LMFDB - Embedded newform 312.2.bk.a.205.3

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			205.3
Root			$0.535233 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	312.205
Dual form			312.2.bk.a.277.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535233 - 1.30902i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.42705 - 1.40126i) q^{4} +2.23607 q^{5} +(-0.190983 - 1.40126i) q^{6} +(3.43649 + 1.98406i) q^{7} +(-2.59808 + 1.11803i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.19682 - 2.92705i) 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} +(0.0729490 + 3.99933i) q^{16} +(-2.93649 + 5.08615i) q^{17} +(-0.866025 - 1.11803i) q^{18} +(-0.252009 + 0.436492i) q^{19} +(-3.19098 - 3.13331i) q^{20} +3.96812 q^{21} +(0.706258 - 0.0962587i) q^{22} +(-4.43649 - 7.68423i) q^{23} +(-1.69098 + 2.26728i) q^{24} +(-4.66312 + 2.06284i) q^{26} -1.00000i q^{27} +(-2.12387 - 7.64677i) q^{28} +(-8.55025 + 4.93649i) q^{29} +(-0.427051 - 3.13331i) q^{30} -4.47214i q^{31} +(5.27424 + 2.04508i) q^{32} +(0.436492 + 0.252009i) q^{33} +(5.08615 + 6.56619i) q^{34} +(7.68423 + 4.43649i) q^{35} +(-1.92705 + 0.535233i) 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} +(2.12387 - 5.19433i) q^{42} +(7.68423 + 4.43649i) q^{43} +(0.252009 - 0.976025i) q^{44} +(1.11803 - 1.93649i) q^{45} +(-12.4333 + 1.69459i) q^{46} -3.96812i q^{47} +(2.06284 + 3.42705i) q^{48} +(4.37298 + 7.57423i) q^{49} +5.87298i q^{51} +(0.204441 + 7.20820i) q^{52} -7.87298i q^{53} +(-1.30902 - 0.535233i) q^{54} +(0.563508 + 0.976025i) q^{55} +(-11.1465 - 1.31262i) q^{56} +0.504017i q^{57} +(1.88557 + 13.8346i) q^{58} +(-1.22803 + 2.12702i) q^{59} +(-4.33013 - 1.11803i) q^{60} +(0.866025 + 0.500000i) q^{61} +(-5.85410 - 2.39364i) 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} +(11.3175 - 3.14342i) q^{68} +(-7.68423 - 4.43649i) q^{69} +(9.92030 - 7.68423i) q^{70} +(-4.30948 - 2.48808i) q^{71} +(-0.330792 + 2.80902i) q^{72} +13.1324i q^{73} +(10.1062 - 1.37741i) q^{74} +(0.971267 - 0.269767i) q^{76} +2.00000i q^{77} +(-3.00696 + 4.11803i) q^{78} +14.0000 q^{79} +(0.163119 + 8.94278i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.234534 - 1.72079i) q^{82} +2.96008 q^{83} +(-5.66271 - 5.56036i) q^{84} +(-6.56619 + 11.3730i) q^{85} +(9.92030 - 7.68423i) q^{86} +(-4.93649 + 8.55025i) q^{87} +(-1.14275 - 0.852284i) 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} +(-5.19433 - 2.12387i) q^{94} +(-0.563508 + 0.976025i) q^{95} +(5.59017 - 0.866025i) q^{96} +(-15.0000 - 8.66025i) q^{97} +(12.2554 - 1.67033i) 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

)

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

$2$	0.535233	−	1.30902i	0.378467	−	0.925615i
$2$	0.535233	−	1.30902i	0.378467	−	0.925615i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.42705	−	1.40126i	−0.713525	−	0.700629i
$5$	2.23607			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$5$	2.23607			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$6$	−0.190983	−	1.40126i	−0.0779685	−	0.572061i
$7$	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
$10$	1.19682	−	2.92705i	0.378467	−	0.925615i
$11$	0.252009	+	0.436492i	0.0759834	+	0.131607i	0.901514	−	0.432751i	$-0.142457\pi$
$11$	0.252009	+	0.436492i	0.0759834	+	0.131607i	−0.825530	+	0.564358i	$0.809124\pi$
$12$	−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
$16$	0.0729490	+	3.99933i	0.0182373	+	0.999834i
$17$	−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	−0.893484	−	0.449095i	$-0.851747\pi$
$19$	−0.252009	+	0.436492i	−0.0578147	+	0.100138i	0.835669	+	0.549233i	$0.185080\pi$
$20$	−3.19098	−	3.13331i	−0.713525	−	0.700629i
$21$	3.96812			0.865915
$22$	0.706258	−	0.0962587i	0.150575	−	0.0205224i
$23$	−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	$-0.542663\pi$
$24$	−1.69098	+	2.26728i	−0.345170	+	0.462807i
$25$		0			0
$26$	−4.66312	+	2.06284i	−0.914513	+	0.404557i
$27$		−	1.00000i		−	0.192450i
$28$	−2.12387	−	7.64677i	−0.401373	−	1.44510i
$29$	−8.55025	+	4.93649i	−1.58774	+	0.916683i	−0.594064	+	0.804418i	$0.702477\pi$
$29$	−8.55025	+	4.93649i	−1.58774	+	0.916683i	−0.993678	+	0.112266i	$0.964189\pi$
$30$	−0.427051	−	3.13331i	−0.0779685	−	0.572061i
$31$		−	4.47214i		−	0.803219i	−0.915811	−	0.401610i	$-0.868451\pi$
$31$		−	4.47214i		−	0.803219i	0.915811	−	0.401610i	$-0.131549\pi$
$32$	5.27424	+	2.04508i	0.932363	+	0.361523i
$33$	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
$36$	−1.92705	+	0.535233i	−0.321175	+	0.0892055i
$37$	3.60611	+	6.24597i	0.592841	+	1.02683i	0.993848	+	0.110756i	$0.0353270\pi$
$37$	3.60611	+	6.24597i	0.592841	+	1.02683i	−0.401007	+	0.916075i	$0.631340\pi$
$38$	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	$0.302763\pi$
$42$	2.12387	−	5.19433i	0.327720	−	0.801503i
$43$	7.68423	+	4.43649i	1.17183	+	0.676559i	0.954111	−	0.299452i	$-0.0968039\pi$
$43$	7.68423	+	4.43649i	1.17183	+	0.676559i	0.217723	+	0.976011i	$0.430137\pi$
$44$	0.252009	−	0.976025i	0.0379917	−	0.147141i
$45$	1.11803	−	1.93649i	0.166667	−	0.288675i
$46$	−12.4333	+	1.69459i	−1.83320	+	0.249854i
$47$		−	3.96812i		−	0.578810i	−0.957207	−	0.289405i	$-0.906543\pi$
$47$		−	3.96812i		−	0.578810i	0.957207	−	0.289405i	$-0.0934574\pi$
$48$	2.06284	+	3.42705i	0.297746	+	0.494652i
$49$	4.37298	+	7.57423i	0.624712	+	1.08203i
$50$		0			0
$51$			5.87298i			0.822382i
$52$	0.204441	+	7.20820i	0.0283508	+	0.999598i
$53$		−	7.87298i		−	1.08144i	−0.841203	−	0.540719i	$-0.818152\pi$
$53$		−	7.87298i		−	1.08144i	0.841203	−	0.540719i	$-0.181848\pi$
$54$	−1.30902	−	0.535233i	−0.178135	−	0.0728360i
$55$	0.563508	+	0.976025i	0.0759834	+	0.131607i
$56$	−11.1465	−	1.31262i	−1.48952	−	0.175407i
$57$			0.504017i			0.0667587i
$58$	1.88557	+	13.8346i	0.247588	+	1.81657i
$59$	−1.22803	+	2.12702i	−0.159876	+	0.276914i	−0.934824	−	0.355112i	$-0.884443\pi$
$59$	−1.22803	+	2.12702i	−0.159876	+	0.276914i	0.774948	+	0.632026i	$0.217776\pi$
$60$	−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	$0.646275\pi$
