3964i	0.368889	−	0.638935i	0.989392	+	0.145269i	$0.0464048\pi$
$830$	−8.89949	−	15.4144i	−0.308906	−	0.535041i
$831$	23.0237	+	3.38943i	0.798685	+	0.117578i
$832$	10.4670	+	18.1294i	0.362878	+	0.628523i
$833$	11.7510	−	9.21958i	0.407147	−	0.319440i
$834$	−54.4932	−	8.02219i	−1.88694	−	0.277786i
$835$	−52.0153			−1.80006
$836$	2.86652	−	4.96495i	0.0991405	−	0.171716i
$837$	−8.37179	−	3.92589i	−0.289372	−	0.135698i
$838$	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	$0.307232\pi$
$840$	−11.7337	+	2.21369i	−0.404851	+	0.0763797i
$841$	−1.19901	−	2.07675i	−0.0413453	−	0.0716122i
$842$	−12.7252	+	22.0407i	−0.438540	+	0.759573i
$843$	−10.3462	−	26.0977i	−0.356341	−	0.898852i
$844$	3.07130	+	5.31966i	0.105719	+	0.183110i
$845$	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
$849$	−21.8954	+	27.6502i	−0.751447	+	0.948953i
$850$	−7.16898			−0.245894
$851$	−6.40584			−0.219589
$852$	−34.9350	+	44.1172i	−1.19685	+	1.51143i
$853$	−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
$857$	19.5408	+	33.8456i	0.667500	+	1.15614i	0.978601	+	0.205767i	$0.0659688\pi$
$857$	19.5408	+	33.8456i	0.667500	+	1.15614i	−0.311101	+	0.950377i	$0.600698\pi$
$858$	2.51024	+	6.33195i	0.0856982	+	0.216169i
$859$	−8.81855	+	15.2742i	−0.300885	+	0.521148i	−0.976337	−	0.216256i	$-0.930615\pi$
$859$	−8.81855	+	15.2742i	−0.300885	+	0.521148i	0.675452	+	0.737404i	$0.263949\pi$
$860$	16.2910	+	28.2168i	0.555517	+	0.962184i
$861$	−14.6253	+	41.7258i	−0.498430	+	1.42201i
$862$	−17.4630	+	30.2468i	−0.594792	+	1.03021i
$863$	0.850995	+	1.47397i	0.0289682	+	0.0501744i	0.880146	−	0.474703i	$-0.157445\pi$
$863$	0.850995	+	1.47397i	0.0289682	+	0.0501744i	−0.851178	+	0.524877i	$0.824111\pi$
$864$	−37.5382	−	17.6032i	−1.27708	−	0.598875i
$865$	−20.1144	+	34.8391i	−0.683909	+	1.18456i
$866$	67.5324			2.29484
$867$	21.3293	+	3.13999i	0.724383	+	0.106640i
$868$	2.21591	−	11.4624i	0.0752129	−	0.389058i
$869$	2.43640	+	4.21997i	0.0826493	+	0.143153i
$870$	−52.1599	−	7.67870i	−1.76839	−	0.260332i
$871$	−2.85967	−	4.95309i	−0.0968962	−	0.167829i
$872$	−3.68732	+	6.38663i	−0.124869	+	0.216279i
$873$	−40.3335	−	12.1384i	−1.36508	−	0.410823i
$874$	8.66323			0.293038
$875$	−4.39843	+	22.7520i	−0.148694	+	0.769160i
$876$	−17.5800	−	44.3447i	−0.593975	−	1.49827i
$877$	20.8181	−	36.0580i	0.702977	−	1.21759i	−0.264440	−	0.964402i	$-0.585187\pi$
$877$	20.8181	−	36.0580i	0.702977	−	1.21759i	0.967417	−	0.253190i	$-0.0814796\pi$
$878$	75.6595			2.55339
$879$	−15.1402	−	2.22886i	−0.510667	−	0.0751775i
$880$	7.21366			0.243172
$881$	21.7833			0.733896			0.366948	−	0.930241i	$-0.380403\pi$
$881$	21.7833			0.733896			0.366948	+	0.930241i	$0.380403\pi$
$882$	6.67107	−	43.9435i	0.224626	−	1.47965i
$883$	−31.8967			−1.07341			−0.536704	−	0.843770i	$-0.680331\pi$
$883$	−31.8967			−1.07341			−0.536704	+	0.843770i	$0.680331\pi$
