LMFDB - Embedded newform 572.2.y.a.391.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(79,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1, 0]))

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

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

chi := DirichletCharacter("572.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.y (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$72$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			391.28
Character	$\chi$	$=$	572.391
Dual form			572.2.y.a.79.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.503593 + 1.32151i) q^{2} +(0.0644943 - 0.0887688i) q^{3} +(-1.49279 - 1.33101i) q^{4} +(-1.31803 + 4.05649i) q^{5} +(0.0848302 + 0.129933i) q^{6} +(0.673809 - 0.489551i) q^{7} +(2.51070 - 1.30245i) q^{8} +(0.923331 + 2.84172i) q^{9} +O(q^{10})$	\(q+(-0.503593 + 1.32151i) q^{2} +(0.0644943 - 0.0887688i) q^{3} +(-1.49279 - 1.33101i) q^{4} +(-1.31803 + 4.05649i) q^{5} +(0.0848302 + 0.129933i) q^{6} +(0.673809 - 0.489551i) q^{7} +(2.51070 - 1.30245i) q^{8} +(0.923331 + 2.84172i) q^{9} +(-4.69695 - 3.78462i) q^{10} +(3.07432 + 1.24440i) q^{11} +(-0.214428 + 0.0466706i) q^{12} +(-0.951057 + 0.309017i) q^{13} +(0.307622 + 1.13698i) q^{14} +(0.275084 + 0.378621i) q^{15} +(0.456834 + 3.97383i) q^{16} +(-0.301881 - 0.0980872i) q^{17} +(-4.22035 - 0.210877i) q^{18} +(-4.60076 - 3.34265i) q^{19} +(7.36677 - 4.30117i) q^{20} -0.0913865i q^{21} +(-3.19270 + 3.43608i) q^{22} +8.65398i q^{23} +(0.0463089 - 0.306873i) q^{24} +(-10.6728 - 7.75426i) q^{25} +(0.0705756 - 1.41245i) q^{26} +(0.624868 + 0.203032i) q^{27} +(-1.65745 - 0.166049i) q^{28} +(-4.91240 - 6.76134i) q^{29} +(-0.638883 + 0.172856i) q^{30} +(4.71670 - 1.53255i) q^{31} +(-5.48152 - 1.39748i) q^{32} +(0.308741 - 0.192647i) q^{33} +(0.281649 - 0.349544i) q^{34} +(1.09776 + 3.37854i) q^{35} +(2.40401 - 5.47105i) q^{36} +(-1.04933 + 0.762385i) q^{37} +(6.73426 - 4.39662i) q^{38} +(-0.0339067 + 0.104354i) q^{39} +(1.97419 + 11.9013i) q^{40} +(-3.10225 + 4.26988i) q^{41} +(0.120768 + 0.0460216i) q^{42} -5.60860 q^{43} +(-2.93301 - 5.94958i) q^{44} -12.7444 q^{45} +(-11.4363 - 4.35808i) q^{46} +(0.974102 - 1.34074i) q^{47} +(0.382215 + 0.215737i) q^{48} +(-1.94876 + 5.99767i) q^{49} +(15.6221 - 10.1993i) q^{50} +(-0.0281767 + 0.0204716i) q^{51} +(1.83103 + 0.804567i) q^{52} +(1.14340 + 3.51901i) q^{53} +(-0.582988 + 0.723525i) q^{54} +(-9.09997 + 10.8308i) q^{55} +(1.05412 - 2.10672i) q^{56} +(-0.593446 + 0.192822i) q^{57} +(11.4090 - 3.08683i) q^{58} +(-1.93389 - 2.66177i) q^{59} +(0.0933051 - 0.931341i) q^{60} +(10.3500 + 3.36292i) q^{61} +(-0.350015 + 7.00496i) q^{62} +(2.01331 + 1.46276i) q^{63} +(4.60724 - 6.54013i) q^{64} -4.26525i q^{65} +(0.0991063 + 0.505020i) q^{66} -6.51462i q^{67} +(0.320090 + 0.548230i) q^{68} +(0.768204 + 0.558133i) q^{69} +(-5.01761 - 0.250714i) q^{70} +(11.1015 + 3.60711i) q^{71} +(6.01941 + 5.93211i) q^{72} +(0.213233 + 0.293490i) q^{73} +(-0.479064 - 1.77064i) q^{74} +(-1.37667 + 0.447308i) q^{75} +(2.41887 + 11.1135i) q^{76} +(2.68070 - 0.666549i) q^{77} +(-0.120830 - 0.0973600i) q^{78} +(1.74509 + 5.37083i) q^{79} +(-16.7219 - 3.38450i) q^{80} +(-7.19361 + 5.22646i) q^{81} +(-4.08043 - 6.24994i) q^{82} +(4.57335 - 14.0753i) q^{83} +(-0.121636 + 0.136421i) q^{84} +(0.795780 - 1.09530i) q^{85} +(2.82445 - 7.41184i) q^{86} -0.917018 q^{87} +(9.33948 - 0.879839i) q^{88} -0.695560 q^{89} +(6.41799 - 16.8419i) q^{90} +(-0.489551 + 0.673809i) q^{91} +(11.5185 - 12.9186i) q^{92} +(0.168158 - 0.517537i) q^{93} +(1.28125 + 1.96247i) q^{94} +(19.6234 - 14.2572i) q^{95} +(-0.477580 + 0.396459i) q^{96} +(-1.57639 - 4.85163i) q^{97} +(-6.94461 - 5.59569i) q^{98} +(-0.697621 + 9.88536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 4 q^{4} + 80 q^{9}+O(q^{10}) $ 288 * q - 4 * q^4 + 80 * q^9	$ 288 q - 4 q^{4} + 80 q^{9} + 8 q^{12} - 6 q^{14} - 32 q^{16} - 50 q^{18} + 16 q^{22} - 88 q^{25} - 50 q^{28} - 20 q^{30} - 4 q^{33} + 30 q^{36} - 48 q^{37} + 38 q^{38} + 70 q^{40} + 56 q^{42} + 66 q^{44} - 96 q^{45} + 70 q^{46} + 76 q^{48} - 56 q^{49} + 70 q^{50} - 20 q^{52} - 80 q^{53} + 44 q^{56} - 20 q^{57} - 2 q^{58} - 144 q^{60} - 150 q^{62} - 100 q^{64} + 30 q^{66} + 24 q^{69} - 28 q^{70} - 100 q^{72} + 40 q^{73} - 140 q^{74} - 24 q^{77} - 40 q^{78} + 118 q^{80} - 76 q^{81} + 56 q^{82} + 120 q^{84} + 80 q^{85} + 44 q^{88} - 8 q^{89} + 80 q^{90} - 14 q^{92} + 72 q^{93} + 50 q^{94} - 140 q^{96} + 116 q^{97}+O(q^{100}) $ 288 * q - 4 * q^4 + 80 * q^9 + 8 * q^12 - 6 * q^14 - 32 * q^16 - 50 * q^18 + 16 * q^22 - 88 * q^25 - 50 * q^28 - 20 * q^30 - 4 * q^33 + 30 * q^36 - 48 * q^37 + 38 * q^38 + 70 * q^40 + 56 * q^42 + 66 * q^44 - 96 * q^45 + 70 * q^46 + 76 * q^48 - 56 * q^49 + 70 * q^50 - 20 * q^52 - 80 * q^53 + 44 * q^56 - 20 * q^57 - 2 * q^58 - 144 * q^60 - 150 * q^62 - 100 * q^64 + 30 * q^66 + 24 * q^69 - 28 * q^70 - 100 * q^72 + 40 * q^73 - 140 * q^74 - 24 * q^77 - 40 * q^78 + 118 * q^80 - 76 * q^81 + 56 * q^82 + 120 * q^84 + 80 * q^85 + 44 * q^88 - 8 * q^89 + 80 * q^90 - 14 * q^92 + 72 * q^93 + 50 * q^94 - 140 * q^96 + 116 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.503593	+	1.32151i	−0.356094	+	0.934450i
$2$	−0.503593	+	1.32151i	−0.356094	+	0.934450i
$3$	0.0644943	−	0.0887688i	0.0372358	−	0.0512507i	−0.789993	−	0.613116i	$-0.789916\pi$
$3$	0.0644943	−	0.0887688i	0.0372358	−	0.0512507i	0.827229	+	0.561865i	$0.189916\pi$
$4$	−1.49279	−	1.33101i	−0.746394	−	0.665504i
$5$	−1.31803	+	4.05649i	−0.589443	+	1.81412i	−0.00879782	+	0.999961i	$0.502800\pi$
$5$	−1.31803	+	4.05649i	−0.589443	+	1.81412i	−0.580645	+	0.814157i	$0.697200\pi$
$6$	0.0848302	+	0.129933i	0.0346318	+	0.0530451i
$7$	0.673809	−	0.489551i	0.254676	−	0.185033i	−0.453121	−	0.891449i	$-0.649689\pi$
$7$	0.673809	−	0.489551i	0.254676	−	0.185033i	0.707796	+	0.706416i	$0.249689\pi$
$8$	2.51070	−	1.30245i	0.887667	−	0.460486i
$9$	0.923331	+	2.84172i	0.307777	+	0.947240i
$10$	−4.69695	−	3.78462i	−1.48531	−	1.19680i
$11$	3.07432	+	1.24440i	0.926943	+	0.375201i
$11$	3.07432	+	1.24440i	0.926943	+	0.375201i
$12$	−0.214428	+	0.0466706i	−0.0619002	+	0.0134726i
$13$	−0.951057	+	0.309017i	−0.263776	+	0.0857059i
$13$	−0.951057	+	0.309017i	−0.263776	+	0.0857059i
$14$	0.307622	+	1.13698i	0.0822154	+	0.303871i
$15$	0.275084	+	0.378621i	0.0710265	+	0.0977595i
$16$	0.456834	+	3.97383i	0.114209	+	0.993457i
$17$	−0.301881	−	0.0980872i	−0.0732170	−	0.0237896i	0.272179	−	0.962246i	$-0.412256\pi$
$17$	−0.301881	−	0.0980872i	−0.0732170	−	0.0237896i	−0.345396	+	0.938457i	$0.612256\pi$
$18$	−4.22035	−	0.210877i	−0.994746	−	0.0497042i
$19$	−4.60076	−	3.34265i	−1.05549	−	0.766856i	−0.0822382	−	0.996613i	$-0.526207\pi$
$19$	−4.60076	−	3.34265i	−1.05549	−	0.766856i	−0.973248	+	0.229757i	$0.926207\pi$
$20$	7.36677	−	4.30117i	1.64726	−	0.961771i
$21$		−	0.0913865i		−	0.0199422i
$22$	−3.19270	+	3.43608i	−0.680686	+	0.732576i
$23$			8.65398i			1.80448i	0.431234	+	0.902240i	$0.358078\pi$
$23$			8.65398i			1.80448i	−0.431234	+	0.902240i	$0.641922\pi$
$24$	0.0463089	−	0.306873i	0.00945276	−	0.0626401i
$25$	−10.6728	−	7.75426i	−2.13457	−	1.55085i
$26$	0.0705756	−	1.41245i	0.0138410	−	0.277005i
$27$	0.624868	+	0.203032i	0.120256	+	0.0390735i
$28$	−1.65745	−	0.166049i	−0.313229	−	0.0313804i
$29$	−4.91240	−	6.76134i	−0.912210	−	1.25555i	−0.966406	−	0.257019i	$-0.917260\pi$
$29$	−4.91240	−	6.76134i	−0.912210	−	1.25555i	0.0541965	−	0.998530i	$-0.482740\pi$
$30$	−0.638883	+	0.172856i	−0.116644	+	0.0315591i
$31$	4.71670	−	1.53255i	0.847144	−	0.275254i	0.146895	−	0.989152i	$-0.453072\pi$
$31$	4.71670	−	1.53255i	0.847144	−	0.275254i	0.700249	+	0.713898i	$0.253072\pi$
$32$	−5.48152	−	1.39748i	−0.969005	−	0.247042i
$33$	0.308741	−	0.192647i	0.0537448	−	0.0335356i
$34$	0.281649	−	0.349544i	0.0483024	−	0.0599463i
$35$	1.09776	+	3.37854i	0.185555	+	0.571078i
$36$	2.40401	−	5.47105i	0.400669	−	0.911841i
$37$	−1.04933	+	0.762385i	−0.172509	+	0.125335i	−0.670690	−	0.741738i	$-0.734002\pi$
$37$	−1.04933	+	0.762385i	−0.172509	+	0.125335i	0.498180	+	0.867073i	$0.334002\pi$
$38$	6.73426	−	4.39662i	1.09244	−	0.713227i
$39$	−0.0339067	+	0.104354i	−0.00542941	+	0.0167100i
$40$	1.97419	+	11.9013i	0.312148	+	1.88176i
$41$	−3.10225	+	4.26988i	−0.484490	+	0.666843i	−0.979360	−	0.202124i	$-0.935216\pi$
$41$	−3.10225	+	4.26988i	−0.484490	+	0.666843i	0.494870	+	0.868967i	$0.335216\pi$
$42$	0.120768	+	0.0460216i	0.0186350	+	0.00710128i
$43$	−5.60860			−0.855304			−0.427652	−	0.903943i	$-0.640659\pi$
$43$	−5.60860			−0.855304			−0.427652	+	0.903943i	$0.640659\pi$
$44$	−2.93301	−	5.94958i	−0.442167	−	0.896933i
$45$	−12.7444			−1.89982
$46$	−11.4363	−	4.35808i	−1.68620	−	0.642564i
$47$	0.974102	−	1.34074i	0.142087	−	0.195566i	−0.732042	−	0.681259i	$-0.761433\pi$
$47$	0.974102	−	1.34074i	0.142087	−	0.195566i	0.874130	+	0.485693i	$0.161433\pi$
$48$	0.382215	+	0.215737i	0.0551680	+	0.0311389i
$49$	−1.94876	+	5.99767i	−0.278394	+	0.856810i
$50$	15.6221	−	10.1993i	2.20930	−	1.44240i
$51$	−0.0281767	+	0.0204716i	−0.00394553	+	0.00286660i
$52$	1.83103	+	0.804567i	0.253918	+	0.111573i
$53$	1.14340	+	3.51901i	0.157058	+	0.483374i	0.998364	−	0.0571855i	$-0.0182126\pi$
$53$	1.14340	+	3.51901i	0.157058	+	0.483374i	−0.841306	+	0.540559i	$0.818213\pi$
$54$	−0.582988	+	0.723525i	−0.0793346	+	0.0984593i
$55$	−9.09997	+	10.8308i	−1.22704	+	1.46043i
$56$	1.05412	−	2.10672i	0.140862	−	0.281522i
$57$	−0.593446	+	0.192822i	−0.0786038	+	0.0255399i
$58$	11.4090	−	3.08683i	1.49808	−	0.405321i
$59$	−1.93389	−	2.66177i	−0.251771	−	0.346533i	0.664359	−	0.747413i	$-0.268704\pi$
