LMFDB - Embedded newform 961.2.d.p.531.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("961.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			531.2
Root			$-2.52368i$ of defining polynomial
Character	$\chi$	$=$	961.531
Dual form			961.2.d.p.628.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.108599 + 0.334232i) q^{2} +(-0.894076 + 2.75168i) q^{3} +(1.51812 - 1.10298i) q^{4} +2.97323 q^{5} -1.01680 q^{6} +(0.875458 - 0.636058i) q^{7} +(1.10215 + 0.800755i) q^{8} +(-4.34534 - 3.15708i) q^{9} +(0.322889 + 0.993749i) q^{10} +(1.96702 - 1.42912i) q^{11} +(1.67773 + 5.16352i) q^{12} +(0.888007 - 2.73301i) q^{13} +(0.307664 + 0.223531i) q^{14} +(-2.65829 + 8.18139i) q^{15} +(1.01179 - 3.11397i) q^{16} +(1.47627 + 1.07257i) q^{17} +(0.583298 - 1.79521i) q^{18} +(0.654583 + 2.01460i) q^{19} +(4.51371 - 3.27940i) q^{20} +(0.967503 + 2.97767i) q^{21} +(0.691275 + 0.502240i) q^{22} +(0.357760 + 0.259928i) q^{23} +(-3.18883 + 2.31682i) q^{24} +3.84010 q^{25} +1.00989 q^{26} +(5.55018 - 4.03244i) q^{27} +(0.627491 - 1.93122i) q^{28} +(-0.976227 - 3.00452i) q^{29} -3.02317 q^{30} +3.87532 q^{32} +(2.17383 + 6.69036i) q^{33} +(-0.198167 + 0.609895i) q^{34} +(2.60294 - 1.89115i) q^{35} -10.0789 q^{36} +3.14675 q^{37} +(-0.602257 + 0.437565i) q^{38} +(6.72642 + 4.88703i) q^{39} +(3.27693 + 2.38083i) q^{40} +(-2.14651 - 6.60626i) q^{41} +(-0.890163 + 0.646741i) q^{42} +(-2.59957 - 8.00065i) q^{43} +(1.40988 - 4.33915i) q^{44} +(-12.9197 - 9.38671i) q^{45} +(-0.0480240 + 0.147803i) q^{46} +(-2.46041 + 7.57236i) q^{47} +(7.66405 + 5.56826i) q^{48} +(-1.80126 + 5.54371i) q^{49} +(0.417029 + 1.28348i) q^{50} +(-4.27127 + 3.10326i) q^{51} +(-1.66634 - 5.12847i) q^{52} +(4.02648 + 2.92541i) q^{53} +(1.95051 + 1.41713i) q^{54} +(5.84840 - 4.24911i) q^{55} +1.47421 q^{56} -6.12878 q^{57} +(0.898189 - 0.652573i) q^{58} +(-3.71251 + 11.4259i) q^{59} +(4.98828 + 15.3523i) q^{60} -14.4351 q^{61} -5.81225 q^{63} +(-1.60273 - 4.93269i) q^{64} +(2.64025 - 8.12585i) q^{65} +(-2.00006 + 1.45313i) q^{66} -6.43759 q^{67} +3.42416 q^{68} +(-1.03510 + 0.752047i) q^{69} +(0.914757 + 0.664610i) q^{70} +(-1.35743 - 0.986230i) q^{71} +(-2.26115 - 6.95911i) q^{72} +(-11.6176 + 8.44069i) q^{73} +(0.341733 + 1.05175i) q^{74} +(-3.43334 + 10.5667i) q^{75} +(3.21579 + 2.33641i) q^{76} +(0.813039 - 2.50228i) q^{77} +(-0.902923 + 2.77891i) q^{78} +(2.78920 + 2.02647i) q^{79} +(3.00829 - 9.25856i) q^{80} +(1.15440 + 3.55287i) q^{81} +(1.97492 - 1.43486i) q^{82} +(3.97199 + 12.2245i) q^{83} +(4.75308 + 3.45331i) q^{84} +(4.38928 + 3.18900i) q^{85} +(2.39176 - 1.73772i) q^{86} +9.14030 q^{87} +3.31232 q^{88} +(-1.82788 + 1.32803i) q^{89} +(1.73428 - 5.33756i) q^{90} +(-0.960936 - 2.95746i) q^{91} +0.829816 q^{92} -2.79812 q^{94} +(1.94622 + 5.98986i) q^{95} +(-3.46483 + 10.6637i) q^{96} +(-2.76106 + 2.00603i) q^{97} -2.04850 q^{98} -13.0592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} - 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} + 4 q^{11} - 5 q^{12} + 9 q^{13} - 18 q^{14} + 4 q^{15} - 2 q^{16} + 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots - 12 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 - 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 + 4 * q^11 - 5 * q^12 + 9 * q^13 - 18 * q^14 + 4 * q^15 - 2 * q^16 + 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 + 2 * q^21 - 8 * q^22 + 21 * q^23 + 5 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 + 20 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 - 56 * q^34 + 21 * q^35 - 2 * q^36 + 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 + 12 * q^42 - 16 * q^43 + 37 * q^44 - 5 * q^45 - 16 * q^46 + 4 * q^47 + 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 - 18 * q^52 + 3 * q^53 + 39 * q^54 + 29 * q^55 + 60 * q^56 + 34 * q^57 + 10 * q^58 - 3 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 9 * q^65 + 20 * q^66 - 26 * q^67 - 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 - 9 * q^73 + 64 * q^74 + 19 * q^75 + 9 * q^76 - 42 * q^77 + 15 * q^78 + 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 + 67 * q^83 + 39 * q^84 - 63 * q^85 - 23 * q^86 - 30 * q^87 + 34 * q^88 + 26 * q^89 - 24 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 + 4 * q^96 - 37 * q^97 + 20 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.108599	+	0.334232i	0.0767908	+	0.236338i	0.982082	−	0.188453i	$-0.0603475\pi$
$2$	0.108599	+	0.334232i	0.0767908	+	0.236338i	−0.905291	+	0.424791i	$0.860347\pi$
$3$	−0.894076	+	2.75168i	−0.516195	+	1.58869i	0.264901	+	0.964275i	$0.414661\pi$
$3$	−0.894076	+	2.75168i	−0.516195	+	1.58869i	−0.781097	+	0.624410i	$0.785339\pi$
$4$	1.51812	−	1.10298i	0.759058	−	0.551488i
$5$	2.97323			1.32967			0.664834	−	0.746991i	$-0.268502\pi$
$5$	2.97323			1.32967			0.664834	+	0.746991i	$0.268502\pi$
$6$	−1.01680			−0.415106
$7$	0.875458	−	0.636058i	0.330892	−	0.240407i	−0.409917	−	0.912123i	$-0.634442\pi$
$7$	0.875458	−	0.636058i	0.330892	−	0.240407i	0.740809	+	0.671716i	$0.234442\pi$
$8$	1.10215	+	0.800755i	0.389667	+	0.283110i
$9$	−4.34534	−	3.15708i	−1.44845	−	1.05236i
$10$	0.322889	+	0.993749i	0.102106	+	0.314251i
$11$	1.96702	−	1.42912i	0.593079	−	0.430897i	−0.250337	−	0.968159i	$-0.580541\pi$
$11$	1.96702	−	1.42912i	0.593079	−	0.430897i	0.843415	+	0.537262i	$0.180541\pi$
$12$	1.67773	+	5.16352i	0.484319	+	1.49058i
$13$	0.888007	−	2.73301i	0.246289	−	0.757999i	−0.749133	−	0.662420i	$-0.769530\pi$
$13$	0.888007	−	2.73301i	0.246289	−	0.757999i	0.995422	−	0.0955796i	$-0.0304705\pi$
$14$	0.307664	+	0.223531i	0.0822268	+	0.0597413i
$15$	−2.65829	+	8.18139i	−0.686369	+	2.11243i
$16$	1.01179	−	3.11397i	0.252948	−	0.778493i
$17$	1.47627	+	1.07257i	0.358047	+	0.260136i	0.752237	−	0.658893i	$-0.228975\pi$
$17$	1.47627	+	1.07257i	0.358047	+	0.260136i	−0.394190	+	0.919029i	$0.628975\pi$
$18$	0.583298	−	1.79521i	0.137485	−	0.423134i
$19$	0.654583	+	2.01460i	0.150172	+	0.462180i	0.997640	−	0.0686657i	$-0.0218742\pi$
$19$	0.654583	+	2.01460i	0.150172	+	0.462180i	−0.847468	+	0.530846i	$0.821874\pi$
$20$	4.51371	−	3.27940i	1.00930	−	0.733297i
$21$	0.967503	+	2.97767i	0.211127	+	0.649781i
$22$	0.691275	+	0.502240i	0.147380	+	0.107078i
$23$	0.357760	+	0.259928i	0.0745981	+	0.0541987i	0.624459	−	0.781057i	$-0.285319\pi$
$23$	0.357760	+	0.259928i	0.0745981	+	0.0541987i	−0.549861	+	0.835256i	$0.685319\pi$
$24$	−3.18883	+	2.31682i	−0.650917	+	0.472919i
$25$	3.84010			0.768019
$26$	1.00989			0.198057
$27$	5.55018	−	4.03244i	1.06813	−	0.776043i
$28$	0.627491	−	1.93122i	0.118585	−	0.364966i
$29$	−0.976227	−	3.00452i	−0.181281	−	0.557925i	0.818584	−	0.574387i	$-0.194760\pi$
$29$	−0.976227	−	3.00452i	−0.181281	−	0.557925i	−0.999864	+	0.0164625i	$0.994760\pi$
$30$	−3.02317			−0.551953
$31$		0			0
$31$		0			0
$32$	3.87532			0.685067
$33$	2.17383	+	6.69036i	0.378415	+	1.16464i
$34$	−0.198167	+	0.609895i	−0.0339854	+	0.104596i
$35$	2.60294	−	1.89115i	0.439977	−	0.319662i
$36$	−10.0789			−1.67982
$37$	3.14675			0.517323			0.258661	−	0.965968i	$-0.416719\pi$
$37$	3.14675			0.517323			0.258661	+	0.965968i	$0.416719\pi$
$38$	−0.602257	+	0.437565i	−0.0976989	+	0.0709824i
$39$	6.72642	+	4.88703i	1.07709	+	0.782551i
$40$	3.27693	+	2.38083i	0.518128	+	0.376442i
$41$	−2.14651	−	6.60626i	−0.335228	−	1.03173i	−0.966610	−	0.256253i	$-0.917512\pi$
$41$	−2.14651	−	6.60626i	−0.335228	−	1.03173i	0.631382	−	0.775472i	$-0.282488\pi$
$42$	−0.890163	+	0.646741i	−0.137355	+	0.0997944i
$43$	−2.59957	−	8.00065i	−0.396430	−	1.22009i	−0.927842	−	0.372974i	$-0.878338\pi$
$43$	−2.59957	−	8.00065i	−0.396430	−	1.22009i	0.531412	−	0.847114i	$-0.321662\pi$
$44$	1.40988	−	4.33915i	0.212547	−	0.654152i
$45$	−12.9197	−	9.38671i	−1.92596	−	1.39929i
$46$	−0.0480240	+	0.147803i	−0.00708075	+	0.0217923i
$47$	−2.46041	+	7.57236i	−0.358888	+	1.10454i	0.594833	+	0.803849i	$0.297218\pi$
$47$	−2.46041	+	7.57236i	−0.358888	+	1.10454i	−0.953721	+	0.300693i	$0.902782\pi$
$48$	7.66405	+	5.56826i	1.10621	+	0.803709i
$49$	−1.80126	+	5.54371i	−0.257323	+	0.791959i
$50$	0.417029	+	1.28348i	0.0589768	+	0.181512i
$51$	−4.27127	+	3.10326i	−0.598097	+	0.434543i
$52$	−1.66634	−	5.12847i	−0.231080	−	0.711191i
$53$	4.02648	+	2.92541i	0.553079	+	0.401835i	0.828919	−	0.559368i	$-0.188956\pi$
$53$	4.02648	+	2.92541i	0.553079	+	0.401835i	−0.275840	+	0.961203i	$0.588956\pi$
$54$	1.95051	+	1.41713i	0.265431	+	0.192847i
$55$	5.84840	−	4.24911i	0.788598	−	0.572950i
$56$	1.47421			0.196999
$57$	−6.12878			−0.811777
$58$	0.898189	−	0.652573i	0.117938	−	0.0856870i
$59$	−3.71251	+	11.4259i	−0.483328	+	1.48753i	0.351061	+	0.936353i	$0.385821\pi$
$59$	−3.71251	+	11.4259i	−0.483328	+	1.48753i	−0.834388	+	0.551177i	$0.814179\pi$
$60$	4.98828	+	15.3523i	0.643984	+	1.98198i
$61$	−14.4351			−1.84823			−0.924115	−	0.382115i	$-0.875196\pi$
$61$	−14.4351			−1.84823			−0.924115	+	0.382115i	$0.875196\pi$
$62$		0			0
$63$	−5.81225			−0.732274
$64$	−1.60273	−	4.93269i	−0.200341	−	0.616586i
$65$	2.64025	−	8.12585i	0.327483	−	1.00789i
$66$	−2.00006	+	1.45313i	−0.246190	+	0.178868i
$67$	−6.43759			−0.786476			−0.393238	−	0.919437i	$-0.628645\pi$
$67$	−6.43759			−0.786476			−0.393238	+	0.919437i	$0.628645\pi$
