LMFDB - Embedded newform 931.2.x.a.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(226,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([6, 10]))

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

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

chi := DirichletCharacter("931.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.x (of order $9$, degree $6$, not 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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			557.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	931.557
Dual form			931.2.x.a.814.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37939 + 0.866025i) q^{2} +(-0.500000 + 0.419550i) q^{3} +(3.37939 + 2.83564i) q^{4} +(-1.03209 + 0.866025i) q^{5} +(-1.55303 + 0.565258i) q^{6} +(3.05303 + 5.28801i) q^{8} +(-0.446967 + 2.53487i) q^{9} +O(q^{10})$	\(q+(2.37939 + 0.866025i) q^{2} +(-0.500000 + 0.419550i) q^{3} +(3.37939 + 2.83564i) q^{4} +(-1.03209 + 0.866025i) q^{5} +(-1.55303 + 0.565258i) q^{6} +(3.05303 + 5.28801i) q^{8} +(-0.446967 + 2.53487i) q^{9} +(-3.20574 + 1.16679i) q^{10} -1.18479 q^{11} -2.87939 q^{12} +(-2.55303 + 0.929228i) q^{13} +(0.152704 - 0.866025i) q^{15} +(1.15270 + 6.53731i) q^{16} +(0.673648 + 3.82045i) q^{17} +(-3.25877 + 5.64436i) q^{18} +(3.29813 - 2.84997i) q^{19} -5.94356 q^{20} +(-2.81908 - 1.02606i) q^{22} +(4.75877 - 1.73205i) q^{23} +(-3.74510 - 1.36310i) q^{24} +(-0.553033 + 3.13641i) q^{25} -6.87939 q^{26} +(-1.81908 - 3.15074i) q^{27} +(-3.56418 - 2.99070i) q^{29} +(1.11334 - 1.92836i) q^{30} +(1.91875 + 3.32337i) q^{31} +(-0.798133 + 4.52644i) q^{32} +(0.592396 - 0.497079i) q^{33} +(-1.70574 + 9.67372i) q^{34} +(-8.69846 + 7.29888i) q^{36} +(2.05303 + 3.55596i) q^{37} +(10.3157 - 3.92490i) q^{38} +(0.886659 - 1.53574i) q^{39} +(-7.73055 - 2.81369i) q^{40} +(9.38326 + 3.41523i) q^{41} +(-1.51114 - 8.57013i) q^{43} +(-4.00387 - 3.35965i) q^{44} +(-1.73396 - 3.00330i) q^{45} +12.8229 q^{46} +(0.0996702 - 0.565258i) q^{47} +(-3.31908 - 2.78504i) q^{48} +(-4.03209 + 6.98378i) q^{50} +(-1.93969 - 1.62760i) q^{51} +(-11.2626 - 4.09927i) q^{52} +(2.25490 + 1.89209i) q^{53} +(-1.59967 - 9.07218i) q^{54} +(1.22281 - 1.02606i) q^{55} +(-0.453363 + 2.80872i) q^{57} +(-5.89053 - 10.2027i) q^{58} +(-0.683448 - 3.87603i) q^{59} +(2.97178 - 2.49362i) q^{60} +(4.24510 - 1.54509i) q^{61} +(1.68732 + 9.56926i) q^{62} +(0.819078 - 1.41868i) q^{64} +(1.83022 - 3.17004i) q^{65} +(1.84002 - 0.669713i) q^{66} +(3.65270 - 1.32948i) q^{67} +(-8.55690 + 14.8210i) q^{68} +(-1.65270 + 2.86257i) q^{69} +(-1.20439 - 6.83045i) q^{71} +(-14.7690 + 5.37549i) q^{72} +(4.69459 - 3.93923i) q^{73} +(1.80541 + 10.2390i) q^{74} +(-1.03936 - 1.80023i) q^{75} +(19.2271 - 0.278817i) q^{76} +(3.43969 - 2.88624i) q^{78} +(1.70321 + 9.65939i) q^{79} +(-6.85117 - 5.74881i) q^{80} +(-5.02481 - 1.82888i) q^{81} +(19.3687 + 16.2523i) q^{82} +(-6.15910 + 10.6679i) q^{83} +(-4.00387 - 3.35965i) q^{85} +(3.82635 - 21.7003i) q^{86} +3.03684 q^{87} +(-3.61721 - 6.26519i) q^{88} +(-1.85844 - 1.55942i) q^{89} +(-1.52481 - 8.64766i) q^{90} +(20.9932 + 7.64090i) q^{92} +(-2.35369 - 0.856674i) q^{93} +(0.726682 - 1.25865i) q^{94} +(-0.935822 + 5.79769i) q^{95} +(-1.50000 - 2.59808i) q^{96} +(5.64543 - 4.73708i) q^{97} +(0.529563 - 3.00330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9	$ 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} - 9 q^{10} - 6 q^{12} - 3 q^{13} + 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{23} - 21 q^{24} + 9 q^{25} - 30 q^{26} + 6 q^{27} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 24 q^{36} + 3 q^{38} + 12 q^{39} - 9 q^{40} + 21 q^{41} - 3 q^{43} - 15 q^{45} + 36 q^{46} + 15 q^{47} - 3 q^{48} - 15 q^{50} - 6 q^{51} - 21 q^{52} + 15 q^{53} - 24 q^{54} + 18 q^{55} + 24 q^{57} - 18 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} - 12 q^{62} - 12 q^{64} - 12 q^{65} - 9 q^{66} + 24 q^{67} - 15 q^{68} - 12 q^{69} - 6 q^{71} - 3 q^{72} + 24 q^{73} + 15 q^{74} - 15 q^{75} + 36 q^{76} + 15 q^{78} + 15 q^{79} - 15 q^{80} - 3 q^{81} + 45 q^{82} + 24 q^{86} + 42 q^{87} + 9 q^{88} - 3 q^{89} + 18 q^{90} + 42 q^{92} + 27 q^{93} - 9 q^{94} - 24 q^{95} - 9 q^{96} + 18 q^{97} + 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9 - 9 * q^10 - 6 * q^12 - 3 * q^13 + 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 + 6 * q^19 - 6 * q^20 + 6 * q^23 - 21 * q^24 + 9 * q^25 - 30 * q^26 + 6 * q^27 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 24 * q^36 + 3 * q^38 + 12 * q^39 - 9 * q^40 + 21 * q^41 - 3 * q^43 - 15 * q^45 + 36 * q^46 + 15 * q^47 - 3 * q^48 - 15 * q^50 - 6 * q^51 - 21 * q^52 + 15 * q^53 - 24 * q^54 + 18 * q^55 + 24 * q^57 - 18 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 - 12 * q^62 - 12 * q^64 - 12 * q^65 - 9 * q^66 + 24 * q^67 - 15 * q^68 - 12 * q^69 - 6 * q^71 - 3 * q^72 + 24 * q^73 + 15 * q^74 - 15 * q^75 + 36 * q^76 + 15 * q^78 + 15 * q^79 - 15 * q^80 - 3 * q^81 + 45 * q^82 + 24 * q^86 + 42 * q^87 + 9 * q^88 - 3 * q^89 + 18 * q^90 + 42 * q^92 + 27 * q^93 - 9 * q^94 - 24 * q^95 - 9 * q^96 + 18 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	2.37939	+	0.866025i	1.68248	+	0.612372i	0.993646	−	0.112548i	$-0.0359011\pi$
$2$	2.37939	+	0.866025i	1.68248	+	0.612372i	0.688833	+	0.724920i	$0.258123\pi$
$3$	−0.500000	+	0.419550i	−0.288675	+	0.242227i	−0.775612	−	0.631210i	$-0.782559\pi$
$3$	−0.500000	+	0.419550i	−0.288675	+	0.242227i	0.486937	+	0.873437i	$0.338114\pi$
$4$	3.37939	+	2.83564i	1.68969	+	1.41782i
$5$	−1.03209	+	0.866025i	−0.461564	+	0.387298i	−0.843706	−	0.536805i	$-0.819631\pi$
$5$	−1.03209	+	0.866025i	−0.461564	+	0.387298i	0.382142	+	0.924104i	$0.375187\pi$
$6$	−1.55303	+	0.565258i	−0.634023	+	0.230766i
$7$		0			0
$7$		0			0
$8$	3.05303	+	5.28801i	1.07941	+	1.86959i
$9$	−0.446967	+	2.53487i	−0.148989	+	0.844958i
$10$	−3.20574	+	1.16679i	−1.01374	+	0.368972i
$11$	−1.18479			−0.357228			−0.178614	−	0.983919i	$-0.557161\pi$
$11$	−1.18479			−0.357228			−0.178614	+	0.983919i	$0.557161\pi$
$12$	−2.87939			−0.831207
$13$	−2.55303	+	0.929228i	−0.708084	+	0.257722i	−0.670859	−	0.741585i	$-0.734074\pi$
$13$	−2.55303	+	0.929228i	−0.708084	+	0.257722i	−0.0372256	+	0.999307i	$0.511852\pi$
$14$		0			0
$15$	0.152704	−	0.866025i	0.0394279	−	0.223607i
$16$	1.15270	+	6.53731i	0.288176	+	1.63433i
$17$	0.673648	+	3.82045i	0.163384	+	0.926595i	0.950715	+	0.310065i	$0.100351\pi$
$17$	0.673648	+	3.82045i	0.163384	+	0.926595i	−0.787332	+	0.616530i	$0.788538\pi$
$18$	−3.25877	+	5.64436i	−0.768100	+	1.33039i
$19$	3.29813	−	2.84997i	0.756644	−	0.653827i
$19$	3.29813	−	2.84997i	0.756644	−	0.653827i
$20$	−5.94356			−1.32902
$21$		0			0
$22$	−2.81908	−	1.02606i	−0.601029	−	0.218757i
$23$	4.75877	−	1.73205i	0.992272	−	0.361158i	0.205673	−	0.978621i	$-0.434062\pi$
$23$	4.75877	−	1.73205i	0.992272	−	0.361158i	0.786600	+	0.617463i	$0.211840\pi$
$24$	−3.74510	−	1.36310i	−0.764465	−	0.278243i
$25$	−0.553033	+	3.13641i	−0.110607	+	0.627282i
$26$	−6.87939			−1.34916
$27$	−1.81908	−	3.15074i	−0.350082	−	0.606359i
$28$		0			0
$29$	−3.56418	−	2.99070i	−0.661851	−	0.555359i	0.248790	−	0.968557i	$-0.419967\pi$
$29$	−3.56418	−	2.99070i	−0.661851	−	0.555359i	−0.910641	+	0.413198i	$0.864412\pi$
$30$	1.11334	−	1.92836i	0.203267	−	0.352069i
$31$	1.91875	+	3.32337i	0.344617	+	0.596895i	0.985284	−	0.170924i	$-0.0546753\pi$
$31$	1.91875	+	3.32337i	0.344617	+	0.596895i	−0.640667	+	0.767819i	$0.721342\pi$
$32$	−0.798133	+	4.52644i	−0.141091	+	0.800169i
$33$	0.592396	−	0.497079i	0.103123	−	0.0865304i
$34$	−1.70574	+	9.67372i	−0.292531	+	1.65903i
$35$		0			0
$36$	−8.69846	+	7.29888i	−1.44974	+	1.21648i
$37$	2.05303	+	3.55596i	0.337517	+	0.584596i	0.983965	−	0.178362i	$-0.0570798\pi$
$37$	2.05303	+	3.55596i	0.337517	+	0.584596i	−0.646448	+	0.762958i	$0.723746\pi$
$38$	10.3157	−	3.92490i	1.67342	−	0.636704i
$39$	0.886659	−	1.53574i	0.141979	−	0.245915i
$40$	−7.73055	−	2.81369i	−1.22231	−	0.444884i
$41$	9.38326	+	3.41523i	1.46542	+	0.533369i	0.946852	−	0.321669i	$-0.104244\pi$
$41$	9.38326	+	3.41523i	1.46542	+	0.533369i	0.518566	+	0.855038i	$0.326466\pi$
$42$		0			0
$43$	−1.51114	−	8.57013i	−0.230447	−	1.30693i	−0.851993	−	0.523554i	$-0.824606\pi$
$43$	−1.51114	−	8.57013i	−0.230447	−	1.30693i	0.621545	−	0.783378i	$-0.286505\pi$
$44$	−4.00387	−	3.35965i	−0.603606	−	0.506486i
$45$	−1.73396	−	3.00330i	−0.258483	−	0.447705i
$46$	12.8229			1.89064
$47$	0.0996702	−	0.565258i	0.0145384	−	0.0824513i	−0.976675	−	0.214722i	$-0.931116\pi$
$47$	0.0996702	−	0.565258i	0.0145384	−	0.0824513i	0.991214	+	0.132270i	$0.0422267\pi$
$48$	−3.31908	−	2.78504i	−0.479068	−	0.401985i
$49$		0			0
$50$	−4.03209	+	6.98378i	−0.570223	+	0.987656i
$51$	−1.93969	−	1.62760i	−0.271611	−	0.227909i
$52$	−11.2626	−	4.09927i	−1.56185	−	0.568466i
$53$	2.25490	+	1.89209i	0.309734	+	0.259898i	0.784382	−	0.620278i	$-0.212980\pi$
$53$	2.25490	+	1.89209i	0.309734	+	0.259898i	−0.474648	+	0.880176i	$0.657425\pi$
$54$	−1.59967	−	9.07218i	−0.217688	−	1.23457i
$55$	1.22281	−	1.02606i	0.164884	−	0.138354i
$56$		0			0
$57$	−0.453363	+	2.80872i	−0.0600494	+	0.372023i
$58$	−5.89053	−	10.2027i	−0.773464	−	1.33968i