$59$	−1.93389	−	2.66177i	−0.251771	−	0.346533i	−0.916131	+	0.400880i	$0.868704\pi$
$60$	0.0933051	−	0.931341i	0.0120456	−	0.120236i
$61$	10.3500	+	3.36292i	1.32518	+	0.430577i	0.884271	−	0.466974i	$-0.154656\pi$
$61$	10.3500	+	3.36292i	1.32518	+	0.430577i	0.440910	+	0.897551i	$0.354656\pi$
$62$	−0.350015	+	7.00496i	−0.0444519	+	0.889630i
$63$	2.01331	+	1.46276i	0.253654	+	0.184290i
$64$	4.60724	−	6.54013i	0.575905	−	0.817517i
$65$		−	4.26525i		−	0.529039i
$66$	0.0991063	+	0.505020i	0.0121991	+	0.0621637i
$67$		−	6.51462i		−	0.795888i	−0.917410	−	0.397944i	$-0.869724\pi$
$67$		−	6.51462i		−	0.795888i	0.917410	−	0.397944i	$-0.130276\pi$
$68$	0.320090	+	0.548230i	0.0388166	+	0.0664827i
$69$	0.768204	+	0.558133i	0.0924809	+	0.0671913i
$70$	−5.01761	−	0.250714i	−0.599719	−	0.0299660i
$71$	11.1015	+	3.60711i	1.31751	+	0.428085i	0.881639	−	0.471924i	$-0.156440\pi$
$71$	11.1015	+	3.60711i	1.31751	+	0.428085i	0.435871	+	0.900009i	$0.356440\pi$
$72$	6.01941	+	5.93211i	0.709394	+	0.699106i
$73$	0.213233	+	0.293490i	0.0249571	+	0.0343504i	0.821313	−	0.570478i	$-0.193242\pi$
$73$	0.213233	+	0.293490i	0.0249571	+	0.0343504i	−0.796356	+	0.604828i	$0.793242\pi$
$74$	−0.479064	−	1.77064i	−0.0556901	−	0.205832i
$75$	−1.37667	+	0.447308i	−0.158965	+	0.0516507i
$76$	2.41887	+	11.1135i	0.277463	+	1.27481i
$77$	2.68070	−	0.666549i	0.305494	−	0.0759603i
$78$	−0.120830	−	0.0973600i	−0.0136813	−	0.0110239i
$79$	1.74509	+	5.37083i	0.196338	+	0.604265i	0.999958	+	0.00912334i	$0.00290409\pi$
$79$	1.74509	+	5.37083i	0.196338	+	0.604265i	−0.803621	+	0.595142i	$0.797096\pi$
$80$	−16.7219	−	3.38450i	−1.86957	−	0.378398i
$81$	−7.19361	+	5.22646i	−0.799290	+	0.580718i
$82$	−4.08043	−	6.24994i	−0.450608	−	0.690190i
$83$	4.57335	−	14.0753i	0.501990	−	1.54497i	−0.303782	−	0.952742i	$-0.598249\pi$
$83$	4.57335	−	14.0753i	0.501990	−	1.54497i	0.805772	−	0.592226i	$-0.201751\pi$
$84$	−0.121636	+	0.136421i	−0.0132716	+	0.0148847i
$85$	0.795780	−	1.09530i	0.0863144	−	0.118802i
$86$	2.82445	−	7.41184i	0.304569	−	0.799239i
$87$	−0.917018			−0.0983147
$88$	9.33948	−	0.879839i	0.995592	−	0.0937912i
$89$	−0.695560			−0.0737293			−0.0368646	−	0.999320i	$-0.511737\pi$
$89$	−0.695560			−0.0737293			−0.0368646	+	0.999320i	$0.511737\pi$
$90$	6.41799	−	16.8419i	0.676515	−	1.77529i
$91$	−0.489551	+	0.673809i	−0.0513188	+	0.0706343i
$92$	11.5185	−	12.9186i	1.20089	−	1.34685i
$93$	0.168158	−	0.517537i	0.0174372	−	0.0536660i
$94$	1.28125	+	1.96247i	0.132151	+	0.202414i
$95$	19.6234	−	14.2572i	2.01332	−	1.46276i
$96$	−0.477580	+	0.396459i	−0.0487428	+	0.0404634i
$97$	−1.57639	−	4.85163i	−0.160058	−	0.492608i	0.838580	−	0.544778i	$-0.183386\pi$
$97$	−1.57639	−	4.85163i	−0.160058	−	0.492608i	−0.998638	+	0.0521701i	$0.983386\pi$
$98$	−6.94461	−	5.59569i	−0.701512	−	0.565250i
$99$	−0.697621	+	9.88536i	−0.0701135	+	0.993516i
$100$	5.61128	+	25.7811i	0.561128	+	2.57811i
$101$	−2.73427	+	0.888417i	−0.272070	+	0.0884008i	−0.441874	−	0.897077i	$-0.645686\pi$
$101$	−2.73427	+	0.888417i	−0.272070	+	0.0884008i	0.169805	+	0.985478i	$0.445686\pi$
$102$	−0.0128639	−	0.0475452i	−0.00127371	−	0.00470768i
$103$	4.49435	+	6.18594i	0.442842	+	0.609519i	0.970841	−	0.239726i	$-0.0770575\pi$
$103$	4.49435	+	6.18594i	0.442842	+	0.609519i	−0.527999	+	0.849245i	$0.677058\pi$
$104$	−1.98534	+	2.01455i	−0.194678	+	0.197543i
$105$	0.370708	+	0.120450i	0.0361774	+	0.0117548i
$106$	−5.22623	−	0.261138i	−0.507616	−	0.0253639i
$107$	7.43033	+	5.39845i	0.718317	+	0.521888i	0.885846	−	0.463979i	$-0.153579\pi$
$107$	7.43033	+	5.39845i	0.718317	+	0.521888i	−0.167529	+	0.985867i	$0.553579\pi$
$108$	−0.662558	−	1.13479i	−0.0637547	−	0.109195i
$109$		−	1.02944i		−	0.0986020i	−0.998784	−	0.0493010i	$-0.984301\pi$
$109$		−	1.02944i		−	0.0986020i	0.998784	−	0.0493010i	$-0.0156994\pi$
$110$	−9.73036	−	17.4800i	−0.927754	−	1.66666i
$111$			0.142318i			0.0135082i
$112$	2.25321	+	2.45396i	0.212908	+	0.231877i
$113$	6.27445	+	4.55865i	0.590250	+	0.428842i	0.842405	−	0.538845i	$-0.181139\pi$
$113$	6.27445	+	4.55865i	0.590250	+	0.428842i	−0.252155	+	0.967687i	$0.581139\pi$
$114$	0.0440382	−	0.881349i	0.00412455	−	0.0825459i
$115$	−35.1048	−	11.4062i	−3.27354	−	1.06364i
$116$	−1.66622	+	16.6317i	−0.154705	+	1.54421i
$117$	−1.75628	−	2.41731i	−0.162368	−	0.223480i
$118$	4.49146	−	1.21521i	0.413472	−	0.111869i
$119$	−0.251429	+	0.0816942i	−0.0230484	+	0.00748890i
$120$	1.18379	+	0.592320i	0.108065	+	0.0540712i
$121$	7.90293	+	7.65138i	0.718448	+	0.695580i
$122$	−9.65632	+	11.9841i	−0.874242	+	1.08499i
$123$	0.178955	+	0.550766i	0.0161358	+	0.0496609i
$124$	−9.08087	−	3.99019i	−0.815486	−	0.358330i
$125$	28.2690	−	20.5386i	2.52845	−	1.83703i
$126$	−2.94694	+	1.92398i	−0.262535	+	0.171402i
$127$	−4.48036	+	13.7891i	−0.397567	+	1.22359i	0.529376	+	0.848387i	$0.322426\pi$
$127$	−4.48036	+	13.7891i	−0.397567	+	1.22359i	−0.926944	+	0.375200i	$0.877574\pi$
$128$	6.32269	+	9.38209i	0.558852	+	0.829267i
$129$	−0.361723	+	0.497869i	−0.0318480	+	0.0438350i
$130$	5.63658	+	2.14795i	0.494360	+	0.188388i
$131$	−5.88784			−0.514423			−0.257211	−	0.966355i	$-0.582804\pi$
$131$	−5.88784			−0.514423			−0.257211	+	0.966355i	$0.582804\pi$
$132$	−0.717299	−	0.123354i	−0.0624329	−	0.0107366i
$133$	−4.73642			−0.410700
$134$	8.60915	+	3.28072i	0.743718	+	0.283411i
$135$	−1.64719	+	2.26717i	−0.141768	+	0.195127i
$136$	−0.885688	+	0.146918i	−0.0759471	+	0.0125981i
$137$	−4.59179	+	14.1321i	−0.392303	+	1.20739i	0.538739	+	0.842473i	$0.318901\pi$
$137$	−4.59179	+	14.1321i	−0.392303	+	1.20739i	−0.931042	+	0.364912i	$0.881099\pi$
$138$	−1.12444	+	0.734119i	−0.0957188	+	0.0624924i
$139$	12.2105	−	8.87146i	1.03568	−	0.752468i	0.0662449	−	0.997803i	$-0.478898\pi$
$139$	12.2105	−	8.87146i	1.03568	−	0.752468i	0.969438	+	0.245336i	$0.0788982\pi$
$140$	2.85815	−	6.50457i	0.241558	−	0.549737i
$141$	−0.0561915	−	0.172940i	−0.00473218	−	0.0145642i
$142$	−10.3575	+	12.8543i	−0.869182	+	1.07871i
$143$	−3.30840	−	0.233477i	−0.276662	−	0.0195244i
$144$	−10.8707	+	4.96735i	−0.905891	+	0.413946i
$145$	33.9020	−	11.0154i	2.81541	−	0.914782i
$146$	−0.495234	+	0.133991i	−0.0409858	+	0.0110891i
$147$	0.406722	+	0.559805i	0.0335459	+	0.0461719i
$148$	2.58117	+	0.258591i	0.212171	+	0.0212561i
$149$	−4.94880	−	1.60796i	−0.405421	−	0.131729i	0.0992056	−	0.995067i	$-0.468370\pi$
$149$	−4.94880	−	1.60796i	−0.405421	−	0.131729i	−0.504627	+	0.863338i	$0.668370\pi$
$150$	0.102160	−	2.04455i	0.00834130	−	0.166937i
$151$	6.50124	+	4.72343i	0.529063	+	0.384387i	0.820007	−	0.572353i	$-0.193969\pi$
$151$	6.50124	+	4.72343i	0.529063	+	0.384387i	−0.290944	+	0.956740i	$0.593969\pi$
$152$	−15.9048	−	2.40012i	−1.29005	−	0.194676i
$153$		−	0.948429i		−	0.0766759i
$154$	−0.469130	+	3.87825i	−0.0378036	+	0.312518i
$155$			21.1532i			1.69907i
$156$	0.189512	−	0.110648i	0.0151731	−	0.00885896i
$157$	13.5260	+	9.82720i	1.07949	+	0.784296i	0.977594	−	0.210499i	$-0.0675090\pi$
$157$	13.5260	+	9.82720i	1.07949	+	0.784296i	0.101896	+	0.994795i	$0.467509\pi$
$158$	−7.97642	−	0.398556i	−0.634570	−	0.0317074i
$159$	0.386121	+	0.125458i	0.0306214	+	0.00994950i
$160$	12.8937	−	20.3938i	1.01934	−	1.61227i
$161$	4.23656	+	5.83113i	0.333888	+	0.459557i
$162$	−3.28418	−	12.1385i	−0.258030	−	0.953687i
$163$	−3.41244	+	1.10877i	−0.267283	+	0.0868454i	−0.439592	−	0.898197i	$-0.644877\pi$
$163$	−3.41244	+	1.10877i	−0.267283	+	0.0868454i	0.172310	+	0.985043i	$0.444877\pi$
$164$	10.3142	−	2.24491i	0.805407	−	0.175298i
$165$	0.374542	+	1.50632i	0.0291580	+	0.117267i
$166$	16.2976	+	13.1320i	1.26494	+	1.01924i
$167$	4.87309	+	14.9978i	0.377091	+	1.16057i	0.942057	+	0.335452i	$0.108889\pi$
$167$	4.87309	+	14.9978i	0.377091	+	1.16057i	−0.564967	+	0.825114i	$0.691111\pi$
$168$	−0.119026	−	0.229444i	−0.00918309	−	0.0177020i
$169$	0.809017	−	0.587785i	0.0622321	−	0.0452143i
$170$	1.04670	+	1.60322i	0.0802782	+	0.122961i
$171$	5.25084	−	16.1604i	0.401542	−	1.23582i
$172$	8.37246	+	7.46510i	0.638394	+	0.569208i
$173$	−6.04951	+	8.32643i	−0.459936	+	0.633047i	−0.974495	−	0.224407i	$-0.927955\pi$
$173$	−6.04951	+	8.32643i	−0.459936	+	0.633047i	0.514560	+	0.857455i	$0.327955\pi$
$174$	0.461804	−	1.21185i	0.0350093	−	0.0918702i
$175$	−10.9875			−0.830580
$176$	−3.54058	+	12.7853i	−0.266881	+	0.963729i
$177$	−0.361007			−0.0271350
$178$	0.350279	−	0.919191i	0.0262545	−	0.0688963i
$179$	7.20941	−	9.92290i	0.538856	−	0.741672i	−0.449591	−	0.893234i	$-0.648430\pi$
$179$	7.20941	−	9.92290i	0.538856	−	0.741672i	0.988448	+	0.151562i	$0.0484304\pi$
$180$	19.0247	+	16.9629i	1.41802	+	1.26434i
$181$	−5.62011	+	17.2969i	−0.417740	+	1.28567i	0.492038	+	0.870574i	$0.336252\pi$
$181$	−5.62011	+	17.2969i	−0.417740	+	1.28567i	−0.909777	+	0.415096i	$0.863748\pi$
$182$	−0.643912	−	0.986272i	−0.0477299	−	0.0731074i
$183$	0.966038	−	0.701868i	0.0714116	−	0.0518836i
$184$	11.2714	+	21.7276i	0.830938	+	1.60178i
$185$	−1.70955	−	5.26146i	−0.125689	−	0.386830i
$186$	0.599248	+	0.482850i	0.0439390	+	0.0354043i
$187$	−0.806021	−	0.677213i	−0.0589421	−	0.0495227i
$188$	−3.23866	+	0.704898i	−0.236203	+	0.0514099i
$189$	0.520436	−	0.169100i	0.0378561	−	0.0123002i
$190$	8.95889	+	33.1124i	0.649946	+	2.40222i
$191$	2.42528	+	3.33811i	0.175487	+	0.241537i	0.887696	−	0.460431i	$-0.152305\pi$
$191$	2.42528	+	3.33811i	0.175487	+	0.241537i	−0.712209	+	0.701968i	$0.752305\pi$
$192$	−0.283419	−	0.830781i	−0.0204540	−	0.0599564i
$193$	−4.43318	−	1.44043i	−0.319108	−	0.103684i	0.145083	−	0.989419i	$-0.453655\pi$
$193$	−4.43318	−	1.44043i	−0.319108	−	0.103684i	−0.464191	+	0.885735i	$0.653655\pi$
