LMFDB - Embedded newform 363.3.h.n.251.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,3,Mod(245,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.245"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.h (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,5,18,0,-32,34] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} - 12x^{14} + 180x^{12} - 2562x^{10} + 25179x^{8} - 96398x^{6} + 239275x^{4} - 536393x^{2} + 1771561 $ x^16 - 12x^14 + 180x^12 - 2562x^10 + 25179x^8 - 96398x^6 + 239275x^4 - 536393*x^2 + 1771561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			251.2
Root			$0.974642 - 1.34148i$ of defining polynomial
Character	$\chi$	$=$	363.251
Dual form			363.3.h.n.269.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.57700 - 0.512399i) q^{2} +(-0.753215 + 2.90391i) q^{3} +(-1.01168 - 0.735029i) q^{4} +(-0.664316 + 0.215849i) q^{5} +(2.67578 - 4.19352i) q^{6} +(2.11081 + 1.53360i) q^{7} +(5.11736 + 7.04345i) q^{8} +(-7.86534 - 4.37453i) q^{9} +1.15823 q^{10} +(2.89647 - 2.38419i) q^{12} +(-5.28943 + 16.2792i) q^{13} +(-2.54295 - 3.50007i) q^{14} +(-0.126434 - 2.09169i) q^{15} +(-2.91533 - 8.97246i) q^{16} +(15.3239 - 4.97905i) q^{17} +(10.1622 + 10.9288i) q^{18} +(-12.8847 + 9.36127i) q^{19} +(0.830732 + 0.269921i) q^{20} +(-6.04332 + 4.97448i) q^{21} -23.1295i q^{23} +(-24.3080 + 9.55511i) q^{24} +(-19.8307 + 14.4078i) q^{25} +(16.6829 - 22.9620i) q^{26} +(18.6275 - 19.5452i) q^{27} +(-1.00823 - 3.10302i) q^{28} +(-3.15401 + 4.34112i) q^{29} +(-0.872396 + 3.36339i) q^{30} +(-1.25541 + 3.86376i) q^{31} -19.1813i q^{32} -26.7172 q^{34} +(-1.73327 - 0.563175i) q^{35} +(4.74180 + 10.2069i) q^{36} +(-51.3978 - 37.3427i) q^{37} +(25.1159 - 8.16065i) q^{38} +(-43.2891 - 27.6217i) q^{39} +(-4.91987 - 3.57450i) q^{40} +(-39.6389 - 54.5583i) q^{41} +(12.0793 - 4.74818i) q^{42} +22.6622 q^{43} +(6.16931 + 1.20834i) q^{45} +(-11.8515 + 36.4752i) q^{46} +(-43.3908 - 59.7223i) q^{47} +(28.2511 - 1.70765i) q^{48} +(-13.0382 - 40.1275i) q^{49} +(38.6557 - 12.5600i) q^{50} +(2.91647 + 48.2496i) q^{51} +(17.3169 - 12.5815i) q^{52} +(40.7539 + 13.2417i) q^{53} +(-39.3906 + 21.2782i) q^{54} +22.7154i q^{56} +(-17.4793 - 44.4670i) q^{57} +(7.19827 - 5.22985i) q^{58} +(-16.8918 + 23.2496i) q^{59} +(-1.40955 + 2.20906i) q^{60} +(14.3079 + 44.0351i) q^{61} +(3.95957 - 5.44989i) q^{62} +(-9.89350 - 21.2961i) q^{63} +(-21.4898 + 66.1388i) q^{64} -11.9562i q^{65} -77.2821 q^{67} +(-19.1627 - 6.22634i) q^{68} +(67.1657 + 17.4214i) q^{69} +(2.44481 + 1.77626i) q^{70} +(-39.2433 + 12.7509i) q^{71} +(-9.43802 - 77.7851i) q^{72} +(-45.9302 - 33.3703i) q^{73} +(61.9201 + 85.2257i) q^{74} +(-26.9023 - 68.4387i) q^{75} +19.9160 q^{76} +(54.1137 + 65.7409i) q^{78} +(15.7368 - 48.4329i) q^{79} +(3.87340 + 5.33128i) q^{80} +(42.7270 + 68.8143i) q^{81} +(34.5551 + 106.350i) q^{82} +(-56.3118 + 18.2968i) q^{83} +(9.77030 - 0.590571i) q^{84} +(-9.10522 + 6.61533i) q^{85} +(-35.7384 - 11.6121i) q^{86} +(-10.2306 - 12.4287i) q^{87} +38.1909i q^{89} +(-9.10987 - 5.06671i) q^{90} +(-36.1307 + 26.2505i) q^{91} +(-17.0008 + 23.3996i) q^{92} +(-10.2744 - 6.55583i) q^{93} +(37.8258 + 116.416i) q^{94} +(6.53888 - 9.00000i) q^{95} +(55.7007 + 14.4476i) q^{96} +(5.03463 - 15.4950i) q^{97} +69.9620i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{3} + 18 q^{4} - 32 q^{6} + 34 q^{7} + 17 q^{9} + 12 q^{10} + 106 q^{12} + 2 q^{13} - 28 q^{15} + 102 q^{16} - 42 q^{18} - 66 q^{19} + 12 q^{21} + 74 q^{24} - 176 q^{25} - 55 q^{27} + 146 q^{28}+ \cdots + 252 q^{97}+O(q^{100}) $ 16 * q + 5 * q^3 + 18 * q^4 - 32 * q^6 + 34 * q^7 + 17 * q^9 + 12 * q^10 + 106 * q^12 + 2 * q^13 - 28 * q^15 + 102 * q^16 - 42 * q^18 - 66 * q^19 + 12 * q^21 + 74 * q^24 - 176 * q^25 - 55 * q^27 + 146 * q^28 - 110 * q^30 - 126 * q^31 - 132 * q^34 + 226 * q^36 - 230 * q^37 - 136 * q^39 - 226 * q^40 - 72 * q^42 + 156 * q^43 - 72 * q^45 - 308 * q^46 + 255 * q^48 + 170 * q^49 + 169 * q^51 + 224 * q^52 - 1046 * q^54 + 259 * q^57 + 184 * q^58 - 316 * q^60 - 104 * q^61 + 108 * q^63 - 184 * q^64 + 368 * q^67 - 22 * q^69 - 52 * q^70 - 73 * q^72 - 354 * q^73 + 54 * q^75 + 900 * q^76 - 492 * q^78 - 566 * q^79 + 377 * q^81 + 200 * q^82 + 720 * q^84 + 162 * q^85 - 132 * q^87 + 774 * q^90 - 226 * q^91 - 370 * q^93 + 530 * q^94 + 67 * q^96 + 252 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.57700	−	0.512399i	−0.788502	−	0.256200i	−0.113036	−	0.993591i	$-0.536057\pi$
$2$	−1.57700	−	0.512399i	−0.788502	−	0.256200i	−0.675466	+	0.737391i	$0.736057\pi$
$3$	−0.753215	+	2.90391i	−0.251072	+	0.967969i
$3$	−0.753215	+	2.90391i	−0.251072	+	0.967969i
$4$	−1.01168	−	0.735029i	−0.252920	−	0.183757i
$5$	−0.664316	+	0.215849i	−0.132863	+	0.0431699i	−0.374694	−	0.927149i	$-0.622252\pi$
$5$	−0.664316	+	0.215849i	−0.132863	+	0.0431699i	0.241831	+	0.970318i	$0.422252\pi$
$6$	2.67578	−	4.19352i	0.445964	−	0.698920i
$7$	2.11081	+	1.53360i	0.301545	+	0.219085i	0.728260	−	0.685301i	$-0.240329\pi$
$7$	2.11081	+	1.53360i	0.301545	+	0.219085i	−0.426715	+	0.904386i	$0.640329\pi$
$8$	5.11736	+	7.04345i	0.639670	+	0.880431i
$9$	−7.86534	−	4.37453i	−0.873926	−	0.486059i
$10$	1.15823			0.115823
$11$		0			0
$11$		0			0
$12$	2.89647	−	2.38419i	0.241372	−	0.198683i
$13$	−5.28943	+	16.2792i	−0.406879	+	1.25224i	0.512437	+	0.858725i	$0.328743\pi$
$13$	−5.28943	+	16.2792i	−0.406879	+	1.25224i	−0.919316	+	0.393520i	$0.871257\pi$
$14$	−2.54295	−	3.50007i	−0.181639	−	0.250005i
$15$	−0.126434	−	2.09169i	−0.00842891	−	0.139446i
$16$	−2.91533	−	8.97246i	−0.182208	−	0.560779i
$17$	15.3239	−	4.97905i	0.901408	−	0.292885i	0.178590	−	0.983924i	$-0.442846\pi$
$17$	15.3239	−	4.97905i	0.901408	−	0.292885i	0.722818	+	0.691038i	$0.242846\pi$
$18$	10.1622	+	10.9288i	0.564564	+	0.607158i
$19$	−12.8847	+	9.36127i	−0.678141	+	0.492698i	−0.872741	−	0.488184i	$-0.837659\pi$
$19$	−12.8847	+	9.36127i	−0.678141	+	0.492698i	0.194599	+	0.980883i	$0.437659\pi$
$20$	0.830732	+	0.269921i	0.0415366	+	0.0134961i
$21$	−6.04332	+	4.97448i	−0.287777	+	0.236880i
$22$		0			0
$23$		−	23.1295i		−	1.00563i	−0.864395	−	0.502814i	$-0.832298\pi$
$23$		−	23.1295i		−	1.00563i	0.864395	−	0.502814i	$-0.167702\pi$
$24$	−24.3080	+	9.55511i	−1.01283	+	0.398130i
$25$	−19.8307	+	14.4078i	−0.793228	+	0.576314i
$26$	16.6829	−	22.9620i	0.641649	−	0.883155i
$27$	18.6275	−	19.5452i	0.689908	−	0.723897i
$28$	−1.00823	−	3.10302i	−0.0360083	−	0.110822i
$29$	−3.15401	+	4.34112i	−0.108759	+	0.149694i	−0.859927	−	0.510418i	$-0.829491\pi$
$29$	−3.15401	+	4.34112i	−0.108759	+	0.149694i	0.751168	+	0.660111i	$0.229491\pi$
$30$	−0.872396	+	3.36339i	−0.0290799	+	0.112113i
$31$	−1.25541	+	3.86376i	−0.0404971	+	0.124637i	−0.969261	−	0.246034i	$-0.920872\pi$
$31$	−1.25541	+	3.86376i	−0.0404971	+	0.124637i	0.928764	+	0.370672i	$0.120872\pi$
$32$		−	19.1813i		−	0.599415i
$33$		0			0
$34$	−26.7172			−0.785799
$35$	−1.73327	−	0.563175i	−0.0495221	−	0.0160907i
$36$	4.74180	+	10.2069i	0.131717	+	0.283524i
$37$	−51.3978	−	37.3427i	−1.38913	−	1.00926i	−0.995960	−	0.0897955i	$-0.971379\pi$
$37$	−51.3978	−	37.3427i	−1.38913	−	1.00926i	−0.393169	−	0.919466i	$-0.628621\pi$
$38$	25.1159	−	8.16065i	0.660945	−	0.214754i
$39$	−43.2891	−	27.6217i	−1.10998	−	0.708249i
$40$	−4.91987	−	3.57450i	−0.122997	−	0.0893624i
$41$	−39.6389	−	54.5583i	−0.966803	−	1.33069i	−0.943645	−	0.330958i	$-0.892628\pi$
$41$	−39.6389	−	54.5583i	−0.966803	−	1.33069i	−0.0231574	−	0.999732i	$-0.507372\pi$
$42$	12.0793	−	4.74818i	0.287601	−	0.113052i
$43$	22.6622			0.527028			0.263514	−	0.964656i	$-0.415118\pi$
$43$	22.6622			0.527028			0.263514	+	0.964656i	$0.415118\pi$
$44$		0			0
$45$	6.16931	+	1.20834i	0.137096	+	0.0268521i
$46$	−11.8515	+	36.4752i	−0.257642	+	0.792940i
$47$	−43.3908	−	59.7223i	−0.923209	−	1.27069i	−0.962450	−	0.271458i	$-0.912494\pi$
