LMFDB - Embedded newform 312.2.bk.a.205.1

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			205.1
Root			$-1.40126 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	312.205
Dual form			312.2.bk.a.277.1

$q$ -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} +(-0.436492 - 0.252009i) q^{7} +(-2.59808 - 1.11803i) q^{8} +(0.500000 - 0.866025i) q^{9} +(3.13331 + 0.427051i) q^{10} +(-1.98406 - 3.43649i) q^{11} +(1.93649 - 0.500000i) q^{12} +(-2.59808 - 2.50000i) q^{13} +(0.563508 + 0.436492i) q^{14} +(-1.93649 + 1.11803i) q^{15} +(3.42705 + 2.06284i) q^{16} +(0.936492 - 1.62205i) q^{17} +(-0.866025 + 1.11803i) q^{18} +(1.98406 - 3.43649i) q^{19} +(-4.30902 - 1.19682i) q^{20} -0.504017 q^{21} +(2.12387 + 5.19433i) q^{22} +(-0.563508 - 0.976025i) q^{23} +(-2.80902 + 0.330792i) q^{24} +(3.16312 + 3.99933i) q^{26} -1.00000i q^{27} +(-0.706258 - 0.719258i) q^{28} +(-1.84205 + 1.06351i) q^{29} +(2.92705 - 1.19682i) q^{30} +4.47214i q^{31} +(-4.40822 - 3.54508i) q^{32} +(-3.43649 - 1.98406i) q^{33} +(-1.62205 + 2.09406i) q^{34} +(0.976025 + 0.563508i) q^{35} +(1.42705 - 1.40126i) q^{36} +(-5.33816 - 9.24597i) q^{37} +(-3.43649 + 4.43649i) q^{38} +(-3.50000 - 0.866025i) q^{39} +(5.80948 + 2.50000i) q^{40} +(4.93649 - 2.85008i) q^{41} +(0.706258 + 0.0962587i) q^{42} +(0.976025 + 0.563508i) q^{43} +(-1.98406 - 7.68423i) q^{44} +(-1.11803 + 1.93649i) q^{45} +(0.603217 + 1.47528i) q^{46} +0.504017i q^{47} +(3.99933 + 0.0729490i) q^{48} +(-3.37298 - 5.84218i) q^{49} -1.87298i q^{51} +(-3.66854 - 6.20820i) q^{52} -0.127017i q^{53} +(-0.190983 + 1.40126i) q^{54} +(4.43649 + 7.68423i) q^{55} +(0.852284 + 1.14275i) q^{56} -3.96812i q^{57} +(2.78430 - 1.13845i) q^{58} +(-5.70017 + 9.87298i) q^{59} +(-4.33013 + 1.11803i) q^{60} +(0.866025 + 0.500000i) q^{61} +(0.854102 - 6.26662i) q^{62} +(-0.436492 + 0.252009i) q^{63} +(5.50000 + 5.80948i) q^{64} +(5.80948 + 5.59017i) q^{65} +(4.43649 + 3.43649i) q^{66} +(7.68423 + 13.3095i) q^{67} +(2.67284 - 2.62453i) q^{68} +(-0.976025 - 0.563508i) q^{69} +(-1.26004 - 0.976025i) q^{70} +(7.30948 + 4.22013i) q^{71} +(-2.26728 + 1.69098i) q^{72} +4.18812i q^{73} +(5.71432 + 13.9755i) q^{74} +(5.66271 - 5.56036i) 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} +(-7.46162 + 3.05092i) q^{82} +7.43222 q^{83} +(-0.971267 - 0.269767i) q^{84} +(-2.09406 + 3.62702i) q^{85} +(-1.26004 - 0.976025i) q^{86} +(-1.06351 + 1.84205i) q^{87} +(1.31262 + 11.1465i) q^{88} +(13.7460 - 7.93624i) q^{89} +(1.93649 - 2.50000i) q^{90} +(0.504017 + 1.74597i) q^{91} +(-0.563508 - 2.18246i) q^{92} +(2.23607 + 3.87298i) q^{93} +(0.0962587 - 0.706258i) q^{94} +(-4.43649 + 7.68423i) q^{95} +(-5.59017 - 0.866025i) q^{96} +(-15.0000 - 8.66025i) q^{97} +(3.61066 + 8.83059i) q^{98} -3.96812 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
$7$	−0.436492	−	0.252009i	−0.164978	−	0.0952503i	0.415238	−	0.909713i	$-0.363698\pi$
$7$	−0.436492	−	0.252009i	−0.164978	−	0.0952503i	−0.580216	+	0.814463i	$0.697032\pi$
$8$	−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
$11$	−1.98406	−	3.43649i	−0.598216	−	1.03614i	−0.993084	−	0.117403i	$-0.962543\pi$
$11$	−1.98406	−	3.43649i	−0.598216	−	1.03614i	0.394868	−	0.918738i	$-0.370790\pi$
$12$	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
$14$	0.563508	+	0.436492i	0.150604	+	0.116657i
$15$	−1.93649	+	1.11803i	−0.500000	+	0.288675i
$16$	3.42705	+	2.06284i	0.856763	+	0.515711i
$17$	0.936492	−	1.62205i	0.227133	−	0.393405i	−0.729825	−	0.683635i	$-0.760398\pi$
$17$	0.936492	−	1.62205i	0.227133	−	0.393405i	0.956957	+	0.290229i	$0.0937316\pi$
$18$	−0.866025	+	1.11803i	−0.204124	+	0.263523i
$19$	1.98406	−	3.43649i	0.455174	−	0.788385i	−0.543524	−	0.839394i	$-0.682910\pi$
$19$	1.98406	−	3.43649i	0.455174	−	0.788385i	0.998698	+	0.0510085i	$0.0162436\pi$
$20$	−4.30902	−	1.19682i	−0.963525	−	0.267617i
$21$	−0.504017			−0.109986
$22$	2.12387	+	5.19433i	0.452810	+	1.10744i
$23$	−0.563508	−	0.976025i	−0.117500	−	0.203515i	0.801277	−	0.598294i	$-0.204155\pi$
$23$	−0.563508	−	0.976025i	−0.117500	−	0.203515i	−0.918776	+	0.394779i	$0.870821\pi$
$24$	−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
$28$	−0.706258	−	0.719258i	−0.133470	−	0.135927i
$29$	−1.84205	+	1.06351i	−0.342060	+	0.197489i	−0.661183	−	0.750225i	$-0.729945\pi$
$29$	−1.84205	+	1.06351i	−0.342060	+	0.197489i	0.319123	+	0.947713i	$0.396612\pi$
$30$	2.92705	−	1.19682i	0.534404	−	0.218508i
$31$			4.47214i			0.803219i	0.915811	+	0.401610i	$0.131549\pi$
$31$			4.47214i			0.803219i	−0.915811	+	0.401610i	$0.868451\pi$
$32$	−4.40822	−	3.54508i	−0.779270	−	0.626688i
$33$	−3.43649	−	1.98406i	−0.598216	−	0.345380i
$34$	−1.62205	+	2.09406i	−0.278179	+	0.359128i
$35$	0.976025	+	0.563508i	0.164978	+	0.0952503i
$36$	1.42705	−	1.40126i	0.237842	−	0.233543i
$37$	−5.33816	−	9.24597i	−0.877588	−	1.52003i	−0.853980	−	0.520306i	$-0.825818\pi$
$37$	−5.33816	−	9.24597i	−0.877588	−	1.52003i	−0.0236086	−	0.999721i	$-0.507516\pi$
$38$	−3.43649	+	4.43649i	−0.557473	+	0.719694i
$39$	−3.50000	−	0.866025i	−0.560449	−	0.138675i
$40$	5.80948	+	2.50000i	0.918559	+	0.395285i
$41$	4.93649	−	2.85008i	0.770950	−	0.445108i	−0.0622631	−	0.998060i	$-0.519832\pi$
$41$	4.93649	−	2.85008i	0.770950	−	0.445108i	0.833214	+	0.552951i	$0.186498\pi$
$42$	0.706258	+	0.0962587i	0.108978	+	0.0148530i
$43$	0.976025	+	0.563508i	0.148842	+	0.0859342i	0.572572	−	0.819855i	$-0.305946\pi$
$43$	0.976025	+	0.563508i	0.148842	+	0.0859342i	−0.423729	+	0.905789i	$0.639279\pi$
$44$	−1.98406	−	7.68423i	−0.299108	−	1.15844i
$45$	−1.11803	+	1.93649i	−0.166667	+	0.288675i
$46$	0.603217	+	1.47528i	0.0889394	+	0.217519i
$47$			0.504017i			0.0735185i	0.999324	+	0.0367592i	$0.0117035\pi$
$47$			0.504017i			0.0735185i	−0.999324	+	0.0367592i	$0.988297\pi$
$48$	3.99933	+	0.0729490i	0.577254	+	0.0105293i
$49$	−3.37298	−	5.84218i	−0.481855	−	0.834597i
$50$		0			0
$51$		−	1.87298i		−	0.262270i
$52$	−3.66854	−	6.20820i	−0.508735	−	0.860923i
$53$		−	0.127017i		−	0.0174471i	−0.999962	−	0.00872354i	$-0.997223\pi$
$53$		−	0.127017i		−	0.0174471i	0.999962	−	0.00872354i	$-0.00277682\pi$
$54$	−0.190983	+	1.40126i	−0.0259895	+	0.190687i
$55$	4.43649	+	7.68423i	0.598216	+	1.03614i
$56$	0.852284	+	1.14275i	0.113891	+	0.152706i
$57$		−	3.96812i		−	0.525590i
$58$	2.78430	−	1.13845i	0.365597	−	0.149486i
$59$	−5.70017	+	9.87298i	−0.742099	+	1.28535i	0.209439	+	0.977822i	$0.432836\pi$
$59$	−5.70017	+	9.87298i	−0.742099	+	1.28535i	−0.951538	+	0.307531i	$0.900497\pi$
$60$	−4.33013	+	1.11803i	−0.559017	+	0.144338i
$61$	0.866025	+	0.500000i	0.110883	+	0.0640184i	0.554416	−	0.832240i	$-0.312942\pi$
$61$	0.866025	+	0.500000i	0.110883	+	0.0640184i	−0.443533	+	0.896258i	$0.646275\pi$
$62$	0.854102	−	6.26662i	0.108471	−	0.795861i
$63$	−0.436492	+	0.252009i	−0.0549928	+	0.0317501i
$64$	5.50000	+	5.80948i	0.687500	+	0.726184i
$65$	5.80948	+	5.59017i	0.720577	+	0.693375i
$66$	4.43649	+	3.43649i	0.546094	+	0.423003i
$67$	7.68423	+	13.3095i	0.938778	+	1.62601i	0.767754	+	0.640744i	$0.221374\pi$
$67$	7.68423	+	13.3095i	0.938778	+	1.62601i	0.171024	+	0.985267i	$0.445293\pi$
$68$	2.67284	−	2.62453i	0.324130	−	0.318271i
$69$	−0.976025	−	0.563508i	−0.117500	−	0.0678384i
$70$	−1.26004	−	0.976025i	−0.150604	−	0.116657i
$71$	7.30948	+	4.22013i	0.867475	+	0.500837i	0.866508	−	0.499163i	$-0.166359\pi$
$71$	7.30948	+	4.22013i	0.867475	+	0.500837i	0.000966726		1.00000i	$0.499692\pi$
$72$	−2.26728	+	1.69098i	−0.267202	+	0.199284i
$73$			4.18812i			0.490182i	0.969500	+	0.245091i	$0.0788179\pi$
$73$			4.18812i			0.490182i	−0.969500	+	0.245091i	$0.921182\pi$
$74$	5.71432	+	13.9755i	0.664276	+	1.62462i
$75$		0			0
$76$	5.66271	−	5.56036i	0.649557	−	0.637817i
$77$			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
$82$	−7.46162	+	3.05092i	−0.823998	+	0.336918i
$83$	7.43222			0.815792			0.407896	−	0.913028i	$-0.366263\pi$
$83$	7.43222			0.815792			0.407896	+	0.913028i	$0.366263\pi$
$84$	−0.971267	−	0.269767i	−0.105974	−	0.0294340i
$85$	−2.09406	+	3.62702i	−0.227133	+	0.393405i
$86$	−1.26004	−	0.976025i	−0.135874	−	0.105247i
$87$	−1.06351	+	1.84205i	−0.114020	+	0.197489i