$62$	−5.85410	−	2.39364i	−0.743472	−	0.303992i
$63$	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	0.919467	−	0.393167i	$-0.128621\pi$
$67$	0.976025	+	1.69052i	0.119240	+	0.206530i	−0.800226	+	0.599698i	$0.795287\pi$
$68$	11.3175	−	3.14342i	1.37245	−	0.381195i
$69$	−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	$0.762080\pi$
$72$	−0.330792	+	2.80902i	−0.0389842	+	0.331046i
$73$			13.1324i			1.53703i	0.639832	+	0.768515i	$0.279004\pi$
$73$			13.1324i			1.53703i	−0.639832	+	0.768515i	$0.720996\pi$
$74$	10.1062	−	1.37741i	1.17482	−	0.160121i
$75$		0			0
$76$	0.971267	−	0.269767i	0.111412	−	0.0309444i
$77$			2.00000i			0.227921i
$78$	−3.00696	+	4.11803i	−0.340471	+	0.466276i
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	0.163119	+	8.94278i	0.0182373	+	0.999834i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.234534	−	1.72079i	−0.0258999	−	0.190030i
$83$	2.96008			0.324911			0.162456	−	0.986716i	$-0.448059\pi$
$83$	2.96008			0.324911			0.162456	+	0.986716i	$0.448059\pi$
$84$	−5.66271	−	5.56036i	−0.617852	−	0.606685i
$85$	−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
$88$	−1.14275	−	0.852284i	−0.121818	−	0.0908538i
$89$	−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
$94$	−5.19433	−	2.12387i	−0.535755	−	0.219060i
$95$	−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	$-0.675333\pi$
$98$	12.2554	−	1.67033i	1.23798	−	0.168729i
$99$	0.504017			0.0506556
$100$		0			0
$101$	6.81820	−	3.93649i	0.678437	−	0.391696i	−0.120829	−	0.992673i	$-0.538555\pi$
$101$	6.81820	−	3.93649i	0.678437	−	0.391696i	0.799266	+	0.600978i	$0.205222\pi$
$102$	7.68784	+	3.14342i	0.761209	+	0.311244i
$103$	10.6190			1.04632			0.523158	−	0.852236i	$-0.324754\pi$
$103$	10.6190			1.04632			0.523158	+	0.852236i	$0.324754\pi$
$104$	9.54508	+	3.59045i	0.935973	+	0.352073i
$105$	8.87298			0.865915
$106$	−10.3059	−	4.21388i	−1.00099	−	0.409288i
$107$	−0.756026	+	0.436492i	−0.0730878	+	0.0421972i	−0.536099	−	0.844155i	$-0.680102\pi$
$107$	−0.756026	+	0.436492i	−0.0730878	+	0.0421972i	0.463011	+	0.886353i	$0.346769\pi$
$108$	−1.40126	+	1.42705i	−0.134836	+	0.137318i
$109$	2.45607			0.235249			0.117624	−	0.993058i	$-0.462472\pi$
$109$	2.45607			0.235249			0.117624	+	0.993058i	$0.462472\pi$
$110$	1.57924	−	0.215241i	0.150575	−	0.0205224i
$111$	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	$0.320392\pi$
$114$	0.659767	+	0.269767i	0.0617928	+	0.0252660i
$115$	−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
$120$	−3.78115	+	5.06980i	−0.345170	+	0.462807i
$121$	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
$124$	−6.26662	+	6.38197i	−0.562759	+	0.573117i
$125$	−11.1803			−1.00000
$126$	−0.757843	−	5.56036i	−0.0675140	−	0.495356i
$127$	−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	$0.865220\pi$
$128$	−4.66092	−	10.3090i	−0.411971	−	0.911197i
$129$	8.87298			0.781223
$130$	−10.4271	+	4.61266i	−0.914513	+	0.404557i
$131$			11.7460i			1.02625i	0.858314	+	0.513125i	$0.171512\pi$
$131$			11.7460i			1.02625i	−0.858314	+	0.513125i	$0.828488\pi$
$132$	−0.269767	−	0.971267i	−0.0234802	−	0.0845379i
$133$	−1.73205	+	1.00000i	−0.150188	+	0.0867110i
$134$	2.73533	−	0.372808i	0.236296	−	0.0322057i
$135$		−	2.23607i		−	0.192450i
$136$	1.94274	−	16.4973i	0.166588	−	1.41463i
$137$	−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	0.0973462	−	0.995251i	$-0.468965\pi$
$139$	−8.44025	−	4.87298i	−0.715893	−	0.413321i	−0.813239	+	0.581930i	$0.802298\pi$
$140$	−4.74911	−	17.0987i	−0.401373	−	1.44510i
$141$	−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
$146$	17.1905	+	7.02889i	1.42270	+	0.581715i
$147$	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	−0.630159	−	0.776466i	$-0.717010\pi$
$149$	4.36214	−	7.55544i	0.357360	−	0.618966i	0.987519	+	0.157500i	$0.0503436\pi$
$150$		0			0
$151$		−	10.8963i		−	0.886730i	−0.896341	−	0.443365i	$-0.853785\pi$
$151$		−	10.8963i		−	0.886730i	0.896341	−	0.443365i	$-0.146215\pi$
$152$	0.166725	−	1.41579i	0.0135232	−	0.114836i
$153$	2.93649	+	5.08615i	0.237401	+	0.411191i
$154$	2.61803	+	1.07047i	0.210967	+	0.0862606i
$155$		−	10.0000i		−	0.803219i
$156$	3.78115	+	6.14027i	0.302735	+	0.491615i
$157$		−	1.25403i		−	0.100083i	−0.998747	−	0.0500414i	$-0.984065\pi$
$157$		−	1.25403i		−	0.100083i	0.998747	−	0.0500414i	$-0.0159353\pi$
$158$	7.49326	−	18.3262i	0.596132	−	1.45796i
$159$	−3.93649	−	6.81820i	−0.312184	−	0.540719i
$160$	11.7936	+	4.57295i	0.932363	+	0.361523i
$161$		−	35.2091i		−	2.77486i
$162$	−1.40126	+	0.190983i	−0.110093	+	0.0150050i
$163$	8.44025	−	14.6190i	0.661092	−	1.14504i	−0.319237	−	0.947675i	$-0.603427\pi$
$163$	8.44025	−	14.6190i	0.661092	−	1.14504i	0.980329	−	0.197370i	$-0.0632399\pi$
$164$	−2.37808	−	0.614017i	−0.185697	−	0.0479467i
$165$	0.976025	+	0.563508i	0.0759834	+	0.0438691i
$166$	1.58434	−	3.87480i	0.122968	−	0.300743i
$167$	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
$172$	−4.74911	−	17.0987i	−0.362117	−	1.30376i
$173$	−15.1485	−	8.74597i	−1.15172	−	0.664944i	−0.202411	−	0.979301i	$-0.564878\pi$
$173$	−15.1485	−	8.74597i	−1.15172	−	0.664944i	−0.949305	+	0.314357i	$0.898211\pi$
$174$	8.55025	+	11.0383i	0.648193	+	0.836814i
$175$		0			0
$176$	−1.72729	+	1.03971i	−0.130200	+	0.0783710i
$177$			2.45607i			0.184609i
$178$	0.385035	+	2.82503i	0.0288596	+	0.211745i
$179$	4.44013	−	2.56351i	0.331871	−	0.191606i	−0.324801	−	0.945782i	$-0.605297\pi$
$179$	4.44013	−	2.56351i	0.331871	−	0.191606i	0.656671	+	0.754177i	$0.271964\pi$
$180$	−4.30902	+	1.19682i	−0.321175	+	0.0892055i
$181$			0.745967i			0.0554473i	0.999616	+	0.0277236i	$0.00882584\pi$
$181$			0.745967i			0.0554473i	−0.999616	+	0.0277236i	$0.991174\pi$
$182$	−20.1176	−	2.16296i	−1.49121	−	0.160329i
$183$	1.00000			0.0739221
$184$	20.1176	+	15.0041i	1.48309	+	1.10611i
$185$	8.06351	+	13.9664i	0.592841	+	1.02683i
$186$	−6.26662	+	0.854102i	−0.459491	+	0.0626258i
$187$	−2.96008			−0.216463
$188$	−5.56036	+	5.66271i	−0.405531	+	0.412995i
