LMFDB - Embedded newform 300.2.w.a.223.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.14
Character	$\chi$	$=$	300.223
Dual form			300.2.w.a.187.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.213085 + 1.39807i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-1.90919 - 0.595816i) q^{4} +(-1.90262 - 1.17475i) q^{5} +(1.34243 - 0.444849i) q^{6} +(2.16308 + 2.16308i) q^{7} +(1.23981 - 2.54222i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(2.04780 - 2.40967i) q^{10} +(3.61787 + 4.97957i) q^{11} +(0.335878 + 1.97159i) q^{12} +(0.749054 + 4.72934i) q^{13} +(-3.48505 + 2.56321i) q^{14} +(-0.182937 + 2.22857i) q^{15} +(3.29001 + 2.27505i) q^{16} +(-3.51342 - 1.79018i) q^{17} +(-1.00581 - 0.994154i) q^{18} +(0.678754 + 2.08899i) q^{19} +(2.93253 + 3.37643i) q^{20} +(0.945301 - 2.90934i) q^{21} +(-7.73269 + 3.99695i) q^{22} +(0.374565 - 2.36491i) q^{23} +(-2.82799 + 0.0494622i) q^{24} +(2.23993 + 4.47020i) q^{25} +(-6.77155 + 0.0394750i) q^{26} +(0.987688 + 0.156434i) q^{27} +(-2.84093 - 5.41853i) q^{28} +(1.48003 + 0.480891i) q^{29} +(-3.07671 - 0.730635i) q^{30} +(8.29187 - 2.69419i) q^{31} +(-3.88173 + 4.11487i) q^{32} +(2.79435 - 5.48422i) q^{33} +(3.25145 - 4.53054i) q^{34} +(-1.57444 - 6.65660i) q^{35} +(1.60422 - 1.19435i) q^{36} +(4.07167 - 0.644890i) q^{37} +(-3.06518 + 0.503811i) q^{38} +(3.87381 - 2.81449i) q^{39} +(-5.34536 + 3.38041i) q^{40} +(-5.32533 - 3.86908i) q^{41} +(3.86602 + 1.94153i) q^{42} +(-8.72991 + 8.72991i) q^{43} +(-3.94029 - 11.6625i) q^{44} +(2.06872 - 0.848752i) q^{45} +(3.22649 + 1.02759i) q^{46} +(-3.47691 + 1.77157i) q^{47} +(0.533453 - 3.96427i) q^{48} +2.35783i q^{49} +(-6.72695 + 2.17904i) q^{50} +3.94320i q^{51} +(1.38773 - 9.47550i) q^{52} +(-5.54447 + 2.82505i) q^{53} +(-0.429168 + 1.34752i) q^{54} +(-1.03369 - 13.7243i) q^{55} +(8.18083 - 2.81721i) q^{56} +(1.55316 - 1.55316i) q^{57} +(-0.987690 + 1.96671i) q^{58} +(7.51879 + 5.46272i) q^{59} +(1.67708 - 4.14577i) q^{60} +(-0.715358 + 0.519738i) q^{61} +(1.99979 + 12.1667i) q^{62} +(-3.02139 + 0.478542i) q^{63} +(-4.92573 - 6.30374i) q^{64} +(4.13062 - 9.87809i) q^{65} +(7.07188 + 5.07530i) q^{66} +(1.52131 - 2.98575i) q^{67} +(5.64117 + 5.51114i) q^{68} +(-2.27720 + 0.739907i) q^{69} +(9.64187 - 0.782756i) q^{70} +(5.96760 + 1.93899i) q^{71} +(1.32795 + 2.49731i) q^{72} +(0.906675 + 0.143603i) q^{73} +(0.0339856 + 5.82989i) q^{74} +(2.96607 - 4.02522i) q^{75} +(-0.0512164 - 4.39269i) q^{76} +(-2.94547 + 18.5969i) q^{77} +(3.10939 + 6.01557i) q^{78} +(2.98135 - 9.17567i) q^{79} +(-3.58702 - 8.19349i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(6.54398 - 6.62073i) q^{82} +(-6.49903 - 3.31142i) q^{83} +(-3.53819 + 4.99125i) q^{84} +(4.58170 + 7.53341i) q^{85} +(-10.3448 - 14.0652i) q^{86} +(-0.243442 - 1.53704i) q^{87} +(17.1446 - 3.02368i) q^{88} +(0.440547 + 0.606362i) q^{89} +(0.745798 + 3.07307i) q^{90} +(-8.60967 + 11.8502i) q^{91} +(-2.12417 + 4.29189i) q^{92} +(-6.16497 - 6.16497i) q^{93} +(-1.73590 - 5.23845i) q^{94} +(1.16263 - 4.77192i) q^{95} +(5.42865 + 1.59053i) q^{96} +(-7.49977 - 14.7191i) q^{97} +(-3.29641 - 0.502419i) q^{98} -6.15509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

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

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

$2$	−0.213085	+	1.39807i	−0.150674	+	0.988583i
$2$	−0.213085	+	1.39807i	−0.150674	+	0.988583i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$4$	−1.90919	−	0.595816i	−0.954595	−	0.297908i
$5$	−1.90262	−	1.17475i	−0.850878	−	0.525364i
$5$	−1.90262	−	1.17475i	−0.850878	−	0.525364i
$6$	1.34243	−	0.444849i	0.548043	−	0.181609i
$7$	2.16308	+	2.16308i	0.817567	+	0.817567i	0.985755	−	0.168188i	$-0.0537915\pi$
$7$	2.16308	+	2.16308i	0.817567	+	0.817567i	−0.168188	+	0.985755i	$0.553791\pi$
$8$	1.23981	−	2.54222i	0.438340	−	0.898809i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$	2.04780	−	2.40967i	0.647571	−	0.762005i
$11$	3.61787	+	4.97957i	1.09083	+	1.50140i	0.847011	+	0.531575i	$0.178400\pi$
$11$	3.61787	+	4.97957i	1.09083	+	1.50140i	0.243817	+	0.969821i	$0.421600\pi$
$12$	0.335878	+	1.97159i	0.0969596	+	0.569150i
$13$	0.749054	+	4.72934i	0.207750	+	1.31168i	0.842387	+	0.538872i	$0.181150\pi$
$13$	0.749054	+	4.72934i	0.207750	+	1.31168i	−0.634637	+	0.772810i	$0.718850\pi$
$14$	−3.48505	+	2.56321i	−0.931420	+	0.685047i
$15$	−0.182937	+	2.22857i	−0.0472343	+	0.575415i
$16$	3.29001	+	2.27505i	0.822502	+	0.568763i
$17$	−3.51342	−	1.79018i	−0.852130	−	0.434182i	−0.0273432	−	0.999626i	$-0.508705\pi$
$17$	−3.51342	−	1.79018i	−0.852130	−	0.434182i	−0.824786	+	0.565444i	$0.808705\pi$
$18$	−1.00581	−	0.994154i	−0.237072	−	0.234324i
$19$	0.678754	+	2.08899i	0.155717	+	0.479247i	0.998233	−	0.0594243i	$-0.0189265\pi$
$19$	0.678754	+	2.08899i	0.155717	+	0.479247i	−0.842516	+	0.538671i	$0.818926\pi$
$20$	2.93253	+	3.37643i	0.655733	+	0.754993i
$21$	0.945301	−	2.90934i	0.206281	−	0.634869i
$22$	−7.73269	+	3.99695i	−1.64862	+	0.852153i
$23$	0.374565	−	2.36491i	0.0781022	−	0.493118i	−0.917368	−	0.398041i	$-0.869690\pi$
$23$	0.374565	−	2.36491i	0.0781022	−	0.493118i	0.995470	−	0.0950770i	$-0.0303097\pi$
$24$	−2.82799	+	0.0494622i	−0.577262	+	0.0100964i
$25$	2.23993	+	4.47020i	0.447986	+	0.894041i
$26$	−6.77155	+	0.0394750i	−1.32801	+	0.00774169i
$27$	0.987688	+	0.156434i	0.190081	+	0.0301058i
$28$	−2.84093	−	5.41853i	−0.536886	−	1.02401i
$29$	1.48003	+	0.480891i	0.274834	+	0.0892991i	0.443192	−	0.896427i	$-0.353846\pi$
$29$	1.48003	+	0.480891i	0.274834	+	0.0892991i	−0.168357	+	0.985726i	$0.553846\pi$
$30$	−3.07671	−	0.730635i	−0.561729	−	0.133395i
$31$	8.29187	−	2.69419i	1.48926	−	0.483891i	0.552398	−	0.833580i	$-0.313713\pi$
$31$	8.29187	−	2.69419i	1.48926	−	0.483891i	0.936866	+	0.349689i	$0.113713\pi$
$32$	−3.88173	+	4.11487i	−0.686199	+	0.727414i
$33$	2.79435	−	5.48422i	0.486434	−	0.954680i
$34$	3.25145	−	4.53054i	0.557619	−	0.776981i
$35$	−1.57444	−	6.65660i	−0.266130	−	1.12517i
$36$	1.60422	−	1.19435i	0.267370	−	0.199059i
$37$	4.07167	−	0.644890i	0.669379	−	0.106019i	0.187510	−	0.982263i	$-0.439958\pi$
$37$	4.07167	−	0.644890i	0.669379	−	0.106019i	0.481869	+	0.876243i	$0.339958\pi$
$38$	−3.06518	+	0.503811i	−0.497238	+	0.0817289i
$39$	3.87381	−	2.81449i	0.620306	−	0.450679i
$40$	−5.34536	+	3.38041i	−0.845175	+	0.534489i
$41$	−5.32533	−	3.86908i	−0.831677	−	0.604248i	0.0883565	−	0.996089i	$-0.471839\pi$
$41$	−5.32533	−	3.86908i	−0.831677	−	0.604248i	−0.920033	+	0.391840i	$0.871839\pi$
$42$	3.86602	+	1.94153i	0.596540	+	0.299585i
$43$	−8.72991	+	8.72991i	−1.33130	+	1.33130i	−0.427088	+	0.904210i	$0.640461\pi$
$43$	−8.72991	+	8.72991i	−1.33130	+	1.33130i	−0.904210	+	0.427088i	$0.859539\pi$
$44$	−3.94029	−	11.6625i	−0.594021	−	1.75819i
$45$	2.06872	−	0.848752i	0.308387	−	0.126524i
$46$	3.22649	+	1.02759i	0.475720	+	0.151511i
$47$	−3.47691	+	1.77157i	−0.507159	+	0.258410i	−0.688796	−	0.724955i	$-0.741860\pi$
$47$	−3.47691	+	1.77157i	−0.507159	+	0.258410i	0.181637	+	0.983366i	$0.441860\pi$
$48$	0.533453	−	3.96427i	0.0769973	−	0.572193i
$49$			2.35783i			0.336833i
$50$	−6.72695	+	2.17904i	−0.951334	+	0.308163i
$51$			3.94320i			0.552159i
$52$	1.38773	−	9.47550i	0.192444	−	1.31402i
$53$	−5.54447	+	2.82505i	−0.761592	+	0.388050i	−0.791237	−	0.611510i	$-0.790562\pi$
$53$	−5.54447	+	2.82505i	−0.761592	+	0.388050i	0.0296448	+	0.999560i	$0.490562\pi$
$54$	−0.429168	+	1.34752i	−0.0584024	+	0.183374i
$55$	−1.03369	−	13.7243i	−0.139382	−	1.85059i
$56$	8.18083	−	2.81721i	1.09321	−	0.376465i
$57$	1.55316	−	1.55316i	0.205720	−	0.205720i
$58$	−0.987690	+	1.96671i	−0.129690	+	0.258242i
$59$	7.51879	+	5.46272i	0.978863	+	0.711186i	0.957454	−	0.288585i	$-0.0931849\pi$
$59$	7.51879	+	5.46272i	0.978863	+	0.711186i	0.0214087	+	0.999771i	$0.493185\pi$
$60$	1.67708	−	4.14577i	0.216510	−	0.535216i
$61$	−0.715358	+	0.519738i	−0.0915921	+	0.0665456i	−0.632639	−	0.774447i	$-0.718028\pi$
$61$	−0.715358	+	0.519738i	−0.0915921	+	0.0665456i	0.541047	+	0.840993i	$0.318028\pi$
$62$	1.99979	+	12.1667i	0.253973	+	1.54517i
$63$	−3.02139	+	0.478542i	−0.380660	+	0.0602906i
$64$	−4.92573	−	6.30374i	−0.615717	−	0.787968i
$65$	4.13062	−	9.87809i	0.512341	−	1.22523i
$66$	7.07188	+	5.07530i	0.870488	+	0.624726i
$67$	1.52131	−	2.98575i	0.185858	−	0.364767i	−0.779211	−	0.626761i	$-0.784380\pi$
$67$	1.52131	−	2.98575i	0.185858	−	0.364767i	0.965069	+	0.261994i	$0.0843801\pi$
$68$	5.64117	+	5.51114i	0.684092	+	0.668324i
$69$	−2.27720	+	0.739907i	−0.274142	+	0.0890743i
$70$	9.64187	−	0.782756i	1.15242	−	0.0935573i
$71$	5.96760	+	1.93899i	0.708224	+	0.230116i	0.640910	−	0.767616i	$-0.278557\pi$
$71$	5.96760	+	1.93899i	0.708224	+	0.230116i	0.0673136	+	0.997732i	$0.478557\pi$
$72$	1.32795	+	2.49731i	0.156501	+	0.294310i
$73$	0.906675	+	0.143603i	0.106118	+	0.0168075i	0.209268	−	0.977858i	$-0.432892\pi$
$73$	0.906675	+	0.143603i	0.106118	+	0.0168075i	−0.103149	+	0.994666i	$0.532892\pi$
$74$	0.0339856	+	5.82989i	0.00395074	+	0.677711i
$75$	2.96607	−	4.02522i	0.342493	−	0.464793i
$76$	−0.0512164	−	4.39269i	−0.00587493	−	0.503876i
$77$	−2.94547	+	18.5969i	−0.335667	+	2.11932i
$78$	3.10939	+	6.01557i	0.352069	+	0.681130i
$79$	2.98135	−	9.17567i	0.335429	−	1.03234i	−0.631082	−	0.775716i	$-0.717389\pi$
