LMFDB - Embedded newform 99.2.g.b.65.7

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			65.7
Root			$1.10617 - 1.91594i$ of defining polynomial
Character	$\chi$	$=$	99.65
Dual form			99.2.g.b.32.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10617 - 1.91594i) q^{2} +(1.59999 + 0.663339i) q^{3} +(-1.44722 - 2.50665i) q^{4} +(-2.54721 + 1.47063i) q^{5} +(3.04078 - 2.33173i) q^{6} +(-1.72189 - 0.994132i) q^{7} -1.97879 q^{8} +(2.11996 + 2.12268i) q^{9} +O(q^{10})$	\(q+(1.10617 - 1.91594i) q^{2} +(1.59999 + 0.663339i) q^{3} +(-1.44722 - 2.50665i) q^{4} +(-2.54721 + 1.47063i) q^{5} +(3.04078 - 2.33173i) q^{6} +(-1.72189 - 0.994132i) q^{7} -1.97879 q^{8} +(2.11996 + 2.12268i) q^{9} +6.50707i q^{10} +(-2.32680 + 2.36347i) q^{11} +(-0.652777 - 4.97063i) q^{12} +(3.09345 - 1.78601i) q^{13} +(-3.80939 + 2.19935i) q^{14} +(-5.05105 + 0.663339i) q^{15} +(0.705560 - 1.22207i) q^{16} -6.08156 q^{17} +(6.41196 - 1.71368i) q^{18} +0.896820i q^{19} +(7.37273 + 4.25665i) q^{20} +(-2.09556 - 2.73280i) q^{21} +(1.95443 + 7.07241i) q^{22} +(4.90171 - 2.83000i) q^{23} +(-3.16605 - 1.31261i) q^{24} +(1.82552 - 3.16190i) q^{25} -7.90249i q^{26} +(1.98387 + 4.80253i) q^{27} +5.75490i q^{28} +(1.60511 - 2.78014i) q^{29} +(-4.31639 + 10.4113i) q^{30} +(-0.278312 - 0.482050i) q^{31} +(-3.53973 - 6.13098i) q^{32} +(-5.29065 + 2.23808i) q^{33} +(-6.72723 + 11.6519i) q^{34} +5.84801 q^{35} +(2.25277 - 8.38598i) q^{36} +2.08674 q^{37} +(1.71825 + 0.992034i) q^{38} +(6.13423 - 0.805590i) q^{39} +(5.04039 - 2.91007i) q^{40} +(4.52912 + 7.84467i) q^{41} +(-7.55393 + 0.992034i) q^{42} +(-2.14823 - 1.24028i) q^{43} +(9.29179 + 2.41203i) q^{44} +(-8.52167 - 2.28922i) q^{45} -12.5218i q^{46} +(-8.77101 - 5.06394i) q^{47} +(1.93954 - 1.48727i) q^{48} +(-1.52340 - 2.63861i) q^{49} +(-4.03867 - 6.99518i) q^{50} +(-9.73046 - 4.03414i) q^{51} +(-8.95379 - 5.16948i) q^{52} -2.18950i q^{53} +(11.3958 + 1.51142i) q^{54} +(2.45106 - 9.44213i) q^{55} +(3.40725 + 1.96718i) q^{56} +(-0.594896 + 1.43491i) q^{57} +(-3.55105 - 6.15060i) q^{58} +(-1.19404 + 0.689379i) q^{59} +(8.97273 + 11.7012i) q^{60} +(9.99879 + 5.77281i) q^{61} -1.23144 q^{62} +(-1.54011 - 5.76253i) q^{63} -12.8399 q^{64} +(-5.25312 + 9.09867i) q^{65} +(-1.56432 + 12.6123i) q^{66} +(-0.471025 - 0.815839i) q^{67} +(8.80134 + 15.2444i) q^{68} +(9.71996 - 1.27649i) q^{69} +(6.46889 - 11.2044i) q^{70} +4.55585i q^{71} +(-4.19496 - 4.20033i) q^{72} +12.7317i q^{73} +(2.30829 - 3.99807i) q^{74} +(5.01824 - 3.84808i) q^{75} +(2.24802 - 1.29789i) q^{76} +(6.35609 - 1.75648i) q^{77} +(5.24203 - 12.6439i) q^{78} +(-10.4939 - 6.05866i) q^{79} +4.15048i q^{80} +(-0.0115201 + 8.99999i) q^{81} +20.0399 q^{82} +(2.60300 - 4.50853i) q^{83} +(-3.81745 + 9.20780i) q^{84} +(15.4910 - 8.94374i) q^{85} +(-4.75262 + 2.74393i) q^{86} +(4.41235 - 3.38347i) q^{87} +(4.60425 - 4.67681i) q^{88} +14.3732i q^{89} +(-13.8124 + 13.7947i) q^{90} -7.10210 q^{91} +(-14.1877 - 8.19126i) q^{92} +(-0.125534 - 0.955892i) q^{93} +(-19.4044 + 11.2031i) q^{94} +(-1.31889 - 2.28439i) q^{95} +(-1.59662 - 12.1576i) q^{96} +(-1.79787 + 3.11401i) q^{97} -6.74056 q^{98} +(-9.94962 + 0.0714190i) 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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.10617	−	1.91594i	0.782179	−	1.35477i	−0.148491	−	0.988914i	$-0.547441\pi$
$2$	1.10617	−	1.91594i	0.782179	−	1.35477i	0.930670	−	0.365860i	$-0.119225\pi$
$3$	1.59999	+	0.663339i	0.923757	+	0.382979i
$3$	1.59999	+	0.663339i	0.923757	+	0.382979i
$4$	−1.44722	−	2.50665i	−0.723608	−	1.25333i
$5$	−2.54721	+	1.47063i	−1.13915	+	0.657687i	−0.946219	−	0.323526i	$-0.895132\pi$
$5$	−2.54721	+	1.47063i	−1.13915	+	0.657687i	−0.192928	+	0.981213i	$0.561798\pi$
$6$	3.04078	−	2.33173i	1.24139	−	0.951924i
$7$	−1.72189	−	0.994132i	−0.650812	−	0.375747i	0.137955	−	0.990438i	$-0.455947\pi$
$7$	−1.72189	−	0.994132i	−0.650812	−	0.375747i	−0.788767	+	0.614692i	$0.789280\pi$
$8$	−1.97879			−0.699607
$9$	2.11996	+	2.12268i	0.706654	+	0.707559i
$10$			6.50707i			2.05772i
$11$	−2.32680	+	2.36347i	−0.701557	+	0.712613i
$11$	−2.32680	+	2.36347i	−0.701557	+	0.712613i
$12$	−0.652777	−	4.97063i	−0.188441	−	1.43490i
$13$	3.09345	−	1.78601i	0.857969	−	0.495349i	−0.00536239	−	0.999986i	$-0.501707\pi$
$13$	3.09345	−	1.78601i	0.857969	−	0.495349i	0.863332	+	0.504637i	$0.168374\pi$
$14$	−3.80939	+	2.19935i	−1.01810	+	0.587802i
$15$	−5.05105	+	0.663339i	−1.30418	+	0.171273i
$16$	0.705560	−	1.22207i	0.176390	−	0.305517i
$17$	−6.08156			−1.47500			−0.737498	−	0.675350i	$-0.763993\pi$
$17$	−6.08156			−1.47500			−0.737498	+	0.675350i	$0.763993\pi$
$18$	6.41196	−	1.71368i	1.51131	−	0.403919i
$19$			0.896820i			0.205745i	0.994695	+	0.102872i	$0.0328033\pi$
$19$			0.896820i			0.205745i	−0.994695	+	0.102872i	$0.967197\pi$
$20$	7.37273	+	4.25665i	1.64859	+	0.951816i
$21$	−2.09556	−	2.73280i	−0.457289	−	0.596346i
$22$	1.95443	+	7.07241i	0.416687	+	1.50784i
$23$	4.90171	−	2.83000i	1.02208	−	0.590096i	0.107372	−	0.994219i	$-0.465756\pi$
$23$	4.90171	−	2.83000i	1.02208	−	0.590096i	0.914705	+	0.404123i	$0.132423\pi$
$24$	−3.16605	−	1.31261i	−0.646267	−	0.267935i
$25$	1.82552	−	3.16190i	0.365105	−	0.632380i
$26$		−	7.90249i		−	1.54981i
$27$	1.98387	+	4.80253i	0.381796	+	0.924246i
$28$			5.75490i			1.08757i
$29$	1.60511	−	2.78014i	0.298062	−	0.516259i	−0.677630	−	0.735403i	$-0.736993\pi$
$29$	1.60511	−	2.78014i	0.298062	−	0.516259i	0.975693	+	0.219144i	$0.0703264\pi$
$30$	−4.31639	+	10.4113i	−0.788062	+	1.90083i
$31$	−0.278312	−	0.482050i	−0.0499862	−	0.0865787i	0.839950	−	0.542664i	$-0.182584\pi$
$31$	−0.278312	−	0.482050i	−0.0499862	−	0.0865787i	−0.889936	+	0.456086i	$0.849251\pi$
$32$	−3.53973	−	6.13098i	−0.625741	−	1.08382i
$33$	−5.29065	+	2.23808i	−0.920984	+	0.389600i
$34$	−6.72723	+	11.6519i	−1.15371	+	1.99829i
$35$	5.84801			0.988495
$36$	2.25277	−	8.38598i	0.375462	−	1.39766i
$37$	2.08674			0.343058			0.171529	−	0.985179i	$-0.445129\pi$
$37$	2.08674			0.343058			0.171529	+	0.985179i	$0.445129\pi$
$38$	1.71825	+	0.992034i	0.278738	+	0.160929i
$39$	6.13423	−	0.805590i	0.982263	−	0.128998i
$40$	5.04039	−	2.91007i	0.796956	−	0.460123i
$41$	4.52912	+	7.84467i	0.707330	+	1.22513i	0.965844	+	0.259124i	$0.0834337\pi$
$41$	4.52912	+	7.84467i	0.707330	+	1.22513i	−0.258514	+	0.966007i	$0.583233\pi$
$42$	−7.55393	+	0.992034i	−1.16560	+	0.153074i
$43$	−2.14823	−	1.24028i	−0.327603	−	0.189141i	0.327174	−	0.944964i	$-0.393904\pi$
$43$	−2.14823	−	1.24028i	−0.327603	−	0.189141i	−0.654776	+	0.755823i	$0.727237\pi$
$44$	9.29179	+	2.41203i	1.40079	+	0.363627i
$45$	−8.52167	−	2.28922i	−1.27034	−	0.341257i
$46$		−	12.5218i		−	1.84624i
$47$	−8.77101	−	5.06394i	−1.27938	−	0.738652i	−0.302648	−	0.953102i	$-0.597871\pi$
$47$	−8.77101	−	5.06394i	−1.27938	−	0.738652i	−0.976735	+	0.214450i	$0.931204\pi$
$48$	1.93954	−	1.48727i	0.279948	−	0.214669i
$49$	−1.52340	−	2.63861i	−0.217629	−	0.376944i
$50$	−4.03867	−	6.99518i	−0.571154	−	0.989268i
$51$	−9.73046	−	4.03414i	−1.36254	−	0.564892i
$52$	−8.95379	−	5.16948i	−1.24167	−	0.716877i
$53$		−	2.18950i		−	0.300751i	−0.988629	−	0.150376i	$-0.951952\pi$
$53$		−	2.18950i		−	0.300751i	0.988629	−	0.150376i	$-0.0480483\pi$
$54$	11.3958	+	1.51142i	1.55078	+	0.205679i
$55$	2.45106	−	9.44213i	0.330500	−	1.27318i
$56$	3.40725	+	1.96718i	0.455313	+	0.262875i
$57$	−0.594896	+	1.43491i	−0.0787959	+	0.190058i
$58$	−3.55105	−	6.15060i	−0.466276	−	0.807613i
$59$	−1.19404	+	0.689379i	−0.155451	+	0.0897496i	−0.575708	−	0.817656i	$-0.695273\pi$
$59$	−1.19404	+	0.689379i	−0.155451	+	0.0897496i	0.420257	+	0.907405i	$0.361940\pi$
$60$	8.97273	+	11.7012i	1.15837	+	1.51062i
$61$	9.99879	+	5.77281i	1.28021	+	0.739132i	0.976887	−	0.213754i	$-0.0685692\pi$
$61$	9.99879	+	5.77281i	1.28021	+	0.739132i	0.303327	+	0.952887i	$0.401903\pi$
$62$	−1.23144			−0.156393
$63$	−1.54011	−	5.76253i	−0.194036	−	0.726011i
$64$	−12.8399			−1.60499
$65$	−5.25312	+	9.09867i	−0.651569	+	1.12855i
$66$	−1.56432	+	12.6123i	−0.192555	+	1.55246i
$67$	−0.471025	−	0.815839i	−0.0575449	−	0.0996706i	0.835818	−	0.549007i	$-0.184994\pi$
$67$	−0.471025	−	0.815839i	−0.0575449	−	0.0996706i	−0.893363	+	0.449336i	$0.851661\pi$
$68$	8.80134	+	15.2444i	1.06732	+	1.84865i
$69$	9.71996	−	1.27649i	1.17015	−	0.153672i
$70$	6.46889	−	11.2044i	0.773180	−	1.33919i
$71$			4.55585i			0.540680i	0.962765	+	0.270340i	$0.0871362\pi$
$71$			4.55585i			0.540680i	−0.962765	+	0.270340i	$0.912864\pi$
$72$	−4.19496	−	4.20033i	−0.494380	−	0.495014i
$73$			12.7317i			1.49014i	0.666988	+	0.745068i	$0.267583\pi$
$73$			12.7317i			1.49014i	−0.666988	+	0.745068i	$0.732417\pi$
$74$	2.30829	−	3.99807i	0.268333	−	0.464766i
$75$	5.01824	−	3.84808i	0.579456	−	0.444338i
$76$	2.24802	−	1.29789i	0.257865	−	0.148879i
