LMFDB - Embedded newform 99.2.g.b.32.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(32,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 15x^{14} + 150x^{12} + 837x^{10} + 3372x^{8} + 8010x^{6} + 13761x^{4} + 13392x^{2} + 8649 $ x^16 + 15x^14 + 150x^12 + 837x^10 + 3372x^8 + 8010x^6 + 13761x^4 + 13392*x^2 + 8649
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			32.3
Root			$-0.679041 - 1.17613i$ of defining polynomial
Character	$\chi$	$=$	99.32
Dual form			99.2.g.b.65.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.679041 - 1.17613i) q^{2} +(-0.323333 - 1.70160i) q^{3} +(0.0778064 - 0.134765i) q^{4} +(0.901139 + 0.520273i) q^{5} +(-1.78176 + 1.53574i) q^{6} +(0.600962 - 0.346965i) q^{7} -2.92750 q^{8} +(-2.79091 + 1.10037i) q^{9} +O(q^{10})$	\(q+(-0.679041 - 1.17613i) q^{2} +(-0.323333 - 1.70160i) q^{3} +(0.0778064 - 0.134765i) q^{4} +(0.901139 + 0.520273i) q^{5} +(-1.78176 + 1.53574i) q^{6} +(0.600962 - 0.346965i) q^{7} -2.92750 q^{8} +(-2.79091 + 1.10037i) q^{9} -1.41315i q^{10} +(-2.59932 - 2.05998i) q^{11} +(-0.254473 - 0.0888218i) q^{12} +(5.22645 + 3.01749i) q^{13} +(-0.816155 - 0.471208i) q^{14} +(0.593931 - 1.70160i) q^{15} +(1.83228 + 3.17360i) q^{16} +3.56351 q^{17} +(3.18933 + 2.53529i) q^{18} -2.26957i q^{19} +(0.140229 - 0.0809611i) q^{20} +(-0.784709 - 0.910413i) q^{21} +(-0.657769 + 4.45596i) q^{22} +(4.37840 + 2.52787i) q^{23} +(0.946557 + 4.98144i) q^{24} +(-1.95863 - 3.39245i) q^{25} -8.19600i q^{26} +(2.77479 + 4.39324i) q^{27} -0.107984i q^{28} +(1.54183 + 2.67053i) q^{29} +(-2.40462 + 0.456917i) q^{30} +(0.0574924 - 0.0995797i) q^{31} +(-0.439113 + 0.760566i) q^{32} +(-2.66483 + 5.08908i) q^{33} +(-2.41977 - 4.19117i) q^{34} +0.722067 q^{35} +(-0.0688598 + 0.461732i) q^{36} -0.416697 q^{37} +(-2.66932 + 1.54113i) q^{38} +(3.44469 - 9.86900i) q^{39} +(-2.63809 - 1.52310i) q^{40} +(1.90286 - 3.29585i) q^{41} +(-0.537919 + 1.54113i) q^{42} +(-7.79291 + 4.49924i) q^{43} +(-0.479856 + 0.190017i) q^{44} +(-3.08749 - 0.460450i) q^{45} -6.86612i q^{46} +(3.70818 - 2.14092i) q^{47} +(4.80778 - 4.14394i) q^{48} +(-3.25923 + 5.64515i) q^{49} +(-2.65998 + 4.60723i) q^{50} +(-1.15220 - 6.06369i) q^{51} +(0.813302 - 0.469560i) q^{52} +6.94682i q^{53} +(3.28284 - 6.24671i) q^{54} +(-1.27060 - 3.20869i) q^{55} +(-1.75932 + 1.01574i) q^{56} +(-3.86191 + 0.733827i) q^{57} +(2.09393 - 3.62679i) q^{58} +(-8.91065 - 5.14457i) q^{59} +(-0.183104 - 0.212436i) q^{60} +(-11.4785 + 6.62714i) q^{61} -0.156159 q^{62} +(-1.29544 + 1.62963i) q^{63} +8.52182 q^{64} +(3.13984 + 5.43836i) q^{65} +(7.79496 - 0.321498i) q^{66} +(6.23818 - 10.8048i) q^{67} +(0.277264 - 0.480235i) q^{68} +(2.88576 - 8.26766i) q^{69} +(-0.490313 - 0.849247i) q^{70} +5.48430i q^{71} +(8.17039 - 3.22133i) q^{72} +9.05590i q^{73} +(0.282954 + 0.490091i) q^{74} +(-5.13932 + 4.42971i) q^{75} +(-0.305857 - 0.176587i) q^{76} +(-2.27684 - 0.336096i) q^{77} +(-13.9464 + 2.65004i) q^{78} +(-0.482139 + 0.278363i) q^{79} +3.81314i q^{80} +(6.57837 - 6.14207i) q^{81} -5.16849 q^{82} +(5.98357 + 10.3638i) q^{83} +(-0.183747 + 0.0349149i) q^{84} +(3.21122 + 1.85400i) q^{85} +(10.5834 + 6.11034i) q^{86} +(4.04565 - 3.48705i) q^{87} +(7.60951 + 6.03060i) q^{88} +6.48257i q^{89} +(1.55498 + 3.94397i) q^{90} +4.18786 q^{91} +(0.681335 - 0.393369i) q^{92} +(-0.188034 - 0.0656318i) q^{93} +(-5.03601 - 2.90754i) q^{94} +(1.18080 - 2.04520i) q^{95} +(1.43616 + 0.501280i) q^{96} +(-5.39453 - 9.34360i) q^{97} +8.85260 q^{98} +(9.52122 + 2.88901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9}+O(q^{10}) $ 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9	$ 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9} - 12 q^{11} + 12 q^{12} - 6 q^{14} - 30 q^{15} - 2 q^{16} + 36 q^{20} + 6 q^{22} + 12 q^{23} - 12 q^{25} + 18 q^{27} - 4 q^{31} + 18 q^{33} - 18 q^{36} - 28 q^{37} + 66 q^{38} - 54 q^{42} - 42 q^{45} - 30 q^{47} + 42 q^{48} + 10 q^{49} + 20 q^{55} - 120 q^{56} - 6 q^{58} - 36 q^{59} + 30 q^{60} + 40 q^{64} + 54 q^{66} + 8 q^{67} + 96 q^{69} + 24 q^{75} + 72 q^{77} - 42 q^{78} + 30 q^{81} + 12 q^{82} - 72 q^{86} - 6 q^{88} - 12 q^{91} + 18 q^{92} - 24 q^{93} - 4 q^{97} - 36 q^{99}+O(q^{100}) $ 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9 - 12 * q^11 + 12 * q^12 - 6 * q^14 - 30 * q^15 - 2 * q^16 + 36 * q^20 + 6 * q^22 + 12 * q^23 - 12 * q^25 + 18 * q^27 - 4 * q^31 + 18 * q^33 - 18 * q^36 - 28 * q^37 + 66 * q^38 - 54 * q^42 - 42 * q^45 - 30 * q^47 + 42 * q^48 + 10 * q^49 + 20 * q^55 - 120 * q^56 - 6 * q^58 - 36 * q^59 + 30 * q^60 + 40 * q^64 + 54 * q^66 + 8 * q^67 + 96 * q^69 + 24 * q^75 + 72 * q^77 - 42 * q^78 + 30 * q^81 + 12 * q^82 - 72 * q^86 - 6 * q^88 - 12 * q^91 + 18 * q^92 - 24 * q^93 - 4 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.679041	−	1.17613i	−0.480155	−	0.831652i	0.519586	−	0.854418i	$-0.326086\pi$
$2$	−0.679041	−	1.17613i	−0.480155	−	0.831652i	−0.999741	+	0.0227659i	$0.992753\pi$
$3$	−0.323333	−	1.70160i	−0.186676	−	0.982421i
$3$	−0.323333	−	1.70160i	−0.186676	−	0.982421i
$4$	0.0778064	−	0.134765i	0.0389032	−	0.0673823i
$5$	0.901139	+	0.520273i	0.403002	+	0.232673i	0.687778	−	0.725921i	$-0.258586\pi$
$5$	0.901139	+	0.520273i	0.403002	+	0.232673i	−0.284777	+	0.958594i	$0.591919\pi$
$6$	−1.78176	+	1.53574i	−0.727399	+	0.626964i
$7$	0.600962	−	0.346965i	0.227142	−	0.131141i	−0.382111	−	0.924117i	$-0.624803\pi$
$7$	0.600962	−	0.346965i	0.227142	−	0.131141i	0.609253	+	0.792976i	$0.291469\pi$
$8$	−2.92750			−1.03503
$9$	−2.79091	+	1.10037i	−0.930304	+	0.366790i
$10$		−	1.41315i		−	0.446876i
$11$	−2.59932	−	2.05998i	−0.783725	−	0.621108i
$11$	−2.59932	−	2.05998i	−0.783725	−	0.621108i
$12$	−0.254473	−	0.0888218i	−0.0734601	−	0.0256406i
$13$	5.22645	+	3.01749i	1.44956	+	0.836902i	0.998455	−	0.0555712i	$-0.0176980\pi$
$13$	5.22645	+	3.01749i	1.44956	+	0.836902i	0.451101	+	0.892473i	$0.351031\pi$
$14$	−0.816155	−	0.471208i	−0.218127	−	0.125936i
$15$	0.593931	−	1.70160i	0.153352	−	0.439352i
$16$	1.83228	+	3.17360i	0.458070	+	0.793400i
$17$	3.56351			0.864279			0.432140	−	0.901807i	$-0.357759\pi$
$17$	3.56351			0.864279			0.432140	+	0.901807i	$0.357759\pi$
$18$	3.18933	+	2.53529i	0.751731	+	0.597573i
$19$		−	2.26957i		−	0.520675i	−0.965518	−	0.260337i	$-0.916166\pi$
$19$		−	2.26957i		−	0.520675i	0.965518	−	0.260337i	$-0.0838338\pi$
$20$	0.140229	−	0.0809611i	0.0313561	−	0.0181035i
$21$	−0.784709	−	0.910413i	−0.171237	−	0.198668i
$22$	−0.657769	+	4.45596i	−0.140237	+	0.950014i
$23$	4.37840	+	2.52787i	0.912960	+	0.527098i	0.881382	−	0.472403i	$-0.156613\pi$
$23$	4.37840	+	2.52787i	0.912960	+	0.527098i	0.0315780	+	0.999501i	$0.489947\pi$
$24$	0.946557	+	4.98144i	0.193215	+	1.01683i
$25$	−1.95863	−	3.39245i	−0.391726	−	0.678490i
$26$		−	8.19600i		−	1.60737i
$27$	2.77479	+	4.39324i	0.534008	+	0.845479i
$28$		−	0.107984i		−	0.0204071i
$29$	1.54183	+	2.67053i	0.286310	+	0.495904i	0.972926	−	0.231116i	$-0.0742378\pi$
$29$	1.54183	+	2.67053i	0.286310	+	0.495904i	−0.686616	+	0.727021i	$0.740904\pi$
$30$	−2.40462	+	0.456917i	−0.439021	+	0.0834213i
$31$	0.0574924	−	0.0995797i	0.0103259	−	0.0178850i	−0.860816	−	0.508916i	$-0.830046\pi$
$31$	0.0574924	−	0.0995797i	0.0103259	−	0.0178850i	0.871142	+	0.491031i	$0.163380\pi$
$32$	−0.439113	+	0.760566i	−0.0776249	+	0.134450i
$33$	−2.66483	+	5.08908i	−0.463887	+	0.885894i
$34$	−2.41977	−	4.19117i	−0.414988	−	0.718780i
$35$	0.722067			0.122052
$36$	−0.0688598	+	0.461732i	−0.0114766	+	0.0769553i
$37$	−0.416697			−0.0685045			−0.0342523	−	0.999413i	$-0.510905\pi$
$37$	−0.416697			−0.0685045			−0.0342523	+	0.999413i	$0.510905\pi$
$38$	−2.66932	+	1.54113i	−0.433020	+	0.250004i
$39$	3.44469	−	9.86900i	0.551592	−	1.58030i
$40$	−2.63809	−	1.52310i	−0.417118	−	0.240823i
$41$	1.90286	−	3.29585i	0.297177	−	0.514726i	−0.678312	−	0.734774i	$-0.737288\pi$
$41$	1.90286	−	3.29585i	0.297177	−	0.514726i	0.975489	+	0.220048i	$0.0706215\pi$
$42$	−0.537919	+	1.54113i	−0.0830026	+	0.237802i
$43$	−7.79291	+	4.49924i	−1.18841	+	0.686128i	−0.957945	−	0.286953i	$-0.907358\pi$
$43$	−7.79291	+	4.49924i	−1.18841	+	0.686128i	−0.230464	+	0.973081i	$0.574024\pi$
$44$	−0.479856	+	0.190017i	−0.0723411	+	0.0286461i
$45$	−3.08749	−	0.460450i	−0.460256	−	0.0686398i
$46$		−	6.86612i		−	1.01235i
$47$	3.70818	−	2.14092i	0.540893	−	0.312285i	−0.204548	−	0.978857i	$-0.565572\pi$
$47$	3.70818	−	2.14092i	0.540893	−	0.312285i	0.745441	+	0.666572i	$0.232239\pi$
$48$	4.80778	−	4.14394i	0.693943	−	0.598127i
$49$	−3.25923	+	5.64515i	−0.465604	+	0.806450i
$50$	−2.65998	+	4.60723i	−0.376178	+	0.651560i
$51$	−1.15220	−	6.06369i	−0.161341	−	0.849086i
$52$	0.813302	−	0.469560i	0.112785	−	0.0651163i
$53$			6.94682i			0.954219i	0.878844	+	0.477110i	$0.158316\pi$
$53$			6.94682i			0.954219i	−0.878844	+	0.477110i	$0.841684\pi$
$54$	3.28284	−	6.24671i	0.446738	−	0.850070i
$55$	−1.27060	−	3.20869i	−0.171327	−	0.432659i
$56$	−1.75932	+	1.01574i	−0.235098	+	0.135734i
$57$	−3.86191	+	0.733827i	−0.511522	+	0.0971977i
$58$	2.09393	−	3.62679i	0.274947	−	0.476221i
$59$	−8.91065	−	5.14457i	−1.16007	−	0.669766i	−0.208748	−	0.977969i	$-0.566939\pi$
$59$	−8.91065	−	5.14457i	−1.16007	−	0.669766i	−0.951320	+	0.308204i	$0.900272\pi$