$194$	7.20534	+	0.360028i	0.517314	+	0.0258485i
$195$	−0.378621	−	0.275084i	−0.0271136	−	0.0196992i
$196$	10.8920	−	6.35943i	0.778002	−	0.454245i
$197$			11.6968i			0.833365i	0.909052	+	0.416682i	$0.136807\pi$
$197$			11.6968i			0.833365i	−0.909052	+	0.416682i	$0.863193\pi$
$198$	−12.7123	−	5.90011i	−0.903424	−	0.419303i
$199$		−	15.8639i		−	1.12456i	−0.826946	−	0.562281i	$-0.809924\pi$
$199$		−	15.8639i		−	1.12456i	0.826946	−	0.562281i	$-0.190076\pi$
$200$	−36.8958	−	5.56779i	−2.60893	−	0.393703i
$201$	−0.578296	−	0.420156i	−0.0407898	−	0.0296355i
$202$	0.202903	−	4.06077i	0.0142762	−	0.285714i
$203$	−6.62004	−	2.15098i	−0.464635	−	0.150969i
$204$	0.0693097	+	0.00694370i	0.00485265	+	0.000486156i
$205$	−13.2319	−	18.2121i	−0.924153	−	1.27199i
$206$	−10.4381	+	2.82414i	−0.727259	+	0.196767i
$207$	−24.5922	+	7.99049i	−1.70928	+	0.555377i
$208$	−1.66246	−	3.63816i	−0.115271	−	0.252261i
$209$	−9.98463	−	16.0016i	−0.690651	−	1.10685i
$210$	−0.345863	+	0.429238i	−0.0238668	+	0.0296202i
$211$	−5.14906	−	15.8472i	−0.354476	−	1.09097i	−0.956313	−	0.292346i	$-0.905564\pi$
$211$	−5.14906	−	15.8472i	−0.354476	−	1.09097i	0.601836	−	0.798619i	$-0.294436\pi$
$212$	2.97699	−	6.77502i	0.204460	−	0.465310i
$213$	1.03619	−	0.752833i	0.0709983	−	0.0515833i
$214$	−10.8760	+	7.10065i	−0.743467	+	0.485390i
$215$	7.39233	−	22.7513i	0.504153	−	1.55162i
$216$	1.83330	−	0.304108i	0.124740	−	0.0206919i
$217$	2.42789	−	3.34171i	0.164816	−	0.226850i
$218$	1.36041	+	0.518416i	0.0921387	+	0.0351116i
$219$	0.0398051			0.00268978
$220$	28.0002	−	4.05597i	1.88777	−	0.273454i
$221$	0.317417			0.0213518
$222$	−0.188074	−	0.0716701i	−0.0126227	−	0.00481018i
$223$	−4.88844	+	6.72836i	−0.327354	+	0.450564i	−0.940695	−	0.339254i	$-0.889825\pi$
$223$	−4.88844	+	6.72836i	−0.327354	+	0.450564i	0.613341	+	0.789818i	$0.289825\pi$
$224$	−4.37763	+	1.74185i	−0.292493	+	0.116382i
$225$	12.1809	−	37.4889i	0.812059	−	2.49926i
$226$	−9.18408	+	5.99605i	−0.610916	+	0.398851i
$227$	10.2124	−	7.41977i	0.677824	−	0.492468i	−0.194811	−	0.980841i	$-0.562409\pi$
$227$	10.2124	−	7.41977i	0.677824	−	0.492468i	0.872635	+	0.488373i	$0.162409\pi$
$228$	1.14254	+	0.502038i	0.0756663	+	0.0332483i
$229$	2.40793	+	7.41084i	0.159120	+	0.489722i	0.998555	−	0.0537386i	$-0.0171138\pi$
$229$	2.40793	+	7.41084i	0.159120	+	0.489722i	−0.839435	+	0.543460i	$0.817114\pi$
$230$	32.7520	−	40.6473i	2.15960	−	2.68021i
$231$	0.113721	−	0.280952i	0.00748232	−	0.0184853i
$232$	−21.1399	−	10.5775i	−1.38790	−	0.694449i
$233$	24.1915	−	7.86030i	1.58484	−	0.514946i	0.621542	−	0.783381i	$-0.286506\pi$
$233$	24.1915	−	7.86030i	1.58484	−	0.514946i	0.963298	+	0.268435i	$0.0865065\pi$
$234$	4.07896	−	1.10360i	0.266650	−	0.0721448i
$235$	4.15478	+	5.71857i	0.271028	+	0.373038i
$236$	−0.655951	+	6.54749i	−0.0426988	+	0.426205i
$237$	0.589310	+	0.191478i	0.0382798	+	0.0124379i
$238$	0.0186579	−	0.373407i	0.00120941	−	0.0242044i
$239$	−6.51146	−	4.73085i	−0.421191	−	0.306013i	0.356926	−	0.934133i	$-0.383825\pi$
$239$	−6.51146	−	4.73085i	−0.421191	−	0.306013i	−0.778117	+	0.628120i	$0.783825\pi$
$240$	−1.37891	+	1.26610i	−0.0890081	+	0.0817267i
$241$		−	13.0733i		−	0.842128i	−0.907031	−	0.421064i	$-0.861657\pi$
$241$		−	13.0733i		−	0.842128i	0.907031	−	0.421064i	$-0.138343\pi$
$242$	−14.0913	+	6.59064i	−0.905820	+	0.423662i
$243$			2.94672i			0.189032i
$244$	−10.9743	−	18.7960i	−0.702556	−	1.20329i
$245$	−21.7610	−	15.8103i	−1.39026	−	1.01008i
$246$	−0.817964	−	0.0408710i	−0.0521515	−	0.00260584i
$247$	5.40852	+	1.75733i	0.344136	+	0.111816i
$248$	9.84615	−	9.99104i	0.625231	−	0.634432i
$249$	−0.954495	−	1.31375i	−0.0604887	−	0.0832555i
$250$	12.9060	+	47.7009i	0.816245	+	3.01687i
$251$	−13.7309	+	4.46143i	−0.866686	+	0.281603i	−0.708418	−	0.705793i	$-0.750591\pi$
$251$	−13.7309	+	4.46143i	−0.866686	+	0.281603i	−0.158268	+	0.987396i	$0.550591\pi$
$252$	−1.05851	−	4.86332i	−0.0666798	−	0.306361i
$253$	−10.7690	+	26.6051i	−0.677043	+	1.67265i
$254$	−15.9662	−	12.8650i	−1.00181	−	0.807219i
$255$	−0.0459049	−	0.141281i	−0.00287468	−	0.00884735i
$256$	−15.5826	+	3.63076i	−0.973913	+	0.226923i
$257$	−21.1572	+	15.3716i	−1.31975	+	0.958856i	−0.319816	+	0.947480i	$0.603621\pi$
$257$	−21.1572	+	15.3716i	−1.31975	+	0.958856i	−0.999935	+	0.0113763i	$0.996379\pi$
$258$	−0.475779	−	0.728745i	−0.0296207	−	0.0453697i
$259$	−0.333824	+	1.02740i	−0.0207428	+	0.0638397i
$260$	−5.67708	+	6.36711i	−0.352078	+	0.394872i
$261$	14.6781	−	20.2026i	0.908549	−	1.25051i
$262$	2.96507	−	7.78085i	0.183183	−	0.480702i
$263$	−12.1003			−0.746136			−0.373068	−	0.927804i	$-0.621694\pi$
$263$	−12.1003			−0.746136			−0.373068	+	0.927804i	$0.621694\pi$
$264$	0.524241	−	0.885799i	0.0322648	−	0.0545172i
$265$	−15.7819			−0.969474
$266$	2.38523	−	6.25924i	0.146248	−	0.383779i
$267$	−0.0448597	+	0.0617441i	−0.00274537	+	0.00377868i
$268$	−8.67102	+	9.72495i	−0.529667	+	0.594046i
$269$	3.44527	−	10.6034i	0.210062	−	0.646503i	−0.789406	−	0.613872i	$-0.789611\pi$
$269$	3.44527	−	10.6034i	0.210062	−	0.646503i	0.999467	−	0.0326314i	$-0.0103887\pi$
$270$	−2.16657	−	3.31852i	−0.131854	−	0.201958i
$271$	22.3611	−	16.2463i	1.35834	−	0.986893i	0.359794	−	0.933032i	$-0.382847\pi$
$271$	22.3611	−	16.2463i	1.35834	−	0.986893i	0.998548	−	0.0538616i	$-0.0171530\pi$
$272$	0.251872	−	1.24443i	0.0152720	−	0.0754549i
$273$	0.0282400	+	0.0869137i	0.00170916	+	0.00526026i
$274$	−16.3633	−	13.1849i	−0.988545	−	0.796530i
$275$	−23.1623	−	37.1204i	−1.39674	−	2.23844i
$276$	−0.403887	−	1.85566i	−0.0243111	−	0.111698i
$277$	0.781619	−	0.253963i	0.0469629	−	0.0152592i	−0.285441	−	0.958396i	$-0.592140\pi$
$277$	0.781619	−	0.253963i	0.0469629	−	0.0152592i	0.332404	+	0.943137i	$0.392140\pi$
$278$	5.57461	+	20.6040i	0.334343	+	1.23574i
$279$	8.71015	+	11.9885i	0.521463	+	0.717732i
$280$	7.15652	+	7.05274i	0.427684	+	0.421482i
$281$	24.6517	+	8.00982i	1.47060	+	0.477826i	0.931288	−	0.364283i	$-0.118686\pi$
$281$	24.6517	+	8.00982i	1.47060	+	0.477826i	0.539308	+	0.842109i	$0.318686\pi$
$282$	0.256840	+	0.0128334i	0.0152946	+	0.000764220i
$283$	5.28000	+	3.83615i	0.313864	+	0.228035i	0.733553	−	0.679633i	$-0.237861\pi$
$283$	5.28000	+	3.83615i	0.313864	+	0.228035i	−0.419689	+	0.907668i	$0.637861\pi$
$284$	−11.7712	−	20.1609i	−0.698490	−	1.19633i
$285$		−	2.66145i		−	0.157651i
$286$	1.97463	−	4.25451i	0.116762	−	0.251574i
$287$			4.39579i			0.259475i
$288$	−1.09001	−	16.8673i	−0.0642295	−	0.993914i
$289$	−13.6718	−	9.93313i	−0.804222	−	0.584302i
$290$	−2.51579	+	50.3492i	−0.147732	+	2.95661i
$291$	−0.532342	−	0.172968i	−0.0312064	−	0.0101396i
$292$	0.0723260	−	0.721934i	0.00423256	−	0.0422480i
$293$	−5.80301	−	7.98716i	−0.339015	−	0.466615i	0.605138	−	0.796120i	$-0.293118\pi$
$293$	−5.80301	−	7.98716i	−0.339015	−	0.466615i	−0.944154	+	0.329506i	$0.893118\pi$
$294$	−0.944611	+	0.255574i	−0.0550909	+	0.0149054i
$295$	13.3464	−	4.33651i	0.777057	−	0.252481i
$296$	−1.64159	+	3.28083i	−0.0954156	+	0.190694i
$297$	1.66839	+	1.40177i	0.0968100	+	0.0813390i
$298$	4.61712	−	5.73014i	0.267462	−	0.331938i
$299$	−2.67423	−	8.23043i	−0.154655	−	0.475978i
$300$	2.65045	+	1.16463i	0.153024	+	0.0672398i
$301$	−3.77913	+	2.74570i	−0.217825	+	0.158259i
$302$	−9.51604	+	6.21278i	−0.547587	+	0.357505i
$303$	−0.0974809	+	0.300015i	−0.00560013	+	0.0172354i
$304$	11.1813	−	19.8097i	0.641292	−	1.13616i
$305$	−27.2833	+	37.5522i	−1.56224	+	2.15023i
$306$	1.25336	+	0.477622i	0.0716498	+	0.0273038i
$307$	−16.7060			−0.953461			−0.476730	−	0.879050i	$-0.658178\pi$
$307$	−16.7060			−0.953461			−0.476730	+	0.879050i	$0.658178\pi$
$308$	−4.88890	−	2.57302i	−0.278571	−	0.146611i
$309$	0.838979			0.0477279
$310$	−27.9542	−	10.6526i	−1.58769	−	0.605027i
$311$	19.8930	−	27.3804i	1.12803	−	1.55260i	0.336269	−	0.941766i	$-0.390835\pi$
$311$	19.8930	−	27.3804i	1.12803	−	1.55260i	0.791760	−	0.610832i	$-0.209165\pi$
$312$	0.0507865	+	0.306164i	0.00287522	+	0.0173331i
$313$	3.45141	−	10.6223i	0.195085	−	0.600411i	−0.804890	−	0.593424i	$-0.797776\pi$
$313$	3.45141	−	10.6223i	0.195085	−	0.600411i	0.999976	−	0.00698709i	$-0.00222408\pi$
$314$	−19.7983	+	12.9258i	−1.11729	+	0.729447i
$315$	−8.58728	+	6.23902i	−0.483838	+	0.351529i
$316$	4.54357	−	10.3402i	0.255596	−	0.581683i
$317$	7.60396	+	23.4026i	0.427081	+	1.31442i	0.900987	+	0.433845i	$0.142843\pi$
$317$	7.60396	+	23.4026i	0.427081	+	1.31442i	−0.473906	+	0.880575i	$0.657157\pi$
$318$	−0.360243	+	0.447084i	−0.0202014	+	0.0250712i
$319$	−6.68849	−	26.8995i	−0.374484	−	1.50609i
$320$	20.4575	+	27.3093i	1.14361	+	1.52664i
$321$	0.958428	−	0.311412i	0.0534943	−	0.0173813i
$322$	−9.83941	+	2.66215i	−0.548329	+	0.148356i
$323$	1.06101	+	1.46036i	0.0590363	+	0.0812565i
$324$	17.6950	+	1.77275i	0.983056	+	0.0984861i
$325$	12.5467	+	4.07666i	0.695963	+	0.226132i
$326$	0.253229	−	5.06794i	0.0140250	−	0.280687i
$327$	−0.0913818	−	0.0663927i	−0.00505342	−	0.00367153i
$328$	−2.22751	+	14.7609i	−0.122994	+	0.815035i
$329$		−	1.38027i		−	0.0760968i
$330$	−2.17924	−	0.263610i	−0.119963	−	0.0145113i
$331$			3.72215i			0.204588i	0.994754	+	0.102294i	$0.0326182\pi$
$331$			3.72215i			0.204588i	−0.994754	+	0.102294i	$0.967382\pi$
$332$	−25.5614	+	14.9243i	−1.40287	+	0.819078i
$333$	−3.13537	−	2.27798i	−0.171817	−	0.124832i
$334$	−22.2738	−	1.11295i	−1.21877	−	0.0608980i
$335$	26.4265	+	8.58650i	1.44383	+	0.469130i
$336$	0.363154	−	0.0417485i	0.0198117	−	0.00227757i
$337$	12.8616	+	17.7024i	0.700614	+	0.964312i	0.999948	+	0.0101639i	$0.00323532\pi$
$337$	12.8616	+	17.7024i	0.700614	+	0.964312i	−0.299335	+	0.954148i	$0.596765\pi$
$338$	0.369350	+	1.36513i	0.0200900	+	0.0742533i