$77$	6.35609	−	1.75648i	0.724344	−	0.200170i
$78$	5.24203	−	12.6439i	0.593543	−	1.43164i
$79$	−10.4939	−	6.05866i	−1.18066	−	0.681653i	−0.224490	−	0.974476i	$-0.572072\pi$
$79$	−10.4939	−	6.05866i	−1.18066	−	0.681653i	−0.956166	+	0.292824i	$0.905405\pi$
$80$			4.15048i			0.464038i
$81$	−0.0115201	+	8.99999i	−0.00128001	+	0.999999i
$82$	20.0399			2.21303
$83$	2.60300	−	4.50853i	0.285717	−	0.494876i	−0.687066	−	0.726595i	$-0.741102\pi$
$83$	2.60300	−	4.50853i	0.285717	−	0.494876i	0.972783	+	0.231719i	$0.0744350\pi$
$84$	−3.81745	+	9.20780i	−0.416518	+	1.00465i
$85$	15.4910	−	8.94374i	1.68024	−	0.970085i
$86$	−4.75262	+	2.74393i	−0.512488	+	0.295885i
$87$	4.41235	−	3.38347i	0.473053	−	0.362746i
$88$	4.60425	−	4.67681i	0.490815	−	0.498550i
$89$			14.3732i			1.52356i	0.647835	+	0.761780i	$0.275674\pi$
$89$			14.3732i			1.52356i	−0.647835	+	0.761780i	$0.724326\pi$
$90$	−13.8124	+	13.7947i	−1.45596	+	1.45409i
$91$	−7.10210			−0.744503
$92$	−14.1877	−	8.19126i	−1.47917	−	0.853997i
$93$	−0.125534	−	0.955892i	−0.0130173	−	0.0991214i
$94$	−19.4044	+	11.2031i	−2.00141	+	1.15552i
$95$	−1.31889	−	2.28439i	−0.135316	−	0.234374i
$96$	−1.59662	−	12.1576i	−0.162954	−	1.24083i
$97$	−1.79787	+	3.11401i	−0.182546	+	0.316180i	−0.942747	−	0.333509i	$-0.891767\pi$
$97$	−1.79787	+	3.11401i	−0.182546	+	0.316180i	0.760201	+	0.649689i	$0.225101\pi$
$98$	−6.74056			−0.680899
$99$	−9.94962	+	0.0714190i	−0.999974	+	0.00717787i
$100$	−10.5677			−1.05677
$101$	−0.543121	+	0.940713i	−0.0540426	+	0.0936045i	−0.891781	−	0.452467i	$-0.850544\pi$
$101$	−0.543121	+	0.940713i	−0.0540426	+	0.0936045i	0.837739	+	0.546072i	$0.183877\pi$
$102$	−18.4927	+	14.1805i	−1.83105	+	1.40408i
$103$	0.454897	+	0.787905i	0.0448223	+	0.0776346i	0.887566	−	0.460680i	$-0.152394\pi$
$103$	0.454897	+	0.787905i	0.0448223	+	0.0776346i	−0.842744	+	0.538315i	$0.819061\pi$
$104$	−6.12129	+	3.53413i	−0.600242	+	0.346550i
$105$	9.35679	+	3.87922i	0.913129	+	0.378573i
$106$	−4.19496	−	2.42196i	−0.407450	−	0.235242i
$107$	14.4638			1.39827			0.699135	−	0.714990i	$-0.253569\pi$
$107$	14.4638			1.39827			0.699135	+	0.714990i	$0.253569\pi$
$108$	9.16717	−	11.9232i	0.882112	−	1.14731i
$109$			4.66346i			0.446678i	0.974741	+	0.223339i	$0.0716957\pi$
$109$			4.66346i			0.446678i	−0.974741	+	0.223339i	$0.928304\pi$
$110$	−15.3793	−	15.1407i	−1.46636	−	1.44361i
$111$	3.33877	+	1.38422i	0.316902	+	0.131384i
$112$	−2.42979	+	1.40284i	−0.229594	+	0.132556i
$113$	14.9126	−	8.60982i	1.40286	−	0.809943i	0.408178	−	0.912903i	$-0.366164\pi$
$113$	14.9126	−	8.60982i	1.40286	−	0.809943i	0.994686	+	0.102959i	$0.0328311\pi$
$114$	2.09114	+	2.72703i	0.195853	+	0.255410i
$115$	−8.32379	+	14.4172i	−0.776197	+	1.34441i
$116$	−9.29179			−0.862721
$117$	10.3491	+	2.78014i	0.956776	+	0.257024i
$118$			3.05028i			0.280801i
$119$	10.4718	+	6.04588i	0.959945	+	0.554224i
$120$	9.99496	−	1.31261i	0.912411	−	0.119824i
$121$	−0.171988	−	10.9987i	−0.0156352	−	0.999878i
$122$	22.1207	−	12.7714i	2.00271	−	1.15627i
$123$	2.04289	+	15.5558i	0.184201	+	1.40262i
$124$	−0.805554	+	1.39526i	−0.0723409	+	0.125298i
$125$		−	3.96763i		−	0.354876i
$126$	−12.7443	−	3.42357i	−1.13535	−	0.304996i
$127$		−	4.30164i		−	0.381709i	−0.981618	−	0.190854i	$-0.938874\pi$
$127$		−	4.30164i		−	0.381709i	0.981618	−	0.190854i	$-0.0611259\pi$
$128$	−7.12363	+	12.3385i	−0.629646	+	1.09058i
$129$	−2.61443	−	3.40945i	−0.230188	−	0.300186i
$130$	11.6217	+	20.1293i	1.01929	+	1.76546i
$131$	−5.42256	−	9.39216i	−0.473772	−	0.820596i	0.525778	−	0.850622i	$-0.323774\pi$
$131$	−5.42256	−	9.39216i	−0.473772	−	0.820596i	−0.999549	+	0.0300257i	$0.990441\pi$
$132$	13.2668	+	10.0228i	1.15473	+	0.872376i
$133$	0.891558	−	1.54422i	0.0773079	−	0.133901i
$134$	−2.08413			−0.180042
$135$	−12.1161	−	9.31550i	−1.04279	−	0.801750i
$136$	12.0341			1.03192
$137$	−2.15433	−	1.24380i	−0.184057	−	0.106265i	0.405141	−	0.914254i	$-0.367223\pi$
$137$	−2.15433	−	1.24380i	−0.184057	−	0.106265i	−0.589197	+	0.807989i	$0.700556\pi$
$138$	8.30623	−	20.0349i	0.707073	−	1.70548i
$139$	1.22677	−	0.708278i	0.104054	−	0.0600754i	−0.447070	−	0.894499i	$-0.647533\pi$
$139$	1.22677	−	0.708278i	0.104054	−	0.0600754i	0.551124	+	0.834424i	$0.314199\pi$
$140$	−8.46334	−	14.6589i	−0.715283	−	1.23891i
$141$	−10.6744	−	13.9204i	−0.898951	−	1.17231i
$142$	8.72874	+	5.03954i	0.732500	+	0.422909i
$143$	−2.97668	+	11.4670i	−0.248922	+	0.958916i
$144$	4.08981	−	1.09306i	0.340818	−	0.0910881i
$145$			9.44213i			0.784126i
$146$	24.3932	+	14.0834i	2.01880	+	1.16555i
$147$	−0.687141	−	5.23229i	−0.0566745	−	0.431552i
$148$	−3.01997	−	5.23074i	−0.248240	−	0.429964i
$149$	0.169446	+	0.293489i	0.0138815	+	0.0240435i	0.872883	−	0.487930i	$-0.162248\pi$
$149$	0.169446	+	0.293489i	0.0138815	+	0.0240435i	−0.859001	+	0.511974i	$0.828915\pi$
$150$	−1.82167	−	13.8713i	−0.148739	−	1.13258i
$151$	0.144791	+	0.0835951i	0.0117829	+	0.00680287i	0.505880	−	0.862604i	$-0.331168\pi$
$151$	0.144791	+	0.0835951i	0.0117829	+	0.00680287i	−0.494097	+	0.869407i	$0.664501\pi$
$152$		−	1.77462i		−	0.143941i
$153$	−12.8927	−	12.9092i	−1.04231	−	1.04365i
$154$	3.66559	−	14.1209i	0.295382	−	1.13789i
$155$	1.41784	+	0.818588i	0.113883	+	0.0657506i
$156$	−10.8969	−	14.2105i	−0.872450	−	1.13775i
$157$	10.4510	+	18.1017i	0.834083	+	1.44467i	0.894775	+	0.446517i	$0.147336\pi$
$157$	10.4510	+	18.1017i	0.834083	+	1.44467i	−0.0606922	+	0.998157i	$0.519331\pi$
$158$	−23.2161	+	13.4038i	−1.84697	+	1.06635i
$159$	1.45238	−	3.50319i	0.115182	−	0.277821i
$160$	18.0329	+	10.4113i	1.42562	+	0.823084i
$161$	−11.2536			−0.886907
$162$	17.2307	+	9.97758i	1.35377	+	0.783913i
$163$	2.63650			0.206506			0.103253	−	0.994655i	$-0.467075\pi$
$163$	2.63650			0.206506			0.103253	+	0.994655i	$0.467075\pi$
$164$	13.1092	−	22.7059i	1.02366	−	1.77303i
$165$	10.1850	−	13.4815i	0.792902	−	1.04953i
$166$	−5.75872	−	9.97439i	−0.446963	−	0.774163i
$167$	−7.68667	−	13.3137i	−0.594813	−	1.03025i	−0.993573	−	0.113191i	$-0.963893\pi$
$167$	−7.68667	−	13.3137i	−0.594813	−	1.03025i	0.398761	−	0.917055i	$-0.369440\pi$
$168$	4.14668	+	5.40764i	0.319923	+	0.417208i
$169$	−0.120368	+	0.208483i	−0.00925905	+	0.0160371i
$170$		−	39.5732i		−	3.03512i
$171$	−1.90366	+	1.90123i	−0.145577	+	0.145390i
$172$			7.17984i			0.547458i
$173$	−5.12402	+	8.87506i	−0.389572	+	0.674758i	−0.992392	−	0.123119i	$-0.960710\pi$
$173$	−5.12402	+	8.87506i	−0.389572	+	0.674758i	0.602820	+	0.797877i	$0.294044\pi$
$174$	−1.60173	−	12.1965i	−0.121427	−	0.924612i
$175$	−6.28669	+	3.62962i	−0.475229	+	0.274374i
$176$	1.24662	+	4.51108i	0.0939674	+	0.340035i
$177$	−2.36775	+	0.310949i	−0.177971	+	0.0233724i
$178$	27.5383	+	15.8992i	2.06408	+	1.19170i
$179$		−	12.8723i		−	0.962123i	−0.876687	−	0.481062i	$-0.840251\pi$
$179$		−	12.8723i		−	0.962123i	0.876687	−	0.481062i	$-0.159749\pi$
$180$	6.59442	+	24.6739i	0.491519	+	1.83908i
$181$	−9.43223			−0.701092			−0.350546	−	0.936545i	$-0.614004\pi$
$181$	−9.43223			−0.701092			−0.350546	+	0.936545i	$0.614004\pi$
$182$	−7.85612	+	13.6072i	−0.582334	+	1.00863i
$183$	12.1687	+	15.8690i	0.899535	+	1.17307i
$184$	−9.69945	+	5.59998i	−0.715053	+	0.412836i
$185$	−5.31537	+	3.06883i	−0.390794	+	0.225625i
$186$	−1.97029	−	0.816861i	−0.144469	−	0.0598952i
$187$	14.1506	−	14.3736i	1.03479	−	1.05110i
$188$			29.3145i			2.13798i
$189$	1.35834	−	10.2416i	0.0988048	−	0.744970i
$190$	−5.83567			−0.423364
$191$	−5.46981	−	3.15800i	−0.395781	−	0.228505i	0.288881	−	0.957365i	$-0.406717\pi$
$191$	−5.46981	−	3.15800i	−0.395781	−	0.228505i	−0.684662	+	0.728861i	$0.740050\pi$
$192$	−20.5437	−	8.51720i	−1.48262	−	0.614676i
$193$	−10.5309	+	6.08001i	−0.758030	+	0.437649i	−0.828588	−	0.559859i	$-0.810855\pi$
$193$	−10.5309	+	6.08001i	−0.758030	+	0.437649i	0.0705580	+	0.997508i	$0.477522\pi$
$194$	3.97750	+	6.88924i	0.285568	+	0.494618i
$195$	−14.4405	+	11.0732i	−1.03410	+	0.792969i
$196$	−4.40939	+	7.63729i	−0.314956	+	0.545520i
$197$	−0.105343			−0.00750541			−0.00375271	−	0.999993i	$-0.501195\pi$
$197$	−0.105343			−0.00750541			−0.00375271	+	0.999993i	$0.501195\pi$
$198$	−10.8691	+	19.1419i	−0.772435	+	1.36035i
$199$	−15.0253			−1.06512			−0.532559	−	0.846393i	$-0.678769\pi$
$199$	−15.0253			−1.06512			−0.532559	+	0.846393i	$0.678769\pi$
$200$	−3.61232	+	6.25673i	−0.255430	+	0.442417i
$201$	−0.212459	−	1.61779i	−0.0149857	−	0.114110i
$202$	1.20157	+	2.08117i	0.0845420	+	0.146431i
$203$	−5.52765	+	3.19139i	−0.387965	+	0.223992i
$204$	3.96990	+	30.2292i	0.277949	+	2.11647i
$205$	−23.0732	−	13.3213i	−1.61151	−	0.930403i
$206$	2.01277			0.140236
$207$	16.3986	+	4.40525i	1.13978	+	0.306186i
$208$		−	5.04054i		−	0.349498i
$209$	−2.11961	−	2.08672i	−0.146616	−	0.144342i
$210$	17.7825	−	13.6360i	1.22711	−	0.940972i
