LMFDB - Embedded newform 961.2.d.q.388.4

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			388.4
Root			$1.14660i$ of defining polynomial
Character	$\chi$	$=$	961.388
Dual form			961.2.d.q.374.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17638 - 1.58123i) q^{2} +(1.14813 + 0.834164i) q^{3} +(1.61830 - 4.98062i) q^{4} +0.608384 q^{5} +3.81777 q^{6} +(-0.533635 + 1.64236i) q^{7} +(-2.69088 - 8.28167i) q^{8} +(-0.304682 - 0.937716i) q^{9} +(1.32408 - 0.961997i) q^{10} +(0.413277 - 1.27194i) q^{11} +(6.01267 - 4.36846i) q^{12} +(2.96963 + 2.15756i) q^{13} +(1.43556 + 4.41820i) q^{14} +(0.698502 + 0.507492i) q^{15} +(-10.4781 - 7.61278i) q^{16} +(0.853758 + 2.62760i) q^{17} +(-2.14585 - 1.55905i) q^{18} +(2.07729 - 1.50924i) q^{19} +(0.984549 - 3.03013i) q^{20} +(-1.98268 + 1.44050i) q^{21} +(-1.11178 - 3.42171i) q^{22} +(0.166641 + 0.512867i) q^{23} +(3.81880 - 11.7530i) q^{24} -4.62987 q^{25} +9.87466 q^{26} +(1.74803 - 5.37989i) q^{27} +(7.31639 + 5.31567i) q^{28} +(-6.57801 + 4.77920i) q^{29} +2.32267 q^{30} -17.4262 q^{32} +(1.53550 - 1.11560i) q^{33} +(6.01295 + 4.36866i) q^{34} +(-0.324655 + 0.999185i) q^{35} -5.16348 q^{36} -7.74498 q^{37} +(2.13452 - 6.56938i) q^{38} +(1.60975 + 4.95432i) q^{39} +(-1.63709 - 5.03843i) q^{40} +(0.0841797 - 0.0611601i) q^{41} +(-2.03730 + 6.27016i) q^{42} +(-2.43086 + 1.76612i) q^{43} +(-5.66623 - 4.11675i) q^{44} +(-0.185364 - 0.570491i) q^{45} +(1.17364 + 0.852697i) q^{46} +(5.44062 + 3.95284i) q^{47} +(-5.67989 - 17.4809i) q^{48} +(3.25054 + 2.36166i) q^{49} +(-10.0764 + 7.32091i) q^{50} +(-1.21162 + 3.72899i) q^{51} +(15.5518 - 11.2990i) q^{52} +(-0.864860 - 2.66177i) q^{53} +(-4.70248 - 14.4727i) q^{54} +(0.251431 - 0.773825i) q^{55} +15.0374 q^{56} +3.64396 q^{57} +(-6.75922 + 20.8027i) q^{58} +(-0.377190 - 0.274045i) q^{59} +(3.65801 - 2.65770i) q^{60} +5.11468 q^{61} +1.70266 q^{63} +(-16.9698 + 12.3293i) q^{64} +(1.80667 + 1.31263i) q^{65} +(1.57780 - 4.85596i) q^{66} +8.29847 q^{67} +14.4687 q^{68} +(-0.236491 + 0.727843i) q^{69} +(0.873372 + 2.68796i) q^{70} +(1.47052 + 4.52580i) q^{71} +(-6.94599 + 5.04656i) q^{72} +(-2.31954 + 7.13881i) q^{73} +(-16.8560 + 12.2466i) q^{74} +(-5.31568 - 3.86207i) q^{75} +(-4.15528 - 12.7886i) q^{76} +(1.86844 + 1.35750i) q^{77} +(11.3374 + 8.23708i) q^{78} +(2.99714 + 9.22426i) q^{79} +(-6.37470 - 4.63149i) q^{80} +(4.10167 - 2.98004i) q^{81} +(0.0864987 - 0.266216i) q^{82} +(-13.4981 + 9.80695i) q^{83} +(3.96601 + 12.2061i) q^{84} +(0.519413 + 1.59859i) q^{85} +(-2.49782 + 7.68750i) q^{86} -11.5390 q^{87} -11.6458 q^{88} +(4.73299 - 14.5666i) q^{89} +(-1.30550 - 0.948503i) q^{90} +(-5.12819 + 3.72585i) q^{91} +2.82407 q^{92} +18.0912 q^{94} +(1.26379 - 0.918199i) q^{95} +(-20.0075 - 14.5363i) q^{96} +(-0.395287 + 1.21657i) q^{97} +10.8087 q^{98} -1.31863 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 $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$ .

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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

)

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

$2$	2.17638	−	1.58123i	1.53893	−	1.11810i	0.587935	−	0.808908i	$-0.299941\pi$
$2$	2.17638	−	1.58123i	1.53893	−	1.11810i	0.950999	−	0.309193i	$-0.100059\pi$
$3$	1.14813	+	0.834164i	0.662872	+	0.481605i	0.867632	−	0.497208i	$-0.165641\pi$
$3$	1.14813	+	0.834164i	0.662872	+	0.481605i	−0.204760	+	0.978812i	$0.565641\pi$
$4$	1.61830	−	4.98062i	0.809151	−	2.49031i
$5$	0.608384			0.272077			0.136039	−	0.990704i	$-0.456563\pi$
$5$	0.608384			0.272077			0.136039	+	0.990704i	$0.456563\pi$
$6$	3.81777			1.55860
$7$	−0.533635	+	1.64236i	−0.201695	+	0.620754i	0.798138	+	0.602475i	$0.205819\pi$
$7$	−0.533635	+	1.64236i	−0.201695	+	0.620754i	−0.999833	+	0.0182787i	$0.994181\pi$
$8$	−2.69088	−	8.28167i	−0.951369	−	2.92801i
$9$	−0.304682	−	0.937716i	−0.101561	−	0.312572i
$10$	1.32408	−	0.961997i	0.418709	−	0.304210i
$11$	0.413277	−	1.27194i	0.124608	−	0.383503i	−0.869222	−	0.494423i	$-0.835380\pi$
$11$	0.413277	−	1.27194i	0.124608	−	0.383503i	0.993829	+	0.110919i	$0.0353796\pi$
$12$	6.01267	−	4.36846i	1.73571	−	1.26107i
$13$	2.96963	+	2.15756i	0.823627	+	0.598400i	0.917749	−	0.397160i	$-0.130004\pi$
$13$	2.96963	+	2.15756i	0.823627	+	0.598400i	−0.0941219	+	0.995561i	$0.530004\pi$
$14$	1.43556	+	4.41820i	0.383670	+	1.18081i
$15$	0.698502	+	0.507492i	0.180353	+	0.131034i
$16$	−10.4781	−	7.61278i	−2.61952	−	1.90319i
$17$	0.853758	+	2.62760i	0.207067	+	0.637286i	0.999622	+	0.0274861i	$0.00875020\pi$
$17$	0.853758	+	2.62760i	0.207067	+	0.637286i	−0.792555	+	0.609800i	$0.791250\pi$
$18$	−2.14585	−	1.55905i	−0.505782	−	0.367472i
$19$	2.07729	−	1.50924i	0.476564	−	0.346244i	−0.323430	−	0.946252i	$-0.604836\pi$
$19$	2.07729	−	1.50924i	0.476564	−	0.346244i	0.799994	+	0.600008i	$0.204836\pi$
$20$	0.984549	−	3.03013i	0.220152	−	0.677558i
$21$	−1.98268	+	1.44050i	−0.432656	+	0.314343i
$22$	−1.11178	−	3.42171i	−0.237032	−	0.729510i
$23$	0.166641	+	0.512867i	0.0347470	+	0.106940i	0.966926	−	0.255058i	$-0.0820946\pi$
$23$	0.166641	+	0.512867i	0.0347470	+	0.106940i	−0.932179	+	0.361998i	$0.882095\pi$
$24$	3.81880	−	11.7530i	0.779509	−	2.39908i
$25$	−4.62987			−0.925974
$26$	9.87466			1.93658
$27$	1.74803	−	5.37989i	0.336409	−	1.03536i
$28$	7.31639	+	5.31567i	1.38267	+	1.00457i
$29$	−6.57801	+	4.77920i	−1.22151	+	0.887476i	−0.996224	−	0.0868178i	$-0.972330\pi$
$29$	−6.57801	+	4.77920i	−1.22151	+	0.887476i	−0.225282	+	0.974294i	$0.572330\pi$
$30$	2.32267			0.424060
$31$		0			0
$31$		0			0
$32$	−17.4262			−3.08054
$33$	1.53550	−	1.11560i	0.267296	−	0.194202i
$34$	6.01295	+	4.36866i	1.03121	+	0.749220i
$35$	−0.324655	+	0.999185i	−0.0548767	+	0.168893i
$36$	−5.16348			−0.860580
$37$	−7.74498			−1.27327			−0.636633	−	0.771167i	$-0.719673\pi$
$37$	−7.74498			−1.27327			−0.636633	+	0.771167i	$0.719673\pi$
$38$	2.13452	−	6.56938i	0.346265	−	1.06569i
$39$	1.60975	+	4.95432i	0.257767	+	0.793326i
$40$	−1.63709	−	5.03843i	−0.258846	−	0.796646i
$41$	0.0841797	−	0.0611601i	0.0131467	−	0.00955161i	−0.581193	−	0.813766i	$-0.697414\pi$
$41$	0.0841797	−	0.0611601i	0.0131467	−	0.00955161i	0.594339	+	0.804214i	$0.297414\pi$
$42$	−2.03730	+	6.27016i	−0.314362	+	0.967506i
$43$	−2.43086	+	1.76612i	−0.370702	+	0.269331i	−0.757502	−	0.652833i	$-0.773580\pi$
$43$	−2.43086	+	1.76612i	−0.370702	+	0.269331i	0.386800	+	0.922164i	$0.373580\pi$
$44$	−5.66623	−	4.11675i	−0.854216	−	0.620624i
$45$	−0.185364	−	0.570491i	−0.0276324	−	0.0850438i
$46$	1.17364	+	0.852697i	0.173043	+	0.125723i
$47$	5.44062	+	3.95284i	0.793597	+	0.576582i	0.909029	−	0.416734i	$-0.136825\pi$
$47$	5.44062	+	3.95284i	0.793597	+	0.576582i	−0.115432	+	0.993315i	$0.536825\pi$
$48$	−5.67989	−	17.4809i	−0.819821	−	2.52315i
$49$	3.25054	+	2.36166i	0.464363	+	0.337379i
$50$	−10.0764	+	7.32091i	−1.42501	+	1.03533i
$51$	−1.21162	+	3.72899i	−0.169661	+	0.522163i
$52$	15.5518	−	11.2990i	2.15664	−	1.56689i
$53$	−0.864860	−	2.66177i	−0.118798	−	0.365622i	0.873923	−	0.486065i	$-0.161568\pi$
$53$	−0.864860	−	2.66177i	−0.118798	−	0.365622i	−0.992720	+	0.120444i	$0.961568\pi$
$54$	−4.70248	−	14.4727i	−0.639926	−	1.96949i
$55$	0.251431	−	0.773825i	0.0339029	−	0.104343i
$56$	15.0374			2.00946
$57$	3.64396			0.482654
$58$	−6.75922	+	20.8027i	−0.887529	+	2.73153i
$59$	−0.377190	−	0.274045i	−0.0491060	−	0.0356776i	0.562962	−	0.826483i	$-0.309662\pi$
$59$	−0.377190	−	0.274045i	−0.0491060	−	0.0356776i	−0.612067	+	0.790806i	$0.709662\pi$
$60$	3.65801	−	2.65770i	0.472247	−	0.343108i
$61$	5.11468			0.654867			0.327434	−	0.944874i	$-0.393816\pi$
$61$	5.11468			0.654867			0.327434	+	0.944874i	$0.393816\pi$
$62$		0			0
$63$	1.70266			0.214514
$64$	−16.9698	+	12.3293i	−2.12123	+	1.54116i
$65$	1.80667	+	1.31263i	0.224090	+	0.162811i
$66$	1.57780	−	4.85596i	0.194213	−	0.597728i
$67$	8.29847			1.01382			0.506910	−	0.861999i	$-0.330788\pi$
$67$	8.29847			1.01382			0.506910	+	0.861999i	$0.330788\pi$
$68$	14.4687			1.75459
$69$	−0.236491	+	0.727843i	−0.0284701	+	0.0876220i
$70$	0.873372	+	2.68796i	0.104388	+	0.321273i
$71$	1.47052	+	4.52580i	0.174519	+	0.537114i	0.999611	−	0.0278842i	$-0.00887696\pi$
$71$	1.47052	+	4.52580i	0.174519	+	0.537114i	−0.825092	+	0.564998i	$0.808877\pi$
$72$	−6.94599	+	5.04656i	−0.818593	+	0.594743i
$73$	−2.31954	+	7.13881i	−0.271482	+	0.835535i	0.718647	+	0.695375i	$0.244762\pi$
$73$	−2.31954	+	7.13881i	−0.271482	+	0.835535i	−0.990129	+	0.140160i	$0.955238\pi$
$74$	−16.8560	+	12.2466i	−1.95947	+	1.42364i
$75$	−5.31568	−	3.86207i	−0.613802	−	0.445953i