$59$	−0.683448	−	3.87603i	−0.0889774	−	0.504616i	−0.996427	−	0.0844555i	$-0.973085\pi$
$59$	−0.683448	−	3.87603i	−0.0889774	−	0.504616i	0.907450	−	0.420160i	$-0.138026\pi$
$60$	2.97178	−	2.49362i	0.383655	−	0.321925i
$61$	4.24510	−	1.54509i	0.543529	−	0.197829i	−0.0556399	−	0.998451i	$-0.517720\pi$
$61$	4.24510	−	1.54509i	0.543529	−	0.197829i	0.599169	+	0.800622i	$0.295498\pi$
$62$	1.68732	+	9.56926i	0.214290	+	1.21530i
$63$		0			0
$64$	0.819078	−	1.41868i	0.102385	−	0.177336i
$65$	1.83022	−	3.17004i	0.227011	−	0.393195i
$66$	1.84002	−	0.669713i	0.226491	−	0.0824360i
$67$	3.65270	−	1.32948i	0.446249	−	0.162421i	−0.109114	−	0.994029i	$-0.534801\pi$
$67$	3.65270	−	1.32948i	0.446249	−	0.162421i	0.555363	+	0.831608i	$0.312579\pi$
$68$	−8.55690	+	14.8210i	−1.03768	+	1.79731i
$69$	−1.65270	+	2.86257i	−0.198962	+	0.344613i
$70$		0			0
$71$	−1.20439	−	6.83045i	−0.142935	−	0.810625i	−0.969002	−	0.247053i	$-0.920538\pi$
$71$	−1.20439	−	6.83045i	−0.142935	−	0.810625i	0.826067	−	0.563572i	$-0.190573\pi$
$72$	−14.7690	+	5.37549i	−1.74055	+	0.633508i
$73$	4.69459	−	3.93923i	0.549461	−	0.461052i	−0.325298	−	0.945612i	$-0.605465\pi$
$73$	4.69459	−	3.93923i	0.549461	−	0.461052i	0.874758	+	0.484560i	$0.161020\pi$
$74$	1.80541	+	10.2390i	0.209874	+	1.19026i
$75$	−1.03936	−	1.80023i	−0.120015	−	0.207873i
$76$	19.2271	−	0.278817i	2.20551	−	0.0319825i
$77$		0			0
$78$	3.43969	−	2.88624i	0.389468	−	0.326803i
$79$	1.70321	+	9.65939i	0.191626	+	1.08677i	0.917142	+	0.398561i	$0.130490\pi$
$79$	1.70321	+	9.65939i	0.191626	+	1.08677i	−0.725516	+	0.688206i	$0.758399\pi$
$80$	−6.85117	−	5.74881i	−0.765984	−	0.642737i
$81$	−5.02481	−	1.82888i	−0.558313	−	0.203209i
$82$	19.3687	+	16.2523i	2.13892	+	1.79476i
$83$	−6.15910	+	10.6679i	−0.676049	+	1.17095i	0.300112	+	0.953904i	$0.402976\pi$
$83$	−6.15910	+	10.6679i	−0.676049	+	1.17095i	−0.976161	+	0.217047i	$0.930357\pi$
$84$		0			0
$85$	−4.00387	−	3.35965i	−0.434281	−	0.364405i
$86$	3.82635	−	21.7003i	0.412606	−	2.34001i
$87$	3.03684			0.325583
$88$	−3.61721	−	6.26519i	−0.385596	−	0.667872i
$89$	−1.85844	−	1.55942i	−0.196994	−	0.165298i	0.538955	−	0.842335i	$-0.318819\pi$
$89$	−1.85844	−	1.55942i	−0.196994	−	0.165298i	−0.735949	+	0.677037i	$0.763264\pi$
$90$	−1.52481	−	8.64766i	−0.160730	−	0.911543i
$91$		0			0
$92$	20.9932	+	7.64090i	2.18869	+	0.796619i
$93$	−2.35369	−	0.856674i	−0.244067	−	0.0888330i
$94$	0.726682	−	1.25865i	0.0749515	−	0.129820i
$95$	−0.935822	+	5.79769i	−0.0960133	+	0.594830i
$96$	−1.50000	−	2.59808i	−0.153093	−	0.265165i
$97$	5.64543	−	4.73708i	0.573207	−	0.480977i	−0.309502	−	0.950899i	$-0.600162\pi$
$97$	5.64543	−	4.73708i	0.573207	−	0.480977i	0.882708	+	0.469922i	$0.155718\pi$
$98$		0			0
$99$	0.529563	−	3.00330i	0.0532231	−	0.301843i
$100$	−10.7626	+	9.03093i	−1.07626	+	0.903093i
$101$	0.376859	−	2.13727i	0.0374989	−	0.212667i	−0.960301	−	0.278966i	$-0.910008\pi$
$101$	0.376859	−	2.13727i	0.0374989	−	0.212667i	0.997800	+	0.0662996i	$0.0211193\pi$
$102$	−3.20574	−	5.55250i	−0.317415	−	0.549779i
$103$	6.23783	−	10.8042i	0.614631	−	1.06457i	−0.375818	−	0.926694i	$-0.622638\pi$
$103$	6.23783	−	10.8042i	0.614631	−	1.06457i	0.990449	−	0.137879i	$-0.0440285\pi$
$104$	−12.7083	−	10.6635i	−1.24615	−	1.04564i
$105$		0			0
$106$	3.72668	+	6.45480i	0.361967	+	0.626946i
$107$	−6.68004			−0.645784			−0.322892	−	0.946436i	$-0.604655\pi$
$107$	−6.68004			−0.645784			−0.322892	+	0.946436i	$0.604655\pi$
$108$	2.78699	−	15.8058i	0.268178	−	1.52091i
$109$	−8.88326	−	3.23324i	−0.850862	−	0.309688i	−0.120470	−	0.992717i	$-0.538440\pi$
$109$	−8.88326	−	3.23324i	−0.850862	−	0.309688i	−0.730392	+	0.683029i	$0.760662\pi$
$110$	3.79813	−	1.38241i	0.362138	−	0.131807i
$111$	−2.51842	−	0.916629i	−0.239038	−	0.0870026i
$112$		0			0
$113$	1.31046			0.123278			0.0616388	−	0.998099i	$-0.480367\pi$
$113$	1.31046			0.123278			0.0616388	+	0.998099i	$0.480367\pi$
$114$	−3.51114	+	6.29039i	−0.328849	+	0.589149i
$115$	−3.41147	+	5.90885i	−0.318122	+	0.551003i
$116$	−3.56418	−	20.2135i	−0.330926	−	1.87677i
$117$	−1.21436	−	6.88695i	−0.112267	−	0.636699i
$118$	1.73055	−	9.81445i	0.159310	−	0.903493i
$119$		0			0
$120$	5.04576	−	1.83651i	0.460613	−	0.167649i
$121$	−9.59627			−0.872388
$122$	11.4388			1.03562
$123$	−6.12449	+	2.22913i	−0.552226	+	0.200994i
$124$	−2.93969	+	16.6718i	−0.263992	+	1.49717i
$125$	−5.51367	−	9.54996i	−0.493158	−	0.854174i
$126$		0			0
$127$	13.6284	−	4.96032i	1.20932	−	0.440157i	0.342853	−	0.939389i	$-0.388607\pi$
$127$	13.6284	−	4.96032i	1.20932	−	0.440157i	0.866468	+	0.499232i	$0.166385\pi$
$128$	10.2194	−	8.57510i	0.903277	−	0.757939i
$129$	4.35117	+	3.65106i	0.383099	+	0.321458i
$130$	7.10014	−	5.95772i	0.622723	−	0.522527i
$131$	18.6138	+	6.77487i	1.62630	+	0.591923i	0.984567	−	0.175008i	$-0.0559952\pi$
$131$	18.6138	+	6.77487i	1.62630	+	0.591923i	0.641729	+	0.766932i	$0.278217\pi$
$132$	3.41147			0.296931
$133$		0			0
$134$	9.84255			0.850267
$135$	4.60607	+	1.67647i	0.396427	+	0.144288i
$136$	−18.1459	+	15.2262i	−1.55600	+	1.30564i
$137$	7.81702	+	6.55926i	0.667853	+	0.560395i	0.912429	−	0.409235i	$-0.134204\pi$
$137$	7.81702	+	6.55926i	0.667853	+	0.560395i	−0.244576	+	0.969630i	$0.578649\pi$
$138$	−6.41147	+	5.37987i	−0.545781	+	0.457965i
$139$	1.56031	−	0.567905i	0.132344	−	0.0481691i	−0.274999	−	0.961444i	$-0.588678\pi$
$139$	1.56031	−	0.567905i	0.132344	−	0.0481691i	0.407343	+	0.913275i	$0.366455\pi$
$140$		0			0
$141$	0.187319	+	0.324446i	0.0157751	+	0.0273232i
$142$	3.04963	−	17.2953i	0.255919	−	1.45139i
$143$	3.02481	−	1.10094i	0.252948	−	0.0920654i
$144$	−17.0865			−1.42387
$145$	6.26857			0.520576
$146$	14.5817	−	5.30731i	1.20679	−	0.439236i
$147$		0			0
$148$	−3.14543	+	17.8386i	−0.258553	+	1.46633i
$149$	1.94609	+	11.0368i	0.159430	+	0.904172i	0.954623	+	0.297816i	$0.0962581\pi$
$149$	1.94609	+	11.0368i	0.159430	+	0.904172i	−0.795194	+	0.606356i	$0.792631\pi$
$150$	−0.914000	−	5.18355i	−0.0746278	−	0.423235i
$151$	5.52094	−	9.56256i	0.449288	−	0.778190i	−0.549052	−	0.835788i	$-0.685011\pi$
$151$	5.52094	−	9.56256i	0.449288	−	0.778190i	0.998340	+	0.0575986i	$0.0183443\pi$
$152$	25.1400	+	8.73951i	2.03912	+	0.708868i
$153$	−9.98545			−0.807276
$154$		0			0
$155$	−4.85844	−	1.76833i	−0.390239	−	0.142036i
$156$	7.35117	−	2.67561i	0.588564	−	0.214220i
$157$	−10.3302	−	3.75989i	−0.824441	−	0.300072i	−0.104866	−	0.994486i	$-0.533441\pi$
$157$	−10.3302	−	3.75989i	−0.824441	−	0.300072i	−0.719576	+	0.694414i	$0.755664\pi$
$158$	−4.31268	+	24.4584i	−0.343098	+	1.94581i
$159$	−1.92127			−0.152367
$160$	−3.09627	−	5.36289i	−0.244781	−	0.423974i
$161$		0			0
$162$	−10.3721	−	8.70323i	−0.814910	−	0.683791i
$163$	3.16637	−	5.48432i	0.248010	−	0.429565i	−0.714964	−	0.699161i	$-0.753557\pi$
$163$	3.16637	−	5.48432i	0.248010	−	0.429565i	0.962973	+	0.269596i	$0.0868902\pi$
$164$	22.0253	+	38.1489i	1.71989	+	2.97893i
$165$	−0.180922	+	1.02606i	−0.0140848	+	0.0798787i
$166$	−23.8935	+	20.0490i	−1.85450	+	1.55611i
$167$	−2.39259	+	13.5690i	−0.185144	+	1.05000i	0.740626	+	0.671917i	$0.234529\pi$
$167$	−2.39259	+	13.5690i	−0.185144	+	1.05000i	−0.925770	+	0.378087i	$0.876582\pi$
$168$		0			0
$169$	−4.30406	+	3.61154i	−0.331082	+	0.277811i
$170$	−6.61721	−	11.4613i	−0.507517	−	0.879045i
$171$	5.75015	+	9.63419i	0.439725	+	0.736745i
$172$	19.1951	−	33.2468i	1.46361	−	2.53505i
$173$	−23.7246	−	8.63506i	−1.80375	−	0.656511i	−0.997927	−	0.0643540i	$-0.979501\pi$
$173$	−23.7246	−	8.63506i	−1.80375	−	0.656511i	−0.805822	−	0.592157i	$-0.798276\pi$
$174$	7.22580	+	2.62998i	0.547787	+	0.199378i
$175$		0			0
$176$	−1.36571	−	7.74535i	−0.102945	−	0.583828i
$177$	1.96791	+	1.65127i	0.147917	+	0.124117i
$178$	−3.07145	−	5.31991i	−0.230215	−	0.398744i
$179$	5.83069			0.435806			0.217903	−	0.975970i	$-0.430078\pi$
$179$	5.83069			0.435806			0.217903	+	0.975970i	$0.430078\pi$
$180$	2.65657	−	15.0662i	0.198009	−	1.12297i
$181$	10.3892	+	8.71756i	0.772222	+	0.647971i	0.941277	−	0.337635i	$-0.109627\pi$
$181$	10.3892	+	8.71756i	0.772222	+	0.647971i	−0.169055	+	0.985607i	$0.554072\pi$
$182$		0			0
$183$	−1.47431	+	2.55358i	−0.108984	+	0.188766i
$184$	23.6878	+	19.8764i	1.74629	+	1.46531i
$185$	−5.19846	−	1.89209i	−0.382199	−	0.139109i
$186$	−4.85844	−	4.07672i	−0.356238	−	0.298919i
$187$	−0.798133	−	4.52644i	−0.0583653	−	0.331006i
$188$	1.93969	−	1.62760i	0.141467	−	0.118705i
$189$		0			0
$190$	−7.24763	+	12.9845i	−0.525798	+	0.941994i
$191$	5.14203	+	8.90625i	0.372064	+	0.644434i	0.989883	−	0.141887i	$-0.0453169\pi$
$191$	5.14203	+	8.90625i	0.372064	+	0.644434i	−0.617819	+	0.786320i	$0.711984\pi$
$192$	0.185670	+	1.05299i	0.0133996	+	0.0759927i
$193$	10.5719	−	8.87089i	0.760983	−	0.638541i	−0.177399	−	0.984139i	$-0.556768\pi$
$193$	10.5719	−	8.87089i	0.760983	−	0.638541i	0.938383	+	0.345598i	$0.112324\pi$
$194$	17.5351	−	6.38225i	1.25895	−	0.458219i
$195$	0.414878	+	2.35289i	0.0297100	+	0.168494i
$196$		0			0
$197$	3.97044	−	6.87700i	0.282882	−	0.489966i	−0.689211	−	0.724560i	$-0.742043\pi$
$197$	3.97044	−	6.87700i	0.282882	−	0.489966i	0.972093	+	0.234594i	$0.0753762\pi$
$198$	3.86097	−	6.68739i	0.274387	−	0.475252i
$199$	−25.4047	+	9.24654i	−1.80089	+	0.655470i	−0.802631	+	0.596476i	$0.796567\pi$