$211$	−18.5712	+	10.7221i	−1.27850	+	0.738141i	−0.976572	−	0.215191i	$-0.930963\pi$
$211$	−18.5712	+	10.7221i	−1.27850	+	0.738141i	−0.301925	+	0.953332i	$0.597629\pi$
$212$	−5.48833	+	3.16869i	−0.376940	+	0.217626i
$213$	−3.02208	+	7.28934i	−0.207069	+	0.499457i
$214$	15.9994	−	27.7118i	1.09370	−	1.89434i
$215$	7.29601			0.497584
$216$	−3.92566	−	9.50318i	−0.267108	−	0.646610i
$217$			1.10671i			0.0751286i
$218$	8.93490	+	5.15857i	0.605148	+	0.349382i
$219$	−8.44546	+	20.3707i	−0.570691	+	1.37652i
$220$	−27.2154	+	7.52086i	−1.83486	+	0.507056i
$221$	−18.8130	+	10.8617i	−1.26550	+	0.730637i
$222$	6.34532	−	4.86571i	0.425870	−	0.326565i
$223$	−4.15489	+	7.19647i	−0.278232	+	0.481911i	−0.970945	−	0.239301i	$-0.923082\pi$
$223$	−4.15489	+	7.19647i	−0.278232	+	0.481911i	0.692714	+	0.721213i	$0.256415\pi$
$224$			14.0758i			0.940480i
$225$	10.5817	−	2.82811i	0.705449	−	0.188541i
$226$		−	38.0956i		−	2.53408i
$227$	10.3771	−	17.9737i	0.688755	−	1.19296i	−0.283486	−	0.958976i	$-0.591491\pi$
$227$	10.3771	−	17.9737i	0.688755	−	1.19296i	0.972241	−	0.233982i	$-0.0751756\pi$
$228$	4.45776	−	0.585424i	0.295222	−	0.0387706i
$229$	−10.1892	−	17.6483i	−0.673325	−	1.16623i	−0.976956	−	0.213443i	$-0.931532\pi$
$229$	−10.1892	−	17.6483i	−0.673325	−	1.16623i	0.303631	−	0.952790i	$-0.401801\pi$
$230$	18.4150	+	31.8958i	1.21425	+	2.10314i
$231$	11.3349	+	1.40588i	0.745779	+	0.0925004i
$232$	−3.17618	+	5.50131i	−0.208526	+	0.361178i
$233$	3.65446			0.239412			0.119706	−	0.992809i	$-0.461805\pi$
$233$	3.65446			0.239412			0.119706	+	0.992809i	$0.461805\pi$
$234$	16.7744	−	16.7530i	1.09658	−	1.09518i
$235$	29.7888			1.94321
$236$	3.45607	+	1.99536i	0.224971	+	0.129887i
$237$	−12.7712	−	16.6548i	−0.829581	−	1.08185i
$238$	23.1671	−	13.3755i	1.50170	−	0.867006i
$239$	1.19109	+	2.06303i	0.0770454	+	0.133447i	0.901974	−	0.431790i	$-0.142118\pi$
$239$	1.19109	+	2.06303i	0.0770454	+	0.133447i	−0.824928	+	0.565237i	$0.808785\pi$
$240$	−2.75318	+	6.64075i	−0.177717	+	0.428658i
$241$	3.51980	+	2.03216i	0.226730	+	0.130903i	0.609063	−	0.793122i	$-0.291546\pi$
$241$	3.51980	+	2.03216i	0.226730	+	0.130903i	−0.382332	+	0.924025i	$0.624879\pi$
$242$	−21.2630	−	11.8368i	−1.36684	−	0.760901i
$243$	−5.98848	+	14.3923i	−0.384161	+	0.923266i
$244$		−	33.4180i		−	2.13937i
$245$	7.76086	+	4.48073i	0.495823	+	0.286264i
$246$	32.0637	+	13.2932i	2.04431	+	0.847546i
$247$	1.60173	+	2.77427i	0.101915	+	0.176523i
$248$	0.550720	+	0.953875i	0.0349707	+	0.0605711i
$249$	7.15548	−	5.48695i	0.453460	−	0.347722i
$250$	−7.60175	−	4.38887i	−0.480777	−	0.277577i
$251$		−	15.0922i		−	0.952613i	−0.879279	−	0.476306i	$-0.841975\pi$
$251$		−	15.0922i		−	0.952613i	0.879279	−	0.476306i	$-0.158025\pi$
$252$	−12.2158	+	12.2002i	−0.769523	+	0.768538i
$253$	−4.71668	+	18.1699i	−0.296535	+	1.14233i
$254$	−8.24169	−	4.75834i	−0.517129	−	0.298565i
$255$	30.7183	−	4.03414i	1.92365	−	0.252628i
$256$	2.91997	+	5.05754i	0.182498	+	0.316096i
$257$	8.44818	−	4.87756i	0.526983	−	0.304254i	−0.212804	−	0.977095i	$-0.568260\pi$
$257$	8.44818	−	4.87756i	0.526983	−	0.304254i	0.739787	+	0.672841i	$0.234926\pi$
$258$	−9.42431	+	1.23767i	−0.586732	+	0.0770538i
$259$	−3.59313	−	2.07450i	−0.223267	−	0.128903i
$260$	30.4096			1.88592
$261$	9.30412	−	2.48665i	0.575910	−	0.153920i
$262$	−23.9931			−1.48230
$263$	−3.83444	+	6.64145i	−0.236442	+	0.409529i	−0.959691	−	0.281058i	$-0.909315\pi$
$263$	−3.83444	+	6.64145i	−0.236442	+	0.409529i	0.723249	+	0.690587i	$0.242648\pi$
$264$	10.4691	−	4.42869i	0.644327	−	0.272567i
$265$	3.21996	+	5.57713i	0.197800	+	0.342600i
$266$	−1.97243	−	3.41634i	−0.120937	−	0.209469i
$267$	−9.53433	+	22.9971i	−0.583492	+	1.40740i
$268$	−1.36335	+	2.36139i	−0.0832799	+	0.144245i
$269$			5.00262i			0.305015i	0.988302	+	0.152507i	$0.0487348\pi$
$269$			5.00262i			0.305015i	−0.988302	+	0.152507i	$0.951265\pi$
$270$	−31.2504	+	12.9092i	−1.90184	+	0.785629i
$271$			7.56909i			0.459789i	0.973216	+	0.229895i	$0.0738381\pi$
$271$			7.56909i			0.459789i	−0.973216	+	0.229895i	$0.926162\pi$
$272$	−4.29091	+	7.43207i	−0.260175	+	0.450636i
$273$	−11.3633	−	4.71110i	−0.687739	−	0.285129i
$274$	−4.76610	+	2.75171i	−0.287930	+	0.166237i
$275$	3.22542	+	11.6717i	0.194500	+	0.703829i
$276$	−17.2666	−	22.5172i	−1.03933	−	1.35538i
$277$	−0.758876	−	0.438137i	−0.0455964	−	0.0263251i	0.477028	−	0.878888i	$-0.341714\pi$
$277$	−0.758876	−	0.438137i	−0.0455964	−	0.0263251i	−0.522625	+	0.852563i	$0.675047\pi$
$278$		−	3.13390i		−	0.187959i
$279$	0.433226	−	1.61269i	0.0259366	−	0.0965494i
$280$	−11.5720			−0.691558
$281$	6.46756	−	11.2022i	0.385823	−	0.668264i	−0.606060	−	0.795419i	$-0.707251\pi$
$281$	6.46756	−	11.2022i	0.385823	−	0.668264i	0.991883	+	0.127154i	$0.0405844\pi$
$282$	−38.4784	+	5.05326i	−2.29136	+	0.300917i
$283$	13.9614	−	8.06064i	0.829921	−	0.479155i	−0.0239043	−	0.999714i	$-0.507610\pi$
$283$	13.9614	−	8.06064i	0.829921	−	0.479155i	0.853826	+	0.520559i	$0.174276\pi$
$284$	11.4199	−	6.59331i	0.677649	−	0.391241i
$285$	−0.594896	−	4.52989i	−0.0352386	−	0.268327i
$286$	18.6773	+	18.3875i	1.10441	+	1.08728i
$287$		−	18.0102i		−	1.06311i
$288$	5.51002	−	20.5112i	0.324681	−	1.20863i
$289$	19.9854			1.17561
$290$	18.0906	+	10.4446i	1.06231	+	0.613327i
$291$	−4.94223	+	3.78980i	−0.289719	+	0.222162i
$292$	31.9140	−	18.4256i	1.86763	−	1.07828i
$293$	−5.39921	−	9.35171i	−0.315425	−	0.546332i	0.664103	−	0.747641i	$-0.268814\pi$
$293$	−5.39921	−	9.35171i	−0.315425	−	0.546332i	−0.979528	+	0.201309i	$0.935480\pi$
$294$	−10.7849	−	4.47128i	−0.628986	−	0.260770i
$295$	2.02765	−	3.51199i	0.118054	−	0.204476i
$296$	−4.12922			−0.240006
$297$	−15.9667	−	6.48570i	−0.926482	−	0.376339i
$298$	0.749742			0.0434314
$299$	10.1088	−	17.5090i	0.584607	−	1.01257i
$300$	−16.9083	−	7.00998i	−0.976199	−	0.404721i
$301$	2.46601	+	4.27126i	0.142139	+	0.246191i
$302$	0.320326	−	0.184940i	0.0184327	−	0.0106421i
$303$	−1.49300	+	1.14486i	−0.0857708	+	0.0657706i
$304$	1.09597	+	0.632761i	0.0628584	+	0.0362913i
$305$	−33.9587			−1.94447
$306$	−38.9947	+	10.4219i	−2.22918	+	0.595778i
$307$		−	28.3264i		−	1.61667i	−0.588721	−	0.808336i	$-0.700368\pi$
$307$		−	28.3264i		−	1.61667i	0.588721	−	0.808336i	$-0.299632\pi$
$308$	−13.6015	−	13.3905i	−0.775019	−	0.762995i
$309$	0.205184	+	1.56239i	0.0116725	+	0.0888815i
$310$	3.13673	−	1.81099i	0.178154	−	0.102857i
$311$	−25.9754	+	14.9969i	−1.47293	+	0.850396i	−0.999536	−	0.0304549i	$-0.990304\pi$
$311$	−25.9754	+	14.9969i	−1.47293	+	0.850396i	−0.473393	+	0.880851i	$0.656971\pi$
$312$	−12.1384	+	1.59409i	−0.687199	+	0.0902477i
$313$	0.529351	−	0.916862i	0.0299207	−	0.0518241i	−0.850677	−	0.525688i	$-0.823808\pi$
$313$	0.529351	−	0.916862i	0.0299207	−	0.0518241i	0.880598	+	0.473864i	$0.157141\pi$
$314$	46.2424			2.60961
$315$	12.3976	+	12.4134i	0.698524	+	0.699419i
$316$			35.0728i			1.97300i
$317$	0.978483	+	0.564927i	0.0549571	+	0.0317295i	0.527227	−	0.849725i	$-0.323232\pi$
$317$	0.978483	+	0.564927i	0.0549571	+	0.0317295i	−0.472270	+	0.881454i	$0.656565\pi$
$318$	−5.10533	−	6.65780i	−0.286292	−	0.373351i
$319$	2.83599	+	10.2625i	0.158785	+	0.574588i
$320$	32.7059	−	18.8828i	1.82832	−	1.05558i
$321$	23.1420	+	9.59441i	1.29166	+	0.535508i
$322$	−12.4484	+	21.5612i	−0.693720	+	1.20156i
$323$		−	5.45407i		−	0.303472i
$324$	22.5765	−	12.9961i	1.25425	−	0.722004i
$325$		−	13.0416i		−	0.723416i
$326$	2.91641	−	5.05137i	0.161525	−	0.279769i
$327$	−3.09345	+	7.46150i	−0.171068	+	0.412622i
$328$	−8.96217	−	15.5229i	−0.494853	−	0.857111i
$329$	10.0685	+	17.4391i	0.555092	+	0.961448i
$330$	−14.5633	−	34.4266i	−0.801686	−	1.89512i
$331$	−6.42264	+	11.1243i	−0.353020	+	0.611449i	−0.986777	−	0.162083i	$-0.948179\pi$
$331$	−6.42264	+	11.1243i	−0.353020	+	0.611449i	0.633757	+	0.773532i	$0.281512\pi$
$332$	−15.0684			−0.826988
$333$	4.42381	+	4.42948i	0.242424	+	0.242734i
$334$	−34.0110			−1.86100
$335$	2.39960	+	1.38541i	0.131104	+	0.0756930i
$336$	−4.81821	+	0.632761i	−0.262855	+	0.0345199i
$337$	11.3658	−	6.56204i	0.619134	−	0.357457i	−0.157398	−	0.987535i	$-0.550310\pi$
$337$	11.3658	−	6.56204i	0.619134	−	0.357457i	0.776532	+	0.630078i	$0.216977\pi$
$338$	0.266294	+	0.461234i	0.0144845	+	0.0250878i
$339$	29.5714	−	3.88352i	1.60610	−	0.210924i
$340$	−44.8377	−	25.8871i	−2.43167	−	1.40392i
$341$	1.78689	+	0.463853i	0.0967653	+	0.0251190i
$342$	1.53686	+	5.75037i	0.0831041	+	0.310945i
$343$			19.9757i			1.07859i
$344$	4.25090	+	2.45426i	0.229193	+	0.132325i
$345$	−22.8815	+	17.5460i	−1.23190	+	0.944644i
$346$	11.3360	+	19.6346i	0.609430	+	1.05556i
$347$	11.3347	+	19.6322i	0.608477	+	1.05391i	0.991492	+	0.130171i	$0.0415527\pi$
$347$	11.3347	+	19.6322i	0.608477	+	1.05391i	−0.383014	+	0.923743i	$0.625114\pi$
$348$	−14.8668	−	6.16361i	−0.796944	−	0.330404i
