LMFDB - Embedded newform 312.2.bk.a.205.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(205,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.205"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$312 = 2^{3} \cdot 3 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	312.bk (of order $6$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12960000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1$ x^8 - 3x^6 + 8x^4 - 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.4
Root			$1.40126 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	312.205
Dual form			312.2.bk.a.277.4

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40126 + 0.190983i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(1.92705 + 0.535233i) q^{4} -2.23607 q^{5} +(-1.30902 + 0.535233i) q^{6} +(3.43649 + 1.98406i) q^{7} +(2.59808 + 1.11803i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.13331 - 0.427051i) q^{10} +(-0.252009 - 0.436492i) q^{11} +(-1.93649 + 0.500000i) q^{12} +(2.59808 + 2.50000i) q^{13} +(4.43649 + 3.43649i) q^{14} +(1.93649 - 1.11803i) q^{15} +(3.42705 + 2.06284i) q^{16} +(-2.93649 + 5.08615i) q^{17} +(0.866025 - 1.11803i) q^{18} +(0.252009 - 0.436492i) q^{19} +(-4.30902 - 1.19682i) q^{20} -3.96812 q^{21} +(-0.269767 - 0.659767i) q^{22} +(-4.43649 - 7.68423i) q^{23} +(-2.80902 + 0.330792i) q^{24} +(3.16312 + 3.99933i) q^{26} +1.00000i q^{27} +(5.56036 + 5.66271i) q^{28} +(8.55025 - 4.93649i) q^{29} +(2.92705 - 1.19682i) q^{30} -4.47214i q^{31} +(4.40822 + 3.54508i) q^{32} +(0.436492 + 0.252009i) q^{33} +(-5.08615 + 6.56619i) q^{34} +(-7.68423 - 4.43649i) q^{35} +(1.42705 - 1.40126i) q^{36} +(-3.60611 - 6.24597i) q^{37} +(0.436492 - 0.563508i) q^{38} +(-3.50000 - 0.866025i) q^{39} +(-5.80948 - 2.50000i) q^{40} +(1.06351 - 0.614017i) q^{41} +(-5.56036 - 0.757843i) q^{42} +(-7.68423 - 4.43649i) q^{43} +(-0.252009 - 0.976025i) q^{44} +(-1.11803 + 1.93649i) q^{45} +(-4.74911 - 11.6149i) q^{46} -3.96812i q^{47} +(-3.99933 - 0.0729490i) q^{48} +(4.37298 + 7.57423i) q^{49} -5.87298i q^{51} +(3.66854 + 6.20820i) q^{52} +7.87298i q^{53} +(-0.190983 + 1.40126i) q^{54} +(0.563508 + 0.976025i) q^{55} +(6.71002 + 8.99685i) q^{56} +0.504017i q^{57} +(12.9239 - 5.28435i) q^{58} +(1.22803 - 2.12702i) q^{59} +(4.33013 - 1.11803i) q^{60} +(-0.866025 - 0.500000i) q^{61} +(0.854102 - 6.26662i) q^{62} +(3.43649 - 1.98406i) q^{63} +(5.50000 + 5.80948i) q^{64} +(-5.80948 - 5.59017i) q^{65} +(0.563508 + 0.436492i) q^{66} +(-0.976025 - 1.69052i) q^{67} +(-8.38105 + 8.22957i) q^{68} +(7.68423 + 4.43649i) q^{69} +(-9.92030 - 7.68423i) q^{70} +(-4.30948 - 2.48808i) q^{71} +(2.26728 - 1.69098i) q^{72} +13.1324i q^{73} +(-3.86022 - 9.44092i) q^{74} +(0.719258 - 0.706258i) q^{76} -2.00000i q^{77} +(-4.73901 - 1.88197i) q^{78} +14.0000 q^{79} +(-7.66312 - 4.61266i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.60752 - 0.657284i) q^{82} -2.96008 q^{83} +(-7.64677 - 2.12387i) q^{84} +(6.56619 - 11.3730i) q^{85} +(-9.92030 - 7.68423i) q^{86} +(-4.93649 + 8.55025i) q^{87} +(-0.166725 - 1.41579i) q^{88} +(-1.74597 + 1.00803i) q^{89} +(-1.93649 + 2.50000i) q^{90} +(3.96812 + 13.7460i) q^{91} +(-4.43649 - 17.1825i) q^{92} +(2.23607 + 3.87298i) q^{93} +(0.757843 - 5.56036i) q^{94} +(-0.563508 + 0.976025i) q^{95} +(-5.59017 - 0.866025i) q^{96} +(-15.0000 - 8.66025i) q^{97} +(4.68113 + 11.4486i) q^{98} -0.504017 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 2 q^{4} - 6 q^{6} + 12 q^{7} + 4 q^{9} + 20 q^{14} + 14 q^{16} - 8 q^{17} - 30 q^{20} - 6 q^{22} - 20 q^{23} - 18 q^{24} - 6 q^{26} + 6 q^{28} + 10 q^{30} - 12 q^{33} - 2 q^{36} - 12 q^{38} - 28 q^{39}+ \cdots + 60 q^{98}+O(q^{100})$ 8 * q + 2 * q^4 - 6 * q^6 + 12 * q^7 + 4 * q^9 + 20 * q^14 + 14 * q^16 - 8 * q^17 - 30 * q^20 - 6 * q^22 - 20 * q^23 - 18 * q^24 - 6 * q^26 + 6 * q^28 + 10 * q^30 - 12 * q^33 - 2 * q^36 - 12 * q^38 - 28 * q^39 + 24 * q^41 - 6 * q^42 - 30 * q^46 + 4 * q^49 - 6 * q^54 + 20 * q^55 - 10 * q^56 + 36 * q^58 - 20 * q^62 + 12 * q^63 + 44 * q^64 + 20 * q^66 + 4 * q^68 + 12 * q^71 - 6 * q^74 + 30 * q^76 + 112 * q^79 - 30 * q^80 - 4 * q^81 - 10 * q^82 - 30 * q^84 - 24 * q^87 + 18 * q^88 + 48 * q^89 - 20 * q^92 - 10 * q^94 - 20 * q^95 - 120 * q^97 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$ .

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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

)

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

$2$	1.40126	+	0.190983i	0.990839	+	0.135045i
$2$	1.40126	+	0.190983i	0.990839	+	0.135045i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	1.92705	+	0.535233i	0.963525	+	0.267617i
$5$	−2.23607			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$5$	−2.23607			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$6$	−1.30902	+	0.535233i	−0.534404	+	0.218508i
$7$	3.43649	+	1.98406i	1.29887	+	0.749904i	0.980209	−	0.197964i	$-0.0634330\pi$
$7$	3.43649	+	1.98406i	1.29887	+	0.749904i	0.318663	+	0.947868i	$0.396766\pi$
$8$	2.59808	+	1.11803i	0.918559	+	0.395285i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−3.13331	−	0.427051i	−0.990839	−	0.135045i
$11$	−0.252009	−	0.436492i	−0.0759834	−	0.131607i	0.825530	−	0.564358i	$-0.190876\pi$
$11$	−0.252009	−	0.436492i	−0.0759834	−	0.131607i	−0.901514	+	0.432751i	$0.857543\pi$
$12$	−1.93649	+	0.500000i	−0.559017	+	0.144338i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$	4.43649	+	3.43649i	1.18570	+	0.918441i
$15$	1.93649	−	1.11803i	0.500000	−	0.288675i
$16$	3.42705	+	2.06284i	0.856763	+	0.515711i
$17$	−2.93649	+	5.08615i	−0.712204	+	1.23357i	0.251824	+	0.967773i	$0.418970\pi$
$17$	−2.93649	+	5.08615i	−0.712204	+	1.23357i	−0.964028	+	0.265800i	$0.914364\pi$
$18$	0.866025	−	1.11803i	0.204124	−	0.263523i
$19$	0.252009	−	0.436492i	0.0578147	−	0.100138i	−0.835669	−	0.549233i	$-0.814920\pi$
$19$	0.252009	−	0.436492i	0.0578147	−	0.100138i	0.893484	+	0.449095i	$0.148253\pi$
$20$	−4.30902	−	1.19682i	−0.963525	−	0.267617i
$21$	−3.96812			−0.865915
$22$	−0.269767	−	0.659767i	−0.0575145	−	0.140663i
$23$	−4.43649	−	7.68423i	−0.925072	−	1.60227i	−0.791445	−	0.611241i	$-0.790671\pi$
$23$	−4.43649	−	7.68423i	−0.925072	−	1.60227i	−0.133628	−	0.991032i	$-0.542663\pi$
$24$	−2.80902	+	0.330792i	−0.573388	+	0.0675227i
$25$		0			0
$26$	3.16312	+	3.99933i	0.620339	+	0.784334i
$27$			1.00000i			0.192450i
$28$	5.56036	+	5.66271i	1.05081	+	1.07015i
$29$	8.55025	−	4.93649i	1.58774	−	0.916683i	0.594064	−	0.804418i	$-0.297523\pi$
$29$	8.55025	−	4.93649i	1.58774	−	0.916683i	0.993678	−	0.112266i	$-0.0358108\pi$
$30$	2.92705	−	1.19682i	0.534404	−	0.218508i
$31$		−	4.47214i		−	0.803219i	−0.915811	−	0.401610i	$-0.868451\pi$
$31$		−	4.47214i		−	0.803219i	0.915811	−	0.401610i	$-0.131549\pi$
$32$	4.40822	+	3.54508i	0.779270	+	0.626688i
$33$	0.436492	+	0.252009i	0.0759834	+	0.0438691i
$34$	−5.08615	+	6.56619i	−0.872268	+	1.12609i
$35$	−7.68423	−	4.43649i	−1.29887	−	0.749904i
$36$	1.42705	−	1.40126i	0.237842	−	0.233543i
$37$	−3.60611	−	6.24597i	−0.592841	−	1.02683i	−0.993848	−	0.110756i	$-0.964673\pi$
$37$	−3.60611	−	6.24597i	−0.592841	−	1.02683i	0.401007	−	0.916075i	$-0.368660\pi$
$38$	0.436492	−	0.563508i	0.0708083	−	0.0914131i
$39$	−3.50000	−	0.866025i	−0.560449	−	0.138675i
$40$	−5.80948	−	2.50000i	−0.918559	−	0.395285i
$41$	1.06351	−	0.614017i	0.166092	−	0.0958933i	−0.414650	−	0.909981i	$-0.636096\pi$
$41$	1.06351	−	0.614017i	0.166092	−	0.0958933i	0.580742	+	0.814088i	$0.302763\pi$
$42$	−5.56036	−	0.757843i	−0.857982	−	0.116938i
$43$	−7.68423	−	4.43649i	−1.17183	−	0.676559i	−0.217723	−	0.976011i	$-0.569863\pi$
$43$	−7.68423	−	4.43649i	−1.17183	−	0.676559i	−0.954111	+	0.299452i	$0.903196\pi$
$44$	−0.252009	−	0.976025i	−0.0379917	−	0.147141i
$45$	−1.11803	+	1.93649i	−0.166667	+	0.288675i
$46$	−4.74911	−	11.6149i	−0.700219	−	1.71252i
$47$		−	3.96812i		−	0.578810i	−0.957207	−	0.289405i	$-0.906543\pi$
$47$		−	3.96812i		−	0.578810i	0.957207	−	0.289405i	$-0.0934574\pi$
$48$	−3.99933	−	0.0729490i	−0.577254	−	0.0105293i
$49$	4.37298	+	7.57423i	0.624712	+	1.08203i
$50$		0			0
$51$		−	5.87298i		−	0.822382i
$52$	3.66854	+	6.20820i	0.508735	+	0.860923i
$53$			7.87298i			1.08144i	0.841203	+	0.540719i	$0.181848\pi$
$53$			7.87298i			1.08144i	−0.841203	+	0.540719i	$0.818152\pi$
$54$	−0.190983	+	1.40126i	−0.0259895	+	0.190687i
$55$	0.563508	+	0.976025i	0.0759834	+	0.131607i
$56$	6.71002	+	8.99685i	0.896664	+	1.20225i
$57$			0.504017i			0.0667587i
$58$	12.9239	−	5.28435i	1.69699	−	0.693869i
$59$	1.22803	−	2.12702i	0.159876	−	0.276914i	−0.774948	−	0.632026i	$-0.782224\pi$
