LMFDB - Embedded newform 804.2.c.b.671.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(671,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("804.671");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.c (of order $2$, degree $1$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			671.9
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38271 - 0.296856i) q^{2} +(-1.71448 + 0.246081i) q^{3} +(1.82375 + 0.820930i) q^{4} -2.85244i q^{5} +(2.44367 + 0.168697i) q^{6} -2.12311i q^{7} +(-2.27802 - 1.67650i) q^{8} +(2.87889 - 0.843802i) q^{9} +O(q^{10})$	\(q+(-1.38271 - 0.296856i) q^{2} +(-1.71448 + 0.246081i) q^{3} +(1.82375 + 0.820930i) q^{4} -2.85244i q^{5} +(2.44367 + 0.168697i) q^{6} -2.12311i q^{7} +(-2.27802 - 1.67650i) q^{8} +(2.87889 - 0.843802i) q^{9} +(-0.846765 + 3.94409i) q^{10} +5.05538 q^{11} +(-3.32880 - 0.958677i) q^{12} +1.45615 q^{13} +(-0.630258 + 2.93564i) q^{14} +(0.701931 + 4.89046i) q^{15} +(2.65215 + 2.99435i) q^{16} -0.803856i q^{17} +(-4.23114 + 0.312114i) q^{18} -3.66618i q^{19} +(2.34165 - 5.20215i) q^{20} +(0.522456 + 3.64003i) q^{21} +(-6.99011 - 1.50072i) q^{22} +2.52796 q^{23} +(4.31817 + 2.31375i) q^{24} -3.13642 q^{25} +(-2.01342 - 0.432266i) q^{26} +(-4.72816 + 2.15512i) q^{27} +(1.74292 - 3.87203i) q^{28} +8.38116i q^{29} +(0.481197 - 6.97044i) q^{30} +2.39032i q^{31} +(-2.77825 - 4.92761i) q^{32} +(-8.66735 + 1.24403i) q^{33} +(-0.238630 + 1.11150i) q^{34} -6.05605 q^{35} +(5.94308 + 0.824479i) q^{36} +1.53809 q^{37} +(-1.08833 + 5.06925i) q^{38} +(-2.49654 + 0.358330i) q^{39} +(-4.78211 + 6.49791i) q^{40} -0.167196i q^{41} +(0.358161 - 5.18819i) q^{42} -11.3226i q^{43} +(9.21977 + 4.15011i) q^{44} +(-2.40690 - 8.21186i) q^{45} +(-3.49542 - 0.750439i) q^{46} +10.3130 q^{47} +(-5.28391 - 4.48110i) q^{48} +2.49241 q^{49} +(4.33675 + 0.931067i) q^{50} +(0.197814 + 1.37820i) q^{51} +(2.65565 + 1.19539i) q^{52} -11.2890i q^{53} +(7.17741 - 1.57632i) q^{54} -14.4202i q^{55} +(-3.55939 + 4.83648i) q^{56} +(0.902176 + 6.28559i) q^{57} +(2.48800 - 11.5887i) q^{58} +4.56971 q^{59} +(-2.73457 + 9.49522i) q^{60} -7.45650 q^{61} +(0.709581 - 3.30511i) q^{62} +(-1.79148 - 6.11219i) q^{63} +(2.37872 + 7.63817i) q^{64} -4.15357i q^{65} +(12.3537 + 0.852826i) q^{66} +1.00000i q^{67} +(0.659909 - 1.46603i) q^{68} +(-4.33413 + 0.622081i) q^{69} +(8.37373 + 1.79777i) q^{70} -15.5562 q^{71} +(-7.97279 - 2.90425i) q^{72} +0.104759 q^{73} +(-2.12672 - 0.456590i) q^{74} +(5.37734 - 0.771814i) q^{75} +(3.00968 - 6.68621i) q^{76} -10.7331i q^{77} +(3.55835 + 0.245647i) q^{78} -6.42169i q^{79} +(8.54120 - 7.56510i) q^{80} +(7.57600 - 4.85842i) q^{81} +(-0.0496331 + 0.231183i) q^{82} -11.4145 q^{83} +(-2.03538 + 7.06741i) q^{84} -2.29295 q^{85} +(-3.36119 + 15.6558i) q^{86} +(-2.06244 - 14.3693i) q^{87} +(-11.5162 - 8.47533i) q^{88} +6.70211i q^{89} +(0.890287 + 12.0691i) q^{90} -3.09156i q^{91} +(4.61037 + 2.07527i) q^{92} +(-0.588211 - 4.09815i) q^{93} +(-14.2599 - 3.06149i) q^{94} -10.4576 q^{95} +(5.97585 + 7.76461i) q^{96} -11.1470 q^{97} +(-3.44627 - 0.739887i) q^{98} +(14.5539 - 4.26574i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) $ 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.38271	−	0.296856i	−0.977721	−	0.209909i
$2$	−1.38271	−	0.296856i	−0.977721	−	0.209909i
$3$	−1.71448	+	0.246081i	−0.989856	+	0.142075i
$3$	−1.71448	+	0.246081i	−0.989856	+	0.142075i
$4$	1.82375	+	0.820930i	0.911876	+	0.410465i
$5$		−	2.85244i		−	1.27565i	−0.770181	−	0.637825i	$-0.779834\pi$
$5$		−	2.85244i		−	1.27565i	0.770181	−	0.637825i	$-0.220166\pi$
$6$	2.44367	+	0.168697i	0.997626	+	0.0688701i
$7$		−	2.12311i		−	0.802460i	−0.915977	−	0.401230i	$-0.868583\pi$
$7$		−	2.12311i		−	0.802460i	0.915977	−	0.401230i	$-0.131417\pi$
$8$	−2.27802	−	1.67650i	−0.805400	−	0.592731i
$9$	2.87889	−	0.843802i	0.959629	−	0.281267i
$10$	−0.846765	+	3.94409i	−0.267771	+	1.24723i
$11$	5.05538			1.52425			0.762127	−	0.647427i	$-0.224155\pi$
$11$	5.05538			1.52425			0.762127	+	0.647427i	$0.224155\pi$
$12$	−3.32880	−	0.958677i	−0.960943	−	0.276746i
$13$	1.45615			0.403862			0.201931	−	0.979400i	$-0.435278\pi$
$13$	1.45615			0.403862			0.201931	+	0.979400i	$0.435278\pi$
$14$	−0.630258	+	2.93564i	−0.168444	+	0.784582i
$15$	0.701931	+	4.89046i	0.181238	+	1.26271i
$16$	2.65215	+	2.99435i	0.663037	+	0.748586i
$17$		−	0.803856i		−	0.194964i	−0.995237	−	0.0974818i	$-0.968921\pi$
$17$		−	0.803856i		−	0.194964i	0.995237	−	0.0974818i	$-0.0310788\pi$
$18$	−4.23114	+	0.312114i	−0.997290	+	0.0735660i
$19$		−	3.66618i		−	0.841079i	−0.907274	−	0.420540i	$-0.861841\pi$
$19$		−	3.66618i		−	0.841079i	0.907274	−	0.420540i	$-0.138159\pi$
$20$	2.34165	−	5.20215i	0.523610	−	1.16324i
$21$	0.522456	+	3.64003i	0.114009	+	0.794320i
$22$	−6.99011	−	1.50072i	−1.49030	−	0.319955i
$23$	2.52796			0.527115			0.263558	−	0.964644i	$-0.415104\pi$
$23$	2.52796			0.527115			0.263558	+	0.964644i	$0.415104\pi$
$24$	4.31817	+	2.31375i	0.881443	+	0.472291i
$25$	−3.13642			−0.627285
$26$	−2.01342	−	0.432266i	−0.394865	−	0.0847744i
$27$	−4.72816	+	2.15512i	−0.909934	+	0.414753i
$28$	1.74292	−	3.87203i	0.329382	−	0.731744i
$29$			8.38116i			1.55634i	0.628052	+	0.778171i	$0.283852\pi$
$29$			8.38116i			1.55634i	−0.628052	+	0.778171i	$0.716148\pi$
$30$	0.481197	−	6.97044i	0.0878542	−	1.27262i
$31$			2.39032i			0.429314i	0.976690	+	0.214657i	$0.0688633\pi$
$31$			2.39032i			0.429314i	−0.976690	+	0.214657i	$0.931137\pi$
$32$	−2.77825	−	4.92761i	−0.491130	−	0.871086i
$33$	−8.66735	+	1.24403i	−1.50879	+	0.216558i
$34$	−0.238630	+	1.11150i	−0.0409246	+	0.190620i
$35$	−6.05605			−1.02366
$36$	5.94308	+	0.824479i	0.990514	+	0.137413i
$37$	1.53809			0.252860			0.126430	−	0.991976i	$-0.459648\pi$
$37$	1.53809			0.252860			0.126430	+	0.991976i	$0.459648\pi$
$38$	−1.08833	+	5.06925i	−0.176550	+	0.822341i
$39$	−2.49654	+	0.358330i	−0.399766	+	0.0573787i
$40$	−4.78211	+	6.49791i	−0.756118	+	1.02741i
$41$		−	0.167196i		−	0.0261116i	−0.999915	−	0.0130558i	$-0.995844\pi$
$41$		−	0.167196i		−	0.0261116i	0.999915	−	0.0130558i	$-0.00415591\pi$
$42$	0.358161	−	5.18819i	0.0552655	−	0.800554i
$43$		−	11.3226i		−	1.72668i	−0.504621	−	0.863341i	$-0.668368\pi$
$43$		−	11.3226i		−	1.72668i	0.504621	−	0.863341i	$-0.331632\pi$
$44$	9.21977	+	4.15011i	1.38993	+	0.625653i
$45$	−2.40690	−	8.21186i	−0.358799	−	1.22415i
$46$	−3.49542	−	0.750439i	−0.515371	−	0.110646i
$47$	10.3130			1.50431			0.752155	−	0.658986i	$-0.229014\pi$
$47$	10.3130			1.50431			0.752155	+	0.658986i	$0.229014\pi$
$48$	−5.28391	−	4.48110i	−0.762667	−	0.646792i
$49$	2.49241			0.356058
$50$	4.33675	+	0.931067i	0.613310	+	0.131673i
$51$	0.197814	+	1.37820i	0.0276994	+	0.192986i
$52$	2.65565	+	1.19539i	0.368273	+	0.165771i
$53$		−	11.2890i		−	1.55066i	−0.631554	−	0.775332i	$-0.717583\pi$
$53$		−	11.2890i		−	1.55066i	0.631554	−	0.775332i	$-0.282417\pi$
$54$	7.17741	−	1.57632i	0.976722	−	0.214510i
$55$		−	14.4202i		−	1.94442i
$56$	−3.55939	+	4.83648i	−0.475643	+	0.646301i
$57$	0.902176	+	6.28559i	0.119496	+	0.832547i
$58$	2.48800	−	11.5887i	0.326690	−	1.52167i
$59$	4.56971			0.594926			0.297463	−	0.954733i	$-0.403860\pi$
$59$	4.56971			0.594926			0.297463	+	0.954733i	$0.403860\pi$
$60$	−2.73457	+	9.49522i	−0.353032	+	1.22583i
$61$	−7.45650			−0.954707			−0.477353	−	0.878711i	$-0.658404\pi$
$61$	−7.45650			−0.954707			−0.477353	+	0.878711i	$0.658404\pi$
$62$	0.709581	−	3.30511i	0.0901168	−	0.419749i
$63$	−1.79148	−	6.11219i	−0.225706	−	0.770064i
$64$	2.37872	+	7.63817i	0.297340	+	0.954772i
$65$		−	4.15357i		−	0.515187i
$66$	12.3537	+	0.852826i	1.52064	+	0.104976i
$67$			1.00000i			0.122169i
$67$			1.00000i			0.122169i
$68$	0.659909	−	1.46603i	0.0800257	−	0.177783i
$69$	−4.33413	+	0.622081i	−0.521768	+	0.0748898i
$70$	8.37373	+	1.79777i	1.00085	+	0.214875i
$71$	−15.5562			−1.84619			−0.923094	−	0.384576i	$-0.874348\pi$
$71$	−15.5562			−1.84619			−0.923094	+	0.384576i	$0.874348\pi$
$72$	−7.97279	−	2.90425i	−0.939602	−	0.342269i
$73$	0.104759			0.0122611			0.00613056	−	0.999981i	$-0.498049\pi$
$73$	0.104759			0.0122611			0.00613056	+	0.999981i	$0.498049\pi$
$74$	−2.12672	−	0.456590i	−0.247226	−	0.0530775i
$75$	5.37734	−	0.771814i	0.620922	−	0.0891214i
$76$	3.00968	−	6.68621i	0.345233	−	0.766960i