$349$	−6.29991	−	3.63726i	−0.337227	−	0.194698i	0.321818	−	0.946801i	$-0.395706\pi$
$349$	−6.29991	−	3.63726i	−0.337227	−	0.194698i	−0.659045	+	0.752104i	$0.729039\pi$
$350$			16.0599i			0.858437i
$351$	14.7144	+	11.3132i	0.785394	+	0.603853i
$352$	22.7266	+	5.89955i	1.21133	+	0.314447i
$353$	9.09981	+	5.25378i	0.484334	+	0.279630i	0.722221	−	0.691662i	$-0.243121\pi$
$353$	9.09981	+	5.25378i	0.484334	+	0.279630i	−0.237887	+	0.971293i	$0.576455\pi$
$354$	−2.02337	+	4.88043i	−0.107541	+	0.259392i
$355$	−6.69999	−	11.6047i	−0.355598	−	0.615915i
$356$	36.0287	−	20.8012i	1.90952	−	1.10246i
$357$	12.7443	+	16.6197i	0.674500	+	0.879608i
$358$	−24.6626	−	14.2390i	−1.30346	−	0.752553i
$359$	−3.88622			−0.205107			−0.102553	−	0.994728i	$-0.532701\pi$
$359$	−3.88622			−0.205107			−0.102553	+	0.994728i	$0.532701\pi$
$360$	16.8626	+	4.52989i	0.888736	+	0.238746i
$361$	18.1957			0.957669
$362$	−10.4336	+	18.0716i	−0.548380	+	0.949822i
$363$	7.02066	−	17.7119i	0.368489	−	0.929632i
$364$	10.2783	+	17.8025i	0.538728	+	0.933105i
$365$	−18.7237	−	32.4304i	−0.980043	−	1.69749i
$366$	43.8648	−	5.76063i	2.29285	−	0.301113i
$367$	5.29444	−	9.17024i	0.276368	−	0.478683i	−0.694112	−	0.719867i	$-0.744203\pi$
$367$	5.29444	−	9.17024i	0.276368	−	0.478683i	0.970479	+	0.241185i	$0.0775360\pi$
$368$		−	7.98695i		−	0.416349i
$369$	−7.05013	+	26.2443i	−0.367015	+	1.36622i
$370$			13.5786i			0.705917i
$371$	−2.17666	+	3.77008i	−0.113006	+	0.195733i
$372$	−2.21441	+	1.69805i	−0.114812	+	0.0880400i
$373$	28.7968	−	16.6259i	1.49104	−	0.860854i	0.491096	−	0.871106i	$-0.336597\pi$
$373$	28.7968	−	16.6259i	1.49104	−	0.860854i	0.999947	+	0.0102516i	$0.00326323\pi$
$374$	−11.8860	−	43.0113i	−0.614611	−	2.22406i
$375$	2.63189	−	6.34819i	0.135910	−	0.327819i
$376$	17.3560	+	10.0205i	0.895066	+	0.516766i
$377$		−	11.4670i		−	0.590579i
$378$	−18.1198	−	13.9315i	−0.931982	−	0.716558i
$379$	−6.30896			−0.324069			−0.162035	−	0.986785i	$-0.551806\pi$
$379$	−6.30896			−0.324069			−0.162035	+	0.986785i	$0.551806\pi$
$380$	−3.81745	+	6.61202i	−0.195831	+	0.339189i
$381$	2.85345	−	6.88260i	0.146187	−	0.352606i
$382$	−12.1011	+	6.98655i	−0.619144	+	0.357463i
$383$	8.24247	−	4.75879i	0.421170	−	0.243163i	−0.274408	−	0.961613i	$-0.588482\pi$
$383$	8.24247	−	4.75879i	0.421170	−	0.243163i	0.695578	+	0.718451i	$0.255148\pi$
$384$	−19.5824	+	15.0161i	−0.999308	+	0.766288i
$385$	−13.6072	+	13.8216i	−0.693485	+	0.704414i
$386$			26.9021i			1.36928i
$387$	−1.92145	−	7.18936i	−0.0976730	−	0.365456i
$388$	10.4077			0.528369
$389$	−24.4361	−	14.1082i	−1.23896	−	0.715313i	−0.270077	−	0.962839i	$-0.587049\pi$
$389$	−24.4361	−	14.1082i	−1.23896	−	0.715313i	−0.968881	+	0.247526i	$0.920382\pi$
$390$	5.24203	+	39.9159i	0.265441	+	2.02122i
$391$	−29.8100	+	17.2108i	−1.50756	+	0.870389i
$392$	3.01449	+	5.22125i	0.152255	+	0.263713i
$393$	−2.44588	−	18.6244i	−0.123379	−	0.939476i
$394$	−0.116528	+	0.201832i	−0.00587058	+	0.0101681i
$395$	35.6403			1.79326
$396$	14.5783	+	24.8369i	0.732586	+	1.24810i
$397$	23.6476			1.18684			0.593419	−	0.804894i	$-0.297778\pi$
$397$	23.6476			1.18684			0.593419	+	0.804894i	$0.297778\pi$
$398$	−16.6205	+	28.7876i	−0.833113	+	1.44299i
$399$	2.45083	−	1.87934i	0.122695	−	0.0940848i
$400$	−2.57603	−	4.46182i	−0.128802	−	0.223091i
$401$	−19.9587	+	11.5231i	−0.996689	+	0.575439i	−0.907267	−	0.420555i	$-0.861835\pi$
$401$	−19.9587	+	11.5231i	−0.996689	+	0.575439i	−0.0894219	+	0.995994i	$0.528502\pi$
$402$	−3.33460	−	1.38249i	−0.166315	−	0.0689522i
$403$	−1.72189	−	0.994132i	−0.0857733	−	0.0495212i
$404$	3.14406			0.156423
$405$	−13.2063	−	22.9418i	−0.656228	−	1.13999i
$406$			14.1209i			0.700806i
$407$	−4.85543	+	4.93195i	−0.240675	+	0.244468i
$408$	19.2545	+	7.98271i	0.953241	+	0.395203i
$409$	−12.2846	+	7.09249i	−0.607432	+	0.350701i	−0.771960	−	0.635671i	$-0.780723\pi$
$409$	−12.2846	+	7.09249i	−0.607432	+	0.350701i	0.164527	+	0.986373i	$0.447390\pi$
$410$	−51.0458	+	29.4713i	−2.52097	+	1.45548i
$411$	−2.62185	−	3.41912i	−0.129326	−	0.168653i
$412$	1.31667	−	2.28054i	0.0648676	−	0.112354i
$413$	2.74134			0.134892
$414$	26.5798	−	26.5458i	1.30633	−	1.30466i
$415$			15.3122i			0.751649i
$416$	−21.8999	−	12.6439i	−1.07373	−	0.619920i
$417$	2.43266	−	0.319474i	0.119128	−	0.0156447i
$418$	−6.34268	+	1.75278i	−0.310231	+	0.0857310i
$419$	13.1460	−	7.58985i	0.642224	−	0.370788i	−0.143247	−	0.989687i	$-0.545754\pi$
$419$	13.1460	−	7.58985i	0.642224	−	0.370788i	0.785471	+	0.618899i	$0.212421\pi$
$420$	−3.81745	−	29.0683i	−0.186272	−	1.41839i
$421$	17.4982	−	30.3078i	0.852812	−	1.47711i	−0.0258482	−	0.999666i	$-0.508229\pi$
$421$	17.4982	−	30.3078i	0.852812	−	1.47711i	0.878660	−	0.477448i	$-0.158438\pi$
$422$			47.4419i			2.30943i
$423$	−7.84509	−	29.3534i	−0.381441	−	1.42721i
$424$			4.33257i			0.210408i
$425$	−11.1020	+	19.2293i	−0.538527	+	0.932757i
$426$	10.6230	+	13.8534i	0.514686	+	0.671197i
$427$	−11.4779	−	19.8802i	−0.555453	−	0.962072i
$428$	−20.9323	−	36.2558i	−1.01180	−	1.75249i
$429$	−12.3692	+	16.3725i	−0.597188	+	0.790473i
$430$	8.07061	−	13.9787i	0.389200	−	0.674113i
$431$	−20.5921			−0.991886			−0.495943	−	0.868355i	$-0.665177\pi$
$431$	−20.5921			−0.991886			−0.495943	+	0.868355i	$0.665177\pi$
$432$	7.26875	+	0.964048i	0.349718	+	0.0463828i
$433$	−27.8883			−1.34023			−0.670113	−	0.742259i	$-0.733755\pi$
$433$	−27.8883			−1.34023			−0.670113	+	0.742259i	$0.733755\pi$
$434$	2.12040	+	1.22421i	0.101782	+	0.0587640i
$435$	−6.26333	+	15.1074i	−0.300304	+	0.724342i
$436$	11.6897	−	6.74903i	0.559833	−	0.323220i
$437$	2.53800	+	4.39595i	0.121409	+	0.210287i
$438$	29.6869	+	38.7144i	1.41850	+	1.84985i
$439$	25.6478	+	14.8078i	1.22410	+	0.706737i	0.965790	−	0.259324i	$-0.0834998\pi$
$439$	25.6478	+	14.8078i	1.22410	+	0.706737i	0.258314	+	0.966061i	$0.416833\pi$
$440$	−4.85012	+	18.6840i	−0.231221	+	0.890724i
$441$	2.37136	−	8.82745i	0.112922	−	0.420355i
$442$			48.0595i			2.28596i
$443$	4.28218	+	2.47232i	0.203453	+	0.117463i	0.598265	−	0.801298i	$-0.295857\pi$
$443$	4.28218	+	2.47232i	0.203453	+	0.117463i	−0.394812	+	0.918762i	$0.629190\pi$
$444$	−1.36218	−	10.3724i	−0.0646461	−	0.492253i
$445$	−21.1378	−	36.6117i	−1.00203	−	1.73556i
$446$	9.19201	+	15.9210i	0.435254	+	0.753882i
$447$	0.0764297	+	0.581980i	0.00361500	+	0.0275267i
$448$	22.1088	+	12.7645i	1.04454	+	0.603068i
$449$			13.9415i			0.657940i	0.944340	+	0.328970i	$0.106701\pi$
$449$			13.9415i			0.657940i	−0.944340	+	0.328970i	$0.893299\pi$
$450$	6.28669	−	23.4023i	0.296357	−	1.10320i
$451$	−29.0790	−	7.54854i	−1.36928	−	0.355447i
$452$	−43.1637	−	24.9205i	−2.03025	−	1.17216i
$453$	0.176213	+	0.229797i	0.00827920	+	0.0107968i
$454$	−22.9577	−	39.7639i	−1.07746	−	1.86621i
$455$	18.0906	−	10.4446i	0.848098	−	0.489650i
$456$	1.17717	−	2.83938i	0.0551262	−	0.132966i
$457$	9.22213	+	5.32440i	0.431393	+	0.249065i	0.699940	−	0.714202i	$-0.253210\pi$
$457$	9.22213	+	5.32440i	0.431393	+	0.249065i	−0.268547	+	0.963267i	$0.586543\pi$
$458$	−45.0841			−2.10664
$459$	−12.0650	−	29.2069i	−0.563148	−	1.36326i
$460$	48.1853			2.24665
$461$	9.36911	−	16.2278i	0.436363	−	0.755803i	−0.561043	−	0.827787i	$-0.689600\pi$
$461$	9.36911	−	16.2278i	0.436363	−	0.755803i	0.997406	+	0.0719837i	$0.0229330\pi$
$462$	15.2318	−	20.1618i	0.708650	−	0.938010i
$463$	13.3731	+	23.1629i	0.621501	+	1.07647i	0.989206	+	0.146529i	$0.0468102\pi$
$463$	13.3731	+	23.1629i	0.621501	+	1.07647i	−0.367705	+	0.929942i	$0.619856\pi$
$464$	−2.26501	−	3.92311i	−0.105150	−	0.182126i
$465$	1.72553	+	2.25024i	0.0800195	+	0.104353i
$466$	4.04245	−	7.00173i	0.187263	−	0.324349i
$467$			39.5871i			1.83187i	0.401322	+	0.915937i	$0.368551\pi$
$467$			39.5871i			1.83187i	−0.401322	+	0.915937i	$0.631449\pi$
$468$	−8.00858	−	29.9651i	−0.370197	−	1.38514i
$469$			1.87304i			0.0864892i
$470$	32.9514	−	57.0736i	1.51994	−	2.63261i
$471$	4.71401	+	35.8952i	0.217210	+	1.65396i
$472$	2.36275	−	1.36414i	0.108755	−	0.0627895i
$473$	7.92989	−	2.19139i	0.364617	−	0.100760i
$474$	−46.0368	+	6.04588i	−2.11454	+	0.277696i
$475$	2.83565	+	1.63717i	0.130109	+	0.0751183i
$476$		−	34.9988i		−	1.60417i
$477$	4.64761	−	4.64167i	0.212799	−	0.212527i
$478$	5.27020			0.241053
$479$	−2.31768	+	4.01434i	−0.105898	+	0.183420i	−0.914105	−	0.405479i	$-0.867105\pi$
$479$	−2.31768	+	4.01434i	−0.105898	+	0.183420i	0.808207	+	0.588898i	$0.200438\pi$
$480$	21.9463	+	28.6199i	1.00171	+	1.30631i
$481$	6.45524	−	3.72693i	0.294333	−	0.169934i
$482$	7.78698	−	4.49582i	0.354687	−	0.204779i
$483$	−18.0057	−	7.46494i	−0.819286	−	0.339667i
$484$	−27.3209	+	16.3486i	−1.24186	+	0.743116i
$485$		−	10.5761i		−	0.480234i
$486$	20.9505	+	27.3939i	0.950334	+	1.24261i
$487$	−6.88070			−0.311794			−0.155897	−	0.987773i	$-0.549827\pi$
$487$	−6.88070			−0.311794			−0.155897	+	0.987773i	$0.549827\pi$