$199$	−25.4047	+	9.24654i	−1.80089	+	0.655470i	−0.998258	+	0.0589938i	$0.981211\pi$
$200$	−18.2738	+	6.65111i	−1.29215	+	0.470305i
$201$	−1.26857	+	2.19723i	−0.0894781	+	0.154981i
$202$	2.74763	−	4.75903i	0.193322	−	0.334844i
$203$		0			0
$204$	−1.93969	−	11.0005i	−0.135806	−	0.770192i
$205$	−12.6420	+	4.60132i	−0.882957	+	0.321370i
$206$	24.1989	−	20.3053i	1.68602	−	1.41474i
$207$	2.26352	+	12.8370i	0.157325	+	0.892237i
$208$	−9.01754	−	15.6188i	−0.625254	−	1.08297i
$209$	−3.90760	+	3.37662i	−0.270295	+	0.233566i
$210$		0			0
$211$	−6.18345	+	5.18853i	−0.425686	+	0.357193i	−0.830321	−	0.557285i	$-0.811843\pi$
$211$	−6.18345	+	5.18853i	−0.425686	+	0.357193i	0.404635	+	0.914478i	$0.367399\pi$
$212$	2.25490	+	12.7882i	0.154867	+	0.878295i
$213$	3.46791	+	2.90992i	0.237617	+	0.199385i
$214$	−15.8944	−	5.78509i	−1.08652	−	0.395461i
$215$	8.98158	+	7.53644i	0.612539	+	0.513981i
$216$	11.1074	−	19.2386i	0.755764	−	1.30902i
$217$		0			0
$218$	−18.3366	−	15.3863i	−1.24191	−	1.04209i
$219$	−0.694593	+	3.93923i	−0.0469362	+	0.266189i
$220$	7.04189			0.474764
$221$	−5.26991	−	9.12776i	−0.354493	−	0.614000i
$222$	−5.19846	−	4.36203i	−0.348898	−	0.292760i
$223$	−2.68732	−	15.2405i	−0.179956	−	1.02058i	−0.932266	−	0.361773i	$-0.882172\pi$
$223$	−2.68732	−	15.2405i	−0.179956	−	1.02058i	0.752310	−	0.658809i	$-0.228940\pi$
$224$		0			0
$225$	−7.70321	−	2.80374i	−0.513547	−	0.186916i
$226$	3.11809	+	1.13489i	0.207412	+	0.0754919i
$227$	−4.93629	+	8.54990i	−0.327633	+	0.567477i	−0.982042	−	0.188664i	$-0.939584\pi$
$227$	−4.93629	+	8.54990i	−0.327633	+	0.567477i	0.654409	+	0.756141i	$0.272918\pi$
$228$	−9.49660	+	8.20616i	−0.628927	+	0.543466i
$229$	−10.0594	−	17.4234i	−0.664746	−	1.15137i	−0.979354	−	0.202152i	$-0.935206\pi$
$229$	−10.0594	−	17.4234i	−0.664746	−	1.15137i	0.314608	−	0.949222i	$-0.398127\pi$
$230$	−13.2344	+	11.1050i	−0.872652	+	0.732242i
$231$		0			0
$232$	4.93330	−	27.9781i	0.323887	−	1.83685i
$233$	2.70780	−	2.27211i	0.177394	−	0.148851i	−0.549768	−	0.835318i	$-0.685284\pi$
$233$	2.70780	−	2.27211i	0.177394	−	0.148851i	0.727161	+	0.686467i	$0.240839\pi$
$234$	3.07486	−	17.4384i	0.201010	−	1.13998i
$235$	0.386659	+	0.669713i	0.0252229	+	0.0436873i
$236$	8.68139	−	15.0366i	0.565110	−	0.978800i
$237$	−4.90420	−	4.11511i	−0.318562	−	0.267305i
$238$		0			0
$239$	−5.98680	−	10.3694i	−0.387254	−	0.670743i	0.604825	−	0.796358i	$-0.293243\pi$
$239$	−5.98680	−	10.3694i	−0.387254	−	0.670743i	−0.992079	+	0.125615i	$0.959910\pi$
$240$	5.83750			0.376809
$241$	2.24035	−	12.7057i	0.144314	−	0.818444i	−0.823602	−	0.567168i	$-0.808039\pi$
$241$	2.24035	−	12.7057i	0.144314	−	0.818444i	0.967916	−	0.251276i	$-0.0808500\pi$
$242$	−22.8332	−	8.31061i	−1.46777	−	0.534226i
$243$	13.5360	−	4.92669i	0.868332	−	0.316047i
$244$	18.7271	+	6.81612i	1.19888	+	0.436358i
$245$		0			0
$246$	−16.5030			−1.05219
$247$	−5.77197	+	10.3408i	−0.367262	+	0.657968i
$248$	−11.7160	+	20.2927i	−0.743967	+	1.28859i
$249$	−1.39615	−	7.91799i	−0.0884777	−	0.501782i
$250$	−4.84864	−	27.4980i	−0.306655	−	1.73913i
$251$	2.49407	−	14.1446i	0.157424	−	0.892798i	−0.799112	−	0.601183i	$-0.794696\pi$
$251$	2.49407	−	14.1446i	0.157424	−	0.892798i	0.956536	−	0.291615i	$-0.0941925\pi$
$252$		0			0
$253$	−5.63816	+	2.05212i	−0.354468	+	0.129016i
$254$	36.7229			2.30420
$255$	3.41147			0.213635
$256$	28.6634	−	10.4326i	1.79146	−	0.652040i
$257$	0.864370	−	4.90209i	0.0539180	−	0.305784i	−0.945908	−	0.324435i	$-0.894826\pi$
$257$	0.864370	−	4.90209i	0.0539180	−	0.305784i	0.999826	+	0.0186508i	$0.00593707\pi$
$258$	7.19119	+	12.4555i	0.447704	+	0.775446i
$259$		0			0
$260$	15.1741	−	5.52293i	0.941059	−	0.342517i
$261$	9.17412	−	7.69800i	0.567863	−	0.476494i
$262$	38.4222	+	32.2401i	2.37373	+	1.99180i
$263$	−18.4179	+	15.4544i	−1.13569	+	0.952961i	−0.999289	−	0.0376922i	$-0.987999\pi$
$263$	−18.4179	+	15.4544i	−1.13569	+	0.952961i	−0.136405	+	0.990653i	$0.543555\pi$
$264$	4.43717	+	1.61500i	0.273089	+	0.0993962i
$265$	−3.96585			−0.243620
$266$		0			0
$267$	1.58347			0.0969070
$268$	16.1138	+	5.86495i	0.984307	+	0.358259i
$269$	−10.0437	+	8.42767i	−0.612375	+	0.513844i	−0.895396	−	0.445270i	$-0.853108\pi$
$269$	−10.0437	+	8.42767i	−0.612375	+	0.513844i	0.283021	+	0.959114i	$0.408663\pi$
$270$	9.50774	+	7.97794i	0.578623	+	0.485522i
$271$	−20.3537	+	17.0788i	−1.23640	+	1.03746i	−0.238602	+	0.971117i	$0.576689\pi$
$271$	−20.3537	+	17.0788i	−1.23640	+	1.03746i	−0.997797	+	0.0663443i	$0.978866\pi$
$272$	−24.1989	+	8.80769i	−1.46728	+	0.534045i
$273$		0			0
$274$	12.9192	+	22.3767i	0.780478	+	1.35183i
$275$	0.655230	−	3.71599i	0.0395118	−	0.224083i
$276$	−13.7023	+	4.98724i	−0.824784	+	0.300197i
$277$	−16.5107			−0.992034			−0.496017	−	0.868313i	$-0.665205\pi$
$277$	−16.5107			−0.992034			−0.496017	+	0.868313i	$0.665205\pi$
$278$	4.20439			0.252163
$279$	−9.28194	+	3.37835i	−0.555695	+	0.202256i
$280$		0			0
$281$	−3.36706	+	19.0955i	−0.200862	+	1.13914i	0.702958	+	0.711231i	$0.251862\pi$
$281$	−3.36706	+	19.0955i	−0.200862	+	1.13914i	−0.903820	+	0.427913i	$0.859249\pi$
$282$	0.164725	+	0.934204i	0.00980925	+	0.0556310i
$283$	−1.96404	−	11.1386i	−0.116750	−	0.662123i	−0.985869	−	0.167519i	$-0.946424\pi$
$283$	−1.96404	−	11.1386i	−0.116750	−	0.662123i	0.869119	−	0.494604i	$-0.164687\pi$
$284$	15.2986	−	26.4980i	0.907805	−	1.57236i
$285$	−1.96451	−	3.29147i	−0.116367	−	0.194970i
$286$	8.15064			0.481958
$287$		0			0
$288$	−11.1172	−	4.04633i	−0.655088	−	0.238433i
$289$	1.83275	−	0.667066i	0.107809	−	0.0392392i
$290$	14.9153	+	5.42874i	0.875859	+	0.318787i
$291$	−0.835275	+	4.73708i	−0.0489647	+	0.277692i
$292$	27.0351			1.58211
$293$	−1.94949	−	3.37662i	−0.113891	−	0.197264i	0.803445	−	0.595379i	$-0.202998\pi$
$293$	−1.94949	−	3.37662i	−0.113891	−	0.197264i	−0.917336	+	0.398115i	$0.869665\pi$
$294$		0			0
$295$	4.06212	+	3.40852i	0.236506	+	0.198452i
$296$	−12.5360	+	21.7129i	−0.728638	+	1.26204i
$297$	2.15523	+	3.73297i	0.125059	+	0.216609i
$298$	−4.92767	+	27.9462i	−0.285452	+	1.61888i
$299$	−10.5398	+	8.84397i	−0.609534	+	0.511460i
$300$	1.59240	−	9.03093i	0.0919370	−	0.521401i
$301$		0			0
$302$	21.4179	−	17.9717i	1.23246	−	1.03416i
$303$	0.708263	+	1.22675i	0.0406887	+	0.0704748i
$304$	22.4329	+	18.2757i	1.28661	+	1.04819i
$305$	−3.04323	+	5.27103i	−0.174255	+	0.301819i
$306$	−23.7592	−	8.64766i	−1.35823	−	0.494354i
$307$	−21.7777	−	7.92642i	−1.24292	−	0.452385i	−0.364914	−	0.931041i	$-0.618902\pi$
$307$	−21.7777	−	7.92642i	−1.24292	−	0.452385i	−0.878002	+	0.478657i	$0.841124\pi$
$308$		0			0
$309$	1.41400	+	8.01919i	0.0804397	+	0.456196i
$310$	−10.0287	−	8.41507i	−0.569591	−	0.477944i
$311$	1.73055	+	2.99740i	0.0981306	+	0.169967i	0.910911	−	0.412603i	$-0.135380\pi$
$311$	1.73055	+	2.99740i	0.0981306	+	0.169967i	−0.812780	+	0.582570i	$0.802047\pi$
$312$	10.8280			0.613015
$313$	−3.97477	+	22.5421i	−0.224668	+	1.27415i	0.638652	+	0.769496i	$0.279492\pi$
$313$	−3.97477	+	22.5421i	−0.224668	+	1.27415i	−0.863320	+	0.504657i	$0.831619\pi$
$314$	−21.3234	−	17.8925i	−1.20335	−	1.00973i
$315$		0			0
$316$	−21.6348	+	37.4725i	−1.21705	+	2.10799i
$317$	20.0096	+	16.7900i	1.12385	+	0.943021i	0.998792	−	0.0491289i	$-0.0156445\pi$
$317$	20.0096	+	16.7900i	1.12385	+	0.943021i	0.125056	+	0.992150i	$0.460089\pi$
$318$	−4.57145	−	1.66387i	−0.256354	−	0.0933053i
$319$	4.22281	+	3.54336i	0.236432	+	0.198390i
$320$	0.383256	+	2.17355i	0.0214246	+	0.121505i
$321$	3.34002	−	2.80261i	0.186422	−	0.156427i
$322$		0			0
$323$	13.1099	+	10.6805i	0.729456	+	0.594277i
$324$	−11.7947	−	20.4291i	−0.655263	−	1.13495i
$325$	−1.50253	−	8.52125i	−0.0833452	−	0.472674i
$326$	12.2836	−	10.3072i	0.680325	−	0.570860i
$327$	5.79813	−	2.11035i	0.320638	−	0.116703i
$328$	10.5876	+	60.0455i	0.584605	+	3.31546i
$329$		0			0
$330$	−1.31908	+	2.28471i	−0.0726128	+	0.125769i
$331$	−9.52229	+	16.4931i	−0.523392	+	0.906542i	0.476237	+	0.879317i	$0.342000\pi$
$331$	−9.52229	+	16.4931i	−0.523392	+	0.906542i	−0.999629	+	0.0272251i	$0.991333\pi$
$332$	−51.0642	+	18.5859i	−2.80251	+	1.02003i
$333$	−9.93154	+	3.61479i	−0.544245	+	0.198089i
$334$	−17.4440	+	30.2139i	−0.954495	+	1.65323i
$335$	−2.61856	+	4.53547i	−0.143067	+	0.247799i
$336$		0			0
$337$	0.295445	+	1.67555i	0.0160939	+	0.0912731i	0.991797	−	0.127825i	$-0.0407996\pi$
$337$	0.295445	+	1.67555i	0.0160939	+	0.0912731i	−0.975703	+	0.219098i	$0.929688\pi$
$338$	−13.3687	+	4.86581i	−0.727162	+	0.264665i
$339$	−0.655230	+	0.549803i	−0.0355872	+	0.0298612i
$340$	−4.00387	−	22.7071i	−0.217140	−	1.23146i
$341$	−2.27332	−	3.93750i	−0.123107	−	0.213228i
$342$	5.33837	+	27.9032i	0.288666	+	1.50883i
$343$		0			0
$344$	40.7053	−	34.1558i	2.19468	−	1.84156i
$345$	−0.773318	−	4.38571i	−0.0416341	−	0.236119i
$346$	−48.9718	−	41.0923i	−2.63274	−	2.20913i
$347$	4.60607	+	1.67647i	0.247267	+	0.0899977i	0.462680	−	0.886525i	$-0.346888\pi$
$347$	4.60607	+	1.67647i	0.247267	+	0.0899977i	−0.215414	+	0.976523i	$0.569110\pi$
$348$	10.2626	+	8.61138i	0.550135	+	0.461618i
$349$	14.0646	−	24.3607i	0.752863	−	1.30400i	−0.193566	−	0.981087i	$-0.562006\pi$
$349$	14.0646	−	24.3607i	0.752863	−	1.30400i	0.946430	−	0.322910i	$-0.104661\pi$
$350$		0			0