$68$	3.42416			0.415241
$69$	−1.03510	+	0.752047i	−0.124612	+	0.0905358i
$70$	0.914757	+	0.664610i	0.109334	+	0.0794361i
$71$	−1.35743	−	0.986230i	−0.161097	−	0.117044i	0.504316	−	0.863519i	$-0.331745\pi$
$71$	−1.35743	−	0.986230i	−0.161097	−	0.117044i	−0.665413	+	0.746475i	$0.731745\pi$
$72$	−2.26115	−	6.95911i	−0.266479	−	0.820139i
$73$	−11.6176	+	8.44069i	−1.35974	+	0.987908i	−0.361278	+	0.932458i	$0.617659\pi$
$73$	−11.6176	+	8.44069i	−1.35974	+	0.987908i	−0.998461	+	0.0554502i	$0.982341\pi$
$74$	0.341733	+	1.05175i	0.0397256	+	0.122263i
$75$	−3.43334	+	10.5667i	−0.396448	+	1.22014i
$76$	3.21579	+	2.33641i	0.368876	+	0.268004i
$77$	0.813039	−	2.50228i	0.0926544	−	0.285161i
$78$	−0.902923	+	2.77891i	−0.102236	+	0.314650i
$79$	2.78920	+	2.02647i	0.313810	+	0.227996i	0.733530	−	0.679658i	$-0.237872\pi$
$79$	2.78920	+	2.02647i	0.313810	+	0.227996i	−0.419720	+	0.907654i	$0.637872\pi$
$80$	3.00829	−	9.25856i	0.336337	−	1.03514i
$81$	1.15440	+	3.55287i	0.128267	+	0.394764i
$82$	1.97492	−	1.43486i	0.218093	−	0.158454i
$83$	3.97199	+	12.2245i	0.435982	+	1.34181i	0.892077	+	0.451884i	$0.149248\pi$
$83$	3.97199	+	12.2245i	0.435982	+	1.34181i	−0.456095	+	0.889931i	$0.650752\pi$
$84$	4.75308	+	3.45331i	0.518604	+	0.376788i
$85$	4.38928	+	3.18900i	0.476084	+	0.345895i
$86$	2.39176	−	1.73772i	0.257911	−	0.187383i
$87$	9.14030			0.979943
$88$	3.31232			0.353094
$89$	−1.82788	+	1.32803i	−0.193755	+	0.140771i	−0.680433	−	0.732810i	$-0.738208\pi$
$89$	−1.82788	+	1.32803i	−0.193755	+	0.140771i	0.486678	+	0.873581i	$0.338208\pi$
$90$	1.73428	−	5.33756i	0.182809	−	0.562629i
$91$	−0.960936	−	2.95746i	−0.100733	−	0.310026i
$92$	0.829816			0.0865143
$93$		0			0
$94$	−2.79812			−0.288604
$95$	1.94622	+	5.98986i	0.199678	+	0.614547i
$96$	−3.46483	+	10.6637i	−0.353628	+	1.08836i
$97$	−2.76106	+	2.00603i	−0.280343	+	0.203681i	−0.719067	−	0.694941i	$-0.755431\pi$
$97$	−2.76106	+	2.00603i	−0.280343	+	0.203681i	0.438724	+	0.898622i	$0.355431\pi$
$98$	−2.04850			−0.206930
$99$	−13.0592			−1.31250
$100$	5.82971	−	4.23553i	0.582971	−	0.423553i
$101$	−14.3336	−	10.4140i	−1.42625	−	1.03623i	−0.990700	−	0.136062i	$-0.956555\pi$
$101$	−14.3336	−	10.4140i	−1.42625	−	1.03623i	−0.435546	−	0.900167i	$-0.643445\pi$
$102$	−1.50106	−	1.09059i	−0.148627	−	0.107984i
$103$	2.49496	+	7.67868i	0.245835	+	0.756603i	0.995498	+	0.0947831i	$0.0302158\pi$
$103$	2.49496	+	7.67868i	0.245835	+	0.756603i	−0.749663	+	0.661820i	$0.769784\pi$
$104$	3.16718	−	2.30109i	0.310568	−	0.225641i
$105$	2.87661	+	8.85329i	0.280728	+	0.863993i
$106$	−0.540495	+	1.66347i	−0.0524975	+	0.161571i
$107$	9.83052	+	7.14229i	0.950352	+	0.690471i	0.950890	−	0.309528i	$-0.100171\pi$
$107$	9.83052	+	7.14229i	0.950352	+	0.690471i	−0.000537750		1.00000i	$0.500171\pi$
$108$	3.97813	−	12.2434i	0.382796	−	1.17812i
$109$	−0.195330	+	0.601165i	−0.0187093	+	0.0575812i	−0.959975	−	0.280085i	$-0.909637\pi$
$109$	−0.195330	+	0.601165i	−0.0187093	+	0.0575812i	0.941266	+	0.337666i	$0.109637\pi$
$110$	2.05532	+	1.49328i	0.195967	+	0.142378i
$111$	−2.81344	+	8.65887i	−0.267040	+	0.821863i
$112$	−1.09489	−	3.36971i	−0.103457	−	0.318408i
$113$	9.14217	−	6.64217i	0.860023	−	0.624843i	−0.0678683	−	0.997694i	$-0.521620\pi$
$113$	9.14217	−	6.64217i	0.860023	−	0.624843i	0.927891	+	0.372851i	$0.121620\pi$
$114$	−0.665577	−	2.04844i	−0.0623370	−	0.191854i
$115$	1.06370	+	0.772825i	0.0991908	+	0.0720663i
$116$	−4.79594	−	3.48445i	−0.445291	−	0.323523i
$117$	−12.4870	+	9.07234i	−1.15442	+	0.838738i
$118$	−4.22209			−0.388675
$119$	1.97463			0.181014
$120$	−9.48112	+	6.88844i	−0.865504	+	0.628825i
$121$	−1.57241	+	4.83939i	−0.142947	+	0.439945i
$122$	−1.56764	−	4.82469i	−0.141927	−	0.436806i
$123$	20.0975			1.81213
$124$		0			0
$125$	−3.44866			−0.308458
$126$	−0.631202	−	1.94264i	−0.0562319	−	0.173064i
$127$	0.0364041	−	0.112040i	0.00323034	−	0.00994197i	−0.949428	−	0.313984i	$-0.898336\pi$
$127$	0.0364041	−	0.112040i	0.00323034	−	0.00994197i	0.952659	+	0.304042i	$0.0983362\pi$
$128$	7.74501	−	5.62708i	0.684569	−	0.497368i
$129$	24.3395			2.14297
$130$	3.00265			0.263350
$131$	−4.67932	+	3.39972i	−0.408834	+	0.297035i	−0.773129	−	0.634248i	$-0.781310\pi$
$131$	−4.67932	+	3.39972i	−0.408834	+	0.297035i	0.364296	+	0.931283i	$0.381310\pi$
$132$	10.6794	+	7.75907i	0.929526	+	0.675340i
$133$	1.85446	+	1.34734i	0.160802	+	0.116830i
$134$	−0.699113	−	2.15165i	−0.0603942	−	0.185874i
$135$	16.5020	−	11.9894i	1.42026	−	1.03188i
$136$	0.768193	+	2.36426i	0.0658720	+	0.202733i
$137$	3.64808	−	11.2276i	0.311676	−	0.959241i	−0.665425	−	0.746465i	$-0.731750\pi$
$137$	3.64808	−	11.2276i	0.311676	−	0.959241i	0.977101	−	0.212776i	$-0.0682504\pi$
$138$	−0.363769	−	0.264294i	−0.0309661	−	0.0224982i
$139$	−4.76566	+	14.6672i	−0.404218	+	1.24406i	0.517328	+	0.855787i	$0.326927\pi$
$139$	−4.76566	+	14.6672i	−0.404218	+	1.24406i	−0.921546	+	0.388268i	$0.873073\pi$
$140$	1.86568	−	5.74196i	0.157678	−	0.485284i
$141$	−18.6370	−	13.5405i	−1.56951	−	1.14032i
$142$	0.182215	−	0.560800i	0.0152911	−	0.0470613i
$143$	−2.15907	−	6.64495i	−0.180551	−	0.555679i
$144$	−14.2276	+	10.3370i	−1.18564	+	0.861415i
$145$	−2.90255	−	8.93312i	−0.241043	−	0.741855i
$146$	−4.08281	−	2.96633i	−0.337896	−	0.245496i
$147$	−13.6441	−	9.91300i	−1.12534	−	0.817611i
$148$	4.77713	−	3.47079i	0.392678	−	0.285297i
$149$	−11.9502			−0.979001			−0.489500	−	0.872003i	$-0.662821\pi$
$149$	−11.9502			−0.979001			−0.489500	+	0.872003i	$0.662821\pi$
$150$	−3.90460			−0.318809
$151$	3.49668	−	2.54048i	0.284556	−	0.206742i	−0.436346	−	0.899779i	$-0.643728\pi$
$151$	3.49668	−	2.54048i	0.284556	−	0.206742i	0.720902	+	0.693037i	$0.243728\pi$
$152$	−0.891755	+	2.74454i	−0.0723309	+	0.222612i
$153$	−3.02870	−	9.32137i	−0.244856	−	0.753588i
$154$	0.924636			0.0745093
$155$		0			0
$156$	15.6018			1.24914
$157$	−2.68982	−	8.27841i	−0.214671	−	0.660689i	−0.999177	−	0.0405678i	$-0.987083\pi$
$157$	−2.68982	−	8.27841i	−0.214671	−	0.660689i	0.784506	−	0.620121i	$-0.212917\pi$
$158$	−0.374409	+	1.15231i	−0.0297864	+	0.0916731i
$159$	−11.6498	+	8.46405i	−0.923887	+	0.671243i
$160$	11.5222			0.910912
$161$	0.478533			0.0377137
$162$	−1.06212	+	0.771674i	−0.0834479	+	0.0606285i
$163$	−2.53053	−	1.83853i	−0.198206	−	0.144005i	0.484255	−	0.874927i	$-0.339091\pi$
$163$	−2.53053	−	1.83853i	−0.198206	−	0.144005i	−0.682462	+	0.730922i	$0.739091\pi$
$164$	−10.5452	−	7.66153i	−0.823442	−	0.598265i
$165$	6.46330	+	19.8920i	0.503167	+	1.54859i
$166$	−3.65447	+	2.65513i	−0.283642	+	0.206078i
$167$	−4.12690	−	12.7013i	−0.319349	−	0.982856i	−0.973927	−	0.226861i	$-0.927154\pi$
$167$	−4.12690	−	12.7013i	−0.319349	−	0.982856i	0.654578	−	0.755995i	$-0.272846\pi$
$168$	−1.31806	+	4.05656i	−0.101690	+	0.312970i
$169$	3.83646	+	2.78735i	0.295112	+	0.214412i
$170$	−0.589196	+	1.81336i	−0.0451893	+	0.139078i
$171$	3.51585	−	10.8207i	0.268864	−	0.827478i
$172$	−12.7710	−	9.27865i	−0.973777	−	0.707491i
$173$	5.88515	−	18.1126i	0.447439	−	1.37708i	−0.432347	−	0.901707i	$-0.642314\pi$
$173$	5.88515	−	18.1126i	0.447439	−	1.37708i	0.879786	−	0.475370i	$-0.157686\pi$
$174$	0.992624	+	3.05498i	0.0752506	+	0.231598i
$175$	3.36184	−	2.44252i	0.254131	−	0.184637i
$176$	−2.46004	−	7.57122i	−0.185432	−	0.570702i
$177$	−28.1213	−	20.4313i	−2.11373	−	1.53571i
$178$	−0.642377	−	0.466714i	−0.0481482	−	0.0349817i
$179$	0.0641793	−	0.0466290i	0.00479699	−	0.00348521i	−0.585384	−	0.810756i	$-0.699056\pi$
$179$	0.0641793	−	0.0466290i	0.00479699	−	0.00348521i	0.590181	+	0.807271i	$0.299056\pi$
$180$	−29.9669			−2.23360
$181$	2.16285			0.160763			0.0803817	−	0.996764i	$-0.474386\pi$
$181$	2.16285			0.160763			0.0803817	+	0.996764i	$0.474386\pi$
$182$	0.884121	−	0.642351i	0.0655354	−	0.0476142i
$183$	12.9061	−	39.7209i	0.954047	−	2.93626i
$184$	0.186165	+	0.572956i	0.0137243	+	0.0422389i
$185$	9.35601			0.687868
$186$		0			0
$187$	4.43668			0.324442
$188$	4.61695	+	14.2095i	0.336725	+	1.03633i
$189$	2.29408	−	7.06046i	0.166870	−	0.513573i
$190$	−1.79065	+	1.30098i	−0.129907	+	0.0943831i
$191$	−5.34169			−0.386511			−0.193256	−	0.981148i	$-0.561905\pi$
$191$	−5.34169			−0.386511			−0.193256	+	0.981148i	$0.561905\pi$
$192$	15.0062			1.08298
$193$	1.72618	−	1.25414i	0.124253	−	0.0902752i	−0.523923	−	0.851766i	$-0.675532\pi$
$193$	1.72618	−	1.25414i	0.124253	−	0.0902752i	0.648176	+	0.761490i	$0.275532\pi$
$194$	−0.970327	−	0.704984i	−0.0696654	−	0.0506149i
$195$	19.9992	+	14.5303i	1.43217	+	1.04053i
$196$	3.38006	+	10.4027i	0.241433	+	0.743053i
$197$	4.75356	−	3.45367i	0.338677	−	0.246064i	−0.405426	−	0.914128i	$-0.632877\pi$
$197$	4.75356	−	3.45367i	0.338677	−	0.246064i	0.744104	+	0.668064i	$0.232877\pi$
$198$	−1.41821	−	4.36481i	−0.100788	−	0.310194i
$199$	2.14086	−	6.58888i	0.151761	−	0.467074i	−0.846057	−	0.533093i	$-0.821030\pi$
$199$	2.14086	−	6.58888i	0.151761	−	0.467074i	0.997818	+	0.0660189i	$0.0210298\pi$
$200$	4.23234	+	3.07498i	0.299272	+	0.217434i
$201$	5.75569	−	17.7142i	0.405975	−	1.24946i
$202$	1.92407	−	5.92169i	0.135377	−	0.416649i
$203$	−2.76569	−	2.00939i	−0.194113	−	0.141032i
$204$	−3.06146	+	9.42221i	−0.214345	+	0.659687i
$205$	−6.38205	−	19.6419i	−0.445742	−	1.37185i
$206$	−2.29551	+	1.66779i	−0.159936	+	0.116200i
