LMFDB - Embedded newform 81.2.g.a.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$81 = 3^{4}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	81.g (of order $27$ , degree $18$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	81.13
Dual form			81.2.g.a.25.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.698417 - 0.350758i) q^{2} +(0.295453 - 1.70667i) q^{3} +(-0.829563 - 1.11430i) q^{4} +(0.424677 + 1.41852i) q^{5} +(-0.804976 + 1.08833i) q^{6} +(-1.50560 - 3.49038i) q^{7} +(0.459961 + 2.60857i) q^{8} +(-2.82541 - 1.00848i) q^{9} +(0.200956 - 1.13968i) q^{10} +(4.91819 - 1.16563i) q^{11} +(-2.14683 + 1.08656i) q^{12} +(3.75323 + 2.46854i) q^{13} +(-0.172741 + 2.96584i) q^{14} +(2.54641 - 0.305675i) q^{15} +(-0.203113 + 0.678443i) q^{16} +(-4.30582 + 1.56719i) q^{17} +(1.61958 + 1.69538i) q^{18} +(4.19524 + 1.52694i) q^{19} +(1.22836 - 1.64997i) q^{20} +(-6.40175 + 1.53832i) q^{21} +(-3.84380 - 0.910998i) q^{22} +(-1.36843 + 3.17237i) q^{23} +(4.58785 - 0.0142893i) q^{24} +(2.34559 - 1.54272i) q^{25} +(-1.75546 - 3.04054i) q^{26} +(-2.55592 + 4.52408i) q^{27} +(-2.64032 + 4.57318i) q^{28} +(-0.0379650 - 0.651834i) q^{29} +(-1.88567 - 0.679686i) q^{30} +(-0.653701 + 0.0764066i) q^{31} +(4.01527 - 4.25594i) q^{32} +(-0.536249 - 8.73810i) q^{33} +(3.55696 + 0.415749i) q^{34} +(4.31178 - 3.61801i) q^{35} +(1.22011 + 3.98495i) q^{36} +(0.766165 + 0.642889i) q^{37} +(-2.39444 - 2.53796i) q^{38} +(5.32187 - 5.67616i) q^{39} +(-3.50497 + 1.76026i) q^{40} +(-0.610184 + 0.306446i) q^{41} +(5.01066 + 1.17108i) q^{42} +(-5.75968 - 6.10490i) q^{43} +(-5.37881 - 4.51336i) q^{44} +(0.230661 - 4.43619i) q^{45} +(2.06847 - 1.73565i) q^{46} +(-7.88112 - 0.921171i) q^{47} +(1.09787 + 0.547094i) q^{48} +(-5.11223 + 5.41864i) q^{49} +(-2.17932 + 0.254726i) q^{50} +(1.40250 + 7.81162i) q^{51} +(-0.362857 - 6.23001i) q^{52} +(-2.07469 + 3.59347i) q^{53} +(3.37195 - 2.26318i) q^{54} +(3.74212 + 6.48154i) q^{55} +(8.41238 - 5.53291i) q^{56} +(3.84548 - 6.70874i) q^{57} +(-0.202121 + 0.468568i) q^{58} +(5.12792 + 1.21534i) q^{59} +(-2.45302 - 2.58388i) q^{60} +(-4.05529 + 5.44719i) q^{61} +(0.483356 + 0.175927i) q^{62} +(0.733974 + 11.3801i) q^{63} +(-2.96617 + 1.07960i) q^{64} +(-1.90776 + 6.37236i) q^{65} +(-2.69043 + 6.29093i) q^{66} +(-0.308237 + 5.29223i) q^{67} +(5.31826 + 3.49787i) q^{68} +(5.00987 + 3.27274i) q^{69} +(-4.28047 + 1.01449i) q^{70} +(-1.06500 + 6.03991i) q^{71} +(1.33111 - 7.83415i) q^{72} +(-0.764322 - 4.33469i) q^{73} +(-0.309604 - 0.717743i) q^{74} +(-1.93989 - 4.45894i) q^{75} +(-1.77875 - 5.94144i) q^{76} +(-11.4734 - 15.4114i) q^{77} +(-5.70784 + 2.09764i) q^{78} +(10.0467 + 5.04564i) q^{79} -1.04864 q^{80} +(6.96594 + 5.69875i) q^{81} +0.533651 q^{82} +(1.44915 + 0.727793i) q^{83} +(7.02479 + 5.85731i) q^{84} +(-4.05167 - 5.44234i) q^{85} +(1.88131 + 6.28402i) q^{86} +(-1.12368 - 0.127793i) q^{87} +(5.30281 + 12.2933i) q^{88} +(-0.181087 - 1.02699i) q^{89} +(-1.71713 + 3.01740i) q^{90} +(2.96526 - 16.8168i) q^{91} +(4.67016 - 1.10685i) q^{92} +(-0.0627375 + 1.13822i) q^{93} +(5.18120 + 3.40773i) q^{94} +(-0.384377 + 6.59950i) q^{95} +(-6.07714 - 8.11016i) q^{96} +(-1.43062 + 4.77859i) q^{97} +(5.47110 - 1.99132i) q^{98} +(-15.0715 - 1.66650i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100})$ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.698417	−	0.350758i	−0.493855	−	0.248023i	0.184398	−	0.982852i	$-0.440966\pi$
$2$	−0.698417	−	0.350758i	−0.493855	−	0.248023i	−0.678253	+	0.734828i	$0.737263\pi$
$3$	0.295453	−	1.70667i	0.170580	−	0.985344i
$3$	0.295453	−	1.70667i	0.170580	−	0.985344i
$4$	−0.829563	−	1.11430i	−0.414781	−	0.557148i
$5$	0.424677	+	1.41852i	0.189921	+	0.634382i	0.998915	+	0.0465645i	$0.0148273\pi$
$5$	0.424677	+	1.41852i	0.189921	+	0.634382i	−0.808994	+	0.587817i	$0.799987\pi$
$6$	−0.804976	+	1.08833i	−0.328630	+	0.444309i
$7$	−1.50560	−	3.49038i	−0.569065	−	1.31924i	−0.923299	−	0.384083i	$-0.874518\pi$
$7$	−1.50560	−	3.49038i	−0.569065	−	1.31924i	0.354234	−	0.935157i	$-0.384742\pi$
$8$	0.459961	+	2.60857i	0.162621	+	0.922268i
$9$	−2.82541	−	1.00848i	−0.941805	−	0.336160i
$10$	0.200956	−	1.13968i	0.0635478	−	0.360398i
$11$	4.91819	−	1.16563i	1.48289	−	0.351452i	0.592100	−	0.805865i	$-0.298299\pi$
$11$	4.91819	−	1.16563i	1.48289	−	0.351452i	0.890791	+	0.454413i	$0.150151\pi$
$12$	−2.14683	+	1.08656i	−0.619736	+	0.313664i
$13$	3.75323	+	2.46854i	1.04096	+	0.684649i	0.950332	−	0.311237i	$-0.100743\pi$
$13$	3.75323	+	2.46854i	1.04096	+	0.684649i	0.0906250	+	0.995885i	$0.471114\pi$
$14$	−0.172741	+	2.96584i	−0.0461669	+	0.792655i
$15$	2.54641	−	0.305675i	0.657481	−	0.0789250i
$16$	−0.203113	+	0.678443i	−0.0507782	+	0.169611i
$17$	−4.30582	+	1.56719i	−1.04431	+	0.380099i	−0.806514	−	0.591215i	$-0.798648\pi$
$17$	−4.30582	+	1.56719i	−1.04431	+	0.380099i	−0.237800	+	0.971314i	$0.576426\pi$
$18$	1.61958	+	1.69538i	0.381740	+	0.399604i
$19$	4.19524	+	1.52694i	0.962455	+	0.350305i	0.774995	−	0.631967i	$-0.217752\pi$
$19$	4.19524	+	1.52694i	0.962455	+	0.350305i	0.187460	+	0.982272i	$0.439975\pi$
$20$	1.22836	−	1.64997i	0.274669	−	0.368944i
$21$	−6.40175	+	1.53832i	−1.39698	+	0.335688i
$22$	−3.84380	−	0.910998i	−0.819502	−	0.194225i
$23$	−1.36843	+	3.17237i	−0.285337	+	0.661486i	−0.999249	−	0.0387500i	$-0.987662\pi$
$23$	−1.36843	+	3.17237i	−0.285337	+	0.661486i	0.713912	+	0.700235i	$0.246922\pi$
$24$	4.58785	−	0.0142893i	0.936491	−	0.00291679i
$25$	2.34559	−	1.54272i	0.469118	−	0.308544i
$26$	−1.75546	−	3.04054i	−0.344273	−	0.596299i
$27$	−2.55592	+	4.52408i	−0.491886	+	0.870659i
$28$	−2.64032	+	4.57318i	−0.498974	+	0.864249i
$29$	−0.0379650	−	0.651834i	−0.00704993	−	0.121043i	−0.999997	−	0.00248341i	$-0.999210\pi$
$29$	−0.0379650	−	0.651834i	−0.00704993	−	0.121043i	0.992947	−	0.118559i	$-0.0378275\pi$
$30$	−1.88567	−	0.679686i	−0.344276	−	0.124093i
$31$	−0.653701	+	0.0764066i	−0.117408	+	0.0137230i	−0.174594	−	0.984641i	$-0.555861\pi$
$31$	−0.653701	+	0.0764066i	−0.117408	+	0.0137230i	0.0571859	+	0.998364i	$0.481787\pi$
$32$	4.01527	−	4.25594i	0.709807	−	0.752351i
$33$	−0.536249	−	8.73810i	−0.0933490	−	1.52111i
$34$	3.55696	+	0.415749i	0.610013	+	0.0713003i
$35$	4.31178	−	3.61801i	0.728824	−	0.611556i
$36$	1.22011	+	3.98495i	0.203352	+	0.664158i
$37$	0.766165	+	0.642889i	0.125957	+	0.105690i	0.703590	−	0.710606i	$-0.251579\pi$
$37$	0.766165	+	0.642889i	0.125957	+	0.105690i	−0.577633	+	0.816296i	$0.696024\pi$
$38$	−2.39444	−	2.53796i	−0.388429	−	0.411711i
$39$	5.32187	−	5.67616i	0.852181	−	0.908914i
$40$	−3.50497	+	1.76026i	−0.554185	+	0.278322i
$41$	−0.610184	+	0.306446i	−0.0952947	+	0.0478588i	−0.495808	−	0.868432i	$-0.665128\pi$
$41$	−0.610184	+	0.306446i	−0.0952947	+	0.0478588i	0.400513	+	0.916291i	$0.368832\pi$
$42$	5.01066	+	1.17108i	0.773162	+	0.180701i
$43$	−5.75968	−	6.10490i	−0.878343	−	0.930989i	0.119745	−	0.992805i	$-0.461792\pi$
$43$	−5.75968	−	6.10490i	−0.878343	−	0.930989i	−0.998088	+	0.0618156i	$0.980311\pi$
$44$	−5.37881	−	4.51336i	−0.810886	−	0.680414i
$45$	0.230661	−	4.43619i	0.0343849	−	0.661308i
$46$	2.06847	−	1.73565i	0.304979	−	0.255908i
$47$	−7.88112	−	0.921171i	−1.14958	−	0.134367i	−0.480111	−	0.877207i	$-0.659404\pi$
$47$	−7.88112	−	0.921171i	−1.14958	−	0.134367i	−0.669468	+	0.742841i	$0.733478\pi$
$48$	1.09787	+	0.547094i	0.158463	+	0.0789662i
$49$	−5.11223	+	5.41864i	−0.730318	+	0.774092i
$50$	−2.17932	+	0.254726i	−0.308202	+	0.0360237i
$51$	1.40250	+	7.81162i	0.196389	+	1.09385i
$52$	−0.362857	−	6.23001i	−0.0503192	−	0.863947i
$53$	−2.07469	+	3.59347i	−0.284981	+	0.493601i	−0.972605	−	0.232466i	$-0.925321\pi$
$53$	−2.07469	+	3.59347i	−0.284981	+	0.493601i	0.687624	+	0.726067i	$0.258654\pi$
$54$	3.37195	−	2.26318i	0.458865	−	0.307980i
$55$	3.74212	+	6.48154i	0.504587	+	0.873971i
$56$	8.41238	−	5.53291i	1.12415	−	0.739366i
$57$	3.84548	−	6.70874i	0.509346	−	0.888594i
$58$	−0.202121	+	0.468568i	−0.0265397	+	0.0615261i
$59$	5.12792	+	1.21534i	0.667598	+	0.158224i	0.550421	−	0.834887i	$-0.314467\pi$
$59$	5.12792	+	1.21534i	0.667598	+	0.158224i	0.117177	+	0.993111i	$0.462615\pi$
$60$	−2.45302	−	2.58388i	−0.316684	−	0.333577i
$61$	−4.05529	+	5.44719i	−0.519226	+	0.697442i	−0.981967	−	0.189052i	$-0.939459\pi$
$61$	−4.05529	+	5.44719i	−0.519226	+	0.697442i	0.462741	+	0.886494i	$0.346866\pi$
$62$	0.483356	+	0.175927i	0.0613862	+	0.0223428i
$63$	0.733974	+	11.3801i	0.0924720	+	1.43376i
$64$	−2.96617	+	1.07960i	−0.370771	+	0.134950i
$65$	−1.90776	+	6.37236i	−0.236628	+	0.790394i
$66$	−2.69043	+	6.29093i	−0.331170	+	0.774360i
$67$	−0.308237	+	5.29223i	−0.0376572	+	0.646549i	0.925689	+	0.378286i	$0.123487\pi$
$67$	−0.308237	+	5.29223i	−0.0376572	+	0.646549i	−0.963346	+	0.268263i	$0.913551\pi$
$68$	5.31826	+	3.49787i	0.644933	+	0.424179i
$69$	5.00987	+	3.27274i	0.603118	+	0.393991i
$70$	−4.28047	+	1.01449i	−0.511614	+	0.121255i
$71$	−1.06500	+	6.03991i	−0.126392	+	0.716805i	0.854079	+	0.520143i	$0.174121\pi$
$71$	−1.06500	+	6.03991i	−0.126392	+	0.716805i	−0.980471	+	0.196662i	$0.936990\pi$
$72$	1.33111	−	7.83415i	0.156873	−	0.923263i