$59$	1.22803	−	2.12702i	0.159876	−	0.276914i	0.934824	+	0.355112i	$0.115557\pi$
$60$	4.33013	−	1.11803i	0.559017	−	0.144338i
$61$	−0.866025	−	0.500000i	−0.110883	−	0.0640184i	0.443533	−	0.896258i	$-0.353725\pi$
$61$	−0.866025	−	0.500000i	−0.110883	−	0.0640184i	−0.554416	+	0.832240i	$0.687058\pi$
$62$	0.854102	−	6.26662i	0.108471	−	0.795861i
$63$	3.43649	−	1.98406i	0.432957	−	0.249968i
$64$	5.50000	+	5.80948i	0.687500	+	0.726184i
$65$	−5.80948	−	5.59017i	−0.720577	−	0.693375i
$66$	0.563508	+	0.436492i	0.0693631	+	0.0537284i
$67$	−0.976025	−	1.69052i	−0.119240	−	0.206530i	0.800226	−	0.599698i	$-0.204713\pi$
$67$	−0.976025	−	1.69052i	−0.119240	−	0.206530i	−0.919467	+	0.393167i	$0.871379\pi$
$68$	−8.38105	+	8.22957i	−1.01635	+	0.997982i
$69$	7.68423	+	4.43649i	0.925072	+	0.534091i
$70$	−9.92030	−	7.68423i	−1.18570	−	0.918441i
$71$	−4.30948	−	2.48808i	−0.511441	−	0.295280i	0.221985	−	0.975050i	$-0.428746\pi$
$71$	−4.30948	−	2.48808i	−0.511441	−	0.295280i	−0.733426	+	0.679770i	$0.762080\pi$
$72$	2.26728	−	1.69098i	0.267202	−	0.199284i
$73$			13.1324i			1.53703i	0.639832	+	0.768515i	$0.279004\pi$
$73$			13.1324i			1.53703i	−0.639832	+	0.768515i	$0.720996\pi$
$74$	−3.86022	−	9.44092i	−0.448741	−	1.09748i
$75$		0			0
$76$	0.719258	−	0.706258i	0.0825046	−	0.0810134i
$77$		−	2.00000i		−	0.227921i
$78$	−4.73901	−	1.88197i	−0.536587	−	0.213091i
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	−7.66312	−	4.61266i	−0.856763	−	0.515711i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.60752	−	0.657284i	0.177521	−	0.0725849i
$83$	−2.96008			−0.324911			−0.162456	−	0.986716i	$-0.551941\pi$
$83$	−2.96008			−0.324911			−0.162456	+	0.986716i	$0.551941\pi$
$84$	−7.64677	−	2.12387i	−0.834331	−	0.231733i
$85$	6.56619	−	11.3730i	0.712204	−	1.23357i
$86$	−9.92030	−	7.68423i	−1.06973	−	0.828612i
$87$	−4.93649	+	8.55025i	−0.529247	+	0.916683i
$88$	−0.166725	−	1.41579i	−0.0177729	−	0.150924i
$89$	−1.74597	+	1.00803i	−0.185072	+	0.106851i	−0.589674	−	0.807642i	$-0.700744\pi$
$89$	−1.74597	+	1.00803i	−0.185072	+	0.106851i	0.404601	+	0.914493i	$0.367410\pi$
$90$	−1.93649	+	2.50000i	−0.204124	+	0.263523i
$91$	3.96812	+	13.7460i	0.415972	+	1.44097i
$92$	−4.43649	−	17.1825i	−0.462536	−	1.79140i
$93$	2.23607	+	3.87298i	0.231869	+	0.401610i
$94$	0.757843	−	5.56036i	0.0781656	−	0.573507i
$95$	−0.563508	+	0.976025i	−0.0578147	+	0.100138i
$96$	−5.59017	−	0.866025i	−0.570544	−	0.0883883i
$97$	−15.0000	−	8.66025i	−1.52302	−	0.879316i	−0.999629	−	0.0272222i	$-0.991334\pi$
$97$	−15.0000	−	8.66025i	−1.52302	−	0.879316i	−0.523390	−	0.852093i	$-0.675333\pi$
$98$	4.68113	+	11.4486i	0.472866	+	1.15649i
$99$	−0.504017			−0.0506556
$100$		0			0
$101$	−6.81820	+	3.93649i	−0.678437	+	0.391696i	−0.799266	−	0.600978i	$-0.794778\pi$
$101$	−6.81820	+	3.93649i	−0.678437	+	0.391696i	0.120829	+	0.992673i	$0.461445\pi$
$102$	1.12164	−	8.22957i	0.111059	−	0.814849i
$103$	10.6190			1.04632			0.523158	−	0.852236i	$-0.324754\pi$
$103$	10.6190			1.04632			0.523158	+	0.852236i	$0.324754\pi$
$104$	3.95492	+	9.39993i	0.387811	+	0.921739i
$105$	8.87298			0.865915
$106$	−1.50361	+	11.0321i	−0.146043	+	1.07153i
$107$	0.756026	−	0.436492i	0.0730878	−	0.0421972i	−0.463011	−	0.886353i	$-0.653231\pi$
$107$	0.756026	−	0.436492i	0.0730878	−	0.0421972i	0.536099	+	0.844155i	$0.319898\pi$
$108$	−0.535233	+	1.92705i	−0.0515028	+	0.185431i
$109$	−2.45607			−0.235249			−0.117624	−	0.993058i	$-0.537528\pi$
$109$	−2.45607			−0.235249			−0.117624	+	0.993058i	$0.537528\pi$
$110$	0.603217	+	1.47528i	0.0575145	+	0.140663i
$111$	6.24597	+	3.60611i	0.592841	+	0.342277i
$112$	7.68423	+	13.8884i	0.726091	+	1.31233i
$113$	−4.93649	+	8.55025i	−0.464386	+	0.804340i	−0.999174	−	0.0406463i	$-0.987058\pi$
$113$	−4.93649	+	8.55025i	−0.464386	+	0.804340i	0.534788	+	0.844987i	$0.320392\pi$
$114$	−0.0962587	+	0.706258i	−0.00901545	+	0.0661472i
$115$	9.92030	+	17.1825i	0.925072	+	1.60227i
$116$	19.1190	−	4.93649i	1.77515	−	0.458342i
$117$	3.46410	−	1.00000i	0.320256	−	0.0924500i
$118$	2.12702	−	2.74597i	0.195808	−	0.252787i
$119$	−20.1825	+	11.6523i	−1.85012	+	1.06817i
$120$	6.28115	−	0.739674i	0.573388	−	0.0675227i
$121$	5.37298	−	9.30628i	0.488453	−	0.846025i
$122$	−1.11803	−	0.866025i	−0.101222	−	0.0784063i
$123$	−0.614017	+	1.06351i	−0.0553640	+	0.0958933i
$124$	2.39364	−	8.61803i	0.214955	−	0.773922i
$125$	11.1803			1.00000
$126$	5.19433	−	2.12387i	0.462748	−	0.189209i
$127$	−1.12702	−	1.95205i	−0.100007	−	0.173216i	0.811681	−	0.584102i	$-0.198553\pi$
$127$	−1.12702	−	1.95205i	−0.100007	−	0.173216i	−0.911687	+	0.410885i	$0.865220\pi$
$128$	6.59741	+	9.19098i	0.583134	+	0.812376i
$129$	8.87298			0.781223
$130$	−7.07295	−	8.94278i	−0.620339	−	0.784334i
$131$		−	11.7460i		−	1.02625i	−0.858314	−	0.513125i	$-0.828488\pi$
$131$		−	11.7460i		−	1.02625i	0.858314	−	0.513125i	$-0.171512\pi$
$132$	0.706258	+	0.719258i	0.0614719	+	0.0626034i
$133$	1.73205	−	1.00000i	0.150188	−	0.0867110i
$134$	−1.04480	−	2.55527i	−0.0902571	−	0.220741i
$135$		−	2.23607i		−	0.192450i
$136$	−13.3157	+	9.93112i	−1.14181	+	0.851586i
$137$	−0.190525	−	0.110000i	−0.0162776	−	0.00939790i	0.491839	−	0.870686i	$-0.336325\pi$
$137$	−0.190525	−	0.110000i	−0.0162776	−	0.00939790i	−0.508117	+	0.861288i	$0.669658\pi$
$138$	9.92030	+	7.68423i	0.844472	+	0.654125i
$139$	8.44025	+	4.87298i	0.715893	+	0.413321i	0.813239	−	0.581930i	$-0.197702\pi$
$139$	8.44025	+	4.87298i	0.715893	+	0.413321i	−0.0973462	+	0.995251i	$0.531035\pi$
$140$	−12.4333	−	12.6622i	−1.05081	−	1.07015i
$141$	1.98406	+	3.43649i	0.167088	+	0.289405i
$142$	−5.56351	−	4.30948i	−0.466879	−	0.361643i
$143$	0.436492	−	1.76406i	0.0365013	−	0.147518i
$144$	3.50000	−	1.93649i	0.291667	−	0.161374i
$145$	−19.1190	+	11.0383i	−1.58774	+	0.916683i
$146$	−2.50806	+	18.4019i	−0.207569	+	1.52295i
$147$	−7.57423	−	4.37298i	−0.624712	−	0.360678i
$148$	−3.60611	−	13.9664i	−0.296420	−	1.14803i
$149$	−4.36214	+	7.55544i	−0.357360	+	0.618966i	−0.987519	−	0.157500i	$-0.949656\pi$
$149$	−4.36214	+	7.55544i	−0.357360	+	0.618966i	0.630159	+	0.776466i	$0.282990\pi$
$150$		0			0
$151$		−	10.8963i		−	0.886730i	−0.896341	−	0.443365i	$-0.853785\pi$
$151$		−	10.8963i		−	0.886730i	0.896341	−	0.443365i	$-0.146215\pi$
$152$	1.14275	−	0.852284i	0.0926893	−	0.0691294i
$153$	2.93649	+	5.08615i	0.237401	+	0.411191i
$154$	0.381966	−	2.80252i	0.0307797	−	0.225833i
$155$			10.0000i			0.803219i
$156$	−6.28115	−	3.54219i	−0.502895	−	0.283602i
$157$			1.25403i			0.100083i	0.998747	+	0.0500414i	$0.0159353\pi$
$157$			1.25403i			0.100083i	−0.998747	+	0.0500414i	$0.984065\pi$
$158$	19.6176	+	2.67376i	1.56069	+	0.212713i
$159$	−3.93649	−	6.81820i	−0.312184	−	0.540719i
$160$	−9.85707	−	7.92705i	−0.779270	−	0.626688i
$161$		−	35.2091i		−	2.77486i
$162$	−0.535233	−	1.30902i	−0.0420519	−	0.102846i
$163$	−8.44025	+	14.6190i	−0.661092	+	1.14504i	0.319237	+	0.947675i	$0.396573\pi$
$163$	−8.44025	+	14.6190i	−0.661092	+	1.14504i	−0.980329	+	0.197370i	$0.936760\pi$
$164$	2.37808	−	0.614017i	0.185697	−	0.0479467i
$165$	−0.976025	−	0.563508i	−0.0759834	−	0.0438691i
$166$	−4.14784	−	0.565326i	−0.321935	−	0.0438778i
$167$	8.12702	−	4.69214i	0.628887	−	0.363088i	−0.151434	−	0.988467i	$-0.548389\pi$
$167$	8.12702	−	4.69214i	0.628887	−	0.363088i	0.780321	+	0.625379i	$0.215056\pi$
$168$	−10.3095	−	4.43649i	−0.795393	−	0.342283i
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	11.3730	−	14.6825i	0.872268	−	1.12609i
$171$	−0.252009	−	0.436492i	−0.0192716	−	0.0333794i
$172$	−12.4333	−	12.6622i	−0.948034	−	0.965484i
$173$	15.1485	+	8.74597i	1.15172	+	0.664944i	0.949305	−	0.314357i	$-0.101789\pi$
$173$	15.1485	+	8.74597i	1.15172	+	0.664944i	0.202411	+	0.979301i	$0.435122\pi$
$174$	−8.55025	+	11.0383i	−0.648193	+	0.836814i
$175$		0			0
$176$	0.0367676	−	2.01573i	0.00277146	−	0.151942i
$177$			2.45607i			0.184609i
$178$	−2.63907	+	1.07907i	−0.197807	+	0.0808795i
$179$	−4.44013	+	2.56351i	−0.331871	+	0.191606i	−0.656671	−	0.754177i	$-0.728036\pi$
$179$	−4.44013	+	2.56351i	−0.331871	+	0.191606i	0.324801	+	0.945782i	$0.394703\pi$
$180$	−3.19098	+	3.13331i	−0.237842	+	0.233543i
$181$		−	0.745967i		−	0.0554473i	−0.999616	−	0.0277236i	$-0.991174\pi$
$181$		−	0.745967i		−	0.0554473i	0.999616	−	0.0277236i	$-0.00882584\pi$
$182$	2.93511	+	20.0195i	0.217565	+	1.48394i
$183$	1.00000			0.0739221
$184$	−2.93511	−	24.9244i	−0.216379	−	1.83745i
$185$	8.06351	+	13.9664i	0.592841	+	1.02683i
$186$	2.39364	+	5.85410i	0.175510	+	0.429244i
$187$	2.96008			0.216463
$188$	2.12387	−	7.64677i	0.154899	−	0.557698i