$207$	−0.733978	−	2.25895i	−0.0510150	−	0.157008i
$208$	−7.61203	−	5.53046i	−0.527799	−	0.383469i
$209$	4.16669	+	3.02727i	0.288216	+	0.209401i
$210$	−2.64666	+	1.92291i	−0.182637	+	0.132693i
$211$	16.7087			1.15028			0.575139	−	0.818056i	$-0.304948\pi$
$211$	16.7087			1.15028			0.575139	+	0.818056i	$0.304948\pi$
$212$	9.33931			0.641427
$213$	3.92744	−	2.85345i	0.269104	−	0.195515i
$214$	−1.31960	+	4.06132i	−0.0902062	+	0.277626i
$215$	−7.72911	−	23.7878i	−0.527121	−	1.62231i
$216$	9.34610			0.635921
$217$		0			0
$218$	−0.222141			−0.0150453
$219$	−12.8391	−	39.5146i	−0.867585	−	2.67015i
$220$	4.19189	−	12.9013i	0.282617	−	0.869805i
$221$	4.24227	−	3.08219i	0.285366	−	0.207331i
$222$	−3.19961			−0.214744
$223$	−6.26156			−0.419305			−0.209653	−	0.977776i	$-0.567233\pi$
$223$	−6.26156			−0.419305			−0.209653	+	0.977776i	$0.567233\pi$
$224$	3.39268	−	2.46493i	0.226683	−	0.164695i
$225$	−16.6865	−	12.1235i	−1.11244	−	0.808232i
$226$	3.21286	+	2.33428i	0.213716	+	0.155274i
$227$	−2.42502	−	7.46343i	−0.160954	−	0.495365i	0.837761	−	0.546036i	$-0.183864\pi$
$227$	−2.42502	−	7.46343i	−0.160954	−	0.495365i	−0.998715	+	0.0506712i	$0.983864\pi$
$228$	−9.30421	+	6.75990i	−0.616186	+	0.447686i
$229$	3.94707	+	12.1478i	0.260830	+	0.802751i	0.992625	+	0.121227i	$0.0386828\pi$
$229$	3.94707	+	12.1478i	0.260830	+	0.802751i	−0.731795	+	0.681525i	$0.761317\pi$
$230$	−0.142786	+	0.439451i	−0.00941506	+	0.0289766i
$231$	6.15855	+	4.47445i	0.405203	+	0.294397i
$232$	1.32994	−	4.09313i	0.0873148	−	0.268727i
$233$	3.92992	−	12.0950i	0.257457	−	0.792372i	−0.735878	−	0.677114i	$-0.763230\pi$
$233$	3.92992	−	12.0950i	0.257457	−	0.792372i	0.993336	−	0.115258i	$-0.0367696\pi$
$234$	−4.38834	−	3.18831i	−0.286875	−	0.208427i
$235$	−7.31536	+	22.5144i	−0.477202	+	1.46868i
$236$	6.96651	+	21.4407i	0.453481	+	1.39567i
$237$	−8.06998	+	5.86318i	−0.524201	+	0.380855i
$238$	0.214442	+	0.659983i	0.0139002	+	0.0427804i
$239$	20.5689	+	14.9442i	1.33049	+	0.966661i	0.999737	+	0.0229450i	$0.00730427\pi$
$239$	20.5689	+	14.9442i	1.33049	+	0.966661i	0.330758	+	0.943716i	$0.392696\pi$
$240$	22.7870	+	16.5557i	1.47089	+	1.06867i
$241$	−1.91007	+	1.38775i	−0.123039	+	0.0893928i	−0.647603	−	0.761978i	$-0.724228\pi$
$241$	−1.91007	+	1.38775i	−0.123039	+	0.0893928i	0.524564	+	0.851371i	$0.324228\pi$
$242$	−1.78824			−0.114953
$243$	9.77268			0.626918
$244$	−21.9142	+	15.9216i	−1.40291	+	1.01928i
$245$	−5.35556	+	16.4827i	−0.342154	+	1.05304i
$246$	2.18256	+	6.71723i	0.139155	+	0.428275i
$247$	6.08718			0.387318
$248$		0			0
$249$	−37.1893			−2.35677
$250$	−0.374520	−	1.15265i	−0.0236867	−	0.0729002i
$251$	0.728241	−	2.24129i	0.0459661	−	0.141469i	−0.925439	−	0.378896i	$-0.876304\pi$
$251$	0.728241	−	2.24129i	0.0459661	−	0.141469i	0.971406	+	0.237427i	$0.0763039\pi$
$252$	−8.82367	+	6.41077i	−0.555839	+	0.403841i
$253$	1.07519			0.0675966
$254$	0.0414009			0.00259772
$255$	−12.6995	+	9.22670i	−0.795271	+	0.577798i
$256$	−5.67014	−	4.11960i	−0.354384	−	0.257475i
$257$	21.0458	+	15.2907i	1.31280	+	0.953805i	0.999992	+	0.00398807i	$0.00126945\pi$
$257$	21.0458	+	15.2907i	1.31280	+	0.953805i	0.312807	+	0.949817i	$0.398731\pi$
$258$	2.64323	+	8.13503i	0.164560	+	0.506465i
$259$	2.75485	−	2.00151i	0.171178	−	0.124368i
$260$	−4.95442	−	15.2481i	−0.307260	−	0.945649i
$261$	−5.24345	+	16.1377i	−0.324561	+	0.998897i
$262$	−1.64446	−	1.19477i	−0.101595	−	0.0738133i
$263$	7.08747	−	21.8130i	0.437032	−	1.34505i	−0.453957	−	0.891023i	$-0.649988\pi$
$263$	7.08747	−	21.8130i	0.437032	−	1.34505i	0.890990	−	0.454024i	$-0.150012\pi$
$264$	−2.96147	+	9.11446i	−0.182266	+	0.560956i
$265$	11.9716	+	8.69791i	0.735412	+	0.534308i
$266$	−0.248934	+	0.766140i	−0.0152631	+	0.0469750i
$267$	−2.02006	−	6.21711i	−0.123626	−	0.380481i
$268$	−9.77301	+	7.10050i	−0.596981	+	0.433732i
$269$	−5.26791	−	16.2130i	−0.321190	−	0.988522i	−0.973131	−	0.230252i	$-0.926045\pi$
$269$	−5.26791	−	16.2130i	−0.321190	−	0.988522i	0.651941	−	0.758270i	$-0.273955\pi$
$270$	5.79932	+	4.21345i	0.352935	+	0.256423i
$271$	−5.86255	−	4.25939i	−0.356124	−	0.258739i	0.395309	−	0.918548i	$-0.370637\pi$
$271$	−5.86255	−	4.25939i	−0.356124	−	0.258739i	−0.751434	+	0.659809i	$0.770637\pi$
$272$	4.83363	−	3.51184i	0.293082	−	0.212936i
$273$	8.99714			0.544531
$274$	4.14881			0.250639
$275$	7.55354	−	5.48797i	0.455496	−	0.330937i
$276$	−0.741919	+	2.28339i	−0.0446583	+	0.137444i
$277$	4.66717	+	14.3641i	0.280423	+	0.863053i	0.987733	+	0.156150i	$0.0499083\pi$
$277$	4.66717	+	14.3641i	0.280423	+	0.863053i	−0.707310	+	0.706903i	$0.750092\pi$
$278$	−5.41979			−0.325058
$279$		0			0
$280$	4.38316			0.261944
$281$	−0.768550	−	2.36535i	−0.0458479	−	0.141105i	0.925512	−	0.378718i	$-0.123635\pi$
$281$	−0.768550	−	2.36535i	−0.0458479	−	0.141105i	−0.971360	+	0.237613i	$0.923635\pi$
$282$	2.50174	−	7.69955i	0.148976	−	0.458502i
$283$	3.82370	−	2.77808i	0.227296	−	0.165140i	−0.468309	−	0.883565i	$-0.655137\pi$
$283$	3.82370	−	2.77808i	0.227296	−	0.165140i	0.695605	+	0.718425i	$0.255137\pi$
$284$	−3.14852			−0.186831
$285$	−18.2223			−1.07939
$286$	1.98648	−	1.44326i	0.117463	−	0.0853420i
$287$	−6.08114	−	4.41821i	−0.358958	−	0.260798i
$288$	−16.8396	−	12.2347i	−0.992283	−	0.720936i
$289$	−4.22433	−	13.0012i	−0.248490	−	0.764774i
$290$	2.67052	−	1.94025i	0.156818	−	0.113935i
$291$	−3.05136	−	9.39111i	−0.178874	−	0.550517i
$292$	−8.32701	+	25.6279i	−0.487302	+	1.49976i
$293$	8.53423	+	6.20048i	0.498575	+	0.362236i	0.808472	−	0.588534i	$-0.200295\pi$
$293$	8.53423	+	6.20048i	0.498575	+	0.362236i	−0.309897	+	0.950770i	$0.600295\pi$
$294$	1.83152	−	5.63683i	0.106816	−	0.328746i
$295$	−11.0381	+	33.9719i	−0.642666	+	1.97792i
$296$	3.46818	+	2.51978i	0.201584	+	0.146459i
$297$	5.15445	−	15.8638i	0.299092	−	0.920510i
$298$	−1.29778	−	3.99415i	−0.0751783	−	0.231375i
$299$	1.02808	−	0.746942i	0.0594553	−	0.0431968i
$300$	6.44264	+	19.8284i	0.371966	+	1.14479i
$301$	−7.36469	−	5.35076i	−0.424493	−	0.308413i
$302$	1.22885	+	0.892809i	0.0707121	+	0.0513754i
$303$	41.4713	−	30.1306i	2.38246	−	1.73096i
$304$	6.93570			0.397790
$305$	−42.9190			−2.45753
$306$	2.78659	−	2.02458i	0.159299	−	0.115737i
$307$	0.818432	−	2.51888i	0.0467104	−	0.143760i	−0.924981	−	0.380013i	$-0.875919\pi$
$307$	0.818432	−	2.51888i	0.0467104	−	0.143760i	0.971692	+	0.236253i	$0.0759195\pi$
$308$	−1.52566	−	4.69551i	−0.0869327	−	0.267551i
$309$	−23.3600			−1.32890
$310$		0			0
$311$	5.51283			0.312604			0.156302	−	0.987709i	$-0.450043\pi$
$311$	5.51283			0.312604			0.156302	+	0.987709i	$0.450043\pi$
$312$	3.50018	+	10.7724i	0.198158	+	0.609869i
$313$	−8.24317	+	25.3699i	−0.465932	+	1.43399i	0.391876	+	0.920018i	$0.371826\pi$
$313$	−8.24317	+	25.3699i	−0.465932	+	1.43399i	−0.857807	+	0.513972i	$0.828174\pi$
$314$	2.47480	−	1.79805i	0.139661	−	0.101470i
$315$	−17.2811			−0.973682
$316$	6.46949			0.363937
$317$	−8.68903	+	6.31295i	−0.488025	+	0.354571i	−0.804424	−	0.594055i	$-0.797526\pi$
$317$	−8.68903	+	6.31295i	−0.488025	+	0.354571i	0.316399	+	0.948626i	$0.397526\pi$
$318$	−4.09411	−	2.97454i	−0.229586	−	0.166804i
$319$	−6.21408	−	4.51480i	−0.347922	−	0.252780i
$320$	−4.76528	−	14.6660i	−0.266387	−	0.819855i
$321$	−28.4426	+	20.6647i	−1.58751	+	1.15339i
$322$	0.0519680	+	0.159941i	0.00289606	+	0.00891317i
$323$	−1.19446	+	3.67617i	−0.0664615	+	0.204547i
$324$	5.67125	+	4.12040i	0.315069	+	0.228911i
$325$	3.41003	−	10.4950i	0.189155	−	0.582158i
$326$	0.339686	−	1.04545i	0.0188135	−	0.0579019i
$327$	−1.47958	−	1.07497i	−0.0818207	−	0.0594462i
$328$	2.92424	−	8.99989i	0.161464	−	0.496936i
$329$	2.66247	+	8.19425i	0.146787	+	0.451764i
$330$	−5.94664	+	4.32048i	−0.327352	+	0.237835i
$331$	6.07145	+	18.6860i	0.333717	+	1.02707i	0.967351	+	0.253442i	$0.0815626\pi$
$331$	6.07145	+	18.6860i	0.333717	+	1.02707i	−0.633634	+	0.773633i	$0.718437\pi$
$332$	19.5133	+	14.1772i	1.07093	+	0.778077i
$333$	−13.6737	−	9.93453i	−0.749315	−	0.544409i
$334$	3.79701	−	2.75869i	0.207763	−	0.150949i
$335$	−19.1404			−1.04575
$336$	10.2513			0.559254
$337$	−15.5159	+	11.2730i	−0.845206	+	0.614078i	−0.923820	−	0.382827i	$-0.874950\pi$
$337$	−15.5159	+	11.2730i	−0.845206	+	0.614078i	0.0786142	+	0.996905i	$0.474950\pi$
$338$	−0.514988	+	1.58497i	−0.0280116	+	0.0862110i
$339$	10.1034	+	31.0950i	0.548740	+	1.68885i
$340$	10.1808			0.552133
$341$		0			0
$342$	3.99844			0.216211
$343$	4.28996	+	13.2031i	0.231636	+	0.712902i
$344$	3.54146	−	10.8995i	0.190943	−	0.587661i
$345$	−3.07760	+	2.23601i	−0.165693	+	0.120383i
$346$	6.69294			0.359815
$347$	10.6600			0.572257			0.286128	−	0.958191i	$-0.407632\pi$
$347$	10.6600			0.572257			0.286128	+	0.958191i	$0.407632\pi$
$348$	13.8760	−	10.0815i	0.743834	−	0.540427i
$349$	15.1299	+	10.9925i	0.809884	+	0.588415i	0.913797	−	0.406171i	$-0.133136\pi$
$349$	15.1299	+	10.9925i	0.809884	+	0.588415i	−0.103913	+	0.994586i	$0.533136\pi$
$350$	1.18146	+	0.858382i	0.0631517	+	0.0458824i
$351$	−6.09208	−	18.7495i	−0.325171	−	1.00077i
$352$	7.62283	−	5.53831i	0.406298	−	0.295193i
$353$	−3.91285	−	12.0425i	−0.208260	−	0.640958i	−0.999564	−	0.0295350i	$-0.990597\pi$
$353$	−3.91285	−	12.0425i	−0.208260	−	0.640958i	0.791304	−	0.611423i	$-0.209403\pi$