$884$	9.83065			0.330641
$885$	−12.7680	−	32.2066i	−0.429192	−	1.08261i
$886$	−84.1952			−2.82859
$887$	−3.11595	+	5.39699i	−0.104623	+	0.181213i	−0.913584	−	0.406649i	$-0.866697\pi$
$887$	−3.11595	+	5.39699i	−0.104623	+	0.181213i	0.808961	+	0.587863i	$0.200030\pi$
$888$	6.29472	+	0.926675i	0.211237	+	0.0310972i
$889$	−2.34210	+	12.1151i	−0.0785516	+	0.406329i
$890$	−65.3631			−2.19098
$891$	−7.50511	−	4.96723i	−0.251430	−	0.166409i
$892$	−29.4228	+	50.9618i	−0.985148	+	1.70633i
$893$	3.08314	+	5.34015i	0.103173	+	0.178701i
$894$	21.0240	+	53.0319i	0.703148	+	1.77365i
$895$	27.2076	+	47.1249i	0.909449	+	1.57521i
$896$	3.96130	−	20.4908i	0.132338	−	0.684551i
$897$	−3.53696	+	4.46660i	−0.118096	+	0.149135i
$898$	61.3828			2.04837
$899$	4.98564	−	8.63539i	0.166280	−	0.288006i
$900$	−8.60118	+	8.09140i	−0.286706	+	0.269713i
$901$	−6.33394	−	10.9707i	−0.211014	−	0.365487i
$902$	−10.2106	+	17.6853i	−0.339975	+	0.588854i
$903$	−23.0537	+	4.34934i	−0.767178	+	0.144737i
$904$	−8.46195	−	14.6565i	−0.281440	−	0.487469i
$905$	−24.7359	+	42.8439i	−0.822251	+	1.42418i
$906$	2.07872	+	0.306017i	0.0690607	+	0.0101667i
$907$	16.9538	+	29.3648i	0.562940	+	0.975041i	0.997238	+	0.0742717i	$0.0236632\pi$
$907$	16.9538	+	29.3648i	0.562940	+	0.975041i	−0.434298	+	0.900769i	$0.643003\pi$
$908$	−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	$0.245499\pi$
$912$	11.1351	+	1.63925i	0.368719	+	0.0542808i
$913$	3.27653			0.108437
$914$	80.2422			2.65418
$915$	−5.57062	−	14.0516i	−0.184159	−	0.464531i
$916$	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	0.897466	−	0.441084i	$-0.145406\pi$
$919$	2.02331	+	3.50447i	0.0667427	+	0.115602i	−0.830723	+	0.556686i	$0.812073\pi$
$920$	−2.30651	−	3.99500i	−0.0760435	−	0.131711i
$921$	30.3548	−	38.3331i	1.00023	−	1.26312i
$922$	−7.83754	+	13.5750i	−0.258116	+	0.447070i
$923$	12.1724	+	21.0832i	0.400660	+	0.693963i
$924$	3.75873	−	10.7236i	0.123653	−	0.352780i
$925$	−2.87195	+	4.97436i	−0.0944291	+	0.163556i
$926$	−44.3531	−	76.8219i	−1.45753	−	2.52452i
$927$	42.7025	+	12.8514i	1.40253	+	0.422094i
$928$	22.3551	−	38.7201i	0.733841	−	1.27105i
$929$	−35.1201			−1.15225			−0.576127	−	0.817360i	$-0.695436\pi$
$929$	−35.1201			−1.15225			−0.576127	+	0.817360i	$0.695436\pi$
$930$	−6.17052	−	15.5648i	−0.202339	−	0.510390i
$931$	2.28514	+	16.0220i	0.0748923	+	0.525099i
$932$	29.5823	+	51.2380i	0.969000	+	1.67836i
$933$	3.70297	−	4.67624i	0.121230	−	0.153093i
$934$	44.4421	+	76.9759i	1.45419	+	2.51873i
$935$	2.73821	−	4.74271i	0.0895489	−	0.155103i
$936$	4.12175	−	3.87746i	0.134724	−	0.126739i
$937$	6.91061			0.225760			0.112880	−	0.993609i	$-0.463992\pi$
$937$	6.91061			0.225760			0.112880	+	0.993609i	$0.463992\pi$
$938$	−3.27172	+	16.9238i	−0.106826	+	0.552583i
$939$	−7.81232	+	9.86567i	−0.254945	+	0.321954i
$940$	8.48698	−	14.6999i	0.276815	−	0.479457i
