LMFDB - Embedded newform 804.2.c.b.671.12

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			671.12
Character	$\chi$	$=$	804.671
Dual form			804.2.c.b.671.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37515 + 0.330103i) q^{2} +(0.355099 - 1.69526i) q^{3} +(1.78206 - 0.907880i) q^{4} -0.0453328i q^{5} +(0.0712965 + 2.44845i) q^{6} -2.82199i q^{7} +(-2.15091 + 1.83673i) q^{8} +(-2.74781 - 1.20397i) q^{9} +O(q^{10})$	\(q+(-1.37515 + 0.330103i) q^{2} +(0.355099 - 1.69526i) q^{3} +(1.78206 - 0.907880i) q^{4} -0.0453328i q^{5} +(0.0712965 + 2.44845i) q^{6} -2.82199i q^{7} +(-2.15091 + 1.83673i) q^{8} +(-2.74781 - 1.20397i) q^{9} +(0.0149645 + 0.0623394i) q^{10} +3.33857 q^{11} +(-0.906284 - 3.34345i) q^{12} -5.31881 q^{13} +(0.931548 + 3.88066i) q^{14} +(-0.0768509 - 0.0160976i) q^{15} +(2.35151 - 3.23580i) q^{16} -0.0462961i q^{17} +(4.17608 + 0.748576i) q^{18} -3.00472i q^{19} +(-0.0411568 - 0.0807860i) q^{20} +(-4.78401 - 1.00209i) q^{21} +(-4.59103 + 1.10207i) q^{22} -8.74554 q^{23} +(2.34996 + 4.29857i) q^{24} +4.99794 q^{25} +(7.31415 - 1.75575i) q^{26} +(-3.01678 + 4.23072i) q^{27} +(-2.56203 - 5.02897i) q^{28} -3.33779i q^{29} +(0.110995 - 0.00323207i) q^{30} -1.84815i q^{31} +(-2.16552 + 5.22595i) q^{32} +(1.18552 - 5.65975i) q^{33} +(0.0152825 + 0.0636640i) q^{34} -0.127929 q^{35} +(-5.98983 + 0.349132i) q^{36} +0.528333 q^{37} +(0.991868 + 4.13194i) q^{38} +(-1.88870 + 9.01677i) q^{39} +(0.0832644 + 0.0975068i) q^{40} +4.07375i q^{41} +(6.90952 - 0.201198i) q^{42} -0.346936i q^{43} +(5.94955 - 3.03102i) q^{44} +(-0.0545793 + 0.124566i) q^{45} +(12.0264 - 2.88693i) q^{46} -0.457301 q^{47} +(-4.65051 - 5.13544i) q^{48} -0.963647 q^{49} +(-6.87291 + 1.64984i) q^{50} +(-0.0784839 - 0.0164397i) q^{51} +(-9.47846 + 4.82884i) q^{52} +2.89403i q^{53} +(2.75195 - 6.81372i) q^{54} -0.151347i q^{55} +(5.18325 + 6.06985i) q^{56} +(-5.09379 - 1.06697i) q^{57} +(1.10182 + 4.58996i) q^{58} -0.226764 q^{59} +(-0.151568 + 0.0410844i) q^{60} -6.11785 q^{61} +(0.610078 + 2.54147i) q^{62} +(-3.39759 + 7.75430i) q^{63} +(1.25281 - 7.90129i) q^{64} +0.241117i q^{65} +(0.238029 + 8.17433i) q^{66} +1.00000i q^{67} +(-0.0420313 - 0.0825027i) q^{68} +(-3.10553 + 14.8260i) q^{69} +(0.175921 - 0.0422297i) q^{70} -7.18463 q^{71} +(8.12166 - 2.45737i) q^{72} -5.00203 q^{73} +(-0.726537 + 0.174404i) q^{74} +(1.77476 - 8.47281i) q^{75} +(-2.72793 - 5.35461i) q^{76} -9.42143i q^{77} +(-0.379213 - 13.0229i) q^{78} -15.3051i q^{79} +(-0.146688 - 0.106600i) q^{80} +(6.10092 + 6.61656i) q^{81} +(-1.34476 - 5.60201i) q^{82} -14.2834 q^{83} +(-9.43519 + 2.55753i) q^{84} -0.00209873 q^{85} +(0.114525 + 0.477088i) q^{86} +(-5.65843 - 1.18525i) q^{87} +(-7.18096 + 6.13207i) q^{88} +0.699578i q^{89} +(0.0339351 - 0.189313i) q^{90} +15.0097i q^{91} +(-15.5851 + 7.93990i) q^{92} +(-3.13309 - 0.656274i) q^{93} +(0.628857 - 0.150956i) q^{94} -0.136213 q^{95} +(8.09036 + 5.52685i) q^{96} +2.90757 q^{97} +(1.32516 - 0.318103i) q^{98} +(-9.17376 - 4.01954i) 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 $

$2$	−1.37515	+	0.330103i	−0.972377	+	0.233418i
$2$	−1.37515	+	0.330103i	−0.972377	+	0.233418i
$3$	0.355099	−	1.69526i	0.205016	−	0.978759i
$3$	0.355099	−	1.69526i	0.205016	−	0.978759i
$4$	1.78206	−	0.907880i	0.891032	−	0.453940i
$5$		−	0.0453328i		−	0.0202735i	−0.999949	−	0.0101367i	$-0.996773\pi$
$5$		−	0.0453328i		−	0.0202735i	0.999949	−	0.0101367i	$-0.00322668\pi$
$6$	0.0712965	+	2.44845i	0.0291067	+	0.999576i
$7$		−	2.82199i		−	1.06661i	−0.845922	−	0.533307i	$-0.820949\pi$
$7$		−	2.82199i		−	1.06661i	0.845922	−	0.533307i	$-0.179051\pi$
$8$	−2.15091	+	1.83673i	−0.760461	+	0.649384i
$9$	−2.74781	−	1.20397i	−0.915937	−	0.401323i
$10$	0.0149645	+	0.0623394i	0.00473219	+	0.0197134i
$11$	3.33857			1.00662			0.503309	−	0.864107i	$-0.332116\pi$
$11$	3.33857			1.00662			0.503309	+	0.864107i	$0.332116\pi$
$12$	−0.906284	−	3.34345i	−0.261622	−	0.965171i
$13$	−5.31881			−1.47517			−0.737586	−	0.675253i	$-0.764035\pi$
$13$	−5.31881			−1.47517			−0.737586	+	0.675253i	$0.764035\pi$
$14$	0.931548	+	3.88066i	0.248967	+	1.03715i
$15$	−0.0768509	−	0.0160976i	−0.0198428	−	0.00415639i
$16$	2.35151	−	3.23580i	0.587877	−	0.808951i
$17$		−	0.0462961i		−	0.0112285i	−0.999984	−	0.00561423i	$-0.998213\pi$
$17$		−	0.0462961i		−	0.0112285i	0.999984	−	0.00561423i	$-0.00178707\pi$
$18$	4.17608	+	0.748576i	0.984311	+	0.176441i
$19$		−	3.00472i		−	0.689331i	−0.938726	−	0.344666i	$-0.887992\pi$
$19$		−	3.00472i		−	0.689331i	0.938726	−	0.344666i	$-0.112008\pi$
$20$	−0.0411568	−	0.0807860i	−0.00920294	−	0.0180643i
$21$	−4.78401	−	1.00209i	−1.04396	−	0.218673i
$22$	−4.59103	+	1.10207i	−0.978811	+	0.234963i
$23$	−8.74554			−1.82357			−0.911786	−	0.410666i	$-0.865296\pi$
$23$	−8.74554			−1.82357			−0.911786	+	0.410666i	$0.865296\pi$
$24$	2.34996	+	4.29857i	0.479683	+	0.877442i
$25$	4.99794			0.999589
$26$	7.31415	−	1.75575i	1.43442	−	0.344332i
$27$	−3.01678	+	4.23072i	−0.580580	+	0.814203i
$28$	−2.56203	−	5.02897i	−0.484179	−	0.950387i
$29$		−	3.33779i		−	0.619813i	−0.950767	−	0.309906i	$-0.899702\pi$
$29$		−	3.33779i		−	0.619813i	0.950767	−	0.309906i	$-0.100298\pi$
$30$	0.110995	−	0.00323207i	0.0202649	−	0.000590093i
$31$		−	1.84815i		−	0.331937i	−0.986131	−	0.165968i	$-0.946925\pi$
$31$		−	1.84815i		−	0.331937i	0.986131	−	0.165968i	$-0.0530750\pi$
$32$	−2.16552	+	5.22595i	−0.382814	+	0.923825i
$33$	1.18552	−	5.65975i	0.206373	−	0.985235i
$34$	0.0152825	+	0.0636640i	0.00262092	+	0.0109183i
$35$	−0.127929			−0.0216239
$36$	−5.98983	+	0.349132i	−0.998306	+	0.0581887i
$37$	0.528333			0.0868575			0.0434287	−	0.999057i	$-0.486172\pi$
$37$	0.528333			0.0868575			0.0434287	+	0.999057i	$0.486172\pi$
$38$	0.991868	+	4.13194i	0.160902	+	0.670289i
$39$	−1.88870	+	9.01677i	−0.302435	+	1.44384i
$40$	0.0832644	+	0.0975068i	0.0131653	+	0.0154172i
$41$			4.07375i			0.636213i	0.948055	+	0.318107i	$0.103047\pi$
$41$			4.07375i			0.636213i	−0.948055	+	0.318107i	$0.896953\pi$
$42$	6.90952	−	0.201198i	1.06616	−	0.0310456i
$43$		−	0.346936i		−	0.0529073i	−0.999650	−	0.0264536i	$-0.991579\pi$
$43$		−	0.346936i		−	0.0529073i	0.999650	−	0.0264536i	$-0.00842143\pi$
$44$	5.94955	−	3.03102i	0.896929	−	0.456944i
$45$	−0.0545793	+	0.124566i	−0.00813621	+	0.0185692i
$46$	12.0264	−	2.88693i	1.77320	−	0.425654i
$47$	−0.457301			−0.0667042			−0.0333521	−	0.999444i	$-0.510618\pi$
$47$	−0.457301			−0.0667042			−0.0333521	+	0.999444i	$0.510618\pi$
$48$	−4.65051	−	5.13544i	−0.671243	−	0.741237i
$49$	−0.963647			−0.137664
$50$	−6.87291	+	1.64984i	−0.971977	+	0.233322i
$51$	−0.0784839	−	0.0164397i	−0.0109899	−	0.00230202i
$52$	−9.47846	+	4.82884i	−1.31443	+	0.669640i
$53$			2.89403i			0.397526i	0.980048	+	0.198763i	$0.0636924\pi$
$53$			2.89403i			0.397526i	−0.980048	+	0.198763i	$0.936308\pi$
$54$	2.75195	−	6.81372i	0.374493	−	0.927230i
$55$		−	0.151347i		−	0.0204076i
$56$	5.18325	+	6.06985i	0.692641	+	0.811118i
$57$	−5.09379	−	1.06697i	−0.674689	−	0.141324i
$58$	1.10182	+	4.58996i	0.144675	+	0.602691i
$59$	−0.226764			−0.0295222			−0.0147611	−	0.999891i	$-0.504699\pi$
$59$	−0.226764			−0.0295222			−0.0147611	+	0.999891i	$0.504699\pi$
$60$	−0.151568	+	0.0410844i	−0.0195673	+	0.00530398i
$61$	−6.11785			−0.783310			−0.391655	−	0.920112i	$-0.628097\pi$
$61$	−6.11785			−0.783310			−0.391655	+	0.920112i	$0.628097\pi$
$62$	0.610078	+	2.54147i	0.0774800	+	0.322767i
$63$	−3.39759	+	7.75430i	−0.428056	+	0.976950i
$64$	1.25281	−	7.90129i	0.156602	−	0.987662i
$65$			0.241117i			0.0299069i
$66$	0.238029	+	8.17433i	0.0292993	+	1.00619i
$67$			1.00000i			0.122169i
$67$			1.00000i			0.122169i
$68$	−0.0420313	−	0.0825027i	−0.00509705	−	0.0100049i
$69$	−3.10553	+	14.8260i	−0.373862	+	1.78484i
$70$	0.175921	−	0.0422297i	0.0210266	−	0.00504741i
$71$	−7.18463			−0.852659			−0.426329	−	0.904568i	$-0.640194\pi$
$71$	−7.18463			−0.852659			−0.426329	+	0.904568i	$0.640194\pi$
$72$	8.12166	−	2.45737i	0.957147	−	0.289604i
$73$	−5.00203			−0.585443			−0.292722	−	0.956198i	$-0.594561\pi$
$73$	−5.00203			−0.585443			−0.292722	+	0.956198i	$0.594561\pi$
$74$	−0.726537	+	0.174404i	−0.0844582	+	0.0202741i
$75$	1.77476	−	8.47281i	0.204932	−	0.978356i
$76$	−2.72793	−	5.35461i	−0.312915	−	0.614216i
$77$		−	9.42143i		−	1.07367i