$351$	7.57192	+	6.35359i	0.404159	+	0.339130i
$352$	0.945622	−	5.36289i	0.0504018	−	0.285843i
$353$	−8.31996			−0.442827			−0.221413	−	0.975180i	$-0.571067\pi$
$353$	−8.31996			−0.442827			−0.221413	+	0.975180i	$0.571067\pi$
$354$	3.25237	+	5.63328i	0.172862	+	0.299405i
$355$	7.15839	+	6.00660i	0.379928	+	0.318797i
$356$	−1.85844	−	10.5397i	−0.0984972	−	0.558605i
$357$		0			0
$358$	13.8735	+	5.04952i	0.733235	+	0.266876i
$359$	−23.4256	−	8.52623i	−1.23636	−	0.449997i	−0.360587	−	0.932726i	$-0.617423\pi$
$359$	−23.4256	−	8.52623i	−1.23636	−	0.449997i	−0.875770	+	0.482729i	$0.839646\pi$
$360$	10.5876	−	18.3383i	0.558018	−	0.966516i
$361$	2.75537	−	18.7991i	0.145019	−	0.989429i
$362$	17.1702	+	29.7397i	0.902448	+	1.56309i
$363$	4.79813	−	4.02611i	0.251837	−	0.211316i
$364$		0			0
$365$	−1.43376	+	8.13127i	−0.0750466	+	0.425610i
$366$	−5.71941	+	4.79915i	−0.298958	+	0.250856i
$367$	−0.449026	+	2.54655i	−0.0234390	+	0.132929i	−0.994282	−	0.106788i	$-0.965943\pi$
$367$	−0.449026	+	2.54655i	−0.0234390	+	0.132929i	0.970843	+	0.239717i	$0.0770546\pi$
$368$	16.8084	+	29.1130i	0.876198	+	1.51762i
$369$	−12.8512	+	22.2589i	−0.669005	+	1.15875i
$370$	−10.7306	−	9.00400i	−0.557855	−	0.468096i
$371$		0			0
$372$	−5.52481	−	9.56926i	−0.286448	−	0.496143i
$373$	−23.3833			−1.21074			−0.605371	−	0.795943i	$-0.706975\pi$
$373$	−23.3833			−1.21074			−0.605371	+	0.795943i	$0.706975\pi$
$374$	2.02094	−	11.4613i	0.104501	−	0.592652i
$375$	6.76352	+	2.46172i	0.349267	+	0.127123i
$376$	3.29339	−	1.19869i	0.169843	−	0.0618179i
$377$	11.8785	+	4.32342i	0.611774	+	0.222668i
$378$		0			0
$379$	25.4388			1.30670			0.653352	−	0.757054i	$-0.273362\pi$
$379$	25.4388			1.30670			0.653352	+	0.757054i	$0.273362\pi$
$380$	−19.6027	+	16.9390i	−1.00560	+	0.868950i
$381$	−4.73308	+	8.19793i	−0.242483	+	0.419993i
$382$	4.52182	+	25.6445i	0.231357	+	1.31209i
$383$	−4.77197	−	27.0632i	−0.243836	−	1.38287i	−0.823179	−	0.567781i	$-0.807802\pi$
$383$	−4.77197	−	27.0632i	−0.243836	−	1.38287i	0.579343	−	0.815084i	$-0.303309\pi$
$384$	−1.51202	+	8.57510i	−0.0771600	+	0.437596i
$385$		0			0
$386$	32.8371	−	11.9517i	1.67136	−	0.608327i
$387$	22.3996			1.13864
$388$	32.5107			1.65048
$389$	3.14068	−	1.14311i	0.159239	−	0.0579582i	−0.261171	−	0.965293i	$-0.584109\pi$
$389$	3.14068	−	1.14311i	0.159239	−	0.0579582i	0.420410	+	0.907334i	$0.361886\pi$
$390$	−1.05051	+	5.95772i	−0.0531945	+	0.301681i
$391$	9.82295	+	17.0138i	0.496768	+	0.860427i
$392$		0			0
$393$	−12.1493	+	4.42198i	−0.612851	+	0.223060i
$394$	15.4029	−	12.9245i	0.775985	−	0.651128i
$395$	−10.1231	−	8.49432i	−0.509351	−	0.427396i
$396$	10.3059	−	8.64766i	0.517890	−	0.434561i
$397$	12.3319	+	4.48843i	0.618919	+	0.225268i	0.632401	−	0.774641i	$-0.282069\pi$
$397$	12.3319	+	4.48843i	0.618919	+	0.225268i	−0.0134823	+	0.999909i	$0.504292\pi$
$398$	−68.4552			−3.43135
$399$		0			0
$400$	−21.1411			−1.05706
$401$	−16.0817	−	5.85327i	−0.803083	−	0.292298i	−0.0923194	−	0.995729i	$-0.529428\pi$
$401$	−16.0817	−	5.85327i	−0.803083	−	0.292298i	−0.710763	+	0.703431i	$0.751650\pi$
$402$	−4.92127	+	4.12944i	−0.245451	+	0.205958i
$403$	−7.98680	−	6.70172i	−0.397851	−	0.333836i
$404$	7.33409	−	6.15403i	0.364885	−	0.306175i
$405$	6.76991	−	2.46405i	0.336400	−	0.122440i
$406$		0			0
$407$	−2.43242	−	4.21307i	−0.120571	−	0.208834i
$408$	2.68479	−	15.2262i	0.132917	−	0.753810i
$409$	8.26739	−	3.00908i	0.408796	−	0.148790i	−0.129433	−	0.991588i	$-0.541316\pi$
$409$	8.26739	−	3.00908i	0.408796	−	0.148790i	0.538229	+	0.842799i	$0.319094\pi$
$410$	−34.0651			−1.68236
$411$	−6.66044			−0.328535
$412$	51.7169	−	18.8234i	2.54791	−	0.927364i
$413$		0			0
$414$	−5.73143	+	32.5046i	−0.281684	+	1.59751i
$415$	−2.88191	−	16.3441i	−0.141467	−	0.802302i
$416$	−2.16843	−	12.2978i	−0.106316	−	0.602949i
$417$	−0.541889	+	0.938579i	−0.0265364	+	0.0459624i
$418$	−12.2219	+	4.65020i	−0.597794	+	0.227449i
$419$	6.84018			0.334165			0.167082	−	0.985943i	$-0.446565\pi$
$419$	6.84018			0.334165			0.167082	+	0.985943i	$0.446565\pi$
$420$		0			0
$421$	4.53209	+	1.64955i	0.220880	+	0.0803939i	0.450090	−	0.892983i	$-0.351392\pi$
$421$	4.53209	+	1.64955i	0.220880	+	0.0803939i	−0.229210	+	0.973377i	$0.573614\pi$
$422$	−19.2062	+	6.99049i	−0.934943	+	0.340292i
$423$	1.38831	+	0.505303i	0.0675018	+	0.0245687i
$424$	−3.12108	+	17.7005i	−0.151573	+	0.859614i
$425$	−12.3550			−0.599307
$426$	5.73143	+	9.92713i	0.277689	+	0.480971i
$427$		0			0
$428$	−22.5744	−	18.9422i	−1.09118	−	0.915606i
$429$	−1.05051	+	1.81953i	−0.0507190	+	0.0878478i
$430$	14.8439	+	25.7104i	0.715836	+	1.23986i
$431$	0.226377	−	1.28385i	0.0109042	−	0.0618407i	−0.978870	−	0.204483i	$-0.934449\pi$
$431$	0.226377	−	1.28385i	0.0109042	−	0.0618407i	0.989774	+	0.142642i	$0.0455598\pi$
$432$	18.5005	−	15.5237i	0.890104	−	0.746886i
$433$	3.44238	−	19.5227i	0.165430	−	0.938202i	−0.783189	−	0.621783i	$-0.786409\pi$
$433$	3.44238	−	19.5227i	0.165430	−	0.938202i	0.948620	−	0.316419i	$-0.102480\pi$
$434$		0			0
$435$	−3.13429	+	2.62998i	−0.150277	+	0.126098i
$436$	−20.8516	−	36.1161i	−0.998612	−	1.72965i
$437$	10.7588	−	19.2749i	0.514662	−	0.922042i
$438$	−5.06418	+	8.77141i	−0.241976	+	0.419114i
$439$	32.4825	+	11.8227i	1.55031	+	0.564265i	0.968489	−	0.249055i	$-0.0801200\pi$
$439$	32.4825	+	11.8227i	1.55031	+	0.564265i	0.581817	+	0.813320i	$0.302342\pi$
$440$	9.15910	+	3.33364i	0.436643	+	0.158925i
$441$		0			0
$442$	−4.63429	−	26.2823i	−0.220430	−	1.25012i
$443$	13.0305	+	10.9339i	0.619098	+	0.519485i	0.897520	−	0.440974i	$-0.145367\pi$
$443$	13.0305	+	10.9339i	0.619098	+	0.519485i	−0.278422	+	0.960459i	$0.589811\pi$
$444$	−5.91147	−	10.2390i	−0.280546	−	0.485920i
$445$	3.26857			0.154945
$446$	6.80453	−	38.5904i	0.322204	−	1.82731i
$447$	−5.60354	−	4.70193i	−0.265038	−	0.222394i
$448$		0			0
$449$	−18.7049	+	32.3978i	−0.882737	+	1.52895i	−0.0344512	+	0.999406i	$0.510968\pi$
$449$	−18.7049	+	32.3978i	−0.882737	+	1.52895i	−0.848286	+	0.529539i	$0.822365\pi$
$450$	−15.9008	−	13.3424i	−0.749571	−	0.628965i
$451$	−11.1172	−	4.04633i	−0.523489	−	0.190534i
$452$	4.42855	+	3.71599i	0.208301	+	0.174786i
$453$	1.25150	+	7.09759i	0.0588004	+	0.333474i
$454$	−19.1498	+	16.0686i	−0.898743	+	0.754135i
$455$		0			0
$456$	−16.2366	+	6.17771i	−0.760351	+	0.289298i
$457$	−4.55556	−	7.89046i	−0.213100	−	0.369100i	0.739583	−	0.673065i	$-0.235023\pi$
$457$	−4.55556	−	7.89046i	−0.213100	−	0.369100i	−0.952683	+	0.303965i	$0.901689\pi$
$458$	−8.84611	−	50.1688i	−0.413352	−	2.34423i
$459$	10.8118	−	9.07218i	0.504652	−	0.423453i
$460$	−28.2841	+	10.2946i	−1.31875	+	0.479986i
$461$	−4.24540	−	24.0769i	−0.197728	−	1.12137i	−0.908480	−	0.417929i	$-0.862756\pi$
$461$	−4.24540	−	24.0769i	−0.197728	−	1.12137i	0.710751	−	0.703443i	$-0.248355\pi$
$462$		0			0
$463$	0.125362	−	0.217134i	0.00582609	−	0.0100911i	−0.863098	−	0.505037i	$-0.831479\pi$
$463$	0.125362	−	0.217134i	0.00582609	−	0.0100911i	0.868924	+	0.494946i	$0.164812\pi$
$464$	15.4427	−	26.7475i	0.716909	−	1.24172i
$465$	3.17112	−	1.15419i	0.147057	−	0.0535245i
$466$	8.41060	−	3.06121i	0.389613	−	0.141808i
$467$	−7.68092	+	13.3037i	−0.355431	+	0.615624i	−0.987192	−	0.159539i	$-0.948999\pi$
$467$	−7.68092	+	13.3037i	−0.355431	+	0.615624i	0.631761	+	0.775163i	$0.282332\pi$
$468$	15.4251	−	26.7171i	0.713028	−	1.23500i
$469$		0			0
$470$	0.340022	+	1.92836i	0.0156841	+	0.0889487i
$471$	6.74257	−	2.45410i	0.310681	−	0.113079i
$472$	18.4099	−	15.4477i	0.847383	−	0.711039i
$473$	1.79039	+	10.1538i	0.0823223	+	0.466873i
$474$	−8.10519	−	14.0386i	−0.372284	−	0.644814i
$475$	7.11468	+	11.9204i	0.326444	+	0.546946i
$476$		0			0
$477$	−5.80406	+	4.87019i	−0.265750	+	0.222991i
$478$	−5.26470	−	29.8576i	−0.240802	−	1.36565i
$479$	−0.550974	−	0.462322i	−0.0251746	−	0.0211240i	0.630114	−	0.776503i	$-0.283008\pi$
$479$	−0.550974	−	0.462322i	−0.0251746	−	0.0211240i	−0.655288	+	0.755379i	$0.727453\pi$
$480$	3.79813	+	1.38241i	0.173360	+	0.0630980i
$481$	−8.54576	−	7.17074i	−0.389653	−	0.326958i
$482$	16.3341	−	28.2915i	0.743998	−	1.28864i
$483$		0			0
$484$	−32.4295	−	27.2116i	−1.47407	−	1.23689i
$485$	−1.72416	+	9.77817i	−0.0782899	+	0.444004i
$486$	36.4739			1.65449
$487$	−5.87346	−	10.1731i	−0.266152	−	0.460988i	0.701713	−	0.712460i	$-0.252419\pi$
$487$	−5.87346	−	10.1731i	−0.266152	−	0.460988i	−0.967865	+	0.251471i	$0.919086\pi$
$488$	21.1309	+	17.7309i	0.956550	+	0.802641i
$489$	0.717759	+	4.07061i	0.0324582	+	0.184079i
$490$		0			0
$491$	−0.0834734	−	0.0303818i	−0.00376710	−	0.00137111i	0.340136	−	0.940376i	$-0.389527\pi$
$491$	−0.0834734	−	0.0303818i	−0.00376710	−	0.00137111i	−0.343903	+	0.939005i	$0.611749\pi$
$492$	−27.0180	−	9.83375i	−1.21807	−	0.443340i
$493$	9.02481	−	15.6314i	0.406457	−	0.704005i
$494$	−22.6891	+	19.6060i	−1.02083	+	0.882117i
$495$	2.05438	+	3.55829i	0.0923374	+	0.159933i
$496$	−19.5141	+	16.3743i	−0.876211	+	0.735228i
$497$		0			0
$498$	3.53519	−	20.0490i	0.158416	−	0.898419i
$499$	11.2536	−	9.44285i	0.503778	−	0.422720i	−0.355155	−	0.934807i	$-0.615572\pi$
$499$	11.2536	−	9.44285i	0.503778	−	0.422720i	0.858934	+	0.512087i	$0.171128\pi$
$500$	8.44743	−	47.9078i	0.377781	−	2.14250i
$501$	−4.49660	−	7.78833i	−0.200893	−	0.347957i