$60$	−0.183104	−	0.212436i	−0.0236387	−	0.0274254i
$61$	−11.4785	+	6.62714i	−1.46968	+	0.848518i	−0.999421	−	0.0340126i	$-0.989171\pi$
$61$	−11.4785	+	6.62714i	−1.46968	+	0.848518i	−0.470255	+	0.882531i	$0.655838\pi$
$62$	−0.156159			−0.0198322
$63$	−1.29544	+	1.62963i	−0.163210	+	0.205314i
$64$	8.52182			1.06523
$65$	3.13984	+	5.43836i	0.389449	+	0.674546i
$66$	7.79496	−	0.321498i	0.959493	−	0.0395736i
$67$	6.23818	−	10.8048i	0.762114	−	1.32002i	−0.179644	−	0.983732i	$-0.557495\pi$
$67$	6.23818	−	10.8048i	0.762114	−	1.32002i	0.941759	−	0.336289i	$-0.109172\pi$
$68$	0.277264	−	0.480235i	0.0336232	−	0.0582371i
$69$	2.88576	−	8.26766i	0.347404	−	0.995309i
$70$	−0.490313	−	0.849247i	−0.0586036	−	0.101504i
$71$			5.48430i			0.650867i	0.945565	+	0.325433i	$0.105510\pi$
$71$			5.48430i			0.650867i	−0.945565	+	0.325433i	$0.894490\pi$
$72$	8.17039	−	3.22133i	0.962890	−	0.379638i
$73$			9.05590i			1.05991i	0.848025	+	0.529956i	$0.177792\pi$
$73$			9.05590i			1.05991i	−0.848025	+	0.529956i	$0.822208\pi$
$74$	0.282954	+	0.490091i	0.0328928	+	0.0569719i
$75$	−5.13932	+	4.42971i	−0.593437	+	0.511498i
$76$	−0.305857	−	0.176587i	−0.0350843	−	0.0202559i
$77$	−2.27684	−	0.336096i	−0.259469	−	0.0383017i
$78$	−13.9464	+	2.65004i	−1.57911	+	0.300058i
$79$	−0.482139	+	0.278363i	−0.0542449	+	0.0313183i	−0.526877	−	0.849941i	$-0.676637\pi$
$79$	−0.482139	+	0.278363i	−0.0542449	+	0.0313183i	0.472632	+	0.881260i	$0.343304\pi$
$80$			3.81314i			0.426322i
$81$	6.57837	−	6.14207i	0.730930	−	0.682452i
$82$	−5.16849			−0.570764
$83$	5.98357	+	10.3638i	0.656782	+	1.13758i	0.981444	+	0.191750i	$0.0614162\pi$
$83$	5.98357	+	10.3638i	0.656782	+	1.13758i	−0.324662	+	0.945830i	$0.605250\pi$
$84$	−0.183747	+	0.0349149i	−0.0200484	+	0.00380953i
$85$	3.21122	+	1.85400i	0.348306	+	0.201095i
$86$	10.5834	+	6.11034i	1.14124	+	0.658895i
$87$	4.04565	−	3.48705i	0.433740	−	0.373851i
$88$	7.60951	+	6.03060i	0.811177	+	0.642864i
$89$			6.48257i			0.687151i	0.939125	+	0.343576i	$0.111638\pi$
$89$			6.48257i			0.687151i	−0.939125	+	0.343576i	$0.888362\pi$
$90$	1.55498	+	3.94397i	0.163910	+	0.415731i
$91$	4.18786			0.439007
$92$	0.681335	−	0.393369i	0.0710341	−	0.0410116i
$93$	−0.188034	−	0.0656318i	−0.0194983	−	0.00680570i
$94$	−5.03601	−	2.90754i	−0.519424	−	0.299890i
$95$	1.18080	−	2.04520i	0.121147	−	0.209833i
$96$	1.43616	+	0.501280i	0.146578	+	0.0511617i
$97$	−5.39453	−	9.34360i	−0.547731	−	0.948699i	−0.998430	−	0.0560222i	$-0.982158\pi$
$97$	−5.39453	−	9.34360i	−0.547731	−	0.948699i	0.450698	−	0.892676i	$-0.351175\pi$
$98$	8.85260			0.894248
$99$	9.52122	+	2.88901i	0.956918	+	0.290357i
$100$	−0.609576			−0.0609576
$101$	−6.25109	−	10.8272i	−0.622006	−	1.07735i	−0.989112	−	0.147167i	$-0.952985\pi$
$101$	−6.25109	−	10.8272i	−0.622006	−	1.07735i	0.367105	−	0.930179i	$-0.380349\pi$
$102$	−6.34932	+	5.47264i	−0.628676	+	0.541872i
$103$	−5.46339	+	9.46287i	−0.538324	+	0.932404i	0.460671	+	0.887571i	$0.347609\pi$
$103$	−5.46339	+	9.46287i	−0.538324	+	0.932404i	−0.998995	+	0.0448329i	$0.985724\pi$
$104$	−15.3004	−	8.83370i	−1.50033	−	0.866216i
$105$	−0.233468	−	1.22867i	−0.0227842	−	0.119906i
$106$	8.17039	−	4.71718i	0.793579	−	0.458173i
$107$	−0.424680			−0.0410554			−0.0205277	−	0.999789i	$-0.506535\pi$
$107$	−0.424680			−0.0410554			−0.0205277	+	0.999789i	$0.506535\pi$
$108$	0.807949	−	0.0321210i	0.0777449	−	0.00309085i
$109$		−	3.07148i		−	0.294195i	−0.989122	−	0.147097i	$-0.953007\pi$
$109$		−	3.07148i		−	0.294195i	0.989122	−	0.147097i	$-0.0469931\pi$
$110$	−2.91106	+	3.67322i	−0.277559	+	0.350228i
$111$	0.134732	+	0.709053i	0.0127882	+	0.0673003i
$112$	2.20226	+	1.27148i	0.208094	+	0.120143i
$113$	−7.91159	−	4.56776i	−0.744260	−	0.429699i	0.0793561	−	0.996846i	$-0.474714\pi$
$113$	−7.91159	−	4.56776i	−0.744260	−	0.429699i	−0.823616	+	0.567148i	$0.808047\pi$
$114$	3.48547	+	4.04382i	0.326444	+	0.378738i
$115$	2.63037	+	4.55593i	0.245283	+	0.424843i
$116$	0.479856			0.0445535
$117$	−17.9069	−	2.67053i	−1.65549	−	0.246890i
$118$			13.9735i			1.28636i
$119$	2.14154	−	1.23642i	0.196314	−	0.113342i
$120$	−1.73873	+	4.98144i	−0.158724	+	0.454742i
$121$	2.51294	+	10.7091i	0.228449	+	0.973556i
$122$	15.5888	+	9.00020i	1.41134	+	0.814840i
$123$	−6.22350	−	2.17226i	−0.561154	−	0.195866i
$124$	−0.00894654	−	0.0154959i	−0.000803423	−	0.00139157i
$125$		−	9.27882i		−	0.829923i
$126$	2.79632	+	0.417026i	0.249116	+	0.0371516i
$127$		−	12.9293i		−	1.14729i	−0.819104	−	0.573645i	$-0.805529\pi$
$127$		−	12.9293i		−	1.14729i	0.819104	−	0.573645i	$-0.194471\pi$
$128$	−4.90844	−	8.50167i	−0.433849	−	0.751449i
$129$	10.1756	+	11.8057i	0.895915	+	1.03943i
$130$	4.26416	−	7.38574i	0.373992	−	0.647772i
$131$	−1.72558	+	2.98878i	−0.150764	+	0.261131i	−0.931509	−	0.363719i	$-0.881507\pi$
$131$	−1.72558	+	2.98878i	−0.150764	+	0.261131i	0.780744	+	0.624851i	$0.214840\pi$
$132$	0.478487	+	0.755087i	0.0416469	+	0.0657219i
$133$	−0.787462	−	1.36392i	−0.0682816	−	0.118267i
$134$	−16.9439			−1.46373
$135$	0.214786	+	5.40257i	0.0184858	+	0.464979i
$136$	−10.4322			−0.894553
$137$	13.7050	−	7.91259i	1.17090	−	0.676018i	0.217007	−	0.976170i	$-0.430371\pi$
$137$	13.7050	−	7.91259i	1.17090	−	0.676018i	0.953892	+	0.300152i	$0.0970373\pi$
$138$	−11.6834	+	2.22004i	−0.994558	+	0.188983i
$139$	−12.5616	−	7.25247i	−1.06546	−	0.615146i	−0.138526	−	0.990359i	$-0.544236\pi$
$139$	−12.5616	−	7.25247i	−1.06546	−	0.615146i	−0.926939	+	0.375213i	$0.877570\pi$
$140$	0.0561814	−	0.0973091i	0.00474820	−	0.00822412i
$141$	−4.84197	−	5.61762i	−0.407767	−	0.473089i
$142$	6.45027	−	3.72407i	0.541295	−	0.312517i
$143$	−7.36924	−	18.6098i	−0.616247	−	1.55623i
$144$	−8.60586	−	6.84106i	−0.717155	−	0.570088i
$145$			3.20869i			0.266467i
$146$	10.6509	−	6.14933i	0.881478	−	0.508922i
$147$	10.6596	+	3.72065i	0.879191	+	0.306874i
$148$	−0.0324217	+	0.0561560i	−0.00266504	+	0.00461599i
$149$	4.86542	−	8.42715i	0.398590	−	0.690379i	−0.594962	−	0.803754i	$-0.702833\pi$
$149$	4.86542	−	8.42715i	0.398590	−	0.690379i	0.993552	+	0.113375i	$0.0361662\pi$
$150$	8.69973	+	3.03657i	0.710330	+	0.247935i
$151$	18.3891	−	10.6169i	1.49648	−	0.863993i	0.496488	−	0.868044i	$-0.334623\pi$
$151$	18.3891	−	10.6169i	1.49648	−	0.863993i	0.999992	+	0.00405067i	$0.00128937\pi$
$152$			6.64416i			0.538913i
$153$	−9.94545	+	3.92118i	−0.804042	+	0.317009i
$154$	1.15077	+	2.90609i	0.0927318	+	0.234179i
$155$	0.103617	−	0.0598235i	0.00832274	−	0.00480514i
$156$	−1.06197	−	1.23209i	−0.0850259	−	0.0986464i
$157$	−2.88726	+	5.00089i	−0.230429	+	0.399114i	−0.957934	−	0.286988i	$-0.907346\pi$
$157$	−2.88726	+	5.00089i	−0.230429	+	0.399114i	0.727506	+	0.686102i	$0.240680\pi$
$158$	0.654784	+	0.378040i	0.0520918	+	0.0300752i
$159$	11.8207	−	2.24614i	0.937446	−	0.178130i
$160$	−0.791404	+	0.456917i	−0.0625660	+	0.0361225i
$161$	3.50834			0.276496
$162$	−11.6909	−	3.56633i	−0.918522	−	0.280197i
$163$	−9.98530			−0.782109			−0.391054	−	0.920368i	$-0.627890\pi$
$163$	−9.98530			−0.782109			−0.391054	+	0.920368i	$0.627890\pi$
$164$	−0.296110	−	0.512877i	−0.0231223	−	0.0400490i
$165$	−5.04909	+	3.19953i	−0.393071	+	0.249083i
$166$	8.12618	−	14.0750i	0.630714	−	1.09243i
$167$	2.02169	−	3.50166i	0.156443	−	0.270967i	−0.777141	−	0.629327i	$-0.783331\pi$
$167$	2.02169	−	3.50166i	0.156443	−	0.270967i	0.933583	+	0.358360i	$0.116664\pi$
$168$	2.29723	+	2.66523i	0.177235	+	0.205627i
$169$	11.7105	+	20.2832i	0.900809	+	1.56025i
$170$		−	5.03577i		−	0.386226i
$171$	2.49736	+	6.33416i	0.190978	+	0.484386i
$172$			1.40028i			0.106770i
$173$	−5.76477	−	9.98487i	−0.438287	−	0.759136i	0.559270	−	0.828985i	$-0.311081\pi$
$173$	−5.76477	−	9.98487i	−0.438287	−	0.759136i	−0.997558	+	0.0698496i	$0.977748\pi$
$174$	−6.84840	−	2.39038i	−0.519176	−	0.181214i
$175$	−2.35413	−	1.35916i	−0.177955	−	0.102742i
$176$	1.77488	−	12.0237i	0.133787	−	0.906319i
$177$	−5.87291	+	16.8258i	−0.441435	+	1.26471i
$178$	7.62437	−	4.40193i	0.571471	−	0.329939i
$179$			13.7069i			1.02450i	0.858837	+	0.512249i	$0.171188\pi$
$179$			13.7069i			1.02450i	−0.858837	+	0.512249i	$0.828812\pi$
$180$	−0.302279	+	0.380259i	−0.0225305	+	0.0283428i
$181$	−0.157093			−0.0116766			−0.00583832	−	0.999983i	$-0.501858\pi$
$181$	−0.157093			−0.0116766			−0.00583832	+	0.999983i	$0.501858\pi$
$182$	−2.84373	−	4.92548i	−0.210791	−	0.365101i
$183$	14.9882	+	17.3892i	1.10796	+	1.28544i
$184$	−12.8178	−	7.40035i	−0.944939	−	0.545561i
$185$	−0.375502	−	0.216796i	−0.0276074	−	0.0159392i
$186$	0.0504913	+	0.265720i	0.00370220	+	0.0194836i
$187$	−9.26272	−	7.34078i	−0.677357	−	0.536811i
$188$		−	0.666307i		−	0.0485955i
$189$	3.19184	+	1.67741i	0.232172	+	0.122014i
$190$	−3.20723			−0.232677
$191$	−19.5206	+	11.2702i	−1.41246	+	0.815486i	−0.995620	−	0.0934929i	$-0.970197\pi$
$191$	−19.5206	+	11.2702i	−1.41246	+	0.815486i	−0.416843	+	0.908979i	$0.636863\pi$
$192$	−2.75539	−	14.5008i	−0.198853	−	1.04650i
$193$	19.8033	+	11.4334i	1.42547	+	0.822998i	0.996759	−	0.0804424i	$-0.0256333\pi$
$193$	19.8033	+	11.4334i	1.42547	+	0.822998i	0.428714	+	0.903440i	$0.358967\pi$
$194$	−7.32621	+	12.6894i	−0.525991	+	0.911044i
$195$	8.23872	−	7.10117i	0.589987	−	0.508525i
$196$	0.507178	+	0.878457i	0.0362270	+	0.0627470i