$78$	−0.379213	−	13.0229i	−0.0429374	−	1.47455i
$79$		−	15.3051i		−	1.72196i	−0.508640	−	0.860979i	$-0.669852\pi$
$79$		−	15.3051i		−	1.72196i	0.508640	−	0.860979i	$-0.330148\pi$
$80$	−0.146688	−	0.106600i	−0.0164002	−	0.0119183i
$81$	6.10092	+	6.61656i	0.677880	+	0.735173i
$82$	−1.34476	−	5.60201i	−0.148504	−	0.618639i
$83$	−14.2834			−1.56781			−0.783904	−	0.620881i	$-0.786775\pi$
$83$	−14.2834			−1.56781			−0.783904	+	0.620881i	$0.786775\pi$
$84$	−9.43519	+	2.55753i	−1.02946	+	0.279049i
$85$	−0.00209873			−0.000227640
$86$	0.114525	+	0.477088i	0.0123495	+	0.0514458i
$87$	−5.65843	−	1.18525i	−0.606647	−	0.127072i
$88$	−7.18096	+	6.13207i	−0.765493	+	0.653681i
$89$			0.699578i			0.0741551i	0.999312	+	0.0370776i	$0.0118049\pi$
$89$			0.699578i			0.0741551i	−0.999312	+	0.0370776i	$0.988195\pi$
$90$	0.0339351	−	0.189313i	0.00357707	−	0.0199554i
$91$			15.0097i			1.57344i
$92$	−15.5851	+	7.93990i	−1.62486	+	0.827792i
$93$	−3.13309	−	0.656274i	−0.324886	−	0.0680524i
$94$	0.628857	−	0.150956i	0.0648616	−	0.0155700i
$95$	−0.136213			−0.0139751
$96$	8.09036	+	5.52685i	0.825719	+	0.564082i
$97$	2.90757			0.295219			0.147610	−	0.989046i	$-0.452842\pi$
$97$	2.90757			0.295219			0.147610	+	0.989046i	$0.452842\pi$
$98$	1.32516	−	0.318103i	0.133861	−	0.0321332i
$99$	−9.17376	−	4.01954i	−0.921998	−	0.403979i
$100$	8.90666	−	4.53754i	0.890666	−	0.453754i
$101$		−	18.8879i		−	1.87941i	−0.341982	−	0.939706i	$-0.611098\pi$
$101$		−	18.8879i		−	1.87941i	0.341982	−	0.939706i	$-0.388902\pi$
$102$	0.113354	−	0.00330075i	0.0112237	−	0.000326823i
$103$			14.3849i			1.41739i	0.705516	+	0.708694i	$0.250715\pi$
$103$			14.3849i			1.41739i	−0.705516	+	0.708694i	$0.749285\pi$
$104$	11.4403	−	9.76924i	1.12181	−	0.957953i
$105$	−0.0454274	+	0.216873i	−0.00443326	+	0.0211646i
$106$	−0.955328	−	3.97972i	−0.0927897	−	0.386545i
$107$	−0.659701			−0.0637757			−0.0318878	−	0.999491i	$-0.510152\pi$
$107$	−0.659701			−0.0637757			−0.0318878	+	0.999491i	$0.510152\pi$
$108$	−1.53511	+	10.2783i	−0.147716	+	0.989030i
$109$	11.4114			1.09301			0.546505	−	0.837456i	$-0.315958\pi$
$109$	11.4114			1.09301			0.546505	+	0.837456i	$0.315958\pi$
$110$	0.0499600	+	0.208124i	0.00476350	+	0.0198439i
$111$	0.187610	−	0.895662i	0.0178072	−	0.0850125i
$112$	−9.13141	−	6.63594i	−0.862837	−	0.627037i
$113$		−	9.58855i		−	0.902015i	−0.892520	−	0.451007i	$-0.851065\pi$
$113$		−	9.58855i		−	0.902015i	0.892520	−	0.451007i	$-0.148935\pi$
$114$	7.35692	−	0.214226i	0.689039	−	0.0200641i
$115$			0.396460i			0.0369701i
$116$	−3.03032	−	5.94816i	−0.281358	−	0.552273i
$117$	14.6151	+	6.40368i	1.35116	+	0.592021i
$118$	0.311834	−	0.0748555i	0.0287067	−	0.00689101i
$119$	−0.130647			−0.0119764
$120$	0.194866	−	0.106530i	0.0177888	−	0.00972483i
$121$	0.146066			0.0132787
$122$	8.41295	−	2.01952i	0.761673	−	0.182839i
$123$	6.90607	+	1.44658i	0.622699	+	0.130434i
$124$	−1.67789	−	3.29351i	−0.150679	−	0.295766i
$125$		−	0.453235i		−	0.0405386i
$126$	2.11248	−	11.7849i	0.188194	−	1.04988i
$127$		−	6.92851i		−	0.614806i	−0.951579	−	0.307403i	$-0.900540\pi$
$127$		−	6.92851i		−	0.614806i	0.951579	−	0.307403i	$-0.0994600\pi$
$128$	0.885434	+	11.2790i	0.0782620	+	0.996933i
$129$	−0.588147	−	0.123197i	−0.0517834	−	0.0108469i
$130$	−0.0795933	−	0.331571i	−0.00698080	−	0.0290807i
$131$	0.832599			0.0727445			0.0363723	−	0.999338i	$-0.488420\pi$
$131$	0.832599			0.0727445			0.0363723	+	0.999338i	$0.488420\pi$
$132$	−3.02570	−	11.1623i	−0.263353	−	0.971557i
$133$	−8.47931			−0.735250
$134$	−0.330103	−	1.37515i	−0.0285165	−	0.118795i
$135$	0.191791	+	0.136759i	0.0165067	+	0.0117704i
$136$	0.0850337	+	0.0995787i	0.00729158	+	0.00853880i
$137$		−	4.92259i		−	0.420565i	−0.977641	−	0.210282i	$-0.932562\pi$
$137$		−	4.92259i		−	0.420565i	0.977641	−	0.210282i	$-0.0674384\pi$
$138$	−0.623527	−	21.4130i	−0.0530781	−	1.82280i
$139$		−	6.30934i		−	0.535151i	−0.963537	−	0.267576i	$-0.913777\pi$
$139$		−	6.30934i		−	0.535151i	0.963537	−	0.267576i	$-0.0862225\pi$
$140$	−0.227978	+	0.116144i	−0.0192676	+	0.00981598i
$141$	−0.162387	+	0.775244i	−0.0136755	+	0.0652873i
$142$	9.87993	−	2.37167i	0.829105	−	0.199026i
$143$	−17.7572			−1.48493
$144$	−10.3573	+	6.06023i	−0.863108	+	0.505019i
$145$	−0.151312			−0.0125658
$146$	6.87853	−	1.65118i	0.569271	−	0.136653i
$147$	−0.342190	+	1.63363i	−0.0282233	+	0.134740i
$148$	0.941524	−	0.479663i	0.0773928	−	0.0394281i
$149$		−	17.5015i		−	1.43378i	−0.697187	−	0.716889i	$-0.745565\pi$
$149$		−	17.5015i		−	1.43378i	0.697187	−	0.716889i	$-0.254435\pi$
$150$	0.356336	+	12.2372i	0.0290947	+	0.999165i
$151$		−	14.7325i		−	1.19891i	−0.800408	−	0.599455i	$-0.795384\pi$
$151$		−	14.7325i		−	1.19891i	0.800408	−	0.599455i	$-0.204616\pi$
$152$	5.51888	+	6.46289i	0.447640	+	0.524209i
$153$	−0.0557391	+	0.127213i	−0.00450624	+	0.0102846i
$154$	3.11004	+	12.9559i	0.250614	+	1.04401i
$155$	−0.0837817			−0.00672951
$156$	4.82035	+	17.7832i	0.385937	+	1.42379i
$157$	12.3226			0.983451			0.491726	−	0.870750i	$-0.336366\pi$
$157$	12.3226			0.983451			0.491726	+	0.870750i	$0.336366\pi$
$158$	5.05226	+	21.0468i	0.401936	+	1.67439i
$159$	4.90614	+	1.02767i	0.389082	+	0.0814993i
$160$	0.236907	+	0.0981693i	0.0187291	+	0.00776096i
$161$			24.6799i			1.94505i
$162$	−10.5738	−	7.08481i	−0.830757	−	0.556636i
$163$			21.0635i			1.64982i	0.565261	+	0.824912i	$0.308775\pi$
$163$			21.0635i			1.64982i	−0.565261	+	0.824912i	$0.691225\pi$
$164$	3.69848	+	7.25969i	0.288803	+	0.566887i
$165$	−0.256572	−	0.0537431i	−0.0199741	−	0.00418390i
$166$	19.6418	−	4.71500i	1.52450	−	0.365955i
$167$	21.7501			1.68308			0.841538	−	0.540198i	$-0.181651\pi$
$167$	21.7501			1.68308			0.841538	+	0.540198i	$0.181651\pi$
$168$	12.1305	−	6.63156i	0.935891	−	0.511636i
$169$	15.2898			1.17614
$170$	0.00288607		0.000692798i	0.000221351		5.31352e-5i
$171$	−3.61760	+	8.25641i	−0.276644	+	0.631384i
$172$	−0.314976	−	0.618262i	−0.0240167	−	0.0471421i
$173$			25.8893i			1.96833i	0.177259	+	0.984164i	$0.443277\pi$
$173$			25.8893i			1.96833i	−0.177259	+	0.984164i	$0.556723\pi$
$174$	8.17243	−	0.237973i	0.619550	−	0.0180407i
$175$		−	14.1042i		−	1.06617i
$176$	7.85067	−	10.8030i	0.591767	−	0.814304i
$177$	−0.0805237	+	0.384424i	−0.00605253	+	0.0288951i
$178$	−0.230933	−	0.962023i	−0.0173091	−	0.0721067i
$179$	1.87615			0.140230			0.0701149	−	0.997539i	$-0.477663\pi$
$179$	1.87615			0.140230			0.0701149	+	0.997539i	$0.477663\pi$
$180$	0.0158272	+	0.271536i	0.00117969	+	0.0202391i
$181$	10.8705			0.808001			0.404000	−	0.914759i	$-0.367619\pi$
$181$	10.8705			0.808001			0.404000	+	0.914759i	$0.367619\pi$
$182$	−4.95473	−	20.6405i	−0.367269	−	1.52998i
$183$	−2.17244	+	10.3713i	−0.160591	+	0.766672i
$184$	18.8109	−	16.0632i	1.38675	−	1.18420i
$185$		−	0.0239508i		−	0.00176090i
$186$	4.52510	−	0.131766i	0.331796	−	0.00966158i
$187$		−	0.154563i		−	0.0113028i
$188$	−0.814940	+	0.415175i	−0.0594356	+	0.0302797i
$189$	11.9391	+	8.51334i	0.868440	+	0.619255i
$190$	0.187313	−	0.0449642i	0.0135891	−	0.00326204i
$191$	−4.00209			−0.289581			−0.144791	−	0.989462i	$-0.546251\pi$
$191$	−4.00209			−0.289581			−0.144791	+	0.989462i	$0.546251\pi$
$192$	−12.9499	−	4.92959i	−0.934577	−	0.355762i
$193$	19.1089			1.37549			0.687743	−	0.725954i	$-0.258602\pi$
$193$	19.1089			1.37549			0.687743	+	0.725954i	$0.258602\pi$
$194$	−3.99834	+	0.959798i	−0.287064	+	0.0689094i
$195$	0.408756	+	0.0856203i	0.0292716	+	0.00613139i
$196$	−1.71728	+	0.874876i	−0.122663	+	0.0624911i
$197$		−	3.18758i		−	0.227105i	−0.993532	−	0.113553i	$-0.963777\pi$
$197$		−	3.18758i		−	0.227105i	0.993532	−	0.113553i	$-0.0362231\pi$
$198$	13.9421	+	2.49918i	0.990825	+	0.177609i
$199$			17.5383i			1.24326i	0.783313	+	0.621628i	$0.213528\pi$
$199$			17.5383i			1.24326i	−0.783313	+	0.621628i	$0.786472\pi$
$200$	−10.7501	+	9.17990i	−0.760148	+	0.649117i
$201$	1.69526	+	0.355099i	0.119574	+	0.0250467i
$202$	6.23494	+	25.9736i	0.438689	+	1.82750i
$203$	−9.41923			−0.661101
$204$	−0.154789	+	0.0419574i	−0.0108374	+	0.00293761i
$205$	0.184675			0.0128982
$206$	−4.74850	−	19.7814i	−0.330844	−	1.37824i
$207$	24.0311	+	10.5294i	1.67028	+	0.731841i
$208$	−12.5072	+	17.2106i	−0.867220	+	1.19334i
$209$		−	10.0315i		−	0.693893i
$210$	−0.00912089	−	0.313228i	−0.000629401	−	0.0216148i