$73$	−0.764322	−	4.33469i	−0.0894571	−	0.507337i	−0.996306	−	0.0858796i	$-0.972630\pi$
$73$	−0.764322	−	4.33469i	−0.0894571	−	0.507337i	0.906848	−	0.421457i	$-0.138481\pi$
$74$	−0.309604	−	0.717743i	−0.0359907	−	0.0834359i
$75$	−1.93989	−	4.45894i	−0.223999	−	0.514874i
$76$	−1.77875	−	5.94144i	−0.204037	−	0.681530i
$77$	−11.4734	−	15.4114i	−1.30751	−	1.75629i
$78$	−5.70784	+	2.09764i	−0.646286	+	0.237511i
$79$	10.0467	+	5.04564i	1.13034	+	0.567679i	0.912814	−	0.408375i	$-0.133904\pi$
$79$	10.0467	+	5.04564i	1.13034	+	0.567679i	0.217528	+	0.976054i	$0.430201\pi$
$80$	−1.04864			−0.117242
$81$	6.96594	+	5.69875i	0.773993	+	0.633194i
$82$	0.533651			0.0589319
$83$	1.44915	+	0.727793i	0.159065	+	0.0798857i	0.526551	−	0.850144i	$-0.323485\pi$
$83$	1.44915	+	0.727793i	0.159065	+	0.0798857i	−0.367486	+	0.930029i	$0.619781\pi$
$84$	7.02479	+	5.85731i	0.766467	+	0.639085i
$85$	−4.05167	−	5.44234i	−0.439465	−	0.590305i
$86$	1.88131	+	6.28402i	0.202867	+	0.677623i
$87$	−1.12368	−	0.127793i	−0.120471	−	0.0137009i
$88$	5.30281	+	12.2933i	0.565281	+	1.31047i
$89$	−0.181087	−	1.02699i	−0.0191952	−	0.108861i	0.973705	−	0.227813i	$-0.0731576\pi$
$89$	−0.181087	−	1.02699i	−0.0191952	−	0.108861i	−0.992900	+	0.118952i	$0.962046\pi$
$90$	−1.71713	+	3.01740i	−0.181001	+	0.318062i
$91$	2.96526	−	16.8168i	0.310844	−	1.76288i
$92$	4.67016	−	1.10685i	0.486898	−	0.115397i
$93$	−0.0627375	+	1.13822i	−0.00650557	+	0.118028i
$94$	5.18120	+	3.40773i	0.534400	+	0.351480i
$95$	−0.384377	+	6.59950i	−0.0394362	+	0.677094i
$96$	−6.07714	−	8.11016i	−0.620246	−	0.827740i
$97$	−1.43062	+	4.77859i	−0.145257	+	0.485192i	−0.999392	−	0.0348588i	$-0.988902\pi$
$97$	−1.43062	+	4.77859i	−0.145257	+	0.485192i	0.854135	+	0.520051i	$0.174087\pi$
$98$	5.47110	−	1.99132i	0.552664	−	0.201153i
$99$	−15.0715	−	1.66650i	−1.51474	−	0.167490i
$100$	−3.66486	−	1.33390i	−0.366486	−	0.133390i
$101$	−5.71510	+	7.67671i	−0.568673	+	0.763861i	−0.989695	−	0.143190i	$-0.954264\pi$
$101$	−5.71510	+	7.67671i	−0.568673	+	0.763861i	0.421022	+	0.907050i	$0.361672\pi$
$102$	1.76046	−	5.94770i	0.174311	−	0.588910i
$103$	3.16740	+	0.750687i	0.312093	+	0.0739673i	0.383677	−	0.923467i	$-0.374657\pi$
$103$	3.16740	+	0.750687i	0.312093	+	0.0739673i	−0.0715847	+	0.997435i	$0.522806\pi$
$104$	−4.71300	+	10.9260i	−0.462148	+	1.07138i
$105$	−4.90081	−	8.42772i	−0.478270	−	0.822461i
$106$	2.70944	−	1.78203i	0.263164	−	0.173086i
$107$	−8.40680	−	14.5610i	−0.812716	−	1.40767i	−0.910956	−	0.412503i	$-0.864655\pi$
$107$	−8.40680	−	14.5610i	−0.812716	−	1.40767i	0.0982402	−	0.995163i	$-0.468679\pi$
$108$	7.16145	−	0.904959i	0.689111	−	0.0870797i
$109$	−3.81772	+	6.61249i	−0.365671	+	0.633361i	−0.988884	−	0.148691i	$-0.952494\pi$
$109$	−3.81772	+	6.61249i	−0.365671	+	0.633361i	0.623212	+	0.782053i	$0.285827\pi$
$110$	−0.340106	−	5.83939i	−0.0324278	−	0.556764i
$111$	1.32356	−	1.11764i	0.125627	−	0.106082i
$112$	2.67383	−	0.312526i	0.252653	−	0.0295310i
$113$	6.87571	−	7.28783i	0.646812	−	0.685581i	−0.318129	−	0.948048i	$-0.603054\pi$
$113$	6.87571	−	7.28783i	0.646812	−	0.685581i	0.964941	+	0.262466i	$0.0845359\pi$
$114$	−5.03889	+	3.33666i	−0.471935	+	0.312507i
$115$	−5.08122	−	0.593909i	−0.473826	−	0.0553823i
$116$	−0.694842	+	0.583042i	−0.0645144	+	0.0541340i
$117$	−8.11495	−	10.7597i	−0.750227	−	0.994734i
$118$	−3.15514	−	2.64747i	−0.290454	−	0.243720i
$119$	11.9529	+	12.6694i	1.09572	+	1.16140i
$120$	1.96862	+	6.50189i	0.179710	+	0.593539i
$121$	13.0000	−	6.52883i	1.18182	−	0.593530i
$122$	4.74293	−	2.38199i	0.429404	−	0.215655i
$123$	0.342720	+	1.13192i	0.0309020	+	0.102062i
$124$	0.627425	+	0.665032i	0.0563444	+	0.0597216i
$125$	8.85601	+	7.43107i	0.792105	+	0.664655i
$126$	3.47906	−	8.20553i	0.309939	−	0.731007i
$127$	2.97665	−	2.49770i	0.264135	−	0.221635i	−0.501096	−	0.865392i	$-0.667070\pi$
$127$	2.97665	−	2.49770i	0.264135	−	0.221635i	0.765230	+	0.643757i	$0.222625\pi$
$128$	−9.17279	−	1.07215i	−0.810768	−	0.0947651i
$129$	−12.1207	+	8.02613i	−1.06717	+	0.706662i
$130$	3.56757	−	3.78140i	0.312896	−	0.331651i
$131$	16.5366	−	1.93285i	1.44481	−	0.168874i	0.642732	−	0.766091i	$-0.277801\pi$
$131$	16.5366	−	1.93285i	1.44481	−	0.168874i	0.802080	+	0.597217i	$0.203727\pi$
$132$	−9.29198	+	7.84634i	−0.808763	+	0.682936i
$133$	−0.986757	−	16.9420i	−0.0855627	−	1.46905i
$134$	2.07157	−	3.58807i	0.178956	−	0.309962i
$135$	−7.50294	−	1.70435i	−0.645750	−	0.146687i
$136$	−6.06863	−	10.5112i	−0.520380	−	0.901325i
$137$	−7.74989	+	5.09718i	−0.662118	+	0.435482i	−0.835587	−	0.549358i	$-0.814873\pi$
$137$	−7.74989	+	5.09718i	−0.662118	+	0.435482i	0.173470	+	0.984839i	$0.444502\pi$
$138$	−2.35104	−	4.04299i	−0.200134	−	0.344162i
$139$	6.30605	−	14.6191i	0.534872	−	1.23997i	−0.409866	−	0.912146i	$-0.634424\pi$
$139$	6.30605	−	14.6191i	0.534872	−	1.23997i	0.944738	−	0.327827i	$-0.106316\pi$
$140$	−7.60843	−	1.80323i	−0.643030	−	0.152401i
$141$	−3.90063	+	13.1783i	−0.328493	+	1.10981i
$142$	2.86236	−	3.84482i	0.240204	−	0.322650i
$143$	21.3365	+	7.76585i	1.78425	+	0.649413i
$144$	1.25807	−	1.71205i	0.104839	−	0.142671i
$145$	0.908517	−	0.330673i	0.0754483	−	0.0274609i
$146$	−0.986611	+	3.29551i	−0.0816525	+	0.272738i
$147$	7.73739	+	10.3258i	0.638169	+	0.851659i
$148$	0.0807865	−	1.38705i	0.00664061	−	0.114015i
$149$	−19.5018	−	12.8265i	−1.59765	−	1.05079i	−0.959823	−	0.280607i	$-0.909464\pi$
$149$	−19.5018	−	12.8265i	−1.59765	−	1.05079i	−0.637824	−	0.770182i	$-0.720165\pi$
$150$	−0.209155	+	3.79463i	−0.0170775	+	0.309830i
$151$	−2.26923	+	0.537818i	−0.184667	+	0.0437670i	−0.321909	−	0.946771i	$-0.604324\pi$
$151$	−2.26923	+	0.537818i	−0.184667	+	0.0437670i	0.137242	+	0.990538i	$0.456176\pi$
$152$	−2.05349	+	11.6459i	−0.166560	+	0.944608i
$153$	13.7462	−	0.0856284i	1.11131	−	0.00692265i
$154$	2.60751	+	14.7879i	0.210119	+	1.19165i
$155$	−0.385996	−	0.894840i	−0.0310040	−	0.0718752i
$156$	−10.7397	−	1.22140i	−0.859868	−	0.0977904i
$157$	5.64522	+	18.8563i	0.450538	+	1.50490i	0.818196	+	0.574939i	$0.194974\pi$
$157$	5.64522	+	18.8563i	0.450538	+	1.50490i	−0.367658	+	0.929961i	$0.619840\pi$
$158$	−5.24698	−	7.04792i	−0.417428	−	0.560702i
$159$	5.51988	+	4.60251i	0.437755	+	0.365003i
$160$	7.74233	+	3.88835i	0.612085	+	0.307401i
$161$	13.1331			1.03503
$162$	−2.86624	−	6.42346i	−0.225193	−	0.504675i
$163$	−17.6622			−1.38341			−0.691707	−	0.722179i	$-0.743141\pi$
$163$	−17.6622			−1.38341			−0.691707	+	0.722179i	$0.743141\pi$
$164$	0.847657	+	0.425709i	0.0661909	+	0.0332423i
$165$	12.1674	−	4.47155i	0.947234	−	0.348110i
$166$	−0.756835	−	1.01661i	−0.0587418	−	0.0789039i
$167$	−0.972303	−	3.24772i	−0.0752391	−	0.251316i	0.912093	−	0.409983i	$-0.134465\pi$
$167$	−0.972303	−	3.24772i	−0.0752391	−	0.251316i	−0.987332	+	0.158667i	$0.949280\pi$
$168$	−6.95736	−	15.9918i	−0.536772	−	1.23380i
$169$	2.84400	+	6.59313i	0.218769	+	0.507164i
$170$	0.920811	+	5.22218i	0.0706230	+	0.400523i
$171$	−10.3134	−	8.54507i	−0.788686	−	0.653458i
$172$	−2.02465	+	11.4824i	−0.154378	+	0.875524i
$173$	−18.1755	+	4.30767i	−1.38186	+	0.327506i	−0.853313	−	0.521399i	$-0.825410\pi$
$173$	−18.1755	+	4.30767i	−1.38186	+	0.327506i	−0.528545	+	0.848906i	$0.677262\pi$
$174$	0.739972	+	0.483393i	0.0560972	+	0.0366459i
$175$	−8.91620	−	5.86428i	−0.674002	−	0.443298i
$176$	−0.208131	+	3.57347i	−0.0156885	+	0.269360i
$177$	3.58924	−	8.39257i	0.269784	−	0.630824i
$178$	−0.233753	+	0.780788i	−0.0175205	+	0.0585225i
$179$	−11.1678	+	4.06476i	−0.834723	+	0.303814i	−0.723796	−	0.690014i	$-0.757604\pi$
$179$	−11.1678	+	4.06476i	−0.834723	+	0.303814i	−0.110927	+	0.993829i	$0.535382\pi$
$180$	−5.13457	+	3.42307i	−0.382708	+	0.255141i
$181$	14.8329	+	5.39873i	1.10252	+	0.401284i	0.828244	−	0.560367i	$-0.189340\pi$
$181$	14.8329	+	5.39873i	1.10252	+	0.401284i	0.274275	+	0.961651i	$0.411562\pi$
$182$	−7.96962	+	10.7051i	−0.590748	+	0.793512i
$183$	8.09839	+	8.53041i	0.598650	+	0.630586i
$184$	−8.90477	−	2.11047i	−0.656469	−	0.155586i
$185$	−0.586578	+	1.35984i	−0.0431261	+	0.0999775i
$186$	0.443058	−	0.772948i	0.0324866	−	0.0566753i
$187$	−19.3501	+	12.7267i	−1.41502	+	0.930672i
$188$	5.51142	+	9.54607i	0.401962	+	0.696219i
$189$	19.6390	+	2.10965i	1.42852	+	0.153455i
$190$	2.58328	−	4.47437i	0.187411	−	0.324605i
$191$	−0.335299	−	5.75686i	−0.0242614	−	0.416552i	−0.988471	−	0.151410i	$-0.951618\pi$
$191$	−0.335299	−	5.75686i	−0.0242614	−	0.416552i	0.964210	−	0.265141i	$-0.0854185\pi$
$192$	0.966146	+	5.38123i	0.0697256	+	0.388357i
$193$	−0.174569	+	0.0204042i	−0.0125657	+	0.00146872i	−0.122373	−	0.992484i	$-0.539051\pi$
$193$	−0.174569	+	0.0204042i	−0.0125657	+	0.00146872i	0.109808	+	0.993953i	$0.464976\pi$
$194$	2.67529	−	2.83565i	0.192075	−	0.203588i
$195$	10.3118	+	5.13864i	0.738445	+	0.367986i
$196$	10.2789	+	1.20143i	0.734206	+	0.0858164i
$197$	8.59155	−	7.20917i	0.612123	−	0.513632i	−0.283194	−	0.959063i	$-0.591394\pi$
$197$	8.59155	−	7.20917i	0.612123	−	0.513632i	0.895316	+	0.445431i	$0.146950\pi$
$198$	9.94162	+	6.45035i	0.706520	+	0.458406i
$199$	−15.6873	−	13.1632i	−1.11204	−	0.933114i	−0.113866	−	0.993496i	$-0.536324\pi$