$189$	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	$0.913374\pi$
$192$	1.85840	−	7.78115i	0.134119	−	0.561556i
$193$	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	0.818957	−	0.573854i	$-0.194552\pi$
$197$	−1.22803	−	2.12702i	−0.0874938	−	0.151544i	−0.906451	+	0.422311i	$0.861219\pi$
$198$	0.269767	−	0.659767i	0.0191715	−	0.0468876i
$199$	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
$202$	−1.50361	−	11.0321i	−0.105793	−	0.776215i
$203$	−39.1772			−2.74970
$204$	8.22957	−	8.38105i	0.576185	−	0.586791i
$205$	2.37808	−	1.37298i	0.166092	−	0.0958933i
$206$	5.68361	−	13.9004i	0.395996	−	0.968486i
$207$	−8.87298			−0.616715
$208$	9.80881	−	10.5729i	0.680119	−	0.733102i
$209$	−0.254033			−0.0175719
$210$	4.74911	−	11.6149i	0.327720	−	0.801503i
$211$	−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	$0.493386\pi$
$212$	−11.0321	+	11.2351i	−0.757687	+	0.771633i
$213$	−4.97615			−0.340960
$214$	0.166725	+	1.22328i	0.0113971	+	0.0836214i
$215$	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
$218$	1.31457	−	3.21503i	0.0890338	−	0.217750i
$219$	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	$0.493774\pi$
$224$	14.0673	+	17.4923i	0.939912	+	1.16876i
$225$		0			0
$226$	8.55025	+	11.0383i	0.568754	+	0.734259i
$227$	−0.976025	+	1.69052i	−0.0647811	+	0.112204i	−0.896597	−	0.442848i	$-0.853968\pi$
$227$	−0.976025	+	1.69052i	−0.0647811	+	0.112204i	0.831816	+	0.555052i	$0.187302\pi$
$228$	0.706258	−	0.719258i	0.0467731	−	0.0476340i
$229$	15.8725			1.04888			0.524441	−	0.851447i	$-0.324274\pi$
$229$	15.8725			1.04888			0.524441	+	0.851447i	$0.324274\pi$
$230$	−27.8018	+	3.78922i	−1.83320	+	0.249854i
$231$	1.00000	+	1.73205i	0.0657952	+	0.113961i
$232$	16.6950	−	22.3849i	1.09608	−	1.46964i
$233$	22.0000			1.44127			0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000			1.44127			0.720634	+	0.693316i	$0.243851\pi$
$234$	−0.545085	+	5.06980i	−0.0356333	+	0.331423i
$235$		−	8.87298i		−	0.578810i
$236$	4.73297	−	1.31457i	0.308090	−	0.0855711i
$237$	12.1244	−	7.00000i	0.787562	−	0.454699i
$238$	4.45080	+	32.6559i	0.288503	+	2.11677i
$239$			1.51205i			0.0978065i	0.998804	+	0.0489032i	$0.0155726\pi$
$239$			1.51205i			0.0978065i	−0.998804	+	0.0489032i	$0.984427\pi$
$240$	4.61266	+	7.66312i	0.297746	+	0.494652i
$241$	−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
$244$	−0.535233	−	1.92705i	−0.0342648	−	0.123367i
$245$	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
$250$	−5.98409	+	14.6353i	−0.378467	+	0.925615i
$251$	13.1964	+	7.61895i	0.832950	+	0.480904i	0.854862	−	0.518856i	$-0.173642\pi$
$251$	13.1964	+	7.61895i	0.832950	+	0.480904i	−0.0219117	+	0.999760i	$0.506975\pi$
$252$	−7.68423	−	1.98406i	−0.484061	−	0.124984i
$253$	2.23607	−	3.87298i	0.140580	−	0.243492i
$254$	−3.15848	+	0.430482i	−0.198181	+	0.0270108i
$255$			13.1324i			0.822382i
$256$	−15.9894	+	0.583495i	−0.999335	+	0.0364684i
$257$	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	$0.674253\pi$
$258$	4.74911	−	11.6149i	0.295667	−	0.723111i
$259$			28.6190i			1.77830i
$260$	0.457144	+	16.1180i	0.0283508	+	0.999598i
$261$			9.87298i			0.611122i
$262$	15.3757	+	6.28683i	0.949912	+	0.388402i
$263$	−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	$0.844396\pi$
$264$	−1.41579	−	0.166725i	−0.0871360	−	0.0102612i
$265$		−	17.6045i		−	1.08144i
$266$	0.381966	+	2.80252i	0.0234198	+	0.171833i
$267$	−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	0.920579	−	0.390557i	$-0.127717\pi$
$269$	17.1005	+	9.87298i	1.04264	+	0.601966i	0.122058	+	0.992523i	$0.461051\pi$
$270$	−2.92705	−	1.19682i	−0.178135	−	0.0728360i
$271$	−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
$276$	4.74911	+	17.0987i	0.285863	+	1.02922i
$277$	−0.646026	−	0.372983i	−0.0388159	−	0.0224104i	0.480466	−	0.877013i	$-0.340467\pi$
$277$	−0.646026	−	0.372983i	−0.0388159	−	0.0224104i	−0.519282	+	0.854603i	$0.673801\pi$
$278$	−10.8963	+	8.44025i	−0.653518	+	0.506213i
$279$	−3.87298	−	2.23607i	−0.231869	−	0.133870i
$280$	−24.9244	−	2.93511i	−1.48952	−	0.175407i
$281$		−	12.1884i		−	0.727097i	−0.931575	−	0.363549i	$-0.881565\pi$
$281$		−	12.1884i		−	0.727097i	0.931575	−	0.363549i	$-0.118435\pi$
$282$	−5.56036	+	0.757843i	−0.331115	+	0.0451289i
$283$	17.8565	−	10.3095i	1.06146	−	0.612835i	0.135625	−	0.990760i	$-0.456696\pi$
$283$	17.8565	−	10.3095i	1.06146	−	0.612835i	0.925836	+	0.377926i	$0.123362\pi$
$284$	2.66340	+	9.58930i	0.158044	+	0.569020i
$285$			1.12702i			0.0667587i
$286$	−2.07556	−	1.51556i	−0.122730	−	0.0896168i
$287$	4.87298			0.287643
$288$	4.40822	−	3.54508i	0.259757	−	0.208896i
$289$	−8.74597	−	15.1485i	−0.514469	−	0.891086i
$290$	4.21627	+	30.9351i	0.247588	+	1.81657i
$291$	−17.3205			−1.01535
$292$	18.4019	−	18.7406i	1.07689	−	1.09671i
$293$	3.07008	−	5.31754i	0.179356	−	0.310654i	−0.762304	−	0.647219i	$-0.775932\pi$
$293$	3.07008	−	5.31754i	0.179356	−	0.310654i	0.941660	+	0.336565i	$0.109265\pi$
$294$	9.77829	−	7.57423i	0.570281	−	0.441738i
$295$	−2.74597	+	4.75615i	−0.159876	+	0.276914i
$296$	−16.3522	−	12.1957i	−0.950450	−	0.708863i
$297$	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
$302$	−14.2635	−	5.83207i	−0.820771	−	0.335598i
$303$	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
$306$	8.22957	−	1.12164i	0.470453	−	0.0641199i
$307$	18.8326			1.07483			0.537415	−	0.843318i	$-0.319401\pi$
$307$	18.8326			1.07483			0.537415	+	0.843318i	$0.319401\pi$
$308$	2.80252	−	2.85410i	0.159688	−	0.162628i
$309$	9.19628	−	5.30948i	0.523158	−	0.302045i
$310$	−13.0902	−	5.35233i	−0.743472	−	0.303992i
$311$	12.6190			0.715555			0.357778	−	0.933807i	$-0.383535\pi$
$311$	12.6190			0.715555			0.357778	+	0.933807i	$0.383535\pi$
$312$	10.0615	−	1.66312i	0.569621	−	0.0941556i
$313$	4.00000			0.226093			0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000			0.226093			0.113047	+	0.993590i	$0.463939\pi$
$314$	−1.64155	−	0.671200i	−0.0926381	−	0.0378780i
$315$	7.68423	−	4.43649i	0.432957	−	0.249968i
$316$	−19.9787	−	19.6176i	−1.12389	−	1.10358i