$339$	0.809333	−	0.262968i	0.0439569	−	0.0142825i
$340$	−2.64578	+	0.575857i	−0.143488	+	0.0312302i
$341$	16.4078	+	1.15791i	0.888530	+	0.0627046i
$342$	18.7119	+	15.0773i	1.01182	+	0.815289i
$343$	3.42467	+	10.5401i	0.184915	+	0.569110i
$344$	−14.0815	+	7.30494i	−0.759225	+	0.393856i
$345$	−3.27658	+	2.38058i	−0.176405	+	0.128166i
$346$	−7.95699	−	12.1876i	−0.427771	−	0.655211i
$347$	−8.35488	+	25.7137i	−0.448514	+	1.38038i	0.430070	+	0.902795i	$0.358489\pi$
$347$	−8.35488	+	25.7137i	−0.448514	+	1.38038i	−0.878584	+	0.477588i	$0.841511\pi$
$348$	1.36891	+	1.22056i	0.0733815	+	0.0654288i
$349$	4.65842	−	6.41176i	0.249359	−	0.343214i	−0.665927	−	0.746016i	$-0.731964\pi$
$349$	4.65842	−	6.41176i	0.249359	−	0.343214i	0.915287	+	0.402803i	$0.131964\pi$
$350$	5.53325	−	14.5202i	0.295765	−	0.776136i
$351$	−0.657025			−0.0350694
$352$	−15.1129	−	11.1175i	−0.805522	−	0.592565i
$353$	18.2794			0.972915			0.486458	−	0.873704i	$-0.338289\pi$
$353$	18.2794			0.972915			0.486458	+	0.873704i	$0.338289\pi$
$354$	0.181801	−	0.477076i	0.00966260	−	0.0253563i
$355$	−29.2644	+	40.2790i	−1.55319	+	2.13779i
$356$	1.03832	+	0.925797i	0.0550311	+	0.0490671i
$357$	−0.00896384	+	0.0275879i	−0.000474417	+	0.00146010i
$358$	9.48262	+	14.5244i	0.501172	+	0.767639i
$359$	11.2244	−	8.15503i	0.592403	−	0.430406i	−0.250771	−	0.968046i	$-0.580684\pi$
$359$	11.2244	−	8.15503i	0.592403	−	0.430406i	0.843174	+	0.537641i	$0.180684\pi$
$360$	−31.9974	+	16.5990i	−1.68641	+	0.874842i
$361$	4.12237	+	12.6873i	0.216967	+	0.667755i
$362$	−20.0278	−	16.1377i	−1.05264	−	0.848176i
$363$	1.18890	−	0.208063i	0.0624010	−	0.0109205i
$364$	1.62764	−	0.354258i	0.0853115	−	0.0185682i
$365$	−1.47159	+	0.478148i	−0.0770265	+	0.0250274i
$366$	0.441037	+	1.63009i	0.0230534	+	0.0852060i
$367$	−20.2556	−	27.8794i	−1.05733	−	1.45530i	−0.882273	−	0.470737i	$-0.843988\pi$
$367$	−20.2556	−	27.8794i	−1.05733	−	1.45530i	−0.175060	−	0.984558i	$-0.556012\pi$
$368$	−34.3894	+	3.95344i	−1.79267	+	0.206087i
$369$	−14.9982	−	4.87321i	−0.780775	−	0.253689i
$370$	7.81400	+	0.390440i	0.406231	+	0.0202980i
$371$	2.49317	+	1.81139i	0.129439	+	0.0940428i
$372$	−0.939870	+	0.548753i	−0.0487300	+	0.0284515i
$373$			21.1404i			1.09461i	0.836935	+	0.547303i	$0.184345\pi$
$373$			21.1404i			1.09461i	−0.836935	+	0.547303i	$0.815655\pi$
$374$	1.30085	−	0.724127i	0.0672655	−	0.0374437i
$375$		−	3.83403i		−	0.197988i
$376$	0.699434	−	4.63491i	0.0360706	−	0.239027i
$377$	6.76134	+	4.91240i	0.348227	+	0.253002i
$378$	−0.0386203	+	0.772920i	−0.00198641	+	0.0397547i
$379$	32.1080	+	10.4325i	1.64928	+	0.535882i	0.978583	−	0.205853i	$-0.0659967\pi$
$379$	32.1080	+	10.4325i	1.64928	+	0.535882i	0.670693	+	0.741735i	$0.265997\pi$
$380$	−48.2700	−	4.83587i	−2.47620	−	0.248075i
$381$	0.935087	+	1.28704i	0.0479060	+	0.0659369i
$382$	−5.63271	+	1.52399i	−0.288195	+	0.0779740i
$383$	18.6863	−	6.07156i	0.954827	−	0.310242i	0.210151	−	0.977669i	$-0.432604\pi$
$383$	18.6863	−	6.07156i	0.954827	−	0.310242i	0.744675	+	0.667427i	$0.232604\pi$
$384$	1.24061	+	0.0438335i	0.0633099	+	0.00223687i
$385$	−0.829407	+	11.7528i	−0.0422705	+	0.598977i
$386$	4.13606	−	5.13312i	0.210520	−	0.261269i
$387$	−5.17860	−	15.9381i	−0.263243	−	0.810178i
$388$	−4.10434	+	9.34064i	−0.208366	+	0.474199i
$389$	−6.51273	+	4.73178i	−0.330209	+	0.239911i	−0.740519	−	0.672035i	$-0.765420\pi$
$389$	−6.51273	+	4.73178i	−0.330209	+	0.239911i	0.410310	+	0.911946i	$0.365420\pi$
$390$	0.554198	−	0.361822i	0.0280629	−	0.0183216i
$391$	0.848845	−	2.61248i	0.0429279	−	0.132119i
$392$	2.91892	+	17.5965i	0.147428	+	0.888758i
$393$	−0.379732	+	0.522656i	−0.0191549	+	0.0263645i
$394$	−15.4575	−	5.89044i	−0.778738	−	0.296756i
$395$	−24.0868			−1.21194
$396$	14.1989	−	13.8282i	0.713521	−	0.694894i
$397$	17.2611			0.866310			0.433155	−	0.901319i	$-0.357400\pi$
$397$	17.2611			0.866310			0.433155	+	0.901319i	$0.357400\pi$
$398$	20.9643	+	7.98895i	1.05085	+	0.400450i
$399$	−0.305473	+	0.420447i	−0.0152928	+	0.0210487i
$400$	25.9384	−	45.9544i	1.29692	−	2.29772i
$401$	4.31276	−	13.2733i	0.215369	−	0.662837i	−0.783758	−	0.621066i	$-0.786700\pi$
$401$	4.31276	−	13.2733i	0.215369	−	0.662837i	0.999127	−	0.0417713i	$-0.0133001\pi$
$402$	0.846467	−	0.552637i	0.0422180	−	0.0275630i
$403$	−4.01226	+	2.91508i	−0.199865	+	0.145211i
$404$	5.26417	+	2.31311i	0.261902	+	0.115082i
$405$	−11.7197	−	36.0695i	−0.582356	−	1.79231i
$406$	6.17635	−	7.66524i	0.306527	−	0.380419i
$407$	−4.17470	+	1.03803i	−0.206932	+	0.0514531i
$408$	−0.0440801	+	0.0880969i	−0.00218229	+	0.00436144i
$409$	−7.95797	+	2.58570i	−0.393496	+	0.127855i	−0.499080	−	0.866556i	$-0.666329\pi$
$409$	−7.95797	+	2.58570i	−0.393496	+	0.127855i	0.105584	+	0.994410i	$0.466329\pi$
$410$	30.7310	−	8.31458i	1.51769	−	0.410628i
$411$	0.958344	+	1.31905i	0.0472716	+	0.0650638i
$412$	1.52443	−	15.2163i	0.0751031	−	0.749655i
$413$	−2.60614	−	0.846788i	−0.128240	−	0.0416677i
$414$	1.82493	−	36.5228i	0.0896903	−	1.79500i
$415$	51.0686	+	37.1035i	2.50686	+	1.82134i
$416$	5.64508	−	0.364801i	0.276773	−	0.0178858i
$417$		−	1.65607i		−	0.0810983i
$418$	26.1744	−	5.13653i	1.28023	−	0.251236i
$419$			1.48226i			0.0724130i	0.999344	+	0.0362065i	$0.0115274\pi$
$419$			1.48226i			0.0724130i	−0.999344	+	0.0362065i	$0.988473\pi$
$420$	−0.393069	−	0.673223i	−0.0191798	−	0.0328499i
$421$	−7.31670	−	5.31589i	−0.356594	−	0.259081i	0.395036	−	0.918666i	$-0.370732\pi$
$421$	−7.31670	−	5.31589i	−0.356594	−	0.259081i	−0.751630	+	0.659585i	$0.770732\pi$
$422$	23.5353	+	1.17598i	1.14568	+	0.0572459i
$423$	4.70941	+	1.53018i	0.228979	+	0.0743999i
$424$	7.45407	+	7.34597i	0.362002	+	0.356752i
$425$	2.46133	+	3.38773i	0.119392	+	0.164329i
$426$	0.473062	+	1.74845i	0.0229199	+	0.0847128i
$427$	8.62023	−	2.80088i	0.417162	−	0.135544i
$428$	−3.90653	−	17.9486i	−0.188829	−	0.867577i
$429$	−0.234098	+	0.278625i	−0.0113024	+	0.0134521i
$430$	26.3433	+	21.2264i	1.27039	+	1.02363i
$431$	−6.10044	−	18.7752i	−0.293848	−	0.904370i	−0.983606	−	0.180331i	$-0.942283\pi$
$431$	−6.10044	−	18.7752i	−0.293848	−	0.904370i	0.689758	−	0.724040i	$-0.257717\pi$
$432$	−0.521353	+	2.57587i	−0.0250836	+	0.123932i
$433$	−12.3335	+	8.96082i	−0.592711	+	0.430630i	−0.843284	−	0.537468i	$-0.819381\pi$
$433$	−12.3335	+	8.96082i	−0.592711	+	0.430630i	0.250573	+	0.968098i	$0.419381\pi$
$434$	3.19344	+	4.89135i	0.153290	+	0.234792i
$435$	1.20866	−	3.71988i	0.0579509	−	0.178354i
$436$	−1.37019	+	1.53673i	−0.0656200	+	0.0735960i
$437$	28.9272	−	39.8149i	1.38378	−	1.90460i
$438$	−0.0200456	+	0.0526030i	−0.000957815	+	0.00251347i
$439$	7.76868			0.370779			0.185389	−	0.982665i	$-0.440645\pi$
$439$	7.76868			0.370779			0.185389	+	0.982665i	$0.440645\pi$
$440$	−8.74069	+	39.0452i	−0.416696	+	1.86141i
$441$	−18.8430			−0.897288
$442$	−0.159849	+	0.419470i	−0.00760324	+	0.0199522i
$443$	14.4040	−	19.8254i	0.684355	−	0.941934i	−0.315621	−	0.948885i	$-0.602213\pi$
$443$	14.4040	−	19.8254i	0.684355	−	0.941934i	0.999976	+	0.00695162i	$0.00221279\pi$
$444$	0.189426	−	0.212450i	0.00898975	−	0.0100824i
$445$	0.916772	−	2.82153i	0.0434592	−	0.133754i
$446$	−6.42982	−	9.84848i	−0.304461	−	0.466339i
$447$	−0.461906	+	0.335594i	−0.0218474	+	0.0158731i
$448$	−0.0973284	−	6.66228i	−0.00459833	−	0.314763i
$449$	2.76670	+	8.51502i	0.130569	+	0.401849i	0.994874	−	0.101118i	$-0.0322419\pi$
$449$	2.76670	+	8.51502i	0.130569	+	0.401849i	−0.864306	+	0.502967i	$0.832242\pi$
$450$	43.4079	+	34.9763i	2.04627	+	1.64880i
$451$	−14.8508	+	9.26655i	−0.699295	+	0.436345i
$452$	−3.29882	−	15.1564i	−0.155163	−	0.712899i
$453$	0.838586	−	0.272473i	0.0394002	−	0.0128019i
$454$	4.66241	+	17.2324i	0.218818	+	0.808757i
$455$	−2.08805	−	2.87396i	−0.0978895	−	0.134733i
$456$	−1.23882	+	1.25705i	−0.0580132	+	0.0588669i
$457$	−15.9127	−	5.17036i	−0.744366	−	0.241859i	−0.0878109	−	0.996137i	$-0.527987\pi$
$457$	−15.9127	−	5.17036i	−0.744366	−	0.241859i	−0.656555	+	0.754278i	$0.727987\pi$
$458$	−11.0061	−	0.549940i	−0.514282	−	0.0256970i
$459$	−0.168721	−	0.122583i	−0.00787523	−	0.00572169i
$460$	37.2222	+	63.7519i	1.73550	+	2.97245i
$461$			1.53052i			0.0712833i	0.999365	+	0.0356416i	$0.0113475\pi$
$461$			1.53052i			0.0712833i	−0.999365	+	0.0356416i	$0.988653\pi$
$462$	0.314012	+	0.291769i	0.0146091	+	0.0135743i
$463$		−	4.36101i		−	0.202673i	−0.994852	−	0.101337i	$-0.967688\pi$
$463$		−	4.36101i		−	0.202673i	0.994852	−	0.101337i	$-0.0323119\pi$
$464$	24.6242	−	22.6098i	1.14315	−	1.04964i
$465$	1.87775	+	1.36426i	0.0870784	+	0.0632661i
$466$	−1.79520	+	35.9278i	−0.0831608	+	1.66432i
$467$	−22.9619	−	7.46078i	−1.06255	−	0.345244i	−0.274969	−	0.961453i	$-0.588667\pi$
$467$	−22.9619	−	7.46078i	−1.06255	−	0.345244i	−0.787582	+	0.616210i	$0.788667\pi$
$468$	−0.595708	+	5.94616i	−0.0275366	+	0.274861i
$469$	−3.18924	−	4.38961i	−0.147265	−	0.202693i
$470$	−9.64948	+	2.61077i	−0.445097	+	0.120426i
$471$	1.74470	−	0.566887i	0.0803914	−	0.0261208i
$472$	−8.32225	−	4.16412i	−0.383063	−	0.191669i
$473$	−17.2427	−	6.97935i	−0.792819	−	0.320911i
$474$	−0.549814	+	0.682353i	−0.0252538	+	0.0313415i
$475$	23.1833	+	71.3510i	1.06372	+	3.27381i
$476$	0.484066	+	0.212702i	0.0221871	+	0.00974917i
$477$	−8.94432	+	6.49843i	−0.409532	+	0.297543i
$478$	9.53100	−	6.22254i	0.435938	−	0.284613i
$479$	−1.48433	+	4.56831i	−0.0678209	+	0.208731i	−0.979223	−	0.202785i	$-0.935001\pi$
$479$	−1.48433	+	4.56831i	−0.0678209	+	0.208731i	0.911402	+	0.411516i	$0.135001\pi$
$480$	−0.978765	−	2.45984i	−0.0446743	−	0.112276i
$481$	0.762385	−	1.04933i	0.0347618	−	0.0478455i
$482$	17.2766	+	6.58365i	0.786927	+	0.299877i