$47$	−43.3908	−	59.7223i	−0.923209	−	1.27069i	0.0392417	−	0.999230i	$-0.487506\pi$
$48$	28.2511	−	1.70765i	0.588564	−	0.0355761i
$49$	−13.0382	−	40.1275i	−0.266086	−	0.818928i
$50$	38.6557	−	12.5600i	0.773113	−	0.251200i
$51$	2.91647	+	48.2496i	0.0571858	+	0.946070i
$52$	17.3169	−	12.5815i	0.333017	−	0.241951i
$53$	40.7539	+	13.2417i	0.768941	+	0.249844i	0.667112	−	0.744958i	$-0.267530\pi$
$53$	40.7539	+	13.2417i	0.768941	+	0.249844i	0.101830	+	0.994802i	$0.467530\pi$
$54$	−39.3906	+	21.2782i	−0.729456	+	0.394040i
$55$		0			0
$56$			22.7154i			0.405632i
$57$	−17.4793	−	44.4670i	−0.306655	−	0.780122i
$58$	7.19827	−	5.22985i	0.124108	−	0.0901698i
$59$	−16.8918	+	23.2496i	−0.286302	+	0.394061i	−0.927809	−	0.373056i	$-0.878310\pi$
$59$	−16.8918	+	23.2496i	−0.286302	+	0.394061i	0.641506	+	0.767118i	$0.278310\pi$
$60$	−1.40955	+	2.20906i	−0.0234924	+	0.0368176i
$61$	14.3079	+	44.0351i	0.234555	+	0.721888i	0.997180	+	0.0750462i	$0.0239104\pi$
$61$	14.3079	+	44.0351i	0.234555	+	0.721888i	−0.762625	+	0.646841i	$0.776090\pi$
$62$	3.95957	−	5.44989i	0.0638641	−	0.0879014i
$63$	−9.89350	−	21.2961i	−0.157040	−	0.338033i
$64$	−21.4898	+	66.1388i	−0.335778	+	1.03342i
$65$		−	11.9562i		−	0.183942i
$66$		0			0
$67$	−77.2821			−1.15346			−0.576732	−	0.816933i	$-0.695672\pi$
$67$	−77.2821			−1.15346			−0.576732	+	0.816933i	$0.695672\pi$
$68$	−19.1627	−	6.22634i	−0.281804	−	0.0915638i
$69$	67.1657	+	17.4214i	0.973417	+	0.252485i
$70$	2.44481	+	1.77626i	0.0349258	+	0.0253751i
$71$	−39.2433	+	12.7509i	−0.552723	+	0.179591i	−0.572044	−	0.820223i	$-0.693849\pi$
$71$	−39.2433	+	12.7509i	−0.552723	+	0.179591i	0.0193214	+	0.999813i	$0.493849\pi$
$72$	−9.43802	−	77.7851i	−0.131084	−	1.08035i
$73$	−45.9302	−	33.3703i	−0.629181	−	0.457127i	0.226935	−	0.973910i	$-0.427129\pi$
$73$	−45.9302	−	33.3703i	−0.629181	−	0.457127i	−0.856117	+	0.516783i	$0.827129\pi$
$74$	61.9201	+	85.2257i	0.836758	+	1.15170i
$75$	−26.9023	−	68.4387i	−0.358697	−	0.912516i
$76$	19.9160			0.262053
$77$		0			0
$78$	54.1137	+	65.7409i	0.693766	+	0.842831i
$79$	15.7368	−	48.4329i	0.199200	−	0.613074i	−0.800702	−	0.599063i	$-0.795540\pi$
$79$	15.7368	−	48.4329i	0.199200	−	0.613074i	0.999902	−	0.0140112i	$-0.00446005\pi$
$80$	3.87340	+	5.33128i	0.0484175	+	0.0666410i
$81$	42.7270	+	68.8143i	0.527494	+	0.849559i
$82$	34.5551	+	106.350i	0.421403	+	1.29695i
$83$	−56.3118	+	18.2968i	−0.678456	+	0.220444i	−0.627919	−	0.778279i	$-0.716093\pi$
$83$	−56.3118	+	18.2968i	−0.678456	+	0.220444i	−0.0505367	+	0.998722i	$0.516093\pi$
$84$	9.77030	−	0.590571i	0.116313	−	0.00703061i
$85$	−9.10522	+	6.61533i	−0.107120	+	0.0778274i
$86$	−35.7384	−	11.6121i	−0.415563	−	0.135024i
$87$	−10.2306	−	12.4287i	−0.117593	−	0.142859i
$88$		0			0
$89$			38.1909i			0.429112i	0.976712	+	0.214556i	$0.0688304\pi$
$89$			38.1909i			0.429112i	−0.976712	+	0.214556i	$0.931170\pi$
$90$	−9.10987	−	5.06671i	−0.101221	−	0.0562968i
$91$	−36.1307	+	26.2505i	−0.397041	+	0.288467i
$92$	−17.0008	+	23.3996i	−0.184792	+	0.254344i
$93$	−10.2744	−	6.55583i	−0.110477	−	0.0704928i
$94$	37.8258	+	116.416i	0.402402	+	1.23847i
$95$	6.53888	−	9.00000i	0.0688303	−	0.0947368i
$96$	55.7007	+	14.4476i	0.580215	+	0.150496i
$97$	5.03463	−	15.4950i	0.0519034	−	0.159742i	−0.921745	−	0.387796i	$-0.873236\pi$
$97$	5.03463	−	15.4950i	0.0519034	−	0.159742i	0.973648	+	0.228054i	$0.0732363\pi$
$98$			69.9620i			0.713898i
$99$		0			0
$100$	30.6525			0.306525
$101$	99.0948	+	32.1979i	0.981137	+	0.318791i	0.755303	−	0.655375i	$-0.227490\pi$
$101$	99.0948	+	32.1979i	0.981137	+	0.318791i	0.225833	+	0.974166i	$0.427490\pi$
$102$	20.1238	−	77.5842i	0.197292	−	0.760629i
$103$	−44.0158	−	31.9793i	−0.427338	−	0.310479i	0.353246	−	0.935531i	$-0.385078\pi$
$103$	−44.0158	−	31.9793i	−0.427338	−	0.310479i	−0.780584	+	0.625052i	$0.785078\pi$
$104$	−141.729	+	46.0507i	−1.36278	+	0.442795i
$105$	2.94093	−	4.60907i	0.0280089	−	0.0438959i
$106$	−57.4840	−	41.7645i	−0.542301	−	0.394005i
$107$	−16.6971	−	22.9816i	−0.156048	−	0.214781i	0.723834	−	0.689974i	$-0.242378\pi$
$107$	−16.6971	−	22.9816i	−0.156048	−	0.214781i	−0.879881	+	0.475193i	$0.842378\pi$
$108$	−33.2114	+	6.08178i	−0.307513	+	0.0563128i
$109$	41.2540			0.378477			0.189238	−	0.981931i	$-0.439398\pi$
$109$	41.2540			0.378477			0.189238	+	0.981931i	$0.439398\pi$
$110$		0			0
$111$	147.153	−	121.127i	1.32570	−	1.09124i
$112$	7.60642	−	23.4101i	0.0679144	−	0.209019i
$113$	85.3335	+	117.451i	0.755164	+	1.03939i	0.997601	+	0.0692265i	$0.0220531\pi$
$113$	85.3335	+	117.451i	0.755164	+	1.03939i	−0.242437	+	0.970167i	$0.577947\pi$
$114$	4.78009	+	79.0809i	0.0419306	+	0.693692i
$115$	4.99248	+	15.3653i	0.0434129	+	0.133611i
$116$	6.38170	−	2.07354i	0.0550146	−	0.0178753i
$117$	112.817	−	104.902i	0.964246	−	0.896602i
$118$	38.5516	−	28.0094i	0.326708	−	0.237367i
$119$	39.9819	+	12.9909i	0.335982	+	0.109167i
$120$	14.0857	−	11.5945i	0.117381	−	0.0966207i
$121$		0			0
$122$		−	76.7749i		−	0.629303i
$123$	188.289	−	74.0136i	1.53080	−	0.601736i
$124$	4.11005	−	2.98613i	0.0331456	−	0.0240817i
$125$	20.3282	−	27.9793i	0.162625	−	0.223835i
$126$	4.68999	+	38.6534i	0.0372222	+	0.306773i
$127$	56.4826	+	173.835i	0.444745	+	1.36878i	0.882763	+	0.469818i	$0.155680\pi$
$127$	56.4826	+	173.835i	0.444745	+	1.36878i	−0.438019	+	0.898966i	$0.644320\pi$
$128$	22.6811	−	31.2178i	0.177196	−	0.243889i
$129$	−17.0695	+	65.8089i	−0.132322	+	0.510147i
$130$	−6.12637	+	18.8550i	−0.0471259	+	0.145039i
$131$		−	84.5109i		−	0.645121i	−0.946549	−	0.322561i	$-0.895456\pi$
$131$		−	84.5109i		−	0.645121i	0.946549	−	0.322561i	$-0.104544\pi$
$132$		0			0
$133$	−41.5536			−0.312433
$134$	121.874	+	39.5993i	0.909508	+	0.295517i
$135$	−8.15573	+	17.0050i	−0.0604128	+	0.125963i
$136$	113.488	+	82.4538i	0.834470	+	0.606278i
$137$	194.370	−	63.1546i	1.41876	−	0.460982i	0.503551	−	0.863966i	$-0.332027\pi$
$137$	194.370	−	63.1546i	1.41876	−	0.460982i	0.915207	+	0.402983i	$0.132027\pi$
$138$	−96.9939	−	61.8894i	−0.702854	−	0.448474i
$139$	−40.6461	−	29.5311i	−0.292418	−	0.212454i	0.431898	−	0.901923i	$-0.357844\pi$
$139$	−40.6461	−	29.5311i	−0.292418	−	0.212454i	−0.724316	+	0.689468i	$0.757844\pi$
$140$	1.33957	+	1.84376i	0.00956836	+	0.0131697i
$141$	206.111	−	81.0191i	1.46178	−	0.574603i
$142$	68.4204			0.481834
$143$		0			0
$144$	−16.3203	+	83.3246i	−0.113335	+	0.578643i
$145$	1.15823	−	3.56467i	0.00798779	−	0.0245839i
$146$	55.3332	+	76.1597i	0.378995	+	0.521642i
$147$	126.347	−	7.63712i	0.859504	−	0.0519532i
$148$	24.5502	+	75.5578i	0.165880	+	0.510526i
$149$	−149.698	+	48.6400i	−1.00469	+	0.326443i	−0.764737	−	0.644343i	$-0.777131\pi$
$149$	−149.698	+	48.6400i	−1.00469	+	0.326443i	−0.239950	+	0.970785i	$0.577131\pi$
$150$	7.35700	+	121.713i	0.0490467	+	0.811418i
$151$	−138.650	+	100.735i	−0.918215	+	0.667122i	−0.943079	−	0.332569i	$-0.892085\pi$
$151$	−138.650	+	100.735i	−0.918215	+	0.667122i	0.0248642	+	0.999691i	$0.492085\pi$
$152$	−131.871	−	42.8476i	−0.867574	−	0.281892i
$153$	−142.309	−	27.8731i	−0.930124	−	0.182177i
$154$		0			0
$155$		−	2.83774i		−	0.0183080i
$156$	23.4920	+	59.7631i	0.150590	+	0.383097i
$157$	52.8595	−	38.4047i	0.336685	−	0.244616i	−0.406577	−	0.913617i	$-0.633278\pi$
$157$	52.8595	−	38.4047i	0.336685	−	0.244616i	0.743262	+	0.669001i	$0.233278\pi$
$158$	−49.6339	+	68.3153i	−0.314139	+	0.432375i
$159$	−69.1492	+	108.372i	−0.434901	+	0.681582i
$160$	4.14027	+	12.7424i	0.0258767	+	0.0796403i
$161$	35.4712	−	48.8220i	0.220318	−	0.303242i
$162$	−32.1202	−	130.414i	−0.198273	−	0.805022i
$163$	−4.77074	+	14.6828i	−0.0292684	+	0.0900787i	−0.964624	−	0.263631i	$-0.915080\pi$
$163$	−4.77074	+	14.6828i	−0.0292684	+	0.0900787i	0.935355	+	0.353710i	$0.115080\pi$
$164$			84.3314i			0.514216i
$165$		0			0
$166$	98.1792			0.591441
