LMFDB - Embedded newform 483.2.i.g.277.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 16 x^{14} - 7 x^{13} + 161 x^{12} - 50 x^{11} + 929 x^{10} - 47 x^{9} + 3741 x^{8} + \cdots + 6400 $ x^16 - x^15 + 16x^14 - 7x^13 + 161x^12 - 50x^11 + 929x^10 - 47x^9 + 3741x^8 - 158x^7 + 8993x^6 + 265x^5 + 15176x^4 + 383x^3 + 12649x^2 + 2960x + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.5
Root			$-0.409272 + 0.708880i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.g.415.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.409272 + 0.708880i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.664993 - 1.15180i) q^{4} +(-1.86020 - 3.22197i) q^{5} -0.818544 q^{6} +(-2.34029 + 1.23412i) q^{7} +2.72574 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.409272 + 0.708880i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.664993 - 1.15180i) q^{4} +(-1.86020 - 3.22197i) q^{5} -0.818544 q^{6} +(-2.34029 + 1.23412i) q^{7} +2.72574 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.52266 - 2.63732i) q^{10} +(-1.85002 + 3.20433i) q^{11} +(0.664993 + 1.15180i) q^{12} -6.90735 q^{13} +(-1.83266 - 1.15389i) q^{14} +3.72041 q^{15} +(-0.214417 - 0.371381i) q^{16} +(1.60886 - 2.78662i) q^{17} +(0.409272 - 0.708880i) q^{18} +(-3.03850 - 5.26284i) q^{19} -4.94809 q^{20} +(0.101365 - 2.64381i) q^{21} -3.02865 q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.36287 + 2.36056i) q^{24} +(-4.42071 + 7.65690i) q^{25} +(-2.82698 - 4.89648i) q^{26} +1.00000 q^{27} +(-0.134814 + 3.51623i) q^{28} -3.33137 q^{29} +(1.52266 + 2.63732i) q^{30} +(-0.319234 + 0.552930i) q^{31} +(2.90125 - 5.02511i) q^{32} +(-1.85002 - 3.20433i) q^{33} +2.63384 q^{34} +(8.32970 + 5.24462i) q^{35} -1.32999 q^{36} +(-3.89016 - 6.73796i) q^{37} +(2.48715 - 4.30786i) q^{38} +(3.45367 - 5.98194i) q^{39} +(-5.07043 - 8.78224i) q^{40} +10.4188 q^{41} +(1.91563 - 1.01018i) q^{42} +4.34017 q^{43} +(2.46050 + 4.26171i) q^{44} +(-1.86020 + 3.22197i) q^{45} +(-0.409272 + 0.708880i) q^{46} +(3.01385 + 5.22014i) q^{47} +0.428834 q^{48} +(3.95390 - 5.77639i) q^{49} -7.23710 q^{50} +(1.60886 + 2.78662i) q^{51} +(-4.59334 + 7.95589i) q^{52} +(-3.63604 + 6.29780i) q^{53} +(0.409272 + 0.708880i) q^{54} +13.7657 q^{55} +(-6.37902 + 3.36389i) q^{56} +6.07700 q^{57} +(-1.36343 - 2.36154i) q^{58} +(2.64831 - 4.58700i) q^{59} +(2.47404 - 4.28517i) q^{60} +(-4.05733 - 7.02750i) q^{61} -0.522615 q^{62} +(2.23892 + 1.40969i) q^{63} +3.89193 q^{64} +(12.8491 + 22.2553i) q^{65} +(1.51432 - 2.62288i) q^{66} +(2.00885 - 3.47943i) q^{67} +(-2.13976 - 3.70617i) q^{68} -1.00000 q^{69} +(-0.308690 + 8.05123i) q^{70} -2.92567 q^{71} +(-1.36287 - 2.36056i) q^{72} +(-4.57491 + 7.92398i) q^{73} +(3.18427 - 5.51531i) q^{74} +(-4.42071 - 7.65690i) q^{75} -8.08232 q^{76} +(0.375056 - 9.78220i) q^{77} +5.65397 q^{78} +(-4.08571 - 7.07666i) q^{79} +(-0.797718 + 1.38169i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.26412 + 7.38567i) q^{82} +6.01247 q^{83} +(-2.97774 - 1.87487i) q^{84} -11.9712 q^{85} +(1.77631 + 3.07666i) q^{86} +(1.66568 - 2.88505i) q^{87} +(-5.04267 + 8.73417i) q^{88} +(-7.21516 - 12.4970i) q^{89} -3.04532 q^{90} +(16.1652 - 8.52449i) q^{91} +1.32999 q^{92} +(-0.319234 - 0.552930i) q^{93} +(-2.46697 + 4.27292i) q^{94} +(-11.3045 + 19.5799i) q^{95} +(2.90125 + 5.02511i) q^{96} -14.8716 q^{97} +(5.71299 + 0.438724i) q^{98} +3.70004 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.409272	+	0.708880i	0.289399	+	0.501254i	0.973666	−	0.227977i	$-0.0732112\pi$
$2$	0.409272	+	0.708880i	0.289399	+	0.501254i	−0.684267	+	0.729231i	$0.739878\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.664993	−	1.15180i	0.332496	−	0.575901i
$5$	−1.86020	−	3.22197i	−0.831908	−	1.44091i	−0.896523	−	0.442997i	$-0.853915\pi$
$5$	−1.86020	−	3.22197i	−0.831908	−	1.44091i	0.0646148	−	0.997910i	$-0.479418\pi$
$6$	−0.818544			−0.334169
$7$	−2.34029	+	1.23412i	−0.884546	+	0.466453i
$7$	−2.34029	+	1.23412i	−0.884546	+	0.466453i
$8$	2.72574			0.963695
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.52266	−	2.63732i	0.481507	−	0.833994i
$11$	−1.85002	+	3.20433i	−0.557802	+	0.966142i	0.439877	+	0.898058i	$0.355022\pi$
$11$	−1.85002	+	3.20433i	−0.557802	+	0.966142i	−0.997680	+	0.0680839i	$0.978311\pi$
$12$	0.664993	+	1.15180i	0.191967	+	0.332496i
$13$	−6.90735			−1.91575			−0.957877	−	0.287179i	$-0.907283\pi$
$13$	−6.90735			−1.91575			−0.957877	+	0.287179i	$0.907283\pi$
$14$	−1.83266	−	1.15389i	−0.489798	−	0.308391i
$15$	3.72041			0.960605
$16$	−0.214417	−	0.371381i	−0.0536042	−	0.0928452i
$17$	1.60886	−	2.78662i	0.390206	−	0.675856i	−0.602271	−	0.798292i	$-0.705737\pi$
$17$	1.60886	−	2.78662i	0.390206	−	0.675856i	0.992476	+	0.122436i	$0.0390706\pi$
$18$	0.409272	−	0.708880i	0.0964663	−	0.167085i
$19$	−3.03850	−	5.26284i	−0.697080	−	1.20738i	−0.969475	−	0.245192i	$-0.921149\pi$
$19$	−3.03850	−	5.26284i	−0.697080	−	1.20738i	0.272395	−	0.962186i	$-0.412184\pi$
$20$	−4.94809			−1.10643
$21$	0.101365	−	2.64381i	0.0221197	−	0.576926i
$22$	−3.02865			−0.645710
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	−1.36287	+	2.36056i	−0.278195	+	0.481847i
$25$	−4.42071	+	7.65690i	−0.884143	+	1.53138i
$26$	−2.82698	−	4.89648i	−0.554417	−	0.960279i
$27$	1.00000			0.192450
$28$	−0.134814	+	3.51623i	−0.0254775	+	0.664505i
$29$	−3.33137			−0.618619			−0.309310	−	0.950961i	$-0.600098\pi$
$29$	−3.33137			−0.618619			−0.309310	+	0.950961i	$0.600098\pi$
$30$	1.52266	+	2.63732i	0.277998	+	0.481507i
$31$	−0.319234	+	0.552930i	−0.0573362	+	0.0993091i	−0.893269	−	0.449523i	$-0.851594\pi$
$31$	−0.319234	+	0.552930i	−0.0573362	+	0.0993091i	0.835933	+	0.548832i	$0.184927\pi$
$32$	2.90125	−	5.02511i	0.512873	−	0.888323i
$33$	−1.85002	−	3.20433i	−0.322047	−	0.557802i
$34$	2.63384			0.451700
$35$	8.32970	+	5.24462i	1.40798	+	0.886502i
$36$	−1.32999			−0.221664
$37$	−3.89016	−	6.73796i	−0.639539	−	1.10771i	−0.985534	−	0.169477i	$-0.945792\pi$
$37$	−3.89016	−	6.73796i	−0.639539	−	1.10771i	0.345996	−	0.938236i	$-0.387541\pi$
$38$	2.48715	−	4.30786i	0.403468	−	0.698828i
$39$	3.45367	−	5.98194i	0.553031	−	0.957877i
$40$	−5.07043	−	8.78224i	−0.801705	−	1.38859i
$41$	10.4188			1.62714			0.813571	−	0.581466i	$-0.197521\pi$
$41$	10.4188			1.62714			0.813571	+	0.581466i	$0.197521\pi$
$42$	1.91563	−	1.01018i	0.295588	−	0.155874i
$43$	4.34017			0.661870			0.330935	−	0.943654i	$-0.392636\pi$
$43$	4.34017			0.661870			0.330935	+	0.943654i	$0.392636\pi$
$44$	2.46050	+	4.26171i	0.370934	+	0.642477i
$45$	−1.86020	+	3.22197i	−0.277303	+	0.480302i
$46$	−0.409272	+	0.708880i	−0.0603439	+	0.104519i
$47$	3.01385	+	5.22014i	0.439615	+	0.761436i	0.997660	−	0.0683752i	$-0.0217815\pi$
$47$	3.01385	+	5.22014i	0.439615	+	0.761436i	−0.558044	+	0.829811i	$0.688448\pi$
$48$	0.428834			0.0618968
$49$	3.95390	−	5.77639i	0.564843	−	0.825199i
$50$	−7.23710			−1.02348
$51$	1.60886	+	2.78662i	0.225285	+	0.390206i
$52$	−4.59334	+	7.95589i	−0.636981	+	1.10328i
$53$	−3.63604	+	6.29780i	−0.499448	+	0.865069i	−1.00000		0.000637367i	$-0.999797\pi$
$53$	−3.63604	+	6.29780i	−0.499448	+	0.865069i	0.500552	+	0.865707i	$0.333130\pi$
$54$	0.409272	+	0.708880i	0.0556949	+	0.0964663i
$55$	13.7657			1.85616
$56$	−6.37902	+	3.36389i	−0.852432	+	0.449519i
$57$	6.07700			0.804918
$58$	−1.36343	−	2.36154i	−0.179028	−	0.310085i
$59$	2.64831	−	4.58700i	0.344780	−	0.597177i	−0.640534	−	0.767930i	$-0.721287\pi$
$59$	2.64831	−	4.58700i	0.344780	−	0.597177i	0.985314	+	0.170753i	$0.0546202\pi$
$60$	2.47404	−	4.28517i	0.319398	−	0.553213i
$61$	−4.05733	−	7.02750i	−0.519488	−	0.899779i	−0.999743	−	0.0226506i	$-0.992789\pi$
$61$	−4.05733	−	7.02750i	−0.519488	−	0.899779i	0.480256	−	0.877129i	$-0.340544\pi$
$62$	−0.522615			−0.0663721
$63$	2.23892	+	1.40969i	0.282078	+	0.177604i
$64$	3.89193			0.486492
$65$	12.8491	+	22.2553i	1.59373	+	2.76042i
$66$	1.51432	−	2.62288i	0.186400	−	0.322855i
$67$	2.00885	−	3.47943i	0.245420	−	0.425081i	−0.716829	−	0.697249i	$-0.754407\pi$
$67$	2.00885	−	3.47943i	0.245420	−	0.425081i	0.962250	+	0.272168i	$0.0877407\pi$
$68$	−2.13976	−	3.70617i	−0.259484	−	0.449439i
$69$	−1.00000			−0.120386
$70$	−0.308690	+	8.05123i	−0.0368955	+	0.962307i
$71$	−2.92567			−0.347213			−0.173606	−	0.984815i	$-0.555542\pi$
$71$	−2.92567			−0.347213			−0.173606	+	0.984815i	$0.555542\pi$
$72$	−1.36287	−	2.36056i	−0.160616	−	0.278195i
$73$	−4.57491	+	7.92398i	−0.535453	+	0.927432i	0.463688	+	0.885998i	$0.346526\pi$