$77$		−	10.7331i		−	1.22315i
$78$	3.55835	+	0.245647i	0.402904	+	0.0278141i
$79$		−	6.42169i		−	0.722496i	−0.932470	−	0.361248i	$-0.882351\pi$
$79$		−	6.42169i		−	0.722496i	0.932470	−	0.361248i	$-0.117649\pi$
$80$	8.54120	−	7.56510i	0.954935	−	0.845804i
$81$	7.57600	−	4.85842i	0.841777	−	0.539825i
$82$	−0.0496331	+	0.231183i	−0.00548106	+	0.0255299i
$83$	−11.4145			−1.25290			−0.626452	−	0.779460i	$-0.715494\pi$
$83$	−11.4145			−1.25290			−0.626452	+	0.779460i	$0.715494\pi$
$84$	−2.03538	+	7.06741i	−0.222078	+	0.771118i
$85$	−2.29295			−0.248706
$86$	−3.36119	+	15.6558i	−0.362446	+	1.68821i
$87$	−2.06244	−	14.3693i	−0.221117	−	1.54055i
$88$	−11.5162	−	8.47533i	−1.22764	−	0.903473i
$89$			6.70211i			0.710422i	0.934786	+	0.355211i	$0.115591\pi$
$89$			6.70211i			0.710422i	−0.934786	+	0.355211i	$0.884409\pi$
$90$	0.890287	+	12.0691i	0.0938445	+	1.27219i
$91$		−	3.09156i		−	0.324083i
$92$	4.61037	+	2.07527i	0.480664	+	0.216362i
$93$	−0.588211	−	4.09815i	−0.0609947	−	0.424959i
$94$	−14.2599	−	3.06149i	−1.47080	−	0.315768i
$95$	−10.4576			−1.07292
$96$	5.97585	+	7.76461i	0.609908	+	0.792472i
$97$	−11.1470			−1.13181			−0.565904	−	0.824471i	$-0.691473\pi$
$97$	−11.1470			−1.13181			−0.565904	+	0.824471i	$0.691473\pi$
$98$	−3.44627	−	0.739887i	−0.348126	−	0.0747398i
$99$	14.5539	−	4.26574i	1.46272	−	0.428723i
$100$	−5.72006	−	2.57478i	−0.572006	−	0.257478i
$101$		−	7.50257i		−	0.746533i	−0.927724	−	0.373267i	$-0.878238\pi$
$101$		−	7.50257i		−	0.746533i	0.927724	−	0.373267i	$-0.121762\pi$
$102$	0.135608	−	1.96436i	0.0134272	−	0.194501i
$103$		−	10.6120i		−	1.04563i	−0.852445	−	0.522817i	$-0.824881\pi$
$103$		−	10.6120i		−	1.04563i	0.852445	−	0.522817i	$-0.175119\pi$
$104$	−3.31713	−	2.44123i	−0.325271	−	0.239382i
$105$	10.3830	−	1.49028i	1.01327	−	0.145436i
$106$	−3.35121	+	15.6094i	−0.325498	+	1.51612i
$107$	8.88638			0.859079			0.429539	−	0.903048i	$-0.358676\pi$
$107$	8.88638			0.859079			0.429539	+	0.903048i	$0.358676\pi$
$108$	−10.3922	+	0.0489252i	−0.999989	+	0.00470783i
$109$	3.23863			0.310205			0.155102	−	0.987898i	$-0.450429\pi$
$109$	3.23863			0.310205			0.155102	+	0.987898i	$0.450429\pi$
$110$	−4.28072	+	19.9389i	−0.408151	+	1.90110i
$111$	−2.63702	+	0.378493i	−0.250295	+	0.0359250i
$112$	6.35732	−	5.63080i	0.600710	−	0.532061i
$113$			11.6367i			1.09469i	0.836908	+	0.547344i	$0.184361\pi$
$113$			11.6367i			1.09469i	−0.836908	+	0.547344i	$0.815639\pi$
$114$	0.618472	−	8.95895i	0.0579252	−	0.839082i
$115$		−	7.21085i		−	0.672415i
$116$	−6.88034	+	15.2852i	−0.638824	+	1.41919i
$117$	4.19208	−	1.22870i	0.387558	−	0.113593i
$118$	−6.31857	−	1.35655i	−0.581671	−	0.124880i
$119$	−1.70667			−0.156451
$120$	6.59982	−	12.3173i	0.602479	−	1.12441i
$121$	14.5569			1.32335
$122$	10.3101	+	2.21351i	0.933437	+	0.200402i
$123$	0.0411437	+	0.286654i	0.00370980	+	0.0258467i
$124$	−1.96228	+	4.35935i	−0.176218	+	0.391481i
$125$		−	5.31574i		−	0.475454i
$126$	0.662652	+	8.98318i	0.0590338	+	0.800285i
$127$			8.64258i			0.766905i	0.923561	+	0.383453i	$0.125265\pi$
$127$			8.64258i			0.766905i	−0.923561	+	0.383453i	$0.874735\pi$
$128$	−1.02163	−	11.2675i	−0.0903001	−	0.995915i
$129$	2.78628	+	19.4124i	0.245318	+	1.70917i
$130$	−1.23301	+	5.74317i	−0.108142	+	0.503710i
$131$	1.46011			0.127570			0.0637851	−	0.997964i	$-0.479683\pi$
$131$	1.46011			0.127570			0.0637851	+	0.997964i	$0.479683\pi$
$132$	−16.8284	−	4.84648i	−1.46472	−	0.421832i
$133$	−7.78370			−0.674932
$134$	0.296856	−	1.38271i	0.0256445	−	0.119448i
$135$	6.14736	+	13.4868i	0.529080	+	1.16076i
$136$	−1.34766	+	1.83120i	−0.115561	+	0.157024i
$137$			15.1807i			1.29697i	0.761226	+	0.648486i	$0.224598\pi$
$137$			15.1807i			1.29697i	−0.761226	+	0.648486i	$0.775402\pi$
$138$	6.17750	+	0.426458i	0.525864	+	0.0363025i
$139$		−	6.98434i		−	0.592404i	−0.955125	−	0.296202i	$-0.904280\pi$
$139$		−	6.98434i		−	0.592404i	0.955125	−	0.296202i	$-0.0957201\pi$
$140$	−11.0447	−	4.97159i	−0.933450	−	0.420176i
$141$	−17.6815	+	2.53784i	−1.48905	+	0.213725i
$142$	21.5097	+	4.61797i	1.80506	+	0.387531i
$143$	7.36138			0.615589
$144$	10.1619	+	6.38250i	0.846823	+	0.531875i
$145$	23.9068			1.98535
$146$	−0.144851	−	0.0310984i	−0.0119880	−	0.00257372i
$147$	−4.27319	+	0.613334i	−0.352446	+	0.0505869i
$148$	2.80509	+	1.26266i	0.230577	+	0.103790i
$149$		−	22.7781i		−	1.86606i	−0.359802	−	0.933029i	$-0.617156\pi$
$149$		−	22.7781i		−	1.86606i	0.359802	−	0.933029i	$-0.382844\pi$
$150$	−7.66440	−	0.529104i	−0.625796	−	0.0432012i
$151$			18.4108i			1.49825i	0.662427	+	0.749126i	$0.269526\pi$
$151$			18.4108i			1.49825i	−0.662427	+	0.749126i	$0.730474\pi$
$152$	−6.14634	+	8.35162i	−0.498534	+	0.677406i
$153$	−0.678295	−	2.31421i	−0.0548369	−	0.187093i
$154$	−3.18619	+	14.8408i	−0.256751	+	1.19590i
$155$	6.81824			0.547654
$156$	−4.84723	−	1.39598i	−0.388089	−	0.111767i
$157$	−20.6893			−1.65119			−0.825595	−	0.564264i	$-0.809160\pi$
$157$	−20.6893			−1.65119			−0.825595	+	0.564264i	$0.809160\pi$
$158$	−1.90632	+	8.87931i	−0.151658	+	0.706400i
$159$	2.77801	+	19.3548i	0.220310	+	1.53493i
$160$	−14.0557	+	7.92481i	−1.11120	+	0.626511i
$161$		−	5.36712i		−	0.422989i
$162$	−11.9176	+	4.46879i	−0.936338	+	0.351101i
$163$			19.3440i			1.51514i	0.652755	+	0.757569i	$0.273613\pi$
$163$			19.3440i			1.51514i	−0.652755	+	0.757569i	$0.726387\pi$
$164$	0.137256	−	0.304924i	0.0107179	−	0.0238106i
$165$	3.54853	+	24.7231i	0.276253	+	1.92469i
$166$	15.7829	+	3.38847i	1.22499	+	0.262996i
$167$	−11.2352			−0.869403			−0.434702	−	0.900575i	$-0.643146\pi$
$167$	−11.2352			−0.869403			−0.434702	+	0.900575i	$0.643146\pi$
$168$	4.91233	−	9.16794i	0.378995	−	0.707322i
$169$	−10.8796			−0.836895
$170$	3.17048	+	0.680677i	0.243165	+	0.0522055i
$171$	−3.09353	−	10.5545i	−0.236568	−	0.807124i
$172$	9.29507	−	20.6496i	0.708742	−	1.57452i
$173$		−	2.96270i		−	0.225250i	−0.993638	−	0.112625i	$-0.964074\pi$
$173$		−	2.96270i		−	0.225250i	0.993638	−	0.112625i	$-0.0359259\pi$
$174$	−1.41387	+	20.4808i	−0.107185	+	1.55265i
$175$			6.65897i			0.503371i
$176$	13.4076	+	15.1376i	1.01064	+	1.14104i
$177$	−7.83468	+	1.12452i	−0.588891	+	0.0845240i
$178$	1.98956	−	9.26705i	0.149124	−	0.694594i
$179$	23.1507			1.73036			0.865182	−	0.501457i	$-0.167203\pi$
$179$	23.1507			1.73036			0.865182	+	0.501457i	$0.167203\pi$
$180$	2.35178	−	16.9523i	0.175291	−	1.26355i
$181$	5.97889			0.444408			0.222204	−	0.975000i	$-0.428675\pi$
$181$	5.97889			0.444408			0.222204	+	0.975000i	$0.428675\pi$
$182$	−0.917748	+	4.27472i	−0.0680280	+	0.316863i
$183$	12.7840	−	1.83490i	0.945022	−	0.135640i
$184$	−5.75872	−	4.23811i	−0.424539	−	0.312438i
$185$		−	4.38730i		−	0.322561i
$186$	−0.403239	+	5.84116i	−0.0295669	+	0.428294i
$187$		−	4.06380i		−	0.297174i
$188$	18.8084	+	8.46627i	1.37175	+	0.617467i
$189$	4.57556	+	10.0384i	0.332823	+	0.730185i
$190$	14.4597	+	3.10439i	1.04902	+	0.225216i
$191$	12.2895			0.889238			0.444619	−	0.895720i	$-0.353339\pi$
$191$	12.2895			0.889238			0.444619	+	0.895720i	$0.353339\pi$
$192$	−5.95787	−	12.5101i	−0.429972	−	0.902842i
$193$	−2.14293			−0.154252			−0.0771259	−	0.997021i	$-0.524574\pi$
$193$	−2.14293			−0.154252			−0.0771259	+	0.997021i	$0.524574\pi$
$194$	15.4131	+	3.30906i	1.10659	+	0.237577i
$195$	1.02211	+	7.12122i	0.0731952	+	0.509961i
$196$	4.54554	+	2.04609i	0.324681	+	0.146149i
$197$			13.7192i			0.977452i	0.872437	+	0.488726i	$0.162538\pi$
$197$			13.7192i			0.977452i	−0.872437	+	0.488726i	$0.837462\pi$
$198$	−21.3900	+	1.57786i	−1.52012	+	0.112133i
$199$			9.05671i			0.642013i	0.947077	+	0.321006i	$0.104021\pi$
$199$			9.05671i			0.642013i	−0.947077	+	0.321006i	$0.895979\pi$
$200$	7.14483	+	5.25821i	0.505216	+	0.371811i
$201$	−0.246081	−	1.71448i	−0.0173572	−	0.120930i
$202$	−2.22718	+	10.3738i	−0.156704	+	0.729901i
$203$	17.7941			1.24890
$204$	−0.770638	+	2.67588i	−0.0539555	+	0.187349i
$205$	−0.476917			−0.0333093
$206$	−3.15025	+	14.6733i	−0.219488	+	1.02234i
$207$	7.27770	−	2.13309i	0.505835	−	0.148260i
$208$	3.86192	+	4.36021i	0.267776	+	0.302326i
$209$		−	18.5339i		−	1.28202i
$210$	−14.7990	−	1.02163i	−1.02123	−	0.0704995i
$211$		−	11.8674i		−	0.816987i	−0.912761	−	0.408494i	$-0.866054\pi$
$211$		−	11.8674i		−	0.816987i	0.912761	−	0.408494i	$-0.133946\pi$
$212$	9.26748	−	20.5884i	0.636493	−	1.41401i