$189$	−1.98406	+	3.43649i	−0.144319	+	0.249968i
$190$	−0.976025	+	1.26004i	−0.0708083	+	0.0914131i
$191$	−9.87298	+	17.1005i	−0.714384	+	1.23735i	0.248813	+	0.968552i	$0.419960\pi$
$191$	−9.87298	+	17.1005i	−0.714384	+	1.23735i	−0.963197	+	0.268798i	$0.913374\pi$
$192$	−7.66788	−	2.28115i	−0.553381	−	0.164628i
$193$	7.11895	−	4.11013i	0.512433	−	0.295853i	−0.221400	−	0.975183i	$-0.571063\pi$
$193$	7.11895	−	4.11013i	0.512433	−	0.295853i	0.733833	+	0.679330i	$0.237729\pi$
$194$	−19.3649	−	15.0000i	−1.39032	−	1.07694i
$195$	7.82624	+	1.93649i	0.560449	+	0.138675i
$196$	4.37298	+	16.9365i	0.312356	+	1.20975i
$197$	1.22803	+	2.12702i	0.0874938	+	0.151544i	0.906451	−	0.422311i	$-0.138781\pi$
$197$	1.22803	+	2.12702i	0.0874938	+	0.151544i	−0.818957	+	0.573854i	$0.805448\pi$
$198$	−0.706258	−	0.0962587i	−0.0501916	−	0.00684081i
$199$	3.43649	−	5.95218i	0.243606	−	0.421939i	−0.718132	−	0.695906i	$-0.755003\pi$
$199$	3.43649	−	5.95218i	0.243606	−	0.421939i	0.961739	+	0.273968i	$0.0883361\pi$
$200$		0			0
$201$	1.69052	+	0.976025i	0.119240	+	0.0688435i
$202$	−10.3059	+	4.21388i	−0.725118	+	0.296488i
$203$	39.1772			2.74970
$204$	3.14342	−	11.3175i	0.220083	−	0.792386i
$205$	−2.37808	+	1.37298i	−0.166092	+	0.0958933i
$206$	14.8799	+	2.02804i	1.03673	+	0.141300i
$207$	−8.87298			−0.616715
$208$	3.74663	+	13.9271i	0.259782	+	0.965667i
$209$	−0.254033			−0.0175719
$210$	12.4333	+	1.69459i	0.857982	+	0.116938i
$211$	12.1244	−	7.00000i	0.834675	−	0.481900i	−0.0207756	−	0.999784i	$-0.506614\pi$
$211$	12.1244	−	7.00000i	0.834675	−	0.481900i	0.855451	+	0.517884i	$0.173280\pi$
$212$	−4.21388	+	15.1716i	−0.289411	+	1.04199i
$213$	4.97615			0.340960
$214$	1.14275	−	0.467250i	0.0781168	−	0.0319405i
$215$	17.1825	+	9.92030i	1.17183	+	0.676559i
$216$	−1.11803	+	2.59808i	−0.0760726	+	0.176777i
$217$	8.87298	−	15.3685i	0.602337	−	1.04328i
$218$	−3.44159	−	0.469067i	−0.233094	−	0.0317692i
$219$	−6.56619	−	11.3730i	−0.443702	−	0.768515i
$220$	0.563508	+	2.18246i	0.0379917	+	0.147141i
$221$	−20.3446	+	5.87298i	−1.36853	+	0.395060i
$222$	8.06351	+	6.24597i	0.541187	+	0.419202i
$223$	−12.4919	+	7.21222i	−0.836522	+	0.482966i	−0.856080	−	0.516843i	$-0.827107\pi$
$223$	−12.4919	+	7.21222i	−0.836522	+	0.482966i	0.0195587	+	0.999809i	$0.493774\pi$
$224$	8.11514	+	20.9288i	0.542216	+	1.39837i
$225$		0			0
$226$	−8.55025	+	11.0383i	−0.568754	+	0.734259i
$227$	0.976025	−	1.69052i	0.0647811	−	0.112204i	−0.831816	−	0.555052i	$-0.812698\pi$
$227$	0.976025	−	1.69052i	0.0647811	−	0.112204i	0.896597	+	0.442848i	$0.146032\pi$
$228$	−0.269767	+	0.971267i	−0.0178657	+	0.0643237i
$229$	−15.8725			−1.04888			−0.524441	−	0.851447i	$-0.675726\pi$
$229$	−15.8725			−1.04888			−0.524441	+	0.851447i	$0.675726\pi$
$230$	10.6193	+	25.9717i	0.700219	+	1.71252i
$231$	1.00000	+	1.73205i	0.0657952	+	0.113961i
$232$	27.7334	−	3.26591i	1.82079	−	0.214417i
$233$	22.0000			1.44127			0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000			1.44127			0.720634	+	0.693316i	$0.243851\pi$
$234$	5.04508	−	0.739674i	0.329808	−	0.0483540i
$235$			8.87298i			0.578810i
$236$	3.50493	−	3.44159i	0.228152	−	0.224028i
$237$	−12.1244	+	7.00000i	−0.787562	+	0.454699i
$238$	−30.5062	+	12.4734i	−1.97743	+	0.808533i
$239$			1.51205i			0.0978065i	0.998804	+	0.0489032i	$0.0155726\pi$
$239$			1.51205i			0.0978065i	−0.998804	+	0.0489032i	$0.984427\pi$
$240$	8.94278	+	0.163119i	0.577254	+	0.0105293i
$241$	−13.5000	−	7.79423i	−0.869611	−	0.502070i	−0.00239235	−	0.999997i	$-0.500762\pi$
$241$	−13.5000	−	7.79423i	−0.869611	−	0.502070i	−0.867219	+	0.497927i	$0.834095\pi$
$242$	9.30628	−	12.0144i	0.598230	−	0.772312i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−1.40126	−	1.42705i	−0.0897064	−	0.0913576i
$245$	−9.77829	−	16.9365i	−0.624712	−	1.08203i
$246$	−1.06351	+	1.37298i	−0.0678068	+	0.0875382i
$247$	1.74597	−	0.504017i	0.111093	−	0.0320698i
$248$	5.00000	−	11.6190i	0.317500	−	0.737804i
$249$	2.56351	−	1.48004i	0.162456	−	0.0937939i
$250$	15.6665	+	2.13525i	0.990839	+	0.135045i
$251$	−13.1964	−	7.61895i	−0.832950	−	0.480904i	0.0219117	−	0.999760i	$-0.493025\pi$
$251$	−13.1964	−	7.61895i	−0.832950	−	0.480904i	−0.854862	+	0.518856i	$0.826358\pi$
$252$	7.68423	−	1.98406i	0.484061	−	0.124984i
$253$	−2.23607	+	3.87298i	−0.140580	+	0.243492i
$254$	−1.20643	−	2.95057i	−0.0756984	−	0.185135i
$255$			13.1324i			0.822382i
$256$	7.48936	+	14.1389i	0.468085	+	0.883684i
$257$	7.68246	+	13.3064i	0.479219	+	0.830031i	0.999716	−	0.0238323i	$-0.00758678\pi$
$257$	7.68246	+	13.3064i	0.479219	+	0.830031i	−0.520497	+	0.853863i	$0.674253\pi$
$258$	12.4333	+	1.69459i	0.774066	+	0.105501i
$259$		−	28.6190i		−	1.77830i
$260$	−8.20311	−	13.8820i	−0.508735	−	0.860923i
$261$		−	9.87298i		−	0.611122i
$262$	2.24328	−	16.4591i	0.138590	−	1.01685i
$263$	−0.563508	−	0.976025i	−0.0347474	−	0.0601843i	0.848129	−	0.529790i	$-0.177729\pi$
$263$	−0.563508	−	0.976025i	−0.0347474	−	0.0601843i	−0.882876	+	0.469606i	$0.844396\pi$
$264$	0.852284	+	1.14275i	0.0524545	+	0.0703314i
$265$		−	17.6045i		−	1.08144i
$266$	2.61803	−	1.07047i	0.160522	−	0.0656345i
$267$	1.00803	−	1.74597i	0.0616907	−	0.106851i
$268$	−0.976025	−	3.78013i	−0.0596202	−	0.230908i
$269$	−17.1005	−	9.87298i	−1.04264	−	0.601966i	−0.122058	−	0.992523i	$-0.538949\pi$
$269$	−17.1005	−	9.87298i	−1.04264	−	0.601966i	−0.920579	+	0.390557i	$0.872283\pi$
$270$	0.427051	−	3.13331i	0.0259895	−	0.190687i
$271$	−26.2379	+	15.1485i	−1.59384	+	0.920203i	−0.601199	+	0.799099i	$0.705310\pi$
$271$	−26.2379	+	15.1485i	−1.59384	+	0.920203i	−0.992640	+	0.121104i	$0.961357\pi$
$272$	−20.5554	+	11.3730i	−1.24636	+	0.689588i
$273$	−10.3095	−	9.92030i	−0.623958	−	0.600404i
$274$	−0.245967	−	0.190525i	−0.0148594	−	0.0115100i
$275$		0			0
$276$	12.4333	+	12.6622i	0.748399	+	0.762175i
$277$	0.646026	+	0.372983i	0.0388159	+	0.0224104i	0.519282	−	0.854603i	$-0.326199\pi$
$277$	0.646026	+	0.372983i	0.0388159	+	0.0224104i	−0.480466	+	0.877013i	$0.659533\pi$
$278$	10.8963	+	8.44025i	0.653518	+	0.506213i
$279$	−3.87298	−	2.23607i	−0.231869	−	0.133870i
$280$	−15.0041	−	20.1176i	−0.896664	−	1.20225i
$281$		−	12.1884i		−	0.727097i	−0.931575	−	0.363549i	$-0.881565\pi$
$281$		−	12.1884i		−	0.727097i	0.931575	−	0.363549i	$-0.118435\pi$
$282$	2.12387	+	5.19433i	0.126475	+	0.309318i
$283$	−17.8565	+	10.3095i	−1.06146	+	0.612835i	−0.925836	−	0.377926i	$-0.876638\pi$
$283$	−17.8565	+	10.3095i	−1.06146	+	0.612835i	−0.135625	+	0.990760i	$0.543304\pi$
$284$	−6.97288	−	7.10122i	−0.413764	−	0.421380i
$285$		−	1.12702i		−	0.0667587i
$286$	0.948543	−	2.38854i	0.0560885	−	0.141237i
$287$	4.87298			0.287643
$288$	5.27424	−	2.04508i	0.310788	−	0.120508i
$289$	−8.74597	−	15.1485i	−0.514469	−	0.891086i
$290$	−28.8987	+	11.8162i	−1.69699	+	0.693869i
$291$	17.3205			1.01535
$292$	−7.02889	+	25.3068i	−0.411335	+	1.48097i
$293$	−3.07008	+	5.31754i	−0.179356	+	0.310654i	−0.941660	−	0.336565i	$-0.890735\pi$
$293$	−3.07008	+	5.31754i	−0.179356	+	0.310654i	0.762304	+	0.647219i	$0.224068\pi$
$294$	−9.77829	−	7.57423i	−0.570281	−	0.441738i
$295$	−2.74597	+	4.75615i	−0.159876	+	0.276914i
$296$	−2.38575	−	20.2593i	−0.138669	−	1.17755i
$297$	0.436492	−	0.252009i	0.0253278	−	0.0146230i
$298$	−7.55544	+	9.75403i	−0.437675	+	0.565036i
$299$	7.68423	−	31.0554i	0.444390	−	1.79598i
$300$		0			0
$301$	−17.6045	−	30.4919i	−1.01471	−	1.75753i
$302$	2.08101	−	15.2686i	0.119749	−	0.878607i
$303$	3.93649	−	6.81820i	0.226146	−	0.391696i
$304$	1.76406	−	0.976025i	0.101176	−	0.0559789i
$305$	1.93649	+	1.11803i	0.110883	+	0.0640184i
$306$	3.14342	+	7.68784i	0.179697	+	0.439484i
$307$	−18.8326			−1.07483			−0.537415	−	0.843318i	$-0.680599\pi$
$307$	−18.8326			−1.07483			−0.537415	+	0.843318i	$0.680599\pi$
$308$	1.07047	−	3.85410i	0.0609955	−	0.219608i
$309$	−9.19628	+	5.30948i	−0.523158	+	0.302045i
$310$	−1.90983	+	14.0126i	−0.108471	+	0.795861i
$311$	12.6190			0.715555			0.357778	−	0.933807i	$-0.383535\pi$
$311$	12.6190			0.715555			0.357778	+	0.933807i	$0.383535\pi$
$312$	−8.12502	−	6.16312i	−0.459989	−	0.348918i
$313$	4.00000			0.226093			0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000			0.226093			0.113047	+	0.993590i	$0.463939\pi$
$314$	−0.239499	+	1.75722i	−0.0135157	+	0.0991659i
$315$	−7.68423	+	4.43649i	−0.432957	+	0.249968i
$316$	26.9787	+	7.49326i	1.51767	+	0.421529i
$317$	18.5485			1.04179			0.520895	−	0.853621i	$-0.325598\pi$
$317$	18.5485			1.04179			0.520895	+	0.853621i	$0.325598\pi$
$318$	−4.21388	−	10.3059i	−0.236303	−	0.577924i
$319$	−4.30948	−	2.48808i	−0.241284	−	0.139306i