$73$	−4.57491	+	7.92398i	−0.535453	+	0.927432i	−0.999141	+	0.0414335i	$0.986808\pi$
$74$	3.18427	−	5.51531i	0.370164	−	0.641142i
$75$	−4.42071	−	7.65690i	−0.510460	−	0.884143i
$76$	−8.08232			−0.927106
$77$	0.375056	−	9.78220i	0.0427416	−	1.11479i
$78$	5.65397			0.640186
$79$	−4.08571	−	7.07666i	−0.459678	−	0.796186i	0.539265	−	0.842136i	$-0.318702\pi$
$79$	−4.08571	−	7.07666i	−0.459678	−	0.796186i	−0.998944	+	0.0459495i	$0.985369\pi$
$80$	−0.797718	+	1.38169i	−0.0891876	+	0.154477i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.26412	+	7.38567i	0.470893	+	0.815611i
$83$	6.01247			0.659954			0.329977	−	0.943989i	$-0.392959\pi$
$83$	6.01247			0.659954			0.329977	+	0.943989i	$0.392959\pi$
$84$	−2.97774	−	1.87487i	−0.324898	−	0.204565i
$85$	−11.9712			−1.29846
$86$	1.77631	+	3.07666i	0.191545	+	0.331765i
$87$	1.66568	−	2.88505i	0.178580	−	0.309310i
$88$	−5.04267	+	8.73417i	−0.537551	+	0.931065i
$89$	−7.21516	−	12.4970i	−0.764805	−	1.32468i	−0.940349	−	0.340210i	$-0.889502\pi$
$89$	−7.21516	−	12.4970i	−0.764805	−	1.32468i	0.175544	−	0.984472i	$-0.443832\pi$
$90$	−3.04532			−0.321005
$91$	16.1652	−	8.52449i	1.69457	−	0.893610i
$92$	1.32999			0.138661
$93$	−0.319234	−	0.552930i	−0.0331030	−	0.0573362i
$94$	−2.46697	+	4.27292i	−0.254448	+	0.440718i
$95$	−11.3045	+	19.5799i	−1.15981	+	2.00885i
$96$	2.90125	+	5.02511i	0.296108	+	0.512873i
$97$	−14.8716			−1.50998			−0.754991	−	0.655735i	$-0.772359\pi$
$97$	−14.8716			−1.50998			−0.754991	+	0.655735i	$0.772359\pi$
$98$	5.71299	+	0.438724i	0.577099	+	0.0443178i
$99$	3.70004			0.371868
$100$	5.87949	+	10.1836i	0.587949	+	1.01836i
$101$	−2.10004	+	3.63738i	−0.208962	+	0.361933i	−0.951388	−	0.307996i	$-0.900342\pi$
$101$	−2.10004	+	3.63738i	−0.208962	+	0.361933i	0.742426	+	0.669928i	$0.233675\pi$
$102$	−1.31692	+	2.28097i	−0.130395	+	0.225850i
$103$	8.72703	+	15.1157i	0.859900	+	1.48939i	0.872023	+	0.489464i	$0.162808\pi$
$103$	8.72703	+	15.1157i	0.859900	+	1.48939i	−0.0121233	+	0.999927i	$0.503859\pi$
$104$	−18.8276			−1.84620
$105$	−8.70682	+	4.59143i	−0.849699	+	0.448077i
$106$	−5.95251			−0.578159
$107$	0.487108	+	0.843697i	0.0470905	+	0.0815632i	0.888610	−	0.458664i	$-0.151672\pi$
$107$	0.487108	+	0.843697i	0.0470905	+	0.0815632i	−0.841519	+	0.540227i	$0.818338\pi$
$108$	0.664993	−	1.15180i	0.0639890	−	0.110832i
$109$	−0.0932707	+	0.161550i	−0.00893371	+	0.0154736i	−0.870458	−	0.492243i	$-0.836177\pi$
$109$	−0.0932707	+	0.161550i	−0.00893371	+	0.0154736i	0.861524	+	0.507717i	$0.169510\pi$
$110$	5.63390	+	9.75820i	0.537171	+	0.930408i
$111$	7.78032			0.738476
$112$	0.960126	+	0.604522i	0.0907233	+	0.0571220i
$113$	2.70857			0.254801			0.127400	−	0.991851i	$-0.459337\pi$
$113$	2.70857			0.254801			0.127400	+	0.991851i	$0.459337\pi$
$114$	2.48715	+	4.30786i	0.232943	+	0.403468i
$115$	1.86020	−	3.22197i	0.173465	−	0.300450i
$116$	−2.21533	+	3.83707i	−0.205689	+	0.356263i
$117$	3.45367	+	5.98194i	0.319292	+	0.553031i
$118$	4.33551			0.399116
$119$	−0.326165	+	8.50703i	−0.0298995	+	0.779838i
$120$	10.1409			0.925730
$121$	−1.34515	−	2.32987i	−0.122286	−	0.211806i
$122$	3.32110	−	5.75232i	0.300678	−	0.520790i
$123$	−5.20940	+	9.02294i	−0.469715	+	0.813571i
$124$	0.424577	+	0.735389i	0.0381281	+	0.0660399i
$125$	14.2917			1.27829
$126$	−0.0829720	+	2.16407i	−0.00739173	+	0.192791i
$127$	6.67778			0.592557			0.296278	−	0.955102i	$-0.404254\pi$
$127$	6.67778			0.592557			0.296278	+	0.955102i	$0.404254\pi$
$128$	−4.20964	−	7.29131i	−0.372083	−	0.644467i
$129$	−2.17009	+	3.75870i	−0.191065	+	0.330935i
$130$	−10.5175	+	18.2169i	−0.922449	+	1.59773i
$131$	−3.85302	−	6.67363i	−0.336640	−	0.583078i	0.647158	−	0.762355i	$-0.275957\pi$
$131$	−3.85302	−	6.67363i	−0.336640	−	0.583078i	−0.983798	+	0.179278i	$0.942624\pi$
$132$	−4.92100			−0.428318
$133$	13.6059	+	8.56668i	1.17978	+	0.742826i
$134$	3.28867			0.284098
$135$	−1.86020	−	3.22197i	−0.160101	−	0.277303i
$136$	4.38533	−	7.59561i	0.376039	−	0.651319i
$137$	10.1975	−	17.6627i	0.871234	−	1.50902i	0.0105139	−	0.999945i	$-0.496653\pi$
$137$	10.1975	−	17.6627i	0.871234	−	1.50902i	0.860721	−	0.509078i	$-0.170013\pi$
$138$	−0.409272	−	0.708880i	−0.0348395	−	0.0603439i
$139$	−12.1820			−1.03326			−0.516632	−	0.856208i	$-0.672814\pi$
$139$	−12.1820			−1.03326			−0.516632	+	0.856208i	$0.672814\pi$
$140$	11.5800	−	6.10653i	0.978685	−	0.516096i
$141$	−6.02770			−0.507624
$142$	−1.19739	−	2.07395i	−0.100483	−	0.174042i
$143$	12.7787	−	22.1334i	1.06861	−	1.85089i
$144$	−0.214417	+	0.371381i	−0.0178681	+	0.0309484i
$145$	6.19702	+	10.7336i	0.514634	+	0.891373i
$146$	−7.48953			−0.619838
$147$	3.02555	+	6.31237i	0.249543	+	0.520636i
$148$	−10.3477			−0.850577
$149$	0.501969	+	0.869437i	0.0411229	+	0.0712270i	0.885854	−	0.463964i	$-0.153573\pi$
$149$	0.501969	+	0.869437i	0.0411229	+	0.0712270i	−0.844731	+	0.535191i	$0.820240\pi$
$150$	3.61855	−	6.26751i	0.295453	−	0.511740i
$151$	1.35532	−	2.34747i	0.110294	−	0.191035i	−0.805595	−	0.592467i	$-0.798154\pi$
$151$	1.35532	−	2.34747i	0.110294	−	0.191035i	0.915889	+	0.401432i	$0.131487\pi$
$152$	−8.28216	−	14.3451i	−0.671772	−	1.16354i
$153$	−3.21772			−0.260137
$154$	7.08791	−	3.73771i	0.571160	−	0.301193i
$155$	2.37536			0.190794
$156$	−4.59334	−	7.95589i	−0.367761	−	0.636981i
$157$	−1.51267	+	2.62001i	−0.120724	+	0.209100i	−0.920053	−	0.391793i	$-0.871855\pi$
$157$	−1.51267	+	2.62001i	−0.120724	+	0.209100i	0.799329	+	0.600893i	$0.205188\pi$
$158$	3.34433	−	5.79256i	0.266061	−	0.460831i
$159$	−3.63604	−	6.29780i	−0.288356	−	0.499448i
$160$	−21.5877			−1.70665
$161$	−2.23892	−	1.40969i	−0.176452	−	0.111099i
$162$	−0.818544			−0.0643109
$163$	−3.84100	−	6.65280i	−0.300850	−	0.521088i	0.675479	−	0.737380i	$-0.263937\pi$
$163$	−3.84100	−	6.65280i	−0.300850	−	0.521088i	−0.976329	+	0.216292i	$0.930604\pi$
$164$	6.92842	−	12.0004i	0.541019	−	0.937072i
$165$	−6.88283	+	11.9214i	−0.535828	+	0.928080i
$166$	2.46074	+	4.26212i	0.190990	+	0.330805i
$167$	4.58319			0.354658			0.177329	−	0.984152i	$-0.443254\pi$
$167$	4.58319			0.354658			0.177329	+	0.984152i	$0.443254\pi$
$168$	0.276296	−	7.20633i	0.0213167	−	0.555981i
$169$	34.7115			2.67011
$170$	−4.89948	−	8.48615i	−0.375773	−	0.650858i
$171$	−3.03850	+	5.26284i	−0.232360	+	0.402459i
$172$	2.88618	−	4.99902i	0.220069	−	0.381171i
$173$	10.0095	+	17.3369i	0.761006	+	1.31810i	0.942332	+	0.334679i	$0.108628\pi$
$173$	10.0095	+	17.3369i	0.761006	+	1.31810i	−0.181326	+	0.983423i	$0.558039\pi$
$174$	2.72687			0.206723
$175$	0.896214	−	23.3750i	0.0677474	−	1.76699i
$176$	1.58670			0.119602
$177$	2.64831	+	4.58700i	0.199059	+	0.344780i
$178$	5.90592	−	10.2294i	0.442668	−	0.766723i
$179$	2.35730	−	4.08296i	0.176193	−	0.305175i	−0.764381	−	0.644765i	$-0.776955\pi$
$179$	2.35730	−	4.08296i	0.176193	−	0.305175i	0.940573	+	0.339590i	$0.110288\pi$
$180$	2.47404	+	4.28517i	0.184404	+	0.319398i
$181$	−1.17108			−0.0870460			−0.0435230	−	0.999052i	$-0.513858\pi$
$181$	−1.17108			−0.0870460			−0.0435230	+	0.999052i	$0.513858\pi$
$182$	12.6588	+	7.97034i	0.938333	+	0.590801i
$183$	8.11466			0.599853
$184$	1.36287	+	2.36056i	0.100472	+	0.174023i
$185$	−14.4730	+	25.0679i	−1.06407	+	1.84303i
$186$	0.261307	−	0.452597i	0.0191600	−	0.0331861i
$187$	5.95284	+	10.3106i	0.435315	+	0.753988i
$188$	8.01676			0.584682
$189$	−2.34029	+	1.23412i	−0.170231	+	0.0897690i
$190$	−18.5064			−1.34259
$191$	−12.0933	−	20.9462i	−0.875039	−	1.51561i	−0.856721	−	0.515780i	$-0.827502\pi$
$191$	−12.0933	−	20.9462i	−0.875039	−	1.51561i	−0.0183179	−	0.999832i	$-0.505831\pi$
$192$	−1.94597	+	3.37051i	−0.140438	+	0.243246i
$193$	−6.16264	+	10.6740i	−0.443597	+	0.768332i	−0.997953	−	0.0639471i	$-0.979631\pi$
$193$	−6.16264	+	10.6740i	−0.443597	+	0.768332i	0.554356	+	0.832279i	$0.312964\pi$
$194$	−6.08653	−	10.5422i	−0.436988	−	0.756885i
$195$	−25.6981			−1.84028
$196$	−4.02394	−	8.39536i	−0.287424	−	0.599669i
$197$	−2.76210			−0.196792			−0.0983958	−	0.995147i	$-0.531371\pi$
$197$	−2.76210			−0.196792			−0.0983958	+	0.995147i	$0.531371\pi$
$198$	1.51432	+	2.62288i	0.107618	+	0.186400i
$199$	−8.29058	+	14.3597i	−0.587704	+	1.01793i	0.406829	+	0.913504i	$0.366635\pi$
$199$	−8.29058	+	14.3597i	−0.587704	+	1.01793i	−0.994532	+	0.104428i	$0.966699\pi$
$200$	−12.0497	+	20.8707i	−0.852044	+	1.47578i
$201$	2.00885	+	3.47943i	0.141694	+	0.245420i
$202$	−3.43795			−0.241893
$203$	7.79636	−	4.11130i	0.547197	−	0.288557i
$204$	4.27952			0.299626
$205$	−19.3811	−	33.5690i	−1.35363	−	2.34456i