$197$	−14.0164			−0.998628			−0.499314	−	0.866421i	$-0.666415\pi$
$197$	−14.0164			−0.998628			−0.499314	+	0.866421i	$0.666415\pi$
$198$	−3.06743	−	13.1600i	−0.217993	−	0.935239i
$199$	15.2365			1.08009			0.540044	−	0.841637i	$-0.318408\pi$
$199$	15.2365			1.08009			0.540044	+	0.841637i	$0.318408\pi$
$200$	5.73389	+	9.93139i	0.405447	+	0.702256i
$201$	−20.4026	−	7.12134i	−1.43909	−	0.502301i
$202$	−8.48949	+	14.7042i	−0.597318	+	1.03459i
$203$	1.85316	+	1.06992i	0.130066	+	0.0750939i
$204$	−0.906819	−	0.316518i	−0.0634900	−	0.0221607i
$205$	3.42949	−	1.98002i	0.239526	−	0.138290i
$206$	14.8395			1.03391
$207$	−15.0013	−	2.23721i	−1.04266	−	0.155497i
$208$			22.1156i			1.53344i
$209$	−4.67527	+	5.89934i	−0.323395	+	0.408066i
$210$	−1.28655	+	1.10891i	−0.0887803	+	0.0765220i
$211$	−5.80210	−	3.34985i	−0.399433	−	0.230613i	0.286806	−	0.957989i	$-0.407406\pi$
$211$	−5.80210	−	3.34985i	−0.399433	−	0.230613i	−0.686239	+	0.727376i	$0.740740\pi$
$212$	0.936185	+	0.540507i	0.0642975	+	0.0371222i
$213$	9.33211	−	1.77326i	0.639425	−	0.121501i
$214$	0.288375	+	0.499481i	0.0197129	+	0.0341438i
$215$	−9.36334			−0.638574
$216$	−8.12319	−	12.8612i	−0.552713	−	0.875094i
$217$		−	0.0797914i		−	0.00541660i
$218$	−3.61248	+	2.08566i	−0.244668	+	0.141259i
$219$	15.4095	−	2.92807i	1.04128	−	0.197861i
$220$	−0.531278	−	0.0784249i	−0.0358188	−	0.00528740i
$221$	18.6245	+	10.7529i	1.25282	+	0.723317i
$222$	0.742452	−	0.639939i	0.0498301	−	0.0429499i
$223$	5.61005	+	9.71690i	0.375677	+	0.650692i	0.990428	−	0.138029i	$-0.0440769\pi$
$223$	5.61005	+	9.71690i	0.375677	+	0.650692i	−0.614751	+	0.788721i	$0.710744\pi$
$224$			0.609428i			0.0407191i
$225$	9.19932	+	7.31281i	0.613288	+	0.487521i
$226$			12.4068i			0.825287i
$227$	2.62493	+	4.54651i	0.174223	+	0.301763i	0.939892	−	0.341472i	$-0.110925\pi$
$227$	2.62493	+	4.54651i	0.174223	+	0.301763i	−0.765669	+	0.643234i	$0.777592\pi$
$228$	−0.201587	+	0.577545i	−0.0133504	+	0.0382488i
$229$	10.5242	−	18.2284i	0.695456	−	1.20456i	−0.274571	−	0.961567i	$-0.588536\pi$
$229$	10.5242	−	18.2284i	0.695456	−	1.20456i	0.970027	−	0.242998i	$-0.0781309\pi$
$230$	3.57226	−	6.18733i	0.235548	−	0.407980i
$231$	0.164274	+	3.98294i	0.0108084	+	0.262058i
$232$	−4.51370	−	7.81796i	−0.296339	−	0.513274i
$233$	26.8309			1.75775			0.878875	−	0.477051i	$-0.158294\pi$
$233$	26.8309			1.75775			0.878875	+	0.477051i	$0.158294\pi$
$234$	9.01863	+	22.8743i	0.589567	+	1.49534i
$235$	4.45544			0.290641
$236$	−1.38661	+	0.800560i	−0.0902607	+	0.0521120i
$237$	0.629555	+	0.730405i	0.0408940	+	0.0474449i
$238$	−2.90838	−	1.67915i	−0.188522	−	0.108843i
$239$	−13.6139	+	23.5799i	−0.880608	+	1.52526i	−0.0299412	+	0.999552i	$0.509532\pi$
$239$	−13.6139	+	23.5799i	−0.880608	+	1.52526i	−0.850667	+	0.525706i	$0.823801\pi$
$240$	6.48846	−	1.23292i	0.418828	−	0.0795843i
$241$	13.6203	−	7.86370i	0.877362	−	0.506545i	0.00757446	−	0.999971i	$-0.497589\pi$
$241$	13.6203	−	7.86370i	0.877362	−	0.506545i	0.869788	+	0.493426i	$0.164256\pi$
$242$	10.8890	−	10.2275i	0.699969	−	0.657448i
$243$	−12.5784	−	9.20785i	−0.806903	−	0.590684i
$244$			2.06253i			0.132040i
$245$	−5.87404	+	3.39138i	−0.375279	+	0.216667i
$246$	1.67114	+	8.79472i	0.106548	+	0.560731i
$247$	6.84840	−	11.8618i	0.435753	−	0.754747i
$248$	−0.168309	+	0.291519i	−0.0106876	+	0.0185115i
$249$	15.7005	−	13.5326i	0.994977	−	0.857596i
$250$	−10.9131	+	6.30070i	−0.690207	+	0.398491i
$251$		−	4.10829i		−	0.259313i	−0.991559	−	0.129657i	$-0.958613\pi$
$251$		−	4.10829i		−	0.259313i	0.991559	−	0.129657i	$-0.0413875\pi$
$252$	0.118823	+	0.301375i	0.00748513	+	0.0189848i
$253$	−6.17351	−	15.5902i	−0.388125	−	0.980147i
$254$	−15.2066	+	8.77952i	−0.954146	+	0.550876i
$255$	2.11648	−	6.06369i	0.132539	−	0.379723i
$256$	1.85575	−	3.21426i	0.115985	−	0.200891i
$257$	6.09755	+	3.52042i	0.380355	+	0.219598i	0.677973	−	0.735087i	$-0.262859\pi$
$257$	6.09755	+	3.52042i	0.380355	+	0.219598i	−0.297618	+	0.954685i	$0.596192\pi$
$258$	6.97541	−	19.9845i	0.434270	−	1.24418i
$259$	−0.250419	+	0.144579i	−0.0155603	+	0.00898372i
$260$	0.977198			0.0606032
$261$	−7.24167	−	5.75662i	−0.448248	−	0.356326i
$262$	4.68695			0.289561
$263$	−6.13973	−	10.6343i	−0.378592	−	0.655740i	0.612266	−	0.790652i	$-0.290258\pi$
$263$	−6.13973	−	10.6343i	−0.378592	−	0.655740i	−0.990858	+	0.134912i	$0.956925\pi$
$264$	7.80128	−	14.8983i	0.480136	−	0.916925i
$265$	−3.61424	+	6.26006i	−0.222021	+	0.384552i
$266$	−1.06944	+	1.85232i	−0.0655714	+	0.113573i
$267$	11.0308	−	2.09603i	0.675072	−	0.128275i
$268$	−0.970739	−	1.68137i	−0.0592974	−	0.102706i
$269$		−	11.5412i		−	0.703680i	−0.936060	−	0.351840i	$-0.885556\pi$
$269$		−	11.5412i		−	0.703680i	0.936060	−	0.351840i	$-0.114444\pi$
$270$	6.20829	−	3.92118i	0.377825	−	0.238636i
$271$			11.8664i			0.720833i	0.932791	+	0.360417i	$0.117365\pi$
$271$			11.8664i			0.720833i	−0.932791	+	0.360417i	$0.882635\pi$
$272$	6.52935	+	11.3092i	0.395900	+	0.685719i
$273$	−1.35407	−	7.12608i	−0.0819523	−	0.431290i
$274$	−18.6125	−	10.7460i	−1.12442	−	0.649187i
$275$	−1.89727	+	12.8528i	−0.114410	+	0.775054i
$276$	−0.889657	−	1.03217i	−0.0535510	−	0.0621296i
$277$	−16.2666	+	9.39155i	−0.977368	+	0.564284i	−0.901474	−	0.432832i	$-0.857514\pi$
$277$	−16.2666	+	9.39155i	−0.977368	+	0.564284i	−0.0758935	+	0.997116i	$0.524181\pi$
$278$			19.6989i			1.18146i
$279$	−0.0508816	+	0.341181i	−0.00304620	+	0.0204260i
$280$	−2.11385			−0.126327
$281$	−8.93966	−	15.4839i	−0.533296	−	0.923695i	−0.999244	−	0.0388830i	$-0.987620\pi$
$281$	−8.93966	−	15.4839i	−0.533296	−	0.923695i	0.465948	−	0.884812i	$-0.345713\pi$
$282$	−3.31917	+	9.50939i	−0.197654	+	0.566276i
$283$	−23.6408	−	13.6490i	−1.40530	−	0.811350i	−0.410370	−	0.911919i	$-0.634600\pi$
$283$	−23.6408	−	13.6490i	−1.40530	−	0.811350i	−0.994930	+	0.100569i	$0.967934\pi$
$284$	0.739089	+	0.426713i	0.0438569	+	0.0253208i
$285$	−3.86191	−	1.34797i	−0.228760	−	0.0798466i
$286$	−16.8836	+	21.3040i	−0.998350	+	1.25973i
$287$		−	2.64091i		−	0.155888i
$288$	0.388622	−	2.60586i	0.0228997	−	0.153552i
$289$	−4.30137			−0.253021
$290$	3.77385	−	2.17883i	0.221608	−	0.127945i
$291$	−14.1549	+	12.2004i	−0.829773	+	0.715203i
$292$	1.22041	+	0.704606i	0.0714193	+	0.0412340i
$293$	6.08847	−	10.5455i	0.355692	−	0.616077i	−0.631544	−	0.775340i	$-0.717579\pi$
$293$	6.08847	−	10.5455i	0.355692	−	0.616077i	0.987236	+	0.159263i	$0.0509119\pi$
$294$	−2.86234	−	15.0636i	−0.166935	−	0.878529i
$295$	−5.35316	−	9.27195i	−0.311673	−	0.539834i
$296$	1.21988			0.0709040
$297$	1.83743	−	17.1355i	0.106619	−	0.994300i
$298$	−13.2153			−0.765540
$299$	15.2557	+	26.4236i	0.882258	+	1.52812i
$300$	0.197096	+	1.03726i	0.0113793	+	0.0598861i
$301$	−3.12216	+	5.40774i	−0.179958	+	0.311697i
$302$	−24.9738	−	14.4187i	−1.43708	−	0.829700i
$303$	−16.4024	+	14.1377i	−0.942294	+	0.812187i
$304$	7.20271	−	4.15848i	0.413104	−	0.238505i
$305$	−13.7917			−0.789710
$306$	11.3652	+	9.03454i	0.649706	+	0.516470i
$307$		−	9.62607i		−	0.549389i	−0.961532	−	0.274694i	$-0.911423\pi$
$307$		−	9.62607i		−	0.549389i	0.961532	−	0.274694i	$-0.0885767\pi$
$308$	−0.222446	+	0.280686i	−0.0126750	+	0.0159936i
$309$	17.8685	+	6.23687i	1.01651	+	0.354803i
$310$	−0.140721	−	0.0812452i	−0.00799240	−	0.00461442i
$311$	−13.5473	−	7.82155i	−0.768198	−	0.443520i	0.0640331	−	0.997948i	$-0.479604\pi$
$311$	−13.5473	−	7.82155i	−0.768198	−	0.443520i	−0.832232	+	0.554428i	$0.812937\pi$
$312$	−10.0843	+	28.8915i	−0.570913	+	1.63566i
$313$	−9.29809	−	16.1048i	−0.525559	−	0.910295i	−0.999557	−	0.0297689i	$-0.990523\pi$
$313$	−9.29809	−	16.1048i	−0.525559	−	0.910295i	0.473998	−	0.880526i	$-0.342810\pi$
$314$	7.84228			0.442566
$315$	−2.01523	+	0.794541i	−0.113545	+	0.0447673i
$316$			0.0866337i			0.00487352i
$317$	19.4271	−	11.2162i	1.09113	−	0.629966i	0.157255	−	0.987558i	$-0.449736\pi$
$317$	19.4271	−	11.2162i	1.09113	−	0.629966i	0.933878	+	0.357592i	$0.116402\pi$
$318$	−10.6685	−	12.3775i	−0.598261	−	0.694099i
$319$	1.49353	−	10.1177i	0.0836215	−	0.566482i
$320$	7.67935	+	4.43367i	0.429289	+	0.247850i
$321$	0.137313	+	0.722638i	0.00766407	+	0.0403337i
$322$	−2.38231	−	4.12627i	−0.132761	−	0.229948i
$323$		−	8.08764i		−	0.450008i
$324$	−0.315894	−	1.36442i	−0.0175497	−	0.0758013i
$325$		−	23.6406i		−	1.31135i
$326$	6.78043	+	11.7440i	0.375533	+	0.650443i
$327$	−5.22645	+	0.993112i	−0.289023	+	0.0549192i
$328$	−5.57063	+	9.64861i	−0.307587	+	0.532755i
$329$	1.48565	−	2.57322i	0.0819064	−	0.141866i
$330$	7.19161	+	3.76579i	0.395885	+	0.207300i
$331$	−2.08619	−	3.61338i	−0.114667	−	0.198609i	0.802979	−	0.596007i	$-0.203247\pi$
$331$	−2.08619	−	3.61338i	−0.114667	−	0.198609i	−0.917647	+	0.397397i	$0.869913\pi$
$332$	1.86224			0.102204
$333$	1.16296	−	0.458520i	0.0637300	−	0.0251268i
$334$	−5.49123			−0.300467
$335$	11.2429	−	6.49111i	0.614267	−	0.354647i
$336$	1.45148	−	4.15848i	0.0791849	−	0.226864i
$337$	11.2856	+	6.51573i	0.614765	+	0.354935i	0.774828	−	0.632172i	$-0.217836\pi$
$337$	11.2856	+	6.51573i	0.614765	+	0.354935i	−0.160063	+	0.987107i	$0.551170\pi$
$338$	15.9038	−	27.5463i	0.865055	−	1.49832i
$339$	−5.21444	+	14.9393i	−0.283209	+	0.811392i
$340$	0.499707	−	0.288506i	0.0271004	−	0.0156464i