$76$	−4.15528	−	12.7886i	−0.476643	−	1.46696i
$77$	1.86844	+	1.35750i	0.212928	+	0.154701i
$78$	11.3374	+	8.23708i	1.28370	+	0.932666i
$79$	2.99714	+	9.22426i	0.337205	+	1.03781i	0.965626	+	0.259936i	$0.0837016\pi$
$79$	2.99714	+	9.22426i	0.337205	+	1.03781i	−0.628421	+	0.777873i	$0.716298\pi$
$80$	−6.37470	−	4.63149i	−0.712713	−	0.517816i
$81$	4.10167	−	2.98004i	0.455741	−	0.331115i
$82$	0.0864987	−	0.266216i	0.00955218	−	0.0293986i
$83$	−13.4981	+	9.80695i	−1.48161	+	1.07645i	−0.504577	+	0.863367i	$0.668352\pi$
$83$	−13.4981	+	9.80695i	−1.48161	+	1.07645i	−0.977033	+	0.213087i	$0.931648\pi$
$84$	3.96601	+	12.2061i	0.432728	+	1.33180i
$85$	0.519413	+	1.59859i	0.0563382	+	0.173391i
$86$	−2.49782	+	7.68750i	−0.269347	+	0.828965i
$87$	−11.5390			−1.23711
$88$	−11.6458			−1.24145
$89$	4.73299	−	14.5666i	0.501696	−	1.54406i	−0.304559	−	0.952493i	$-0.598509\pi$
$89$	4.73299	−	14.5666i	0.501696	−	1.54406i	0.806255	−	0.591568i	$-0.201491\pi$
$90$	−1.30550	−	0.948503i	−0.137612	−	0.0999810i
$91$	−5.12819	+	3.72585i	−0.537581	+	0.390575i
$92$	2.82407			0.294430
$93$		0			0
$94$	18.0912			1.86597
$95$	1.26379	−	0.918199i	0.129662	−	0.0942052i
$96$	−20.0075	−	14.5363i	−2.04201	−	1.48360i
$97$	−0.395287	+	1.21657i	−0.0401353	+	0.123524i	−0.969117	−	0.246603i	$-0.920686\pi$
$97$	−0.395287	+	1.21657i	−0.0401353	+	0.123524i	0.928981	+	0.370127i	$0.120686\pi$
$98$	10.8087			1.09185
$99$	−1.31863			−0.132528
$100$	−7.49253	+	23.0596i	−0.749253	+	2.30596i
$101$	2.50929	+	7.72281i	0.249684	+	0.768448i	0.994831	+	0.101547i	$0.0323794\pi$
$101$	2.50929	+	7.72281i	0.249684	+	0.768448i	−0.745147	+	0.666900i	$0.767621\pi$
$102$	3.25945	+	10.0316i	0.322734	+	0.993273i
$103$	−12.2586	+	8.90642i	−1.20788	+	0.877576i	−0.995037	−	0.0995106i	$-0.968272\pi$
$103$	−12.2586	+	8.90642i	−1.20788	+	0.877576i	−0.212843	+	0.977086i	$0.568272\pi$
$104$	9.87731	−	30.3992i	0.968550	−	2.98089i
$105$	−1.20623	+	0.876377i	−0.117716	+	0.0855256i
$106$	−6.09114	−	4.42547i	−0.591624	−	0.429840i
$107$	−3.82427	−	11.7699i	−0.369707	−	1.13784i	−0.946981	−	0.321290i	$-0.895884\pi$
$107$	−3.82427	−	11.7699i	−0.369707	−	1.13784i	0.577274	−	0.816550i	$-0.304116\pi$
$108$	−23.9664	−	17.4126i	−2.30616	−	1.67553i
$109$	−5.83267	−	4.23769i	−0.558669	−	0.405897i	0.272303	−	0.962212i	$-0.412215\pi$
$109$	−5.83267	−	4.23769i	−0.558669	−	0.405897i	−0.830971	+	0.556315i	$0.812215\pi$
$110$	−0.676389	−	2.08171i	−0.0644911	−	0.198483i
$111$	−8.89222	−	6.46058i	−0.844013	−	0.613211i
$112$	18.0944	−	13.1463i	1.70976	−	1.24221i
$113$	5.15187	−	15.8558i	0.484647	−	1.49159i	−0.347844	−	0.937552i	$-0.613086\pi$
$113$	5.15187	−	15.8558i	0.484647	−	1.49159i	0.832491	−	0.554038i	$-0.186914\pi$
$114$	7.93064	−	5.76195i	0.742772	−	0.539656i
$115$	0.101381	+	0.312020i	0.00945387	+	0.0290960i
$116$	13.1582	+	40.4968i	1.22171	+	3.76003i
$117$	1.11839	−	3.44204i	0.103395	−	0.318217i
$118$	−1.25424			−0.115462
$119$	−4.77105			−0.437362
$120$	2.32329	−	7.15036i	0.212087	−	0.652736i
$121$	7.45216	+	5.41431i	0.677469	+	0.492210i
$122$	11.1315	−	8.08750i	1.00780	−	0.732208i
$123$	0.147667			0.0133147
$124$		0			0
$125$	−5.85866			−0.524014
$126$	3.70563	−	2.69230i	0.330124	−	0.239849i
$127$	−10.4440	−	7.58798i	−0.926751	−	0.673324i	0.0184442	−	0.999830i	$-0.494129\pi$
$127$	−10.4440	−	7.58798i	−0.926751	−	0.673324i	−0.945195	+	0.326506i	$0.894129\pi$
$128$	−6.66735	+	20.5200i	−0.589316	+	1.81373i
$129$	−4.26417			−0.375439
$130$	6.00758			0.526900
$131$	−0.753317	+	2.31847i	−0.0658176	+	0.202566i	−0.978557	−	0.205977i	$-0.933963\pi$
$131$	−0.753317	+	2.31847i	−0.0658176	+	0.202566i	0.912739	+	0.408543i	$0.133963\pi$
$132$	−3.07150	−	9.45312i	−0.267340	−	0.822789i
$133$	1.37020	+	4.21705i	0.118812	+	0.365665i
$134$	18.0606	−	13.1218i	1.56020	−	1.13355i
$135$	1.06347	−	3.27304i	0.0915293	−	0.281698i
$136$	19.4635	−	14.1411i	1.66898	−	1.21259i
$137$	6.58849	+	4.78682i	0.562893	+	0.408966i	0.832517	−	0.554000i	$-0.186899\pi$
$137$	6.58849	+	4.78682i	0.562893	+	0.408966i	−0.269624	+	0.962966i	$0.586899\pi$
$138$	0.636196	+	1.95801i	0.0541566	+	0.166677i
$139$	−1.09489	−	0.795487i	−0.0928677	−	0.0674723i	0.540382	−	0.841420i	$-0.318280\pi$
$139$	−1.09489	−	0.795487i	−0.0928677	−	0.0674723i	−0.633250	+	0.773947i	$0.718280\pi$
$140$	4.45117	+	3.23397i	0.376193	+	0.273320i
$141$	2.94921	+	9.07674i	0.248368	+	0.764400i
$142$	10.3568	+	7.52463i	0.869120	+	0.631453i
$143$	3.97156	−	2.88551i	0.332119	−	0.241298i
$144$	−3.94613	+	12.1450i	−0.328845	+	1.01208i
$145$	−4.00195	+	2.90759i	−0.332344	+	0.241462i
$146$	6.23992	+	19.2045i	0.516420	+	1.58938i
$147$	1.76203	+	5.42297i	0.145330	+	0.447279i
$148$	−12.5337	+	38.5748i	−1.03027	+	3.17083i
$149$	−9.00385			−0.737624			−0.368812	−	0.929504i	$-0.620235\pi$
$149$	−9.00385			−0.737624			−0.368812	+	0.929504i	$0.620235\pi$
$150$	−17.6758			−1.44322
$151$	0.991453	−	3.05138i	0.0806833	−	0.248318i	−0.902576	−	0.430531i	$-0.858326\pi$
$151$	0.991453	−	3.05138i	0.0806833	−	0.248318i	0.983259	+	0.182214i	$0.0583262\pi$
$152$	−18.0888	−	13.1423i	−1.46720	−	1.06598i
$153$	2.20381	−	1.60117i	0.178168	−	0.129447i
$154$	6.21295			0.500654
$155$		0			0
$156$	27.2807			2.18420
$157$	2.69141	−	1.95543i	0.214798	−	0.156060i	−0.475184	−	0.879887i	$-0.657618\pi$
$157$	2.69141	−	1.95543i	0.214798	−	0.156060i	0.689982	+	0.723827i	$0.257618\pi$
$158$	21.1086	+	15.3363i	1.67931	+	1.22009i
$159$	1.22738	−	3.77748i	0.0973374	−	0.299574i
$160$	−10.6018			−0.838146
$161$	−0.931238			−0.0733918
$162$	4.21466	−	12.9714i	0.331135	−	1.01913i
$163$	0.537796	+	1.65517i	0.0421235	+	0.129643i	0.969907	−	0.243477i	$-0.0782881\pi$
$163$	0.537796	+	1.65517i	0.0421235	+	0.129643i	−0.927783	+	0.373120i	$0.878288\pi$
$164$	−0.168387	−	0.518243i	−0.0131488	−	0.0404680i
$165$	0.934172	−	0.678716i	0.0727252	−	0.0528379i
$166$	−13.8700	+	42.6873i	−1.07652	+	3.31318i
$167$	−11.3396	+	8.23868i	−0.877482	+	0.637528i	−0.932584	−	0.360953i	$-0.882452\pi$
$167$	−11.3396	+	8.23868i	−0.877482	+	0.637528i	0.0551021	+	0.998481i	$0.482452\pi$
$168$	17.2649	+	12.5437i	1.33202	+	0.967766i
$169$	0.146407	+	0.450593i	0.0112620	+	0.0346610i
$170$	3.65818	+	2.65782i	0.280570	+	0.203846i
$171$	−2.04816	−	1.48807i	−0.156626	−	0.113796i
$172$	4.86252	+	14.9653i	0.370764	+	1.14109i
$173$	0.00969274	+	0.00704219i	0.000736925	+	0.000535408i	0.588154	−	0.808749i	$-0.299855\pi$
$173$	0.00969274	+	0.00704219i	0.000736925	+	0.000535408i	−0.587417	+	0.809285i	$0.699855\pi$
$174$	−25.1133	+	18.2459i	−1.90384	+	1.38322i
$175$	2.47066	−	7.60391i	0.186764	−	0.574802i
$176$	−14.0133	+	10.1813i	−1.05629	+	0.767442i
$177$	−0.204464	−	0.629277i	−0.0153685	−	0.0472993i
$178$	−12.7325	−	39.1865i	−0.954339	−	2.93715i
$179$	3.08337	−	9.48965i	0.230462	−	0.709289i	−0.767229	−	0.641373i	$-0.778365\pi$
$179$	3.08337	−	9.48965i	0.230462	−	0.709289i	0.997691	−	0.0679161i	$-0.0216350\pi$
$180$	−3.14138			−0.234144
$181$	18.6032			1.38276			0.691381	−	0.722490i	$-0.257003\pi$
$181$	18.6032			1.38276			0.691381	+	0.722490i	$0.257003\pi$
$182$	−5.26946	+	16.2177i	−0.390599	+	1.20214i
$183$	5.87230	+	4.26648i	0.434093	+	0.315387i
$184$	3.79899	−	2.76013i	0.280065	−	0.203479i
$185$	−4.71192			−0.346427
$186$		0			0
$187$	3.69497			0.270203
$188$	28.4922	−	20.7008i	2.07801	−	1.50976i
$189$	7.90290	+	5.74179i	0.574851	+	0.417654i
$190$	1.29861	−	3.99670i	0.0942109	−	0.289951i
$191$	1.19812			0.0866928			0.0433464	−	0.999060i	$-0.486198\pi$
$191$	1.19812			0.0866928			0.0433464	+	0.999060i	$0.486198\pi$
$192$	−29.7682			−2.14834
$193$	3.93272	−	12.1037i	0.283084	−	0.871242i	−0.703883	−	0.710316i	$-0.748552\pi$
$193$	3.93272	−	12.1037i	0.283084	−	0.871242i	0.986967	−	0.160926i	$-0.0514479\pi$
$194$	1.06338	+	3.27276i	0.0763465	+	0.234971i
$195$	0.979349	+	3.01413i	0.0701326	+	0.215846i
$196$	17.0229	−	12.3678i	1.21592	−	0.883417i
$197$	0.917347	−	2.82330i	0.0653582	−	0.201152i	−0.913044	−	0.407860i	$-0.866275\pi$
$197$	0.917347	−	2.82330i	0.0653582	−	0.201152i	0.978403	+	0.206708i	$0.0662751\pi$
$198$	−2.86985	+	2.08507i	−0.203951	+	0.148179i
$199$	−10.6661	−	7.74939i	−0.756101	−	0.549340i	0.141611	−	0.989922i	$-0.454772\pi$
$199$	−10.6661	−	7.74939i	−0.756101	−	0.549340i	−0.897712	+	0.440583i	$0.854772\pi$
$200$	12.4584	+	38.3430i	0.880943	+	2.71126i
$201$	9.52770	+	6.92228i	0.672032	+	0.488260i
$202$	17.6727	+	12.8400i	1.24345	+	0.903419i
$203$	−4.33892	−	13.3538i	−0.304532	−	0.937254i
$204$	16.6119	+	12.0693i	1.16307	+	0.845018i
$205$	0.0512136	−	0.0372088i	0.00357691	−	0.00259878i
$206$	−12.5963	+	38.7675i	−0.877628	+	2.70106i