$206$	−7.14346	+	12.3728i	−0.497708	+	0.862056i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	1.48105	+	2.56526i	0.102692	+	0.177869i
$209$	22.4851			1.55533
$210$	−6.81823	−	4.29295i	−0.470503	−	0.296242i
$211$	2.75812			0.189877			0.0949386	−	0.995483i	$-0.469735\pi$
$211$	2.75812			0.189877			0.0949386	+	0.995483i	$0.469735\pi$
$212$	4.83588	+	8.37598i	0.332129	+	0.575265i
$213$	1.46283	−	2.53370i	0.100232	−	0.173606i
$214$	−0.398720	+	0.690603i	−0.0272559	+	0.0472086i
$215$	−8.07360	−	13.9839i	−0.550615	−	0.953694i
$216$	2.72574			0.185463
$217$	0.0647186	−	1.68799i	0.00439338	−	0.114588i
$218$	−0.152692			−0.0103416
$219$	−4.57491	−	7.92398i	−0.309144	−	0.535453i
$220$	9.15406	−	15.8553i	0.617167	−	1.06896i
$221$	−11.1129	+	19.2482i	−0.747538	+	1.29477i
$222$	3.18427	+	5.51531i	0.213714	+	0.370164i
$223$	−25.8192			−1.72898			−0.864490	−	0.502650i	$-0.832358\pi$
$223$	−25.8192			−1.72898			−0.864490	+	0.502650i	$0.832358\pi$
$224$	−0.588172	+	15.3407i	−0.0392989	+	1.02499i
$225$	8.84143			0.589429
$226$	1.10854	+	1.92005i	0.0737391	+	0.127720i
$227$	−4.18548	+	7.24946i	−0.277800	+	0.481164i	−0.970838	−	0.239738i	$-0.922939\pi$
$227$	−4.18548	+	7.24946i	−0.277800	+	0.481164i	0.693038	+	0.720901i	$0.256272\pi$
$228$	4.04116	−	6.99950i	0.267632	−	0.463553i
$229$	−9.75934	−	16.9037i	−0.644915	−	1.11703i	−0.984321	−	0.176386i	$-0.943559\pi$
$229$	−9.75934	−	16.9037i	−0.644915	−	1.11703i	0.339406	−	0.940640i	$-0.389774\pi$
$230$	3.04532			0.200802
$231$	8.28411	+	5.21591i	0.545054	+	0.343182i
$232$	−9.08044			−0.596160
$233$	−3.12934	−	5.42018i	−0.205010	−	0.355088i	0.745126	−	0.666924i	$-0.232389\pi$
$233$	−3.12934	−	5.42018i	−0.205010	−	0.355088i	−0.950136	+	0.311836i	$0.899056\pi$
$234$	−2.82698	+	4.89648i	−0.184806	+	0.320093i
$235$	11.2127	−	19.4211i	0.731439	−	1.26689i
$236$	−3.52221	−	6.10065i	−0.229276	−	0.397118i
$237$	8.17142			0.530791
$238$	−6.16395	+	3.25048i	−0.399550	+	0.210697i
$239$	−4.53876			−0.293588			−0.146794	−	0.989167i	$-0.546895\pi$
$239$	−4.53876			−0.293588			−0.146794	+	0.989167i	$0.546895\pi$
$240$	−0.797718	−	1.38169i	−0.0514925	−	0.0891876i
$241$	9.83855	−	17.0409i	0.633756	−	1.09770i	−0.353021	−	0.935616i	$-0.614845\pi$
$241$	9.83855	−	17.0409i	0.633756	−	1.09770i	0.986777	−	0.162083i	$-0.0518212\pi$
$242$	1.10107	−	1.90710i	0.0707792	−	0.122593i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−10.7924			−0.690911
$245$	−25.9664	−	1.99407i	−1.65893	−	0.127396i
$246$	−8.52824			−0.543741
$247$	20.9880	+	36.3522i	1.33543	+	2.31304i
$248$	−0.870149	+	1.50714i	−0.0552545	+	0.0957037i
$249$	−3.00623	+	5.20695i	−0.190512	+	0.329977i
$250$	5.84918	+	10.1311i	0.369935	+	0.640746i
$251$	−10.3015			−0.650226			−0.325113	−	0.945675i	$-0.605402\pi$
$251$	−10.3015			−0.650226			−0.325113	+	0.945675i	$0.605402\pi$
$252$	3.11255	−	1.64136i	0.196072	−	0.103396i
$253$	−3.70004			−0.232620
$254$	2.73303	+	4.73374i	0.171485	+	0.297021i
$255$	5.98561	−	10.3674i	0.374833	−	0.649230i
$256$	7.33771	−	12.7093i	0.458607	−	0.794330i
$257$	−7.65741	−	13.2630i	−0.477656	−	0.827324i	0.522016	−	0.852936i	$-0.325180\pi$
$257$	−7.65741	−	13.2630i	−0.477656	−	0.827324i	−0.999672	+	0.0256113i	$0.991847\pi$
$258$	−3.55262			−0.221177
$259$	17.4195	+	10.9678i	1.08240	+	0.681508i
$260$	34.1782			2.11964
$261$	1.66568	+	2.88505i	0.103103	+	0.178580i
$262$	3.15387	−	5.46266i	0.194847	−	0.337484i
$263$	2.65875	−	4.60509i	0.163945	−	0.283962i	−0.772335	−	0.635216i	$-0.780911\pi$
$263$	2.65875	−	4.60509i	0.163945	−	0.283962i	0.936280	+	0.351254i	$0.114245\pi$
$264$	−5.04267	−	8.73417i	−0.310355	−	0.537551i
$265$	27.0551			1.66198
$266$	−0.504221	+	13.1511i	−0.0309158	+	0.806344i
$267$	14.4303			0.883121
$268$	−2.67175	−	4.62760i	−0.163203	−	0.282676i
$269$	0.882323	−	1.52823i	0.0537962	−	0.0931777i	−0.837873	−	0.545865i	$-0.816201\pi$
$269$	0.882323	−	1.52823i	0.0537962	−	0.0931777i	0.891669	+	0.452687i	$0.149535\pi$
$270$	1.52266	−	2.63732i	0.0926660	−	0.160502i
$271$	−8.30828	−	14.3904i	−0.504692	−	0.874152i	−0.999985	−	0.00542626i	$-0.998273\pi$
$271$	−8.30828	−	14.3904i	−0.504692	−	0.874152i	0.495293	−	0.868726i	$-0.335061\pi$
$272$	−1.37987			−0.0836666
$273$	−0.700166	+	18.2617i	−0.0423760	+	1.10525i
$274$	16.6943			1.00854
$275$	−16.3568	−	28.3308i	−0.986353	−	1.70841i
$276$	−0.664993	+	1.15180i	−0.0400279	+	0.0693303i
$277$	−0.976477	+	1.69131i	−0.0586708	+	0.101621i	−0.893869	−	0.448328i	$-0.852020\pi$
$277$	−0.976477	+	1.69131i	−0.0586708	+	0.101621i	0.835198	+	0.549949i	$0.185353\pi$
$278$	−4.98575	−	8.63557i	−0.299025	−	0.517927i
$279$	0.638468			0.0382241
$280$	22.7046	+	14.2955i	1.35686	+	0.854317i
$281$	13.1183			0.782575			0.391287	−	0.920268i	$-0.372030\pi$
$281$	13.1183			0.782575			0.391287	+	0.920268i	$0.372030\pi$
$282$	−2.46697	−	4.27292i	−0.146906	−	0.254448i
$283$	−0.489936	+	0.848594i	−0.0291237	+	0.0504437i	−0.880220	−	0.474566i	$-0.842605\pi$
$283$	−0.489936	+	0.848594i	−0.0291237	+	0.0504437i	0.851096	+	0.525010i	$0.175938\pi$
$284$	−1.94555	+	3.36979i	−0.115447	+	0.199960i
$285$	−11.3045	−	19.5799i	−0.669618	−	1.15981i
$286$	20.9199			1.23702
$287$	−24.3830	+	12.8580i	−1.43928	+	0.758986i
$288$	−5.80250			−0.341916
$289$	3.32315	+	5.75586i	0.195479	+	0.338580i
$290$	−5.07253	+	8.78588i	−0.297869	+	0.515925i
$291$	7.43580	−	12.8792i	0.435895	−	0.754991i
$292$	6.08457	+	10.5388i	0.356072	+	0.616736i
$293$	−22.4505			−1.31157			−0.655786	−	0.754947i	$-0.727663\pi$
$293$	−22.4505			−1.31157			−0.655786	+	0.754947i	$0.727663\pi$
$294$	−3.23644	+	4.72823i	−0.188753	+	0.275756i
$295$	−19.7056			−1.14730
$296$	−10.6036	−	18.3659i	−0.616320	−	1.06750i
$297$	−1.85002	+	3.20433i	−0.107349	+	0.185934i
$298$	−0.410884	+	0.711672i	−0.0238019	+	0.0412261i
$299$	−3.45367	−	5.98194i	−0.199731	−	0.345945i
$300$	−11.7590			−0.678905
$301$	−10.1573	+	5.35629i	−0.585454	+	0.308732i
$302$	2.21877			0.127676
$303$	−2.10004	−	3.63738i	−0.120644	−	0.208962i
$304$	−1.30301	+	2.25688i	−0.0747328	+	0.129441i
$305$	−15.0949	+	26.1452i	−0.864332	+	1.49707i
$306$	−1.31692	−	2.28097i	−0.0752834	−	0.130395i
$307$	29.2019			1.66664			0.833322	−	0.552789i	$-0.186436\pi$
$307$	29.2019			1.66664			0.833322	+	0.552789i	$0.186436\pi$
$308$	−11.0177	−	6.93708i	−0.627794	−	0.395277i
$309$	−17.4541			−0.992927
$310$	0.972169	+	1.68385i	0.0552155	+	0.0956361i
$311$	−0.895965	+	1.55186i	−0.0508055	+	0.0879977i	−0.890310	−	0.455355i	$-0.849512\pi$
$311$	−0.895965	+	1.55186i	−0.0508055	+	0.0879977i	0.839504	+	0.543353i	$0.182846\pi$
$312$	9.41382	−	16.3052i	0.532953	−	0.923101i
$313$	4.41582	+	7.64843i	0.249597	+	0.432315i	0.963414	−	0.268017i	$-0.0863685\pi$
$313$	4.41582	+	7.64843i	0.249597	+	0.432315i	−0.713817	+	0.700332i	$0.753035\pi$
$314$	−2.47637			−0.139750
$315$	0.377120	−	9.83604i	0.0212483	−	0.554198i
$316$	−10.8679			−0.611366
$317$	10.7748	+	18.6624i	0.605170	+	1.04819i	0.992025	+	0.126045i	$0.0402283\pi$
$317$	10.7748	+	18.6624i	0.605170	+	1.04819i	−0.386854	+	0.922141i	$0.626438\pi$
$318$	2.97626	−	5.15503i	0.166900	−	0.289079i
$319$	6.16310	−	10.6748i	0.345067	−	0.597674i
$320$	−7.23979	−	12.5397i	−0.404716	−	0.700989i
$321$	−0.974217			−0.0543755
$322$	0.0829720	−	2.16407i	0.00462385	−	0.120599i
$323$	−19.5541			−1.08802
$324$	0.664993	+	1.15180i	0.0369440	+	0.0639890i
$325$	30.5354	−	52.8889i	1.69380	−	2.93375i
$326$	3.14403	−	5.44561i	0.174131	−	0.301605i
$327$	−0.0932707	−	0.161550i	−0.00515788	−	0.00893371i
$328$	28.3989			1.56807
$329$	−13.4956	−	8.49718i	−0.744034	−	0.468465i
$330$	−11.2678			−0.620272
$331$	−11.5543	−	20.0127i	−0.635082	−	1.09999i	−0.986498	−	0.163775i	$-0.947633\pi$
$331$	−11.5543	−	20.0127i	−0.635082	−	1.09999i	0.351415	−	0.936220i	$-0.385701\pi$
$332$	3.99825	−	6.92517i	0.219432	−	0.380068i
$333$	−3.89016	+	6.73796i	−0.213180	+	0.369238i
$334$	1.87577	+	3.24893i	0.102638	+	0.177774i
$335$	−14.9475			−0.816669
$336$	−1.00359	+	0.529232i	−0.0547506	+	0.0288720i
$337$	4.83315			0.263279			0.131639	−	0.991298i	$-0.457976\pi$
$337$	4.83315			0.263279			0.131639	+	0.991298i	$0.457976\pi$
$338$	14.2064	+	24.6063i	0.772728	+	1.33840i
$339$	−1.35429	+	2.34569i	−0.0735547	+	0.127400i
$340$	−7.96077	+	13.7885i	−0.431734	+	0.747785i
$341$	−1.18118	−	2.04586i	−0.0639645	−	0.110790i
$342$	−4.97429			−0.268979
$343$	−2.12451	+	18.3980i	−0.114713	+	0.993399i
$344$	11.8302			0.637841
$345$	1.86020	+	3.22197i	0.100150	+	0.173465i