$167$	−146.561	−	47.6206i	−0.877612	−	0.285154i	−0.164647	−	0.986353i	$-0.552648\pi$
$167$	−146.561	−	47.6206i	−0.877612	−	0.285154i	−0.712966	+	0.701199i	$0.752648\pi$
$168$	−65.9633	−	17.1096i	−0.392639	−	0.101843i
$169$	−100.310	−	72.8793i	−0.593549	−	0.431238i
$170$	17.7487	−	5.76689i	0.104404	−	0.0339229i
$171$	142.294	−	17.2651i	0.832126	−	0.100966i
$172$	−22.9269	−	16.6574i	−0.133296	−	0.0968453i
$173$	−14.7552	−	20.3087i	−0.0852900	−	0.117392i	0.764240	−	0.644932i	$-0.223114\pi$
$173$	−14.7552	−	20.3087i	−0.0852900	−	0.117392i	−0.849530	+	0.527540i	$0.823114\pi$
$174$	9.76514	+	24.8423i	0.0561215	+	0.142772i
$175$	−63.9548			−0.365456
$176$		0			0
$177$	−54.7915	−	66.5642i	−0.309556	−	0.376069i
$178$	19.5690	−	60.2272i	0.109938	−	0.338355i
$179$	−36.3280	−	50.0013i	−0.202950	−	0.279337i	0.695395	−	0.718628i	$-0.255230\pi$
$179$	−36.3280	−	50.0013i	−0.202950	−	0.279337i	−0.898345	+	0.439291i	$0.855230\pi$
$180$	−5.35321	−	5.75708i	−0.0297400	−	0.0319838i
$181$	−45.8596	−	141.141i	−0.253368	−	0.779786i	−0.994147	−	0.108037i	$-0.965544\pi$
$181$	−45.8596	−	141.141i	−0.253368	−	0.779786i	0.740779	−	0.671749i	$-0.234456\pi$
$182$	70.4290	−	22.8838i	0.386972	−	0.125735i
$183$	−138.651	+	8.38083i	−0.757655	+	0.0457969i
$184$	162.911	−	118.362i	0.885386	−	0.643271i
$185$	42.2048	+	13.7132i	0.228134	+	0.0741252i
$186$	12.8435	+	15.6032i	0.0690513	+	0.0838880i
$187$		0			0
$188$			92.3135i			0.491029i
$189$	69.2937	−	12.6893i	0.366633	−	0.0671391i
$190$	−14.9234	+	10.8425i	−0.0785444	+	0.0570658i
$191$	−33.0352	+	45.4691i	−0.172959	+	0.238058i	−0.886692	−	0.462360i	$-0.847003\pi$
$191$	−33.0352	+	45.4691i	−0.172959	+	0.238058i	0.713733	+	0.700418i	$0.247003\pi$
$192$	−175.874	−	112.221i	−0.916013	−	0.584485i
$193$	−46.6529	−	143.583i	−0.241725	−	0.743953i	−0.996158	−	0.0875759i	$-0.972088\pi$
$193$	−46.6529	−	143.583i	−0.241725	−	0.743953i	0.754433	−	0.656377i	$-0.227912\pi$
$194$	−15.8793	+	21.8559i	−0.0818519	+	0.112659i
$195$	34.7198	+	9.00562i	0.178050	+	0.0461827i
$196$	−16.3044	+	50.1797i	−0.0831856	+	0.256019i
$197$			22.3374i			0.113388i	0.998392	+	0.0566938i	$0.0180559\pi$
$197$			22.3374i			0.113388i	−0.998392	+	0.0566938i	$0.981944\pi$
$198$		0			0
$199$	−150.930			−0.758444			−0.379222	−	0.925306i	$-0.623808\pi$
$199$	−150.930			−0.758444			−0.379222	+	0.925306i	$0.623808\pi$
$200$	−202.962	−	65.9463i	−1.01481	−	0.329731i
$201$	58.2100	−	224.420i	0.289602	−	1.11652i
$202$	−139.775	−	101.552i	−0.691954	−	0.502734i
$203$	−13.3150	+	4.32632i	−0.0655914	+	0.0213119i
$204$	32.5143	−	50.9569i	0.159384	−	0.249789i
$205$	38.1092	+	27.6879i	0.185898	+	0.135063i
$206$	53.0269	+	72.9852i	0.257412	+	0.354297i
$207$	−101.180	+	181.921i	−0.488794	+	0.878845i
$208$	161.485			0.776369
$209$		0			0
$210$	−6.99955	+	5.76159i	−0.0333312	+	0.0274362i
$211$	−56.1107	+	172.691i	−0.265927	+	0.818440i	0.725551	+	0.688168i	$0.241585\pi$
$211$	−56.1107	+	172.691i	−0.265927	+	0.818440i	−0.991478	+	0.130272i	$0.958415\pi$
$212$	−31.4969	−	43.3517i	−0.148570	−	0.204489i
$213$	−7.46884	−	123.563i	−0.0350650	−	0.580108i
$214$	14.5556	+	44.7976i	0.0680169	+	0.209335i
$215$	−15.0549	+	4.89162i	−0.0700227	+	0.0227517i
$216$	232.989	+	31.1818i	1.07866	+	0.144360i
$217$	−8.57538	+	6.23038i	−0.0395179	+	0.0287114i
$218$	−65.0577	−	21.1385i	−0.298430	−	0.0969657i
$219$	131.499	−	108.242i	0.600454	−	0.494256i
$220$		0			0
$221$			275.798i			1.24795i
$222$	−294.127	+	115.617i	−1.32489	+	0.520797i
$223$	−152.123	+	110.524i	−0.682166	+	0.495623i	−0.874076	−	0.485790i	$-0.838532\pi$
$223$	−152.123	+	110.524i	−0.682166	+	0.495623i	0.191909	+	0.981413i	$0.438532\pi$
$224$	29.4164	−	40.4882i	0.131323	−	0.180751i
$225$	219.003	−	26.5726i	0.973345	−	0.118100i
$226$	−74.3891	−	228.946i	−0.329155	−	1.01304i
$227$	−252.293	+	347.252i	−1.11142	+	1.52974i	−0.292122	+	0.956381i	$0.594361\pi$
$227$	−252.293	+	347.252i	−1.11142	+	1.52974i	−0.819302	+	0.573362i	$0.805639\pi$
$228$	−15.0010	+	57.8342i	−0.0657940	+	0.253659i
$229$	41.9569	−	129.130i	0.183218	−	0.563887i	−0.816695	−	0.577069i	$-0.804196\pi$
$229$	41.9569	−	129.130i	0.183218	−	0.563887i	0.999913	+	0.0131824i	$0.00419621\pi$
$230$		−	26.7892i		−	0.116475i
$231$		0			0
$232$	−46.7166			−0.201365
$233$	−310.890	−	101.014i	−1.33429	−	0.433538i	−0.446913	−	0.894577i	$-0.647477\pi$
$233$	−310.890	−	101.014i	−1.33429	−	0.433538i	−0.887380	+	0.461039i	$0.847477\pi$
$234$	−231.665	+	107.624i	−0.990019	+	0.459933i
$235$	41.7162	+	30.3086i	0.177516	+	0.128973i
$236$	34.1783	−	11.1052i	0.144823	−	0.0470559i
$237$	128.791	+	82.1785i	0.543423	+	0.346745i
$238$	−56.3950	−	40.9734i	−0.236954	−	0.172157i
$239$	−54.9303	−	75.6050i	−0.229834	−	0.316339i	0.678488	−	0.734612i	$-0.262636\pi$
$239$	−54.9303	−	75.6050i	−0.229834	−	0.316339i	−0.908322	+	0.418273i	$0.862636\pi$
$240$	−18.3990	+	7.23240i	−0.0766627	+	0.0301350i
$241$	−206.766			−0.857952			−0.428976	−	0.903316i	$-0.641125\pi$
$241$	−206.766			−0.857952			−0.428976	+	0.903316i	$0.641125\pi$
$242$		0			0
$243$	−232.013	+	72.2432i	−0.954785	+	0.297297i
$244$	17.8921	−	55.0662i	0.0733283	−	0.225681i
$245$	17.3230	+	23.8431i	0.0707061	+	0.0973186i
$246$	−334.857	+	20.2406i	−1.36121	+	0.0822789i
$247$	−84.2412	−	259.268i	−0.341058	−	1.04967i
$248$	−33.6386	+	10.9298i	−0.135639	+	0.0440719i
$249$	−10.7173	−	177.306i	−0.0430416	−	0.712071i
$250$	−46.3942	+	33.7074i	−0.185577	+	0.134829i
$251$	2.65372	+	0.862246i	0.0105726	+	0.00343524i	0.314299	−	0.949324i	$-0.398231\pi$
$251$	2.65372	+	0.862246i	0.0105726	+	0.00343524i	−0.303726	+	0.952759i	$0.598231\pi$
$252$	−5.64417	+	28.8168i	−0.0223975	+	0.114353i
$253$		0			0
$254$		−	303.081i		−	1.19323i
$255$	−12.3521	−	31.4235i	−0.0484396	−	0.123229i
$256$	173.280	−	125.895i	0.676875	−	0.491779i
$257$	235.235	−	323.774i	0.915313	−	1.25982i	−0.0500071	−	0.998749i	$-0.515924\pi$
$257$	235.235	−	323.774i	0.915313	−	1.25982i	0.965320	−	0.261071i	$-0.0840756\pi$
$258$	60.6391	−	95.0345i	0.235035	−	0.368351i
$259$	−51.2226	−	157.647i	−0.197771	−	0.608675i
$260$	−8.78819	+	12.0959i	−0.0338007	+	0.0465227i
$261$	43.7977	−	20.3471i	0.167807	−	0.0779581i
$262$	−43.3033	+	133.274i	−0.165280	+	0.508679i
$263$			379.212i			1.44187i	0.693003	+	0.720935i	$0.256287\pi$
$263$			379.212i			1.44187i	−0.693003	+	0.720935i	$0.743713\pi$
$264$		0			0
$265$	−29.9317			−0.112950
$266$	65.5302	+	21.2920i	0.246354	+	0.0800453i
$267$	−110.903	−	28.7660i	−0.415366	−	0.107738i
$268$	78.1848	+	56.8046i	0.291734	+	0.211957i
$269$	−29.6737	+	9.64156i	−0.110311	+	0.0358422i	−0.363652	−	0.931535i	$-0.618470\pi$
$269$	−29.6737	+	9.64156i	−0.110311	+	0.0358422i	0.253341	+	0.967377i	$0.418470\pi$
$270$	21.5749	−	22.6379i	0.0799072	−	0.0838440i
$271$	419.157	+	304.535i	1.54670	+	1.12375i	0.945950	+	0.324312i	$0.105133\pi$
$271$	419.157	+	304.535i	1.54670	+	1.12375i	0.600754	+	0.799434i	$0.294867\pi$
$272$	−89.3487	−	122.978i	−0.328488	−	0.452125i
$273$	−49.0148	−	124.692i	−0.179541	−	0.456749i
$274$	−338.882			−1.23680
$275$		0			0
$276$	−55.1450	−	66.9937i	−0.199801	−	0.242731i
$277$	−113.705	+	349.949i	−0.410488	+	1.26335i	0.505737	+	0.862688i	$0.331221\pi$
$277$	−113.705	+	349.949i	−0.410488	+	1.26335i	−0.916225	+	0.400664i	$0.868779\pi$
$278$	48.9673	+	67.3977i	0.176141	+	0.242438i
$279$	26.7763	−	24.8979i	0.0959726	−	0.0892398i
$280$	−4.90310	−	15.0902i	−0.0175111	−	0.0538936i
$281$	304.711	−	99.0066i	1.08438	−	0.352337i	0.288308	−	0.957538i	$-0.406907\pi$
$281$	304.711	−	99.0066i	1.08438	−	0.352337i	0.796073	+	0.605201i	$0.206907\pi$
$282$	−366.551	+	22.1564i	−1.29983	+	0.0785688i
$283$	−130.086	+	94.5128i	−0.459667	+	0.333968i	−0.793401	−	0.608700i	$-0.791691\pi$
$283$	−130.086	+	94.5128i	−0.459667	+	0.333968i	0.333734	+	0.942667i	$0.391691\pi$