$207$	0.430151	−	0.312523i	0.0298976	−	0.0217219i
$208$	−14.6910	−	45.2143i	−1.01864	−	3.13505i
$209$	−1.06116	−	3.26592i	−0.0734021	−	0.225908i
$210$	−1.23946	+	3.81466i	−0.0855307	+	0.263237i
$211$	18.3323			1.26205			0.631023	−	0.775764i	$-0.282635\pi$
$211$	18.3323			1.26205			0.631023	+	0.775764i	$0.282635\pi$
$212$	−14.6569			−1.00664
$213$	−2.08691	+	6.42285i	−0.142993	+	0.440087i
$214$	−26.9341	−	19.5687i	−1.84117	−	1.33769i
$215$	−1.47889	+	1.07448i	−0.100860	+	0.0732788i
$216$	−49.2582			−3.35160
$217$		0			0
$218$	−19.3949			−1.31359
$219$	−8.61807	+	6.26139i	−0.582355	+	0.423106i
$220$	−3.44724	−	2.50457i	−0.232413	−	0.168858i
$221$	−3.13386	+	9.64503i	−0.210806	+	0.648795i
$222$	−29.5686			−1.98451
$223$	−9.39601			−0.629203			−0.314602	−	0.949224i	$-0.601871\pi$
$223$	−9.39601			−0.629203			−0.314602	+	0.949224i	$0.601871\pi$
$224$	9.29922	−	28.6201i	0.621330	−	1.91226i
$225$	1.41064	+	4.34150i	0.0940426	+	0.289433i
$226$	−13.8593	−	42.6546i	−0.921909	−	2.83734i
$227$	−6.84382	+	4.97232i	−0.454240	+	0.330025i	−0.791268	−	0.611470i	$-0.790578\pi$
$227$	−6.84382	+	4.97232i	−0.454240	+	0.330025i	0.337028	+	0.941495i	$0.390578\pi$
$228$	5.89702	−	18.1492i	0.390540	−	1.20196i
$229$	18.4807	−	13.4270i	1.22124	−	0.887283i	0.225038	−	0.974350i	$-0.427749\pi$
$229$	18.4807	−	13.4270i	1.22124	−	0.887283i	0.996203	+	0.0870664i	$0.0277492\pi$
$230$	0.714022	+	0.518767i	0.0470812	+	0.0342065i
$231$	1.01283	+	3.11716i	0.0666392	+	0.205094i
$232$	57.2804	+	41.6167i	3.76064	+	2.73227i
$233$	−13.1493	−	9.55355i	−0.861442	−	0.625874i	0.0668349	−	0.997764i	$-0.478710\pi$
$233$	−13.1493	−	9.55355i	−0.861442	−	0.625874i	−0.928277	+	0.371890i	$0.878710\pi$
$234$	−3.00863	−	9.25963i	−0.196681	−	0.605321i
$235$	3.30999	+	2.40485i	0.215920	+	0.156875i
$236$	−1.97532	+	1.43515i	−0.128582	+	0.0934206i
$237$	−4.25344	+	13.0907i	−0.276290	+	0.850334i
$238$	−10.3836	+	7.54415i	−0.673071	+	0.489015i
$239$	−5.64667	−	17.3786i	−0.365252	−	1.12413i	−0.949823	−	0.312788i	$-0.898737\pi$
$239$	−5.64667	−	17.3786i	−0.365252	−	1.12413i	0.584570	−	0.811343i	$-0.301263\pi$
$240$	−3.45555	−	10.6351i	−0.223055	−	0.686492i
$241$	5.61532	−	17.2822i	0.361714	−	1.11324i	−0.590299	−	0.807185i	$-0.700990\pi$
$241$	5.61532	−	17.2822i	0.361714	−	1.11324i	0.952013	−	0.306057i	$-0.0990100\pi$
$242$	24.7800			1.59292
$243$	−9.77517			−0.627078
$244$	8.27710	−	25.4743i	0.529887	−	1.63082i
$245$	1.97758	+	1.43679i	0.126343	+	0.0917933i
$246$	0.321379	−	0.233496i	0.0204904	−	0.0148871i
$247$	9.42508			0.599704
$248$		0			0
$249$	−23.6782			−1.50054
$250$	−12.7507	+	9.26390i	−0.806423	+	0.585901i
$251$	−18.5509	−	13.4780i	−1.17092	−	0.850726i	−0.179805	−	0.983702i	$-0.557547\pi$
$251$	−18.5509	−	13.4780i	−1.17092	−	0.850726i	−0.991119	+	0.132976i	$0.957547\pi$
$252$	2.75541	−	8.48029i	0.173575	−	0.534208i
$253$	0.721203			0.0453417
$254$	−34.7284			−2.17905
$255$	−0.737132	+	2.26866i	−0.0461610	+	0.142069i
$256$	4.97240	+	15.3035i	0.310775	+	0.956467i
$257$	0.0328155	+	0.100996i	0.00204697	+	0.00629993i	0.952075	−	0.305865i	$-0.0989457\pi$
$257$	0.0328155	+	0.100996i	0.00204697	+	0.00629993i	−0.950028	+	0.312165i	$0.898946\pi$
$258$	−9.28046	+	6.74265i	−0.577776	+	0.419779i
$259$	4.13299	−	12.7200i	0.256812	−	0.790385i
$260$	9.46144	−	6.87414i	0.586774	−	0.426316i
$261$	6.48574	+	4.71217i	0.401457	+	0.291676i
$262$	2.02654	+	6.23705i	0.125200	+	0.385326i
$263$	−5.90365	−	4.28925i	−0.364034	−	0.264486i	0.390698	−	0.920519i	$-0.372234\pi$
$263$	−5.90365	−	4.28925i	−0.364034	−	0.264486i	−0.754733	+	0.656032i	$0.772234\pi$
$264$	−13.3709	−	9.71453i	−0.822922	−	0.597888i
$265$	−0.526167	−	1.61937i	−0.0323222	−	0.0994774i
$266$	9.65022	+	7.01130i	0.591693	+	0.429890i
$267$	17.5850	−	12.7763i	1.07619	−	0.781896i
$268$	13.4294	−	41.3315i	0.820333	−	2.52473i
$269$	13.1217	−	9.53350i	0.800047	−	0.581268i	−0.110881	−	0.993834i	$-0.535367\pi$
$269$	13.1217	−	9.53350i	0.800047	−	0.581268i	0.910928	+	0.412566i	$0.135367\pi$
$270$	−2.86091	−	8.80498i	−0.174109	−	0.535854i
$271$	1.59009	+	4.89379i	0.0965911	+	0.297277i	0.987665	−	0.156581i	$-0.0500473\pi$
$271$	1.59009	+	4.89379i	0.0965911	+	0.297277i	−0.891074	+	0.453858i	$0.850047\pi$
$272$	11.0576	−	34.0317i	0.670463	−	2.06347i
$273$	−8.99579			−0.544450
$274$	21.9082			1.32352
$275$	−1.91342	+	5.88890i	−0.115383	+	0.355114i
$276$	3.24240	+	2.35574i	0.195169	+	0.141799i
$277$	−13.6909	+	9.94699i	−0.822604	+	0.597657i	−0.917457	−	0.397835i	$-0.869762\pi$
$277$	−13.6909	+	9.94699i	−0.822604	+	0.597657i	0.0948533	+	0.995491i	$0.469762\pi$
$278$	−3.64076			−0.218358
$279$		0			0
$280$	9.14853			0.546729
$281$	−1.54253	+	1.12071i	−0.0920194	+	0.0668560i	−0.632844	−	0.774280i	$-0.718112\pi$
$281$	−1.54253	+	1.12071i	−0.0920194	+	0.0668560i	0.540824	+	0.841136i	$0.318112\pi$
$282$	20.7711	+	15.0911i	1.23690	+	0.898660i
$283$	−4.73099	+	14.5605i	−0.281228	+	0.865532i	0.706276	+	0.707937i	$0.250374\pi$
$283$	−4.73099	+	14.5605i	−0.281228	+	0.865532i	−0.987504	+	0.157595i	$0.949626\pi$
$284$	24.9211			1.47879
$285$	2.21692			0.131319
$286$	4.08097	−	12.5599i	0.241313	−	0.742684i
$287$	0.0555257	+	0.170891i	0.00327758	+	0.0100874i
$288$	5.30945	+	16.3408i	0.312862	+	0.962891i
$289$	7.57792	−	5.50568i	0.445760	−	0.323864i
$290$	−4.11220	+	12.6561i	−0.241477	+	0.743189i
$291$	−1.46866	+	1.06704i	−0.0860943	+	0.0625512i
$292$	31.8020	+	23.1055i	1.86107	+	1.35215i
$293$	8.27970	+	25.4823i	0.483705	+	1.48869i	0.833847	+	0.551995i	$0.186133\pi$
$293$	8.27970	+	25.4823i	0.483705	+	1.48869i	−0.350142	+	0.936697i	$0.613867\pi$
$294$	12.4098	+	9.01626i	0.723756	+	0.525839i
$295$	−0.229476	−	0.166724i	−0.0133606	−	0.00970706i
$296$	20.8408	+	64.1413i	1.21135	+	3.72814i
$297$	−6.12045	−	4.44677i	−0.355145	−	0.258028i
$298$	−19.5958	+	14.2372i	−1.13515	+	0.824738i
$299$	−0.611682	+	1.88256i	−0.0353745	+	0.108872i
$300$	−27.8379	+	20.2254i	−1.60722	+	1.16771i
$301$	−1.60341	−	4.93480i	−0.0924193	−	0.284437i
$302$	−2.66716	−	8.20868i	−0.153478	−	0.472356i
$303$	−3.56110	+	10.9599i	−0.204580	+	0.629632i
$304$	−33.2556			−1.90734
$305$	3.11169			0.178175
$306$	2.26453	−	6.96949i	0.129454	−	0.398419i
$307$	−7.24172	−	5.26142i	−0.413307	−	0.300285i	0.361632	−	0.932321i	$-0.382220\pi$
$307$	−7.24172	−	5.26142i	−0.413307	−	0.300285i	−0.774939	+	0.632036i	$0.782220\pi$
$308$	9.78489	−	7.10914i	0.557546	−	0.405081i
$309$	−21.5039			−1.22331
$310$		0			0
$311$	20.6556			1.17127			0.585637	−	0.810574i	$-0.300844\pi$
$311$	20.6556			1.17127			0.585637	+	0.810574i	$0.300844\pi$
$312$	36.6984	−	26.6629i	2.07764	−	1.50949i
$313$	0.365126	+	0.265280i	0.0206382	+	0.0149945i	0.598057	−	0.801454i	$-0.295940\pi$
$313$	0.365126	+	0.265280i	0.0206382	+	0.0149945i	−0.577418	+	0.816448i	$0.695940\pi$
$314$	2.76556	−	8.51151i	0.156069	−	0.480332i
$315$	1.03587			0.0583646
$316$	50.7928			2.85732
$317$	−1.72458	+	5.30770i	−0.0968618	+	0.298110i	−0.987734	−	0.156143i	$-0.950094\pi$
$317$	−1.72458	+	5.30770i	−0.0968618	+	0.298110i	0.890873	+	0.454253i	$0.150094\pi$
$318$	−3.30184	−	10.1620i	−0.185158	−	0.569857i
$319$	3.36030	+	10.3419i	0.188141	+	0.579038i
$320$	−10.3242	+	7.50095i	−0.577139	+	0.419316i
$321$	5.42727	−	16.7034i	0.302921	−	0.932295i
$322$	−2.02673	+	1.47250i	−0.112945	+	0.0820595i
$323$	5.73919	+	4.16977i	0.319337	+	0.232012i
$324$	−8.20469	−	25.2515i	−0.455816	−	1.40286i
$325$	−13.7490	−	9.98923i	−0.762657	−	0.554103i
$326$	3.78766	+	2.75189i	0.209779	+	0.152413i
$327$	−3.16173	−	9.73081i	−0.174844	−	0.538115i
$328$	−0.733025	−	0.532574i	−0.0404746	−	0.0294065i
$329$	−9.39530	+	6.82608i	−0.517980	+	0.376334i
$330$	0.959906	−	2.95429i	0.0528411	−	0.162628i
$331$	19.5826	−	14.2276i	1.07636	−	0.782020i	0.0993141	−	0.995056i	$-0.468335\pi$
$331$	19.5826	−	14.2276i	1.07636	−	0.782020i	0.977044	+	0.213036i	$0.0683352\pi$
$332$	27.0007	+	83.0996i	1.48186	+	4.56068i
$333$	2.35976	+	7.26259i	0.129314	+	0.397987i
$334$	−11.6519	+	35.8610i	−0.637566	+	1.96223i
$335$	5.04865			0.275837
$336$	31.7409			1.73161
$337$	−3.41031	+	10.4958i	−0.185771	+	0.571745i	−0.999961	−	0.00885416i	$-0.997182\pi$
$337$	−3.41031	+	10.4958i	−0.185771	+	0.571745i	0.814190	+	0.580599i	$0.197182\pi$
$338$	1.03113	+	0.749160i	0.0560861	+	0.0407489i
$339$	19.1414	−	13.9070i	1.03962	−	0.755325i
$340$	8.80253			0.477384
$341$		0			0
$342$	−6.81056			−0.368273
$343$	−15.3928	+	11.1835i	−0.831134	+	0.603854i
$344$	21.1676	+	15.3791i	1.14128	+	0.829187i
$345$	−0.143877	+	0.442808i	−0.00774608	+	0.0238400i
$346$	0.0322304			0.00173272