$317$	−18.5485			−1.04179			−0.520895	−	0.853621i	$-0.674402\pi$
$317$	−18.5485			−1.04179			−0.520895	+	0.853621i	$0.674402\pi$
$318$	−11.0321	+	1.50361i	−0.618649	+	0.0843180i
$319$	−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
$322$	−46.0892	−	18.8451i	−2.56845	−	1.05019i
$323$	−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
$328$	−2.07658	+	2.78430i	−0.114660	+	0.153737i
$329$	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	−0.969759	−	0.244064i	$-0.921519\pi$
$331$	−4.97615	+	8.61895i	−0.273514	+	0.473740i	0.696245	+	0.717804i	$0.254853\pi$
$332$	−4.22419	−	4.14784i	−0.231833	−	0.227642i
$333$	7.21222			0.395227
$334$	−1.79224	−	13.1498i	−0.0980668	−	0.719524i
$335$	2.18246	+	3.78013i	0.119240	+	0.206530i
$336$	0.289470	+	15.8698i	0.0157919	+	0.865770i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	17.2722	+	6.29837i	0.939486	+	0.342586i
$339$			9.87298i			0.536227i
$340$	25.3068	−	7.02889i	1.37245	−	0.381195i
$341$	1.95205	−	1.12702i	0.105709	−	0.0610314i
$342$	0.706258	−	0.0962587i	0.0381901	−	0.00520508i
$343$			6.92820i			0.374088i
$344$	−24.9244	−	2.93511i	−1.34383	−	0.158251i
$345$	−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	0.325096	−	0.945681i	$-0.394603\pi$
$347$	−6.17218	−	3.56351i	−0.331340	−	0.191299i	−0.656436	+	0.754382i	$0.727937\pi$
$348$	19.0257	−	5.28435i	1.01989	−	0.283271i
$349$	13.6364	+	23.6190i	0.729940	+	1.26429i	0.956908	+	0.290391i	$0.0937854\pi$
$349$	13.6364	+	23.6190i	0.729940	+	1.26429i	−0.226968	+	0.973902i	$0.572881\pi$
$350$		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	$0.594582\pi$
$354$	3.21503	+	1.31457i	0.170877	+	0.0698685i
$355$	−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
$358$	−0.979173	−	7.18428i	−0.0517509	−	0.379701i
$359$			13.9204i			0.734692i	0.930084	+	0.367346i	$0.119733\pi$
$359$			13.9204i			0.734692i	−0.930084	+	0.367346i	$0.880267\pi$
$360$	−0.739674	+	6.28115i	−0.0389842	+	0.331046i
$361$	9.37298	+	16.2345i	0.493315	+	0.854446i
$362$	0.976483	+	0.399266i	0.0513228	+	0.0209850i
$363$		−	10.7460i		−	0.564017i
$364$	−13.5989	+	25.1766i	−0.712778	+	1.31961i
$365$			29.3649i			1.53703i
$366$	0.535233	−	1.30902i	0.0279771	−	0.0684234i
$367$	−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	$0.838476\pi$
$368$	30.4082	−	18.3036i	1.58514	−	0.954140i
$369$		−	1.22803i		−	0.0639289i
$370$	22.5981	−	3.07999i	1.17482	−	0.160121i
$371$	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	−0.376710	−	0.926331i	$-0.622945\pi$
$373$	−26.4068	−	15.2460i	−1.36729	−	0.789406i	−0.990581	+	0.136925i	$0.956278\pi$
$374$	−1.58434	+	3.87480i	−0.0819240	+	0.200361i
$375$	−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	0.690256	−	0.723565i	$-0.257498\pi$
$379$	−5.48017	−	9.49193i	−0.281497	−	0.487568i	−0.971754	+	0.235997i	$0.924164\pi$
$380$	2.17182	−	0.603217i	0.111412	−	0.0309444i
$381$	−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	$0.864604\pi$
$384$	−9.19098	−	6.59741i	−0.469025	−	0.336673i
$385$			4.47214i			0.227921i
$386$	−1.56993	−	11.5187i	−0.0799073	−	0.586287i
$387$	7.68423	−	4.43649i	0.390611	−	0.225520i
$388$	9.27051	+	33.3775i	0.470639	+	1.69449i
$389$		−	11.6190i		−	0.589104i	−0.955635	−	0.294552i	$-0.904830\pi$
$389$		−	11.6190i		−	0.589104i	0.955635	−	0.294552i	$-0.0951704\pi$
$390$	−6.72376	+	9.20820i	−0.340471	+	0.466276i
$391$	52.1109			2.63536
$392$	−19.8296	−	14.7893i	−1.00155	−	0.746971i
$393$	5.87298	+	10.1723i	0.296253	+	0.513125i
$394$	−3.44159	+	0.469067i	−0.173385	+	0.0236313i
$395$	31.3050			1.57512
$396$	−0.719258	−	0.706258i	−0.0361441	−	0.0354908i
$397$	−3.74812	+	6.49193i	−0.188113	+	0.325821i	−0.944621	−	0.328163i	$-0.893570\pi$
$397$	−3.74812	+	6.49193i	−0.188113	+	0.325821i	0.756508	+	0.653984i	$0.226904\pi$
$398$	−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
$406$	−20.9689	+	51.2836i	−1.04067	+	2.54516i
$407$	−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	$0.622167\pi$
$410$	−0.524433	−	3.84781i	−0.0258999	−	0.190030i
$411$	−0.219999			−0.0108518
$412$	−15.1538	−	14.8799i	−0.746573	−	0.733080i
$413$	−8.44025	+	4.87298i	−0.415318	+	0.239784i
$414$	−4.74911	+	11.6149i	−0.233406	+	0.570841i
$415$	6.61895			0.324911
$416$	−8.59017	−	18.4989i	−0.421168	−	0.906983i
$417$	−9.74597			−0.477262
$418$	−0.135967	+	0.332534i	−0.00665037	+	0.0162648i
$419$	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	$0.114296\pi$
$420$	−12.6622	−	12.4333i	−0.617852	−	0.606685i
$421$	12.1244			0.590905			0.295452	−	0.955357i	$-0.404530\pi$
$421$	12.1244			0.590905			0.295452	+	0.955357i	$0.404530\pi$
$422$	2.67376	+	19.6176i	0.130157	+	0.954971i
$423$	−3.43649	−	1.98406i	−0.167088	−	0.0964683i
$424$	8.80226	+	20.4546i	0.427476	+	0.993364i
$425$		0			0
$426$	−2.66340	+	6.51387i	−0.129042	+	0.315598i
$427$	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	$0.209005\pi$
$432$	3.99933	−	0.0729490i	0.192418	−	0.00350976i
$433$	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
$436$	−3.50493	−	3.44159i	−0.167856	−	0.164822i
$437$	4.47214			0.213931
$438$	18.4019	−	2.50806i	0.879276	−	0.119840i
$439$	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	$0.701422\pi$
$440$	−2.55527	−	1.90577i	−0.121818	−	0.0908538i
$441$	8.74597			0.416475
$442$	3.20127	−	29.7749i	0.152269	−	1.41625i
$443$		−	40.7298i		−	1.93513i	−0.252617	−	0.967566i	$-0.581291\pi$
$443$		−	40.7298i		−	1.93513i	0.252617	−	0.967566i	$-0.418709\pi$
$444$	−3.86022	−	13.8983i	−0.183198	−	0.659585i
$445$	−3.90410	+	2.25403i	−0.185072	+	0.106851i
$446$	2.75482	+	20.2124i	0.130445	+	0.957084i
$447$		−	8.72427i		−	0.412644i
$448$	30.4270	−	9.05189i	1.43754	−	0.427661i
$449$	−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
$452$	19.0257	−	5.28435i	0.894896	−	0.248555i
$453$	−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	$0.976257\pi$
$458$	8.49547	−	20.7773i	0.396967	−	0.970861i
$459$	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	$-0.510826\pi$
$461$	18.2185	−	31.5554i	0.848522	−	1.46968i	0.882527	−	0.470262i	$-0.155841\pi$