$211$		−	3.20034i		−	0.220321i	−0.993914	−	0.110160i	$-0.964864\pi$
$211$		−	3.20034i		−	0.220321i	0.993914	−	0.110160i	$-0.0351364\pi$
$212$	2.62744	+	5.15735i	0.180453	+	0.354208i
$213$	−2.55125	+	12.1798i	−0.174809	+	0.834547i
$214$	0.907186	−	0.217769i	0.0620140	−	0.0148864i
$215$	−0.0157276			−0.00107261
$216$	−1.28189	−	14.6409i	−0.0872214	−	0.996189i
$217$	−5.21545			−0.354048
$218$	−15.6923	+	3.76692i	−1.06282	+	0.255128i
$219$	−1.77621	+	8.47974i	−0.120025	+	0.573008i
$220$	−0.137405	−	0.269710i	−0.00926384	−	0.0181838i
$221$			0.246240i			0.0165639i
$222$	0.0376683	+	1.29360i	0.00252813	+	0.0868207i
$223$		−	23.6656i		−	1.58476i	−0.610026	−	0.792382i	$-0.708841\pi$
$223$		−	23.6656i		−	1.58476i	0.610026	−	0.792382i	$-0.291159\pi$
$224$	14.7476	+	6.11109i	0.985365	+	0.408314i
$225$	−13.7334	−	6.01737i	−0.915560	−	0.401158i
$226$	3.16521	+	13.1857i	0.210546	+	0.877098i
$227$	25.7062			1.70618			0.853091	−	0.521762i	$-0.174725\pi$
$227$	25.7062			1.70618			0.853091	+	0.521762i	$0.174725\pi$
$228$	−10.0461	+	2.72313i	−0.665322	+	0.180344i
$229$	−11.9383			−0.788906			−0.394453	−	0.918916i	$-0.629066\pi$
$229$	−11.9383			−0.788906			−0.394453	+	0.918916i	$0.629066\pi$
$230$	−0.130873	−	0.545191i	−0.00862948	−	0.0359489i
$231$	−15.9718	−	3.34554i	−1.05087	−	0.220120i
$232$	6.13064	+	7.17929i	0.402496	+	0.471344i
$233$		−	17.8239i		−	1.16769i	−0.811867	−	0.583843i	$-0.801548\pi$
$233$		−	17.8239i		−	1.16769i	0.811867	−	0.583843i	$-0.198452\pi$
$234$	−22.2118	−	3.98153i	−1.45203	−	0.260281i
$235$			0.0207308i			0.00135233i
$236$	−0.404108	+	0.205875i	−0.0263052	+	0.0134013i
$237$	−25.9461	−	5.43482i	−1.68538	−	0.353030i
$238$	0.179659	−	0.0431270i	0.0116456	−	0.00279551i
$239$	22.2718			1.44064			0.720320	−	0.693642i	$-0.243995\pi$
$239$	22.2718			1.44064			0.720320	+	0.693642i	$0.243995\pi$
$240$	−0.232804	+	0.210821i	−0.0150274	+	0.0136084i
$241$	19.3681			1.24761			0.623804	−	0.781580i	$-0.285586\pi$
$241$	19.3681			1.24761			0.623804	+	0.781580i	$0.285586\pi$
$242$	−0.200863	+	0.0482169i	−0.0129119	+	0.00309950i
$243$	13.3832	−	7.99311i	0.858533	−	0.512758i
$244$	−10.9024	+	5.55428i	−0.697955	+	0.355576i
$245$			0.0436848i			0.00279092i
$246$	−9.97439	+	0.290445i	−0.635944	+	0.0185181i
$247$			15.9816i			1.01688i
$248$	3.39455	+	3.97519i	0.215554	+	0.252425i
$249$	−5.07202	+	24.2141i	−0.321426	+	1.53451i
$250$	0.149614	+	0.623265i	0.00946243	+	0.0394188i
$251$	−12.1468			−0.766701			−0.383350	−	0.923603i	$-0.625230\pi$
$251$	−12.1468			−0.766701			−0.383350	+	0.923603i	$0.625230\pi$
$252$	0.985249	+	16.9033i	0.0620649	+	1.06481i
$253$	−29.1976			−1.83564
$254$	2.28712	+	9.52773i	0.143507	+	0.597823i
$255$	−0.000745258		0.00355790i	−4.66699e−5		0.000222804i
$256$	−4.94083	−	15.2180i	−0.308802	−	0.951126i
$257$		−	22.4036i		−	1.39750i	−0.715367	−	0.698748i	$-0.753741\pi$
$257$		−	22.4036i		−	1.39750i	0.715367	−	0.698748i	$-0.246259\pi$
$258$	0.849456	−	0.0247353i	0.0528848	−	0.00153996i
$259$		−	1.49095i		−	0.0926433i
$260$	0.218905	+	0.429686i	0.0135759	+	0.0266480i
$261$	−4.01860	+	9.17162i	−0.248745	+	0.567709i
$262$	−1.14495	+	0.274843i	−0.0707351	+	0.0169799i
$263$	26.2457			1.61838			0.809189	−	0.587548i	$-0.199907\pi$
$263$	26.2457			1.61838			0.809189	+	0.587548i	$0.199907\pi$
$264$	7.84550	+	14.3511i	0.482857	+	0.883248i
$265$	0.131195			0.00805923
$266$	11.6603	−	2.79904i	0.714940	−	0.171620i
$267$	1.18597	+	0.248419i	0.0725800	+	0.0152030i
$268$	0.907880	+	1.78206i	0.0554576	+	0.108857i
$269$			16.0941i			0.981276i	0.871364	+	0.490638i	$0.163236\pi$
$269$			16.0941i			0.981276i	−0.871364	+	0.490638i	$0.836764\pi$
$270$	−0.308885	−	0.124754i	−0.0187982	−	0.00759227i
$271$		−	13.4888i		−	0.819383i	−0.912224	−	0.409692i	$-0.865636\pi$
$271$		−	13.4888i		−	0.819383i	0.912224	−	0.409692i	$-0.134364\pi$
$272$	−0.149805	−	0.108866i	−0.00908327	−	0.00660095i
$273$	25.4453	+	5.32991i	1.54002	+	0.322581i
$274$	1.62496	+	6.76928i	0.0981674	+	0.408947i
$275$	16.6860			1.00620
$276$	7.92594	+	29.2403i	0.477086	+	1.76006i
$277$	−13.5911			−0.816609			−0.408304	−	0.912846i	$-0.633880\pi$
$277$	−13.5911			−0.816609			−0.408304	+	0.912846i	$0.633880\pi$
$278$	2.08273	+	8.67628i	0.124914	+	0.520369i
$279$	−2.22511	+	5.07835i	−0.133214	+	0.304033i
$280$	0.275163	−	0.234971i	0.0164442	−	0.0140422i
$281$		−	14.2655i		−	0.851007i	−0.904957	−	0.425504i	$-0.860097\pi$
$281$		−	14.2655i		−	0.851007i	0.904957	−	0.425504i	$-0.139903\pi$
$282$	−0.0326040	−	1.11968i	−0.00194154	−	0.0666760i
$283$		−	2.05619i		−	0.122228i	−0.998131	−	0.0611138i	$-0.980535\pi$
$283$		−	2.05619i		−	0.122228i	0.998131	−	0.0611138i	$-0.0194653\pi$
$284$	−12.8035	+	6.52278i	−0.759746	+	0.387056i
$285$	−0.0483689	+	0.230916i	−0.00286513	+	0.0136783i
$286$	24.4188	−	5.86171i	1.44392	−	0.346610i
$287$	11.4961			0.678594
$288$	12.2423	−	11.7527i	0.721386	−	0.692534i
$289$	16.9979			0.999874
$290$	0.208076	−	0.0499484i	0.0122186	−	0.00293307i
$291$	1.03248	−	4.92909i	0.0605248	−	0.288948i
$292$	−8.91394	+	4.54124i	−0.521649	+	0.265756i
$293$		−	30.5801i		−	1.78651i	−0.449554	−	0.893253i	$-0.648417\pi$
$293$		−	30.5801i		−	1.78651i	0.449554	−	0.893253i	$-0.351583\pi$
$294$	−0.0687047	−	2.35944i	−0.00400694	−	0.137606i
$295$			0.0102799i			0.000598517i
$296$	−1.13640	+	0.970408i	−0.0660517	+	0.0564038i
$297$	−10.0718	+	14.1246i	−0.584422	+	0.819591i
$298$	5.77729	+	24.0671i	0.334669	+	1.39417i
$299$	46.5159			2.69008
$300$	−4.52956	−	16.7104i	−0.261514	−	0.964774i
$301$	−0.979051			−0.0564316
$302$	4.86322	+	20.2593i	0.279847	+	1.16579i
$303$	−32.0198	−	6.70706i	−1.83949	−	0.385310i
$304$	−9.72270	−	7.06563i	−0.557635	−	0.405242i
$305$			0.277339i			0.0158804i
$306$	0.0346562	−	0.193336i	0.00198116	−	0.0110523i
$307$			17.9892i			1.02670i	0.858181	+	0.513348i	$0.171595\pi$
$307$			17.9892i			1.02670i	−0.858181	+	0.513348i	$0.828405\pi$
$308$	−8.55353	−	16.7896i	−0.487383	−	0.956676i
$309$	24.3862	+	5.10807i	1.38728	+	0.290588i
$310$	0.115212	−	0.0276566i	0.00654361	−	0.00157079i
$311$	−26.8825			−1.52436			−0.762182	−	0.647363i	$-0.775872\pi$
$311$	−26.8825			−1.52436			−0.762182	+	0.647363i	$0.775872\pi$
$312$	−12.4990	−	22.8633i	−0.707615	−	1.29438i
$313$	−14.6195			−0.826344			−0.413172	−	0.910653i	$-0.635579\pi$
$313$	−14.6195			−0.826344			−0.413172	+	0.910653i	$0.635579\pi$
$314$	−16.9454	+	4.06773i	−0.956285	+	0.229555i
$315$	0.351524	+	0.154022i	0.0198062	+	0.00867818i
$316$	−13.8952	−	27.2747i	−0.781666	−	1.53432i
$317$		−	16.4279i		−	0.922683i	−0.887223	−	0.461341i	$-0.847368\pi$
$317$		−	16.4279i		−	0.922683i	0.887223	−	0.461341i	$-0.152632\pi$
$318$	−7.08590	+	0.206335i	−0.397358	+	0.0115707i
$319$		−	11.1435i		−	0.623914i
$320$	−0.358188	−	0.0567936i	−0.0200233	−	0.00317486i
$321$	−0.234259	+	1.11836i	−0.0130751	+	0.0624210i
$322$	−8.14689	−	33.9385i	−0.454008	−	1.89132i
$323$	−0.139107			−0.00774013
$324$	16.8793	+	6.25222i	0.937737	+	0.347346i
$325$	−26.5831			−1.47457
$326$	−6.95313	−	28.9655i	−0.385098	−	1.60425i
$327$	4.05216	−	19.3452i	0.224085	−	1.06979i
$328$	−7.48240	−	8.76227i	−0.413147	−	0.483815i
$329$			1.29050i			0.0711476i
$330$	0.370566	−	0.0107905i	0.0203990	−	0.000593998i
$331$			18.0323i			0.991146i	0.868566	+	0.495573i	$0.165042\pi$
$331$			18.0323i			0.991146i	−0.868566	+	0.495573i	$0.834958\pi$
$332$	−25.4540	+	12.9676i	−1.39697	+	0.711691i
$333$	−1.45176	−	0.636097i	−0.0795559	−	0.0348579i
$334$	−29.9097	+	7.17978i	−1.63658	+	0.392860i
$335$	0.0453328			0.00247680
$336$	−14.4922	+	13.1237i	−0.790614	+	0.715957i
$337$	21.9123			1.19364			0.596821	−	0.802375i	$-0.296430\pi$
$337$	21.9123			1.19364			0.596821	+	0.802375i	$0.296430\pi$
$338$	−21.0257	+	5.04719i	−1.14365	+	0.274531i
$339$	−16.2551	−	3.40488i	−0.882855	−	0.184928i
$340$	−0.00374008	+	0.00190540i	−0.000202834	+	0.000103335i
$341$		−	6.17017i		−	0.334133i
$342$	2.24926	−	12.5480i	0.121626	−	0.678516i
$343$		−	17.0345i		−	0.919779i
$344$	0.637229	+	0.746228i	0.0343571	+	0.0402339i
$345$	0.672103	+	0.140782i	0.0361848	+	0.00757947i
$346$	−8.54614	−	35.6016i	−0.459443	−	1.91396i
$347$	−8.77121			−0.470863			−0.235432	−	0.971891i	$-0.575650\pi$
$347$	−8.77121			−0.470863			−0.235432	+	0.971891i	$0.575650\pi$
$348$	−11.1597	+	3.02499i	−0.598225	+	0.162156i