$341$	−0.354574	+	0.140406i	−0.0192012	+	0.00760343i
$342$	5.75401	−	7.23839i	0.311141	−	0.391407i
$343$			9.38088i			0.506520i
$344$	22.8138	−	13.1715i	1.23004	−	0.710161i
$345$	6.90191	−	5.94893i	0.371586	−	0.320280i
$346$	−7.82903	+	13.5603i	−0.420891	+	0.729005i
$347$	−6.70335	+	11.6105i	−0.359855	+	0.623287i	−0.987936	−	0.154861i	$-0.950507\pi$
$347$	−6.70335	+	11.6105i	−0.359855	+	0.623287i	0.628081	+	0.778148i	$0.283840\pi$
$348$	−0.155153	−	0.816525i	−0.00831710	−	0.0437704i
$349$	−4.98969	+	2.88080i	−0.267092	+	0.154206i	−0.627565	−	0.778564i	$-0.715949\pi$
$349$	−4.98969	+	2.88080i	−0.267092	+	0.154206i	0.360473	+	0.932770i	$0.382615\pi$
$350$			3.69169i			0.197329i
$351$	1.24572	+	31.3339i	0.0664916	+	1.67248i
$352$	2.70815	−	1.07239i	0.144345	−	0.0571586i
$353$	−15.4546	+	8.92269i	−0.822563	+	0.474907i	−0.851300	−	0.524680i	$-0.824185\pi$
$353$	−15.4546	+	8.92269i	−0.822563	+	0.474907i	0.0287365	+	0.999587i	$0.490852\pi$
$354$	23.7773	−	4.51809i	1.26375	−	0.240134i
$355$	−2.85333	+	4.94212i	−0.151439	+	0.262300i
$356$	0.873621	+	0.504385i	0.0463018	+	0.0267324i
$357$	−2.79632	−	3.24427i	−0.147997	−	0.171705i
$358$	16.1211	−	9.30752i	0.852026	−	0.491918i
$359$	−3.75055			−0.197946			−0.0989732	−	0.995090i	$-0.531556\pi$
$359$	−3.75055			−0.197946			−0.0989732	+	0.995090i	$0.531556\pi$
$360$	9.03863	+	1.34797i	0.476378	+	0.0710440i
$361$	13.8491			0.728898
$362$	0.106673	+	0.184763i	0.00560659	+	0.00971090i
$363$	17.4102	−	7.73864i	0.913796	−	0.406173i
$364$	0.325842	−	0.564375i	0.0170788	−	0.0295813i
$365$	−4.71154	+	8.16062i	−0.246613	+	0.427147i
$366$	10.2744	−	29.4360i	0.537051	−	1.53865i
$367$	4.16772	+	7.21870i	0.217553	+	0.376813i	0.954059	−	0.299618i	$-0.0968591\pi$
$367$	4.16772	+	7.21870i	0.217553	+	0.376813i	−0.736506	+	0.676431i	$0.763526\pi$
$368$			18.5271i			0.965791i
$369$	−1.68406	+	11.2923i	−0.0876688	+	0.587853i
$370$			0.588854i			0.0306131i
$371$	2.41031	+	4.17477i	0.125137	+	0.216743i
$372$	−0.0234751	+	0.0202338i	−0.00121713	+	0.00104907i
$373$	18.9150	+	10.9206i	0.979381	+	0.565446i	0.902083	−	0.431562i	$-0.142037\pi$
$373$	18.9150	+	10.9206i	0.979381	+	0.565446i	0.0772977	+	0.997008i	$0.475371\pi$
$374$	−2.34397	+	15.8789i	−0.121204	+	0.821078i
$375$	−15.7889	+	3.00015i	−0.815334	+	0.154927i
$376$	−10.8557	+	6.26753i	−0.559839	+	0.323223i
$377$			18.6098i			0.958455i
$378$	−0.194530	−	4.89307i	−0.0100055	−	0.251672i
$379$	−0.619089			−0.0318005			−0.0159002	−	0.999874i	$-0.505061\pi$
$379$	−0.619089			−0.0318005			−0.0159002	+	0.999874i	$0.505061\pi$
$380$	−0.183747	−	0.318259i	−0.00942601	−	0.0163263i
$381$	−22.0005	+	4.18047i	−1.12712	+	0.214172i
$382$	26.5106	+	15.3059i	1.35640	+	0.783118i
$383$	−8.24928	−	4.76273i	−0.421519	−	0.243364i	0.274208	−	0.961670i	$-0.411584\pi$
$383$	−8.24928	−	4.76273i	−0.421519	−	0.243364i	−0.695727	+	0.718306i	$0.744918\pi$
$384$	−12.8794	+	11.1011i	−0.657250	+	0.566500i
$385$	−1.87688	−	1.48745i	−0.0956549	−	0.0758073i
$386$		−	31.0551i		−	1.58066i
$387$	16.7985	−	21.1321i	0.853916	−	1.07420i
$388$	−1.67891			−0.0852340
$389$	−12.9643	+	7.48494i	−0.657316	+	0.379502i	−0.791254	−	0.611488i	$-0.790571\pi$
$389$	−12.9643	+	7.48494i	−0.657316	+	0.379502i	0.133937	+	0.990990i	$0.457238\pi$
$390$	−13.9464	−	4.86786i	−0.706201	−	0.246493i
$391$	15.6025	+	9.00811i	0.789053	+	0.455560i
$392$	9.54139	−	16.5262i	0.481913	−	0.834698i
$393$	5.64366	+	1.96987i	0.284685	+	0.0993670i
$394$	9.51772	+	16.4852i	0.479496	+	0.830511i
$395$	−0.579299			−0.0291477
$396$	1.13015	−	1.05834i	0.0567921	−	0.0531835i
$397$	1.73926			0.0872911			0.0436455	−	0.999047i	$-0.486103\pi$
$397$	1.73926			0.0872911			0.0436455	+	0.999047i	$0.486103\pi$
$398$	−10.3462	−	17.9202i	−0.518609	−	0.898258i
$399$	−2.06625	+	1.78095i	−0.103442	+	0.0891590i
$400$	7.17752	−	12.4318i	0.358876	−	0.621592i
$401$	7.38951	+	4.26634i	0.369015	+	0.213051i	0.673028	−	0.739617i	$-0.264993\pi$
$401$	7.38951	+	4.26634i	0.369015	+	0.213051i	−0.304013	+	0.952668i	$0.598327\pi$
$402$	5.47853	+	28.8318i	0.273244	+	1.43800i
$403$	0.600962	−	0.346965i	0.0299360	−	0.0172836i
$404$	−1.94550			−0.0967921
$405$	9.12358	−	2.11231i	0.453355	−	0.104962i
$406$		−	2.90609i		−	0.144227i
$407$	1.08313	+	0.858388i	0.0536887	+	0.0425487i
$408$	3.37307	+	17.7514i	0.166992	+	0.878828i
$409$	−3.44798	−	1.99069i	−0.170492	−	0.0984334i	0.412326	−	0.911036i	$-0.364716\pi$
$409$	−3.44798	−	1.99069i	−0.170492	−	0.0984334i	−0.582818	+	0.812603i	$0.698050\pi$
$410$	−4.65753	−	2.68903i	−0.230019	−	0.132801i
$411$	−17.8954	−	20.7621i	−0.882714	−	1.02412i
$412$	0.850173	+	1.47254i	0.0418850	+	0.0725470i
$413$	−7.13995			−0.351334
$414$	7.55527	+	19.1627i	0.371321	+	0.941797i
$415$			12.4524i			0.611262i
$416$	−4.59000	+	2.65004i	−0.225043	+	0.129929i
$417$	−8.27923	+	23.7199i	−0.405436	+	1.16157i
$418$	10.1131	+	1.49285i	0.494648	+	0.0730178i
$419$	−2.91792	−	1.68466i	−0.142550	−	0.0823010i	0.427029	−	0.904238i	$-0.359560\pi$
$419$	−2.91792	−	1.68466i	−0.142550	−	0.0823010i	−0.569579	+	0.821937i	$0.692894\pi$
$420$	−0.183747	−	0.0641353i	−0.00896592	−	0.00312948i
$421$	0.711598	+	1.23252i	0.0346811	+	0.0600695i	0.882845	−	0.469664i	$-0.155625\pi$
$421$	0.711598	+	1.23252i	0.0346811	+	0.0600695i	−0.848164	+	0.529734i	$0.822292\pi$
$422$			9.09873i			0.442919i
$423$	−7.99339	+	10.0555i	−0.388652	+	0.488914i
$424$		−	20.3368i		−	0.987643i
$425$	−6.97961	−	12.0890i	−0.338561	−	0.586405i
$426$	−8.42247	−	9.77169i	−0.408070	−	0.473440i
$427$	−4.59878	+	7.96531i	−0.222550	+	0.385468i
$428$	−0.0330428	+	0.0572318i	−0.00159719	+	0.00276641i
$429$	−29.2838	+	18.5567i	−1.41384	+	0.895926i
$430$	6.35809	+	11.0125i	0.306614	+	0.531072i
$431$	−11.6399			−0.560674			−0.280337	−	0.959902i	$-0.590446\pi$
$431$	−11.6399			−0.560674			−0.280337	+	0.959902i	$0.590446\pi$
$432$	−8.85821	+	16.8557i	−0.426191	+	0.810971i
$433$	17.6818			0.849731			0.424866	−	0.905256i	$-0.360321\pi$
$433$	17.6818			0.849731			0.424866	+	0.905256i	$0.360321\pi$
$434$	−0.0938454	+	0.0541817i	−0.00450472	+	0.00260080i
$435$	5.45992	−	1.03748i	0.261783	−	0.0497431i
$436$	−0.413927	−	0.238981i	−0.0198235	−	0.0114451i
$437$	5.73718	−	9.93709i	0.274447	−	0.475355i
$438$	−13.9075	−	16.1354i	−0.664527	−	0.770980i
$439$	12.7573	−	7.36543i	0.608873	−	0.351533i	−0.163651	−	0.986518i	$-0.552327\pi$
$439$	12.7573	−	7.36543i	0.608873	−	0.351533i	0.772524	+	0.634985i	$0.218994\pi$
$440$	3.71967	+	9.39343i	0.177328	+	0.447814i
$441$	2.88447	−	19.3415i	0.137356	−	0.921023i
$442$		−	29.2066i		−	1.38922i
$443$	11.3664	−	6.56238i	0.540033	−	0.311788i	−0.205059	−	0.978750i	$-0.565739\pi$
$443$	11.3664	−	6.56238i	0.540033	−	0.311788i	0.745092	+	0.666961i	$0.232405\pi$
$444$	0.106038	+	0.0370117i	0.00503235	+	0.00175650i
$445$	−3.37271	+	5.84170i	−0.159882	+	0.276923i
$446$	7.61892	−	13.1963i	0.360766	−	0.624865i
$447$	−15.9128	−	5.55423i	−0.752650	−	0.262706i
$448$	5.12129	−	2.95678i	0.241958	−	0.139695i
$449$		−	0.195055i		−	0.00920521i	−0.999989	−	0.00460260i	$-0.998535\pi$
$449$		−	0.195055i		−	0.00920521i	0.999989	−	0.00460260i	$-0.00146506\pi$
$450$	2.35413	−	15.7853i	0.110975	−	0.744127i
$451$	−11.7356	+	4.64712i	−0.552606	+	0.218824i
$452$	−1.23114	+	0.710802i	−0.0579082	+	0.0334333i
$453$	−24.0116	−	27.8581i	−1.12816	−	1.30889i
$454$	3.56487	−	6.17454i	0.167308	−	0.289785i
$455$	3.77385	+	2.17883i	0.176921	+	0.102145i
$456$	11.3057	−	2.14828i	0.529439	−	0.100602i
$457$	−13.4440	+	7.76192i	−0.628886	+	0.363087i	−0.780320	−	0.625380i	$-0.784944\pi$
$457$	−13.4440	+	7.76192i	−0.628886	+	0.363087i	0.151435	+	0.988467i	$0.451611\pi$
$458$	−28.5853			−1.33571
$459$	9.88799	+	15.6554i	0.461532	+	0.730730i
$460$	0.818638			0.0381692
$461$	−6.99529	−	12.1162i	−0.325803	−	0.564307i	0.655872	−	0.754872i	$-0.272301\pi$
$461$	−6.99529	−	12.1162i	−0.325803	−	0.564307i	−0.981675	+	0.190565i	$0.938968\pi$
$462$	4.57292	−	2.89779i	0.212752	−	0.134817i
$463$	−10.3960	+	18.0065i	−0.483145	+	0.836831i	−0.999813	−	0.0193546i	$-0.993839\pi$
$463$	−10.3960	+	18.0065i	−0.483145	+	0.836831i	0.516668	+	0.856186i	$0.327172\pi$
$464$	−5.65012	+	9.78630i	−0.262300	+	0.454318i
$465$	−0.135299	−	0.156973i	−0.00627433	−	0.00727943i
$466$	−18.2193	−	31.5567i	−0.843992	−	1.46184i
$467$			29.5307i			1.36652i	0.730176	+	0.683259i	$0.239438\pi$
$467$			29.5307i			1.36652i	−0.730176	+	0.683259i	$0.760562\pi$
$468$	−1.75316	+	2.20543i	−0.0810400	+	0.101946i
$469$		−	8.65773i		−	0.399777i
$470$	−3.02543	−	5.24020i	−0.139553	−	0.241712i
$471$	9.44307	+	3.29603i	0.435114	+	0.151873i
$472$	26.0859	+	15.0607i	1.20070	+	0.693226i
$473$	29.5246	+	4.35829i	1.35754	+	0.200395i
$474$	0.431561	−	1.23642i	0.0198222	−	0.0567905i
$475$	−7.69940	+	4.44525i	−0.353273	+	0.203962i
$476$		−	0.384804i		−	0.0176375i
$477$	−7.64407	−	19.3880i	−0.349998	−	0.887714i
$478$	36.9775			1.69131
$479$	−12.6583	−	21.9249i	−0.578374	−	1.00177i	−0.995666	−	0.0930005i	$-0.970354\pi$
$479$	−12.6583	−	21.9249i	−0.578374	−	1.00177i	0.417292	−	0.908772i	$-0.362979\pi$
$480$	1.03338	+	1.19892i	0.0471671	+	0.0547229i
$481$	−2.17784	−	1.25738i	−0.0993011	−	0.0573315i
$482$	−18.4975	−	10.6795i	−0.842539	−	0.486440i
$483$	−1.13436	−	5.96980i	−0.0516153	−	0.271635i