$88$	1.31262	+	11.1465i	0.139926	+	1.18822i
$89$	13.7460	−	7.93624i	1.45707	−	0.841239i	0.458203	−	0.888847i	$-0.348493\pi$
$89$	13.7460	−	7.93624i	1.45707	−	0.841239i	0.998866	+	0.0476078i	$0.0151598\pi$
$90$	1.93649	−	2.50000i	0.204124	−	0.263523i
$91$	0.504017	+	1.74597i	0.0528354	+	0.183027i
$92$	−0.563508	−	2.18246i	−0.0587498	−	0.227537i
$93$	2.23607	+	3.87298i	0.231869	+	0.401610i
$94$	0.0962587	−	0.706258i	0.00992833	−	0.0728450i
$95$	−4.43649	+	7.68423i	−0.455174	+	0.788385i
$96$	−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	$-0.675333\pi$
$98$	3.61066	+	8.83059i	0.364732	+	0.892024i
$99$	−3.96812			−0.398811
$100$		0			0
$101$	0.110000	−	0.0635083i	0.0109454	−	0.00631931i	−0.494517	−	0.869168i	$-0.664655\pi$
$101$	0.110000	−	0.0635083i	0.0109454	−	0.00631931i	0.505463	+	0.862848i	$0.331322\pi$
$102$	−0.357708	+	2.62453i	−0.0354184	+	0.259868i
$103$	−12.6190			−1.24338			−0.621691	−	0.783263i	$-0.713554\pi$
$103$	−12.6190			−1.24338			−0.621691	+	0.783263i	$0.713554\pi$
$104$	3.95492	+	9.39993i	0.387811	+	0.921739i
$105$	1.12702			0.109986
$106$	−0.0242580	+	0.177983i	−0.00235615	+	0.0172873i
$107$	5.95218	−	3.43649i	0.575419	−	0.332218i	−0.183892	−	0.982946i	$-0.558870\pi$
$107$	5.95218	−	3.43649i	0.575419	−	0.332218i	0.759311	+	0.650728i	$0.225536\pi$
$108$	0.535233	−	1.92705i	0.0515028	−	0.185431i
$109$	11.4003			1.09195			0.545977	−	0.837800i	$-0.316159\pi$
$109$	11.4003			1.09195			0.545977	+	0.837800i	$0.316159\pi$
$110$	−4.74911	−	11.6149i	−0.452810	−	1.10744i
$111$	−9.24597	−	5.33816i	−0.877588	−	0.506676i
$112$	−0.976025	−	1.76406i	−0.0922257	−	0.166688i
$113$	−1.06351	+	1.84205i	−0.100046	+	0.173286i	−0.911704	−	0.410849i	$-0.865232\pi$
$113$	−1.06351	+	1.84205i	−0.100046	+	0.173286i	0.811657	+	0.584134i	$0.198566\pi$
$114$	−0.757843	+	5.56036i	−0.0709785	+	0.520775i
$115$	1.26004	+	2.18246i	0.117500	+	0.203515i
$116$	−4.11895	+	1.06351i	−0.382435	+	0.0987443i
$117$	−3.46410	+	1.00000i	−0.320256	+	0.0924500i
$118$	9.87298	−	12.7460i	0.908882	−	1.17336i
$119$	−0.817542	+	0.472008i	−0.0749439	+	0.0432689i
$120$	6.28115	−	0.739674i	0.573388	−	0.0675227i
$121$	−2.37298	+	4.11013i	−0.215726	+	0.373648i
$122$	−1.11803	−	0.866025i	−0.101222	−	0.0784063i
$123$	2.85008	−	4.93649i	0.256983	−	0.445108i
$124$	−2.39364	+	8.61803i	−0.214955	+	0.773922i
$125$	11.1803			1.00000
$126$	0.659767	−	0.269767i	0.0587767	−	0.0240327i
$127$	−8.87298	−	15.3685i	−0.787350	−	1.36373i	−0.927585	−	0.373612i	$-0.878119\pi$
$127$	−8.87298	−	15.3685i	−0.787350	−	1.36373i	0.140235	−	0.990118i	$-0.455214\pi$
$128$	−6.59741	−	9.19098i	−0.583134	−	0.812376i
$129$	1.12702			0.0992283
$130$	−7.07295	−	8.94278i	−0.620339	−	0.784334i
$131$		−	3.74597i		−	0.327287i	−0.986520	−	0.163643i	$-0.947675\pi$
$131$		−	3.74597i		−	0.327287i	0.986520	−	0.163643i	$-0.0523246\pi$
$132$	−5.56036	−	5.66271i	−0.483967	−	0.492875i
$133$	−1.73205	+	1.00000i	−0.150188	+	0.0867110i
$134$	−8.22571	−	20.1176i	−0.710593	−	1.73789i
$135$			2.23607i			0.192450i
$136$	−4.24659	+	3.16718i	−0.364142	+	0.271584i
$137$	−11.8095	−	6.81820i	−1.00895	−	0.582518i	−0.0980670	−	0.995180i	$-0.531266\pi$
$137$	−11.8095	−	6.81820i	−1.00895	−	0.582518i	−0.910885	+	0.412661i	$0.864599\pi$
$138$	1.26004	+	0.976025i	0.107262	+	0.0830848i
$139$	4.97615	+	2.87298i	0.422072	+	0.243683i	0.695963	−	0.718077i	$-0.254978\pi$
$139$	4.97615	+	2.87298i	0.422072	+	0.243683i	−0.273892	+	0.961761i	$0.588311\pi$
$140$	1.57924	+	1.60831i	0.133470	+	0.135927i
$141$	0.252009	+	0.436492i	0.0212230	+	0.0367592i
$142$	−9.43649	−	7.30948i	−0.791893	−	0.613398i
$143$	−3.43649	+	13.8884i	−0.287374	+	1.16141i
$144$	3.50000	−	1.93649i	0.291667	−	0.161374i
$145$	4.11895	−	2.37808i	0.342060	−	0.197489i
$146$	0.799859	−	5.86864i	0.0661968	−	0.485692i
$147$	−5.84218	−	3.37298i	−0.481855	−	0.278199i
$148$	−5.33816	−	20.6746i	−0.438794	−	1.69944i
$149$	−11.2903	+	19.5554i	−0.924941	+	1.60204i	−0.133284	+	0.991078i	$0.542552\pi$
$149$	−11.2903	+	19.5554i	−0.924941	+	1.60204i	−0.791657	+	0.610966i	$0.790781\pi$
$150$		0			0
$151$		−	6.42419i		−	0.522793i	−0.965232	−	0.261396i	$-0.915817\pi$
$151$		−	6.42419i		−	0.522793i	0.965232	−	0.261396i	$-0.0841830\pi$
$152$	−8.99685	+	6.71002i	−0.729741	+	0.544255i
$153$	−0.936492	−	1.62205i	−0.0757109	−	0.131135i
$154$	0.381966	−	2.80252i	0.0307797	−	0.225833i
$155$		−	10.0000i		−	0.803219i
$156$	−6.28115	−	3.54219i	−0.502895	−	0.283602i
$157$		−	16.7460i		−	1.33647i	−0.743949	−	0.668237i	$-0.767049\pi$
$157$		−	16.7460i		−	1.33647i	0.743949	−	0.668237i	$-0.232951\pi$
$158$	−19.6176	−	2.67376i	−1.56069	−	0.212713i
$159$	−0.0635083	−	0.110000i	−0.00503654	−	0.00872354i
$160$	9.85707	+	7.92705i	0.779270	+	0.626688i
$161$			0.568036i			0.0447675i
$162$	0.535233	+	1.30902i	0.0420519	+	0.102846i
$163$	−4.97615	+	8.61895i	−0.389762	+	0.675088i	−0.992417	−	0.122914i	$-0.960776\pi$
$163$	−4.97615	+	8.61895i	−0.389762	+	0.675088i	0.602655	+	0.798002i	$0.294110\pi$
$164$	11.0383	−	2.85008i	0.861949	−	0.222554i
$165$	7.68423	+	4.43649i	0.598216	+	0.345380i
$166$	−10.4145	−	1.41943i	−0.808319	−	0.110169i
$167$	15.8730	−	9.16427i	1.22829	−	0.709153i	0.261617	−	0.965172i	$-0.415744\pi$
$167$	15.8730	−	9.16427i	1.22829	−	0.709153i	0.966672	+	0.256019i	$0.0824111\pi$
$168$	1.30948	+	0.563508i	0.101028	+	0.0434756i
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	3.62702	−	4.68246i	0.278179	−	0.359128i
$171$	−1.98406	−	3.43649i	−0.151725	−	0.262795i
$172$	1.57924	+	1.60831i	0.120416	+	0.122633i
$173$	11.6844	+	6.74597i	0.888345	+	0.512886i	0.873401	−	0.487002i	$-0.161910\pi$
$173$	11.6844	+	6.74597i	0.888345	+	0.512886i	0.0149443	+	0.999888i	$0.495243\pi$
$174$	1.84205	−	2.37808i	0.139645	−	0.180282i
$175$		0			0
$176$	0.289470	−	15.8698i	0.0218196	−	1.19623i
$177$			11.4003i			0.856902i
$178$	−20.7773	+	8.49547i	−1.55733	+	0.636763i
$179$	11.1483	−	6.43649i	0.833265	−	0.481086i	−0.0217040	−	0.999764i	$-0.506909\pi$
$179$	11.1483	−	6.43649i	0.833265	−	0.481086i	0.854969	+	0.518678i	$0.173576\pi$
$180$	−3.19098	+	3.13331i	−0.237842	+	0.233543i
$181$		−	14.7460i		−	1.09606i	−0.836459	−	0.548030i	$-0.815378\pi$
$181$		−	14.7460i		−	1.09606i	0.836459	−	0.548030i	$-0.184622\pi$
$182$	−0.372808	−	2.54281i	−0.0276344	−	0.188486i
$183$	1.00000			0.0739221
$184$	0.372808	+	3.16581i	0.0274838	+	0.233387i
$185$	11.9365	+	20.6746i	0.877588	+	1.52003i
$186$	−2.39364	−	5.85410i	−0.175510	−	0.429244i
$187$	−7.43222			−0.543498
$188$	−0.269767	+	0.971267i	−0.0196748	+	0.0708369i
$189$	−0.252009	+	0.436492i	−0.0183309	+	0.0317501i
$190$	7.68423	−	9.92030i	0.557473	−	0.719694i
$191$	−2.12702	+	3.68410i	−0.153906	+	0.266572i	−0.932660	−	0.360757i	$-0.882518\pi$
$191$	−2.12702	+	3.68410i	−0.153906	+	0.266572i	0.778754	+	0.627329i	$0.215852\pi$
$192$	7.66788	+	2.28115i	0.553381	+	0.164628i
$193$	−16.1190	+	9.30628i	−1.16027	+	0.669881i	−0.951368	−	0.308056i	$-0.900321\pi$
$193$	−16.1190	+	9.30628i	−1.16027	+	0.669881i	−0.208899	+	0.977937i	$0.566988\pi$
$194$	19.3649	+	15.0000i	1.39032	+	1.07694i
$195$	7.82624	+	1.93649i	0.560449	+	0.138675i
$196$	−3.37298	−	13.0635i	−0.240927	−	0.933108i
$197$	−5.70017	−	9.87298i	−0.406120	−	0.703421i	0.588331	−	0.808620i	$-0.299785\pi$
$197$	−5.70017	−	9.87298i	−0.406120	−	0.703421i	−0.994451	+	0.105199i	$0.966452\pi$
$198$	5.56036	+	0.757843i	0.395158	+	0.0538576i
$199$	−0.436492	+	0.756026i	−0.0309421	+	0.0535932i	−0.881082	−	0.472964i	$-0.843184\pi$
$199$	−0.436492	+	0.756026i	−0.0309421	+	0.0535932i	0.850140	+	0.526557i	$0.176517\pi$
$200$		0			0
$201$	13.3095	+	7.68423i	0.938778	+	0.542004i
$202$	−0.166267	+	0.0679835i	−0.0116985	+	0.00478330i
$203$	1.07205			0.0752434
$204$	1.00248	−	3.60933i	0.0701878	−	0.252704i
$205$	−11.0383	+	6.37298i	−0.770950	+	0.445108i
$206$	17.6824	+	2.41001i	1.23199	+	0.167913i
$207$	−1.12702			−0.0783331
$208$	−3.74663	−	13.9271i	−0.259782	−	0.965667i
$209$	−15.7460			−1.08917
$210$	−1.57924	−	0.215241i	−0.108978	−	0.0148530i
$211$	−12.1244	+	7.00000i	−0.834675	+	0.481900i	−0.855451	−	0.517884i	$-0.826720\pi$