$354$	3.77487	−	11.6179i	0.200632	−	0.617482i
$355$	−4.03595	−	2.93229i	−0.214206	−	0.155630i
$356$	−1.31015	+	4.03222i	−0.0694377	+	0.213707i
$357$	−1.76547	+	5.43355i	−0.0934384	+	0.287574i
$358$	0.0225547	+	0.0163869i	0.00119205	+	0.000866077i
$359$	−7.00793	+	21.5682i	−0.369864	+	1.13832i	0.577015	+	0.816734i	$0.304218\pi$
$359$	−7.00793	+	21.5682i	−0.369864	+	1.13832i	−0.946879	+	0.321591i	$0.895782\pi$
$360$	−6.72293	−	20.6910i	−0.354329	−	1.09051i
$361$	11.7412	−	8.53048i	0.617958	−	0.448973i
$362$	0.234883	+	0.722895i	0.0123452	+	0.0379945i
$363$	−11.9106	−	8.65357i	−0.625146	−	0.454195i
$364$	−4.72082	−	3.42987i	−0.247438	−	0.179774i
$365$	−34.5418	+	25.0961i	−1.80800	+	1.31359i
$366$	14.6776			0.767210
$367$	8.71968			0.455164			0.227582	−	0.973759i	$-0.426918\pi$
$367$	8.71968			0.455164			0.227582	+	0.973759i	$0.426918\pi$
$368$	1.17139	−	0.851062i	0.0610628	−	0.0443647i
$369$	−11.5292	+	35.4832i	−0.600185	+	1.84718i
$370$	1.01605	+	3.12708i	0.0528219	+	0.162569i
$371$	5.38574			0.279614
$372$		0			0
$373$	25.4134			1.31586			0.657928	−	0.753081i	$-0.271433\pi$
$373$	25.4134			1.31586			0.657928	+	0.753081i	$0.271433\pi$
$374$	0.481817	+	1.48288i	0.0249142	+	0.0766779i
$375$	3.08337	−	9.48963i	0.159224	−	0.490042i
$376$	−8.77534	+	6.37566i	−0.452553	+	0.328799i
$377$	−9.07826			−0.467554
$378$	2.60897			0.134191
$379$	−17.8776	+	12.9888i	−0.918309	+	0.667190i	−0.943102	−	0.332502i	$-0.892107\pi$
$379$	−17.8776	+	12.9888i	−0.918309	+	0.667190i	0.0247939	+	0.999693i	$0.492107\pi$
$380$	9.56127	+	6.94667i	0.490483	+	0.356357i
$381$	0.275752	+	0.200345i	0.0141272	+	0.0102640i
$382$	−0.580101	−	1.78537i	−0.0296805	−	0.0913473i
$383$	21.5543	−	15.6601i	1.10138	−	0.800196i	0.120092	−	0.992763i	$-0.461681\pi$
$383$	21.5543	−	15.6601i	1.10138	−	0.800196i	0.981284	+	0.192567i	$0.0616812\pi$
$384$	8.55932	+	26.3429i	0.436791	+	1.34430i
$385$	2.41735	−	7.43984i	0.123200	−	0.379169i
$386$	0.606636	+	0.440747i	0.0308769	+	0.0224334i
$387$	−13.9626	+	42.9726i	−0.709761	+	2.18442i
$388$	−1.97901	+	6.09077i	−0.100469	+	0.309212i
$389$	10.4809	+	7.61479i	0.531401	+	0.386085i	0.820881	−	0.571099i	$-0.193483\pi$
$389$	10.4809	+	7.61479i	0.531401	+	0.386085i	−0.289481	+	0.957184i	$0.593483\pi$
$390$	−2.68460	+	8.26234i	−0.135940	+	0.418380i
$391$	0.249358	+	0.767445i	0.0126106	+	0.0388114i
$392$	−6.42441	+	4.66761i	−0.324482	+	0.235750i
$393$	−5.17130	−	15.9156i	−0.260857	−	0.802836i
$394$	1.67056	+	1.21373i	0.0841614	+	0.0611469i
$395$	8.29294	+	6.02517i	0.417263	+	0.303159i
$396$	−19.8254	+	14.4040i	−0.996265	+	0.723829i
$397$	−2.92725			−0.146915			−0.0734574	−	0.997298i	$-0.523403\pi$
$397$	−2.92725			−0.146915			−0.0734574	+	0.997298i	$0.523403\pi$
$398$	2.43471			0.122041
$399$	−5.36549	+	3.89826i	−0.268611	+	0.195157i
$400$	3.88537	−	11.9580i	0.194269	−	0.597898i
$401$	−3.79302	−	11.6737i	−0.189414	−	0.582957i	0.810582	−	0.585625i	$-0.199151\pi$
$401$	−3.79302	−	11.6737i	−0.189414	−	0.582957i	−0.999996	+	0.00266786i	$0.999151\pi$
$402$	6.54572			0.326471
$403$		0			0
$404$	−33.2464			−1.65407
$405$	3.43229	+	10.5635i	0.170552	+	0.524905i
$406$	0.371253	−	1.14260i	0.0184250	−	0.0567063i
$407$	6.18972	−	4.49710i	0.306813	−	0.222913i
$408$	−7.19251			−0.356082
$409$	−17.1972			−0.850348			−0.425174	−	0.905112i	$-0.639787\pi$
$409$	−17.1972			−0.850348			−0.425174	+	0.905112i	$0.639787\pi$
$410$	5.87189	−	4.26617i	0.289992	−	0.210691i
$411$	27.6332	+	20.0767i	1.36305	+	0.990311i
$412$	12.2570	+	8.90526i	0.603861	+	0.438731i
$413$	4.01740	+	12.3643i	0.197684	+	0.608407i
$414$	0.675305	−	0.490638i	0.0331894	−	0.0241135i
$415$	11.8096	+	36.3463i	0.579712	+	1.78417i
$416$	3.44131	−	10.5913i	0.168724	−	0.519280i
$417$	−36.0986	−	26.2272i	−1.76776	−	1.28435i
$418$	−0.559316	+	1.72140i	−0.0273571	+	0.0841963i
$419$	7.15236	−	22.0127i	0.349416	−	1.07539i	−0.609762	−	0.792585i	$-0.708735\pi$
$419$	7.15236	−	22.0127i	0.349416	−	1.07539i	0.959177	−	0.282806i	$-0.0912652\pi$
$420$	14.1320	+	10.2675i	0.689571	+	0.501003i
$421$	9.01781	−	27.7540i	0.439501	−	1.35264i	−0.448902	−	0.893581i	$-0.648185\pi$
$421$	9.01781	−	27.7540i	0.439501	−	1.35264i	0.888403	−	0.459064i	$-0.151815\pi$
$422$	1.81455	+	5.58460i	0.0883307	+	0.271854i
$423$	34.5978	−	25.1368i	1.68220	−	1.22219i
$424$	2.09523	+	6.44844i	0.101753	+	0.313164i
$425$	5.66900	+	4.11877i	0.274987	+	0.199790i
$426$	1.38023	+	1.00280i	0.0668723	+	0.0485856i
$427$	−12.6374	+	9.18158i	−0.611564	+	0.444328i
$428$	22.8017			1.10216
$429$	20.2152			0.975998
$430$	7.11126	−	5.16664i	0.342936	−	0.249157i
$431$	9.37935	−	28.8667i	0.451787	−	1.39046i	−0.423078	−	0.906093i	$-0.639050\pi$
$431$	9.37935	−	28.8667i	0.451787	−	1.39046i	0.874866	−	0.484366i	$-0.160950\pi$
$432$	−6.94129	−	21.3631i	−0.333963	−	1.02783i
$433$	−13.8400			−0.665107			−0.332553	−	0.943084i	$-0.607910\pi$
$433$	−13.8400			−0.665107			−0.332553	+	0.943084i	$0.607910\pi$
$434$		0			0
$435$	27.1762			1.30300
$436$	0.366536	+	1.12808i	0.0175539	+	0.0540254i
$437$	−0.289467	+	0.890887i	−0.0138471	+	0.0426169i
$438$	11.8128	−	8.58247i	0.564435	−	0.410086i
$439$	12.9201			0.616644			0.308322	−	0.951282i	$-0.400233\pi$
$439$	12.9201			0.616644			0.308322	+	0.951282i	$0.400233\pi$
$440$	9.84829			0.469499
$441$	25.3290	−	18.4026i	1.20614	−	0.876315i
$442$	1.49087	+	1.08318i	0.0709136	+	0.0515218i
$443$	−19.2208	−	13.9648i	−0.913210	−	0.663486i	0.0286150	−	0.999591i	$-0.490890\pi$
$443$	−19.2208	−	13.9648i	−0.913210	−	0.663486i	−0.941825	+	0.336105i	$0.890890\pi$
$444$	5.27940	+	16.2483i	0.250549	+	0.771111i
$445$	−5.43471	+	3.94855i	−0.257630	+	0.187179i
$446$	−0.679997	−	2.09282i	−0.0321988	−	0.0990977i
$447$	10.6844	−	32.8833i	0.505356	−	1.55532i
$448$	−4.54060	−	3.29894i	−0.214523	−	0.155860i
$449$	−5.99891	+	18.4627i	−0.283106	+	0.871311i	0.703854	+	0.710345i	$0.251461\pi$
$449$	−5.99891	+	18.4627i	−0.283106	+	0.871311i	−0.986960	+	0.160966i	$0.948539\pi$
$450$	2.23992	−	6.89377i	0.105591	−	0.324975i
$451$	−13.6634	−	9.92703i	−0.643384	−	0.467446i
$452$	6.55272	−	20.1672i	0.308214	−	0.948585i
$453$	3.86431	+	11.8931i	0.181561	+	0.558788i
$454$	2.23116	−	1.62104i	0.104714	−	0.0760790i
$455$	−2.85708	−	8.79320i	−0.133942	−	0.412231i
$456$	−6.75481	−	4.90766i	−0.316323	−	0.229822i
$457$	−19.6931	−	14.3078i	−0.921202	−	0.669293i	0.0226207	−	0.999744i	$-0.492799\pi$
$457$	−19.6931	−	14.3078i	−0.921202	−	0.669293i	−0.943823	+	0.330452i	$0.892799\pi$
$458$	−3.63155	+	2.63847i	−0.169691	+	0.123288i
$459$	12.5186			0.584319
$460$	2.46723			0.115035
$461$	31.0202	−	22.5375i	1.44476	−	1.04968i	0.457734	−	0.889089i	$-0.348661\pi$
$461$	31.0202	−	22.5375i	1.44476	−	1.04968i	0.987022	−	0.160587i	$-0.0513388\pi$
$462$	−0.826695	+	2.54431i	−0.0384613	+	0.118372i
$463$	−2.03775	−	6.27154i	−0.0947022	−	0.291463i	0.892474	−	0.451099i	$-0.148968\pi$
$463$	−2.03775	−	6.27154i	−0.0947022	−	0.291463i	−0.987176	+	0.159636i	$0.948968\pi$
$464$	−10.3437			−0.480195
$465$		0			0
$466$	4.46933			0.207038
$467$	11.8667	+	36.5219i	0.549125	+	1.69003i	0.710975	+	0.703217i	$0.248254\pi$
$467$	11.8667	+	36.5219i	0.549125	+	1.69003i	−0.161850	+	0.986815i	$0.551746\pi$
$468$	−8.95015	+	27.5457i	−0.413721	+	1.27330i
$469$	−5.63584	+	4.09468i	−0.260239	+	0.189075i
$470$	−8.31947			−0.383748
$471$	25.1845			1.16044
$472$	−13.2411	+	9.62022i	−0.609471	+	0.442807i
$473$	−16.5473	−	12.0223i	−0.760846	−	0.552787i
$474$	−2.83605	−	2.06051i	−0.130264	−	0.0946425i
$475$	2.51366	+	7.73625i	0.115335	+	0.354963i
$476$	2.99771	−	2.17796i	0.137400	−	0.0998269i
$477$	−8.26069	−	25.4238i	−0.378231	−	1.16408i
$478$	−2.76108	+	8.49772i	−0.126289	+	0.388677i
$479$	−6.08797	−	4.42317i	−0.278167	−	0.202100i	0.439951	−	0.898022i	$-0.354996\pi$
$479$	−6.08797	−	4.42317i	−0.278167	−	0.202100i	−0.718117	+	0.695922i	$0.754996\pi$
$480$	−10.3017	+	31.7055i	−0.470208	+	1.44715i
$481$	2.79434	−	8.60009i	0.127411	−	0.392130i
$482$	−0.671262	−	0.487700i	−0.0305751	−	0.0222141i
$483$	−0.427845	+	1.31677i	−0.0194676	+	0.0599152i
$484$	2.95063	+	9.08110i	0.134119	+	0.412777i
$485$	−8.20927	+	5.96439i	−0.372764	+	0.270829i
$486$	1.06130	+	3.26634i	0.0481415	+	0.148164i
$487$	−20.2515	−	14.7136i	−0.917684	−	0.666736i	0.0252625	−	0.999681i	$-0.491958\pi$
$487$	−20.2515	−	14.7136i	−0.917684	−	0.666736i	−0.942946	+	0.332944i	$0.891958\pi$
$488$	−15.9096	−	11.5590i	−0.720194	−	0.523252i
$489$	7.32155	−	5.31942i	0.331092	−	0.240552i
$490$	−6.09066			−0.275148
$491$	−39.7100			−1.79209			−0.896044	−	0.443964i	$-0.853572\pi$
$491$	−39.7100			−1.79209			−0.896044	+	0.443964i	$0.853572\pi$
$492$	30.5103	−	22.1671i	1.37551	−	0.999368i
$493$	1.78138	−	5.48254i	0.0802295	−	0.246921i
$494$	0.661059	+	2.03453i	0.0297425	+	0.0915379i
$495$	−38.8281			−1.74519
$496$		0			0
$497$	−1.81567			−0.0814440
$498$	−4.03870	−	12.4298i	−0.180979	−	0.556995i
$499$	−7.30951	+	22.4964i	−0.327219	+	1.00708i	0.643210	+	0.765689i	$0.277602\pi$
$499$	−7.30951	+	22.4964i	−0.327219	+	1.00708i	−0.970429	+	0.241386i	$0.922398\pi$
$500$	−5.23547	+	3.80379i	−0.234137	+	0.170111i
$501$	38.6397			1.72630
$502$	0.828199			0.0369643
$503$	16.3312	−	11.8653i	0.728171	−	0.529047i	−0.160814	−	0.986985i	$-0.551412\pi$