$484$	1.63873	+	0.494581i	0.0744878	+	0.0224810i
$485$		−	11.2265i		−	0.509770i
$486$	−2.28843	+	21.0464i	−0.103805	+	0.954682i
$487$	15.0628			0.682563			0.341281	−	0.939961i	$-0.389139\pi$
$487$	15.0628			0.682563			0.341281	+	0.939961i	$0.389139\pi$
$488$	33.6034	−	19.4009i	1.52116	−	0.878239i
$489$	3.22858	+	16.9910i	0.146001	+	0.768361i
$490$	7.97743	+	4.60577i	0.360384	+	0.208068i
$491$	0.00646000	−	0.0111891i	0.000291536	−	0.000504955i	−0.865880	−	0.500252i	$-0.833241\pi$
$491$	0.00646000	−	0.0111891i	0.000291536	−	0.000504955i	0.866171	+	0.499748i	$0.166574\pi$
$492$	−0.776971	+	0.669691i	−0.0350286	+	0.0301920i
$493$	5.49433	+	9.51646i	0.247452	+	0.428600i
$494$	−18.6014			−0.836916
$495$	7.07687	+	7.55704i	0.318082	+	0.339664i
$496$	0.421368			0.0189200
$497$	1.90286	+	3.29585i	0.0853551	+	0.147839i
$498$	−26.5775	−	9.27664i	−1.19096	−	0.415696i
$499$	9.57743	−	16.5886i	0.428745	−	0.742608i	−0.568017	−	0.823017i	$-0.692289\pi$
$499$	9.57743	−	16.5886i	0.428745	−	0.742608i	0.996762	+	0.0804090i	$0.0256226\pi$
$500$	−1.25046	−	0.721952i	−0.0559221	−	0.0322867i
$501$	−6.61212	−	2.30790i	−0.295408	−	0.103110i
$502$	−4.83190	+	2.78970i	−0.215658	+	0.124510i
$503$	10.5101			0.468621			0.234311	−	0.972162i	$-0.424717\pi$
$503$	10.5101			0.468621			0.234311	+	0.972162i	$0.424717\pi$
$504$	3.79240	−	4.77074i	0.168927	−	0.212506i
$505$		−	13.0091i		−	0.578897i
$506$	−14.1441	+	17.8472i	−0.628781	+	0.793407i
$507$	30.7276	−	26.4849i	1.36466	−	1.17623i
$508$	−1.74241	−	1.00598i	−0.0773070	−	0.0446332i
$509$	−33.3204	−	19.2375i	−1.47690	−	0.852689i	−0.477241	−	0.878773i	$-0.658363\pi$
$509$	−33.3204	−	19.2375i	−1.47690	−	0.852689i	−0.999660	+	0.0260838i	$0.991696\pi$
$510$	−8.56889	+	1.62823i	−0.379437	+	0.0720993i
$511$	3.14208	+	5.44225i	0.138998	+	0.240751i
$512$	−24.6743			−1.09046
$513$	9.97076	−	6.29757i	0.440220	−	0.278044i
$514$		−	9.56205i		−	0.421764i
$515$	−9.84655	+	5.68491i	−0.433891	+	0.250507i
$516$	2.38272	−	0.452756i	0.104893	−	0.0199315i
$517$	−14.0490	−	2.07385i	−0.617874	−	0.0912077i
$518$	0.340089	+	0.196351i	0.0149427	+	0.00862715i
$519$	−15.1264	+	13.0378i	−0.663973	+	0.572296i
$520$	−9.19188	−	15.9208i	−0.403090	−	0.698173i
$521$		−	20.5746i		−	0.901390i	−0.892678	−	0.450695i	$-0.851176\pi$
$521$		−	20.5746i		−	0.901390i	0.892678	−	0.450695i	$-0.148824\pi$
$522$	−1.85316	+	12.4262i	−0.0811106	+	0.543878i
$523$			17.8181i			0.779132i	0.920999	+	0.389566i	$0.127375\pi$
$523$			17.8181i			0.779132i	−0.920999	+	0.389566i	$0.872625\pi$
$524$	0.268522	+	0.465093i	0.0117304	+	0.0203177i
$525$	−1.55158	+	4.44525i	−0.0677164	+	0.194007i
$526$	−8.33826	+	14.4423i	−0.363565	+	0.629713i
$527$	0.204875	−	0.354854i	0.00892449	−	0.0154577i
$528$	−21.0334	+	0.867509i	−0.915362	+	0.0377535i
$529$	1.28028	+	2.21752i	0.0556645	+	0.0964138i
$530$	9.81688			0.426418
$531$	30.5298	+	4.55302i	1.32488	+	0.197584i
$532$	−0.245078			−0.0106255
$533$	19.8904	−	11.4837i	0.861550	−	0.497416i
$534$	−9.95556	−	11.5504i	−0.430819	−	0.499833i
$535$	−0.382696	−	0.220950i	−0.0165454	−	0.00955249i
$536$	−18.2623	+	31.6312i	−0.788809	+	1.36626i
$537$	23.3236	−	4.43188i	1.00649	−	0.191250i
$538$	−13.5740	+	7.83696i	−0.585217	+	0.337875i
$539$	20.1007	−	7.95961i	0.865798	−	0.342845i
$540$	0.744787	+	0.391409i	0.0320505	+	0.0168435i
$541$			6.50298i			0.279585i	0.990181	+	0.139793i	$0.0446436\pi$
$541$			6.50298i			0.279585i	−0.990181	+	0.139793i	$0.955356\pi$
$542$	13.9565	−	8.05778i	0.599483	−	0.346111i
$543$	0.0507934	+	0.267310i	0.00217975	+	0.0114714i
$544$	−1.56479	+	2.71029i	−0.0670896	+	0.116203i
$545$	1.59801	−	2.76784i	0.0684512	−	0.118561i
$546$	−7.46175	+	6.43147i	−0.319333	+	0.275242i
$547$	−3.53074	+	2.03848i	−0.150964	+	0.0871589i	−0.573579	−	0.819150i	$-0.694445\pi$
$547$	−3.53074	+	2.03848i	−0.150964	+	0.0871589i	0.422615	+	0.906309i	$0.361112\pi$
$548$		−	2.46260i		−	0.105197i
$549$	24.7433	−	31.1264i	1.05602	−	1.32844i
$550$	16.4050	−	6.49614i	0.699510	−	0.276996i
$551$	6.06094	−	3.49929i	0.258205	−	0.149075i
$552$	−8.44805	+	24.2036i	−0.359573	+	1.03017i
$553$	−0.193165	+	0.334571i	−0.00821420	+	0.0142274i
$554$	22.0914	+	12.7545i	0.938575	+	0.541887i
$555$	−0.247489	+	0.709053i	−0.0105053	+	0.0300976i
$556$	−1.95475	+	1.12858i	−0.0828999	+	0.0478623i
$557$	18.2643			0.773883			0.386942	−	0.922104i	$-0.373531\pi$
$557$	18.2643			0.773883			0.386942	+	0.922104i	$0.373531\pi$
$558$	0.435825	−	0.171832i	0.0184499	−	0.00727424i
$559$	−54.3057			−2.29689
$560$	1.32303	+	2.29155i	0.0559082	+	0.0968358i
$561$	−9.49615	+	18.1350i	−0.400928	+	0.765660i
$562$	−12.1408	+	21.0285i	−0.512129	+	0.887033i
$563$	11.4489	−	19.8301i	0.482515	−	0.835741i	−0.517283	−	0.855814i	$-0.673057\pi$
$563$	11.4489	−	19.8301i	0.482515	−	0.835741i	0.999799	+	0.0200732i	$0.00638994\pi$
$564$	−1.13379	+	0.215439i	−0.0477412	+	0.00907163i
$565$	−4.75297	−	8.23238i	−0.199959	−	0.346339i
$566$			37.0730i			1.55829i
$567$	1.82227	−	5.97362i	0.0765279	−	0.250868i
$568$		−	16.0553i		−	0.673665i
$569$	15.8852	+	27.5140i	0.665943	+	1.15345i	0.979029	+	0.203723i	$0.0653041\pi$
$569$	15.8852	+	27.5140i	0.665943	+	1.15345i	−0.313085	+	0.949725i	$0.601363\pi$
$570$	1.03701	+	5.45744i	0.0434354	+	0.228587i
$571$	2.09799	+	1.21127i	0.0877981	+	0.0506903i	0.543256	−	0.839567i	$-0.317191\pi$
$571$	2.09799	+	1.21127i	0.0877981	+	0.0506903i	−0.455458	+	0.890257i	$0.650525\pi$
$572$	−3.08132	−	0.454850i	−0.128836	−	0.0190182i
$573$	25.4891	+	29.5723i	1.06482	+	1.23540i
$574$	−3.10606	+	1.79329i	−0.129645	+	0.0748503i
$575$		−	19.8047i		−	0.825913i
$576$	−23.7836	+	9.37715i	−0.990985	+	0.390715i
$577$	−23.1471			−0.963625			−0.481812	−	0.876274i	$-0.660021\pi$
$577$	−23.1471			−0.963625			−0.481812	+	0.876274i	$0.660021\pi$
$578$	2.92080	+	5.05898i	0.121489	+	0.210426i
$579$	13.0521	−	37.3942i	0.542428	−	1.55405i
$580$	0.432418	+	0.249656i	0.0179552	+	0.0103664i
$581$	7.19179	+	4.15218i	0.298366	+	0.172262i
$582$	23.9611	+	8.36342i	0.993219	+	0.346675i
$583$	14.3103	−	18.0570i	0.592673	−	0.747845i
$584$		−	26.5111i		−	1.09704i
$585$	−14.7472	−	11.7230i	−0.609723	−	0.484686i
$586$	−16.5373			−0.683149
$587$	−29.5082	+	17.0366i	−1.21794	+	0.703175i	−0.964476	−	0.264171i	$-0.914902\pi$
$587$	−29.5082	+	17.0366i	−1.21794	+	0.703175i	−0.253459	+	0.967346i	$0.581568\pi$
$588$	1.33080	−	1.14705i	0.0548812	−	0.0473035i
$589$	−0.226003	−	0.130483i	−0.00931229	−	0.00537645i
$590$	−7.27003	+	12.5921i	−0.299302	+	0.518407i
$591$	4.53197	+	23.8504i	0.186420	+	0.981074i
$592$	−0.763505	−	1.32243i	−0.0313799	−	0.0543515i
$593$	36.2236			1.48752			0.743762	−	0.668445i	$-0.233040\pi$
$593$	36.2236			1.48752			0.743762	+	0.668445i	$0.233040\pi$
$594$	−21.4013	+	9.47461i	−0.878105	+	0.388748i
$595$	2.57310			0.105487
$596$	−0.757120	−	1.31137i	−0.0310129	−	0.0537159i
$597$	−4.92647	−	25.9265i	−0.201627	−	1.06110i
$598$	20.7185	−	35.8854i	0.847241	−	1.46746i
$599$	14.2534	+	8.22918i	0.582376	+	0.336235i	0.762077	−	0.647486i	$-0.224180\pi$
$599$	14.2534	+	8.22918i	0.582376	+	0.336235i	−0.179701	+	0.983721i	$0.557513\pi$
$600$	15.0453	−	12.9680i	0.614223	−	0.529415i
$601$	−8.79918	+	5.08021i	−0.358926	+	0.207226i	−0.668609	−	0.743614i	$-0.733110\pi$
$601$	−8.79918	+	5.08021i	−0.358926	+	0.207226i	0.309684	+	0.950840i	$0.399777\pi$
$602$	8.48031			0.345631
$603$	−5.52088	+	37.0196i	−0.224828	+	1.50756i
$604$		−	3.30426i		−	0.134448i
$605$	−3.30715	+	10.9578i	−0.134455	+	0.445499i
$606$	27.7657	+	9.69138i	1.12790	+	0.393686i
$607$	−3.41583	−	1.97213i	−0.138644	−	0.0800462i	0.429074	−	0.903270i	$-0.358840\pi$
$607$	−3.41583	−	1.97213i	−0.138644	−	0.0800462i	−0.567718	+	0.823223i	$0.692173\pi$
$608$	1.72616	+	0.996597i	0.0700049	+	0.0404173i
$609$	1.22140	−	3.49929i	0.0494935	−	0.141798i
$610$	9.36512	+	16.2209i	0.379183	+	0.656764i
$611$	25.8408			1.04541
$612$	−0.245383	+	1.64539i	−0.00991902	+	0.0665109i
$613$		−	8.98271i		−	0.362808i	−0.983409	−	0.181404i	$-0.941936\pi$
$613$		−	8.98271i		−	0.362808i	0.983409	−	0.181404i	$-0.0580642\pi$
$614$	−11.3215	+	6.53649i	−0.456900	+	0.263791i
$615$	−4.47807	−	5.19543i	−0.180573	−	0.209500i
$616$	6.66543	+	0.983921i	0.268558	+	0.0396433i
$617$	−31.8577	−	18.3930i	−1.28254	−	0.740475i	−0.305229	−	0.952279i	$-0.598733\pi$
$617$	−31.8577	−	18.3930i	−1.28254	−	0.740475i	−0.977312	+	0.211804i	$0.932066\pi$
$618$	−4.79809	−	25.2509i	−0.193007	−	1.01574i
$619$	3.35792	+	5.81608i	0.134966	+	0.233768i	0.925585	−	0.378541i	$-0.123574\pi$
$619$	3.35792	+	5.81608i	0.134966	+	0.233768i	−0.790618	+	0.612309i	$0.790241\pi$
$620$		−	0.0186186i		−	0.000747740i
$621$	1.04359	+	26.2497i	0.0418778	+	1.05336i
$622$			21.2446i			0.851832i
$623$	2.24923	+	3.89578i	0.0901134	+	0.156081i
$624$	37.6319	−	7.15069i	1.50648	−	0.286257i
$625$	−4.96564	+	8.60073i	−0.198625	+	0.344029i
$626$	−12.6276	+	21.8716i	−0.504699	+	0.874165i
$627$	11.5500	+	6.04801i	0.461263	+	0.241534i
$628$	0.449295	+	0.778201i	0.0179288	+	0.0310536i
$629$	−1.48490			−0.0592070
$630$	2.30291	+	1.83065i	0.0917500	+	0.0729348i
$631$	−4.73839			−0.188632			−0.0943162	−	0.995542i	$-0.530066\pi$
$631$	−4.73839			−0.188632			−0.0943162	+	0.995542i	$0.530066\pi$
$632$	1.41146	−	0.814908i	0.0561449	−	0.0324153i