$502$	18.1839	−	31.4955i	0.811588	−	1.40571i
$503$	−3.75671	−	3.15225i	−0.167503	−	0.140552i	0.555183	−	0.831728i	$-0.312648\pi$
$503$	−3.75671	−	3.15225i	−0.167503	−	0.140552i	−0.722686	+	0.691176i	$0.757093\pi$
$504$		0			0
$505$	1.46198	+	2.53223i	0.0650573	+	0.112683i
$506$	−15.1925			−0.675390
$507$	0.636812	−	3.61154i	0.0282818	−	0.160394i
$508$	60.1211	+	21.8823i	2.66744	+	0.970870i
$509$	−6.02704	+	2.19366i	−0.267144	+	0.0972324i	−0.472119	−	0.881535i	$-0.656511\pi$
$509$	−6.02704	+	2.19366i	−0.267144	+	0.0972324i	0.204975	+	0.978767i	$0.434289\pi$
$510$	8.11721	+	2.95442i	0.359436	+	0.130824i
$511$		0			0
$512$	50.5553			2.23425
$513$	−14.9791	−	5.20723i	−0.661341	−	0.229905i
$514$	6.30200	−	10.9154i	0.277969	−	0.481457i
$515$	2.91875	+	16.5530i	0.128615	+	0.729414i
$516$	4.35117	+	24.6767i	0.191549	+	1.08633i
$517$	−0.118089	+	0.669713i	−0.00519353	+	0.0294540i
$518$		0			0
$519$	15.4851	−	5.63613i	0.679723	−	0.247399i
$520$	22.3509			0.980153
$521$	−35.8135			−1.56902			−0.784508	−	0.620119i	$-0.787084\pi$
$521$	−35.8135			−1.56902			−0.784508	+	0.620119i	$0.787084\pi$
$522$	28.4954	−	10.3715i	1.24721	−	0.453947i
$523$	6.73277	−	38.1835i	0.294404	−	1.66965i	−0.375213	−	0.926939i	$-0.622430\pi$
$523$	6.73277	−	38.1835i	0.294404	−	1.66965i	0.669616	−	0.742707i	$-0.266459\pi$
$524$	43.6921	+	75.6770i	1.90870	+	3.30596i
$525$		0			0
$526$	−57.2071	+	20.8217i	−2.49435	+	0.907869i
$527$	−11.4042	+	9.56926i	−0.496775	+	0.416844i
$528$	3.93242	+	3.29969i	0.171137	+	0.143601i
$529$	2.02687	−	1.70075i	0.0881250	−	0.0739456i
$530$	−9.43629	−	3.43453i	−0.409886	−	0.149186i
$531$	10.1307			0.439636
$532$		0			0
$533$	−27.1293			−1.17510
$534$	3.76769	+	1.37133i	0.163044	+	0.0593432i
$535$	6.89440	−	5.78509i	0.298071	−	0.250111i
$536$	18.1821	+	15.2566i	0.785347	+	0.658985i
$537$	−2.91534	+	2.44626i	−0.125806	+	0.105564i
$538$	−31.1964	+	11.3546i	−1.34497	+	0.489530i
$539$		0			0
$540$	10.8118	+	18.7266i	0.465266	+	0.805864i
$541$	1.64796	−	9.34602i	0.0708512	−	0.401817i	−0.928671	−	0.370905i	$-0.879048\pi$
$541$	1.64796	−	9.34602i	0.0708512	−	0.401817i	0.999522	−	0.0309122i	$-0.00984123\pi$
$542$	−63.2199	+	23.0102i	−2.71553	+	0.988372i
$543$	−8.85204			−0.379878
$544$	−17.8307			−0.764484
$545$	11.9684	−	4.35613i	0.512669	−	0.186596i
$546$		0			0
$547$	2.46791	−	13.9962i	0.105520	−	0.598435i	−0.885491	−	0.464657i	$-0.846178\pi$
$547$	2.46791	−	13.9962i	0.105520	−	0.598435i	0.991011	−	0.133779i	$-0.0427111\pi$
$548$	7.81702	+	44.3325i	0.333926	+	1.89379i
$549$	2.01919	+	11.4514i	0.0861769	+	0.488734i
$550$	4.77719	−	8.27433i	0.203700	−	0.352819i
$551$	−20.2785	+	0.294064i	−0.863895	+	0.0125275i
$552$	−20.1830			−0.859047
$553$		0			0
$554$	−39.2854	−	14.2987i	−1.66908	−	0.607494i
$555$	3.39306	−	1.23497i	0.144027	−	0.0524216i
$556$	6.88326	+	2.50530i	0.291915	+	0.106248i
$557$	3.91400	−	22.1974i	0.165842	−	0.940534i	−0.782351	−	0.622838i	$-0.785980\pi$
$557$	3.91400	−	22.1974i	0.165842	−	0.940534i	0.948193	−	0.317696i	$-0.102909\pi$
$558$	−25.0110			−1.05880
$559$	11.8216	+	20.4756i	0.500001	+	0.866026i
$560$		0			0
$561$	2.29813	+	1.92836i	0.0970273	+	0.0814155i
$562$	−24.5488	+	42.5197i	−1.03553	+	1.79358i
$563$	21.4859	+	37.2147i	0.905524	+	1.56841i	0.820213	+	0.572058i	$0.193855\pi$
$563$	21.4859	+	37.2147i	0.905524	+	1.56841i	0.0853106	+	0.996354i	$0.472812\pi$
$564$	−0.286989	+	1.62760i	−0.0120844	+	0.0685341i
$565$	−1.35251	+	1.13489i	−0.0569006	+	0.0477452i
$566$	4.97313	−	28.2040i	0.209036	−	1.18550i
$567$		0			0
$568$	32.4424	−	27.2224i	1.36125	−	1.14223i
$569$	−3.71348	−	6.43193i	−0.155677	−	0.269641i	0.777628	−	0.628724i	$-0.216423\pi$
$569$	−3.71348	−	6.43193i	−0.155677	−	0.269641i	−0.933305	+	0.359084i	$0.883089\pi$
$570$	−1.82383	−	9.53298i	−0.0763916	−	0.399293i
$571$	−2.02229	+	3.50271i	−0.0846301	+	0.146584i	−0.905234	−	0.424914i	$-0.860304\pi$
$571$	−2.02229	+	3.50271i	−0.0846301	+	0.146584i	0.820603	+	0.571498i	$0.193638\pi$
$572$	13.3439	+	4.85678i	0.557936	+	0.203072i
$573$	−6.30763	−	2.29579i	−0.263505	−	0.0959080i
$574$		0			0
$575$	2.80066	+	15.8833i	0.116796	+	0.662381i
$576$	3.23009	+	2.71036i	0.134587	+	0.112932i
$577$	−1.61721	−	2.80109i	−0.0673254	−	0.116611i	0.830398	−	0.557171i	$-0.188113\pi$
$577$	−1.61721	−	2.80109i	−0.0673254	−	0.116611i	−0.897723	+	0.440560i	$0.854780\pi$
$578$	4.93851			0.205415
$579$	−1.56418	+	8.87089i	−0.0650050	+	0.368662i
$580$	21.1839	+	17.7754i	0.879614	+	0.738084i
$581$		0			0
$582$	−6.08987	+	10.5480i	−0.252433	+	0.437227i
$583$	−2.67159	−	2.24173i	−0.110646	−	0.0928429i
$584$	35.1634	+	12.7984i	1.45507	+	0.529603i
$585$	7.21760	+	6.05628i	0.298411	+	0.250396i
$586$	−1.71436	−	9.72259i	−0.0708194	−	0.401637i
$587$	−31.2610	+	26.2311i	−1.29028	+	1.08267i	−0.298543	+	0.954396i	$0.596501\pi$
$587$	−31.2610	+	26.2311i	−1.29028	+	1.08267i	−0.991738	+	0.128279i	$0.959055\pi$
$588$		0			0
$589$	15.7998	+	5.49254i	0.651019	+	0.226316i
$590$	6.71348	+	11.6281i	0.276390	+	0.478721i
$591$	0.900025	+	5.10430i	0.0370221	+	0.209963i
$592$	−20.8799	+	17.5203i	−0.858157	+	0.720079i
$593$	10.3969	−	3.78417i	0.426951	−	0.155397i	−0.119602	−	0.992822i	$-0.538162\pi$
$593$	10.3969	−	3.78417i	0.426951	−	0.155397i	0.546553	+	0.837425i	$0.315940\pi$
$594$	1.89528	+	10.7487i	0.0777642	+	0.441023i
$595$		0			0
$596$	−24.7199	+	42.8161i	−1.01257	+	1.75381i
$597$	8.82295	−	15.2818i	0.361099	−	0.625442i
$598$	−32.7374	+	11.9154i	−1.33873	+	0.487259i
$599$	41.8705	−	15.2396i	1.71078	−	0.622674i	0.713804	−	0.700346i	$-0.246971\pi$
$599$	41.8705	−	15.2396i	1.71078	−	0.622674i	0.996979	+	0.0776714i	$0.0247485\pi$
$600$	6.34642	−	10.9923i	0.259091	−	0.448760i
$601$	2.49953	−	4.32932i	0.101958	−	0.176597i	−0.810533	−	0.585693i	$-0.800823\pi$
$601$	2.49953	−	4.32932i	0.101958	−	0.176597i	0.912491	+	0.409096i	$0.134156\pi$
$602$		0			0
$603$	1.73742	+	9.85337i	0.0707530	+	0.401260i
$604$	45.7734	−	16.6601i	1.86249	−	0.677892i
$605$	9.90420	−	8.31061i	0.402663	−	0.337874i
$606$	0.622836	+	3.53228i	0.0253010	+	0.143489i
$607$	15.5940	+	27.0097i	0.632943	+	1.09629i	0.986947	+	0.161045i	$0.0514865\pi$
$607$	15.5940	+	27.0097i	0.632943	+	1.09629i	−0.354004	+	0.935244i	$0.615180\pi$
$608$	10.2679	+	17.2035i	0.416417	+	0.697692i
$609$		0			0
$610$	−11.8059	+	9.90630i	−0.478006	+	0.401095i
$611$	0.270792	+	1.53574i	0.0109551	+	0.0621293i
$612$	−33.7447	−	28.3152i	−1.36405	−	1.14457i
$613$	−15.3824	−	5.59873i	−0.621288	−	0.226130i	0.0121468	−	0.999926i	$-0.496133\pi$
$613$	−15.3824	−	5.59873i	−0.621288	−	0.226130i	−0.633435	+	0.773796i	$0.718356\pi$
$614$	−44.9530	−	37.7200i	−1.81415	−	1.52226i
$615$	4.39053	−	7.60462i	0.177043	−	0.306648i
$616$		0			0
$617$	12.3014	+	10.3221i	0.495235	+	0.415551i	0.855898	−	0.517145i	$-0.173005\pi$
$617$	12.3014	+	10.3221i	0.495235	+	0.415551i	−0.360663	+	0.932696i	$0.617450\pi$
$618$	−3.58037	+	20.3053i	−0.144024	+	0.816799i
$619$	23.8425			0.958313			0.479156	−	0.877730i	$-0.340943\pi$
$619$	23.8425			0.958313			0.479156	+	0.877730i	$0.340943\pi$
$620$	−11.4042	−	19.7527i	−0.458004	−	0.793286i
$621$	−14.1138	−	11.8429i	−0.566368	−	0.475239i
$622$	1.52182	+	8.63068i	0.0610195	+	0.346059i
$623$		0			0
$624$	11.0617	+	4.02611i	0.442820	+	0.161173i
$625$	−1.00253	−	0.364890i	−0.0401010	−	0.0145956i
$626$	−28.9795	+	50.1940i	−1.15825	+	2.00616i
$627$	0.537141	−	3.32774i	0.0214514	−	0.132897i
$628$	−24.2481	−	41.9989i	−0.967604	−	1.67594i
$629$	−12.2023	+	10.2390i	−0.486539	+	0.408255i
$630$		0			0
$631$	3.72874	−	21.1467i	0.148439	−	0.841838i	−0.816103	−	0.577907i	$-0.803870\pi$
$631$	3.72874	−	21.1467i	0.148439	−	0.841838i	0.964541	−	0.263931i	$-0.0850193\pi$
$632$	−45.8790	+	38.4970i	−1.82497	+	1.53133i
$633$	0.914878	−	5.18853i	0.0363631	−	0.206226i
$634$	33.0699	+	57.2787i	1.31337	+	2.27483i
$635$	−9.76991	+	16.9220i	−0.387707	+	0.671529i
$636$	−6.49273	−	5.44804i	−0.257453	−	0.216029i
$637$		0			0
$638$	6.97906	+	12.0881i	0.276303	+	0.478572i
$639$	17.8527			0.706240
$640$	−3.12108	+	17.7005i	−0.123372	+	0.699675i
$641$	−11.9846	−	4.36203i	−0.473362	−	0.172290i	0.0943126	−	0.995543i	$-0.469935\pi$
$641$	−11.9846	−	4.36203i	−0.473362	−	0.172290i	−0.567675	+	0.823253i	$0.692157\pi$
$642$	10.3743	−	3.77595i	0.409442	−	0.149025i
$643$	−26.8828	−	9.78456i	−1.06016	−	0.385865i	−0.247669	−	0.968845i	$-0.579665\pi$
$643$	−26.8828	−	9.78456i	−1.06016	−	0.385865i	−0.812487	+	0.582979i	$0.801887\pi$
$644$		0			0
$645$	−7.65270			−0.301325
$646$	21.9440	+	36.7665i	0.863376	+	1.44656i
$647$	−8.35638	+	14.4737i	−0.328523	+	0.569019i	−0.982219	−	0.187738i	$-0.939884\pi$
$647$	−8.35638	+	14.4737i	−0.328523	+	0.569019i	0.653696	+	0.756757i	$0.273218\pi$
$648$	−5.66978	−	32.1549i	−0.222730	−	1.26316i
$649$	0.809745	+	4.59229i	0.0317853	+	0.180263i
$650$	3.80453	−	21.5766i	0.149226	−	0.846302i
$651$		0			0
$652$	26.2520	−	9.55493i	1.02811	−	0.374200i
$653$	27.0000			1.05659			0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000			1.05659			0.528296	+	0.849060i	$0.322831\pi$
$654$	15.6236			0.610931
$655$	−25.0783	+	9.12776i	−0.979891	+	0.356651i
$656$	−11.5103	+	65.2780i	−0.449400	+	2.54868i
$657$	7.88713	+	13.6609i	0.307706	+	0.532963i