$320$	−12.2984	−	12.9904i	−0.687500	−	0.726184i
$321$	−0.436492	+	0.756026i	−0.0243626	+	0.0421972i
$322$	6.72433	−	49.3370i	0.374732	−	2.74944i
$323$	1.48004	+	2.56351i	0.0823518	+	0.142637i
$324$	−0.500000	−	1.93649i	−0.0277778	−	0.107583i
$325$		0			0
$326$	−14.6190	+	18.8730i	−0.809669	+	1.04528i
$327$	2.12702	−	1.22803i	0.117624	−	0.0679104i
$328$	3.44957	−	0.406224i	0.190470	−	0.0224300i
$329$	7.87298	−	13.6364i	0.434052	−	0.751799i
$330$	−1.26004	−	0.976025i	−0.0693631	−	0.0537284i
$331$	4.97615	−	8.61895i	0.273514	−	0.473740i	−0.696245	−	0.717804i	$-0.745147\pi$
$331$	4.97615	−	8.61895i	0.273514	−	0.473740i	0.969759	+	0.244064i	$0.0784806\pi$
$332$	−5.70423	−	1.58434i	−0.313060	−	0.0869517i
$333$	−7.21222			−0.395227
$334$	12.2842	−	5.02277i	0.672160	−	0.274834i
$335$	2.18246	+	3.78013i	0.119240	+	0.206530i
$336$	−13.5989	−	8.18561i	−0.741883	−	0.446561i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	−1.78031	+	18.2984i	−0.0968362	+	0.995300i
$339$		−	9.87298i		−	0.536227i
$340$	18.7406	−	18.4019i	1.01635	−	0.997982i
$341$	−1.95205	+	1.12702i	−0.105709	+	0.0610314i
$342$	−0.269767	−	0.659767i	−0.0145873	−	0.0356761i
$343$			6.92820i			0.374088i
$344$	−15.0041	−	20.1176i	−0.808965	−	1.08467i
$345$	−17.1825	−	9.92030i	−0.925072	−	0.534091i
$346$	19.5566	+	15.1485i	1.05137	+	0.814386i
$347$	6.17218	+	3.56351i	0.331340	+	0.191299i	0.656436	−	0.754382i	$-0.272063\pi$
$347$	6.17218	+	3.56351i	0.331340	+	0.191299i	−0.325096	+	0.945681i	$0.605397\pi$
$348$	−14.0893	+	13.8346i	−0.755263	+	0.741613i
$349$	−13.6364	−	23.6190i	−0.729940	−	1.26429i	−0.956908	−	0.290391i	$-0.906215\pi$
$349$	−13.6364	−	23.6190i	−0.729940	−	1.26429i	0.226968	−	0.973902i	$-0.427119\pi$
$350$		0			0
$351$	−2.50000	+	2.59808i	−0.133440	+	0.138675i
$352$	0.436492	−	2.81754i	0.0232651	−	0.150175i
$353$	−23.8095	+	13.7464i	−1.26725	+	0.731647i	−0.974467	−	0.224531i	$-0.927915\pi$
$353$	−23.8095	+	13.7464i	−1.26725	+	0.731647i	−0.292784	+	0.956179i	$0.594582\pi$
$354$	−0.469067	+	3.44159i	−0.0249306	+	0.182918i
$355$	9.63628	+	5.56351i	0.511441	+	0.295280i
$356$	−3.90410	+	1.00803i	−0.206917	+	0.0534257i
$357$	11.6523	−	20.1825i	0.616708	−	1.06817i
$358$	−6.71135	+	2.74415i	−0.354706	+	0.145033i
$359$			13.9204i			0.734692i	0.930084	+	0.367346i	$0.119733\pi$
$359$			13.9204i			0.734692i	−0.930084	+	0.367346i	$0.880267\pi$
$360$	−5.06980	+	3.78115i	−0.267202	+	0.199284i
$361$	9.37298	+	16.2345i	0.493315	+	0.854446i
$362$	0.142467	−	1.04529i	0.00748790	−	0.0549393i
$363$			10.7460i			0.564017i
$364$	0.289470	+	28.6130i	0.0151724	+	1.49973i
$365$		−	29.3649i		−	1.53703i
$366$	1.40126	+	0.190983i	0.0732450	+	0.00998284i
$367$	−0.309475	−	0.536026i	−0.0161545	−	0.0279804i	0.857835	−	0.513925i	$-0.171809\pi$
$367$	−0.309475	−	0.536026i	−0.0161545	−	0.0279804i	−0.873990	+	0.485945i	$0.838476\pi$
$368$	0.647275	−	35.4860i	0.0337416	−	1.84984i
$369$		−	1.22803i		−	0.0639289i
$370$	8.63171	+	21.1105i	0.448741	+	1.09748i
$371$	−15.6205	+	27.0554i	−0.810974	+	1.40465i
$372$	2.23607	+	8.66025i	0.115935	+	0.449013i
$373$	26.4068	+	15.2460i	1.36729	+	0.789406i	0.990581	−	0.136925i	$-0.0437219\pi$
$373$	26.4068	+	15.2460i	1.36729	+	0.789406i	0.376710	+	0.926331i	$0.377055\pi$
$374$	4.14784	+	0.565326i	0.214480	+	0.0292323i
$375$	−9.68246	+	5.59017i	−0.500000	+	0.288675i
$376$	4.43649	−	10.3095i	0.228795	−	0.531671i
$377$	34.5554	+	8.55025i	1.77970	+	0.440361i
$378$	−3.43649	+	4.43649i	−0.176754	+	0.228189i
$379$	5.48017	+	9.49193i	0.281497	+	0.487568i	0.971754	−	0.235997i	$-0.0758356\pi$
$379$	5.48017	+	9.49193i	0.281497	+	0.487568i	−0.690256	+	0.723565i	$0.742502\pi$
$380$	−1.60831	+	1.57924i	−0.0825046	+	0.0810134i
$381$	1.95205	+	1.12702i	0.100007	+	0.0577388i
$382$	−17.1005	+	22.0767i	−0.874938	+	1.12954i
$383$	−19.7460	−	11.4003i	−1.00897	−	0.582530i	−0.0980813	−	0.995178i	$-0.531271\pi$
$383$	−19.7460	−	11.4003i	−1.00897	−	0.582530i	−0.910890	+	0.412648i	$0.864604\pi$
$384$	−10.3090	−	4.66092i	−0.526080	−	0.237852i
$385$			4.47214i			0.227921i
$386$	10.7605	−	4.39975i	0.547693	−	0.223942i
$387$	−7.68423	+	4.43649i	−0.390611	+	0.225520i
$388$	−24.2705	−	24.7172i	−1.23215	−	1.25483i
$389$			11.6190i			0.589104i	0.955635	+	0.294552i	$0.0951704\pi$
$389$			11.6190i			0.589104i	−0.955635	+	0.294552i	$0.904830\pi$
$390$	10.5967	+	4.20820i	0.536587	+	0.213091i
$391$	52.1109			2.63536
$392$	2.89310	+	24.5676i	0.146124	+	1.24085i
$393$	5.87298	+	10.1723i	0.296253	+	0.513125i
$394$	1.31457	+	3.21503i	0.0662270	+	0.161971i
$395$	−31.3050			−1.57512
$396$	−0.971267	−	0.269767i	−0.0488080	−	0.0135563i
$397$	3.74812	−	6.49193i	0.188113	−	0.325821i	−0.756508	−	0.653984i	$-0.773096\pi$
$397$	3.74812	−	6.49193i	0.188113	−	0.325821i	0.944621	+	0.328163i	$0.106430\pi$
$398$	5.95218	−	7.68423i	0.298356	−	0.385176i
$399$	−1.00000	+	1.73205i	−0.0500626	+	0.0867110i
$400$		0			0
$401$	−3.19052	+	1.84205i	−0.159327	+	0.0919876i	−0.577544	−	0.816360i	$-0.695989\pi$
$401$	−3.19052	+	1.84205i	−0.159327	+	0.0919876i	0.418216	+	0.908347i	$0.362655\pi$
$402$	2.18246	+	1.69052i	0.108851	+	0.0843157i
$403$	11.1803	−	11.6190i	0.556932	−	0.578781i
$404$	−15.2460	+	3.93649i	−0.758515	+	0.195848i
$405$	1.11803	+	1.93649i	0.0555556	+	0.0962250i
$406$	54.8973	+	7.48217i	2.72451	+	0.371334i
$407$	−1.81754	+	3.14807i	−0.0900922	+	0.156044i
$408$	6.56619	−	15.2585i	0.325075	−	0.755406i
$409$	4.88105	+	2.81808i	0.241352	+	0.139345i	0.615798	−	0.787904i	$-0.288834\pi$
$409$	4.88105	+	2.81808i	0.241352	+	0.139345i	−0.374446	+	0.927249i	$0.622167\pi$
$410$	−3.59452	+	1.46973i	−0.177521	+	0.0725849i
$411$	0.219999			0.0108518
$412$	20.4633	+	5.68361i	1.00815	+	0.280012i
$413$	8.44025	−	4.87298i	0.415318	−	0.239784i
$414$	−12.4333	−	1.69459i	−0.611066	−	0.0832845i
$415$	6.61895			0.324911
$416$	2.59017	+	20.2309i	0.126994	+	0.991904i
$417$	−9.74597			−0.477262
$418$	−0.355966	−	0.0485160i	−0.0174109	−	0.00237300i
$419$	−22.5167	+	13.0000i	−1.10001	+	0.635092i	−0.936224	−	0.351404i	$-0.885704\pi$
$419$	−22.5167	+	13.0000i	−1.10001	+	0.635092i	−0.163787	+	0.986496i	$0.552371\pi$
$420$	17.0987	+	4.74911i	0.834331	+	0.231733i
$421$	−12.1244			−0.590905			−0.295452	−	0.955357i	$-0.595470\pi$
$421$	−12.1244			−0.590905			−0.295452	+	0.955357i	$0.595470\pi$
$422$	18.3262	−	7.49326i	0.892107	−	0.364766i
$423$	−3.43649	−	1.98406i	−0.167088	−	0.0964683i
$424$	−8.80226	+	20.4546i	−0.427476	+	0.993364i
$425$		0			0
$426$	6.97288	+	0.950361i	0.337837	+	0.0460451i
$427$	−1.98406	−	3.43649i	−0.0960154	−	0.166303i
$428$	1.69052	−	0.436492i	0.0817146	−	0.0210986i
$429$	0.504017	+	1.74597i	0.0243342	+	0.0842961i
$430$	22.1825	+	17.1825i	1.06973	+	0.828612i
$431$	13.6905	−	7.90423i	0.659449	−	0.380733i	−0.132618	−	0.991167i	$-0.542338\pi$
$431$	13.6905	−	7.90423i	0.659449	−	0.380733i	0.792067	+	0.610434i	$0.209005\pi$
$432$	−2.06284	+	3.42705i	−0.0992486	+	0.164884i
$433$	13.3730	−	23.1627i	0.642665	−	1.11313i	−0.342171	−	0.939638i	$-0.611162\pi$
$433$	13.3730	−	23.1627i	0.642665	−	1.11313i	0.984836	−	0.173490i	$-0.0555044\pi$
$434$	15.3685	−	19.8406i	0.737710	−	0.952379i
$435$	11.0383	−	19.1190i	0.529247	−	0.916683i
$436$	−4.73297	−	1.31457i	−0.226668	−	0.0629564i
$437$	−4.47214			−0.213931
$438$	−7.02889	−	17.1905i	−0.335853	−	0.821395i
$439$	8.43649	+	14.6124i	0.402652	+	0.697413i	0.994045	−	0.108970i	$-0.0347552\pi$
$439$	8.43649	+	14.6124i	0.402652	+	0.697413i	−0.591393	+	0.806383i	$0.701422\pi$
$440$	0.372808	+	3.16581i	0.0177729	+	0.150924i
$441$	8.74597			0.416475
$442$	−29.6297	+	4.34409i	−1.40934	+	0.206627i
$443$			40.7298i			1.93513i	0.252617	+	0.967566i	$0.418709\pi$
$443$			40.7298i			1.93513i	−0.252617	+	0.967566i	$0.581291\pi$
$444$	10.1062	+	10.2922i	0.479618	+	0.488447i
$445$	3.90410	−	2.25403i	0.185072	−	0.106851i
$446$	−18.8818	+	7.72044i	−0.894081	+	0.365573i
$447$		−	8.72427i		−	0.412644i
$448$	7.37436	+	30.8765i	0.348406	+	1.45878i
$449$	−4.25403	−	2.45607i	−0.200760	−	0.115909i	0.396250	−	0.918143i	$-0.370311\pi$
$449$	−4.25403	−	2.45607i	−0.200760	−	0.115909i	−0.597010	+	0.802234i	$0.703645\pi$
$450$		0			0
$451$	−0.536026	−	0.309475i	−0.0252405	−	0.0145726i
$452$	−14.0893	+	13.8346i	−0.662703	+	0.650725i
$453$	5.44816	+	9.43649i	0.255977	+	0.443365i
$454$	1.69052	−	2.18246i	0.0793403	−	0.102428i
$455$	−8.87298	−	30.7369i	−0.415972	−	1.44097i
$456$	−0.563508	+	1.30948i	−0.0263887	+	0.0613218i
$457$	−33.3569	+	19.2586i	−1.56037	+	0.900879i	−0.563148	+	0.826356i	$0.690410\pi$
$457$	−33.3569	+	19.2586i	−1.56037	+	0.900879i	−0.997219	+	0.0745228i	$0.976257\pi$