$633$	−3.82410	+	10.9560i	−0.151994	+	0.435462i
$634$	−26.3836	−	15.2326i	−1.04782	−	0.604962i
$635$	6.72676	−	11.6511i	0.266944	−	0.462360i
$636$	0.617029	−	1.76778i	0.0244668	−	0.0700971i
$637$	−34.0684	+	19.6694i	−1.34984	+	0.779330i
$638$	−12.9139	+	5.11374i	−0.511267	+	0.202455i
$639$	−6.03476	−	15.3062i	−0.238731	−	0.605504i
$640$		−	10.2149i		−	0.403780i
$641$	−10.8179	+	6.24571i	−0.427281	+	0.246691i	−0.698187	−	0.715915i	$-0.746010\pi$
$641$	−10.8179	+	6.24571i	−0.427281	+	0.246691i	0.270907	+	0.962606i	$0.412676\pi$
$642$	0.756677	−	0.652199i	0.0298637	−	0.0257403i
$643$	7.61387	−	13.1876i	0.300262	−	0.520069i	−0.675933	−	0.736963i	$-0.736259\pi$
$643$	7.61387	−	13.1876i	0.300262	−	0.520069i	0.976195	+	0.216894i	$0.0695926\pi$
$644$	0.272971	−	0.472800i	0.0107566	−	0.0186309i
$645$	3.02748	+	15.9327i	0.119207	+	0.627349i
$646$	−9.51215	+	5.49184i	−0.374250	+	0.216074i
$647$		−	1.84588i		−	0.0725689i	−0.999342	−	0.0362844i	$-0.988448\pi$
$647$		−	1.84588i		−	0.0725689i	0.999342	−	0.0362844i	$-0.0115522\pi$
$648$	−19.2582	+	17.9809i	−0.756533	+	0.706357i
$649$	12.5639	+	31.7282i	0.493177	+	1.24544i
$650$	−27.8045	+	16.0530i	−1.09058	+	0.629649i
$651$	−0.135773	+	0.0257992i	−0.00532138	+	0.00101115i
$652$	−0.776920	+	1.34566i	−0.0304265	+	0.0527003i
$653$	22.3987	+	12.9319i	0.876530	+	0.506065i	0.869513	−	0.493910i	$-0.164433\pi$
$653$	22.3987	+	12.9319i	0.876530	+	0.506065i	0.00701753	+	0.999975i	$0.497766\pi$
$654$	4.71701	+	5.47264i	0.184450	+	0.213997i
$655$	−3.10997	+	1.79554i	−0.121517	+	0.0701576i
$656$	13.9463			0.544512
$657$	−9.96483	−	25.2742i	−0.388765	−	0.986041i
$658$	−4.03526			−0.157311
$659$	10.7085	+	18.5477i	0.417144	+	0.722514i	0.995651	−	0.0931630i	$-0.0296978\pi$
$659$	10.7085	+	18.5477i	0.417144	+	0.722514i	−0.578507	+	0.815677i	$0.696364\pi$
$660$	0.0383317	+	0.929382i	0.00149206	+	0.0361762i
$661$	−9.79157	+	16.9595i	−0.380848	+	0.659648i	−0.991184	−	0.132495i	$-0.957701\pi$
$661$	−9.79157	+	16.9595i	−0.380848	+	0.659648i	0.610336	+	0.792143i	$0.291034\pi$
$662$	−2.83321	+	4.90727i	−0.110116	+	0.190726i
$663$	12.2752	−	35.1683i	0.476730	−	1.36582i
$664$	−17.5169	−	30.3402i	−0.679787	−	1.17743i
$665$		−	1.63878i		−	0.0635492i
$666$	−1.32898	−	1.05645i	−0.0514970	−	0.0409365i
$667$			15.5902i			0.603655i
$668$	−0.314600	−	0.544903i	−0.0121722	−	0.0210829i
$669$	14.7204	−	12.6879i	0.569123	−	0.490542i
$670$	−15.2688	−	8.81546i	−0.589886	−	0.340571i
$671$	43.4882	+	6.41953i	1.67884	+	0.247823i
$672$	1.03701	−	0.197048i	0.0400033	−	0.00760130i
$673$	17.9430	−	10.3594i	0.691651	−	0.399325i	−0.112579	−	0.993643i	$-0.535911\pi$
$673$	17.9430	−	10.3594i	0.691651	−	0.399325i	0.804230	+	0.594318i	$0.202578\pi$
$674$		−	17.6978i		−	0.681694i
$675$	9.46906	−	18.0181i	0.364464	−	0.693516i
$676$	3.64461			0.140177
$677$	23.6132	+	40.8993i	0.907530	+	1.57189i	0.817485	+	0.575950i	$0.195368\pi$
$677$	23.6132	+	40.8993i	0.907530	+	1.57189i	0.0900445	+	0.995938i	$0.471299\pi$
$678$	21.1114	−	4.01153i	0.810780	−	0.154062i
$679$	−6.48381	−	3.74343i	−0.248826	−	0.143660i
$680$	−9.40085	−	5.42759i	−0.360506	−	0.208138i
$681$	6.88764	−	5.93663i	0.263935	−	0.227492i
$682$	0.405907	+	0.321684i	0.0155430	+	0.0123179i
$683$		−	18.5786i		−	0.710889i	−0.934697	−	0.355445i	$-0.884329\pi$
$683$		−	18.5786i		−	0.710889i	0.934697	−	0.355445i	$-0.115671\pi$
$684$	1.04793	+	0.156282i	0.0400687	+	0.00597559i
$685$	16.4668			0.629166
$686$	11.0332	−	6.37000i	0.421248	−	0.243208i
$687$	−34.4203	−	12.0141i	−1.31322	−	0.458367i
$688$	−28.5576	−	16.4877i	−1.08875	−	0.628589i
$689$	−20.9620	+	36.3072i	−0.798588	+	1.38319i
$690$	−11.6834	−	4.07800i	−0.444780	−	0.155247i
$691$	12.5064	+	21.6616i	0.475764	+	0.824048i	0.999615	−	0.0277627i	$-0.00883828\pi$
$691$	12.5064	+	21.6616i	0.475764	+	0.824048i	−0.523850	+	0.851810i	$0.675505\pi$
$692$	−1.79414			−0.0682031
$693$	6.72428	−	1.56735i	0.255434	−	0.0595386i
$694$	18.2074			0.691144
$695$	−7.54653	−	13.0710i	−0.286256	−	0.495810i
$696$	−11.8436	+	10.2083i	−0.448932	+	0.386946i
$697$	6.78088	−	11.7448i	0.256844	−	0.444867i
$698$	6.77641	+	3.91236i	0.256491	+	0.148085i
$699$	−8.67532	−	45.6556i	−0.328131	−	1.72685i
$700$	−0.366332	+	0.211502i	−0.0138460	+	0.00799402i
$701$	−21.8969			−0.827033			−0.413516	−	0.910497i	$-0.635700\pi$
$701$	−21.8969			−0.827033			−0.413516	+	0.910497i	$0.635700\pi$
$702$	36.0070	−	22.7422i	1.35900	−	0.858348i
$703$			0.945722i			0.0356686i
$704$	−22.1510	−	17.5548i	−0.834845	−	0.661622i
$705$	−1.44059	−	7.58140i	−0.0542558	−	0.285532i
$706$	20.9886	+	12.1178i	0.789915	+	0.456058i
$707$	−7.51333	−	4.33782i	−0.282568	−	0.163141i
$708$	1.81057	+	2.10061i	0.0680455	+	0.0789459i
$709$	−21.8109	−	37.7776i	−0.819125	−	1.41877i	−0.906328	−	0.422575i	$-0.861126\pi$
$709$	−21.8109	−	37.7776i	−0.819125	−	1.41877i	0.0872032	−	0.996191i	$-0.472207\pi$
$710$	7.75012			0.290857
$711$	1.03930	−	1.30742i	0.0389770	−	0.0490320i
$712$		−	18.9777i		−	0.711220i
$713$	0.503450	−	0.290667i	0.0188543	−	0.0108856i
$714$	−1.91688	+	5.49184i	−0.0717375	+	0.205527i
$715$	3.04148	−	20.6041i	0.113745	−	0.770548i
$716$	1.84720	+	1.06648i	0.0690331	+	0.0398563i
$717$	44.5255	+	15.5412i	1.66283	+	0.580398i
$718$	2.54678	+	4.41115i	0.0950449	+	0.164623i
$719$			33.0842i			1.23383i	0.787029	+	0.616916i	$0.211618\pi$
$719$			33.0842i			1.23383i	−0.787029	+	0.616916i	$0.788382\pi$
$720$	−4.19587	−	10.6421i	−0.156371	−	0.396609i
$721$			7.58243i			0.282384i
$722$	−9.40408	−	16.2883i	−0.349984	−	0.606189i
$723$	−17.7848	−	20.6338i	−0.661424	−	0.767379i
$724$	−0.0122228	+	0.0211706i	−0.000454258	+	0.000786799i
$725$	6.03975	−	10.4612i	0.224311	−	0.388518i
$726$	−20.9239	−	15.2218i	−0.776558	−	0.564934i
$727$	18.1836	+	31.4949i	0.674392	+	1.16808i	0.976646	+	0.214854i	$0.0689275\pi$
$727$	18.1836	+	31.4949i	0.674392	+	1.16808i	−0.302254	+	0.953227i	$0.597739\pi$
$728$	−12.2600			−0.454384
$729$	−11.6011	+	24.3806i	−0.429671	+	0.902986i
$730$	12.7973			0.473650
$731$	−27.7702	+	16.0331i	−1.02712	+	0.593006i
$732$	3.50962	−	0.666885i	0.129719	−	0.0246488i
$733$	0.0497214	+	0.0287067i	0.00183650	+	0.00106030i	0.500918	−	0.865495i	$-0.332996\pi$
$733$	0.0497214	+	0.0287067i	0.00183650	+	0.00106030i	−0.499081	+	0.866555i	$0.666329\pi$
$734$	5.66011	−	9.80359i	0.208918	−	0.361857i
$735$	7.67006	+	8.89875i	0.282914	+	0.328235i
$736$	−3.84523	+	2.22004i	−0.141737	+	0.0818319i
$737$	−38.4728	+	15.2347i	−1.41716	+	0.561178i
$738$	14.4248	−	5.68725i	0.530984	−	0.209350i
$739$			32.6312i			1.20036i	0.799865	+	0.600180i	$0.204904\pi$
$739$			32.6312i			1.20036i	−0.799865	+	0.600180i	$0.795096\pi$
$740$	−0.0584329	+	0.0337362i	−0.00214803	+	0.00124017i
$741$	−22.3984	−	7.81796i	−0.822825	−	0.287200i
$742$	3.27340	−	5.66969i	0.120170	−	0.208141i
$743$	−0.609704	+	1.05604i	−0.0223679	+	0.0387423i	−0.876993	−	0.480504i	$-0.840454\pi$
$743$	−0.609704	+	1.05604i	−0.0223679	+	0.0387423i	0.854625	+	0.519246i	$0.173787\pi$
$744$	0.550470	+	0.192137i	0.0201812	+	0.00704409i
$745$	8.76884	−	5.06269i	0.321265	−	0.185483i
$746$		−	29.6621i		−	1.08601i
$747$	−28.1037	−	22.3404i	−1.02826	−	0.817394i
$748$	−1.70998	+	0.677127i	−0.0625229	+	0.0247582i
$749$	−0.255217	+	0.147349i	−0.00932541	+	0.00538403i
$750$	14.2499	+	16.5326i	0.520332	+	0.603686i
$751$	14.0648	−	24.3609i	0.513231	−	0.888943i	−0.486651	−	0.873597i	$-0.661782\pi$
$751$	14.0648	−	24.3609i	0.513231	−	0.888943i	0.999882	−	0.0153462i	$-0.00488503\pi$
$752$	13.5888	+	7.84551i	0.495534	+	0.286096i
$753$	−6.99069	+	1.32835i	−0.254755	+	0.0484077i
$754$	21.8876	−	12.6368i	0.797101	−	0.460206i
$755$	22.0948			0.804112
$756$	0.474402	−	0.299634i	0.0172538	−	0.0108976i
$757$	45.1173			1.63982			0.819908	−	0.572495i	$-0.194024\pi$
$757$	45.1173			1.63982			0.819908	+	0.572495i	$0.194024\pi$
$758$	0.420387	+	0.728132i	0.0152691	+	0.0264469i
$759$	−24.5322	+	15.5457i	−0.890464	+	0.564273i
$760$	−3.45678	+	5.98731i	−0.125391	+	0.217183i
$761$	3.65931	−	6.33812i	0.132650	−	0.229757i	−0.792047	−	0.610460i	$-0.790985\pi$
$761$	3.65931	−	6.33812i	0.132650	−	0.229757i	0.924697	+	0.380703i	$0.124318\pi$
$762$	19.8561	+	23.0369i	0.719309	+	0.834538i
$763$	−1.06570	−	1.84584i	−0.0385809	−	0.0668241i
$764$			3.50758i			0.126900i
$765$	−11.0023	−	1.64082i	−0.397790	−	0.0593239i
$766$			12.9363i			0.467409i
$767$	−31.0474	−	53.7756i	−1.12106	−	1.94173i
$768$	−6.06943	−	2.11848i	−0.219012	−	0.0764441i
$769$	−25.6578	−	14.8136i	−0.925245	−	0.534191i	−0.0399407	−	0.999202i	$-0.512717\pi$
$769$	−25.6578	−	14.8136i	−0.925245	−	0.534191i	−0.885305	+	0.465011i	$0.846050\pi$
$770$	−0.474953	+	3.21750i	−0.0171161	+	0.115951i
$771$	4.01883	−	11.5139i	0.144735	−	0.414663i
$772$	3.08165	−	1.77919i	0.110911	−	0.0640344i
$773$			35.5682i			1.27930i	0.768667	+	0.639650i	$0.220921\pi$
$773$			35.5682i			1.27930i	−0.768667	+	0.639650i	$0.779079\pi$
$774$	−36.2610	−	5.40774i	−1.30338	−	0.194377i
$775$	−0.450425			−0.0161798
$776$	15.7925	+	27.3534i	0.566917	+	0.981929i
$777$	0.326985	+	0.379366i	0.0117305	+	0.0136097i
$778$	17.6066	+	10.1652i	0.631227	+	0.364439i
$779$	−7.48017	−	4.31868i	−0.268005	−	0.154733i
$780$	−0.315960	−	1.66280i	−0.0113132	−	0.0595379i