$483$	0.790857			0.0359852
$484$	−1.61335	−	21.9408i	−0.0733343	−	0.997307i
$485$	21.7583			0.987995
$486$	−3.89413	−	1.48395i	−0.176641	−	0.0673132i
$487$	−13.9336	+	19.1780i	−0.631394	+	0.869039i	−0.998120	−	0.0612898i	$-0.980479\pi$
$487$	−13.9336	+	19.1780i	−0.631394	+	0.869039i	0.366726	+	0.930329i	$0.380479\pi$
$488$	30.3658	−	5.03709i	1.37459	−	0.228018i
$489$	−0.121659	+	0.374427i	−0.00550160	+	0.0169322i
$490$	31.8521	−	20.7954i	1.43893	−	0.939442i
$491$	−29.2102	+	21.2224i	−1.31824	+	0.957754i	−0.318283	+	0.947996i	$0.603106\pi$
$491$	−29.2102	+	21.2224i	−1.31824	+	0.957754i	−0.999952	+	0.00975860i	$0.996894\pi$
$492$	0.465933	−	1.06037i	0.0210059	−	0.0478051i
$493$	0.819761	+	2.52297i	0.0369202	+	0.113629i
$494$	−5.04603	+	6.26244i	−0.227031	+	0.281760i
$495$	−39.1804	−	15.8591i	−1.76103	−	0.712815i
$496$	8.24483	+	18.0432i	0.370204	+	0.810165i
$497$	9.24618	−	3.00427i	0.414748	−	0.134760i
$498$	2.21681	−	0.599782i	0.0993378	−	0.0268769i
$499$	−12.0369	−	16.5674i	−0.538846	−	0.741658i	0.449600	−	0.893230i	$-0.351566\pi$
$499$	−12.0369	−	16.5674i	−0.538846	−	0.741658i	−0.988446	+	0.151572i	$0.951566\pi$
$500$	−69.5366	−	6.96643i	−3.10977	−	0.311548i
$501$	1.64563	+	0.534696i	0.0735211	+	0.0238885i
$502$	1.01894	−	20.3923i	0.0454773	−	0.910152i
$503$	4.88408	+	3.54849i	0.217770	+	0.158219i	0.691322	−	0.722546i	$-0.257028\pi$
$503$	4.88408	+	3.54849i	0.217770	+	0.158219i	−0.473552	+	0.880766i	$0.657028\pi$
$504$	6.96000	+	1.05030i	0.310023	+	0.0467843i
$505$		−	12.2625i		−	0.545674i
$506$	−29.7358	−	27.6296i	−1.32192	−	1.22828i
$507$		−	0.109724i		−	0.00487303i
$508$	25.0417	−	14.6209i	1.11104	−	0.648695i
$509$	10.5403	+	7.65799i	0.467191	+	0.339434i	0.796346	−	0.604842i	$-0.206764\pi$
$509$	10.5403	+	7.65799i	0.467191	+	0.339434i	−0.329154	+	0.944276i	$0.606764\pi$
$510$	0.209822	+	0.0104841i	0.00929107	+	0.000464244i
$511$	0.287357	+	0.0933678i	0.0127119	+	0.00413035i
$512$	3.04919	−	22.4210i	0.134757	−	0.990879i
$513$	−2.19620	−	3.02281i	−0.0969647	−	0.133460i
$514$	−9.65916	−	35.7006i	−0.426047	−	1.57468i
$515$	−31.0169	+	10.0780i	−1.36677	+	0.444090i
$516$	1.20264	−	0.261757i	0.0529435	−	0.0115232i
$517$	4.66312	−	2.90968i	0.205084	−	0.127968i
$518$	−1.18961	−	0.958545i	−0.0522687	−	0.0421160i
$519$	0.348969	+	1.07402i	0.0153180	+	0.0471441i
$520$	−5.55528	−	10.7088i	−0.243615	−	0.469610i
$521$	10.6026	−	7.70321i	0.464507	−	0.337484i	−0.330790	−	0.943704i	$-0.607315\pi$
$521$	10.6026	−	7.70321i	0.464507	−	0.337484i	0.795297	+	0.606221i	$0.207315\pi$
$522$	19.3062	+	29.5711i	0.845011	+	1.29429i
$523$	−6.57912	+	20.2484i	−0.287685	+	0.885402i	0.697896	+	0.716199i	$0.254120\pi$
$523$	−6.57912	+	20.2484i	−0.287685	+	0.885402i	−0.985581	+	0.169204i	$0.945880\pi$
$524$	8.78929	+	7.83676i	0.383962	+	0.342350i
$525$	−0.708634	+	0.975352i	−0.0309273	+	0.0425678i
$526$	6.09362	−	15.9907i	0.265694	−	0.697227i
$527$	−1.57421			−0.0685735
$528$	0.906591	+	1.13887i	0.0394543	+	0.0495631i
$529$	−51.8914			−2.25615
$530$	7.94765	−	20.8560i	0.345224	−	0.905925i
$531$	5.77839	−	7.95327i	0.250761	−	0.345143i
$532$	7.07048	+	6.30422i	0.306544	+	0.273323i
$533$	1.63095	−	5.01954i	0.0706442	−	0.217421i
$534$	−0.0590045	−	0.0903765i	−0.00255338	−	0.00391098i
$535$	−31.6922	+	23.0257i	−1.37017	+	0.995489i
$536$	−8.48498	−	16.3563i	−0.366495	−	0.706483i
$537$	−0.415878	−	1.27994i	−0.0179465	−	0.0552335i
$538$	12.2776	+	9.89277i	0.529323	+	0.426508i
$539$	−13.4546	+	16.0137i	−0.579532	+	0.689760i
$540$	5.47653	−	1.19197i	0.235672	−	0.0512944i
$541$	−9.17399	+	2.98081i	−0.394420	+	0.128155i	−0.499511	−	0.866308i	$-0.666487\pi$
$541$	−9.17399	+	2.98081i	−0.394420	+	0.128155i	0.105090	+	0.994463i	$0.466487\pi$
$542$	10.2088	+	37.7320i	0.438505	+	1.62073i
$543$	1.17296	+	1.61444i	0.0503366	+	0.0692824i
$544$	1.51769	+	0.959540i	0.0650706	+	0.0411399i
$545$	4.17590	+	1.35683i	0.178876	+	0.0581202i
$546$	−0.129079	−	0.00644966i	−0.00552407	−	0.000276020i
$547$	25.4845	+	18.5155i	1.08964	+	0.791668i	0.979338	−	0.202231i	$-0.0648191\pi$
$547$	25.4845	+	18.5155i	1.08964	+	0.791668i	0.110299	+	0.993898i	$0.464819\pi$
$548$	25.6645	−	14.9845i	1.09633	−	0.640106i
$549$			32.5169i			1.38779i
$550$	60.7194	−	11.9157i	2.58908	−	0.508088i
$551$			47.5277i			2.02475i
$552$	2.65567	+	0.400756i	0.113033	+	0.0170573i
$553$	3.80515	+	2.76460i	0.161811	+	0.117563i
$554$	−0.0580021	+	1.16081i	−0.00246427	+	0.0493182i
$555$	−0.577310	−	0.187579i	−0.0245054	−	0.00796230i
$556$	−30.0357	−	3.00909i	−1.27380	−	0.127614i
$557$	19.0461	+	26.2148i	0.807011	+	1.11076i	0.991778	+	0.127973i	$0.0408470\pi$
$557$	19.0461	+	26.2148i	0.807011	+	1.11076i	−0.184767	+	0.982782i	$0.559153\pi$
$558$	−20.2293	+	5.47325i	−0.856374	+	0.231701i
$559$	5.33410	−	1.73315i	0.225608	−	0.0733046i
$560$	−12.9243	+	5.90572i	−0.546149	+	0.249562i
$561$	−0.112099	+	0.0278732i	−0.00473283	+	0.00117681i
$562$	−22.9995	+	28.5438i	−0.970174	+	1.20405i
$563$	9.66803	+	29.7551i	0.407459	+	1.25403i	0.918825	+	0.394666i	$0.129140\pi$
$563$	9.66803	+	29.7551i	0.407459	+	1.25403i	−0.511366	+	0.859363i	$0.670860\pi$
$564$	−0.146302	+	0.332954i	−0.00616043	+	0.0140199i
$565$	−26.7621	+	19.4438i	−1.12589	+	0.818006i
$566$	−7.72849	+	5.04573i	−0.324853	+	0.212088i
$567$	−2.28850	+	7.04327i	−0.0961079	+	0.295790i
$568$	32.5707	−	5.40285i	1.36664	−	0.226698i
$569$	8.24351	−	11.3462i	0.345586	−	0.475658i	−0.600476	−	0.799642i	$-0.705022\pi$
$569$	8.24351	−	11.3462i	0.345586	−	0.475658i	0.946063	+	0.323984i	$0.105022\pi$
$570$	3.51714	+	1.34029i	0.147317	+	0.0561385i
$571$	10.6526			0.445798			0.222899	−	0.974842i	$-0.428448\pi$
$571$	10.6526			0.445798			0.222899	+	0.974842i	$0.428448\pi$
$572$	4.62798	+	4.75204i	0.193505	+	0.198693i
$573$	0.452737			0.0189134
$574$	−5.80909	−	2.21369i	−0.242467	−	0.0923976i
$575$	67.1052	−	92.3624i	2.79848	−	3.85178i
$576$	22.8392	+	7.05378i	0.951635	+	0.293907i
$577$	10.8036	−	33.2502i	0.449761	−	1.38422i	−0.427416	−	0.904055i	$-0.640576\pi$
$577$	10.8036	−	33.2502i	0.449761	−	1.38422i	0.877177	−	0.480167i	$-0.159424\pi$
$578$	20.0118	−	13.0652i	0.832379	−	0.543439i
$579$	−0.413781	+	0.300629i	−0.0171961	+	0.0124937i
$580$	−65.2702	−	28.6802i	−2.71020	−	1.19088i
$581$	−3.80902	−	11.7230i	−0.158025	−	0.486350i
$582$	0.496663	−	0.616390i	0.0205874	−	0.0255502i
$583$	−0.863892	+	12.2414i	−0.0357787	+	0.506988i
$584$	0.917622	+	0.459140i	0.0379715	+	0.0189994i
$585$	12.1206	−	3.93823i	0.501127	−	0.162826i
$586$	13.4775	−	3.64647i	0.556749	−	0.150634i
$587$	−7.24065	−	9.96590i	−0.298854	−	0.411337i	0.633011	−	0.774143i	$-0.281819\pi$
$587$	−7.24065	−	9.96590i	−0.298854	−	0.411337i	−0.931865	+	0.362806i	$0.881819\pi$
$588$	0.137955	−	1.37702i	0.00568917	−	0.0567874i
$589$	−26.8232	−	8.71537i	−1.10523	−	0.359111i
$590$	−0.990404	+	19.8212i	−0.0407743	+	0.816028i
$591$	1.03831	+	0.754379i	0.0427105	+	0.0310310i
$592$	−3.50896	−	3.82158i	−0.144217	−	0.157066i
$593$		−	10.6600i		−	0.437752i	−0.975753	−	0.218876i	$-0.929761\pi$
$593$		−	10.6600i		−	0.437752i	0.975753	−	0.218876i	$-0.0702390\pi$
$594$	−2.69265	+	1.49888i	−0.110481	+	0.0614998i
$595$		−	1.12759i		−	0.0462269i
$596$	5.24730	+	8.98723i	0.214938	+	0.368131i
$597$	−1.40822	−	1.02313i	−0.0576346	−	0.0418740i
$598$	12.2233	+	0.610760i	0.499849	+	0.0249758i
$599$	31.6717	+	10.2907i	1.29407	+	0.420469i	0.873514	−	0.486799i	$-0.161835\pi$
$599$	31.6717	+	10.2907i	1.29407	+	0.420469i	0.420555	+	0.907267i	$0.361835\pi$
$600$	−2.87382	+	2.91611i	−0.117323	+	0.119050i
$601$	12.9774	+	17.8618i	0.529358	+	0.728599i	0.987032	−	0.160521i	$-0.0513175\pi$
$601$	12.9774	+	17.8618i	0.529358	+	0.728599i	−0.457675	+	0.889120i	$0.651318\pi$
$602$	−1.72533	−	6.37687i	−0.0703192	−	0.259902i
$603$	18.5127	−	6.01515i	0.753897	−	0.244956i
$604$	−3.41805	−	15.7043i	−0.139079	−	0.638998i
$605$	−41.4541	+	21.9734i	−1.68535	+	0.893346i
$606$	−0.347383	−	0.279908i	−0.0141115	−	0.0113705i
$607$	−2.03948	−	6.27687i	−0.0827798	−	0.254770i	0.901097	−	0.433618i	$-0.142763\pi$
$607$	−2.03948	−	6.27687i	−0.0827798	−	0.254770i	−0.983877	+	0.178847i	$0.942763\pi$
$608$	20.5479	+	24.7522i	0.833326	+	1.00384i
$609$	−0.617895	+	0.448927i	−0.0250384	+	0.0181914i
$610$	−35.8860	−	54.9662i	−1.45298	−	2.22552i
$611$	−0.512115	+	1.57613i	−0.0207180	+	0.0637634i
$612$	−1.26237	+	1.41580i	−0.0510282	+	0.0572305i
$613$	2.34232	−	3.22392i	0.0946053	−	0.130213i	−0.759090	−	0.650985i	$-0.774356\pi$
$613$	2.34232	−	3.22392i	0.0946053	−	0.130213i	0.853696	+	0.520772i	$0.174356\pi$
$614$	8.41302	−	22.0772i	0.339522	−	0.890962i
$615$	−2.47005			−0.0996019
$616$	5.86230	−	5.16499i	0.236199	−	0.208103i
$617$	−7.76299			−0.312526			−0.156263	−	0.987715i	$-0.549945\pi$
$617$	−7.76299			−0.312526			−0.156263	+	0.987715i	$0.549945\pi$
$618$	−0.422504	+	1.10872i	−0.0169956	+	0.0445993i
$619$	26.1306	−	35.9656i	1.05028	−	1.44558i	0.161706	−	0.986839i	$-0.448300\pi$
$619$	26.1306	−	35.9656i	1.05028	−	1.44558i	0.888570	−	0.458741i	$-0.151700\pi$
$620$	28.1551	−	31.5773i	1.13074	−	1.26817i
$621$	−1.75703	+	5.40760i	−0.0705074	+	0.216999i
$622$	26.1655	+	40.0774i	1.04914	+	1.60696i
$623$	−0.468675	+	0.340512i	−0.0187771	+	0.0136423i
$624$	−0.430175	−	0.0870668i	−0.0172208	−	0.00348546i
$625$	25.6719	+	79.0101i	1.02688	+	3.16040i
$626$	12.2995	+	9.91042i	0.491585	+	0.396100i
$627$	−2.06439	−	0.145686i	−0.0824439	−	0.00581816i
$628$	−7.11134	−	32.6731i	−0.283773	−	1.30380i
$629$	0.391554	−	0.127224i	0.0156123	−	0.00507274i
$630$	−3.92045	−	14.4901i	−0.156195	−	0.577300i
$631$	−22.3449	−	30.7551i	−0.889537	−	1.22434i	−0.973687	−	0.227889i	$-0.926818\pi$