$284$	49.0740	+	15.9451i	0.172796	+	0.0561448i
$285$	21.2100	+	25.7672i	0.0744209	+	0.0904113i
$286$		0			0
$287$		−	175.953i		−	0.613075i
$288$	−83.9091	+	150.867i	−0.291351	+	0.523845i
$289$	−23.7736	+	17.2725i	−0.0822616	+	0.0597665i
$290$	−3.65307	+	5.02801i	−0.0125968	+	0.0173380i
$291$	41.2039	+	26.2912i	0.141594	+	0.0903476i
$292$	21.9386	+	67.5202i	0.0751323	+	0.231233i
$293$	171.011	−	235.377i	0.583657	−	0.803335i	−0.410434	−	0.911891i	$-0.634623\pi$
$293$	171.011	−	235.377i	0.583657	−	0.803335i	0.994090	+	0.108556i	$0.0346226\pi$
$294$	−203.163	−	52.6964i	−0.691030	−	0.179239i
$295$	6.20310	−	19.0912i	0.0210275	−	0.0647159i
$296$		−	553.114i		−	1.86863i
$297$		0			0
$298$	260.998			0.875832
$299$	376.528	+	122.342i	1.25929	+	0.409169i
$300$	−23.0879	+	89.0121i	−0.0769598	+	0.296707i
$301$	47.8357	+	34.7547i	0.158923	+	0.115464i
$302$	270.269	−	87.8157i	0.894931	−	0.290781i
$303$	−168.139	+	263.510i	−0.554915	+	0.869670i
$304$	121.557	+	88.3162i	0.399858	+	0.290514i
$305$	−19.0099	−	26.1649i	−0.0623276	−	0.0857866i
$306$	210.140	+	116.875i	0.686731	+	0.381945i
$307$	281.800			0.917915			0.458957	−	0.888458i	$-0.348223\pi$
$307$	281.800			0.917915			0.458957	+	0.888458i	$0.348223\pi$
$308$		0			0
$309$	126.018	−	103.730i	0.407826	−	0.335697i
$310$	−1.45405	+	4.47512i	−0.00469050	+	0.0144359i
$311$	−278.465	−	383.274i	−0.895385	−	1.23239i	−0.971917	−	0.235325i	$-0.924385\pi$
$311$	−278.465	−	383.274i	−0.895385	−	1.23239i	0.0765316	−	0.997067i	$-0.475615\pi$
$312$	−26.9741	−	446.255i	−0.0864556	−	1.43030i
$313$	−9.26252	−	28.5071i	−0.0295927	−	0.0910771i	0.935169	−	0.354201i	$-0.115247\pi$
$313$	−9.26252	−	28.5071i	−0.0295927	−	0.0910771i	−0.964762	+	0.263124i	$0.915247\pi$
$314$	−103.038	+	33.4791i	−0.328147	+	0.106621i
$315$	11.1692	+	12.0118i	0.0354576	+	0.0381328i
$316$	−51.5202	+	37.4316i	−0.163039	+	0.118454i
$317$	151.481	+	49.2192i	0.477858	+	0.155266i	0.538036	−	0.842922i	$-0.319167\pi$
$317$	151.481	+	49.2192i	0.477858	+	0.155266i	−0.0601773	+	0.998188i	$0.519167\pi$
$318$	164.578	−	135.470i	0.517541	−	0.426007i
$319$		0			0
$320$		−	48.5757i		−	0.151799i
$321$	79.3128	−	31.1767i	0.247080	−	0.0971237i
$322$	−80.9546	+	58.8170i	−0.251412	+	0.182661i
$323$	−150.834	+	207.605i	−0.466978	+	0.642740i
$324$	7.35442	−	101.024i	0.0226988	−	0.311802i
$325$	−129.655	−	399.037i	−0.398938	−	1.22781i
$326$	15.0470	−	20.7104i	0.0461563	−	0.0635287i
$327$	−31.0731	+	119.798i	−0.0950248	+	0.366354i
$328$	181.432	−	558.389i	0.553145	−	1.70241i
$329$		−	192.607i		−	0.585431i
$330$		0			0
$331$	332.709			1.00516			0.502582	−	0.864530i	$-0.332384\pi$
$331$	332.709			1.00516			0.502582	+	0.864530i	$0.332384\pi$
$332$	70.4183	+	22.8803i	0.212103	+	0.0689166i
$333$	240.904	+	518.554i	0.723436	+	1.55722i
$334$	206.727	+	150.196i	0.618943	+	0.449688i
$335$	51.3397	−	16.6813i	0.153253	−	0.0497949i
$336$	62.2516	+	39.7212i	0.185273	+	0.118218i
$337$	44.8239	+	32.5664i	0.133008	+	0.0966363i	0.652300	−	0.757961i	$-0.273804\pi$
$337$	44.8239	+	32.5664i	0.133008	+	0.0966363i	−0.519292	+	0.854597i	$0.673804\pi$
$338$	120.846	+	166.330i	0.357531	+	0.492099i
$339$	−405.342	+	159.334i	−1.19570	+	0.470012i
$340$	14.0740			0.0413942
$341$		0			0
$342$	−233.244	−	45.6840i	−0.682000	−	0.133579i
$343$	73.5248	−	226.286i	0.214358	−	0.659727i
$344$	115.971	+	159.620i	0.337124	+	0.464012i
$345$	−48.3797	+	2.92434i	−0.140231	+	0.00847635i
$346$	12.8628	+	39.5875i	0.0371756	+	0.114415i
$347$	131.761	−	42.8117i	0.379714	−	0.123377i	−0.112940	−	0.993602i	$-0.536027\pi$
$347$	131.761	−	42.8117i	0.379714	−	0.123377i	0.492654	+	0.870225i	$0.336027\pi$
$348$	1.21457	+	20.0937i	0.00349016	+	0.0577404i
$349$	183.255	−	133.143i	0.525087	−	0.381498i	−0.293430	−	0.955981i	$-0.594797\pi$
$349$	183.255	−	133.143i	0.525087	−	0.381498i	0.818517	+	0.574482i	$0.194797\pi$
$350$	100.857	+	32.7704i	0.288162	+	0.0936297i
$351$	219.652	+	406.624i	0.625788	+	1.15847i
$352$		0			0
$353$		−	258.939i		−	0.733538i	−0.930312	−	0.366769i	$-0.880464\pi$
$353$		−	258.939i		−	0.733538i	0.930312	−	0.366769i	$-0.119536\pi$
$354$	52.2989	+	133.047i	0.147737	+	0.375839i
$355$	23.3177	−	16.9413i	0.0656836	−	0.0477220i
$356$	28.0715	−	38.6370i	0.0788524	−	0.108531i
$357$	−67.8393	+	106.319i	−0.190026	+	0.297811i
$358$	31.6688	+	97.4666i	0.0884604	+	0.272253i
$359$	152.258	−	209.565i	0.424116	−	0.583745i	−0.542474	−	0.840072i	$-0.682512\pi$
$359$	152.258	−	209.565i	0.424116	−	0.583745i	0.966590	+	0.256327i	$0.0825124\pi$
$360$	23.0597	+	49.6367i	0.0640547	+	0.137880i
$361$	−33.1734	+	102.097i	−0.0918932	+	0.282818i
$362$			246.079i			0.679775i
$363$		0			0
$364$	55.8476			0.153428
$365$	37.7152	+	12.2544i	0.103329	+	0.0335737i
$366$	222.947	+	57.8280i	0.609145	+	0.158000i
$367$	160.814	+	116.838i	0.438186	+	0.318361i	0.784914	−	0.619605i	$-0.212707\pi$
$367$	160.814	+	116.838i	0.438186	+	0.318361i	−0.346728	+	0.937966i	$0.612707\pi$
$368$	−207.528	+	67.4300i	−0.563935	+	0.183234i
$369$	73.1066	+	602.521i	0.198121	+	1.63285i
$370$	−59.5305	−	43.2514i	−0.160893	−	0.116896i
$371$	65.7164	+	90.4509i	0.177133	+	0.243803i
$372$	5.57568	+	14.1844i	0.0149884	+	0.0381301i
$373$	−670.467			−1.79750			−0.898750	−	0.438462i	$-0.855523\pi$
$373$	−670.467			−1.79750			−0.898750	+	0.438462i	$0.855523\pi$
$374$		0			0
$375$	65.9379	+	80.1056i	0.175834	+	0.213615i
$376$	198.604	−	611.242i	0.528203	−	1.62564i
$377$	−53.9870	−	74.3067i	−0.143201	−	0.197100i
$378$	−115.778	−	15.4950i	−0.306292	−	0.0409921i
$379$	121.255	+	373.186i	0.319935	+	0.984659i	0.973675	+	0.227940i	$0.0731990\pi$
$379$	121.255	+	373.186i	0.319935	+	0.984659i	−0.653740	+	0.756719i	$0.726801\pi$
$380$	−13.2305	+	4.29886i	−0.0348172	+	0.0113128i
$381$	−547.345	+	33.0846i	−1.43660	+	0.0868363i
$382$	75.3950	−	54.7777i	0.197369	−	0.143397i
$383$	−473.343	−	153.798i	−1.23588	−	0.401562i	−0.383040	−	0.923732i	$-0.625123\pi$
$383$	−473.343	−	153.798i	−1.23588	−	0.401562i	−0.852842	+	0.522170i	$0.825123\pi$
$384$	73.5699	+	89.3774i	0.191588	+	0.232754i
$385$		0			0
$386$			250.336i			0.648538i
$387$	−178.246	−	99.1365i	−0.460584	−	0.256167i
$388$	−16.4827	+	11.9754i	−0.0424813	+	0.0308644i
$389$	−242.332	+	333.541i	−0.622961	+	0.857433i	−0.997564	−	0.0697526i	$-0.977779\pi$
$389$	−242.332	+	333.541i	−0.622961	+	0.857433i	0.374603	+	0.927185i	$0.377779\pi$
$390$	−50.1388	−	31.9923i	−0.128561	−	0.0820315i
$391$	−115.163	−	354.434i	−0.294534	−	0.906482i
$392$	215.915	−	297.181i	0.550802	−	0.758115i
$393$	245.412	+	63.6548i	0.624457	+	0.161972i
$394$	11.4456	−	35.2261i	0.0290499	−	0.0894063i
$395$			35.5715i			0.0900544i
$396$		0			0
$397$	171.230			0.431310			0.215655	−	0.976470i	$-0.430811\pi$
$397$	171.230			0.431310			0.215655	+	0.976470i	$0.430811\pi$
$398$	238.018	+	77.3366i	0.598034	+	0.194313i
$399$	31.2988	−	120.668i	0.0784430	−	0.302425i
$400$	187.087	+	135.927i	0.467717	+	0.339816i
$401$	−690.485	+	224.352i	−1.72191	+	0.559482i	−0.992242	−	0.124323i	$-0.960324\pi$
$401$	−690.485	+	224.352i	−1.72191	+	0.559482i	−0.729665	+	0.683804i	$0.760324\pi$
$402$	−206.790	+	324.084i	−0.514403	+	0.806179i
$403$	−56.2584	−	40.8741i	−0.139599	−	0.101425i
$404$	−76.5860	−	105.412i	−0.189569	−	0.260920i
$405$	−43.2378	−	36.4918i	−0.106760	−	0.0901033i
$406$	23.2147			0.0571790
$407$		0			0
$408$	−324.919	+	267.453i	−0.796369	+	0.655521i
$409$	−93.1348	+	286.639i	−0.227713	+	0.700830i	0.770291	+	0.637692i	$0.220111\pi$
$409$	−93.1348	+	286.639i	−0.227713	+	0.700830i	−0.998005	+	0.0631377i	$0.979889\pi$
$410$	−45.9110	−	63.1911i	−0.111978	−	0.154125i
$411$	36.9927	+	612.001i	0.0900067	+	1.48905i
$412$	21.0242	+	64.7058i	0.0510296	+	0.157053i
$413$	−71.3110	+	23.1704i	−0.172666	+	0.0561026i
$414$	252.778	−	235.045i	0.610575	−	0.567742i