$462$	2.80252	−	0.381966i	0.130385	−	0.0177707i
$463$		−	18.3926i		−	0.854775i	−0.904069	−	0.427387i	$-0.859434\pi$
$463$		−	18.3926i		−	0.854775i	0.904069	−	0.427387i	$-0.140566\pi$
$464$	−20.3664	−	33.8352i	−0.945487	−	1.57076i
$465$	−5.00000	−	8.66025i	−0.231869	−	0.401610i
$466$	11.7751	−	28.7984i	0.545472	−	1.33406i
$467$			12.3649i			0.572180i	0.958203	+	0.286090i	$0.0923557\pi$
$467$			12.3649i			0.572180i	−0.958203	+	0.286090i	$0.907644\pi$
$468$	6.34471	+	3.42705i	0.293284	+	0.158415i
$469$			7.74597i			0.357676i
$470$	−11.6149	−	4.74911i	−0.535755	−	0.219060i
$471$	−0.627017	−	1.08602i	−0.0288914	−	0.0500414i
$472$	0.812448	−	6.89913i	0.0373960	−	0.317558i
$473$			4.47214i			0.205629i
$474$	−2.67376	−	19.6176i	−0.122810	−	0.901067i
$475$		0			0
$476$	45.1293	+	11.6523i	2.06850	+	0.534084i
$477$	−6.81820	−	3.93649i	−0.312184	−	0.180240i
$478$	1.97930	+	0.809300i	0.0905311	+	0.0370165i
$479$	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
$484$	−20.7080	+	5.75160i	−0.941274	+	0.261436i
$485$	−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	$0.927459\pi$
$488$	−2.80902	−	0.330792i	−0.127158	−	0.0149743i
$489$		−	16.8805i		−	0.763363i
$490$	27.4038	−	3.73497i	1.23798	−	0.168729i
$491$	−32.7850	+	18.9284i	−1.47957	+	0.854228i	−0.999732	−	0.0231316i	$-0.992636\pi$
$491$	−32.7850	+	18.9284i	−1.47957	+	0.854228i	−0.479834	+	0.877359i	$0.659303\pi$
$492$	−2.36648	+	0.657284i	−0.106689	+	0.0296327i
$493$		−	57.9839i		−	2.61146i
$494$	0.274732	−	2.55527i	0.0123608	−	0.114967i
$495$	1.12702			0.0506556
$496$	17.8856	−	0.326238i	0.803086	−	0.0146485i
$497$	−9.87298	−	17.1005i	−0.442864	−	0.767063i
$498$	−0.565326	−	4.14784i	−0.0253329	−	0.185869i
$499$	2.01607			0.0902516			0.0451258	−	0.998981i	$-0.485631\pi$
$499$	2.01607			0.0902516			0.0451258	+	0.998981i	$0.485631\pi$
$500$	15.9549	+	15.6665i	0.713525	+	0.700629i
$501$	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	$0.318701\pi$
$504$	−6.71002	+	8.99685i	−0.298888	+	0.400752i
$505$	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	0.946358	−	0.323121i	$-0.104732\pi$
$509$	4.36214	+	7.55544i	0.193348	+	0.334889i	−0.753010	+	0.658010i	$0.771399\pi$
$510$	17.1905	+	7.02889i	0.761209	+	0.311244i
$511$	−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
$514$	21.5302	−	2.93444i	0.949657	−	0.129433i
$515$	23.7447			1.04632
$516$	−12.6622	−	12.4333i	−0.557422	−	0.547347i
$517$	1.73205	−	1.00000i	0.0761755	−	0.0439799i
$518$	37.4627	+	15.3178i	1.64602	+	0.673026i
$519$	−17.4919			−0.767811
$520$	21.3435	+	8.02850i	0.935973	+	0.352073i
$521$	5.61895			0.246171			0.123085	−	0.992396i	$-0.460721\pi$
$521$	5.61895			0.246171			0.123085	+	0.992396i	$0.460721\pi$
$522$	12.9239	+	5.28435i	0.565664	+	0.231290i
$523$	−29.7609	+	17.1825i	−1.30135	+	0.751336i	−0.980636	−	0.195839i	$-0.937257\pi$
$523$	−29.7609	+	17.1825i	−1.30135	+	0.751336i	−0.320717	+	0.947175i	$0.603924\pi$
$524$	16.4591	−	16.7621i	0.719021	−	0.732255i
$525$		0			0
$526$	−1.57924	+	0.215241i	−0.0688582	+	0.00938495i
$527$	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
$530$	−23.0446	−	9.42253i	−1.00099	−	0.409288i
$531$	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
$536$	−4.42585	−	3.30088i	−0.191168	−	0.142576i
$537$	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
$540$	−3.13331	+	3.19098i	−0.134836	+	0.137318i
$541$	−29.4449			−1.26593			−0.632967	−	0.774179i	$-0.718163\pi$
$541$	−29.4449			−1.26593			−0.632967	+	0.774179i	$0.718163\pi$
$542$	5.78620	+	42.4538i	0.248538	+	1.82355i
$543$	0.372983	+	0.646026i	0.0160062	+	0.0277236i
$544$	−25.8894	+	20.8202i	−1.11000	+	0.892660i
$545$	5.49193			0.235249
$546$	−18.5038	+	8.18561i	−0.791890	+	0.350312i
$547$		−	24.3649i		−	1.04177i	−0.853627	−	0.520884i	$-0.825602\pi$
$547$		−	24.3649i		−	1.04177i	0.853627	−	0.520884i	$-0.174398\pi$
$548$	0.117751	+	0.423950i	0.00503007	+	0.0181102i
$549$	0.866025	−	0.500000i	0.0369611	−	0.0213395i
$550$		0			0
$551$		−	4.97615i		−	0.211991i
$552$	24.9244	+	2.93511i	1.06085	+	0.124927i
$553$	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
$556$	5.21636	+	18.7810i	0.221223	+	0.796491i
$557$	−2.85008	−	4.93649i	−0.120762	−	0.209166i	0.799306	−	0.600924i	$-0.205200\pi$
$557$	−2.85008	−	4.93649i	−0.120762	−	0.209166i	−0.920068	+	0.391758i	$0.871867\pi$
$558$	−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
$562$	−15.9548	−	6.52362i	−0.673012	−	0.275182i
$563$	−21.6367	−	12.4919i	−0.911877	−	0.526472i	−0.0308422	−	0.999524i	$-0.509819\pi$
$563$	−21.6367	−	12.4919i	−0.911877	−	0.526472i	−0.881034	+	0.473052i	$0.843152\pi$
$564$	−1.98406	+	7.68423i	−0.0835440	+	0.323564i
$565$	−11.0383	+	19.1190i	−0.464386	+	0.804340i
$566$	−3.93787	−	28.8925i	−0.165521	−	1.21444i
$567$		−	3.96812i		−	0.166645i
$568$	13.9781	+	1.64607i	0.586508	+	0.0690677i
$569$	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	$0.528889\pi$
$570$	1.47528	+	0.603217i	0.0617928	+	0.0252660i
$571$		−	16.6190i		−	0.695481i	−0.937591	−	0.347741i	$-0.886949\pi$
$571$		−	16.6190i		−	0.695481i	0.937591	−	0.347741i	$-0.113051\pi$
$572$	−3.09480	+	1.90577i	−0.129400	+	0.0796841i
$573$			19.7460i			0.824900i
$574$	2.60818	−	6.37882i	0.108863	−	0.266247i
$575$		0			0
$576$	−2.28115	−	7.66788i	−0.0950480	−	0.319495i
$577$			18.6126i			0.774851i	0.921901	+	0.387426i	$0.126636\pi$
$577$			18.6126i			0.774851i	−0.921901	+	0.387426i	$0.873364\pi$
$578$	−24.5107	+	3.34066i	−1.01951	+	0.138953i
$579$	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
$582$	−9.27051	+	22.6728i	−0.384275	+	0.939819i
$583$	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	0.943437	−	0.331553i	$-0.107573\pi$
$587$	4.47214	+	7.74597i	0.184585	+	0.319710i	−0.758852	+	0.651263i	$0.774239\pi$
$588$	−4.68113	−	16.8539i	−0.193047	−	0.695044i
$589$	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
$592$	−24.7166	+	14.8777i	−1.01585	+	0.611469i
$593$		−	19.5566i		−	0.803092i	−0.915839	−	0.401546i	$-0.868473\pi$