$213$	26.6709	−	3.82809i	1.82746	−	0.262297i
$214$	−12.2873	−	2.63798i	−0.839939	−	0.180328i
$215$	−32.2971			−2.20264
$216$	14.3839	+	3.01734i	0.978698	+	0.205304i
$217$	5.07491			0.344507
$218$	−4.47808	−	0.961408i	−0.303294	−	0.0651147i
$219$	−0.179607	+	0.0257792i	−0.0121367	+	0.00174200i
$220$	11.8380	−	26.2988i	0.798115	−	1.77307i
$221$		−	1.17053i		−	0.0787385i
$222$	3.75858	+	0.259470i	0.252259	+	0.0174145i
$223$			3.55716i			0.238205i	0.992882	+	0.119102i	$0.0380017\pi$
$223$			3.55716i			0.238205i	−0.992882	+	0.119102i	$0.961998\pi$
$224$	−10.4618	+	5.89853i	−0.699012	+	0.394112i
$225$	−9.02942	+	2.64652i	−0.601961	+	0.176435i
$226$	3.45442	−	16.0901i	0.229785	−	1.07030i
$227$	−7.87327			−0.522567			−0.261284	−	0.965262i	$-0.584146\pi$
$227$	−7.87327			−0.522567			−0.261284	+	0.965262i	$0.584146\pi$
$228$	−3.51468	+	12.2040i	−0.232766	+	0.808229i
$229$	−9.51932			−0.629054			−0.314527	−	0.949248i	$-0.601846\pi$
$229$	−9.51932			−0.629054			−0.314527	+	0.949248i	$0.601846\pi$
$230$	−2.14058	+	9.97048i	−0.141146	+	0.657434i
$231$	2.64122	+	18.4017i	0.173779	+	1.21075i
$232$	14.0510	−	19.0924i	0.922492	−	1.25348i
$233$			21.2749i			1.39376i	0.717186	+	0.696882i	$0.245430\pi$
$233$			21.2749i			1.39376i	−0.717186	+	0.696882i	$0.754570\pi$
$234$	−6.16117	+	0.454484i	−0.402768	+	0.0297105i
$235$		−	29.4173i		−	1.91897i
$236$	8.33402	+	3.75141i	0.542499	+	0.244196i
$237$	1.58025	+	11.0099i	0.102649	+	0.715167i
$238$	2.35983	+	0.506637i	0.152965	+	0.0328404i
$239$	−2.42407			−0.156800			−0.0783999	−	0.996922i	$-0.524981\pi$
$239$	−2.42407			−0.156800			−0.0783999	+	0.996922i	$0.524981\pi$
$240$	−12.7821	+	15.0720i	−0.825080	+	0.972896i
$241$	−7.40619			−0.477075			−0.238537	−	0.971133i	$-0.576668\pi$
$241$	−7.40619			−0.477075			−0.238537	+	0.971133i	$0.576668\pi$
$242$	−20.1279	−	4.32130i	−1.29387	−	0.277784i
$243$	−11.7933	+	10.1940i	−0.756543	+	0.653944i
$244$	−13.5988	−	6.12126i	−0.870575	−	0.391874i
$245$		−	7.10945i		−	0.454206i
$246$	0.0282054	−	0.408572i	0.00179831	−	0.0260496i
$247$		−	5.33850i		−	0.339680i
$248$	4.00736	−	5.44518i	0.254468	−	0.345769i
$249$	19.5699	−	2.80889i	1.24020	−	0.178006i
$250$	−1.57801	+	7.35011i	−0.0998021	+	0.464862i
$251$	−3.61478			−0.228163			−0.114081	−	0.993471i	$-0.536392\pi$
$251$	−3.61478			−0.228163			−0.114081	+	0.993471i	$0.536392\pi$
$252$	1.75046	−	12.6178i	0.110269	−	0.794848i
$253$	12.7798			0.803458
$254$	2.56560	−	11.9502i	0.160980	−	0.749819i
$255$	3.93122	−	0.564252i	0.246183	−	0.0353348i
$256$	−1.93221	+	15.8829i	−0.120763	+	0.992681i
$257$			6.59715i			0.411519i	0.978603	+	0.205759i	$0.0659664\pi$
$257$			6.59715i			0.411519i	−0.978603	+	0.205759i	$0.934034\pi$
$258$	1.91009	−	27.6688i	0.118917	−	1.72258i
$259$		−	3.26552i		−	0.202910i
$260$	3.40979	−	7.57509i	0.211466	−	0.469787i
$261$	7.07204	+	24.1284i	0.437748	+	1.49351i
$262$	−2.01890	−	0.433442i	−0.124728	−	0.0267781i
$263$	−23.6376			−1.45756			−0.728780	−	0.684748i	$-0.759912\pi$
$263$	−23.6376			−1.45756			−0.728780	+	0.684748i	$0.759912\pi$
$264$	21.8300	+	11.6969i	1.34354	+	0.719892i
$265$	−32.2012			−1.97811
$266$	10.7626	+	2.31064i	0.659895	+	0.141674i
$267$	−1.64926	−	11.4906i	−0.100933	−	0.703215i
$268$	−0.820930	+	1.82375i	−0.0501463	+	0.111403i
$269$		−	18.1628i		−	1.10741i	−0.832714	−	0.553704i	$-0.813214\pi$
$269$		−	18.1628i		−	1.10741i	0.832714	−	0.553704i	$-0.186786\pi$
$270$	−4.49635	−	20.4731i	−0.273639	−	1.24596i
$271$			14.8714i			0.903373i	0.892177	+	0.451687i	$0.149178\pi$
$271$			14.8714i			0.903373i	−0.892177	+	0.451687i	$0.850822\pi$
$272$	2.40702	−	2.13195i	0.145947	−	0.129268i
$273$	0.760773	+	5.30042i	0.0460441	+	0.320796i
$274$	4.50648	−	20.9904i	0.272246	−	1.26808i
$275$	−15.8558			−0.956142
$276$	−8.41507	−	2.42349i	−0.506528	−	0.145877i
$277$	−1.90014			−0.114168			−0.0570842	−	0.998369i	$-0.518180\pi$
$277$	−1.90014			−0.114168			−0.0570842	+	0.998369i	$0.518180\pi$
$278$	−2.07334	+	9.65729i	−0.124351	+	0.579206i
$279$	2.01695	+	6.88146i	0.120752	+	0.411982i
$280$	13.7958	+	10.1529i	0.824455	+	0.606754i
$281$			16.5030i			0.984487i	0.870458	+	0.492243i	$0.163823\pi$
$281$			16.5030i			0.984487i	−0.870458	+	0.492243i	$0.836177\pi$
$282$	25.2017	+	1.73977i	1.50074	+	0.103602i
$283$		−	1.11291i		−	0.0661559i	−0.999453	−	0.0330780i	$-0.989469\pi$
$283$		−	1.11291i		−	0.0661559i	0.999453	−	0.0330780i	$-0.0105310\pi$
$284$	−28.3708	−	12.7706i	−1.68349	−	0.757795i
$285$	17.9293	−	2.57341i	1.06204	−	0.152435i
$286$	−10.1786	−	2.18527i	−0.601875	−	0.129218i
$287$	−0.354975			−0.0209535
$288$	−12.1562	−	11.8417i	−0.716311	−	0.697781i
$289$	16.3538			0.961989
$290$	−33.0560	−	7.09687i	−1.94112	−	0.416743i
$291$	19.1114	−	2.74307i	1.12033	−	0.160802i
$292$	0.191055	+	0.0859998i	0.0111806	+	0.00503276i
$293$		−	27.9266i		−	1.63149i	−0.578411	−	0.815745i	$-0.696327\pi$
$293$		−	27.9266i		−	1.63149i	0.578411	−	0.815745i	$-0.303673\pi$
$294$	6.09063	+	0.420461i	0.355213	+	0.0245218i
$295$		−	13.0348i		−	0.758917i
$296$	−3.50379	−	2.57860i	−0.203653	−	0.149878i
$297$	−23.9026	+	10.8950i	−1.38697	+	0.632190i
$298$	−6.76183	+	31.4955i	−0.391702	+	1.82448i
$299$	3.68107			0.212882
$300$	10.4405	+	3.00682i	0.602785	+	0.173599i
$301$	−24.0391			−1.38559
$302$	5.46537	−	25.4568i	0.314497	−	1.46487i
$303$	1.84624	+	12.8630i	0.106064	+	0.738960i
$304$	10.9778	−	9.72325i	0.629620	−	0.557667i
$305$			21.2692i			1.21787i
$306$	0.250895	+	3.40123i	0.0143427	+	0.194435i
$307$			28.0248i			1.59946i	0.600358	+	0.799731i	$0.295025\pi$
$307$			28.0248i			1.59946i	−0.600358	+	0.799731i	$0.704975\pi$
$308$	8.81114	−	19.5746i	0.502061	−	1.11536i
$309$	2.61142	+	18.1941i	0.148558	+	1.03503i
$310$	−9.42763	−	2.02404i	−0.535453	−	0.114958i
$311$	18.7867			1.06529			0.532647	−	0.846338i	$-0.321197\pi$
$311$	18.7867			1.06529			0.532647	+	0.846338i	$0.321197\pi$
$312$	6.28789	+	3.36915i	0.355982	+	0.190741i
$313$	23.2463			1.31396			0.656980	−	0.753908i	$-0.271833\pi$
$313$	23.2463			1.31396			0.656980	+	0.753908i	$0.271833\pi$
$314$	28.6073	+	6.14176i	1.61440	+	0.346599i
$315$	−17.4347	+	5.11010i	−0.982333	+	0.287922i
$316$	5.27175	−	11.7116i	0.296559	−	0.658827i
$317$		−	10.0106i		−	0.562254i	−0.959671	−	0.281127i	$-0.909292\pi$
$317$		−	10.0106i		−	0.562254i	0.959671	−	0.281127i	$-0.0907082\pi$
$318$	1.90442	−	27.5866i	0.106794	−	1.54698i
$319$			42.3700i			2.37226i
$320$	21.7874	−	6.78515i	1.21796	−	0.379302i
$321$	−15.2355	+	2.18677i	−0.850364	+	0.122053i
$322$	−1.59326	+	7.42116i	−0.0887891	+	0.413565i
$323$	−2.94708			−0.163980
$324$	17.8052	−	2.64120i	0.989176	−	0.146733i
$325$	−4.56709			−0.253337
$326$	5.74238	−	26.7471i	0.318041	−	1.48138i
$327$	−5.55257	+	0.796965i	−0.307058	+	0.0440723i
$328$	−0.280303	+	0.380875i	−0.0154772	+	0.0210303i
$329$		−	21.8957i		−	1.20715i
$330$	2.43264	−	35.2382i	0.133912	−	1.93980i
$331$		−	8.21433i		−	0.451500i	−0.974185	−	0.225750i	$-0.927517\pi$
$331$		−	8.21433i		−	0.451500i	0.974185	−	0.225750i	$-0.0724833\pi$
$332$	−20.8172	−	9.37050i	−1.14249	−	0.514273i
$333$	4.42798	−	1.29784i	0.242652	−	0.0711212i
$334$	15.5349	+	3.33523i	0.850034	+	0.182496i
$335$	2.85244			0.155846
$336$	−9.51387	+	11.2183i	−0.519024	+	0.612009i
$337$	−4.38801			−0.239030			−0.119515	−	0.992832i	$-0.538134\pi$
$337$	−4.38801			−0.239030			−0.119515	+	0.992832i	$0.538134\pi$
$338$	15.0433	+	3.22969i	0.818250	+	0.175672i
$339$	−2.86357	−	19.9509i	−0.155528	−	1.08358i
$340$	−4.18178	−	1.88235i	−0.226789	−	0.102085i
$341$			12.0840i			0.654384i
$342$	1.14427	+	15.5121i	0.0618748	+	0.838800i
$343$		−	20.1534i		−	1.08818i
$344$	−18.9823	+	25.7931i	−1.02346	+	1.39067i
$345$	1.77445	+	12.3629i	0.0955332	+	0.665594i
$346$	−0.879496	+	4.09655i	−0.0472820	+	0.220232i
$347$	32.4290			1.74088			0.870441	−	0.492273i	$-0.163834\pi$
$347$	32.4290			1.74088			0.870441	+	0.492273i	$0.163834\pi$
$348$	8.03483	−	27.8992i	0.430712	−	1.49556i
$349$	−9.03367			−0.483562			−0.241781	−	0.970331i	$-0.577731\pi$
$349$	−9.03367			−0.483562			−0.241781	+	0.970331i	$0.577731\pi$
$350$	1.97676	−	9.20740i	0.105662	−	0.492156i
$351$	−6.88489	+	3.13817i	−0.367488	+	0.167503i
$352$	−14.0451	−	24.9109i	−0.748608	−	1.32776i
$353$		−	37.0762i		−	1.97337i	−0.162653	−	0.986683i	$-0.552005\pi$