$458$	−22.2414	−	3.03137i	−1.03927	−	0.141647i
$459$	−5.08615	−	2.93649i	−0.237401	−	0.137064i
$460$	9.92030	+	38.4211i	0.462536	+	1.79140i
$461$	−18.2185	+	31.5554i	−0.848522	+	1.46968i	0.0340048	+	0.999422i	$0.489174\pi$
$461$	−18.2185	+	31.5554i	−0.848522	+	1.46968i	−0.882527	+	0.470262i	$0.844159\pi$
$462$	1.07047	+	2.61803i	0.0498026	+	0.121802i
$463$		−	18.3926i		−	0.854775i	−0.904069	−	0.427387i	$-0.859434\pi$
$463$		−	18.3926i		−	0.854775i	0.904069	−	0.427387i	$-0.140566\pi$
$464$	39.4854	+	0.720224i	1.83306	+	0.0334356i
$465$	−5.00000	−	8.66025i	−0.231869	−	0.401610i
$466$	30.8277	+	4.20163i	1.42807	+	0.194637i
$467$		−	12.3649i		−	0.572180i	−0.958203	−	0.286090i	$-0.907644\pi$
$467$		−	12.3649i		−	0.572180i	0.958203	−	0.286090i	$-0.0923557\pi$
$468$	7.21073	−	0.0729490i	0.333316	−	0.00337207i
$469$		−	7.74597i		−	0.357676i
$470$	−1.69459	+	12.4333i	−0.0781656	+	0.573507i
$471$	−0.627017	−	1.08602i	−0.0288914	−	0.0500414i
$472$	5.56860	−	4.15317i	0.256316	−	0.191165i
$473$			4.47214i			0.205629i
$474$	−18.3262	+	7.49326i	−0.841752	+	0.344177i
$475$		0			0
$476$	−45.1293	+	11.6523i	−2.06850	+	0.534084i
$477$	6.81820	+	3.93649i	0.312184	+	0.180240i
$478$	−0.288776	+	2.11878i	−0.0132083	+	0.0969105i
$479$	36.1109	−	20.8486i	1.64995	−	0.952598i	0.672858	−	0.739771i	$-0.265066\pi$
$479$	36.1109	−	20.8486i	1.64995	−	0.952598i	0.977090	−	0.212827i	$-0.0682670\pi$
$480$	12.5000	+	1.93649i	0.570544	+	0.0883883i
$481$	6.24597	−	25.2428i	0.284792	−	1.15097i
$482$	−17.4284	−	13.5000i	−0.793843	−	0.614908i
$483$	17.6045	+	30.4919i	0.801034	+	1.38743i
$484$	15.3350	−	15.0579i	0.697047	−	0.684449i
$485$	33.5410	+	19.3649i	1.52302	+	0.879316i
$486$	1.11803	+	0.866025i	0.0507151	+	0.0392837i
$487$	−27.9284	−	16.1245i	−1.26556	−	0.730670i	−0.291414	−	0.956597i	$-0.594126\pi$
$487$	−27.9284	−	16.1245i	−1.26556	−	0.730670i	−0.974144	+	0.225927i	$0.927459\pi$
$488$	−1.69098	−	2.26728i	−0.0765472	−	0.102635i
$489$		−	16.8805i		−	0.763363i
$490$	−10.4673	−	25.5999i	−0.472866	−	1.15649i
$491$	32.7850	−	18.9284i	1.47957	−	0.854228i	0.479834	−	0.877359i	$-0.340697\pi$
$491$	32.7850	−	18.9284i	1.47957	−	0.854228i	0.999732	+	0.0231316i	$0.00736368\pi$
$492$	−1.75247	+	1.72079i	−0.0790073	+	0.0775793i
$493$			57.9839i			2.61146i
$494$	2.54281	−	0.372808i	0.114406	−	0.0167734i
$495$	1.12702			0.0506556
$496$	9.22531	−	15.3262i	0.414229	−	0.688168i
$497$	−9.87298	−	17.1005i	−0.442864	−	0.767063i
$498$	3.87480	−	1.58434i	0.173634	−	0.0709958i
$499$	−2.01607			−0.0902516			−0.0451258	−	0.998981i	$-0.514369\pi$
$499$	−2.01607			−0.0902516			−0.0451258	+	0.998981i	$0.514369\pi$
$500$	21.5451	+	5.98409i	0.963525	+	0.267617i
$501$	−4.69214	+	8.12702i	−0.209629	+	0.363088i
$502$	−17.0365	−	13.1964i	−0.760376	−	0.588985i
$503$	−10.3095	+	17.8565i	−0.459677	+	0.796184i	−0.998944	−	0.0459514i	$-0.985368\pi$
$503$	−10.3095	+	17.8565i	−0.459677	+	0.796184i	0.539267	+	0.842135i	$0.318701\pi$
$504$	11.1465	−	1.31262i	0.496505	−	0.0584689i
$505$	15.2460	−	8.80226i	0.678437	−	0.391696i
$506$	−3.87298	+	5.00000i	−0.172175	+	0.222277i
$507$	−6.92820	−	11.0000i	−0.307692	−	0.488527i
$508$	−1.12702	−	4.36492i	−0.0500033	−	0.193662i
$509$	−4.36214	−	7.55544i	−0.193348	−	0.334889i	0.753010	−	0.658010i	$-0.228601\pi$
$509$	−4.36214	−	7.55544i	−0.193348	−	0.334889i	−0.946358	+	0.323121i	$0.895268\pi$
$510$	−2.50806	+	18.4019i	−0.111059	+	0.814849i
$511$	−26.0554	+	45.1293i	−1.15262	+	1.99640i
$512$	7.79423	+	21.2426i	0.344459	+	0.938801i
$513$	0.436492	+	0.252009i	0.0192716	+	0.0111265i
$514$	8.22381	+	20.1129i	0.362737	+	0.887144i
$515$	−23.7447			−1.04632
$516$	17.0987	+	4.74911i	0.752728	+	0.209068i
$517$	−1.73205	+	1.00000i	−0.0761755	+	0.0439799i
$518$	5.46573	−	40.1025i	0.240151	−	1.76200i
$519$	−17.4919			−0.767811
$520$	−8.84346	−	21.0189i	−0.387811	−	0.921739i
$521$	5.61895			0.246171			0.123085	−	0.992396i	$-0.460721\pi$
$521$	5.61895			0.246171			0.123085	+	0.992396i	$0.460721\pi$
$522$	1.88557	−	13.8346i	0.0825292	−	0.605524i
$523$	29.7609	−	17.1825i	1.30135	−	0.751336i	0.320717	−	0.947175i	$-0.396076\pi$
$523$	29.7609	−	17.1825i	1.30135	−	0.751336i	0.980636	+	0.195839i	$0.0627429\pi$
$524$	6.28683	−	22.6351i	0.274641	−	0.988818i
$525$		0			0
$526$	−0.603217	−	1.47528i	−0.0263015	−	0.0643254i
$527$	22.7460	+	13.1324i	0.990830	+	0.572056i
$528$	0.976025	+	1.76406i	0.0424760	+	0.0767709i
$529$	−27.8649	+	48.2635i	−1.21152	+	2.09841i
$530$	3.36217	−	24.6685i	0.146043	−	1.07153i
$531$	−1.22803	−	2.12702i	−0.0532921	−	0.0923047i
$532$	3.87298	−	1.00000i	0.167915	−	0.0433555i
$533$	4.29812	+	1.06351i	0.186172	+	0.0460657i
$534$	1.74597	−	2.25403i	0.0755554	−	0.0975416i
$535$	−1.69052	+	0.976025i	−0.0730878	+	0.0421972i
$536$	−0.645723	−	5.48334i	−0.0278910	−	0.236844i
$537$	2.56351	−	4.44013i	0.110624	−	0.191606i
$538$	−22.0767	−	17.1005i	−0.951792	−	0.737255i
$539$	2.20406	−	3.81754i	0.0949355	−	0.164433i
$540$	1.19682	−	4.30902i	0.0515028	−	0.185431i
$541$	29.4449			1.26593			0.632967	−	0.774179i	$-0.281837\pi$
$541$	29.4449			1.26593			0.632967	+	0.774179i	$0.281837\pi$
$542$	−39.6592	+	16.2159i	−1.70351	+	0.696533i
$543$	0.372983	+	0.646026i	0.0160062	+	0.0277236i
$544$	−30.9755	+	12.0107i	−1.32807	+	0.514957i
$545$	5.49193			0.235249
$546$	−12.5516	−	15.8698i	−0.537160	−	0.679166i
$547$			24.3649i			1.04177i	0.853627	+	0.520884i	$0.174398\pi$
$547$			24.3649i			1.04177i	−0.853627	+	0.520884i	$0.825602\pi$
$548$	−0.308276	−	0.313950i	−0.0131689	−	0.0134113i
$549$	−0.866025	+	0.500000i	−0.0369611	+	0.0213395i
$550$		0			0
$551$		−	4.97615i		−	0.211991i
$552$	15.0041	+	20.1176i	0.638615	+	0.856261i
$553$	48.1109	+	27.7768i	2.04588	+	1.18119i
$554$	0.834016	+	0.646026i	0.0354339	+	0.0274470i
$555$	−13.9664	−	8.06351i	−0.592841	−	0.342277i
$556$	13.6566	+	13.9080i	0.579170	+	0.589830i
$557$	2.85008	+	4.93649i	0.120762	+	0.209166i	0.920068	−	0.391758i	$-0.128133\pi$
$557$	2.85008	+	4.93649i	0.120762	+	0.209166i	−0.799306	+	0.600924i	$0.794800\pi$
$558$	−5.00000	−	3.87298i	−0.211667	−	0.163956i
$559$	−8.87298	−	30.7369i	−0.375287	−	1.30003i
$560$	−17.1825	−	31.0554i	−0.726091	−	1.31233i
$561$	−2.56351	+	1.48004i	−0.108231	+	0.0624874i
$562$	2.32777	−	17.0791i	0.0981911	−	0.720437i
$563$	21.6367	+	12.4919i	0.911877	+	0.526472i	0.881034	−	0.473052i	$-0.156848\pi$
$563$	21.6367	+	12.4919i	0.911877	+	0.526472i	0.0308422	+	0.999524i	$0.490181\pi$
$564$	1.98406	+	7.68423i	0.0835440	+	0.323564i
$565$	11.0383	−	19.1190i	0.464386	−	0.804340i
$566$	−26.9906	+	11.0359i	−1.13450	+	0.463875i
$567$		−	3.96812i		−	0.166645i
$568$	−8.41459	−	11.2824i	−0.353068	−	0.473397i
$569$	19.4919	+	33.7610i	0.817144	+	1.41534i	0.907778	+	0.419451i	$0.137777\pi$
$569$	19.4919	+	33.7610i	0.817144	+	1.41534i	−0.0906335	+	0.995884i	$0.528889\pi$
$570$	0.215241	−	1.57924i	0.00901545	−	0.0661472i
$571$			16.6190i			0.695481i	0.937591	+	0.347741i	$0.113051\pi$
$571$			16.6190i			0.695481i	−0.937591	+	0.347741i	$0.886949\pi$
$572$	1.78533	−	3.16581i	0.0746482	−	0.132369i
$573$		−	19.7460i		−	0.824900i
$574$	6.82831	+	0.930657i	0.285008	+	0.0388449i
$575$		0			0
$576$	7.78115	−	1.85840i	0.324215	−	0.0774334i
$577$			18.6126i			0.774851i	0.921901	+	0.387426i	$0.126636\pi$
$577$			18.6126i			0.774851i	−0.921901	+	0.387426i	$0.873364\pi$
$578$	−9.36226	−	22.8972i	−0.389419	−	0.952400i
$579$	−4.11013	+	7.11895i	−0.170811	+	0.295853i
$580$	−42.7513	+	11.0383i	−1.77515	+	0.458342i
$581$	−10.1723	−	5.87298i	−0.422018	−	0.243652i
$582$	24.2705	+	3.30792i	1.00605	+	0.137118i
$583$	3.43649	−	1.98406i	0.142325	−	0.0821713i
$584$	−14.6825	+	34.1190i	−0.607564	+	1.41185i
$585$	−7.74597	+	2.23607i	−0.320256	+	0.0924500i
$586$	−5.31754	+	6.86492i	−0.219666	+	0.283587i
$587$	−4.47214	−	7.74597i	−0.184585	−	0.319710i	0.758852	−	0.651263i	$-0.225761\pi$
$587$	−4.47214	−	7.74597i	−0.184585	−	0.319710i	−0.943437	+	0.331553i	$0.892427\pi$
$588$	−12.2554	−	12.4809i	−0.505403	−	0.514705i
$589$	−1.95205	−	1.12702i	−0.0804328	−	0.0464379i
$590$	−4.75615	+	6.14017i	−0.195808	+	0.252787i
$591$	−2.12702	−	1.22803i	−0.0874938	−	0.0505146i
$592$	0.526124	−	28.8441i	0.0216236	−	1.18548i
$593$		−	19.5566i		−	0.803092i	−0.915839	−	0.401546i	$-0.868473\pi$
$593$		−	19.5566i		−	0.803092i	0.915839	−	0.401546i	$-0.131527\pi$
$594$	0.659767	−	0.269767i	0.0270706	−	0.0110687i
$595$	45.1293	−	26.0554i	1.85012	−	1.06817i
$596$	−12.4500	+	12.2250i	−0.509971	+	0.500754i
$597$			6.87298i			0.281292i
$598$	16.6987	−	42.0491i	0.682859	−	1.71952i