$199$	−15.6873	−	13.1632i	−1.11204	−	0.933114i	−0.998175	+	0.0603824i	$0.980768\pi$
$200$	5.10316	+	5.40904i	0.360848	+	0.382477i
$201$	8.94100	+	2.08967i	0.630649	+	0.147394i
$202$	6.68418	−	3.35692i	0.470298	−	0.236192i
$203$	−2.21799	+	1.11392i	−0.155672	+	0.0781816i
$204$	7.54100	−	8.04303i	0.527975	−	0.563125i
$205$	−0.693831	−	0.735418i	−0.0484593	−	0.0513638i
$206$	−1.94885	−	1.63528i	−0.135783	−	0.113935i
$207$	7.06565	−	7.58324i	0.491097	−	0.527071i
$208$	−2.43709	+	2.04496i	−0.168982	+	0.141792i
$209$	22.4129	+	2.61969i	1.55033	+	0.181208i
$210$	0.466716	+	7.60506i	0.0322064	+	0.524799i
$211$	−0.817579	+	0.866583i	−0.0562844	+	0.0596580i	−0.754904	−	0.655835i	$-0.772317\pi$
$211$	−0.817579	+	0.866583i	−0.0562844	+	0.0596580i	0.698620	+	0.715493i	$0.253798\pi$
$212$	5.72528	−	0.669189i	0.393214	−	0.0459601i
$213$	9.99345	+	3.60211i	0.684740	+	0.246812i
$214$	0.764060	+	13.1184i	0.0522301	+	0.896756i
$215$	6.21393	−	10.7628i	0.423786	−	0.734019i
$216$	−12.9770	−	4.58638i	−0.882972	−	0.312064i
$217$	1.25090	+	2.16663i	0.0849168	+	0.147080i
$218$	4.98574	−	3.27918i	0.337677	−	0.222094i
$219$	−7.62368	+	0.0237447i	−0.515161	+	0.00160452i
$220$	4.11803	−	9.54667i	0.277638	−	0.643636i
$221$	−20.0294	−	4.74705i	−1.34732	−	0.319321i
$222$	−1.31642	+	0.316331i	−0.0883524	+	0.0212307i
$223$	−8.89760	+	11.9515i	−0.595827	+	0.800335i	−0.993088	−	0.117371i	$-0.962553\pi$
$223$	−8.89760	+	11.9515i	−0.595827	+	0.800335i	0.397261	+	0.917706i	$0.369961\pi$
$224$	−20.9003	−	7.60707i	−1.39646	−	0.508269i
$225$	−8.18306	+	1.99334i	−0.545538	+	0.132889i
$226$	−7.35838	+	2.67823i	−0.489472	+	0.178153i
$227$	7.05501	−	23.5654i	0.468258	−	1.56409i	−0.319179	−	0.947694i	$-0.603407\pi$
$227$	7.05501	−	23.5654i	0.468258	−	1.56409i	0.787437	−	0.616395i	$-0.211408\pi$
$228$	−10.6656	+	1.28031i	−0.706346	+	0.0847908i
$229$	−0.0887860	+	1.52440i	−0.00586714	+	0.100735i	−0.999970	−	0.00770332i	$-0.997548\pi$
$229$	−0.0887860	+	1.52440i	−0.00586714	+	0.100735i	0.994103	+	0.108438i	$0.0345850\pi$
$230$	3.34049	+	2.19707i	0.220265	+	0.144871i
$231$	−29.6919	+	15.0278i	−1.95359	+	0.988759i
$232$	1.68289	−	0.398853i	0.110487	−	0.0261860i
$233$	2.44148	−	13.8463i	0.159946	−	0.907101i	−0.794177	−	0.607687i	$-0.792098\pi$
$233$	2.44148	−	13.8463i	0.159946	−	0.907101i	0.954123	−	0.299414i	$-0.0967912\pi$
$234$	1.89357	+	10.3611i	0.123786	+	0.677328i
$235$	−2.04023	−	11.5707i	−0.133090	−	0.754791i
$236$	−2.89968	−	6.72222i	−0.188753	−	0.437579i
$237$	11.5796	−	15.6556i	0.752173	−	1.01694i
$238$	−3.90425	−	13.0411i	−0.253075	−	0.845329i
$239$	−13.6853	−	18.3826i	−0.885229	−	1.18907i	−0.981066	−	0.193672i	$-0.937960\pi$
$239$	−13.6853	−	18.3826i	−0.885229	−	1.18907i	0.0958376	−	0.995397i	$-0.469447\pi$
$240$	−0.309825	+	1.78968i	−0.0199991	+	0.115524i
$241$	−6.31686	−	3.17245i	−0.406905	−	0.204355i	0.233561	−	0.972342i	$-0.424962\pi$
$241$	−6.31686	−	3.17245i	−0.406905	−	0.204355i	−0.640465	+	0.767987i	$0.721259\pi$
$242$	−11.3694			−0.730855
$243$	11.7840	−	10.2048i	0.755942	−	0.654639i
$244$	9.43390			0.603943
$245$	−9.85750	−	4.95062i	−0.629773	−	0.316284i
$246$	0.157669	−	0.910764i	0.0100526	−	0.0580682i
$247$	11.9764	+	16.0871i	0.762039	+	1.02360i
$248$	−0.499989	−	1.67008i	−0.0317493	−	0.106050i
$249$	1.67026	−	2.25819i	0.105848	−	0.143107i
$250$	−3.57867	−	8.29630i	−0.226335	−	0.524704i
$251$	0.0115419	+	0.0654574i	0.000728518	+	0.00413163i	0.985170	−	0.171582i	$-0.0548878\pi$
$251$	0.0115419	+	0.0654574i	0.000728518	+	0.00413163i	−0.984441	+	0.175714i	$0.943777\pi$
$252$	12.0720	−	10.2584i	0.760463	−	0.646219i
$253$	−3.03237	+	17.1974i	−0.190644	+	1.08119i
$254$	−2.95503	+	0.700355i	−0.185415	+	0.0439442i
$255$	−10.4853	+	5.30689i	−0.656617	+	0.332330i
$256$	11.3048	+	7.43532i	0.706553	+	0.464707i
$257$	−1.12474	+	19.3110i	−0.0701591	+	1.20459i	0.761075	+	0.648663i	$0.224672\pi$
$257$	−1.12474	+	19.3110i	−0.0701591	+	1.20459i	−0.831235	+	0.555922i	$0.812365\pi$
$258$	11.2806	−	1.35414i	0.702297	−	0.0843048i
$259$	1.09039	−	3.64214i	0.0677533	−	0.226312i
$260$	8.68330	−	3.16046i	0.538515	−	0.196003i
$261$	−0.550095	+	1.87999i	−0.0340500	+	0.116368i
$262$	−12.2274	−	4.45042i	−0.755413	−	0.274948i
$263$	8.99328	−	12.0801i	0.554549	−	0.744889i	−0.433139	−	0.901327i	$-0.642594\pi$
$263$	8.99328	−	12.0801i	0.554549	−	0.744889i	0.987688	+	0.156439i	$0.0500013\pi$
$264$	22.5473	−	5.41803i	1.38769	−	0.333456i
$265$	−5.97849	−	1.41693i	−0.367256	−	0.0870412i
$266$	−5.25336	+	12.1787i	−0.322104	+	0.746722i
$267$	−1.80624	+	0.00562570i	−0.110540	+	0.000344287i
$268$	6.15281	−	4.04677i	0.375843	−	0.247196i
$269$	5.86823	+	10.1641i	0.357792	+	0.619715i	0.987592	−	0.157043i	$-0.0501962\pi$
$269$	5.86823	+	10.1641i	0.357792	+	0.619715i	−0.629799	+	0.776758i	$0.716863\pi$
$270$	4.64236	+	3.82206i	0.282525	+	0.232603i
$271$	1.44013	−	2.49438i	0.0874817	−	0.151523i	−0.818964	−	0.573844i	$-0.805451\pi$
$271$	1.44013	−	2.49438i	0.0874817	−	0.151523i	0.906446	+	0.422322i	$0.138785\pi$
$272$	−0.188683	−	3.23957i	−0.0114406	−	0.196428i
$273$	−27.8246	−	10.0293i	−1.68402	−	0.607000i
$274$	7.20053	−	0.841621i	0.435000	−	0.0508442i
$275$	9.73782	−	10.3215i	0.587213	−	0.622409i
$276$	−0.509205	−	8.29742i	−0.0306506	−	0.499446i
$277$	2.28547	+	0.267133i	0.137320	+	0.0160504i	0.184475	−	0.982837i	$-0.440941\pi$
$277$	2.28547	+	0.267133i	0.137320	+	0.0160504i	−0.0471550	+	0.998888i	$0.515015\pi$
$278$	−9.53200	+	7.99830i	−0.571692	+	0.479706i
$279$	1.92403	+	0.443364i	0.115189	+	0.0265435i
$280$	11.4211	+	9.58343i	0.682540	+	0.572719i
$281$	−4.35455	−	4.61556i	−0.259771	−	0.275341i	0.584341	−	0.811508i	$-0.301353\pi$
$281$	−4.35455	−	4.61556i	−0.259771	−	0.275341i	−0.844112	+	0.536167i	$0.819872\pi$
$282$	7.34665	−	7.83575i	0.437487	−	0.466612i
$283$	−13.1201	+	6.58917i	−0.779910	+	0.391686i	−0.793770	−	0.608218i	$-0.791885\pi$
$283$	−13.1201	+	6.58917i	−0.779910	+	0.391686i	0.0138596	+	0.999904i	$0.495588\pi$
$284$	7.61373	−	3.82376i	0.451792	−	0.226898i
$285$	11.1496	+	2.60585i	0.660443	+	0.154357i
$286$	−12.1778	−	12.9077i	−0.720090	−	0.763251i
$287$	1.98831	+	1.66839i	0.117366	+	0.0984819i
$288$	−15.6368	+	7.97547i	−0.921410	+	0.469959i
$289$	3.06122	−	2.56867i	0.180072	−	0.151098i
$290$	−0.750510	−	0.0877220i	−0.0440715	−	0.00515121i
$291$	7.73277	+	3.85343i	0.453303	+	0.225892i
$292$	−4.19607	+	4.44757i	−0.245556	+	0.260275i
$293$	25.1838	−	2.94357i	1.47125	−	0.171965i	0.657623	−	0.753347i	$-0.271562\pi$
$293$	25.1838	−	2.94357i	1.47125	−	0.171965i	0.813631	+	0.581382i	$0.197488\pi$
$294$	−1.78206	−	9.92567i	−0.103932	−	0.578877i
$295$	0.453727	+	7.79019i	0.0264170	+	0.453562i
$296$	−1.32461	+	2.29430i	−0.0769916	+	0.133353i
$297$	−7.29707	+	25.2296i	−0.423419	+	1.46397i
$298$	9.12136	+	15.7987i	0.528386	+	0.915191i
$299$	−12.9671	+	8.52862i	−0.749909	+	0.493223i
$300$	−3.35931	+	5.86058i	−0.193950	+	0.338361i
$301$	−12.6366	+	29.2950i	−0.728364	+	1.68854i
$302$	1.77351	+	0.420330i	0.102054	+	0.0241873i
$303$	11.4130	+	12.0219i	0.655661	+	0.690638i
$304$	−1.88805	+	2.53609i	−0.108287	+	0.145455i
$305$	−9.44914	−	3.43921i	−0.541056	−	0.196928i
$306$	−9.63061	−	4.76179i	−0.550545	−	0.272213i
$307$	11.4486	−	4.16694i	0.653405	−	0.237820i	0.00601852	−	0.999982i	$-0.498084\pi$
$307$	11.4486	−	4.16694i	0.653405	−	0.237820i	0.647386	+	0.762162i	$0.275862\pi$
$308$	−7.65498	+	25.5694i	−0.436183	+	1.45695i
$309$	2.21699	−	5.18389i	0.126120	−	0.294901i
$310$	−0.0442860	+	0.760362i	−0.00251528	+	0.0431857i
$311$	21.0005	+	13.8123i	1.19083	+	0.783221i	0.980903	−	0.194496i	$-0.0623070\pi$
$311$	21.0005	+	13.8123i	1.19083	+	0.783221i	0.209927	+	0.977717i	$0.432677\pi$
$312$	17.2545	+	11.2716i	0.976844	+	0.638131i
$313$	28.7660	−	6.81767i	1.62595	−	0.385358i	0.686254	−	0.727362i	$-0.259254\pi$
$313$	28.7660	−	6.81767i	1.62595	−	0.385358i	0.939698	+	0.342005i	$0.111106\pi$
$314$	2.67130	−	15.1497i	0.150750	−	0.854947i
$315$	−15.8313	+	5.87404i	−0.891991	+	0.330965i
$316$	−2.71203	−	15.3807i	−0.152563	−	0.865230i
$317$	1.69844	+	3.93743i	0.0953940	+	0.221148i	0.959231	−	0.282623i	$-0.0912046\pi$
$317$	1.69844	+	3.93743i	0.0953940	+	0.221148i	−0.863837	+	0.503771i	$0.831945\pi$
$318$	−2.24081	−	5.15061i	−0.125658	−	0.288832i
$319$	−0.946519	−	3.16159i	−0.0529949	−	0.177015i
$320$	−2.79109	−	3.74909i	−0.156027	−	0.209580i
$321$	−27.3346	+	10.0455i	−1.52567	+	0.560685i
$322$	−9.17238	−	4.60654i	−0.511157	−	0.256712i
$323$	−20.4570			−1.13826
$324$	0.571413	−	12.4896i	0.0317452	−	0.693866i
$325$	12.6118			0.699576
$326$	12.3356	+	6.19517i	0.683206	+	0.343119i
$327$	10.1573	+	8.46926i	0.561703	+	0.468351i
$328$	−1.08005	−	1.45075i	−0.0596355	−	0.0801044i
$329$	8.65060	+	28.8950i	0.476923	+	1.59303i
$330$	−10.0664	−	1.14482i	−0.554136	−	0.0630203i
$331$	−11.0234	−	25.5552i	−0.605903	−	1.40464i	−0.894447	−	0.447174i	$-0.852431\pi$
$331$	−11.0234	−	25.5552i	−0.605903	−	1.40464i	0.288545	−	0.957466i	$-0.406829\pi$
$332$	−0.391188	−	2.21854i	−0.0214692	−	0.121758i
$333$	−1.51639	−	2.58909i	−0.0830978	−	0.141881i
$334$	−0.460091	+	2.60930i	−0.0251750	+	0.142775i