$415$	33.4595	−	24.3098i	0.0806253	−	0.0585777i
$416$	312.256	+	101.458i	0.750615	+	0.243889i
$417$	116.371	−	95.7892i	0.279067	−	0.229710i
$418$		0			0
$419$			573.195i			1.36801i	0.729478	+	0.684004i	$0.239763\pi$
$419$			573.195i			1.36801i	−0.729478	+	0.684004i	$0.760237\pi$
$420$	−6.36309	+	2.50124i	−0.0151502	+	0.00595533i
$421$	452.468	−	328.737i	1.07475	−	0.780849i	0.0979865	−	0.995188i	$-0.468760\pi$
$421$	452.468	−	328.737i	1.07475	−	0.780849i	0.976759	+	0.214339i	$0.0687598\pi$
$422$	176.973	−	243.583i	0.419368	−	0.577211i
$423$	80.0262	+	659.550i	0.189187	+	1.55922i
$424$	115.285	+	354.811i	0.271898	+	0.836817i
$425$	−232.147	+	319.523i	−0.546229	+	0.751819i
$426$	−51.5353	+	198.686i	−0.120975	+	0.466400i
$427$	−37.3308	+	114.893i	−0.0874259	+	0.269069i
$428$			35.5229i			0.0829973i
$429$		0			0
$430$	26.2480			0.0610420
$431$	190.066	+	61.7562i	0.440988	+	0.143286i	0.521092	−	0.853501i	$-0.325525\pi$
$431$	190.066	+	61.7562i	0.440988	+	0.143286i	−0.0801033	+	0.996787i	$0.525525\pi$
$432$	−229.674	−	110.154i	−0.531653	−	0.254986i
$433$	83.7223	+	60.8278i	0.193354	+	0.140480i	0.680250	−	0.732980i	$-0.261871\pi$
$433$	83.7223	+	60.8278i	0.193354	+	0.140480i	−0.486896	+	0.873460i	$0.661871\pi$
$434$	16.7159	−	5.43131i	0.0385158	−	0.0125145i
$435$	9.47906	+	6.04835i	0.0217909	+	0.0139043i
$436$	−41.7359	−	30.3229i	−0.0957245	−	0.0695479i
$437$	216.521	+	298.016i	0.495472	+	0.681958i
$438$	−262.838	+	103.318i	−0.600087	+	0.235886i
$439$	662.550			1.50923			0.754613	−	0.656171i	$-0.227825\pi$
$439$	662.550			1.50923			0.754613	+	0.656171i	$0.227825\pi$
$440$		0			0
$441$	−72.9890	+	372.652i	−0.165508	+	0.845016i
$442$	141.319	−	434.934i	0.319725	−	0.984013i
$443$	123.922	+	170.565i	0.279735	+	0.385022i	0.925646	−	0.378391i	$-0.123522\pi$
$443$	123.922	+	170.565i	0.279735	+	0.385022i	−0.645911	+	0.763412i	$0.723522\pi$
$444$	−237.904	+	14.3803i	−0.535820	+	0.0323880i
$445$	−8.24349	−	25.3709i	−0.0185247	−	0.0570132i
$446$	296.531	−	96.3488i	0.664868	−	0.216029i
$447$	−28.4908	−	471.346i	−0.0637378	−	1.05447i
$448$	−146.791	+	106.650i	−0.327659	+	0.238058i
$449$	227.560	+	73.9387i	0.506815	+	0.164674i	0.551253	−	0.834338i	$-0.314150\pi$
$449$	227.560	+	73.9387i	0.506815	+	0.164674i	−0.0444383	+	0.999012i	$0.514150\pi$
$450$	−358.984	−	70.3118i	−0.797742	−	0.156248i
$451$		0			0
$452$		−	181.546i		−	0.401651i
$453$	−188.093	−	478.503i	−0.415216	−	1.05630i
$454$	575.799	−	418.342i	1.26828	−	0.921459i
$455$	18.3361	−	25.2374i	0.0402990	−	0.0554668i
$456$	223.753	−	350.668i	0.490685	−	0.769009i
$457$	−8.24694	−	25.3815i	−0.0180458	−	0.0555393i	0.941628	−	0.336655i	$-0.109296\pi$
$457$	−8.24694	−	25.3815i	−0.0180458	−	0.0555393i	−0.959674	+	0.281116i	$0.909296\pi$
$458$	−132.332	+	182.140i	−0.288935	+	0.397685i
$459$	188.130	−	392.257i	0.409870	−	0.854591i
$460$	6.24313	−	19.2144i	0.0135720	−	0.0417704i
$461$		−	393.125i		−	0.852766i	−0.904543	−	0.426383i	$-0.859788\pi$
$461$		−	393.125i		−	0.852766i	0.904543	−	0.426383i	$-0.140212\pi$
$462$		0			0
$463$	106.954			0.231002			0.115501	−	0.993307i	$-0.463153\pi$
$463$	106.954			0.231002			0.115501	+	0.993307i	$0.463153\pi$
$464$	48.1455	+	15.6434i	0.103762	+	0.0337143i
$465$	8.24052	+	2.13742i	0.0177215	+	0.00459661i
$466$	438.515	+	318.600i	0.941020	+	0.683691i
$467$	−402.211	+	130.686i	−0.861265	+	0.279842i	−0.706157	−	0.708055i	$-0.749573\pi$
$467$	−402.211	+	130.686i	−0.861265	+	0.279842i	−0.155108	+	0.987897i	$0.549573\pi$
$468$	−191.241	+	23.2041i	−0.408635	+	0.0495815i
$469$	−163.128	−	118.520i	−0.347821	−	0.252707i
$470$	−50.2565	−	69.1722i	−0.106929	−	0.147175i
$471$	71.7090	+	182.426i	0.152248	+	0.387316i
$472$	−250.199			−0.530083
$473$		0			0
$474$	−160.996	−	195.588i	−0.339654	−	0.412634i
$475$	120.637	−	371.281i	0.253972	−	0.781644i
$476$	−30.9002	−	42.5305i	−0.0649164	−	0.0893498i
$477$	−262.617	−	282.430i	−0.550559	−	0.592096i
$478$	47.8853	+	147.376i	0.100178	+	0.308317i
$479$	−513.299	+	166.781i	−1.07161	+	0.348186i	−0.791113	−	0.611670i	$-0.790498\pi$
$479$	−513.299	+	166.781i	−1.07161	+	0.348186i	−0.280493	+	0.959856i	$0.590498\pi$
$480$	−40.1214	+	2.42516i	−0.0835862	+	0.00505242i
$481$	879.773	−	639.192i	1.82905	−	1.32888i
$482$	326.071	+	105.947i	0.676497	+	0.219807i
$483$	115.057	+	139.779i	0.238213	+	0.289397i
$484$		0			0
$485$			11.3803i			0.0234645i
$486$	402.902	+	4.95537i	0.829017	+	0.0101962i
$487$	−494.023	+	358.929i	−1.01442	+	0.737020i	−0.965132	−	0.261765i	$-0.915696\pi$
$487$	−494.023	+	358.929i	−1.01442	+	0.737020i	−0.0492892	+	0.998785i	$0.515696\pi$
$488$	−236.940	+	326.121i	−0.485534	+	0.668280i
$489$	−39.0442	−	24.9131i	−0.0798449	−	0.0509471i
$490$	−15.1013	−	46.4769i	−0.0308189	−	0.0948508i
$491$	33.4298	−	46.0121i	0.0680851	−	0.0937111i	−0.773616	−	0.633654i	$-0.781554\pi$
$491$	33.4298	−	46.0121i	0.0680851	−	0.0937111i	0.841702	+	0.539943i	$0.181554\pi$
$492$	−244.890	−	63.5196i	−0.497745	−	0.129105i
$493$	−26.7172	+	82.2270i	−0.0541931	+	0.166789i
$494$			452.031i			0.915043i
$495$		0			0
$496$	38.3274			0.0772729
$497$	−102.390	−	33.2686i	−0.206016	−	0.0669388i
$498$	−73.9501	+	285.103i	−0.148494	+	0.572497i
$499$	−379.330	−	275.600i	−0.760181	−	0.552304i	0.138785	−	0.990323i	$-0.455680\pi$
$499$	−379.330	−	275.600i	−0.760181	−	0.552304i	−0.898966	+	0.438019i	$0.855680\pi$
$500$	−41.1313	+	13.3644i	−0.0822626	+	0.0267287i
$501$	248.678	−	389.731i	0.496363	−	0.777907i
$502$	−3.74311	−	2.71953i	−0.00745640	−	0.00541739i
$503$	−269.307	−	370.669i	−0.535401	−	0.736916i	0.452540	−	0.891744i	$-0.350518\pi$
$503$	−269.307	−	370.669i	−0.535401	−	0.736916i	−0.987942	+	0.154827i	$0.950518\pi$
$504$	99.3691	−	178.664i	0.197161	−	0.354492i
$505$	−72.7802			−0.144119
$506$		0			0
$507$	287.189	−	236.396i	0.566448	−	0.466265i
$508$	70.6318	−	217.382i	0.139039	−	0.427918i
$509$	161.552	+	222.357i	0.317391	+	0.436851i	0.937668	−	0.347531i	$-0.112980\pi$
$509$	161.552	+	222.357i	0.317391	+	0.436851i	−0.620277	+	0.784383i	$0.712980\pi$
$510$	3.37795	+	55.8841i	0.00662343	+	0.109577i
$511$	−45.7737	−	140.877i	−0.0895767	−	0.275689i
$512$	−484.567	+	157.445i	−0.946420	+	0.307510i
$513$	−57.0413	+	426.211i	−0.111192	+	0.830821i
$514$	−536.868	+	390.058i	−1.04449	+	0.758867i
$515$	36.1431	+	11.7436i	0.0701808	+	0.0228031i
$516$	65.6404	−	54.0310i	0.127210	−	0.104711i
$517$		0			0
$518$			274.856i			0.530610i
$519$	70.0885	−	27.5508i	0.135045	−	0.0530843i
$520$	84.2131	−	61.1844i	0.161948	−	0.117662i
$521$	−146.004	+	200.957i	−0.280237	+	0.385714i	−0.925812	−	0.377983i	$-0.876618\pi$
$521$	−146.004	+	200.957i	−0.280237	+	0.385714i	0.645575	+	0.763697i	$0.276618\pi$
$522$	−79.4949	+	9.64547i	−0.152289	+	0.0184779i
$523$	−43.4437	−	133.706i	−0.0830663	−	0.255652i	0.900894	−	0.434039i	$-0.142912\pi$
$523$	−43.4437	−	133.706i	−0.0830663	−	0.255652i	−0.983960	+	0.178387i	$0.942912\pi$
$524$	−62.1180	+	85.4981i	−0.118546	+	0.163164i
$525$	48.1717	−	185.719i	0.0917555	−	0.353750i
$526$	194.308	−	598.018i	0.369407	−	1.13692i
$527$			65.4587i			0.124210i
$528$		0			0
$529$	−5.97152			−0.0112883
$530$	47.2024	+	15.3370i	0.0890611	+	0.0289377i
$531$	234.566	−	108.972i	0.441744	−	0.205221i
$532$	42.0390	+	30.5431i	0.0790207	+	0.0574119i
$533$	1097.83	−	356.707i	2.05972	−	0.669244i
$534$	160.155	+	102.191i	0.299915	+	0.191368i
$535$	16.0527	+	11.6630i	0.0300051	+	0.0217999i
$536$	−395.480	−	544.332i	−0.737837	−	1.01555i
$537$	172.562	−	67.8315i	0.321344	−	0.126316i
$538$	51.7358			0.0961633
$539$		0			0
$540$	20.7501	−	11.2089i	0.0384262	−	0.0207572i
$541$	−185.692	+	571.503i	−0.343239	+	1.05638i	0.619280	+	0.785170i	$0.287424\pi$
$541$	−185.692	+	571.503i	−0.343239	+	1.05638i	−0.962520	+	0.271212i	$0.912576\pi$
$542$	−504.968	−	695.029i	−0.931675	−	1.28234i
$543$	444.403	−	26.8622i	0.818421	−	0.0494700i