$349$	−24.2036			−1.29559			−0.647794	−	0.761815i	$-0.724308\pi$
$349$	−24.2036			−1.29559			−0.647794	+	0.761815i	$0.724308\pi$
$350$	4.65582	+	19.3953i	0.248864	+	1.03672i
$351$	16.0457	−	22.5024i	0.856456	−	1.20109i
$352$	−7.22975	+	17.4472i	−0.385347	+	0.929939i
$353$		−	30.4426i		−	1.62030i	−0.586225	−	0.810148i	$-0.699387\pi$
$353$		−	30.4426i		−	1.62030i	0.586225	−	0.810148i	$-0.300613\pi$
$354$	−0.0161675	−	0.555221i	−0.000859293	−	0.0295097i
$355$			0.325700i			0.0172863i
$356$	0.635133	+	1.24669i	0.0336620	+	0.0660746i
$357$	−0.0463927	+	0.221481i	−0.00245536	+	0.0117220i
$358$	−2.57998	+	0.619322i	−0.136356	+	0.0327322i
$359$	17.3593			0.916188			0.458094	−	0.888904i	$-0.348532\pi$
$359$	17.3593			0.916188			0.458094	+	0.888904i	$0.348532\pi$
$360$	−0.111400	−	0.368178i	−0.00587127	−	0.0194047i
$361$	9.97163			0.524823
$362$	−14.9486	+	3.58840i	−0.785681	+	0.188602i
$363$	0.0518679	−	0.247620i	0.00272236	−	0.0129967i
$364$	13.6270	+	26.7482i	0.714247	+	1.40198i
$365$			0.226756i			0.0118690i
$366$	−0.436182	−	14.9793i	−0.0227996	−	0.782978i
$367$		−	20.2091i		−	1.05491i	−0.849584	−	0.527453i	$-0.823147\pi$
$367$		−	20.2091i		−	1.05491i	0.849584	−	0.527453i	$-0.176853\pi$
$368$	−20.5652	+	28.2988i	−1.07203	+	1.47518i
$369$	4.90467	−	11.1939i	0.255327	−	0.582731i
$370$	0.00790624	+	0.0329360i	0.000411026	+	0.00171226i
$371$	8.16694			0.424007
$372$	−6.17918	+	1.67494i	−0.320376	+	0.0868418i
$373$	−9.05088			−0.468637			−0.234318	−	0.972160i	$-0.575286\pi$
$373$	−9.05088			−0.468637			−0.234318	+	0.972160i	$0.575286\pi$
$374$	0.0510217	+	0.212547i	0.00263827	+	0.0109905i
$375$	−0.768351	−	0.160943i	−0.0396775	−	0.00831107i
$376$	0.983613	−	0.839941i	0.0507260	−	0.0433166i
$377$			17.7531i			0.914331i
$378$	−19.2283	−	7.76599i	−0.988996	−	0.399439i
$379$		−	21.7509i		−	1.11727i	−0.829415	−	0.558634i	$-0.811326\pi$
$379$		−	21.7509i		−	1.11727i	0.829415	−	0.558634i	$-0.188674\pi$
$380$	−0.242740	+	0.123665i	−0.0124523	+	0.00634387i
$381$	−11.7456	−	2.46031i	−0.601747	−	0.126045i
$382$	5.50347	−	1.32110i	0.281582	−	0.0675934i
$383$	14.9683			0.764845			0.382423	−	0.923987i	$-0.375090\pi$
$383$	14.9683			0.764845			0.382423	+	0.923987i	$0.375090\pi$
$384$	19.4353	+	2.50412i	0.991802	+	0.127788i
$385$	−0.427100			−0.0217670
$386$	−26.2775	+	6.30789i	−1.33749	+	0.321063i
$387$	−0.417700	+	0.953314i	−0.0212329	+	0.0484597i
$388$	5.18148	−	2.63973i	0.263050	−	0.134012i
$389$			26.1553i			1.32613i	0.748564	+	0.663063i	$0.230744\pi$
$389$			26.1553i			1.32613i	−0.748564	+	0.663063i	$0.769256\pi$
$390$	−0.590363	+	0.0171908i	−0.0298942	+	0.000870490i
$391$			0.404885i			0.0204759i
$392$	2.07272	−	1.76996i	0.104688	−	0.0893966i
$393$	0.295655	−	1.41147i	0.0149138	−	0.0711993i
$394$	1.05223	+	4.38339i	0.0530105	+	0.220832i
$395$	−0.693823			−0.0349100
$396$	−19.9975	+	1.16560i	−1.00491	+	0.0585738i
$397$	−21.6228			−1.08522			−0.542610	−	0.839985i	$-0.682564\pi$
$397$	−21.6228			−1.08522			−0.542610	+	0.839985i	$0.682564\pi$
$398$	−5.78944	−	24.1177i	−0.290198	−	1.20891i
$399$	−3.01099	+	14.3746i	−0.150738	+	0.719632i
$400$	11.7527	−	16.1724i	0.587635	−	0.808618i
$401$		−	30.4479i		−	1.52050i	−0.649633	−	0.760248i	$-0.725077\pi$
$401$		−	30.4479i		−	1.52050i	0.649633	−	0.760248i	$-0.274923\pi$
$402$	−2.44845	+	0.0712965i	−0.122118	+	0.00355595i
$403$			9.82994i			0.489664i
$404$	−17.1479	−	33.6594i	−0.853141	−	1.67462i
$405$	0.299947	−	0.276572i	0.0149045	−	0.0137430i
$406$	12.9528	−	3.10932i	0.642839	−	0.154313i
$407$	1.76388			0.0874322
$408$	0.199007	−	0.108794i	0.00985232	−	0.00538610i
$409$	−9.38435			−0.464026			−0.232013	−	0.972713i	$-0.574531\pi$
$409$	−9.38435			−0.464026			−0.232013	+	0.972713i	$0.574531\pi$
$410$	−0.253955	+	0.0609617i	−0.0125420	+	0.00301068i
$411$	−8.34506	−	1.74800i	−0.411631	−	0.0862227i
$412$	13.0598	+	25.6349i	0.643410	+	1.26294i
$413$			0.639927i			0.0314888i
$414$	−36.5221	−	6.54670i	−1.79496	−	0.321753i
$415$			0.647508i			0.0317849i
$416$	11.5180	−	27.7958i	0.564717	−	1.36280i
$417$	−10.6960	−	2.24044i	−0.523784	−	0.109715i
$418$	3.31142	+	13.7948i	0.161967	+	0.674725i
$419$	14.5317			0.709920			0.354960	−	0.934881i	$-0.384494\pi$
$419$	14.5317			0.709920			0.354960	+	0.934881i	$0.384494\pi$
$420$	0.115940	+	0.427724i	0.00565729	+	0.0208708i
$421$	7.75853			0.378127			0.189064	−	0.981965i	$-0.439455\pi$
$421$	7.75853			0.378127			0.189064	+	0.981965i	$0.439455\pi$
$422$	1.05644	+	4.40095i	0.0514268	+	0.214235i
$423$	1.25658	+	0.550576i	0.0610969	+	0.0267699i
$424$	−5.31557	−	6.22480i	−0.258147	−	0.302303i
$425$		−	0.231385i		−	0.0112238i
$426$	−0.512239	−	17.5912i	−0.0248181	−	0.852297i
$427$			17.2645i			0.835489i
$428$	−1.17563	+	0.598929i	−0.0568262	+	0.0289503i
$429$	−6.30557	+	30.1031i	−0.304436	+	1.45339i
$430$	0.0216278	−	0.00519172i	0.00104298	−	0.000250367i
$431$	−24.2429			−1.16774			−0.583869	−	0.811848i	$-0.698462\pi$
$431$	−24.2429			−1.16774			−0.583869	+	0.811848i	$0.698462\pi$
$432$	6.59580	+	19.7103i	0.317340	+	0.948312i
$433$	30.8720			1.48361			0.741806	−	0.670614i	$-0.233969\pi$
$433$	30.8720			1.48361			0.741806	+	0.670614i	$0.233969\pi$
$434$	7.17202	−	1.72164i	0.344268	−	0.0826412i
$435$	−0.0537306	+	0.256513i	−0.00257618	+	0.0122988i
$436$	20.3358	−	10.3602i	0.973907	−	0.496161i
$437$			26.2779i			1.25704i
$438$	−0.356627	−	12.2472i	−0.0170403	−	0.585195i
$439$			36.8150i			1.75708i	0.477665	+	0.878542i	$0.341483\pi$
$439$			36.8150i			1.75708i	−0.477665	+	0.878542i	$0.658517\pi$
$440$	0.277984	+	0.325533i	0.0132524	+	0.0155192i
$441$	2.64792	+	1.16020i	0.126091	+	0.0552477i
$442$	−0.0812846	−	0.338617i	−0.00386631	−	0.0161064i
$443$	−20.0252			−0.951425			−0.475712	−	0.879601i	$-0.657810\pi$
$443$	−20.0252			−0.951425			−0.475712	+	0.879601i	$0.657810\pi$
$444$	−0.478820	−	1.76646i	−0.0227238	−	0.0838323i
$445$	0.0317139			0.00150338
$446$	7.81207	+	32.5436i	0.369912	+	1.54099i
$447$	−29.6696	−	6.21476i	−1.40332	−	0.293948i
$448$	−22.2974	−	3.53543i	−1.05345	−	0.167034i
$449$			19.0841i			0.900634i	0.892869	+	0.450317i	$0.148689\pi$
$449$			19.0841i			0.900634i	−0.892869	+	0.450317i	$0.851311\pi$
$450$	20.8718	+	3.74134i	0.983907	+	0.176369i
$451$			13.6005i			0.640424i
$452$	−8.70526	−	17.0874i	−0.409461	−	0.803724i
$453$	−24.9753	−	5.23148i	−1.17344	−	0.245796i
$454$	−35.3499	+	8.48570i	−1.65905	+	0.398253i
$455$	0.680430			0.0318991
$456$	12.9160	−	7.06097i	0.604848	−	0.330660i
$457$	−14.3677			−0.672092			−0.336046	−	0.941846i	$-0.609090\pi$
$457$	−14.3677			−0.672092			−0.336046	+	0.941846i	$0.609090\pi$
$458$	16.4170	−	3.94087i	0.767114	−	0.184145i
$459$	0.195866	+	0.139665i	0.00914224	+	0.00651902i
$460$	0.359938	+	0.706517i	0.0167822	+	0.0329415i
$461$			24.9347i			1.16132i	0.814145	+	0.580661i	$0.197206\pi$
$461$			24.9347i			1.16132i	−0.814145	+	0.580661i	$0.802794\pi$
$462$	23.0679	−	0.671715i	1.07322	−	0.0312510i
$463$		−	15.6605i		−	0.727807i	−0.931437	−	0.363904i	$-0.881444\pi$
$463$		−	15.6605i		−	0.727807i	0.931437	−	0.363904i	$-0.118556\pi$
$464$	−10.8004	−	7.84885i	−0.501398	−	0.364374i
$465$	−0.0297508	+	0.142032i	−0.00137966	+	0.00658656i
$466$	5.88373	+	24.5106i	0.272559	+	1.13543i
$467$	−0.0672601			−0.00311243			−0.00155621	−	0.999999i	$-0.500495\pi$
$467$	−0.0672601			−0.00311243			−0.00155621	+	0.999999i	$0.500495\pi$
$468$	31.8588	−	1.85697i	1.47267	−	0.0858384i
$469$	2.82199			0.130308
$470$	−0.00684328	−	0.0285079i	−0.000315657	−	0.00131497i
$471$	4.37574	−	20.8900i	0.201624	−	0.962561i
$472$	0.487749	−	0.416506i	0.0224505	−	0.0191712i
$473$		−	1.15827i		−	0.0532574i
$474$	37.4738	−	1.09120i	1.72123	−	0.0501205i
$475$		−	15.0174i		−	0.689048i
$476$	−0.232822	+	0.118612i	−0.0106714	+	0.00543658i
$477$	3.48433	−	7.95225i	0.159536	−	0.364109i
$478$	−30.6270	+	7.35197i	−1.40085	+	0.336271i
$479$	10.4537			0.477640			0.238820	−	0.971064i	$-0.423239\pi$
$479$	10.4537			0.477640			0.238820	+	0.971064i	$0.423239\pi$
$480$	0.250548	−	0.366759i	0.0114359	−	0.0167402i
$481$	−2.81011			−0.128130
$482$	−26.6340	+	6.39346i	−1.21315	+	0.291214i
$483$	41.8388	+	8.76379i	1.90373	+	0.398766i
$484$	0.260299	−	0.132611i	0.0118318	−	0.00602776i
$485$		−	0.131808i		−	0.00598511i
$486$	−15.7653	+	15.4095i	−0.715131	+	0.698991i