$79$	2.98135	−	9.17567i	0.335429	−	1.03234i	0.966511	−	0.256627i	$-0.0826112\pi$
$80$	−3.58702	−	8.19349i	−0.401041	−	0.916060i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	6.54398	−	6.62073i	0.722662	−	0.731137i
$83$	−6.49903	−	3.31142i	−0.713361	−	0.363476i	0.0593466	−	0.998237i	$-0.481098\pi$
$83$	−6.49903	−	3.31142i	−0.713361	−	0.363476i	−0.772708	+	0.634762i	$0.781098\pi$
$84$	−3.53819	+	4.99125i	−0.386048	+	0.544590i
$85$	4.58170	+	7.53341i	0.496955	+	0.817114i
$86$	−10.3448	−	14.0652i	−1.11551	−	1.51669i
$87$	−0.243442	−	1.53704i	−0.0260998	−	0.164787i
$88$	17.1446	−	3.02368i	1.82762	−	0.322325i
$89$	0.440547	+	0.606362i	0.0466979	+	0.0642742i	0.831727	−	0.555184i	$-0.187352\pi$
$89$	0.440547	+	0.606362i	0.0466979	+	0.0642742i	−0.785029	+	0.619458i	$0.787352\pi$
$90$	0.745798	+	3.07307i	0.0786140	+	0.323930i
$91$	−8.60967	+	11.8502i	−0.902539	+	1.24224i
$92$	−2.12417	+	4.29189i	−0.221460	+	0.447460i
$93$	−6.16497	−	6.16497i	−0.639278	−	0.639278i
$94$	−1.73590	−	5.23845i	−0.179045	−	0.540305i
$95$	1.16263	−	4.77192i	0.119283	−	0.489589i
$96$	5.42865	+	1.59053i	0.554059	+	0.162333i
$97$	−7.49977	−	14.7191i	−0.761486	−	1.49450i	−0.866036	−	0.499981i	$-0.833340\pi$
$97$	−7.49977	−	14.7191i	−0.761486	−	1.49450i	0.104550	−	0.994520i	$-0.466660\pi$
$98$	−3.29641	−	0.502419i	−0.332987	−	0.0507520i
$99$	−6.15509			−0.618609
$100$	−1.61303	−	9.86905i	−0.161303	−	0.986905i
$101$	11.9475			1.18882			0.594411	−	0.804162i	$-0.297385\pi$
$101$	11.9475			1.18882			0.594411	+	0.804162i	$0.297385\pi$
$102$	−5.51287	−	0.840239i	−0.545855	−	0.0831961i
$103$	−2.47283	−	4.85319i	−0.243655	−	0.478199i	0.736499	−	0.676439i	$-0.236478\pi$
$103$	−2.47283	−	4.85319i	−0.243655	−	0.478199i	−0.980154	+	0.198239i	$0.936478\pi$
$104$	12.9517	+	3.95923i	1.27002	+	0.388235i
$105$	−5.21629	+	4.42487i	−0.509058	+	0.431823i
$106$	−2.76817	−	8.35353i	−0.268868	−	0.811366i
$107$	−0.462862	−	0.462862i	−0.0447466	−	0.0447466i	0.684379	−	0.729126i	$-0.260073\pi$
$107$	−0.462862	−	0.462862i	−0.0447466	−	0.0447466i	−0.729126	+	0.684379i	$0.760073\pi$
$108$	−1.79248	−	0.887143i	−0.172481	−	0.0853654i
$109$	2.19584	−	3.02232i	0.210324	−	0.289486i	−0.690802	−	0.723044i	$-0.742742\pi$
$109$	2.19584	−	3.02232i	0.210324	−	0.289486i	0.901125	+	0.433559i	$0.142742\pi$
$110$	19.4078	+	1.47929i	1.85046	+	0.141045i
$111$	−2.42310	−	3.33511i	−0.229991	−	0.316555i
$112$	2.19543	+	12.0377i	0.207449	+	1.13745i
$113$	0.121019	+	0.764081i	0.0113845	+	0.0718787i	0.992726	−	0.120392i	$-0.0384150\pi$
$113$	0.121019	+	0.764081i	0.0113845	+	0.0718787i	−0.981342	+	0.192270i	$0.938415\pi$
$114$	1.84046	+	2.50237i	0.172375	+	0.234369i
$115$	−3.49083	+	4.05951i	−0.325522	+	0.378551i
$116$	−2.53913	−	1.79994i	−0.235753	−	0.167120i
$117$	−4.26640	−	2.17384i	−0.394429	−	0.200971i
$118$	−9.23940	+	9.34775i	−0.850556	+	0.860530i
$119$	−3.72751	−	11.4721i	−0.341701	−	1.05165i
$120$	5.43871	+	3.22808i	0.496484	+	0.294682i
$121$	−8.30794	+	25.5692i	−0.755268	+	2.32448i
$122$	−0.574196	−	1.11087i	−0.0519853	−	0.100573i
$123$	−1.02972	+	6.50143i	−0.0928472	+	0.586214i
$124$	−17.4360	+	0.203294i	−1.56580	+	0.0182564i
$125$	0.989632	−	11.1365i	0.0885154	−	0.996075i
$126$	−0.0252191	−	4.32609i	−0.00224669	−	0.385398i
$127$	6.14470	+	0.973224i	0.545254	+	0.0863597i	0.422984	−	0.906137i	$-0.360983\pi$
$127$	6.14470	+	0.973224i	0.545254	+	0.0863597i	0.122270	+	0.992497i	$0.460983\pi$
$128$	9.86266	−	5.54328i	0.871744	−	0.489961i
$129$	11.7417	+	3.81511i	1.03380	+	0.335902i
$130$	12.9301	+	7.87977i	1.13404	+	0.691101i
$131$	−1.58146	+	0.513847i	−0.138173	+	0.0448950i	−0.377287	−	0.926096i	$-0.623143\pi$
$131$	−1.58146	+	0.513847i	−0.138173	+	0.0448950i	0.239114	+	0.970991i	$0.423143\pi$
$132$	−8.60253	+	8.80550i	−0.748754	+	0.766420i
$133$	−3.05045	+	5.98685i	−0.264508	+	0.519126i
$134$	3.85011	+	2.76312i	0.332599	+	0.238697i
$135$	−1.69542	−	1.45792i	−0.145919	−	0.125478i
$136$	−8.90700	+	6.71239i	−0.763769	+	0.575583i
$137$	3.67379	−	0.581872i	0.313873	−	0.0497127i	0.00248964	−	0.999997i	$-0.499208\pi$
$137$	3.67379	−	0.581872i	0.313873	−	0.0497127i	0.311384	+	0.950284i	$0.399208\pi$
$138$	−0.549202	−	3.34134i	−0.0467512	−	0.284434i
$139$	−1.16095	+	0.843477i	−0.0984702	+	0.0715428i	−0.635931	−	0.771746i	$-0.719384\pi$
$139$	−1.16095	+	0.843477i	−0.0984702	+	0.0715428i	0.537461	+	0.843289i	$0.319384\pi$
$140$	−0.960194	+	13.6468i	−0.0811512	+	1.15336i
$141$	3.15697	+	2.29367i	0.265864	+	0.193162i
$142$	−3.98245	+	7.92994i	−0.334200	+	0.665466i
$143$	−20.8401	+	20.8401i	−1.74274	+	1.74274i
$144$	−3.77437	+	1.32443i	−0.314531	+	0.110369i
$145$	−2.25101	−	2.65361i	−0.186936	−	0.220371i
$146$	−0.393966	+	1.23699i	−0.0326049	+	0.102374i
$147$	2.10084	−	1.07043i	0.173274	−	0.0882877i
$148$	−8.15783	−	1.19475i	−0.670569	−	0.0982079i
$149$		−	20.6530i		−	1.69196i	−0.533217	−	0.845979i	$-0.679017\pi$
$149$		−	20.6530i		−	1.69196i	0.533217	−	0.845979i	$-0.320983\pi$
$150$	4.99551	+	5.00449i	0.407881	+	0.408615i
$151$			16.4775i			1.34092i	0.741946	+	0.670459i	$0.233903\pi$
$151$			16.4775i			1.34092i	−0.741946	+	0.670459i	$0.766097\pi$
$152$	6.15219	+	0.864414i	0.499009	+	0.0701132i
$153$	3.51342	−	1.79018i	0.284043	−	0.144727i
$154$	−25.3722	−	8.08070i	−2.04455	−	0.651161i
$155$	−18.9413	−	4.61484i	−1.52140	−	0.370673i
$156$	−9.07275	+	3.06531i	−0.726401	+	0.245421i
$157$	5.04582	−	5.04582i	0.402700	−	0.402700i	−0.476483	−	0.879184i	$-0.658089\pi$
$157$	5.04582	−	5.04582i	0.402700	−	0.402700i	0.879184	+	0.476483i	$0.158089\pi$
$158$	12.1929	+	6.12334i	0.970017	+	0.487147i
$159$	5.03428	+	3.65762i	0.399244	+	0.290068i
$160$	12.2194	−	3.26899i	0.966028	−	0.258436i
$161$	5.92570	−	4.30527i	0.467011	−	0.339303i
$162$	1.39549	−	0.229371i	0.109640	−	0.0180211i
$163$	−9.51202	+	1.50656i	−0.745039	+	0.118003i	−0.517401	−	0.855743i	$-0.673100\pi$
$163$	−9.51202	+	1.50656i	−0.745039	+	0.118003i	−0.227638	+	0.973746i	$0.573100\pi$
$164$	7.86180	+	10.5597i	0.613904	+	0.824575i
$165$	−11.7592	+	7.15173i	−0.915450	+	0.556761i
$166$	6.01444	−	8.38047i	0.466811	−	0.650451i
$167$	8.48953	−	16.6616i	0.656939	−	1.28932i	−0.286598	−	0.958051i	$-0.592525\pi$
$167$	8.48953	−	16.6616i	0.656939	−	1.28932i	0.943538	−	0.331265i	$-0.107475\pi$
$168$	−6.22417	−	6.01019i	−0.480205	−	0.463696i
$169$	−9.44183	+	3.06784i	−0.726294	+	0.235987i
$170$	−11.5085	+	4.80026i	−0.882663	+	0.368163i
$171$	−2.08899	−	0.678754i	−0.159749	−	0.0519056i
$172$	21.8685	−	11.4656i	1.66745	−	0.874246i
$173$	1.08740	+	0.172227i	0.0826731	+	0.0130941i	0.197634	−	0.980276i	$-0.436674\pi$
$173$	1.08740	+	0.172227i	0.0826731	+	0.0130941i	−0.114961	+	0.993370i	$0.536674\pi$
$174$	2.20075	−	0.0128294i	0.166839	−	0.000972593i
$175$	−4.82426	+	14.5146i	−0.364680	+	1.09720i
$176$	0.574042	+	24.6136i	0.0432701	+	1.85532i
$177$	1.45386	−	9.17931i	0.109279	−	0.689959i
$178$	−0.941609	+	0.486709i	−0.0705766	+	0.0364804i
$179$	−3.43461	+	10.5706i	−0.256715	+	0.790086i	0.736772	+	0.676141i	$0.236349\pi$
$179$	−3.43461	+	10.5706i	−0.256715	+	0.790086i	−0.993487	+	0.113945i	$0.963651\pi$
$180$	−4.45529	+	0.387850i	−0.332077	+	0.0289086i
$181$	−3.67610	−	11.3139i	−0.273242	−	0.840952i	−0.989679	−	0.143301i	$-0.954228\pi$
$181$	−3.67610	−	11.3139i	−0.273242	−	0.840952i	0.716437	−	0.697652i	$-0.245772\pi$
$182$	−14.7328	−	14.5620i	−1.09207	−	1.07941i
$183$	0.787855	+	0.401432i	0.0582399	+	0.0296747i
$184$	−5.54772	−	3.88427i	−0.408984	−	0.286352i
$185$	−8.50443	−	3.55621i	−0.625258	−	0.261458i
$186$	9.93272	−	7.30539i	0.728302	−	0.535657i
$187$	−3.79678	−	23.9719i	−0.277648	−	1.75300i
$188$	7.69360	−	1.31067i	0.561114	−	0.0955905i
$189$	1.79807	+	2.47483i	0.130790	+	0.180017i
$190$	6.42373	+	2.64226i	0.466026	+	0.191690i
$191$	−12.4784	+	17.1750i	−0.902904	+	1.24274i	0.0666283	+	0.997778i	$0.478776\pi$
$191$	−12.4784	+	17.1750i	−0.902904	+	1.24274i	−0.969532	+	0.244963i	$0.921224\pi$
$192$	−3.38044	+	7.25070i	−0.243962	+	0.523274i
$193$	7.90062	+	7.90062i	0.568699	+	0.568699i	0.931764	−	0.363065i	$-0.118270\pi$
$193$	7.90062	+	7.90062i	0.568699	+	0.568699i	−0.363065	+	0.931764i	$0.618270\pi$
$194$	22.1764	−	7.34876i	1.59217	−	0.527610i
$195$	−10.6767	+	0.804147i	−0.764575	+	0.0575861i
$196$	1.40483	−	4.50154i	0.100345	−	0.321539i
$197$	7.05910	+	13.8543i	0.502940	+	0.987076i	0.993301	+	0.115556i	$0.0368651\pi$
$197$	7.05910	+	13.8543i	0.502940	+	0.987076i	−0.490361	+	0.871520i	$0.663135\pi$
$198$	1.31156	−	8.60523i	0.0932084	−	0.611547i
$199$	12.4250			0.880782			0.440391	−	0.897806i	$-0.354840\pi$
$199$	12.4250			0.880782			0.440391	+	0.897806i	$0.354840\pi$
$200$	14.1413	−	0.152176i	0.999942	−	0.0107605i
$201$	−3.35098			−0.236360
$202$	−2.54584	+	16.7034i	−0.179125	+	1.17525i
$203$	2.16122	+	4.24163i	0.151688	+	0.297704i
$204$	2.34942	−	7.52832i	0.164493	−	0.527088i
$205$	5.58688	+	13.6173i	0.390205	+	0.951074i
$206$	7.31202	−	2.42303i	0.509452	−	0.168821i
$207$	1.69309	+	1.69309i	0.117678	+	0.117678i
$208$	−8.29509	+	17.2637i	−0.575161	+	1.19702i
$209$	−7.94662	+	10.9376i	−0.549679	+	0.756569i
$210$	−5.07476	−	8.23560i	−0.350191	−	0.568311i
$211$	−5.73506	−	7.89363i	−0.394818	−	0.543420i	0.564616	−	0.825354i	$-0.309024\pi$
$211$	−5.73506	−	7.89363i	−0.394818	−	0.543420i	−0.959434	+	0.281934i	$0.909024\pi$