$347$	18.5674			0.996749			0.498375	−	0.866962i	$-0.333930\pi$
$347$	18.5674			0.996749			0.498375	+	0.866962i	$0.333930\pi$
$348$	−18.6737	+	57.4716i	−1.00101	+	3.08080i
$349$	−9.94251	−	30.5999i	−0.532210	−	1.63797i	−0.749601	−	0.661890i	$-0.769755\pi$
$349$	−9.94251	−	30.5999i	−0.532210	−	1.63797i	0.217391	−	0.976085i	$-0.430245\pi$
$350$	−6.64646	−	20.4557i	−0.355268	−	1.09340i
$351$	16.7985	−	12.2048i	0.896635	−	0.651444i
$352$	−7.20184	+	22.1650i	−0.383859	+	1.18140i
$353$	26.0612	−	18.9346i	1.38710	−	1.00778i	0.390920	−	0.920425i	$-0.372157\pi$
$353$	26.0612	−	18.9346i	1.38710	−	1.00778i	0.996177	−	0.0873596i	$-0.0278429\pi$
$354$	−1.44003	−	1.04624i	−0.0765365	−	0.0556070i
$355$	0.894642	+	2.75342i	0.0474826	+	0.146137i
$356$	−64.8915	−	47.1465i	−3.43924	−	2.49876i
$357$	−5.47778	−	3.97984i	−0.289915	−	0.210636i
$358$	−8.29475	−	25.5286i	−0.438391	−	1.34923i
$359$	−17.1206	−	12.4389i	−0.903592	−	0.656498i	0.0357939	−	0.999359i	$-0.488604\pi$
$359$	−17.1206	−	12.4389i	−0.903592	−	0.656498i	−0.939386	+	0.342861i	$0.888604\pi$
$360$	−4.22583	+	3.07024i	−0.222721	+	0.161816i
$361$	−3.83398	+	11.7998i	−0.201789	+	0.621042i
$362$	40.4876	−	29.4160i	2.12798	−	1.54607i
$363$	4.03961	+	12.4327i	0.212025	+	0.652545i
$364$	10.2581	+	31.5711i	0.537670	+	1.65478i
$365$	−1.41117	+	4.34314i	−0.0738640	+	0.227330i
$366$	19.5267			1.02068
$367$	−12.9964			−0.678408			−0.339204	−	0.940713i	$-0.610158\pi$
$367$	−12.9964			−0.678408			−0.339204	+	0.940713i	$0.610158\pi$
$368$	2.15827	−	6.64247i	0.112508	−	0.346263i
$369$	−0.0829989	−	0.0603022i	−0.00432075	−	0.00313921i
$370$	−10.2549	+	7.45064i	−0.533129	+	0.387341i
$371$	4.83309			0.250922
$372$		0			0
$373$	−4.42592			−0.229166			−0.114583	−	0.993414i	$-0.536553\pi$
$373$	−4.42592			−0.229166			−0.114583	+	0.993414i	$0.536553\pi$
$374$	8.04167	−	5.84262i	0.415825	−	0.302115i
$375$	−6.72649	−	4.88708i	−0.347354	−	0.252368i
$376$	18.0961	−	55.6941i	0.933235	−	2.87220i
$377$	−29.8457			−1.53713
$378$	26.2788			1.35164
$379$	−4.62158	+	14.2238i	−0.237394	+	0.730625i	0.759400	+	0.650624i	$0.225492\pi$
$379$	−4.62158	+	14.2238i	−0.237394	+	0.730625i	−0.996795	+	0.0800014i	$0.974508\pi$
$380$	−2.52800	−	7.78040i	−0.129684	−	0.399126i
$381$	−5.66138	−	17.4239i	−0.290041	−	0.892655i
$382$	2.60756	−	1.89451i	0.133415	−	0.0969313i
$383$	3.60015	−	11.0801i	0.183959	−	0.566169i	−0.815970	−	0.578095i	$-0.803796\pi$
$383$	3.60015	−	11.0801i	0.183959	−	0.566169i	0.999929	+	0.0119263i	$0.00379635\pi$
$384$	−24.7720	+	17.9979i	−1.26414	+	0.918452i
$385$	1.13673	+	0.825880i	0.0579330	+	0.0420908i
$386$	−10.5796	−	32.5608i	−0.538489	−	1.65730i
$387$	2.39676	+	1.74135i	0.121834	+	0.0885176i
$388$	5.41958	+	3.93755i	0.275137	+	0.199899i
$389$	−4.45044	−	13.6970i	−0.225646	−	0.694468i	−0.998225	−	0.0595494i	$-0.981034\pi$
$389$	−4.45044	−	13.6970i	−0.225646	−	0.694468i	0.772579	−	0.634919i	$-0.218966\pi$
$390$	6.89747	+	5.01131i	0.349267	+	0.253757i
$391$	−1.20534	+	0.875729i	−0.0609566	+	0.0442875i
$392$	10.8116	−	33.2748i	0.546071	−	1.68063i
$393$	−2.79889	+	2.03351i	−0.141185	+	0.102577i
$394$	−2.46780	−	7.59512i	−0.124326	−	0.382637i
$395$	1.82341	+	5.61189i	0.0917458	+	0.282365i
$396$	−2.13395	+	6.56761i	−0.107235	+	0.330035i
$397$	15.7901			0.792484			0.396242	−	0.918146i	$-0.370314\pi$
$397$	15.7901			0.792484			0.396242	+	0.918146i	$0.370314\pi$
$398$	−35.4672			−1.77781
$399$	−1.94454	+	5.98469i	−0.0973489	+	0.299609i
$400$	48.5122	+	35.2462i	2.42561	+	1.76231i
$401$	25.0983	−	18.2350i	1.25335	−	0.910612i	0.254938	−	0.966957i	$-0.417945\pi$
$401$	25.0983	−	18.2350i	1.25335	−	0.910612i	0.998411	+	0.0563457i	$0.0179449\pi$
$402$	31.6817			1.58014
$403$		0			0
$404$	42.5252			2.11571
$405$	2.49539	−	1.81301i	0.123997	−	0.0900889i
$406$	−30.5586	−	22.2021i	−1.51660	−	1.10187i
$407$	−3.20082	+	9.85111i	−0.158659	+	0.488302i
$408$	34.1426			1.69031
$409$	−6.58582			−0.325648			−0.162824	−	0.986655i	$-0.552060\pi$
$409$	−6.58582			−0.325648			−0.162824	+	0.986655i	$0.552060\pi$
$410$	0.0526244	−	0.161961i	0.00259893	−	0.00799870i
$411$	3.57144	+	10.9918i	0.176166	+	0.542184i
$412$	24.5213	+	75.4689i	1.20808	+	3.71809i
$413$	0.651362	−	0.473242i	0.0320514	−	0.0232867i
$414$	0.442001	−	1.36034i	0.0217232	−	0.0668571i
$415$	−8.21203	+	5.96639i	−0.403113	+	0.292879i
$416$	−51.7493	−	37.5981i	−2.53722	−	1.84340i
$417$	−0.593512	−	1.82664i	−0.0290644	−	0.0894510i
$418$	−7.47368	−	5.42994i	−0.365550	−	0.265587i
$419$	11.8699	+	8.62397i	0.579882	+	0.421309i	0.838681	−	0.544622i	$-0.183327\pi$
$419$	11.8699	+	8.62397i	0.579882	+	0.421309i	−0.258800	+	0.965931i	$0.583327\pi$
$420$	2.41286	+	7.42601i	0.117735	+	0.362352i
$421$	21.6136	+	15.7032i	1.05338	+	0.765327i	0.972853	−	0.231425i	$-0.0743389\pi$
$421$	21.6136	+	15.7032i	1.05338	+	0.765327i	0.0805294	+	0.996752i	$0.474339\pi$
$422$	39.8980	−	28.9876i	1.94221	−	1.41110i
$423$	2.04898	−	6.30612i	0.0996250	−	0.306614i
$424$	−19.7166	+	14.3250i	−0.957524	+	0.695682i
$425$	−3.95279	−	12.1654i	−0.191738	−	0.590110i
$426$	5.61412	+	17.2785i	0.272005	+	0.837145i
$427$	−2.72937	+	8.40014i	−0.132084	+	0.406511i
$428$	−64.8103			−3.13272
$429$	6.96685			0.336363
$430$	−1.51963	+	4.67695i	−0.0732832	+	0.225543i
$431$	−3.22637	−	2.34409i	−0.155409	−	0.112911i	0.507363	−	0.861732i	$-0.330620\pi$
$431$	−3.22637	−	2.34409i	−0.155409	−	0.112911i	−0.662772	+	0.748821i	$0.730620\pi$
$432$	−59.2719	+	43.0636i	−2.85172	+	2.07190i
$433$	−18.0766			−0.868704			−0.434352	−	0.900743i	$-0.643023\pi$
$433$	−18.0766			−0.868704			−0.434352	+	0.900743i	$0.643023\pi$
$434$		0			0
$435$	−7.02016			−0.336591
$436$	−30.5453	+	22.1925i	−1.46286	+	1.06283i
$437$	1.12020	+	0.813875i	0.0535866	+	0.0389329i
$438$	−8.85548	+	27.2544i	−0.423131	+	1.30226i
$439$	22.9086			1.09337			0.546684	−	0.837339i	$-0.315890\pi$
$439$	22.9086			1.09337			0.546684	+	0.837339i	$0.315890\pi$
$440$	−7.08513			−0.337771
$441$	1.22418	−	3.76764i	0.0582943	−	0.179411i
$442$	8.43057	+	25.9466i	0.401001	+	1.23416i
$443$	−6.64118	−	20.4395i	−0.315532	−	0.971108i	−0.975535	−	0.219845i	$-0.929445\pi$
$443$	−6.64118	−	20.4395i	−0.315532	−	0.971108i	0.660003	−	0.751263i	$-0.270555\pi$
$444$	−46.5680	+	33.8336i	−2.21002	+	1.60567i
$445$	2.87947	−	8.86211i	0.136500	−	0.420104i
$446$	−20.4493	+	14.8573i	−0.968303	+	0.703513i
$447$	−10.3376	−	7.51068i	−0.488950	−	0.355243i
$448$	−11.1935	−	34.4499i	−0.528841	−	1.62761i
$449$	15.2092	+	11.0501i	0.717767	+	0.521488i	0.885670	−	0.464315i	$-0.153700\pi$
$449$	15.2092	+	11.0501i	0.717767	+	0.521488i	−0.167903	+	0.985804i	$0.553700\pi$
$450$	9.93502	+	7.21821i	0.468341	+	0.340270i
$451$	−0.0430022	−	0.132347i	−0.00202490	−	0.00623199i
$452$	−70.6346	−	51.3190i	−3.32237	−	2.41384i
$453$	3.68366	−	2.67634i	0.173074	−	0.125745i
$454$	−7.03235	+	21.6433i	−0.330045	+	1.01577i
$455$	−3.11991	+	2.26675i	−0.146264	+	0.106267i
$456$	−9.80544	−	30.1780i	−0.459182	−	1.41322i
$457$	−1.26882	−	3.90503i	−0.0593530	−	0.182670i	0.916984	−	0.398924i	$-0.130616\pi$
$457$	−1.26882	−	3.90503i	−0.0593530	−	0.182670i	−0.976337	+	0.216254i	$0.930616\pi$
$458$	18.9898	−	58.4447i	0.887337	−	2.73094i
$459$	15.6286			0.729480
$460$	1.71812			0.0801078
$461$	7.06878	−	21.7555i	0.329226	−	1.01325i	−0.640271	−	0.768149i	$-0.721178\pi$
$461$	7.06878	−	21.7555i	0.329226	−	1.01325i	0.969497	−	0.245104i	$-0.0788220\pi$
$462$	7.13327	+	5.18262i	0.331870	+	0.241117i
$463$	−13.4030	+	9.73782i	−0.622888	+	0.452555i	−0.853929	−	0.520389i	$-0.825787\pi$
$463$	−13.4030	+	9.73782i	−0.622888	+	0.452555i	0.231041	+	0.972944i	$0.425787\pi$
$464$	105.308			4.88880
$465$		0			0
$466$	−43.7244			−2.02549
$467$	−30.8610	+	22.4218i	−1.42808	+	1.03756i	−0.437704	+	0.899119i	$0.644208\pi$
$467$	−30.8610	+	22.4218i	−1.42808	+	1.03756i	−0.990371	+	0.138438i	$0.955792\pi$
$468$	−15.3336	−	11.1405i	−0.708797	−	0.514971i
$469$	−4.42835	+	13.6291i	−0.204482	+	0.629332i
$470$	11.0064			0.507688
$471$	4.72123			0.217543
$472$	−1.25457	+	3.86118i	−0.0577465	+	0.177725i
$473$	1.24177	+	3.82179i	0.0570969	+	0.175726i
$474$	11.4424	+	35.2161i	0.525567	+	1.61753i
$475$	−9.61760	+	6.98760i	−0.441286	+	0.320613i
$476$	−7.72101	+	23.7628i	−0.353892	+	1.08917i
$477$	−2.23247	+	1.62199i	−0.102218	+	0.0742656i
$478$	−39.7690	−	28.8939i	−1.81899	−	1.32158i
$479$	−10.4092	−	32.0361i	−0.475607	−	1.46377i	−0.845138	−	0.534549i	$-0.820482\pi$
$479$	−10.4092	−	32.0361i	−0.475607	−	1.46377i	0.369531	−	0.929218i	$-0.379518\pi$
$480$	−12.1722	−	8.84364i	−0.555584	−	0.403655i
$481$	−22.9997	−	16.7103i	−1.04870	−	0.761923i