$353$		−	37.0762i		−	1.97337i	0.162653	−	0.986683i	$-0.447995\pi$
$354$	11.1669	+	0.770895i	0.593513	+	0.0409726i
$355$			44.3733i			2.35509i
$356$	−5.50196	+	12.2230i	−0.291603	+	0.647817i
$357$	2.92606	−	0.419980i	0.154863	−	0.0222277i
$358$	−32.0106	−	6.87243i	−1.69181	−	0.363219i
$359$	−6.59057			−0.347837			−0.173918	−	0.984760i	$-0.555643\pi$
$359$	−6.59057			−0.347837			−0.173918	+	0.984760i	$0.555643\pi$
$360$	−8.28421	+	22.7419i	−0.436616	+	1.19860i
$361$	5.55913			0.292586
$362$	−8.26705	−	1.77487i	−0.434507	−	0.0932852i
$363$	−24.9575	+	3.58217i	−1.30993	+	0.188015i
$364$	2.53795	−	5.63824i	0.133025	−	0.295524i
$365$		−	0.298819i		−	0.0156409i
$366$	−18.2213	−	1.25789i	−0.952440	−	0.0657508i
$367$		−	10.1782i		−	0.531298i	−0.964070	−	0.265649i	$-0.914414\pi$
$367$		−	10.1782i		−	0.531298i	0.964070	−	0.265649i	$-0.0855862\pi$
$368$	6.70451	+	7.56957i	0.349497	+	0.394591i
$369$	−0.141080	−	0.481338i	−0.00734434	−	0.0250575i
$370$	−1.30240	+	6.06635i	−0.0677084	+	0.315374i
$371$	−23.9678			−1.24435
$372$	2.29154	−	7.95690i	0.118811	−	0.412546i
$373$	1.30447			0.0675429			0.0337715	−	0.999430i	$-0.489248\pi$
$373$	1.30447			0.0675429			0.0337715	+	0.999430i	$0.489248\pi$
$374$	−1.20636	+	5.61904i	−0.0623796	+	0.290554i
$375$	1.30810	+	9.11373i	0.0675501	+	0.470631i
$376$	−23.4933	−	17.2898i	−1.21157	−	0.891652i
$377$			12.2042i			0.628548i
$378$	−3.34669	−	15.2384i	−0.172135	−	0.783780i
$379$			16.4614i			0.845567i	0.906231	+	0.422783i	$0.138947\pi$
$379$			16.4614i			0.845567i	−0.906231	+	0.422783i	$0.861053\pi$
$380$	−19.0720	−	8.58492i	−0.978374	−	0.440397i
$381$	−2.12677	−	14.8175i	−0.108958	−	0.759126i
$382$	−16.9928	−	3.64822i	−0.869427	−	0.186659i
$383$	−34.5749			−1.76669			−0.883347	−	0.468719i	$-0.844716\pi$
$383$	−34.5749			−1.76669			−0.883347	+	0.468719i	$0.844716\pi$
$384$	4.52428	+	19.0665i	0.230878	+	0.972983i
$385$	−30.6156			−1.56032
$386$	2.96305	+	0.636143i	0.150815	+	0.0323788i
$387$	−9.55404	−	32.5965i	−0.485659	−	1.65698i
$388$	−20.3294	−	9.15092i	−1.03207	−	0.464568i
$389$		−	19.6800i		−	0.997815i	−0.866655	−	0.498908i	$-0.833735\pi$
$389$		−	19.6800i		−	0.997815i	0.866655	−	0.498908i	$-0.166265\pi$
$390$	0.700694	−	10.1500i	0.0354810	−	0.513964i
$391$		−	2.03211i		−	0.102768i
$392$	−5.67775	−	4.17851i	−0.286769	−	0.211047i
$393$	−2.50333	+	0.359304i	−0.126276	+	0.0181245i
$394$	4.07262	−	18.9696i	0.205176	−	0.955675i
$395$	−18.3175			−0.921653
$396$	30.0445	+	4.16806i	1.50980	+	0.209453i
$397$	35.8383			1.79867			0.899337	−	0.437256i	$-0.144050\pi$
$397$	35.8383			1.79867			0.899337	+	0.437256i	$0.144050\pi$
$398$	2.68854	−	12.5228i	0.134764	−	0.627709i
$399$	13.3450	−	1.91542i	0.668086	−	0.0958909i
$400$	−8.31827	−	9.39154i	−0.415913	−	0.469577i
$401$		−	4.40721i		−	0.220086i	−0.993927	−	0.110043i	$-0.964901\pi$
$401$		−	4.40721i		−	0.220086i	0.993927	−	0.110043i	$-0.0350988\pi$
$402$	−0.168697	+	2.44367i	−0.00841382	+	0.121879i
$403$			3.48065i			0.173384i
$404$	6.15908	−	13.6828i	0.306426	−	0.680746i
$405$	−13.8584	−	21.6101i	−0.688628	−	1.07381i
$406$	−24.6040	−	5.28229i	−1.22108	−	0.262156i
$407$	7.77561			0.385423
$408$	1.85992	−	3.47119i	0.0920796	−	0.171849i
$409$	36.5773			1.80863			0.904316	−	0.426864i	$-0.140382\pi$
$409$	36.5773			1.80863			0.904316	+	0.426864i	$0.140382\pi$
$410$	0.659436	+	0.141576i	0.0325672	+	0.00699192i
$411$	−3.73567	−	26.0270i	−0.184267	−	1.28382i
$412$	8.71173	−	19.3537i	0.429196	−	0.953490i
$413$		−	9.70200i		−	0.477404i
$414$	−10.6961	+	0.789011i	−0.525687	+	0.0387778i
$415$			32.5592i			1.59827i
$416$	−4.04554	−	7.17532i	−0.198349	−	0.351799i
$417$	1.71871	+	11.9745i	0.0841657	+	0.586395i
$418$	−5.50191	+	25.6270i	−0.269107	+	1.25346i
$419$	−4.31729			−0.210914			−0.105457	−	0.994424i	$-0.533630\pi$
$419$	−4.31729			−0.210914			−0.105457	+	0.994424i	$0.533630\pi$
$420$	20.1594	+	5.80579i	0.983677	+	0.283294i
$421$	1.17156			0.0570982			0.0285491	−	0.999592i	$-0.490911\pi$
$421$	1.17156			0.0570982			0.0285491	+	0.999592i	$0.490911\pi$
$422$	−3.52292	+	16.4092i	−0.171493	+	0.798786i
$423$	29.6901	−	8.70215i	1.44358	−	0.423113i
$424$	−18.9260	+	25.7165i	−0.919127	+	1.24891i
$425$			2.52123i			0.122298i
$426$	−38.0144	−	2.62429i	−1.84180	−	0.127147i
$427$			15.8310i			0.766114i
$428$	16.2066	+	7.29509i	0.783374	+	0.352622i
$429$	−12.6209	+	1.81149i	−0.609345	+	0.0874597i
$430$	44.6574	+	9.58759i	2.15357	+	0.462355i
$431$	20.4106			0.983144			0.491572	−	0.870837i	$-0.336423\pi$
$431$	20.4106			0.983144			0.491572	+	0.870837i	$0.336423\pi$
$432$	−18.9929	−	8.44203i	−0.913799	−	0.406167i
$433$	9.00788			0.432891			0.216445	−	0.976295i	$-0.430554\pi$
$433$	9.00788			0.432891			0.216445	+	0.976295i	$0.430554\pi$
$434$	−7.01710	−	1.50652i	−0.336832	−	0.0723151i
$435$	−40.9877	+	5.88300i	−1.96521	+	0.282068i
$436$	5.90646	+	2.65869i	0.282868	+	0.127328i
$437$		−	9.26794i		−	0.443346i
$438$	0.255997	+	0.0176725i	0.0122320	+	0.000844425i
$439$		−	21.3555i		−	1.01924i	−0.860399	−	0.509621i	$-0.829786\pi$
$439$		−	21.3555i		−	1.01924i	0.860399	−	0.509621i	$-0.170214\pi$
$440$	−24.1754	+	32.8494i	−1.15252	+	1.56603i
$441$	7.17536	−	2.10310i	0.341684	−	0.100148i
$442$	−0.347480	+	1.61850i	−0.0165279	+	0.0769843i
$443$	13.0837			0.621625			0.310812	−	0.950471i	$-0.399399\pi$
$443$	13.0837			0.621625			0.310812	+	0.950471i	$0.399399\pi$
$444$	−5.11999	−	1.47453i	−0.242984	−	0.0699780i
$445$	19.1174			0.906250
$446$	1.05596	−	4.91850i	0.0500013	−	0.232898i
$447$	5.60526	+	39.0527i	0.265120	+	1.84713i
$448$	16.2167	−	5.05028i	0.766166	−	0.238603i
$449$			28.1175i			1.32695i	0.748199	+	0.663474i	$0.230919\pi$
$449$			28.1175i			1.32695i	−0.748199	+	0.663474i	$0.769081\pi$
$450$	13.2707	−	0.978922i	0.625585	−	0.0461468i
$451$		−	0.845239i		−	0.0398008i
$452$	−9.55290	+	21.2224i	−0.449331	+	0.998220i
$453$	−4.53055	−	31.5650i	−0.212864	−	1.48305i
$454$	10.8864	+	2.33723i	0.510925	+	0.109692i
$455$	−8.81849			−0.413417
$456$	8.48260	−	15.8312i	0.397234	−	0.741363i
$457$	27.2212			1.27336			0.636678	−	0.771130i	$-0.280308\pi$
$457$	27.2212			1.27336			0.636678	+	0.771130i	$0.280308\pi$
$458$	13.1624	+	2.82587i	0.615040	+	0.132044i
$459$	1.73241	+	3.80076i	0.0808618	+	0.177404i
$460$	5.91960	−	13.1508i	0.276003	−	0.613159i
$461$		−	18.3120i		−	0.852877i	−0.904517	−	0.426438i	$-0.859768\pi$
$461$		−	18.3120i		−	0.852877i	0.904517	−	0.426438i	$-0.140232\pi$
$462$	1.81064	−	26.2283i	0.0842387	−	1.22025i
$463$			10.0274i			0.466012i	0.972475	+	0.233006i	$0.0748562\pi$
$463$			10.0274i			0.466012i	−0.972475	+	0.233006i	$0.925144\pi$
$464$	−25.0961	+	22.2281i	−1.16506	+	1.03191i
$465$	−11.6897	+	1.67784i	−0.542099	+	0.0778079i
$466$	6.31558	−	29.4169i	0.292563	−	1.36271i
$467$	13.3284			0.616765			0.308383	−	0.951262i	$-0.400212\pi$
$467$	13.3284			0.616765			0.308383	+	0.951262i	$0.400212\pi$
$468$	8.65400	+	1.20056i	0.400031	+	0.0554960i
$469$	2.12311			0.0980361
$470$	−8.73271	+	40.6755i	−0.402810	+	1.87622i
$471$	35.4715	−	5.09125i	1.63444	−	0.234592i
$472$	−10.4099	−	7.66111i	−0.479153	−	0.352631i
$473$		−	57.2401i		−	2.63190i
$474$	1.08332	−	15.6925i	0.0497584	−	0.720781i
$475$			11.4987i			0.527596i
$476$	−3.11255	−	1.40106i	−0.142664	−	0.0642174i
$477$	−9.52568	−	32.4998i	−0.436151	−	1.48806i
$478$	3.35177	+	0.719599i	0.153306	+	0.0329137i
$479$	7.57165			0.345958			0.172979	−	0.984926i	$-0.444661\pi$
$479$	7.57165			0.345958			0.172979	+	0.984926i	$0.444661\pi$
$480$	22.1481	−	17.0458i	1.01092	−	0.778029i
$481$	2.23968			0.102121
$482$	10.2406	+	2.19857i	0.466446	+	0.100142i
$483$	1.32075	+	9.20183i	0.0600960	+	0.418698i
$484$	26.5481	+	11.9502i	1.20673	+	0.543190i
$485$			31.7962i			1.44379i
$486$	19.3329	−	10.5944i	0.876957	−	0.480570i
$487$			27.0871i			1.22743i	0.789527	+	0.613716i	$0.210326\pi$
$487$			27.0871i			1.22743i	−0.789527	+	0.613716i	$0.789674\pi$
$488$	16.9860	+	12.5008i	0.768921	+	0.565884i
$489$	−4.76019	−	33.1649i	−0.215263	−	1.49977i
$490$	−2.11048	+	9.83028i	−0.0953419	+	0.444087i
$491$	−5.08156			−0.229328			−0.114664	−	0.993404i	$-0.536579\pi$
$491$	−5.08156			−0.229328			−0.114664	+	0.993404i	$0.536579\pi$
$492$	−0.160287	+	0.556563i	−0.00722630	+	0.0250918i
$493$	6.73724			0.303430