$346$	−8.19320	+	14.1910i	−0.440469	+	0.762915i
$347$	−1.15792	+	2.00558i	−0.0621605	+	0.107665i	−0.895431	−	0.445201i	$-0.853132\pi$
$347$	−1.15792	+	2.00558i	−0.0621605	+	0.107665i	0.833270	+	0.552866i	$0.186466\pi$
$348$	−2.21533	−	3.83707i	−0.118754	−	0.205689i
$349$	2.05541			0.110024			0.0550119	−	0.998486i	$-0.482480\pi$
$349$	2.05541			0.110024			0.0550119	+	0.998486i	$0.482480\pi$
$350$	16.9369	−	8.93144i	0.905315	−	0.477406i
$351$	−6.90735			−0.368687
$352$	10.7347	+	18.5931i	0.572164	+	0.991017i
$353$	−9.28196	+	16.0768i	−0.494029	+	0.855683i	−0.999976	−	0.00688094i	$-0.997810\pi$
$353$	−9.28196	+	16.0768i	−0.494029	+	0.855683i	0.505947	+	0.862564i	$0.331143\pi$
$354$	−2.16775	+	3.75466i	−0.115215	+	0.199558i
$355$	5.44234	+	9.42640i	0.288849	+	0.500302i
$356$	−19.1921			−1.01718
$357$	−7.20422	−	4.53598i	−0.381288	−	0.240070i
$358$	3.85910			0.203960
$359$	3.63704	+	6.29954i	0.191956	+	0.332477i	0.945898	−	0.324463i	$-0.105184\pi$
$359$	3.63704	+	6.29954i	0.191956	+	0.332477i	−0.753943	+	0.656940i	$0.771850\pi$
$360$	−5.07043	+	8.78224i	−0.267235	+	0.462865i
$361$	−8.96497	+	15.5278i	−0.471840	+	0.817251i
$362$	−0.479292	−	0.830158i	−0.0251910	−	0.0436321i
$363$	2.69030			0.141204
$364$	0.931211	−	24.2878i	0.0488087	−	1.27303i
$365$	34.0411			1.78179
$366$	3.32110	+	5.75232i	0.173597	+	0.300678i
$367$	10.1199	−	17.5281i	0.528253	−	0.914961i	−0.471204	−	0.882024i	$-0.656181\pi$
$367$	10.1199	−	17.5281i	0.528253	−	0.914961i	0.999457	−	0.0329370i	$-0.0104861\pi$
$368$	0.214417	−	0.371381i	0.0111773	−	0.0193596i
$369$	−5.20940	−	9.02294i	−0.271190	−	0.469715i
$370$	−23.6935			−1.23177
$371$	0.737136	−	19.2260i	0.0382702	−	0.998162i
$372$	−0.849154			−0.0440266
$373$	−6.66186	−	11.5387i	−0.344938	−	0.597450i	0.640405	−	0.768038i	$-0.278767\pi$
$373$	−6.66186	−	11.5387i	−0.344938	−	0.597450i	−0.985342	+	0.170588i	$0.945433\pi$
$374$	−4.87266	+	8.43970i	−0.251959	+	0.436407i
$375$	−7.14584	+	12.3770i	−0.369009	+	0.639143i
$376$	8.21497	+	14.2287i	0.423655	+	0.733792i
$377$	23.0109			1.18512
$378$	−1.83266	−	1.15389i	−0.0942617	−	0.0593498i
$379$	9.15684			0.470355			0.235178	−	0.971952i	$-0.424433\pi$
$379$	9.15684			0.470355			0.235178	+	0.971952i	$0.424433\pi$
$380$	15.0348	+	26.0410i	0.771267	+	1.33587i
$381$	−3.33889	+	5.78313i	−0.171056	+	0.296278i
$382$	9.89888	−	17.1454i	0.506471	−	0.877233i
$383$	−4.49277	−	7.78171i	−0.229570	−	0.397627i	0.728111	−	0.685459i	$-0.240399\pi$
$383$	−4.49277	−	7.78171i	−0.229570	−	0.397627i	−0.957681	+	0.287833i	$0.907065\pi$
$384$	8.41928			0.429645
$385$	−32.2156	+	16.9885i	−1.64186	+	0.865812i
$386$	−10.0888			−0.513506
$387$	−2.17009	−	3.75870i	−0.110312	−	0.191065i
$388$	−9.88951	+	17.1291i	−0.502064	+	0.869600i
$389$	8.18621	−	14.1789i	0.415057	−	0.718900i	−0.580377	−	0.814348i	$-0.697095\pi$
$389$	8.18621	−	14.1789i	0.415057	−	0.718900i	0.995434	+	0.0954475i	$0.0304282\pi$
$390$	−10.5175	−	18.2169i	−0.532576	−	0.922449i
$391$	3.21772			0.162727
$392$	10.7773	−	15.7449i	0.544336	−	0.795239i
$393$	7.70604			0.388718
$394$	−1.13045	−	1.95800i	−0.0569513	−	0.0986425i
$395$	−15.2005	+	26.3281i	−0.764821	+	1.32471i
$396$	2.46050	−	4.26171i	0.123645	−	0.214159i
$397$	−4.84245	−	8.38738i	−0.243036	−	0.420950i	0.718542	−	0.695484i	$-0.244810\pi$
$397$	−4.84245	−	8.38738i	−0.243036	−	0.420950i	−0.961578	+	0.274533i	$0.911477\pi$
$398$	−13.5724			−0.680323
$399$	−14.2219	+	7.49974i	−0.711987	+	0.375457i
$400$	3.79150			0.189575
$401$	−5.73309	−	9.93000i	−0.286297	−	0.495881i	0.686626	−	0.727011i	$-0.259091\pi$
$401$	−5.73309	−	9.93000i	−0.286297	−	0.495881i	−0.972923	+	0.231130i	$0.925758\pi$
$402$	−1.64433	+	2.84807i	−0.0820119	+	0.142049i
$403$	2.20506	−	3.81928i	0.109842	−	0.190252i
$404$	2.79302	+	4.83766i	0.138958	+	0.240683i
$405$	3.72041			0.184869
$406$	6.10525	+	3.84404i	0.302999	+	0.190776i
$407$	28.7875			1.42694
$408$	4.38533	+	7.59561i	0.217106	+	0.376039i
$409$	19.3266	−	33.4747i	0.955639	−	1.65522i	0.222740	−	0.974878i	$-0.428500\pi$
$409$	19.3266	−	33.4747i	0.955639	−	1.65522i	0.732899	−	0.680337i	$-0.238167\pi$
$410$	15.8643	−	27.4777i	0.783480	−	1.35703i
$411$	10.1975	+	17.6627i	0.503007	+	0.871234i
$412$	23.2137			1.14365
$413$	−0.536893	+	14.0032i	−0.0264188	+	0.689054i
$414$	0.818544			0.0402292
$415$	−11.1844	−	19.3720i	−0.549021	−	0.950933i
$416$	−20.0399	+	34.7102i	−0.982539	+	1.70181i
$417$	6.09100	−	10.5499i	0.298277	−	0.516632i
$418$	9.20254	+	15.9393i	0.450111	+	0.779615i
$419$	−6.70860			−0.327736			−0.163868	−	0.986482i	$-0.552397\pi$
$419$	−6.70860			−0.327736			−0.163868	+	0.986482i	$0.552397\pi$
$420$	−0.501565	+	13.0818i	−0.0244738	+	0.638326i
$421$	−34.0515			−1.65957			−0.829783	−	0.558086i	$-0.811536\pi$
$421$	−34.0515			−1.65957			−0.829783	+	0.558086i	$0.811536\pi$
$422$	1.12882	+	1.95518i	0.0549502	+	0.0951766i
$423$	3.01385	−	5.22014i	0.146538	−	0.253812i
$424$	−9.91089	+	17.1662i	−0.481315	+	0.833662i
$425$	14.2246	+	24.6377i	0.689995	+	1.19511i
$426$	2.39479			0.116028
$427$	18.1681	+	11.4391i	0.879216	+	0.553579i
$428$	1.29569			0.0626298
$429$	12.7787	+	22.1334i	0.616963	+	1.06861i
$430$	6.60860	−	11.4464i	0.318695	−	0.551996i
$431$	−3.73449	+	6.46832i	−0.179884	+	0.311568i	−0.941841	−	0.336060i	$-0.890906\pi$
$431$	−3.73449	+	6.46832i	−0.179884	+	0.311568i	0.761957	+	0.647628i	$0.224239\pi$
$432$	−0.214417	−	0.371381i	−0.0103161	−	0.0178681i
$433$	−25.8698			−1.24322			−0.621611	−	0.783326i	$-0.713522\pi$
$433$	−25.8698			−1.24322			−0.621611	+	0.783326i	$0.713522\pi$
$434$	1.22307	−	0.644969i	0.0587092	−	0.0309595i
$435$	−12.3940			−0.594249
$436$	0.124049	+	0.214859i	0.00594086	+	0.0102899i
$437$	3.03850	−	5.26284i	0.145351	−	0.251756i
$438$	3.74477	−	6.48613i	0.178932	−	0.309919i
$439$	7.98617	+	13.8324i	0.381159	+	0.660187i	0.991228	−	0.132161i	$-0.0421917\pi$
$439$	7.98617	+	13.8324i	0.381159	+	0.660187i	−0.610069	+	0.792348i	$0.708858\pi$
$440$	37.5216			1.78877
$441$	−6.97945	−	0.535981i	−0.332355	−	0.0255229i
$442$	−18.1929			−0.865347
$443$	−15.3142	−	26.5249i	−0.727598	−	1.26024i	−0.957896	−	0.287116i	$-0.907303\pi$
$443$	−15.3142	−	26.5249i	−0.727598	−	1.26024i	0.230298	−	0.973120i	$-0.426030\pi$
$444$	5.17386	−	8.96139i	0.245540	−	0.425289i
$445$	−26.8433	+	46.4940i	−1.27250	+	2.20403i
$446$	−10.5671	−	18.3027i	−0.500365	−	0.866658i
$447$	−1.00394			−0.0474847
$448$	−9.10825	+	4.80311i	−0.430324	+	0.226926i
$449$	−7.12584			−0.336289			−0.168144	−	0.985762i	$-0.553778\pi$
$449$	−7.12584			−0.336289			−0.168144	+	0.985762i	$0.553778\pi$
$450$	3.61855	+	6.26751i	0.170580	+	0.295453i
$451$	−19.2750	+	33.3852i	−0.907623	+	1.57205i
$452$	1.80118	−	3.11974i	0.0847204	−	0.146740i
$453$	1.35532	+	2.34747i	0.0636783	+	0.110294i
$454$	−6.85200			−0.321580
$455$	−57.5362	−	36.2264i	−2.69734	−	1.69832i
$456$	16.5643			0.775695
$457$	−10.3426	−	17.9138i	−0.483805	−	0.837974i	0.516022	−	0.856575i	$-0.327412\pi$
$457$	−10.3426	−	17.9138i	−0.483805	−	0.837974i	−0.999827	+	0.0186008i	$0.994079\pi$
$458$	7.98845	−	13.8364i	0.373276	−	0.646532i
$459$	1.60886	−	2.78662i	0.0750951	−	0.130069i
$460$	−2.47404	−	4.28517i	−0.115353	−	0.199797i
$461$	12.1611			0.566401			0.283200	−	0.959061i	$-0.408604\pi$
$461$	12.1611			0.566401			0.283200	+	0.959061i	$0.408604\pi$
$462$	−0.307000	+	8.00716i	−0.0142829	+	0.372527i
$463$	−1.96022			−0.0910992			−0.0455496	−	0.998962i	$-0.514504\pi$
$463$	−1.96022			−0.0910992			−0.0455496	+	0.998962i	$0.514504\pi$
$464$	0.714301	+	1.23721i	0.0331606	+	0.0574358i
$465$	−1.18768	+	2.05712i	−0.0550774	+	0.0953969i
$466$	2.56150	−	4.43666i	0.118659	−	0.205524i
$467$	19.6961	+	34.1146i	0.911427	+	1.57864i	0.812050	+	0.583587i	$0.198351\pi$
$467$	19.6961	+	34.1146i	0.911427	+	1.57864i	0.0993764	+	0.995050i	$0.468315\pi$
$468$	9.18668			0.424654
$469$	−0.407256	+	10.6220i	−0.0188053	+	0.490480i
$470$	18.3563			0.846711
$471$	−1.51267	−	2.62001i	−0.0697000	−	0.120724i
$472$	7.21859	−	12.5030i	0.332263	−	0.575496i
$473$	−8.02941	+	13.9073i	−0.369193	+	0.639460i
$474$	3.34433	+	5.79256i	0.153610	+	0.266061i
$475$	53.7294			2.46527
$476$	9.58151	+	6.03279i	0.439168	+	0.276513i
$477$	7.27207			0.332965
$478$	−1.85759	−	3.21743i	−0.0849640	−	0.147162i
$479$	1.41366	−	2.44853i	0.0645917	−	0.111876i	−0.831921	−	0.554894i	$-0.812759\pi$
$479$	1.41366	−	2.44853i	0.0645917	−	0.111876i	0.896513	+	0.443018i	$0.146092\pi$
$480$	10.7938	−	18.6955i	0.492669	−	0.853327i
$481$	26.8707	+	46.5414i	1.22520	+	2.12211i