$211$	−12.1244	+	7.00000i	−0.834675	+	0.481900i	0.0207756	+	0.999784i	$0.493386\pi$
$212$	0.0679835	−	0.244768i	0.00466913	−	0.0168107i
$213$	8.44025			0.578317
$214$	−8.99685	+	3.67865i	−0.615012	+	0.251467i
$215$	−2.18246	−	1.26004i	−0.148842	−	0.0859342i
$216$	−1.11803	+	2.59808i	−0.0760726	+	0.176777i
$217$	1.12702	−	1.95205i	0.0765069	−	0.132514i
$218$	−15.9748	−	2.17727i	−1.08195	−	0.147463i
$219$	2.09406	+	3.62702i	0.141503	+	0.245091i
$220$	4.43649	+	17.1825i	0.299108	+	1.15844i
$221$	−6.48820	+	1.87298i	−0.436444	+	0.125990i
$222$	11.9365	+	9.24597i	0.801125	+	0.620549i
$223$	18.4919	−	10.6763i	1.23831	−	0.714939i	0.269563	−	0.962983i	$-0.413121\pi$
$223$	18.4919	−	10.6763i	1.23831	−	0.714939i	0.968749	+	0.248043i	$0.0797876\pi$
$224$	1.03076	+	2.65831i	0.0688704	+	0.177616i
$225$		0			0
$226$	1.84205	−	2.37808i	0.122531	−	0.158187i
$227$	−7.68423	+	13.3095i	−0.510020	+	0.883381i	0.489912	+	0.871772i	$0.337029\pi$
$227$	−7.68423	+	13.3095i	−0.510020	+	0.883381i	−0.999933	+	0.0116092i	$0.996305\pi$
$228$	2.12387	−	7.64677i	0.140657	−	0.506420i
$229$	−2.01607			−0.133226			−0.0666128	−	0.997779i	$-0.521219\pi$
$229$	−2.01607			−0.133226			−0.0666128	+	0.997779i	$0.521219\pi$
$230$	−1.34883	−	3.29884i	−0.0889394	−	0.217519i
$231$	1.00000	+	1.73205i	0.0657952	+	0.113961i
$232$	5.97483	−	0.703601i	0.392267	−	0.0461936i
$233$	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
$235$		−	1.12702i		−	0.0735185i
$236$	−16.2689	+	15.9748i	−1.05901	+	1.03987i
$237$	12.1244	−	7.00000i	0.787562	−	0.454699i
$238$	1.23573	−	0.505269i	0.0801007	−	0.0327517i
$239$		−	11.9044i		−	0.770029i	−0.922911	−	0.385014i	$-0.874196\pi$
$239$		−	11.9044i		−	0.770029i	0.922911	−	0.385014i	$-0.125804\pi$
$240$	−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	$0.834095\pi$
$242$	4.11013	−	5.30615i	0.264209	−	0.341092i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	1.40126	+	1.42705i	0.0897064	+	0.0913576i
$245$	7.54222	+	13.0635i	0.481855	+	0.834597i
$246$	−4.93649	+	6.37298i	−0.314739	+	0.406327i
$247$	−13.7460	+	3.96812i	−0.874635	+	0.252485i
$248$	5.00000	−	11.6190i	0.317500	−	0.737804i
$249$	6.43649	−	3.71611i	0.407896	−	0.235499i
$250$	−15.6665	−	2.13525i	−0.990839	−	0.135045i
$251$	−27.0528	−	15.6190i	−1.70756	−	0.985859i	−0.937567	−	0.347806i	$-0.886927\pi$
$251$	−27.0528	−	15.6190i	−1.70756	−	0.985859i	−0.769992	−	0.638054i	$-0.779740\pi$
$252$	−0.976025	+	0.252009i	−0.0614838	+	0.0158750i
$253$	−2.23607	+	3.87298i	−0.140580	+	0.243492i
$254$	9.49823	+	23.2298i	0.595972	+	1.45757i
$255$			4.18812i			0.262270i
$256$	7.48936	+	14.1389i	0.468085	+	0.883684i
$257$	−11.6825	−	20.2346i	−0.728732	−	1.26220i	−0.957419	−	0.288701i	$-0.906777\pi$
$257$	−11.6825	−	20.2346i	−0.728732	−	1.26220i	0.228688	−	0.973500i	$-0.426557\pi$
$258$	−1.57924	−	0.215241i	−0.0983193	−	0.0134003i
$259$			5.38105i			0.334362i
$260$	8.20311	+	13.8820i	0.508735	+	0.860923i
$261$			2.12702i			0.131659i
$262$	−0.715416	+	5.24907i	−0.0441985	+	0.324288i
$263$	−4.43649	−	7.68423i	−0.273566	−	0.473830i	0.696206	−	0.717842i	$-0.254870\pi$
$263$	−4.43649	−	7.68423i	−0.273566	−	0.473830i	−0.969772	+	0.244012i	$0.921536\pi$
$264$	6.71002	+	8.99685i	0.412973	+	0.553718i
$265$			0.284018i			0.0174471i
$266$	2.61803	−	1.07047i	0.160522	−	0.0656345i
$267$	7.93624	−	13.7460i	0.485690	−	0.841239i
$268$	7.68423	+	29.7609i	0.469389	+	1.81794i
$269$	3.68410	+	2.12702i	0.224624	+	0.129686i	0.608089	−	0.793869i	$-0.291936\pi$
$269$	3.68410	+	2.12702i	0.224624	+	0.129686i	−0.383466	+	0.923555i	$0.625270\pi$
$270$	0.427051	−	3.13331i	0.0259895	−	0.190687i
$271$	20.2379	−	11.6844i	1.22936	−	0.709774i	0.262468	−	0.964941i	$-0.415464\pi$
$271$	20.2379	−	11.6844i	1.22936	−	0.709774i	0.966897	+	0.255167i	$0.0821303\pi$
$272$	6.55544	−	3.62702i	0.397482	−	0.219920i
$273$	1.30948	+	1.26004i	0.0792530	+	0.0762613i
$274$	15.2460	+	11.8095i	0.921043	+	0.713436i
$275$		0			0
$276$	−1.57924	−	1.60831i	−0.0950592	−	0.0968089i
$277$	12.7704	+	7.37298i	0.767298	+	0.443000i	0.831910	−	0.554911i	$-0.187248\pi$
$277$	12.7704	+	7.37298i	0.767298	+	0.443000i	−0.0646120	+	0.997910i	$0.520581\pi$
$278$	−6.42419	−	4.97615i	−0.385297	−	0.298450i
$279$	3.87298	+	2.23607i	0.231869	+	0.133870i
$280$	−1.90577	−	2.55527i	−0.113891	−	0.152706i
$281$			19.1166i			1.14040i	0.821506	+	0.570200i	$0.193134\pi$
$281$			19.1166i			1.14040i	−0.821506	+	0.570200i	$0.806866\pi$
$282$	−0.269767	−	0.659767i	−0.0160644	−	0.0392886i
$283$	−2.26808	+	1.30948i	−0.134823	+	0.0778402i	−0.565895	−	0.824478i	$-0.691469\pi$
$283$	−2.26808	+	1.30948i	−0.134823	+	0.0778402i	0.431071	+	0.902318i	$0.358136\pi$
$284$	11.8270	+	12.0447i	0.701802	+	0.714720i
$285$			8.87298i			0.525590i
$286$	7.46786	−	18.8049i	0.441584	−	1.11196i
$287$	−2.87298			−0.169587
$288$	−5.27424	+	2.04508i	−0.310788	+	0.120508i
$289$	6.74597	+	11.6844i	0.396822	+	0.687315i
$290$	−6.22589	+	2.54565i	−0.365597	+	0.149486i
$291$	−17.3205			−1.01535
$292$	−2.24162	+	8.07072i	−0.131181	+	0.472303i
$293$	14.2504	−	24.6825i	0.832519	−	1.44196i	−0.0635162	−	0.997981i	$-0.520231\pi$
$293$	14.2504	−	24.6825i	0.832519	−	1.44196i	0.896035	−	0.443984i	$-0.146435\pi$
$294$	7.54222	+	5.84218i	0.439871	+	0.340723i
$295$	12.7460	−	22.0767i	0.742099	−	1.28535i
$296$	3.53165	+	29.9900i	0.205273	+	1.74313i
$297$	−3.43649	+	1.98406i	−0.199405	+	0.115127i
$298$	19.5554	−	25.2460i	1.13282	−	1.46246i
$299$	−0.976025	+	3.94456i	−0.0564450	+	0.228120i
$300$		0			0
$301$	−0.284018	−	0.491933i	−0.0163705	−	0.0283546i
$302$	−1.22691	+	9.00195i	−0.0706008	+	0.518004i
$303$	0.0635083	−	0.110000i	0.00364846	−	0.00631931i
$304$	13.8884	−	7.68423i	0.796555	−	0.440721i
$305$	−1.93649	−	1.11803i	−0.110883	−	0.0640184i
$306$	1.00248	+	2.45177i	0.0573081	+	0.140158i
$307$	5.41615			0.309116			0.154558	−	0.987984i	$-0.450605\pi$
$307$	5.41615			0.309116			0.154558	+	0.987984i	$0.450605\pi$
$308$	−1.07047	+	3.85410i	−0.0609955	+	0.219608i
$309$	−10.9283	+	6.30948i	−0.621691	+	0.358933i
$310$	−1.90983	+	14.0126i	−0.108471	+	0.795861i
$311$	−10.6190			−0.602145			−0.301073	−	0.953601i	$-0.597345\pi$
$311$	−10.6190			−0.602145			−0.301073	+	0.953601i	$0.597345\pi$
$312$	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	$0.463939\pi$
$314$	−3.19820	+	23.4654i	−0.180485	+	1.32423i
$315$	0.976025	−	0.563508i	0.0549928	−	0.0317501i
$316$	26.9787	+	7.49326i	1.51767	+	0.421529i
$317$	−23.0207			−1.29297			−0.646485	−	0.762927i	$-0.723762\pi$
$317$	−23.0207			−1.29297			−0.646485	+	0.762927i	$0.723762\pi$
$318$	0.0679835	+	0.166267i	0.00381233	+	0.00932379i
$319$	7.30948	+	4.22013i	0.409252	+	0.236282i
$320$	−12.2984	−	12.9904i	−0.687500	−	0.726184i
$321$	3.43649	−	5.95218i	0.191806	−	0.332218i
$322$	0.108485	−	0.795965i	0.00604564	−	0.0443574i
$323$	−3.71611	−	6.43649i	−0.206770	−	0.358136i
$324$	−0.500000	−	1.93649i	−0.0277778	−	0.107583i
$325$		0			0
$326$	8.61895	−	11.1270i	0.477359	−	0.616268i
$327$	9.87298	−	5.70017i	0.545977	−	0.315220i
$328$	−16.0119	+	1.88557i	−0.884108	+	0.104113i
$329$	0.127017	−	0.219999i	0.00700265	−	0.0121290i
$330$	−9.92030	−	7.68423i	−0.546094	−	0.423003i
$331$	8.44025	−	14.6190i	0.463918	−	0.803530i	−0.535234	−	0.844704i	$-0.679776\pi$
$331$	8.44025	−	14.6190i	0.463918	−	0.803530i	0.999152	+	0.0411739i	$0.0131098\pi$
$332$	14.3223	+	3.97797i	0.786037	+	0.218320i
$333$	−10.6763			−0.585059
$334$	−23.9924	+	9.81004i	−1.31280	+	0.536782i
$335$	−17.1825	−	29.7609i	−0.938778	−	1.62601i
$336$	−1.72729	−	1.03971i	−0.0942315	−	0.0567207i
$337$	−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
$339$			2.12702i			0.115524i
$340$	−5.97666	+	5.86864i	−0.324130	+	0.318271i
$341$	15.3685	−	8.87298i	0.832249	−	0.480499i
$342$	2.12387	+	5.19433i	0.114846	+	0.280877i
$343$			6.92820i			0.374088i
$344$	−1.90577	−	2.55527i	−0.102752	−	0.137771i
$345$	2.18246	+	1.26004i	0.117500	+	0.0678384i
$346$	−15.0844	−	11.6844i	−0.810945	−	0.628155i
$347$	−12.8804	−	7.43649i	−0.691455	−	0.399212i	0.112702	−	0.993629i	$-0.464050\pi$
$347$	−12.8804	−	7.43649i	−0.691455	−	0.399212i	−0.804157	+	0.594417i	$0.797383\pi$