$631$	−22.3449	−	30.7551i	−0.889537	−	1.22434i	0.0841503	−	0.996453i	$-0.473182\pi$
$632$	11.3766	+	11.2116i	0.452538	+	0.445975i
$633$	−1.73882	−	0.564978i	−0.0691120	−	0.0224558i
$634$	−34.7561	−	1.73665i	−1.38034	−	0.0689712i
$635$	−50.0302	−	36.3491i	−1.98539	−	1.44247i
$636$	−0.409411	−	0.701214i	−0.0162342	−	0.0278049i
$637$		−	6.30632i		−	0.249866i
$638$	38.9163	+	4.70749i	1.54071	+	0.186371i
$639$			34.8780i			1.37975i
$640$	−46.3919	+	13.2820i	−1.83380	+	0.525019i
$641$	23.3897	+	16.9936i	0.923838	+	0.671207i	0.944476	−	0.328580i	$-0.106570\pi$
$641$	23.3897	+	16.9936i	0.923838	+	0.671207i	−0.0206386	+	0.999787i	$0.506570\pi$
$642$	−0.0711227	+	1.42340i	−0.00280699	+	0.0561771i
$643$	10.0341	+	3.26028i	0.395707	+	0.128573i	0.500110	−	0.865962i	$-0.333293\pi$
$643$	10.0341	+	3.26028i	0.395707	+	0.128573i	−0.104403	+	0.994535i	$0.533293\pi$
$644$	1.43699	−	14.3435i	0.0566253	−	0.565215i
$645$	−1.54284	−	2.12354i	−0.0607492	−	0.0836142i
$646$	−2.46420	+	0.666715i	−0.0969526	+	0.0262315i
$647$	29.8120	−	9.68650i	1.17203	−	0.380816i	0.342630	−	0.939470i	$-0.388682\pi$
$647$	29.8120	−	9.68650i	1.17203	−	0.380816i	0.829400	+	0.558655i	$0.188682\pi$
$648$	−11.2538	+	22.4914i	−0.442091	+	0.883546i
$649$	−2.63309	−	10.5897i	−0.103358	−	0.415681i
$650$	−11.7058	+	14.5276i	−0.459138	+	0.569819i
$651$	−0.140054	−	0.431042i	−0.00548916	−	0.0168939i
$652$	6.56983	+	2.88683i	0.257294	+	0.113057i
$653$	1.82531	−	1.32616i	0.0714299	−	0.0518968i	−0.551497	−	0.834177i	$-0.685943\pi$
$653$	1.82531	−	1.32616i	0.0714299	−	0.0518968i	0.622927	+	0.782280i	$0.285943\pi$
$654$	0.133758	−	0.0873272i	0.00523035	−	0.00341476i
$655$	7.76037	−	23.8840i	0.303223	−	0.933223i
$656$	−18.3850	−	10.3772i	−0.717813	−	0.405161i
$657$	−0.637132	+	0.876937i	−0.0248569	+	0.0342126i
$658$	1.82405	+	0.695095i	0.0711087	+	0.0270976i
$659$	−9.62701			−0.375015			−0.187508	−	0.982263i	$-0.560041\pi$
$659$	−9.62701			−0.375015			−0.187508	+	0.982263i	$0.560041\pi$
$660$	1.44581	−	2.74713i	0.0562781	−	0.106932i
$661$	34.4602			1.34035			0.670173	−	0.742205i	$-0.266220\pi$
$661$	34.4602			1.34035			0.670173	+	0.742205i	$0.266220\pi$
$662$	−4.91887	−	1.87445i	−0.191177	−	0.0728525i
$663$	0.0204716	−	0.0281767i	0.000795051	−	0.00109429i
$664$	−6.85011	−	41.2955i	−0.265836	−	1.60258i
$665$	6.24277	−	19.2133i	0.242084	−	0.745059i
$666$	4.58932	−	2.99625i	0.177833	−	0.116102i
$667$	58.5125	−	42.5118i	2.26561	−	1.64606i
$668$	12.6877	−	28.8747i	0.490903	−	1.11719i
$669$	0.281992	+	0.867882i	0.0109024	+	0.0335543i
$670$	−24.6554	+	30.5989i	−0.952520	+	1.18214i
$671$	27.6344	+	23.2182i	1.06681	+	0.896330i
$672$	−0.127711	+	0.500937i	−0.00492655	+	0.0193240i
$673$	−25.0698	+	8.14569i	−0.966372	+	0.313993i	−0.749350	−	0.662174i	$-0.769634\pi$
$673$	−25.0698	+	8.14569i	−0.966372	+	0.313993i	−0.217021	+	0.976167i	$0.569634\pi$
$674$	−29.8709	+	8.08189i	−1.15059	+	0.311303i
$675$	−5.09474	−	7.01231i	−0.196097	−	0.269904i
$676$	−1.99004	−	0.199369i	−0.0765399	−	0.00766805i
$677$	−6.36829	−	2.06918i	−0.244753	−	0.0795251i	0.184072	−	0.982913i	$-0.441072\pi$
$677$	−6.36829	−	2.06918i	−0.244753	−	0.0795251i	−0.428825	+	0.903388i	$0.641072\pi$
$678$	−0.0600586	+	1.20197i	−0.00230654	+	0.0461614i
$679$	−3.43730	−	2.49735i	−0.131912	−	0.0958394i
$680$	0.571394	−	3.78643i	0.0219120	−	0.145203i
$681$		−	1.38508i		−	0.0530764i
$682$	−9.79303	+	21.0999i	−0.374995	+	0.807959i
$683$			9.31128i			0.356286i	0.984005	+	0.178143i	$0.0570090\pi$
$683$			9.31128i			0.356286i	−0.984005	+	0.178143i	$0.942991\pi$
$684$	−29.3481	+	17.1352i	−1.12215	+	0.655180i
$685$	−51.2745	−	37.2531i	−1.95910	−	1.42337i
$686$	−15.6535	−	0.782153i	−0.597652	−	0.0298627i
$687$	0.813149	+	0.264208i	0.0310236	+	0.0100802i
$688$	−2.56220	−	22.2876i	−0.0976831	−	0.849708i
$689$	−2.17487	−	2.99345i	−0.0828560	−	0.114041i
$690$	−1.49590	−	5.52888i	−0.0569478	−	0.210481i
$691$	−24.9130	+	8.09472i	−0.947734	+	0.307938i	−0.741795	−	0.670627i	$-0.766025\pi$
$691$	−24.9130	+	8.09472i	−0.947734	+	0.307938i	−0.205940	+	0.978565i	$0.566025\pi$
$692$	20.1132	−	4.37766i	0.764589	−	0.166414i
$693$	4.36932	+	7.00236i	0.165977	+	0.265998i
$694$	−29.7735	−	23.9903i	−1.13019	−	0.910660i
$695$	19.8931	+	61.2248i	0.754590	+	2.32239i
$696$	−2.30236	+	1.19437i	−0.0872707	+	0.0452726i
$697$	1.35533	−	0.984706i	0.0513368	−	0.0372984i
$698$	6.12727	+	9.38507i	0.231921	+	0.355230i
$699$	0.862467	−	2.65440i	0.0326215	−	0.100399i
$700$	16.4021	+	14.6245i	0.619940	+	0.552755i
$701$	−5.96809	+	8.21436i	−0.225411	+	0.310252i	−0.906711	−	0.421752i	$-0.861415\pi$
$701$	−5.96809	+	8.21436i	−0.225411	+	0.310252i	0.681300	+	0.732005i	$0.261415\pi$
$702$	0.330873	−	0.868266i	0.0124880	−	0.0327706i
$703$	7.37611			0.278195
$704$	22.3027	−	14.3732i	0.840564	−	0.541712i
$705$	0.775591			0.0292104
$706$	−9.20538	+	24.1565i	−0.346449	+	0.909141i
$707$	−1.40745	+	1.93718i	−0.0529325	+	0.0728553i
$708$	0.538908	+	0.480504i	0.0202534	+	0.0180584i
$709$	7.70391	−	23.7102i	0.289326	−	0.890455i	−0.695742	−	0.718292i	$-0.744924\pi$
$709$	7.70391	−	23.7102i	0.289326	−	0.890455i	0.985068	−	0.172163i	$-0.0550757\pi$
$710$	−38.4919	−	58.9575i	−1.44457	−	2.21264i
$711$	−13.6511	+	9.91809i	−0.511956	+	0.371958i
$712$	−1.74634	+	0.905934i	−0.0654470	+	0.0339513i
$713$	13.2626	+	40.8182i	0.496690	+	1.52865i
$714$	−0.0319436	−	0.0257389i	−0.00119546	−	0.000963253i
$715$	5.30768	−	13.1128i	0.198496	−	0.490389i
$716$	−23.9696	+	5.21701i	−0.895785	+	0.194969i
$717$	−0.839904	+	0.272901i	−0.0313668	+	0.0101917i
$718$	5.12442	+	18.9400i	0.191242	+	0.706836i
$719$	3.43070	+	4.72195i	0.127943	+	0.176099i	0.868183	−	0.496244i	$-0.165288\pi$
$719$	3.43070	+	4.72195i	0.127943	+	0.176099i	−0.740240	+	0.672343i	$0.765288\pi$
$720$	−5.82208	−	50.6440i	−0.216976	−	1.88739i
$721$	6.05667	+	1.96793i	0.225562	+	0.0732895i
$722$	−18.8425	−	0.941497i	−0.701244	−	0.0350389i
$723$	−1.16051	−	0.843157i	−0.0431597	−	0.0313573i
$724$	31.4120	−	18.3402i	1.16742	−	0.681609i
$725$			110.255i			4.09475i
$726$	−0.323763	+	1.67592i	−0.0120160	+	0.0621993i
$727$		−	23.3279i		−	0.865183i	−0.901590	−	0.432592i	$-0.857599\pi$
$727$		−	23.3279i		−	0.865183i	0.901590	−	0.432592i	$-0.142401\pi$
$728$	−0.351512	+	2.32935i	−0.0130279	+	0.0863314i
$729$	−21.3193	−	15.4893i	−0.789602	−	0.573679i
$730$	0.109203	−	2.18552i	0.00404179	−	0.0808896i
$731$	1.69313	+	0.550132i	0.0626228	+	0.0203474i
$732$	−2.37628	−	0.238065i	−0.0878299	−	0.00879912i
$733$	−23.0234	−	31.6890i	−0.850389	−	1.17046i	−0.983777	−	0.179396i	$-0.942586\pi$
$733$	−23.0234	−	31.6890i	−0.850389	−	1.17046i	0.133388	−	0.991064i	$-0.457414\pi$
$734$	47.0436	−	12.7281i	1.73641	−	0.469804i
$735$	−2.80692	+	0.912023i	−0.103535	+	0.0336405i
$736$	12.0938	−	47.4370i	0.445782	−	1.74855i
$737$	8.10680	−	20.0281i	0.298618	−	0.737743i
$738$	13.9930	−	17.3662i	0.515089	−	0.639258i
$739$	−6.18826	−	19.0455i	−0.227639	−	0.700600i	−0.998013	−	0.0630081i	$-0.979931\pi$
$739$	−6.18826	−	19.0455i	−0.227639	−	0.700600i	0.770374	−	0.637592i	$-0.220069\pi$
$740$	−4.45105	+	10.1297i	−0.163624	+	0.372374i
$741$	0.504815	−	0.366770i	0.0185448	−	0.0134736i
$742$	−3.64932	+	2.38255i	−0.133971	+	0.0874660i
$743$	−10.7473	+	33.0767i	−0.394280	+	1.21347i	0.535242	+	0.844699i	$0.320221\pi$
$743$	−10.7473	+	33.0767i	−0.394280	+	1.21347i	−0.929521	+	0.368769i	$0.879779\pi$
$744$	−0.251872	−	1.51840i	−0.00923409	−	0.0556671i
$745$	13.0454	−	17.9554i	0.477945	−	0.657835i
$746$	−27.9372	−	10.6461i	−1.02285	−	0.389783i
$747$	44.2208			1.61796
$748$	0.301843	+	2.08376i	0.0110365	+	0.0761897i
$749$	7.64943			0.279504
$750$	5.06671	+	1.93079i	0.185010	+	0.0705024i
$751$	0.418833	−	0.576475i	0.0152834	−	0.0210359i	−0.801307	−	0.598254i	$-0.795862\pi$
$751$	0.418833	−	0.576475i	0.0152834	−	0.0210359i	0.816590	+	0.577218i	$0.195862\pi$
$752$	5.77286	+	3.25842i	0.210514	+	0.118822i
$753$	−0.489528	+	1.50661i	−0.0178394	+	0.0549040i
$754$	−9.89676	+	6.46134i	−0.360419	+	0.235308i
$755$	−27.7294	+	20.1466i	−1.00918	+	0.733209i
$756$	−1.00197	−	0.440274i	−0.0364414	−	0.0160126i
$757$	−12.5584	−	38.6509i	−0.456444	−	1.40479i	−0.869431	−	0.494054i	$-0.835514\pi$
$757$	−12.5584	−	38.6509i	−0.456444	−	1.40479i	0.412987	−	0.910737i	$-0.364486\pi$
$758$	−29.9560	+	37.1773i	−1.08805	+	1.35034i
$759$	1.66717	+	2.67183i	0.0605143	+	0.0969815i
$760$	30.6991	−	61.3541i	1.11357	−	2.22555i
$761$	25.5026	−	8.28629i	0.924467	−	0.300378i	0.192169	−	0.981362i	$-0.438448\pi$
$761$	25.5026	−	8.28629i	0.924467	−	0.300378i	0.732298	+	0.680984i	$0.238448\pi$
$762$	−2.17174	+	0.587586i	−0.0786738	+	0.0212860i
$763$	−0.503961	−	0.693642i	−0.0182446	−	0.0251115i
$764$	0.822624	−	8.21116i	0.0297615	−	0.297070i
$765$	3.84729	+	1.25006i	0.139099	+	0.0451961i
$766$	−1.38667	+	27.7518i	−0.0501023	+	1.00271i
$767$	2.66177	+	1.93389i	0.0961110	+	0.0698287i
$768$	−0.682691	+	1.61741i	−0.0246345	+	0.0583634i
$769$		−	46.9938i		−	1.69464i	−0.531082	−	0.847320i	$-0.678215\pi$
$769$		−	46.9938i		−	1.69464i	0.531082	−	0.847320i	$-0.321785\pi$
$770$	−15.1138	−	7.01469i	−0.544662	−	0.252792i
$771$			2.86949i			0.103342i
$772$	4.70058	+	8.05086i	0.169178	+	0.289757i
$773$	−33.8711	−	24.6088i	−1.21826	−	0.885116i	−0.222304	−	0.974978i	$-0.571358\pi$
$773$	−33.8711	−	24.6088i	−1.21826	−	0.885116i	−0.995954	+	0.0898614i	$0.971358\pi$
$774$	23.6703	+	1.18273i	0.850810	+	0.0425122i
$775$	−62.2243	−	20.2179i	−2.23516	−	0.726248i
$776$	−10.2769	−	10.1278i	−0.368918	−	0.363567i
$777$	0.0696717	+	0.0958948i	0.00249946	+	0.00344021i
$778$	−2.97334	−	10.9895i	−0.106599	−	0.393994i