$482$	16.1066			0.733634
$483$	2.34029	−	1.23412i	0.106487	−	0.0561544i
$484$	−3.57806			−0.162639
$485$	27.6642	+	47.9158i	1.25617	+	2.17575i
$486$	0.409272	−	0.708880i	0.0185650	−	0.0321554i
$487$	12.3924	−	21.4643i	0.561554	−	0.972640i	−0.435807	−	0.900040i	$-0.643537\pi$
$487$	12.3924	−	21.4643i	0.561554	−	0.972640i	0.997361	−	0.0725997i	$-0.0231296\pi$
$488$	−11.0592	−	19.1551i	−0.500627	−	0.867112i
$489$	7.68199			0.347392
$490$	−9.21376	−	19.2232i	−0.416235	−	0.868414i
$491$	13.1356			0.592802			0.296401	−	0.955064i	$-0.404214\pi$
$491$	13.1356			0.592802			0.296401	+	0.955064i	$0.404214\pi$
$492$	6.92842	+	12.0004i	0.312357	+	0.541019i
$493$	−5.35970	+	9.28327i	−0.241389	+	0.418097i
$494$	−17.1796	+	29.7559i	−0.772946	+	1.33878i
$495$	−6.88283	−	11.9214i	−0.309360	−	0.535828i
$496$	0.273797			0.0122938
$497$	6.84690	−	3.61062i	0.307126	−	0.161959i
$498$	−4.92147			−0.220536
$499$	−8.24049	−	14.2730i	−0.368895	−	0.638945i	0.620498	−	0.784208i	$-0.286931\pi$
$499$	−8.24049	−	14.2730i	−0.368895	−	0.638945i	−0.989393	+	0.145263i	$0.953597\pi$
$500$	9.50386	−	16.4612i	0.425026	−	0.736166i
$501$	−2.29159	+	3.96916i	−0.102381	+	0.177329i
$502$	−4.21612	−	7.30254i	−0.188175	−	0.325928i
$503$	17.3522			0.773696			0.386848	−	0.922144i	$-0.373564\pi$
$503$	17.3522			0.773696			0.386848	+	0.922144i	$0.373564\pi$
$504$	6.10272	+	3.84245i	0.271837	+	0.171156i
$505$	15.6260			0.695348
$506$	−1.51432	−	2.62288i	−0.0673199	−	0.116601i
$507$	−17.3557	+	30.0610i	−0.770795	+	1.33506i
$508$	4.44067	−	7.69147i	0.197023	−	0.341254i
$509$	17.4049	+	30.1462i	0.771461	+	1.33621i	0.936762	+	0.349966i	$0.113807\pi$
$509$	17.4049	+	30.1462i	0.771461	+	1.33621i	−0.165302	+	0.986243i	$0.552860\pi$
$510$	9.79897			0.433906
$511$	0.927475	−	24.1904i	0.0410291	−	1.07012i
$512$	−4.82609			−0.213285
$513$	−3.03850	−	5.26284i	−0.134153	−	0.232360i
$514$	6.26792	−	10.8564i	0.276466	−	0.478854i
$515$	32.4681	−	56.2364i	1.43072	−	2.47807i
$516$	2.88618	+	4.99902i	0.127057	+	0.220069i
$517$	−22.3027			−0.980873
$518$	−0.645549	+	16.8372i	−0.0283638	+	0.739784i
$519$	−20.0190			−0.878735
$520$	35.0232	+	60.6620i	1.53587	+	2.66021i
$521$	−8.45741	+	14.6487i	−0.370526	+	0.641770i	−0.989647	−	0.143526i	$-0.954156\pi$
$521$	−8.45741	+	14.6487i	−0.370526	+	0.641770i	0.619120	+	0.785296i	$0.287489\pi$
$522$	−1.36343	+	2.36154i	−0.0596759	+	0.103362i
$523$	14.5236	+	25.1555i	0.635071	+	1.09997i	0.986500	+	0.163761i	$0.0523624\pi$
$523$	14.5236	+	25.1555i	0.635071	+	1.09997i	−0.351429	+	0.936214i	$0.614304\pi$
$524$	−10.2489			−0.447726
$525$	19.7953	+	12.4637i	0.863937	+	0.543959i
$526$	4.35260			0.189783
$527$	1.02721	+	1.77917i	0.0447458	+	0.0775020i
$528$	−0.793351	+	1.37412i	−0.0345262	+	0.0598011i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	11.0729	+	19.1788i	0.480975	+	0.833073i
$531$	−5.29661			−0.229853
$532$	18.9150	−	9.97455i	0.820068	−	0.432452i
$533$	−71.9662			−3.11720
$534$	5.90592	+	10.2294i	0.255574	+	0.442668i
$535$	1.81224	−	3.13889i	0.0783500	−	0.135706i
$536$	5.47561	−	9.48403i	0.236510	−	0.409648i
$537$	2.35730	+	4.08296i	0.101725	+	0.176193i
$538$	1.44444			0.0622743
$539$	11.1947	+	23.3560i	0.482188	+	1.00602i
$540$	−4.94809			−0.212932
$541$	1.89782	+	3.28713i	0.0815938	+	0.141325i	0.903935	−	0.427671i	$-0.140666\pi$
$541$	1.89782	+	3.28713i	0.0815938	+	0.141325i	−0.822341	+	0.568995i	$0.807332\pi$
$542$	6.80069	−	11.7791i	0.292115	−	0.505957i
$543$	0.585542	−	1.01419i	0.0251280	−	0.0435230i
$544$	−9.33540	−	16.1694i	−0.400252	−	0.693257i
$545$	0.694010			0.0297281
$546$	−13.2319	+	6.97767i	−0.566274	+	0.298617i
$547$	3.31002			0.141526			0.0707630	−	0.997493i	$-0.477457\pi$
$547$	3.31002			0.141526			0.0707630	+	0.997493i	$0.477457\pi$
$548$	−13.5626	−	23.4911i	−0.579365	−	1.00349i
$549$	−4.05733	+	7.02750i	−0.173163	+	0.299926i
$550$	13.3888	−	23.1900i	0.570899	−	0.988827i
$551$	10.1224	+	17.5324i	0.431227	+	0.746907i
$552$	−2.72574			−0.116015
$553$	18.2952	+	11.5192i	0.777990	+	0.489845i
$554$	−1.59858			−0.0679171
$555$	−14.4730	−	25.0679i	−0.614344	−	1.06407i
$556$	−8.10094	+	14.0312i	−0.343556	+	0.595057i
$557$	3.87634	−	6.71401i	0.164246	−	0.284482i	−0.772141	−	0.635451i	$-0.780814\pi$
$557$	3.87634	−	6.71401i	0.164246	−	0.284482i	0.936387	+	0.350969i	$0.114148\pi$
$558$	0.261307	+	0.452597i	0.0110620	+	0.0191600i
$559$	−29.9791			−1.26798
$560$	0.161722	−	4.21803i	0.00683400	−	0.178244i
$561$	−11.9057			−0.502658
$562$	5.36897	+	9.29933i	0.226476	+	0.392269i
$563$	8.10901	−	14.0452i	0.341754	−	0.591935i	−0.643005	−	0.765862i	$-0.722312\pi$
$563$	8.10901	−	14.0452i	0.341754	−	0.591935i	0.984759	+	0.173927i	$0.0556457\pi$
$564$	−4.00838	+	6.94271i	−0.168783	+	0.292341i
$565$	−5.03849	−	8.72693i	−0.211971	−	0.367145i
$566$	−0.802068			−0.0337134
$567$	0.101365	−	2.64381i	0.00425694	−	0.111030i
$568$	−7.97461			−0.334607
$569$	12.0269	+	20.8313i	0.504196	+	0.873293i	0.999988	+	0.00485179i	$0.00154438\pi$
$569$	12.0269	+	20.8313i	0.504196	+	0.873293i	−0.495792	+	0.868441i	$0.665122\pi$
$570$	9.25319	−	16.0270i	0.387574	−	0.671297i
$571$	−21.9667	+	38.0474i	−0.919276	+	1.59223i	−0.118759	+	0.992923i	$0.537892\pi$
$571$	−21.9667	+	38.0474i	−0.919276	+	1.59223i	−0.800517	+	0.599310i	$0.795442\pi$
$572$	−16.9955	−	29.4371i	−0.710619	−	1.23083i
$573$	24.1866			1.01041
$574$	−19.0941	−	12.0222i	−0.796971	−	0.501796i
$575$	−8.84143			−0.368713
$576$	−1.94597	−	3.37051i	−0.0810819	−	0.140438i
$577$	9.02413	−	15.6303i	0.375679	−	0.650696i	−0.614749	−	0.788723i	$-0.710743\pi$
$577$	9.02413	−	15.6303i	0.375679	−	0.650696i	0.990428	+	0.138027i	$0.0440761\pi$
$578$	−2.72014	+	4.71143i	−0.113143	+	0.195969i
$579$	−6.16264	−	10.6740i	−0.256111	−	0.443597i
$580$	16.4839			0.684456
$581$	−14.0709	+	7.42010i	−0.583760	+	0.307838i
$582$	12.1731			0.504590
$583$	−13.4535	−	23.3021i	−0.557186	−	0.965075i
$584$	−12.4700	+	21.5987i	−0.516013	+	0.893761i
$585$	12.8491	−	22.2553i	0.531244	−	0.920141i
$586$	−9.18836	−	15.9147i	−0.379568	−	0.657431i
$587$	−0.826642			−0.0341192			−0.0170596	−	0.999854i	$-0.505431\pi$
$587$	−0.826642			−0.0341192			−0.0170596	+	0.999854i	$0.505431\pi$
$588$	9.28257	+	0.712847i	0.382807	+	0.0293973i
$589$	3.87997			0.159871
$590$	−8.06493	−	13.9689i	−0.332028	−	0.575089i
$591$	1.38105	−	2.39205i	0.0568089	−	0.0983958i
$592$	−1.66823	+	2.88946i	−0.0685639	+	0.118756i
$593$	0.342732	+	0.593629i	0.0140743	+	0.0243774i	0.872977	−	0.487762i	$-0.162187\pi$
$593$	0.342732	+	0.593629i	0.0140743	+	0.0243774i	−0.858902	+	0.512139i	$0.828853\pi$
$594$	−3.02865			−0.124267
$595$	28.0161	−	14.7739i	1.14855	−	0.605671i
$596$	1.33522			0.0546929
$597$	−8.29058	−	14.3597i	−0.339311	−	0.587704i
$598$	2.82698	−	4.89648i	0.115604	−	0.200232i
$599$	13.6846	−	23.7024i	0.559137	−	0.968454i	−0.438432	−	0.898764i	$-0.644466\pi$
$599$	13.6846	−	23.7024i	0.559137	−	0.968454i	0.997569	−	0.0696892i	$-0.0222007\pi$
$600$	−12.0497	−	20.8707i	−0.491928	−	0.852044i
$601$	−10.3969			−0.424096			−0.212048	−	0.977259i	$-0.568013\pi$
$601$	−10.3969			−0.424096			−0.212048	+	0.977259i	$0.568013\pi$
$602$	−7.95405	−	5.00809i	−0.324183	−	0.204115i
$603$	−4.01771			−0.163614
$604$	−1.80255	−	3.12211i	−0.0733447	−	0.127037i
$605$	−5.00451	+	8.66807i	−0.203462	+	0.352407i
$606$	1.71898	−	2.97735i	0.0698286	−	0.120947i
$607$	−7.92909	−	13.7336i	−0.321832	−	0.557429i	0.659034	−	0.752113i	$-0.270965\pi$
$607$	−7.92909	−	13.7336i	−0.321832	−	0.557429i	−0.980866	+	0.194684i	$0.937632\pi$
$608$	−35.2618			−1.43005
$609$	−0.337685	+	8.80750i	−0.0136837	+	0.356898i
$610$	−24.7117			−1.00055
$611$	−20.8177	−	36.0573i	−0.842195	−	1.45872i
$612$	−2.13976	+	3.70617i	−0.0864946	+	0.149813i
$613$	−4.24670	+	7.35551i	−0.171523	+	0.297086i	−0.938952	−	0.344047i	$-0.888202\pi$
$613$	−4.24670	+	7.35551i	−0.171523	+	0.297086i	0.767430	+	0.641133i	$0.221535\pi$
$614$	11.9515	+	20.7007i	0.482325	+	0.835411i
$615$	38.7621			1.56304
$616$	1.02230	−	26.6637i	0.0411898	−	1.07431i
$617$	−20.0404			−0.806797			−0.403399	−	0.915024i	$-0.632171\pi$
$617$	−20.0404			−0.806797			−0.403399	+	0.915024i	$0.632171\pi$
$618$	−7.14346	−	12.3728i	−0.287352	−	0.497708i
$619$	13.6695	−	23.6763i	0.549424	−	0.951630i	−0.448890	−	0.893587i	$-0.648181\pi$
$619$	13.6695	−	23.6763i	0.549424	−	0.951630i	0.998314	−	0.0580430i	$-0.0184860\pi$
$620$	1.57960	−	2.73595i	0.0634382	−	0.109878i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	−1.46677			−0.0588123