$658$		0			0
$659$	41.2533	−	15.0150i	1.60700	−	0.584900i	0.626157	−	0.779697i	$-0.284627\pi$
$659$	41.2533	−	15.0150i	1.60700	−	0.584900i	0.980844	+	0.194797i	$0.0624047\pi$
$660$	−3.52094	+	2.95442i	−0.137053	+	0.115001i
$661$	−8.23964	−	6.91388i	−0.320485	−	0.268919i	0.468325	−	0.883556i	$-0.344858\pi$
$661$	−8.23964	−	6.91388i	−0.320485	−	0.268919i	−0.788809	+	0.614638i	$0.789302\pi$
$662$	−36.9406	+	30.9969i	−1.43574	+	1.20473i
$663$	6.46451	+	2.35289i	0.251061	+	0.0913786i
$664$	−75.2158			−2.91894
$665$		0			0
$666$	−26.7615			−1.03699
$667$	−22.1411	−	8.05872i	−0.857309	−	0.312035i
$668$	−46.5624	+	39.0705i	−1.80155	+	1.51168i
$669$	7.73783	+	6.49281i	0.299162	+	0.251026i
$670$	−10.1584	+	8.52390i	−0.392453	+	0.329307i
$671$	−5.02956	+	1.83061i	−0.194164	+	0.0706700i
$672$		0			0
$673$	−2.32888	−	4.03374i	−0.0897717	−	0.155489i	0.817643	−	0.575726i	$-0.195280\pi$
$673$	−2.32888	−	4.03374i	−0.0897717	−	0.155489i	−0.907415	+	0.420237i	$0.861947\pi$
$674$	−0.748093	+	4.24265i	−0.0288155	+	0.163421i
$675$	10.8880	−	3.96291i	0.419079	−	0.152532i
$676$	−24.7861			−0.953312
$677$	3.26857			0.125621			0.0628107	−	0.998025i	$-0.479994\pi$
$677$	3.26857			0.125621			0.0628107	+	0.998025i	$0.479994\pi$
$678$	−2.03519	+	0.740748i	−0.0781609	+	0.0284482i
$679$		0			0
$680$	5.54189	−	31.4296i	0.212522	−	1.20527i
$681$	−1.11897	−	6.34597i	−0.0428789	−	0.243178i
$682$	−1.99912	−	11.3376i	−0.0765504	−	0.434139i
$683$	−3.10947	+	5.38576i	−0.118981	+	0.206080i	−0.919364	−	0.393408i	$-0.871296\pi$
$683$	−3.10947	+	5.38576i	−0.118981	+	0.206080i	0.800383	+	0.599488i	$0.204629\pi$
$684$	−7.88713	+	48.8630i	−0.301572	+	1.86832i
$685$	−13.7483			−0.525297
$686$		0			0
$687$	12.3397	+	4.49129i	0.470790	+	0.171353i
$688$	54.2836	−	19.7576i	2.06954	−	0.753253i
$689$	−7.51501	−	2.73524i	−0.286299	−	0.104204i
$690$	1.95811	−	11.1050i	0.0745440	−	0.422760i
$691$	22.2175			0.845194			0.422597	−	0.906318i	$-0.361119\pi$
$691$	22.2175			0.845194			0.422597	+	0.906318i	$0.361119\pi$
$692$	−55.6887	−	96.4557i	−2.11697	−	3.66670i
$693$		0			0
$694$	9.50774	+	7.97794i	0.360909	+	0.302839i
$695$	−1.11856	+	1.93739i	−0.0424292	+	0.0734896i
$696$	9.27156	+	16.0588i	0.351438	+	0.608708i
$697$	−6.72668	+	38.1489i	−0.254791	+	1.44499i
$698$	54.5622	−	45.7831i	2.06521	−	1.73292i
$699$	−0.400634	+	2.27211i	−0.0151534	+	0.0859391i
$700$		0			0
$701$	−21.2750	+	17.8518i	−0.803544	+	0.674254i	−0.949058	−	0.315102i	$-0.897961\pi$
$701$	−21.2750	+	17.8518i	−0.803544	+	0.674254i	0.145513	+	0.989356i	$0.453517\pi$
$702$	12.5141	+	21.6751i	0.472316	+	0.818075i
$703$	16.9055	+	5.87695i	0.637605	+	0.221653i
$704$	−0.970437	+	1.68085i	−0.0365747	+	0.0633493i
$705$	−0.474308	−	0.172634i	−0.0178635	−	0.00650177i
$706$	−19.7964	−	7.20529i	−0.745047	−	0.271175i
$707$		0			0
$708$	1.96791	+	11.1606i	0.0739586	+	0.419440i
$709$	−4.67886	−	3.92603i	−0.175718	−	0.147445i	0.550687	−	0.834712i	$-0.314366\pi$
$709$	−4.67886	−	3.92603i	−0.175718	−	0.147445i	−0.726405	+	0.687267i	$0.758810\pi$
$710$	11.8307	+	20.4914i	0.443998	+	0.769027i
$711$	−25.2466			−0.946822
$712$	2.57233	−	14.5884i	0.0964021	−	0.546724i
$713$	14.8871	+	12.4918i	0.557527	+	0.467821i
$714$		0			0
$715$	−2.16843	+	3.75584i	−0.0810948	+	0.140460i
$716$	19.7041	+	16.5337i	0.736378	+	0.617895i
$717$	7.34389	+	2.67296i	0.274263	+	0.0998235i
$718$	−48.3546	−	40.5743i	−1.80458	−	1.51422i
$719$	6.72432	+	38.1355i	0.250775	+	1.42221i	0.806690	+	0.590975i	$0.201257\pi$
$719$	6.72432	+	38.1355i	0.250775	+	1.42221i	−0.555915	+	0.831239i	$0.687632\pi$
$720$	17.6348	−	14.7973i	0.657208	−	0.551463i
$721$		0			0
$722$	22.8366	−	42.3442i	0.849891	−	1.57589i
$723$	4.21048	+	7.29277i	0.156590	+	0.271221i
$724$	10.3892	+	58.9200i	0.386111	+	2.18974i
$725$	11.3512	−	9.52476i	0.421572	−	0.353741i
$726$	14.9033	−	5.42437i	0.553114	−	0.201317i
$727$	−1.92366	−	10.9096i	−0.0713445	−	0.404615i	−0.999476	−	0.0323628i	$-0.989697\pi$
$727$	−1.92366	−	10.9096i	−0.0713445	−	0.404615i	0.928132	−	0.372252i	$-0.121414\pi$
$728$		0			0
$729$	3.31996	−	5.75033i	0.122961	−	0.212975i
$730$	−10.4534	+	18.1058i	−0.386896	+	0.670124i
$731$	31.7237	−	11.5465i	1.17335	−	0.427063i
$732$	−12.2233	+	4.44891i	−0.451785	+	0.164436i
$733$	7.90373	−	13.6897i	0.291931	−	0.505639i	−0.682335	−	0.731039i	$-0.739036\pi$
$733$	7.90373	−	13.6897i	0.291931	−	0.505639i	0.974266	+	0.225400i	$0.0723689\pi$
$734$	−3.27379	+	5.67036i	−0.120838	+	0.209297i
$735$		0			0
$736$	4.04189	+	22.9227i	0.148986	+	0.844942i
$737$	−4.32770	+	1.57515i	−0.159413	+	0.0580215i
$738$	−49.8546	+	41.8330i	−1.83517	+	1.53989i
$739$	0.269037	+	1.52579i	0.00989670	+	0.0561270i	0.989356	−	0.145514i	$-0.0464836\pi$
$739$	0.269037	+	1.52579i	0.00989670	+	0.0561270i	−0.979459	+	0.201641i	$0.935373\pi$
$740$	−12.2023	−	21.1351i	−0.448567	−	0.776940i
$741$	−1.45249	−	7.59202i	−0.0533584	−	0.278900i
$742$		0			0
$743$	29.2349	−	24.5310i	1.07252	−	0.899955i	0.0772453	−	0.997012i	$-0.475388\pi$
$743$	29.2349	−	24.5310i	1.07252	−	0.899955i	0.995279	+	0.0970576i	$0.0309431\pi$
$744$	−2.65580	−	15.0618i	−0.0973664	−	0.552193i
$745$	−11.5667	−	9.70562i	−0.423771	−	0.355586i
$746$	−55.6379	−	20.2505i	−2.03705	−	0.741425i
$747$	−24.2888	−	20.3807i	−0.888681	−	0.745692i
$748$	10.1382	−	17.5598i	0.370688	−	0.642050i
$749$		0			0
$750$	13.9611	+	11.7148i	0.509787	+	0.427762i
$751$	−4.40167	+	24.9631i	−0.160619	+	0.910918i	0.792848	+	0.609420i	$0.208598\pi$
$751$	−4.40167	+	24.9631i	−0.160619	+	0.910918i	−0.953467	+	0.301498i	$0.902513\pi$
$752$	3.81016			0.138942
$753$	4.68732	+	8.11867i	0.170815	+	0.295861i
$754$	24.5194	+	20.5742i	0.892942	+	0.749267i
$755$	2.58331	+	14.6507i	0.0940163	+	0.533193i
$756$		0			0
$757$	−39.8153	−	14.4916i	−1.44711	−	0.526705i	−0.505328	−	0.862927i	$-0.668628\pi$
$757$	−39.8153	−	14.4916i	−1.44711	−	0.526705i	−0.941783	+	0.336222i	$0.890851\pi$
$758$	60.5287	+	22.0307i	2.19850	+	0.800190i
$759$	1.95811	−	3.39155i	0.0710749	−	0.123105i
$760$	−33.5153	+	12.7519i	−1.21573	+	0.462560i
$761$	1.42855	+	2.47432i	0.0517848	+	0.0896940i	0.890756	−	0.454482i	$-0.150176\pi$
$761$	1.42855	+	2.47432i	0.0517848	+	0.0896940i	−0.838971	+	0.544176i	$0.816842\pi$
$762$	−18.3614	+	15.4071i	−0.665165	+	0.558139i
$763$		0			0
$764$	−7.87804	+	44.6786i	−0.285018	+	1.61641i
$765$	10.3059	−	8.64766i	0.372610	−	0.312657i
$766$	12.0831	−	68.5265i	0.436579	−	2.47596i
$767$	5.34658	+	9.26055i	0.193054	+	0.334379i
$768$	−9.95471	+	17.2421i	−0.359210	+	0.622169i
$769$	14.6472	+	12.2905i	0.528193	+	0.443207i	0.867477	−	0.497477i	$-0.165740\pi$
$769$	14.6472	+	12.2905i	0.528193	+	0.443207i	−0.339284	+	0.940684i	$0.610185\pi$
$770$		0			0
$771$	1.62449	+	2.81369i	0.0585044	+	0.101333i
$772$	60.8813			2.19116
$773$	0.436700	−	2.47665i	0.0157070	−	0.0890788i	−0.975947	−	0.218010i	$-0.930043\pi$
$773$	0.436700	−	2.47665i	0.0157070	−	0.0890788i	0.991654	+	0.128931i	$0.0411546\pi$
$774$	53.2973	+	19.3986i	1.91573	+	0.697270i
$775$	−11.4846	+	4.18004i	−0.412538	+	0.150152i
$776$	42.2854	+	15.3906i	1.51796	+	0.552491i
$777$		0			0
$778$	8.46286			0.303408
$779$	40.6805	−	15.4781i	1.45753	−	0.554561i
$780$	−5.26991	+	9.12776i	−0.188693	+	0.326826i
$781$	1.42696	+	8.09267i	0.0510605	+	0.289578i
$782$	8.63816	+	48.9894i	0.308900	+	1.75186i
$783$	−2.93939	+	16.6701i	−0.105045	+	0.595741i
$784$		0			0
$785$	13.9179	−	5.06569i	0.496750	−	0.180802i
$786$	−32.7374			−1.16770
$787$	2.72605			0.0971733			0.0485866	−	0.998819i	$-0.484528\pi$
$787$	2.72605			0.0971733			0.0485866	+	0.998819i	$0.484528\pi$
$788$	32.9183	−	11.9813i	1.17267	−	0.426816i
$789$	2.72503	−	15.4544i	0.0970137	−	0.550192i
$790$	−16.7306	−	28.9782i	−0.595246	−	1.03100i
$791$		0			0
$792$	17.4982	−	6.36884i	0.621773	−	0.226307i
$793$	−9.40214	+	7.88933i	−0.333880	+	0.280158i
$794$	25.4552	+	21.3594i	0.903370	+	0.758018i
$795$	1.98293	−	1.66387i	0.0703271	−	0.0590115i
$796$	−112.072	−	40.7909i	−3.97229	−	1.44579i
$797$	22.0327			0.780439			0.390219	−	0.920722i	$-0.372399\pi$
$797$	22.0327			0.780439			0.390219	+	0.920722i	$0.372399\pi$
$798$		0			0
$799$	2.22668			0.0787743
$800$	−13.7554	−	5.00654i	−0.486326	−	0.177008i
$801$	4.78359	−	4.01390i	0.169020	−	0.141824i
$802$	−33.1955	−	27.8544i	−1.17217	−	0.983571i
$803$	−5.56212	+	4.66717i	−0.196283	+	0.164701i
$804$	−10.5175	+	3.82807i	−0.370925	+	0.135006i
$805$		0			0
$806$	−13.1998	−	22.8627i	−0.464943	−	0.805306i
$807$	1.48602	−	8.42767i	0.0523105	−	0.296668i
$808$	12.4525	−	4.53233i	0.438077	−	0.159447i
$809$	54.7205			1.92387			0.961935	−	0.273278i	$-0.0881077\pi$
$809$	54.7205			1.92387			0.961935	+	0.273278i	$0.0881077\pi$
$810$	18.2422			0.640964
$811$	2.17112	−	0.790224i	0.0762384	−	0.0277485i	−0.303619	−	0.952793i	$-0.598195\pi$
$811$	2.17112	−	0.790224i	0.0762384	−	0.0277485i	0.379858	+	0.925045i	$0.375973\pi$
$812$		0			0
$813$	3.01145	−	17.0788i	0.105616	−	0.598979i
$814$	−2.13903	−	12.1311i	−0.0749731	−	0.425193i
$815$	1.48158	+	8.40247i	0.0518975	+	0.294326i
$816$	8.40420	−	14.5565i	0.294206	−	0.509579i
$817$	−29.4085	−	23.9587i	−1.02887	−	0.838209i
$818$	22.2772			0.778906
$819$		0			0
$820$	−55.7700	−	20.2986i	−1.94757	−	0.708858i