$482$	−15.1061	−	46.4917i	−0.688063	−	2.11764i
$483$	−1.06918	−	0.776805i	−0.0486494	−	0.0353459i
$484$	39.0265	−	28.3544i	1.77393	−	1.28884i
$485$	−0.240486	+	0.740141i	−0.0109199	+	0.0336081i
$486$	−21.2745	+	15.4568i	−0.965031	+	0.701136i
$487$	6.38944	+	19.6647i	0.289533	+	0.891092i	0.985003	+	0.172537i	$0.0551963\pi$
$487$	6.38944	+	19.6647i	0.289533	+	0.891092i	−0.695470	+	0.718555i	$0.744804\pi$
$488$	−13.7630	−	42.3581i	−0.623020	−	1.91746i
$489$	−0.763222	+	2.34895i	−0.0345141	+	0.106223i
$490$	6.57587			0.297067
$491$	−24.7327			−1.11617			−0.558087	−	0.829783i	$-0.688464\pi$
$491$	−24.7327			−1.11617			−0.558087	+	0.829783i	$0.688464\pi$
$492$	0.238969	−	0.735472i	0.0107736	−	0.0331576i
$493$	−18.1739	−	13.2041i	−0.818509	−	0.594682i
$494$	20.5126	−	14.9033i	0.922905	−	0.670529i
$495$	−0.802235			−0.0360578
$496$		0			0
$497$	−8.21771			−0.368615
$498$	−51.5327	+	37.4407i	−2.30924	+	1.67776i
$499$	−19.8696	−	14.4361i	−0.889485	−	0.646249i	0.0462585	−	0.998930i	$-0.485270\pi$
$499$	−19.8696	−	14.4361i	−0.889485	−	0.646249i	−0.935744	+	0.352681i	$0.885270\pi$
$500$	−9.48108	+	29.1798i	−0.424007	+	1.30496i
$501$	−19.8917			−0.888695
$502$	−61.6858			−2.75317
$503$	4.55464	−	14.0177i	0.203081	−	0.625020i	−0.796705	−	0.604368i	$-0.793426\pi$
$503$	4.55464	−	14.0177i	0.203081	−	0.625020i	0.999787	−	0.0206524i	$-0.00657432\pi$
$504$	−4.58164	−	14.1008i	−0.204082	−	0.628101i
$505$	1.52661	+	4.69843i	0.0679334	+	0.209077i
$506$	1.56961	−	1.14039i	0.0697778	−	0.0506966i
$507$	−0.207775	+	0.639466i	−0.00922761	+	0.0283997i
$508$	−54.6943	+	39.7377i	−2.42667	+	1.76308i
$509$	12.5449	+	9.11437i	0.556041	+	0.403987i	0.830008	−	0.557752i	$-0.188336\pi$
$509$	12.5449	+	9.11437i	0.556041	+	0.403987i	−0.273967	+	0.961739i	$0.588336\pi$
$510$	1.98300	+	6.10304i	0.0878087	+	0.270247i
$511$	−10.4867	−	7.61904i	−0.463905	−	0.337046i
$512$	0.109537	+	0.0795830i	0.00484088	+	0.00351710i
$513$	−4.48838	−	13.8138i	−0.198167	−	0.609895i
$514$	0.231117	+	0.167916i	0.0101941	+	0.00740646i
$515$	−7.45796	+	5.41852i	−0.328637	+	0.238769i
$516$	−6.90071	+	21.2382i	−0.303787	+	0.934960i
$517$	7.27625	−	5.28650i	0.320009	−	0.232500i
$518$	−11.1184	−	34.2189i	−0.488514	−	1.50349i
$519$	0.00525417	+	0.0161707i	0.000230632	+	0.000709813i
$520$	6.00920	−	18.4944i	0.263521	−	0.811033i
$521$	29.4146			1.28867			0.644337	−	0.764741i	$-0.277133\pi$
$521$	29.4146			1.28867			0.644337	+	0.764741i	$0.277133\pi$
$522$	21.5665			0.943939
$523$	−13.9138	+	42.8222i	−0.608408	+	1.87249i	−0.136999	+	0.990571i	$0.543746\pi$
$523$	−13.9138	+	42.8222i	−0.608408	+	1.87249i	−0.471409	+	0.881915i	$0.656254\pi$
$524$	10.3283	+	7.50397i	0.451195	+	0.327813i
$525$	9.17954	−	6.66933i	0.400628	−	0.291073i
$526$	−19.6309			−0.855947
$527$		0			0
$528$	−24.5819			−1.06979
$529$	18.3721	−	13.3481i	0.798788	−	0.580354i
$530$	−3.70575	−	2.69238i	−0.160967	−	0.116950i
$531$	−0.142053	+	0.437194i	−0.00616457	+	0.0189726i
$532$	23.2209			1.00676
$533$	0.381940			0.0165436
$534$	18.0695	−	55.6121i	0.781943	−	2.40657i
$535$	−2.32663	−	7.16062i	−0.100589	−	0.309581i
$536$	−22.3302	−	68.7252i	−0.964516	−	2.96848i
$537$	11.4560	−	8.32329i	0.494364	−	0.359177i
$538$	13.4832	−	41.4971i	0.581303	−	1.78907i
$539$	4.34725	−	3.15846i	0.187249	−	0.136045i
$540$	−14.5807	−	10.5935i	−0.627455	−	0.455873i
$541$	11.6743	+	35.9297i	0.501916	+	1.54474i	0.805894	+	0.592059i	$0.201685\pi$
$541$	11.6743	+	35.9297i	0.501916	+	1.54474i	−0.303979	+	0.952679i	$0.598315\pi$
$542$	11.1989	+	8.13646i	0.481033	+	0.349491i
$543$	21.3588	+	15.5181i	0.916595	+	0.665945i
$544$	−14.8777	−	45.7890i	−0.637878	−	1.96319i
$545$	−3.54850	−	2.57814i	−0.152001	−	0.110435i
$546$	−19.5783	+	14.2244i	−0.837873	+	0.608750i
$547$	−5.62682	+	17.3176i	−0.240585	+	0.740445i	0.755746	+	0.654865i	$0.227274\pi$
$547$	−5.62682	+	17.3176i	−0.240585	+	0.740445i	−0.996331	+	0.0855805i	$0.972726\pi$
$548$	34.5035	−	25.0683i	1.47392	−	1.07086i
$549$	−1.55835	−	4.79611i	−0.0665088	−	0.204693i
$550$	5.14739	+	15.8420i	0.219486	+	0.675507i
$551$	−6.45149	+	19.8556i	−0.274843	+	0.845878i
$552$	6.66412			0.283644
$553$	−16.7489			−0.712237
$554$	−14.0680	+	43.2969i	−0.597693	+	1.83951i
$555$	−5.40989	−	3.93051i	−0.229637	−	0.166841i
$556$	−5.73389	+	4.16591i	−0.243171	+	0.176674i
$557$	9.19760			0.389715			0.194857	−	0.980832i	$-0.437576\pi$
$557$	9.19760			0.389715			0.194857	+	0.980832i	$0.437576\pi$
$558$		0			0
$559$	−11.0293			−0.466488
$560$	11.0083	−	7.99802i	0.465187	−	0.337978i
$561$	4.24230	+	3.08221i	0.179110	+	0.130131i
$562$	−1.58502	+	4.87819i	−0.0668600	+	0.205774i
$563$	−36.1618			−1.52404			−0.762019	−	0.647555i	$-0.775792\pi$
$563$	−36.1618			−1.52404			−0.762019	+	0.647555i	$0.775792\pi$
$564$	49.9805			2.10456
$565$	3.13431	−	9.64643i	0.131862	−	0.405828i
$566$	12.7271	+	39.1700i	0.534960	+	1.64644i
$567$	2.70550	+	8.32666i	0.113620	+	0.349687i
$568$	33.5242	−	24.3568i	1.40664	−	1.02199i
$569$	−12.8241	+	39.4686i	−0.537616	+	1.65461i	0.200313	+	0.979732i	$0.435804\pi$
$569$	−12.8241	+	39.4686i	−0.537616	+	1.65461i	−0.737929	+	0.674879i	$0.764196\pi$
$570$	4.82487	−	3.50547i	0.202092	−	0.146828i
$571$	−26.2066	−	19.0402i	−1.09671	−	0.796808i	−0.116192	−	0.993227i	$-0.537069\pi$
$571$	−26.2066	−	19.0402i	−1.09671	−	0.796808i	−0.980520	+	0.196419i	$0.937069\pi$
$572$	−7.94444	−	24.4505i	−0.332174	−	1.02233i
$573$	1.37559	+	0.999427i	0.0574662	+	0.0417517i
$574$	0.391063	+	0.284124i	0.0163227	+	0.0118591i
$575$	−0.771525	−	2.37451i	−0.0321748	−	0.0990239i
$576$	16.7318	+	12.1564i	0.697158	+	0.506515i
$577$	−33.1556	+	24.0889i	−1.38028	+	1.00284i	−0.383431	+	0.923570i	$0.625257\pi$
$577$	−33.1556	+	24.0889i	−1.38028	+	1.00284i	−0.996854	+	0.0792655i	$0.974743\pi$
$578$	7.78668	−	23.9649i	0.323883	−	0.996810i
$579$	14.6117	−	10.6160i	0.607242	−	0.441187i
$580$	8.00524	+	24.6376i	0.332399	+	1.02302i
$581$	−8.90348	−	27.4021i	−0.369379	−	1.13683i
$582$	−1.50912	+	4.64458i	−0.0625549	+	0.192524i
$583$	−3.74302			−0.155020
$584$	65.3629			2.70474
$585$	0.680408	−	2.09408i	0.0281314	−	0.0865796i
$586$	58.3132	+	42.3671i	2.40890	+	1.75017i
$587$	20.6553	−	15.0070i	0.852537	−	0.619404i	−0.0733077	−	0.997309i	$-0.523356\pi$
$587$	20.6553	−	15.0070i	0.852537	−	0.619404i	0.925844	+	0.377905i	$0.123356\pi$
$588$	29.8612			1.23146
$589$		0			0
$590$	−0.763058			−0.0314146
$591$	3.40833	−	2.47630i	0.140200	−	0.101861i
$592$	81.1526	+	58.9608i	3.33535	+	2.42327i
$593$	13.7611	−	42.3522i	0.565099	−	1.73920i	−0.102557	−	0.994727i	$-0.532702\pi$
$593$	13.7611	−	42.3522i	0.565099	−	1.73920i	0.667656	−	0.744470i	$-0.267298\pi$
$594$	−20.3518			−0.835045
$595$	−2.90263			−0.118996
$596$	−14.5709	+	44.8448i	−0.596849	+	1.83691i
$597$	−5.78181	−	17.7946i	−0.236634	−	0.728284i
$598$	1.64552	+	5.06439i	0.0672903	+	0.207098i
$599$	−15.3551	+	11.1561i	−0.627393	+	0.455827i	−0.855496	−	0.517810i	$-0.826748\pi$
$599$	−15.3551	+	11.1561i	−0.627393	+	0.455827i	0.228103	+	0.973637i	$0.426748\pi$
$600$	−17.6805	+	54.4151i	−0.721805	+	2.22149i
$601$	−10.3876	+	7.54705i	−0.423720	+	0.307851i	−0.779133	−	0.626859i	$-0.784340\pi$
$601$	−10.3876	+	7.54705i	−0.423720	+	0.307851i	0.355413	+	0.934709i	$0.384340\pi$
$602$	−11.2927	−	8.20464i	−0.460257	−	0.334396i
$603$	−2.52840	−	7.78161i	−0.102964	−	0.316891i
$604$	−13.5933	−	9.87610i	−0.553103	−	0.401853i
$605$	4.53378	+	3.29398i	0.184324	+	0.133919i
$606$	9.57991	+	29.4839i	0.389157	+	1.19770i
$607$	30.8553	+	22.4177i	1.25238	+	0.909907i	0.998357	−	0.0572916i	$-0.0182465\pi$
$607$	30.8553	+	22.4177i	1.25238	+	0.909907i	0.254022	+	0.967198i	$0.418246\pi$
$608$	−36.1993	+	26.3003i	−1.46808	+	1.06662i
$609$	6.15763	−	18.9512i	0.249520	−	0.767943i
$610$	6.77222	−	4.92030i	0.274199	−	0.199217i
$611$	7.62813	+	23.4770i	0.308601	+	0.949777i
$612$	−4.40836	−	13.5675i	−0.178197	−	0.548435i
$613$	5.72991	−	17.6348i	0.231429	−	0.712265i	−0.766146	−	0.642666i	$-0.777828\pi$
$613$	5.72991	−	17.6348i	0.231429	−	0.712265i	0.997575	−	0.0695985i	$-0.0221718\pi$
$614$	−24.0803			−0.971801
$615$	0.0898380			0.00362262
$616$	6.21462	−	19.1266i	0.250394	−	0.770634i
$617$	−6.58180	−	4.78195i	−0.264973	−	0.192514i	0.447363	−	0.894352i	$-0.352363\pi$
$617$	−6.58180	−	4.78195i	−0.264973	−	0.192514i	−0.712337	+	0.701838i	$0.752363\pi$
$618$	−46.8007	+	34.0027i	−1.88260	+	1.36779i
$619$	5.36063			0.215462			0.107731	−	0.994180i	$-0.465641\pi$
$619$	5.36063			0.215462			0.107731	+	0.994180i	$0.465641\pi$
$620$		0			0
$621$	3.05046			0.122411
$622$	44.9545	−	32.6614i	1.80251	−	1.30960i