$212$	12.2687	−	2.09007i	0.842615	−	0.143547i
$213$	−0.981580	−	6.19745i	−0.0672567	−	0.424642i
$214$	0.745742	−	0.548484i	0.0509779	−	0.0374936i
$215$	26.8651	−	6.35425i	1.83219	−	0.433356i
$216$	1.62224	−	2.31697i	0.110379	−	0.157650i
$217$	23.7637	+	12.1082i	1.61319	+	0.821960i
$218$	3.75751	+	3.71395i	0.254490	+	0.251541i
$219$	−0.283670	−	0.873048i	−0.0191687	−	0.0589951i
$220$	−6.20366	+	26.8182i	−0.418251	+	1.80808i
$221$	5.83461	−	17.9571i	0.392479	−	1.20792i
$222$	5.17904	−	2.67700i	0.347595	−	0.179668i
$223$	2.05317	−	12.9632i	0.137490	−	0.868081i	−0.818462	−	0.574560i	$-0.805173\pi$
$223$	2.05317	−	12.9632i	0.137490	−	0.868081i	0.955953	−	0.293520i	$-0.0948269\pi$
$224$	−17.2973	+	0.504313i	−1.15572	+	0.0336958i
$225$	−4.93307	−	0.815379i	−0.328871	−	0.0543586i
$226$	−1.09402	+	0.00637766i	−0.0727734	+	0.000424235i
$227$	20.8358	+	3.30006i	1.38292	+	0.219033i	0.803164	−	0.595759i	$-0.203148\pi$
$227$	20.8358	+	3.30006i	1.38292	+	0.219033i	0.579754	+	0.814791i	$0.303148\pi$
$228$	−3.89066	+	2.03987i	−0.257665	+	0.135094i
$229$	−10.1735	−	3.30556i	−0.672281	−	0.218437i	−0.0470685	−	0.998892i	$-0.514988\pi$
$229$	−10.1735	−	3.30556i	−0.672281	−	0.218437i	−0.625213	+	0.780454i	$0.714988\pi$
$230$	−4.93162	−	5.74544i	−0.325181	−	0.378843i
$231$	17.9072	−	5.81841i	1.17821	−	0.382823i
$232$	3.05749	−	3.16634i	0.200734	−	0.207880i
$233$	1.31152	−	2.57401i	0.0859207	−	0.168629i	−0.844048	−	0.536268i	$-0.819834\pi$
$233$	1.31152	−	2.57401i	0.0859207	−	0.168629i	0.929969	+	0.367639i	$0.119834\pi$
$234$	3.94828	−	5.50150i	0.258107	−	0.359644i
$235$	8.69639	+	0.713863i	0.567290	+	0.0465673i
$236$	−11.1000	−	14.9092i	−0.722549	−	0.970505i
$237$	−9.52909	+	1.50926i	−0.618981	+	0.0980369i
$238$	16.8331	−	2.76678i	1.09113	−	0.179344i
$239$	10.0152	−	7.27645i	0.647828	−	0.470675i	−0.214703	−	0.976679i	$-0.568878\pi$
$239$	10.0152	−	7.27645i	0.647828	−	0.470675i	0.862531	+	0.506005i	$0.168878\pi$
$240$	−5.67198	+	6.91583i	−0.366125	+	0.446415i
$241$	−13.7385	−	9.98161i	−0.884975	−	0.642972i	0.0495877	−	0.998770i	$-0.484209\pi$
$241$	−13.7385	−	9.98161i	−0.884975	−	0.642972i	−0.934563	+	0.355798i	$0.884209\pi$
$242$	−33.9772	−	17.0635i	−2.18414	−	1.09688i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	1.67542	−	0.566056i	0.107258	−	0.0362380i
$245$	2.76986	−	4.48605i	0.176960	−	0.286603i
$246$	−8.87002	−	2.82499i	−0.565532	−	0.180114i
$247$	−9.37111	+	4.77482i	−0.596270	+	0.303815i
$248$	3.43114	−	24.4200i	0.217877	−	1.55067i
$249$			7.29403i			0.462241i
$250$	15.3586	+	3.75659i	0.971366	+	0.237588i
$251$		−	15.2933i		−	0.965305i	−0.875812	−	0.482653i	$-0.839673\pi$
$251$		−	15.2933i		−	0.965305i	0.875812	−	0.482653i	$-0.160327\pi$
$252$	6.05354	+	0.886568i	0.381337	+	0.0558485i
$253$	13.1314	−	6.69076i	0.825561	−	0.420644i
$254$	−2.66998	+	8.38333i	−0.167529	+	0.526017i
$255$	4.63227	−	7.50242i	0.290084	−	0.469820i
$256$	5.64829	+	14.9699i	0.353018	+	0.935616i
$257$	−5.22988	+	5.22988i	−0.326231	+	0.326231i	−0.851151	−	0.524920i	$-0.824095\pi$
$257$	−5.22988	+	5.22988i	−0.326231	+	0.326231i	0.524920	+	0.851151i	$0.324095\pi$
$258$	−7.83577	+	15.6027i	−0.487833	+	0.971385i
$259$	10.2023	+	7.41241i	0.633940	+	0.460584i
$260$	−13.7717	+	16.3980i	−0.854082	+	1.01696i
$261$	−1.25899	+	0.914708i	−0.0779294	+	0.0566190i
$262$	−0.381407	−	2.32048i	−0.0235634	−	0.143360i
$263$	28.6588	−	4.53910i	1.76718	−	0.279893i	0.813683	−	0.581309i	$-0.197459\pi$
$263$	28.6588	−	4.53910i	1.76718	−	0.279893i	0.953493	+	0.301415i	$0.0974591\pi$
$264$	−10.4776	−	13.9032i	−0.644852	−	0.855686i
$265$	13.8678	+	1.13837i	0.851889	+	0.0699293i
$266$	−7.72002	−	5.54045i	−0.473345	−	0.339707i
$267$	0.340268	−	0.667813i	0.0208240	−	0.0408695i
$268$	−4.68343	+	4.79393i	−0.286086	+	0.292836i
$269$	3.35427	−	1.08987i	0.204514	−	0.0664505i	−0.204969	−	0.978768i	$-0.565709\pi$
$269$	3.35427	−	1.08987i	0.204514	−	0.0664505i	0.409482	+	0.912318i	$0.365709\pi$
$270$	2.39954	−	2.05966i	0.146032	−	0.125347i
$271$	−5.83745	−	1.89670i	−0.354600	−	0.115216i	0.126300	−	0.991992i	$-0.459690\pi$
$271$	−5.83745	−	1.89670i	−0.354600	−	0.115216i	−0.480900	+	0.876776i	$0.659690\pi$
$272$	−7.48643	−	13.8829i	−0.453932	−	0.841775i
$273$	14.4673	+	2.29140i	0.875602	+	0.138682i
$274$	0.0306646	+	5.26020i	0.00185251	+	0.317781i
$275$	−14.1559	+	27.3265i	−0.853634	+	1.64785i
$276$	4.78845	−	0.0558308i	0.288231	−	0.00336062i
$277$	3.23161	−	20.4036i	0.194169	−	1.22593i	−0.677384	−	0.735630i	$-0.736886\pi$
$277$	3.23161	−	20.4036i	0.194169	−	1.22593i	0.871552	−	0.490302i	$-0.163114\pi$
$278$	−0.931858	−	1.80282i	−0.0558891	−	0.108126i
$279$	−2.69419	+	8.29187i	−0.161297	+	0.496421i
$280$	−18.8745	−	4.25035i	−1.12797	−	0.254007i
$281$	5.87134	+	18.0701i	0.350255	+	1.07797i	0.958710	+	0.284385i	$0.0917895\pi$
$281$	5.87134	+	18.0701i	0.350255	+	1.07797i	−0.608455	+	0.793588i	$0.708211\pi$
$282$	−3.87941	+	3.92491i	−0.231015	+	0.233725i
$283$	13.1812	+	6.71617i	0.783543	+	0.399235i	0.799522	−	0.600637i	$-0.205086\pi$
$283$	13.1812	+	6.71617i	0.783543	+	0.399235i	−0.0159788	+	0.999872i	$0.505086\pi$
$284$	−10.2380	−	7.25749i	−0.607513	−	0.430653i
$285$	−4.77963	+	1.13050i	−0.283121	+	0.0669649i
$286$	−24.6951	−	33.5766i	−1.46025	−	1.98543i
$287$	−3.14999	−	19.8882i	−0.185938	−	1.17397i
$288$	−1.04738	−	5.55905i	−0.0617175	−	0.327570i
$289$	−0.852962	−	1.17400i	−0.0501742	−	0.0690589i
$290$	4.18959	−	2.58162i	0.246021	−	0.151598i
$291$	−9.71001	+	13.3647i	−0.569211	+	0.783452i
$292$	−1.64545	−	0.814377i	−0.0962929	−	0.0476578i
$293$	−3.69461	−	3.69461i	−0.215842	−	0.215842i	0.590902	−	0.806743i	$-0.298772\pi$
$293$	−3.69461	−	3.69461i	−0.215842	−	0.215842i	−0.806743	+	0.590902i	$0.798772\pi$
$294$	1.04888	+	3.16521i	0.0611718	+	0.184599i
$295$	−7.88808	−	19.2262i	−0.459262	−	1.11939i
$296$	3.40866	−	11.1506i	0.198124	−	0.648116i
$297$	2.79435	+	5.48422i	0.162145	+	0.318227i
$298$	28.8743	+	4.40085i	1.67264	+	0.254934i
$299$	11.4650			0.663040
$300$	−8.06109	+	5.91768i	−0.465407	+	0.341657i
$301$	−37.7670			−2.17685
$302$	−23.0367	−	3.51111i	−1.32561	−	0.202042i
$303$	−5.42405	−	10.6453i	−0.311604	−	0.611557i
$304$	−2.51945	+	8.41699i	−0.144500	+	0.482747i
$305$	1.97162	−	0.148498i	0.112894	−	0.00850297i
$306$	1.75413	+	5.29346i	0.100277	+	0.302607i
$307$	5.17718	+	5.17718i	0.295477	+	0.295477i	0.839239	−	0.543762i	$-0.183001\pi$
$307$	5.17718	+	5.17718i	0.295477	+	0.295477i	−0.543762	+	0.839239i	$0.683001\pi$
$308$	16.7038	−	33.7501i	0.951788	−	1.92309i
$309$	−3.20159	+	4.40661i	−0.182132	+	0.250683i
$310$	10.4880	−	25.4979i	0.595677	−	1.44818i
$311$	−2.74588	−	3.77938i	−0.155705	−	0.214309i	0.724037	−	0.689761i	$-0.242285\pi$
$311$	−2.74588	−	3.77938i	−0.155705	−	0.214309i	−0.879742	+	0.475452i	$0.842285\pi$
$312$	−2.35224	−	13.3375i	−0.133170	−	0.755087i
$313$	−3.67466	−	23.2009i	−0.207704	−	1.31139i	−0.842493	−	0.538707i	$-0.818913\pi$
$313$	−3.67466	−	23.2009i	−0.207704	−	1.31139i	0.634789	−	0.772686i	$-0.281087\pi$
$314$	5.97921	+	8.12959i	0.337426	+	0.458780i
$315$	6.31073	+	2.63890i	0.355570	+	0.148685i
$316$	−11.1590	+	15.7417i	−0.627742	+	0.885542i
$317$	4.91790	+	2.50580i	0.276217	+	0.140740i	0.586612	−	0.809868i	$-0.300461\pi$
$317$	4.91790	+	2.50580i	0.276217	+	0.140740i	−0.310395	+	0.950608i	$0.600461\pi$
$318$	−6.18633	+	6.25888i	−0.346912	+	0.350980i
$319$	2.95992	+	9.10970i	0.165724	+	0.510046i
$320$	1.96649	+	17.7801i	0.109930	+	0.993939i
$321$	−0.202278	+	0.622549i	−0.0112901	+	0.0347473i
$322$	4.75639	+	9.20193i	0.265063	+	0.512803i
$323$	1.35491	−	8.55459i	0.0753894	−	0.475990i
$324$	0.0233174	+	1.99986i	0.00129541	+	0.111104i
$325$	−19.4633	+	13.9418i	−1.07963	+	0.773352i
$326$	−0.0793953	−	13.6195i	−0.00439730	−	0.754313i
$327$	−3.68980	−	0.584407i	−0.204046	−	0.0323178i
$328$	−16.4384	+	8.74121i	−0.907661	+	0.482653i
$329$	−11.3529	−	3.68877i	−0.625905	−	0.203369i
$330$	−7.49290	−	17.9641i	−0.412471	−	0.988889i
$331$	22.9947	−	7.47144i	1.26390	−	0.410668i	0.401020	−	0.916069i	$-0.368656\pi$
$331$	22.9947	−	7.47144i	1.26390	−	0.410668i	0.862884	+	0.505402i	$0.168656\pi$
$332$	10.4349	+	10.1944i	0.572689	+	0.559488i
$333$	−1.87154	+	3.67311i	−0.102560	+	0.201285i
$334$	21.4851	+	15.4193i	1.17561	+	0.843706i
$335$	−6.40199	+	3.89358i	−0.349778	+	0.212729i
$336$	9.72893	−	7.42113i	0.530757	−	0.404856i
$337$	−25.8855	+	4.09986i	−1.41007	+	0.223334i	−0.814591	−	0.580035i	$-0.803039\pi$
$337$	−25.8855	+	4.09986i	−1.41007	+	0.223334i	−0.595482	+	0.803369i	$0.703039\pi$
$338$	−2.27713	−	13.8540i	−0.123859	−	0.753560i
$339$	0.625860	−	0.454714i	0.0339920	−	0.0246967i
$340$	−4.25880	−	17.1126i	−0.230966	−	0.928059i
$341$	43.4148	+	31.5427i	2.35104	+	1.70813i
$342$	1.39408	−	2.77592i	0.0753831	−	0.150104i
$343$	10.0414	−	10.0414i	0.542184	−	0.542184i
$344$	11.3699	+	33.0168i	0.613023	+	1.78014i
$345$	5.20185	+	1.26738i	0.280058	+	0.0682332i
$346$	−0.472492	+	1.48355i	−0.0254014	+	0.0797564i
$347$	−17.8899	+	9.11535i	−0.960379	+	0.489337i	−0.862609	−	0.505872i	$-0.831171\pi$
$347$	−17.8899	+	9.11535i	−0.960379	+	0.489337i	−0.0977699	+	0.995209i	$0.531171\pi$
$348$	−0.451012	+	3.07954i	−0.0241768	+	0.165081i
$349$		−	1.31111i		−	0.0701821i	−0.999384	−	0.0350910i	$-0.988828\pi$
$349$		−	1.31111i		−	0.0701821i	0.999384	−	0.0350910i	$-0.0111721\pi$