$348$	−3.03536	+	2.98050i	−0.162712	+	0.159772i
$349$	0.219999	+	0.381050i	0.0117763	+	0.0203971i	0.871853	−	0.489767i	$-0.162918\pi$
$349$	0.219999	+	0.381050i	0.0117763	+	0.0203971i	−0.860077	+	0.510164i	$0.829585\pi$
$350$		0			0
$351$	−2.50000	+	2.59808i	−0.133440	+	0.138675i
$352$	−3.43649	+	22.1825i	−0.183166	+	1.18233i
$353$	−12.1905	+	7.03820i	−0.648836	+	0.374606i	−0.788010	−	0.615662i	$-0.788889\pi$
$353$	−12.1905	+	7.03820i	−0.648836	+	0.374606i	0.139174	+	0.990268i	$0.455555\pi$
$354$	2.17727	−	15.9748i	0.115721	−	0.849052i
$355$	−16.3445	−	9.43649i	−0.867475	−	0.500837i
$356$	30.7369	−	7.93624i	1.62905	−	0.420620i
$357$	−0.472008	+	0.817542i	−0.0249813	+	0.0432689i
$358$	−16.8510	+	6.89005i	−0.890601	+	0.364150i
$359$		−	17.3845i		−	0.917520i	−0.888560	−	0.458760i	$-0.848294\pi$
$359$		−	17.3845i		−	0.917520i	0.888560	−	0.458760i	$-0.151706\pi$
$360$	5.06980	−	3.78115i	0.267202	−	0.199284i
$361$	1.62702	+	2.81808i	0.0856325	+	0.148320i
$362$	−2.81623	+	20.6629i	−0.148018	+	1.08602i
$363$			4.74597i			0.249099i
$364$	0.0367676	+	3.63433i	0.00192714	+	0.190491i
$365$		−	9.36492i		−	0.490182i
$366$	−1.40126	−	0.190983i	−0.0732450	−	0.00998284i
$367$	11.3095	+	19.5886i	0.590350	+	1.02252i	0.994185	+	0.107684i	$0.0343435\pi$
$367$	11.3095	+	19.5886i	0.590350	+	1.02252i	−0.403835	+	0.914832i	$0.632323\pi$
$368$	0.0822148	−	4.50732i	0.00428574	−	0.234960i
$369$		−	5.70017i		−	0.296739i
$370$	−12.7776	−	31.2501i	−0.664276	−	1.62462i
$371$	−0.0320093	+	0.0554417i	−0.00166184	+	0.00287839i
$372$	2.23607	+	8.66025i	0.115935	+	0.449013i
$373$	0.426027	+	0.245967i	0.0220588	+	0.0127357i	0.510989	−	0.859587i	$-0.329279\pi$
$373$	0.426027	+	0.245967i	0.0220588	+	0.0127357i	−0.488930	+	0.872323i	$0.662613\pi$
$374$	10.4145	+	1.41943i	0.538519	+	0.0733969i
$375$	9.68246	−	5.59017i	0.500000	−	0.288675i
$376$	0.563508	−	1.30948i	0.0290607	−	0.0675310i
$377$	7.44456	+	1.84205i	0.383414	+	0.0948704i
$378$	0.436492	−	0.563508i	0.0224507	−	0.0289837i
$379$	12.4084	+	21.4919i	0.637375	+	1.10397i	0.986007	+	0.166706i	$0.0533132\pi$
$379$	12.4084	+	21.4919i	0.637375	+	1.10397i	−0.348631	+	0.937260i	$0.613353\pi$
$380$	−12.6622	+	12.4333i	−0.649557	+	0.637817i
$381$	−15.3685	−	8.87298i	−0.787350	−	0.454577i
$382$	3.68410	−	4.75615i	0.188495	−	0.243346i
$383$	−4.25403	−	2.45607i	−0.217371	−	0.125499i	0.387361	−	0.921928i	$-0.373387\pi$
$383$	−4.25403	−	2.45607i	−0.217371	−	0.125499i	−0.604732	+	0.796429i	$0.706720\pi$
$384$	−10.3090	−	4.66092i	−0.526080	−	0.237852i
$385$		−	4.47214i		−	0.227921i
$386$	24.3642	−	9.96206i	1.24010	−	0.507055i
$387$	0.976025	−	0.563508i	0.0496141	−	0.0286447i
$388$	−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
$391$	−2.11088			−0.106752
$392$	2.23151	+	18.9495i	0.112708	+	0.957096i
$393$	−1.87298	−	3.24410i	−0.0944795	−	0.163643i
$394$	6.10184	+	14.9232i	0.307406	+	0.751822i
$395$	−31.3050			−1.57512
$396$	−7.64677	−	2.12387i	−0.384265	−	0.106728i
$397$	14.1404	−	24.4919i	0.709688	−	1.22921i	−0.255285	−	0.966866i	$-0.582169\pi$
$397$	14.1404	−	24.4919i	0.709688	−	1.22921i	0.964973	−	0.262349i	$-0.0844972\pi$
$398$	0.756026	−	0.976025i	0.0378961	−	0.0489237i
$399$	−1.00000	+	1.73205i	−0.0500626	+	0.0867110i
$400$		0			0
$401$	−14.8095	+	8.55025i	−0.739550	+	0.426979i	−0.821906	−	0.569624i	$-0.807089\pi$
$401$	−14.8095	+	8.55025i	−0.739550	+	0.426979i	0.0823557	+	0.996603i	$0.473756\pi$
$402$	−17.1825	−	13.3095i	−0.856983	−	0.663816i
$403$	11.1803	−	11.6190i	0.556932	−	0.578781i
$404$	0.245967	−	0.0635083i	0.0122373	−	0.00315966i
$405$	1.11803	+	1.93649i	0.0555556	+	0.0962250i
$406$	−1.50222	−	0.204744i	−0.0745541	−	0.0101613i
$407$	−21.1825	+	36.6891i	−1.04998	+	1.81861i
$408$	−2.09406	+	4.86615i	−0.103671	+	0.240910i
$409$	28.1190	+	16.2345i	1.39039	+	0.802744i	0.993359	−	0.115060i	$-0.0367061\pi$
$409$	28.1190	+	16.2345i	1.39039	+	0.802744i	0.397034	+	0.917804i	$0.370039\pi$
$410$	16.6847	−	6.82206i	0.823998	−	0.336918i
$411$	−13.6364			−0.672634
$412$	−24.3174	−	6.75408i	−1.19803	−	0.332750i
$413$	4.97615	−	2.87298i	0.244860	−	0.141370i
$414$	1.57924	+	0.215241i	0.0776155	+	0.0105785i
$415$	−16.6190			−0.815792
$416$	2.59017	+	20.2309i	0.126994	+	0.991904i
$417$	5.74597			0.281381
$418$	22.0642	+	3.00721i	1.07919	+	0.147088i
$419$	22.5167	−	13.0000i	1.10001	−	0.635092i	0.163787	−	0.986496i	$-0.447629\pi$
$419$	22.5167	−	13.0000i	1.10001	−	0.635092i	0.936224	+	0.351404i	$0.114296\pi$
$420$	2.17182	+	0.603217i	0.105974	+	0.0294340i
$421$	12.1244			0.590905			0.295452	−	0.955357i	$-0.404530\pi$
$421$	12.1244			0.590905			0.295452	+	0.955357i	$0.404530\pi$
$422$	18.3262	−	7.49326i	0.892107	−	0.364766i
$423$	0.436492	+	0.252009i	0.0212230	+	0.0122531i
$424$	−0.142009	+	0.329999i	−0.00689656	+	0.0160262i
$425$		0			0
$426$	−11.8270	−	1.61195i	−0.573019	−	0.0780990i
$427$	−0.252009	−	0.436492i	−0.0121956	−	0.0211233i
$428$	13.3095	−	3.43649i	0.643338	−	0.166109i
$429$	3.96812	+	13.7460i	0.191583	+	0.663662i
$430$	2.81754	+	2.18246i	0.135874	+	0.105247i
$431$	25.3095	−	14.6124i	1.21911	−	0.703856i	0.254386	−	0.967103i	$-0.418127\pi$
$431$	25.3095	−	14.6124i	1.21911	−	0.703856i	0.964729	+	0.263247i	$0.0847933\pi$
$432$	2.06284	−	3.42705i	0.0992486	−	0.164884i
$433$	5.62702	−	9.74628i	0.270417	−	0.468376i	−0.698552	−	0.715560i	$-0.746172\pi$
$433$	5.62702	−	9.74628i	0.270417	−	0.468376i	0.968969	+	0.247183i	$0.0795050\pi$
$434$	−1.95205	+	2.52009i	−0.0937014	+	0.120968i
$435$	2.37808	−	4.11895i	0.114020	−	0.197489i
$436$	21.9690	+	6.10184i	1.05213	+	0.292225i
$437$	−4.47214			−0.213931
$438$	−2.24162	−	5.48232i	−0.107109	−	0.261955i
$439$	4.56351	+	7.90423i	0.217804	+	0.377248i	0.954136	−	0.299372i	$-0.0967772\pi$
$439$	4.56351	+	7.90423i	0.217804	+	0.377248i	−0.736332	+	0.676620i	$0.763444\pi$
$440$	−2.93511	−	24.9244i	−0.139926	−	1.18822i
$441$	−6.74597			−0.321237
$442$	9.44936	−	1.38540i	0.449460	−	0.0658966i
$443$			36.7298i			1.74509i	0.488536	+	0.872544i	$0.337531\pi$
$443$			36.7298i			1.74509i	−0.488536	+	0.872544i	$0.662469\pi$
$444$	−14.9603	−	15.2357i	−0.709984	−	0.723052i
$445$	−30.7369	+	17.7460i	−1.45707	+	0.841239i
$446$	−27.9510	+	11.4286i	−1.32352	+	0.541162i
$447$			22.5807i			1.06803i
$448$	−0.936667	−	3.92183i	−0.0442533	−	0.185289i
$449$	−19.7460	−	11.4003i	−0.931870	−	0.538015i	−0.0444673	−	0.999011i	$-0.514159\pi$
$449$	−19.7460	−	11.4003i	−0.931870	−	0.538015i	−0.887402	+	0.460996i	$0.847492\pi$
$450$		0			0
$451$	−19.5886	−	11.3095i	−0.922390	−	0.532542i
$452$	−3.03536	+	2.98050i	−0.142771	+	0.140191i
$453$	−3.21209	−	5.56351i	−0.150917	−	0.261396i
$454$	13.3095	−	17.1825i	0.624645	−	0.806413i
$455$	−1.12702	−	3.90410i	−0.0528354	−	0.183027i
$456$	−4.43649	+	10.3095i	−0.207758	+	0.482785i
$457$	36.3569	−	20.9906i	1.70070	−	0.981901i	0.755652	−	0.654973i	$-0.227320\pi$
$457$	36.3569	−	20.9906i	1.70070	−	0.981901i	0.945049	−	0.326928i	$-0.106013\pi$
$458$	2.82503	+	0.385035i	0.132005	+	0.0179915i
$459$	−1.62205	−	0.936492i	−0.0757109	−	0.0437117i
$460$	1.26004	+	4.88013i	0.0587498	+	0.227537i
$461$	2.56607	−	4.44456i	0.119514	−	0.207004i	−0.800061	−	0.599918i	$-0.795200\pi$
$461$	2.56607	−	4.44456i	0.119514	−	0.207004i	0.919575	+	0.392914i	$0.128533\pi$
$462$	−1.07047	−	2.61803i	−0.0498026	−	0.121802i
$463$			21.8567i			1.01577i	0.861426	+	0.507883i	$0.169572\pi$
$463$			21.8567i			1.01577i	−0.861426	+	0.507883i	$0.830428\pi$
$464$	−8.50665	−	0.155164i	−0.394911	−	0.00720330i
$465$	−5.00000	−	8.66025i	−0.231869	−	0.401610i
$466$	−30.8277	−	4.20163i	−1.42807	−	0.194637i
$467$		−	26.3649i		−	1.22002i	−0.792393	−	0.610011i	$-0.791165\pi$
$467$		−	26.3649i		−	1.22002i	0.792393	−	0.610011i	$-0.208835\pi$
$468$	−7.21073	+	0.0729490i	−0.333316	+	0.00337207i
$469$		−	7.74597i		−	0.357676i
$470$	−0.215241	+	1.57924i	−0.00992833	+	0.0728450i
$471$	−8.37298	−	14.5024i	−0.385807	−	0.668237i
$472$	25.8478	−	19.2778i	1.18974	−	0.887332i
$473$		−	4.47214i		−	0.205629i
$474$	−18.3262	+	7.49326i	−0.841752	+	0.344177i
$475$		0			0
$476$	−1.82808	+	0.472008i	−0.0837898	+	0.0216344i
$477$	−0.110000	−	0.0635083i	−0.00503654	−	0.00290785i