$623$	32.3084	+	20.3423i	1.29441	+	0.814996i
$624$	−2.96210			−0.118579
$625$	−4.48185	−	7.76280i	−0.179274	−	0.310512i
$626$	−3.61455	+	6.26058i	−0.144466	+	0.250223i
$627$	−11.2426	+	19.4727i	−0.448985	+	0.777665i
$628$	2.01182	+	3.48458i	0.0802805	+	0.139050i
$629$	−25.0349			−0.998206
$630$	7.12692	−	3.75828i	0.283943	−	0.149734i
$631$	−12.7286			−0.506717			−0.253358	−	0.967373i	$-0.581535\pi$
$631$	−12.7286			−0.506717			−0.253358	+	0.967373i	$0.581535\pi$
$632$	−11.1366	−	19.2891i	−0.442990	−	0.767280i
$633$	−1.37906	+	2.38861i	−0.0548128	+	0.0949386i
$634$	−8.81961	+	15.2760i	−0.350271	+	0.606688i
$635$	−12.4220	−	21.5156i	−0.492953	−	0.853820i
$636$	−9.67175			−0.383510
$637$	−27.3110	+	39.8995i	−1.08210	+	1.58088i
$638$	10.0895			0.399448
$639$	1.46283	+	2.53370i	0.0578688	+	0.100232i
$640$	−15.6616	+	27.1266i	−0.619078	+	1.07227i
$641$	−7.00976	+	12.1413i	−0.276869	+	0.479551i	−0.970605	−	0.240678i	$-0.922630\pi$
$641$	−7.00976	+	12.1413i	−0.276869	+	0.479551i	0.693736	+	0.720229i	$0.255963\pi$
$642$	−0.398720	−	0.690603i	−0.0157362	−	0.0272559i
$643$	10.2819			0.405477			0.202738	−	0.979233i	$-0.435016\pi$
$643$	10.2819			0.405477			0.202738	+	0.979233i	$0.435016\pi$
$644$	−3.11255	+	1.64136i	−0.122652	+	0.0646787i
$645$	16.1472			0.635796
$646$	−8.00293	−	13.8615i	−0.314871	−	0.545373i
$647$	−17.7597	+	30.7607i	−0.698207	+	1.20933i	0.270881	+	0.962613i	$0.412685\pi$
$647$	−17.7597	+	30.7607i	−0.698207	+	1.20933i	−0.969088	+	0.246717i	$0.920648\pi$
$648$	−1.36287	+	2.36056i	−0.0535386	+	0.0927316i
$649$	9.79884	+	16.9721i	0.384638	+	0.666213i
$650$	49.9892			1.96074
$651$	1.42948	+	0.900042i	0.0560258	+	0.0352754i
$652$	−10.2169			−0.400126
$653$	−13.7068	−	23.7409i	−0.536389	−	0.929053i	−0.999095	−	0.0425411i	$-0.986455\pi$
$653$	−13.7068	−	23.7409i	−0.536389	−	0.929053i	0.462706	−	0.886512i	$-0.346879\pi$
$654$	0.0763462	−	0.132235i	0.00298537	−	0.00517081i
$655$	−14.3348	+	24.8286i	−0.560107	+	0.970134i
$656$	−2.23396	−	3.86934i	−0.0872217	−	0.151072i
$657$	9.14983			0.356969
$658$	0.500130	−	13.0444i	0.0194971	−	0.508523i
$659$	32.7484			1.27570			0.637848	−	0.770162i	$-0.279825\pi$
$659$	32.7484			1.27570			0.637848	+	0.770162i	$0.279825\pi$
$660$	9.15406	+	15.8553i	0.356321	+	0.617167i
$661$	19.1523	−	33.1727i	0.744936	−	1.29027i	−0.205288	−	0.978702i	$-0.565813\pi$
$661$	19.1523	−	33.1727i	0.744936	−	1.29027i	0.950225	−	0.311566i	$-0.100853\pi$
$662$	9.45771	−	16.3812i	0.367584	−	0.636675i
$663$	−11.1129	−	19.2482i	−0.431591	−	0.747538i
$664$	16.3884			0.635994
$665$	2.29176	−	59.7736i	0.0888706	−	2.31792i
$666$	−6.36854			−0.246776
$667$	−1.66568	−	2.88505i	−0.0644955	−	0.111709i
$668$	3.04779	−	5.27892i	0.117922	−	0.204248i
$669$	12.9096	−	22.3601i	0.499114	−	0.864490i
$670$	−6.11759	−	10.5960i	−0.236343	−	0.409358i
$671$	30.0246			1.15909
$672$	−12.9913	−	8.17972i	−0.501152	−	0.315540i
$673$	−0.487689			−0.0187990			−0.00939951	−	0.999956i	$-0.502992\pi$
$673$	−0.487689			−0.0187990			−0.00939951	+	0.999956i	$0.502992\pi$
$674$	1.97807	+	3.42613i	0.0761926	+	0.131969i
$675$	−4.42071	+	7.65690i	−0.170153	+	0.294714i
$676$	23.0829	−	39.9807i	0.887803	−	1.53772i
$677$	23.6713	+	40.9999i	0.909763	+	1.57575i	0.814394	+	0.580313i	$0.197070\pi$
$677$	23.6713	+	40.9999i	0.909763	+	1.57575i	0.0953689	+	0.995442i	$0.469597\pi$
$678$	−2.21708			−0.0851466
$679$	34.8038	−	18.3533i	1.33565	−	0.704337i
$680$	−32.6304			−1.25132
$681$	−4.18548	−	7.24946i	−0.160388	−	0.277800i
$682$	0.966848	−	1.67463i	0.0370225	−	0.0641249i
$683$	−19.3546	+	33.5231i	−0.740582	+	1.28273i	0.211649	+	0.977346i	$0.432117\pi$
$683$	−19.3546	+	33.5231i	−0.740582	+	1.28273i	−0.952231	+	0.305380i	$0.901217\pi$
$684$	4.04116	+	6.99950i	0.154518	+	0.267632i
$685$	−75.8780			−2.89915
$686$	−13.9115	+	6.02377i	−0.531143	+	0.229988i
$687$	19.5187			0.744684
$688$	−0.930606	−	1.61186i	−0.0354790	−	0.0614515i
$689$	25.1154	−	43.5011i	0.956819	−	1.65726i
$690$	−1.52266	+	2.63732i	−0.0579666	+	0.100401i
$691$	10.9784	+	19.0152i	0.417639	+	0.723371i	0.995701	−	0.0926209i	$-0.0295245\pi$
$691$	10.9784	+	19.0152i	0.417639	+	0.723371i	−0.578063	+	0.815992i	$0.696191\pi$
$692$	26.6249			1.01213
$693$	−8.65916	+	4.56629i	−0.328934	+	0.173459i
$694$	−1.89562			−0.0719567
$695$	22.6610	+	39.2500i	0.859580	+	1.48884i
$696$	4.54022	−	7.86389i	0.172097	−	0.298080i
$697$	16.7624	−	29.0333i	0.634920	−	1.09971i
$698$	0.841223	+	1.45704i	0.0318408	+	0.0551498i
$699$	6.25868			0.236725
$700$	−26.3274	−	16.5765i	−0.995083	−	0.626533i
$701$	7.52091			0.284061			0.142031	−	0.989862i	$-0.454637\pi$
$701$	7.52091			0.284061			0.142031	+	0.989862i	$0.454637\pi$
$702$	−2.82698	−	4.89648i	−0.106698	−	0.184806i
$703$	−23.6405	+	40.9466i	−0.891619	+	1.54433i
$704$	−7.20016	+	12.4710i	−0.271366	+	0.470020i
$705$	11.2127	+	19.4211i	0.422297	+	0.731439i
$706$	−15.1954			−0.571886
$707$	0.425743	−	11.1042i	0.0160117	−	0.417617i
$708$	7.04442			0.264745
$709$	−0.346957	−	0.600947i	−0.0130302	−	0.0225690i	0.859437	−	0.511242i	$-0.170814\pi$
$709$	−0.346957	−	0.600947i	−0.0130302	−	0.0225690i	−0.872467	+	0.488673i	$0.837481\pi$
$710$	−4.45479	+	7.71593i	−0.167185	+	0.289574i
$711$	−4.08571	+	7.07666i	−0.153226	+	0.265395i
$712$	−19.6666	−	34.0636i	−0.737039	−	1.27659i
$713$	−0.638468			−0.0239108
$714$	0.266980	−	6.96338i	0.00999149	−	0.260598i
$715$	−95.0842			−3.55595
$716$	−3.13517	−	5.43028i	−0.117167	−	0.202939i
$717$	2.26938	−	3.93068i	0.0847515	−	0.146794i
$718$	−2.97708	+	5.15645i	−0.111104	+	0.192437i
$719$	4.68815	+	8.12011i	0.174838	+	0.302829i	0.940105	−	0.340884i	$-0.110726\pi$
$719$	4.68815	+	8.12011i	0.174838	+	0.302829i	−0.765267	+	0.643713i	$0.777393\pi$
$720$	1.59544			0.0594584
$721$	−39.0783	−	24.6048i	−1.45535	−	0.916331i
$722$	−14.6764			−0.546200
$723$	9.83855	+	17.0409i	0.365899	+	0.633756i
$724$	−0.778763	+	1.34886i	−0.0289425	+	0.0501299i
$725$	14.7270	−	25.5079i	0.546948	−	0.947341i
$726$	1.10107	+	1.90710i	0.0408644	+	0.0707792i
$727$	−18.9568			−0.703069			−0.351535	−	0.936175i	$-0.614340\pi$
$727$	−18.9568			−0.703069			−0.351535	+	0.936175i	$0.614340\pi$
$728$	44.0621	−	23.2356i	1.63305	−	0.861167i
$729$	1.00000			0.0370370
$730$	13.9321	+	24.1310i	0.515649	+	0.893130i
$731$	6.98272	−	12.0944i	0.258265	−	0.447329i
$732$	5.39619	−	9.34647i	0.199449	−	0.345456i
$733$	3.19807	+	5.53923i	0.118124	+	0.204596i	0.919024	−	0.394201i	$-0.128979\pi$
$733$	3.19807	+	5.53923i	0.118124	+	0.204596i	−0.800900	+	0.598797i	$0.795645\pi$
$734$	16.5671			0.611504
$735$	14.7101	−	21.4905i	0.542591	−	0.792690i
$736$	5.80250			0.213883
$737$	7.43284	+	12.8741i	0.273792	+	0.474222i
$738$	4.26412	−	7.38567i	0.156964	−	0.271870i
$739$	−14.9428	+	25.8818i	−0.549682	+	0.952076i	0.448615	+	0.893725i	$0.351918\pi$
$739$	−14.9428	+	25.8818i	−0.549682	+	0.952076i	−0.998296	+	0.0583511i	$0.981416\pi$
$740$	19.2489	+	33.3400i	0.707602	+	1.22560i
$741$	−41.9760			−1.54203
$742$	13.9306	−	7.34611i	0.511408	−	0.269684i
$743$	16.7564			0.614731			0.307366	−	0.951591i	$-0.400553\pi$
$743$	16.7564			0.614731			0.307366	+	0.951591i	$0.400553\pi$
$744$	−0.870149	−	1.50714i	−0.0319012	−	0.0552545i
$745$	1.86753	−	3.23466i	0.0684210	−	0.118509i
$746$	5.45302	−	9.44491i	0.199649	−	0.345803i
$747$	−3.00623	−	5.20695i	−0.109992	−	0.190512i
$748$	15.8344			0.578963
$749$	−2.18120	−	1.37334i	−0.0796992	−	0.0501809i
$750$	−11.6984			−0.427164
$751$	9.56890	+	16.5738i	0.349174	+	0.604787i	0.986103	−	0.166135i	$-0.0531289\pi$
$751$	9.56890	+	16.5738i	0.349174	+	0.604787i	−0.636929	+	0.770923i	$0.719796\pi$
$752$	1.29244	−	2.23857i	0.0471305	−	0.0816323i
$753$	5.15076	−	8.92137i	0.187704	−	0.325113i
$754$	9.41772	+	16.3120i	0.342973	+	0.594047i
$755$	−10.0846			−0.367018
$756$	−0.134814	+	3.51623i	−0.00490315	+	0.127884i
$757$	−43.3744			−1.57647			−0.788234	−	0.615376i	$-0.789004\pi$
$757$	−43.3744			−1.57647			−0.788234	+	0.615376i	$0.789004\pi$
$758$	3.74764	+	6.49110i	0.136120	+	0.235767i
$759$	1.85002	−	3.20433i	0.0671515	−	0.116310i
$760$	−30.8130	+	53.3697i	−1.11771	+	1.93592i
$761$	−3.08216	−	5.33845i	−0.111728	−	0.193519i	0.804739	−	0.593629i	$-0.202305\pi$
$761$	−3.08216	−	5.33845i	−0.111728	−	0.193519i	−0.916467	+	0.400110i	$0.868972\pi$
$762$	−5.46606			−0.198014
$763$	0.0189088	−	0.493180i	0.000684546	−	0.0178543i
$764$	−32.1678			−1.16379
$765$	5.98561	+	10.3674i	0.216410	+	0.374833i
$766$	3.67753	−	6.36967i	0.132875	−	0.230146i