$503$	16.3312	−	11.8653i	0.728171	−	0.529047i	0.888984	+	0.457938i	$0.151412\pi$
$504$	−6.40594	−	4.65419i	−0.285343	−	0.207314i
$505$	−42.6171	−	30.9631i	−1.89643	−	1.37784i
$506$	0.116764	+	0.359363i	0.00519080	+	0.0159756i
$507$	−11.1000	+	8.06462i	−0.492968	+	0.358162i
$508$	−0.0683121	−	0.210243i	−0.00303086	−	0.00932803i
$509$	3.65846	−	11.2596i	0.162158	−	0.499072i	−0.836657	−	0.547726i	$-0.815493\pi$
$509$	3.65846	−	11.2596i	0.162158	−	0.499072i	0.998816	+	0.0486549i	$0.0154935\pi$
$510$	−4.46300	−	3.24256i	−0.197625	−	0.143583i
$511$	−4.80197	+	14.7789i	−0.212427	+	0.653782i
$512$	6.67779	−	20.5521i	0.295120	−	0.908285i
$513$	11.7568	+	8.54181i	0.519075	+	0.377130i
$514$	−2.82509	+	8.69472i	−0.124609	+	0.383508i
$515$	7.41808	+	22.8305i	0.326880	+	1.00603i
$516$	36.9501	−	26.8459i	1.62664	−	1.18182i
$517$	5.98217	+	18.4112i	0.263095	+	0.809724i
$518$	0.968143	+	0.703397i	0.0425378	+	0.0309055i
$519$	44.5784	+	32.3881i	1.95678	+	1.42168i
$520$	9.41676	−	6.84168i	0.412952	−	0.300027i
$521$	−32.7484			−1.43474			−0.717368	−	0.696695i	$-0.754653\pi$
$521$	−32.7484			−1.43474			−0.717368	+	0.696695i	$0.754653\pi$
$522$	−5.96316			−0.261000
$523$	23.8682	−	17.3412i	1.04368	−	0.758279i	0.0726806	−	0.997355i	$-0.476845\pi$
$523$	23.8682	−	17.3412i	1.04368	−	0.758279i	0.971001	+	0.239076i	$0.0768446\pi$
$524$	−3.35393	+	10.3223i	−0.146517	+	0.450934i
$525$	3.71530	+	11.4345i	0.162149	+	0.499044i
$526$	8.06030			0.351446
$527$		0			0
$528$	23.0331			1.00239
$529$	−7.04696	−	21.6883i	−0.306390	−	0.942970i
$530$	−1.60702	+	4.94589i	−0.0698043	+	0.214836i
$531$	52.2047	−	37.9289i	2.26549	−	1.64597i
$532$	4.30138			0.186488
$533$	−19.9611			−0.864610
$534$	1.85858	−	1.35034i	0.0804288	−	0.0584349i
$535$	29.2284	+	21.2357i	1.26365	+	0.918098i
$536$	−7.09515	−	5.15493i	−0.306464	−	0.222659i
$537$	0.0709271	+	0.218291i	0.00306073	+	0.00941995i
$538$	4.84681	−	3.52141i	0.208961	−	0.151819i
$539$	4.37953	+	13.4788i	0.188640	+	0.580574i
$540$	11.8279	−	36.4025i	0.508992	−	1.56652i
$541$	−10.7323	−	7.79746i	−0.461417	−	0.335239i	0.332670	−	0.943043i	$-0.392050\pi$
$541$	−10.7323	−	7.79746i	−0.461417	−	0.335239i	−0.794087	+	0.607804i	$0.792050\pi$
$542$	0.786961	−	2.42202i	0.0338028	−	0.104034i
$543$	−1.93375	+	5.95148i	−0.0829853	+	0.255403i
$544$	5.72101	+	4.15655i	0.245286	+	0.178211i
$545$	−0.580762	+	1.78740i	−0.0248771	+	0.0765639i
$546$	0.977076	+	3.00713i	0.0418150	+	0.128693i
$547$	−30.5516	+	22.1970i	−1.30629	+	0.949077i	−0.999996	−	0.00285966i	$-0.999090\pi$
$547$	−30.5516	+	22.1970i	−1.30629	+	0.949077i	−0.306296	+	0.951936i	$0.599090\pi$
$548$	−6.84560	−	21.0686i	−0.292429	−	0.900005i
$549$	62.7256	+	45.5728i	2.67706	+	1.94500i
$550$	2.65456	+	1.92865i	0.113191	+	0.0822380i
$551$	5.41387	−	3.93341i	0.230639	−	0.167569i
$552$	−1.74304			−0.0741887
$553$	3.73078			0.158649
$554$	−4.29408	+	3.11983i	−0.182438	+	0.132549i
$555$	−8.36499	+	25.7448i	−0.355074	+	1.09281i
$556$	8.94274	+	27.5229i	0.379257	+	1.16723i
$557$	−11.3637			−0.481496			−0.240748	−	0.970588i	$-0.577393\pi$
$557$	−11.3637			−0.481496			−0.240748	+	0.970588i	$0.577393\pi$
$558$		0			0
$559$	−24.1743			−1.02246
$560$	−3.25535	−	10.0189i	−0.137563	−	0.423377i
$561$	−3.96673	+	12.2083i	−0.167475	+	0.515437i
$562$	0.707114	−	0.513748i	0.0298278	−	0.0216712i
$563$	−20.1865			−0.850762			−0.425381	−	0.905014i	$-0.639860\pi$
$563$	−20.1865			−0.850762			−0.425381	+	0.905014i	$0.639860\pi$
$564$	−43.2280			−1.82023
$565$	27.1818	−	19.7487i	1.14355	−	0.830835i
$566$	1.34377	+	0.976309i	0.0564830	+	0.0410373i
$567$	3.27046	+	2.37613i	0.137346	+	0.0997880i
$568$	−0.706355	−	2.17394i	−0.0296380	−	0.0912164i
$569$	25.0712	−	18.2153i	1.05104	−	0.763624i	0.0786282	−	0.996904i	$-0.474946\pi$
$569$	25.0712	−	18.2153i	1.05104	−	0.763624i	0.972409	+	0.233280i	$0.0749460\pi$
$570$	−1.97891	−	6.09047i	−0.0828876	−	0.255102i
$571$	−3.21368	+	9.89070i	−0.134489	+	0.413913i	−0.995510	−	0.0946553i	$-0.969825\pi$
$571$	−3.21368	+	9.89070i	−0.134489	+	0.413913i	0.861022	+	0.508568i	$0.169825\pi$
$572$	−10.6069	−	7.70640i	−0.443499	−	0.322221i
$573$	4.77588	−	14.6987i	0.199515	−	0.614045i
$574$	0.816303	−	2.51232i	0.0340718	−	0.104862i
$575$	1.37383	+	0.998148i	0.0572928	+	0.0416256i
$576$	−8.60847	+	26.4942i	−0.358686	+	1.10392i
$577$	1.67297	+	5.14889i	0.0696468	+	0.214351i	0.979822	−	0.199873i	$-0.0640530\pi$
$577$	1.67297	+	5.14889i	0.0696468	+	0.214351i	−0.910175	+	0.414224i	$0.864053\pi$
$578$	3.88665	−	2.82382i	0.161663	−	0.117455i
$579$	1.90767	+	5.87120i	0.0792800	+	0.243999i
$580$	−14.2594	−	10.3601i	−0.592090	−	0.430179i
$581$	11.2528	+	8.17564i	0.466845	+	0.339183i
$582$	2.80744	−	2.03972i	0.116372	−	0.0845493i
$583$	12.1009			0.501169
$584$	−19.5632			−0.809532
$585$	−37.1267	+	26.9741i	−1.53500	+	1.11524i
$586$	−1.14559	+	3.52578i	−0.0473241	+	0.145649i
$587$	−3.88212	−	11.9479i	−0.160232	−	0.493145i	0.838421	−	0.545023i	$-0.183479\pi$
$587$	−3.88212	−	11.9479i	−0.160232	−	0.493145i	−0.998653	+	0.0518785i	$0.983479\pi$
$588$	−31.6471			−1.30510
$589$		0			0
$590$	−12.5532			−0.516809
$591$	5.25335	+	16.1682i	0.216094	+	0.665069i
$592$	3.18385	−	9.79890i	0.130856	−	0.402732i
$593$	−21.9001	+	15.9114i	−0.899330	+	0.653401i	−0.938294	−	0.345839i	$-0.887594\pi$
$593$	−21.9001	+	15.9114i	−0.899330	+	0.653401i	0.0389638	+	0.999241i	$0.487594\pi$
$594$	5.86195			0.240519
$595$	5.87102			0.240688
$596$	−18.1418	+	13.1808i	−0.743119	+	0.539907i
$597$	16.2164	+	11.7819i	0.663695	+	0.482202i
$598$	0.361300	+	0.262500i	0.0147747	+	0.0107344i
$599$	−4.43596	−	13.6525i	−0.181249	−	0.557826i	0.818615	−	0.574343i	$-0.194742\pi$
$599$	−4.43596	−	13.6525i	−0.181249	−	0.557826i	−0.999864	+	0.0165169i	$0.994742\pi$
$600$	−12.2454	+	8.89681i	−0.499916	+	0.363211i
$601$	0.197776	+	0.608692i	0.00806745	+	0.0248291i	0.955009	−	0.296576i	$-0.0958449\pi$
$601$	0.197776	+	0.608692i	0.00806745	+	0.0248291i	−0.946942	+	0.321405i	$0.895845\pi$
$602$	0.988601	−	3.04260i	0.0402924	−	0.124007i
$603$	27.9735	+	20.3239i	1.13917	+	0.827655i
$604$	2.50627	−	7.71350i	0.101979	−	0.313858i
$605$	−4.67515	+	14.3886i	−0.190072	+	0.584981i
$606$	14.5744	+	10.5889i	0.592043	+	0.430144i
$607$	−2.01412	+	6.19882i	−0.0817505	+	0.251602i	−0.983575	−	0.180501i	$-0.942228\pi$
$607$	−2.01412	+	6.19882i	−0.0817505	+	0.251602i	0.901824	+	0.432103i	$0.142228\pi$
$608$	2.53672	+	7.80721i	0.102877	+	0.316624i
$609$	8.00195	−	5.81376i	0.324255	−	0.235585i
$610$	−4.66094	−	14.3449i	−0.188716	−	0.580808i
$611$	18.5104	+	13.4486i	0.748853	+	0.544073i
$612$	−14.8792	−	10.8103i	−0.601454	−	0.436982i
$613$	−8.45044	+	6.13961i	−0.341310	+	0.247976i	−0.745214	−	0.666825i	$-0.767653\pi$
$613$	−8.45044	+	6.13961i	−0.341310	+	0.247976i	0.403904	+	0.914801i	$0.367653\pi$
$614$	0.930770			0.0375628
$615$	59.7545			2.40953
$616$	2.89980	−	2.10683i	0.116836	−	0.0848864i
$617$	6.70671	−	20.6411i	0.270002	−	0.830980i	−0.720497	−	0.693458i	$-0.756086\pi$
$617$	6.70671	−	20.6411i	0.270002	−	0.830980i	0.990499	−	0.137522i	$-0.0439138\pi$
$618$	−2.53686	−	7.80766i	−0.102048	−	0.314070i
$619$	28.5478			1.14743			0.573716	−	0.819054i	$-0.305501\pi$
$619$	28.5478			1.14743			0.573716	+	0.819054i	$0.305501\pi$
$620$		0			0
$621$	3.03377			0.121741
$622$	0.598686	+	1.84257i	0.0240051	+	0.0738802i
$623$	−0.755528	+	2.32528i	−0.0302696	+	0.0931602i
$624$	22.0238	−	16.0012i	0.881658	−	0.640562i
$625$	−29.4541			−1.17817
$626$	−9.37462			−0.374685
$627$	−12.0554	+	8.75879i	−0.481448	+	0.349792i
$628$	−13.2143	−	9.60079i	−0.527310	−	0.383113i
$629$	4.64544	+	3.37511i	0.185226	+	0.134574i
$630$	−1.87671	−	5.77592i	−0.0747699	−	0.230118i
$631$	−22.0380	+	16.0116i	−0.877320	+	0.637410i	−0.932541	−	0.361064i	$-0.882414\pi$
$631$	−22.0380	+	16.0116i	−0.877320	+	0.637410i	0.0552209	+	0.998474i	$0.482414\pi$
$632$	1.45140	+	4.46694i	0.0577334	+	0.177685i
$633$	−14.9389	+	45.9772i	−0.593768	+	1.82743i
$634$	−3.05361	−	2.21858i	−0.121274	−	0.0881109i
$635$	0.108238	−	0.333122i	0.00429529	−	0.0132195i
$636$	−8.35006	+	25.6988i	−0.331101	+	1.01903i
$637$	13.5515	+	9.84571i	0.536929	+	0.390101i
$638$	0.834149	−	2.56725i	0.0330243	−	0.101638i
$639$	2.78489	+	8.57101i	0.110169	+	0.339064i
$640$	23.0277	−	16.7306i	0.910250	−	0.661335i
$641$	12.7340	+	39.1912i	0.502963	+	1.54796i	0.804169	+	0.594401i	$0.202611\pi$
$641$	12.7340	+	39.1912i	0.502963	+	1.54796i	−0.301206	+	0.953559i	$0.597389\pi$
$642$	−9.99564	−	7.26226i	−0.394497	−	0.286619i
$643$	24.9278	+	18.1111i	0.983055	+	0.714232i	0.958389	−	0.285464i	$-0.0921478\pi$
$643$	24.9278	+	18.1111i	0.983055	+	0.714232i	0.0246661	+	0.999696i	$0.492148\pi$
$644$	0.726469	−	0.527811i	0.0286269	−	0.0207986i
$645$	72.3668			2.84944
$646$	−1.35841			−0.0534459
$647$	−7.21333	+	5.24079i	−0.283585	+	0.206037i	−0.720480	−	0.693476i	$-0.756078\pi$
$647$	−7.21333	+	5.24079i	−0.283585	+	0.206037i	0.436894	+	0.899513i	$0.356078\pi$
$648$	−1.57267	+	4.84017i	−0.0617802	+	0.190140i
$649$	9.02649	+	27.7807i	0.354321	+	1.09049i
$650$	3.87809			0.152111
$651$		0			0
$652$	−5.86949			−0.229867
$653$	12.1263	+	37.3208i	0.474537	+	1.46047i	0.846581	+	0.532260i	$0.178657\pi$