$623$	21.3980	+	15.5465i	0.857292	+	0.622859i
$624$	20.8490	−	64.1665i	0.834626	−	2.56872i
$625$	19.5850			0.783401
$626$	1.21412			0.0485261
$627$	1.50596	−	4.63488i	0.0601424	−	0.185099i
$628$	−5.38372	−	16.5694i	−0.214834	−	0.661191i
$629$	−6.61234	−	20.3507i	−0.263651	−	0.811435i
$630$	2.25444	−	1.63795i	0.0898192	−	0.0652575i
$631$	−8.97602	+	27.6254i	−0.357330	+	1.09975i	0.597317	+	0.802006i	$0.296234\pi$
$631$	−8.97602	+	27.6254i	−0.357330	+	1.09975i	−0.954646	+	0.297742i	$0.903766\pi$
$632$	68.3273	−	49.6427i	2.71791	−	1.97468i
$633$	21.0478	+	15.2921i	0.836575	+	0.607807i
$634$	4.63938	+	14.2785i	0.184253	+	0.567073i
$635$	−6.35393	−	4.61640i	−0.252148	−	0.183196i
$636$	−16.8279	−	12.2262i	−0.667271	−	0.484801i
$637$	4.55748	+	14.0265i	0.180574	+	0.555750i
$638$	23.6663	+	17.1946i	0.936959	+	0.680740i
$639$	3.79587	−	2.75786i	0.150162	−	0.109099i
$640$	−4.05631	+	12.4840i	−0.160340	+	0.493474i
$641$	−22.3334	+	16.2261i	−0.882114	+	0.640894i	−0.933810	−	0.357769i	$-0.883537\pi$
$641$	−22.3334	+	16.2261i	−0.882114	+	0.640894i	0.0516957	+	0.998663i	$0.483537\pi$
$642$	−14.6002	−	44.9348i	−0.576224	−	1.77344i
$643$	1.30684	+	4.02205i	0.0515369	+	0.158614i	0.973513	−	0.228634i	$-0.0734258\pi$
$643$	1.30684	+	4.02205i	0.0515369	+	0.158614i	−0.921976	+	0.387248i	$0.873426\pi$
$644$	−1.50702	+	4.63814i	−0.0593851	+	0.182769i
$645$	−2.59425			−0.102148
$646$	19.0840			0.750852
$647$	8.12124	−	24.9946i	0.319279	−	0.982639i	−0.654679	−	0.755907i	$-0.727196\pi$
$647$	8.12124	−	24.9946i	0.319279	−	0.982639i	0.973957	−	0.226732i	$-0.0728040\pi$
$648$	−35.7168	−	25.9497i	−1.40309	−	1.01940i
$649$	−0.504451	+	0.366505i	−0.0198014	+	0.0143866i
$650$	−45.7184			−1.79322
$651$		0			0
$652$	9.11408			0.356935
$653$	10.8018	−	7.84796i	0.422707	−	0.307114i	−0.356019	−	0.934479i	$-0.615866\pi$
$653$	10.8018	−	7.84796i	0.422707	−	0.307114i	0.778726	+	0.627364i	$0.215866\pi$
$654$	−22.2678	−	16.1785i	−0.870741	−	0.632630i
$655$	−0.458306	+	1.41052i	−0.0179075	+	0.0551136i
$656$	−1.34764			−0.0526166
$657$	7.40090			0.288737
$658$	−9.65412	+	29.7123i	−0.376357	+	1.15831i
$659$	−4.76375	−	14.6613i	−0.185569	−	0.571124i	0.814388	−	0.580320i	$-0.197073\pi$
$659$	−4.76375	−	14.6613i	−0.185569	−	0.571124i	−0.999958	+	0.00919639i	$0.997073\pi$
$660$	−1.86865	−	5.75112i	−0.0727372	−	0.223862i
$661$	3.82104	−	2.77615i	0.148621	−	0.107980i	−0.510990	−	0.859587i	$-0.670721\pi$
$661$	3.82104	−	2.77615i	0.148621	−	0.107980i	0.659611	+	0.751607i	$0.270721\pi$
$662$	20.1221	−	61.9294i	0.782067	−	2.40696i
$663$	−11.6436	+	8.45958i	−0.452200	+	0.328543i
$664$	117.540	+	85.3976i	4.56143	+	3.31407i
$665$	0.833609	+	2.56558i	0.0323260	+	0.0994891i
$666$	16.6196	+	12.0748i	0.643996	+	0.467890i
$667$	−3.54726	−	2.57724i	−0.137351	−	0.0997910i
$668$	22.6829	+	69.8108i	0.877628	+	2.70106i
$669$	−10.7878	−	7.83781i	−0.417081	−	0.303027i
$670$	10.9878	−	7.98310i	0.424496	−	0.308414i
$671$	2.11378	−	6.50554i	0.0816015	−	0.251144i
$672$	34.5505	−	25.1024i	1.33281	−	0.968347i
$673$	9.60209	+	29.5522i	0.370133	+	1.13915i	0.946704	+	0.322106i	$0.104391\pi$
$673$	9.60209	+	29.5522i	0.370133	+	1.13915i	−0.576570	+	0.817047i	$0.695609\pi$
$674$	9.17425	+	28.2354i	0.353379	+	1.08759i
$675$	−8.09316	+	24.9082i	−0.311506	+	0.958716i
$676$	2.48116			0.0954294
$677$	9.03995			0.347434			0.173717	−	0.984796i	$-0.444422\pi$
$677$	9.03995			0.347434			0.173717	+	0.984796i	$0.444422\pi$
$678$	19.6687	−	60.5339i	0.755371	−	2.32479i
$679$	−1.78710	−	1.29841i	−0.0685828	−	0.0498283i
$680$	11.8413	−	8.60321i	0.454093	−	0.329918i
$681$	−12.0053			−0.460044
$682$		0			0
$683$	7.13535			0.273027			0.136513	−	0.990638i	$-0.456410\pi$
$683$	7.13535			0.273027			0.136513	+	0.990638i	$0.456410\pi$
$684$	−10.7261	+	7.79294i	−0.410121	+	0.297971i
$685$	4.00833	+	2.91222i	0.153150	+	0.111270i
$686$	−15.8169	+	48.6793i	−0.603890	+	1.85858i
$687$	32.4186			1.23685
$688$	38.9158			1.48365
$689$	3.17461	−	9.77045i	0.120943	−	0.372224i
$690$	0.387051	+	1.19122i	0.0147348	+	0.0453490i
$691$	11.2715	+	34.6902i	0.428789	+	1.31968i	0.899319	+	0.437293i	$0.144063\pi$
$691$	11.2715	+	34.6902i	0.428789	+	1.31968i	−0.470530	+	0.882384i	$0.655937\pi$
$692$	0.0507603	−	0.0368795i	0.00192962	−	0.00140195i
$693$	0.703669	−	2.16567i	0.0267302	−	0.0822670i
$694$	40.4097	−	29.3594i	1.53393	−	1.11447i
$695$	−0.666115	−	0.483961i	−0.0252672	−	0.0183577i
$696$	31.0501	+	95.5625i	1.17695	+	3.62229i
$697$	0.232573	+	0.168974i	0.00880934	+	0.00640036i
$698$	−70.0243	−	50.8756i	−2.65046	−	1.92567i
$699$	−7.12790	−	21.9374i	−0.269602	−	0.829749i
$700$	−33.8739	−	24.6109i	−1.28031	−	0.930203i
$701$	1.30611	−	0.948944i	0.0493311	−	0.0358411i	−0.562846	−	0.826561i	$-0.690294\pi$
$701$	1.30611	−	0.948944i	0.0493311	−	0.0358411i	0.612178	+	0.790720i	$0.290294\pi$
$702$	17.2612	−	53.1246i	0.651483	−	2.00506i
$703$	−16.0886	+	11.6891i	−0.606793	+	0.440861i
$704$	8.66884	+	26.6800i	0.326719	+	1.00554i
$705$	1.79425	+	5.52214i	0.0675755	+	0.207976i
$706$	26.7791	−	82.4176i	1.00784	−	3.10183i
$707$	−14.0227			−0.527377
$708$	−3.46507			−0.130225
$709$	−3.54997	+	10.9257i	−0.133322	+	0.410323i	−0.995325	−	0.0965797i	$-0.969210\pi$
$709$	−3.54997	+	10.9257i	−0.133322	+	0.410323i	0.862003	+	0.506903i	$0.169210\pi$
$710$	6.30089	+	4.57786i	0.236468	+	0.171804i
$711$	7.73655	−	5.62094i	0.290143	−	0.210802i
$712$	−133.372			−4.99833
$713$		0			0
$714$	−18.2148			−0.681672
$715$	2.41623	−	1.75550i	0.0903620	−	0.0656518i
$716$	−42.2745	−	30.7142i	−1.57987	−	1.14784i
$717$	8.01355	−	24.6632i	0.299271	−	0.921063i
$718$	−56.9298			−2.12460
$719$	14.1710			0.528489			0.264244	−	0.964456i	$-0.414877\pi$
$719$	14.1710			0.528489			0.264244	+	0.964456i	$0.414877\pi$
$720$	−2.40076	+	7.38879i	−0.0894712	+	0.275364i
$721$	−8.08591	−	24.8859i	−0.301135	−	0.926798i
$722$	10.3140	+	31.7433i	0.383848	+	1.18136i
$723$	20.8633	−	15.1580i	0.775913	−	0.563734i
$724$	30.1056	−	92.6554i	1.11886	−	3.44351i
$725$	30.4553	−	22.1271i	1.13108	−	0.821779i
$726$	28.4507	+	20.6706i	1.05590	+	0.767159i
$727$	−8.32731	−	25.6288i	−0.308843	−	0.950520i	−0.978215	−	0.207593i	$-0.933437\pi$
$727$	−8.32731	−	25.6288i	−0.308843	−	0.950520i	0.669373	−	0.742927i	$-0.266563\pi$
$728$	44.6556	+	32.4442i	1.65505	+	1.20246i
$729$	−23.5282	−	17.0942i	−0.871413	−	0.633119i
$730$	3.79627	+	11.6837i	0.140506	+	0.432434i
$731$	−6.71602	−	4.87947i	−0.248401	−	0.180474i
$732$	30.7529	−	22.3433i	1.13666	−	0.825831i
$733$	−8.78336	+	27.0324i	−0.324421	+	0.998464i	0.647281	+	0.762252i	$0.275906\pi$
$733$	−8.78336	+	27.0324i	−0.324421	+	0.998464i	−0.971701	+	0.236212i	$0.924094\pi$
$734$	−28.2852	+	20.5504i	−1.04403	+	0.758529i
$735$	1.07199	+	3.29924i	0.0395409	+	0.121694i
$736$	−2.90391	−	8.93732i	−0.107040	−	0.329434i
$737$	3.42957	−	10.5551i	0.126330	−	0.388803i
$738$	−0.275989			−0.0101593
$739$	0.697306			0.0256508			0.0128254	−	0.999918i	$-0.495917\pi$
$739$	0.697306			0.0256508			0.0128254	+	0.999918i	$0.495917\pi$
$740$	−7.62531	+	23.4683i	−0.280312	+	0.862711i
$741$	10.8212	+	7.86206i	0.397527	+	0.288820i
$742$	10.5187	−	7.64225i	0.386152	−	0.280556i
$743$	18.1815			0.667015			0.333508	−	0.942747i	$-0.391768\pi$
$743$	18.1815			0.667015			0.333508	+	0.942747i	$0.391768\pi$
$744$		0			0
$745$	−5.47779			−0.200691
$746$	−9.63250	+	6.99842i	−0.352671	+	0.256230i
$747$	13.3088	+	9.66939i	0.486943	+	0.353785i
$748$	5.97959	−	18.4033i	0.218635	−	0.672890i
$749$	21.3712			0.780886
$750$	−22.3670			−0.816728
$751$	−11.4540	+	35.2519i	−0.417963	+	1.28636i	0.491610	+	0.870815i	$0.336408\pi$
$751$	−11.4540	+	35.2519i	−0.417963	+	1.28636i	−0.909573	+	0.415543i	$0.863592\pi$
$752$	−26.9152	−	82.8365i	−0.981497	−	3.02074i
$753$	−10.0560	−	30.9490i	−0.366459	−	1.12785i
$754$	−64.9556	+	47.1930i	−2.36554	+	1.71867i
$755$	0.603184	−	1.85641i	0.0219521	−	0.0675616i
$756$	41.3870	−	30.0694i	1.50523	−	1.09361i
$757$	5.17933	+	3.76300i	0.188246	+	0.136769i	0.677917	−	0.735139i	$-0.262883\pi$
$757$	5.17933	+	3.76300i	0.188246	+	0.136769i	−0.489671	+	0.871907i	$0.662883\pi$
$758$	12.4328	+	38.2641i	0.451578	+	1.38981i
$759$	0.828034	+	0.601602i	0.0300557	+	0.0218368i
$760$	−11.0049	−	7.99555i	−0.399191	−	0.290029i
$761$	6.59406	+	20.2944i	0.239035	+	0.735673i	0.996561	+	0.0828677i	$0.0264079\pi$
$761$	6.59406	+	20.2944i	0.239035	+	0.735673i	−0.757526	+	0.652805i	$0.773592\pi$
$762$	−39.8726	−	28.9692i	−1.44443	−	1.04944i
$763$	10.0723	−	7.31797i	0.364643	−	0.264928i
$764$	1.93892	−	5.96738i	0.0701476	−	0.215892i
$765$	1.34077	−	0.974123i	0.0484755	−	0.0352195i