$488$	−19.7855	−	11.4232i	−0.895648	−	0.517102i
$489$	4.21838	+	1.74889i	0.190762	+	0.0790876i
$490$	17.1696	−	9.91289i	0.775645	−	0.447819i
$491$	4.71089	+	8.15951i	0.212600	+	0.368233i	0.952527	−	0.304453i	$-0.0984737\pi$
$491$	4.71089	+	8.15951i	0.212600	+	0.368233i	−0.739928	+	0.672686i	$0.765140\pi$
$492$	36.0364	−	27.6334i	1.62465	−	1.24581i
$493$	−9.76160	+	16.9076i	−0.439640	+	0.761479i
$494$	7.08712			0.318864
$495$	25.2387	−	14.8142i	1.13440	−	0.665847i
$496$	−0.785462			−0.0352683
$497$	4.52912	−	7.84467i	0.203159	−	0.351881i
$498$	−2.59751	−	19.7790i	−0.116397	−	0.886316i
$499$	18.0952	+	31.3417i	0.810051	+	1.40305i	0.912828	+	0.408344i	$0.133894\pi$
$499$	18.0952	+	31.3417i	0.810051	+	1.40305i	−0.102777	+	0.994704i	$0.532773\pi$
$500$	−9.94548	+	5.74203i	−0.444776	+	0.256791i
$501$	−3.46713	−	26.4007i	−0.154900	−	1.17950i
$502$	−28.9158	−	16.6945i	−1.29058	−	0.745114i
$503$	−15.9118			−0.709472			−0.354736	−	0.934966i	$-0.615429\pi$
$503$	−15.9118			−0.709472			−0.354736	+	0.934966i	$0.615429\pi$
$504$	3.04756	+	11.4028i	0.135749	+	0.507923i
$505$		−	3.19493i		−	0.142172i
$506$	29.5950	+	29.1358i	1.31566	+	1.29525i
$507$	−0.330882	+	0.253727i	−0.0146950	+	0.0112684i
$508$	−10.7827	+	6.22541i	−0.478406	+	0.276208i
$509$	−0.497111	+	0.287007i	−0.0220340	+	0.0127214i	−0.510977	−	0.859595i	$-0.670716\pi$
$509$	−0.497111	+	0.287007i	−0.0220340	+	0.0127214i	0.488943	+	0.872316i	$0.337383\pi$
$510$	26.2504	−	63.3168i	1.16239	−	2.80372i
$511$	12.6570	−	21.9226i	0.559914	−	0.969799i
$512$	−15.5746			−0.688306
$513$	−4.30700	+	1.77918i	−0.190159	+	0.0785526i
$514$		−	21.5816i		−	0.951924i
$515$	−2.31744	−	1.33797i	−0.102118	−	0.0589581i
$516$	−4.76267	+	11.4877i	−0.209665	+	0.505718i
$517$	32.3769	−	8.94723i	1.42393	−	0.393499i
$518$	−7.94922	+	4.58949i	−0.349269	+	0.201650i
$519$	−14.0856	+	10.8011i	−0.618288	+	0.474115i
$520$	10.3948	−	18.0043i	0.455843	−	0.789542i
$521$		−	22.0365i		−	0.965437i	−0.875775	−	0.482719i	$-0.839649\pi$
$521$		−	22.0365i		−	0.965437i	0.875775	−	0.482719i	$-0.160351\pi$
$522$	5.52765	−	20.5768i	0.241939	−	0.900621i
$523$		−	42.1305i		−	1.84224i	−0.389280	−	0.921119i	$-0.627276\pi$
$523$		−	42.1305i		−	1.84224i	0.389280	−	0.921119i	$-0.372724\pi$
$524$	−15.6953	+	27.1850i	−0.685650	+	1.18758i
$525$	−12.4663	+	1.63717i	−0.544075	+	0.0714518i
$526$	8.48307	+	14.6931i	0.369880	+	0.640650i
$527$	1.69257	+	2.93162i	0.0737295	+	0.127703i
$528$	−0.997791	+	8.04463i	−0.0434233	+	0.350097i
$529$	4.51783	−	7.82511i	0.196427	−	0.340222i
$530$	14.2473			0.618861
$531$	−3.99465	−	1.07310i	−0.173353	−	0.0465687i
$532$	−5.16111			−0.223763
$533$	28.0212	+	16.1781i	1.21373	+	0.700750i
$534$	33.5145	+	43.7059i	1.45031	+	1.89134i
$535$	−36.8424	+	21.2710i	−1.59284	+	0.919624i
$536$	0.932059	+	1.61437i	0.0402588	+	0.0697303i
$537$	8.53872	−	20.5957i	0.368473	−	0.888768i
$538$	9.58471	+	5.53373i	0.413226	+	0.238576i
$539$	9.78094	+	2.53901i	0.421295	+	0.109363i
$540$	−5.81611	+	43.8524i	−0.250286	+	1.88711i
$541$			29.4484i			1.26608i	0.774117	+	0.633042i	$0.218194\pi$
$541$			29.4484i			1.26608i	−0.774117	+	0.633042i	$0.781806\pi$
$542$	14.5019	+	8.37268i	0.622910	+	0.359638i
$543$	−15.0915	−	6.25677i	−0.647639	−	0.268504i
$544$	21.5271	+	37.2860i	0.922965	+	1.59862i
$545$	−6.85823	−	11.8788i	−0.293774	−	0.508832i
$546$	−21.5959	+	16.5602i	−0.924221	+	0.708710i
$547$	−20.0426	−	11.5716i	−0.856960	−	0.494766i	0.00603338	−	0.999982i	$-0.498080\pi$
$547$	−20.0426	−	11.5716i	−0.856960	−	0.494766i	−0.862993	+	0.505216i	$0.831413\pi$
$548$			7.20020i			0.307577i
$549$	8.94326	+	33.4623i	0.381689	+	1.42814i
$550$	25.9301	+	6.73112i	1.10566	+	0.287016i
$551$	2.49328	+	1.43950i	0.106217	+	0.0613247i
$552$	−19.2337	+	2.52591i	−0.818642	+	0.107510i
$553$	12.0462	+	20.8647i	0.512257	+	0.887256i
$554$	−1.67889	+	0.969307i	−0.0713292	+	0.0411819i
$555$	−10.5402	+	1.38422i	−0.447408	+	0.0587568i
$556$	−3.55082	−	2.05007i	−0.150588	−	0.0869421i
$557$	43.6929			1.85133			0.925665	−	0.378345i	$-0.123507\pi$
$557$	43.6929			1.85133			0.925665	+	0.378345i	$0.123507\pi$
$558$	−2.61060	−	2.61395i	−0.110516	−	0.110657i
$559$	−8.86062			−0.374764
$560$	4.12613	−	7.14666i	0.174361	−	0.302002i
$561$	32.1754	−	13.6110i	1.35845	−	0.574658i
$562$	−14.3084	−	24.7829i	−0.603565	−	1.04540i
$563$	14.6859	+	25.4368i	0.618938	+	1.07203i	0.989680	+	0.143296i	$0.0457702\pi$
$563$	14.6859	+	25.4368i	0.618938	+	1.07203i	−0.370742	+	0.928736i	$0.620896\pi$
$564$	−19.4455	+	46.9030i	−0.818801	+	1.97497i
$565$	−25.3238	+	43.8620i	−1.06538	+	1.84529i
$566$		−	35.6657i		−	1.49914i
$567$	8.96702	−	15.4855i	0.376579	−	0.650331i
$568$		−	9.01507i		−	0.378264i
$569$	−2.66244	+	4.61148i	−0.111615	+	0.193323i	−0.916422	−	0.400214i	$-0.868936\pi$
$569$	−2.66244	+	4.61148i	−0.111615	+	0.193323i	0.804806	+	0.593537i	$0.202269\pi$
$570$	−9.33704	−	3.87103i	−0.391086	−	0.162140i
$571$	−4.63953	+	2.67863i	−0.194158	+	0.112097i	−0.593928	−	0.804518i	$-0.702424\pi$
$571$	−4.63953	+	2.67863i	−0.194158	+	0.112097i	0.399769	+	0.916616i	$0.369090\pi$
$572$	33.0516	−	9.13369i	1.38196	−	0.381899i
$573$	−6.65684	−	8.68111i	−0.278093	−	0.362659i
$574$	−34.5064	−	19.9223i	−1.44027	−	0.831540i
$575$		−	20.6649i		−	0.861787i
$576$	−27.2201	−	27.2549i	−1.13417	−	1.13562i
$577$	−21.0970			−0.878280			−0.439140	−	0.898419i	$-0.644717\pi$
$577$	−21.0970			−0.878280			−0.439140	+	0.898419i	$0.644717\pi$
$578$	22.1072	−	38.2908i	0.919539	−	1.59269i
$579$	−20.8825	+	2.74243i	−0.867846	+	0.113972i
$580$	23.6681	−	13.6648i	0.982766	−	0.567400i
$581$	−8.96416	+	5.17546i	−0.371896	+	0.214714i
$582$	1.79408	+	13.6612i	0.0743670	+	0.566274i
$583$	5.17483	+	5.09454i	0.214319	+	0.210994i
$584$		−	25.1934i		−	1.04251i
$585$	−30.4499	+	8.13815i	−1.25895	+	0.336471i
$586$	−23.8897			−0.986876
$587$	8.35543	+	4.82401i	0.344865	+	0.199108i	0.662421	−	0.749131i	$-0.269529\pi$
$587$	8.35543	+	4.82401i	0.344865	+	0.199108i	−0.317556	+	0.948240i	$0.602862\pi$
$588$	−12.1211	+	9.29469i	−0.499866	+	0.383307i
$589$	0.432312	−	0.249595i	0.0178131	−	0.0102844i
$590$	−4.48584	−	7.76970i	−0.184679	−	0.319874i
$591$	−0.168549	−	0.0698784i	−0.00693318	−	0.00287441i
$592$	1.47232	−	2.55014i	0.0605121	−	0.104810i
$593$	−17.3131			−0.710964			−0.355482	−	0.934683i	$-0.615683\pi$
$593$	−17.3131			−0.710964			−0.355482	+	0.934683i	$0.615683\pi$
$594$	−30.0881	+	23.4170i	−1.23453	+	0.960810i
$595$	−35.5651			−1.45803
$596$	0.490449	−	0.849483i	0.0200896	−	0.0347962i
$597$	−24.0404	−	9.96689i	−0.983910	−	0.407918i
$598$	−22.3641	−	38.7357i	−0.914535	−	1.58402i
$599$	18.5318	−	10.6994i	0.757190	−	0.437164i	−0.0710961	−	0.997469i	$-0.522650\pi$
$599$	18.5318	−	10.6994i	0.757190	−	0.437164i	0.828286	+	0.560306i	$0.189316\pi$
$600$	−9.93003	+	7.61453i	−0.405392	+	0.310862i
$601$	28.1701	+	16.2640i	1.14908	+	0.663424i	0.948664	−	0.316286i	$-0.102436\pi$
$601$	28.1701	+	16.2640i	1.14908	+	0.663424i	0.200420	+	0.979710i	$0.435769\pi$
$602$	10.9113			0.444711
$603$	0.733209	−	2.72938i	0.0298586	−	0.111149i
$604$		−	0.483921i		−	0.0196905i
$605$	16.6131	+	27.7630i	0.675418	+	1.12873i
$606$	0.541975	+	4.12691i	0.0220162	+	0.167644i
$607$	29.8728	−	17.2471i	1.21250	−	0.700038i	0.249198	−	0.968453i	$-0.419833\pi$
$607$	29.8728	−	17.2471i	1.21250	−	0.700038i	0.963303	+	0.268415i	$0.0864997\pi$
$608$	5.49839	−	3.17450i	0.222989	−	0.128743i
$609$	−10.9612	+	1.43950i	−0.444169	+	0.0583314i
$610$	−37.5641	+	65.0629i	−1.52092	+	2.63432i
$611$	−36.1769			−1.46356
$612$	−13.7004	+	50.9999i	−0.553805	+	2.06155i
$613$		−	5.37093i		−	0.216930i	−0.994100	−	0.108465i	$-0.965407\pi$
$613$		−	5.37093i		−	0.216930i	0.994100	−	0.108465i	$-0.0345935\pi$
$614$	−54.2717	−	31.3338i	−2.19023	−	1.26453i
$615$	−28.0805	−	36.6195i	−1.13231	−	1.47664i
$616$	−12.5774	+	3.47571i	−0.506756	+	0.140040i
$617$	−14.5460	+	8.39813i	−0.585600	+	0.338096i	−0.763356	−	0.645978i	$-0.776450\pi$
$617$	−14.5460	+	8.39813i	−0.585600	+	0.338096i	0.177756	+	0.984075i	$0.443116\pi$
$618$	3.22042	+	1.33515i	0.129544	+	0.0537076i
$619$	−6.15702	+	10.6643i	−0.247472	+	0.428633i	−0.962824	−	0.270131i	$-0.912933\pi$
$619$	−6.15702	+	10.6643i	−0.247472	+	0.428633i	0.715352	+	0.698764i	$0.246266\pi$
$620$		−	4.73870i		−	0.190311i
$621$	23.3155	+	17.9262i	0.935620	+	0.719354i
$622$			66.3564i			2.66065i
$623$	14.2889	−	24.7491i	0.572473	−	0.991552i
$624$	3.34359	−	8.06483i	0.133851	−	0.322852i
$625$	14.9625	+	25.9159i	0.598502	+	1.03664i
$626$	−1.17110	−	2.02841i	−0.0468067	−	0.0810715i
$627$	−2.00716	−	4.74476i	−0.0801581	−	0.189488i
$628$	30.2498	−	52.3942i	1.20710	−	2.09076i
$629$	−12.6906			−0.506009
$630$	37.4972	−	10.0216i	1.49392	−	0.399271i
$631$	47.5795			1.89411			0.947056	−	0.321069i	$-0.104042\pi$