$487$		−	23.8327i		−	1.07996i	−0.841677	−	0.539982i	$-0.818431\pi$
$487$		−	23.8327i		−	1.07996i	0.841677	−	0.539982i	$-0.181569\pi$
$488$	13.1589	−	11.2369i	0.595677	−	0.508669i
$489$	35.7082	+	7.47964i	1.61478	+	0.338241i
$490$	−0.0144205	−	0.0600731i	−0.000651451	−	0.00271383i
$491$	−29.4130			−1.32739			−0.663694	−	0.748004i	$-0.731012\pi$
$491$	−29.4130			−1.32739			−0.663694	+	0.748004i	$0.731012\pi$
$492$	13.6204	−	3.69198i	0.614054	−	0.166447i
$493$	−0.154527			−0.00695954
$494$	−5.27556	−	21.9770i	−0.237359	−	0.988793i
$495$	−0.182217	+	0.415873i	−0.00819005	+	0.0186921i
$496$	−5.98023	−	4.34593i	−0.268520	−	0.195138i
$497$			20.2750i			0.909457i
$498$	−1.01836	−	34.9723i	−0.0456337	−	1.56714i
$499$			39.5774i			1.77173i	0.463946	+	0.885864i	$0.346433\pi$
$499$			39.5774i			1.77173i	−0.463946	+	0.885864i	$0.653567\pi$
$500$	−0.411483	−	0.807694i	−0.0184021	−	0.0361212i
$501$	7.72344	−	36.8721i	0.345058	−	1.64732i
$502$	16.7037	−	4.00970i	0.745522	−	0.178962i
$503$	−6.34209			−0.282780			−0.141390	−	0.989954i	$-0.545157\pi$
$503$	−6.34209			−0.282780			−0.141390	+	0.989954i	$0.545157\pi$
$504$	−6.93468	−	22.9193i	−0.308895	−	1.02091i
$505$	−0.856240			−0.0381022
$506$	40.1511	−	9.63822i	1.78493	−	0.428471i
$507$	5.42937	−	25.9201i	0.241127	−	1.15115i
$508$	−6.29026	−	12.3471i	−0.279085	−	0.547812i
$509$			27.5700i			1.22202i	0.791623	+	0.611009i	$0.209236\pi$
$509$			27.5700i			1.22202i	−0.791623	+	0.611009i	$0.790764\pi$
$510$	−0.000149632	−	0.00513865i	−6.62584e−6	−	0.000227543i
$511$			14.1157i			0.624441i
$512$	11.8179	+	19.2960i	0.522282	+	0.852773i
$513$	12.7122	+	9.06460i	0.561255	+	0.400212i
$514$	7.39548	+	30.8082i	0.326201	+	1.35889i
$515$	0.652109			0.0287354
$516$	−1.15996	+	0.314423i	−0.0510645	+	0.0138417i
$517$	−1.52673			−0.0671456
$518$	0.492168	+	2.05028i	0.0216246	+	0.0900842i
$519$	43.8891	+	9.19326i	1.92652	+	0.403539i
$520$	−0.442867	−	0.518620i	−0.0194210	−	0.0227430i
$521$			27.0474i			1.18497i	0.805581	+	0.592485i	$0.201853\pi$
$521$			27.0474i			1.18497i	−0.805581	+	0.592485i	$0.798147\pi$
$522$	2.49859	−	13.9389i	0.109360	−	0.610089i
$523$		−	5.32931i		−	0.233035i	−0.993189	−	0.116517i	$-0.962827\pi$
$523$		−	5.32931i		−	0.233035i	0.993189	−	0.116517i	$-0.0371730\pi$
$524$	1.48375	−	0.755901i	0.0648177	−	0.0330217i
$525$	−23.9102	−	5.00837i	−1.04353	−	0.218583i
$526$	−36.0917	+	8.66378i	−1.57367	+	0.377759i
$527$	−0.0855620			−0.00372714
$528$	−15.5261	−	17.1450i	−0.675685	−	0.746142i
$529$	53.4845			2.32541
$530$	−0.180412	+	0.0433077i	−0.00783660	+	0.00188117i
$531$	0.623105	+	0.273017i	0.0270405	+	0.0118479i
$532$	−15.1107	+	7.69820i	−0.655131	+	0.333759i
$533$		−	21.6675i		−	0.938525i
$534$	−1.71288	+	0.0498775i	−0.0741237	+	0.00215841i
$535$			0.0299061i			0.00129295i
$536$	−1.83673	−	2.15091i	−0.0793348	−	0.0929051i
$537$	0.666218	−	3.18056i	0.0287494	−	0.137251i
$538$	−5.31271	−	22.1318i	−0.229047	−	0.954170i
$539$	−3.21721			−0.138575
$540$	0.465944	+	0.0695910i	0.0200511	+	0.00299472i
$541$	−18.5591			−0.797920			−0.398960	−	0.916968i	$-0.630629\pi$
$541$	−18.5591			−0.797920			−0.398960	+	0.916968i	$0.630629\pi$
$542$	4.45267	+	18.5490i	0.191259	+	0.796749i
$543$	3.86012	−	18.4284i	0.165653	−	0.790838i
$544$	0.241941	+	0.100255i	0.0103731	+	0.00429841i
$545$		−	0.517309i		−	0.0221591i
$546$	−36.7504	+	1.07014i	−1.57277	+	0.0457976i
$547$		−	16.1107i		−	0.688845i	−0.938815	−	0.344423i	$-0.888075\pi$
$547$		−	16.1107i		−	0.688845i	0.938815	−	0.344423i	$-0.111925\pi$
$548$	−4.46912	−	8.77236i	−0.190911	−	0.374737i
$549$	16.8107	+	7.36570i	0.717463	+	0.314360i
$550$	−22.9457	+	5.50810i	−0.978409	+	0.234866i
$551$	−10.0292			−0.427256
$552$	−20.5516	−	37.5933i	−0.874736	−	1.60008i
$553$	−43.1909			−1.83666
$554$	18.6897	−	4.48645i	0.794051	−	0.190611i
$555$	−0.0406029	−	0.00850491i	−0.00172350	−	0.000361014i
$556$	−5.72813	−	11.2437i	−0.242927	−	0.476837i
$557$		−	0.882960i		−	0.0374122i	−0.999825	−	0.0187061i	$-0.994045\pi$
$557$		−	0.882960i		−	0.0374122i	0.999825	−	0.0187061i	$-0.00595469\pi$
$558$	1.38348	−	7.71800i	0.0585673	−	0.326729i
$559$			1.84529i			0.0780473i
$560$	−0.300826	+	0.413953i	−0.0127122	+	0.0174927i
$561$	−0.262024	−	0.0548851i	−0.0110627	−	0.00231725i
$562$	4.70908	+	19.6172i	0.198640	+	0.827500i
$563$	4.74187			0.199846			0.0999230	−	0.994995i	$-0.468140\pi$
$563$	4.74187			0.199846			0.0999230	+	0.994995i	$0.468140\pi$
$564$	0.414445	+	1.52896i	0.0174513	+	0.0643810i
$565$	−0.434676			−0.0182870
$566$	0.678753	+	2.82756i	0.0285301	+	0.118851i
$567$	18.6719	−	17.2167i	0.784145	−	0.723035i
$568$	15.4535	−	13.1963i	0.648414	−	0.553702i
$569$			29.6251i			1.24195i	0.783830	+	0.620975i	$0.213263\pi$
$569$			29.6251i			1.24195i	−0.783830	+	0.620975i	$0.786737\pi$
$570$	−0.00971149	−	0.333510i	−0.000406770	−	0.0139692i
$571$			7.09982i			0.297118i	0.988904	+	0.148559i	$0.0474635\pi$
$571$			7.09982i			0.297118i	−0.988904	+	0.148559i	$0.952536\pi$
$572$	−31.6445	+	16.1214i	−1.32312	+	0.674072i
$573$	−1.42114	+	6.78458i	−0.0593689	+	0.283430i
$574$	−15.8088	+	3.79490i	−0.659849	+	0.158396i
$575$	−43.7097			−1.82282
$576$	−12.9554	+	20.2029i	−0.539809	+	0.841788i
$577$	−45.0273			−1.87451			−0.937256	−	0.348641i	$-0.886643\pi$
$577$	−45.0273			−1.87451			−0.937256	+	0.348641i	$0.886643\pi$
$578$	−23.3746	+	5.61104i	−0.972254	+	0.233388i
$579$	6.78553	−	32.3945i	0.281997	−	1.34627i
$580$	−0.269647	+	0.137373i	−0.0111965	+	0.00570410i
$581$			40.3077i			1.67225i
$582$	0.207300	+	7.11905i	0.00859285	+	0.295094i
$583$			9.66194i			0.400157i
$584$	10.7589	−	9.18740i	0.445207	−	0.380177i
$585$	0.290297	−	0.662543i	0.0120023	−	0.0273928i
$586$	10.0946	+	42.0521i	0.417003	+	1.73716i
$587$	34.7911			1.43598			0.717990	−	0.696053i	$-0.245062\pi$
$587$	34.7911			1.43598			0.717990	+	0.696053i	$0.245062\pi$
$588$	0.873338	+	3.22190i	0.0360158	+	0.132869i
$589$	−5.55317			−0.228814
$590$	−0.00339341	−	0.0141363i	−0.000139705	−	0.000581984i
$591$	−5.40377	−	1.13190i	−0.222281	−	0.0465603i
$592$	1.24238	−	1.70958i	0.0510615	−	0.0702634i
$593$			22.8534i			0.938475i	0.883072	+	0.469237i	$0.155471\pi$
$593$			22.8534i			0.938475i	−0.883072	+	0.469237i	$0.844529\pi$
$594$	9.18759	−	22.7481i	0.376971	−	0.933366i
$595$			0.00592261i			0.000242803i
$596$	−15.8893	−	31.1888i	−0.650850	−	1.27754i
$597$	29.7319	+	6.22782i	1.21685	+	0.254888i
$598$	−63.9662	+	15.3550i	−2.61577	+	0.627914i
$599$	27.3056			1.11568			0.557838	−	0.829950i	$-0.311631\pi$
$599$	27.3056			1.11568			0.557838	+	0.829950i	$0.311631\pi$
$600$	11.7450	+	21.4840i	0.479486	+	0.877081i
$601$	35.2624			1.43838			0.719192	−	0.694812i	$-0.244512\pi$
$601$	35.2624			1.43838			0.719192	+	0.694812i	$0.244512\pi$
$602$	1.34634	−	0.323188i	0.0548727	−	0.0131721i
$603$	1.20397	−	2.74781i	0.0490294	−	0.111899i
$604$	−13.3753	−	26.2542i	−0.544234	−	1.06827i
$605$		−	0.00662160i		−	0.000269206i
$606$	46.2460	−	1.34664i	1.87862	−	0.0547035i
$607$			23.8874i			0.969560i	0.874636	+	0.484780i	$0.161100\pi$
$607$			23.8874i			0.969560i	−0.874636	+	0.484780i	$0.838900\pi$
$608$	15.7025	+	6.50680i	0.636822	+	0.263886i
$609$	−3.34476	+	15.9680i	−0.135536	+	0.647058i
$610$	−0.0915505	−	0.381383i	−0.00370677	−	0.0154417i
$611$	2.43230			0.0984003
$612$	0.0161635	+	0.277306i	0.000653370	+	0.0112094i
$613$	−32.2630			−1.30309			−0.651545	−	0.758610i	$-0.725879\pi$
$613$	−32.2630			−1.30309			−0.651545	+	0.758610i	$0.725879\pi$
$614$	−5.93827	−	24.7377i	−0.239649	−	0.998334i
$615$	0.0655778	−	0.313072i	0.00264435	−	0.0126243i
$616$	17.3047	+	20.2646i	0.697225	+	0.816485i
$617$		−	42.1094i		−	1.69526i	−0.530587	−	0.847630i	$-0.678029\pi$
$617$		−	42.1094i		−	1.69526i	0.530587	−	0.847630i	$-0.321971\pi$
$618$	−35.2208	+	1.02560i	−1.41679	+	0.0412555i
$619$			8.85623i			0.355962i	0.984034	+	0.177981i	$0.0569566\pi$
$619$			8.85623i			0.355962i	−0.984034	+	0.177981i	$0.943043\pi$
$620$	−0.149304	+	0.0760637i	−0.00599621	+	0.00305479i
$621$	26.3834	−	37.0000i	1.05873	−	1.48476i
$622$	36.9673	−	8.87397i	1.48226	−	0.355814i
$623$	1.97420			0.0790948
$624$	24.7352	+	27.3145i	0.990200	+	1.09345i
$625$	24.9692			0.998767
$626$	20.1040	−	4.82594i	0.803518	−	0.192884i
$627$	−17.0060	−	3.56217i	−0.679153	−	0.142259i