$653$	12.1263	+	37.3208i	0.474537	+	1.46047i	−0.372044	+	0.928215i	$0.621343\pi$
$654$	0.198611	−	0.611263i	0.00776631	−	0.0239023i
$655$	−13.9127	+	10.1082i	−0.543613	+	0.394958i
$656$	−22.7435			−0.887986
$657$	77.1304			3.00914
$658$	−2.44964	+	1.77977i	−0.0954969	+	0.0693826i
$659$	−26.6600	−	19.3696i	−1.03853	−	0.754533i	−0.0685280	−	0.997649i	$-0.521830\pi$
$659$	−26.6600	−	19.3696i	−1.03853	−	0.754533i	−0.969997	+	0.243117i	$0.921830\pi$
$660$	31.7524	+	23.0695i	1.23596	+	0.897979i
$661$	−0.0524325	−	0.161371i	−0.00203939	−	0.00627659i	0.950032	−	0.312154i	$-0.101050\pi$
$661$	−0.0524325	−	0.161371i	−0.00203939	−	0.00627659i	−0.952071	+	0.305877i	$0.901050\pi$
$662$	−5.58611	+	4.05854i	−0.217110	+	0.157740i
$663$	4.68830	+	14.4291i	0.182079	+	0.560380i
$664$	−5.41114	+	16.6538i	−0.209993	+	0.646292i
$665$	5.51374	+	4.00596i	0.213814	+	0.155345i
$666$	1.83549	−	5.64907i	0.0711240	−	0.218897i
$667$	0.431703	−	1.32864i	0.0167156	−	0.0514453i
$668$	−20.2743	−	14.7302i	−0.784438	−	0.569927i
$669$	5.59832	−	17.2298i	0.216443	−	0.666144i
$670$	−2.07862	−	6.39734i	−0.0803042	−	0.247151i
$671$	−28.3942	+	20.6296i	−1.09615	+	0.796396i
$672$	3.74939	+	11.5394i	0.144636	+	0.445143i
$673$	11.8006	+	8.57364i	0.454880	+	0.330490i	0.791519	−	0.611144i	$-0.209290\pi$
$673$	11.8006	+	8.57364i	0.454880	+	0.330490i	−0.336640	+	0.941634i	$0.609290\pi$
$674$	−5.45280	−	3.96169i	−0.210034	−	0.152599i
$675$	21.3132	−	15.4850i	0.820346	−	0.596016i
$676$	8.89857			0.342253
$677$	15.7668			0.605968			0.302984	−	0.952996i	$-0.402017\pi$
$677$	15.7668			0.605968			0.302984	+	0.952996i	$0.402017\pi$
$678$	−9.29573	+	6.75374i	−0.357000	+	0.259376i
$679$	−1.14124	+	3.51239i	−0.0437969	+	0.134793i
$680$	2.28401	+	7.02948i	0.0875880	+	0.269568i
$681$	22.7051			0.870063
$682$		0			0
$683$	20.5935			0.787988			0.393994	−	0.919113i	$-0.371093\pi$
$683$	20.5935			0.787988			0.393994	+	0.919113i	$0.371093\pi$
$684$	−6.59748	−	20.3050i	−0.252261	−	0.776380i
$685$	10.8466	−	33.3823i	0.414426	−	1.27547i
$686$	−3.94703	+	2.86768i	−0.150698	+	0.109489i
$687$	−36.9560			−1.40996
$688$	−27.5440			−1.05011
$689$	11.5707	−	8.40660i	0.440808	−	0.320266i
$690$	−1.08157	−	0.785806i	−0.0411746	−	0.0299151i
$691$	4.81503	+	3.49833i	0.183173	+	0.133083i	0.675593	−	0.737275i	$-0.263888\pi$
$691$	4.81503	+	3.49833i	0.183173	+	0.133083i	−0.492420	+	0.870358i	$0.663888\pi$
$692$	−11.0435	−	33.9882i	−0.419809	−	1.29204i
$693$	−11.4328	+	8.30642i	−0.434296	+	0.315535i
$694$	1.15766	+	3.56290i	0.0439440	+	0.135246i
$695$	−14.1694	+	43.6089i	−0.537476	+	1.65418i
$696$	10.0739	+	7.31914i	0.381852	+	0.277431i
$697$	3.91687	−	12.0549i	0.148362	−	0.456611i
$698$	−2.03096	+	6.25066i	−0.0768731	+	0.236591i
$699$	29.7681	+	21.6278i	1.12593	+	0.818038i
$700$	2.40963	−	7.41607i	0.0910753	−	0.280301i
$701$	−8.22925	−	25.3270i	−0.310814	−	0.956589i	−0.977443	−	0.211199i	$-0.932263\pi$
$701$	−8.22925	−	25.3270i	−0.310814	−	0.956589i	0.666629	−	0.745390i	$-0.267737\pi$
$702$	5.60509	−	4.07234i	0.211551	−	0.153701i
$703$	2.05981	+	6.33944i	0.0776871	+	0.239096i
$704$	−10.2020	−	7.41220i	−0.384503	−	0.279358i
$705$	−55.4120	−	40.2591i	−2.08693	−	1.51625i
$706$	3.60006	−	2.61560i	0.135490	−	0.0984394i
$707$	−19.1723			−0.721050
$708$	−65.2266			−2.45137
$709$	2.13805	−	1.55338i	0.0802962	−	0.0583386i	−0.546913	−	0.837189i	$-0.684197\pi$
$709$	2.13805	−	1.55338i	0.0802962	−	0.0583386i	0.627209	+	0.778851i	$0.284197\pi$
$710$	0.541767	−	1.66739i	0.0203321	−	0.0625759i
$711$	−5.72231	−	17.6114i	−0.214603	−	0.660481i
$712$	−3.07802			−0.115354
$713$		0			0
$714$	−2.00779			−0.0751398
$715$	−6.41943	−	19.7570i	−0.240073	−	0.738868i
$716$	0.0460010	−	0.141576i	0.00171914	−	0.00529096i
$717$	−59.5120	+	43.2380i	−2.22251	+	1.61475i
$718$	−7.96983			−0.297431
$719$	5.19824			0.193862			0.0969308	−	0.995291i	$-0.469097\pi$
$719$	5.19824			0.193862			0.0969308	+	0.995291i	$0.469097\pi$
$720$	−42.3020	+	30.7342i	−1.57650	+	1.14540i
$721$	7.06832	+	5.13543i	0.263238	+	0.191253i
$722$	4.12624	+	2.99789i	0.153563	+	0.111570i
$723$	−2.11090	−	6.49667i	−0.0785051	−	0.241614i
$724$	3.28346	−	2.38557i	0.122029	−	0.0886592i
$725$	−3.74880	−	11.5376i	−0.139227	−	0.428497i
$726$	1.59883	−	4.92068i	0.0593380	−	0.182624i
$727$	−19.5834	−	14.2282i	−0.726309	−	0.527694i	0.162085	−	0.986777i	$-0.448178\pi$
$727$	−19.5834	−	14.2282i	−0.726309	−	0.527694i	−0.888394	+	0.459083i	$0.848178\pi$
$728$	1.30911	−	4.02902i	0.0485188	−	0.149325i
$729$	−12.2007	+	37.5499i	−0.451878	+	1.39074i
$730$	−12.1391	−	8.81959i	−0.449289	−	0.326428i
$731$	4.74360	−	14.5993i	0.175448	−	0.539975i
$732$	−24.2183	−	74.5361i	−0.895132	−	2.75493i
$733$	−32.6542	+	23.7246i	−1.20611	+	0.876289i	−0.994872	−	0.101146i	$-0.967749\pi$
$733$	−32.6542	+	23.7246i	−1.20611	+	0.876289i	−0.211237	+	0.977435i	$0.567749\pi$
$734$	0.946946	+	2.91440i	0.0349524	+	0.107572i
$735$	−40.5670	−	29.4736i	−1.49634	−	1.08715i
$736$	1.38644	+	1.00730i	0.0511047	+	0.0371297i
$737$	−12.6629	+	9.20011i	−0.466442	+	0.338890i
$738$	−13.1117			−0.482647
$739$	6.09785			0.224313			0.112157	−	0.993691i	$-0.464224\pi$
$739$	6.09785			0.224313			0.112157	+	0.993691i	$0.464224\pi$
$740$	14.2035	−	10.3195i	0.522132	−	0.379351i
$741$	−5.44241	+	16.7500i	−0.199932	+	0.615327i
$742$	0.584884	+	1.80009i	0.0214718	+	0.0660833i
$743$	16.2263			0.595284			0.297642	−	0.954678i	$-0.403800\pi$
$743$	16.2263			0.595284			0.297642	+	0.954678i	$0.403800\pi$
$744$		0			0
$745$	−35.5308			−1.30175
$746$	2.75986	+	8.49397i	0.101046	+	0.310986i
$747$	21.3341	−	65.6596i	0.780573	−	2.40236i
$748$	6.73540	−	4.89355i	0.246270	−	0.178926i
$749$	13.1491			0.480458
$750$	3.50659			0.128043
$751$	−29.4842	+	21.4215i	−1.07589	+	0.781682i	−0.976962	−	0.213412i	$-0.931542\pi$
$751$	−29.4842	+	21.4215i	−1.07589	+	0.781682i	−0.0989310	+	0.995094i	$0.531542\pi$
$752$	21.0907	+	15.3233i	0.769099	+	0.558783i
$753$	5.51623	+	4.00778i	0.201023	+	0.146052i
$754$	−0.985886	−	3.03425i	−0.0359039	−	0.110501i
$755$	10.3964	−	7.55344i	0.378365	−	0.274898i
$756$	−4.30484	−	13.2489i	−0.156565	−	0.481859i
$757$	13.4615	−	41.4301i	0.489265	−	1.50580i	−0.336442	−	0.941704i	$-0.609224\pi$
$757$	13.4615	−	41.4301i	0.489265	−	1.50580i	0.825707	−	0.564099i	$-0.190776\pi$
$758$	−6.28275	−	4.56469i	−0.228200	−	0.165797i
$759$	−0.961302	+	2.95858i	−0.0348931	+	0.107390i
$760$	−2.65139	+	8.16015i	−0.0961761	+	0.296000i
$761$	−2.66917	−	1.93927i	−0.0967574	−	0.0702984i	0.538355	−	0.842718i	$-0.319046\pi$
$761$	−2.66917	−	1.93927i	−0.0967574	−	0.0702984i	−0.635112	+	0.772420i	$0.719046\pi$
$762$	−0.0370156	+	0.113922i	−0.00134093	+	0.00412697i
$763$	0.211372	+	0.650536i	0.00765218	+	0.0235510i
$764$	−8.10931	+	5.89176i	−0.293385	+	0.213156i
$765$	−9.00501	−	27.7146i	−0.325577	−	1.00202i
$766$	7.57490	+	5.50348i	0.273692	+	0.198849i
$767$	27.9304	+	20.2926i	1.00851	+	0.732724i
$768$	16.4054	−	11.9192i	0.591978	−	0.430097i
$769$	−45.7136			−1.64847			−0.824237	−	0.566244i	$-0.808396\pi$
$769$	−45.7136			−1.64847			−0.824237	+	0.566244i	$0.808396\pi$
$770$	2.74916			0.0990727
$771$	−60.8916	+	44.2403i	−2.19296	+	1.59328i
$772$	1.23725	−	3.80787i	0.0445297	−	0.137048i
$773$	9.27071	+	28.5323i	0.333444	+	1.02624i	0.967483	+	0.252935i	$0.0813959\pi$
$773$	9.27071	+	28.5323i	0.333444	+	1.02624i	−0.634039	+	0.773301i	$0.718604\pi$
$774$	−15.8791			−0.570764
$775$		0			0
$776$	−4.64943			−0.166905
$777$	3.04449	+	9.36998i	0.109221	+	0.336146i
$778$	−1.40690	+	4.33000i	−0.0504398	+	0.155238i
$779$	11.9039	−	8.64869i	0.426501	−	0.309871i
$780$	46.3877			1.66094
$781$	−4.07953			−0.145977
$782$	−0.229425	+	0.166687i	−0.00820422	+	0.00596071i
$783$	−17.5338	−	12.7390i	−0.626605	−	0.455256i
$784$	15.4405	+	11.2182i	0.551445	+	0.400648i
$785$	−7.99745	−	24.6136i	−0.285441	−	0.878498i
$786$	4.75791	−	3.45683i	0.169709	−	0.123301i
$787$	−13.3594	−	41.1161i	−0.476212	−	1.46563i	−0.844317	−	0.535845i	$-0.819993\pi$
$787$	−13.3594	−	41.1161i	−0.476212	−	1.46563i	0.368105	−	0.929784i	$-0.380007\pi$
$788$	3.40715	−	10.4861i	0.121375	−	0.373553i
$789$	53.6857	+	39.0050i	1.91126	+	1.38861i
$790$	−1.11320	+	3.42609i	−0.0396061	+	0.121895i
$791$	3.77878	−	11.6299i	0.134358	−	0.413511i
$792$	−14.3932	−	10.4572i	−0.511439	−	0.371582i
$793$	−12.8185	+	39.4513i	−0.455198	+	1.40096i
$794$	−0.317896	−	0.978383i	−0.0112817	−	0.0347215i
$795$	−34.6374	+	25.1656i	−1.22846	+	0.892531i
$796$	−4.01731	−	12.3640i	−0.142390	−	0.438231i
$797$	−18.4648	−	13.4155i	−0.654057	−	0.475200i	0.210594	−	0.977574i	$-0.432460\pi$
$797$	−18.4648	−	13.4155i	−0.654057	−	0.475200i	−0.864651	+	0.502374i	$0.832460\pi$
$798$	−1.88561	−	1.36998i	−0.0667498	−	0.0484966i
$799$	−11.7541	+	8.53986i	−0.415830	+	0.302118i
$800$	14.8816			0.526144
$801$	12.1355			0.428786
$802$	3.48981	−	2.53550i	0.123230	−	0.0895315i
$803$	−10.7893	+	33.2060i	−0.380746	+	1.17182i
$804$	−10.8005	−	33.2406i	−0.380905	−	1.17231i
$805$	1.42279			0.0501467
$806$		0			0
$807$	49.3229			1.73625
$808$	−7.45866	−	22.9554i	−0.262395	−	0.807568i
$809$	−6.56303	+	20.1989i	−0.230744	+	0.710157i	0.766914	+	0.641750i	$0.221791\pi$
$809$	−6.56303	+	20.1989i	−0.230744	+	0.710157i	−0.997658	+	0.0684064i	$0.978209\pi$