$631$	47.5795			1.89411			0.947056	+	0.321069i	$0.104042\pi$
$632$	20.7652	+	11.9888i	0.825996	+	0.476889i
$633$	−36.8263	+	4.83628i	−1.46371	+	0.192225i
$634$	2.16473	−	1.24981i	0.0859725	−	0.0496363i
$635$	6.32614	+	10.9572i	0.251045	+	0.434823i
$636$	−10.8832	+	1.42926i	−0.431547	+	0.0566738i
$637$	−9.42515	−	5.44161i	−0.373438	−	0.215605i
$638$	22.7994	+	5.91842i	0.902635	+	0.234313i
$639$	−9.67061	+	9.65824i	−0.382563	+	0.382074i
$640$		−	41.9050i		−	1.65644i
$641$	33.8812	+	19.5613i	1.33823	+	0.772625i	0.986544	−	0.163495i	$-0.0522767\pi$
$641$	33.8812	+	19.5613i	1.33823	+	0.772625i	0.351681	+	0.936120i	$0.385610\pi$
$642$	43.9813	−	33.7257i	1.73580	−	1.33105i
$643$	10.8224	+	18.7450i	0.426795	+	0.739230i	0.996586	−	0.0825593i	$-0.0263094\pi$
$643$	10.8224	+	18.7450i	0.426795	+	0.739230i	−0.569792	+	0.821789i	$0.692976\pi$
$644$	16.2864	+	28.2088i	0.641773	+	1.11158i
$645$	11.6736	+	4.83973i	0.459646	+	0.190564i
$646$	−10.4497	−	6.03312i	−0.411137	−	0.237370i
$647$			34.3499i			1.35043i	0.737619	+	0.675217i	$0.235950\pi$
$647$			34.3499i			1.35043i	−0.737619	+	0.675217i	$0.764050\pi$
$648$	0.0227959	−	17.8091i	0.000895506	−	0.699607i
$649$	1.14897	−	4.42613i	0.0451009	−	0.173741i
$650$	−24.9869	−	14.4262i	−0.980066	−	0.565841i
$651$	−0.734127	+	1.77074i	−0.0287727	+	0.0694006i
$652$	−3.81558	−	6.60878i	−0.149430	−	0.258820i
$653$	15.4832	−	8.93925i	0.605906	−	0.349820i	−0.165455	−	0.986217i	$-0.552909\pi$
$653$	15.4832	−	8.93925i	0.605906	−	0.349820i	0.771361	+	0.636397i	$0.219576\pi$
$654$	10.8739	+	14.1805i	0.425203	+	0.554503i
$655$	27.6248	+	15.9492i	1.07939	+	0.623187i
$656$	12.7823			0.499064
$657$	−27.0254	+	26.9908i	−1.05436	+	1.05301i
$658$	44.5496			1.73673
$659$	−18.9301	+	32.7879i	−0.737413	+	1.27724i	0.216243	+	0.976340i	$0.430620\pi$
$659$	−18.9301	+	32.7879i	−0.737413	+	1.27724i	−0.953656	+	0.300898i	$0.902714\pi$
$660$	−48.5333	−	6.01968i	−1.88916	−	0.234316i
$661$	−14.4740	−	25.0697i	−0.562974	−	0.975100i	−0.997235	−	0.0743129i	$-0.976324\pi$
$661$	−14.4740	−	25.0697i	−0.562974	−	0.975100i	0.434261	−	0.900787i	$-0.357010\pi$
$662$	14.2090	+	24.6108i	0.552250	+	0.956525i
$663$	−37.3057	+	4.89925i	−1.44883	+	0.190271i
$664$	−5.15079	+	8.92144i	−0.199890	+	0.346219i
$665$			5.24462i			0.203378i
$666$	13.3801	−	3.57601i	0.518468	−	0.138568i
$667$		−	18.1699i		−	0.703541i
$668$	−22.2486	+	38.5357i	−0.860823	+	1.49099i
$669$	−11.4215	+	8.75821i	−0.441580	+	0.338612i
$670$	5.30872	−	3.06499i	0.205094	−	0.118411i
$671$	−36.9091	+	10.1997i	−1.42486	+	0.393754i
$672$	−9.33704	+	22.5212i	−0.360184	+	0.868775i
$673$	−30.3229	−	17.5070i	−1.16886	−	0.674844i	−0.215452	−	0.976515i	$-0.569122\pi$
$673$	−30.3229	−	17.5070i	−1.16886	−	0.674844i	−0.953412	+	0.301671i	$0.902456\pi$
$674$		−	29.0349i		−	1.11838i
$675$	18.8067	+	2.49432i	0.723870	+	0.0960064i
$676$	0.696792			0.0267997
$677$	−16.5475	+	28.6610i	−0.635970	+	1.10153i	0.350338	+	0.936623i	$0.386067\pi$
$677$	−16.5475	+	28.6610i	−0.635970	+	1.10153i	−0.986309	+	0.164910i	$0.947267\pi$
$678$	25.2703	−	60.9528i	0.970501	−	2.34088i
$679$	6.19147	−	3.57465i	0.237607	−	0.137182i
$680$	−30.6535	+	17.6978i	−1.17551	+	0.678679i
$681$	28.5260	−	21.8743i	1.09312	−	0.838225i
$682$	2.86531	−	2.91047i	0.109718	−	0.111448i
$683$		−	37.8518i		−	1.44836i	−0.689612	−	0.724179i	$-0.742219\pi$
$683$		−	37.8518i		−	1.44836i	0.689612	−	0.724179i	$-0.257781\pi$
$684$	7.52072	+	2.02033i	0.287562	+	0.0772493i
$685$	7.31670			0.279557
$686$	38.2722	+	22.0965i	1.46124	+	0.843648i
$687$	−4.59593	−	34.9961i	−0.175346	−	1.33518i
$688$	−3.03142	+	1.75019i	−0.115572	+	0.0667254i
$689$	−3.91047	−	6.77313i	−0.148977	−	0.258036i
$690$	8.30623	+	63.2484i	0.316213	+	2.40783i
$691$	4.85793	−	8.41419i	0.184804	−	0.320091i	−0.758706	−	0.651433i	$-0.774168\pi$
$691$	4.85793	−	8.41419i	0.184804	−	0.320091i	0.943511	+	0.331342i	$0.107501\pi$
$692$	29.6623			1.12759
$693$	17.2031	+	9.76826i	0.653493	+	0.371065i
$694$	50.1523			1.90375
$695$	−2.08324	+	3.60827i	−0.0790216	+	0.136869i
$696$	−8.73110	+	6.69517i	−0.330952	+	0.253780i
$697$	−27.5441	−	47.7078i	−1.04331	−	1.80706i
$698$	−13.9375	+	8.04684i	−0.527543	+	0.304577i
$699$	5.84712	+	2.42415i	0.221158	+	0.0916897i
$700$	18.1964	+	10.5057i	0.687759	+	0.397078i
$701$	47.1521			1.78091			0.890454	−	0.455073i	$-0.150387\pi$
$701$	47.1521			1.78091			0.890454	+	0.455073i	$0.150387\pi$
$702$	37.9519	−	15.6775i	1.43240	−	0.591710i
$703$			1.87143i			0.0705824i
$704$	29.8759	−	30.3467i	1.12599	−	1.14373i
$705$	47.6619	+	19.7601i	1.79505	+	0.744208i
$706$	20.1318	−	11.6231i	0.757672	−	0.437442i
$707$	1.87039	−	1.07987i	0.0703431	−	0.0406126i
$708$	4.20609	+	5.48512i	0.158075	+	0.206143i
$709$	6.74414	−	11.6812i	0.253282	−	0.438696i	−0.711146	−	0.703045i	$-0.751823\pi$
$709$	6.74414	−	11.6812i	0.253282	−	0.438696i	0.964427	+	0.264348i	$0.0851568\pi$
$710$	−29.6453			−1.11257
$711$	−9.38611	−	35.1193i	−0.352006	−	1.31708i
$712$		−	28.4416i		−	1.06589i
$713$	−2.72840	−	1.57525i	−0.102180	−	0.0589934i
$714$	45.9397	−	6.03312i	1.71925	−	0.225784i
$715$	−9.28147	−	33.5864i	−0.347107	−	1.25606i
$716$	−32.2665	+	18.6291i	−1.20585	+	0.696200i
$717$	0.537251	+	4.09094i	0.0200640	+	0.152779i
$718$	−4.29881	+	7.44576i	−0.160430	+	0.277873i
$719$			26.1982i			0.977028i	0.872556	+	0.488514i	$0.162461\pi$
$719$			26.1982i			0.977028i	−0.872556	+	0.488514i	$0.837539\pi$
$720$	−8.81013	+	8.79886i	−0.328334	+	0.327914i
$721$		−	1.80891i		−	0.0673674i
$722$	20.1275	−	34.8619i	0.749069	−	1.29743i
$723$	4.28365	+	5.58626i	0.159311	+	0.207755i
$724$	13.6505	+	23.6433i	0.507316	+	0.878698i
$725$	−5.86034	−	10.1504i	−0.217648	−	0.376977i
$726$	−26.1688	−	33.0435i	−0.971217	−	1.22636i
$727$	7.39362	−	12.8061i	0.274214	−	0.474953i	−0.695722	−	0.718311i	$-0.744916\pi$
$727$	7.39362	−	12.8061i	0.274214	−	0.474953i	0.969937	+	0.243358i	$0.0782489\pi$
$728$	14.0536			0.520860
$729$	−19.1285	+	19.0552i	−0.708463	+	0.705748i
$730$	−82.8463			−3.06628
$731$	13.0646	+	7.54286i	0.483212	+	0.278983i
$732$	22.1675	−	53.4686i	0.819334	−	1.97626i
$733$	−13.1742	+	7.60615i	−0.486602	+	0.280940i	−0.723164	−	0.690677i	$-0.757313\pi$
$733$	−13.1742	+	7.60615i	−0.486602	+	0.280940i	0.236562	+	0.971616i	$0.423979\pi$
$734$	−11.7131	−	20.2877i	−0.432338	−	0.748831i
$735$	9.44508	+	12.3172i	0.348387	+	0.454328i
$736$	−34.7014	−	20.0349i	−1.27911	−	0.738495i
$737$	3.02419	+	0.785042i	0.111398	+	0.0289174i
$738$	42.4838	+	42.5382i	1.56385	+	1.56585i
$739$		−	50.1272i		−	1.84396i	−0.387241	−	0.921979i	$-0.626572\pi$
$739$		−	50.1272i		−	1.84396i	0.387241	−	0.921979i	$-0.373428\pi$
$740$	15.3850	+	8.88253i	0.565564	+	0.326528i
$741$	0.722470	+	5.50131i	0.0265406	+	0.202095i
$742$	4.81550	+	8.34068i	0.176782	+	0.306196i
$743$	−22.7747	−	39.4469i	−0.835523	−	1.44717i	−0.893604	−	0.448856i	$-0.851832\pi$
$743$	−22.7747	−	39.4469i	−0.835523	−	1.44717i	0.0580813	−	0.998312i	$-0.481502\pi$
$744$	0.248406	+	1.89151i	0.00910701	+	0.0693460i
$745$	−0.863228	−	0.498385i	−0.0316262	−	0.0182594i
$746$		−	73.5640i		−	2.69337i
$747$	15.0884	−	4.03258i	0.552057	−	0.147545i
$748$	−56.5086	−	14.6689i	−2.06616	−	0.536348i
$749$	−24.9051	−	14.3789i	−0.910011	−	0.525395i
$750$	−9.25144	−	12.0647i	−0.337815	−	0.440541i
$751$	−9.02706	−	15.6353i	−0.329402	−	0.570541i	0.652991	−	0.757365i	$-0.273514\pi$
$751$	−9.02706	−	15.6353i	−0.329402	−	0.570541i	−0.982393	+	0.186824i	$0.940180\pi$
$752$	−12.3769	+	7.14584i	−0.451341	+	0.260582i
$753$	10.0113	−	24.1475i	0.364831	−	0.879983i
$754$	−21.9700	−	12.6844i	−0.800101	−	0.461938i
$755$	−0.491751			−0.0178966
$756$	−27.6380	+	11.4170i	−1.00519	+	0.415232i
$757$	−40.8091			−1.48323			−0.741617	−	0.670824i	$-0.765941\pi$
$757$	−40.8091			−1.48323			−0.741617	+	0.670824i	$0.765941\pi$
$758$	−6.97877	+	12.0876i	−0.253480	+	0.439041i
$759$	−19.5995	+	25.9430i	−0.711415	+	0.941670i
$760$	2.60981	+	4.52033i	0.0946678	+	0.163969i
$761$	18.6880	+	32.3686i	0.677440	+	1.17336i	0.975749	+	0.218892i	$0.0702441\pi$
$761$	18.6880	+	32.3686i	0.677440	+	1.17336i	−0.298309	+	0.954469i	$0.596423\pi$
$762$	−10.0303	−	13.0803i	−0.363358	−	0.473851i
$763$	4.63609	−	8.02994i	0.167838	−	0.290703i
$764$			18.2812i			0.661391i
$765$	51.8251	+	13.9220i	1.87374	+	0.503352i
$766$		−	21.0561i		−	0.760788i
$767$	−2.46247	+	4.26513i	−0.0889147	+	0.154005i
$768$	1.31707	+	10.0290i	0.0475258	+	0.361889i
$769$	−43.1053	+	24.8869i	−1.55442	+	0.897443i	−0.556644	+	0.830751i	$0.687911\pi$
$769$	−43.1053	+	24.8869i	−1.55442	+	0.897443i	−0.997774	+	0.0666919i	$0.978756\pi$
$770$	11.4296	+	41.3595i	0.411892	+	1.49049i
$771$	16.7525	−	2.20006i	0.603327	−	0.0792331i
$772$	30.4810	+	17.5982i	1.09703	+	0.633373i
$773$		−	22.0442i		−	0.792876i	−0.918062	−	0.396438i	$-0.870246\pi$