$593$		−	19.5566i		−	0.803092i	0.915839	−	0.401546i	$-0.131527\pi$
$594$	−0.0962587	−	0.706258i	−0.00394954	−	0.0289781i
$595$	−45.1293	+	26.0554i	−1.85012	+	1.06817i
$596$	−16.8121	+	4.66952i	−0.688651	+	0.191271i
$597$		−	6.87298i		−	0.281292i
$598$	36.5392	+	26.6807i	1.49420	+	1.09105i
$599$	−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	$0.724137\pi$
$602$	49.3370	−	6.72433i	2.01083	−	0.274063i
$603$	1.95205			0.0794936
$604$	−15.2686	+	15.5496i	−0.621269	+	0.632705i
$605$	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	$0.0372114\pi$
$608$	−2.22182	+	1.78678i	−0.0901066	+	0.0724636i
$609$	−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	0.678422	−	0.734673i	$-0.262664\pi$
$613$	−7.35423	−	12.7379i	−0.297035	−	0.514479i	−0.975456	+	0.220194i	$0.929331\pi$
$614$	10.0798	−	24.6521i	0.406788	−	0.994879i
$615$	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	$0.706937\pi$
$618$	−2.02804	−	14.8799i	−0.0815797	−	0.598557i
$619$	22.2326			0.893605			0.446803	−	0.894633i	$-0.352563\pi$
$619$	22.2326			0.893605			0.446803	+	0.894633i	$0.352563\pi$
$620$	−14.0126	+	14.2705i	−0.562759	+	0.573117i
$621$	−7.68423	+	4.43649i	−0.308357	+	0.178030i
$622$	6.75408	−	16.5184i	0.270814	−	0.662328i
$623$	−8.00000			−0.320513
$624$	3.20820	−	14.0608i	0.128431	−	0.562884i
$625$	−25.0000			−1.00000
$626$	2.14093	−	5.23607i	0.0855689	−	0.209275i
$627$	−0.219999	+	0.127017i	−0.00878593	+	0.00507256i
$628$	−1.75722	+	1.78957i	−0.0701209	+	0.0714116i
$629$	−42.3573			−1.68889
$630$	−1.69459	−	12.4333i	−0.0675140	−	0.495356i
$631$	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
$634$	−9.92779	+	24.2804i	−0.394283	+	0.964296i
$635$	−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
$640$	−10.4221	−	23.0517i	−0.411971	−	0.911197i
$641$	−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	−0.808422	−	0.588603i	$-0.799678\pi$
$643$	2.67607	−	4.63508i	0.105534	−	0.182790i	0.913956	+	0.405813i	$0.133012\pi$
$644$	−49.3370	+	50.2451i	−1.94415	+	1.97993i
$645$	19.8406			0.781223
$646$	−4.14784	+	0.565326i	−0.163195	+	0.0222424i
$647$	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	$0.729816\pi$
$648$	2.26728	+	1.69098i	0.0890673	+	0.0664281i
$649$	−1.23790			−0.0485918
$650$		0			0
$651$		−	17.7460i		−	0.695519i
$652$	−32.5296	+	9.03501i	−1.27396	+	0.353838i
$653$	16.6605	−	9.61895i	0.651976	−	0.376419i	−0.137237	−	0.990538i	$-0.543822\pi$
$653$	16.6605	−	9.61895i	0.651976	−	0.376419i	0.789213	+	0.614120i	$0.210489\pi$
$654$	−0.469067	−	3.44159i	−0.0183420	−	0.134577i
$655$			26.2648i			1.02625i
$656$	2.53324	+	4.20853i	0.0989064	+	0.164316i
$657$	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	$0.666667\pi$
$660$	−0.603217	−	2.17182i	−0.0234802	−	0.0845379i
$661$	−16.2345	−	28.1190i	−0.631448	−	1.09370i	−0.987256	−	0.159141i	$-0.949127\pi$
$661$	−16.2345	−	28.1190i	−0.631448	−	1.09370i	0.355808	−	0.934559i	$-0.384206\pi$
$662$	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
$666$	3.86022	−	9.44092i	0.149580	−	0.365828i
$667$	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
$670$	6.11638	−	0.833625i	0.236296	−	0.0322057i
$671$			0.504017i			0.0194574i
$672$	20.9288	+	8.11514i	0.807347	+	0.313048i
$673$	−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	$0.974328\pi$
$674$	−6.95803	+	17.0172i	−0.268013	+	0.655479i
$675$		0			0
$676$	17.4894	−	19.2386i	0.672668	−	0.739945i
$677$			15.7460i			0.605167i	0.953123	+	0.302583i	$0.0978491\pi$
$677$			15.7460i			0.605167i	−0.953123	+	0.302583i	$0.902151\pi$
$678$	12.9239	+	5.28435i	0.496340	+	0.202944i
$679$	−34.3649	−	59.5218i	−1.31880	−	2.28424i
$680$	4.34409	−	36.8891i	0.166588	−	1.41463i
$681$			1.95205i			0.0748027i
$682$	−0.430482	−	3.15848i	−0.0164840	−	0.120945i
$683$	4.25214	−	7.36492i	0.162703	−	0.281811i	−0.773134	−	0.634243i	$-0.781312\pi$
$683$	4.25214	−	7.36492i	0.162703	−	0.281811i	0.935837	+	0.352432i	$0.114645\pi$
$684$	0.252009	−	0.976025i	0.00963579	−	0.0373193i
$685$	−0.426027	−	0.245967i	−0.0162776	−	0.00939790i
$686$	9.06914	+	3.70820i	0.346261	+	0.141580i
$687$	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	$0.134451\pi$
$691$	21.3206	+	36.9284i	0.811075	+	1.40482i	−0.101037	+	0.994883i	$0.532216\pi$
$692$	9.36226	+	33.7078i	0.355900	+	1.28138i
$693$	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
$696$	3.26591	−	27.7334i	0.123794	−	1.05123i
$697$			7.21222i			0.273182i
$698$	38.2163	−	5.20864i	1.44651	−	0.197150i
$699$	19.0526	−	11.0000i	0.720634	−	0.416058i
$700$		0			0
$701$			43.7460i			1.65226i	0.563478	+	0.826131i	$0.309463\pi$
$701$			43.7460i			1.65226i	−0.563478	+	0.826131i	$0.690537\pi$
$702$	2.06284	+	4.66312i	0.0778570	+	0.175998i
$703$	−3.63508			−0.137100
$704$	3.92183	+	0.936667i	0.147810	+	0.0353020i
$705$	−4.43649	−	7.68423i	−0.167088	−	0.289405i
$706$	5.25066	+	38.5245i	0.197611	+	1.44989i
$707$	31.2409			1.17494
$708$	3.44159	−	3.50493i	0.129343	−	0.131723i
$709$	−24.8947	+	43.1190i	−0.934941	+	1.61937i	−0.160203	+	0.987084i	$0.551215\pi$
$709$	−24.8947	+	43.1190i	−0.934941	+	1.61937i	−0.774738	+	0.632282i	$0.782118\pi$
$710$	−12.4404	+	9.63628i	−0.466879	+	0.361643i
$711$	7.00000	−	12.1244i	0.262521	−	0.454699i
$712$	3.40914	−	4.57100i	0.127763	−	0.171305i
$713$	−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
$718$	18.2221	+	7.45067i	0.680042	+	0.278057i
$719$	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
$722$	26.2679	−	3.58016i	0.977592	−	0.133240i
$723$	−15.5885			−0.579741
$724$	1.04529	−	1.06453i	0.0388480	−	0.0395630i
$725$		0			0
$726$	−14.0667	−	5.75160i	−0.522062	−	0.213462i
$727$	−25.1270			−0.931909			−0.465955	−	0.884809i	$-0.654289\pi$
$727$	−25.1270			−0.931909			−0.465955	+	0.884809i	$0.654289\pi$
$728$	25.6779	+	31.2766i	0.951688	+	1.15919i
$729$	−1.00000			−0.0370370
$730$	38.4392	+	15.7171i	1.42270	+	0.581715i
$731$	−45.1293	+	26.0554i	−1.66917	+	0.963695i
$732$	−1.42705	−	1.40126i	−0.0527453	−	0.0517920i
$733$	−30.5809			−1.12953			−0.564766	−	0.825251i	$-0.691034\pi$