$767$	−18.2928	+	31.6840i	−0.660514	+	1.14404i
$768$	7.33771	+	12.7093i	0.264777	+	0.458607i
$769$	2.61523			0.0943076			0.0471538	−	0.998888i	$-0.484985\pi$
$769$	2.61523			0.0943076			0.0471538	+	0.998888i	$0.484985\pi$
$770$	−25.2277	−	15.8841i	−0.909144	−	0.572423i
$771$	15.3148			0.551550
$772$	8.19623	+	14.1963i	0.294989	+	0.510936i
$773$	26.2277	−	45.4278i	0.943346	−	1.63392i	0.184318	−	0.982867i	$-0.440992\pi$
$773$	26.2277	−	45.4278i	0.943346	−	1.63392i	0.759029	−	0.651057i	$-0.225674\pi$
$774$	1.77631	−	3.07666i	0.0638482	−	0.110588i
$775$	−2.82249	−	4.88869i	−0.101387	−	0.175607i
$776$	−40.5361			−1.45516
$777$	−18.2082	+	9.60185i	−0.653215	+	0.344464i
$778$	13.4015			0.480469
$779$	−31.6575	−	54.8324i	−1.13425	−	1.96457i
$780$	−17.0891	+	29.5992i	−0.611887	+	1.05982i
$781$	5.41254	−	9.37480i	0.193676	−	0.335457i
$782$	1.31692	+	2.28097i	0.0470930	+	0.0815675i
$783$	−3.33137			−0.119053
$784$	−2.99302	−	0.229847i	−0.106894	−	0.00820881i
$785$	11.2555			0.401725
$786$	3.15387	+	5.46266i	0.112495	+	0.194847i
$787$	16.6426	−	28.8259i	0.593246	−	1.02753i	−0.400546	−	0.916277i	$-0.631180\pi$
$787$	16.6426	−	28.8259i	0.593246	−	1.02753i	0.993792	−	0.111255i	$-0.0354871\pi$
$788$	−1.83678	+	3.18139i	−0.0654325	+	0.113332i
$789$	2.65875	+	4.60509i	0.0946539	+	0.163945i
$790$	−24.8846			−0.885353
$791$	−6.33884	+	3.34270i	−0.225383	+	0.118853i
$792$	10.0853			0.358367
$793$	28.0254	+	48.5414i	0.995211	+	1.72376i
$794$	3.96376	−	6.86544i	0.140669	−	0.243645i
$795$	−13.5275	+	23.4304i	−0.479772	+	0.830990i
$796$	11.0264	+	19.0982i	0.390819	+	0.676918i
$797$	−26.0207			−0.921702			−0.460851	−	0.887477i	$-0.652456\pi$
$797$	−26.0207			−0.921702			−0.460851	+	0.887477i	$0.652456\pi$
$798$	−11.1371	−	7.01221i	−0.394248	−	0.248229i
$799$	19.3954			0.686161
$800$	25.6512	+	44.4292i	0.906906	+	1.57081i
$801$	−7.21516	+	12.4970i	−0.254935	+	0.441561i
$802$	4.69278	−	8.12814i	0.165708	−	0.287015i
$803$	−16.9274	−	29.3191i	−0.597354	−	1.03465i
$804$	5.34349			0.188450
$805$	−0.377120	+	9.83604i	−0.0132917	+	0.346675i
$806$	3.60988			0.127153
$807$	0.882323	+	1.52823i	0.0310592	+	0.0537962i
$808$	−5.72416	+	9.91454i	−0.201375	+	0.348792i
$809$	20.9252	−	36.2435i	0.735691	−	1.27425i	−0.218729	−	0.975786i	$-0.570191\pi$
$809$	20.9252	−	36.2435i	0.735691	−	1.27425i	0.954420	−	0.298468i	$-0.0964757\pi$
$810$	1.52266	+	2.63732i	0.0535008	+	0.0926660i
$811$	−17.1370			−0.601760			−0.300880	−	0.953662i	$-0.597280\pi$
$811$	−17.1370			−0.601760			−0.300880	+	0.953662i	$0.597280\pi$
$812$	0.449116	−	11.7138i	0.0157609	−	0.411075i
$813$	16.6166			0.582768
$814$	11.7819	+	20.4069i	0.412956	+	0.715261i
$815$	−14.2901	+	24.7511i	−0.500559	+	0.866994i
$816$	0.689933	−	1.19500i	0.0241525	−	0.0418333i
$817$	−13.1876	−	22.8416i	−0.461376	−	0.799127i
$818$	31.6393			1.10624
$819$	−15.4650	−	9.73722i	−0.540392	−	0.340246i
$820$	−51.5531			−1.80031
$821$	2.38038	+	4.12293i	0.0830757	+	0.143891i	0.904570	−	0.426326i	$-0.140192\pi$
$821$	2.38038	+	4.12293i	0.0830757	+	0.143891i	−0.821494	+	0.570217i	$0.806859\pi$
$822$	−8.34713	+	14.4577i	−0.291140	+	0.504269i
$823$	23.4907	−	40.6871i	0.818835	−	1.41826i	−0.0877056	−	0.996146i	$-0.527953\pi$
$823$	23.4907	−	40.6871i	0.818835	−	1.41826i	0.906541	−	0.422118i	$-0.138713\pi$
$824$	23.7876	+	41.2014i	0.828681	+	1.43532i
$825$	32.7136			1.13894
$826$	−10.1463	+	5.35054i	−0.353036	+	0.186169i
$827$	−13.3820			−0.465336			−0.232668	−	0.972556i	$-0.574746\pi$
$827$	−13.3820			−0.465336			−0.232668	+	0.972556i	$0.574746\pi$
$828$	−0.664993	−	1.15180i	−0.0231101	−	0.0400279i
$829$	0.185848	−	0.321899i	0.00645478	−	0.0111800i	−0.862780	−	0.505580i	$-0.831279\pi$
$829$	0.185848	−	0.321899i	0.00645478	−	0.0111800i	0.869235	+	0.494400i	$0.164612\pi$
$830$	9.15494	−	15.8568i	0.317772	−	0.550398i
$831$	−0.976477	−	1.69131i	−0.0338736	−	0.0586708i
$832$	−26.8829			−0.931998
$833$	−9.73537	−	20.3114i	−0.337311	−	0.703749i
$834$	9.97150			0.345285
$835$	−8.52566	−	14.7669i	−0.295043	−	0.511029i
$836$	14.9525	−	25.8984i	0.517142	−	0.895716i
$837$	−0.319234	+	0.552930i	−0.0110343	+	0.0191121i
$838$	−2.74564	−	4.75559i	−0.0948466	−	0.164279i
$839$	45.6631			1.57647			0.788233	−	0.615377i	$-0.210996\pi$
$839$	45.6631			1.57647			0.788233	+	0.615377i	$0.210996\pi$
$840$	−23.7325	+	12.5150i	−0.818850	+	0.431810i
$841$	−17.9020			−0.617310
$842$	−13.9363	−	24.1384i	−0.480277	−	0.831864i
$843$	−6.55917	+	11.3608i	−0.225910	+	0.391287i
$844$	1.83413	−	3.17681i	0.0631335	−	0.109350i
$845$	−64.5704	−	111.839i	−2.22129	−	3.84739i
$846$	4.93394			0.169632
$847$	6.02338	+	3.79249i	0.206966	+	0.130312i
$848$	3.11851			0.107090
$849$	−0.489936	−	0.848594i	−0.0168146	−	0.0291237i
$850$	−11.6435	+	20.1671i	−0.399368	+	0.691725i
$851$	3.89016	−	6.73796i	0.133353	−	0.230974i
$852$	−1.94555	−	3.36979i	−0.0666534	−	0.115447i
$853$	42.5768			1.45780			0.728901	−	0.684619i	$-0.240031\pi$
$853$	42.5768			1.45780			0.728901	+	0.684619i	$0.240031\pi$
$854$	−0.673289	+	17.5607i	−0.0230395	+	0.600915i
$855$	22.6089			0.773209
$856$	1.32773	+	2.29970i	0.0453809	+	0.0786020i
$857$	−20.6961	+	35.8467i	−0.706965	+	1.22450i	0.259012	+	0.965874i	$0.416603\pi$
$857$	−20.6961	+	35.8467i	−0.706965	+	1.22450i	−0.965978	+	0.258626i	$0.916730\pi$
$858$	−10.4600	+	18.1172i	−0.357097	+	0.618510i
$859$	26.3774	+	45.6869i	0.899984	+	1.55882i	0.827512	+	0.561448i	$0.189755\pi$
$859$	26.3774	+	45.6869i	0.899984	+	1.55882i	0.0724717	+	0.997370i	$0.476911\pi$
$860$	−21.4756			−0.732310
$861$	1.05610	−	27.5453i	0.0359919	−	0.938741i
$862$	−6.11368			−0.208233
$863$	−11.3720	−	19.6969i	−0.387109	−	0.670492i	0.604951	−	0.796263i	$-0.293193\pi$
$863$	−11.3720	−	19.6969i	−0.387109	−	0.670492i	−0.992059	+	0.125771i	$0.959859\pi$
$864$	2.90125	−	5.02511i	0.0987025	−	0.170958i
$865$	37.2393	−	64.5004i	1.26618	−	2.19308i
$866$	−10.5878	−	18.3386i	−0.359787	−	0.623170i
$867$	−6.64630			−0.225720
$868$	−1.90119	−	1.19704i	−0.0645306	−	0.0406303i
$869$	30.2346			1.02564
$870$	−5.07253	−	8.78588i	−0.171975	−	0.297869i
$871$	−13.8758	+	24.0337i	−0.470165	+	0.814350i
$872$	−0.254232	+	0.440342i	−0.00860937	+	0.0149119i
$873$	7.43580	+	12.8792i	0.251664	+	0.435895i
$874$	4.97429			0.168258
$875$	−33.4466	+	17.6376i	−1.13070	+	0.596261i
$876$	−12.1691			−0.411157
$877$	−2.64296	−	4.57774i	−0.0892464	−	0.154579i	0.817946	−	0.575294i	$-0.195113\pi$
$877$	−2.64296	−	4.57774i	−0.0892464	−	0.154579i	−0.907193	+	0.420715i	$0.861779\pi$
$878$	−6.53703	+	11.3225i	−0.220614	+	0.382115i
$879$	11.2253	−	19.4427i	0.378618	−	0.655786i
$880$	−2.95159	−	5.11230i	−0.0994980	−	0.172336i
$881$	−51.9769			−1.75115			−0.875573	−	0.483086i	$-0.839516\pi$
$881$	−51.9769			−1.75115			−0.875573	+	0.483086i	$0.839516\pi$
$882$	−2.47655	−	5.16695i	−0.0833897	−	0.173980i
$883$	13.0607			0.439526			0.219763	−	0.975553i	$-0.429472\pi$
$883$	13.0607			0.439526			0.219763	+	0.975553i	$0.429472\pi$
$884$	14.7801	+	25.5998i	0.497107	+	0.861015i
$885$	9.85278	−	17.0655i	0.331197	−	0.573651i
$886$	12.5353	−	21.7118i	0.421132	−	0.729422i
$887$	24.5844	+	42.5815i	0.825464	+	1.42975i	0.901564	+	0.432646i	$0.142420\pi$
$887$	24.5844	+	42.5815i	0.825464	+	1.42975i	−0.0760999	+	0.997100i	$0.524247\pi$
$888$	21.2071			0.711665
$889$	−15.6279	+	8.24118i	−0.524144	+	0.276400i
$890$	−43.9449			−1.47304
$891$	−1.85002	−	3.20433i	−0.0619780	−	0.107349i
$892$	−17.1696	+	29.7386i	−0.574880	+	0.995721i
$893$	18.3152	−	31.7228i	0.612894	−	1.06156i
$894$	−0.410884	−	0.711672i	−0.0137420	−	0.0238019i
$895$	−17.5402			−0.586305
$896$	18.8501	+	11.8686i	0.629738	+	0.396501i
$897$	6.90735			0.230630
$898$	−2.91640	−	5.05136i	−0.0973217	−	0.168566i
$899$	1.06349	−	1.84201i	0.0354692	−	0.0614345i
$900$	5.87949	−	10.1836i	0.195983	−	0.339452i
$901$	11.6997	+	20.2645i	0.389775	+	0.675110i
$902$	−31.5548			−1.05066
$903$	0.439943	−	11.4746i	0.0146404	−	0.381850i
$904$	7.38286			0.245550
$905$	2.17846	+	3.77320i	0.0724143	+	0.125425i
$906$	−1.10939	+	1.92151i	−0.0368569	+	0.0638379i
$907$	25.5561	−	44.2644i	0.848575	−	1.46978i	−0.0339041	−	0.999425i	$-0.510794\pi$
$907$	25.5561	−	44.2644i	0.848575	−	1.46978i	0.882480	−	0.470351i	$-0.155873\pi$
$908$	5.56663	+	9.64168i	0.184735	+	0.319970i
$909$	4.20008			0.139308
$910$	2.13223	−	55.6127i	0.0706826	−	1.84354i
$911$	10.9073			0.361376			0.180688	−	0.983540i	$-0.442168\pi$
$911$	10.9073			0.361376			0.180688	+	0.983540i	$0.442168\pi$