$773$		−	22.0442i		−	0.792876i	0.918062	−	0.396438i	$-0.129754\pi$
$774$	−15.8998	−	4.27126i	−0.571508	−	0.153527i
$775$	−2.03226			−0.0730008
$776$	3.55761	−	6.16197i	0.127711	−	0.221202i
$777$	−4.37290	−	5.70265i	−0.156877	−	0.204581i
$778$	−54.0608	+	31.2120i	−1.93817	+	1.11901i
$779$	−7.03526	+	4.06181i	−0.252064	+	0.145529i
$780$	48.6552	+	20.1719i	1.74214	+	0.722269i
$781$	−10.7676	−	10.6006i	−0.385296	−	0.379318i
$782$			76.1523i			2.72320i
$783$	16.5360	+	2.19316i	0.590949	+	0.0783772i
$784$	−4.29941			−0.153550
$785$	−53.2419	−	30.7393i	−1.90029	−	1.09713i
$786$	−38.3888	−	15.9155i	−1.36928	−	0.567689i
$787$	0.904779	−	0.522374i	0.0322519	−	0.0186206i	−0.483787	−	0.875186i	$-0.660739\pi$
$787$	0.904779	−	0.522374i	0.0322519	−	0.0186206i	0.516039	+	0.856565i	$0.327406\pi$
$788$	0.152455	+	0.264059i	0.00543098	+	0.00940673i
$789$	−10.5406	+	8.08274i	−0.375256	+	0.287753i
$790$	39.4241	−	68.2846i	1.40265	−	2.42946i
$791$	−34.2372			−1.21733
$792$	19.6882	−	0.141323i	0.699589	−	0.00502169i
$793$	41.2411			1.46451
$794$	26.1582	−	45.3073i	0.928320	−	1.60790i
$795$	1.45238	+	11.0593i	0.0515107	+	0.392233i
$796$	21.7449	+	37.6633i	0.770728	+	1.33494i
$797$	9.71423	−	5.60851i	0.344096	−	0.198664i	−0.317986	−	0.948095i	$-0.603007\pi$
$797$	9.71423	−	5.60851i	0.344096	−	0.198664i	0.662082	+	0.749432i	$0.269673\pi$
$798$	−0.889677	−	6.77452i	−0.0314942	−	0.239815i
$799$	53.3414	+	30.7967i	1.88708	+	1.08951i
$800$	−25.8474			−0.913843
$801$	−30.5098	+	30.4707i	−1.07801	+	1.07663i
$802$			50.9862i			1.80038i
$803$	−30.0911	−	29.6242i	−1.06189	−	1.04542i
$804$	−3.74776	+	2.87385i	−0.132173	+	0.101353i
$805$	28.6653	−	16.5499i	1.01032	−	0.583307i
$806$	−3.80939	+	2.19935i	−0.134180	+	0.0774690i
$807$	−3.31843	+	8.00415i	−0.116814	+	0.281760i
$808$	1.07472	−	1.86147i	0.0378086	−	0.0654864i
$809$	42.4243			1.49156			0.745779	−	0.666194i	$-0.232078\pi$
$809$	42.4243			1.49156			0.745779	+	0.666194i	$0.232078\pi$
$810$	−58.5636	−	0.0749622i	−2.05771	−	0.00263390i
$811$		−	14.9819i		−	0.526084i	−0.964784	−	0.263042i	$-0.915274\pi$
$811$		−	14.9819i		−	0.526084i	0.964784	−	0.263042i	$-0.0847258\pi$
$812$	15.9994	+	9.23726i	0.561469	+	0.324164i
$813$	−5.02087	+	12.1105i	−0.176090	+	0.424733i
$814$	4.07840	+	14.7583i	0.142948	+	0.517278i
$815$	−6.71571	+	3.87732i	−0.235241	+	0.135817i
$816$	−11.7954	+	9.04494i	−0.412922	+	0.316636i
$817$	1.11231	−	1.92658i	0.0389149	−	0.0674025i
$818$			31.3820i			1.09724i
$819$	−15.0562	−	15.0755i	−0.526106	−	0.526780i
$820$			77.1155i			2.69299i
$821$	−13.6808	+	23.6958i	−0.477463	+	0.826989i	−0.999666	−	0.0258314i	$-0.991777\pi$
$821$	−13.6808	+	23.6958i	−0.477463	+	0.826989i	0.522204	+	0.852821i	$0.325110\pi$
$822$	−9.45104	+	1.24118i	−0.329643	+	0.0432910i
$823$	−3.62185	−	6.27322i	−0.126250	−	0.218671i	0.795971	−	0.605335i	$-0.206961\pi$
$823$	−3.62185	−	6.27322i	−0.126250	−	0.218671i	−0.922221	+	0.386664i	$0.873627\pi$
$824$	−0.900145	−	1.55910i	−0.0313580	−	0.0543137i
$825$	−2.58162	+	20.8142i	−0.0898806	+	0.724656i
$826$	3.03238	−	5.25224i	0.105510	−	0.182749i
$827$	11.5567			0.401866			0.200933	−	0.979605i	$-0.435603\pi$
$827$	11.5567			0.401866			0.200933	+	0.979605i	$0.435603\pi$
$828$	−12.6899	−	47.4810i	−0.441006	−	1.65008i
$829$	33.2245			1.15393			0.576967	−	0.816767i	$-0.304236\pi$
$829$	33.2245			1.15393			0.576967	+	0.816767i	$0.304236\pi$
$830$	29.3373	+	16.9379i	1.01831	+	0.587924i
$831$	−0.923564	−	1.20441i	−0.0320381	−	0.0417805i
$832$	−39.7196	+	22.9321i	−1.37703	+	0.795028i
$833$	9.26467	+	16.0469i	0.321002	+	0.555991i
$834$	2.07884	−	5.01422i	0.0719843	−	0.173628i
$835$	39.1592	+	22.6086i	1.35516	+	0.782401i
$836$	−2.16316	+	8.33306i	−0.0748144	+	0.288205i
$837$	1.76292	−	2.29292i	0.0609355	−	0.0792550i
$838$		−	33.5826i		−	1.16009i
$839$	−15.5480	−	8.97664i	−0.536776	−	0.309908i	0.206995	−	0.978342i	$-0.433632\pi$
$839$	−15.5480	−	8.97664i	−0.536776	−	0.309908i	−0.743771	+	0.668434i	$0.766965\pi$
$840$	−18.5151	−	7.67615i	−0.638832	−	0.264852i
$841$	9.34722	+	16.1899i	0.322318	+	0.558271i
$842$	−38.7120	−	67.0511i	−1.33410	−	2.31073i
$843$	17.7789	−	13.6332i	0.612338	−	0.469552i
$844$	53.7533	+	31.0345i	1.85026	+	1.06825i
$845$		−	0.708066i		−	0.0243582i
$846$	−64.9173	−	17.4391i	−2.23190	−	0.599568i
$847$	−10.6380	+	19.1094i	−0.365525	+	0.656608i
$848$	−2.67572	−	1.54483i	−0.0918846	−	0.0530496i
$849$	27.6852	−	3.63581i	0.950152	−	0.124781i
$850$	24.5614	+	42.5416i	0.842450	+	1.45917i
$851$	10.2286	−	5.90549i	0.350632	−	0.202437i
$852$	22.6454	−	2.97396i	0.775820	−	0.101886i
$853$	0.526130	+	0.303761i	0.0180144	+	0.0104006i	0.508980	−	0.860778i	$-0.330023\pi$
$853$	0.526130	+	0.303761i	0.0180144	+	0.0104006i	−0.490966	+	0.871179i	$0.663356\pi$
$854$	−50.7858			−1.73785
$855$	2.05302	−	7.64241i	0.0702118	−	0.261365i
$856$	−28.6208			−0.978240
$857$	17.3174	−	29.9945i	0.591550	−	1.02459i	−0.402474	−	0.915431i	$-0.631850\pi$
$857$	17.3174	−	29.9945i	0.591550	−	1.02459i	0.994024	−	0.109163i	$-0.0348169\pi$
$858$	17.6864	+	41.8093i	0.603804	+	1.42735i
$859$	−1.79581	−	3.11043i	−0.0612722	−	0.106127i	0.833762	−	0.552124i	$-0.186182\pi$
$859$	−1.79581	−	3.11043i	−0.0612722	−	0.106127i	−0.895034	+	0.445997i	$0.852849\pi$
$860$	−10.5589	−	18.2886i	−0.360056	−	0.623635i
$861$	11.9469	−	28.8162i	0.407148	−	0.982053i
$862$	−22.7783	+	39.4532i	−0.775832	+	1.34378i
$863$		−	34.2857i		−	1.16710i	−0.812078	−	0.583549i	$-0.801664\pi$
$863$		−	34.2857i		−	1.16710i	0.812078	−	0.583549i	$-0.198336\pi$
$864$	22.4218	−	29.1627i	0.762807	−	0.992136i
$865$		−	30.1422i		−	1.02487i
$866$	−30.8492	+	53.4323i	−1.04830	+	1.81570i
$867$	31.9765	+	13.2571i	1.08598	+	0.450234i
$868$	2.77415	−	1.60165i	0.0941607	−	0.0543637i
$869$	38.7367	−	10.7047i	1.31405	−	0.363134i
$870$	22.0165	+	28.7114i	0.746428	+	0.973409i
$871$	−2.91419	−	1.68251i	−0.0987435	−	0.0570096i
$872$		−	9.22799i		−	0.312499i
$873$	−10.4215	+	2.78528i	−0.352713	+	0.0942673i
$874$	11.2298			0.379855
$875$	−3.94435	+	6.83182i	−0.133343	+	0.230958i
$876$	63.2847	−	8.31098i	2.13819	−	0.280802i
$877$	−40.3773	+	23.3118i	−1.36344	+	0.787185i	−0.990081	−	0.140500i	$-0.955129\pi$
$877$	−40.3773	+	23.3118i	−1.36344	+	0.787185i	−0.373363	+	0.927685i	$0.621796\pi$
$878$	56.7416	−	32.7598i	1.91494	−	1.10559i
$879$	−2.43535	−	18.5442i	−0.0821424	−	0.625480i
$880$	−9.80954	−	9.65735i	−0.330680	−	0.325549i
$881$			11.2898i			0.380365i	0.981749	+	0.190182i	$0.0609079\pi$
$881$			11.2898i			0.380365i	−0.981749	+	0.190182i	$0.939092\pi$
$882$	−14.2897	−	14.3080i	−0.481160	−	0.481777i
$883$	38.7208			1.30306			0.651530	−	0.758623i	$-0.274128\pi$
$883$	38.7208			1.30306			0.651530	+	0.758623i	$0.274128\pi$
$884$	54.4530	+	31.4385i	1.83145	+	1.05739i
$885$	5.57387	−	4.27414i	0.187363	−	0.143674i
$886$	9.47363	−	5.46960i	0.318273	−	0.183755i
$887$	−8.61024	−	14.9134i	−0.289104	−	0.500742i	0.684492	−	0.729020i	$-0.260024\pi$
$887$	−8.61024	−	14.9134i	−0.289104	−	0.500742i	−0.973596	+	0.228278i	$0.926691\pi$
$888$	−6.60673	−	2.73907i	−0.221707	−	0.0919173i
$889$	−4.27640	+	7.40694i	−0.143426	+	0.248421i
$890$	−93.5277			−3.13506
$891$	−21.2444	−	20.9684i	−0.711715	−	0.702469i
$892$	24.0521			0.805323
$893$	4.54145	−	7.86602i	0.151974	−	0.263226i
$894$	1.19958	+	0.497333i	0.0401201	+	0.0166333i
$895$	18.9305	+	32.7885i	0.632776	+	1.09600i
$896$	24.5322	−	14.1637i	0.819562	−	0.473174i
$897$	27.7884	−	21.3087i	0.927828	−	0.711476i
$898$	26.7111	+	15.4216i	0.891360	+	0.514627i
$899$	−1.78689			−0.0595960
$900$	−22.4031	−	22.4318i	−0.746771	−	0.747728i
$901$			13.3156i			0.443607i
$902$	−46.6288	+	47.3637i	−1.55257	+	1.57704i
$903$	1.11231	+	8.46979i	0.0370154	+	0.281857i
$904$	−29.5090	+	17.0370i	−0.981454	+	0.566642i
$905$	24.0259	−	13.8714i	0.798647	−	0.461099i
$906$	0.635199	−	0.0834187i	0.0211031	−	0.00277140i
$907$	−16.1880	+	28.0385i	−0.537515	+	0.931003i	0.461522	+	0.887129i	$0.347303\pi$
$907$	−16.1880	+	28.0385i	−0.537515	+	0.931003i	−0.999037	+	0.0438743i	$0.986030\pi$
$908$	−60.0719			−1.99355
$909$	−3.14823	+	0.841406i	−0.104420	+	0.0279077i
$910$		−	46.2139i		−	1.53198i
$911$	2.39925	+	1.38521i	0.0794908	+	0.0458941i	0.539219	−	0.842166i	$-0.318720\pi$
$911$	2.39925	+	1.38521i	0.0794908	+	0.0458941i	−0.459728	+	0.888060i	$0.652053\pi$
$912$	1.33382	+	1.73942i	0.0441671	+	0.0575978i
$913$	4.59912	+	16.6426i	0.152208	+	0.550789i
$914$	20.4024	−	11.7794i	0.674853	−	0.389627i
$915$	−54.3338	−	22.5261i	−1.79622	−	0.744692i
$916$	−29.4921	+	51.0818i	−0.974447	+	1.68779i
$917$			21.5630i			0.712072i
$918$	−69.3045	−	9.19181i	−2.28739	−	0.303375i
$919$			27.3707i			0.902876i	0.892302	+	0.451438i	$0.149089\pi$
$919$			27.3707i			0.902876i	−0.892302	+	0.451438i	$0.850911\pi$