$478$	−2.27353	+	16.6811i	−0.103989	+	0.762975i
$479$	−18.1109	+	10.4563i	−0.827507	+	0.477762i	−0.852998	−	0.521913i	$-0.825218\pi$
$479$	−18.1109	+	10.4563i	−0.827507	+	0.477762i	0.0254911	+	0.999675i	$0.491885\pi$
$480$	12.5000	+	1.93649i	0.570544	+	0.0883883i
$481$	−9.24597	+	37.3671i	−0.421580	+	1.70379i
$482$	17.4284	+	13.5000i	0.793843	+	0.614908i
$483$	0.284018	+	0.491933i	0.0129233	+	0.0223837i
$484$	−6.77274	+	6.65033i	−0.307852	+	0.302288i
$485$	33.5410	+	19.3649i	1.52302	+	0.879316i
$486$	1.11803	+	0.866025i	0.0507151	+	0.0392837i
$487$	6.92843	+	4.00013i	0.313957	+	0.181263i	0.648696	−	0.761048i	$-0.275315\pi$
$487$	6.92843	+	4.00013i	0.313957	+	0.181263i	−0.334739	+	0.942311i	$0.608648\pi$
$488$	−1.69098	−	2.26728i	−0.0765472	−	0.102635i
$489$			9.95231i			0.450059i
$490$	−8.07369	−	19.7458i	−0.364732	−	0.892024i
$491$	27.5888	−	15.9284i	1.24507	−	0.718840i	0.274946	−	0.961460i	$-0.411340\pi$
$491$	27.5888	−	15.9284i	1.24507	−	0.718840i	0.970121	+	0.242620i	$0.0780068\pi$
$492$	8.13443	−	7.98741i	0.366729	−	0.360100i
$493$			3.98387i			0.179424i
$494$	20.0195	−	2.93511i	0.900720	−	0.132057i
$495$	8.87298			0.398811
$496$	−9.22531	+	15.3262i	−0.414229	+	0.688168i
$497$	−2.12702	−	3.68410i	−0.0954097	−	0.165255i
$498$	−9.72890	+	3.97797i	−0.435963	+	0.178257i
$499$	−15.8725			−0.710550			−0.355275	−	0.934762i	$-0.615613\pi$
$499$	−15.8725			−0.710550			−0.355275	+	0.934762i	$0.615613\pi$
$500$	21.5451	+	5.98409i	0.963525	+	0.267617i
$501$	9.16427	−	15.8730i	0.409429	−	0.709153i
$502$	34.9250	+	27.0528i	1.55878	+	1.20743i
$503$	1.30948	−	2.26808i	0.0583866	−	0.101129i	−0.835355	−	0.549711i	$-0.814738\pi$
$503$	1.30948	−	2.26808i	0.0583866	−	0.101129i	0.893741	+	0.448583i	$0.148071\pi$
$504$	1.41579	−	0.166725i	0.0630644	−	0.00742652i
$505$	−0.245967	+	0.142009i	−0.0109454	+	0.00631931i
$506$	3.87298	−	5.00000i	0.172175	−	0.222277i
$507$	6.92820	+	11.0000i	0.307692	+	0.488527i
$508$	−8.87298	−	34.3649i	−0.393675	−	1.52470i
$509$	−11.2903	−	19.5554i	−0.500436	−	0.866780i	−1.00000		0.000502947i	$-0.999840\pi$
$509$	−11.2903	−	19.5554i	−0.500436	−	0.866780i	0.499564	−	0.866277i	$-0.333493\pi$
$510$	0.799859	−	5.86864i	0.0354184	−	0.259868i
$511$	1.05544	−	1.82808i	0.0466900	−	0.0808694i
$512$	−7.79423	−	21.2426i	−0.344459	−	0.938801i
$513$	−3.43649	−	1.98406i	−0.151725	−	0.0875984i
$514$	12.5057	+	30.5851i	0.551602	+	1.34905i
$515$	28.2168			1.24338
$516$	2.17182	+	0.603217i	0.0956090	+	0.0265551i
$517$	1.73205	−	1.00000i	0.0761755	−	0.0439799i
$518$	1.02769	−	7.54024i	0.0451541	−	0.331299i
$519$	13.4919			0.592230
$520$	−8.84346	−	21.0189i	−0.387811	−	0.921739i
$521$	−17.6190			−0.771900			−0.385950	−	0.922520i	$-0.626126\pi$
$521$	−17.6190			−0.771900			−0.385950	+	0.922520i	$0.626126\pi$
$522$	0.406224	−	2.98050i	0.0177799	−	0.130453i
$523$	3.78013	−	2.18246i	0.165293	−	0.0954322i	−0.415071	−	0.909789i	$-0.636243\pi$
$523$	3.78013	−	2.18246i	0.165293	−	0.0954322i	0.580365	+	0.814357i	$0.302910\pi$
$524$	2.00497	−	7.21867i	0.0875873	−	0.315349i
$525$		0			0
$526$	4.74911	+	11.6149i	0.207071	+	0.506433i
$527$	7.25403	+	4.18812i	0.315991	+	0.182437i
$528$	−7.68423	−	13.8884i	−0.334413	−	0.604416i
$529$	10.8649	−	18.8186i	0.472388	−	0.818199i
$530$	0.0542426	−	0.397982i	0.00235615	−	0.0172873i
$531$	5.70017	+	9.87298i	0.247366	+	0.428451i
$532$	−3.87298	+	1.00000i	−0.167915	+	0.0433555i
$533$	−19.9506	−	4.93649i	−0.864156	−	0.213823i
$534$	−13.7460	+	17.7460i	−0.594846	+	0.767943i
$535$	−13.3095	+	7.68423i	−0.575419	+	0.332218i
$536$	−5.08377	−	43.1703i	−0.219585	−	1.86467i
$537$	6.43649	−	11.1483i	0.277755	−	0.481086i
$538$	−4.75615	−	3.68410i	−0.205052	−	0.158833i
$539$	−13.3844	+	23.1825i	−0.576507	+	0.998539i
$540$	−1.19682	+	4.30902i	−0.0515028	+	0.185431i
$541$	−29.4449			−1.26593			−0.632967	−	0.774179i	$-0.718163\pi$
$541$	−29.4449			−1.26593			−0.632967	+	0.774179i	$0.718163\pi$
$542$	−30.5900	+	12.5077i	−1.31395	+	0.537252i
$543$	−7.37298	−	12.7704i	−0.316405	−	0.548030i
$544$	−9.87857	+	3.83041i	−0.423540	+	0.164227i
$545$	−25.4919			−1.09195
$546$	−1.59427	−	2.01573i	−0.0682283	−	0.0862654i
$547$			14.3649i			0.614199i	0.951677	+	0.307100i	$0.0993585\pi$
$547$			14.3649i			0.614199i	−0.951677	+	0.307100i	$0.900641\pi$
$548$	−19.1081	−	19.4598i	−0.816259	−	0.831284i
$549$	0.866025	−	0.500000i	0.0369611	−	0.0213395i
$550$		0			0
$551$			8.44025i			0.359567i
$552$	1.90577	+	2.55527i	0.0811148	+	0.108759i
$553$	−6.11088	−	3.52812i	−0.259861	−	0.150031i
$554$	−16.4865	−	12.7704i	−0.700444	−	0.542562i
$555$	20.6746	+	11.9365i	0.877588	+	0.506676i
$556$	8.05158	+	8.19979i	0.341463	+	0.347748i
$557$	−0.614017	−	1.06351i	−0.0260167	−	0.0450623i	0.852724	−	0.522362i	$-0.174949\pi$
$557$	−0.614017	−	1.06351i	−0.0260167	−	0.0450623i	−0.878741	+	0.477300i	$0.841616\pi$
$558$	−5.00000	−	3.87298i	−0.211667	−	0.163956i
$559$	−1.12702	−	3.90410i	−0.0476677	−	0.165126i
$560$	2.18246	+	3.94456i	0.0922257	+	0.166688i
$561$	−6.43649	+	3.71611i	−0.271749	+	0.156894i
$562$	3.65094	−	26.7873i	0.154006	−	1.12995i
$563$	32.0290	+	18.4919i	1.34986	+	0.779342i	0.988229	−	0.152979i	$-0.0488868\pi$
$563$	32.0290	+	18.4919i	1.34986	+	0.779342i	0.361631	+	0.932321i	$0.382220\pi$
$564$	0.252009	+	0.976025i	0.0106115	+	0.0410981i
$565$	2.37808	−	4.11895i	0.100046	−	0.173286i
$566$	3.42825	−	1.40175i	0.144100	−	0.0589199i
$567$			0.504017i			0.0211667i
$568$	−14.2723	−	19.1365i	−0.598854	−	0.802948i
$569$	−11.4919	−	19.9046i	−0.481767	−	0.834445i	0.518014	−	0.855372i	$-0.326671\pi$
$569$	−11.4919	−	19.9046i	−0.481767	−	0.834445i	−0.999781	+	0.0209273i	$0.993338\pi$
$570$	1.69459	−	12.4333i	0.0709785	−	0.520775i
$571$			6.61895i			0.276994i	0.990363	+	0.138497i	$0.0442272\pi$
$571$			6.61895i			0.276994i	−0.990363	+	0.138497i	$0.955773\pi$
$572$	−14.0558	+	24.9244i	−0.587704	+	1.04214i
$573$			4.25403i			0.177715i
$574$	4.02579	+	0.548691i	0.168033	+	0.0229019i
$575$		0			0
$576$	7.78115	−	1.85840i	0.324215	−	0.0774334i
$577$		−	8.22026i		−	0.342214i	−0.985252	−	0.171107i	$-0.945266\pi$
$577$		−	8.22026i		−	0.342214i	0.985252	−	0.171107i	$-0.0547343\pi$
$578$	−7.22133	−	17.6612i	−0.300368	−	0.734608i
$579$	−9.30628	+	16.1190i	−0.386756	+	0.669881i
$580$	9.21025	−	2.37808i	0.382435	−	0.0987443i
$581$	−3.24410	−	1.87298i	−0.134588	−	0.0777044i
$582$	24.2705	+	3.30792i	1.00605	+	0.137118i
$583$	−0.436492	+	0.252009i	−0.0180776	+	0.0104371i
$584$	4.68246	−	10.8810i	0.193762	−	0.450261i
$585$	7.74597	−	2.23607i	0.320256	−	0.0924500i
$586$	−24.6825	+	31.8649i	−1.01962	+	1.31633i
$587$	−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	$0.892427\pi$
$588$	−9.45284	−	9.62684i	−0.389829	−	0.397004i
$589$	15.3685	+	8.87298i	0.633246	+	0.365605i
$590$	−22.0767	+	28.5008i	−0.908882	+	1.17336i
$591$	−9.87298	−	5.70017i	−0.406120	−	0.234474i
$592$	0.778827	−	42.6982i	0.0320096	−	1.75488i
$593$		−	15.0844i		−	0.619444i	−0.950827	−	0.309722i	$-0.899764\pi$
$593$		−	15.0844i		−	0.619444i	0.950827	−	0.309722i	$-0.100236\pi$
$594$	5.19433	−	2.12387i	0.213126	−	0.0871434i
$595$	1.82808	−	1.05544i	0.0749439	−	0.0432689i
$596$	−32.2238	+	31.6414i	−1.31994	+	1.29608i
$597$			0.872983i			0.0357288i
$598$	2.12101	−	5.34094i	0.0867344	−	0.218407i
$599$	−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
$601$	−7.24597	−	12.5504i	−0.295569	−	0.511941i	0.679548	−	0.733631i	$-0.262176\pi$
$601$	−7.24597	−	12.5504i	−0.295569	−	0.511941i	−0.975117	+	0.221690i	$0.928843\pi$
$602$	0.304032	+	0.743568i	0.0123914	+	0.0303056i
$603$	15.3685			0.625852
$604$	3.43844	−	12.3797i	0.139908	−	0.503724i
$605$	5.30615	−	9.19052i	0.215726	−	0.373648i
$606$	−0.110000	+	0.142009i	−0.00446843	+	0.00576872i
$607$	−5.74597	+	9.95231i	−0.233222	+	0.403952i	−0.958754	−	0.284236i	$-0.908260\pi$
$607$	−5.74597	+	9.95231i	−0.233222	+	0.403952i	0.725533	+	0.688188i	$0.241593\pi$
$608$	−20.9288	+	8.11514i	−0.848776	+	0.329112i
$609$	0.928425	−	0.536026i	0.0376217	−	0.0217209i
$610$	2.50000	+	1.93649i	0.101222	+	0.0784063i
$611$	1.26004	−	1.30948i	0.0509759	−	0.0529757i
$612$	−0.936492	−	3.62702i	−0.0378554	−	0.146613i