$350$	−19.2644	−	9.83749i	−1.02972	−	0.525836i
$351$			4.78829i			0.255580i
$352$	−34.5339	−	4.44226i	−1.84066	−	0.236773i
$353$	−26.1678	+	13.3332i	−1.39277	+	0.709654i	−0.979592	−	0.200995i	$-0.935583\pi$
$353$	−26.1678	+	13.3332i	−1.39277	+	0.709654i	−0.413182	+	0.910649i	$0.635583\pi$
$354$	12.5235	+	3.98857i	0.665617	+	0.211990i
$355$	−9.07625	−	10.6996i	−0.481717	−	0.567875i
$356$	−0.479809	−	1.42014i	−0.0254298	−	0.0752675i
$357$	−8.52946	+	8.52946i	−0.451427	+	0.451427i
$358$	−14.0466	−	7.05426i	−0.742386	−	0.372829i
$359$	2.37394	+	1.72477i	0.125292	+	0.0910299i	0.648666	−	0.761073i	$-0.275327\pi$
$359$	2.37394	+	1.72477i	0.125292	+	0.0910299i	−0.523374	+	0.852103i	$0.675327\pi$
$360$	0.407116	−	6.31144i	0.0214569	−	0.332642i
$361$	11.4682	−	8.33210i	0.603587	−	0.438532i
$362$	16.6009	−	2.72861i	0.872522	−	0.143413i
$363$	26.5541	−	4.20575i	1.39373	−	0.220745i
$364$	23.4980	−	17.4945i	1.23163	−	0.916961i
$365$	−1.55636	−	1.33834i	−0.0814637	−	0.0700518i
$366$	−0.729110	+	1.01594i	−0.0381112	+	0.0531038i
$367$	1.44407	−	2.83414i	0.0753796	−	0.147941i	−0.850241	−	0.526394i	$-0.823544\pi$
$367$	1.44407	−	2.83414i	0.0753796	−	0.147941i	0.925621	+	0.378453i	$0.123544\pi$
$368$	6.61261	−	6.92841i	0.344706	−	0.361169i
$369$	6.26030	−	2.03409i	0.325898	−	0.105891i
$370$	6.78400	−	11.1320i	0.352683	−	0.578725i
$371$	−18.1039	−	5.88233i	−0.939910	−	0.305395i
$372$	8.09691	+	15.4433i	0.419805	+	0.800697i
$373$	8.95416	+	1.41820i	0.463629	+	0.0734316i	0.383879	−	0.923383i	$-0.374588\pi$
$373$	8.95416	+	1.41820i	0.463629	+	0.0734316i	0.0797497	+	0.996815i	$0.474588\pi$
$374$	34.3234	−	0.200090i	1.77482	−	0.0103464i
$375$	−10.3719	+	4.17408i	−0.535605	+	0.215548i
$376$	0.193013	+	11.0355i	0.00995386	+	0.569111i
$377$	−1.16567	+	7.35977i	−0.0600352	+	0.379047i
$378$	−3.84312	+	1.98647i	−0.197669	+	0.102173i
$379$	−9.24861	+	28.4643i	−0.475069	+	1.46211i	0.370795	+	0.928715i	$0.379085\pi$
$379$	−9.24861	+	28.4643i	−0.475069	+	1.46211i	−0.845864	+	0.533398i	$0.820915\pi$
$380$	−5.06286	+	8.41778i	−0.259719	+	0.431823i
$381$	−1.92248	−	5.91680i	−0.0984919	−	0.303127i
$382$	−21.3529	−	21.1054i	−1.09251	−	1.07984i
$383$	−15.4391	−	7.86660i	−0.788900	−	0.401965i	0.0126293	−	0.999920i	$-0.495980\pi$
$383$	−15.4391	−	7.86660i	−0.788900	−	0.401965i	−0.801529	+	0.597956i	$0.795980\pi$
$384$	−9.41665	−	6.27110i	−0.480541	−	0.320021i
$385$	27.4508	−	31.9227i	1.39902	−	1.62693i
$386$	−12.7291	+	9.36210i	−0.647895	+	0.476518i
$387$	−1.93133	−	12.1940i	−0.0981751	−	0.619853i
$388$	5.54859	+	32.5701i	0.281687	+	1.65349i
$389$	−2.48759	−	3.42387i	−0.126126	−	0.173597i	0.741284	−	0.671191i	$-0.234217\pi$
$389$	−2.48759	−	3.42387i	−0.126126	−	0.173597i	−0.867410	+	0.497594i	$0.834217\pi$
$390$	1.15080	−	15.0981i	0.0582729	−	0.764523i
$391$	−5.54961	+	7.63838i	−0.280656	+	0.386290i
$392$	5.99411	+	2.92326i	0.302748	+	0.147647i
$393$	1.17581	+	1.17581i	0.0593117	+	0.0593117i
$394$	−20.8734	+	6.91697i	−1.05159	+	0.348472i
$395$	−16.4515	+	13.9555i	−0.827764	+	0.702176i
$396$	11.7512	+	3.66730i	0.590521	+	0.184289i
$397$	−10.9532	−	21.4968i	−0.549723	−	1.07889i	−0.984009	−	0.178118i	$-0.942999\pi$
$397$	−10.9532	−	21.4968i	−0.549723	−	1.07889i	0.434286	−	0.900775i	$-0.357001\pi$
$398$	−2.64758	+	17.3709i	−0.132711	+	0.870726i
$399$	6.71920			0.336381
$400$	−2.80056	+	19.8030i	−0.140028	+	0.990148i
$401$	11.0326			0.550942			0.275471	−	0.961309i	$-0.411166\pi$
$401$	11.0326			0.550942			0.275471	+	0.961309i	$0.411166\pi$
$402$	0.714045	−	4.68490i	0.0356133	−	0.233662i
$403$	18.9528	+	37.1970i	0.944107	+	1.85291i
$404$	−22.8100	−	7.11851i	−1.13484	−	0.354159i
$405$	−0.529311	+	2.17252i	−0.0263017	+	0.107953i
$406$	−6.39061	+	2.11770i	−0.317160	+	0.105100i
$407$	17.9420	+	17.9420i	0.889354	+	0.889354i
$408$	10.0245	+	4.88883i	0.496286	+	0.242033i
$409$	17.6926	−	24.3518i	0.874843	−	1.20412i	−0.102980	−	0.994683i	$-0.532838\pi$
$409$	17.6926	−	24.3518i	0.874843	−	1.20412i	0.977823	−	0.209435i	$-0.0671624\pi$
$410$	−20.2284	+	4.90919i	−0.999010	+	0.242448i
$411$	−2.18632	−	3.00921i	−0.107843	−	0.148433i
$412$	1.82948	+	10.7390i	0.0901321	+	0.529073i
$413$	4.44744	+	28.0800i	0.218844	+	1.38173i
$414$	−2.72782	+	2.00628i	−0.134065	+	0.0986033i
$415$	8.47510	+	13.9351i	0.416026	+	0.684048i
$416$	−22.3683	−	15.2757i	−1.09669	−	0.748955i
$417$	1.27860	+	0.651480i	0.0626134	+	0.0319031i
$418$	−13.5982	−	13.4406i	−0.665109	−	0.657399i
$419$	4.26390	+	13.1229i	0.208305	+	0.641097i	0.999561	+	0.0296124i	$0.00942730\pi$
$419$	4.26390	+	13.1229i	0.208305	+	0.641097i	−0.791256	+	0.611484i	$0.790573\pi$
$420$	12.5953	−	5.33997i	0.614587	−	0.260564i
$421$	4.03666	−	12.4236i	0.196735	−	0.605487i	−0.803217	−	0.595686i	$-0.796880\pi$
$421$	4.03666	−	12.4236i	0.196735	−	0.605487i	0.999952	−	0.00980083i	$-0.00311975\pi$
$422$	12.2579	−	6.33598i	0.596705	−	0.308431i
$423$	0.610442	−	3.85418i	0.0296807	−	0.187397i
$424$	0.307789	+	17.5978i	0.0149475	+	0.854624i
$425$	0.132643	−	19.7156i	0.00643413	−	0.956346i
$426$	8.87362	−	0.0517291i	0.429928	−	0.00250628i
$427$	−2.67161	−	0.423141i	−0.129288	−	0.0204772i
$428$	0.607911	+	1.15947i	0.0293845	+	0.0560452i
$429$	28.0299	+	9.10745i	1.35329	+	0.439712i
$430$	3.15910	+	38.9133i	0.152345	+	1.87657i
$431$	23.7995	−	7.73293i	1.14638	−	0.372482i	0.326603	−	0.945162i	$-0.394096\pi$
$431$	23.7995	−	7.73293i	1.14638	−	0.372482i	0.819779	+	0.572680i	$0.194096\pi$
$432$	2.89361	+	2.76171i	0.139219	+	0.132873i
$433$	−8.85686	+	17.3826i	−0.425634	+	0.835353i	0.574228	+	0.818696i	$0.305302\pi$
$433$	−8.85686	+	17.3826i	−0.425634	+	0.835353i	−0.999861	+	0.0166575i	$0.994698\pi$
$434$	−21.9918	+	30.6432i	−1.05564	+	1.47092i
$435$	−1.34245	+	3.21038i	−0.0643657	+	0.153926i
$436$	−5.99303	+	4.46186i	−0.287014	+	0.213684i
$437$	5.19451	−	0.822729i	0.248487	−	0.0393565i
$438$	1.28103	−	0.210557i	0.0612098	−	0.0100608i
$439$	5.96431	−	4.33333i	0.284661	−	0.206818i	−0.436287	−	0.899808i	$-0.643707\pi$
$439$	5.96431	−	4.33333i	0.284661	−	0.206818i	0.720948	+	0.692989i	$0.243707\pi$
$440$	−36.1718	−	14.3877i	−1.72442	−	0.685907i
$441$	−1.90752	−	1.38590i	−0.0908345	−	0.0659951i
$442$	23.8620	+	11.9836i	1.13500	+	0.570001i
$443$	11.9556	−	11.9556i	0.568027	−	0.568027i	−0.363548	−	0.931575i	$-0.618435\pi$
$443$	11.9556	−	11.9556i	0.568027	−	0.568027i	0.931575	+	0.363548i	$0.118435\pi$
$444$	2.63905	+	7.81108i	0.125244	+	0.370698i
$445$	−0.125872	−	1.67121i	−0.00596690	−	0.0792229i
$446$	17.6859	+	5.63274i	0.837454	+	0.266718i
$447$	−18.4019	+	9.37625i	−0.870382	+	0.443482i
$448$	2.98074	−	24.2903i	0.140827	−	1.14761i
$449$		−	17.9404i		−	0.846658i	−0.905976	−	0.423329i	$-0.860861\pi$
$449$		−	17.9404i		−	0.846658i	0.905976	−	0.423329i	$-0.139139\pi$
$450$	2.19112	−	6.72302i	0.103290	−	0.316926i
$451$		−	40.5157i		−	1.90781i
$452$	0.224204	−	1.53088i	0.0105457	−	0.0720065i
$453$	14.6815	−	7.48062i	0.689799	−	0.351470i
$454$	−9.05351	+	28.4266i	−0.424902	+	1.33413i
$455$	30.3020	−	12.4322i	1.42058	−	0.582832i
$456$	−2.02284	−	5.87408i	−0.0947281	−	0.275079i
$457$	15.2228	−	15.2228i	0.712092	−	0.712092i	−0.254880	−	0.966973i	$-0.582036\pi$
$457$	15.2228	−	15.2228i	0.712092	−	0.712092i	0.966973	+	0.254880i	$0.0820360\pi$
$458$	6.78921	−	13.5188i	0.317239	−	0.631693i
$459$	−3.19012	−	2.31776i	−0.148902	−	0.108184i
$460$	9.08337	−	5.67047i	0.423514	−	0.264387i
$461$	−10.4823	+	7.61580i	−0.488207	+	0.354703i	−0.804494	−	0.593960i	$-0.797564\pi$
$461$	−10.4823	+	7.61580i	−0.488207	+	0.354703i	0.316287	+	0.948663i	$0.397564\pi$
$462$	4.31876	+	26.2753i	0.200927	+	1.22244i
$463$	−1.76416	+	0.279416i	−0.0819876	+	0.0129856i	−0.197293	−	0.980344i	$-0.563215\pi$
$463$	−1.76416	+	0.279416i	−0.0819876	+	0.0129856i	0.115306	+	0.993330i	$0.463215\pi$
$464$	3.77526	+	4.94927i	0.175262	+	0.229764i
$465$	4.48731	+	18.9719i	0.208094	+	0.879801i
$466$	3.31917	+	2.38208i	0.153758	+	0.110348i
$467$	−9.95367	+	19.5352i	−0.460601	+	0.903980i	0.537552	+	0.843230i	$0.319349\pi$
$467$	−9.95367	+	19.5352i	−0.460601	+	0.903980i	−0.998153	+	0.0607495i	$0.980651\pi$
$468$	6.85015	+	6.69226i	0.316648	+	0.309350i
$469$	9.74913	−	3.16768i	0.450173	−	0.146270i
$470$	−2.85110	+	12.0060i	−0.131512	+	0.553797i
$471$	−6.78662	−	2.20511i	−0.312711	−	0.101606i
$472$	23.2093	−	12.3416i	1.06829	−	0.568070i
$473$	−75.0548	−	11.8875i	−3.45102	−	0.546588i
$474$	−0.0795377	−	13.6439i	−0.00365329	−	0.626686i
$475$	−7.81785	+	7.71335i	−0.358707	+	0.353913i
$476$	0.281265	+	24.1233i	0.0128918	+	1.10569i
$477$	0.973446	−	6.14610i	0.0445710	−	0.281410i
$478$	8.03889	+	15.5524i	0.367690	+	0.711351i
$479$	1.58785	−	4.88691i	0.0725509	−	0.223289i	−0.908205	−	0.418525i	$-0.862547\pi$
$479$	1.58785	−	4.88691i	0.0725509	−	0.223289i	0.980756	+	0.195236i	$0.0625473\pi$
$480$	−8.46018	−	9.40348i	−0.386153	−	0.429208i
$481$	6.09980	+	18.7733i	0.278127	+	0.855987i
$482$	16.8825	−	17.0804i	0.768975	−	0.777993i
$483$	−6.52624	−	3.32529i	−0.296954	−	0.151306i
$484$	31.0960	−	43.8665i	1.41345	−	1.99393i
$485$	−3.02206	+	36.8152i	−0.137225	+	1.67169i
$486$	−0.837909	−	1.13926i	−0.0380083	−	0.0516778i
$487$	2.07383	+	13.0936i	0.0939741	+	0.593329i	0.989069	+	0.147453i	$0.0471076\pi$
$487$	2.07383	+	13.0936i	0.0939741	+	0.593329i	−0.895095	+	0.445876i	$0.852892\pi$