$599$	−10.0000			−0.408589			−0.204294	−	0.978909i	$-0.565490\pi$
$599$	−10.0000			−0.408589			−0.204294	+	0.978909i	$0.565490\pi$
$600$		0			0
$601$	8.24597	+	14.2824i	0.336360	+	0.582593i	0.983745	−	0.179570i	$-0.0574708\pi$
$601$	8.24597	+	14.2824i	0.336360	+	0.582593i	−0.647385	+	0.762163i	$0.724137\pi$
$602$	−18.8451	−	46.0892i	−0.768067	−	1.87846i
$603$	−1.95205			−0.0794936
$604$	5.83207	−	20.9978i	0.237304	−	0.854387i
$605$	−12.0144	+	20.8095i	−0.488453	+	0.846025i
$606$	6.81820	−	8.80226i	0.276971	−	0.357567i
$607$	9.74597	−	16.8805i	0.395577	−	0.685159i	−0.597598	−	0.801796i	$-0.703878\pi$
$607$	9.74597	−	16.8805i	0.395577	−	0.685159i	0.993175	+	0.116637i	$0.0372114\pi$
$608$	2.65831	−	1.03076i	0.107809	−	0.0418028i
$609$	−33.9284	+	19.5886i	−1.37485	+	0.793770i
$610$	2.50000	+	1.93649i	0.101222	+	0.0784063i
$611$	9.92030	−	10.3095i	0.401332	−	0.417077i
$612$	2.93649	+	11.3730i	0.118701	+	0.459726i
$613$	7.35423	+	12.7379i	0.297035	+	0.514479i	0.975456	−	0.220194i	$-0.0706690\pi$
$613$	7.35423	+	12.7379i	0.297035	+	0.514479i	−0.678422	+	0.734673i	$0.737336\pi$
$614$	−26.3893	−	3.59670i	−1.06498	−	0.145151i
$615$	1.37298	−	2.37808i	0.0553640	−	0.0958933i
$616$	2.23607	−	5.19615i	0.0900937	−	0.209359i
$617$	−5.42843	−	3.13410i	−0.218540	−	0.126174i	0.386734	−	0.922191i	$-0.373603\pi$
$617$	−5.42843	−	3.13410i	−0.218540	−	0.126174i	−0.605274	+	0.796017i	$0.706937\pi$
$618$	−13.9004	+	5.68361i	−0.559156	+	0.228628i
$619$	−22.2326			−0.893605			−0.446803	−	0.894633i	$-0.647437\pi$
$619$	−22.2326			−0.893605			−0.446803	+	0.894633i	$0.647437\pi$
$620$	−5.35233	+	19.2705i	−0.214955	+	0.773922i
$621$	7.68423	−	4.43649i	0.308357	−	0.178030i
$622$	17.6824	+	2.41001i	0.709000	+	0.0966324i
$623$	−8.00000			−0.320513
$624$	−10.2082	−	10.1879i	−0.408655	−	0.407841i
$625$	−25.0000			−1.00000
$626$	5.60503	+	0.763932i	0.224022	+	0.0305329i
$627$	0.219999	−	0.127017i	0.00878593	−	0.00507256i
$628$	−0.671200	+	2.41659i	−0.0267838	+	0.0964323i
$629$	42.3573			1.68889
$630$	−11.6149	+	4.74911i	−0.462748	+	0.189209i
$631$	12.0000	+	6.92820i	0.477712	+	0.275807i	0.719463	−	0.694531i	$-0.244388\pi$
$631$	12.0000	+	6.92820i	0.477712	+	0.275807i	−0.241750	+	0.970339i	$0.577721\pi$
$632$	36.3731	+	15.6525i	1.44684	+	0.622622i
$633$	−7.00000	+	12.1244i	−0.278225	+	0.481900i
$634$	25.9913	+	3.54246i	1.03225	+	0.140689i
$635$	2.52009	+	4.36492i	0.100007	+	0.173216i
$636$	−3.93649	−	15.2460i	−0.156092	−	0.604542i
$637$	−7.57423	+	30.6109i	−0.300102	+	1.21285i
$638$	−5.56351	−	4.30948i	−0.220261	−	0.170614i
$639$	−4.30948	+	2.48808i	−0.170480	+	0.0984268i
$640$	−14.7523	−	20.5517i	−0.583134	−	0.812376i
$641$	−9.68246	+	16.7705i	−0.382434	+	0.662395i	−0.991410	−	0.130794i	$-0.958247\pi$
$641$	−9.68246	+	16.7705i	−0.382434	+	0.662395i	0.608975	+	0.793189i	$0.291581\pi$
$642$	−0.756026	+	0.976025i	−0.0298380	+	0.0385206i
$643$	−2.67607	+	4.63508i	−0.105534	+	0.182790i	−0.913956	−	0.405813i	$-0.866988\pi$
$643$	−2.67607	+	4.63508i	−0.105534	+	0.182790i	0.808422	+	0.588603i	$0.200322\pi$
$644$	18.8451	−	67.8496i	0.742599	−	2.67365i
$645$	−19.8406			−0.781223
$646$	1.58434	+	3.87480i	0.0623348	+	0.152452i
$647$	8.12702	+	14.0764i	0.319506	+	0.553401i	0.980385	−	0.197092i	$-0.0631497\pi$
$647$	8.12702	+	14.0764i	0.319506	+	0.553401i	−0.660879	+	0.750492i	$0.729816\pi$
$648$	−0.330792	−	2.80902i	−0.0129947	−	0.110349i
$649$	−1.23790			−0.0485918
$650$		0			0
$651$			17.7460i			0.695519i
$652$	−24.0893	+	23.6540i	−0.943412	+	0.926360i
$653$	−16.6605	+	9.61895i	−0.651976	+	0.376419i	−0.789213	−	0.614120i	$-0.789511\pi$
$653$	−16.6605	+	9.61895i	−0.651976	+	0.376419i	0.137237	+	0.990538i	$0.456178\pi$
$654$	3.21503	−	1.31457i	0.125718	−	0.0514037i
$655$			26.2648i			1.02625i
$656$	4.91132	+	0.0895838i	0.191755	+	0.00349766i
$657$	11.3730	+	6.56619i	0.443702	+	0.256172i
$658$	13.6364	−	17.6045i	0.531602	−	0.686296i
$659$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$659$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$660$	−1.57924	−	1.60831i	−0.0614719	−	0.0626034i
$661$	16.2345	+	28.1190i	0.631448	+	1.09370i	0.987256	+	0.159141i	$0.0508725\pi$
$661$	16.2345	+	28.1190i	0.631448	+	1.09370i	−0.355808	+	0.934559i	$0.615794\pi$
$662$	8.61895	−	11.1270i	0.334985	−	0.432464i
$663$	14.6825	−	15.2585i	0.570219	−	0.592589i
$664$	−7.69052	−	3.30948i	−0.298450	−	0.128433i
$665$	−3.87298	+	2.23607i	−0.150188	+	0.0867110i
$666$	−10.1062	−	1.37741i	−0.391607	−	0.0533736i
$667$	−75.8663	−	43.8014i	−2.93755	−	1.69600i
$668$	18.1726	−	4.69214i	0.703118	−	0.181544i
$669$	7.21222	−	12.4919i	0.278841	−	0.482966i
$670$	2.33625	+	5.71375i	0.0902571	+	0.220741i
$671$			0.504017i			0.0194574i
$672$	−17.4923	−	14.0673i	−0.674781	−	0.542659i
$673$	−11.1190	−	19.2586i	−0.428604	−	0.742364i	0.568145	−	0.822928i	$-0.307661\pi$
$673$	−11.1190	−	19.2586i	−0.428604	−	0.742364i	−0.996749	+	0.0805642i	$0.974328\pi$
$674$	−18.2164	−	2.48278i	−0.701668	−	0.0956331i
$675$		0			0
$676$	−5.98936	+	25.3007i	−0.230360	+	0.973106i
$677$		−	15.7460i		−	0.605167i	−0.953123	−	0.302583i	$-0.902151\pi$
$677$		−	15.7460i		−	0.605167i	0.953123	−	0.302583i	$-0.0978491\pi$
$678$	1.88557	−	13.8346i	0.0724150	−	0.531315i
$679$	−34.3649	−	59.5218i	−1.31880	−	2.28424i
$680$	29.7749	−	22.2066i	1.14181	−	0.851586i
$681$			1.95205i			0.0748027i
$682$	−2.95057	+	1.20643i	−0.112983	+	0.0461967i
$683$	−4.25214	+	7.36492i	−0.162703	+	0.281811i	−0.935837	−	0.352432i	$-0.885355\pi$
$683$	−4.25214	+	7.36492i	−0.162703	+	0.281811i	0.773134	+	0.634243i	$0.218688\pi$
$684$	−0.252009	−	0.976025i	−0.00963579	−	0.0373193i
$685$	0.426027	+	0.245967i	0.0162776	+	0.00939790i
$686$	−1.32317	+	9.70820i	−0.0505188	+	0.370661i
$687$	13.7460	−	7.93624i	0.524441	−	0.302786i
$688$	−17.1825	−	31.0554i	−0.655075	−	1.18398i
$689$	−19.6825	+	20.4546i	−0.749842	+	0.779259i
$690$	−22.1825	−	17.1825i	−0.844472	−	0.654125i
$691$	−21.3206	−	36.9284i	−0.811075	−	1.40482i	−0.912112	−	0.409941i	$-0.865549\pi$
$691$	−21.3206	−	36.9284i	−0.811075	−	1.40482i	0.101037	−	0.994883i	$-0.467784\pi$
$692$	24.5107	+	24.9619i	0.931758	+	0.948908i
$693$	−1.73205	−	1.00000i	−0.0657952	−	0.0379869i
$694$	7.96825	+	6.17218i	0.302471	+	0.234293i
$695$	−18.8730	−	10.8963i	−0.715893	−	0.413321i
$696$	−22.3849	+	16.6950i	−0.848496	+	0.632824i
$697$			7.21222i			0.273182i
$698$	−14.5973	−	35.7006i	−0.552516	−	1.35129i
$699$	−19.0526	+	11.0000i	−0.720634	+	0.416058i
$700$		0			0
$701$		−	43.7460i		−	1.65226i	−0.563478	−	0.826131i	$-0.690537\pi$
$701$		−	43.7460i		−	1.65226i	0.563478	−	0.826131i	$-0.309463\pi$
$702$	−3.99933	+	3.16312i	−0.150945	+	0.119384i
$703$	−3.63508			−0.137100
$704$	1.14974	−	3.86474i	0.0433325	−	0.145658i
$705$	−4.43649	−	7.68423i	−0.167088	−	0.289405i
$706$	−35.9886	+	14.7151i	−1.35445	+	0.553809i
$707$	−31.2409			−1.17494
$708$	−1.31457	+	4.73297i	−0.0494045	+	0.177876i
$709$	24.8947	−	43.1190i	0.934941	−	1.61937i	0.160203	−	0.987084i	$-0.448785\pi$
$709$	24.8947	−	43.1190i	0.934941	−	1.61937i	0.774738	−	0.632282i	$-0.217882\pi$
$710$	12.4404	+	9.63628i	0.466879	+	0.361643i
$711$	7.00000	−	12.1244i	0.262521	−	0.454699i
$712$	−5.66317	+	0.666900i	−0.212236	+	0.0249931i
$713$	−34.3649	+	19.8406i	−1.28698	+	0.743036i
$714$	20.1825	−	26.0554i	0.755310	−	0.975100i
$715$	−0.976025	+	3.94456i	−0.0365013	+	0.147518i
$716$	−9.92843	+	2.56351i	−0.371043	+	0.0958028i
$717$	−0.756026	−	1.30948i	−0.0282343	−	0.0489032i
$718$	−2.65856	+	19.5061i	−0.0992168	+	0.727962i
$719$	6.49193	−	11.2444i	0.242108	−	0.419344i	−0.719206	−	0.694797i	$-0.755494\pi$
$719$	6.49193	−	11.2444i	0.242108	−	0.419344i	0.961315	+	0.275453i	$0.0888277\pi$
$720$	−7.82624	+	4.33013i	−0.291667	+	0.161374i
$721$	36.4919	+	21.0686i	1.35903	+	0.784637i
$722$	10.0335	+	24.5388i	0.373407	+	0.913239i
$723$	15.5885			0.579741
$724$	0.399266	−	1.43752i	0.0148386	−	0.0534249i
$725$		0			0
$726$	−2.05230	+	15.0579i	−0.0761679	+	0.558850i
$727$	−25.1270			−0.931909			−0.465955	−	0.884809i	$-0.654289\pi$
$727$	−25.1270			−0.931909			−0.465955	+	0.884809i	$0.654289\pi$
$728$	−5.05898	+	40.1496i	−0.187498	+	1.48804i
$729$	−1.00000			−0.0370370
$730$	5.60820	−	41.1478i	0.207569	−	1.52295i
$731$	45.1293	−	26.0554i	1.66917	−	0.963695i
$732$	1.92705	+	0.535233i	0.0712259	+	0.0197828i
$733$	30.5809			1.12953			0.564766	−	0.825251i	$-0.308966\pi$
$733$	30.5809			1.12953			0.564766	+	0.825251i	$0.308966\pi$
$734$	−0.331283	−	0.810216i	−0.0122279	−	0.0299056i
$735$	16.9365	+	9.77829i	0.624712	+	0.360678i
$736$	7.68423	−	49.6015i	0.283244	−	1.82833i