$810$	−3.15792	+	2.29437i	−0.110958	+	0.0806158i
$811$	2.12314			0.0745534			0.0372767	−	0.999305i	$-0.488132\pi$
$811$	2.12314			0.0745534			0.0372767	+	0.999305i	$0.488132\pi$
$812$	−6.41495			−0.225121
$813$	16.9621	−	12.3237i	0.594885	−	0.432210i
$814$	2.17527	+	1.58043i	0.0762431	+	0.0553939i
$815$	−7.52384	−	5.46639i	−0.263548	−	0.191479i
$816$	5.34183	+	16.4405i	0.187001	+	0.575531i
$817$	14.4165	−	10.4742i	0.504368	−	0.366445i
$818$	−1.86759	−	5.74787i	−0.0652989	−	0.200969i
$819$	−5.16132	+	15.8849i	−0.180351	+	0.555064i
$820$	−31.3533	−	22.7795i	−1.09490	−	0.795495i
$821$	12.9144	−	39.7465i	0.450716	−	1.38716i	−0.425376	−	0.905017i	$-0.639858\pi$
$821$	12.9144	−	39.7465i	0.450716	−	1.38716i	0.876092	−	0.482144i	$-0.160142\pi$
$822$	−3.70935	+	11.4162i	−0.129379	+	0.398186i
$823$	−13.1858	−	9.58002i	−0.459627	−	0.333938i	0.333758	−	0.942659i	$-0.391683\pi$
$823$	−13.1858	−	9.58002i	−0.459627	−	0.333938i	−0.793385	+	0.608720i	$0.791683\pi$
$824$	−3.39894	+	10.4609i	−0.118408	+	0.364422i
$825$	8.34772	+	25.6916i	0.290630	+	0.894468i
$826$	−3.69626	+	2.68549i	−0.128609	+	0.0934402i
$827$	−9.60719	−	29.5679i	−0.334075	−	1.02818i	−0.967176	−	0.254107i	$-0.918218\pi$
$827$	−9.60719	−	29.5679i	−0.334075	−	1.02818i	0.633101	−	0.774069i	$-0.281782\pi$
$828$	−3.60583	−	2.61979i	−0.125311	−	0.0910440i
$829$	22.6920	+	16.4867i	0.788125	+	0.572606i	0.907406	−	0.420254i	$-0.138059\pi$
$829$	22.6920	+	16.4867i	0.788125	+	0.572606i	−0.119282	+	0.992860i	$0.538059\pi$
$830$	−10.8656	+	7.89431i	−0.377150	+	0.274016i
$831$	−43.6982			−1.51587
$832$	−14.9043			−0.516714
$833$	−8.60516	+	6.25201i	−0.298151	+	0.216619i
$834$	4.84571	−	14.9136i	0.167793	−	0.516414i
$835$	−12.2702	−	37.7639i	−0.424629	−	1.30687i
$836$	9.66453			0.334255
$837$		0			0
$838$	8.13409			0.280987
$839$	−7.12828	−	21.9386i	−0.246096	−	0.757404i	−0.995454	−	0.0952401i	$-0.969638\pi$
$839$	−7.12828	−	21.9386i	−0.246096	−	0.757404i	0.749359	−	0.662164i	$-0.230362\pi$
$840$	−3.91888	+	12.0611i	−0.135214	+	0.416147i
$841$	15.3874	−	11.1796i	0.530600	−	0.385503i
$842$	10.2556			0.353431
$843$	7.19585			0.247838
$844$	25.3658	−	18.4293i	0.873128	−	0.634364i
$845$	11.4067	+	8.28743i	0.392401	+	0.285096i
$846$	12.1588	+	8.83389i	0.418028	+	0.303715i
$847$	1.70155	+	5.23683i	0.0584659	+	0.179940i
$848$	13.1836	−	9.57844i	0.452726	−	0.328925i
$849$	4.22573	+	13.0054i	0.145027	+	0.446346i
$850$	−0.760980	+	2.34206i	−0.0261014	+	0.0803318i
$851$	1.12578	+	0.817928i	0.0385913	+	0.0280382i
$852$	2.81502	−	8.66374i	0.0964410	−	0.296815i
$853$	9.27697	−	28.5516i	0.317637	−	0.977587i	−0.657018	−	0.753875i	$-0.728182\pi$
$853$	9.27697	−	28.5516i	0.317637	−	0.977587i	0.974655	−	0.223712i	$-0.0718176\pi$
$854$	−4.44118	−	3.22670i	−0.151974	−	0.110416i
$855$	10.4534	−	32.1724i	0.357500	−	1.10027i
$856$	5.11543	+	15.7437i	0.174842	+	0.538108i
$857$	44.1621	−	32.0857i	1.50855	−	1.09603i	0.541734	−	0.840550i	$-0.317768\pi$
$857$	44.1621	−	32.0857i	1.50855	−	1.09603i	0.966816	−	0.255475i	$-0.0822318\pi$
$858$	2.19534	+	6.75656i	0.0749477	+	0.230665i
$859$	−7.55331	−	5.48780i	−0.257716	−	0.187241i	0.451424	−	0.892310i	$-0.350916\pi$
$859$	−7.55331	−	5.48780i	−0.257716	−	0.187241i	−0.709139	+	0.705068i	$0.750916\pi$
$860$	−37.9710	−	27.5876i	−1.29480	−	0.940728i
$861$	17.5945	−	12.7832i	0.599619	−	0.435649i
$862$	10.6668			0.363311
$863$	13.3167			0.453307			0.226653	−	0.973975i	$-0.427222\pi$
$863$	13.3167			0.453307			0.226653	+	0.973975i	$0.427222\pi$
$864$	21.5087	−	15.6270i	0.731741	−	0.531641i
$865$	17.4979	−	53.8530i	0.594946	−	1.83106i
$866$	−1.50300	−	4.62577i	−0.0510741	−	0.157190i
$867$	39.5520			1.34326
$868$		0			0
$869$	8.38250			0.284357
$870$	2.95130	+	9.08317i	0.100058	+	0.307948i
$871$	−5.71662	+	17.5940i	−0.193700	+	0.596149i
$872$	−0.696668	+	0.506159i	−0.0235922	+	0.0171407i
$873$	18.3309			0.620409
$874$	−0.329199			−0.0111353
$875$	−3.01916	+	2.19355i	−0.102066	+	0.0741555i
$876$	−63.0749	−	45.8266i	−2.13110	−	1.54834i
$877$	34.4367	+	25.0197i	1.16284	+	0.844855i	0.990135	−	0.140118i	$-0.0447481\pi$
$877$	34.4367	+	25.0197i	1.16284	+	0.844855i	0.172709	+	0.984973i	$0.444748\pi$
$878$	1.40311	+	4.31832i	0.0473526	+	0.145736i
$879$	−24.6920	+	17.9398i	−0.832841	+	0.605095i
$880$	−7.31426	−	22.5110i	−0.246564	−	0.758845i
$881$	−1.78400	+	5.49057i	−0.0601043	+	0.184982i	−0.976601	−	0.215061i	$-0.931005\pi$
$881$	−1.78400	+	5.49057i	−0.0601043	+	0.184982i	0.916496	+	0.400043i	$0.131005\pi$
$882$	8.90144	+	6.46727i	0.299727	+	0.217764i
$883$	8.40436	−	25.8660i	0.282829	−	0.870459i	−0.704212	−	0.709990i	$-0.748699\pi$
$883$	8.40436	−	25.8660i	0.282829	−	0.870459i	0.987041	−	0.160469i	$-0.0513006\pi$
$884$	3.04068	−	9.35826i	0.102269	−	0.314752i
$885$	−83.6111	−	60.7470i	−2.81055	−	2.04199i
$886$	2.58011	−	7.94078i	0.0866806	−	0.266776i
$887$	−2.27798	−	7.01089i	−0.0764870	−	0.235403i	0.905502	−	0.424343i	$-0.139495\pi$
$887$	−2.27798	−	7.01089i	−0.0764870	−	0.235403i	−0.981989	+	0.188940i	$0.939495\pi$
$888$	−10.0344	+	7.29045i	−0.336734	+	0.244652i
$889$	−0.0393938	−	0.121242i	−0.00132123	−	0.00406632i
$890$	−1.90993	−	1.38765i	−0.0640211	−	0.0465141i
$891$	7.34822	+	5.33880i	0.246175	+	0.178856i
$892$	−9.50578	+	6.90636i	−0.318277	+	0.231242i
$893$	−16.8658			−0.564393
$894$	12.1510			0.406389
$895$	0.190820	−	0.138639i	0.00637840	−	0.00463418i
$896$	3.20129	−	9.85255i	0.106947	−	0.329150i
$897$	1.13617	+	3.49677i	0.0379356	+	0.116754i
$898$	−6.82232			−0.227664
$899$		0			0
$900$	−38.7040			−1.29013
$901$	2.80645	+	8.63736i	0.0934963	+	0.287752i
$902$	1.83411	−	5.64480i	0.0610691	−	0.187951i
$903$	21.3082	−	15.4813i	0.709092	−	0.515186i
$904$	15.3948			0.512022
$905$	6.43065			0.213762
$906$	−3.55541	+	2.58316i	−0.118121	+	0.0858196i
$907$	−13.3350	−	9.68848i	−0.442783	−	0.321701i	0.343957	−	0.938985i	$-0.388233\pi$
$907$	−13.3350	−	9.68848i	−0.442783	−	0.321701i	−0.786740	+	0.617285i	$0.788233\pi$
$908$	−11.9134	−	8.65562i	−0.395361	−	0.287247i
$909$	29.4067	+	90.5045i	0.975358	+	3.00184i
$910$	2.62869	−	1.90986i	0.0871404	−	0.0633112i
$911$	13.8461	+	42.6140i	0.458743	+	1.41187i	0.866684	+	0.498857i	$0.166247\pi$
$911$	13.8461	+	42.6140i	0.458743	+	1.41187i	−0.407941	+	0.913008i	$0.633753\pi$
$912$	−6.20105	+	19.0849i	−0.205337	+	0.631963i
$913$	25.2833	+	18.3694i	0.836756	+	0.607939i
$914$	2.64350	−	8.13586i	0.0874393	−	0.269110i
$915$	38.3728	−	118.099i	1.26857	−	3.90425i
$916$	19.3909	+	14.0883i	0.640693	+	0.465490i
$917$	−1.93413	+	5.95263i	−0.0638705	+	0.196573i
$918$	1.35950	+	4.18412i	0.0448703	+	0.138097i
$919$	8.37884	−	6.08758i	0.276392	−	0.200811i	−0.440950	−	0.897532i	$-0.645358\pi$
$919$	8.37884	−	6.08758i	0.276392	−	0.200811i	0.717342	+	0.696721i	$0.245358\pi$
$920$	0.553511	+	1.70353i	0.0182487	+	0.0561638i
$921$	6.19941	+	4.50413i	0.204277	+	0.148416i
$922$	10.9015	+	7.92041i	0.359022	+	0.260845i
$923$	−3.90078	+	2.83408i	−0.128396	+	0.0932849i
$924$	14.2846			0.469929
$925$	12.0838			0.397314
$926$	1.87486	−	1.36216i	0.0616116	−	0.0447634i
$927$	13.4008	−	41.2433i	0.440139	−	1.35461i
$928$	−3.78319	−	11.6435i	−0.124189	−	0.382216i
$929$	44.0624			1.44564			0.722820	−	0.691037i	$-0.242846\pi$
$929$	44.0624			1.44564			0.722820	+	0.691037i	$0.242846\pi$
$930$		0			0
$931$	−12.3474			−0.404671
$932$	−7.37447	−	22.6963i	−0.241559	−	0.743441i
$933$	−4.92889	+	15.1696i	−0.161365	+	0.496630i
$934$	−10.9181	+	7.93246i	−0.357251	+	0.259558i
$935$	13.1913			0.431401
$936$	−21.0272			−0.687296
$937$	27.9652	−	20.3179i	0.913585	−	0.663758i	−0.0283343	−	0.999599i	$-0.509020\pi$
$937$	27.9652	−	20.3179i	0.913585	−	0.663758i	0.941919	+	0.335840i	$0.109020\pi$
$938$	−1.98062	−	1.43900i	−0.0646694	−	0.0469851i
$939$	−62.4398	−	45.3652i	−2.03765	−	1.48044i
$940$	13.7272	+	42.2481i	0.447733	+	1.37798i
$941$	17.9190	−	13.0189i	0.584142	−	0.424404i	−0.256073	−	0.966657i	$-0.582429\pi$
$941$	17.9190	−	13.0189i	0.584142	−	0.424404i	0.840215	+	0.542254i	$0.182429\pi$
$942$	2.73500	+	8.41746i	0.0891111	+	0.274256i
$943$	0.949218	−	2.92139i	0.0309108	−	0.0951337i
$944$	31.8238	+	23.1213i	1.03578	+	0.752535i
$945$	6.82084	−	20.9924i	0.221882	−	0.682882i
$946$	2.22123	−	6.83625i	0.0722185	−	0.222266i
$947$	22.7193	+	16.5065i	0.738277	+	0.536390i	0.892171	−	0.451698i	$-0.149181\pi$
$947$	22.7193	+	16.5065i	0.738277	+	0.536390i	−0.153894	+	0.988087i	$0.549181\pi$
$948$	−5.78422	+	17.8020i	−0.187863	+	0.578182i
$949$	12.7519	+	39.2464i	0.413945	+	1.27399i
$950$	−2.31272	+	1.68029i	−0.0750346	+	0.0545159i
$951$	−9.60259	−	29.5537i	−0.311385	−	0.958345i
$952$	2.17632	+	1.58119i	0.0705351	+	0.0512467i
$953$	−6.20254	−	4.50641i	−0.200920	−	0.145977i	0.482776	−	0.875744i	$-0.339629\pi$
$953$	−6.20254	−	4.50641i	−0.200920	−	0.145977i	−0.683696	+	0.729767i	$0.739629\pi$
$954$	7.60035	−	5.52198i	0.246070	−	0.178781i
$955$	−15.8821			−0.513932
$956$	47.7092			1.54302
$957$	17.9792	−	13.0626i	0.581184	−	0.422255i
$958$	0.817221	−	2.51515i	0.0264032	−	0.0812607i
$959$	−3.94768	−	12.1497i	−0.127477	−	0.392334i
$960$	44.6168			1.44000
$961$		0			0
$962$	3.17789			0.102459
$963$	−20.1682	−	62.0714i	−0.649912	−	2.00022i
$964$	−1.36906	+	4.21353i	−0.0440944	+	0.135709i