$488$	0.434377	+	2.46297i	0.0196633	+	0.111493i
$489$	5.66072	+	7.79131i	0.255987	+	0.352335i
$490$	5.68159	+	4.82836i	0.256668	+	0.218123i
$491$	−4.99246	+	6.87153i	−0.225307	+	0.310108i	−0.906673	−	0.421835i	$-0.861386\pi$
$491$	−4.99246	+	6.87153i	−0.225307	+	0.310108i	0.681366	+	0.731943i	$0.261386\pi$
$492$	5.83959	−	11.7989i	0.263269	−	0.531937i
$493$	−4.33908	−	4.33908i	−0.195423	−	0.195423i
$494$	−4.67868	−	14.1189i	−0.210504	−	0.635239i
$495$	11.7108	+	7.23068i	0.526361	+	0.324995i
$496$	33.4097	+	10.0005i	1.50014	+	0.449036i
$497$	8.71420	+	17.1026i	0.390885	+	0.767156i
$498$	−10.1976	−	1.55425i	−0.456963	−	0.0696477i
$499$	−25.0509			−1.12143			−0.560716	−	0.828008i	$-0.689474\pi$
$499$	−25.0509			−1.12143			−0.560716	+	0.828008i	$0.689474\pi$
$500$	−8.52467	+	20.6720i	−0.381235	+	0.924478i
$501$	−18.6998			−0.835445
$502$	21.3811	+	3.25878i	0.954285	+	0.145446i
$503$	−1.99779	−	3.92088i	−0.0890770	−	0.174823i	0.842170	−	0.539212i	$-0.181278\pi$
$503$	−1.99779	−	3.92088i	−0.0890770	−	0.174823i	−0.931247	+	0.364389i	$0.881278\pi$
$504$	−2.52940	+	8.27434i	−0.112669	+	0.368569i
$505$	−22.7316	−	14.0353i	−1.01154	−	0.624564i
$506$	6.55604	+	19.7842i	0.291451	+	0.879516i
$507$	7.01996	+	7.01996i	0.311767	+	0.311767i
$508$	−11.1515	−	5.51918i	−0.494769	−	0.244874i
$509$	−21.3937	+	29.4458i	−0.948257	+	1.30516i	0.00404015	+	0.999992i	$0.498714\pi$
$509$	−21.3937	+	29.4458i	−0.948257	+	1.30516i	−0.952297	+	0.305172i	$0.901286\pi$
$510$	9.50182	+	8.07489i	0.420748	+	0.357562i
$511$	1.65059	+	2.27184i	0.0730176	+	0.100500i
$512$	−22.1325	+	4.70684i	−0.978126	+	0.208015i
$513$	0.343607	+	2.16945i	0.0151706	+	0.0957836i
$514$	−6.19732	−	8.42614i	−0.273352	−	0.371661i
$515$	−0.996436	+	12.1387i	−0.0439082	+	0.534897i
$516$	−20.1440	−	14.2797i	−0.886791	−	0.628627i
$517$	−21.4007	−	10.9042i	−0.941200	−	0.479565i
$518$	−12.5370	+	12.6840i	−0.550845	+	0.557305i
$519$	−0.340212	−	1.04707i	−0.0149337	−	0.0459611i
$520$	−19.9910	−	22.7479i	−0.876665	−	0.997562i
$521$	6.05775	−	18.6438i	0.265395	−	0.816801i	−0.726208	−	0.687476i	$-0.758719\pi$
$521$	6.05775	−	18.6438i	0.265395	−	0.816801i	0.991602	−	0.129325i	$-0.0412811\pi$
$522$	−1.01055	−	1.95506i	−0.0442307	−	0.0855707i
$523$	4.80315	−	30.3259i	0.210027	−	1.32606i	−0.627052	−	0.778978i	$-0.715738\pi$
$523$	4.80315	−	30.3259i	0.210027	−	1.32606i	0.837079	−	0.547082i	$-0.184262\pi$
$524$	3.32546	−	0.0387731i	0.145273	−	0.00169381i
$525$	15.1227	−	2.29102i	0.660010	−	0.0999883i
$526$	0.239210	+	41.0341i	0.0104301	+	1.78917i
$527$	−33.9559	−	5.37809i	−1.47914	−	0.234273i
$528$	21.6703	−	11.6858i	0.943079	−	0.508561i
$529$	16.4218	+	5.33577i	0.713991	+	0.231990i
$530$	−4.54653	+	19.1455i	−0.197489	+	0.831627i
$531$	−8.83887	+	2.87192i	−0.383574	+	0.124631i
$532$	9.39095	−	9.61252i	0.407149	−	0.416756i
$533$	14.3092	−	28.0834i	0.619801	−	1.21643i
$534$	0.861142	+	0.618019i	0.0372653	+	0.0267443i
$535$	0.336904	+	1.42440i	0.0145656	+	0.0615821i
$536$	−5.70427	−	7.56927i	−0.246387	−	0.326943i
$537$	10.9778	−	1.73871i	0.473726	−	0.0750309i
$538$	0.808965	+	4.92174i	0.0348769	+	0.212191i
$539$	−11.7410	+	8.53032i	−0.505719	+	0.367427i
$540$	2.36823	+	3.79361i	0.101913	+	0.163251i
$541$	−22.0987	−	16.0556i	−0.950098	−	0.690286i	0.000732404	−	1.00000i	$-0.499767\pi$
$541$	−22.0987	−	16.0556i	−0.950098	−	0.690286i	−0.950830	+	0.309713i	$0.899767\pi$
$542$	3.89559	−	7.75699i	0.167330	−	0.333191i
$543$	−8.41181	+	8.41181i	−0.360985	+	0.360985i
$544$	21.0045	−	7.50830i	0.900560	−	0.321916i
$545$	−7.72833	+	3.17076i	−0.331045	+	0.135821i
$546$	−6.28630	+	19.7380i	−0.269029	+	0.844710i
$547$	−20.0141	+	10.1977i	−0.855739	+	0.436021i	−0.826089	−	0.563539i	$-0.809439\pi$
$547$	−20.0141	+	10.1977i	−0.855739	+	0.436021i	−0.0296502	+	0.999560i	$0.509439\pi$
$548$	−7.36066	−	1.07800i	−0.314432	−	0.0460499i
$549$		−	0.884231i		−	0.0377380i
$550$	−35.1879	−	25.6138i	−1.50042	−	1.09218i
$551$			3.41817i			0.145619i
$552$	−0.942294	+	6.70648i	−0.0401067	+	0.285447i
$553$	26.2966	−	13.3988i	1.11825	−	0.569775i
$554$	27.8370	+	8.86571i	1.18268	+	0.376668i
$555$	0.692321	+	9.19199i	0.0293874	+	0.390178i
$556$	2.71902	−	0.918647i	0.115312	−	0.0389593i
$557$	−1.72925	+	1.72925i	−0.0732707	+	0.0732707i	−0.742792	−	0.669522i	$-0.766499\pi$
$557$	−1.72925	+	1.72925i	−0.0732707	+	0.0732707i	0.669522	+	0.742792i	$0.266499\pi$
$558$	−11.0185	−	5.53354i	−0.466451	−	0.234254i
$559$	−47.8258	−	34.7475i	−2.02282	−	1.46966i
$560$	9.96416	−	25.4822i	0.421063	−	1.07682i
$561$	−19.6355	+	14.2660i	−0.829009	+	0.602311i
$562$	−26.5144	+	4.35805i	−1.11844	+	0.183833i
$563$	10.7903	−	1.70902i	0.454758	−	0.0720266i	0.0751463	−	0.997173i	$-0.476058\pi$
$563$	10.7903	−	1.70902i	0.454758	−	0.0720266i	0.379612	+	0.925146i	$0.376058\pi$
$564$	−4.66064	−	6.26002i	−0.196248	−	0.263594i
$565$	0.667351	−	1.59592i	0.0280757	−	0.0671410i
$566$	−12.1984	+	16.9971i	−0.512737	+	0.714443i
$567$	1.38878	−	2.72564i	0.0583234	−	0.114466i
$568$	12.3280	−	12.7669i	0.517273	−	0.535689i
$569$	−40.3160	+	13.0995i	−1.69014	+	0.549158i	−0.986834	−	0.161734i	$-0.948291\pi$
$569$	−40.3160	+	13.0995i	−1.69014	+	0.549158i	−0.703301	+	0.710892i	$0.748291\pi$
$570$	−0.562042	−	6.92314i	−0.0235414	−	0.289979i
$571$	−22.9908	−	7.47016i	−0.962135	−	0.312617i	−0.214498	−	0.976724i	$-0.568812\pi$
$571$	−22.9908	−	7.47016i	−0.962135	−	0.312617i	−0.747637	+	0.664108i	$0.768812\pi$
$572$	52.2045	−	27.3708i	2.18278	−	1.14443i
$573$	20.9681	+	3.32102i	0.875956	+	0.138738i
$574$	28.4763	−	0.166004i	1.18858	−	0.00692887i
$575$	11.4106	−	3.62285i	0.475856	−	0.151083i
$576$	7.99511	−	0.279758i	0.333129	−	0.0116566i
$577$	−2.35827	+	14.8895i	−0.0981760	+	0.619859i	0.888714	+	0.458463i	$0.151600\pi$
$577$	−2.35827	+	14.8895i	−0.0981760	+	0.619859i	−0.986890	+	0.161396i	$0.948400\pi$
$578$	1.82309	−	0.942336i	0.0758304	−	0.0391960i
$579$	3.45270	−	10.6263i	0.143489	−	0.441615i
$580$	2.71653	+	6.40744i	0.112798	+	0.266054i
$581$	−6.89505	−	21.2208i	−0.286055	−	0.880387i
$582$	−16.6157	−	16.4231i	−0.688742	−	0.680758i
$583$	−34.1267	−	17.3884i	−1.41338	−	0.720155i
$584$	1.48918	−	2.12692i	0.0616226	−	0.0880127i
$585$	5.56362	+	9.14794i	0.230027	+	0.378221i
$586$	5.95259	−	4.37805i	0.245899	−	0.180856i
$587$	−5.76093	−	36.3731i	−0.237779	−	1.50128i	−0.760815	−	0.648968i	$-0.775201\pi$
$587$	−5.76093	−	36.3731i	−0.237779	−	1.50128i	0.523036	−	0.852310i	$-0.324799\pi$
$588$	−4.64868	+	0.791943i	−0.191708	+	0.0326592i
$589$	11.2563	+	15.4929i	0.463807	+	0.638375i
$590$	28.5603	−	6.93125i	1.17581	−	0.285355i
$591$	9.13948	−	12.5794i	0.375948	−	0.517448i
$592$	14.8630	+	7.14157i	0.610865	+	0.293517i
$593$	31.3538	+	31.3538i	1.28755	+	1.28755i	0.936273	+	0.351274i	$0.114251\pi$
$593$	31.3538	+	31.3538i	1.28755	+	1.28755i	0.351274	+	0.936273i	$0.385749\pi$
$594$	−8.26275	+	2.73808i	−0.339025	+	0.112345i
$595$	−6.38480	+	26.2060i	−0.261751	+	1.07434i
$596$	−12.3054	+	39.4304i	−0.504048	+	1.61513i
$597$	−5.64081	−	11.0707i	−0.230863	−	0.453094i
$598$	−2.44303	+	16.0289i	−0.0999029	+	0.655470i
$599$	−44.9068			−1.83484			−0.917421	−	0.397917i	$-0.869733\pi$
$599$	−44.9068			−1.83484			−0.917421	+	0.397917i	$0.869733\pi$
$600$	−6.55561	−	12.5309i	−0.267632	−	0.511573i
$601$	33.0206			1.34694			0.673468	−	0.739216i	$-0.264804\pi$
$601$	33.0206			1.34694			0.673468	+	0.739216i	$0.264804\pi$
$602$	8.04759	−	52.8008i	0.327995	−	2.15200i
$603$	1.52131	+	2.98575i	0.0619527	+	0.121589i
$604$	9.81755	−	31.4586i	0.399470	−	1.28003i
$605$	45.8443	−	38.8888i	1.86384	−	1.58105i
$606$	16.0386	−	5.31484i	0.651526	−	0.215901i
$607$	25.5333	+	25.5333i	1.03636	+	1.03636i	0.999313	+	0.0370508i	$0.0117963\pi$
$607$	25.5333	+	25.5333i	1.03636	+	1.03636i	0.0370508	+	0.999313i	$0.488204\pi$
$608$	−11.2307	−	5.31590i	−0.455464	−	0.215588i
$609$	2.79814	−	3.85132i	0.113387	−	0.156063i
$610$	−0.212512	+	2.78810i	−0.00860437	+	0.112887i
$611$	−10.9828	−	15.1165i	−0.444315	−	0.611547i
$612$	−7.77440	+	1.32444i	−0.314261	+	0.0535371i
$613$	1.23030	+	7.76779i	0.0496912	+	0.313738i	0.999997	+	0.00242026i	$0.000770394\pi$
$613$	1.23030	+	7.76779i	0.0496912	+	0.313738i	−0.950306	+	0.311318i	$0.899230\pi$
$614$	−8.34123	+	6.13487i	−0.336625	+	0.247583i
$615$	9.59672	−	11.1601i	0.386977	−	0.450018i
$616$	43.6256	+	30.5447i	1.75773	+	1.23068i
$617$	7.71828	+	3.93266i	0.310726	+	0.158323i	0.602399	−	0.798195i	$-0.294212\pi$
$617$	7.71828	+	3.93266i	0.310726	+	0.158323i	−0.291672	+	0.956518i	$0.594212\pi$
$618$	−5.47853	−	5.41502i	−0.220379	−	0.217824i
$619$	−1.99490	−	6.13966i	−0.0801817	−	0.246774i	0.902928	−	0.429792i	$-0.141413\pi$
$619$	−1.99490	−	6.13966i	−0.0801817	−	0.246774i	−0.983109	+	0.183018i	$0.941413\pi$
$620$	33.4129	+	20.0961i	1.34189	+	0.807080i
$621$	0.739907	−	2.27720i	0.0296914	−	0.0913808i
$622$	5.86894	−	3.03360i	0.235323	−	0.121636i
$623$	−0.358669	+	2.26455i	−0.0143698	+	0.0907272i
$624$	19.1480	−	0.446571i	0.766532	−	0.0178771i
$625$	−14.9654	+	20.0259i	−0.598617	+	0.801035i
$626$	33.2195	−	0.193654i	1.32772	−	0.00773997i
$627$	13.3532	+	2.11493i	0.533274	+	0.0844622i
$628$	−12.6398	+	6.62705i	−0.504383	+	0.264448i
$629$	−15.4600	−	5.02325i	−0.616429	−	0.200290i
$630$	−5.03408	+	8.26053i	−0.200563	+	0.329107i