$494$	−1.58477	+	7.38157i	−0.0713020	+	0.332113i
$495$	−12.1678	−	41.5141i	−0.546901	−	1.86592i
$496$	−7.15744	+	6.33948i	−0.321378	+	0.284651i
$497$			33.0276i			1.48149i
$498$	−27.8933	−	1.92559i	−1.24993	−	0.0862877i
$499$			15.9343i			0.713318i	0.934235	+	0.356659i	$0.116084\pi$
$499$			15.9343i			0.713318i	−0.934235	+	0.356659i	$0.883916\pi$
$500$	4.36385	−	9.69460i	0.195157	−	0.433556i
$501$	19.2625	−	2.76476i	0.860584	−	0.123520i
$502$	4.99818	+	1.07307i	0.223080	+	0.0478934i
$503$	39.2197			1.74872			0.874359	−	0.485280i	$-0.161282\pi$
$503$	39.2197			1.74872			0.874359	+	0.485280i	$0.161282\pi$
$504$	−6.16605	+	16.9271i	−0.274658	+	0.753993i
$505$	−21.4006			−0.952316
$506$	−17.6707	−	3.79376i	−0.785557	−	0.168653i
$507$	18.6529	−	2.67727i	0.828406	−	0.118902i
$508$	−7.09495	+	15.7619i	−0.314788	+	0.699323i
$509$		−	7.49202i		−	0.332078i	−0.986119	−	0.166039i	$-0.946902\pi$
$509$		−	7.49202i		−	0.332078i	0.986119	−	0.166039i	$-0.0530978\pi$
$510$	−5.60323	−	0.386813i	−0.248115	−	0.0171284i
$511$		−	0.222415i		−	0.00983905i
$512$	7.38662	−	21.3878i	0.326445	−	0.945216i
$513$	7.90106	+	17.3343i	0.348840	+	0.765327i
$514$	1.95840	−	9.12192i	0.0863815	−	0.402351i
$515$	−30.2702			−1.33386
$516$	−10.8547	+	37.6908i	−0.477853	+	1.65924i
$517$	52.1363			2.29295
$518$	−0.969391	+	4.51526i	−0.0425926	+	0.198389i
$519$	0.729064	+	5.07950i	0.0320024	+	0.222965i
$520$	−6.96345	+	9.46191i	−0.305368	+	0.414932i
$521$		−	6.35296i		−	0.278328i	−0.990269	−	0.139164i	$-0.955558\pi$
$521$		−	6.35296i		−	0.278328i	0.990269	−	0.139164i	$-0.0444416\pi$
$522$	−2.61588	−	35.4619i	−0.114494	−	1.55213i
$523$			11.5021i			0.502952i	0.967864	+	0.251476i	$0.0809159\pi$
$523$			11.5021i			0.502952i	−0.967864	+	0.251476i	$0.919084\pi$
$524$	2.66287	+	1.19865i	0.116328	+	0.0523631i
$525$	−1.63865	−	11.4167i	−0.0715163	−	0.498265i
$526$	32.6839	+	7.01698i	1.42509	+	0.305955i
$527$	1.92147			0.0837006
$528$	−26.7122	−	22.6537i	−1.16250	−	0.985875i
$529$	−16.6094			−0.722150
$530$	44.5248	+	9.55913i	1.93404	+	0.415222i
$531$	13.1557	−	3.85593i	0.570908	−	0.167333i
$532$	−14.1955	−	6.38987i	−0.615455	−	0.277036i
$533$		−	0.243462i		−	0.0105455i
$534$	−1.13062	+	16.3778i	−0.0489268	+	0.708735i
$535$		−	25.3479i		−	1.09588i
$536$	1.67650	−	2.27802i	0.0724136	−	0.0983953i
$537$	−39.6914	+	5.69694i	−1.71281	+	0.245841i
$538$	−5.39175	+	25.1139i	−0.232455	+	1.08274i
$539$	12.6001			0.542723
$540$	0.139556	+	29.6431i	0.00600555	+	1.27564i
$541$	−23.7717			−1.02202			−0.511012	−	0.859573i	$-0.670729\pi$
$541$	−23.7717			−1.02202			−0.511012	+	0.859573i	$0.670729\pi$
$542$	4.41467	−	20.5628i	0.189626	−	0.883247i
$543$	−10.2507	+	1.47129i	−0.439900	+	0.0631391i
$544$	−3.96109	+	2.23331i	−0.169830	+	0.0957526i
$545$		−	9.23801i		−	0.395713i
$546$	0.521536	−	7.55476i	0.0223197	−	0.323314i
$547$		−	6.10422i		−	0.260998i	−0.991448	−	0.130499i	$-0.958342\pi$
$547$		−	6.10422i		−	0.260998i	0.991448	−	0.130499i	$-0.0416579\pi$
$548$	−12.4623	+	27.6858i	−0.532362	+	1.18268i
$549$	−21.4664	+	6.29181i	−0.916165	+	0.268528i
$550$	21.9239	+	4.70690i	0.934840	+	0.200703i
$551$	30.7268			1.30901
$552$	10.9161	+	5.84904i	0.464622	+	0.248952i
$553$	−13.6339			−0.579774
$554$	2.62734	+	0.564069i	0.111625	+	0.0239650i
$555$	1.07963	+	7.52194i	0.0458278	+	0.319289i
$556$	5.73365	−	12.7377i	0.243161	−	0.540199i
$557$			21.7496i			0.921561i	0.887514	+	0.460781i	$0.152430\pi$
$557$			21.7496i			0.921561i	−0.887514	+	0.460781i	$0.847570\pi$
$558$	−0.746052	−	10.1138i	−0.0315829	−	0.428150i
$559$		−	16.4874i		−	0.697342i
$560$	−16.0615	−	18.1339i	−0.678724	−	0.766297i
$561$	1.00002	+	6.96730i	0.0422210	+	0.294160i
$562$	4.89902	−	22.8188i	0.206653	−	0.962553i
$563$	−32.0628			−1.35128			−0.675642	−	0.737230i	$-0.736134\pi$
$563$	−32.0628			−1.35128			−0.675642	+	0.737230i	$0.736134\pi$
$564$	−34.3301	−	9.88687i	−1.44556	−	0.416312i
$565$	33.1930			1.39644
$566$	−0.330376	+	1.53883i	−0.0138867	+	0.0646820i
$567$	−10.3150	−	16.0847i	−0.433188	−	0.675493i
$568$	35.4374	+	26.0800i	1.48692	+	1.09429i
$569$			17.3619i			0.727850i	0.931428	+	0.363925i	$0.118564\pi$
$569$			17.3619i			0.727850i	−0.931428	+	0.363925i	$0.881436\pi$
$570$	−25.5549	−	1.76416i	−1.07038	−	0.0738924i
$571$		−	8.49419i		−	0.355471i	−0.984078	−	0.177735i	$-0.943123\pi$
$571$		−	8.49419i		−	0.355471i	0.984078	−	0.177735i	$-0.0568771\pi$
$572$	13.4253	+	6.04317i	0.561341	+	0.252678i
$573$	−21.0701	+	3.02421i	−0.880218	+	0.126338i
$574$	0.490826	+	0.105377i	0.0204867	+	0.00439833i
$575$	−7.92874			−0.330651
$576$	13.2932	+	19.9823i	0.553882	+	0.832595i
$577$	−26.2794			−1.09402			−0.547012	−	0.837125i	$-0.684235\pi$
$577$	−26.2794			−1.09402			−0.547012	+	0.837125i	$0.684235\pi$
$578$	−22.6125	−	4.85473i	−0.940557	−	0.201930i
$579$	3.67402	−	0.527335i	0.152687	−	0.0219153i
$580$	43.6000	+	19.6258i	1.81039	+	0.814916i
$581$			24.2342i			1.00541i
$582$	−27.2397	−	1.88047i	−1.12912	−	0.0779478i
$583$		−	57.0702i		−	2.36361i
$584$	−0.238643	−	0.175628i	−0.00987511	−	0.00726755i
$585$	−3.50479	−	11.9577i	−0.144905	−	0.494389i
$586$	−8.29019	+	38.6143i	−0.342464	+	1.59514i
$587$	−22.2560			−0.918602			−0.459301	−	0.888281i	$-0.651900\pi$
$587$	−22.2560			−0.918602			−0.459301	+	0.888281i	$0.651900\pi$
$588$	−8.29674	−	2.38942i	−0.342152	−	0.0985378i
$589$	8.76333			0.361087
$590$	−3.86947	+	18.0233i	−0.159304	+	0.742009i
$591$	−3.37603	−	23.5213i	−0.138871	−	0.967536i
$592$	4.07923	+	4.60556i	0.167655	+	0.189287i
$593$		−	24.8234i		−	1.01937i	−0.860360	−	0.509687i	$-0.829761\pi$
$593$		−	24.8234i		−	1.01937i	0.860360	−	0.509687i	$-0.170239\pi$
$594$	36.2845	−	7.96888i	1.48877	−	0.326967i
$595$			4.86819i			0.199576i
$596$	18.6992	−	41.5417i	0.765951	−	1.70161i
$597$	−2.22868	−	15.5275i	−0.0912139	−	0.635500i
$598$	−5.08984	−	1.09275i	−0.208139	−	0.0446858i
$599$	−44.5649			−1.82087			−0.910436	−	0.413649i	$-0.864254\pi$
$599$	−44.5649			−1.82087			−0.910436	+	0.413649i	$0.864254\pi$
$600$	−13.5436	−	7.25689i	−0.552916	−	0.296261i
$601$	25.2111			1.02838			0.514190	−	0.857676i	$-0.328093\pi$
$601$	25.2111			1.02838			0.514190	+	0.857676i	$0.328093\pi$
$602$	33.2391	+	7.13617i	1.35472	+	0.290848i
$603$	0.843802	+	2.87889i	0.0343623	+	0.117237i
$604$	−15.1140	+	33.5768i	−0.614980	+	1.36622i
$605$		−	41.5226i		−	1.68814i
$606$	1.26566	−	18.3338i	0.0514138	−	0.744761i
$607$		−	5.55928i		−	0.225644i	−0.993615	−	0.112822i	$-0.964011\pi$
$607$		−	5.55928i		−	0.225644i	0.993615	−	0.112822i	$-0.0359890\pi$
$608$	−18.0655	+	10.1856i	−0.732652	+	0.413080i
$609$	−30.5077	+	4.37879i	−1.23623	+	0.177438i
$610$	6.31390	−	29.4091i	0.255642	−	1.19074i
$611$	15.0173			0.607535
$612$	0.662762	−	4.77738i	0.0267906	−	0.193114i
$613$	7.97048			0.321925			0.160962	−	0.986961i	$-0.448540\pi$
$613$	7.97048			0.321925			0.160962	+	0.986961i	$0.448540\pi$
$614$	8.31935	−	38.7501i	0.335742	−	1.56383i
$615$	0.817665	−	0.117360i	0.0329714	−	0.00473241i
$616$	−17.9940	+	24.4502i	−0.725001	+	0.985128i
$617$			42.4971i			1.71087i	0.517911	+	0.855435i	$0.326710\pi$
$617$			42.4971i			1.71087i	−0.517911	+	0.855435i	$0.673290\pi$
$618$	1.79021	−	25.9323i	0.0720130	−	1.04315i
$619$			22.5315i			0.905619i	0.891607	+	0.452810i	$0.149578\pi$
$619$			22.5315i			0.905619i	−0.891607	+	0.452810i	$0.850422\pi$
$620$	12.4348	+	5.59730i	0.499393	+	0.224793i
$621$	−11.9526	+	5.44805i	−0.479640	+	0.218623i
$622$	−25.9764	−	5.57693i	−1.04156	−	0.223615i
$623$	14.2293			0.570085
$624$	−7.69415	−	6.52515i	−0.308012	−	0.261215i
$625$	−30.8450			−1.23380
$626$	−32.1429	−	6.90082i	−1.28469	−	0.275812i
$627$	4.56085	+	31.7761i	0.182143	+	1.26901i
$628$	−37.7322	−	16.9845i	−1.50568	−	0.677755i
$629$		−	1.23640i		−	0.0492985i
$630$	25.6240	−	1.89018i	1.02088	−	0.0753065i
$631$		−	21.5848i		−	0.859278i	−0.903001	−	0.429639i	$-0.858641\pi$
$631$		−	21.5848i		−	0.859278i	0.903001	−	0.429639i	$-0.141359\pi$
$632$	−10.7659	+	14.6287i	−0.428246	+	0.581899i
$633$	2.92035	+	20.3465i	0.116073	+	0.808700i
$634$	−2.97172	+	13.8418i	−0.118022	+	0.549728i
$635$	24.6525			0.978303
$636$	−10.8225	+	37.5789i	−0.429141	+	1.49010i
$637$	3.62931			0.143799
$638$	12.5778	−	58.5852i	0.497959	−	2.31941i
$639$	−44.7847	+	13.1264i	−1.77166	+	0.519272i
$640$	−32.1399	+	2.91414i	−1.27044	+	0.115191i