$781$	11.2976	−	14.2555i	0.404259	−	0.510100i
$782$		−	24.4675i		−	0.874956i
$783$	−7.45401	+	14.1838i	−0.266385	+	0.506886i
$784$	−23.8873			−0.853117
$785$	−5.20365	+	3.00433i	−0.185726	+	0.107229i
$786$	−1.51545	−	7.97533i	−0.0540541	−	0.284471i
$787$	−45.9910	−	26.5529i	−1.63940	−	0.946509i	−0.981039	−	0.193808i	$-0.937916\pi$
$787$	−45.9910	−	26.5529i	−1.63940	−	0.946509i	−0.658363	−	0.752701i	$-0.728751\pi$
$788$	−1.09057	+	1.88892i	−0.0388498	+	0.0672898i
$789$	−16.1102	+	13.8858i	−0.573539	+	0.494348i
$790$	0.393368	+	0.681333i	0.0139954	+	0.0242408i
$791$	−6.33942			−0.225404
$792$	−27.8734	−	8.45759i	−0.990437	−	0.300527i
$793$	−79.9893			−2.84050
$794$	−1.18103	−	2.04561i	−0.0419132	−	0.0725958i
$795$	11.8207	+	4.12593i	0.419238	+	0.146332i
$796$	1.18550	−	2.05334i	0.0420189	−	0.0727788i
$797$	−15.1077	−	8.72246i	−0.535144	−	0.308965i	0.207965	−	0.978136i	$-0.433316\pi$
$797$	−15.1077	−	8.72246i	−0.535144	−	0.308965i	−0.743109	+	0.669171i	$0.766649\pi$
$798$	3.49770	+	1.22084i	0.123817	+	0.0432174i
$799$	13.2141	−	7.62918i	0.467482	−	0.269901i
$800$	3.44024			0.121631
$801$	−7.13322	−	18.0923i	−0.252040	−	0.639259i
$802$		−	11.5881i		−	0.409189i
$803$	18.6550	−	23.5392i	0.658320	−	0.830680i
$804$	−2.54715	+	2.19546i	−0.0898312	+	0.0774278i
$805$	3.16150	+	1.82529i	0.111428	+	0.0643332i
$806$	−0.816155	−	0.471208i	−0.0287479	−	0.0165976i
$807$	−19.6386	+	3.73166i	−0.691311	+	0.131361i
$808$	18.3000	+	31.6966i	0.643793	+	1.11508i
$809$	1.79521			0.0631163			0.0315581	−	0.999502i	$-0.489953\pi$
$809$	1.79521			0.0631163			0.0315581	+	0.999502i	$0.489953\pi$
$810$	−8.67965	−	9.29621i	−0.304972	−	0.326636i
$811$			18.6459i			0.654746i	0.944895	+	0.327373i	$0.106163\pi$
$811$			18.6459i			0.654746i	−0.944895	+	0.327373i	$0.893837\pi$
$812$	0.288375	−	0.166494i	0.0101200	−	0.00584278i
$813$	20.1919	−	3.83680i	0.708162	−	0.134563i
$814$	0.274090	−	1.85678i	0.00960686	−	0.0650803i
$815$	−8.99815	−	5.19508i	−0.315191	−	0.181976i
$816$	17.1326	−	14.7670i	0.599760	−	0.516949i
$817$	10.2113	+	17.6866i	0.357249	+	0.618774i
$818$			5.40705i			0.189053i
$819$	−11.6879	+	4.60820i	−0.408410	+	0.161023i
$820$		−	0.616231i		−	0.0215197i
$821$	4.24825	+	7.35818i	0.148265	+	0.256802i	0.930586	−	0.366073i	$-0.119298\pi$
$821$	4.24825	+	7.35818i	0.148265	+	0.256802i	−0.782321	+	0.622875i	$0.785965\pi$
$822$	−12.2673	+	35.1457i	−0.427871	+	1.22585i
$823$	−18.8954	+	32.7278i	−0.658652	+	1.14082i	0.322313	+	0.946633i	$0.395540\pi$
$823$	−18.8954	+	32.7278i	−0.658652	+	1.14082i	−0.980965	+	0.194185i	$0.937794\pi$
$824$	15.9941	−	27.7025i	0.557180	−	0.965064i
$825$	22.4839	−	0.927331i	0.782787	−	0.0322855i
$826$	4.84832	+	8.39753i	0.168695	+	0.292188i
$827$	−24.4842			−0.851400			−0.425700	−	0.904864i	$-0.639972\pi$
$827$	−24.4842			−0.851400			−0.425700	+	0.904864i	$0.639972\pi$
$828$	−1.46870	+	1.84758i	−0.0510407	+	0.0642078i
$829$	12.9560			0.449981			0.224990	−	0.974361i	$-0.427765\pi$
$829$	12.9560			0.449981			0.224990	+	0.974361i	$0.427765\pi$
$830$	14.6456	−	8.45566i	0.508358	−	0.293500i
$831$	21.2402	+	24.6428i	0.736816	+	0.854849i
$832$	44.5389	+	25.7145i	1.54411	+	0.891491i
$833$	−11.6143	+	20.1166i	−0.402412	+	0.696998i
$834$	33.5197	−	6.36930i	1.16069	−	0.220551i
$835$	3.64364	−	2.10366i	0.126093	−	0.0728001i
$836$	0.431256	+	1.08907i	0.0149153	+	0.0376662i
$837$	0.597007	−	0.0237347i	0.0206356	−	0.000820392i
$838$			4.57581i			0.158069i
$839$	41.7035	−	24.0775i	1.43976	−	0.831248i	0.441931	−	0.897049i	$-0.354294\pi$
$839$	41.7035	−	24.0775i	1.43976	−	0.831248i	0.997833	+	0.0658009i	$0.0209602\pi$
$840$	0.683478	+	3.59694i	0.0235822	+	0.124106i
$841$	9.74553	−	16.8797i	0.336053	−	0.582060i
$842$	0.966408	−	1.67387i	0.0333046	−	0.0576853i
$843$	−23.4571	+	20.2182i	−0.807904	+	0.696353i
$844$	−0.902881	+	0.521279i	−0.0310785	+	0.0179432i
$845$			24.3707i			0.838376i
$846$	17.2544	+	2.57322i	0.593219	+	0.0884690i
$847$	5.22587	+	5.56386i	0.179563	+	0.191177i
$848$	−22.0464	+	12.7285i	−0.757078	+	0.437099i
$849$	−15.5814	+	44.6405i	−0.534752	+	1.53206i
$850$	−9.47889	+	16.4179i	−0.325123	+	0.563130i
$851$	−1.82447	−	1.05336i	−0.0625419	−	0.0361086i
$852$	0.487125	−	1.39561i	0.0166886	−	0.0478127i
$853$	0.295104	−	0.170379i	0.0101042	−	0.00583365i	−0.494939	−	0.868927i	$-0.664810\pi$
$853$	0.295104	−	0.170379i	0.0101042	−	0.00583365i	0.505044	+	0.863094i	$0.331476\pi$
$854$	12.4910			0.427434
$855$	−1.04502	+	7.00728i	−0.0357390	+	0.239644i
$856$	1.24325			0.0424934
$857$	7.22929	+	12.5215i	0.246948	+	0.427726i	0.962677	−	0.270651i	$-0.0872390\pi$
$857$	7.22929	+	12.5215i	0.246948	+	0.427726i	−0.715730	+	0.698377i	$0.753906\pi$
$858$	41.7101	+	21.8409i	1.42396	+	0.745637i
$859$	7.07652	−	12.2569i	0.241448	−	0.418200i	−0.719679	−	0.694307i	$-0.755711\pi$
$859$	7.07652	−	12.2569i	0.241448	−	0.418200i	0.961127	+	0.276107i	$0.0890444\pi$
$860$	−0.728527	+	1.26185i	−0.0248426	+	0.0430286i
$861$	−4.49378	+	0.853894i	−0.153148	+	0.0291006i
$862$	7.90396	+	13.6901i	0.269210	+	0.466286i
$863$		−	11.2286i		−	0.382225i	−0.981568	−	0.191112i	$-0.938791\pi$
$863$		−	11.2286i		−	0.382225i	0.981568	−	0.191112i	$-0.0612095\pi$
$864$	−4.55979	+	0.181280i	−0.155127	+	0.00616728i
$865$		−	11.9970i		−	0.407911i
$866$	−12.0066	−	20.7961i	−0.408002	−	0.706681i
$867$	1.39077	+	7.31922i	0.0472332	+	0.248574i
$868$	−0.0107531	−	0.00620828i	−0.000364983	−	0.000210723i
$869$	1.82666	+	0.269643i	0.0619651	+	0.00914701i
$870$	−4.92772	−	5.71710i	−0.167065	−	0.193828i
$871$	65.2070	−	37.6473i	2.20946	−	1.27563i
$872$			8.99177i			0.304500i
$873$	25.3371	+	20.1412i	0.857530	+	0.681676i
$874$	−15.5831			−0.527107
$875$	−3.21943	−	5.57622i	−0.108837	−	0.188511i
$876$	0.804361	−	2.30448i	0.0271768	−	0.0778613i
$877$	28.4903	+	16.4489i	0.962048	+	0.555439i	0.896803	−	0.442430i	$-0.145884\pi$
$877$	28.4903	+	16.4489i	0.962048	+	0.555439i	0.0652454	+	0.997869i	$0.479217\pi$
$878$	−17.3255	−	10.0029i	−0.584706	−	0.337580i
$879$	−19.9129	−	6.95044i	−0.671646	−	0.234432i
$880$	7.85501	−	9.91158i	0.264792	−	0.334119i
$881$		−	24.6878i		−	0.831754i	−0.909421	−	0.415877i	$-0.863475\pi$
$881$		−	24.6878i		−	0.831754i	0.909421	−	0.415877i	$-0.136525\pi$
$882$	−24.7068	+	9.74114i	−0.831922	+	0.328001i
$883$	2.21112			0.0744101			0.0372050	−	0.999308i	$-0.488155\pi$
$883$	2.21112			0.0744101			0.0372050	+	0.999308i	$0.488155\pi$
$884$	2.89821	−	1.67328i	0.0974774	−	0.0562786i
$885$	−14.0463	+	12.1069i	−0.472162	+	0.406969i
$886$	−15.4365	−	8.91226i	−0.518599	−	0.299413i
$887$	23.2619	−	40.2908i	0.781059	−	1.35283i	−0.150266	−	0.988646i	$-0.548013\pi$
$887$	23.2619	−	40.2908i	0.781059	−	1.35283i	0.931325	−	0.364189i	$-0.118654\pi$
$888$	−0.394427	−	2.07575i	−0.0132361	−	0.0696577i
$889$	−4.48602	−	7.77001i	−0.150456	−	0.260598i
$890$	9.16083			0.307072
$891$	−29.7519	+	2.41388i	−0.996725	+	0.0808679i
$892$	1.74599			0.0584601
$893$	−4.85896	−	8.41596i	−0.162599	−	0.281629i
$894$	4.27293	+	22.4872i	0.142908	+	0.752083i
$895$	−7.13131	+	12.3518i	−0.238373	+	0.412875i
$896$	−5.89957	−	3.40612i	−0.197091	−	0.113790i
$897$	40.0298	−	34.5027i	1.33656	−	1.15201i
$898$	−0.229411	+	0.132450i	−0.00765553	+	0.00441992i
$899$	0.354574			0.0118257
$900$	1.70127	−	0.670759i	0.0567091	−	0.0223586i
$901$			24.7551i			0.824712i
$902$	13.4346	+	10.6470i	0.447322	+	0.354506i
$903$	10.2113	+	3.56418i	0.339812	+	0.118609i
$904$	23.1612	+	13.3721i	0.770330	+	0.444750i
$905$	−0.141563	−	0.0817313i	−0.00470571	−	0.00271684i
$906$	−16.4600	+	47.1576i	−0.546846	+	1.56671i
$907$	−16.2346	−	28.1192i	−0.539062	−	0.933683i	−0.998955	−	0.0457088i	$-0.985445\pi$
$907$	−16.2346	−	28.1192i	−0.539062	−	0.933683i	0.459892	−	0.887975i	$-0.347888\pi$
$908$	0.816945			0.0271113
$909$	29.3601	+	23.3392i	0.973815	+	0.774114i
$910$		−	5.91806i		−	0.196182i
$911$	37.3959	−	21.5905i	1.23898	−	0.715326i	0.270094	−	0.962834i	$-0.412945\pi$
$911$	37.3959	−	21.5905i	1.23898	−	0.715326i	0.968886	+	0.247508i	$0.0796117\pi$
$912$	−9.40497	−	10.9116i	−0.311430	−	0.361318i
$913$	5.79612	−	39.2650i	0.191824	−	1.29948i
$914$	18.2581	+	10.5413i	0.603925	+	0.348676i
$915$	4.45931	+	23.4680i	0.147420	+	0.775828i
$916$	−1.63769	−	2.83657i	−0.0541109	−	0.0937228i
$917$			2.39486i			0.0790853i
$918$	11.6985	−	22.2602i	0.386107	−	0.734698i
$919$			32.5278i			1.07299i	0.843903	+	0.536496i	$0.180252\pi$
$919$			32.5278i			1.07299i	−0.843903	+	0.536496i	$0.819748\pi$
$920$	−7.70040	−	13.3375i	−0.253875	−	0.439724i
$921$	−16.3798	+	3.11243i	−0.539731	+	0.102558i
$922$	−9.50017	+	16.4548i	−0.312872	+	0.541909i
$923$	−16.5488	+	28.6634i	−0.544711	+	0.943468i
$924$	0.549541	+	0.287760i	0.0180786	+	0.00946661i
$925$	0.816155	+	1.41362i	0.0268350	+	0.0464796i
$926$	28.2373			0.927937
$927$	4.83518	−	32.4218i	0.158808	−	1.06487i
$928$	−2.70815			−0.0888993
$929$	37.3218	−	21.5478i	1.22449	−	0.706959i	0.258618	−	0.965980i	$-0.416733\pi$
$929$	37.3218	−	21.5478i	1.22449	−	0.706959i	0.965872	+	0.259020i	$0.0833997\pi$
$930$	−0.0927474	+	0.265720i	−0.00304131	+	0.00871331i
$931$	12.8121	+	7.39705i	0.419898	+	0.242428i
$932$	2.08761	−	3.61585i	0.0683821	−	0.118441i
$933$	−8.92889	+	25.5812i	−0.292319	+	0.837489i