$335$	−7.63804	+	1.81025i	−0.417311	+	0.0989044i
$336$	0.256615	−	4.65568i	0.0139995	−	0.253988i
$337$	−22.4760	−	14.7827i	−1.22435	−	0.805267i	−0.238214	−	0.971213i	$-0.576562\pi$
$337$	−22.4760	−	14.7827i	−1.22435	−	0.805267i	−0.986135	+	0.165946i	$0.946932\pi$
$338$	0.326297	−	5.60231i	0.0177482	−	0.304725i
$339$	−10.4064	−	13.8878i	−0.565200	−	0.754279i
$340$	−2.70326	+	9.02952i	−0.146605	+	0.489695i
$341$	−3.12596	+	1.13776i	−0.169280	+	0.0616130i
$342$	4.20581	+	9.58553i	0.227424	+	0.518326i
$343$	1.60598	+	0.584529i	0.0867148	+	0.0315616i
$344$	13.2758	−	17.8325i	0.715785	−	0.961466i
$345$	−2.51487	+	8.49646i	−0.135396	+	0.457434i
$346$	14.2050	+	3.36665i	0.763667	+	0.180992i
$347$	−12.0799	+	28.0044i	−0.648485	+	1.50336i	0.203109	+	0.979156i	$0.434895\pi$
$347$	−12.0799	+	28.0044i	−0.648485	+	1.50336i	−0.851594	+	0.524201i	$0.824364\pi$
$348$	0.789764	+	1.35812i	0.0423358	+	0.0728031i
$349$	6.66329	−	4.38252i	0.356678	−	0.234591i	−0.358506	−	0.933528i	$-0.616714\pi$
$349$	6.66329	−	4.38252i	0.356678	−	0.234591i	0.715183	+	0.698937i	$0.246343\pi$
$350$	4.17028	+	7.22314i	0.222911	+	0.386093i
$351$	−20.7608	+	10.6705i	−1.10813	+	0.569550i
$352$	14.7870	−	25.6119i	0.788151	−	1.36512i
$353$	1.26931	+	21.7932i	0.0675587	+	1.15994i	0.846340	+	0.532643i	$0.178801\pi$
$353$	1.26931	+	21.7932i	0.0675587	+	1.15994i	−0.778782	+	0.627295i	$0.784162\pi$
$354$	−5.45055	+	4.60256i	−0.289693	+	0.244623i
$355$	−9.02001	+	1.05429i	−0.478733	+	0.0559558i
$356$	−0.994153	+	1.05374i	−0.0526900	+	0.0558481i
$357$	25.1539	−	16.6565i	1.33129	−	0.881553i
$358$	9.22555	+	1.07831i	0.487585	+	0.0569906i
$359$	−13.2606	+	11.1269i	−0.699866	+	0.587258i	−0.921736	−	0.387819i	$-0.873229\pi$
$359$	−13.2606	+	11.1269i	−0.699866	+	0.587258i	0.221869	+	0.975076i	$0.428784\pi$
$360$	11.6782	−	1.43878i	0.615494	−	0.0758303i
$361$	0.713665	+	0.598836i	0.0375613	+	0.0315177i
$362$	−8.46589	−	8.97332i	−0.444957	−	0.471627i
$363$	−7.30164	−	24.1156i	−0.383237	−	1.26574i
$364$	−21.1988	+	10.6464i	−1.11112	+	0.558024i
$365$	5.82425	−	2.92505i	0.304855	−	0.153104i
$366$	−2.66394	−	8.79836i	−0.139246	−	0.459897i
$367$	16.4058	+	17.3891i	0.856376	+	0.907705i	0.996598	−	0.0824149i	$-0.0262633\pi$
$367$	16.4058	+	17.3891i	0.856376	+	0.907705i	−0.140222	+	0.990120i	$0.544782\pi$
$368$	−1.87433	−	1.57275i	−0.0977062	−	0.0819853i
$369$	2.03307	−	0.250478i	0.105837	−	0.0130394i
$370$	0.886651	−	0.743989i	0.0460948	−	0.0386781i
$371$	15.6663	+	1.83112i	0.813351	+	0.0950671i
$372$	1.32036	−	0.874319i	0.0684576	−	0.0453313i
$373$	7.91296	−	8.38725i	0.409718	−	0.434275i	−0.489348	−	0.872088i	$-0.662765\pi$
$373$	7.91296	−	8.38725i	0.409718	−	0.434275i	0.899066	+	0.437813i	$0.144247\pi$
$374$	17.9784	−	2.10138i	0.929642	−	0.108660i
$375$	15.2989	−	12.9187i	0.790031	−	0.667119i
$376$	−1.22207	−	20.9821i	−0.0630235	−	1.08207i
$377$	1.46658	−	2.54020i	0.0755329	−	0.130827i
$378$	−12.9762	−	8.36194i	−0.667424	−	0.430092i
$379$	−10.3656	−	17.9537i	−0.532443	−	0.922218i	−0.999282	−	0.0378763i	$-0.987941\pi$
$379$	−10.3656	−	17.9537i	−0.532443	−	0.922218i	0.466839	−	0.884342i	$-0.345393\pi$
$380$	7.67266	−	5.04638i	0.393599	−	0.258874i
$381$	−3.38328	−	5.81810i	−0.173331	−	0.298070i
$382$	−1.78509	+	4.13829i	−0.0913329	+	0.211734i
$383$	−15.4278	−	3.65646i	−0.788324	−	0.186836i	−0.183314	−	0.983054i	$-0.558683\pi$
$383$	−15.4278	−	3.65646i	−0.788324	−	0.186836i	−0.605010	+	0.796218i	$0.706831\pi$
$384$	−4.53992	+	15.3381i	−0.231677	+	0.782720i
$385$	16.9889	−	22.8200i	0.865834	−	1.16302i
$386$	0.129079	+	0.0469808i	0.00656994	+	0.00239126i
$387$	10.1168	+	23.0574i	0.514266	+	1.17207i
$388$	6.51155	−	2.37001i	0.330574	−	0.120319i
$389$	8.17648	−	27.3114i	0.414564	−	1.38474i	−0.454811	−	0.890588i	$-0.650293\pi$
$389$	8.17648	−	27.3114i	0.414564	−	1.38474i	0.869375	−	0.494153i	$-0.164522\pi$
$390$	−5.39953	−	7.20587i	−0.273416	−	0.364883i
$391$	0.920492	−	15.8042i	0.0465513	−	0.799255i
$392$	−16.4863	−	10.8432i	−0.832685	−	0.547665i
$393$	1.58707	−	28.7936i	0.0800569	−	1.45244i
$394$	−8.52915	+	2.02145i	−0.429693	+	0.101839i
$395$	−2.89074	+	16.3942i	−0.145449	+	0.824882i
$396$	10.6457	+	18.1765i	0.534968	+	0.913405i
$397$	5.49087	+	31.1403i	0.275579	+	1.56289i	0.737117	+	0.675765i	$0.236187\pi$
$397$	5.49087	+	31.1403i	0.275579	+	1.56289i	−0.461538	+	0.887120i	$0.652702\pi$
$398$	6.33916	+	14.6958i	0.317753	+	0.736635i
$399$	−29.2058	−	3.32150i	−1.46212	−	0.166283i
$400$	0.570228	+	1.90470i	0.0285114	+	0.0952348i
$401$	10.1802	+	13.6744i	0.508376	+	0.682867i	0.980015	−	0.198924i	$-0.0637449\pi$
$401$	10.1802	+	13.6744i	0.508376	+	0.682867i	−0.471639	+	0.881792i	$0.656337\pi$
$402$	−5.51158	−	4.59558i	−0.274892	−	0.229207i
$403$	−2.64210	−	1.32691i	−0.131612	−	0.0660982i
$404$	13.2952			0.661458
$405$	−5.12552	+	12.3014i	−0.254689	+	0.611264i
$406$	1.93980			0.0962705
$407$	4.51752	+	2.26878i	0.223925	+	0.112459i
$408$	−19.7320	+	7.25155i	−0.976882	+	0.359005i
$409$	−14.2344	−	19.1202i	−0.703848	−	0.945432i	0.296105	−	0.955155i	$-0.404312\pi$
$409$	−14.2344	−	19.1202i	−0.703848	−	0.945432i	−0.999953	+	0.00972374i	$0.996905\pi$
$410$	0.226629	+	0.756995i	0.0111924	+	0.0373853i
$411$	6.40945	+	14.7324i	0.316155	+	0.726698i
$412$	−1.79107	−	4.15216i	−0.0882395	−	0.204562i
$413$	−3.47862	−	19.7282i	−0.171172	−	0.970762i
$414$	−7.59465	+	2.81792i	−0.373257	+	0.138493i
$415$	−0.416966	+	2.36473i	−0.0204681	+	0.116080i
$416$	25.5762	−	6.06166i	1.25397	−	0.297197i
$417$	−23.0867	−	15.0816i	−1.13056	−	0.738548i
$418$	−14.7346	−	9.69113i	−0.720695	−	0.474009i
$419$	0.914980	−	15.7096i	0.0446997	−	0.767464i	−0.899262	−	0.437410i	$-0.855896\pi$
$419$	0.914980	−	15.7096i	0.0446997	−	0.767464i	0.943962	−	0.330054i	$-0.107067\pi$
$420$	−5.32545	+	12.4523i	−0.259855	+	0.607609i
$421$	6.75647	−	22.5682i	0.329290	−	1.09991i	−0.619763	−	0.784789i	$-0.712771\pi$
$421$	6.75647	−	22.5682i	0.329290	−	1.09991i	0.949053	−	0.315116i	$-0.102044\pi$
$422$	0.874971	−	0.318464i	0.0425929	−	0.0155026i
$423$	21.3384	+	10.5506i	1.03751	+	0.512990i
$424$	−10.3281	−	3.75912i	−0.501577	−	0.182559i
$425$	−7.68195	+	10.3186i	−0.372629	+	0.500528i
$426$	−5.71612	−	6.02105i	−0.276947	−	0.291721i
$427$	25.1184	+	5.95318i	1.21557	+	0.288094i
$428$	−9.25130	+	21.4469i	−0.447179	+	1.03668i
$429$	19.5576	−	34.1198i	0.944252	−	1.64732i
$430$	−8.11506	+	5.33736i	−0.391343	+	0.257390i
$431$	0.705848	+	1.22256i	0.0339995	+	0.0588888i	0.882524	−	0.470267i	$-0.155842\pi$
$431$	0.705848	+	1.22256i	0.0339995	+	0.0588888i	−0.848525	+	0.529155i	$0.822509\pi$
$432$	−2.55019	−	2.65294i	−0.122696	−	0.127640i
$433$	−6.50524	+	11.2674i	−0.312622	+	0.541477i	−0.978929	−	0.204200i	$-0.934541\pi$
$433$	−6.50524	+	11.2674i	−0.312622	+	0.541477i	0.666307	+	0.745677i	$0.267874\pi$
$434$	−0.113689	−	1.95197i	−0.00545727	−	0.0936977i
$435$	−0.295924	−	1.64823i	−0.0141885	−	0.0790268i
$436$	10.5353	−	1.23140i	0.504550	−	0.0589734i
$437$	−10.5849	+	11.2194i	−0.506346	+	0.536695i
$438$	5.33284	+	2.65748i	0.254813	+	0.126979i
$439$	−20.5982	−	2.40758i	−0.983097	−	0.114908i	−0.390669	−	0.920531i	$-0.627756\pi$
$439$	−20.5982	−	2.40758i	−0.983097	−	0.114908i	−0.592428	+	0.805624i	$0.701830\pi$
$440$	−15.1863	+	12.7428i	−0.723979	+	0.607490i
$441$	19.9088	−	10.1543i	0.948036	−	0.483540i
$442$	12.3238	+	10.3409i	0.586182	+	0.491865i
$443$	−23.3099	−	24.7070i	−1.10749	−	1.17387i	−0.983373	−	0.181599i	$-0.941873\pi$
$443$	−23.3099	−	24.7070i	−1.10749	−	1.17387i	−0.124113	−	0.992268i	$-0.539609\pi$
$444$	−2.34336	−	0.547684i	−0.111211	−	0.0259920i
$445$	1.37991	−	0.693016i	0.0654140	−	0.0328521i
$446$	10.4063	−	5.22626i	0.492754	−	0.247470i
$447$	−27.6524	+	29.4934i	−1.30791	+	1.39499i
$448$	8.23407	+	8.72761i	0.389023	+	0.412341i
$449$	0.919709	+	0.771727i	0.0434038	+	0.0364201i	0.664231	−	0.747527i	$-0.268759\pi$
$449$	0.919709	+	0.771727i	0.0434038	+	0.0364201i	−0.620828	+	0.783947i	$0.713203\pi$
$450$	6.41437	+	1.47809i	0.302376	+	0.0696780i
$451$	−2.64380	+	2.21841i	−0.124492	+	0.104461i
$452$	−13.8246	−	1.61587i	−0.650256	−	0.0760040i
$453$	0.247423	+	4.03172i	0.0116249	+	0.189427i
$454$	−13.1931	+	13.9839i	−0.619182	+	0.656295i
$455$	25.1143	−	2.93544i	1.17738	−	0.137615i
$456$	19.2690	+	6.94544i	0.902352	+	0.325250i
$457$	1.86373	+	31.9990i	0.0871815	+	1.49685i	0.704257	+	0.709945i	$0.251280\pi$
$457$	1.86373	+	31.9990i	0.0871815	+	1.49685i	−0.617076	+	0.786904i	$0.711683\pi$
$458$	0.596704	−	1.03352i	0.0278821	−	0.0482933i
$459$	3.91522	−	23.4855i	0.182747	−	1.09621i
$460$	3.55340	+	6.15466i	0.165678	+	0.286963i
$461$	−0.281296	+	0.185011i	−0.0131013	+	0.00861684i	−0.556043	−	0.831154i	$-0.687681\pi$
$461$	−0.281296	+	0.185011i	−0.0131013	+	0.00861684i	0.542941	+	0.839771i	$0.317311\pi$
$462$	26.0085	−	0.0810058i	1.21002	−	0.00376873i
$463$	−1.16952	+	2.71124i	−0.0543520	+	0.126002i	−0.943228	−	0.332145i	$-0.892228\pi$
$463$	−1.16952	+	2.71124i	−0.0543520	+	0.126002i	0.888876	+	0.458147i	$0.151487\pi$
$464$	0.449944	+	0.106639i	0.0208881	+	0.00495057i
$465$	−1.64124	+	0.394383i	−0.0761105	+	0.0182891i
$466$	−6.56187	+	8.81412i	−0.303973	+	0.408306i