$733$	−30.5809			−1.12953			−0.564766	+	0.825251i	$0.691034\pi$
$734$	−0.867309	+	0.118209i	−0.0320130	+	0.00436317i
$735$	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
$738$	−1.60752	−	0.657284i	−0.0591735	−	0.0241950i
$739$	−16.3765	−	28.3649i	−0.602419	−	1.04342i	−0.992454	−	0.122620i	$-0.960870\pi$
$739$	−16.3765	−	28.3649i	−0.602419	−	1.04342i	0.390035	−	0.920800i	$-0.372463\pi$
$740$	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	$0.114157\pi$
$744$	10.1396	+	7.56231i	0.371736	+	0.277248i
$745$	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
$748$	4.22419	+	4.14784i	0.154452	+	0.151660i
$749$	−3.46410			−0.126576
$750$	2.13525	+	15.6665i	0.0779685	+	0.572061i
$751$	−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	$0.946804\pi$
$752$	15.8698	−	0.289470i	0.578713	−	0.0105559i
$753$	15.2379			0.555300
$754$	29.6876	−	40.6573i	1.08116	−	1.48065i
$755$		−	24.3649i		−	0.886730i
$756$	−7.64677	+	2.12387i	−0.278110	+	0.0772444i
$757$	−2.39205	+	1.38105i	−0.0869405	+	0.0501951i	−0.542840	−	0.839836i	$-0.682651\pi$
$757$	−2.39205	+	1.38105i	−0.0869405	+	0.0501951i	0.455899	+	0.890031i	$0.349318\pi$
$758$	−15.3583	+	2.09324i	−0.557838	+	0.0760299i
$759$		−	4.47214i		−	0.162328i
$760$	0.372808	−	3.16581i	0.0135232	−	0.114836i
$761$	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
$764$	38.0515	−	10.5687i	1.37665	−	0.382362i
$765$	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	$0.163010\pi$
$770$	5.85410	+	2.39364i	0.210967	+	0.0862606i
$771$	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	−0.837551	−	0.546359i	$-0.816014\pi$
$773$	1.51205	−	2.61895i	0.0543847	−	0.0941971i	0.891936	+	0.452161i	$0.149347\pi$
$774$	−1.69459	−	12.4333i	−0.0609107	−	0.446907i
$775$		0			0
$776$	48.6536	+	5.72949i	1.74656	+	0.205677i
$777$	14.3095	+	24.7847i	0.513350	+	0.889148i
$778$	−15.2094	−	6.21885i	−0.545284	−	0.222956i
$779$			0.618950i			0.0221762i
$780$	8.45492	+	13.7301i	0.302735	+	0.491615i
$781$		−	2.50807i		−	0.0897457i
$782$	27.8915	−	68.2140i	0.997397	−	2.43933i
$783$	4.93649	+	8.55025i	0.176416	+	0.305561i
$784$	−29.9729	+	18.0416i	−1.07046	+	0.644341i
$785$		−	2.80410i		−	0.100083i
$786$	16.4591	−	2.24328i	0.587078	−	0.0800151i
$787$	3.24410	−	5.61895i	0.115640	−	0.200294i	−0.802396	−	0.596793i	$-0.796442\pi$
$787$	3.24410	−	5.61895i	0.115640	−	0.200294i	0.918035	+	0.396499i	$0.129775\pi$
$788$	−1.22803	+	4.75615i	−0.0437469	+	0.169431i
$789$	−0.976025	−	0.563508i	−0.0347474	−	0.0200614i
$790$	16.7554	−	40.9787i	0.596132	−	1.45796i
$791$	−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
$796$	−13.2446	+	3.67865i	−0.469442	+	0.130386i
$797$	−27.2728	−	15.7460i	−0.966053	−	0.557751i	−0.0680221	−	0.997684i	$-0.521669\pi$
$797$	−27.2728	−	15.7460i	−0.966053	−	0.557751i	−0.898031	+	0.439933i	$0.855002\pi$
$798$	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
$802$	0.703601	+	5.16238i	0.0248450	+	0.182290i
$803$	−5.73218	+	3.30948i	−0.202284	+	0.116789i
$804$	−1.04480	−	3.76170i	−0.0368473	−	0.132665i
$805$		−	78.7298i		−	2.77486i
$806$	9.22531	+	20.8541i	0.324948	+	0.734554i
$807$	19.7460			0.695091
$808$	−13.3131	+	17.8503i	−0.468353	+	0.627971i
$809$	−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	$0.996330\pi$
$810$	−3.13331	+	0.427051i	−0.110093	+	0.0150050i
$811$	36.2171			1.27175			0.635877	−	0.771790i	$-0.280639\pi$
$811$	36.2171			1.27175			0.635877	+	0.771790i	$0.280639\pi$
$812$	55.9078	+	54.8973i	1.96198	+	1.92652i
$813$	−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
$816$	−23.4880	+	0.428428i	−0.822245	+	0.0149980i
$817$	−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	$0.204239\pi$
$821$	26.3288	+	45.6028i	0.918881	+	1.59155i	0.117764	+	0.993042i	$0.462427\pi$
$822$	−0.117751	+	0.287983i	−0.00410703	+	0.0100446i
$823$	−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
$826$	1.86131	+	13.6566i	0.0647634	+	0.475175i
$827$	−35.2091			−1.22434			−0.612169	−	0.790727i	$-0.709703\pi$
$827$	−35.2091			−1.22434			−0.612169	+	0.790727i	$0.709703\pi$
$828$	12.6622	+	12.4333i	0.440042	+	0.432089i
$829$	26.1868	−	15.1190i	0.909505	−	0.525103i	0.0292330	−	0.999573i	$-0.490694\pi$
$829$	26.1868	−	15.1190i	0.909505	−	0.525103i	0.880272	+	0.474470i	$0.157360\pi$
$830$	3.54268	−	8.66432i	0.122968	−	0.300743i
$831$	−0.745967			−0.0258773
$832$	−28.8131	+	1.34346i	−0.998915	+	0.0465761i
$833$	−51.3649			−1.77969
$834$	−5.21636	+	12.7576i	−0.180628	+	0.441761i
$835$	18.1726	−	10.4919i	0.628887	−	0.363088i
$836$	0.362518	+	0.355966i	0.0125380	+	0.0123114i
$837$	−4.47214			−0.154580
$838$	−4.96556	−	36.4327i	−0.171532	−	1.25855i
$839$	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
$842$	6.48936	−	15.8710i	0.223638	−	0.546950i
$843$	−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
$848$	31.4867	−	0.574326i	1.08126	−	0.0197224i
$849$	10.3095	−	17.8565i	0.353820	−	0.612835i
$850$		0			0
$851$	31.9970	−	55.4204i	1.09684	−	1.89979i
$852$	7.10122	+	6.97288i	0.243284	+	0.238887i
$853$	25.5408			0.874499			0.437250	−	0.899340i	$-0.355953\pi$
$853$	25.5408			0.874499			0.437250	+	0.899340i	$0.355953\pi$
$854$	5.56036	−	0.757843i	0.190272	−	0.0259329i
$855$	0.563508	+	0.976025i	0.0192716	+	0.0333794i
$856$	1.47620	−	1.97930i	0.0504555	−	0.0676511i
$857$	−15.6190			−0.533533			−0.266767	−	0.963761i	$-0.585955\pi$
$857$	−15.6190			−0.533533			−0.266767	+	0.963761i	$0.585955\pi$
$858$	−2.55527	−	0.274732i	−0.0872354	−	0.00937920i
$859$			43.6028i			1.48771i	0.668342	+	0.743854i	$0.267004\pi$
$859$			43.6028i			1.48771i	−0.668342	+	0.743854i	$0.732996\pi$
$860$	−10.6193	−	38.2338i	−0.362117	−	1.30376i
$861$	4.22013	−	2.43649i	0.143822	−	0.0830354i
$862$	−3.01915	−	22.1517i	−0.102833	−	0.754491i
$863$			17.2565i			0.587418i	0.955895	+	0.293709i	$0.0948896\pi$
$863$			17.2565i			0.587418i	−0.955895	+	0.293709i	$0.905110\pi$
$864$	2.04508	−	5.27424i	0.0695752	−	0.179433i
$865$	−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
$868$	−34.1974	+	9.49823i	−1.16073	+	0.322391i