$934$	34.7320	−	20.0526i	1.13647	−	0.656140i
$935$	−4.52779	−	11.4342i	−0.148075	−	0.373939i
$936$	52.4225	+	7.81796i	1.71348	+	0.255538i
$937$		−	11.5132i		−	0.376121i	−0.982157	−	0.188061i	$-0.939780\pi$
$937$		−	11.5132i		−	0.376121i	0.982157	−	0.188061i	$-0.0602201\pi$
$938$	−10.1826	+	5.87895i	−0.332475	+	0.191955i
$939$	−24.3975	+	21.0289i	−0.796184	+	0.686251i
$940$	0.346662	−	0.600436i	0.0113069	−	0.0195841i
$941$	−18.7501	+	32.4761i	−0.611235	+	1.05869i	0.379797	+	0.925070i	$0.375994\pi$
$941$	−18.7501	+	32.4761i	−0.611235	+	1.05869i	−0.991033	+	0.133621i	$0.957340\pi$
$942$	−2.53567	−	13.3445i	−0.0826166	−	0.434786i
$943$	16.6630	−	9.62039i	0.542622	−	0.313283i
$944$		−	37.7051i		−	1.22720i
$945$	2.00358	+	3.17221i	0.0651765	+	0.103192i
$946$	−14.9225	−	37.6844i	−0.485173	−	1.22523i
$947$	1.64407	−	0.949205i	0.0534252	−	0.0308450i	−0.473050	−	0.881036i	$-0.656847\pi$
$947$	1.64407	−	0.949205i	0.0534252	−	0.0308450i	0.526475	+	0.850191i	$0.323513\pi$
$948$	0.147416	−	0.0280115i	0.00478785	−	0.000909772i
$949$	−27.3261	+	47.3302i	−0.887042	+	1.53640i
$950$	10.4564	+	6.03701i	0.339251	+	0.195867i
$951$	−25.3670	−	29.4306i	−0.822581	−	0.954352i
$952$	−6.26934	+	3.61961i	−0.203191	+	0.117312i
$953$	−29.2413			−0.947219			−0.473610	−	0.880735i	$-0.657049\pi$
$953$	−29.2413			−0.947219			−0.473610	+	0.880735i	$0.657049\pi$
$954$	−17.6122	+	22.1557i	−0.570216	+	0.717316i
$955$	−23.4544			−0.758967
$956$	2.11849	+	3.66933i	0.0685169	+	0.118675i
$957$	−17.6992	+	0.729992i	−0.572134	+	0.0235973i
$958$	−17.1911	+	29.7758i	−0.555418	+	0.962012i
$959$	5.49079	−	9.51033i	0.177307	−	0.307105i
$960$	5.06137	−	14.5008i	0.163355	−	0.468010i
$961$	15.4934	+	26.8353i	0.499787	+	0.865656i
$962$			3.41525i			0.110112i
$963$	1.18524	−	0.467305i	0.0381940	−	0.0150587i
$964$		−	2.44738i		−	0.0788249i
$965$	11.8970	+	20.6063i	0.382979	+	0.663339i
$966$	−6.25101	+	5.38790i	−0.201123	+	0.173353i
$967$	4.76099	+	2.74876i	0.153103	+	0.0883941i	0.574594	−	0.818438i	$-0.305160\pi$
$967$	4.76099	+	2.74876i	0.153103	+	0.0883941i	−0.421491	+	0.906832i	$0.638493\pi$
$968$	−7.35664	−	31.3509i	−0.236451	−	1.00766i
$969$	−13.7620	+	2.61500i	−0.442098	+	0.0840060i
$970$	−13.2039	+	7.62326i	−0.423951	+	0.244768i
$971$			23.7715i			0.762863i	0.924397	+	0.381432i	$0.124569\pi$
$971$			23.7715i			0.762863i	−0.924397	+	0.381432i	$0.875431\pi$
$972$	−2.21957	+	0.978690i	−0.0711927	+	0.0313915i
$973$	−10.0654			−0.322683
$974$	−10.2283	−	17.7159i	−0.327736	−	0.567655i
$975$	−40.2270	+	7.64379i	−1.28829	+	0.244797i
$976$	−42.0638	−	24.2855i	−1.34643	−	0.777361i
$977$	−18.5423	−	10.7054i	−0.593220	−	0.342496i	0.173150	−	0.984896i	$-0.444606\pi$
$977$	−18.5423	−	10.7054i	−0.593220	−	0.342496i	−0.766370	+	0.642400i	$0.777939\pi$
$978$	17.7914	−	15.3348i	0.568905	−	0.490354i
$979$	13.3540	−	16.8503i	0.426795	−	0.538537i
$980$			1.05548i			0.0337162i
$981$	3.37977	+	8.57224i	0.107908	+	0.273691i
$982$	−0.0175464			−0.000559929
$983$	−2.31814	+	1.33838i	−0.0739373	+	0.0426877i	−0.536513	−	0.843892i	$-0.680259\pi$
$983$	−2.31814	+	1.33838i	−0.0739373	+	0.0426877i	0.462576	+	0.886580i	$0.346925\pi$
$984$	18.2193	+	6.35929i	0.580810	+	0.202727i
$985$	−12.6307	−	7.29236i	−0.402449	−	0.232354i
$986$	7.46175	−	12.9241i	0.237631	−	0.411588i
$987$	−4.85896	−	1.69598i	−0.154662	−	0.0539836i
$988$	−1.06570	−	1.84584i	−0.0339044	−	0.0587241i
$989$	−45.4940			−1.44663
$990$	4.08260	−	13.4549i	0.129754	−	0.427624i
$991$	33.1201			1.05209			0.526047	−	0.850456i	$-0.323674\pi$
$991$	33.1201			1.05209			0.526047	+	0.850456i	$0.323674\pi$
$992$	0.0504913	+	0.0874535i	0.00160310	+	0.00277665i
$993$	−5.47401	+	4.71819i	−0.173712	+	0.149727i
$994$	2.58424	−	4.47604i	0.0819672	−	0.141971i
$995$	13.7302	+	7.92715i	0.435278	+	0.251308i
$996$	−0.602123	−	3.16879i	−0.0190790	−	0.100407i
$997$	−30.9584	+	17.8739i	−0.980463	+	0.566071i	−0.902410	−	0.430878i	$-0.858204\pi$
$997$	−30.9584	+	17.8739i	−0.980463	+	0.566071i	−0.0780533	+	0.996949i	$0.524870\pi$
$998$	−26.0139			−0.823455
$999$	−1.15624	−	1.83065i	−0.0365820	−	0.0579192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.g.b.32.3	✓	16
3.2	odd	2		297.2.g.b.98.6		16
9.2	odd	6	inner	99.2.g.b.65.6	yes	16
9.4	even	3		891.2.d.b.890.11		16
9.5	odd	6		891.2.d.b.890.6		16
9.7	even	3		297.2.g.b.197.3		16
11.10	odd	2	inner	99.2.g.b.32.6	yes	16
33.32	even	2		297.2.g.b.98.3		16
99.32	even	6		891.2.d.b.890.12		16
99.43	odd	6		297.2.g.b.197.6		16
99.65	even	6	inner	99.2.g.b.65.3	yes	16
99.76	odd	6		891.2.d.b.890.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.g.b.32.3	✓	16	1.1	even	1	trivial
99.2.g.b.32.6	yes	16	11.10	odd	2	inner
99.2.g.b.65.3	yes	16	99.65	even	6	inner
99.2.g.b.65.6	yes	16	9.2	odd	6	inner
297.2.g.b.98.3		16	33.32	even	2
297.2.g.b.98.6		16	3.2	odd	2
297.2.g.b.197.3		16	9.7	even	3
297.2.g.b.197.6		16	99.43	odd	6
891.2.d.b.890.5		16	99.76	odd	6
891.2.d.b.890.6		16	9.5	odd	6
891.2.d.b.890.11		16	9.4	even	3
891.2.d.b.890.12		16	99.32	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.679041 - 1.17613i) q^{2} +(-0.323333 - 1.70160i) q^{3} +(0.0778064 - 0.134765i) q^{4} +(0.901139 + 0.520273i) q^{5} +(-1.78176 + 1.53574i) q^{6} +(0.600962 - 0.346965i) q^{7} -2.92750 q^{8} +(-2.79091 + 1.10037i) q^{9} +O(q^{10})\)	\(q+(-0.679041 - 1.17613i) q^{2} +(-0.323333 - 1.70160i) q^{3} +(0.0778064 - 0.134765i) q^{4} +(0.901139 + 0.520273i) q^{5} +(-1.78176 + 1.53574i) q^{6} +(0.600962 - 0.346965i) q^{7} -2.92750 q^{8} +(-2.79091 + 1.10037i) q^{9} -1.41315i q^{10} +(-2.59932 - 2.05998i) q^{11} +(-0.254473 - 0.0888218i) q^{12} +(5.22645 + 3.01749i) q^{13} +(-0.816155 - 0.471208i) q^{14} +(0.593931 - 1.70160i) q^{15} +(1.83228 + 3.17360i) q^{16} +3.56351 q^{17} +(3.18933 + 2.53529i) q^{18} -2.26957i q^{19} +(0.140229 - 0.0809611i) q^{20} +(-0.784709 - 0.910413i) q^{21} +(-0.657769 + 4.45596i) q^{22} +(4.37840 + 2.52787i) q^{23} +(0.946557 + 4.98144i) q^{24} +(-1.95863 - 3.39245i) q^{25} -8.19600i q^{26} +(2.77479 + 4.39324i) q^{27} -0.107984i q^{28} +(1.54183 + 2.67053i) q^{29} +(-2.40462 + 0.456917i) q^{30} +(0.0574924 - 0.0995797i) q^{31} +(-0.439113 + 0.760566i) q^{32} +(-2.66483 + 5.08908i) q^{33} +(-2.41977 - 4.19117i) q^{34} +0.722067 q^{35} +(-0.0688598 + 0.461732i) q^{36} -0.416697 q^{37} +(-2.66932 + 1.54113i) q^{38} +(3.44469 - 9.86900i) q^{39} +(-2.63809 - 1.52310i) q^{40} +(1.90286 - 3.29585i) q^{41} +(-0.537919 + 1.54113i) q^{42} +(-7.79291 + 4.49924i) q^{43} +(-0.479856 + 0.190017i) q^{44} +(-3.08749 - 0.460450i) q^{45} -6.86612i q^{46} +(3.70818 - 2.14092i) q^{47} +(4.80778 - 4.14394i) q^{48} +(-3.25923 + 5.64515i) q^{49} +(-2.65998 + 4.60723i) q^{50} +(-1.15220 - 6.06369i) q^{51} +(0.813302 - 0.469560i) q^{52} +6.94682i q^{53} +(3.28284 - 6.24671i) q^{54} +(-1.27060 - 3.20869i) q^{55} +(-1.75932 + 1.01574i) q^{56} +(-3.86191 + 0.733827i) q^{57} +(2.09393 - 3.62679i) q^{58} +(-8.91065 - 5.14457i) q^{59} +(-0.183104 - 0.212436i) q^{60} +(-11.4785 + 6.62714i) q^{61} -0.156159 q^{62} +(-1.29544 + 1.62963i) q^{63} +8.52182 q^{64} +(3.13984 + 5.43836i) q^{65} +(7.79496 - 0.321498i) q^{66} +(6.23818 - 10.8048i) q^{67} +(0.277264 - 0.480235i) q^{68} +(2.88576 - 8.26766i) q^{69} +(-0.490313 - 0.849247i) q^{70} +5.48430i q^{71} +(8.17039 - 3.22133i) q^{72} +9.05590i q^{73} +(0.282954 + 0.490091i) q^{74} +(-5.13932 + 4.42971i) q^{75} +(-0.305857 - 0.176587i) q^{76} +(-2.27684 - 0.336096i) q^{77} +(-13.9464 + 2.65004i) q^{78} +(-0.482139 + 0.278363i) q^{79} +3.81314i q^{80} +(6.57837 - 6.14207i) q^{81} -5.16849 q^{82} +(5.98357 + 10.3638i) q^{83} +(-0.183747 + 0.0349149i) q^{84} +(3.21122 + 1.85400i) q^{85} +(10.5834 + 6.11034i) q^{86} +(4.04565 - 3.48705i) q^{87} +(7.60951 + 6.03060i) q^{88} +6.48257i q^{89} +(1.55498 + 3.94397i) q^{90} +4.18786 q^{91} +(0.681335 - 0.393369i) q^{92} +(-0.188034 - 0.0656318i) q^{93} +(-5.03601 - 2.90754i) q^{94} +(1.18080 - 2.04520i) q^{95} +(1.43616 + 0.501280i) q^{96} +(-5.39453 - 9.34360i) q^{97} +8.85260 q^{98} +(9.52122 + 2.88901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9	\( 16 q - 6 q^{3} - 14 q^{4} + 6 q^{9} - 12 q^{11} + 12 q^{12} - 6 q^{14} - 30 q^{15} - 2 q^{16} + 36 q^{20} + 6 q^{22} + 12 q^{23} - 12 q^{25} + 18 q^{27} - 4 q^{31} + 18 q^{33} - 18 q^{36} - 28 q^{37} + 66 q^{38} - 54 q^{42} - 42 q^{45} - 30 q^{47} + 42 q^{48} + 10 q^{49} + 20 q^{55} - 120 q^{56} - 6 q^{58} - 36 q^{59} + 30 q^{60} + 40 q^{64} + 54 q^{66} + 8 q^{67} + 96 q^{69} + 24 q^{75} + 72 q^{77} - 42 q^{78} + 30 q^{81} + 12 q^{82} - 72 q^{86} - 6 q^{88} - 12 q^{91} + 18 q^{92} - 24 q^{93} - 4 q^{97} - 36 q^{99}+O(q^{100}) \) 16 * q - 6 * q^3 - 14 * q^4 + 6 * q^9 - 12 * q^11 + 12 * q^12 - 6 * q^14 - 30 * q^15 - 2 * q^16 + 36 * q^20 + 6 * q^22 + 12 * q^23 - 12 * q^25 + 18 * q^27 - 4 * q^31 + 18 * q^33 - 18 * q^36 - 28 * q^37 + 66 * q^38 - 54 * q^42 - 42 * q^45 - 30 * q^47 + 42 * q^48 + 10 * q^49 + 20 * q^55 - 120 * q^56 - 6 * q^58 - 36 * q^59 + 30 * q^60 + 40 * q^64 + 54 * q^66 + 8 * q^67 + 96 * q^69 + 24 * q^75 + 72 * q^77 - 42 * q^78 + 30 * q^81 + 12 * q^82 - 72 * q^86 - 6 * q^88 - 12 * q^91 + 18 * q^92 - 24 * q^93 - 4 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more