$613$	19.4786	+	33.7379i	0.786733	+	1.36266i	0.927958	+	0.372684i	$0.121562\pi$
$613$	19.4786	+	33.7379i	0.786733	+	1.36266i	−0.141226	+	0.989977i	$0.545104\pi$
$614$	−7.58943	−	1.03439i	−0.306284	−	0.0417447i
$615$	−6.37298	+	11.0383i	−0.256983	+	0.445108i
$616$	2.23607	−	5.19615i	0.0900937	−	0.209359i
$617$	29.4284	+	16.9905i	1.18474	+	0.684012i	0.957107	−	0.289734i	$-0.0935668\pi$
$617$	29.4284	+	16.9905i	1.18474	+	0.684012i	0.227637	+	0.973746i	$0.426900\pi$
$618$	16.5184	−	6.75408i	0.664468	−	0.271689i
$619$	40.1212			1.61261			0.806303	−	0.591502i	$-0.201465\pi$
$619$	40.1212			1.61261			0.806303	+	0.591502i	$0.201465\pi$
$620$	5.35233	−	19.2705i	0.214955	−	0.773922i
$621$	−0.976025	+	0.563508i	−0.0391665	+	0.0226128i
$622$	14.8799	+	2.02804i	0.596629	+	0.0813170i
$623$	−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
$627$	−13.6364	+	7.87298i	−0.544586	+	0.314417i
$628$	8.96300	−	32.2703i	0.357662	−	1.28773i
$629$	−19.9966			−0.797316
$630$	−1.47528	+	0.603217i	−0.0587767	+	0.0240327i
$631$	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
$634$	32.2579	+	4.39656i	1.28113	+	0.174610i
$635$	19.8406	+	34.3649i	0.787350	+	1.36373i
$636$	−0.0635083	−	0.245967i	−0.00251827	−	0.00975321i
$637$	−5.84218	+	23.6109i	−0.231476	+	0.935497i
$638$	−9.43649	−	7.30948i	−0.373594	−	0.289385i
$639$	7.30948	−	4.22013i	0.289158	−	0.166946i
$640$	14.7523	+	20.5517i	0.583134	+	0.812376i
$641$	9.68246	−	16.7705i	0.382434	−	0.662395i	−0.608975	−	0.793189i	$-0.708419\pi$
$641$	9.68246	−	16.7705i	0.382434	−	0.662395i	0.991410	+	0.130794i	$0.0417526\pi$
$642$	−5.95218	+	7.68423i	−0.234914	+	0.303272i
$643$	25.0367	−	43.3649i	0.987353	−	1.71015i	0.356379	−	0.934342i	$-0.384011\pi$
$643$	25.0367	−	43.3649i	0.987353	−	1.71015i	0.630974	−	0.775804i	$-0.282655\pi$
$644$	−0.304032	+	1.09463i	−0.0119805	+	0.0431346i
$645$	−2.52009			−0.0992283
$646$	3.97797	+	9.72890i	0.156511	+	0.382779i
$647$	15.8730	+	27.4928i	0.624031	+	1.08085i	0.988727	+	0.149727i	$0.0478396\pi$
$647$	15.8730	+	27.4928i	0.624031	+	1.08085i	−0.364696	+	0.931127i	$0.618827\pi$
$648$	0.330792	+	2.80902i	0.0129947	+	0.110349i
$649$	45.2379			1.77574
$650$		0			0
$651$		−	2.25403i		−	0.0883425i
$652$	−14.2024	+	13.9458i	−0.556211	+	0.546158i
$653$	−23.5887	+	13.6190i	−0.923098	+	0.532951i	−0.884622	−	0.466309i	$-0.845584\pi$
$653$	−23.5887	+	13.6190i	−0.923098	+	0.532951i	−0.0384757	+	0.999260i	$0.512250\pi$
$654$	−14.9232	+	6.10184i	−0.583545	+	0.238601i
$655$			8.37624i			0.327287i
$656$	22.7969	+	0.415822i	0.890069	+	0.0162351i
$657$	3.62702	+	2.09406i	0.141503	+	0.0816970i
$658$	−0.219999	+	0.284018i	−0.00857647	+	0.0110722i
$659$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$659$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$660$	12.4333	+	12.6622i	0.483967	+	0.492875i
$661$	−2.81808	−	4.88105i	−0.109610	−	0.189851i	0.806002	−	0.591913i	$-0.201627\pi$
$661$	−2.81808	−	4.88105i	−0.109610	−	0.189851i	−0.915612	+	0.402062i	$0.868294\pi$
$662$	−14.6190	+	18.8730i	−0.568182	+	0.733519i
$663$	−4.68246	+	4.86615i	−0.181852	+	0.188986i
$664$	−19.3095	−	8.30948i	−0.749353	−	0.322470i
$665$	3.87298	−	2.23607i	0.150188	−	0.0867110i
$666$	14.9603	+	2.03900i	0.579699	+	0.0790095i
$667$	2.07602	+	1.19859i	0.0803839	+	0.0464097i
$668$	35.4931	−	9.16427i	1.37327	−	0.354576i
$669$	10.6763	−	18.4919i	0.412770	−	0.714939i
$670$	18.3932	+	44.9843i	0.710593	+	1.73789i
$671$		−	3.96812i		−	0.153188i
$672$	2.22182	+	1.78678i	0.0857084	+	0.0689267i
$673$	12.1190	+	20.9906i	0.467151	+	0.809130i	0.999296	−	0.0375239i	$-0.0119470\pi$
$673$	12.1190	+	20.9906i	0.467151	+	0.809130i	−0.532145	+	0.846654i	$0.678614\pi$
$674$	18.2164	+	2.48278i	0.701668	+	0.0956331i
$675$		0			0
$676$	−5.98936	+	25.3007i	−0.230360	+	0.973106i
$677$			0.254033i			0.00976329i	0.999988	+	0.00488165i	$0.00155388\pi$
$677$			0.254033i			0.00976329i	−0.999988	+	0.00488165i	$0.998446\pi$
$678$	0.406224	−	2.98050i	0.0156009	−	0.114465i
$679$	4.36492	+	7.56026i	0.167510	+	0.290136i
$680$	9.49565	−	7.08204i	0.364142	−	0.271584i
$681$			15.3685i			0.588921i
$682$	−23.2298	+	9.49823i	−0.889514	+	0.363706i
$683$	−18.1085	+	31.3649i	−0.692904	+	1.20015i	0.277978	+	0.960587i	$0.410336\pi$
$683$	−18.1085	+	31.3649i	−0.692904	+	1.20015i	−0.970882	+	0.239558i	$0.922998\pi$
$684$	−1.98406	−	7.68423i	−0.0758624	−	0.293814i
$685$	26.4068	+	15.2460i	1.00895	+	0.582518i
$686$	1.32317	−	9.70820i	0.0505188	−	0.370661i
$687$	−1.74597	+	1.00803i	−0.0666128	+	0.0384589i
$688$	2.18246	+	3.94456i	0.0832054	+	0.150385i
$689$	−0.317542	+	0.329999i	−0.0120974	+	0.0125720i
$690$	−2.81754	−	2.18246i	−0.107262	−	0.0830848i
$691$	1.19602	+	2.07157i	0.0454989	+	0.0788064i	0.887878	−	0.460079i	$-0.152179\pi$
$691$	1.19602	+	2.07157i	0.0454989	+	0.0788064i	−0.842379	+	0.538885i	$0.818846\pi$
$692$	18.9057	+	19.2537i	0.718686	+	0.731915i
$693$	1.73205	+	1.00000i	0.0657952	+	0.0379869i
$694$	16.6285	+	12.8804i	0.631209	+	0.488933i
$695$	−11.1270	−	6.42419i	−0.422072	−	0.243683i
$696$	4.82255	−	3.59675i	0.182798	−	0.136334i
$697$		−	10.6763i		−	0.404395i
$698$	−0.235502	−	0.575966i	−0.00891388	−	0.0218006i
$699$	19.0526	−	11.0000i	0.720634	−	0.416058i
$700$		0			0
$701$			28.2540i			1.06714i	0.845756	+	0.533570i	$0.179150\pi$
$701$			28.2540i			1.06714i	−0.845756	+	0.533570i	$0.820850\pi$
$702$	3.99933	−	3.16312i	0.150945	−	0.119384i
$703$	−42.3649			−1.59782
$704$	9.05189	−	30.4270i	0.341156	−	1.14676i
$705$	−0.563508	−	0.976025i	−0.0212230	−	0.0367592i
$706$	18.4263	−	7.53416i	0.693481	−	0.283552i
$707$	−0.0640186			−0.00240767
$708$	−6.10184	+	21.9690i	−0.229321	+	0.825647i
$709$	−11.4783	+	19.8810i	−0.431078	+	0.746649i	−0.996966	−	0.0778331i	$-0.975200\pi$
$709$	−11.4783	+	19.8810i	−0.431078	+	0.746649i	0.565889	+	0.824482i	$0.308533\pi$
$710$	21.1006	+	16.3445i	0.791893	+	0.613398i
$711$	7.00000	−	12.1244i	0.262521	−	0.454699i
$712$	−44.5861	+	5.25049i	−1.67093	+	0.196771i
$713$	4.36492	−	2.52009i	0.163467	−	0.0943780i
$714$	0.817542	−	1.05544i	0.0305957	−	0.0394989i
$715$	7.68423	−	31.0554i	0.287374	−	1.16141i
$716$	24.9284	−	6.43649i	0.931619	−	0.240543i
$717$	−5.95218	−	10.3095i	−0.222288	−	0.385014i
$718$	−3.32015	+	24.3602i	−0.123907	+	0.909115i
$719$	−24.4919	+	42.4213i	−0.913395	+	1.58205i	−0.104161	+	0.994560i	$0.533216\pi$
$719$	−24.4919	+	42.4213i	−0.913395	+	1.58205i	−0.809234	+	0.587486i	$0.800118\pi$
$720$	−7.82624	+	4.33013i	−0.291667	+	0.161374i
$721$	5.50807	+	3.18008i	0.205131	+	0.118433i
$722$	−1.74167	−	4.25958i	−0.0648181	−	0.158525i
$723$	−15.5885			−0.579741
$724$	7.89253	−	28.4162i	0.293324	−	1.05608i
$725$		0			0
$726$	0.906399	−	6.65033i	0.0336396	−	0.246817i
$727$	−32.8730			−1.21919			−0.609596	−	0.792712i	$-0.708668\pi$
$727$	−32.8730			−1.21919			−0.609596	+	0.792712i	$0.708668\pi$
$728$	0.642575	−	5.09966i	0.0238154	−	0.189006i
$729$	−1.00000			−0.0370370
$730$	−1.78854	+	13.1227i	−0.0661968	+	0.485692i
$731$	1.82808	−	1.05544i	0.0676139	−	0.0390369i
$732$	1.92705	+	0.535233i	0.0712259	+	0.0197828i
$733$	40.9732			1.51338			0.756691	−	0.653773i	$-0.226815\pi$
$733$	40.9732			1.51338			0.756691	+	0.653773i	$0.226815\pi$
$734$	−12.1064	−	29.6086i	−0.446856	−	1.09287i
$735$	13.0635	+	7.54222i	0.481855	+	0.278199i
$736$	−0.976025	+	6.30021i	−0.0359768	+	0.232229i
$737$	30.4919	−	52.8136i	1.12318	−	1.94541i
$738$	−1.08864	+	7.98741i	−0.0400732	+	0.294021i
$739$	5.98419	+	10.3649i	0.220132	+	0.381280i	0.954848	−	0.297095i	$-0.0960179\pi$
$739$	5.98419	+	10.3649i	0.220132	+	0.381280i	−0.734716	+	0.678375i	$0.762685\pi$
$740$	11.9365	+	46.2298i	0.438794	+	1.69944i
$741$	−9.92030	+	10.3095i	−0.364431	+	0.378728i
$742$	0.0554417	−	0.0715749i	0.00203533	−	0.00262760i
$743$	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
$745$	25.2460	−	43.7273i	0.924941	−	1.60204i
$746$	−0.549998	−	0.426027i	−0.0201369	−	0.0155979i
$747$	3.71611	−	6.43649i	0.135965	−	0.235499i
$748$	−14.3223	−	3.97797i	−0.523674	−	0.145449i
$749$	−3.46410			−0.126576
$750$	−14.6353	+	5.98409i	−0.534404	+	0.218508i