$941$	−28.7020			−0.935658			−0.467829	−	0.883819i	$-0.654964\pi$
$941$	−28.7020			−0.935658			−0.467829	+	0.883819i	$0.654964\pi$
$942$	−16.2649	+	20.5399i	−0.529940	+	0.669227i
$943$	−17.0814			−0.556248
$944$	21.9039			0.712910
$945$	−14.3149	−	32.2507i	−0.465664	−	1.04912i
$946$	−10.8355			−0.352292
$947$	29.0156			0.942882			0.471441	−	0.881898i	$-0.343734\pi$
$947$	29.0156			0.942882			0.471441	+	0.881898i	$0.343734\pi$
$948$	12.9923	−	16.4071i	0.421969	−	0.532877i
$949$	−20.6366			−0.669891
$950$	3.88401	−	6.72730i	0.126014	−	0.218263i
$951$	27.1163	−	34.2434i	0.879306	−	1.11042i
$952$	−4.32926	−	3.75561i	−0.140312	−	0.121720i
$953$	43.0740			1.39530			0.697651	−	0.716437i	$-0.254228\pi$
$953$	43.0740			1.39530			0.697651	+	0.716437i	$0.254228\pi$
$954$	−36.0980	−	10.8637i	−1.16872	−	0.351726i
$955$	−20.9378	+	36.2653i	−0.677530	+	1.17352i
$956$	7.43423	+	12.8765i	0.240440	+	0.416455i
$957$	6.02510	−	7.60870i	0.194764	−	0.245954i
$958$	18.2665	+	31.6386i	0.590165	+	1.02220i
$959$	47.5894	−	16.4408i	1.53674	−	0.530900i
$960$	−18.4587	−	46.5610i	−0.595751	−	1.50275i
$961$	−27.8334			−0.897850
$962$	7.11466	−	12.3230i	0.229386	−	0.397308i
$963$	−29.3721	+	27.6312i	−0.946501	+	0.890403i
$964$	19.0825	+	33.0518i	0.614605	+	1.06453i
$965$	3.76126	−	6.51469i	0.121079	−	0.209715i
$966$	16.8735	−	3.18337i	0.542895	−	0.102423i
$967$	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	$0.794059\pi$
$968$	0.507612	−	0.879209i	0.0163153	−	0.0282589i
$969$	5.30447	−	6.69866i	0.170404	−	0.215192i
$970$	−38.1349	−	66.0515i	−1.22444	−	2.12079i
$971$	−16.0197	−	27.7469i	−0.514096	−	0.890441i	−0.999866	−	0.0163541i	$-0.994794\pi$
$971$	−16.0197	−	27.7469i	−0.514096	−	0.890441i	0.485770	−	0.874087i	$-0.338539\pi$
$972$	−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
$975$	1.88273	+	4.74909i	0.0602957	+	0.152093i
$976$	9.55656			0.305898
$977$	43.0720			1.37799			0.688997	−	0.724764i	$-0.258051\pi$
$977$	43.0720			1.37799			0.688997	+	0.724764i	$0.258051\pi$
$978$	−16.8665	−	2.48299i	−0.539330	−	0.0793972i
$979$	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
$983$	−5.89523	−	10.2108i	−0.188029	−	0.325675i	0.756564	−	0.653919i	$-0.226876\pi$
$983$	−5.89523	−	10.2108i	−0.188029	−	0.325675i	−0.944593	+	0.328244i	$0.893543\pi$
$984$	16.7851	+	2.47101i	0.535090	+	0.0787730i
$985$	27.1314	−	46.9930i	0.864479	−	1.49732i
$986$	−12.6527	−	21.9150i	−0.402943	−	0.697917i
$987$	7.96733	+	9.26814i	0.253603	+	0.295008i
$988$	−5.32606	+	9.22500i	−0.169444	+	0.293486i
$989$	−4.53170	−	7.84914i	−0.144100	−	0.249588i
$990$	−3.73544	−	15.8629i	−0.118720	−	0.504157i
$991$	−28.5783	+	49.4990i	−0.907819	+	1.57239i	−0.0907302	+	0.995876i	$0.528920\pi$
$991$	−28.5783	+	49.4990i	−0.907819	+	1.57239i	−0.817088	+	0.576512i	$0.804413\pi$
$992$	14.1989			0.450816
$993$	−7.98037	+	10.0779i	−0.253249	+	0.319812i