$628$	21.9597	−	11.1875i	0.876287	−	0.446428i
$629$		−	0.0244598i		−	0.000975275i
$630$	−0.534241	−	0.0957645i	−0.0212847	−	0.00381535i
$631$			45.1892i			1.79895i	0.436970	+	0.899476i	$0.356051\pi$
$631$			45.1892i			1.79895i	−0.436970	+	0.899476i	$0.643949\pi$
$632$	28.1114	+	32.9199i	1.11821	+	1.30948i
$633$	−5.42541	−	1.13644i	−0.215641	−	0.0451694i
$634$	5.42290	+	22.5908i	0.215371	+	0.897195i
$635$	−0.314089			−0.0124642
$636$	9.67605	−	2.62282i	0.383680	−	0.104001i
$637$	5.12546			0.203078
$638$	3.67849	+	15.3239i	0.145633	+	0.606680i
$639$	19.7420	+	8.65007i	0.780981	+	0.342191i
$640$	0.511309	−	0.0401392i	0.0202113	−	0.00158664i
$641$		−	15.8749i		−	0.627021i	−0.949585	−	0.313510i	$-0.898495\pi$
$641$		−	15.8749i		−	0.627021i	0.949585	−	0.313510i	$-0.101505\pi$
$642$	−0.0470344	−	1.61525i	−0.00185630	−	0.0637487i
$643$		−	11.1940i		−	0.441449i	−0.975336	−	0.220725i	$-0.929158\pi$
$643$		−	11.1940i		−	0.441449i	0.975336	−	0.220725i	$-0.0708422\pi$
$644$	22.4064	+	43.9811i	0.882934	+	1.73310i
$645$	−0.00558485	+	0.0266624i	−0.000219903	+	0.00104983i
$646$	0.191293	−	0.0459196i	0.00752632	−	0.00180668i
$647$	9.10556			0.357977			0.178988	−	0.983851i	$-0.442718\pi$
$647$	9.10556			0.357977			0.178988	+	0.983851i	$0.442718\pi$
$648$	−25.2754	−	3.02584i	−0.992910	−	0.118866i
$649$	−0.757069			−0.0297176
$650$	36.5557	−	8.77516i	1.43383	−	0.344190i
$651$	−1.85200	+	8.84155i	−0.0725856	+	0.346528i
$652$	19.1232	+	37.5366i	0.748921	+	1.47005i
$653$		−	23.2914i		−	0.911461i	−0.890118	−	0.455731i	$-0.849378\pi$
$653$		−	23.2914i		−	0.911461i	0.890118	−	0.455731i	$-0.150622\pi$
$654$	0.813591	+	27.9402i	0.0318139	+	1.09255i
$655$		−	0.0377441i		−	0.00147478i
$656$	13.1819	+	9.57946i	0.514665	+	0.374015i
$657$	13.7446	+	6.02229i	0.536229	+	0.234952i
$658$	−0.425998	−	1.77463i	−0.0166071	−	0.0691823i
$659$	−31.9785			−1.24571			−0.622853	−	0.782339i	$-0.714026\pi$
$659$	−31.9785			−1.24571			−0.622853	+	0.782339i	$0.714026\pi$
$660$	−0.506021	+	0.137163i	−0.0196968	+	0.00533908i
$661$	0.528143			0.0205424			0.0102712	−	0.999947i	$-0.496731\pi$
$661$	0.528143			0.0205424			0.0102712	+	0.999947i	$0.496731\pi$
$662$	−5.95252	−	24.7971i	−0.231351	−	0.963767i
$663$	0.417441	+	0.0874396i	0.0162121	+	0.00339587i
$664$	30.7223	−	26.2348i	1.19226	−	1.01811i
$665$			0.384391i			0.0149061i
$666$	2.20636	+	0.395498i	0.0854948	+	0.0153252i
$667$			29.1908i			1.13027i
$668$	38.7601	−	19.7465i	1.49967	−	0.764016i
$669$	−40.1193	−	8.40361i	−1.55110	−	0.324902i
$670$	−0.0623394	+	0.0149645i	−0.00240838	+	0.000578129i
$671$	−20.4249			−0.788494
$672$	15.5967	−	22.8309i	0.601657	−	0.880723i
$673$	14.1935			0.547121			0.273561	−	0.961855i	$-0.411799\pi$
$673$	14.1935			0.547121			0.273561	+	0.961855i	$0.411799\pi$
$674$	−30.1327	+	7.23333i	−1.16067	+	0.278617i
$675$	−15.0777	+	21.1449i	−0.580342	+	0.813868i
$676$	27.2473	−	13.8813i	1.04797	−	0.533895i
$677$		−	5.83261i		−	0.224165i	−0.993699	−	0.112083i	$-0.964248\pi$
$677$		−	5.83261i		−	0.224165i	0.993699	−	0.112083i	$-0.0357521\pi$
$678$	23.4771	−	0.683631i	0.901633	−	0.0262547i
$679$		−	8.20515i		−	0.314885i
$680$	0.00451418	−	0.00385482i	0.000173111	−	0.000147825i
$681$	9.12825	−	43.5787i	0.349795	−	1.66994i
$682$	2.03679	+	8.48489i	0.0779927	+	0.324903i
$683$	20.2308			0.774110			0.387055	−	0.922057i	$-0.373492\pi$
$683$	20.2308			0.774110			0.387055	+	0.922057i	$0.373492\pi$
$684$	1.04905	+	17.9978i	0.0401113	+	0.688163i
$685$	−0.223155			−0.00852630
$686$	5.62315	+	23.4250i	0.214693	+	0.894372i
$687$	−4.23928	+	20.2385i	−0.161739	+	0.772149i
$688$	−1.12262	−	0.815822i	−0.0427994	−	0.0311029i
$689$		−	15.3928i		−	0.586420i
$690$	−0.970714	+	0.0282662i	−0.0369544	+	0.00107608i
$691$		−	27.2492i		−	1.03661i	−0.855196	−	0.518305i	$-0.826563\pi$
$691$		−	27.2492i		−	1.03661i	0.855196	−	0.518305i	$-0.173437\pi$
$692$	23.5044	+	46.1364i	0.893503	+	1.75384i
$693$	−11.3431	+	25.8883i	−0.430889	+	0.983415i
$694$	12.0617	−	2.89540i	0.457856	−	0.109908i
$695$	−0.286020			−0.0108494
$696$	14.3477	−	7.84367i	0.543850	−	0.297314i
$697$	0.188599			0.00714370
$698$	33.2835	−	7.98967i	1.25980	−	0.302413i
$699$	−30.2162	−	6.32926i	−1.14288	−	0.239395i
$700$	−12.8049	−	25.1345i	−0.483980	−	0.949996i
$701$			1.36934i			0.0517193i	0.999666	+	0.0258596i	$0.00823230\pi$
$701$			1.36934i			0.0517193i	−0.999666	+	0.0258596i	$0.991768\pi$
$702$	−14.6371	+	36.2409i	−0.552442	+	1.36782i
$703$		−	1.58750i		−	0.0598735i
$704$	4.18261	−	26.3790i	0.157638	−	0.994198i
$705$	0.0351440	+	0.00736147i	0.00132360	+	0.000277249i
$706$	10.0492	+	41.8631i	0.378206	+	1.57554i
$707$	−53.3014			−2.00461
$708$	0.205513	+	0.758175i	0.00772364	+	0.0284939i
$709$	−9.08190			−0.341078			−0.170539	−	0.985351i	$-0.554551\pi$
$709$	−9.08190			−0.341078			−0.170539	+	0.985351i	$0.554551\pi$
$710$	−0.107514	−	0.447885i	−0.00403494	−	0.0168088i
$711$	−18.4269	+	42.0555i	−0.691061	+	1.57720i
$712$	−1.28494	−	1.50473i	−0.0481551	−	0.0563921i
$713$			16.1630i			0.605310i
$714$	−0.00931470	−	0.319884i	−0.000348594	−	0.0119713i
$715$			0.804986i			0.0301048i
$716$	3.34342	−	1.70332i	0.124949	−	0.0636560i
$717$	7.90868	−	37.7564i	0.295355	−	1.41004i
$718$	−23.8716	+	5.73035i	−0.890880	+	0.213855i
$719$	−3.80251			−0.141810			−0.0709048	−	0.997483i	$-0.522589\pi$
$719$	−3.80251			−0.141810			−0.0709048	+	0.997483i	$0.522589\pi$
$720$	0.274727	+	0.469526i	0.0102385	+	0.0174982i
$721$	40.5942			1.51181
$722$	−13.7125	+	3.29166i	−0.510325	+	0.122503i
$723$	6.87759	−	32.8340i	0.255780	−	1.22111i
$724$	19.3720	−	9.86915i	0.719955	−	0.366784i
$725$		−	16.6821i		−	0.619558i
$726$	0.0104140	+	0.357636i	0.000386500	+	0.0132731i
$727$			7.17785i			0.266212i	0.991102	+	0.133106i	$0.0424950\pi$
$727$			7.17785i			0.266212i	−0.991102	+	0.133106i	$0.957505\pi$
$728$	−27.5687	−	32.2844i	−1.02177	−	1.19654i
$729$	−8.79803	−	25.5264i	−0.325853	−	0.945420i
$730$	−0.0748528	−	0.311823i	−0.00277043	−	0.0115411i
$731$	−0.0160618			−0.000594067
$732$	5.54451	+	20.4547i	0.204931	+	0.756028i
$733$	−2.44611			−0.0903492			−0.0451746	−	0.998979i	$-0.514384\pi$
$733$	−2.44611			−0.0903492			−0.0451746	+	0.998979i	$0.514384\pi$
$734$	6.67107	+	27.7905i	0.246234	+	1.02576i
$735$	0.0740571	+	0.0155124i	0.00273164	+	0.000572185i
$736$	18.9387	−	45.7037i	0.698088	−	1.68466i
$737$			3.33857i			0.122978i
$738$	−3.04951	+	17.0123i	−0.112254	+	0.626232i
$739$		−	49.4937i		−	1.82065i	−0.413890	−	0.910327i	$-0.635830\pi$
$739$		−	49.4937i		−	1.82065i	0.413890	−	0.910327i	$-0.364170\pi$
$740$	−0.0217445	−	0.0426819i	−0.000799344	−	0.00156902i
$741$	27.0929	+	5.67503i	0.995283	+	0.208478i
$742$	−11.2308	+	2.69593i	−0.412294	+	0.0989707i
$743$	−47.0335			−1.72549			−0.862746	−	0.505638i	$-0.831257\pi$
$743$	−47.0335			−1.72549			−0.862746	+	0.505638i	$0.831257\pi$
$744$	7.94438	−	4.34306i	0.291255	−	0.159224i
$745$	−0.793392			−0.0290676
$746$	12.4463	−	2.98772i	0.455691	−	0.109388i
$747$	39.2481	+	17.1968i	1.43601	+	0.629198i
$748$	−0.140325	−	0.275441i	−0.00513078	−	0.0100711i
$749$			1.86167i			0.0680240i
$750$	1.10972	−	0.0323141i	0.0405214	−	0.00117994i
$751$			43.9718i			1.60455i	0.596952	+	0.802277i	$0.296378\pi$
$751$			43.9718i			1.60455i	−0.596952	+	0.802277i	$0.703622\pi$
$752$	−1.07535	+	1.47974i	−0.0392139	+	0.0539604i
$753$	−4.31332	+	20.5920i	−0.157186	+	0.750415i
$754$	−5.86035	−	24.4131i	−0.213421	−	0.889074i
$755$	−0.667864			−0.0243061
$756$	29.0053	+	4.33208i	1.05491	+	0.157556i
$757$	18.1609			0.660068			0.330034	−	0.943969i	$-0.392940\pi$
$757$	18.1609			0.660068			0.330034	+	0.943969i	$0.392940\pi$
$758$	7.18002	+	29.9107i	0.260790	+	1.08640i
$759$	−10.3680	+	49.4975i	−0.376336	+	1.79665i
$760$	0.292981	−	0.250186i	0.0106275	−	0.00907522i
$761$		−	33.2514i		−	1.20536i	−0.797982	−	0.602681i	$-0.794099\pi$
$761$		−	33.2514i		−	1.20536i	0.797982	−	0.602681i	$-0.205901\pi$
$762$	16.9641	−	0.493979i	0.614546	−	0.0178950i
$763$		−	32.2028i		−	1.16582i
$764$	−7.13198	+	3.63342i	−0.258026	+	0.131453i
$765$	0.00576692	+	0.00252681i	0.000208504	+	9.13570e-5i
$766$	−20.5837	+	4.94108i	−0.743718	+	0.178529i
$767$	1.20612			0.0435503
$768$	−27.5530	+	2.97210i	−0.994232	+	0.107246i
$769$	−43.4416			−1.56655			−0.783273	−	0.621678i	$-0.786451\pi$
$769$	−43.4416			−1.56655			−0.783273	+	0.621678i	$0.786451\pi$