$467$	−3.55605	−	1.29430i	−0.164554	−	0.0598929i	0.258429	−	0.966030i	$-0.416795\pi$
$467$	−3.55605	−	1.29430i	−0.164554	−	0.0598929i	−0.422984	+	0.906137i	$0.639017\pi$
$468$	−5.25762	+	17.9683i	−0.243034	+	0.830584i
$469$	18.9360	−	6.89213i	0.874382	−	0.318249i
$470$	−2.63359	+	8.79682i	−0.121479	+	0.405767i
$471$	33.8494	−	4.06333i	1.55970	−	0.187228i
$472$	−0.811652	+	13.9355i	−0.0373593	+	0.641435i
$473$	−35.4433	−	23.3114i	−1.62968	−	1.07186i
$474$	−13.5787	+	6.87251i	−0.623690	+	0.315665i
$475$	12.1960	−	2.89050i	0.559589	−	0.132625i
$476$	4.20172	−	23.8292i	0.192586	−	1.09221i
$477$	9.48581	−	8.06076i	0.434326	−	0.369077i
$478$	3.11022	+	17.6389i	0.142258	+	0.806785i
$479$	−1.25429	−	2.90777i	−0.0573100	−	0.132859i	0.887155	−	0.461472i	$-0.152678\pi$
$479$	−1.25429	−	2.90777i	−0.0573100	−	0.132859i	−0.944465	+	0.328612i	$0.893419\pi$
$480$	8.92360	−	12.0647i	0.407305	−	0.550678i
$481$	1.28860	+	4.30421i	0.0587549	+	0.196255i
$482$	3.29904	+	4.43138i	0.150267	+	0.201844i
$483$	3.88022	−	22.4138i	0.176556	−	1.01986i
$484$	−18.0593	−	9.06974i	−0.820879	−	0.412261i
$485$	−7.38607			−0.335384
$486$	−11.8095	+	2.99389i	−0.535692	+	0.135805i
$487$	1.22501			0.0555106			0.0277553	−	0.999615i	$-0.491164\pi$
$487$	1.22501			0.0555106			0.0277553	+	0.999615i	$0.491164\pi$
$488$	−16.0746	−	8.07299i	−0.727665	−	0.365447i
$489$	−5.21837	+	30.1435i	−0.235983	+	1.36314i
$490$	5.14817	+	6.91520i	0.232571	+	0.312397i
$491$	11.6292	+	38.8443i	0.524819	+	1.75302i	0.649032	+	0.760761i	$0.275174\pi$
$491$	11.6292	+	38.8443i	0.524819	+	1.75302i	−0.124213	+	0.992256i	$0.539641\pi$
$492$	0.976987	−	1.32089i	0.0440460	−	0.0595503i
$493$	1.18502	+	2.74718i	0.0533705	+	0.123727i
$494$	−2.72183	−	15.4363i	−0.122461	−	0.694512i
$495$	−4.03653	−	22.0869i	−0.181429	−	0.992732i
$496$	0.0809373	−	0.459018i	0.00363419	−	0.0206105i
$497$	22.6850	−	5.37646i	1.01756	−	0.241167i
$498$	−1.95861	+	0.991304i	−0.0877676	+	0.0444214i
$499$	34.3817	+	22.6132i	1.53914	+	1.01231i	0.983506	+	0.180876i	$0.0578934\pi$
$499$	34.3817	+	22.6132i	1.53914	+	1.01231i	0.555630	+	0.831429i	$0.312477\pi$
$500$	0.933801	−	16.0328i	0.0417609	−	0.717006i
$501$	−5.83004	+	0.699847i	−0.260467	+	0.0312669i
$502$	0.0148986	−	0.0497649i	0.000664959	−	0.00222112i
$503$	9.54144	−	3.47280i	0.425432	−	0.154845i	−0.120426	−	0.992722i	$-0.538426\pi$
$503$	9.54144	−	3.47280i	0.425432	−	0.154845i	0.545858	+	0.837878i	$0.316204\pi$
$504$	−29.3483	+	7.14904i	−1.30728	+	0.318444i
$505$	−13.3166	−	4.84686i	−0.592582	−	0.215682i
$506$	8.15000	−	10.9473i	0.362311	−	0.486669i
$507$	12.0925	−	2.90579i	0.537048	−	0.129051i
$508$	−5.25250	−	1.24486i	−0.233042	−	0.0552319i
$509$	9.60383	−	22.2642i	0.425682	−	0.986842i	−0.561534	−	0.827454i	$-0.689789\pi$
$509$	9.60383	−	22.2642i	0.425682	−	0.986842i	0.987216	−	0.159388i	$-0.0509522\pi$
$510$	9.18457	−	0.0286062i	0.406699	−	0.00126670i
$511$	−13.9789	+	9.19409i	−0.618392	+	0.406723i
$512$	3.94773	+	6.83768i	0.174467	+	0.302186i
$513$	−17.6307	+	15.0769i	−0.778415	+	0.665660i
$514$	7.55901	−	13.0926i	0.333414	−	0.577490i
$515$	0.280256	+	4.81181i	0.0123496	+	0.212034i
$516$	18.9984	+	6.84792i	0.836358	+	0.301463i
$517$	−39.8346	+	4.65600i	−1.75192	+	0.204771i
$518$	−2.03905	+	2.16127i	−0.0895909	+	0.0949608i
$519$	1.98174	+	32.2922i	0.0869889	+	1.41747i
$520$	−17.5002	−	2.04548i	−0.767435	−	0.0897003i
$521$	−4.86477	+	4.08202i	−0.213129	+	0.178837i	−0.743102	−	0.669178i	$-0.766646\pi$
$521$	−4.86477	+	4.08202i	−0.213129	+	0.178837i	0.529973	+	0.848014i	$0.322202\pi$
$522$	1.04362	−	1.12007i	0.0456779	−	0.0490239i
$523$	21.5335	+	18.0688i	0.941595	+	0.790092i	0.977862	−	0.209250i	$-0.0671024\pi$
$523$	21.5335	+	18.0688i	0.941595	+	0.790092i	−0.0362674	+	0.999342i	$0.511547\pi$
$524$	−15.8719	−	16.8233i	−0.693369	−	0.734928i
$525$	−12.6427	+	13.4844i	−0.551772	+	0.588506i
$526$	−10.5182	+	5.28246i	−0.458617	+	0.230326i
$527$	2.69497	−	1.35347i	0.117395	−	0.0589579i
$528$	6.03723	+	1.41100i	0.262737	+	0.0614061i
$529$	7.59220	+	8.04726i	0.330096	+	0.349881i
$530$	3.67848	+	3.08661i	0.159783	+	0.134074i
$531$	−13.2629	−	8.60524i	−0.575559	−	0.373436i
$532$	−18.0598	+	15.1540i	−0.782991	+	0.657008i
$533$	−3.04663	−	0.356100i	−0.131964	−	0.0154244i
$534$	1.26348	+	0.629624i	0.0546762	+	0.0272465i
$535$	17.0849	−	18.1089i	0.738645	−	0.782918i
$536$	−13.9469	+	1.63016i	−0.602415	+	0.0704122i
$537$	3.63761	+	20.2607i	0.156974	+	0.874314i
$538$	−0.533340	−	9.15709i	−0.0229939	−	0.394790i
$539$	−18.8268	+	32.6089i	−0.810926	+	1.40457i
$540$	4.32501	+	9.77435i	0.186119	+	0.420621i
$541$	−1.34390	−	2.32771i	−0.0577788	−	0.100076i	0.835689	−	0.549203i	$-0.185068\pi$
$541$	−1.34390	−	2.32771i	−0.0577788	−	0.100076i	−0.893468	+	0.449127i	$0.851735\pi$
$542$	−1.88074	+	1.23698i	−0.0807845	+	0.0531328i
$543$	13.5962	−	23.7197i	0.583471	−	1.01791i
$544$	−10.6192	+	24.6180i	−0.455293	+	1.05549i
$545$	−11.0012	−	2.60734i	−0.471242	−	0.111686i
$546$	15.9153	+	16.7643i	0.681112	+	0.717447i
$547$	19.5913	−	26.3156i	0.837662	−	1.12518i	−0.152918	−	0.988239i	$-0.548867\pi$
$547$	19.5913	−	26.3156i	0.837662	−	1.12518i	0.990580	−	0.136937i	$-0.0437257\pi$
$548$	12.1088	+	4.40724i	0.517262	+	0.188268i
$549$	16.9513	−	11.3009i	0.723462	−	0.482311i
$550$	−10.4214	+	3.79308i	−0.444370	+	0.161737i
$551$	0.836042	−	2.79257i	0.0356166	−	0.118968i
$552$	−6.23281	+	14.5739i	−0.265286	+	0.620307i
$553$	2.48487	−	42.6635i	0.105667	−	1.81424i
$554$	−1.50251	−	0.988215i	−0.0638355	−	0.0419852i
$555$	2.14749	+	1.40286i	0.0911557	+	0.0595482i
$556$	−21.5212	+	5.10062i	−0.912703	+	0.216315i
$557$	1.71906	−	9.74928i	0.0728390	−	0.413090i	−0.926485	−	0.376331i	$-0.877185\pi$
$557$	1.71906	−	9.74928i	0.0728390	−	0.413090i	0.999324	−	0.0367591i	$-0.0117034\pi$
$558$	−1.18826	−	0.984522i	−0.0503031	−	0.0416781i
$559$	−6.54721	−	37.1311i	−0.276917	−	1.57048i
$560$	1.57884	+	3.66016i	0.0667182	+	0.154670i
$561$	16.0032	+	36.7843i	0.675658	+	1.55303i
$562$	1.42235	+	4.75098i	0.0599982	+	0.200408i
$563$	−4.20131	−	5.64334i	−0.177064	−	0.237838i	0.704727	−	0.709479i	$-0.251070\pi$
$563$	−4.20131	−	5.64334i	−0.177064	−	0.237838i	−0.881791	+	0.471640i	$0.843662\pi$
$564$	17.9203	−	6.58574i	0.754581	−	0.277310i
$565$	13.2579	+	6.65836i	0.557764	+	0.280119i
$566$	11.4745			0.482310
$567$	9.40287	−	32.8938i	0.394883	−	1.38141i
$568$	−16.2454			−0.681640
$569$	3.51923	+	1.76742i	0.147534	+	0.0740943i	0.521034	−	0.853536i	$-0.325546\pi$
$569$	3.51923	+	1.76742i	0.147534	+	0.0740943i	−0.373501	+	0.927630i	$0.621843\pi$
$570$	−6.87302	−	5.73077i	−0.287879	−	0.240035i
$571$	15.2678	+	20.5083i	0.638939	+	0.858244i	0.997154	−	0.0753955i	$-0.0240219\pi$
$571$	15.2678	+	20.5083i	0.638939	+	0.858244i	−0.358215	+	0.933639i	$0.616615\pi$
$572$	−9.04650	−	30.2174i	−0.378253	−	1.26345i
$573$	−9.92409	−	1.12864i	−0.414585	−	0.0471496i
$574$	−0.803467	−	1.86265i	−0.0335361	−	0.0777453i
$575$	1.68431	+	9.55219i	0.0702405	+	0.398354i
$576$	9.46940	−	0.0589873i	0.394559	−	0.00245780i
$577$	0.816045	−	4.62802i	0.0339724	−	0.192667i	−0.963099	−	0.269149i	$-0.913258\pi$
$577$	0.816045	−	4.62802i	0.0339724	−	0.192667i	0.997071	+	0.0764818i	$0.0243687\pi$
$578$	−3.03899	+	0.720254i	−0.126405	+	0.0299586i
$579$	−0.0167539	+	0.303959i	−0.000696267	+	0.0126321i
$580$	−1.12214	−	0.738043i	−0.0465943	−	0.0306456i
$581$	0.358422	−	6.15387i	0.0148699	−	0.255306i
$582$	−4.04907	−	5.40363i	−0.167840	−	0.223988i
$583$	−6.01507	+	20.0917i	−0.249119	+	0.832114i
$584$	10.9558	−	3.98757i	0.453353	−	0.165007i
$585$	11.8166	−	16.0806i	0.488556	−	0.664852i
$586$	−18.6213	−	6.77759i	−0.769238	−	0.279980i
$587$	16.5849	−	22.2775i	0.684534	−	0.919489i	−0.315028	−	0.949082i	$-0.602014\pi$
$587$	16.5849	−	22.2775i	0.684534	−	0.919489i	0.999562	+	0.0295936i	$0.00942131\pi$
$588$	5.08737	−	17.1876i	0.209800	−	0.708807i
$589$	−2.85910	−	0.677620i	−0.117807	−	0.0279208i
$590$	2.41558	−	5.59994i	0.0994479	−	0.230546i
$591$	−9.76523	−	16.7929i	−0.401688	−	0.690766i
$592$	−0.591781	+	0.389221i	−0.0243221	+	0.0159969i
$593$	7.16631	+	12.4124i	0.294285	+	0.509717i	0.974818	−	0.223000i	$-0.0715851\pi$
$593$	7.16631	+	12.4124i	0.294285	+	0.509717i	−0.680533	+	0.732717i	$0.738252\pi$
$594$	13.9459	−	15.0612i	0.572206	−	0.617970i
$595$	−12.8956	+	22.3359i	−0.528669	+	0.915682i
$596$	1.88540	+	32.3711i	0.0772291	+	1.32597i
$597$	−27.1000	+	22.8838i	−1.10913	+	0.936573i
$598$	12.0479	−	1.40820i	0.492677	−	0.0575857i
$599$	−18.8738	+	20.0050i	−0.771161	+	0.817383i	−0.987281	−	0.158983i	$-0.949178\pi$
$599$	−18.8738	+	20.0050i	−0.771161	+	0.817383i	0.216120	+	0.976367i	$0.430660\pi$
$600$	10.7392	−	7.11128i	0.438425	−	0.290317i
$601$	−18.6234	−	2.17676i	−0.759665	−	0.0887921i	−0.272564	−	0.962138i	$-0.587872\pi$
$601$	−18.6234	−	2.17676i	−0.759665	−	0.0887921i	−0.487101	+	0.873346i	$0.661946\pi$
$602$	19.1011	−	16.0277i	0.778503	−	0.653242i
$603$	6.20801	−	14.6419i	0.252810	−	0.596264i
$604$	2.48176	+	2.08244i	0.100981	+	0.0847333i
$605$	14.7821	+	15.6681i	0.600976	+	0.636998i
$606$	−3.75428	−	12.3995i	−0.152507	−	0.503695i