$641$		−	5.43407i		−	0.214633i	−0.994225	−	0.107316i	$-0.965774\pi$
$641$		−	5.43407i		−	0.214633i	0.994225	−	0.107316i	$-0.0342258\pi$
$642$	21.7154	+	1.49910i	0.857039	+	0.0591648i
$643$			26.2544i			1.03537i	0.855570	+	0.517687i	$0.173207\pi$
$643$			26.2544i			1.03537i	−0.855570	+	0.517687i	$0.826793\pi$
$644$	4.40603	−	9.78831i	0.173622	−	0.385713i
$645$	55.3728	−	7.94770i	2.18030	−	0.312940i
$646$	4.07495	+	0.874859i	0.160327	+	0.0344209i
$647$	19.5905			0.770181			0.385090	−	0.922879i	$-0.374170\pi$
$647$	19.5905			0.770181			0.385090	+	0.922879i	$0.374170\pi$
$648$	−25.4034	−	1.63357i	−0.997939	−	0.0641727i
$649$	23.1016			0.906818
$650$	6.31495	+	1.35577i	0.247693	+	0.0531777i
$651$	−8.70083	+	1.24884i	−0.341012	+	0.0489458i
$652$	−15.8801	+	35.2787i	−0.621911	+	1.38162i
$653$			37.5923i			1.47110i	0.677470	+	0.735550i	$0.263076\pi$
$653$			37.5923i			1.47110i	−0.677470	+	0.735550i	$0.736924\pi$
$654$	7.91416	+	0.546346i	0.309468	+	0.0213638i
$655$		−	4.16487i		−	0.162735i
$656$	0.500642	−	0.443429i	0.0195468	−	0.0173130i
$657$	0.301590	−	0.0883959i	0.0117661	−	0.00344865i
$658$	−6.49987	+	30.2753i	−0.253391	+	1.18025i
$659$	13.5327			0.527157			0.263579	−	0.964638i	$-0.415097\pi$
$659$	13.5327			0.527157			0.263579	+	0.964638i	$0.415097\pi$
$660$	−13.8243	+	48.0020i	−0.538110	+	1.86847i
$661$	1.18561			0.0461147			0.0230573	−	0.999734i	$-0.492660\pi$
$661$	1.18561			0.0461147			0.0230573	+	0.999734i	$0.492660\pi$
$662$	−2.43847	+	11.3580i	−0.0947739	+	0.441441i
$663$	0.288046	+	2.00685i	0.0111868	+	0.0779398i
$664$	26.0024	+	19.1364i	1.00909	+	0.742636i
$665$			22.2025i			0.860978i
$666$	−6.50786	+	0.480058i	−0.252175	+	0.0186019i
$667$			21.1872i			0.820372i
$668$	−20.4902	−	9.22328i	−0.792788	−	0.356859i
$669$	−0.875348	−	6.09868i	−0.0338429	−	0.235788i
$670$	−3.94409	−	0.846765i	−0.152373	−	0.0327134i
$671$	−37.6954			−1.45522
$672$	16.4851	−	12.6874i	0.635927	−	0.489426i
$673$	28.8260			1.11116			0.555581	−	0.831463i	$-0.312496\pi$
$673$	28.8260			1.11116			0.555581	+	0.831463i	$0.312496\pi$
$674$	6.06733	+	1.30261i	0.233705	+	0.0501746i
$675$	14.8295	−	6.75937i	0.570788	−	0.260168i
$676$	−19.8418	−	8.93142i	−0.763145	−	0.343516i
$677$		−	2.13643i		−	0.0821098i	−0.999157	−	0.0410549i	$-0.986928\pi$
$677$		−	2.13643i		−	0.0821098i	0.999157	−	0.0410549i	$-0.0130719\pi$
$678$	−1.96307	+	28.4363i	−0.0753912	+	1.09209i
$679$			23.6663i			0.908231i
$680$	5.22338	+	3.84413i	0.200308	+	0.147416i
$681$	13.4986	−	1.93746i	0.517266	−	0.0742436i
$682$	3.58720	−	16.7086i	0.137361	−	0.639805i
$683$	27.8685			1.06636			0.533179	−	0.846003i	$-0.320997\pi$
$683$	27.8685			1.06636			0.533179	+	0.846003i	$0.320997\pi$
$684$	3.02269	−	21.7884i	0.115575	−	0.833101i
$685$	43.3020			1.65448
$686$	−5.98267	+	27.8663i	−0.228419	+	1.06394i
$687$	16.3207	−	2.34252i	0.622673	−	0.0893728i
$688$	33.9038	−	30.0293i	1.29257	−	1.14485i
$689$		−	16.4384i		−	0.626255i
$690$	1.21645	−	17.6210i	0.0463093	−	0.670818i
$691$			0.711215i			0.0270559i	0.999908	+	0.0135280i	$0.00430621\pi$
$691$			0.711215i			0.0270559i	−0.999908	+	0.0135280i	$0.995694\pi$
$692$	2.43217	−	5.40324i	0.0924572	−	0.205400i
$693$	−9.05663	−	30.8995i	−0.344033	−	1.17377i
$694$	−44.8398	−	9.62676i	−1.70210	−	0.365427i
$695$	−19.9224			−0.755701
$696$	−19.3919	+	36.1913i	−0.735047	+	1.37183i
$697$	−0.134401			−0.00509082
$698$	12.4909	+	2.68170i	0.472788	+	0.101504i
$699$	−5.23534	−	36.4754i	−0.198019	−	1.37963i
$700$	−5.46655	+	12.1443i	−0.206616	+	0.459012i
$701$			6.63817i			0.250720i	0.992111	+	0.125360i	$0.0400086\pi$
$701$			6.63817i			0.250720i	−0.992111	+	0.125360i	$0.959991\pi$
$702$	10.4514	−	2.29535i	0.394461	−	0.0866324i
$703$		−	5.63890i		−	0.212675i
$704$	12.0253	+	38.6139i	0.453221	+	1.45532i
$705$	7.23904	+	50.4354i	0.272638	+	1.89951i
$706$	−11.0063	+	51.2655i	−0.414227	+	1.92940i
$707$	−15.9288			−0.599063
$708$	−15.2117	−	4.38088i	−0.571690	−	0.164644i
$709$	7.64531			0.287126			0.143563	−	0.989641i	$-0.454144\pi$
$709$	7.64531			0.287126			0.143563	+	0.989641i	$0.454144\pi$
$710$	13.1725	−	61.3552i	0.494355	−	2.30262i
$711$	−5.41863	−	18.4873i	−0.203214	−	0.693329i
$712$	11.2361	−	15.2675i	0.421089	−	0.572174i
$713$			6.04262i			0.226298i
$714$	−4.17055	−	0.287910i	−0.156079	−	0.0107748i
$715$		−	20.9979i		−	0.785277i
$716$	42.2212	+	19.0051i	1.57788	+	0.710254i
$717$	4.15601	−	0.596516i	0.155209	−	0.0222773i
$718$	9.11282	+	1.95645i	0.340088	+	0.0730141i
$719$	−34.9849			−1.30472			−0.652359	−	0.757910i	$-0.726220\pi$
$719$	−34.9849			−1.30472			−0.652359	+	0.757910i	$0.726220\pi$
$720$	18.2057	−	28.9862i	0.678487	−	1.08025i
$721$	−22.5305			−0.839080
$722$	−7.68664	−	1.65026i	−0.286067	−	0.0614164i
$723$	12.6978	−	1.82252i	0.472235	−	0.0677803i
$724$	10.9040	+	4.90825i	0.405245	+	0.182414i
$725$		−	26.2869i		−	0.976270i
$726$	35.5723	+	2.45570i	1.32021	+	0.0911394i
$727$			25.8783i			0.959773i	0.877330	+	0.479887i	$0.159322\pi$
$727$			25.8783i			0.959773i	−0.877330	+	0.479887i	$0.840678\pi$
$728$	−5.18299	+	7.04262i	−0.192094	+	0.261017i
$729$	17.7109	−	20.3795i	0.655960	−	0.754796i
$730$	−0.0887063	+	0.413179i	−0.00328317	+	0.0152924i
$731$	−9.10175			−0.336640
$732$	24.8212	+	7.14838i	0.917419	+	0.264212i
$733$	−28.6885			−1.05964			−0.529818	−	0.848112i	$-0.677740\pi$
$733$	−28.6885			−1.05964			−0.529818	+	0.848112i	$0.677740\pi$
$734$	−3.02146	+	14.0735i	−0.111524	+	0.519461i
$735$	1.74950	+	12.1890i	0.0645312	+	0.449598i
$736$	−7.02330	−	12.4568i	−0.258882	−	0.459163i
$737$			5.05538i			0.186217i
$738$	0.0521842	+	0.707430i	0.00192093	+	0.0260409i
$739$		−	32.7425i		−	1.20445i	−0.798326	−	0.602226i	$-0.794281\pi$
$739$		−	32.7425i		−	1.20445i	0.798326	−	0.602226i	$-0.205719\pi$
$740$	3.60167	−	8.00135i	0.132400	−	0.294136i
$741$	1.31370	+	9.15275i	0.0482600	+	0.336235i
$742$	33.1404	+	7.11498i	1.21662	+	0.261199i
$743$	−12.8638			−0.471927			−0.235963	−	0.971762i	$-0.575825\pi$
$743$	−12.8638			−0.471927			−0.235963	+	0.971762i	$0.575825\pi$
$744$	−5.53059	+	10.3218i	−0.202761	+	0.378415i
$745$	−64.9733			−2.38044
$746$	−1.80370	−	0.387240i	−0.0660381	−	0.0141779i
$747$	−32.8611	+	9.63158i	−1.20232	+	0.352401i
$748$	3.33609	−	7.41136i	0.121980	−	0.270986i
$749$		−	18.8668i		−	0.689376i
$750$	0.896748	−	12.9899i	0.0327446	−	0.474325i
$751$		−	22.4339i		−	0.818623i	−0.912395	−	0.409312i	$-0.865769\pi$
$751$		−	22.4339i		−	0.818623i	0.912395	−	0.409312i	$-0.134231\pi$
$752$	27.3517	+	30.8808i	0.997414	+	1.12611i
$753$	6.19747	−	0.889528i	0.225848	−	0.0324162i
$754$	3.62289	−	16.8748i	0.131938	−	0.614545i
$755$	52.5158			1.91125
$756$	0.103874	+	22.0638i	0.00377785	+	0.802451i
$757$	−16.4339			−0.597301			−0.298651	−	0.954363i	$-0.596537\pi$
$757$	−16.4339			−0.597301			−0.298651	+	0.954363i	$0.596537\pi$
$758$	4.88668	−	22.7613i	0.177492	−	0.826728i
$759$	−21.9107	+	3.14486i	−0.795307	+	0.114151i
$760$	23.8225	+	17.5321i	0.864133	+	0.635955i
$761$			43.7728i			1.58676i	0.608724	+	0.793382i	$0.291682\pi$
$761$			43.7728i			1.58676i	−0.608724	+	0.793382i	$0.708318\pi$
$762$	−1.45797	+	21.1197i	−0.0528169	+	0.765084i
$763$		−	6.87597i		−	0.248927i
$764$	22.4130	+	10.0888i	0.810875	+	0.365001i
$765$	−6.60115	+	1.93480i	−0.238665	+	0.0699527i
$766$	47.8069	+	10.2638i	1.72733	+	0.370845i
$767$	6.65417			0.240268
$768$	−0.595740	−	27.7064i	−0.0214969	−	0.999769i
$769$	30.2331			1.09023			0.545116	−	0.838361i	$-0.316486\pi$
$769$	30.2331			1.09023			0.545116	+	0.838361i	$0.316486\pi$
$770$	42.3324	+	9.08843i	1.52555	+	0.327524i
$771$	−1.62343	−	11.3107i	−0.0584665	−	0.407344i
$772$	−3.90818	−	1.75920i	−0.140659	−	0.0633149i
$773$			43.3489i			1.55915i	0.626308	+	0.779575i	$0.284565\pi$
$773$			43.3489i			1.55915i	−0.626308	+	0.779575i	$0.715435\pi$
$774$	3.53395	+	47.9076i	0.127025	+	1.72200i
$775$		−	7.49705i		−	0.269302i
$776$	25.3931	+	18.6879i	0.911559	+	0.670858i
$777$	0.803583	+	5.59868i	0.0288284	+	0.200851i
$778$	−5.84213	+	27.2116i	−0.209450	+	0.975585i
$779$	−0.612970			−0.0219619
$780$	−3.98194	+	13.8264i	−0.142576	+	0.495066i
$781$	−78.6428			−2.81406
$782$	−0.603245	+	2.80981i	−0.0215720	+	0.100479i
$783$	−18.0624	−	39.6274i	−0.645498	−	1.41617i
$784$	6.61024	+	7.46313i	0.236080	+	0.266540i