$869$	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
$874$	2.39364	−	5.85410i	0.0809659	−	0.198018i
$875$	−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	−0.818821	−	0.574049i	$-0.805372\pi$
$877$	2.59808	−	4.50000i	0.0877308	−	0.151954i	0.906552	+	0.422095i	$0.138705\pi$
$878$	23.6434	−	3.22245i	0.797927	−	0.108753i
$879$		−	6.14017i		−	0.207103i
$880$	−3.86234	+	2.32486i	−0.130200	+	0.0783710i
$881$	−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	$0.893264\pi$
$882$	4.68113	−	11.4486i	0.157622	−	0.385495i
$883$			50.9839i			1.71574i	0.513864	+	0.857872i	$0.328214\pi$
$883$			50.9839i			1.71574i	−0.513864	+	0.857872i	$0.671786\pi$
$884$	−37.2624	−	20.1270i	−1.25327	−	0.676945i
$885$			5.49193i			0.184609i
$886$	−53.3160	−	21.8000i	−1.79119	−	0.732384i
$887$	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	$0.628454\pi$
$888$	−20.2593	−	2.38575i	−0.679856	−	0.0800604i
$889$		−	8.94427i		−	0.299981i
$890$	0.860964	+	6.31697i	0.0288596	+	0.211745i
$891$	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
$894$	−11.4202	−	4.66952i	−0.381949	−	0.156172i
$895$	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
$904$	3.26591	−	27.7334i	0.108622	−	0.922398i
$905$			1.66803i			0.0554473i
$906$	−15.2686	+	2.08101i	−0.507264	+	0.0691370i
$907$	27.2728	−	15.7460i	0.905579	−	0.522836i	0.0265729	−	0.999647i	$-0.491541\pi$
$907$	27.2728	−	15.7460i	0.905579	−	0.522836i	0.879006	+	0.476811i	$0.158207\pi$
$908$	3.76170	−	1.04480i	0.124836	−	0.0346730i
$909$		−	7.87298i		−	0.261130i
$910$	−44.9843	−	4.83653i	−1.49121	−	0.160329i
$911$	−38.7298			−1.28318			−0.641588	−	0.767049i	$-0.721724\pi$
$911$	−38.7298			−1.28318			−0.641588	+	0.767049i	$0.721724\pi$
$912$	−2.01573	+	0.0367676i	−0.0667476	+	0.00121750i
$913$	0.745967	+	1.29205i	0.0246879	+	0.0427607i
$914$	7.35613	+	53.9725i	0.243319	+	1.78525i
$915$	2.23607			0.0739221
$916$	−22.6508	−	22.2414i	−0.748405	−	0.734878i
$917$	−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	$0.894541\pi$
$920$	44.9843	+	33.5501i	1.48309	+	1.10611i
$921$	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
$926$	−24.0762	−	9.84431i	−0.791192	−	0.323504i
$927$	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	$0.520301\pi$
$930$	−14.0126	+	1.90983i	−0.459491	+	0.0626258i
$931$	−4.40812			−0.144470
$932$	−31.3951	−	30.8277i	−1.02838	−	1.00979i
$933$	10.9283	−	6.30948i	0.357778	−	0.206563i
$934$	16.1859	+	6.61811i	0.529618	+	0.216551i
$935$	−6.61895			−0.216463
$936$	7.88197	−	6.47106i	0.257630	−	0.211513i
$937$	12.2379			0.399795			0.199897	−	0.979817i	$-0.435939\pi$
$937$	12.2379			0.399795			0.199897	+	0.979817i	$0.435939\pi$
$938$	10.1396	+	4.14590i	0.331070	+	0.135368i
$939$	3.46410	−	2.00000i	0.113047	−	0.0652675i
$940$	−12.4333	+	12.6622i	−0.405531	+	0.412995i
$941$	34.6410			1.12926			0.564632	−	0.825342i	$-0.309018\pi$
$941$	34.6410			1.12926			0.564632	+	0.825342i	$0.309018\pi$
$942$	−1.75722	+	0.239499i	−0.0572535	+	0.00780330i
$943$	−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
$946$	5.85410	+	2.39364i	0.190333	+	0.0778238i
$947$	−0.504017	−	0.872983i	−0.0163784	−	0.0283681i	0.857720	−	0.514117i	$-0.171880\pi$
$947$	−0.504017	−	0.872983i	−0.0163784	−	0.0283681i	−0.874098	+	0.485749i	$0.838547\pi$
$948$	−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
$952$	39.4078	−	52.8384i	1.27722	−	1.71250i
$953$	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
$956$	2.11878	−	2.15777i	0.0685261	−	0.0697874i
$957$	−4.97615			−0.160856
$958$	−7.96347	−	58.4286i	−0.257288	−	1.88774i
$959$	−0.436492	−	0.756026i	−0.0140951	−	0.0244133i
$960$	4.15551	−	17.3992i	0.134119	−	0.561556i
$961$	11.0000			0.354839
$962$	−29.7002	−	21.6868i	−0.957572	−	0.699212i
$963$			0.872983i			0.0281315i
$964$	8.34346	+	30.0398i	0.268725	+	0.967515i
$965$	15.9185	−	9.19052i	0.512433	−	0.295853i
$966$	−49.3370	+	6.72433i	−1.58739	+	0.216352i
$967$		−	11.3363i		−	0.364551i	−0.983247	−	0.182276i	$-0.941654\pi$
$967$		−	11.3363i		−	0.364551i	0.983247	−	0.182276i	$-0.0583464\pi$
$968$	−3.55468	+	30.1856i	−0.114252	+	0.970202i
$969$	−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	$0.0542564\pi$
$971$	50.6415	+	29.2379i	1.62516	+	0.938289i	0.639656	+	0.768662i	$0.279077\pi$
$972$	0.535233	+	1.92705i	0.0171676	+	0.0618102i
$973$	−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	$0.165089\pi$
$978$	−22.0969	−	9.03501i	−0.706580	−	0.288908i
$979$	−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
$982$	7.23002	+	53.0472i	0.230719	+	1.69281i
$983$		−	27.2728i		−	0.869868i	−0.900462	−	0.434934i	$-0.856772\pi$
$983$		−	27.2728i		−	0.869868i	0.900462	−	0.434934i	$-0.143228\pi$
$984$	−0.406224	+	3.44957i	−0.0129499	+	0.109968i
$985$	−2.74597	−	4.75615i	−0.0874938	−	0.151544i
$986$	−75.9019	−	31.0349i	−2.41721	−	0.988352i
$987$		−	15.7460i		−	0.501200i
$988$	−3.19784	−	1.72729i	−0.101737	−	0.0549525i
$989$		−	78.7298i		−	2.50346i
$990$	0.603217	−	1.47528i	0.0191715	−	0.0468876i
$991$	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	$0.770411\pi$
$992$	9.14590	−	23.5871i	0.290383	−	0.748892i
$993$			9.95231i			0.315827i
$994$	−27.6692	+	3.77114i	−0.877614	+	0.119613i
$995$	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	0.393491	−	0.919329i	$-0.371267\pi$
$997$	−6.50218	−	3.75403i	−0.205926	−	0.118891i	−0.599417	+	0.800437i	$0.704601\pi$
$998$	1.07907	−	2.63907i	0.0341573	−	0.0835382i
$999$	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.205.3	✓	8
3.2	odd	2		936.2.dg.c.829.2		8
4.3	odd	2		1248.2.ca.a.49.2		8
8.3	odd	2		1248.2.ca.a.49.3		8
8.5	even	2	inner	312.2.bk.a.205.4	yes	8
13.4	even	6	inner	312.2.bk.a.277.4	yes	8
24.5	odd	2		936.2.dg.c.829.1		8
39.17	odd	6		936.2.dg.c.901.1		8
52.43	odd	6		1248.2.ca.a.433.3		8
104.43	odd	6		1248.2.ca.a.433.2		8
104.69	even	6	inner	312.2.bk.a.277.3	yes	8
312.173	odd	6		936.2.dg.c.901.2		8

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

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