$631$	13.7963	−	4.48269i	0.549222	−	0.178453i	−0.0212442	−	0.999774i	$-0.506763\pi$
$631$	13.7963	−	4.48269i	0.549222	−	0.178453i	0.570466	+	0.821321i	$0.306763\pi$
$632$	−19.6302	−	18.9553i	−0.780848	−	0.754003i
$633$	−4.42961	+	8.69361i	−0.176061	+	0.345540i
$634$	−4.55121	+	6.34162i	−0.180752	+	0.251858i
$635$	−10.5477	−	9.07015i	−0.418574	−	0.359938i
$636$	−7.43212	−	9.98258i	−0.294703	−	0.395835i
$637$	−11.1510	+	1.76614i	−0.441818	+	0.0699770i
$638$	−13.3667	+	2.19703i	−0.529193	+	0.0869812i
$639$	−5.07634	+	3.68818i	−0.200817	+	0.145902i
$640$	−25.2769	−	1.03940i	−0.999156	−	0.0410858i
$641$	−15.6806	−	11.3926i	−0.619348	−	0.449982i	0.233346	−	0.972394i	$-0.425033\pi$
$641$	−15.6806	−	11.3926i	−0.619348	−	0.449982i	−0.852694	+	0.522411i	$0.825033\pi$
$642$	−0.827263	−	0.415455i	−0.0326495	−	0.0163967i
$643$	7.59067	−	7.59067i	0.299347	−	0.299347i	−0.541411	−	0.840758i	$-0.682110\pi$
$643$	7.59067	−	7.59067i	0.299347	−	0.299347i	0.840758	+	0.541411i	$0.182110\pi$
$644$	−13.8784	+	4.68896i	−0.546887	+	0.184771i
$645$	−17.8582	−	21.0523i	−0.703166	−	0.828932i
$646$	11.6712	+	3.71712i	0.459197	+	0.146248i
$647$	−21.3418	+	10.8742i	−0.839034	+	0.427509i	−0.820037	−	0.572310i	$-0.806047\pi$
$647$	−21.3418	+	10.8742i	−0.839034	+	0.427509i	−0.0189968	+	0.999820i	$0.506047\pi$
$648$	−2.80091	−	0.393543i	−0.110030	−	0.0154598i
$649$			57.2037i			2.24544i
$650$	−15.3443	−	30.1818i	−0.601851	−	1.18383i
$651$		−	26.6707i		−	1.04531i
$652$	19.0579	+	2.79111i	0.746364	+	0.109308i
$653$	−9.13921	+	4.65666i	−0.357645	+	0.182229i	−0.623576	−	0.781763i	$-0.714321\pi$
$653$	−9.13921	+	4.65666i	−0.357645	+	0.182229i	0.265931	+	0.963992i	$0.414321\pi$
$654$	1.60328	−	5.03406i	0.0626933	−	0.196847i
$655$	3.61256	+	0.880161i	0.141154	+	0.0343907i
$656$	−8.71802	−	24.8447i	−0.340382	−	0.970022i
$657$	−0.649108	+	0.649108i	−0.0253241	+	0.0253241i
$658$	7.57629	−	15.0861i	0.295355	−	0.588117i
$659$	−34.9138	−	25.3664i	−1.36005	−	0.988134i	−0.998442	−	0.0558045i	$-0.982228\pi$
$659$	−34.9138	−	25.3664i	−1.36005	−	0.988134i	−0.361609	−	0.932330i	$-0.617772\pi$
$660$	26.7116	−	6.64771i	1.03975	−	0.258762i
$661$	−8.24772	+	5.99232i	−0.320799	+	0.233074i	−0.736516	−	0.676420i	$-0.763531\pi$
$661$	−8.24772	+	5.99232i	−0.320799	+	0.233074i	0.415717	+	0.909494i	$0.363531\pi$
$662$	5.54574	+	33.7403i	0.215541	+	1.31135i
$663$	−18.6487	+	2.95367i	−0.724257	+	0.114711i
$664$	−16.4759	+	12.4164i	−0.639390	+	0.481850i
$665$	12.8369	−	7.80719i	0.497794	−	0.302750i
$666$	−4.73646	−	3.39923i	−0.183534	−	0.131717i
$667$	1.69163	−	3.32001i	0.0655002	−	0.128551i
$668$	−26.1354	+	26.7520i	−1.01121	+	1.03507i
$669$	−12.4824	+	4.05579i	−0.482598	+	0.156806i
$670$	−4.07932	−	9.78008i	−0.157598	−	0.377837i
$671$	−5.17614	−	1.68183i	−0.199823	−	0.0649263i
$672$	8.30215	+	15.1830i	0.320262	+	0.585699i
$673$	−0.702378	−	0.111246i	−0.0270747	−	0.00428821i	0.142882	−	0.989740i	$-0.454363\pi$
$673$	−0.702378	−	0.111246i	−0.0270747	−	0.00428821i	−0.169957	+	0.985451i	$0.554363\pi$
$674$	−0.216062	−	37.0633i	−0.00832240	−	1.42763i
$675$	1.51306	+	4.76557i	0.0582376	+	0.183427i
$676$	19.8541	−	0.231488i	0.763619	−	0.00890340i
$677$	−0.150123	+	0.947838i	−0.00576969	+	0.0364284i	−0.990405	−	0.138194i	$-0.955870\pi$
$677$	−0.150123	+	0.947838i	−0.00576969	+	0.0364284i	0.984636	+	0.174622i	$0.0558704\pi$
$678$	0.502359	+	0.971888i	0.0192930	+	0.0373251i
$679$	15.6160	−	48.0612i	0.599289	−	1.84442i
$680$	24.8320	−	2.30765i	0.952264	−	0.0884944i
$681$	−6.51886	−	20.0630i	−0.249803	−	0.768816i
$682$	−53.3499	+	53.9756i	−2.04287	+	2.06683i
$683$	31.1864	+	15.8902i	1.19331	+	0.608023i	0.933827	−	0.357724i	$-0.116447\pi$
$683$	31.1864	+	15.8902i	1.19331	+	0.608023i	0.259485	+	0.965747i	$0.416447\pi$
$684$	3.58386	+	2.54052i	0.137032	+	0.0971393i
$685$	−7.67339	−	3.20871i	−0.293185	−	0.122598i
$686$	11.8989	+	16.1782i	0.454301	+	0.617687i
$687$	1.67338	+	10.5653i	0.0638435	+	0.403092i
$688$	−48.5824	+	8.86047i	−1.85219	+	0.337802i
$689$	−17.5137	−	24.1056i	−0.667220	−	0.918349i
$690$	−2.88032	+	7.00248i	−0.109652	+	0.266580i
$691$	−13.7471	+	18.9213i	−0.522964	+	0.719799i	−0.986038	−	0.166521i	$-0.946747\pi$
$691$	−13.7471	+	18.9213i	−0.522964	+	0.719799i	0.463074	+	0.886320i	$0.346747\pi$
$692$	−1.97343	−	0.976700i	−0.0750185	−	0.0371286i
$693$	−13.3139	−	13.3139i	−0.505755	−	0.505755i
$694$	−8.93180	−	26.9536i	−0.339047	−	1.02314i
$695$	3.19971	−	0.240996i	0.121372	−	0.00914149i
$696$	−4.20930	−	1.28675i	−0.159553	−	0.0487742i
$697$	11.7838	+	23.1270i	0.446343	+	0.875997i
$698$	1.83302	+	0.279378i	0.0693808	+	0.0105746i
$699$	−2.88888			−0.109267
$700$	17.8584	−	24.8367i	0.674985	−	0.938737i
$701$	41.4474			1.56545			0.782723	−	0.622370i	$-0.213830\pi$
$701$	41.4474			1.56545			0.782723	+	0.622370i	$0.213830\pi$
$702$	−6.69436	−	1.02031i	−0.252662	−	0.0385093i
$703$	4.11083	+	8.06796i	0.155043	+	0.304289i
$704$	13.5692	−	47.3341i	0.511410	−	1.78397i
$705$	−3.31202	−	8.07263i	−0.124738	−	0.304033i
$706$	−13.0647	−	39.4255i	−0.491697	−	1.48380i
$707$	25.8434	+	25.8434i	0.971941	+	0.971941i
$708$	−8.24487	+	16.6588i	−0.309861	+	0.626076i
$709$	13.9526	−	19.2041i	0.524001	−	0.721226i	−0.462200	−	0.886776i	$-0.652940\pi$
$709$	13.9526	−	19.2041i	0.524001	−	0.721226i	0.986201	+	0.165550i	$0.0529399\pi$
$710$	16.8928	−	10.4093i	0.633975	−	0.390653i
$711$	5.67087	+	7.80529i	0.212674	+	0.292721i
$712$	2.08770	−	0.368193i	0.0782398	−	0.0137986i
$713$	−3.26568	−	20.6187i	−0.122301	−	0.772175i
$714$	−10.1073	−	13.7423i	−0.378255	−	0.514292i
$715$	64.1327	−	15.1689i	2.39843	−	0.567285i
$716$	12.8555	−	18.1349i	0.480431	−	0.677735i
$717$	−11.0302	−	5.62015i	−0.411929	−	0.209888i
$718$	−2.91720	+	2.95141i	−0.108869	+	0.110146i
$719$	0.654007	+	2.01283i	0.0243904	+	0.0750658i	0.962511	−	0.271243i	$-0.0874348\pi$
$719$	0.654007	+	2.01283i	0.0243904	+	0.0750658i	−0.938120	+	0.346309i	$0.887435\pi$
$720$	8.73707	+	1.91405i	0.325611	+	0.0713325i
$721$	5.14893	−	15.8468i	0.191756	−	0.590164i
$722$	9.20515	+	17.8087i	0.342580	+	0.662772i
$723$	−2.65653	+	16.7727i	−0.0987974	+	0.623782i
$724$	0.277385	+	23.7906i	0.0103090	+	0.884170i
$725$	1.16548	+	7.69319i	0.0432849	+	0.285718i
$726$	0.221642	+	38.0206i	0.00822592	+	1.41108i
$727$	12.6019	+	1.99595i	0.467379	+	0.0740255i	0.385682	−	0.922632i	$-0.373966\pi$
$727$	12.6019	+	1.99595i	0.467379	+	0.0740255i	0.0816966	+	0.996657i	$0.473966\pi$
$728$	19.4514	+	36.5797i	0.720917	+	1.35573i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$	2.20273	−	1.89072i	0.0815265	−	0.0699786i
$731$	46.2999	−	15.0437i	1.71246	−	0.556413i
$732$	−1.26498	−	1.23583i	−0.0467552	−	0.0456775i
$733$	−8.55620	+	16.7925i	−0.316030	+	0.620245i	−0.993310	−	0.115481i	$-0.963159\pi$
$733$	−8.55620	+	16.7925i	−0.316030	+	0.620245i	0.677279	+	0.735726i	$0.263159\pi$
$734$	3.65461	+	2.62282i	0.134894	+	0.0968099i
$735$	−5.25459	−	0.431335i	−0.193819	−	0.0159100i
$736$	8.27734	+	10.7212i	0.305107	+	0.395189i
$737$	20.3716	−	3.22655i	0.750399	−	0.118852i
$738$	1.50982	+	9.18576i	0.0555774	+	0.338133i
$739$	−14.1263	+	10.2634i	−0.519645	+	0.377544i	−0.816470	−	0.577387i	$-0.804072\pi$
$739$	−14.1263	+	10.2634i	−0.519645	+	0.377544i	0.296825	+	0.954932i	$0.404072\pi$
$740$	14.1177	+	11.8566i	0.518978	+	0.435856i
$741$	8.50879	+	6.18200i	0.312578	+	0.227101i
$742$	12.0816	−	24.0571i	0.443529	−	0.883164i
$743$	15.1611	−	15.1611i	0.556207	−	0.556207i	−0.372019	−	0.928225i	$-0.621334\pi$
$743$	15.1611	−	15.1611i	0.556207	−	0.556207i	0.928225	+	0.372019i	$0.121334\pi$
$744$	−23.3161	+	8.02930i	−0.854810	+	0.294368i
$745$	−24.2621	+	39.2948i	−0.888893	+	1.43965i
$746$	−3.89074	+	12.2163i	−0.142450	+	0.447272i
$747$	6.49903	−	3.31142i	0.237787	−	0.121159i
$748$	−7.03409	+	48.0292i	−0.257192	+	1.75612i
$749$		−	2.00242i		−	0.0731667i
$750$	−3.62553	−	15.3901i	−0.132386	−	0.561967i
$751$			5.28907i			0.193001i	0.995333	+	0.0965004i	$0.0307649\pi$
$751$			5.28907i			0.193001i	−0.995333	+	0.0965004i	$0.969235\pi$
$752$	−15.4695	−	2.08165i	−0.564113	−	0.0759101i
$753$	−13.6264	+	6.94302i	−0.496575	+	0.253018i
$754$	−10.0411	−	3.19795i	−0.365674	−	0.116462i
$755$	19.3569	−	31.3504i	0.704470	−	1.14096i
$756$	−1.95831	−	5.79623i	−0.0712231	−	0.210807i
$757$	11.0805	−	11.0805i	0.402727	−	0.402727i	−0.476466	−	0.879193i	$-0.658082\pi$
$757$	11.0805	−	11.0805i	0.402727	−	0.402727i	0.879193	+	0.476466i	$0.158082\pi$
$758$	−37.8243	−	18.9955i	−1.37384	−	0.689948i
$759$	−11.9230	−	8.66258i	−0.432778	−	0.314432i
$760$	−10.6898	−	8.87193i	−0.387760	−	0.321819i
$761$	−4.11949	+	2.99298i	−0.149331	+	0.108496i	−0.659942	−	0.751316i	$-0.729419\pi$
$761$	−4.11949	+	2.99298i	−0.149331	+	0.108496i	0.510611	+	0.859812i	$0.329419\pi$
$762$	8.68174	−	1.42698i	0.314506	−	0.0516941i
$763$	11.2873	−	1.78773i	0.408628	−	0.0647203i
$764$	34.0567	−	25.3555i	1.23213	−	0.917331i
$765$	−8.78771	−	0.721360i	−0.317720	−	0.0260808i
$766$	14.2879	−	19.9086i	0.516242	−	0.719328i
$767$	−20.2031	+	39.6508i	−0.729491	+	1.43171i
$768$	10.7740	−	11.8288i	0.388772	−	0.426836i
$769$	34.6499	−	11.2584i	1.24951	−	0.405990i	0.391763	−	0.920066i	$-0.371865\pi$
$769$	34.6499	−	11.2584i	1.24951	−	0.405990i	0.857744	+	0.514076i	$0.171865\pi$
$770$	38.7808	+	45.1804i	1.39756	+	1.62819i