$785$			59.0151i			2.10634i
$786$	3.56803	+	0.246315i	0.127267	+	0.00878577i
$787$			7.62023i			0.271632i	0.990734	+	0.135816i	$0.0433656\pi$
$787$			7.62023i			0.271632i	−0.990734	+	0.135816i	$0.956634\pi$
$788$	−11.2625	+	25.0204i	−0.401209	+	0.891315i
$789$	40.5263	−	5.81677i	1.44277	−	0.207082i
$790$	25.3277	+	5.43766i	0.901119	+	0.193463i
$791$	24.7060			0.878443
$792$	−40.3055	−	14.6821i	−1.43219	−	0.521706i
$793$	−10.8578			−0.385570
$794$	−49.5539	−	10.6388i	−1.75860	−	0.377558i
$795$	55.2084	−	7.92410i	1.95804	−	0.281039i
$796$	−7.43492	+	16.5172i	−0.263524	+	0.585436i
$797$			27.1456i			0.961546i	0.876845	+	0.480773i	$0.159644\pi$
$797$			27.1456i			0.961546i	−0.876845	+	0.480773i	$0.840356\pi$
$798$	−19.0208	−	1.31308i	−0.673330	−	0.0464827i
$799$		−	8.29019i		−	0.293286i
$800$	8.71378	+	15.4551i	0.308079	+	0.546419i
$801$	5.65525	+	19.2946i	0.199818	+	0.681742i
$802$	−1.30831	+	6.09388i	−0.0461980	+	0.215182i
$803$	0.529597			0.0186891
$804$	0.958677	−	3.32880i	0.0338099	−	0.117398i
$805$	−15.3094			−0.539586
$806$	1.03325	−	4.81272i	0.0363948	−	0.169521i
$807$	4.46952	+	31.1398i	0.157335	+	1.09617i
$808$	−12.5780	+	17.0910i	−0.442493	+	0.601258i
$809$			40.2746i			1.41598i	0.706224	+	0.707989i	$0.250397\pi$
$809$			40.2746i			1.41598i	−0.706224	+	0.707989i	$0.749603\pi$
$810$	12.7470	+	33.9943i	0.447883	+	1.19444i
$811$		−	7.23609i		−	0.254093i	−0.991897	−	0.127047i	$-0.959450\pi$
$811$		−	7.23609i		−	0.254093i	0.991897	−	0.127047i	$-0.0405498\pi$
$812$	32.4521	+	14.6077i	1.13884	+	0.512630i
$813$	−3.65957	−	25.4967i	−0.128347	−	0.894209i
$814$	−10.7514	−	2.30824i	−0.376836	−	0.0809037i
$815$	55.1776			1.93279
$816$	−3.60216	+	4.24750i	−0.126101	+	0.148692i
$817$	−41.5107			−1.45228
$818$	−50.5757	−	10.8582i	−1.76834	−	0.379648i
$819$	−2.60866	−	8.90025i	−0.0911540	−	0.311000i
$820$	−0.869778	−	0.391515i	−0.0303740	−	0.0136723i
$821$			45.0469i			1.57215i	0.618132	+	0.786074i	$0.287890\pi$
$821$			45.0469i			1.57215i	−0.618132	+	0.786074i	$0.712110\pi$
$822$	−2.56093	+	37.0966i	−0.0893227	+	1.29389i
$823$		−	42.4821i		−	1.48083i	−0.672149	−	0.740416i	$-0.734629\pi$
$823$		−	42.4821i		−	1.48083i	0.672149	−	0.740416i	$-0.265371\pi$
$824$	−17.7910	+	24.1744i	−0.619780	+	0.842155i
$825$	27.1845	−	3.90181i	0.946443	−	0.135844i
$826$	−2.88010	+	13.4150i	−0.100211	+	0.466768i
$827$	36.9614			1.28527			0.642637	−	0.766171i	$-0.277841\pi$
$827$	36.9614			1.28527			0.642637	+	0.766171i	$0.277841\pi$
$828$	15.0238	+	2.08425i	0.522115	+	0.0724326i
$829$	41.2643			1.43317			0.716585	−	0.697500i	$-0.245704\pi$
$829$	41.2643			1.43317			0.716585	+	0.697500i	$0.245704\pi$
$830$	9.66540	−	45.0198i	0.335491	−	1.56266i
$831$	3.25776	−	0.467588i	0.113010	−	0.0162205i
$832$	3.46376	+	11.1223i	0.120084	+	0.385596i
$833$		−	2.00354i		−	0.0694184i
$834$	1.17823	−	17.0674i	0.0407989	−	0.590997i
$835$			32.0477i			1.10905i
$836$	15.2151	−	33.8013i	0.526224	−	1.16904i
$837$	−5.15142	−	11.3018i	−0.178059	−	0.390647i
$838$	5.96955	+	1.28161i	0.206215	+	0.0442726i
$839$	25.0777			0.865779			0.432890	−	0.901447i	$-0.357494\pi$
$839$	25.0777			0.865779			0.432890	+	0.901447i	$0.357494\pi$
$840$	−26.1510	−	14.0121i	−0.902296	−	0.483465i
$841$	−41.2438			−1.42220
$842$	−1.61992	−	0.347784i	−0.0558261	−	0.0119854i
$843$	−4.06107	−	28.2941i	−0.139871	−	0.974500i
$844$	9.74232	−	21.6433i	0.335345	−	0.744991i
$845$			31.0335i			1.06759i
$846$	−43.6359	+	3.21884i	−1.50023	+	0.110666i
$847$		−	30.9058i		−	1.06194i
$848$	33.8032	−	29.9401i	1.16081	−	1.02815i
$849$	0.273867	+	1.90807i	0.00939909	+	0.0654848i
$850$	0.748444	−	3.48612i	0.0256714	−	0.119573i
$851$	3.88821			0.133286
$852$	51.7837	+	14.9134i	1.77408	+	0.510925i
$853$	−17.3445			−0.593864			−0.296932	−	0.954899i	$-0.595963\pi$
$853$	−17.3445			−0.593864			−0.296932	+	0.954899i	$0.595963\pi$
$854$	4.69952	−	21.8896i	0.160814	−	0.749046i
$855$	−30.1062	+	8.82411i	−1.02961	+	0.301778i
$856$	−20.2433	−	14.8980i	−0.691902	−	0.509203i
$857$			26.7099i			0.912393i	0.889879	+	0.456196i	$0.150789\pi$
$857$			26.7099i			0.912393i	−0.889879	+	0.456196i	$0.849211\pi$
$858$	17.9888	+	1.24184i	0.614128	+	0.0423957i
$859$			55.4006i			1.89024i	0.326718	+	0.945122i	$0.394057\pi$
$859$			55.4006i			1.89024i	−0.326718	+	0.945122i	$0.605943\pi$
$860$	−58.9019	−	26.5136i	−2.00854	−	0.904108i
$861$	0.608598	−	0.0873526i	0.0207410	−	0.00297697i
$862$	−28.2219	−	6.05901i	−0.961240	−	0.206371i
$863$	37.6023			1.28000			0.639999	−	0.768376i	$-0.278935\pi$
$863$	37.6023			1.28000			0.639999	+	0.768376i	$0.278935\pi$
$864$	23.7556	+	17.3110i	0.808182	+	0.588933i
$865$	−8.45093			−0.287340
$866$	−12.4552	−	2.67404i	−0.423247	−	0.0908677i
$867$	−28.0383	+	4.02436i	−0.952231	+	0.136674i
$868$	9.25537	+	4.16614i	0.314148	+	0.141408i
$869$		−	32.4641i		−	1.10127i
$870$	58.4203	+	4.03299i	1.98064	+	0.136731i
$871$			1.45615i			0.0493397i
$872$	−7.37766	−	5.42955i	−0.249839	−	0.183868i
$873$	−32.0910	+	9.40588i	−1.08612	+	0.318341i
$874$	−2.75124	+	12.8148i	−0.0930622	+	0.433468i
$875$	−11.2859			−0.381533
$876$	−0.348722	−	0.100430i	−0.0117822	−	0.00339322i
$877$	36.3860			1.22867			0.614334	−	0.789046i	$-0.289425\pi$
$877$	36.3860			1.22867			0.614334	+	0.789046i	$0.289425\pi$
$878$	−6.33950	+	29.5284i	−0.213948	+	0.996534i
$879$	6.87221	+	47.8796i	0.231794	+	1.61494i
$880$	43.1790	−	38.2445i	1.45556	−	1.28922i
$881$			38.2118i			1.28739i	0.765283	+	0.643694i	$0.222599\pi$
$881$			38.2118i			1.28739i	−0.765283	+	0.643694i	$0.777401\pi$
$882$	−10.5457	+	0.777916i	−0.355093	+	0.0261938i
$883$		−	24.9656i		−	0.840160i	−0.907487	−	0.420080i	$-0.862002\pi$
$883$		−	24.9656i		−	0.840160i	0.907487	−	0.420080i	$-0.137998\pi$
$884$	0.960924	−	2.13476i	0.0323194	−	0.0717998i
$885$	3.20762	+	22.3480i	0.107823	+	0.751219i
$886$	−18.0909	−	3.88397i	−0.607776	−	0.130485i
$887$	19.0263			0.638842			0.319421	−	0.947613i	$-0.396512\pi$
$887$	19.0263			0.638842			0.319421	+	0.947613i	$0.396512\pi$
$888$	6.64172	+	3.55874i	0.222881	+	0.119423i
$889$	18.3492			0.615411
$890$	−26.4337	−	5.67511i	−0.886060	−	0.190230i
$891$	38.2996	−	24.5612i	1.28308	−	0.822830i
$892$	−2.92018	+	6.48738i	−0.0977747	+	0.217213i
$893$		−	37.8094i		−	1.26524i
$894$	3.84260	−	55.6623i	0.128516	−	1.86163i
$895$		−	66.0360i		−	2.20734i
$896$	−23.9221	+	2.16903i	−0.799181	+	0.0724622i
$897$	−6.31113	+	0.905842i	−0.210723	+	0.0302452i
$898$	8.34686	−	38.8783i	0.278538	−	1.29738i
$899$	−20.0336			−0.668159
$900$	−18.6400	−	2.58592i	−0.621334	−	0.0861972i
$901$	−9.07473			−0.302323
$902$	−0.250914	+	1.16872i	−0.00835454	+	0.0389140i
$903$	41.2147	−	5.91557i	1.37154	−	0.196858i
$904$	19.5089	−	26.5086i	0.648855	−	0.881662i
$905$		−	17.0544i		−	0.566909i
$906$	−3.10585	+	44.9901i	−0.103185	+	1.49470i
$907$			12.2295i			0.406076i	0.979171	+	0.203038i	$0.0650814\pi$
$907$			12.2295i			0.406076i	−0.979171	+	0.203038i	$0.934919\pi$
$908$	−14.3589	−	6.46340i	−0.476517	−	0.214495i
$909$	−6.33068	−	21.5991i	−0.209975	−	0.716395i
$910$	12.1934	+	2.61782i	0.404207	+	0.0867800i
$911$	−21.0362			−0.696959			−0.348479	−	0.937316i	$-0.613302\pi$
$911$	−21.0362			−0.696959			−0.348479	+	0.937316i	$0.613302\pi$
$912$	−16.4285	+	19.3718i	−0.544003	+	0.641463i
$913$	−57.7047			−1.90975
$914$	−37.6390	−	8.08079i	−1.24499	−	0.267289i
$915$	−5.23395	−	36.4657i	−0.173029	−	1.20552i
$916$	−17.3609	−	7.81469i	−0.573620	−	0.258205i
$917$		−	3.09997i		−	0.102370i
$918$	−1.26713	−	5.76960i	−0.0418216	−	0.190425i
$919$		−	49.5124i		−	1.63326i	−0.577158	−	0.816632i	$-0.695838\pi$
$919$		−	49.5124i		−	1.63326i	0.577158	−	0.816632i	$-0.304162\pi$
$920$	−12.0890	+	16.4264i	−0.398561	+	0.541563i
$921$	−6.89638	−	48.0481i	−0.227243	−	1.58324i
$922$	−5.43604	+	25.3202i	−0.179026	+	0.833875i
$923$	−22.6522			−0.745606
$924$	−10.2896	+	35.7285i	−0.338503	+	1.17538i
$925$	−4.82409			−0.158615
$926$	2.97669	−	13.8649i	0.0978201	−	0.455630i
$927$	−8.95445	−	30.5509i	−0.294103	−	1.00342i
$928$	41.2991	−	23.2850i	1.35571	−	0.764367i
$929$			51.0406i			1.67459i	0.546754	+	0.837293i	$0.315863\pi$
$929$			51.0406i			1.67459i	−0.546754	+	0.837293i	$0.684137\pi$
$930$	16.6616	+	1.15021i	0.546354	+	0.0377170i
$931$		−	9.13761i		−	0.299473i
$932$	−17.4652	+	38.8001i	−0.572091	+	1.27094i