$737$	−0.491933	+	0.852054i	−0.0181206	+	0.0313858i
$738$	0.234534	−	1.72079i	0.00863330	−	0.0633433i
$739$	16.3765	+	28.3649i	0.602419	+	1.04342i	0.992454	+	0.122620i	$0.0391297\pi$
$739$	16.3765	+	28.3649i	0.602419	+	1.04342i	−0.390035	+	0.920800i	$0.627537\pi$
$740$	8.06351	+	31.2298i	0.296420	+	1.14803i
$741$	−1.26004	+	1.30948i	−0.0462888	+	0.0481048i
$742$	−27.0554	+	34.9284i	−0.993237	+	1.28226i
$743$	30.0000	−	17.3205i	1.10059	−	0.635428i	0.164216	−	0.986424i	$-0.447490\pi$
$743$	30.0000	−	17.3205i	1.10059	−	0.635428i	0.936377	+	0.350997i	$0.114157\pi$
$744$	1.47935	+	12.5623i	0.0542355	+	0.460556i
$745$	9.75403	−	16.8945i	0.357360	−	0.618966i
$746$	34.0910	+	26.4068i	1.24816	+	0.966821i
$747$	−1.48004	+	2.56351i	−0.0541519	+	0.0937939i
$748$	5.70423	+	1.58434i	0.208567	+	0.0579290i
$749$	3.46410			0.126576
$750$	−14.6353	+	5.98409i	−0.534404	+	0.218508i
$751$	−9.56351	−	16.5645i	−0.348977	−	0.604447i	0.637091	−	0.770789i	$-0.280138\pi$
$751$	−9.56351	−	16.5645i	−0.348977	−	0.604447i	−0.986068	+	0.166342i	$0.946804\pi$
$752$	8.18561	−	13.5989i	0.298498	−	0.495903i
$753$	15.2379			0.555300
$754$	46.7882	+	18.5806i	1.70392	+	0.676666i
$755$			24.3649i			0.886730i
$756$	−5.66271	+	5.56036i	−0.205951	+	0.202228i
$757$	2.39205	−	1.38105i	0.0869405	−	0.0501951i	−0.455899	−	0.890031i	$-0.650682\pi$
$757$	2.39205	−	1.38105i	0.0869405	−	0.0501951i	0.542840	+	0.839836i	$0.317349\pi$
$758$	5.86634	+	14.3473i	0.213075	+	0.521116i
$759$		−	4.47214i		−	0.162328i
$760$	−2.55527	+	1.90577i	−0.0926893	+	0.0691294i
$761$	5.12702	+	2.96008i	0.185854	+	0.107303i	0.590040	−	0.807374i	$-0.299112\pi$
$761$	5.12702	+	2.96008i	0.185854	+	0.107303i	−0.404186	+	0.914677i	$0.632445\pi$
$762$	2.52009	+	1.95205i	0.0912931	+	0.0707153i
$763$	−8.44025	−	4.87298i	−0.305558	−	0.176414i
$764$	−28.1785	+	27.6692i	−1.01946	+	1.00104i
$765$	−6.56619	−	11.3730i	−0.237401	−	0.411191i
$766$	−25.4919	−	19.7460i	−0.921061	−	0.713451i
$767$	8.50807	−	2.45607i	0.307208	−	0.0886834i
$768$	−13.5554	−	8.50000i	−0.489140	−	0.306717i
$769$	24.4919	−	14.1404i	0.883202	−	0.509917i	0.0114890	−	0.999934i	$-0.496343\pi$
$769$	24.4919	−	14.1404i	0.883202	−	0.509917i	0.871713	+	0.490017i	$0.163010\pi$
$770$	−0.854102	+	6.26662i	−0.0307797	+	0.225833i
$771$	−13.3064	−	7.68246i	−0.479219	−	0.276677i
$772$	15.9185	−	4.11013i	0.572918	−	0.147927i
$773$	−1.51205	+	2.61895i	−0.0543847	+	0.0941971i	−0.891936	−	0.452161i	$-0.850653\pi$
$773$	−1.51205	+	2.61895i	−0.0543847	+	0.0941971i	0.837551	+	0.546359i	$0.183986\pi$
$774$	−11.6149	+	4.74911i	−0.417488	+	0.170703i
$775$		0			0
$776$	−29.2887	−	39.2705i	−1.05140	−	1.40973i
$777$	14.3095	+	24.7847i	0.513350	+	0.889148i
$778$	−2.21902	+	16.2812i	−0.0795558	+	0.583708i
$779$		−	0.618950i		−	0.0221762i
$780$	14.0451	+	7.92058i	0.502895	+	0.283602i
$781$			2.50807i			0.0897457i
$782$	73.0208	+	9.95229i	2.61122	+	0.355893i
$783$	4.93649	+	8.55025i	0.176416	+	0.305561i
$784$	−0.638010	+	34.9780i	−0.0227861	+	1.24922i
$785$		−	2.80410i		−	0.100083i
$786$	6.28683	+	15.3757i	0.224244	+	0.548432i
$787$	−3.24410	+	5.61895i	−0.115640	+	0.200294i	−0.918035	−	0.396499i	$-0.870225\pi$
$787$	−3.24410	+	5.61895i	−0.115640	+	0.200294i	0.802396	+	0.596793i	$0.203558\pi$
$788$	1.22803	+	4.75615i	0.0437469	+	0.169431i
$789$	0.976025	+	0.563508i	0.0347474	+	0.0200614i
$790$	−43.8663	−	5.97871i	−1.56069	−	0.212713i
$791$	−33.9284	+	19.5886i	−1.20636	+	0.696490i
$792$	−1.30948	−	0.563508i	−0.0465302	−	0.0200234i
$793$	−1.00000	−	3.46410i	−0.0355110	−	0.123014i
$794$	6.49193	−	8.38105i	0.230390	−	0.297432i
$795$	8.80226	+	15.2460i	0.312184	+	0.540719i
$796$	9.80810	−	9.63083i	0.347639	−	0.341356i
$797$	27.2728	+	15.7460i	0.966053	+	0.557751i	0.898031	−	0.439933i	$-0.144998\pi$
$797$	27.2728	+	15.7460i	0.966053	+	0.557751i	0.0680221	+	0.997684i	$0.478331\pi$
$798$	−1.73205	+	2.23607i	−0.0613139	+	0.0791559i
$799$	20.1825	+	11.6523i	0.714004	+	0.412230i
$800$		0			0
$801$			2.01607i			0.0712343i
$802$	−4.82255	+	1.97185i	−0.170290	+	0.0696285i
$803$	5.73218	−	3.30948i	0.202284	−	0.116789i
$804$	2.73533	+	2.78568i	0.0964675	+	0.0982432i
$805$			78.7298i			2.77486i
$806$	17.8856	−	14.1459i	0.629992	−	0.498268i
$807$	19.7460			0.695091
$808$	−22.1153	+	2.60432i	−0.778015	+	0.0916197i
$809$	−13.9365	−	24.1387i	−0.489981	−	0.848672i	0.509953	−	0.860203i	$-0.329663\pi$
$809$	−13.9365	−	24.1387i	−0.489981	−	0.848672i	−0.999934	+	0.0115306i	$0.996330\pi$
$810$	1.19682	+	2.92705i	0.0420519	+	0.102846i
$811$	−36.2171			−1.27175			−0.635877	−	0.771790i	$-0.719361\pi$
$811$	−36.2171			−1.27175			−0.635877	+	0.771790i	$0.719361\pi$
$812$	75.4964	+	20.9689i	2.64940	+	0.735865i
$813$	15.1485	−	26.2379i	0.531280	−	0.920203i
$814$	−3.14807	+	4.06415i	−0.110340	+	0.142448i
$815$	18.8730	−	32.6890i	0.661092	−	1.14504i
$816$	12.1150	−	20.1270i	0.424111	−	0.704586i
$817$	−3.87298	+	2.23607i	−0.135499	+	0.0782301i
$818$	6.30141	+	4.88105i	0.220324	+	0.170662i
$819$	13.8884	+	3.43649i	0.485301	+	0.120081i
$820$	−5.31754	+	1.37298i	−0.185697	+	0.0479467i
$821$	−26.3288	−	45.6028i	−0.918881	−	1.59155i	−0.801117	−	0.598508i	$-0.795761\pi$
$821$	−26.3288	−	45.6028i	−0.918881	−	1.59155i	−0.117764	−	0.993042i	$-0.537573\pi$
$822$	0.308276	+	0.0420161i	0.0107524	+	0.00146548i
$823$	−23.8730	+	41.3492i	−0.832160	+	1.44134i	0.0641621	+	0.997939i	$0.479563\pi$
$823$	−23.8730	+	41.3492i	−0.832160	+	1.44134i	−0.896322	+	0.443404i	$0.853771\pi$
$824$	27.5888	+	11.8723i	0.961103	+	0.413593i
$825$		0			0
$826$	12.7576	−	5.21636i	0.443895	−	0.181501i
$827$	35.2091			1.22434			0.612169	−	0.790727i	$-0.290297\pi$
$827$	35.2091			1.22434			0.612169	+	0.790727i	$0.290297\pi$
$828$	−17.0987	−	4.74911i	−0.594221	−	0.165043i
$829$	−26.1868	+	15.1190i	−0.909505	+	0.525103i	−0.880272	−	0.474470i	$-0.842640\pi$
$829$	−26.1868	+	15.1190i	−0.909505	+	0.525103i	−0.0292330	+	0.999573i	$0.509306\pi$
$830$	9.27486	+	1.26411i	0.321935	+	0.0438778i
$831$	−0.745967			−0.0258773
$832$	−0.234268	+	28.8435i	−0.00812179	+	0.999967i
$833$	−51.3649			−1.77969
$834$	−13.6566	−	1.86131i	−0.472890	−	0.0644520i
$835$	−18.1726	+	10.4919i	−0.628887	+	0.363088i
$836$	−0.489535	−	0.135967i	−0.0169309	−	0.00470252i
$837$	4.47214			0.154580
$838$	−34.0344	+	13.9161i	−1.17570	+	0.480722i
$839$	6.00000	+	3.46410i	0.207143	+	0.119594i	0.599983	−	0.800013i	$-0.295174\pi$
$839$	6.00000	+	3.46410i	0.207143	+	0.119594i	−0.392840	+	0.919607i	$0.628507\pi$
$840$	23.0527	+	9.92030i	0.795393	+	0.342283i
$841$	34.2379	−	59.3018i	1.18062	−	2.04489i
$842$	−16.9894	−	2.31555i	−0.585492	−	0.0797990i
$843$	6.09419	+	10.5554i	0.209895	+	0.363549i
$844$	27.1109	−	7.00000i	0.933195	−	0.240950i
$845$	−1.11803	−	29.0474i	−0.0384615	−	0.999260i
$846$	−4.43649	−	3.43649i	−0.152530	−	0.118149i
$847$	36.9284	−	21.3206i	1.26888	−	0.732586i
$848$	−16.2407	+	26.9811i	−0.557709	+	0.926535i
$849$	10.3095	−	17.8565i	0.353820	−	0.612835i
$850$		0			0
$851$	−31.9970	+	55.4204i	−1.09684	+	1.89979i
$852$	9.58930	+	2.66340i	0.328524	+	0.0912467i
$853$	−25.5408			−0.874499			−0.437250	−	0.899340i	$-0.644047\pi$
$853$	−25.5408			−0.874499			−0.437250	+	0.899340i	$0.644047\pi$
$854$	−2.12387	−	5.19433i	−0.0726773	−	0.177746i
$855$	0.563508	+	0.976025i	0.0192716	+	0.0333794i
$856$	2.45223	−	0.288776i	0.0838153	−	0.00987017i
$857$	−15.6190			−0.533533			−0.266767	−	0.963761i	$-0.585955\pi$
$857$	−15.6190			−0.533533			−0.266767	+	0.963761i	$0.585955\pi$
$858$	0.372808	+	2.54281i	0.0127275	+	0.0868101i
$859$		−	43.6028i		−	1.48771i	−0.668342	−	0.743854i	$-0.732996\pi$
$859$		−	43.6028i		−	1.48771i	0.668342	−	0.743854i	$-0.267004\pi$
$860$	27.8018	+	28.3135i	0.948034	+	0.965484i
$861$	−4.22013	+	2.43649i	−0.143822	+	0.0830354i
$862$	20.6935	−	8.46121i	0.704825	−	0.288190i
$863$			17.2565i			0.587418i	0.955895	+	0.293709i	$0.0948896\pi$
$863$			17.2565i			0.587418i	−0.955895	+	0.293709i	$0.905110\pi$
$864$	−3.54508	+	4.40822i	−0.120606	+	0.149971i
$865$	−33.8730	−	19.5566i	−1.15172	−	0.664944i
$866$	23.1627	−	29.9029i	0.787100	−	1.01614i
$867$	15.1485	+	8.74597i	0.514469	+	0.297029i
$868$	25.3244	−	24.8667i	0.859566	−	0.844030i
$869$	−3.52812	−	6.11088i	−0.119683	−	0.207298i
$870$	19.1190	−	24.6825i	0.648193	−	0.836814i
$871$	1.69052	−	6.83218i	0.0572813	−	0.231499i
$872$	−6.38105	−	2.74597i	−0.216090	−	0.0929902i
$873$	−15.0000	+	8.66025i	−0.507673	+	0.293105i
$874$	−6.26662	−	0.854102i	−0.211972	−	0.0288904i
$875$	38.4211	+	22.1825i	1.29887	+	0.749904i
$876$	−6.56619	−	25.4308i	−0.221851	−	0.859226i
$877$	−2.59808	+	4.50000i	−0.0877308	+	0.151954i	−0.906552	−	0.422095i	$-0.861295\pi$