$912$	−1.30301	−	2.25688i	−0.0431470	−	0.0747328i
$913$	−11.1232	+	19.2659i	−0.368124	+	0.637609i
$914$	8.46584	−	14.6633i	0.280025	−	0.485018i
$915$	−15.0949	−	26.1452i	−0.499022	−	0.864332i
$916$	−25.9596			−0.857728
$917$	17.2532	+	10.8631i	0.569752	+	0.358732i
$918$	2.63384			0.0869298
$919$	17.4016	+	30.1405i	0.574027	+	0.994244i	0.996147	+	0.0877036i	$0.0279528\pi$
$919$	17.4016	+	30.1405i	0.574027	+	0.994244i	−0.422120	+	0.906540i	$0.638714\pi$
$920$	5.07043	−	8.78224i	0.167167	−	0.289542i
$921$	−14.6010	+	25.2896i	−0.481118	+	0.833322i
$922$	4.97721	+	8.62079i	0.163916	+	0.283910i
$923$	20.2086			0.665174
$924$	11.5166	−	6.07310i	0.378867	−	0.199790i
$925$	68.7892			2.26177
$926$	−0.802264	−	1.38956i	−0.0263640	−	0.0456638i
$927$	8.72703	−	15.1157i	0.286633	−	0.496464i
$928$	−9.66512	+	16.7405i	−0.317273	+	0.549533i
$929$	3.56249	+	6.17041i	0.116882	+	0.202445i	0.918530	−	0.395351i	$-0.129377\pi$
$929$	3.56249	+	6.17041i	0.116882	+	0.202445i	−0.801649	+	0.597795i	$0.796044\pi$
$930$	−1.94434			−0.0637574
$931$	−42.4141	−	3.25716i	−1.39007	−	0.106749i
$932$	−8.32396			−0.272660
$933$	−0.895965	−	1.55186i	−0.0293326	−	0.0508055i
$934$	−16.1221	+	27.9243i	−0.527532	+	0.913712i
$935$	22.1470	−	38.3597i	0.724284	−	1.25450i
$936$	9.41382	+	16.3052i	0.307700	+	0.532953i
$937$	−2.12786			−0.0695142			−0.0347571	−	0.999396i	$-0.511066\pi$
$937$	−2.12786			−0.0695142			−0.0347571	+	0.999396i	$0.511066\pi$
$938$	−7.69643	+	4.05861i	−0.251297	+	0.132518i
$939$	−8.83165			−0.288210
$940$	−14.9128	−	25.8297i	−0.486402	−	0.842473i
$941$	23.3782	−	40.4923i	0.762109	−	1.32001i	−0.179653	−	0.983730i	$-0.557497\pi$
$941$	23.3782	−	40.4923i	0.762109	−	1.32001i	0.941762	−	0.336281i	$-0.109169\pi$
$942$	1.23818	−	2.14460i	0.0403422	−	0.0698748i
$943$	5.20940	+	9.02294i	0.169641	+	0.293827i
$944$	−2.27137			−0.0739267
$945$	8.32970	+	5.24462i	0.270965	+	0.170607i
$946$	−13.1448			−0.427376
$947$	−14.9787	−	25.9439i	−0.486744	−	0.843065i	0.513140	−	0.858305i	$-0.328482\pi$
$947$	−14.9787	−	25.9439i	−0.486744	−	0.843065i	−0.999884	+	0.0152402i	$0.995149\pi$
$948$	5.43394	−	9.41186i	0.176486	−	0.305683i
$949$	31.6005	−	54.7337i	1.02580	−	1.77673i
$950$	21.9899	+	38.0877i	0.713447	+	1.23573i
$951$	−21.5495			−0.698791
$952$	−0.889041	+	23.1879i	−0.0288140	+	0.751526i
$953$	60.6214			1.96372			0.981860	−	0.189605i	$-0.0607207\pi$
$953$	60.6214			1.96372			0.981860	+	0.189605i	$0.0607207\pi$
$954$	2.97626	+	5.15503i	0.0963598	+	0.166900i
$955$	−44.9919	+	77.9283i	−1.45590	+	2.52170i
$956$	−3.01824	+	5.22775i	−0.0976169	+	0.169077i
$957$	6.16310	+	10.6748i	0.199225	+	0.345067i
$958$	2.31428			0.0747711
$959$	−2.06735	+	53.9207i	−0.0667583	+	1.74119i
$960$	14.4796			0.467326
$961$	15.2962	+	26.4938i	0.493425	+	0.854637i
$962$	−21.9949	+	38.0962i	−0.709142	+	1.22827i
$963$	0.487108	−	0.843697i	0.0156968	−	0.0271877i
$964$	−13.0851	−	22.6641i	−0.421444	−	0.729962i
$965$	45.8551			1.47613
$966$	1.83266	+	1.15389i	0.0589648	+	0.0371259i
$967$	6.34634			0.204084			0.102042	−	0.994780i	$-0.467462\pi$
$967$	6.34634			0.204084			0.102042	+	0.994780i	$0.467462\pi$
$968$	−3.66653	−	6.35062i	−0.117847	−	0.204117i
$969$	9.77703	−	16.9343i	0.314084	−	0.544009i
$970$	−22.6444	+	39.2212i	−0.727067	+	1.25932i
$971$	15.6672	+	27.1364i	0.502784	+	0.870847i	0.999995	+	0.00321760i	$0.00102420\pi$
$971$	15.6672	+	27.1364i	0.502784	+	0.870847i	−0.497211	+	0.867630i	$0.665642\pi$
$972$	−1.32999			−0.0426593
$973$	28.5094	−	15.0340i	0.913969	−	0.481969i
$974$	20.2875			0.650052
$975$	30.5354	+	52.8889i	0.977916	+	1.69380i
$976$	−1.73992	+	3.01363i	−0.0556935	+	0.0964639i
$977$	8.82750	−	15.2897i	0.282417	−	0.489160i	−0.689563	−	0.724226i	$-0.742197\pi$
$977$	8.82750	−	15.2897i	0.282417	−	0.489160i	0.971979	+	0.235066i	$0.0755306\pi$
$978$	3.14403	+	5.44561i	0.100535	+	0.174131i
$979$	53.3928			1.70644
$980$	−19.5642	+	28.5821i	−0.624957	+	0.913021i
$981$	0.186541			0.00595581
$982$	5.37604	+	9.31157i	0.171556	+	0.297144i
$983$	−1.70377	+	2.95102i	−0.0543420	+	0.0941230i	−0.891917	−	0.452200i	$-0.850639\pi$
$983$	−1.70377	+	2.95102i	−0.0543420	+	0.0941230i	0.837575	+	0.546323i	$0.183973\pi$
$984$	−14.1995	+	24.5942i	−0.452662	+	0.784034i
$985$	5.13807	+	8.89940i	0.163713	+	0.283559i
$986$	−8.77430			−0.279431
$987$	14.1066	−	7.43890i	0.449017	−	0.236783i
$988$	55.8274			1.77611
$989$	2.17009	+	3.75870i	0.0690047	+	0.119520i
$990$	5.63390	−	9.75820i	0.179057	−	0.310136i
$991$	−0.526481	+	0.911892i	−0.0167242	+	0.0289672i	−0.874266	−	0.485446i	$-0.838657\pi$
$991$	−0.526481	+	0.911892i	−0.0167242	+	0.0289672i	0.857542	+	0.514414i	$0.171990\pi$
$992$	1.85236	+	3.20838i	0.0588124	+	0.101866i
$993$	23.1086			0.733330
$994$	5.36174	+	3.37591i	0.170064	+	0.107077i
$995$	61.6887			1.95566
$996$	3.99825	+	6.92517i	0.126689	+	0.219432i
$997$	27.4735	−	47.5855i	0.870095	−	1.50705i	0.00819818	−	0.999966i	$-0.497390\pi$
$997$	27.4735	−	47.5855i	0.870095	−	1.50705i	0.861897	−	0.507083i	$-0.169276\pi$
$998$	6.74521	−	11.6830i	0.213516	−	0.369820i
$999$	−3.89016	−	6.73796i	−0.123079	−	0.213180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.g.277.5	✓	16
7.2	even	3	inner	483.2.i.g.415.5	yes	16
7.3	odd	6		3381.2.a.be.1.4		8
7.4	even	3		3381.2.a.bf.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.5	✓	16	1.1	even	1	trivial
483.2.i.g.415.5	yes	16	7.2	even	3	inner
3381.2.a.be.1.4		8	7.3	odd	6
3381.2.a.bf.1.4		8	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.409272 + 0.708880i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.664993 - 1.15180i) q^{4} +(-1.86020 - 3.22197i) q^{5} -0.818544 q^{6} +(-2.34029 + 1.23412i) q^{7} +2.72574 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.409272 + 0.708880i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.664993 - 1.15180i) q^{4} +(-1.86020 - 3.22197i) q^{5} -0.818544 q^{6} +(-2.34029 + 1.23412i) q^{7} +2.72574 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.52266 - 2.63732i) q^{10} +(-1.85002 + 3.20433i) q^{11} +(0.664993 + 1.15180i) q^{12} -6.90735 q^{13} +(-1.83266 - 1.15389i) q^{14} +3.72041 q^{15} +(-0.214417 - 0.371381i) q^{16} +(1.60886 - 2.78662i) q^{17} +(0.409272 - 0.708880i) q^{18} +(-3.03850 - 5.26284i) q^{19} -4.94809 q^{20} +(0.101365 - 2.64381i) q^{21} -3.02865 q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.36287 + 2.36056i) q^{24} +(-4.42071 + 7.65690i) q^{25} +(-2.82698 - 4.89648i) q^{26} +1.00000 q^{27} +(-0.134814 + 3.51623i) q^{28} -3.33137 q^{29} +(1.52266 + 2.63732i) q^{30} +(-0.319234 + 0.552930i) q^{31} +(2.90125 - 5.02511i) q^{32} +(-1.85002 - 3.20433i) q^{33} +2.63384 q^{34} +(8.32970 + 5.24462i) q^{35} -1.32999 q^{36} +(-3.89016 - 6.73796i) q^{37} +(2.48715 - 4.30786i) q^{38} +(3.45367 - 5.98194i) q^{39} +(-5.07043 - 8.78224i) q^{40} +10.4188 q^{41} +(1.91563 - 1.01018i) q^{42} +4.34017 q^{43} +(2.46050 + 4.26171i) q^{44} +(-1.86020 + 3.22197i) q^{45} +(-0.409272 + 0.708880i) q^{46} +(3.01385 + 5.22014i) q^{47} +0.428834 q^{48} +(3.95390 - 5.77639i) q^{49} -7.23710 q^{50} +(1.60886 + 2.78662i) q^{51} +(-4.59334 + 7.95589i) q^{52} +(-3.63604 + 6.29780i) q^{53} +(0.409272 + 0.708880i) q^{54} +13.7657 q^{55} +(-6.37902 + 3.36389i) q^{56} +6.07700 q^{57} +(-1.36343 - 2.36154i) q^{58} +(2.64831 - 4.58700i) q^{59} +(2.47404 - 4.28517i) q^{60} +(-4.05733 - 7.02750i) q^{61} -0.522615 q^{62} +(2.23892 + 1.40969i) q^{63} +3.89193 q^{64} +(12.8491 + 22.2553i) q^{65} +(1.51432 - 2.62288i) q^{66} +(2.00885 - 3.47943i) q^{67} +(-2.13976 - 3.70617i) q^{68} -1.00000 q^{69} +(-0.308690 + 8.05123i) q^{70} -2.92567 q^{71} +(-1.36287 - 2.36056i) q^{72} +(-4.57491 + 7.92398i) q^{73} +(3.18427 - 5.51531i) q^{74} +(-4.42071 - 7.65690i) q^{75} -8.08232 q^{76} +(0.375056 - 9.78220i) q^{77} +5.65397 q^{78} +(-4.08571 - 7.07666i) q^{79} +(-0.797718 + 1.38169i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.26412 + 7.38567i) q^{82} +6.01247 q^{83} +(-2.97774 - 1.87487i) q^{84} -11.9712 q^{85} +(1.77631 + 3.07666i) q^{86} +(1.66568 - 2.88505i) q^{87} +(-5.04267 + 8.73417i) q^{88} +(-7.21516 - 12.4970i) q^{89} -3.04532 q^{90} +(16.1652 - 8.52449i) q^{91} +1.32999 q^{92} +(-0.319234 - 0.552930i) q^{93} +(-2.46697 + 4.27292i) q^{94} +(-11.3045 + 19.5799i) q^{95} +(2.90125 + 5.02511i) q^{96} -14.8716 q^{97} +(5.71299 + 0.438724i) q^{98} +3.70004 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

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