$544$	−95.5046	−	293.933i	−0.175560	−	0.540318i
$545$	−27.4057	+	8.90465i	−0.0502857	+	0.0163388i
$546$	13.4041	+	221.755i	0.0245497	+	0.406145i
$547$	−502.297	+	364.940i	−0.918276	+	0.667166i	−0.943094	−	0.332526i	$-0.892099\pi$
$547$	−502.297	+	364.940i	−0.918276	+	0.667166i	0.0248187	+	0.999692i	$0.492099\pi$
$548$	−243.061	−	78.9752i	−0.443542	−	0.144115i
$549$	80.0967	−	408.941i	0.145896	−	0.744884i
$550$		0			0
$551$		−	85.4594i		−	0.155099i
$552$	221.005	+	562.230i	0.400370	+	1.01853i
$553$	107.494	−	78.0989i	0.194383	−	0.141228i
$554$	358.627	−	493.608i	0.647341	−	0.890988i
$555$	−71.6110	+	112.230i	−0.129029	+	0.202216i
$556$	19.4147	+	59.7522i	0.0349185	+	0.107468i
$557$	317.419	−	436.890i	0.569873	−	0.784363i	−0.422666	−	0.906285i	$-0.638906\pi$
$557$	317.419	−	436.890i	0.569873	−	0.784363i	0.992540	+	0.121922i	$0.0389058\pi$
$558$	−54.9841	+	25.5439i	−0.0985377	+	0.0457776i
$559$	−119.870	+	368.922i	−0.214437	+	0.659968i
$560$			17.1936i			0.0307028i
$561$		0			0
$562$	−531.261			−0.945305
$563$	−265.027	−	86.1126i	−0.470741	−	0.152953i	0.0640335	−	0.997948i	$-0.479604\pi$
$563$	−265.027	−	86.1126i	−0.470741	−	0.152953i	−0.534775	+	0.844995i	$0.679604\pi$
$564$	−268.070	−	69.5319i	−0.475301	−	0.123283i
$565$	−82.0403	−	59.6057i	−0.145204	−	0.105497i
$566$	253.574	−	82.3912i	0.448011	−	0.145567i
$567$	−15.3446	+	210.780i	−0.0270627	+	0.371746i
$568$	−290.633	−	211.157i	−0.511677	−	0.371755i
$569$	628.675	+	865.297i	1.10488	+	1.52073i	0.828755	+	0.559611i	$0.189050\pi$
$569$	628.675	+	865.297i	1.10488	+	1.52073i	0.276122	+	0.961122i	$0.410950\pi$
$570$	−20.2451	−	51.5030i	−0.0355177	−	0.0903561i
$571$	−470.660			−0.824274			−0.412137	−	0.911122i	$-0.635217\pi$
$571$	−470.660			−0.824274			−0.412137	+	0.911122i	$0.635217\pi$
$572$		0			0
$573$	−107.155	−	130.179i	−0.187007	−	0.227189i
$574$	−90.1580	+	277.478i	−0.157070	+	0.483411i
$575$	333.246	+	458.673i	0.579558	+	0.797693i
$576$	458.351	−	426.196i	0.795748	−	0.739924i
$577$	70.8100	+	217.931i	0.122721	+	0.377696i	0.993479	−	0.114015i	$-0.0363714\pi$
$577$	70.8100	+	217.931i	0.122721	+	0.377696i	−0.870758	+	0.491712i	$0.836371\pi$
$578$	46.3415	−	15.0573i	0.0801756	−	0.0260506i
$579$	452.091	−	27.3269i	0.780814	−	0.0471967i
$580$	−3.79189	+	2.75497i	−0.00653775	+	0.00474995i
$581$	−146.924	−	47.7384i	−0.252881	−	0.0821660i
$582$	−51.5071	−	62.5741i	−0.0885001	−	0.107516i
$583$		0			0
$584$		−	494.275i		−	0.846361i
$585$	−52.3029	+	94.0399i	−0.0894067	+	0.160752i
$586$	−390.293	+	283.564i	−0.666029	+	0.483898i
$587$	−0.435454	+	0.599351i	−0.000741830	+	0.00102104i	−0.809388	−	0.587275i	$-0.800201\pi$
$587$	−0.435454	+	0.599351i	−0.000741830	+	0.00102104i	0.808646	+	0.588296i	$0.200201\pi$
$588$	−133.436	−	85.1424i	−0.226933	−	0.144800i
$589$	−19.9941	−	61.5355i	−0.0339458	−	0.104475i
$590$	−19.5646	+	26.9284i	−0.0331604	+	0.0456414i
$591$	−64.8656	−	16.8248i	−0.109756	−	0.0284684i
$592$	−185.214	+	570.031i	−0.312862	+	0.962890i
$593$		−	498.413i		−	0.840494i	−0.907410	−	0.420247i	$-0.861943\pi$
$593$		−	498.413i		−	0.840494i	0.907410	−	0.420247i	$-0.138057\pi$
$594$		0			0
$595$	−29.3647			−0.0493524
$596$	187.199	+	60.8246i	0.314092	+	0.102055i
$597$	113.683	−	438.287i	0.190424	−	0.734150i
$598$	−531.099	−	385.866i	−0.888125	−	0.645261i
$599$	−182.035	+	59.1467i	−0.303898	+	0.0987425i	−0.456997	−	0.889468i	$-0.651075\pi$
$599$	−182.035	+	59.1467i	−0.303898	+	0.0987425i	0.153098	+	0.988211i	$0.451075\pi$
$600$	344.376	−	539.710i	0.573959	−	0.899517i
$601$	672.631	+	488.695i	1.11919	+	0.813137i	0.984086	−	0.177695i	$-0.0568640\pi$
$601$	672.631	+	488.695i	1.11919	+	0.813137i	0.135101	+	0.990832i	$0.456864\pi$
$602$	−57.6288	−	79.3192i	−0.0957289	−	0.131760i
$603$	607.849	+	338.073i	1.00804	+	0.560651i
$604$	214.314			0.354824
$605$		0			0
$606$	400.178	−	329.402i	0.660361	−	0.543567i
$607$	−244.029	+	751.044i	−0.402025	+	1.23731i	0.521329	+	0.853356i	$0.325436\pi$
$607$	−244.029	+	751.044i	−0.402025	+	1.23731i	−0.923354	+	0.383950i	$0.874564\pi$
$608$	179.561	+	247.145i	0.295331	+	0.406488i
$609$	−2.53414	−	41.9243i	−0.00416115	−	0.0688412i
$610$	16.5718	+	51.0028i	0.0271669	+	0.0836112i
$611$	1201.74	−	390.470i	1.96685	−	0.639067i
$612$	123.484	+	132.800i	0.201771	+	0.216993i
$613$	−224.256	+	162.932i	−0.365834	+	0.265794i	−0.755481	−	0.655170i	$-0.772597\pi$
$613$	−224.256	+	162.932i	−0.365834	+	0.265794i	0.389647	+	0.920964i	$0.372597\pi$
$614$	−444.399	−	144.394i	−0.723777	−	0.235170i
$615$	−109.107	+	89.8104i	−0.177411	+	0.146033i
$616$		0			0
$617$		−	928.547i		−	1.50494i	−0.658628	−	0.752469i	$-0.728863\pi$
$617$		−	928.547i		−	1.50494i	0.658628	−	0.752469i	$-0.271137\pi$
$618$	−251.883	+	99.0115i	−0.407577	+	0.160213i
$619$	−773.156	+	561.731i	−1.24904	+	0.907481i	−0.998166	−	0.0605380i	$-0.980718\pi$
$619$	−773.156	+	561.731i	−1.24904	+	0.907481i	−0.250875	+	0.968019i	$0.580718\pi$
$620$	−2.08582	+	2.87088i	−0.00336423	+	0.00463046i
$621$	−452.070	−	430.844i	−0.727972	−	0.693791i
$622$	242.751	+	747.109i	0.390274	+	1.20114i
$623$	−58.5695	+	80.6140i	−0.0940120	+	0.129396i
$624$	−121.633	+	468.936i	−0.194924	+	0.751501i
$625$	181.901	−	559.835i	0.291042	−	0.895735i
$626$			49.7019i			0.0793961i
$627$		0			0
$628$	−81.7055			−0.130104
$629$	−973.548	−	316.325i	−1.54777	−	0.502901i
$630$	−11.4590	−	24.6658i	−0.0181888	−	0.0391520i
$631$	4.25502	+	3.09145i	0.00674330	+	0.00489929i	0.591152	−	0.806560i	$-0.298673\pi$
$631$	4.25502	+	3.09145i	0.00674330	+	0.00489929i	−0.584409	+	0.811460i	$0.698673\pi$
$632$	421.665	−	137.007i	0.667192	−	0.216784i
$633$	−459.215	−	293.013i	−0.725458	−	0.462896i
$634$	−213.666	−	155.238i	−0.337013	−	0.244854i
$635$	−75.0446	−	103.290i	−0.118180	−	0.162661i
$636$	149.613	−	58.8108i	0.235241	−	0.0924698i
$637$	722.207			1.13376
$638$		0			0
$639$	364.441	+	71.3807i	0.570330	+	0.111707i
$640$	−8.32906	+	25.6342i	−0.0130141	+	0.0400534i
$641$	285.666	+	393.185i	0.445657	+	0.613394i	0.971457	−	0.237214i	$-0.0762343\pi$
$641$	285.666	+	393.185i	0.445657	+	0.613394i	−0.525801	+	0.850608i	$0.676234\pi$
$642$	−141.051	+	8.52594i	−0.219706	+	0.0132803i
$643$	−228.326	−	702.715i	−0.355095	−	1.09287i	−0.955955	−	0.293515i	$-0.905175\pi$
$643$	−228.326	−	702.715i	−0.355095	−	1.09287i	0.600860	−	0.799354i	$-0.294825\pi$
$644$	−71.7712	+	23.3199i	−0.111446	+	0.0362110i
$645$	−2.86526	−	47.4024i	−0.00444227	−	0.0734920i
$646$	344.242	−	250.107i	0.532883	−	0.387162i
$647$	−1093.99	−	355.458i	−1.69086	−	0.549394i	−0.703892	−	0.710307i	$-0.748556\pi$
$647$	−1093.99	−	355.458i	−1.69086	−	0.549394i	−0.986969	+	0.160913i	$0.948556\pi$
$648$	−266.040	+	653.093i	−0.410556	+	1.00786i
$649$		0			0
$650$			695.717i			1.07033i
$651$	−11.6333	−	29.5949i	−0.0178699	−	0.0454607i
$652$	15.6188	−	11.3477i	0.0239552	−	0.0174045i
$653$	355.641	−	489.498i	0.544626	−	0.749614i	−0.444645	−	0.895707i	$-0.646670\pi$
$653$	355.641	−	489.498i	0.544626	−	0.749614i	0.989271	+	0.146093i	$0.0466700\pi$
$654$	110.387	−	172.999i	0.168787	−	0.264525i
$655$	18.2416	+	56.1419i	0.0278498	+	0.0857129i
$656$	−373.962	+	514.714i	−0.570064	+	0.784625i
$657$	215.278	+	463.392i	0.327667	+	0.705314i
$658$	−98.6916	+	303.741i	−0.149987	+	0.461613i
$659$			956.314i			1.45116i	0.688138	+	0.725580i	$0.258428\pi$
$659$			956.314i			1.45116i	−0.688138	+	0.725580i	$0.741572\pi$
$660$		0			0
$661$	57.8747			0.0875563			0.0437781	−	0.999041i	$-0.486061\pi$
$661$	57.8747			0.0875563			0.0437781	+	0.999041i	$0.486061\pi$
$662$	−524.684	−	170.480i	−0.792573	−	0.257523i
$663$	−800.890	−	207.735i	−1.20798	−	0.313325i
$664$	−417.041	−	302.998i	−0.628074	−	0.456322i
$665$	27.6047	−	8.96932i	0.0415109	−	0.0134877i
$666$	−114.200	−	941.200i	−0.171472	−	1.41321i