$877$	−2.59808	+	4.50000i	−0.0877308	+	0.151954i	0.818821	+	0.574049i	$0.194628\pi$
$878$	9.03098	+	22.0870i	0.304781	+	0.745401i
$879$		−	6.14017i		−	0.207103i
$880$	−0.0822148	+	4.50732i	−0.00277146	+	0.151942i
$881$	−5.55544	−	9.62231i	−0.187168	−	0.324184i	0.757137	−	0.653256i	$-0.226597\pi$
$881$	−5.55544	−	9.62231i	−0.187168	−	0.324184i	−0.944305	+	0.329072i	$0.893264\pi$
$882$	12.2554	+	1.67033i	0.412659	+	0.0562430i
$883$		−	50.9839i		−	1.71574i	−0.513864	−	0.857872i	$-0.671786\pi$
$883$		−	50.9839i		−	1.71574i	0.513864	−	0.857872i	$-0.328214\pi$
$884$	−42.3485	+	0.428428i	−1.42433	+	0.0144096i
$885$		−	5.49193i		−	0.184609i
$886$	−7.77871	+	57.0730i	−0.261331	+	1.91741i
$887$	17.8730	+	30.9569i	0.600116	+	1.03943i	0.992803	+	0.119759i	$0.0382123\pi$
$887$	17.8730	+	30.9569i	0.600116	+	1.03943i	−0.392687	+	0.919672i	$0.628454\pi$
$888$	12.1957	+	16.3522i	0.409262	+	0.548742i
$889$		−	8.94427i		−	0.299981i
$890$	5.90114	−	2.41287i	0.197807	−	0.0808795i
$891$	−0.252009	+	0.436492i	−0.00844261	+	0.0146230i
$892$	−27.9328	+	7.21222i	−0.935260	+	0.241483i
$893$	−1.73205	−	1.00000i	−0.0579609	−	0.0334637i
$894$	1.66619	−	12.2250i	0.0557257	−	0.408864i
$895$	9.92843	−	5.73218i	0.331871	−	0.191606i
$896$	4.43649	+	44.6744i	0.148213	+	1.49247i
$897$	8.87298	+	30.7369i	0.296260	+	1.02628i
$898$	−5.49193	−	4.25403i	−0.183268	−	0.141959i
$899$	−22.0767	−	38.2379i	−0.736298	−	1.27531i
$900$		0			0
$901$	−40.0432	−	23.1190i	−1.33403	−	0.770204i
$902$	−0.692007	−	0.536026i	−0.0230413	−	0.0178477i
$903$	30.4919	+	17.6045i	1.01471	+	0.585842i
$904$	−22.3849	+	16.6950i	−0.744509	+	0.555269i
$905$			1.66803i			0.0554473i
$906$	5.83207	+	14.2635i	0.193758	+	0.473872i
$907$	−27.2728	+	15.7460i	−0.905579	+	0.522836i	−0.879006	−	0.476811i	$-0.841793\pi$
$907$	−27.2728	+	15.7460i	−0.905579	+	0.522836i	−0.0265729	+	0.999647i	$0.508459\pi$
$908$	2.78568	−	2.73533i	0.0924459	−	0.0907750i
$909$			7.87298i			0.261130i
$910$	−6.56312	−	44.7650i	−0.217565	−	1.48394i
$911$	−38.7298			−1.28318			−0.641588	−	0.767049i	$-0.721724\pi$
$911$	−38.7298			−1.28318			−0.641588	+	0.767049i	$0.721724\pi$
$912$	−1.03971	+	1.72729i	−0.0344282	+	0.0571964i
$913$	0.745967	+	1.29205i	0.0246879	+	0.0427607i
$914$	−50.4196	+	20.6157i	−1.66773	+	0.681906i
$915$	−2.23607			−0.0739221
$916$	−30.5871	−	8.49547i	−1.01063	−	0.280698i
$917$	23.3047	−	40.3649i	0.769589	−	1.33297i
$918$	−6.56619	−	5.08615i	−0.216717	−	0.167868i
$919$	−22.8730	+	39.6172i	−0.754510	+	1.30685i	0.191107	+	0.981569i	$0.438792\pi$
$919$	−22.8730	+	39.6172i	−0.754510	+	1.30685i	−0.945618	+	0.325281i	$0.894541\pi$
$920$	6.56312	+	55.7326i	0.216379	+	1.83745i
$921$	16.3095	−	9.41628i	0.537415	−	0.310277i
$922$	−31.5554	+	40.7379i	−1.03922	+	1.34163i
$923$	−4.97615	−	17.2379i	−0.163792	−	0.567392i
$924$	1.00000	+	3.87298i	0.0328976	+	0.127412i
$925$		0			0
$926$	3.51267	−	25.7727i	0.115433	−	0.846945i
$927$	5.30948	−	9.19628i	0.174386	−	0.302045i
$928$	55.1917	+	8.55025i	1.81175	+	0.280676i
$929$	23.4284	+	13.5264i	0.768662	+	0.443787i	0.832397	−	0.554180i	$-0.186968\pi$
$929$	23.4284	+	13.5264i	0.768662	+	0.443787i	−0.0637353	+	0.997967i	$0.520301\pi$
$930$	−5.35233	−	13.0902i	−0.175510	−	0.429244i
$931$	4.40812			0.144470
$932$	42.3951	+	11.7751i	1.38870	+	0.385707i
$933$	−10.9283	+	6.30948i	−0.357778	+	0.206563i
$934$	2.36149	−	17.3264i	0.0772703	−	0.566939i
$935$	−6.61895			−0.216463
$936$	10.1180	+	1.27491i	0.330718	+	0.0416716i
$937$	12.2379			0.399795			0.199897	−	0.979817i	$-0.435939\pi$
$937$	12.2379			0.399795			0.199897	+	0.979817i	$0.435939\pi$
$938$	1.47935	−	10.8541i	0.0483024	−	0.354399i
$939$	−3.46410	+	2.00000i	−0.113047	+	0.0652675i
$940$	−4.74911	+	17.0987i	−0.154899	+	0.557698i
$941$	−34.6410			−1.12926			−0.564632	−	0.825342i	$-0.690982\pi$
$941$	−34.6410			−1.12926			−0.564632	+	0.825342i	$0.690982\pi$
$942$	−0.671200	−	1.64155i	−0.0218689	−	0.0534846i
$943$	−9.43649	−	5.44816i	−0.307294	−	0.177417i
$944$	8.59624	−	4.75615i	0.279784	−	0.154800i
$945$	4.43649	−	7.68423i	0.144319	−	0.249968i
$946$	−0.854102	+	6.26662i	−0.0277693	+	0.203745i
$947$	0.504017	+	0.872983i	0.0163784	+	0.0283681i	0.874098	−	0.485749i	$-0.161453\pi$
$947$	0.504017	+	0.872983i	0.0163784	+	0.0283681i	−0.857720	+	0.514117i	$0.828120\pi$
$948$	−27.1109	+	7.00000i	−0.880521	+	0.227349i
$949$	−32.8310	+	34.1190i	−1.06574	+	1.10755i
$950$		0			0
$951$	−16.0635	+	9.27427i	−0.520895	+	0.300739i
$952$	−65.4633	+	7.70901i	−2.12168	+	0.249851i
$953$	17.7460	−	30.7369i	0.574848	−	0.995666i	−0.421210	−	0.906963i	$-0.638394\pi$
$953$	17.7460	−	30.7369i	0.574848	−	0.995666i	0.996058	−	0.0887032i	$-0.0282723\pi$
$954$	8.80226	+	6.81820i	0.284984	+	0.220747i
$955$	22.0767	−	38.2379i	0.714384	−	1.23735i
$956$	−0.809300	+	2.91380i	−0.0261746	+	0.0942390i
$957$	4.97615			0.160856
$958$	54.5824	−	22.3178i	1.76348	−	0.721054i
$959$	−0.436492	−	0.756026i	−0.0140951	−	0.0244133i
$960$	17.1459	+	5.10081i	0.553381	+	0.164628i
$961$	11.0000			0.354839
$962$	13.5732	−	34.1788i	0.437616	−	1.10197i
$963$		−	0.872983i		−	0.0281315i
$964$	−21.8435	−	22.2455i	−0.703530	−	0.716480i
$965$	−15.9185	+	9.19052i	−0.512433	+	0.295853i
$966$	18.8451	+	46.0892i	0.606330	+	1.48290i
$967$		−	11.3363i		−	0.364551i	−0.983247	−	0.182276i	$-0.941654\pi$
$967$		−	11.3363i		−	0.364551i	0.983247	−	0.182276i	$-0.0583464\pi$
$968$	24.3642	−	18.1712i	0.783094	−	0.584046i
$969$	−2.56351	−	1.48004i	−0.0823518	−	0.0475458i
$970$	43.3013	+	33.5410i	1.39032	+	1.07694i
$971$	−50.6415	−	29.2379i	−1.62516	−	0.938289i	−0.985508	−	0.169627i	$-0.945744\pi$
$971$	−50.6415	−	29.2379i	−1.62516	−	0.938289i	−0.639656	−	0.768662i	$-0.720923\pi$
$972$	1.40126	+	1.42705i	0.0449454	+	0.0457727i
$973$	19.3366	+	33.4919i	0.619902	+	1.07370i
$974$	−36.0554	−	27.9284i	−1.15529	−	0.894884i
$975$		0			0
$976$	−1.93649	−	3.50000i	−0.0619856	−	0.112032i
$977$	27.3014	−	15.7625i	0.873449	−	0.504286i	0.00495645	−	0.999988i	$-0.498422\pi$
$977$	27.3014	−	15.7625i	0.873449	−	0.504286i	0.868493	+	0.495701i	$0.165089\pi$
$978$	3.22389	−	23.6540i	0.103089	−	0.756370i
$979$	0.879997	+	0.508067i	0.0281248	+	0.0162379i
$980$	−9.77829	−	37.8711i	−0.312356	−	1.20975i
$981$	−1.22803	+	2.12702i	−0.0392081	+	0.0679104i
$982$	49.5553	−	20.2622i	1.58137	−	0.646594i
$983$		−	27.2728i		−	0.869868i	−0.900462	−	0.434934i	$-0.856772\pi$
$983$		−	27.2728i		−	0.869868i	0.900462	−	0.434934i	$-0.143228\pi$
$984$	−2.78430	+	2.07658i	−0.0887603	+	0.0661991i
$985$	−2.74597	−	4.75615i	−0.0874938	−	0.151544i
$986$	−11.0739	+	81.2504i	−0.352666	+	2.58754i
$987$			15.7460i			0.501200i
$988$	3.63433	−	0.0367676i	0.115624	−	0.00116973i
$989$			78.7298i			2.50346i
$990$	1.57924	+	0.215241i	0.0501916	+	0.00684081i
$991$	6.18246	+	10.7083i	0.196392	+	0.340161i	0.947356	−	0.320182i	$-0.103744\pi$
$991$	6.18246	+	10.7083i	0.196392	+	0.340161i	−0.750964	+	0.660343i	$0.770411\pi$
$992$	15.8541	−	19.7141i	0.503368	−	0.625925i
$993$			9.95231i			0.315827i
$994$	−10.5687	−	25.8478i	−0.335219	−	0.819843i
$995$	−7.68423	+	13.3095i	−0.243606	+	0.421939i
$996$	5.73218	−	1.48004i	0.181631	−	0.0468969i
$997$	6.50218	+	3.75403i	0.205926	+	0.118891i	0.599417	−	0.800437i	$-0.295399\pi$
$997$	6.50218	+	3.75403i	0.205926	+	0.118891i	−0.393491	+	0.919329i	$0.628733\pi$
$998$	−2.82503	−	0.385035i	−0.0894249	−	0.0121881i
$999$	6.24597	−	3.60611i	0.197614	−	0.114092i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bk.a.205.4	yes	8
3.2	odd	2		936.2.dg.c.829.1		8
4.3	odd	2		1248.2.ca.a.49.3		8
8.3	odd	2		1248.2.ca.a.49.2		8
8.5	even	2	inner	312.2.bk.a.205.3	✓	8
13.4	even	6	inner	312.2.bk.a.277.3	yes	8
24.5	odd	2		936.2.dg.c.829.2		8
39.17	odd	6		936.2.dg.c.901.2		8
52.43	odd	6		1248.2.ca.a.433.2		8
104.43	odd	6		1248.2.ca.a.433.3		8
104.69	even	6	inner	312.2.bk.a.277.4	yes	8
312.173	odd	6		936.2.dg.c.901.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.a.205.3	✓	8	8.5	even	2	inner
312.2.bk.a.205.4	yes	8	1.1	even	1	trivial
312.2.bk.a.277.3	yes	8	13.4	even	6	inner
312.2.bk.a.277.4	yes	8	104.69	even	6	inner
936.2.dg.c.829.1		8	3.2	odd	2
936.2.dg.c.829.2		8	24.5	odd	2
936.2.dg.c.901.1		8	312.173	odd	6
936.2.dg.c.901.2		8	39.17	odd	6
1248.2.ca.a.49.2		8	8.3	odd	2
1248.2.ca.a.49.3		8	4.3	odd	2
1248.2.ca.a.433.2		8	52.43	odd	6
1248.2.ca.a.433.3		8	104.43	odd	6

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	312.2.bk.a.205.4

Level	$312$
Weight	$2$
Character	312.205
Analytic conductor	$2.491$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$