$607$	23.5997	−	11.8522i	0.957881	−	0.481066i	0.100041	−	0.994983i	$-0.468103\pi$
$607$	23.5997	−	11.8522i	0.957881	−	0.481066i	0.857840	+	0.513918i	$0.171806\pi$
$608$	23.3436	−	11.7236i	0.946709	−	0.475455i
$609$	1.24577	+	4.11448i	0.0504811	+	0.166727i
$610$	5.39311	+	5.71636i	0.218361	+	0.231449i
$611$	−27.3057	−	22.9122i	−1.10467	−	0.926928i
$612$	−11.4987	−	15.2463i	−0.464809	−	0.616295i
$613$	−26.7821	+	22.4728i	−1.08172	+	0.907670i	−0.996062	−	0.0886553i	$-0.971743\pi$
$613$	−26.7821	+	22.4728i	−1.08172	+	0.907670i	−0.0856560	+	0.996325i	$0.527299\pi$
$614$	−9.45747	−	1.10542i	−0.381672	−	0.0446111i
$615$	−1.46011	+	0.966856i	−0.0588772	+	0.0389874i
$616$	34.9243	−	37.0176i	1.40714	−	1.49148i
$617$	7.10306	−	0.830228i	0.285958	−	0.0334237i	0.0280954	−	0.999605i	$-0.491056\pi$
$617$	7.10306	−	0.830228i	0.285958	−	0.0334237i	0.257863	+	0.966182i	$0.416982\pi$
$618$	−3.36667	+	2.84289i	−0.135427	+	0.114358i
$619$	1.09438	+	18.7898i	0.0439868	+	0.755224i	0.946130	+	0.323787i	$0.104956\pi$
$619$	1.09438	+	18.7898i	0.0439868	+	0.755224i	−0.902143	+	0.431437i	$0.858007\pi$
$620$	−0.676908	+	1.17244i	−0.0271853	+	0.0470863i
$621$	−10.8545	−	14.2992i	−0.435575	−	0.573807i
$622$	−9.82235	−	17.0128i	−0.393841	−	0.682152i
$623$	−3.31196	+	2.17831i	−0.132691	+	0.0872721i
$624$	2.77002	+	4.76349i	0.110889	+	0.190692i
$625$	−1.22031	+	2.82901i	−0.0488126	+	0.113160i
$626$	−22.4820	−	5.32834i	−0.898562	−	0.212963i
$627$	11.0929	−	37.4773i	0.443007	−	1.49670i
$628$	16.3285	−	21.9330i	0.651578	−	0.875221i
$629$	−4.30649	−	1.56744i	−0.171711	−	0.0624978i
$630$	13.1172	+	1.45041i	0.522601	+	0.0577858i
$631$	−22.0642	+	8.03070i	−0.878361	+	0.319697i	−0.741548	−	0.670900i	$-0.765908\pi$
$631$	−22.0642	+	8.03070i	−0.878361	+	0.319697i	−0.136813	+	0.990597i	$0.543686\pi$
$632$	−8.54081	+	28.5283i	−0.339735	+	1.13479i
$633$	1.23741	+	1.65137i	0.0491827	+	0.0656360i
$634$	0.194865	−	3.34571i	0.00773909	−	0.132875i
$635$	4.80716	+	3.16172i	0.190766	+	0.125469i
$636$	0.549471	−	9.96885i	0.0217879	−	0.395291i
$637$	−32.5634	+	7.71768i	−1.29021	+	0.305786i
$638$	−0.447890	+	2.54011i	−0.0177321	+	0.100564i
$639$	9.10019	−	15.9912i	0.359998	−	0.632603i
$640$	−2.37461	−	13.4671i	−0.0938648	−	0.532334i
$641$	−1.72652	−	4.00251i	−0.0681933	−	0.158090i	0.880711	−	0.473654i	$-0.157065\pi$
$641$	−1.72652	−	4.00251i	−0.0681933	−	0.158090i	−0.948904	+	0.315565i	$0.897806\pi$
$642$	22.6145	+	2.57188i	0.892522	+	0.101504i
$643$	−5.45270	−	18.2133i	−0.215034	−	0.718262i	−0.995643	−	0.0932433i	$-0.970277\pi$
$643$	−5.45270	−	18.2133i	−0.215034	−	0.718262i	0.780610	−	0.625019i	$-0.214909\pi$
$644$	−10.8947	−	14.6342i	−0.429312	−	0.576667i
$645$	−16.5326	−	13.7850i	−0.650972	−	0.542784i
$646$	14.2875	+	7.17544i	0.562133	+	0.282314i
$647$	−20.6268			−0.810924			−0.405462	−	0.914112i	$-0.632889\pi$
$647$	−20.6268			−0.810924			−0.405462	+	0.914112i	$0.632889\pi$
$648$	−11.6615	+	20.7923i	−0.458108	+	0.816799i
$649$	26.6367			1.04558
$650$	−8.80828	−	4.42368i	−0.345489	−	0.173511i
$651$	4.06729	−	1.49473i	0.159410	−	0.0585833i
$652$	14.6519	+	19.6810i	0.573814	+	0.770766i
$653$	−1.71817	−	5.73909i	−0.0672372	−	0.224588i	0.917767	−	0.397120i	$-0.129990\pi$
$653$	−1.71817	−	5.73909i	−0.0672372	−	0.224588i	−0.985004	+	0.172532i	$0.944805\pi$
$654$	−4.12340	−	9.47784i	−0.161238	−	0.370613i
$655$	9.76452	+	22.6367i	0.381531	+	0.884489i
$656$	−0.0839701	−	0.476218i	−0.00327848	−	0.0185932i
$657$	−2.21192	+	13.0181i	−0.0862951	+	0.507884i
$658$	4.09344	−	23.2150i	0.159579	−	0.905016i
$659$	−37.7920	+	8.95688i	−1.47217	+	0.348910i	−0.886912	−	0.461938i	$-0.847154\pi$
$659$	−37.7920	+	8.95688i	−1.47217	+	0.348910i	−0.585256	+	0.810848i	$0.699006\pi$
$660$	−15.0763	−	9.84870i	−0.586844	−	0.383360i
$661$	−25.8965	−	17.0324i	−1.00726	−	0.662483i	−0.0651777	−	0.997874i	$-0.520761\pi$
$661$	−25.8965	−	17.0324i	−1.00726	−	0.662483i	−0.942079	+	0.335390i	$0.891132\pi$
$662$	−1.26474	+	21.7147i	−0.0491555	+	0.843967i
$663$	−14.0194	+	32.7809i	−0.544467	+	1.27310i
$664$	−1.23194	+	4.11497i	−0.0478086	+	0.159692i
$665$	23.6135	−	8.59460i	0.915691	−	0.333284i
$666$	0.150930	+	2.34015i	0.00584843	+	0.0906790i
$667$	2.11981	+	0.771549i	0.0820795	+	0.0298745i
$668$	−2.81233	+	3.77762i	−0.108812	+	0.146160i
$669$	17.7685	+	18.7163i	0.686969	+	0.723616i
$670$	5.96949	+	1.41480i	0.230622	+	0.0546583i
$671$	−13.5952	+	31.5173i	−0.524839	+	1.21671i
$672$	−19.1578	+	33.4222i	−0.739027	+	1.28929i
$673$	32.2411	−	21.2053i	1.24280	−	0.817405i	0.254085	−	0.967182i	$-0.418226\pi$
$673$	32.2411	−	21.2053i	1.24280	−	0.817405i	0.988720	+	0.149777i	$0.0478554\pi$
$674$	10.5125	+	18.2082i	0.404926	+	0.701352i
$675$	0.984249	+	14.5547i	0.0378838	+	0.560210i
$676$	4.98742	−	8.63847i	0.191824	−	0.332249i
$677$	−0.231922	−	3.98194i	−0.00891348	−	0.153039i	−0.999828	−	0.0185455i	$-0.994096\pi$
$677$	−0.231922	−	3.98194i	−0.00891348	−	0.153039i	0.990915	−	0.134493i	$-0.0429406\pi$
$678$	2.39679	+	13.3496i	0.0920480	+	0.512687i
$679$	18.8330	−	2.20127i	0.722745	−	0.0844768i
$680$	12.3331	−	13.0723i	0.472953	−	0.501301i
$681$	−38.1338	−	19.0030i	−1.46129	−	0.728197i
$682$	2.58230	+	0.301828i	0.0988815	+	0.0115576i
$683$	32.2624	−	27.0713i	1.23449	−	1.03586i	0.236551	−	0.971619i	$-0.423983\pi$
$683$	32.2624	−	27.0713i	1.23449	−	1.03586i	0.997935	−	0.0642370i	$-0.0204614\pi$
$684$	−0.966116	+	18.5809i	−0.0369404	+	0.710457i
$685$	−10.5217	−	8.82872i	−0.402012	−	0.337328i
$686$	−0.916615	−	0.971555i	−0.0349965	−	0.0370941i
$687$	2.57540	+	0.601916i	0.0982577	+	0.0229645i
$688$	5.31170	−	2.66763i	0.202506	−	0.101703i
$689$	−16.6574	+	8.36566i	−0.634597	+	0.318706i
$690$	4.73663	−	5.05196i	0.180320	−	0.192325i
$691$	5.86779	+	6.21949i	0.223221	+	0.236601i	0.829300	−	0.558804i	$-0.188740\pi$
$691$	5.86779	+	6.21949i	0.223221	+	0.236601i	−0.606078	+	0.795405i	$0.707258\pi$
$692$	19.8777	+	16.6794i	0.755638	+	0.634056i
$693$	16.8749	+	55.1142i	0.641024	+	2.09362i
$694$	18.2596	−	15.3216i	0.693125	−	0.581601i
$695$	23.4155	+	2.73688i	0.888200	+	0.103816i
$696$	−0.183492	−	2.98997i	−0.00695525	−	0.113335i
$697$	2.14708	−	2.27577i	0.0813265	−	0.0862011i
$698$	−6.19096	+	0.723619i	−0.234331	+	0.0273894i
$699$	−22.9097	−	8.25772i	−0.866523	−	0.312336i
$700$	0.862006	+	14.8001i	0.0325808	+	0.559390i
$701$	−0.440975	+	0.763791i	−0.0166554	+	0.0288480i	−0.874233	−	0.485507i	$-0.838635\pi$
$701$	−0.440975	+	0.763791i	−0.0166554	+	0.0288480i	0.857578	+	0.514355i	$0.171968\pi$
$702$	18.2424	−	0.170458i	0.688517	−	0.00643351i
$703$	2.23259	+	3.86697i	0.0842039	+	0.145845i
$704$	−13.3298	+	8.76713i	−0.502385	+	0.330424i
$705$	−20.3502	+	0.0633825i	−0.766431	+	0.00238712i
$706$	6.75765	−	15.6660i	0.254327	−	0.589597i
$707$	35.3993	+	8.38979i	1.33133	+	0.315530i
$708$	−12.3293	+	2.96269i	−0.463364	+	0.111345i
$709$	−24.0259	+	32.2724i	−0.902312	+	1.21202i	0.0743501	+	0.997232i	$0.476312\pi$
$709$	−24.0259	+	32.2724i	−0.902312	+	1.21202i	−0.976662	+	0.214783i	$0.931096\pi$
$710$	6.66953	+	2.42751i	0.250303	+	0.0911028i
$711$	−23.2977	−	24.3879i	−0.873730	−	0.914619i
$712$	2.59569	−	0.944754i	0.0972777	−	0.0354062i
$713$	0.652152	−	2.17834i	0.0244233	−	0.0815795i
$714$	−23.4103	+	2.81021i	−0.876109	+	0.105169i
$715$	−1.95489	+	33.5642i	−0.0731089	+	1.25523i
$716$	13.7938	+	9.07230i	0.515497	+	0.339048i
$717$	−35.4162	+	17.9251i	−1.32264	+	0.669423i
$718$	13.1643	−	3.11999i	0.491286	−	0.116437i
$719$	−2.39151	+	13.5629i	−0.0891883	+	0.505812i	0.907186	+	0.420730i	$0.138226\pi$
$719$	−2.39151	+	13.5629i	−0.0891883	+	0.505812i	−0.996374	+	0.0850815i	$0.972885\pi$
$720$	2.96285	+	1.05754i	0.110419	+	0.0394120i
$721$	−2.14866	−	12.1857i	−0.0800203	−	0.453817i
$722$	−0.288389	−	0.668561i	−0.0107327	−	0.0248813i
$723$	−7.28064	+	9.84345i	−0.270770	+	0.366082i
$724$	−6.28902	−	21.0068i	−0.233730	−	0.780712i
$725$	−1.09465	−	1.47037i	−0.0406542	−	0.0546080i
$726$	−3.35914	+	19.4038i	−0.124669	+	0.720143i
$727$	−11.1569	−	5.60321i	−0.413787	−	0.207812i	0.229712	−	0.973259i	$-0.426222\pi$
$727$	−11.1569	−	5.60321i	−0.413787	−	0.207812i	−0.643499	+	0.765447i	$0.722518\pi$
$728$	45.2317			1.67640
$729$	−13.9346	−	23.1263i	−0.516096	−	0.856531i
$730$	−5.09374			−0.188528
$731$	34.3677	+	17.2601i	1.27113	+	0.638388i
$732$	2.78728	−	16.1005i	0.103021	−	0.595092i
$733$	−16.0474	−	21.5554i	−0.592725	−	0.796168i	0.400007	−	0.916512i	$-0.369008\pi$
$733$	−16.0474	−	21.5554i	−0.592725	−	0.796168i	−0.992732	+	0.120344i	$0.961600\pi$
$734$	−5.35871	−	17.8993i	−0.197793	−	0.660676i
$735$	−11.3615	+	15.3608i	−0.419075	+	0.566591i
$736$	8.00682	+	18.5619i	0.295135	+	0.684200i
$737$	4.65283	+	26.3875i	0.171389	+	0.971996i
$738$	−1.50779	−	0.538177i	−0.0555024	−	0.0198106i
$739$	−4.23374	+	24.0107i	−0.155740	+	0.883248i	0.802365	+	0.596833i	$0.203575\pi$
$739$	−4.23374	+	24.0107i	−0.155740	+	0.883248i	−0.958106	+	0.286415i	$0.907536\pi$
$740$	2.00187	−	0.474451i	0.0735901	−	0.0174412i
$741$	30.9937	−	15.6867i	1.13858	−	0.576265i
$742$	−10.2993	−	6.77395i	−0.378099	−	0.248680i
$743$	2.09728	−	36.0090i	0.0769418	−	1.32104i	−0.710082	−	0.704118i	$-0.751342\pi$