$771$	7.03417	+	2.28554i	0.253329	+	0.0823117i
$772$	−10.3765	−	19.7911i	−0.373457	−	0.712297i
$773$	32.6907	+	5.17769i	1.17580	+	0.186229i	0.713604	−	0.700549i	$-0.247061\pi$
$773$	32.6907	+	5.17769i	1.17580	+	0.186229i	0.462197	+	0.886777i	$0.347061\pi$
$774$	17.4595	−	0.101781i	0.627569	−	0.00365844i
$775$	30.6168	+	31.0316i	1.09979	+	1.11469i
$776$	−46.7175	+	0.817098i	−1.67706	+	0.0293321i
$777$	1.97275	−	12.4555i	0.0707722	−	0.446838i
$778$	5.31688	−	2.74824i	0.190619	−	0.0985293i
$779$	4.46787	−	13.7507i	0.160078	−	0.492670i
$780$	20.8630	+	4.82608i	0.747014	+	0.172801i
$781$	11.9346	+	36.7311i	0.427055	+	1.31434i
$782$	−9.49644	−	9.38636i	−0.339592	−	0.335656i
$783$	1.38658	+	0.706498i	0.0495523	+	0.0252482i
$784$	−5.36418	+	7.75727i	−0.191578	+	0.277046i
$785$	−15.5279	+	3.67271i	−0.554213	+	0.131085i
$786$	−1.89441	+	1.39331i	−0.0675713	+	0.0496978i
$787$	−5.67435	−	35.8265i	−0.202269	−	1.27708i	−0.854658	−	0.519191i	$-0.826233\pi$
$787$	−5.67435	−	35.8265i	−0.202269	−	1.27708i	0.652389	−	0.757884i	$-0.273767\pi$
$788$	−5.22257	−	30.6564i	−0.186046	−	1.09209i
$789$	−17.0552	−	23.4744i	−0.607181	−	0.835713i
$790$	−16.0051	−	25.9740i	−0.569437	−	0.924114i
$791$	−1.39100	+	1.91454i	−0.0494581	+	0.0680732i
$792$	−7.63115	+	15.6476i	−0.271161	+	0.556012i
$793$	−2.99386	−	2.99386i	−0.106315	−	0.106315i
$794$	32.3879	−	10.7326i	1.14940	−	0.380886i
$795$	−5.28154	−	12.8731i	−0.187317	−	0.456561i
$796$	−23.7216	−	7.40299i	−0.840789	−	0.262392i
$797$	−5.84580	−	11.4730i	−0.207069	−	0.406395i	0.763993	−	0.645225i	$-0.223236\pi$
$797$	−5.84580	−	11.4730i	−0.207069	−	0.406395i	−0.971062	+	0.238830i	$0.923236\pi$
$798$	−1.43176	+	9.39390i	−0.0506839	+	0.332540i
$799$	15.3873			0.544362
$800$	−27.0891	−	8.13509i	−0.957745	−	0.287619i
$801$	−0.749504			−0.0264824
$802$	−2.35089	+	15.4243i	−0.0830127	+	0.544652i
$803$	2.56515	+	5.03439i	0.0905221	+	0.177660i
$804$	6.39766	+	1.99657i	0.225628	+	0.0704135i
$805$	−16.3320	+	1.23009i	−0.575627	+	0.0433550i
$806$	−56.0425	+	18.5712i	−1.97401	+	0.654142i
$807$	−2.49389	−	2.49389i	−0.0877890	−	0.0877890i
$808$	14.8127	−	30.3732i	0.521107	−	1.06852i
$809$	22.9504	−	31.5886i	0.806894	−	1.11059i	−0.184901	−	0.982757i	$-0.559196\pi$
$809$	22.9504	−	31.5886i	0.806894	−	1.11059i	0.991795	−	0.127837i	$-0.0408036\pi$
$810$	−2.92454	−	1.20294i	−0.102758	−	0.0422671i
$811$	−3.23075	−	4.44674i	−0.113447	−	0.156146i	0.748518	−	0.663115i	$-0.230766\pi$
$811$	−3.23075	−	4.44674i	−0.113447	−	0.156146i	−0.861964	+	0.506969i	$0.830766\pi$
$812$	−1.59894	−	9.38575i	−0.0561119	−	0.329375i
$813$	0.960172	+	6.06229i	0.0336747	+	0.212614i
$814$	−28.9074	+	21.2610i	−1.01320	+	0.745198i
$815$	19.8676	+	8.30784i	0.695932	+	0.291011i
$816$	−8.97099	+	12.9732i	−0.314047	+	0.454152i
$817$	−24.1621	−	12.3112i	−0.845326	−	0.430715i
$818$	30.2754	+	29.9245i	1.05856	+	1.04628i
$819$	−4.52637	−	13.9307i	−0.158164	−	0.486780i
$820$	−2.55301	−	29.3268i	−0.0891549	−	1.02414i
$821$	−6.85514	+	21.0979i	−0.239246	+	0.736323i	0.757284	+	0.653086i	$0.226526\pi$
$821$	−6.85514	+	21.0979i	−0.239246	+	0.736323i	−0.996530	+	0.0832374i	$0.973474\pi$
$822$	4.67295	−	2.41540i	0.162988	−	0.0842469i
$823$	−3.98090	+	25.1344i	−0.138765	+	0.876130i	0.815845	+	0.578271i	$0.196272\pi$
$823$	−3.98090	+	25.1344i	−0.138765	+	0.876130i	−0.954610	+	0.297859i	$0.903728\pi$
$824$	−15.4037	+	0.269414i	−0.536614	+	0.00938548i
$825$	30.7747	+	0.207047i	1.07144	+	0.00720845i
$826$	−40.2055	+	0.234379i	−1.39893	+	0.00815510i
$827$	37.7357	+	5.97675i	1.31220	+	0.207832i	0.773032	−	0.634367i	$-0.218739\pi$
$827$	37.7357	+	5.97675i	1.31220	+	0.207832i	0.539167	+	0.842199i	$0.318739\pi$
$828$	−2.22366	−	4.24119i	−0.0772774	−	0.147392i
$829$	−41.3764	−	13.4440i	−1.43706	−	0.466929i	−0.516081	−	0.856540i	$-0.672610\pi$
$829$	−41.3764	−	13.4440i	−1.43706	−	0.466929i	−0.920980	+	0.389610i	$0.872610\pi$
$830$	−21.2882	+	8.87940i	−0.738923	+	0.308208i
$831$	−19.6468	+	6.38364i	−0.681541	+	0.221446i
$832$	26.1229	−	28.0173i	0.905648	−	0.971325i
$833$	4.22093	−	8.28404i	0.146247	−	0.287025i
$834$	−1.18327	+	1.64875i	−0.0409731	+	0.0570916i
$835$	−35.7256	+	21.7277i	−1.23633	+	0.751918i
$836$	21.6884	−	16.1472i	0.750109	−	0.558463i
$837$	8.61125	−	1.36389i	0.297648	−	0.0471429i
$838$	−19.2553	+	3.16491i	−0.665164	+	0.109330i
$839$	−4.45082	+	3.23371i	−0.153659	+	0.111640i	−0.661958	−	0.749541i	$-0.730274\pi$
$839$	−4.45082	+	3.23371i	−0.153659	+	0.111640i	0.508299	+	0.861181i	$0.330274\pi$
$840$	4.78177	+	18.7469i	0.164987	+	0.646831i
$841$	−21.5023	−	15.6223i	−0.741457	−	0.538700i
$842$	16.5088	+	8.29080i	0.568932	+	0.285720i
$843$	13.4351	−	13.4351i	0.462728	−	0.462728i
$844$	6.24616	+	18.4875i	0.215002	+	0.636365i
$845$	21.5682	+	5.25485i	0.741967	+	0.180772i
$846$	5.25833	+	1.67471i	0.180785	+	0.0575777i
$847$	−73.2790	+	37.3375i	−2.51790	+	1.28293i
$848$	−24.6685	−	3.31952i	−0.847119	−	0.113993i
$849$		−	14.7936i		−	0.507716i
$850$	27.5354	+	4.38654i	0.944458	+	0.150457i
$851$		−	9.87069i		−	0.338363i
$852$	−1.81852	+	12.4169i	−0.0623014	+	0.425398i
$853$	−4.42032	+	2.25226i	−0.151349	+	0.0771161i	−0.528025	−	0.849229i	$-0.677067\pi$
$853$	−4.42032	+	2.25226i	−0.151349	+	0.0771161i	0.376676	+	0.926345i	$0.377067\pi$
$854$	1.16086	−	3.64493i	0.0397239	−	0.124727i
$855$	3.17719	+	3.74545i	0.108658	+	0.128092i
$856$	−1.75056	+	0.602834i	−0.0598329	+	0.0206045i
$857$	−10.3827	+	10.3827i	−0.354667	+	0.354667i	−0.861843	−	0.507176i	$-0.830689\pi$
$857$	−10.3827	+	10.3827i	−0.354667	+	0.354667i	0.507176	+	0.861843i	$0.330689\pi$
$858$	−18.7056	+	37.2470i	−0.638598	+	1.27159i
$859$	34.9173	+	25.3689i	1.19136	+	0.865575i	0.993408	−	0.114636i	$-0.0365702\pi$
$859$	34.9173	+	25.3689i	1.19136	+	0.865575i	0.197954	+	0.980211i	$0.436570\pi$
$860$	−55.0766	−	3.87522i	−1.87810	−	0.132144i
$861$	−16.2905	+	11.8357i	−0.555178	+	0.403361i
$862$	5.73983	+	34.9211i	0.195500	+	1.18942i
$863$	−52.7195	+	8.34994i	−1.79459	+	0.284235i	−0.962674	−	0.270664i	$-0.912757\pi$
$863$	−52.7195	+	8.34994i	−1.79459	+	0.284235i	−0.831917	+	0.554899i	$0.812757\pi$
$864$	−4.47765	+	3.45698i	−0.152333	+	0.117609i
$865$	−1.86658	−	1.60510i	−0.0634655	−	0.0545750i
$866$	−22.4148	−	16.0865i	−0.761684	−	0.546641i
$867$	−0.658806	+	1.29298i	−0.0223742	+	0.0439119i
$868$	−38.1552	−	37.2757i	−1.29507	−	1.26522i
$869$	56.4770	−	18.3505i	1.91585	−	0.622498i
$870$	−4.20227	−	2.56092i	−0.142470	−	0.0868235i
$871$	15.2602	+	4.95832i	0.517071	+	0.168006i
$872$	−4.96096	−	9.32942i	−0.167999	−	0.315934i
$873$	16.3163	+	2.58424i	0.552222	+	0.0874634i
$874$	0.0433577	+	7.43759i	0.00146660	+	0.251580i
$875$	26.2297	−	21.9484i	0.886726	−	0.741991i
$876$	0.0214048	+	1.83583i	0.000723201	+	0.0620269i
$877$	−8.50704	+	53.7113i	−0.287262	+	1.81370i	0.247711	+	0.968834i	$0.420322\pi$
$877$	−8.50704	+	53.7113i	−0.287262	+	1.81370i	−0.534973	+	0.844869i	$0.679678\pi$
$878$	4.78738	+	9.26189i	0.161566	+	0.312574i
$879$	−1.61460	+	4.96924i	−0.0544593	+	0.167608i
$880$	27.8227	−	47.5048i	0.937902	−	1.60139i
$881$	3.94503	+	12.1416i	0.132912	+	0.409060i	0.995259	−	0.0972568i	$-0.0310068\pi$
$881$	3.94503	+	12.1416i	0.132912	+	0.409060i	−0.862348	+	0.506316i	$0.831007\pi$
$882$	2.34404	−	2.37153i	0.0789281	−	0.0798537i
$883$	13.0041	+	6.62594i	0.437624	+	0.222980i	0.658900	−	0.752231i	$-0.271022\pi$
$883$	13.0041	+	6.62594i	0.437624	+	0.222980i	−0.221276	+	0.975211i	$0.571022\pi$
$884$	−21.8385	+	30.8071i	−0.734508	+	1.03616i
$885$	−13.5495	+	15.7568i	−0.455463	+	0.529660i
$886$	14.1672	+	19.2623i	0.475955	+	0.647129i
$887$	6.89961	+	43.5624i	0.231666	+	1.46268i	0.779661	+	0.626202i	$0.215391\pi$
$887$	6.89961	+	43.5624i	0.231666	+	1.46268i	−0.547995	+	0.836482i	$0.684609\pi$
$888$	−11.4828	+	2.02514i	−0.385337	+	0.0679592i
$889$	11.1863	+	15.3966i	0.375177	+	0.516386i
$890$	2.36329	+	0.180133i	0.0792175	+	0.00603806i
$891$	3.61787	−	4.97957i	0.121203	−	0.166822i
$892$	−11.6436	+	23.5259i	−0.389856	+	0.787706i
$893$	−6.06076	−	6.06076i	−0.202816	−	0.202816i
$894$	−9.18746	−	27.7251i	−0.307275	−	0.927266i
$895$	18.9526	−	16.0771i	0.633515	−	0.537398i
$896$	33.3243	+	9.34317i	1.11329	+	0.312133i
$897$	−5.20501	−	10.2154i	−0.173790	−	0.341083i
$898$	25.0818	+	3.82283i	0.836992	+	0.127569i
$899$	13.5678			0.452512
$900$	8.93234	+	4.49591i	0.297745	+	0.149864i
$901$	24.5374			0.817459
$902$	56.6436	+	8.63330i	1.88603	+	0.287457i
$903$	17.1458	+	33.6506i	0.570578	+	1.11982i
$904$	2.09250	+	0.639661i	0.0695955	+	0.0212748i
$905$	−6.29673	+	25.8445i	−0.209310	+	0.859099i
$906$	7.33000	+	22.1198i	0.243523	+	0.734882i
$907$	4.84284	+	4.84284i	0.160804	+	0.160804i	0.782923	−	0.622119i	$-0.213728\pi$
$907$	4.84284	+	4.84284i	0.160804	+	0.160804i	−0.622119	+	0.782923i	$0.713728\pi$
$908$	−37.8132	−	18.7147i	−1.25487	−	0.621070i
$909$	−7.02257	+	9.66573i	−0.232924	+	0.320592i
$910$	10.9242	+	45.0133i	0.362134	+	1.49218i
$911$	8.76056	+	12.0579i	0.290250	+	0.399495i	0.929095	−	0.369840i	$-0.120588\pi$
$911$	8.76056	+	12.0579i	0.290250	+	0.399495i	−0.638845	+	0.769335i	$0.720588\pi$
$912$	8.64340	−	1.57638i	0.286211	−	0.0521993i
$913$	−7.02319	−	44.3427i	−0.232434	−	1.46753i
$914$	18.0388	+	24.5263i	0.596669	+	0.811257i
$915$	−1.02741	−	1.68931i	−0.0339650	−	0.0558467i