$994$	13.9263	−	72.0377i	0.441717	−	2.28490i
$995$	8.25044	+	14.2902i	0.261556	+	0.453029i
$996$	−5.18619	−	13.0819i	−0.164331	−	0.414515i
$997$	−1.50661	−	2.60953i	−0.0477149	−	0.0826446i	0.841182	−	0.540753i	$-0.181861\pi$
$997$	−1.50661	−	2.60953i	−0.0477149	−	0.0826446i	−0.888896	+	0.458108i	$0.848527\pi$
$998$	−16.3553	+	28.3283i	−0.517719	+	0.896716i
$999$	1.59817	+	18.7334i	0.0505637	+	0.592699i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.k.c.67.35	✓	80	9.4	even	3
693.2.k.c.331.35	yes	80	7.2	even	3
693.2.l.c.529.6	yes	80	1.1	even	1	trivial
693.2.l.c.562.6	yes	80	63.58	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.11652 q^{2} +(1.07526 - 1.35787i) q^{3} +2.47967 q^{4} +(-1.28330 + 2.22274i) q^{5} +(-2.27581 + 2.87397i) q^{6} +(0.502180 - 2.59766i) q^{7} -1.01522 q^{8} +(-0.687640 - 2.92013i) q^{9} +O(q^{10})\)	\(q-2.11652 q^{2} +(1.07526 - 1.35787i) q^{3} +2.47967 q^{4} +(-1.28330 + 2.22274i) q^{5} +(-2.27581 + 2.87397i) q^{6} +(0.502180 - 2.59766i) q^{7} -1.01522 q^{8} +(-0.687640 - 2.92013i) q^{9} +(2.71613 - 4.70448i) q^{10} +(0.500000 + 0.866025i) q^{11} +(2.66628 - 3.36707i) q^{12} +(-0.929012 - 1.60910i) q^{13} +(-1.06287 + 5.49800i) q^{14} +(1.63832 + 4.13258i) q^{15} -2.81059 q^{16} +(-1.06686 + 1.84786i) q^{17} +(1.45541 + 6.18052i) q^{18} +(-1.15601 - 2.00227i) q^{19} +(-3.18216 + 5.51166i) q^{20} +(-2.98731 - 3.47505i) q^{21} +(-1.05826 - 1.83296i) q^{22} +(0.885189 - 1.53319i) q^{23} +(-1.09163 + 1.37855i) q^{24} +(-0.793718 - 1.37476i) 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} +(-3.46754 - 8.74670i) q^{30} +1.77951 q^{31} +7.97912 q^{32} +(1.71358 + 0.252264i) 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} +(2.44672 + 4.23784i) q^{38} +(-3.18388 - 0.468713i) q^{39} +(1.30284 - 2.25658i) q^{40} +(-4.82423 - 8.35581i) q^{41} +(6.32272 + 7.35501i) q^{42} +(2.55974 - 4.43359i) q^{43} +(1.23983 + 2.14745i) q^{44} +(7.37314 + 2.21896i) q^{45} +(-1.87352 + 3.24504i) q^{46} -2.66705 q^{47} +(-3.02211 + 3.81642i) q^{48} +(-6.49563 - 2.60898i) q^{49} +(1.67992 + 2.90971i) q^{50} +(1.36201 + 3.43559i) q^{51} +(-2.30364 - 3.99002i) q^{52} +(-2.96849 + 5.14158i) q^{53} +(9.95730 + 4.66939i) q^{54} -2.56660 q^{55} +(-0.509825 + 2.63720i) q^{56} +(-3.96183 - 0.583239i) q^{57} +(-5.92985 + 10.2708i) q^{58} -7.79334 q^{59} +(4.06249 + 10.2474i) q^{60} -3.40020 q^{61} -3.76637 q^{62} +(-7.93081 + 0.319823i) q^{63} -11.2668 q^{64} +4.76881 q^{65} +(-3.62683 - 0.533923i) q^{66} +3.07818 q^{67} +(-2.64546 + 4.58207i) q^{68} +(-1.13007 - 2.85055i) q^{69} +(-10.8566 - 9.41807i) q^{70} -13.1025 q^{71} +(0.698109 + 2.96458i) q^{72} +(5.55336 - 9.61870i) q^{73} +(3.82915 + 6.63229i) q^{74} +(-2.72020 - 0.400453i) q^{75} +(-2.86652 - 4.96495i) q^{76} +(2.50073 - 0.863928i) q^{77} +(6.73875 + 0.992041i) q^{78} +4.87281 q^{79} +(3.60683 - 6.24721i) q^{80} +(-8.05430 + 4.01600i) q^{81} +(10.2106 + 17.6853i) q^{82} +(1.63826 - 2.83756i) q^{83} +(-7.40754 - 8.61696i) q^{84} +(-2.73821 - 4.74271i) q^{85} +(-5.41774 + 9.38380i) q^{86} +(-3.57678 - 9.02224i) q^{87} +(-0.507612 - 0.879209i) 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} +(1.91343 - 2.41635i) q^{93} +5.64488 q^{94} +5.93403 q^{95} +(8.57961 - 10.8346i) q^{96} +(7.02007 - 12.1591i) q^{97} +(13.7481 + 5.52196i) q^{98} +(2.18509 - 2.05558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 80 q^{4} - 4 q^{5} + 6 q^{6} - q^{7} - 4 q^{9}+O(q^{10}) \) 80 * q + 80 * q^4 - 4 * q^5 + 6 * q^6 - q^7 - 4 * q^9	\( 80 q + 80 q^{4} - 4 q^{5} + 6 q^{6} - q^{7} - 4 q^{9} + 12 q^{10} + 40 q^{11} + 5 q^{12} + 21 q^{13} + 7 q^{14} - 5 q^{15} + 80 q^{16} - 3 q^{17} - 10 q^{18} + 18 q^{19} - 12 q^{20} - 33 q^{21} + 4 q^{23} - 2 q^{24} - 40 q^{25} - 12 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} + 14 q^{30} - 64 q^{31} - 70 q^{32} + 28 q^{34} - 18 q^{35} - 16 q^{36} - 7 q^{37} - 23 q^{38} + 42 q^{39} + 51 q^{40} - 2 q^{41} + 25 q^{42} + 9 q^{43} + 40 q^{44} - 14 q^{45} - 6 q^{46} + 52 q^{47} - 28 q^{48} - q^{49} + 2 q^{50} - 20 q^{51} + 44 q^{52} + 4 q^{53} - 2 q^{54} - 8 q^{55} + 6 q^{56} + 16 q^{57} - 16 q^{58} + 48 q^{59} - 70 q^{60} - 138 q^{61} + 12 q^{62} + 95 q^{63} + 44 q^{64} + 14 q^{65} + 3 q^{66} - 14 q^{67} - 17 q^{68} + 15 q^{69} - 40 q^{70} + 34 q^{71} - 19 q^{72} + 26 q^{73} - 4 q^{74} + 14 q^{75} + 52 q^{76} - 2 q^{77} - 60 q^{78} + 10 q^{79} - 47 q^{80} - 44 q^{81} + 60 q^{82} + 4 q^{83} - 205 q^{84} + 13 q^{85} + 82 q^{87} - 38 q^{89} - 43 q^{90} + 13 q^{91} - 21 q^{92} + 44 q^{93} - 112 q^{94} + 40 q^{95} - 78 q^{96} + 49 q^{97} - 84 q^{98} - 2 q^{99}+O(q^{100}) \) 80 * q + 80 * q^4 - 4 * q^5 + 6 * q^6 - q^7 - 4 * q^9 + 12 * q^10 + 40 * q^11 + 5 * q^12 + 21 * q^13 + 7 * q^14 - 5 * q^15 + 80 * q^16 - 3 * q^17 - 10 * q^18 + 18 * q^19 - 12 * q^20 - 33 * q^21 + 4 * q^23 - 2 * q^24 - 40 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 + 14 * q^30 - 64 * q^31 - 70 * q^32 + 28 * q^34 - 18 * q^35 - 16 * q^36 - 7 * q^37 - 23 * q^38 + 42 * q^39 + 51 * q^40 - 2 * q^41 + 25 * q^42 + 9 * q^43 + 40 * q^44 - 14 * q^45 - 6 * q^46 + 52 * q^47 - 28 * q^48 - q^49 + 2 * q^50 - 20 * q^51 + 44 * q^52 + 4 * q^53 - 2 * q^54 - 8 * q^55 + 6 * q^56 + 16 * q^57 - 16 * q^58 + 48 * q^59 - 70 * q^60 - 138 * q^61 + 12 * q^62 + 95 * q^63 + 44 * q^64 + 14 * q^65 + 3 * q^66 - 14 * q^67 - 17 * q^68 + 15 * q^69 - 40 * q^70 + 34 * q^71 - 19 * q^72 + 26 * q^73 - 4 * q^74 + 14 * q^75 + 52 * q^76 - 2 * q^77 - 60 * q^78 + 10 * q^79 - 47 * q^80 - 44 * q^81 + 60 * q^82 + 4 * q^83 - 205 * q^84 + 13 * q^85 + 82 * q^87 - 38 * q^89 - 43 * q^90 + 13 * q^91 - 21 * q^92 + 44 * q^93 - 112 * q^94 + 40 * q^95 - 78 * q^96 + 49 * q^97 - 84 * q^98 - 2 * q^99

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