$743$	2.09728	−	36.0090i	0.0769418	−	1.32104i	0.787024	−	0.616922i	$-0.211621\pi$
$744$	−2.99799	+	0.359883i	−0.109912	+	0.0131940i
$745$	9.91272	−	33.1108i	0.363174	−	1.21308i
$746$	−8.46844	+	3.08226i	−0.310052	+	0.112850i
$747$	−3.36050	−	3.51776i	−0.122954	−	0.128708i
$748$	30.2335	+	11.0041i	1.10544	+	0.402349i
$749$	−38.1661	+	51.2660i	−1.39456	+	1.87322i
$750$	−15.2163	+	3.65643i	−0.555622	+	0.133514i
$751$	−2.27344	−	0.538814i	−0.0829588	−	0.0196616i	0.188927	−	0.981991i	$-0.439499\pi$
$751$	−2.27344	−	0.538814i	−0.0829588	−	0.0196616i	−0.271886	+	0.962330i	$0.587647\pi$
$752$	2.22572	−	5.15979i	0.0811635	−	0.188158i
$753$	0.115124		0.000358564i	0.00419535		1.30668e-5i
$754$	−1.91528	+	1.25970i	−0.0697505	+	0.0458756i
$755$	−1.72660	−	2.99055i	−0.0628372	−	0.108837i
$756$	−13.9410	−	23.6337i	−0.507028	−	0.859549i
$757$	8.08646	−	14.0062i	0.293907	−	0.509063i	−0.680823	−	0.732448i	$-0.738378\pi$
$757$	8.08646	−	14.0062i	0.293907	−	0.509063i	0.974730	+	0.223386i	$0.0717109\pi$
$758$	0.942084	+	16.1750i	0.0342180	+	0.587501i
$759$	28.4543	+	10.2563i	1.03283	+	0.372279i
$760$	−17.3920	+	2.03284i	−0.630875	+	0.0737387i
$761$	31.1257	−	32.9914i	1.12831	−	1.19594i	0.150020	−	0.988683i	$-0.452066\pi$
$761$	31.1257	−	32.9914i	1.12831	−	1.19594i	0.978287	−	0.207253i	$-0.0664523\pi$
$762$	0.322198	+	5.25017i	0.0116720	+	0.190194i
$763$	28.8281	+	3.36952i	1.04365	+	0.121985i
$764$	−6.13669	+	5.14929i	−0.222018	+	0.186295i
$765$	5.95916	+	19.4629i	0.215454	+	0.703682i
$766$	9.49250	+	7.96515i	0.342978	+	0.287793i
$767$	16.2461	+	17.2199i	0.586614	+	0.621774i
$768$	16.0297	−	17.0968i	0.578420	−	0.616928i
$769$	16.4123	−	8.24257i	0.591843	−	0.297235i	−0.127557	−	0.991831i	$-0.540713\pi$
$769$	16.4123	−	8.24257i	0.591843	−	0.297235i	0.719399	+	0.694597i	$0.244417\pi$
$770$	−19.8696	+	9.97891i	−0.716052	+	0.359615i
$771$	32.6251	+	7.62504i	1.17496	+	0.274609i
$772$	0.167552	+	0.177595i	0.00603033	+	0.00639178i
$773$	22.5821	+	18.9486i	0.812222	+	0.681536i	0.951137	−	0.308769i	$-0.0999169\pi$
$773$	22.5821	+	18.9486i	0.812222	+	0.681536i	−0.138915	+	0.990304i	$0.544361\pi$
$774$	1.02182	−	19.6522i	0.0367287	−	0.706385i
$775$	−1.41544	+	1.18769i	−0.0508441	+	0.0426633i
$776$	−13.1233	−	1.53389i	−0.471099	−	0.0550636i
$777$	−5.89376	−	2.93701i	−0.211438	−	0.105365i
$778$	−15.2903	+	16.2067i	−0.548183	+	0.581040i
$779$	−3.02780	+	0.353899i	−0.108482	+	0.0126797i
$780$	−2.82834	−	15.7533i	−0.101271	−	0.564057i
$781$	1.80245	+	30.9468i	0.0644967	+	1.10736i
$782$	−6.18635	+	10.7151i	−0.221224	+	0.383170i
$783$	3.04599	+	1.49428i	0.108855	+	0.0534011i
$784$	−2.63788	−	4.56895i	−0.0942102	−	0.163177i
$785$	−24.3507	+	16.0157i	−0.869114	+	0.571626i
$786$	−11.2080	+	19.5532i	−0.399776	+	0.697441i
$787$	12.6971	−	29.4351i	0.452601	−	1.04925i	−0.527284	−	0.849689i	$-0.676790\pi$
$787$	12.6971	−	29.4351i	0.452601	−	1.04925i	0.979886	−	0.199559i	$-0.0639510\pi$
$788$	−15.1604	−	3.59307i	−0.540066	−	0.127998i
$789$	−17.9595	−	18.9176i	−0.639376	−	0.673485i
$790$	7.76935	−	10.4360i	0.276421	−	0.371298i
$791$	−35.7894	−	13.0263i	−1.27252	−	0.463161i
$792$	−2.58509	−	40.0814i	−0.0918573	−	1.42423i
$793$	−28.6670	+	10.4339i	−1.01799	+	0.370520i
$794$	7.08779	−	23.6749i	0.251536	−	0.840189i
$795$	−4.18459	+	9.78464i	−0.148412	+	0.347026i
$796$	−1.65411	+	28.4000i	−0.0586283	+	1.00661i
$797$	−9.84741	−	6.47674i	−0.348813	−	0.229418i	0.362996	−	0.931791i	$-0.381754\pi$
$797$	−9.84741	−	6.47674i	−0.348813	−	0.229418i	−0.711810	+	0.702373i	$0.752124\pi$
$798$	19.2328	+	12.5640i	0.680833	+	0.444759i
$799$	35.3783	−	8.38481i	1.25159	−	0.296633i
$800$	2.85246	−	16.1771i	0.100850	−	0.571948i
$801$	−0.524058	+	3.08431i	−0.0185167	+	0.108979i
$802$	−2.31363	−	13.1212i	−0.0816970	−	0.463327i
$803$	−8.81174	−	20.4279i	−0.310960	−	0.720885i
$804$	−5.08861	−	11.6964i	−0.179461	−	0.412501i
$805$	5.57733	+	18.6296i	0.196575	+	0.656606i
$806$	1.37986	+	1.85347i	0.0486035	+	0.0652859i
$807$	19.0805	−	7.01210i	0.671664	−	0.246838i
$808$	−22.6539	−	11.3772i	−0.796962	−	0.400249i
$809$	21.4155			0.752929			0.376464	−	0.926431i	$-0.377140\pi$
$809$	21.4155			0.752929			0.376464	+	0.926431i	$0.377140\pi$
$810$	7.89458	−	6.79372i	0.277387	−	0.238707i
$811$	1.73790			0.0610258			0.0305129	−	0.999534i	$-0.490286\pi$
$811$	1.73790			0.0610258			0.0305129	+	0.999534i	$0.490286\pi$
$812$	3.08119	+	1.54743i	0.108129	+	0.0543043i
$813$	−3.83158	−	3.19480i	−0.134379	−	0.112046i
$814$	−2.35932	−	3.16911i	−0.0826940	−	0.111077i
$815$	−7.50075	−	25.0542i	−0.262740	−	0.877612i
$816$	−5.58461	−	0.635122i	−0.195500	−	0.0222337i
$817$	−14.8414	−	34.4063i	−0.519235	−	1.20372i
$818$	3.23502	+	18.3467i	0.113110	+	0.641477i
$819$	−25.3375	+	44.5241i	−0.885365	+	1.55580i
$820$	−0.243897	+	1.38321i	−0.00851725	+	0.0483037i
$821$	−8.67839	+	2.05682i	−0.302878	+	0.0717834i	−0.379245	−	0.925296i	$-0.623816\pi$
$821$	−8.67839	+	2.05682i	−0.302878	+	0.0717834i	0.0763667	+	0.997080i	$0.475668\pi$
$822$	0.691055	−	12.5376i	0.0241033	−	0.437297i
$823$	−1.54747	−	1.01779i	−0.0539414	−	0.0354778i	0.522252	−	0.852791i	$-0.325092\pi$
$823$	−1.54747	−	1.01779i	−0.0539414	−	0.0354778i	−0.576193	+	0.817313i	$0.695462\pi$
$824$	−0.501339	+	8.60765i	−0.0174650	+	0.299862i
$825$	−14.7383	−	19.6687i	−0.513120	−	0.684777i
$826$	−4.49031	+	14.9987i	−0.156238	+	0.521870i
$827$	−19.7686	+	7.19517i	−0.687420	+	0.250200i	−0.662030	−	0.749477i	$-0.730305\pi$
$827$	−19.7686	+	7.19517i	−0.687420	+	0.250200i	−0.0253900	+	0.999678i	$0.508083\pi$
$828$	−14.3114	−	1.58246i	−0.497354	−	0.0549942i
$829$	−5.33030	−	1.94007i	−0.185129	−	0.0673814i	0.247792	−	0.968813i	$-0.420295\pi$
$829$	−5.33030	−	1.94007i	−0.185129	−	0.0673814i	−0.432921	+	0.901432i	$0.642517\pi$
$830$	1.12067	−	1.50531i	0.0388989	−	0.0522502i
$831$	1.13115	−	3.82160i	0.0392393	−	0.132570i
$832$	−13.7977	−	3.27012i	−0.478350	−	0.113371i
$833$	13.5203	−	31.3435i	0.468450	−	1.08599i
$834$	10.8342	+	18.6311i	0.375156	+	0.645141i
$835$	4.19404	−	2.75846i	0.145141	−	0.0954606i
$836$	−15.6738	−	27.1478i	−0.542089	−	0.938925i
$837$	1.32513	−	3.15268i	0.0458034	−	0.108973i
$838$	−6.14931	+	10.6509i	−0.212424	+	0.367930i
$839$	−1.39131	−	23.8879i	−0.0480334	−	0.824701i	−0.933184	−	0.359398i	$-0.882982\pi$
$839$	−1.39131	−	23.8879i	−0.0480334	−	0.824701i	0.885151	−	0.465304i	$-0.154055\pi$
$840$	19.7301	−	16.6605i	0.680753	−	0.574842i
$841$	28.3805	−	3.31720i	0.978637	−	0.114386i
$842$	−12.6348	+	13.3921i	−0.435424	+	0.461522i
$843$	−9.16378	+	6.06809i	−0.315617	+	0.208996i
$844$	1.64386	+	0.192140i	0.0565841	+	0.00661373i
$845$	−8.14471	+	6.83422i	−0.280186	+	0.235104i
$846$	−11.2024	−	14.8534i	−0.385147	−	0.510670i
$847$	−42.3609	−	35.5450i	−1.45554	−	1.22134i
$848$	−2.01657	−	2.13744i	−0.0692494	−	0.0734000i
$849$	7.36913	+	24.3384i	0.252908	+	0.835293i
$850$	8.98455	−	4.51221i	0.308168	−	0.154768i
$851$	−3.08792	+	1.55081i	−0.105853	+	0.0531612i
$852$	−4.27637	−	14.1238i	−0.146506	−	0.483874i
$853$	−4.63443	−	4.91221i	−0.158680	−	0.168191i	0.643156	−	0.765735i	$-0.277625\pi$
$853$	−4.63443	−	4.91221i	−0.158680	−	0.168191i	−0.801836	+	0.597544i	$0.796143\pi$
$854$	−15.4550	−	12.9683i	−0.528860	−	0.443766i
$855$	7.74148	−	18.2587i	0.264753	−	0.624434i
$856$	34.1166	−	28.6272i	1.16608	−	0.978457i
$857$	18.7289	+	2.18910i	0.639768	+	0.0747782i	0.429791	−	0.902928i	$-0.358587\pi$
$857$	18.7289	+	2.18910i	0.639768	+	0.0747782i	0.209977	+	0.977706i	$0.432661\pi$
$858$	−25.6272	+	16.9698i	−0.874898	+	0.579341i
$859$	−22.2456	+	23.5790i	−0.759010	+	0.804503i	−0.985530	−	0.169503i	$-0.945784\pi$
$859$	−22.2456	+	23.5790i	−0.759010	+	0.804503i	0.226520	+	0.974007i	$0.427265\pi$
$860$	−17.1478	+	2.00429i	−0.584736	+	0.0683458i
$861$	3.43483	−	2.90045i	0.117059	−	0.0988469i
$862$	−0.0641516	−	1.10144i	−0.00218501	−	0.0375152i
$863$	23.6121	−	40.8973i	0.803765	−	1.39216i	−0.113357	−	0.993554i	$-0.536160\pi$
$863$	23.6121	−	40.8973i	0.803765	−	1.39216i	0.917122	−	0.398607i	$-0.130506\pi$
$864$	8.99151	+	29.0432i	0.305897	+	0.988071i
$865$	−13.8292	−	23.9529i	−0.470208	−	0.814424i
$866$	8.49550	−	5.58758i	0.288689	−	0.189874i
$867$	−3.47941	−	5.98340i	−0.118167	−	0.203207i
$868$	1.37656	−	3.19123i	0.0467235	−	0.108317i
$869$	55.2930	+	13.1047i	1.87569	+	0.444546i
$870$	−0.371453	+	1.25495i	−0.0125934	+	0.0425468i
$871$	−14.2209	+	19.1020i	−0.481858	+	0.647248i
$872$	−19.0051	−	6.91730i	−0.643595	−	0.234249i
$873$	8.86119	−	12.0587i	0.299906	−	0.408127i
$874$	11.3280	−	4.12304i	0.383174	−	0.139464i
$875$	12.6036	−	42.0991i	0.426081	−	1.42321i
$876$	6.35078	+	8.47534i	0.214573	+	0.286355i
$877$	−0.327452	+	5.62213i	−0.0110573	+	0.189846i	0.988256	+	0.152804i	$0.0488304\pi$
$877$	−0.327452	+	5.62213i	−0.0110573	+	0.189846i	−0.999314	+	0.0370415i	$0.988207\pi$
$878$	13.5416	+	8.90647i	0.457008	+	0.300579i
$879$	2.41696	−	43.8500i	0.0815220	−	1.47902i
$880$	−5.15743	+	1.22233i	−0.173857	+	0.0412048i
$881$	−0.984686	+	5.58443i	−0.0331749	+	0.188144i	−0.996892	−	0.0787820i	$-0.974897\pi$