$933$	−32.2094	+	4.62303i	−1.05449	+	0.151351i
$934$	−18.4293	−	3.95662i	−0.603024	−	0.129465i
$935$	−11.5917			−0.379091
$936$	−11.6095	−	4.22902i	−0.379470	−	0.138230i
$937$	26.2752			0.858372			0.429186	−	0.903216i	$-0.358800\pi$
$937$	26.2752			0.858372			0.429186	+	0.903216i	$0.358800\pi$
$938$	−2.93564	−	0.630258i	−0.0958519	−	0.0205787i
$939$	−39.8554	+	5.72048i	−1.30063	+	0.186681i
$940$	24.1496	−	53.6499i	0.787672	−	1.74987i
$941$		−	28.1175i		−	0.916603i	−0.888797	−	0.458301i	$-0.848458\pi$
$941$		−	28.1175i		−	0.916603i	0.888797	−	0.458301i	$-0.151542\pi$
$942$	−50.5580	−	3.49022i	−1.64727	−	0.113718i
$943$		−	0.422664i		−	0.0137638i
$944$	12.1196	+	13.6833i	0.394458	+	0.445353i
$945$	28.6339	−	13.0515i	0.931462	−	0.424566i
$946$	−16.9921	+	79.1463i	−0.552460	+	2.57327i
$947$	48.9353			1.59018			0.795092	−	0.606488i	$-0.207422\pi$
$947$	48.9353			1.59018			0.795092	+	0.606488i	$0.207422\pi$
$948$	−6.15633	+	21.3765i	−0.199948	+	0.694278i
$949$	0.152545			0.00495181
$950$	3.41346	−	15.8993i	0.110747	−	0.515842i
$951$	2.46343	+	17.1631i	0.0798821	+	0.556550i
$952$	3.88783	+	2.86123i	0.126005	+	0.0927331i
$953$		−	43.3385i		−	1.40387i	−0.712240	−	0.701936i	$-0.752319\pi$
$953$		−	43.3385i		−	1.40387i	0.712240	−	0.701936i	$-0.247681\pi$
$954$	3.52346	+	47.7654i	0.114076	+	1.54646i
$955$		−	35.0551i		−	1.13436i
$956$	−4.42090	−	1.98999i	−0.142982	−	0.0643608i
$957$	−10.4264	−	72.6425i	−0.337039	−	2.34820i
$958$	−10.4694	−	2.24769i	−0.338250	−	0.0726196i
$959$	32.2302			1.04077
$960$	−35.6845	+	16.9945i	−1.15171	+	0.548495i
$961$	25.2864			0.815690
$962$	−3.09682	−	0.664862i	−0.0998454	−	0.0214360i
$963$	25.5829	−	7.49834i	0.824397	−	0.241631i
$964$	−13.5071	−	6.07996i	−0.435033	−	0.195822i
$965$			6.11260i			0.196771i
$966$	0.905416	−	13.1155i	0.0291313	−	0.421984i
$967$			16.4142i			0.527846i	0.964544	+	0.263923i	$0.0850165\pi$
$967$			16.4142i			0.527846i	−0.964544	+	0.263923i	$0.914984\pi$
$968$	−33.1608	−	24.4046i	−1.06583	−	0.784392i
$969$	5.05271	−	0.725220i	0.162316	−	0.0232974i
$970$	9.43891	−	43.9649i	0.303065	−	1.41163i
$971$	−8.16524			−0.262035			−0.131017	−	0.991380i	$-0.541824\pi$
$971$	−8.16524			−0.262035			−0.131017	+	0.991380i	$0.541824\pi$
$972$	−29.8767	+	8.90980i	−0.958295	+	0.285782i
$973$	−14.8285			−0.475380
$974$	8.04096	−	37.4535i	0.257649	−	1.20009i
$975$	7.83020	−	1.12387i	0.250767	−	0.0359928i
$976$	−19.7757	−	22.3273i	−0.633006	−	0.714681i
$977$		−	8.80600i		−	0.281729i	−0.990029	−	0.140865i	$-0.955012\pi$
$977$		−	8.80600i		−	0.281729i	0.990029	−	0.140865i	$-0.0449882\pi$
$978$	−3.26327	+	47.2704i	−0.104348	+	1.51154i
$979$			33.8817i			1.08286i
$980$	5.83636	−	12.9659i	0.186436	−	0.414180i
$981$	9.32366	−	2.73276i	0.297681	−	0.0872504i
$982$	7.02631	+	1.50849i	0.224219	+	0.0481380i
$983$	5.32687			0.169901			0.0849504	−	0.996385i	$-0.472927\pi$
$983$	5.32687			0.169901			0.0849504	+	0.996385i	$0.472927\pi$
$984$	0.386849	−	0.721980i	0.0123323	−	0.0230159i
$985$	39.1332			1.24689
$986$	−9.31563	−	1.99999i	−0.296670	−	0.0636927i
$987$	5.38811	+	37.5397i	0.171505	+	1.19490i
$988$	4.38253	−	9.73610i	0.139427	−	0.309746i
$989$		−	28.6231i		−	0.910160i
$990$	4.50074	+	61.0139i	0.143043	+	1.93915i
$991$		−	4.36278i		−	0.138588i	−0.997596	−	0.0692941i	$-0.977925\pi$
$991$		−	4.36278i		−	0.138588i	0.997596	−	0.0692941i	$-0.0220747\pi$
$992$	11.7785	−	6.64091i	0.373969	−	0.210849i
$993$	2.02139	+	14.0833i	0.0641468	+	0.446920i
$994$	9.80445	−	45.6675i	0.310978	−	1.44848i
$995$	25.8337			0.818984
$996$	37.9967	+	10.9428i	1.20397	+	0.346737i
$997$	−31.9210			−1.01095			−0.505474	−	0.862842i	$-0.668682\pi$
$997$	−31.9210			−1.01095			−0.505474	+	0.862842i	$0.668682\pi$
$998$	4.73020	−	22.0325i	0.149732	−	0.697426i
$999$	−7.27231	+	3.31476i	−0.230086	+	0.104874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.9	✓	128
3.2	odd	2	inner	804.2.c.b.671.120	yes	128
4.3	odd	2	inner	804.2.c.b.671.119	yes	128
12.11	even	2	inner	804.2.c.b.671.10	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.9	✓	128	1.1	even	1	trivial
804.2.c.b.671.10	yes	128	12.11	even	2	inner
804.2.c.b.671.119	yes	128	4.3	odd	2	inner
804.2.c.b.671.120	yes	128	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38271 - 0.296856i) q^{2} +(-1.71448 + 0.246081i) q^{3} +(1.82375 + 0.820930i) q^{4} -2.85244i q^{5} +(2.44367 + 0.168697i) q^{6} -2.12311i q^{7} +(-2.27802 - 1.67650i) q^{8} +(2.87889 - 0.843802i) q^{9} +O(q^{10})\)	\(q+(-1.38271 - 0.296856i) q^{2} +(-1.71448 + 0.246081i) q^{3} +(1.82375 + 0.820930i) q^{4} -2.85244i q^{5} +(2.44367 + 0.168697i) q^{6} -2.12311i q^{7} +(-2.27802 - 1.67650i) q^{8} +(2.87889 - 0.843802i) q^{9} +(-0.846765 + 3.94409i) q^{10} +5.05538 q^{11} +(-3.32880 - 0.958677i) q^{12} +1.45615 q^{13} +(-0.630258 + 2.93564i) q^{14} +(0.701931 + 4.89046i) q^{15} +(2.65215 + 2.99435i) q^{16} -0.803856i q^{17} +(-4.23114 + 0.312114i) q^{18} -3.66618i q^{19} +(2.34165 - 5.20215i) q^{20} +(0.522456 + 3.64003i) q^{21} +(-6.99011 - 1.50072i) q^{22} +2.52796 q^{23} +(4.31817 + 2.31375i) q^{24} -3.13642 q^{25} +(-2.01342 - 0.432266i) q^{26} +(-4.72816 + 2.15512i) q^{27} +(1.74292 - 3.87203i) q^{28} +8.38116i q^{29} +(0.481197 - 6.97044i) q^{30} +2.39032i q^{31} +(-2.77825 - 4.92761i) q^{32} +(-8.66735 + 1.24403i) q^{33} +(-0.238630 + 1.11150i) q^{34} -6.05605 q^{35} +(5.94308 + 0.824479i) q^{36} +1.53809 q^{37} +(-1.08833 + 5.06925i) q^{38} +(-2.49654 + 0.358330i) q^{39} +(-4.78211 + 6.49791i) q^{40} -0.167196i q^{41} +(0.358161 - 5.18819i) q^{42} -11.3226i q^{43} +(9.21977 + 4.15011i) q^{44} +(-2.40690 - 8.21186i) q^{45} +(-3.49542 - 0.750439i) q^{46} +10.3130 q^{47} +(-5.28391 - 4.48110i) q^{48} +2.49241 q^{49} +(4.33675 + 0.931067i) q^{50} +(0.197814 + 1.37820i) q^{51} +(2.65565 + 1.19539i) q^{52} -11.2890i q^{53} +(7.17741 - 1.57632i) q^{54} -14.4202i q^{55} +(-3.55939 + 4.83648i) q^{56} +(0.902176 + 6.28559i) q^{57} +(2.48800 - 11.5887i) q^{58} +4.56971 q^{59} +(-2.73457 + 9.49522i) q^{60} -7.45650 q^{61} +(0.709581 - 3.30511i) q^{62} +(-1.79148 - 6.11219i) q^{63} +(2.37872 + 7.63817i) q^{64} -4.15357i q^{65} +(12.3537 + 0.852826i) q^{66} +1.00000i q^{67} +(0.659909 - 1.46603i) q^{68} +(-4.33413 + 0.622081i) q^{69} +(8.37373 + 1.79777i) q^{70} -15.5562 q^{71} +(-7.97279 - 2.90425i) q^{72} +0.104759 q^{73} +(-2.12672 - 0.456590i) q^{74} +(5.37734 - 0.771814i) q^{75} +(3.00968 - 6.68621i) q^{76} -10.7331i q^{77} +(3.55835 + 0.245647i) q^{78} -6.42169i q^{79} +(8.54120 - 7.56510i) q^{80} +(7.57600 - 4.85842i) q^{81} +(-0.0496331 + 0.231183i) q^{82} -11.4145 q^{83} +(-2.03538 + 7.06741i) q^{84} -2.29295 q^{85} +(-3.36119 + 15.6558i) q^{86} +(-2.06244 - 14.3693i) q^{87} +(-11.5162 - 8.47533i) q^{88} +6.70211i q^{89} +(0.890287 + 12.0691i) q^{90} -3.09156i q^{91} +(4.61037 + 2.07527i) q^{92} +(-0.588211 - 4.09815i) q^{93} +(-14.2599 - 3.06149i) q^{94} -10.4576 q^{95} +(5.97585 + 7.76461i) q^{96} -11.1470 q^{97} +(-3.44627 - 0.739887i) q^{98} +(14.5539 - 4.26574i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 128 q + 4 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{16} + 18 q^{18} - 8 q^{21} - 8 q^{22} - 24 q^{24} - 136 q^{25} + 14 q^{30} - 32 q^{33} + 34 q^{36} - 48 q^{37} + 16 q^{40} - 28 q^{42} - 16 q^{45} - 28 q^{46} - 22 q^{48} - 152 q^{49} + 8 q^{52} - 16 q^{54} - 32 q^{57} - 20 q^{58} - 14 q^{60} + 8 q^{61} + 16 q^{64} + 14 q^{66} + 56 q^{69} - 4 q^{70} - 8 q^{72} - 48 q^{73} - 36 q^{76} + 40 q^{78} + 44 q^{81} + 60 q^{82} + 46 q^{84} + 64 q^{85} - 28 q^{88} - 14 q^{90} + 32 q^{93} - 8 q^{96} + 64 q^{97}+O(q^{100}) \) 128 * q + 4 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^10 + 4 * q^12 - 8 * q^13 - 4 * q^16 + 18 * q^18 - 8 * q^21 - 8 * q^22 - 24 * q^24 - 136 * q^25 + 14 * q^30 - 32 * q^33 + 34 * q^36 - 48 * q^37 + 16 * q^40 - 28 * q^42 - 16 * q^45 - 28 * q^46 - 22 * q^48 - 152 * q^49 + 8 * q^52 - 16 * q^54 - 32 * q^57 - 20 * q^58 - 14 * q^60 + 8 * q^61 + 16 * q^64 + 14 * q^66 + 56 * q^69 - 4 * q^70 - 8 * q^72 - 48 * q^73 - 36 * q^76 + 40 * q^78 + 44 * q^81 + 60 * q^82 + 46 * q^84 + 64 * q^85 - 28 * q^88 - 14 * q^90 + 32 * q^93 - 8 * q^96 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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