$766$	−9.68498	−	29.8073i	−0.349932	−	1.07698i
$767$	−0.528847	−	1.62762i	−0.0190955	−	0.0587700i
$768$	−7.05666	+	21.7182i	−0.254635	+	0.783686i
$769$	−12.2566			−0.441983			−0.220991	−	0.975276i	$-0.570929\pi$
$769$	−12.2566			−0.441983			−0.220991	+	0.975276i	$0.570929\pi$
$770$	3.77986			0.136217
$771$	−0.0465705	+	0.143329i	−0.00167720	+	0.00516188i
$772$	−53.9195	−	39.1748i	−1.94061	−	1.40993i
$773$	−28.0757	+	20.3982i	−1.00981	+	0.733672i	−0.964170	−	0.265286i	$-0.914534\pi$
$773$	−28.0757	+	20.3982i	−1.00981	+	0.733672i	−0.0456427	+	0.998958i	$0.514534\pi$
$774$	7.96974			0.286466
$775$		0			0
$776$	11.1389			0.399863
$777$	15.3558	−	11.1566i	0.550886	−	0.400242i
$778$	−31.3441	−	22.7728i	−1.12374	−	0.816445i
$779$	0.0825606	−	0.254095i	0.00295804	−	0.00910391i
$780$	16.5971			0.594272
$781$	6.36426			0.227731
$782$	−1.23854	+	3.81184i	−0.0442902	+	0.136311i
$783$	14.2130	+	43.7432i	0.507932	+	1.56325i
$784$	−16.0807	−	49.4913i	−0.574311	−	1.76755i
$785$	1.63741	−	1.18965i	0.0584418	−	0.0424604i
$786$	−2.87599	+	8.85139i	−0.102583	+	0.315719i
$787$	−16.2760	+	11.8252i	−0.580175	+	0.421522i	−0.838787	−	0.544459i	$-0.816735\pi$
$787$	−16.2760	+	11.8252i	−0.580175	+	0.421522i	0.258612	+	0.965981i	$0.416735\pi$
$788$	−12.5773	−	9.13791i	−0.448046	−	0.325525i
$789$	−3.20020	−	9.84921i	−0.113930	−	0.350641i
$790$	12.8421	+	9.33037i	0.456903	+	0.331960i
$791$	23.2917	+	16.9224i	0.828159	+	0.601693i
$792$	3.54828	+	10.9205i	0.126083	+	0.388042i
$793$	15.1887	+	11.0352i	0.539367	+	0.391873i
$794$	34.3653	−	24.9679i	1.21958	−	0.886077i
$795$	0.746717	−	2.29816i	0.0264833	−	0.0815073i
$796$	−55.8578	+	40.5831i	−1.97983	+	1.43843i
$797$	−8.09685	−	24.9195i	−0.286805	−	0.882695i	−0.985852	−	0.167619i	$-0.946392\pi$
$797$	−8.09685	−	24.9195i	−0.286805	−	0.882695i	0.699047	−	0.715076i	$-0.253608\pi$
$798$	5.23112	+	16.0997i	0.185180	+	0.569924i
$799$	−5.74151	+	17.6705i	−0.203120	+	0.625139i
$800$	80.6809			2.85250
$801$	−15.1014			−0.533583
$802$	25.7897	−	79.3726i	0.910666	−	2.80274i
$803$	8.12150	+	5.90061i	0.286601	+	0.208228i
$804$	49.8960	−	36.2516i	1.75970	−	1.27849i
$805$	−0.566550			−0.0199683
$806$		0			0
$807$	23.0179			0.810270
$808$	57.2055	−	41.5623i	2.01248	−	1.46216i
$809$	29.4888	+	21.4249i	1.03677	+	0.753258i	0.969653	−	0.244487i	$-0.0786196\pi$
$809$	29.4888	+	21.4249i	1.03677	+	0.753258i	0.0671181	+	0.997745i	$0.478620\pi$
$810$	2.56413	−	7.89158i	0.0900944	−	0.277282i
$811$	−19.1064			−0.670918			−0.335459	−	0.942055i	$-0.608891\pi$
$811$	−19.1064			−0.670918			−0.335459	+	0.942055i	$0.608891\pi$
$812$	−73.5320			−2.58047
$813$	−2.25660	+	6.94510i	−0.0791424	+	0.243575i
$814$	8.61071	+	26.5010i	0.301805	+	0.928861i
$815$	0.327187	+	1.00698i	0.0114608	+	0.0352729i
$816$	41.0835	−	29.8489i	1.43821	−	1.04492i
$817$	−2.38410	+	7.33750i	−0.0834091	+	0.256707i
$818$	−14.3333	+	10.4137i	−0.501151	+	0.364107i
$819$	5.05626	+	3.67359i	0.176680	+	0.128366i
$820$	−0.102444	−	0.315291i	−0.00357750	−	0.0110104i
$821$	31.9236	+	23.1939i	1.11414	+	0.809472i	0.983311	−	0.181933i	$-0.0582353\pi$
$821$	31.9236	+	23.1939i	1.11414	+	0.809472i	0.130831	+	0.991405i	$0.458235\pi$
$822$	25.1534	+	18.2750i	0.877324	+	0.637413i
$823$	9.76122	+	30.0420i	0.340255	+	1.04720i	0.964075	+	0.265629i	$0.0855796\pi$
$823$	9.76122	+	30.0420i	0.340255	+	1.04720i	−0.623820	+	0.781568i	$0.714420\pi$
$824$	106.747	+	77.5559i	3.71869	+	2.70179i
$825$	−7.10915	+	5.16510i	−0.247509	+	0.179826i
$826$	0.669305	−	2.05991i	0.0232881	−	0.0716734i
$827$	16.0427	−	11.6557i	0.557859	−	0.405308i	−0.272816	−	0.962066i	$-0.587955\pi$
$827$	16.0427	−	11.6557i	0.557859	−	0.405308i	0.830675	+	0.556758i	$0.187955\pi$
$828$	−0.860446	−	2.64818i	−0.0299026	−	0.0920306i
$829$	−2.78111	−	8.55938i	−0.0965920	−	0.297280i	0.891073	−	0.453859i	$-0.149953\pi$
$829$	−2.78111	−	8.55938i	−0.0965920	−	0.297280i	−0.987665	+	0.156580i	$0.949953\pi$
$830$	−8.43826	+	25.9703i	−0.292896	+	0.901442i
$831$	−24.0163			−0.833115
$832$	−76.9954			−2.66933
$833$	−3.43031	+	10.5574i	−0.118853	+	0.365792i
$834$	−4.18005	−	3.03699i	−0.144743	−	0.105162i
$835$	−6.89881	+	5.01228i	−0.238743	+	0.173457i
$836$	−17.9836			−0.621976
$837$		0			0
$838$	39.4699			1.36347
$839$	25.7633	−	18.7181i	0.889448	−	0.646222i	−0.0462862	−	0.998928i	$-0.514739\pi$
$839$	25.7633	−	18.7181i	0.889448	−	0.646222i	0.935734	+	0.352707i	$0.114739\pi$
$840$	10.5037	+	7.63137i	0.362411	+	0.263307i
$841$	11.4679	−	35.2947i	0.395446	−	1.21706i
$842$	71.8698			2.47680
$843$	−2.70587			−0.0931953
$844$	29.6672	−	91.3062i	1.02119	−	3.14289i
$845$	0.0890714	+	0.274134i	0.00306415	+	0.00943048i
$846$	−5.51208	−	16.9644i	−0.189509	−	0.583250i
$847$	−12.8690	+	9.34987i	−0.442184	+	0.321265i
$848$	−11.2013	+	34.4742i	−0.384656	+	1.18385i
$849$	−17.5776	+	12.7709i	−0.603262	+	0.438296i
$850$	−27.8392	−	20.2263i	−0.954876	−	0.693758i
$851$	−1.29063	−	3.97215i	−0.0442422	−	0.136163i
$852$	28.6126	+	20.7882i	0.980250	+	0.712193i
$853$	39.7160	+	28.8554i	1.35985	+	0.987989i	0.998454	+	0.0555768i	$0.0176998\pi$
$853$	39.7160	+	28.8554i	1.35985	+	0.987989i	0.361396	+	0.932412i	$0.382300\pi$
$854$	7.34243	+	22.5977i	0.251253	+	0.773277i
$855$	−1.24606	−	0.905319i	−0.0426145	−	0.0309613i
$856$	−87.1838	+	63.3428i	−2.97988	+	2.16501i
$857$	5.94563	−	18.2988i	0.203099	−	0.625074i	−0.796687	−	0.604392i	$-0.793416\pi$
$857$	5.94563	−	18.2988i	0.203099	−	0.625074i	0.999786	−	0.0206823i	$-0.00658385\pi$
$858$	15.1625	−	11.0162i	0.517640	−	0.376087i
$859$	−1.43450	−	4.41494i	−0.0489446	−	0.150636i	0.923597	−	0.383364i	$-0.125235\pi$
$859$	−1.43450	−	4.41494i	−0.0489446	−	0.150636i	−0.972542	+	0.232728i	$0.925235\pi$
$860$	2.95828	+	9.10464i	0.100876	+	0.310466i
$861$	−0.0788001	+	0.242522i	−0.00268550	+	0.00826512i
$862$	−10.7284			−0.365410
$863$	38.5304			1.31159			0.655795	−	0.754939i	$-0.272333\pi$
$863$	38.5304			1.31159			0.655795	+	0.754939i	$0.272333\pi$
$864$	−30.4615	+	93.7509i	−1.03632	+	3.18947i
$865$	0.00589690	+	0.00428435i	0.000200501	+	0.000145672i
$866$	−39.3415	+	28.5833i	−1.33688	+	0.971299i
$867$	13.2931			0.451456
$868$		0			0
$869$	12.9713			0.440022
$870$	−15.2786	+	11.1005i	−0.517991	+	0.376343i
$871$	24.6434	+	17.9045i	0.835009	+	0.606670i
$872$	−19.4001	+	59.7074i	−0.656970	+	2.02195i
$873$	1.26123			0.0426863
$874$	3.72492			0.125997
$875$	3.12638	−	9.62202i	0.105691	−	0.325284i
$876$	17.2390	+	53.0562i	0.582452	+	1.79260i
$877$	−2.86099	−	8.80521i	−0.0966086	−	0.297331i	0.891061	−	0.453884i	$-0.149962\pi$
$877$	−2.86099	−	8.80521i	−0.0966086	−	0.297331i	−0.987670	+	0.156553i	$0.949962\pi$
$878$	49.8578	−	36.2238i	1.68262	−	1.22250i
$879$	−11.7503	+	36.1636i	−0.396326	+	1.21977i
$880$	−8.52548	+	6.19412i	−0.287394	+	0.208804i
$881$	−14.4645	−	10.5091i	−0.487321	−	0.354059i	0.316832	−	0.948482i	$-0.397381\pi$
$881$	−14.4645	−	10.5091i	−0.487321	−	0.354059i	−0.804153	+	0.594422i	$0.797381\pi$
$882$	−3.29323	−	10.1355i	−0.110889	−	0.341281i
$883$	−39.0881	−	28.3992i	−1.31542	−	0.955709i	−0.999977	−	0.00676442i	$-0.997847\pi$
$883$	−39.0881	−	28.3992i	−1.31542	−	0.955709i	−0.315443	−	0.948944i	$-0.602153\pi$
$884$	42.9667	+	31.2172i	1.44513	+	1.04995i
$885$	−0.124393	−	0.382842i	−0.00418142	−	0.0128691i
$886$	−46.7733	−	33.9828i	−1.57138	−	1.14167i
$887$	−19.0218	+	13.8201i	−0.638689	+	0.464035i	−0.859400	−	0.511305i	$-0.829162\pi$
$887$	−19.0218	+	13.8201i	−0.638689	+	0.464035i	0.220711	+	0.975339i	$0.429162\pi$
$888$	−29.5765	+	91.0271i	−0.992522	+	3.05467i
$889$	18.0354	−	13.1035i	0.604889	−	0.439478i
$890$	−7.74623	−	23.8404i	−0.259654	−	0.799134i
$891$	−2.09529	−	6.44864i	−0.0701948	−	0.216037i
$892$	−15.2056	+	46.7980i	−0.509121	+	1.56691i
$893$	17.2676			0.577838
$894$	−34.3746			−1.14966
$895$	1.87587	−	5.77335i	0.0627036	−	0.192982i
$896$	−30.1433	−	21.9004i	−1.00702	−	0.731640i
$897$	−2.27266	+	1.65118i	−0.0758818	+	0.0551313i
$898$	50.5739			1.68767
$899$		0			0
$900$	23.9062			0.796874
$901$	6.25567	−	4.54501i	0.208406	−	0.151416i
$902$	−0.302861	−	0.220042i	−0.0100842	−	0.00732658i
$903$	2.27551	−	7.00330i	0.0757242	−	0.233055i
$904$	−145.176			−4.82847
$905$	11.3179			0.376219
$906$	3.78514	−	11.6495i	0.125753	−	0.387028i
$907$	−3.88809	−	11.9663i	−0.129102	−	0.397335i	0.865524	−	0.500867i	$-0.166986\pi$
$907$	−3.88809	−	11.9663i	−0.129102	−	0.397335i	−0.994626	+	0.103532i	$0.966986\pi$
$908$	13.6899	+	42.1332i	0.454315	+	1.39824i
$909$	6.47726	−	4.70601i	0.214837	−	0.156088i
$910$	−3.20586	+	9.86661i	−0.106273	+	0.327075i