$881$	−0.984686	+	5.58443i	−0.0331749	+	0.188144i	0.963717	+	0.266926i	$0.0860080\pi$
$882$	−17.4663	+	0.108802i	−0.588122	+	0.00366355i
$883$	5.95650	+	33.7810i	0.200452	+	1.13682i	0.904437	+	0.426606i	$0.140291\pi$
$883$	5.95650	+	33.7810i	0.200452	+	1.13682i	−0.703985	+	0.710215i	$0.748598\pi$
$884$	11.3260	+	26.2566i	0.380934	+	0.883105i
$885$	13.4293	+	1.52728i	0.451421	+	0.0513389i
$886$	7.61382	+	25.4319i	0.255791	+	0.854403i
$887$	16.0539	+	21.5641i	0.539037	+	0.724053i	0.985297	−	0.170851i	$-0.0546516\pi$
$887$	16.0539	+	21.5641i	0.539037	+	0.724053i	−0.446260	+	0.894904i	$0.647244\pi$
$888$	3.52424	+	2.93853i	0.118266	+	0.0986106i
$889$	−13.1996	−	6.62908i	−0.442700	−	0.222332i
$890$	−1.20683			−0.0404531
$891$	40.9025	+	19.9078i	1.37028	+	0.666937i
$892$	20.6987			0.693043
$893$	−31.6566	−	15.8986i	−1.05935	−	0.532025i
$894$	29.6579	−	10.8993i	0.991910	−	0.364528i
$895$	−10.5087	−	14.1156i	−0.351266	−	0.471832i
$896$	10.0684	+	33.6307i	0.336361	+	1.12352i
$897$	10.7243	+	24.6504i	0.358075	+	0.823052i
$898$	−0.371650	−	0.861583i	−0.0124021	−	0.0287514i
$899$	0.0746222	+	0.423204i	0.00248879	+	0.0141146i
$900$	9.00953	+	7.46476i	0.300318	+	0.248825i
$901$	3.30159	−	18.7243i	0.109992	−	0.623796i
$902$	2.62460	−	0.622041i	0.0873896	−	0.0207117i
$903$	46.2633	+	30.2218i	1.53955	+	1.00572i
$904$	22.1733	+	14.5836i	0.737475	+	0.485045i
$905$	−1.35902	+	23.3335i	−0.0451753	+	0.775631i
$906$	1.24135	−	2.90260i	0.0412412	−	0.0964326i
$907$	−8.72987	+	29.1598i	−0.289871	+	0.968235i	0.681729	+	0.731605i	$0.261228\pi$
$907$	−8.72987	+	29.1598i	−0.289871	+	0.968235i	−0.971600	+	0.236631i	$0.923957\pi$
$908$	−32.1114	+	11.6876i	−1.06565	+	0.387866i
$909$	23.8893	−	15.9263i	0.792359	−	0.528243i
$910$	−18.5699	−	6.75888i	−0.615585	−	0.224055i
$911$	8.39961	−	11.2826i	0.278291	−	0.373810i	−0.640898	−	0.767626i	$-0.721438\pi$
$911$	8.39961	−	11.2826i	0.278291	−	0.373810i	0.919189	+	0.393816i	$0.128845\pi$
$912$	3.77043	+	3.97157i	0.124851	+	0.131512i
$913$	7.97556	+	1.89024i	0.263953	+	0.0625579i
$914$	9.92224	−	23.0023i	0.328199	−	0.760850i
$915$	−8.66136	+	15.1104i	−0.286336	+	0.499534i
$916$	1.77228	−	1.16565i	0.0585578	−	0.0385141i
$917$	−31.6440	−	54.8090i	−1.04498	−	1.80995i
$918$	−10.9722	+	15.0293i	−0.362136	+	0.496042i
$919$	−14.5007	+	25.1160i	−0.478335	+	0.828501i	−0.999691	−	0.0248384i	$-0.992093\pi$
$919$	−14.5007	+	25.1160i	−0.478335	+	0.828501i	0.521356	+	0.853339i	$0.325426\pi$
$920$	−0.787909	−	13.5279i	−0.0259766	−	0.446001i
$921$	−3.72906	−	20.7700i	−0.122877	−	0.684396i
$922$	0.261356	−	0.0305482i	0.00860731	−	0.00100605i
$923$	−18.9069	+	20.0402i	−0.622329	+	0.659630i
$924$	41.3768	+	20.6191i	1.36120	+	0.678317i
$925$	2.78891	+	0.325976i	0.0916986	+	0.0107180i
$926$	1.76780	−	1.48336i	0.0580935	−	0.0487462i
$927$	−8.19215	−	5.31526i	−0.269066	−	0.174576i
$928$	−2.92661	−	2.45572i	−0.0960706	−	0.0806128i
$929$	30.5782	+	32.4109i	1.00324	+	1.06337i	0.997989	+	0.0633825i	$0.0201888\pi$
$929$	30.5782	+	32.4109i	1.00324	+	1.06337i	0.00524738	+	0.999986i	$0.498330\pi$
$930$	1.28460	+	0.300233i	0.0421237	+	0.00984503i
$931$	−29.7210	+	14.9264i	−0.974066	+	0.489194i
$932$	−17.4542	+	8.76584i	−0.571732	+	0.287135i
$933$	29.7776	−	31.7600i	0.974874	−	1.03978i
$934$	2.02962	+	2.15127i	0.0664112	+	0.0703918i
$935$	−26.2707	−	22.0437i	−0.859143	−	0.720907i
$936$	24.3348	−	26.1174i	0.795408	−	0.853675i
$937$	−15.7744	+	13.2363i	−0.515326	+	0.432409i	−0.862999	−	0.505206i	$-0.831416\pi$
$937$	−15.7744	+	13.2363i	−0.515326	+	0.432409i	0.347673	+	0.937616i	$0.386972\pi$
$938$	−15.6427	−	1.82837i	−0.510752	−	0.0596983i
$939$	−3.13647	−	51.1083i	−0.102355	−	1.66786i
$940$	−11.2007	+	11.8721i	−0.365327	+	0.387224i
$941$	−56.3981	+	6.59199i	−1.83852	+	0.214893i	−0.963226	−	0.268691i	$-0.913409\pi$
$941$	−56.3981	+	6.59199i	−1.83852	+	0.214893i	−0.875298	+	0.483584i	$0.839335\pi$
$942$	−25.0662	−	9.03504i	−0.816702	−	0.294378i
$943$	−0.137168	−	2.35508i	−0.00446680	−	0.0766920i
$944$	−1.86608	+	3.23215i	−0.0607359	+	0.105198i
$945$	5.34763	+	28.7542i	0.173958	+	0.935374i
$946$	16.5775	+	28.7131i	0.538982	+	0.933544i
$947$	13.1803	−	8.66883i	0.428303	−	0.281699i	−0.317000	−	0.948426i	$-0.602675\pi$
$947$	13.1803	−	8.66883i	0.428303	−	0.281699i	0.745302	+	0.666727i	$0.232305\pi$
$948$	−27.0509	+	0.0842527i	−0.878574	+	0.00273640i
$949$	7.83165	−	18.1558i	0.254226	−	0.589363i
$950$	−9.53173	−	2.25906i	−0.309250	−	0.0732936i
$951$	7.22169	−	1.73534i	0.234179	−	0.0562724i
$952$	−27.5510	+	37.0075i	−0.892934	+	1.19942i
$953$	47.3933	+	17.2497i	1.53522	+	0.558774i	0.964893	−	0.262645i	$-0.0845947\pi$
$953$	47.3933	+	17.2497i	1.53522	+	0.558774i	0.570326	+	0.821418i	$0.306817\pi$
$954$	−9.45243	+	2.30255i	−0.306034	+	0.0745477i
$955$	8.02382	−	2.92043i	0.259645	−	0.0945030i
$956$	−9.13079	+	30.4990i	−0.295311	+	0.986407i
$957$	−5.67543	+	0.681288i	−0.183461	+	0.0220229i
$958$	−0.143907	+	2.47079i	−0.00464942	+	0.0798275i
$959$	29.4594	+	19.3757i	0.951293	+	0.625675i
$960$	−7.22308	+	3.65578i	−0.233124	+	0.117990i
$961$	−29.7429	+	7.04920i	−0.959449	+	0.227393i
$962$	0.609760	−	3.45812i	0.0196594	−	0.111494i
$963$	9.06821	+	49.6190i	0.292219	+	1.59895i
$964$	1.70519	+	9.67059i	0.0549203	+	0.311469i
$965$	−0.103079	−	0.238964i	−0.00331824	−	0.00769253i
$966$	−10.5718	+	14.2932i	−0.340143	+	0.459875i
$967$	−6.27933	−	20.9744i	−0.201930	−	0.674492i	−0.997630	−	0.0688018i	$-0.978082\pi$
$967$	−6.27933	−	20.9744i	−0.201930	−	0.674492i	0.795701	−	0.605690i	$-0.207103\pi$
$968$	23.0104	+	30.9083i	0.739581	+	0.993430i
$969$	−6.04408	+	34.9132i	−0.194164	+	1.12157i
$970$	5.15856	+	2.59072i	0.165631	+	0.0831832i
$971$	−21.3313			−0.684555			−0.342277	−	0.939599i	$-0.611198\pi$
$971$	−21.3313			−0.684555			−0.342277	+	0.939599i	$0.611198\pi$
$972$	−21.1467	−	4.66530i	−0.678281	−	0.149640i
$973$	−60.5205			−1.94020
$974$	−0.855569	−	0.429683i	−0.0274142	−	0.0137679i
$975$	3.72619	−	21.5241i	0.119334	−	0.689323i
$976$	−2.87193	−	3.85768i	−0.0919283	−	0.123481i
$977$	−2.05675	−	6.87002i	−0.0658012	−	0.219791i	0.918765	−	0.394806i	$-0.129188\pi$
$977$	−2.05675	−	6.87002i	−0.0658012	−	0.219791i	−0.984566	+	0.175014i	$0.944003\pi$
$978$	14.2177	−	19.2224i	0.454631	−	0.614663i
$979$	−2.08772	−	4.83988i	−0.0667238	−	0.154683i
$980$	2.66095	+	15.0910i	0.0850011	+	0.482065i
$981$	17.4552	−	14.8329i	0.557302	−	0.473579i
$982$	5.50290	−	31.2085i	0.175605	−	0.995904i
$983$	−40.2972	+	9.55061i	−1.28528	+	0.304617i	−0.815805	−	0.578328i	$-0.803705\pi$
$983$	−40.2972	+	9.55061i	−1.28528	+	0.304617i	−0.469477	+	0.882945i	$0.655557\pi$
$984$	−2.79505	+	1.41465i	−0.0891030	+	0.0450973i
$985$	13.8750	+	9.12572i	0.442094	+	0.290770i
$986$	0.135959	−	2.33433i	0.00432983	−	0.0743403i
$987$	51.8700	−	6.22655i	1.65104	−	0.198193i
$988$	7.99060	−	26.6905i	0.254215	−	0.849137i
$989$	27.2487	−	9.91773i	0.866460	−	0.315365i
$990$	−4.92797	+	16.8417i	−0.156621	+	0.535264i
$991$	51.2878	+	18.6672i	1.62921	+	0.592984i	0.985105	−	0.171953i	$-0.0550079\pi$
$991$	51.2878	+	18.6672i	1.62921	+	0.592984i	0.644105	+	0.764937i	$0.277230\pi$
$992$	−2.29960	+	3.08890i	−0.0730125	+	0.0980728i
$993$	−46.8711	+	11.2629i	−1.48741	+	0.357419i
$994$	−17.7295	−	4.20196i	−0.562344	−	0.133278i
$995$	12.0102	−	27.8428i	0.380750	−	0.882677i
$996$	−3.90188	+	0.0121528i	−0.123636	+	0.000385075i
$997$	22.1506	−	14.5687i	0.701516	−	0.461395i	−0.147979	−	0.988990i	$-0.547277\pi$
$997$	22.1506	−	14.5687i	0.701516	−	0.461395i	0.849495	+	0.527596i	$0.176906\pi$
$998$	−16.0810	−	27.8531i	−0.509035	−	0.881674i
$999$	−4.86673	+	1.82302i	−0.153977	+	0.0576778i

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	81.2.g.a.13.4	✓	144
3.2	odd	2		243.2.g.a.10.5		144
9.2	odd	6		729.2.g.a.514.4		144
9.4	even	3		729.2.g.c.28.5		144
9.5	odd	6		729.2.g.b.28.4		144
9.7	even	3		729.2.g.d.514.5		144
81.2	odd	54		729.2.g.b.703.4		144
81.5	odd	54		6561.2.a.d.1.43		72
81.25	even	27	inner	81.2.g.a.25.4	yes	144
81.29	odd	54		729.2.g.a.217.4		144
81.52	even	27		729.2.g.d.217.5		144
81.56	odd	54		243.2.g.a.73.5		144
81.76	even	27		6561.2.a.c.1.30		72
81.79	even	27		729.2.g.c.703.5		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.4	✓	144	1.1	even	1	trivial
81.2.g.a.25.4	yes	144	81.25	even	27	inner
243.2.g.a.10.5		144	3.2	odd	2
243.2.g.a.73.5		144	81.56	odd	54
729.2.g.a.217.4		144	81.29	odd	54
729.2.g.a.514.4		144	9.2	odd	6
729.2.g.b.28.4		144	9.5	odd	6
729.2.g.b.703.4		144	81.2	odd	54
729.2.g.c.28.5		144	9.4	even	3
729.2.g.c.703.5		144	81.79	even	27
729.2.g.d.217.5		144	81.52	even	27
729.2.g.d.514.5		144	9.7	even	3
6561.2.a.c.1.30		72	81.76	even	27
6561.2.a.d.1.43		72	81.5	odd	54

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Hilbert	Bianchi

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

Introduction

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Modular forms

Varieties

Fields

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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	81.2.g.a.13.4

Level	$81$
Weight	$2$
Character	81.13
Analytic conductor	$0.647$
Analytic rank	$0$
Dimension	$144$
Inner twists	$2$