$667$	100.408	+	72.9505i	0.150536	+	0.109371i
$668$	113.271	+	155.904i	0.169567	+	0.233389i
$669$	−206.370	−	524.999i	−0.308475	−	0.784753i
$670$	−89.5104			−0.133598
$671$		0			0
$672$	95.4169	+	115.919i	0.141989	+	0.172498i
$673$	−263.174	+	809.965i	−0.391045	+	1.20351i	0.540953	+	0.841053i	$0.318064\pi$
$673$	−263.174	+	809.965i	−0.391045	+	1.20351i	−0.931999	+	0.362461i	$0.881936\pi$
$674$	−54.0004	−	74.3251i	−0.0801192	−	0.110275i
$675$	−87.7918	+	655.978i	−0.130062	+	0.971819i
$676$	47.9131	+	147.461i	0.0708773	+	0.218138i
$677$	−256.528	+	83.3509i	−0.378918	+	0.123118i	−0.492282	−	0.870436i	$-0.663837\pi$
$677$	−256.528	+	83.3509i	−0.378918	+	0.123118i	0.113364	+	0.993553i	$0.463837\pi$
$678$	720.869	−	43.5734i	1.06323	−	0.0642675i
$679$	34.3903	−	24.9860i	0.0506484	−	0.0367982i
$680$	−93.1894	−	30.2791i	−0.137043	−	0.0445281i
$681$	−818.355	−	994.191i	−1.20170	−	1.45990i
$682$		0			0
$683$			254.016i			0.371913i	0.982558	+	0.185956i	$0.0595383\pi$
$683$			254.016i			0.371913i	−0.982558	+	0.185956i	$0.940462\pi$
$684$	−156.646	−	87.1231i	−0.229015	−	0.127373i
$685$	−115.491	+	83.9092i	−0.168600	+	0.122495i
$686$	−231.898	+	319.180i	−0.338044	+	0.465277i
$687$	343.379	+	219.102i	0.499824	+	0.318925i
$688$	−66.0678	−	203.336i	−0.0960288	−	0.295546i
$689$	−431.129	+	593.399i	−0.625732	+	0.861246i
$690$	77.7934	+	20.1780i	0.112744	+	0.0292435i
$691$	−116.992	+	360.065i	−0.169309	+	0.521078i	−0.999328	−	0.0366564i	$-0.988329\pi$
$691$	−116.992	+	360.065i	−0.169309	+	0.521078i	0.830019	+	0.557735i	$0.188329\pi$
$692$			31.3914i			0.0453634i
$693$		0			0
$694$	−229.724			−0.331014
$695$	33.3762	+	10.8446i	0.0480232	+	0.0156037i
$696$	35.1877	−	135.661i	0.0505570	−	0.194915i
$697$	−879.073	−	638.684i	−1.26122	−	0.916333i
$698$	−357.217	+	116.067i	−0.511772	+	0.166285i
$699$	527.503	−	826.711i	0.754654	−	1.18270i
$700$	64.7018	+	47.0086i	0.0924312	+	0.0671552i
$701$	188.061	+	258.843i	0.268275	+	0.369249i	0.921806	−	0.387651i	$-0.126713\pi$
$701$	188.061	+	258.843i	0.268275	+	0.369249i	−0.653531	+	0.756899i	$0.726713\pi$
$702$	−138.037	−	753.796i	−0.196635	−	1.07378i
$703$	1011.82			1.43929
$704$		0			0
$705$	−119.435	+	98.3111i	−0.169411	+	0.139448i
$706$	−132.680	+	408.347i	−0.187932	+	0.578396i
$707$	159.792	+	219.935i	0.226014	+	0.311082i
$708$	6.50486	+	107.615i	0.00918766	+	0.151999i
$709$	−70.6162	−	217.334i	−0.0995997	−	0.306536i	0.888825	−	0.458246i	$-0.151522\pi$
$709$	−70.6162	−	217.334i	−0.0995997	−	0.306536i	−0.988425	+	0.151710i	$0.951522\pi$
$710$	−45.4528	+	14.7685i	−0.0640180	+	0.0208007i
$711$	−335.646	+	312.100i	−0.472076	+	0.438959i
$712$	−268.996	+	195.437i	−0.377803	+	0.274490i
$713$	89.3666	+	29.0370i	0.125339	+	0.0407251i
$714$	161.460	−	132.904i	0.226135	−	0.186140i
$715$		0			0
$716$			77.2875i			0.107943i
$717$	260.924	−	102.566i	0.363911	−	0.143048i
$718$	−347.492	+	252.467i	−0.483972	+	0.351626i
$719$	473.254	−	651.379i	0.658212	−	0.905951i	−0.341209	−	0.939988i	$-0.610836\pi$
$719$	473.254	−	651.379i	0.658212	−	0.905951i	0.999421	+	0.0340364i	$0.0108362\pi$
$720$	−7.14377	−	58.8766i	−0.00992190	−	0.0817731i
$721$	−43.8658	−	135.005i	−0.0608402	−	0.187247i
$722$	104.629	−	144.010i	0.144916	−	0.199460i
$723$	155.739	−	600.430i	0.215407	−	0.830470i
$724$	−57.3477	+	176.498i	−0.0792095	+	0.243782i
$725$		−	131.530i		−	0.181420i
$726$		0			0
$727$	−1002.31			−1.37869			−0.689345	−	0.724434i	$-0.742101\pi$
$727$	−1002.31			−1.37869			−0.689345	+	0.724434i	$0.742101\pi$
$728$	−369.788	−	120.151i	−0.507950	−	0.165043i
$729$	−35.0321	−	728.158i	−0.0480550	−	0.998845i
$730$	−53.1978	−	38.6505i	−0.0728737	−	0.0529458i
$731$	347.274	−	112.836i	0.475068	−	0.154359i
$732$	146.431	+	93.4337i	0.200042	+	0.127642i
$733$	−586.218	−	425.913i	−0.799752	−	0.581054i	0.111089	−	0.993810i	$-0.464566\pi$
$733$	−586.218	−	425.913i	−0.799752	−	0.581054i	−0.910841	+	0.412757i	$0.864566\pi$
$734$	−193.737	−	266.656i	−0.263946	−	0.363291i
$735$	−82.2859	+	32.3454i	−0.111954	+	0.0440073i
$736$	−443.653			−0.602789
$737$		0			0
$738$	193.442	−	987.637i	0.262117	−	1.33826i
$739$	265.858	−	818.228i	0.359754	−	1.10721i	−0.593447	−	0.804873i	$-0.702233\pi$
$739$	265.858	−	818.228i	0.359754	−	1.10721i	0.953201	−	0.302337i	$-0.0977666\pi$
$740$	−32.6182	−	44.8951i	−0.0440787	−	0.0606691i
$741$	816.341	−	49.3442i	1.10167	−	0.0665914i
$742$	−57.2880	−	176.314i	−0.0772076	−	0.237620i
$743$	−371.211	+	120.614i	−0.499611	+	0.162333i	−0.547972	−	0.836497i	$-0.684600\pi$
$743$	−371.211	+	120.614i	−0.499611	+	0.162333i	0.0483616	+	0.998830i	$0.484600\pi$
$744$	−6.40214	−	105.916i	−0.00860502	−	0.142360i
$745$	88.9482	−	64.6246i	0.119394	−	0.0867445i
$746$	1057.33	+	343.547i	1.41733	+	0.460519i
$747$	522.951	+	102.427i	0.700069	+	0.137118i
$748$		0			0
$749$		−	74.1164i		−	0.0989538i
$750$	−62.9382	−	160.113i	−0.0839176	−	0.213484i
$751$	698.777	−	507.691i	0.930461	−	0.676020i	−0.0156443	−	0.999878i	$-0.504980\pi$
$751$	698.777	−	507.691i	0.930461	−	0.676020i	0.946106	+	0.323858i	$0.104980\pi$
$752$	−409.358	+	563.433i	−0.544359	+	0.749246i
$753$	−4.50270	+	7.05669i	−0.00597968	+	0.00937144i
$754$	47.0629	+	144.845i	0.0624177	+	0.192102i
$755$	70.3641	−	96.8478i	0.0931974	−	0.128275i
$756$	−79.4301	−	38.0954i	−0.105066	−	0.0503907i
$757$	−261.252	+	804.051i	−0.345115	+	1.06215i	0.616408	+	0.787427i	$0.288587\pi$
$757$	−261.252	+	804.051i	−0.345115	+	1.06215i	−0.961522	+	0.274727i	$0.911413\pi$
$758$		−	650.647i		−	0.858373i
$759$		0			0
$760$	96.8528			0.127438
$761$	167.271	+	54.3497i	0.219805	+	0.0714188i	0.416849	−	0.908976i	$-0.363134\pi$
$761$	167.271	+	54.3497i	0.219805	+	0.0714188i	−0.197045	+	0.980395i	$0.563134\pi$
$762$	880.118	+	228.285i	1.15501	+	0.299587i
$763$	87.0795	+	63.2670i	0.114128	+	0.0829187i
$764$	66.8422	−	21.7184i	0.0874898	−	0.0284272i
$765$	100.555	−	12.2007i	0.131444	−	0.0159487i
$766$	667.657	+	485.081i	0.871614	+	0.633265i
$767$	−289.136	−	397.962i	−0.376971	−	0.518856i
$768$	235.071	+	598.015i	0.306082	+	0.778665i
$769$	−1341.04			−1.74388			−0.871941	−	0.489611i	$-0.837139\pi$
$769$	−1341.04			−1.74388			−0.871941	+	0.489611i	$0.837139\pi$
$770$		0			0
$771$	763.025	+	926.972i	0.989657	+	1.20230i
$772$	−58.3398	+	179.551i	−0.0755697	+	0.232580i
$773$	−461.195	−	634.781i	−0.596630	−	0.821191i	0.398764	−	0.917054i	$-0.369439\pi$
$773$	−461.195	−	634.781i	−0.596630	−	0.821191i	−0.995395	+	0.0958621i	$0.969439\pi$
$774$	230.297	+	247.672i	0.297541	+	0.319989i
$775$	−30.7727	−	94.7088i	−0.0397068	−	0.122205i
$776$	134.902	−	43.8324i	0.173843	−	0.0564851i
$777$	496.373	−	30.0036i	0.638833	−	0.0386147i
$778$	553.065	−	401.825i	0.710880	−	0.516485i
$779$	1021.47	+	331.896i	1.31126	+	0.426053i
$780$	−28.5060	−	34.6309i	−0.0365461	−	0.0443986i
$781$		0			0
$782$			617.954i			0.790222i
$783$	26.0969	+	142.510i	0.0333293	+	0.182005i
$784$	−322.032	+	233.970i	−0.410755	+	0.298431i
$785$	−26.8258	+	36.9225i	−0.0341730	+	0.0470351i
$786$	−354.398	−	226.133i	−0.450888	−	0.287701i
$787$	447.595	+	1377.55i	0.568735	+	1.75039i	0.656584	+	0.754253i	$0.272001\pi$
$787$	447.595	+	1377.55i	0.568735	+	1.75039i	−0.0878489	+	0.996134i	$0.527999\pi$
$788$	16.4186	−	22.5983i	0.0208358	−	0.0286780i
$789$	−1101.20	−	285.628i	−1.39568	−	0.362013i
$790$	18.2268	−	56.0964i	0.0230719	−	0.0710081i
$791$			378.785i			0.478869i
$792$		0			0
$793$	−792.536			−0.999415
$794$	−270.030	−	87.7382i	−0.340089	−	0.110501i
$795$	22.5450	−	86.9188i	0.0283585	−	0.109332i
$796$	152.693	+	110.938i	0.191826	+	0.139370i
$797$	−329.440	+	107.041i	−0.413350	+	0.134305i	−0.508307	−	0.861176i	$-0.669728\pi$
$797$	−329.440	+	107.041i	−0.413350	+	0.134305i	0.0949575	+	0.995481i	$0.469728\pi$
$798$	−111.188	+	174.256i	−0.139334	+	0.218366i
$799$	−962.279	−	699.136i	−1.20435	−	0.875014i