$911$	−38.2539	+	27.7931i	−1.26741	+	0.920827i	−0.999096	−	0.0425044i	$-0.986466\pi$
$911$	−38.2539	+	27.7931i	−1.26741	+	0.920827i	−0.268314	+	0.963332i	$0.586466\pi$
$912$	−38.1817	−	27.7406i	−1.26432	−	0.918584i
$913$	6.89536	+	21.2217i	0.228203	+	0.702337i
$914$	−8.93621	−	6.49254i	−0.295584	−	0.214754i
$915$	3.57261	+	2.59566i	0.118107	+	0.0858098i
$916$	−36.9676	−	113.775i	−1.22144	−	3.75922i
$917$	−3.40577	−	2.47443i	−0.112468	−	0.0817130i
$918$	34.0138	−	24.7124i	1.12262	−	0.815632i
$919$	−7.14814	+	21.9997i	−0.235795	+	0.725704i	0.761219	+	0.648494i	$0.224601\pi$
$919$	−7.14814	+	21.9997i	−0.235795	+	0.725704i	−0.997015	+	0.0772094i	$0.975399\pi$
$920$	2.31124	−	1.67922i	0.0761994	−	0.0553621i
$921$	−3.92554	−	12.0816i	−0.129351	−	0.398101i
$922$	−19.0161	−	58.5256i	−0.626262	−	1.92744i
$923$	−5.39779	+	16.6127i	−0.177671	+	0.546814i
$924$	17.1645			0.564670
$925$	35.8582			1.17901
$926$	−13.7722	+	42.3864i	−0.452582	+	1.39290i
$927$	12.0867	+	8.78149i	0.396979	+	0.288422i
$928$	114.630	−	83.2833i	3.76290	−	2.73391i
$929$	−1.68694			−0.0553468			−0.0276734	−	0.999617i	$-0.508810\pi$
$929$	−1.68694			−0.0553468			−0.0276734	+	0.999617i	$0.508810\pi$
$930$		0			0
$931$	10.3166			0.338114
$932$	−68.8623	+	50.0314i	−2.25566	+	1.63883i
$933$	23.7153	+	17.2302i	0.776404	+	0.564091i
$934$	−31.7111	+	97.5968i	−1.03762	+	3.19346i
$935$	2.24796			0.0735162
$936$	−31.5153			−1.03011
$937$	6.09587	−	18.7612i	0.199143	−	0.612900i	−0.800760	−	0.598986i	$-0.795571\pi$
$937$	6.09587	−	18.7612i	0.199143	−	0.612900i	0.999903	−	0.0139148i	$-0.00442936\pi$
$938$	11.9130	+	36.6643i	0.388972	+	1.19713i
$939$	0.197925	+	0.609150i	0.00645903	+	0.0198789i
$940$	17.3342	−	12.5940i	0.565379	−	0.410772i
$941$	2.72654	−	8.39142i	0.0888826	−	0.273552i	−0.896729	−	0.442581i	$-0.854063\pi$
$941$	2.72654	−	8.39142i	0.0888826	−	0.273552i	0.985611	+	0.169028i	$0.0540630\pi$
$942$	10.2752	−	7.46537i	0.334784	−	0.243235i
$943$	0.0453948	+	0.0329813i	0.00147826	+	0.00107402i
$944$	1.86599	+	5.74293i	0.0607328	+	0.186916i
$945$	4.80800	+	3.49321i	0.156404	+	0.113634i
$946$	8.74572	+	6.35414i	0.284348	+	0.206591i
$947$	−4.80867	−	14.7996i	−0.156261	−	0.480921i	0.842026	−	0.539437i	$-0.181363\pi$
$947$	−4.80867	−	14.7996i	−0.156261	−	0.480921i	−0.998286	+	0.0585164i	$0.981363\pi$
$948$	58.3167	+	42.3695i	1.89404	+	1.37610i
$949$	−22.2906	+	16.1951i	−0.723584	+	0.525714i
$950$	−9.88255	+	30.4154i	−0.320632	+	0.986804i
$951$	−6.40752	+	4.65534i	−0.207778	+	0.150960i
$952$	12.8383	+	39.5123i	0.416093	+	1.28060i
$953$	−2.98255	−	9.17933i	−0.0966141	−	0.297348i	0.891057	−	0.453892i	$-0.149965\pi$
$953$	−2.98255	−	9.17933i	−0.0966141	−	0.297348i	−0.987671	+	0.156544i	$0.949965\pi$
$954$	−2.29397	+	7.06012i	−0.0742701	+	0.228580i
$955$	0.728916			0.0235872
$956$	−95.6945			−3.09498
$957$	−4.76882	+	14.6769i	−0.154154	+	0.474437i
$958$	−73.3109	−	53.2635i	−2.36857	−	1.72086i
$959$	−11.3775	+	8.26626i	−0.367400	+	0.266931i
$960$	−18.1105			−0.584514
$961$		0			0
$962$	−76.4790			−2.46578
$963$	−9.87164	+	7.17217i	−0.318109	+	0.231120i
$964$	−76.9887	−	55.9356i	−2.47964	−	1.80156i
$965$	2.39260	−	7.36368i	0.0770207	−	0.237045i
$966$	−3.55525			−0.114388
$967$	−28.3976			−0.913204			−0.456602	−	0.889671i	$-0.650934\pi$
$967$	−28.3976			−0.913204			−0.456602	+	0.889671i	$0.650934\pi$
$968$	24.7867	−	76.2856i	0.796675	−	2.45191i
$969$	3.11106	+	9.57485i	0.0999416	+	0.307588i
$970$	0.646946	+	1.99109i	0.0207722	+	0.0639302i
$971$	17.9012	−	13.0060i	0.574476	−	0.417381i	−0.262252	−	0.964999i	$-0.584465\pi$
$971$	17.9012	−	13.0060i	0.574476	−	0.417381i	0.836728	+	0.547618i	$0.184465\pi$
$972$	−15.8192	+	48.6865i	−0.507401	+	1.56162i
$973$	1.89075	−	1.37371i	0.0606146	−	0.0440391i
$974$	45.0003	+	32.6947i	1.44190	+	1.04760i
$975$	−7.45296	−	22.9378i	−0.238686	−	0.734599i
$976$	−53.5921	−	38.9369i	−1.71544	−	1.24634i
$977$	16.1094	+	11.7042i	0.515385	+	0.374449i	0.814862	−	0.579654i	$-0.196812\pi$
$977$	16.1094	+	11.7042i	0.515385	+	0.374449i	−0.299478	+	0.954103i	$0.596812\pi$
$978$	2.05318	+	6.31905i	0.0656536	+	0.202061i
$979$	−16.5718	−	12.0401i	−0.529637	−	0.384804i
$980$	10.3564	−	7.52439i	0.330824	−	0.240358i
$981$	−2.19663	+	6.76054i	−0.0701331	+	0.215847i
$982$	−53.8279	+	39.1083i	−1.71772	+	1.24799i
$983$	7.70391	+	23.7102i	0.245717	+	0.756238i	0.995518	+	0.0945747i	$0.0301491\pi$
$983$	7.70391	+	23.7102i	0.245717	+	0.756238i	−0.749801	+	0.661663i	$0.769851\pi$
$984$	−0.397353	−	1.22293i	−0.0126671	−	0.0389855i
$985$	0.558099	−	1.71765i	0.0177825	−	0.0547289i
$986$	−60.4320			−1.92455
$987$	−16.4811			−0.524598
$988$	15.2526	−	46.9428i	0.485251	−	1.49345i
$989$	−1.31087	−	0.952399i	−0.0416831	−	0.0302845i
$990$	−1.74597	+	1.26852i	−0.0554905	+	0.0403162i
$991$	42.0512			1.33580			0.667900	−	0.744251i	$-0.267193\pi$
$991$	42.0512			1.33580			0.667900	+	0.744251i	$0.267193\pi$
$992$		0			0
$993$	34.3515			1.09011
$994$	−17.8849	+	12.9941i	−0.567274	+	0.412149i
$995$	−6.48910	−	4.71460i	−0.205718	−	0.149463i
$996$	−38.3184	+	117.932i	−1.21417	+	3.73682i
$997$	14.4647			0.458100			0.229050	−	0.973415i	$-0.426438\pi$
$997$	14.4647			0.458100			0.229050	+	0.973415i	$0.426438\pi$
$998$	−66.0707			−2.09143
$999$	−13.5385	+	41.6671i	−0.428338	+	1.31829i

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.q.388.4		16
31.2	even	5	inner	961.2.d.q.374.4		16
31.3	odd	30		31.2.g.a.20.1	yes	16
31.4	even	5		961.2.d.n.628.1		16
31.5	even	3		961.2.g.n.338.2		16
31.6	odd	6		961.2.g.s.235.2		16
31.7	even	15		961.2.g.j.846.1		16
31.8	even	5		961.2.a.j.1.1		8
31.9	even	15		961.2.c.i.521.1		16
31.10	even	15		961.2.g.m.732.2		16
31.11	odd	30		31.2.g.a.14.1	✓	16
31.12	odd	30		961.2.g.t.816.2		16
31.13	odd	30		961.2.g.k.844.1		16
31.14	even	15		961.2.c.i.439.1		16
31.15	odd	10		961.2.d.o.531.1		16
31.16	even	5		961.2.d.n.531.1		16
31.17	odd	30		961.2.c.j.439.1		16
31.18	even	15		961.2.g.j.844.1		16
31.19	even	15		961.2.g.n.816.2		16
31.20	even	15		961.2.g.l.448.1		16
31.21	odd	30		961.2.g.s.732.2		16
31.22	odd	30		961.2.c.j.521.1		16
31.23	odd	10		961.2.a.i.1.1		8
31.24	odd	30		961.2.g.k.846.1		16
31.25	even	3		961.2.g.m.235.2		16
31.26	odd	6		961.2.g.t.338.2		16
31.27	odd	10		961.2.d.o.628.1		16
31.28	even	15		961.2.g.l.547.1		16
31.29	odd	10		961.2.d.p.374.4		16
31.30	odd	2		961.2.d.p.388.4		16
93.8	odd	10		8649.2.a.be.1.8		8
93.11	even	30		279.2.y.c.262.2		16
93.23	even	10		8649.2.a.bf.1.8		8
93.65	even	30		279.2.y.c.82.2		16
124.3	even	30		496.2.bg.c.113.1		16
124.11	even	30		496.2.bg.c.417.1		16
155.3	even	60		775.2.ck.a.299.1		32
155.34	odd	30		775.2.bl.a.51.2		16
155.42	even	60		775.2.ck.a.324.1		32
155.73	even	60		775.2.ck.a.324.4		32
155.104	odd	30		775.2.bl.a.76.2		16
155.127	even	60		775.2.ck.a.299.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	31.11	odd	30
31.2.g.a.20.1	yes	16	31.3	odd	30
279.2.y.c.82.2		16	93.65	even	30
279.2.y.c.262.2		16	93.11	even	30
496.2.bg.c.113.1		16	124.3	even	30
496.2.bg.c.417.1		16	124.11	even	30
775.2.bl.a.51.2		16	155.34	odd	30
775.2.bl.a.76.2		16	155.104	odd	30
775.2.ck.a.299.1		32	155.3	even	60
775.2.ck.a.299.4		32	155.127	even	60
775.2.ck.a.324.1		32	155.42	even	60
775.2.ck.a.324.4		32	155.73	even	60
961.2.a.i.1.1		8	31.23	odd	10
961.2.a.j.1.1		8	31.8	even	5
961.2.c.i.439.1		16	31.14	even	15
961.2.c.i.521.1		16	31.9	even	15
961.2.c.j.439.1		16	31.17	odd	30
961.2.c.j.521.1		16	31.22	odd	30
961.2.d.n.531.1		16	31.16	even	5
961.2.d.n.628.1		16	31.4	even	5
961.2.d.o.531.1		16	31.15	odd	10
961.2.d.o.628.1		16	31.27	odd	10
961.2.d.p.374.4		16	31.29	odd	10
961.2.d.p.388.4		16	31.30	odd	2
961.2.d.q.374.4		16	31.2	even	5	inner
961.2.d.q.388.4		16	1.1	even	1	trivial
961.2.g.j.844.1		16	31.18	even	15
961.2.g.j.846.1		16	31.7	even	15
961.2.g.k.844.1		16	31.13	odd	30
961.2.g.k.846.1		16	31.24	odd	30
961.2.g.l.448.1		16	31.20	even	15
961.2.g.l.547.1		16	31.28	even	15
961.2.g.m.235.2		16	31.25	even	3
961.2.g.m.732.2		16	31.10	even	15
961.2.g.n.338.2		16	31.5	even	3
961.2.g.n.816.2		16	31.19	even	15
961.2.g.s.235.2		16	31.6	odd	6
961.2.g.s.732.2		16	31.21	odd	30
961.2.g.t.338.2		16	31.26	odd	6
961.2.g.t.816.2		16	31.12	odd	30
8649.2.a.be.1.8		8	93.8	odd	10
8649.2.a.bf.1.8		8	93.23	even	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 $\F_{q}$

Introduction

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Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	961.2.d.q.388.4

Level	$961$
Weight	$2$
Character	961.388
Analytic conductor	$7.674$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$