$920$	16.4710	−	28.5286i	0.543034	−	0.940562i
$921$	18.7900	−	45.3221i	0.619152	−	1.49341i
$922$	−20.7276	−	35.9013i	−0.682628	−	1.18235i
$923$	8.13678	+	14.0933i	0.267825	+	0.463887i
$924$	−12.8799	−	30.4472i	−0.423718	−	1.00164i
$925$	3.80939	−	6.59806i	0.125252	−	0.216943i
$926$	59.1716			1.94450
$927$	−0.708103	+	2.63593i	−0.0232572	+	0.0865752i
$928$	−22.7266			−0.746039
$929$	−36.5817	−	21.1205i	−1.20021	−	0.692940i	−0.239606	−	0.970870i	$-0.577018\pi$
$929$	−36.5817	−	21.1205i	−1.20021	−	0.692940i	−0.960601	+	0.277930i	$0.910352\pi$
$930$	6.22006	−	0.816861i	0.203964	−	0.0267859i
$931$	2.36636	−	1.36622i	0.0775543	−	0.0447760i
$932$	−5.28880	−	9.16047i	−0.173240	−	0.300061i
$933$	−51.5085	+	6.76446i	−1.68631	+	0.221458i
$934$	75.8466	+	43.7900i	2.48178	+	1.43285i
$935$	−14.9063	+	57.4229i	−0.487487	+	1.87793i
$936$	−20.4787	−	5.50131i	−0.669368	−	0.179816i
$937$		−	4.97330i		−	0.162471i	−0.996695	−	0.0812353i	$-0.974113\pi$
$937$		−	4.97330i		−	0.162471i	0.996695	−	0.0812353i	$-0.0258865\pi$
$938$	3.58864	+	2.07190i	0.117173	+	0.0676500i
$939$	1.45515	−	1.11584i	0.0474870	−	0.0364139i
$940$	−43.1109	−	74.6702i	−1.40612	−	2.43547i
$941$	−3.06880	−	5.31531i	−0.100040	−	0.173274i	0.811661	−	0.584129i	$-0.198564\pi$
$941$	−3.06880	−	5.31531i	−0.100040	−	0.173274i	−0.911701	+	0.410855i	$0.865230\pi$
$942$	73.9875	+	30.6744i	2.41064	+	0.999425i
$943$	44.4009	+	25.6348i	1.44589	+	0.834785i
$944$			1.94560i			0.0633237i
$945$	11.6017	+	28.0852i	0.377404	+	0.913613i
$946$	4.57321	−	17.6172i	0.148688	−	0.572786i
$947$	−10.6476	−	6.14740i	−0.346001	−	0.199764i	0.316922	−	0.948452i	$-0.397351\pi$
$947$	−10.6476	−	6.14740i	−0.346001	−	0.199764i	−0.662922	+	0.748688i	$0.730684\pi$
$948$	−23.2652	+	56.1162i	−0.755617	+	1.82257i
$949$	22.7389	+	39.3850i	0.738137	+	1.27849i
$950$	6.27342	−	3.62196i	0.203537	−	0.117512i
$951$	1.19083	+	1.55295i	0.0386152	+	0.0503577i
$952$	−20.7214	−	11.9635i	−0.671585	−	0.387740i
$953$	−9.06757			−0.293727			−0.146864	−	0.989157i	$-0.546918\pi$
$953$	−9.06757			−0.293727			−0.146864	+	0.989157i	$0.546918\pi$
$954$	−3.75211	−	14.0390i	−0.121479	−	0.454530i
$955$	18.5770			0.601138
$956$	3.44754	−	5.97132i	0.111501	−	0.193126i
$957$	−2.26992	+	18.3011i	−0.0733762	+	0.591591i
$958$	5.12749	+	8.88107i	0.165662	+	0.286934i
$959$	2.47300	+	4.28337i	0.0798575	+	0.138317i
$960$	64.8549	−	8.51720i	2.09318	−	0.274891i
$961$	15.3451	−	26.5785i	0.495003	−	0.857370i
$962$		−	16.4905i		−	0.531674i
$963$	30.6627	+	30.7020i	0.988093	+	0.989358i
$964$		−	11.7639i		−	0.378889i
$965$	17.8829	−	30.9741i	0.575672	−	0.997093i
$966$	−34.2197	+	26.2403i	−1.10100	+	0.844268i
$967$	−41.5070	+	23.9641i	−1.33477	+	0.770632i	−0.986027	−	0.166585i	$-0.946726\pi$
$967$	−41.5070	+	23.9641i	−1.33477	+	0.770632i	−0.348747	+	0.937217i	$0.613393\pi$
$968$	0.340327	+	21.7640i	0.0109385	+	0.699522i
$969$	3.61790	−	8.72648i	0.116224	−	0.280335i
$970$	−20.2631	−	11.6989i	−0.650608	−	0.375629i
$971$			38.7369i			1.24313i	0.783364	+	0.621564i	$0.213502\pi$
$971$			38.7369i			1.24313i	−0.783364	+	0.621564i	$0.786498\pi$
$972$	44.7431	−	5.81773i	1.43514	−	0.186604i
$973$	−2.81649			−0.0902925
$974$	−7.61121	+	13.1830i	−0.243879	+	0.422410i
$975$	8.65099	−	20.8664i	0.277053	−	0.668261i
$976$	14.1095	−	8.14613i	0.451634	−	0.260751i
$977$	−39.7165	+	22.9303i	−1.27064	+	0.733606i	−0.975109	−	0.221726i	$-0.928831\pi$
$977$	−39.7165	+	22.9303i	−1.27064	+	0.733606i	−0.295534	+	0.955332i	$0.595498\pi$
$978$	8.01701	−	6.14759i	0.256356	−	0.196578i
$979$	−33.9707	−	33.4437i	−1.08571	−	1.06886i
$980$		−	25.9384i		−	0.828571i
$981$	−9.89901	+	9.88635i	−0.316051	+	0.315647i
$982$	20.8442			0.665164
$983$	16.4952	+	9.52353i	0.526116	+	0.303753i	0.739434	−	0.673230i	$-0.235093\pi$
$983$	16.4952	+	9.52353i	0.526116	+	0.303753i	−0.213317	+	0.976983i	$0.568427\pi$
$984$	−4.04245	−	30.7816i	−0.128869	−	0.981281i
$985$	0.268332	−	0.154922i	0.00854977	−	0.00493621i
$986$	21.5959	+	37.4053i	0.687755	+	1.19123i
$987$	4.54145	+	34.5812i	0.144556	+	1.10073i
$988$	4.63609	−	8.02994i	0.147494	−	0.255467i
$989$	−14.0400			−0.446447
$990$	−0.464728	−	64.7429i	−0.0147700	−	2.05766i
$991$	−8.79537			−0.279394			−0.139697	−	0.990194i	$-0.544613\pi$
$991$	−8.79537			−0.279394			−0.139697	+	0.990194i	$0.544613\pi$
$992$	−1.97029	+	3.41265i	−0.0625569	+	0.108352i
$993$	−17.6554	+	13.5385i	−0.560277	+	0.429631i
$994$	−10.0199	−	17.3550i	−0.317813	−	0.550469i
$995$	38.2727	−	22.0967i	1.21333	−	0.700514i
$996$	−24.1094	−	9.99549i	−0.763936	−	0.316719i
$997$	−37.0500	−	21.3908i	−1.17338	−	0.677454i	−0.218910	−	0.975745i	$-0.570250\pi$
$997$	−37.0500	−	21.3908i	−1.17338	−	0.677454i	−0.954475	+	0.298291i	$0.903583\pi$
$998$	80.0652			2.53442
$999$	4.13983	+	10.0216i	0.130978	+	0.317070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.g.b.65.7	yes	16
3.2	odd	2		297.2.g.b.197.2		16
9.2	odd	6		891.2.d.b.890.14		16
9.4	even	3		297.2.g.b.98.7		16
9.5	odd	6	inner	99.2.g.b.32.2	✓	16
9.7	even	3		891.2.d.b.890.3		16
11.10	odd	2	inner	99.2.g.b.65.2	yes	16
33.32	even	2		297.2.g.b.197.7		16
99.32	even	6	inner	99.2.g.b.32.7	yes	16
99.43	odd	6		891.2.d.b.890.13		16
99.65	even	6		891.2.d.b.890.4		16
99.76	odd	6		297.2.g.b.98.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.g.b.32.2	✓	16	9.5	odd	6	inner
99.2.g.b.32.7	yes	16	99.32	even	6	inner
99.2.g.b.65.2	yes	16	11.10	odd	2	inner
99.2.g.b.65.7	yes	16	1.1	even	1	trivial
297.2.g.b.98.2		16	99.76	odd	6
297.2.g.b.98.7		16	9.4	even	3
297.2.g.b.197.2		16	3.2	odd	2
297.2.g.b.197.7		16	33.32	even	2
891.2.d.b.890.3		16	9.7	even	3
891.2.d.b.890.4		16	99.65	even	6
891.2.d.b.890.13		16	99.43	odd	6
891.2.d.b.890.14		16	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.10617 - 1.91594i) q^{2} +(1.59999 + 0.663339i) q^{3} +(-1.44722 - 2.50665i) q^{4} +(-2.54721 + 1.47063i) q^{5} +(3.04078 - 2.33173i) q^{6} +(-1.72189 - 0.994132i) q^{7} -1.97879 q^{8} +(2.11996 + 2.12268i) q^{9} +O(q^{10})\)	\(q+(1.10617 - 1.91594i) q^{2} +(1.59999 + 0.663339i) q^{3} +(-1.44722 - 2.50665i) q^{4} +(-2.54721 + 1.47063i) q^{5} +(3.04078 - 2.33173i) q^{6} +(-1.72189 - 0.994132i) q^{7} -1.97879 q^{8} +(2.11996 + 2.12268i) q^{9} +6.50707i q^{10} +(-2.32680 + 2.36347i) q^{11} +(-0.652777 - 4.97063i) q^{12} +(3.09345 - 1.78601i) q^{13} +(-3.80939 + 2.19935i) q^{14} +(-5.05105 + 0.663339i) q^{15} +(0.705560 - 1.22207i) q^{16} -6.08156 q^{17} +(6.41196 - 1.71368i) q^{18} +0.896820i q^{19} +(7.37273 + 4.25665i) q^{20} +(-2.09556 - 2.73280i) q^{21} +(1.95443 + 7.07241i) q^{22} +(4.90171 - 2.83000i) q^{23} +(-3.16605 - 1.31261i) q^{24} +(1.82552 - 3.16190i) q^{25} -7.90249i q^{26} +(1.98387 + 4.80253i) q^{27} +5.75490i q^{28} +(1.60511 - 2.78014i) q^{29} +(-4.31639 + 10.4113i) q^{30} +(-0.278312 - 0.482050i) q^{31} +(-3.53973 - 6.13098i) q^{32} +(-5.29065 + 2.23808i) q^{33} +(-6.72723 + 11.6519i) q^{34} +5.84801 q^{35} +(2.25277 - 8.38598i) q^{36} +2.08674 q^{37} +(1.71825 + 0.992034i) q^{38} +(6.13423 - 0.805590i) q^{39} +(5.04039 - 2.91007i) q^{40} +(4.52912 + 7.84467i) q^{41} +(-7.55393 + 0.992034i) q^{42} +(-2.14823 - 1.24028i) q^{43} +(9.29179 + 2.41203i) q^{44} +(-8.52167 - 2.28922i) q^{45} -12.5218i q^{46} +(-8.77101 - 5.06394i) q^{47} +(1.93954 - 1.48727i) q^{48} +(-1.52340 - 2.63861i) q^{49} +(-4.03867 - 6.99518i) q^{50} +(-9.73046 - 4.03414i) q^{51} +(-8.95379 - 5.16948i) q^{52} -2.18950i q^{53} +(11.3958 + 1.51142i) q^{54} +(2.45106 - 9.44213i) q^{55} +(3.40725 + 1.96718i) q^{56} +(-0.594896 + 1.43491i) q^{57} +(-3.55105 - 6.15060i) q^{58} +(-1.19404 + 0.689379i) q^{59} +(8.97273 + 11.7012i) q^{60} +(9.99879 + 5.77281i) q^{61} -1.23144 q^{62} +(-1.54011 - 5.76253i) q^{63} -12.8399 q^{64} +(-5.25312 + 9.09867i) q^{65} +(-1.56432 + 12.6123i) q^{66} +(-0.471025 - 0.815839i) q^{67} +(8.80134 + 15.2444i) q^{68} +(9.71996 - 1.27649i) q^{69} +(6.46889 - 11.2044i) q^{70} +4.55585i q^{71} +(-4.19496 - 4.20033i) q^{72} +12.7317i q^{73} +(2.30829 - 3.99807i) q^{74} +(5.01824 - 3.84808i) q^{75} +(2.24802 - 1.29789i) q^{76} +(6.35609 - 1.75648i) q^{77} +(5.24203 - 12.6439i) q^{78} +(-10.4939 - 6.05866i) q^{79} +4.15048i q^{80} +(-0.0115201 + 8.99999i) q^{81} +20.0399 q^{82} +(2.60300 - 4.50853i) q^{83} +(-3.81745 + 9.20780i) q^{84} +(15.4910 - 8.94374i) q^{85} +(-4.75262 + 2.74393i) q^{86} +(4.41235 - 3.38347i) q^{87} +(4.60425 - 4.67681i) q^{88} +14.3732i q^{89} +(-13.8124 + 13.7947i) q^{90} -7.10210 q^{91} +(-14.1877 - 8.19126i) q^{92} +(-0.125534 - 0.955892i) q^{93} +(-19.4044 + 11.2031i) q^{94} +(-1.31889 - 2.28439i) q^{95} +(-1.59662 - 12.1576i) q^{96} +(-1.79787 + 3.11401i) q^{97} -6.74056 q^{98} +(-9.94962 + 0.0714190i) 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

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