$751$	−13.4365	−	23.2727i	−0.490305	−	0.849232i	0.509633	−	0.860392i	$-0.329781\pi$
$751$	−13.4365	−	23.2727i	−0.490305	−	0.849232i	−0.999938	+	0.0111594i	$0.996448\pi$
$752$	−1.03971	+	1.72729i	−0.0379143	+	0.0629879i
$753$	−31.2379			−1.13837
$754$	−10.0800	−	4.00297i	−0.367090	−	0.145780i
$755$			14.3649i			0.522793i
$756$	−0.719258	+	0.706258i	−0.0261592	+	0.0256864i
$757$	−42.6413	+	24.6190i	−1.54982	+	0.894791i	−0.551669	+	0.834063i	$0.686009\pi$
$757$	−42.6413	+	24.6190i	−1.54982	+	0.894791i	−0.998154	+	0.0607279i	$0.980658\pi$
$758$	−13.2827	−	32.4855i	−0.482451	−	1.17993i
$759$			4.47214i			0.162328i
$760$	20.1176	−	15.0041i	0.729741	−	0.544255i
$761$	12.8730	+	7.43222i	0.466645	+	0.269418i	0.714834	−	0.699294i	$-0.246502\pi$
$761$	12.8730	+	7.43222i	0.466645	+	0.269418i	−0.248189	+	0.968712i	$0.579835\pi$
$762$	19.8406	+	15.3685i	0.718749	+	0.556740i
$763$	−4.97615	−	2.87298i	−0.180149	−	0.104009i
$764$	−6.07072	+	5.96100i	−0.219631	+	0.215661i
$765$	2.09406	+	3.62702i	0.0757109	+	0.131135i
$766$	5.49193	+	4.25403i	0.198432	+	0.153704i
$767$	39.4919	−	11.4003i	1.42597	−	0.411642i
$768$	13.5554	+	8.50000i	0.489140	+	0.306717i
$769$	−6.49193	+	3.74812i	−0.234105	+	0.135161i	−0.612464	−	0.790498i	$-0.709822\pi$
$769$	−6.49193	+	3.74812i	−0.234105	+	0.135161i	0.378359	+	0.925659i	$0.376488\pi$
$770$	−0.854102	+	6.26662i	−0.0307797	+	0.225833i
$771$	−20.2346	−	11.6825i	−0.728732	−	0.420733i
$772$	−36.0431	+	9.30628i	−1.29722	+	0.334940i
$773$	−11.9044	+	20.6190i	−0.428170	+	0.741612i	−0.996711	−	0.0810431i	$-0.974175\pi$
$773$	−11.9044	+	20.6190i	−0.428170	+	0.741612i	0.568541	+	0.822655i	$0.307508\pi$
$774$	−1.47528	+	0.603217i	−0.0530280	+	0.0216822i
$775$		0			0
$776$	29.2887	+	39.2705i	1.05140	+	1.40973i
$777$	2.69052	+	4.66013i	0.0965220	+	0.167181i
$778$	2.21902	−	16.2812i	0.0795558	−	0.583708i
$779$		−	22.6190i		−	0.810408i
$780$	14.0451	+	7.92058i	0.502895	+	0.283602i
$781$		−	33.4919i		−	1.19844i
$782$	2.95789	+	0.403143i	0.105774	+	0.0144164i
$783$	1.06351	+	1.84205i	0.0380067	+	0.0658295i
$784$	0.492112	−	26.9794i	0.0175754	−	0.963549i
$785$			37.4451i			1.33647i
$786$	2.00497	+	4.90353i	0.0715148	+	0.174903i
$787$	−10.1723	+	17.6190i	−0.362604	+	0.628048i	−0.988389	−	0.151948i	$-0.951445\pi$
$787$	−10.1723	+	17.6190i	−0.362604	+	0.628048i	0.625785	+	0.779996i	$0.284779\pi$
$788$	−5.70017	−	22.0767i	−0.203060	−	0.786449i
$789$	−7.68423	−	4.43649i	−0.273566	−	0.157943i
$790$	43.8663	+	5.97871i	1.56069	+	0.212713i
$791$	0.928425	−	0.536026i	0.0330110	−	0.0190589i
$792$	10.3095	+	4.43649i	0.366331	+	0.157644i
$793$	−1.00000	−	3.46410i	−0.0355110	−	0.123014i
$794$	−24.4919	+	31.6190i	−0.869186	+	1.12211i
$795$	0.142009	+	0.245967i	0.00503654	+	0.00872354i
$796$	−1.24579	+	1.22328i	−0.0441559	+	0.0433578i
$797$	−0.439999	−	0.254033i	−0.0155855	−	0.00899832i	0.492187	−	0.870490i	$-0.336198\pi$
$797$	−0.439999	−	0.254033i	−0.0155855	−	0.00899832i	−0.507773	+	0.861491i	$0.669531\pi$
$798$	1.73205	−	2.23607i	0.0613139	−	0.0791559i
$799$	0.817542	+	0.472008i	0.0289225	+	0.0166984i
$800$		0			0
$801$		−	15.8725i		−	0.560826i
$802$	22.3849	−	9.15276i	0.790437	−	0.323195i
$803$	14.3924	−	8.30948i	0.507898	−	0.293235i
$804$	21.5352	+	21.9316i	0.759487	+	0.773467i
$805$		−	1.27017i		−	0.0447675i
$806$	−17.8856	+	14.1459i	−0.629992	+	0.498268i
$807$	4.25403			0.149749
$808$	−0.356792	+	0.0420161i	−0.0125519	+	0.00147812i
$809$	−10.0635	−	17.4305i	−0.353814	−	0.612824i	0.633100	−	0.774070i	$-0.281782\pi$
$809$	−10.0635	−	17.4305i	−0.353814	−	0.612824i	−0.986914	+	0.161246i	$0.948449\pi$
$810$	−1.19682	−	2.92705i	−0.0420519	−	0.102846i
$811$	−8.50427			−0.298625			−0.149313	−	0.988790i	$-0.547706\pi$
$811$	−8.50427			−0.298625			−0.149313	+	0.988790i	$0.547706\pi$
$812$	2.06590	+	0.573798i	0.0724989	+	0.0201364i
$813$	11.6844	−	20.2379i	0.409788	−	0.709774i
$814$	36.6891	−	47.3654i	1.28595	−	1.66016i
$815$	11.1270	−	19.2726i	0.389762	−	0.675088i
$816$	3.86367	−	6.41881i	0.135256	−	0.224703i
$817$	3.87298	−	2.23607i	0.135499	−	0.0782301i
$818$	−36.3014	−	28.1190i	−1.26925	−	0.983156i
$819$	1.76406	+	0.436492i	0.0616412	+	0.0152523i
$820$	−24.6825	+	6.37298i	−0.861949	+	0.222554i
$821$	−22.8647	−	39.6028i	−0.797983	−	1.38215i	−0.920927	−	0.389734i	$-0.872567\pi$
$821$	−22.8647	−	39.6028i	−0.797983	−	1.38215i	0.122944	−	0.992414i	$-0.460766\pi$
$822$	19.1081	+	2.60432i	0.666473	+	0.0908362i
$823$	−16.1270	+	27.9328i	−0.562152	+	0.973677i	0.435156	+	0.900355i	$0.356693\pi$
$823$	−16.1270	+	27.9328i	−0.562152	+	0.973677i	−0.997308	+	0.0733215i	$0.976640\pi$
$824$	32.7850	+	14.1084i	1.14212	+	0.491490i
$825$		0			0
$826$	−7.52157	+	3.07543i	−0.261709	+	0.107008i
$827$	0.568036			0.0197525			0.00987627	−	0.999951i	$-0.496856\pi$
$827$	0.568036			0.0197525			0.00987627	+	0.999951i	$0.496856\pi$
$828$	−2.17182	−	0.603217i	−0.0754759	−	0.0209632i
$829$	−14.0624	+	8.11895i	−0.488409	+	0.281983i	−0.723914	−	0.689890i	$-0.757659\pi$
$829$	−14.0624	+	8.11895i	−0.488409	+	0.281983i	0.235505	+	0.971873i	$0.424325\pi$
$830$	23.2874	+	3.17394i	0.808319	+	0.110169i
$831$	14.7460			0.511532
$832$	0.234268	−	28.8435i	0.00812179	−	0.999967i
$833$	−12.6351			−0.437780
$834$	−8.05158	−	1.09738i	−0.278804	−	0.0379992i
$835$	−35.4931	+	20.4919i	−1.22829	+	0.709153i
$836$	−30.3433	−	8.42776i	−1.04944	−	0.291480i
$837$	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	$0.628507\pi$
$840$	−2.92808	−	1.26004i	−0.101028	−	0.0434756i
$841$	−12.2379	+	21.1967i	−0.421997	+	0.730919i
$842$	−16.9894	−	2.31555i	−0.585492	−	0.0797990i
$843$	9.55829	+	16.5554i	0.329205	+	0.570200i
$844$	−27.1109	+	7.00000i	−0.933195	+	0.240950i
$845$	−1.11803	−	29.0474i	−0.0384615	−	0.999260i
$846$	−0.563508	−	0.436492i	−0.0193738	−	0.0150069i
$847$	2.07157	−	1.19602i	0.0711802	−	0.0410959i
$848$	0.262015	−	0.435293i	0.00899765	−	0.0149480i
$849$	−1.30948	+	2.26808i	−0.0449411	+	0.0778402i
$850$		0			0
$851$	−6.01620	+	10.4204i	−0.206233	+	0.357205i
$852$	16.2648	+	4.51750i	0.557223	+	0.154767i
$853$	−1.29205			−0.0442390			−0.0221195	−	0.999755i	$-0.507041\pi$
$853$	−1.29205			−0.0442390			−0.0221195	+	0.999755i	$0.507041\pi$
$854$	0.269767	+	0.659767i	0.00923123	+	0.0225768i
$855$	4.43649	+	7.68423i	0.151725	+	0.262795i
$856$	−19.3063	+	2.27353i	−0.659877	+	0.0777076i
$857$	7.61895			0.260258			0.130129	−	0.991497i	$-0.458461\pi$
$857$	7.61895			0.260258			0.130129	+	0.991497i	$0.458461\pi$
$858$	−2.93511	−	20.0195i	−0.100203	−	0.683454i
$859$		−	41.6028i		−	1.41947i	−0.704469	−	0.709735i	$-0.748815\pi$
$859$		−	41.6028i		−	1.41947i	0.704469	−	0.709735i	$-0.251185\pi$
$860$	−3.53129	−	3.59629i	−0.120416	−	0.122633i
$861$	−2.48808	+	1.43649i	−0.0847934	+	0.0489555i
$862$	−38.2558	+	15.6421i	−1.30300	+	0.532773i
$863$			48.5614i			1.65305i	0.562900	+	0.826525i	$0.309686\pi$
$863$			48.5614i			1.65305i	−0.562900	+	0.826525i	$0.690314\pi$
$864$	−3.54508	+	4.40822i	−0.120606	+	0.149971i
$865$	−26.1270	−	15.0844i	−0.888345	−	0.512886i
$866$	−9.74628	+	12.5824i	−0.331192	+	0.427567i
$867$	11.6844	+	6.74597i	0.396822	+	0.229105i
$868$	3.21662	−	3.15848i	0.109179	−	0.107206i
$869$	−27.7768	−	48.1109i	−0.942264	−	1.63205i
$870$	−4.11895	+	5.31754i	−0.139645	+	0.180282i
$871$	13.3095	−	53.7896i	0.450974	−	1.82259i
$872$	−29.6190	−	12.7460i	−1.00302	−	0.431633i
$873$	−15.0000	+	8.66025i	−0.507673	+	0.293105i
$874$	6.26662	+	0.854102i	0.211972	+	0.0288904i
$875$	−4.88013	−	2.81754i	−0.164978	−	0.0952503i
$876$	2.09406	+	8.11026i	0.0707517	+	0.274020i
$877$	2.59808	−	4.50000i	0.0877308	−	0.151954i	−0.818821	−	0.574049i	$-0.805372\pi$
$877$	2.59808	−	4.50000i	0.0877308	−	0.151954i	0.906552	+	0.422095i	$0.138705\pi$
$878$	−4.88508	−	11.9474i	−0.164864	−	0.403206i
$879$		−	28.5008i		−	0.961310i
$880$	−0.647275	+	35.4860i	−0.0218196	+	1.19623i
$881$	21.5554	+	37.3351i	0.726221	+	1.25785i	0.958469	+	0.285196i	$0.0920586\pi$
$881$	21.5554	+	37.3351i	0.726221	+	1.25785i	−0.232248	+	0.972657i	$0.574608\pi$
$882$	9.45284	+	1.28836i	0.318294	+	0.0433815i
$883$		−	10.9839i		−	0.369637i	−0.982773	−	0.184818i	$-0.940830\pi$