$821$	−1.04411	+	0.380025i	−0.0364397	+	0.0132630i	−0.360176	−	0.932884i	$-0.617283\pi$
$821$	−1.04411	+	0.380025i	−0.0364397	+	0.0132630i	0.323736	+	0.946147i	$0.395061\pi$
$822$	−15.8478	−	5.76811i	−0.552754	−	0.201186i
$823$	3.58543	−	20.3340i	0.124980	−	0.708798i	−0.856340	−	0.516413i	$-0.827267\pi$
$823$	3.58543	−	20.3340i	0.124980	−	0.708798i	0.981320	−	0.192384i	$-0.0616220\pi$
$824$	76.1772			2.65376
$825$	1.23143	+	2.13290i	0.0428729	+	0.0742580i
$826$		0			0
$827$	27.8116	+	23.3367i	0.967103	+	0.811495i	0.982094	−	0.188392i	$-0.0603276\pi$
$827$	27.8116	+	23.3367i	0.967103	+	0.811495i	−0.0149913	+	0.999888i	$0.504772\pi$
$828$	−28.7520	+	49.7999i	−0.999200	+	1.73066i
$829$	3.57486	+	6.19183i	0.124160	+	0.215051i	0.921404	−	0.388606i	$-0.127043\pi$
$829$	3.57486	+	6.19183i	0.124160	+	0.215051i	−0.797244	+	0.603657i	$0.793710\pi$
$830$	7.29726	−	41.3848i	0.253291	−	1.43649i
$831$	8.25537	−	6.92708i	0.286376	−	0.240298i
$832$	−0.772852	+	4.38306i	−0.0267938	+	0.151955i
$833$		0			0
$834$	−2.10220	+	1.76395i	−0.0727931	+	0.0610807i
$835$	−9.28177	−	16.0765i	−0.321209	−	0.556350i
$836$	−22.7802	+	0.330341i	−0.787869	+	0.0114251i
$837$	6.98070	−	12.0909i	0.241288	−	0.417924i
$838$	16.2754	+	5.92377i	0.562226	+	0.204633i
$839$	32.5197	+	11.8362i	1.12270	+	0.408631i	0.835638	−	0.549280i	$-0.185098\pi$
$839$	32.5197	+	11.8362i	1.12270	+	0.408631i	0.287065	+	0.957911i	$0.407320\pi$
$840$		0			0
$841$	−1.27672	−	7.24065i	−0.0440249	−	0.249678i
$842$	9.35504	+	7.84981i	0.322396	+	0.270522i
$843$	−6.32800	−	10.9604i	−0.217948	−	0.377497i
$844$	−35.6091			−1.22571
$845$	1.31449	−	7.45486i	0.0452199	−	0.256455i
$846$	2.86571	+	2.40462i	0.0985253	+	0.0826725i
$847$		0			0
$848$	−9.76991	+	16.9220i	−0.335500	+	0.581103i
$849$	5.65523	+	4.74530i	0.194087	+	0.162858i
$850$	−29.3974	−	10.6998i	−1.00832	−	0.366999i
$851$	15.9290	+	13.3660i	0.546040	+	0.458182i
$852$	3.46791	+	19.6675i	0.118809	+	0.673797i
$853$	25.4716	−	21.3732i	0.872132	−	0.731805i	−0.0924142	−	0.995721i	$-0.529458\pi$
$853$	25.4716	−	21.3732i	0.872132	−	0.731805i	0.964546	+	0.263915i	$0.0850139\pi$
$854$		0			0
$855$	−14.2781	−	4.96356i	−0.488301	−	0.169750i
$856$	−20.3944	−	35.3241i	−0.697066	−	1.20735i
$857$	−0.674830	−	3.82715i	−0.0230518	−	0.130733i	0.971110	−	0.238632i	$-0.0766989\pi$
$857$	−0.674830	−	3.82715i	−0.0230518	−	0.130733i	−0.994162	+	0.107899i	$0.965588\pi$
$858$	−4.07532	+	3.41960i	−0.139129	+	0.116743i
$859$	−1.55778	+	0.566986i	−0.0531508	+	0.0193453i	−0.368459	−	0.929644i	$-0.620114\pi$
$859$	−1.55778	+	0.566986i	−0.0531508	+	0.0193453i	0.315308	+	0.948989i	$0.397892\pi$
$860$	8.98158	+	50.9371i	0.306269	+	1.73694i
$861$		0			0
$862$	1.65048	−	2.85872i	0.0562156	−	0.0973684i
$863$	26.3594	−	45.6558i	0.897284	−	1.55414i	0.0663308	−	0.997798i	$-0.478871\pi$
$863$	26.3594	−	45.6558i	0.897284	−	1.55414i	0.830953	−	0.556343i	$-0.187796\pi$
$864$	15.7135	−	5.71924i	0.534583	−	0.194572i
$865$	31.9641	−	11.6340i	1.08681	−	0.395567i
$866$	25.0979	−	43.4709i	0.852862	−	1.47720i
$867$	−0.636507	+	1.10246i	−0.0216169	+	0.0374416i
$868$		0			0
$869$	−2.01795	−	11.4444i	−0.0684543	−	0.388224i
$870$	−9.73530	+	3.54336i	−0.330058	+	0.120131i
$871$	−8.09009	+	6.78839i	−0.274122	+	0.230016i
$872$	−10.0235	−	56.8459i	−0.339438	−	1.92505i
$873$	9.48457	+	16.4278i	0.321004	+	0.555996i
$874$	42.2918	−	36.5450i	1.43054	−	1.23615i
$875$		0			0
$876$	−13.5175	+	11.3426i	−0.456715	+	0.383230i
$877$	−3.67958	−	20.8679i	−0.124251	−	0.704660i	−0.981750	−	0.190175i	$-0.939094\pi$
$877$	−3.67958	−	20.8679i	−0.124251	−	0.704660i	0.857500	−	0.514485i	$-0.172017\pi$
$878$	67.0497	+	56.2614i	2.26282	+	1.89873i
$879$	2.39141	+	0.870401i	0.0806602	+	0.0293579i
$880$	8.11721	+	6.81115i	0.273631	+	0.229604i
$881$	−16.0505	+	27.8003i	−0.540755	+	0.936616i	0.458106	+	0.888898i	$0.348528\pi$
$881$	−16.0505	+	27.8003i	−0.540755	+	0.936616i	−0.998861	+	0.0477179i	$0.984805\pi$
$882$		0			0
$883$	−36.2315	−	30.4018i	−1.21929	−	1.02310i	−0.998862	−	0.0476989i	$-0.984811\pi$
$883$	−36.2315	−	30.4018i	−1.21929	−	1.02310i	−0.220425	−	0.975404i	$-0.570744\pi$
$884$	8.07398	−	45.7898i	0.271557	−	1.54008i
$885$	−3.46110			−0.116344
$886$	21.5355	+	37.3007i	0.723501	+	1.25314i
$887$	8.09177	+	6.78980i	0.271695	+	0.227979i	0.768447	−	0.639913i	$-0.221030\pi$
$887$	8.09177	+	6.78980i	0.271695	+	0.227979i	−0.496752	+	0.867892i	$0.665474\pi$
$888$	−2.84167	−	16.1159i	−0.0953602	−	0.540815i
$889$		0			0
$890$	7.77719	+	2.83067i	0.260692	+	0.0948841i
$891$	5.95336	+	2.16685i	0.199445	+	0.0725921i
$892$	34.1352	−	59.1239i	1.14293	−	1.97962i
$893$	−1.28224	−	2.14835i	−0.0429086	−	0.0718919i
$894$	−9.26099	−	16.0405i	−0.309734	−	0.536475i
$895$	−6.01779	+	5.04952i	−0.201153	+	0.168787i
$896$		0			0
$897$	1.55943	−	8.84397i	0.0520679	−	0.295291i
$898$	−72.5634	+	60.8879i	−2.42147	+	2.03186i
$899$	3.10044	−	17.5835i	0.103406	−	0.586442i
$900$	−18.0817	−	31.3185i	−0.602724	−	1.04395i
$901$	−5.70961	+	9.88933i	−0.190215	+	0.329461i
$902$	−22.9479	−	19.2556i	−0.764081	−	0.641141i
$903$		0			0
$904$	4.00088	+	6.92972i	0.133067	+	0.230479i
$905$	−18.2722			−0.607388
$906$	−3.16890	+	17.9717i	−0.105280	+	0.597071i
$907$	−40.3320	−	14.6797i	−1.33920	−	0.487430i	−0.429642	−	0.902999i	$-0.641360\pi$
$907$	−40.3320	−	14.6797i	−1.33920	−	0.487430i	−0.909561	+	0.415569i	$0.863582\pi$
$908$	−40.9261	+	14.8959i	−1.35818	+	0.494337i
$909$	5.24928	+	1.91058i	0.174107	+	0.0633699i
$910$		0			0
$911$	−55.1411			−1.82691			−0.913454	−	0.406942i	$-0.866595\pi$
$911$	−55.1411			−1.82691			−0.913454	+	0.406942i	$0.866595\pi$
$912$	−18.8840	+	0.273842i	−0.625313	+	0.00906780i
$913$	7.29726	−	12.6392i	0.241504	−	0.418297i
$914$	−4.00609	−	22.7197i	−0.132510	−	0.751500i
$915$	−0.689845	−	3.91231i	−0.0228056	−	0.129337i
$916$	15.4119	−	87.4055i	0.509225	−	2.88796i
$917$		0			0
$918$	33.5822	−	12.2229i	1.10838	−	0.403416i
$919$	−24.5577			−0.810083			−0.405041	−	0.914298i	$-0.632743\pi$
$919$	−24.5577			−0.810083			−0.405041	+	0.914298i	$0.632743\pi$
$920$	−41.6614			−1.37353
$921$	14.2144	−	5.17360i	0.468379	−	0.170476i
$922$	10.7497	−	60.9648i	0.354024	−	2.00777i
$923$	9.42190	+	16.3192i	0.310126	+	0.537154i
$924$		0			0
$925$	−12.2883	+	4.47259i	−0.404038	+	0.147058i
$926$	0.486329	−	0.408079i	0.0159818	−	0.0134103i
$927$	24.5993	+	20.6412i	0.807946	+	0.677947i
$928$	16.3819	−	13.7461i	0.537763	−	0.451236i
$929$	20.9338	+	7.61927i	0.686814	+	0.249980i	0.661771	−	0.749706i	$-0.269805\pi$
$929$	20.9338	+	7.61927i	0.686814	+	0.249980i	0.0250438	+	0.999686i	$0.492027\pi$
$930$	8.54488			0.280198
$931$		0			0
$932$	15.5936			0.510785
$933$	−2.12284	−	0.772649i	−0.0694985	−	0.0252954i
$934$	−29.7973	+	25.0029i	−0.974996	+	0.818119i
$935$	4.74376	+	3.98048i	0.155137	+	0.130176i
$936$	32.7108	−	27.4476i	1.06919	−	0.897153i
$937$	8.97565	−	3.26687i	0.293222	−	0.106724i	−0.191221	−	0.981547i	$-0.561245\pi$
$937$	8.97565	−	3.26687i	0.293222	−	0.106724i	0.484443	+	0.874823i	$0.339022\pi$
$938$		0			0
$939$	−7.47013	−	12.9386i	−0.243779	−	0.422237i
$940$	−0.592396	+	3.35965i	−0.0193218	+	0.109580i
$941$	52.3649	−	19.0593i	1.70705	−	0.621314i	0.710450	−	0.703748i	$-0.248491\pi$
$941$	52.3649	−	19.0593i	1.70705	−	0.621314i	0.996597	+	0.0824333i	$0.0262691\pi$
$942$	18.1685			0.591961
$943$	50.5681			1.64672
$944$	24.5510	−	8.93582i	0.799066	−	0.290836i
$945$		0			0
$946$	−4.53343	+	25.7104i	−0.147395	+	0.835916i
$947$	−4.69594	−	26.6320i	−0.152597	−	0.865423i	−0.960950	−	0.276724i	$-0.910751\pi$
$947$	−4.69594	−	26.6320i	−0.152597	−	0.865423i	0.808352	−	0.588699i	$-0.200360\pi$
$948$	−4.90420	−	27.8131i	−0.159281	−	0.903328i
$949$	−8.32501	+	14.4193i	−0.270241	+	0.468071i
$950$	6.60519	+	34.5248i	0.214301	+	1.12013i
$951$	−17.0490			−0.552852
$952$		0			0
$953$	−21.7361	−	7.91128i	−0.704100	−	0.256272i	−0.0349398	−	0.999389i	$-0.511124\pi$
$953$	−21.7361	−	7.91128i	−0.704100	−	0.256272i	−0.669161	+	0.743118i	$0.733346\pi$
$954$	−18.0278	+	6.56159i	−0.583672	+	0.212439i
$955$	−13.0201	−	4.73892i	−0.421319	−	0.153348i
$956$	9.17230	−	52.0187i	0.296654	−	1.68241i
$957$	−3.59802			−0.116308
$958$	−0.910597	−	1.57720i	−0.0294200	−	0.0509570i
$959$		0			0
$960$	−1.10354	−	0.925981i	−0.0356166	−	0.0298859i
$961$	8.13681	−	14.0934i	0.262478	−	0.454625i
$962$	−14.1236	−	24.4628i	−0.455363	−	0.788713i
$963$	2.98576	−	16.9331i	0.0962147	−	0.545660i
$964$	43.5997	−	36.5845i	1.40425	−	1.17831i
$965$	−3.22874	+	18.3111i	−0.103937	+	0.589455i
$966$		0			0
$967$	29.9026	−	25.0913i	0.961603	−	0.806881i	−0.0196101	−	0.999808i	$-0.506242\pi$
$967$	29.9026	−	25.0913i	0.961603	−	0.806881i	0.981213	+	0.192927i	$0.0617980\pi$
$968$	−29.2977	−	50.7451i	−0.941664	−	1.63101i
$969$	−11.0360	+	0.160035i	−0.354526	+	0.00514107i
$970$	−12.5706	+	21.7729i	−0.403617	+	0.699085i
$971$	38.7178	+	14.0921i	1.24251	+	0.452238i	0.877865	−	0.478907i	$-0.158967\pi$
$971$	38.7178	+	14.0921i	1.24251	+	0.452238i	0.364648	+	0.931145i	$0.381189\pi$
$972$	59.7135	+	21.7339i	1.91531	+	0.697117i
$973$		0			0
$974$	−5.16503	−	29.2923i	−0.165498	−	0.938587i
$975$	4.32635	+	3.63024i	0.138554	+	0.116261i
$976$	14.9941	+	25.9705i	0.479948	+	0.831295i