$965$	5.13233	−	3.72886i	0.165216	−	0.120036i
$966$	−0.486571			−0.0156552
$967$	−1.85036			−0.0595037			−0.0297518	−	0.999557i	$-0.509472\pi$
$967$	−1.85036			−0.0595037			−0.0297518	+	0.999557i	$0.509472\pi$
$968$	−5.60820	+	4.07459i	−0.180254	+	0.130962i
$969$	−9.04772	−	6.57355i	−0.290654	−	0.211173i
$970$	−2.88500	−	2.09608i	−0.0926319	−	0.0673010i
$971$	15.2566	+	46.9550i	0.489608	+	1.50686i	0.825194	+	0.564850i	$0.191066\pi$
$971$	15.2566	+	46.9550i	0.489608	+	1.50686i	−0.335586	+	0.942010i	$0.608934\pi$
$972$	14.8361	−	10.7790i	0.475867	−	0.345738i
$973$	5.15704	+	15.8718i	0.165327	+	0.508825i
$974$	2.71847	−	8.36658i	0.0871053	−	0.268083i
$975$	25.8301	+	18.7667i	0.827225	+	0.601014i
$976$	−14.6053	+	44.9506i	−0.467505	+	1.43883i
$977$	−11.0079	+	33.8790i	−0.352175	+	1.08388i	0.605454	+	0.795880i	$0.292992\pi$
$977$	−11.0079	+	33.8790i	−0.352175	+	1.08388i	−0.957629	+	0.288004i	$0.907008\pi$
$978$	2.57303	+	1.86942i	0.0822764	+	0.0597773i
$979$	−1.69755	+	5.22454i	−0.0542541	+	0.166977i
$980$	10.0497	+	30.9298i	0.321026	+	0.988015i
$981$	2.74670	−	1.99559i	0.0876954	−	0.0637144i
$982$	−4.31245	−	13.2724i	−0.137616	−	0.423538i
$983$	5.16443	+	3.75218i	0.164720	+	0.119676i	0.667091	−	0.744976i	$-0.267539\pi$
$983$	5.16443	+	3.75218i	0.164720	+	0.119676i	−0.502372	+	0.864652i	$0.667539\pi$
$984$	22.1504	+	16.0932i	0.706127	+	0.513032i
$985$	14.1334	−	10.2685i	0.450329	−	0.327183i
$986$	2.02590			0.0645177
$987$	−24.9284			−0.793481
$988$	9.24105	−	6.71402i	0.293997	−	0.213601i
$989$	1.14957	−	3.53801i	0.0365542	−	0.112502i
$990$	−4.21668	−	12.9776i	−0.134015	−	0.412455i
$991$	−44.2919			−1.40698			−0.703489	−	0.710706i	$-0.748376\pi$
$991$	−44.2919			−1.40698			−0.703489	+	0.710706i	$0.748376\pi$
$992$		0			0
$993$	−56.8463			−1.80396
$994$	−0.197179	−	0.606856i	−0.00625415	−	0.0192483i
$995$	6.36526	−	19.5903i	0.201792	−	0.621053i
$996$	−56.4576	+	41.0189i	−1.78893	+	1.29973i
$997$	5.32316			0.168586			0.0842931	−	0.996441i	$-0.473137\pi$
$997$	5.32316			0.168586			0.0842931	+	0.996441i	$0.473137\pi$
$998$	−8.31281			−0.263137
$999$	17.4650	−	12.6891i	0.552569	−	0.401465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.p.531.2		16
31.2	even	5		961.2.d.o.388.3		16
31.3	odd	30		961.2.c.i.439.4		16
31.4	even	5		961.2.d.o.374.3		16
31.5	even	3		961.2.g.t.844.1		16
31.6	odd	6		961.2.g.m.547.1		16
31.7	even	15		31.2.g.a.10.2	✓	16
31.8	even	5	inner	961.2.d.p.628.2		16
31.9	even	15		961.2.g.s.448.1		16
31.10	even	15		31.2.g.a.28.2	yes	16
31.11	odd	30		961.2.g.j.732.2		16
31.12	odd	30		961.2.g.j.235.2		16
31.13	odd	30		961.2.c.i.521.4		16
31.14	even	15		961.2.g.t.846.1		16
31.15	odd	10		961.2.a.j.1.4		8
31.16	even	5		961.2.a.i.1.4		8
31.17	odd	30		961.2.g.n.846.1		16
31.18	even	15		961.2.c.j.521.4		16
31.19	even	15		961.2.g.k.235.2		16
31.20	even	15		961.2.g.k.732.2		16
31.21	odd	30		961.2.g.l.338.2		16
31.22	odd	30		961.2.g.m.448.1		16
31.23	odd	10		961.2.d.q.628.2		16
31.24	odd	30		961.2.g.l.816.2		16
31.25	even	3		961.2.g.s.547.1		16
31.26	odd	6		961.2.g.n.844.1		16
31.27	odd	10		961.2.d.n.374.3		16
31.28	even	15		961.2.c.j.439.4		16
31.29	odd	10		961.2.d.n.388.3		16
31.30	odd	2		961.2.d.q.531.2		16
93.38	odd	30		279.2.y.c.10.1		16
93.41	odd	30		279.2.y.c.28.1		16
93.47	odd	10		8649.2.a.bf.1.5		8
93.77	even	10		8649.2.a.be.1.5		8
124.7	odd	30		496.2.bg.c.289.1		16
124.103	odd	30		496.2.bg.c.369.1		16
155.7	odd	60		775.2.ck.a.599.3		32
155.38	odd	60		775.2.ck.a.599.2		32
155.69	even	30		775.2.bl.a.351.1		16
155.72	odd	60		775.2.ck.a.524.2		32
155.103	odd	60		775.2.ck.a.524.3		32
155.134	even	30		775.2.bl.a.276.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	31.7	even	15
31.2.g.a.28.2	yes	16	31.10	even	15
279.2.y.c.10.1		16	93.38	odd	30
279.2.y.c.28.1		16	93.41	odd	30
496.2.bg.c.289.1		16	124.7	odd	30
496.2.bg.c.369.1		16	124.103	odd	30
775.2.bl.a.276.1		16	155.134	even	30
775.2.bl.a.351.1		16	155.69	even	30
775.2.ck.a.524.2		32	155.72	odd	60
775.2.ck.a.524.3		32	155.103	odd	60
775.2.ck.a.599.2		32	155.38	odd	60
775.2.ck.a.599.3		32	155.7	odd	60
961.2.a.i.1.4		8	31.16	even	5
961.2.a.j.1.4		8	31.15	odd	10
961.2.c.i.439.4		16	31.3	odd	30
961.2.c.i.521.4		16	31.13	odd	30
961.2.c.j.439.4		16	31.28	even	15
961.2.c.j.521.4		16	31.18	even	15
961.2.d.n.374.3		16	31.27	odd	10
961.2.d.n.388.3		16	31.29	odd	10
961.2.d.o.374.3		16	31.4	even	5
961.2.d.o.388.3		16	31.2	even	5
961.2.d.p.531.2		16	1.1	even	1	trivial
961.2.d.p.628.2		16	31.8	even	5	inner
961.2.d.q.531.2		16	31.30	odd	2
961.2.d.q.628.2		16	31.23	odd	10
961.2.g.j.235.2		16	31.12	odd	30
961.2.g.j.732.2		16	31.11	odd	30
961.2.g.k.235.2		16	31.19	even	15
961.2.g.k.732.2		16	31.20	even	15
961.2.g.l.338.2		16	31.21	odd	30
961.2.g.l.816.2		16	31.24	odd	30
961.2.g.m.448.1		16	31.22	odd	30
961.2.g.m.547.1		16	31.6	odd	6
961.2.g.n.844.1		16	31.26	odd	6
961.2.g.n.846.1		16	31.17	odd	30
961.2.g.s.448.1		16	31.9	even	15
961.2.g.s.547.1		16	31.25	even	3
961.2.g.t.844.1		16	31.5	even	3
961.2.g.t.846.1		16	31.14	even	15
8649.2.a.be.1.5		8	93.77	even	10
8649.2.a.bf.1.5		8	93.47	odd	10

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.108599 + 0.334232i) q^{2} +(-0.894076 + 2.75168i) q^{3} +(1.51812 - 1.10298i) q^{4} +2.97323 q^{5} -1.01680 q^{6} +(0.875458 - 0.636058i) q^{7} +(1.10215 + 0.800755i) q^{8} +(-4.34534 - 3.15708i) q^{9} +(0.322889 + 0.993749i) q^{10} +(1.96702 - 1.42912i) q^{11} +(1.67773 + 5.16352i) q^{12} +(0.888007 - 2.73301i) q^{13} +(0.307664 + 0.223531i) q^{14} +(-2.65829 + 8.18139i) q^{15} +(1.01179 - 3.11397i) q^{16} +(1.47627 + 1.07257i) q^{17} +(0.583298 - 1.79521i) q^{18} +(0.654583 + 2.01460i) q^{19} +(4.51371 - 3.27940i) q^{20} +(0.967503 + 2.97767i) q^{21} +(0.691275 + 0.502240i) q^{22} +(0.357760 + 0.259928i) q^{23} +(-3.18883 + 2.31682i) q^{24} +3.84010 q^{25} +1.00989 q^{26} +(5.55018 - 4.03244i) q^{27} +(0.627491 - 1.93122i) q^{28} +(-0.976227 - 3.00452i) q^{29} -3.02317 q^{30} +3.87532 q^{32} +(2.17383 + 6.69036i) q^{33} +(-0.198167 + 0.609895i) q^{34} +(2.60294 - 1.89115i) q^{35} -10.0789 q^{36} +3.14675 q^{37} +(-0.602257 + 0.437565i) q^{38} +(6.72642 + 4.88703i) q^{39} +(3.27693 + 2.38083i) q^{40} +(-2.14651 - 6.60626i) q^{41} +(-0.890163 + 0.646741i) q^{42} +(-2.59957 - 8.00065i) q^{43} +(1.40988 - 4.33915i) q^{44} +(-12.9197 - 9.38671i) q^{45} +(-0.0480240 + 0.147803i) q^{46} +(-2.46041 + 7.57236i) q^{47} +(7.66405 + 5.56826i) q^{48} +(-1.80126 + 5.54371i) q^{49} +(0.417029 + 1.28348i) q^{50} +(-4.27127 + 3.10326i) q^{51} +(-1.66634 - 5.12847i) q^{52} +(4.02648 + 2.92541i) q^{53} +(1.95051 + 1.41713i) q^{54} +(5.84840 - 4.24911i) q^{55} +1.47421 q^{56} -6.12878 q^{57} +(0.898189 - 0.652573i) q^{58} +(-3.71251 + 11.4259i) q^{59} +(4.98828 + 15.3523i) q^{60} -14.4351 q^{61} -5.81225 q^{63} +(-1.60273 - 4.93269i) q^{64} +(2.64025 - 8.12585i) q^{65} +(-2.00006 + 1.45313i) q^{66} -6.43759 q^{67} +3.42416 q^{68} +(-1.03510 + 0.752047i) q^{69} +(0.914757 + 0.664610i) q^{70} +(-1.35743 - 0.986230i) q^{71} +(-2.26115 - 6.95911i) q^{72} +(-11.6176 + 8.44069i) q^{73} +(0.341733 + 1.05175i) q^{74} +(-3.43334 + 10.5667i) q^{75} +(3.21579 + 2.33641i) q^{76} +(0.813039 - 2.50228i) q^{77} +(-0.902923 + 2.77891i) q^{78} +(2.78920 + 2.02647i) q^{79} +(3.00829 - 9.25856i) q^{80} +(1.15440 + 3.55287i) q^{81} +(1.97492 - 1.43486i) q^{82} +(3.97199 + 12.2245i) q^{83} +(4.75308 + 3.45331i) q^{84} +(4.38928 + 3.18900i) q^{85} +(2.39176 - 1.73772i) q^{86} +9.14030 q^{87} +3.31232 q^{88} +(-1.82788 + 1.32803i) q^{89} +(1.73428 - 5.33756i) q^{90} +(-0.960936 - 2.95746i) q^{91} +0.829816 q^{92} -2.79812 q^{94} +(1.94622 + 5.98986i) q^{95} +(-3.46483 + 10.6637i) q^{96} +(-2.76106 + 2.00603i) q^{97} -2.04850 q^{98} -13.0592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{5} - 22 q^{6} - 9 q^{7} - 8 q^{8} - 10 q^{9} - 6 q^{10} + 4 q^{11} - 5 q^{12} + 9 q^{13} - 18 q^{14} + 4 q^{15} - 2 q^{16} + 17 q^{17} - 14 q^{18} - 7 q^{19} + 36 q^{20}+ \cdots - 12 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^5 - 22 * q^6 - 9 * q^7 - 8 * q^8 - 10 * q^9 - 6 * q^10 + 4 * q^11 - 5 * q^12 + 9 * q^13 - 18 * q^14 + 4 * q^15 - 2 * q^16 + 17 * q^17 - 14 * q^18 - 7 * q^19 + 36 * q^20 + 2 * q^21 - 8 * q^22 + 21 * q^23 + 5 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 + 20 * q^28 + 26 * q^29 - 22 * q^30 - 42 * q^32 + 7 * q^33 - 56 * q^34 + 21 * q^35 - 2 * q^36 + 16 * q^37 + 24 * q^38 + 2 * q^39 - 13 * q^40 + 6 * q^41 + 12 * q^42 - 16 * q^43 + 37 * q^44 - 5 * q^45 - 16 * q^46 + 4 * q^47 + 37 * q^48 - 39 * q^49 - 21 * q^50 - 11 * q^51 - 18 * q^52 + 3 * q^53 + 39 * q^54 + 29 * q^55 + 60 * q^56 + 34 * q^57 + 10 * q^58 - 3 * q^59 + 35 * q^60 - 60 * q^61 - 46 * q^63 - 32 * q^64 + 9 * q^65 + 20 * q^66 - 26 * q^67 - 60 * q^68 - 21 * q^69 + 27 * q^70 + 18 * q^71 - 4 * q^72 - 9 * q^73 + 64 * q^74 + 19 * q^75 + 9 * q^76 - 42 * q^77 + 15 * q^78 + 14 * q^79 + 18 * q^80 + 29 * q^81 + 32 * q^82 + 67 * q^83 + 39 * q^84 - 63 * q^85 - 23 * q^86 - 30 * q^87 + 34 * q^88 + 26 * q^89 - 24 * q^90 + 8 * q^91 - 64 * q^92 + 44 * q^94 + 28 * q^95 + 4 * q^96 - 37 * q^97 + 20 * q^98 - 12 * q^99

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