$916$	17.4536	+	12.3724i	0.576682	+	0.408797i
$917$	−4.53231	−	2.30933i	−0.149670	−	0.0762607i
$918$	3.92015	−	3.96612i	0.129384	−	0.130902i
$919$	−7.90817	−	24.3388i	−0.260866	−	0.802864i	−0.992617	−	0.121292i	$-0.961296\pi$
$919$	−7.90817	−	24.3388i	−0.260866	−	0.802864i	0.731751	−	0.681572i	$-0.238704\pi$
$920$	5.99217	+	13.9075i	0.197556	+	0.458516i
$921$	2.26251	−	6.96329i	0.0745522	−	0.229448i
$922$	−8.41380	−	16.2777i	−0.277094	−	0.536078i
$923$	−4.70009	+	29.6752i	−0.154705	+	0.976771i
$924$	−37.6550	+	0.439037i	−1.23876	+	0.0144433i
$925$	12.0030	+	16.7567i	0.394658	+	0.550957i
$926$	−0.0147252	−	2.52596i	−0.000483899	−	0.0830081i
$927$	5.37981	+	0.852078i	0.176696	+	0.0279859i
$928$	−7.72387	+	4.22345i	−0.253549	+	0.138641i
$929$	−14.8414	−	4.82227i	−0.486931	−	0.158214i	0.0552544	−	0.998472i	$-0.482403\pi$
$929$	−14.8414	−	4.82227i	−0.486931	−	0.158214i	−0.542186	+	0.840259i	$0.682403\pi$
$930$	−27.4802	+	2.23093i	−0.901111	+	0.0731550i
$931$	−4.92548	+	1.60039i	−0.161426	+	0.0524505i
$932$	−4.03758	+	4.13284i	−0.132255	+	0.135376i
$933$	−2.12085	+	4.16240i	−0.0694335	+	0.136271i
$934$	−25.1905	−	18.0786i	−0.824259	−	0.591549i
$935$	−20.9372	+	50.0698i	−0.684719	+	1.63746i
$936$	−10.8159	+	8.15096i	−0.353529	+	0.266422i
$937$	13.6370	−	2.15989i	0.445502	−	0.0705605i	0.0703466	−	0.997523i	$-0.477589\pi$
$937$	13.6370	−	2.15989i	0.445502	−	0.0705605i	0.375155	+	0.926962i	$0.377589\pi$
$938$	2.35124	+	14.3049i	0.0767708	+	0.467073i
$939$	−19.0039	+	13.8071i	−0.620169	+	0.450579i
$940$	−16.1777	−	6.54435i	−0.527659	−	0.213453i
$941$	19.0308	+	13.8267i	0.620386	+	0.450737i	0.853056	−	0.521819i	$-0.174746\pi$
$941$	19.0308	+	13.8267i	0.620386	+	0.450737i	−0.232671	+	0.972556i	$0.574746\pi$
$942$	4.52902	−	9.01828i	0.147563	−	0.293831i
$943$	−11.1447	+	11.1447i	−0.362921	+	0.362921i
$944$	12.3089	+	35.0780i	0.400621	+	1.14169i
$945$	−0.513739	−	6.82094i	−0.0167119	−	0.221885i
$946$	32.6126	−	102.399i	1.06033	−	3.32927i
$947$	−22.7069	+	11.5698i	−0.737877	+	0.375967i	−0.782181	−	0.623051i	$-0.785893\pi$
$947$	−22.7069	+	11.5698i	−0.737877	+	0.375967i	0.0443045	+	0.999018i	$0.485893\pi$
$948$	19.0921	+	2.79612i	0.620082	+	0.0908137i
$949$			4.39554i			0.142685i
$950$	−9.11793	−	12.5735i	−0.295825	−	0.407938i
$951$		−	5.51949i		−	0.178982i
$952$	−33.7860	−	4.74710i	−1.09501	−	0.153854i
$953$	−18.7735	+	9.56559i	−0.608134	+	0.309860i	−0.730804	−	0.682588i	$-0.760854\pi$
$953$	−18.7735	+	9.56559i	−0.608134	+	0.309860i	0.122670	+	0.992448i	$0.460854\pi$
$954$	8.38523	+	2.67059i	0.271482	+	0.0864634i
$955$	43.9180	−	18.0186i	1.42115	−	0.583067i
$956$	−23.4563	+	7.92492i	−0.758631	+	0.256310i
$957$	6.77303	−	6.77303i	0.218941	−	0.218941i
$958$	6.49388	+	3.26126i	0.209808	+	0.105366i
$959$	9.20535	+	6.68808i	0.297256	+	0.215969i
$960$	14.9494	−	9.82416i	0.482491	−	0.317074i
$961$	36.4169	−	26.4585i	1.17474	−	0.853499i
$962$	−27.5461	+	4.52763i	−0.888121	+	0.145977i
$963$	0.646527	−	0.102400i	0.0208340	−	0.00329979i
$964$	20.2822	+	27.2424i	0.653246	+	0.877419i
$965$	−5.75064	−	24.3131i	−0.185120	−	0.782668i
$966$	6.03962	−	8.41556i	0.194322	−	0.270766i
$967$	−12.9924	+	25.4990i	−0.417808	+	0.819994i	0.582168	+	0.813068i	$0.302204\pi$
$967$	−12.9924	+	25.4990i	−0.417808	+	0.819994i	−0.999976	+	0.00692551i	$0.997796\pi$
$968$	54.7022	+	52.8216i	1.75820	+	1.69775i
$969$	−8.23731	+	2.67646i	−0.264621	+	0.0859804i
$970$	−50.8263	−	12.0698i	−1.63193	−	0.387539i
$971$	−12.1175	−	3.93722i	−0.388869	−	0.126351i	0.108056	−	0.994145i	$-0.465538\pi$
$971$	−12.1175	−	3.93722i	−0.388869	−	0.126351i	−0.496925	+	0.867794i	$0.665538\pi$
$972$	1.77131	−	0.928695i	0.0568147	−	0.0297879i
$973$	−4.33573	−	0.686712i	−0.138997	−	0.0220150i
$974$	−18.7477	+	0.109290i	−0.600715	+	0.00350189i
$975$	21.2584	+	11.0125i	0.680813	+	0.352681i
$976$	−3.53596	+	0.0824661i	−0.113183	+	0.00263967i
$977$	7.04607	−	44.4872i	0.225424	−	1.42327i	−0.572200	−	0.820114i	$-0.693910\pi$
$977$	7.04607	−	44.4872i	0.225424	−	1.42327i	0.797623	−	0.603156i	$-0.206090\pi$
$978$	−12.0990	+	6.25386i	−0.386883	+	0.199976i
$979$	−1.42558	+	4.38747i	−0.0455616	+	0.140224i
$980$	−7.96104	+	6.91440i	−0.254306	+	0.220872i
$981$	1.15442	+	3.55295i	0.0368579	+	0.113437i
$982$	−8.54305	−	8.44402i	−0.272620	−	0.269460i
$983$	−18.7209	−	9.53878i	−0.597104	−	0.304240i	0.129194	−	0.991619i	$-0.458761\pi$
$983$	−18.7209	−	9.53878i	−0.597104	−	0.304240i	−0.726298	+	0.687379i	$0.758761\pi$
$984$	15.2514	+	10.6783i	0.486196	+	0.340413i
$985$	2.84450	−	34.6521i	0.0906332	−	1.10411i
$986$	6.99093	−	5.14174i	0.222637	−	0.163746i
$987$	1.86738	+	11.7902i	0.0594393	+	0.375285i
$988$	20.7361	−	3.53258i	0.659705	−	0.112386i
$989$	17.3755	+	23.9153i	0.552509	+	0.760464i
$990$	−12.6044	+	14.8317i	−0.400594	+	0.471383i
$991$	6.89129	−	9.48504i	0.218909	−	0.301302i	−0.685412	−	0.728155i	$-0.740378\pi$
$991$	6.89129	−	9.48504i	0.218909	−	0.301302i	0.904321	+	0.426853i	$0.140378\pi$
$992$	−21.1005	+	44.5781i	−0.669943	+	1.41536i
$993$	−17.0965	−	17.0965i	−0.542541	−	0.542541i
$994$	−25.7674	+	8.53874i	−0.817294	+	0.270832i
$995$	−23.6400	−	14.5962i	−0.749438	−	0.462731i
$996$	4.34590	−	13.9257i	0.137705	−	0.441252i
$997$	24.9244	+	48.9168i	0.789362	+	1.54921i	0.834998	+	0.550253i	$0.185469\pi$
$997$	24.9244	+	48.9168i	0.789362	+	1.54921i	−0.0456360	+	0.998958i	$0.514531\pi$
$998$	5.33798	−	35.0228i	0.168971	−	1.10863i
$999$	4.12243			0.130428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.223.14	yes	240
3.2	odd	2		900.2.bj.f.523.17		240
4.3	odd	2	inner	300.2.w.a.223.13	yes	240
12.11	even	2		900.2.bj.f.523.18		240
25.12	odd	20	inner	300.2.w.a.187.13	✓	240
75.62	even	20		900.2.bj.f.487.18		240
100.87	even	20	inner	300.2.w.a.187.14	yes	240
300.287	odd	20		900.2.bj.f.487.17		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.13	✓	240	25.12	odd	20	inner
300.2.w.a.187.14	yes	240	100.87	even	20	inner
300.2.w.a.223.13	yes	240	4.3	odd	2	inner
300.2.w.a.223.14	yes	240	1.1	even	1	trivial
900.2.bj.f.487.17		240	300.287	odd	20
900.2.bj.f.487.18		240	75.62	even	20
900.2.bj.f.523.17		240	3.2	odd	2
900.2.bj.f.523.18		240	12.11	even	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.213085 + 1.39807i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-1.90919 - 0.595816i) q^{4} +(-1.90262 - 1.17475i) q^{5} +(1.34243 - 0.444849i) q^{6} +(2.16308 + 2.16308i) q^{7} +(1.23981 - 2.54222i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(2.04780 - 2.40967i) q^{10} +(3.61787 + 4.97957i) q^{11} +(0.335878 + 1.97159i) q^{12} +(0.749054 + 4.72934i) q^{13} +(-3.48505 + 2.56321i) q^{14} +(-0.182937 + 2.22857i) q^{15} +(3.29001 + 2.27505i) q^{16} +(-3.51342 - 1.79018i) q^{17} +(-1.00581 - 0.994154i) q^{18} +(0.678754 + 2.08899i) q^{19} +(2.93253 + 3.37643i) q^{20} +(0.945301 - 2.90934i) q^{21} +(-7.73269 + 3.99695i) q^{22} +(0.374565 - 2.36491i) q^{23} +(-2.82799 + 0.0494622i) q^{24} +(2.23993 + 4.47020i) q^{25} +(-6.77155 + 0.0394750i) q^{26} +(0.987688 + 0.156434i) q^{27} +(-2.84093 - 5.41853i) q^{28} +(1.48003 + 0.480891i) q^{29} +(-3.07671 - 0.730635i) q^{30} +(8.29187 - 2.69419i) q^{31} +(-3.88173 + 4.11487i) q^{32} +(2.79435 - 5.48422i) q^{33} +(3.25145 - 4.53054i) q^{34} +(-1.57444 - 6.65660i) q^{35} +(1.60422 - 1.19435i) q^{36} +(4.07167 - 0.644890i) q^{37} +(-3.06518 + 0.503811i) q^{38} +(3.87381 - 2.81449i) q^{39} +(-5.34536 + 3.38041i) q^{40} +(-5.32533 - 3.86908i) q^{41} +(3.86602 + 1.94153i) q^{42} +(-8.72991 + 8.72991i) q^{43} +(-3.94029 - 11.6625i) q^{44} +(2.06872 - 0.848752i) q^{45} +(3.22649 + 1.02759i) q^{46} +(-3.47691 + 1.77157i) q^{47} +(0.533453 - 3.96427i) q^{48} +2.35783i q^{49} +(-6.72695 + 2.17904i) q^{50} +3.94320i q^{51} +(1.38773 - 9.47550i) q^{52} +(-5.54447 + 2.82505i) q^{53} +(-0.429168 + 1.34752i) q^{54} +(-1.03369 - 13.7243i) q^{55} +(8.18083 - 2.81721i) q^{56} +(1.55316 - 1.55316i) q^{57} +(-0.987690 + 1.96671i) q^{58} +(7.51879 + 5.46272i) q^{59} +(1.67708 - 4.14577i) q^{60} +(-0.715358 + 0.519738i) q^{61} +(1.99979 + 12.1667i) q^{62} +(-3.02139 + 0.478542i) q^{63} +(-4.92573 - 6.30374i) q^{64} +(4.13062 - 9.87809i) q^{65} +(7.07188 + 5.07530i) q^{66} +(1.52131 - 2.98575i) q^{67} +(5.64117 + 5.51114i) q^{68} +(-2.27720 + 0.739907i) q^{69} +(9.64187 - 0.782756i) q^{70} +(5.96760 + 1.93899i) q^{71} +(1.32795 + 2.49731i) q^{72} +(0.906675 + 0.143603i) q^{73} +(0.0339856 + 5.82989i) q^{74} +(2.96607 - 4.02522i) q^{75} +(-0.0512164 - 4.39269i) q^{76} +(-2.94547 + 18.5969i) q^{77} +(3.10939 + 6.01557i) q^{78} +(2.98135 - 9.17567i) q^{79} +(-3.58702 - 8.19349i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(6.54398 - 6.62073i) q^{82} +(-6.49903 - 3.31142i) q^{83} +(-3.53819 + 4.99125i) q^{84} +(4.58170 + 7.53341i) q^{85} +(-10.3448 - 14.0652i) q^{86} +(-0.243442 - 1.53704i) q^{87} +(17.1446 - 3.02368i) q^{88} +(0.440547 + 0.606362i) q^{89} +(0.745798 + 3.07307i) q^{90} +(-8.60967 + 11.8502i) q^{91} +(-2.12417 + 4.29189i) q^{92} +(-6.16497 - 6.16497i) q^{93} +(-1.73590 - 5.23845i) q^{94} +(1.16263 - 4.77192i) q^{95} +(5.42865 + 1.59053i) q^{96} +(-7.49977 - 14.7191i) q^{97} +(-3.29641 - 0.502419i) q^{98} -6.15509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

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