$977$	22.4938			0.719641			0.359821	−	0.933022i	$-0.382838\pi$
$977$	22.4938			0.719641			0.359821	+	0.933022i	$0.382838\pi$
$978$	−1.81743	+	10.3072i	−0.0581150	+	0.329586i
$979$	2.20187	+	1.84759i	0.0703720	+	0.0590491i
$980$		0			0
$981$	12.1664	−	21.0728i	0.388442	−	0.672802i
$982$	−0.172304	−	0.144580i	−0.00549844	−	0.00461374i
$983$	41.8597	+	15.2357i	1.33512	+	0.485943i	0.908271	−	0.418382i	$-0.137403\pi$
$983$	41.8597	+	15.2357i	1.33512	+	0.485943i	0.426845	+	0.904325i	$0.359625\pi$
$984$	−30.4859	−	25.5807i	−0.971856	−	0.815484i
$985$	1.85781	+	10.5362i	0.0591948	+	0.335710i
$986$	35.0107	−	29.3775i	1.11497	−	0.935570i
$987$		0			0
$988$	−48.8285	+	18.5782i	−1.55344	+	0.591052i
$989$	−22.0351	−	38.1659i	−0.700675	−	1.21360i
$990$	1.80659	+	10.2457i	0.0574172	+	0.325629i
$991$	−34.7245	+	29.1373i	−1.10306	+	0.925576i	−0.997627	−	0.0688503i	$-0.978067\pi$
$991$	−34.7245	+	29.1373i	−1.10306	+	0.925576i	−0.105432	+	0.994427i	$0.533622\pi$
$992$	−16.5744	+	6.03260i	−0.526239	+	0.191535i
$993$	−2.15853	−	12.2416i	−0.0684988	−	0.388476i
$994$		0			0
$995$	18.2121	−	31.5443i	0.577363	−	1.00002i
$996$	17.7344	−	30.7169i	0.561937	−	0.973303i
$997$	9.85844	−	3.58818i	0.312220	−	0.113639i	−0.181157	−	0.983454i	$-0.557984\pi$
$997$	9.85844	−	3.58818i	0.312220	−	0.113639i	0.493377	+	0.869815i	$0.335762\pi$
$998$	34.9543	−	12.7223i	1.10646	−	0.402718i
$999$	7.46926	−	12.9371i	0.236317	−	0.409313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.x.a.557.1		6
7.2	even	3		931.2.v.b.177.1		6
7.3	odd	6		931.2.w.a.785.1		6
7.4	even	3		19.2.e.a.6.1	✓	6
7.5	odd	6		931.2.v.a.177.1		6
7.6	odd	2		931.2.x.b.557.1		6
19.16	even	9		931.2.v.b.263.1		6
21.11	odd	6		171.2.u.c.82.1		6
28.11	odd	6		304.2.u.b.177.1		6
35.4	even	6		475.2.l.a.101.1		6
35.18	odd	12		475.2.u.a.424.2		12
35.32	odd	12		475.2.u.a.424.1		12
133.4	even	9		361.2.a.g.1.1		3
133.11	even	3		361.2.e.g.99.1		6
133.16	even	9	inner	931.2.x.a.814.1		6
133.18	odd	6		361.2.e.h.234.1		6
133.25	even	9		361.2.c.i.292.3		6
133.32	odd	18		361.2.c.h.292.1		6
133.46	odd	6		361.2.e.a.99.1		6
133.53	odd	18		361.2.a.h.1.3		3
133.54	odd	18		931.2.x.b.814.1		6
133.60	odd	18		361.2.e.h.54.1		6
133.67	odd	18		361.2.c.h.68.1		6
133.73	odd	18		931.2.w.a.491.1		6
133.74	even	9		361.2.e.g.62.1		6
133.81	even	9		361.2.e.f.245.1		6
133.88	odd	6		361.2.e.b.28.1		6
133.102	even	3		361.2.e.f.28.1		6
133.109	odd	18		361.2.e.b.245.1		6
133.111	odd	18		931.2.v.a.263.1		6
133.116	odd	18		361.2.e.a.62.1		6
133.123	even	9		361.2.c.i.68.3		6
133.130	even	9		19.2.e.a.16.1	yes	6
399.53	even	18		3249.2.a.s.1.1		3
399.137	odd	18		3249.2.a.z.1.3		3
399.263	odd	18		171.2.u.c.73.1		6
532.263	odd	18		304.2.u.b.225.1		6
532.319	even	18		5776.2.a.bi.1.2		3
532.403	odd	18		5776.2.a.br.1.2		3
665.4	even	18		9025.2.a.bd.1.3		3
665.263	odd	36		475.2.u.a.149.1		12
665.319	odd	18		9025.2.a.x.1.1		3
665.529	even	18		475.2.l.a.301.1		6
665.662	odd	36		475.2.u.a.149.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	7.4	even	3
19.2.e.a.16.1	yes	6	133.130	even	9
171.2.u.c.73.1		6	399.263	odd	18
171.2.u.c.82.1		6	21.11	odd	6
304.2.u.b.177.1		6	28.11	odd	6
304.2.u.b.225.1		6	532.263	odd	18
361.2.a.g.1.1		3	133.4	even	9
361.2.a.h.1.3		3	133.53	odd	18
361.2.c.h.68.1		6	133.67	odd	18
361.2.c.h.292.1		6	133.32	odd	18
361.2.c.i.68.3		6	133.123	even	9
361.2.c.i.292.3		6	133.25	even	9
361.2.e.a.62.1		6	133.116	odd	18
361.2.e.a.99.1		6	133.46	odd	6
361.2.e.b.28.1		6	133.88	odd	6
361.2.e.b.245.1		6	133.109	odd	18
361.2.e.f.28.1		6	133.102	even	3
361.2.e.f.245.1		6	133.81	even	9
361.2.e.g.62.1		6	133.74	even	9
361.2.e.g.99.1		6	133.11	even	3
361.2.e.h.54.1		6	133.60	odd	18
361.2.e.h.234.1		6	133.18	odd	6
475.2.l.a.101.1		6	35.4	even	6
475.2.l.a.301.1		6	665.529	even	18
475.2.u.a.149.1		12	665.263	odd	36
475.2.u.a.149.2		12	665.662	odd	36
475.2.u.a.424.1		12	35.32	odd	12
475.2.u.a.424.2		12	35.18	odd	12
931.2.v.a.177.1		6	7.5	odd	6
931.2.v.a.263.1		6	133.111	odd	18
931.2.v.b.177.1		6	7.2	even	3
931.2.v.b.263.1		6	19.16	even	9
931.2.w.a.491.1		6	133.73	odd	18
931.2.w.a.785.1		6	7.3	odd	6
931.2.x.a.557.1		6	1.1	even	1	trivial
931.2.x.a.814.1		6	133.16	even	9	inner
931.2.x.b.557.1		6	7.6	odd	2
931.2.x.b.814.1		6	133.54	odd	18
3249.2.a.s.1.1		3	399.53	even	18
3249.2.a.z.1.3		3	399.137	odd	18
5776.2.a.bi.1.2		3	532.319	even	18
5776.2.a.br.1.2		3	532.403	odd	18
9025.2.a.x.1.1		3	665.319	odd	18
9025.2.a.bd.1.3		3	665.4	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.x (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.37939 + 0.866025i) q^{2} +(-0.500000 + 0.419550i) q^{3} +(3.37939 + 2.83564i) q^{4} +(-1.03209 + 0.866025i) q^{5} +(-1.55303 + 0.565258i) q^{6} +(3.05303 + 5.28801i) q^{8} +(-0.446967 + 2.53487i) q^{9} +O(q^{10})\)	\(q+(2.37939 + 0.866025i) q^{2} +(-0.500000 + 0.419550i) q^{3} +(3.37939 + 2.83564i) q^{4} +(-1.03209 + 0.866025i) q^{5} +(-1.55303 + 0.565258i) q^{6} +(3.05303 + 5.28801i) q^{8} +(-0.446967 + 2.53487i) q^{9} +(-3.20574 + 1.16679i) q^{10} -1.18479 q^{11} -2.87939 q^{12} +(-2.55303 + 0.929228i) q^{13} +(0.152704 - 0.866025i) q^{15} +(1.15270 + 6.53731i) q^{16} +(0.673648 + 3.82045i) q^{17} +(-3.25877 + 5.64436i) q^{18} +(3.29813 - 2.84997i) q^{19} -5.94356 q^{20} +(-2.81908 - 1.02606i) q^{22} +(4.75877 - 1.73205i) q^{23} +(-3.74510 - 1.36310i) q^{24} +(-0.553033 + 3.13641i) q^{25} -6.87939 q^{26} +(-1.81908 - 3.15074i) q^{27} +(-3.56418 - 2.99070i) q^{29} +(1.11334 - 1.92836i) q^{30} +(1.91875 + 3.32337i) q^{31} +(-0.798133 + 4.52644i) q^{32} +(0.592396 - 0.497079i) q^{33} +(-1.70574 + 9.67372i) q^{34} +(-8.69846 + 7.29888i) q^{36} +(2.05303 + 3.55596i) q^{37} +(10.3157 - 3.92490i) q^{38} +(0.886659 - 1.53574i) q^{39} +(-7.73055 - 2.81369i) q^{40} +(9.38326 + 3.41523i) q^{41} +(-1.51114 - 8.57013i) q^{43} +(-4.00387 - 3.35965i) q^{44} +(-1.73396 - 3.00330i) q^{45} +12.8229 q^{46} +(0.0996702 - 0.565258i) q^{47} +(-3.31908 - 2.78504i) q^{48} +(-4.03209 + 6.98378i) q^{50} +(-1.93969 - 1.62760i) q^{51} +(-11.2626 - 4.09927i) q^{52} +(2.25490 + 1.89209i) q^{53} +(-1.59967 - 9.07218i) q^{54} +(1.22281 - 1.02606i) q^{55} +(-0.453363 + 2.80872i) q^{57} +(-5.89053 - 10.2027i) q^{58} +(-0.683448 - 3.87603i) q^{59} +(2.97178 - 2.49362i) q^{60} +(4.24510 - 1.54509i) q^{61} +(1.68732 + 9.56926i) q^{62} +(0.819078 - 1.41868i) q^{64} +(1.83022 - 3.17004i) q^{65} +(1.84002 - 0.669713i) q^{66} +(3.65270 - 1.32948i) q^{67} +(-8.55690 + 14.8210i) q^{68} +(-1.65270 + 2.86257i) q^{69} +(-1.20439 - 6.83045i) q^{71} +(-14.7690 + 5.37549i) q^{72} +(4.69459 - 3.93923i) q^{73} +(1.80541 + 10.2390i) q^{74} +(-1.03936 - 1.80023i) q^{75} +(19.2271 - 0.278817i) q^{76} +(3.43969 - 2.88624i) q^{78} +(1.70321 + 9.65939i) q^{79} +(-6.85117 - 5.74881i) q^{80} +(-5.02481 - 1.82888i) q^{81} +(19.3687 + 16.2523i) q^{82} +(-6.15910 + 10.6679i) q^{83} +(-4.00387 - 3.35965i) q^{85} +(3.82635 - 21.7003i) q^{86} +3.03684 q^{87} +(-3.61721 - 6.26519i) q^{88} +(-1.85844 - 1.55942i) q^{89} +(-1.52481 - 8.64766i) q^{90} +(20.9932 + 7.64090i) q^{92} +(-2.35369 - 0.856674i) q^{93} +(0.726682 - 1.25865i) q^{94} +(-0.935822 + 5.79769i) q^{95} +(-1.50000 - 2.59808i) q^{96} +(5.64543 - 4.73708i) q^{97} +(0.529563 - 3.00330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9	\( 6 q + 3 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} + 6 q^{8} - 15 q^{9} - 9 q^{10} - 6 q^{12} - 3 q^{13} + 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} + 6 q^{19} - 6 q^{20} + 6 q^{23} - 21 q^{24} + 9 q^{25} - 30 q^{26} + 6 q^{27} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 24 q^{36} + 3 q^{38} + 12 q^{39} - 9 q^{40} + 21 q^{41} - 3 q^{43} - 15 q^{45} + 36 q^{46} + 15 q^{47} - 3 q^{48} - 15 q^{50} - 6 q^{51} - 21 q^{52} + 15 q^{53} - 24 q^{54} + 18 q^{55} + 24 q^{57} - 18 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} - 12 q^{62} - 12 q^{64} - 12 q^{65} - 9 q^{66} + 24 q^{67} - 15 q^{68} - 12 q^{69} - 6 q^{71} - 3 q^{72} + 24 q^{73} + 15 q^{74} - 15 q^{75} + 36 q^{76} + 15 q^{78} + 15 q^{79} - 15 q^{80} - 3 q^{81} + 45 q^{82} + 24 q^{86} + 42 q^{87} + 9 q^{88} - 3 q^{89} + 18 q^{90} + 42 q^{92} + 27 q^{93} - 9 q^{94} - 24 q^{95} - 9 q^{96} + 18 q^{97} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 + 6 * q^8 - 15 * q^9 - 9 * q^10 - 6 * q^12 - 3 * q^13 + 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 + 6 * q^19 - 6 * q^20 + 6 * q^23 - 21 * q^24 + 9 * q^25 - 30 * q^26 + 6 * q^27 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 24 * q^36 + 3 * q^38 + 12 * q^39 - 9 * q^40 + 21 * q^41 - 3 * q^43 - 15 * q^45 + 36 * q^46 + 15 * q^47 - 3 * q^48 - 15 * q^50 - 6 * q^51 - 21 * q^52 + 15 * q^53 - 24 * q^54 + 18 * q^55 + 24 * q^57 - 18 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 - 12 * q^62 - 12 * q^64 - 12 * q^65 - 9 * q^66 + 24 * q^67 - 15 * q^68 - 12 * q^69 - 6 * q^71 - 3 * q^72 + 24 * q^73 + 15 * q^74 - 15 * q^75 + 36 * q^76 + 15 * q^78 + 15 * q^79 - 15 * q^80 - 3 * q^81 + 45 * q^82 + 24 * q^86 + 42 * q^87 + 9 * q^88 - 3 * q^89 + 18 * q^90 + 42 * q^92 + 27 * q^93 - 9 * q^94 - 24 * q^95 - 9 * q^96 + 18 * q^97 + 9 * q^99

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