$770$	0.587326	−	0.140987i	0.0211658	−	0.00508082i
$771$	−37.9799	−	7.95548i	−1.36781	−	0.286510i
$772$	34.0532	−	17.3486i	1.22560	−	0.624388i
$773$			6.95049i			0.249992i	0.992157	+	0.124996i	$0.0398918\pi$
$773$			6.95049i			0.249992i	−0.992157	+	0.124996i	$0.960108\pi$
$774$	0.259708	−	1.44883i	0.00933501	−	0.0520772i
$775$		−	9.23693i		−	0.331800i
$776$	−6.25392	+	5.34044i	−0.224503	+	0.191711i
$777$	−2.52755	−	0.529436i	−0.0906754	−	0.0189934i
$778$	−8.63393	−	35.9674i	−0.309541	−	1.28949i
$779$	12.2405			0.438562
$780$	0.806162	−	0.218520i	0.0288652	−	0.00782428i
$781$	−23.9864			−0.858301
$782$	−0.133654	−	0.556776i	−0.00477944	−	0.0199103i
$783$	14.1213	+	10.0694i	0.504654	+	0.359851i
$784$	−2.26602	+	3.11817i	−0.0809294	+	0.111363i
$785$		−	0.558619i		−	0.0199380i
$786$	0.0593615	+	2.03858i	0.00211735	+	0.0727137i
$787$		−	6.96183i		−	0.248162i	−0.992272	−	0.124081i	$-0.960402\pi$
$787$		−	6.96183i		−	0.248162i	0.992272	−	0.124081i	$-0.0395983\pi$
$788$	−2.89394	−	5.68047i	−0.103092	−	0.202358i
$789$	9.31981	−	44.4933i	0.331794	−	1.58400i
$790$	0.954110	−	0.229033i	0.0339457	−	0.00814863i
$791$	−27.0588			−0.962101
$792$	27.1147	−	8.20411i	0.963481	−	0.291520i
$793$	32.5397			1.15552
$794$	29.7346	−	7.13776i	1.05524	−	0.253310i
$795$	0.0465871	−	0.222409i	0.00165227	−	0.00788804i
$796$	15.9227	+	31.2543i	0.564364	+	1.10778i
$797$			39.3251i			1.39297i	0.717574	+	0.696483i	$0.245253\pi$
$797$			39.3251i			1.39297i	−0.717574	+	0.696483i	$0.754747\pi$
$798$	−0.604546	−	20.7612i	−0.0214007	−	0.734938i
$799$			0.0211713i			0.000748986i
$800$	−10.8232	+	26.1190i	−0.382657	+	0.923446i
$801$	0.842270	−	1.92231i	0.0297602	−	0.0679214i
$802$	10.0509	+	41.8704i	0.354911	+	1.47849i
$803$	−16.6996			−0.589317
$804$	3.34345	−	0.906284i	0.117914	−	0.0319622i
$805$	1.11881			0.0394328
$806$	−3.24489	−	13.5176i	−0.114296	−	0.476138i
$807$	27.2837	+	5.71500i	0.960432	+	0.201178i
$808$	34.6920	+	40.6261i	1.22046	+	1.42922i
$809$			1.17193i			0.0412029i	0.999788	+	0.0206014i	$0.00655811\pi$
$809$			1.17193i			0.0412029i	−0.999788	+	0.0206014i	$0.993442\pi$
$810$	−0.321175	+	0.479341i	−0.0112849	+	0.0168423i
$811$			18.4901i			0.649274i	0.945839	+	0.324637i	$0.105242\pi$
$811$			18.4901i			0.649274i	−0.945839	+	0.324637i	$0.894758\pi$
$812$	−16.7857	+	8.55154i	−0.589062	+	0.300100i
$813$	−22.8669	−	4.78984i	−0.801978	−	0.167987i
$814$	−2.42559	+	0.582261i	−0.0850171	+	0.0204083i
$815$	0.954870			0.0334476
$816$	−0.237751	+	0.215300i	−0.00832295	+	0.00753702i
$817$	−1.04245			−0.0364706
$818$	12.9049	−	3.09780i	0.451208	−	0.108312i
$819$	18.0712	−	41.2437i	0.631457	−	1.44117i
$820$	0.329102	−	0.167663i	0.0114928	−	0.00585503i
$821$		−	21.7270i		−	0.758278i	−0.925340	−	0.379139i	$-0.876220\pi$
$821$		−	21.7270i		−	0.758278i	0.925340	−	0.379139i	$-0.123780\pi$
$822$	12.0527	−	0.350963i	0.420387	−	0.0122413i
$823$			4.79475i			0.167135i	0.996502	+	0.0835673i	$0.0266314\pi$
$823$			4.79475i			0.167135i	−0.996502	+	0.0835673i	$0.973369\pi$
$824$	−26.4213	−	30.9407i	−0.920429	−	1.07787i
$825$	5.92518	−	28.2871i	0.206288	−	0.984831i
$826$	−0.211242	−	0.879995i	−0.00735004	−	0.0306189i
$827$	−54.0235			−1.87858			−0.939290	−	0.343124i	$-0.888515\pi$
$827$	−54.0235			−1.87858			−0.939290	+	0.343124i	$0.888515\pi$
$828$	52.3843	−	3.05335i	1.82048	−	0.106111i
$829$	2.34284			0.0813702			0.0406851	−	0.999172i	$-0.487046\pi$
$829$	2.34284			0.0813702			0.0406851	+	0.999172i	$0.487046\pi$
$830$	−0.213744	−	0.890419i	−0.00741917	−	0.0309069i
$831$	−4.82617	+	23.0404i	−0.167418	+	0.799263i
$832$	−6.66348	+	42.0255i	−0.231015	+	1.45697i
$833$			0.0446131i			0.00154575i
$834$	15.4481	−	0.449834i	0.534925	−	0.0155765i
$835$		−	0.985995i		−	0.0341218i
$836$	−9.10739	−	17.8768i	−0.314986	−	0.618281i
$837$	7.81899	+	5.57545i	0.270264	+	0.192716i
$838$	−19.9832	+	4.79696i	−0.690310	+	0.165708i
$839$	16.2551			0.561190			0.280595	−	0.959826i	$-0.409468\pi$
$839$	16.2551			0.561190			0.280595	+	0.959826i	$0.409468\pi$
$840$	−0.300627	−	0.549912i	−0.0103726	−	0.0189738i
$841$	17.8591			0.615832
$842$	−10.6691	+	2.56111i	−0.367682	+	0.0882617i
$843$	−24.1837	−	5.06566i	−0.832931	−	0.174470i
$844$	−2.90553	−	5.70322i	−0.100012	−	0.196313i
$845$		−	0.693128i		−	0.0238443i
$846$	−1.90973	−	0.342325i	−0.0656577	−	0.0117694i
$847$		−	0.412198i		−	0.0141633i
$848$	9.36452	+	6.80534i	0.321579	+	0.233696i
$849$	−3.48577	−	0.730149i	−0.119631	−	0.0250587i
$850$	0.0763810	+	0.318189i	0.00261985	+	0.0109138i
$851$	−4.62056			−0.158391
$852$	6.51131	+	24.0214i	0.223074	+	0.822961i
$853$	43.8622			1.50181			0.750906	−	0.660409i	$-0.229617\pi$
$853$	43.8622			1.50181			0.750906	+	0.660409i	$0.229617\pi$
$854$	−5.69907	−	23.7413i	−0.195018	−	0.812410i
$855$	0.374287	+	0.163996i	0.0128003	+	0.00560854i
$856$	1.41896	−	1.21170i	0.0484989	−	0.0414149i
$857$			4.50112i			0.153755i	0.997041	+	0.0768777i	$0.0244951\pi$
$857$			4.50112i			0.153755i	−0.997041	+	0.0768777i	$0.975505\pi$
$858$	−1.26603	−	43.4777i	−0.0432215	−	1.48431i
$859$			4.27027i			0.145700i	0.997343	+	0.0728499i	$0.0232094\pi$
$859$			4.27027i			0.145700i	−0.997343	+	0.0728499i	$0.976791\pi$
$860$	−0.0280276	+	0.0142788i	−0.000955733	+	0.000486902i
$861$	4.08225	−	19.4889i	0.139123	−	0.664179i
$862$	33.3375	−	8.00264i	1.13548	−	0.272571i
$863$	11.8273			0.402606			0.201303	−	0.979529i	$-0.435482\pi$
$863$	11.8273			0.402606			0.201303	+	0.979529i	$0.435482\pi$
$864$	−15.5766	−	24.9273i	−0.529927	−	0.848043i
$865$	1.17364			0.0399048
$866$	−42.4535	+	10.1909i	−1.44263	+	0.346302i
$867$	6.03592	−	28.8158i	0.204990	−	0.978635i
$868$	−9.29427	+	4.73501i	−0.315468	+	0.160717i
$869$		−	51.0972i		−	1.73335i
$870$	−0.0107880	−	0.370479i	−0.000365747	−	0.0125604i
$871$		−	5.31881i		−	0.180221i
$872$	−24.5448	+	20.9596i	−0.831192	+	0.709783i
$873$	−7.98945	−	3.50063i	−0.270402	−	0.118478i
$874$	−8.67442	−	36.1361i	−0.293417	−	1.22232i
$875$	−1.27903			−0.0432390
$876$	4.53326	+	16.7240i	0.153165	+	0.565052i
$877$	37.0994			1.25276			0.626380	−	0.779518i	$-0.284536\pi$
$877$	37.0994			1.25276			0.626380	+	0.779518i	$0.284536\pi$
$878$	−12.1527	−	50.6261i	−0.410135	−	1.70855i
$879$	−51.8411	−	10.8589i	−1.74856	−	0.366263i
$880$	−0.489729	−	0.355893i	−0.0165088	−	0.0119972i
$881$		−	6.46201i		−	0.217711i	−0.994058	−	0.108855i	$-0.965281\pi$
$881$		−	6.46201i		−	0.217711i	0.994058	−	0.108855i	$-0.0347185\pi$
$882$	−4.02427	−	0.721363i	−0.135504	−	0.0242896i
$883$			18.6252i			0.626789i	0.949623	+	0.313395i	$0.101466\pi$
$883$			18.6252i			0.626789i	−0.949623	+	0.313395i	$0.898534\pi$
$884$	0.223557	+	0.438816i	0.00751903	+	0.0147590i
$885$	0.0174270	+	0.00365037i	0.000585804	+	0.000122706i
$886$	27.5376	−	6.61037i	0.925143	−	0.222080i
$887$	−3.54980			−0.119190			−0.0595952	−	0.998223i	$-0.518981\pi$
$887$	−3.54980			−0.119190			−0.0595952	+	0.998223i	$0.518981\pi$
$888$	1.24156	+	2.27108i	0.0416640	+	0.0762124i
$889$	−19.5522			−0.655760
$890$	−0.0436112	+	0.0104688i	−0.00146185	+	0.000350916i
$891$	20.3684	+	22.0899i	0.682366	+	0.740038i
$892$	−21.4855	−	42.1735i	−0.719388	−	1.41207i
$893$			1.37406i			0.0459813i
$894$	42.8516	−	1.24780i	1.43317	−	0.0417325i
$895$		−	0.0850511i		−	0.00284294i
$896$	31.8293	−	2.49869i	1.06334	−	0.0834753i
$897$	16.5177	−	78.8565i	0.551511	−	2.63294i
$898$	−6.29971	−	26.2435i	−0.210224	−	0.875756i
$899$	−6.16873			−0.205739
$900$	−29.9369	+	1.74494i	−0.997895	+	0.0581648i
$901$	0.133982			0.00446360
$902$	−4.48957	−	18.7027i	−0.149486	−	0.622733i
$903$	−0.347660	+	1.65975i	−0.0115694	+	0.0552329i
$904$	17.6116	+	20.6241i	0.585754	+	0.685947i
$905$		−	0.492792i		−	0.0163810i
$906$	36.0717	−	1.05037i	1.19840	−	0.0348963i
$907$			18.7682i			0.623187i	0.950216	+	0.311593i	$0.100863\pi$
$907$			18.7682i			0.623187i	−0.950216	+	0.311593i	$0.899137\pi$
$908$	45.8101	−	23.3382i	1.52026	−	0.774505i
$909$	−22.7404	+	51.9003i	−0.754252	+	1.72142i
$910$	−0.935692	+	0.224612i	−0.0310179	+	0.00744581i
$911$	−18.4902			−0.612609			−0.306305	−	0.951934i	$-0.599093\pi$
$911$	−18.4902			−0.612609			−0.306305	+	0.951934i	$0.599093\pi$
$912$	−15.4306	+	13.9735i	−0.510958	+	0.462709i
$913$	−47.6862			−1.57818
$914$	19.7577	−	4.74282i	0.653527	−	0.156878i