$883$		−	10.9839i		−	0.369637i	0.982773	−	0.184818i	$-0.0591697\pi$
$884$	−13.5056	+	0.136632i	−0.454242	+	0.00459544i
$885$		−	25.4919i		−	0.856902i
$886$	7.01477	−	51.4680i	0.235666	−	1.72910i
$887$	10.1270	+	17.5405i	0.340032	+	0.588953i	0.984438	−	0.175731i	$-0.0562288\pi$
$887$	10.1270	+	17.5405i	0.340032	+	0.588953i	−0.644406	+	0.764683i	$0.722895\pi$
$888$	18.0535	+	24.2063i	0.605835	+	0.812309i
$889$			8.94427i			0.299981i
$890$	46.4595	−	18.9965i	1.55733	−	0.636763i
$891$	−1.98406	+	3.43649i	−0.0664685	+	0.115127i
$892$	41.3492	−	10.6763i	1.38447	−	0.357470i
$893$	1.73205	+	1.00000i	0.0579609	+	0.0334637i
$894$	4.31253	−	31.6414i	0.144232	−	1.05825i
$895$	−24.9284	+	14.3924i	−0.833265	+	0.481086i
$896$	0.563508	+	5.67439i	0.0188255	+	0.189568i
$897$	1.12702	+	3.90410i	0.0376300	+	0.130354i
$898$	25.4919	+	19.7460i	0.850677	+	0.658931i
$899$	−4.75615	−	8.23790i	−0.158627	−	0.274749i
$900$		0			0
$901$	−0.206028	−	0.118950i	−0.00686377	−	0.00396280i
$902$	25.2888	+	19.5886i	0.842023	+	0.652229i
$903$	−0.491933	−	0.284018i	−0.0163705	−	0.00945152i
$904$	4.82255	−	3.59675i	0.160396	−	0.119626i
$905$			32.9730i			1.09606i
$906$	3.43844	+	8.40937i	0.114234	+	0.279383i
$907$	0.439999	−	0.254033i	0.0146099	−	0.00843504i	−0.492677	−	0.870212i	$-0.663982\pi$
$907$	0.439999	−	0.254033i	0.0146099	−	0.00843504i	0.507287	+	0.861777i	$0.330648\pi$
$908$	−21.9316	+	21.5352i	−0.727825	+	0.714670i
$909$		−	0.127017i		−	0.00421288i
$910$	0.833625	+	5.68589i	0.0276344	+	0.188486i
$911$	38.7298			1.28318			0.641588	−	0.767049i	$-0.278276\pi$
$911$	38.7298			1.28318			0.641588	+	0.767049i	$0.278276\pi$
$912$	8.18561	−	13.5989i	0.271053	−	0.450306i
$913$	−14.7460	−	25.5408i	−0.488020	−	0.845276i
$914$	−54.9542	+	22.4698i	−1.81772	+	0.743234i
$915$	−2.23607			−0.0739221
$916$	−3.88507	−	1.07907i	−0.128366	−	0.0356534i
$917$	−0.944016	+	1.63508i	−0.0311741	+	0.0539952i
$918$	2.09406	+	1.62205i	0.0691142	+	0.0535357i
$919$	−15.1270	+	26.2008i	−0.498994	+	0.864283i	−0.999999	−	0.00116097i	$-0.999630\pi$
$919$	−15.1270	+	26.2008i	−0.498994	+	0.864283i	0.501005	+	0.865444i	$0.332964\pi$
$920$	−0.833625	−	7.07896i	−0.0274838	−	0.233387i
$921$	4.69052	−	2.70808i	0.154558	−	0.0892341i
$922$	−4.44456	+	5.73790i	−0.146374	+	0.188968i
$923$	−8.44025	−	29.2379i	−0.277814	−	0.962377i
$924$	1.00000	+	3.87298i	0.0328976	+	0.127412i
$925$		0			0
$926$	4.17425	−	30.6268i	0.137174	−	1.00646i
$927$	−6.30948	+	10.9283i	−0.207230	+	0.358933i
$928$	11.8904	+	1.84205i	0.390321	+	0.0604683i
$929$	−11.4284	−	6.59820i	−0.374954	−	0.216480i	0.300666	−	0.953729i	$-0.402791\pi$
$929$	−11.4284	−	6.59820i	−0.374954	−	0.216480i	−0.675621	+	0.737249i	$0.736124\pi$
$930$	5.35233	+	13.0902i	0.175510	+	0.429244i
$931$	−26.7688			−0.877312
$932$	42.3951	+	11.7751i	1.38870	+	0.385707i
$933$	−9.19628	+	5.30948i	−0.301073	+	0.173824i
$934$	−5.03525	+	36.9441i	−0.164758	+	1.20885i
$935$	16.6190			0.543498
$936$	10.1180	+	1.27491i	0.330718	+	0.0416716i
$937$	−34.2379			−1.11850			−0.559252	−	0.828998i	$-0.688911\pi$
$937$	−34.2379			−1.11850			−0.559252	+	0.828998i	$0.688911\pi$
$938$	−1.47935	+	10.8541i	−0.0483024	+	0.354399i
$939$	3.46410	−	2.00000i	0.113047	−	0.0652675i
$940$	0.603217	−	2.17182i	0.0196748	−	0.0708369i
$941$	34.6410			1.12926			0.564632	−	0.825342i	$-0.309018\pi$
$941$	34.6410			1.12926			0.564632	+	0.825342i	$0.309018\pi$
$942$	8.96300	+	21.9208i	0.292030	+	0.714217i
$943$	−5.56351	−	3.21209i	−0.181173	−	0.104600i
$944$	−39.9012	+	22.0767i	−1.29867	+	0.718534i
$945$	0.563508	−	0.976025i	0.0183309	−	0.0317501i
$946$	−0.854102	+	6.26662i	−0.0277693	+	0.203745i
$947$	3.96812	+	6.87298i	0.128947	+	0.223342i	0.923269	−	0.384155i	$-0.125507\pi$
$947$	3.96812	+	6.87298i	0.128947	+	0.223342i	−0.794322	+	0.607497i	$0.792174\pi$
$948$	27.1109	−	7.00000i	0.880521	−	0.227349i
$949$	10.4703	−	10.8810i	0.339880	−	0.353214i
$950$		0			0
$951$	−19.9365	+	11.5103i	−0.646485	+	0.373248i
$952$	2.65176	−	0.312273i	0.0859439	−	0.0101208i
$953$	2.25403	−	3.90410i	0.0730153	−	0.126466i	−0.827206	−	0.561899i	$-0.810071\pi$
$953$	2.25403	−	3.90410i	0.0730153	−	0.126466i	0.900221	+	0.435432i	$0.143404\pi$
$954$	0.142009	+	0.110000i	0.00459771	+	0.00356137i
$955$	4.75615	−	8.23790i	0.153906	−	0.266572i
$956$	6.37161	−	22.9403i	0.206072	−	0.741942i
$957$	8.44025			0.272835
$958$	27.3750	−	11.1931i	0.884446	−	0.361634i
$959$	3.43649	+	5.95218i	0.110970	+	0.192206i
$960$	−17.1459	−	5.10081i	−0.553381	−	0.164628i
$961$	11.0000			0.354839
$962$	20.0925	−	50.5952i	0.647807	−	1.63125i
$963$		−	6.87298i		−	0.221479i
$964$	−21.8435	−	22.2455i	−0.703530	−	0.716480i
$965$	36.0431	−	20.8095i	1.16027	−	0.669881i
$966$	−0.304032	−	0.743568i	−0.00978205	−	0.0239239i
$967$		−	33.6970i		−	1.08362i	−0.840500	−	0.541811i	$-0.817739\pi$
$967$		−	33.6970i		−	1.08362i	0.840500	−	0.541811i	$-0.182261\pi$
$968$	10.7605	−	8.02535i	0.345854	−	0.257944i
$969$	−6.43649	−	3.71611i	−0.206770	−	0.119379i
$970$	−43.3013	−	33.5410i	−1.39032	−	1.07694i
$971$	−29.8569	−	17.2379i	−0.958154	−	0.553191i	−0.0625497	−	0.998042i	$-0.519923\pi$
$971$	−29.8569	−	17.2379i	−0.958154	−	0.553191i	−0.895604	+	0.444851i	$0.853257\pi$
$972$	−1.40126	−	1.42705i	−0.0449454	−	0.0457727i
$973$	−1.44803	−	2.50807i	−0.0464218	−	0.0804049i
$974$	−8.94456	−	6.92843i	−0.286602	−	0.222001i
$975$		0			0
$976$	1.93649	+	3.50000i	0.0619856	+	0.112032i
$977$	−15.3014	+	8.83427i	−0.489535	+	0.282633i	−0.724382	−	0.689399i	$-0.757875\pi$
$977$	−15.3014	+	8.83427i	−0.489535	+	0.282633i	0.234846	+	0.972033i	$0.424541\pi$
$978$	1.90072	−	13.9458i	0.0607784	−	0.445936i
$979$	−54.5456	−	31.4919i	−1.74329	−	1.00649i
$980$	7.54222	+	29.2109i	0.240927	+	0.933108i
$981$	5.70017	−	9.87298i	0.181992	−	0.315220i
$982$	−41.7012	+	17.0508i	−1.33074	+	0.544114i
$983$		−	0.439999i		−	0.0140338i	−0.999975	−	0.00701689i	$-0.997766\pi$
$983$		−	0.439999i		−	0.0140338i	0.999975	−	0.00701689i	$-0.00223356\pi$
$984$	−12.9239	+	9.63889i	−0.411999	+	0.307277i
$985$	12.7460	+	22.0767i	0.406120	+	0.703421i
$986$	0.760851	−	5.58243i	0.0242304	−	0.177781i
$987$		−	0.254033i		−	0.00808597i
$988$	−28.6130	+	0.289470i	−0.910302	+	0.00920928i
$989$		−	1.27017i		−	0.0403889i
$990$	−12.4333	−	1.69459i	−0.395158	−	0.0538576i
$991$	−13.1825	−	22.8327i	−0.418755	−	0.725304i	0.577060	−	0.816702i	$-0.304200\pi$
$991$	−13.1825	−	22.8327i	−0.418755	−	0.725304i	−0.995814	+	0.0913976i	$0.970867\pi$
$992$	15.8541	−	19.7141i	0.503368	−	0.625925i
$993$		−	16.8805i		−	0.535687i
$994$	2.27690	+	5.56860i	0.0722189	+	0.176625i
$995$	0.976025	−	1.69052i	0.0309421	−	0.0535932i
$996$	14.3924	−	3.71611i	0.456042	−	0.117749i
$997$	−33.3350	−	19.2460i	−1.05573	−	0.609526i	−0.131482	−	0.991319i	$-0.541973\pi$
$997$	−33.3350	−	19.2460i	−1.05573	−	0.609526i	−0.924248	+	0.381793i	$0.875307\pi$
$998$	22.2414	+	3.03137i	0.704041	+	0.0959564i
$999$	−9.24597	+	5.33816i	−0.292529	+	0.168892i

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.205.1	✓	8
3.2	odd	2		936.2.dg.c.829.4		8
4.3	odd	2		1248.2.ca.a.49.1		8
8.3	odd	2		1248.2.ca.a.49.4		8
8.5	even	2	inner	312.2.bk.a.205.2	yes	8
13.4	even	6	inner	312.2.bk.a.277.2	yes	8
24.5	odd	2		936.2.dg.c.829.3		8
39.17	odd	6		936.2.dg.c.901.3		8
52.43	odd	6		1248.2.ca.a.433.4		8
104.43	odd	6		1248.2.ca.a.433.1		8
104.69	even	6	inner	312.2.bk.a.277.1	yes	8
312.173	odd	6		936.2.dg.c.901.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.a.205.1	✓	8	1.1	even	1	trivial
312.2.bk.a.205.2	yes	8	8.5	even	2	inner
312.2.bk.a.277.1	yes	8	104.69	even	6	inner
312.2.bk.a.277.2	yes	8	13.4	even	6	inner
936.2.dg.c.829.3		8	24.5	odd	2
936.2.dg.c.829.4		8	3.2	odd	2
936.2.dg.c.901.3		8	39.17	odd	6
936.2.dg.c.901.4		8	312.173	odd	6
1248.2.ca.a.49.1		8	4.3	odd	2
1248.2.ca.a.49.4		8	8.3	odd	2
1248.2.ca.a.433.1		8	104.43	odd	6
1248.2.ca.a.433.4		8	52.43	odd	6

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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

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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.205.1

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