$779$	28.5454	−	9.27496i	1.02274	−	0.332310i
$780$	0.199062	+	0.914590i	0.00712755	+	0.0327476i
$781$	29.6410	+	24.9042i	1.06064	+	0.891142i
$782$	3.02495	+	2.43738i	0.108172	+	0.0871606i
$783$	−1.69683	−	5.22232i	−0.0606399	−	0.186630i
$784$	−24.7240	−	5.00410i	−0.882999	−	0.178718i
$785$	−57.6916	+	41.9154i	−2.05910	+	1.49603i
$786$	−0.499466	−	0.765027i	−0.0178154	−	0.0272876i
$787$	−10.9846	+	33.8071i	−0.391558	+	1.20509i	0.540051	+	0.841632i	$0.318405\pi$
$787$	−10.9846	+	33.8071i	−0.391558	+	1.20509i	−0.931610	+	0.363460i	$0.881595\pi$
$788$	15.5686	−	17.4609i	0.554608	−	0.622019i
$789$	−0.780400	+	1.07413i	−0.0277830	+	0.0382400i
$790$	12.1299	−	31.8310i	0.431564	−	1.13250i
$791$	6.45947			0.229672
$792$	11.1237	+	25.7278i	0.395263	+	0.914198i
$793$	−10.8826			−0.386453
$794$	−8.69257	+	22.8108i	−0.308488	+	0.809524i
$795$	−1.01784	+	1.40094i	−0.0360992	+	0.0496862i
$796$	−21.1150	+	23.6814i	−0.748401	+	0.839367i
$797$	3.23025	−	9.94169i	0.114421	−	0.352153i	−0.877405	−	0.479751i	$-0.840727\pi$
$797$	3.23025	−	9.94169i	0.114421	−	0.352153i	0.991826	+	0.127599i	$0.0407269\pi$
$798$	−0.401792	−	0.615420i	−0.0142233	−	0.0217856i
$799$	−0.425572	+	0.309196i	−0.0150557	+	0.0109386i
$800$	47.6669	+	57.4202i	1.68528	+	2.03011i
$801$	−0.642232	−	1.97659i	−0.0226922	−	0.0698393i
$802$	15.3690	+	12.3837i	0.542697	+	0.437284i
$803$	0.290328	+	1.16763i	0.0102455	+	0.0412048i
$804$	0.304041	+	1.39692i	0.0107227	+	0.0492656i
$805$	−29.2379	+	9.49996i	−1.03050	+	0.334829i
$806$	−1.83177	−	6.77027i	−0.0645212	−	0.238473i
$807$	−0.719055	−	0.989694i	−0.0253119	−	0.0348389i
$808$	−5.70780	+	5.79180i	−0.200800	+	0.203755i
$809$	19.9897	+	6.49505i	0.702801	+	0.228354i	0.638550	−	0.769580i	$-0.279534\pi$
$809$	19.9897	+	6.49505i	0.702801	+	0.228354i	0.0642502	+	0.997934i	$0.479534\pi$
$810$	53.5682	+	2.67663i	1.88219	+	0.0940472i
$811$	−10.4007	−	7.55656i	−0.365219	−	0.265347i	0.390007	−	0.920812i	$-0.372473\pi$
$811$	−10.4007	−	7.55656i	−0.365219	−	0.265347i	−0.755225	+	0.655465i	$0.772473\pi$
$812$	7.01934	+	12.0223i	0.246331	+	0.421899i
$813$		−	3.03277i		−	0.106364i
$814$	0.730584	−	6.03966i	0.0256070	−	0.211690i
$815$		−	15.3039i		−	0.536073i
$816$	−0.0942227	−	0.102617i	−0.00329845	−	0.00359232i
$817$	25.8038	+	18.7476i	0.902762	+	0.655895i
$818$	0.590542	−	11.8187i	0.0206478	−	0.413231i
$819$	−2.36679	−	0.769017i	−0.0827024	−	0.0268716i
$820$	−4.48808	+	44.7985i	−0.156731	+	1.56443i
$821$	−10.5539	−	14.5263i	−0.368335	−	0.506970i	0.584112	−	0.811673i	$-0.301443\pi$
$821$	−10.5539	−	14.5263i	−0.368335	−	0.506970i	−0.952447	+	0.304703i	$0.901443\pi$
$822$	−2.22575	+	0.602200i	−0.0776320	+	0.0210041i
$823$	−16.4856	+	5.35648i	−0.574650	+	0.186715i	−0.581903	−	0.813258i	$-0.697692\pi$
$823$	−16.4856	+	5.35648i	−0.574650	+	0.186715i	0.00725227	+	0.999974i	$0.497692\pi$
$824$	19.3409	+	9.67738i	0.673771	+	0.337128i
$825$	−4.78897	−	0.337963i	−0.166731	−	0.0117664i
$826$	2.43148	−	3.01762i	0.0846019	−	0.104996i
$827$	−8.93235	−	27.4909i	−0.310608	−	0.955954i	−0.977525	−	0.210821i	$-0.932386\pi$
$827$	−8.93235	−	27.4909i	−0.310608	−	0.955954i	0.666916	−	0.745132i	$-0.267614\pi$
$828$	47.3463	+	20.8043i	1.64540	+	0.722999i
$829$	12.3236	−	8.95363i	0.428017	−	0.310972i	−0.352839	−	0.935684i	$-0.614784\pi$
$829$	12.3236	−	8.95363i	0.428017	−	0.310972i	0.780855	+	0.624712i	$0.214784\pi$
$830$	−74.7505	+	48.8027i	−2.59463	+	1.69397i
$831$	0.0278660	−	0.0857626i	0.000966660	−	0.00297507i
$832$	−2.36073	+	7.64375i	−0.0818437	+	0.264999i
$833$	1.17659	−	1.61944i	0.0407664	−	0.0561101i
$834$	2.18852	+	0.833987i	0.0757823	+	0.0288786i
$835$	−67.2614			−2.32768
$836$	−6.39328	+	37.1766i	−0.221116	+	1.28578i
$837$	3.25847			0.112629
$838$	−1.95882	−	0.746454i	−0.0676664	−	0.0257858i
$839$	−21.8925	+	30.1324i	−0.755812	+	1.04029i	0.241739	+	0.970341i	$0.422282\pi$
$839$	−21.8925	+	30.1324i	−0.755812	+	1.04029i	−0.997551	+	0.0699444i	$0.977718\pi$
$840$	1.08762	−	0.180415i	0.0375264	−	0.00622490i
$841$	−12.6225	+	38.8482i	−0.435260	+	1.33959i
$842$	10.7097	−	6.99206i	0.369079	−	0.240962i
$843$	2.30092	−	1.67171i	0.0792477	−	0.0575769i
$844$	−13.4063	+	30.5099i	−0.461463	+	1.05020i
$845$	1.31803	+	4.05649i	0.0453417	+	0.139548i
$846$	−4.39378	+	5.45296i	−0.151061	+	0.187477i
$847$	9.07080	+	1.28668i	0.311676	+	0.0442109i
$848$	−13.4616	+	6.15127i	−0.462274	+	0.211235i
$849$	0.681061	−	0.221290i	0.0233739	−	0.00759466i
$850$	−5.71644	+	1.54664i	−0.196072	+	0.0530494i
$851$	−6.59767	−	9.08091i	−0.226165	−	0.311290i
$852$	−2.54883	−	0.255351i	−0.0873216	−	0.00874819i
$853$	−2.15621	−	0.700597i	−0.0738274	−	0.0239880i	0.271870	−	0.962334i	$-0.412358\pi$
$853$	−2.15621	−	0.700597i	−0.0738274	−	0.0239880i	−0.345698	+	0.938346i	$0.612358\pi$
$854$	−0.639687	+	12.8022i	−0.0218896	+	0.438084i
$855$	58.6339	+	42.6000i	2.00524	+	1.45689i
$856$	25.6866	+	3.87625i	0.877948	+	0.132488i
$857$			16.1535i			0.551792i	0.961187	+	0.275896i	$0.0889745\pi$
$857$			16.1535i			0.551792i	−0.961187	+	0.275896i	$0.911025\pi$
$858$	−0.250315	−	0.449677i	−0.00854563	−	0.0153517i
$859$		−	3.91888i		−	0.133711i	−0.997763	−	0.0668553i	$-0.978703\pi$
$859$		−	3.91888i		−	0.133711i	0.997763	−	0.0668553i	$-0.0212966\pi$
$860$	−41.3173	+	24.1236i	−1.40891	+	0.822607i
$861$	0.390209	+	0.283504i	0.0132983	+	0.00966177i
$862$	27.8838	+	1.39326i	0.949726	+	0.0474548i
$863$	13.8782	+	4.50929i	0.472418	+	0.153498i	0.535544	−	0.844508i	$-0.320107\pi$
$863$	13.8782	+	4.50929i	0.472418	+	0.153498i	−0.0631252	+	0.998006i	$0.520107\pi$
$864$	−3.14149	−	1.98616i	−0.106876	−	0.0675706i
$865$	−25.8027	−	35.5143i	−0.877317	−	1.20752i
$866$	−5.63077	−	20.8115i	−0.191341	−	0.707203i
$867$	−1.76350	+	0.572997i	−0.0598918	+	0.0194600i
$868$	−8.07217	+	1.75692i	−0.273987	+	0.0596337i
$869$	−1.31850	+	18.6832i	−0.0447270	+	0.633786i
$870$	4.30719	+	3.47056i	0.146027	+	0.117663i
$871$	2.01313	+	6.19578i	0.0682123	+	0.209936i
$872$	−1.34079	−	2.58460i	−0.0454049	−	0.0875257i
$873$	12.3314	−	8.95931i	0.417356	−	0.303227i
$874$	38.0483	+	58.2781i	1.28700	+	1.97129i
$875$	8.99318	−	27.6782i	0.304025	−	0.935693i
$876$	−0.0594206	−	0.0529809i	−0.00200764	−	0.00179006i
$877$	9.77616	−	13.4557i	0.330118	−	0.454368i	−0.611405	−	0.791318i	$-0.709395\pi$
$877$	9.77616	−	13.4557i	0.330118	−	0.454368i	0.941523	+	0.336950i	$0.109395\pi$
$878$	−3.91225	+	10.2664i	−0.132032	+	0.346474i
$879$	−1.08327			−0.0365379
$880$	−47.1969	−	31.2138i	−1.59101	−	1.05222i
$881$	20.4818			0.690048			0.345024	−	0.938594i	$-0.387871\pi$
$881$	20.4818			0.690048			0.345024	+	0.938594i	$0.387871\pi$
$882$	9.48922	−	24.9013i	0.319519	−	0.838471i
$883$	−15.8280	+	21.7853i	−0.532653	+	0.733135i	−0.987532	−	0.157419i	$-0.949683\pi$
$883$	−15.8280	+	21.7853i	−0.532653	+	0.733135i	0.454878	+	0.890554i	$0.349683\pi$
$884$	−0.473836	−	0.422484i	−0.0159368	−	0.0142097i
$885$	0.475820	−	1.46442i	0.0159945	−	0.0492261i
$886$	18.9458	+	29.0190i	0.636495	+	0.974912i
$887$	2.48706	−	1.80695i	0.0835072	−	0.0606715i	−0.545248	−	0.838275i	$-0.683565\pi$
$887$	2.48706	−	1.80695i	0.0835072	−	0.0606715i	0.628756	+	0.777603i	$0.283565\pi$
$888$	0.185362	+	0.357317i	0.00622033	+	0.0119908i
$889$	3.73157	+	11.4846i	0.125153	+	0.385181i
$890$	3.26701	+	2.63243i	0.109511	+	0.0882393i
$891$	−28.6193	+	7.11611i	−0.958783	+	0.238399i
$892$	16.2529	−	3.53746i	0.544187	−	0.118443i
$893$	−8.96321	+	2.91232i	−0.299942	+	0.0974572i
$894$	−0.210879	−	0.779418i	−0.00705286	−	0.0260676i
$895$	30.7499	+	42.3236i	1.02786	+	1.41472i
$896$	8.85329	+	3.22645i	0.295768	+	0.107788i
$897$	−0.903078	−	0.293428i	−0.0301529	−	0.00979727i
$898$	−12.6460	−	0.631879i	−0.422002	−	0.0210861i
$899$	−33.5324	−	24.3627i	−1.11837	−	0.812542i
$900$	−68.0816	+	39.7502i	−2.26939	+	1.32501i
$901$		−	1.17448i		−	0.0391275i
$902$	−4.76712	−	24.2920i	−0.158728	−	0.808836i
$903$			0.512550i			0.0170566i
$904$	21.6907	+	3.27325i	0.721421	+	0.108867i
$905$	−62.7573	−	45.5959i	−2.08612	−	1.51566i
$906$	−0.0622295	+	1.24542i	−0.00206744	+	0.0413762i
$907$	2.69229	+	0.874778i	0.0893960	+	0.0290465i	0.353374	−	0.935482i	$-0.385034\pi$
$907$	2.69229	+	0.874778i	0.0893960	+	0.0290465i	−0.263978	+	0.964529i	$0.585034\pi$
$908$	−25.1208	−	2.51669i	−0.833663	−	0.0835194i
$909$	−5.04926	−	6.94971i	−0.167473	−	0.230507i
$910$	4.84950	−	1.31208i	0.160759	−	0.0434951i
$911$	−30.4506	+	9.89401i	−1.00887	+	0.327803i	−0.766406	−	0.642356i	$-0.777957\pi$
$911$	−30.4506	+	9.89401i	−1.00887	+	0.327803i	−0.242468	+	0.970159i	$0.577957\pi$
$912$	−1.03735	−	2.27016i	−0.0343500	−	0.0751726i
$913$	31.5753	−	37.5810i	1.04499	−	1.24375i
$914$	14.8462	−	18.4251i	0.491070	−	0.609448i
$915$	1.57385	+	4.84381i	0.0520299	+	0.160131i
$916$	6.26936	−	14.2678i	0.207145	−	0.471421i
$917$	−3.96727	+	2.88239i	−0.131011	+	0.0951850i
$918$	0.246962	−	0.161235i	0.00815095	−	0.00532155i
$919$	−8.21731	+	25.2903i	−0.271064	+	0.834250i	0.719170	+	0.694834i	$0.244522\pi$
$919$	−8.21731	+	25.2903i	−0.271064	+	0.834250i	−0.990234	+	0.139415i	$0.955478\pi$
$920$	−102.994	+	17.0846i	−3.39560	+	0.563264i
$921$	−1.07744	+	1.48297i	−0.0355029	+	0.0488656i
$922$	−2.02260	−	0.770758i	−0.0666107	−	0.0253835i
$923$	−11.6729			−0.384217
$924$	−0.543711	+	0.268037i	−0.0178868	+	0.00881777i
$925$	17.1111			0.562609
$926$	5.76313	+	2.19617i	0.189388	+	0.0721707i
$927$	−13.4289	+	18.4834i	−0.441064	+	0.607073i
$928$	17.4786	+	43.9274i	0.573763	+	1.44199i
$929$	−15.1415	+	46.6007i	−0.496776	+	1.52892i	0.317395	+	0.948293i	$0.397192\pi$
$929$	−15.1415	+	46.6007i	−0.496776	+	1.52892i	−0.814171	+	0.580625i	$0.802808\pi$