$915$	0.470162	+	0.0984829i	0.0155431	+	0.00325574i
$916$	−21.2749	+	10.8386i	−0.702941	+	0.358116i
$917$		−	2.34959i		−	0.0775903i
$918$	−0.315449	−	0.127405i	−0.0104114	−	0.00420498i
$919$		−	47.1741i		−	1.55613i	−0.628183	−	0.778065i	$-0.716201\pi$
$919$		−	47.1741i		−	1.55613i	0.628183	−	0.778065i	$-0.283799\pi$
$920$	−0.728192	−	0.852749i	−0.0240078	−	0.0281143i
$921$	30.4963	+	6.38793i	1.00489	+	0.210489i
$922$	−8.23100	−	34.2888i	−0.271074	−	1.12924i
$923$	38.2137			1.25782
$924$	−31.5001	+	8.53849i	−1.03628	+	0.280896i
$925$	2.64058			0.0868218
$926$	5.16959	+	21.5356i	0.169883	+	0.707703i
$927$	17.3190	−	39.5270i	0.568831	−	1.29824i
$928$	17.4431	+	7.22807i	0.572599	+	0.237273i
$929$			60.1181i			1.97241i	0.165522	+	0.986206i	$0.447069\pi$
$929$			60.1181i			1.97241i	−0.165522	+	0.986206i	$0.552931\pi$
$930$	−0.00597334	−	0.205135i	−0.000195874	−	0.00672665i
$931$			2.89549i			0.0948960i
$932$	−16.1820	−	31.7634i	−0.530059	−	1.04045i
$933$	−9.54592	+	45.5727i	−0.312520	+	1.49198i
$934$	0.0924926	−	0.0222027i	0.00302645	−	0.000726496i
$935$	−0.00700678			−0.000229146
$936$	−43.1976	+	13.0703i	−1.41196	+	0.427216i
$937$	12.3494			0.403438			0.201719	−	0.979443i	$-0.435347\pi$
$937$	12.3494			0.403438			0.201719	+	0.979443i	$0.435347\pi$
$938$	−3.88066	+	0.931548i	−0.126708	+	0.0304161i
$939$	−5.19137	+	24.7839i	−0.169414	+	0.808792i
$940$	0.0188210	+	0.0369435i	0.000613875	+	0.00120497i
$941$		−	24.8282i		−	0.809376i	−0.914455	−	0.404688i	$-0.867380\pi$
$941$		−	24.8282i		−	0.809376i	0.914455	−	0.404688i	$-0.132620\pi$
$942$	0.878559	+	30.1713i	0.0286250	+	0.983034i
$943$		−	35.6272i		−	1.16018i
$944$	−0.533238	+	0.733764i	−0.0173554	+	0.0238820i
$945$	0.385934	−	0.541232i	0.0125544	−	0.0176063i
$946$	0.382349	+	1.59279i	0.0124312	+	0.0517862i
$947$	−11.3420			−0.368564			−0.184282	−	0.982873i	$-0.558996\pi$
$947$	−11.3420			−0.368564			−0.184282	+	0.982873i	$0.558996\pi$
$948$	−51.1718	+	13.8708i	−1.66198	+	0.450502i
$949$	26.6048			0.863630
$950$	4.95730	+	20.6512i	0.160836	+	0.670014i
$951$	−27.8496	−	5.83353i	−0.903084	−	0.189165i
$952$	0.281010	−	0.239964i	0.00910760	−	0.00777729i
$953$		−	29.4402i		−	0.953663i	−0.878995	−	0.476831i	$-0.841785\pi$
$953$		−	29.4402i		−	0.953663i	0.878995	−	0.476831i	$-0.158215\pi$
$954$	−2.16640	+	12.0857i	−0.0701399	+	0.391289i
$955$			0.181426i			0.00587081i
$956$	39.6897	−	20.2201i	1.28366	−	0.653965i
$957$	−18.8911	−	3.95703i	−0.610662	−	0.127913i
$958$	−14.3753	+	3.45078i	−0.464445	+	0.111490i
$959$	−13.8915			−0.448580
$960$	−0.223472	+	0.587054i	−0.00721253	+	0.0189471i
$961$	27.5844			0.889818
$962$	3.86431	−	0.927624i	0.124590	−	0.0299078i
$963$	1.81273	+	0.794259i	0.0584145	+	0.0255947i
$964$	34.5152	−	17.5839i	1.11166	−	0.566340i
$965$		−	0.866259i		−	0.0278858i
$966$	−60.4274	+	1.75959i	−1.94422	+	0.0566138i
$967$			29.6692i			0.954097i	0.878877	+	0.477049i	$0.158293\pi$
$967$			29.6692i			0.954097i	−0.878877	+	0.477049i	$0.841707\pi$
$968$	−0.314175	+	0.268285i	−0.0100980	+	0.00862300i
$969$	−0.0493967	+	0.235823i	−0.00158685	+	0.00757571i
$970$	0.0435103	+	0.181256i	0.00139703	+	0.00581978i
$971$	32.1612			1.03210			0.516050	−	0.856558i	$-0.327402\pi$
$971$	32.1612			1.03210			0.516050	+	0.856558i	$0.327402\pi$
$972$	16.5930	−	26.3946i	0.532219	−	0.846607i
$973$	−17.8049			−0.570799
$974$	7.86725	+	32.7735i	0.252083	+	1.05013i
$975$	−9.43964	+	45.0653i	−0.302310	+	1.44324i
$976$	−14.3862	+	19.7962i	−0.460490	+	0.633659i
$977$		−	18.5520i		−	0.593531i	−0.954950	−	0.296766i	$-0.904092\pi$
$977$		−	18.5520i		−	0.593531i	0.954950	−	0.296766i	$-0.0959080\pi$
$978$	−51.5731	+	1.50176i	−1.64912	+	0.0480209i
$979$			2.33559i			0.0746458i
$980$	0.0396606	+	0.0778492i	0.00126691	+	0.00248680i
$981$	−31.3563	−	13.7389i	−1.00113	−	0.438650i
$982$	40.4472	−	9.70930i	1.29072	−	0.309836i
$983$	−49.7253			−1.58599			−0.792995	−	0.609228i	$-0.791479\pi$
$983$	−49.7253			−1.58599			−0.792995	+	0.609228i	$0.791479\pi$
$984$	−17.5113	+	9.57314i	−0.558240	+	0.305181i
$985$	−0.144502			−0.00460421
$986$	0.212497	−	0.0510098i	0.00676730	−	0.00162448i
$987$	2.18773	+	0.458255i	0.0696363	+	0.0145864i
$988$	14.5093	+	28.4802i	0.461604	+	0.906075i
$989$			3.03414i			0.0964801i
$990$	0.113295	−	0.632037i	0.00360074	−	0.0200874i
$991$			2.66567i			0.0846779i	0.999103	+	0.0423389i	$0.0134809\pi$
$991$			2.66567i			0.0846779i	−0.999103	+	0.0423389i	$0.986519\pi$
$992$	9.65831	+	4.00220i	0.306652	+	0.127070i
$993$	30.5695	+	6.40326i	0.970093	+	0.203201i
$994$	−6.69283	−	27.8811i	−0.212284	−	0.884335i
$995$	0.795060			0.0252051
$996$	12.9448	+	47.7559i	0.410173	+	1.51320i
$997$	11.0297			0.349315			0.174657	−	0.984629i	$-0.444118\pi$
$997$	11.0297			0.349315			0.174657	+	0.984629i	$0.444118\pi$
$998$	−13.0646	−	54.4248i	−0.413553	−	1.72279i
$999$	−1.59387	+	2.23523i	−0.0504277	+	0.0707196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.c.b.671.12	yes	128
3.2	odd	2	inner	804.2.c.b.671.117	yes	128
4.3	odd	2	inner	804.2.c.b.671.118	yes	128
12.11	even	2	inner	804.2.c.b.671.11	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.c.b.671.11	✓	128	12.11	even	2	inner
804.2.c.b.671.12	yes	128	1.1	even	1	trivial
804.2.c.b.671.117	yes	128	3.2	odd	2	inner
804.2.c.b.671.118	yes	128	4.3	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)

\(f(q)\)	\(=\)	\(q+(-1.37515 + 0.330103i) q^{2} +(0.355099 - 1.69526i) q^{3} +(1.78206 - 0.907880i) q^{4} -0.0453328i q^{5} +(0.0712965 + 2.44845i) q^{6} -2.82199i q^{7} +(-2.15091 + 1.83673i) q^{8} +(-2.74781 - 1.20397i) q^{9} +O(q^{10})\)	\(q+(-1.37515 + 0.330103i) q^{2} +(0.355099 - 1.69526i) q^{3} +(1.78206 - 0.907880i) q^{4} -0.0453328i q^{5} +(0.0712965 + 2.44845i) q^{6} -2.82199i q^{7} +(-2.15091 + 1.83673i) q^{8} +(-2.74781 - 1.20397i) q^{9} +(0.0149645 + 0.0623394i) q^{10} +3.33857 q^{11} +(-0.906284 - 3.34345i) q^{12} -5.31881 q^{13} +(0.931548 + 3.88066i) q^{14} +(-0.0768509 - 0.0160976i) q^{15} +(2.35151 - 3.23580i) q^{16} -0.0462961i q^{17} +(4.17608 + 0.748576i) q^{18} -3.00472i q^{19} +(-0.0411568 - 0.0807860i) q^{20} +(-4.78401 - 1.00209i) q^{21} +(-4.59103 + 1.10207i) q^{22} -8.74554 q^{23} +(2.34996 + 4.29857i) q^{24} +4.99794 q^{25} +(7.31415 - 1.75575i) q^{26} +(-3.01678 + 4.23072i) q^{27} +(-2.56203 - 5.02897i) q^{28} -3.33779i q^{29} +(0.110995 - 0.00323207i) q^{30} -1.84815i q^{31} +(-2.16552 + 5.22595i) q^{32} +(1.18552 - 5.65975i) q^{33} +(0.0152825 + 0.0636640i) q^{34} -0.127929 q^{35} +(-5.98983 + 0.349132i) q^{36} +0.528333 q^{37} +(0.991868 + 4.13194i) q^{38} +(-1.88870 + 9.01677i) q^{39} +(0.0832644 + 0.0975068i) q^{40} +4.07375i q^{41} +(6.90952 - 0.201198i) q^{42} -0.346936i q^{43} +(5.94955 - 3.03102i) q^{44} +(-0.0545793 + 0.124566i) q^{45} +(12.0264 - 2.88693i) q^{46} -0.457301 q^{47} +(-4.65051 - 5.13544i) q^{48} -0.963647 q^{49} +(-6.87291 + 1.64984i) q^{50} +(-0.0784839 - 0.0164397i) q^{51} +(-9.47846 + 4.82884i) q^{52} +2.89403i q^{53} +(2.75195 - 6.81372i) q^{54} -0.151347i q^{55} +(5.18325 + 6.06985i) q^{56} +(-5.09379 - 1.06697i) q^{57} +(1.10182 + 4.58996i) q^{58} -0.226764 q^{59} +(-0.151568 + 0.0410844i) q^{60} -6.11785 q^{61} +(0.610078 + 2.54147i) q^{62} +(-3.39759 + 7.75430i) q^{63} +(1.25281 - 7.90129i) q^{64} +0.241117i q^{65} +(0.238029 + 8.17433i) q^{66} +1.00000i q^{67} +(-0.0420313 - 0.0825027i) q^{68} +(-3.10553 + 14.8260i) q^{69} +(0.175921 - 0.0422297i) q^{70} -7.18463 q^{71} +(8.12166 - 2.45737i) q^{72} -5.00203 q^{73} +(-0.726537 + 0.174404i) q^{74} +(1.77476 - 8.47281i) q^{75} +(-2.72793 - 5.35461i) q^{76} -9.42143i q^{77} +(-0.379213 - 13.0229i) q^{78} -15.3051i q^{79} +(-0.146688 - 0.106600i) q^{80} +(6.10092 + 6.61656i) q^{81} +(-1.34476 - 5.60201i) q^{82} -14.2834 q^{83} +(-9.43519 + 2.55753i) q^{84} -0.00209873 q^{85} +(0.114525 + 0.477088i) q^{86} +(-5.65843 - 1.18525i) q^{87} +(-7.18096 + 6.13207i) q^{88} +0.699578i q^{89} +(0.0339351 - 0.189313i) q^{90} +15.0097i q^{91} +(-15.5851 + 7.93990i) q^{92} +(-3.13309 - 0.656274i) q^{93} +(0.628857 - 0.150956i) q^{94} -0.136213 q^{95} +(8.09036 + 5.52685i) q^{96} +2.90757 q^{97} +(1.32516 - 0.318103i) q^{98} +(-9.17376 - 4.01954i) 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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