$930$	−2.74851	+	1.79443i	−0.0901271	+	0.0588417i
$931$	29.0139	−	21.0798i	0.950891	−	0.690863i
$932$	−46.5750	−	20.4654i	−1.52561	−	0.670365i
$933$	−1.14754	−	3.53176i	−0.0375687	−	0.115625i
$934$	21.4230	−	26.5873i	0.700981	−	0.869962i
$935$	3.80947	−	2.37703i	0.124583	−	0.0777371i
$936$	−7.55792	−	3.78168i	−0.247038	−	0.123608i
$937$	−12.4092	+	4.03201i	−0.405392	+	0.131720i	−0.504613	−	0.863345i	$-0.668365\pi$
$937$	−12.4092	+	4.03201i	−0.405392	+	0.131720i	0.0992209	+	0.995065i	$0.468365\pi$
$938$	7.40700	−	2.00404i	0.241847	−	0.0654342i
$939$	−0.720337	−	0.991459i	−0.0235073	−	0.0323550i
$940$	1.40925	−	14.0667i	0.0459647	−	0.458804i
$941$	−8.39051	−	2.72624i	−0.273523	−	0.0888729i	0.169044	−	0.985609i	$-0.445932\pi$
$941$	−8.39051	−	2.72624i	−0.273523	−	0.0888729i	−0.442567	+	0.896736i	$0.645932\pi$
$942$	−0.129470	+	2.59112i	−0.00421835	+	0.0844232i
$943$	−36.9515	−	26.8468i	−1.20331	−	0.874252i
$944$	9.69396	−	8.90094i	0.315511	−	0.289701i
$945$			2.33402i			0.0759258i
$946$	17.9066	−	19.2716i	0.582193	−	0.626575i
$947$		−	35.9330i		−	1.16766i	−0.811874	−	0.583832i	$-0.801553\pi$
$947$		−	35.9330i		−	1.16766i	0.811874	−	0.583832i	$-0.198447\pi$
$948$	−0.624856	−	1.07021i	−0.0202944	−	0.0347589i
$949$	−0.293490	−	0.213233i	−0.00952710	−	0.00692184i
$950$	−105.966	−	5.29478i	−3.43799	−	0.171785i
$951$	2.56783	+	0.834340i	0.0832677	+	0.0270553i
$952$	−0.524860	+	0.532584i	−0.0170108	+	0.0172611i
$953$	21.4852	+	29.5718i	0.695974	+	0.957926i	0.999986	+	0.00525754i	$0.00167353\pi$
$953$	21.4852	+	29.5718i	0.695974	+	0.957926i	−0.304013	+	0.952668i	$0.598326\pi$
$954$	−4.08346	−	15.0926i	−0.132207	−	0.488641i
$955$	−16.7376	+	5.43839i	−0.541617	+	0.175982i
$956$	3.42343	+	15.7290i	0.110721	+	0.508711i
$957$	−2.81921	−	1.14114i	−0.0911322	−	0.0368878i
$958$	−5.28957	−	4.26213i	−0.170898	−	0.137703i
$959$	3.82438	+	11.7702i	0.123496	+	0.380081i
$960$	3.74361	−	0.0546900i	0.120825	−	0.00176511i
$961$	−5.18098	+	3.76420i	−0.167128	+	0.121426i
$962$	1.00277	+	1.53594i	0.0323307	+	0.0495206i
$963$	−8.48023	+	26.0995i	−0.273272	+	0.841044i
$964$	−17.4007	+	19.5157i	−0.560440	+	0.628560i
$965$	11.6862	−	16.0846i	0.376191	−	0.517783i
$966$	−0.398270	+	1.04513i	−0.0128141	+	0.0336264i
$967$	−3.21941			−0.103529			−0.0517647	−	0.998659i	$-0.516485\pi$
$967$	−3.21941			−0.103529			−0.0517647	+	0.998659i	$0.516485\pi$
$968$	29.8075	+	8.91715i	0.958048	+	0.286608i
$969$	0.198064			0.00636272
$970$	−10.9573	+	28.7539i	−0.351819	+	0.923232i
$971$	28.6738	−	39.4661i	0.920187	−	1.26653i	−0.0433793	−	0.999059i	$-0.513812\pi$
$971$	28.6738	−	39.4661i	0.920187	−	1.26653i	0.963566	−	0.267470i	$-0.0861876\pi$
$972$	3.92211	−	4.39883i	0.125802	−	0.141093i
$973$	3.88452	−	11.9553i	0.124532	−	0.383271i
$974$	−18.3271	−	28.0714i	−0.587238	−	0.899466i
$975$	1.17107	−	0.850831i	0.0375042	−	0.0272484i
$976$	−8.63542	+	42.6654i	−0.276413	+	1.36569i
$977$	10.9434	+	33.6804i	0.350112	+	1.07753i	0.958790	+	0.284116i	$0.0916999\pi$
$977$	10.9434	+	33.6804i	0.350112	+	1.07753i	−0.608679	+	0.793417i	$0.708300\pi$
$978$	−0.433544	−	0.349333i	−0.0138632	−	0.0111704i
$979$	−2.13838	−	0.865556i	−0.0683429	−	0.0276633i
$980$	11.4409	+	52.5654i	0.365467	+	1.67914i
$981$	2.92537	−	0.950509i	0.0933997	−	0.0303474i
$982$	−13.3357	−	49.2890i	−0.425558	−	1.57288i
$983$	10.6975	+	14.7238i	0.341196	+	0.469616i	0.944790	−	0.327676i	$-0.106265\pi$
$983$	10.6975	+	14.7238i	0.341196	+	0.469616i	−0.603595	+	0.797291i	$0.706265\pi$
$984$	1.16665	+	1.14973i	0.0371914	+	0.0366520i
$985$	−47.4481	−	15.4168i	−1.51182	−	0.491221i
$986$	−3.74696	−	0.187223i	−0.119327	−	0.00596240i
$987$	−0.122525	−	0.0890197i	−0.00390002	−	0.00283353i
$988$	−5.73474	−	9.82210i	−0.182447	−	0.312483i
$989$		−	48.5368i		−	1.54338i
$990$	40.6890	−	43.7908i	1.29318	−	1.39176i
$991$		−	40.7398i		−	1.29414i	−0.762429	−	0.647072i	$-0.775993\pi$
$991$		−	40.7398i		−	1.29414i	0.762429	−	0.647072i	$-0.224007\pi$
$992$	−27.9964	+	1.80920i	−0.888886	+	0.0574423i
$993$	0.330411	+	0.240058i	0.0104853	+	0.00761800i
$994$	−0.686137	+	13.7319i	−0.0217629	+	0.435548i
$995$	64.3518	+	20.9092i	2.04009	+	0.662865i
$996$	−0.323753	+	3.23159i	−0.0102585	+	0.102397i
$997$	2.13995	+	2.94538i	0.0677728	+	0.0932813i	0.841558	−	0.540167i	$-0.181639\pi$
$997$	2.13995	+	2.94538i	0.0677728	+	0.0932813i	−0.773785	+	0.633448i	$0.781639\pi$
$998$	27.9557	−	7.56370i	0.884922	−	0.239425i
$999$	−0.810483	+	0.263342i	−0.0256425	+	0.00833177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.y.a.391.28	yes	288
4.3	odd	2	inner	572.2.y.a.391.14	yes	288
11.2	odd	10	inner	572.2.y.a.79.14	✓	288
44.35	even	10	inner	572.2.y.a.79.28	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.y.a.79.14	✓	288	11.2	odd	10	inner
572.2.y.a.79.28	yes	288	44.35	even	10	inner
572.2.y.a.391.14	yes	288	4.3	odd	2	inner
572.2.y.a.391.28	yes	288	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.503593 + 1.32151i) q^{2} +(0.0644943 - 0.0887688i) q^{3} +(-1.49279 - 1.33101i) q^{4} +(-1.31803 + 4.05649i) q^{5} +(0.0848302 + 0.129933i) q^{6} +(0.673809 - 0.489551i) q^{7} +(2.51070 - 1.30245i) q^{8} +(0.923331 + 2.84172i) q^{9} +O(q^{10})\)	\(q+(-0.503593 + 1.32151i) q^{2} +(0.0644943 - 0.0887688i) q^{3} +(-1.49279 - 1.33101i) q^{4} +(-1.31803 + 4.05649i) q^{5} +(0.0848302 + 0.129933i) q^{6} +(0.673809 - 0.489551i) q^{7} +(2.51070 - 1.30245i) q^{8} +(0.923331 + 2.84172i) q^{9} +(-4.69695 - 3.78462i) q^{10} +(3.07432 + 1.24440i) q^{11} +(-0.214428 + 0.0466706i) q^{12} +(-0.951057 + 0.309017i) q^{13} +(0.307622 + 1.13698i) q^{14} +(0.275084 + 0.378621i) q^{15} +(0.456834 + 3.97383i) q^{16} +(-0.301881 - 0.0980872i) q^{17} +(-4.22035 - 0.210877i) q^{18} +(-4.60076 - 3.34265i) q^{19} +(7.36677 - 4.30117i) q^{20} -0.0913865i q^{21} +(-3.19270 + 3.43608i) q^{22} +8.65398i q^{23} +(0.0463089 - 0.306873i) q^{24} +(-10.6728 - 7.75426i) q^{25} +(0.0705756 - 1.41245i) q^{26} +(0.624868 + 0.203032i) q^{27} +(-1.65745 - 0.166049i) q^{28} +(-4.91240 - 6.76134i) q^{29} +(-0.638883 + 0.172856i) q^{30} +(4.71670 - 1.53255i) q^{31} +(-5.48152 - 1.39748i) q^{32} +(0.308741 - 0.192647i) q^{33} +(0.281649 - 0.349544i) q^{34} +(1.09776 + 3.37854i) q^{35} +(2.40401 - 5.47105i) q^{36} +(-1.04933 + 0.762385i) q^{37} +(6.73426 - 4.39662i) q^{38} +(-0.0339067 + 0.104354i) q^{39} +(1.97419 + 11.9013i) q^{40} +(-3.10225 + 4.26988i) q^{41} +(0.120768 + 0.0460216i) q^{42} -5.60860 q^{43} +(-2.93301 - 5.94958i) q^{44} -12.7444 q^{45} +(-11.4363 - 4.35808i) q^{46} +(0.974102 - 1.34074i) q^{47} +(0.382215 + 0.215737i) q^{48} +(-1.94876 + 5.99767i) q^{49} +(15.6221 - 10.1993i) q^{50} +(-0.0281767 + 0.0204716i) q^{51} +(1.83103 + 0.804567i) q^{52} +(1.14340 + 3.51901i) q^{53} +(-0.582988 + 0.723525i) q^{54} +(-9.09997 + 10.8308i) q^{55} +(1.05412 - 2.10672i) q^{56} +(-0.593446 + 0.192822i) q^{57} +(11.4090 - 3.08683i) q^{58} +(-1.93389 - 2.66177i) q^{59} +(0.0933051 - 0.931341i) q^{60} +(10.3500 + 3.36292i) q^{61} +(-0.350015 + 7.00496i) q^{62} +(2.01331 + 1.46276i) q^{63} +(4.60724 - 6.54013i) q^{64} -4.26525i q^{65} +(0.0991063 + 0.505020i) q^{66} -6.51462i q^{67} +(0.320090 + 0.548230i) q^{68} +(0.768204 + 0.558133i) q^{69} +(-5.01761 - 0.250714i) q^{70} +(11.1015 + 3.60711i) q^{71} +(6.01941 + 5.93211i) q^{72} +(0.213233 + 0.293490i) q^{73} +(-0.479064 - 1.77064i) q^{74} +(-1.37667 + 0.447308i) q^{75} +(2.41887 + 11.1135i) q^{76} +(2.68070 - 0.666549i) q^{77} +(-0.120830 - 0.0973600i) q^{78} +(1.74509 + 5.37083i) q^{79} +(-16.7219 - 3.38450i) q^{80} +(-7.19361 + 5.22646i) q^{81} +(-4.08043 - 6.24994i) q^{82} +(4.57335 - 14.0753i) q^{83} +(-0.121636 + 0.136421i) q^{84} +(0.795780 - 1.09530i) q^{85} +(2.82445 - 7.41184i) q^{86} -0.917018 q^{87} +(9.33948 - 0.879839i) q^{88} -0.695560 q^{89} +(6.41799 - 16.8419i) q^{90} +(-0.489551 + 0.673809i) q^{91} +(11.5185 - 12.9186i) q^{92} +(0.168158 - 0.517537i) q^{93} +(1.28125 + 1.96247i) q^{94} +(19.6234 - 14.2572i) q^{95} +(-0.477580 + 0.396459i) q^{96} +(-1.57639 - 4.85163i) q^{97} +(-6.94461 - 5.59569i) q^{98} +(-0.697621 + 9.88536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 4 q^{4} + 80 q^{9}+O(q^{10}) \) 288 * q - 4 * q^4 + 80 * q^9	\( 288 q - 4 q^{4} + 80 q^{9} + 8 q^{12} - 6 q^{14} - 32 q^{16} - 50 q^{18} + 16 q^{22} - 88 q^{25} - 50 q^{28} - 20 q^{30} - 4 q^{33} + 30 q^{36} - 48 q^{37} + 38 q^{38} + 70 q^{40} + 56 q^{42} + 66 q^{44} - 96 q^{45} + 70 q^{46} + 76 q^{48} - 56 q^{49} + 70 q^{50} - 20 q^{52} - 80 q^{53} + 44 q^{56} - 20 q^{57} - 2 q^{58} - 144 q^{60} - 150 q^{62} - 100 q^{64} + 30 q^{66} + 24 q^{69} - 28 q^{70} - 100 q^{72} + 40 q^{73} - 140 q^{74} - 24 q^{77} - 40 q^{78} + 118 q^{80} - 76 q^{81} + 56 q^{82} + 120 q^{84} + 80 q^{85} + 44 q^{88} - 8 q^{89} + 80 q^{90} - 14 q^{92} + 72 q^{93} + 50 q^{94} - 140 q^{96} + 116 q^{97}+O(q^{100}) \) 288 * q - 4 * q^4 + 80 * q^9 + 8 * q^12 - 6 * q^14 - 32 * q^16 - 50 * q^18 + 16 * q^22 - 88 * q^25 - 50 * q^28 - 20 * q^30 - 4 * q^33 + 30 * q^36 - 48 * q^37 + 38 * q^38 + 70 * q^40 + 56 * q^42 + 66 * q^44 - 96 * q^45 + 70 * q^46 + 76 * q^48 - 56 * q^49 + 70 * q^50 - 20 * q^52 - 80 * q^53 + 44 * q^56 - 20 * q^57 - 2 * q^58 - 144 * q^60 - 150 * q^62 - 100 * q^64 + 30 * q^66 + 24 * q^69 - 28 * q^70 - 100 * q^72 + 40 * q^73 - 140 * q^74 - 24 * q^77 - 40 * q^78 + 118 * q^80 - 76 * q^81 + 56 * q^82 + 120 * q^84 + 80 * q^85 + 44 * q^88 - 8 * q^89 + 80 * q^90 - 14 * q^92 + 72 * q^93 + 50 * q^94 - 140 * q^96 + 116 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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