$800$	276.361	+	380.378i	0.345451	+	0.475473i
$801$	167.067	−	300.384i	0.208573	−	0.375012i
$802$	1203.85			1.50107
$803$		0			0
$804$	−223.845	+	184.255i	−0.278414	+	0.229173i
$805$	−13.0259	+	40.0897i	−0.0161813	+	0.0498009i
$806$	67.7758	+	93.2854i	0.0840891	+	0.115739i
$807$	−5.64754	−	93.4317i	−0.00699819	−	0.115777i
$808$	280.320	+	862.737i	0.346931	+	1.06774i
$809$	−497.588	+	161.676i	−0.615066	+	0.199847i	−0.599948	−	0.800039i	$-0.704812\pi$
$809$	−497.588	+	161.676i	−0.615066	+	0.199847i	−0.0151173	+	0.999886i	$0.504812\pi$
$810$	49.4877	+	79.7028i	0.0610959	+	0.0983985i
$811$	−836.093	+	607.457i	−1.03094	+	0.749022i	−0.968497	−	0.249026i	$-0.919889\pi$
$811$	−836.093	+	607.457i	−1.03094	+	0.749022i	−0.0624439	+	0.998048i	$0.519889\pi$
$812$	16.6506	+	5.41009i	0.0205056	+	0.00666268i
$813$	−1200.06	+	987.811i	−1.47608	+	1.21502i
$814$		0			0
$815$		−	10.7838i		−	0.0132317i
$816$	424.415	−	166.831i	0.520117	−	0.204450i
$817$	−291.995	+	212.147i	−0.357399	+	0.259666i
$818$	293.748	−	404.309i	0.359105	−	0.494265i
$819$	399.013	−	48.4141i	0.487196	−	0.0591137i
$820$	−18.2029	−	56.0227i	−0.0221986	−	0.0683204i
$821$	57.4727	−	79.1044i	0.0700033	−	0.0963513i	−0.772580	−	0.634918i	$-0.781034\pi$
$821$	57.4727	−	79.1044i	0.0700033	−	0.0963513i	0.842583	+	0.538567i	$0.181034\pi$
$822$	255.251	−	984.082i	0.310524	−	1.19718i
$823$	223.007	−	686.344i	0.270968	−	0.833954i	−0.719290	−	0.694710i	$-0.755533\pi$
$823$	223.007	−	686.344i	0.270968	−	0.833954i	0.990258	−	0.139244i	$-0.0444672\pi$
$824$		−	473.673i		−	0.574846i
$825$		0			0
$826$	124.330			0.150521
$827$	1169.10	+	379.865i	1.41367	+	0.459328i	0.913584	−	0.406649i	$-0.133303\pi$
$827$	1169.10	+	379.865i	1.41367	+	0.459328i	0.500083	+	0.865978i	$0.333303\pi$
$828$	236.080	−	109.675i	0.285120	−	0.132458i
$829$	156.467	+	113.680i	0.188742	+	0.137129i	0.678144	−	0.734929i	$-0.262785\pi$
$829$	156.467	+	113.680i	0.188742	+	0.137129i	−0.489402	+	0.872059i	$0.662785\pi$
$830$	−65.2221	+	21.1919i	−0.0785808	+	0.0255325i
$831$	−930.573	−	593.775i	−1.11982	−	0.714531i
$832$	−963.017	−	699.673i	−1.15747	−	0.840953i
$833$	−399.594	−	549.994i	−0.479704	−	0.660256i
$834$	−232.600	+	91.4315i	−0.278896	+	0.109630i
$835$	107.642			0.128912
$836$		0			0
$837$	52.1329	+	96.5094i	0.0622854	+	0.115304i
$838$	293.705	−	903.931i	0.350483	−	1.07868i
$839$	−342.849	−	471.891i	−0.408640	−	0.562445i	0.554246	−	0.832353i	$-0.313007\pi$
$839$	−342.849	−	471.891i	−0.408640	−	0.562445i	−0.962886	+	0.269908i	$0.913007\pi$
$840$	47.5136	−	2.87199i	0.0565638	−	0.00341903i
$841$	250.986	+	772.455i	0.298437	+	0.918495i
$842$	−881.988	+	286.575i	−1.04749	+	0.340351i
$843$	57.9930	+	959.425i	0.0687936	+	1.13811i
$844$	183.699	−	133.465i	0.217653	−	0.158134i
$845$	82.3684	+	26.7631i	0.0974773	+	0.0316723i
$846$	211.752	−	1081.12i	0.250297	−	1.27792i
$847$		0			0
$848$		−	404.267i		−	0.476730i
$849$	−176.474	−	448.945i	−0.207861	−	0.528793i
$850$	529.820	−	384.937i	0.623318	−	0.452867i
$851$	−863.716	+	1188.80i	−1.01494	+	1.39695i
$852$	−83.2664	+	130.496i	−0.0977305	+	0.153165i
$853$	133.256	+	410.119i	0.156220	+	0.480796i	0.998282	−	0.0585840i	$-0.0186586\pi$
$853$	133.256	+	410.119i	0.156220	+	0.480796i	−0.842062	+	0.539380i	$0.818659\pi$
$854$	117.742	−	162.058i	0.137871	−	0.189763i
$855$	−90.8012	+	42.1835i	−0.106200	+	0.0493374i
$856$	76.4244	−	235.210i	0.0892808	−	0.274778i
$857$			580.461i			0.677317i	0.940909	+	0.338659i	$0.109973\pi$
$857$			580.461i			0.677317i	−0.940909	+	0.338659i	$0.890027\pi$
$858$		0			0
$859$	−812.241			−0.945566			−0.472783	−	0.881179i	$-0.656751\pi$
$859$	−812.241			−0.945566			−0.472783	+	0.881179i	$0.656751\pi$
$860$	18.8262	+	6.11701i	0.0218910	+	0.00711280i
$861$	510.950	+	132.530i	0.593437	+	0.153926i
$862$	−268.091	−	194.779i	−0.311010	−	0.225962i
$863$	597.471	−	194.130i	0.692318	−	0.224948i	0.0583378	−	0.998297i	$-0.481420\pi$
$863$	597.471	−	194.130i	0.692318	−	0.224948i	0.633980	+	0.773349i	$0.281420\pi$
$864$	−374.903	−	357.300i	−0.433915	−	0.413541i
$865$	14.1857	+	10.3065i	0.0163997	+	0.0119151i
$866$	−100.862	−	138.825i	−0.116469	−	0.160306i
$867$	−32.2512	−	82.0462i	−0.0371986	−	0.0946323i
$868$	13.2551			0.0152708
$869$		0			0
$870$	−11.8493	−	14.3953i	−0.0136199	−	0.0165464i
$871$	408.778	−	1258.09i	0.469320	−	1.44442i
$872$	211.112	+	290.570i	0.242100	+	0.333223i
$873$	−107.382	+	99.8493i	−0.123004	+	0.114375i
$874$	−188.751	−	580.917i	−0.215963	−	0.664665i
$875$	85.8180	−	27.8840i	0.0980778	−	0.0318674i
$876$	−212.597	+	12.8505i	−0.242690	+	0.0146696i
$877$	971.470	−	705.814i	1.10772	−	0.804805i	0.125416	−	0.992104i	$-0.459973\pi$
$877$	971.470	−	705.814i	1.10772	−	0.804805i	0.982303	+	0.187299i	$0.0599734\pi$
$878$	−1044.84	−	339.490i	−1.19003	−	0.386663i
$879$	554.704	+	673.891i	0.631063	+	0.766656i
$880$		0			0
$881$			131.219i			0.148943i	0.997223	+	0.0744714i	$0.0237269\pi$
$881$			131.219i			0.148943i	−0.997223	+	0.0744714i	$0.976273\pi$
$882$	306.051	−	550.274i	0.346996	−	0.623894i
$883$	102.745	−	74.6486i	0.116359	−	0.0845398i	−0.528084	−	0.849192i	$-0.677089\pi$
$883$	102.745	−	74.6486i	0.116359	−	0.0845398i	0.644443	+	0.764652i	$0.277089\pi$
$884$	202.719	−	279.019i	0.229320	−	0.315633i
$885$	50.7667	+	32.3930i	0.0573635	+	0.0366022i
$886$	−108.029	−	332.479i	−0.121929	−	0.375258i
$887$	702.278	−	966.602i	0.791745	−	1.08974i	−0.202144	−	0.979356i	$-0.564791\pi$
$887$	702.278	−	966.602i	0.791745	−	1.08974i	0.993889	−	0.110388i	$-0.0352092\pi$
$888$	1606.19	+	416.613i	1.80877	+	0.469159i
$889$	−147.369	+	453.556i	−0.165770	+	0.510187i
$890$			44.2339i			0.0497010i
$891$		0			0
$892$	235.138			0.263608
$893$	1118.15	+	363.310i	1.25213	+	0.406842i
$894$	−196.587	+	757.913i	−0.219897	+	0.847778i
$895$	34.9261	+	25.3753i	0.0390235	+	0.0283522i
$896$	95.7511	−	31.1114i	0.106865	−	0.0347226i
$897$	−638.875	+	1001.25i	−0.712235	+	1.11622i
$898$	−320.977	−	233.203i	−0.357435	−	0.259692i
$899$	−12.8135	−	17.6362i	−0.0142530	−	0.0196176i
$900$	−241.092	−	134.090i	−0.267881	−	0.148989i
$901$	690.442			0.766306
$902$		0			0
$903$	−136.955	+	112.733i	−0.151667	+	0.124842i
$904$	−390.581	+	1202.08i	−0.432058	+	1.32974i
$905$	60.9305	+	83.8636i	0.0673265	+	0.0926670i
$906$	51.4380	+	850.980i	0.0567748	+	0.939271i
$907$	162.105	+	498.908i	0.178727	+	0.550064i	0.999784	−	0.0207814i	$-0.00661541\pi$
$907$	162.105	+	498.908i	0.178727	+	0.550064i	−0.821057	+	0.570846i	$0.806615\pi$
$908$	510.481	−	165.865i	0.562203	−	0.182671i
$909$	−638.563	−	686.740i	−0.702490	−	0.755489i
$910$	−41.8477	+	30.4041i	−0.0459864	+	0.0334111i
$911$	167.014	+	54.2660i	0.183330	+	0.0595675i	0.399243	−	0.916845i	$-0.369273\pi$
$911$	167.014	+	54.2660i	0.183330	+	0.0595675i	−0.215913	+	0.976413i	$0.569273\pi$
$912$	−348.020	+	286.468i	−0.381601	+	0.314110i
$913$		0			0
$914$			44.2524i			0.0484162i
$915$	90.2990	−	35.4952i	0.0986874	−	0.0387926i
$916$	−137.361	+	99.7989i	−0.149958	+	0.108951i
$917$	129.606	−	178.387i	0.141337	−	0.194533i
$918$	−497.674	+	522.193i	−0.542129	+	0.568838i
$919$	403.301	+	1241.23i	0.438848	+	1.35063i	0.889092	+	0.457729i	$0.151337\pi$
$919$	403.301	+	1241.23i	0.438848	+	1.35063i	−0.450244	+	0.892905i	$0.648663\pi$
$920$	−82.6761	+	113.794i	−0.0898654	+	0.123689i
$921$	−212.256	+	818.320i	−0.230462	+	0.888513i
$922$	−201.437	+	619.960i	−0.218478	+	0.672407i
$923$		−	706.294i		−	0.765216i
$924$		0			0
$925$	1557.28			1.68355
$926$	−168.667	−	54.8031i	−0.182145	−	0.0591826i
$927$	206.304	+	444.077i	0.222551	+	0.479047i
$928$	83.2683	+	60.4979i	0.0897287	+	0.0651917i
$929$	−1483.17	+	481.913i	−1.59653	+	0.518743i	−0.966246	−	0.257623i	$-0.917061\pi$
$929$	−1483.17	+	481.913i	−1.59653	+	0.518743i	−0.630282	+	0.776366i	$0.717061\pi$
$930$	−11.9001	−	7.59316i	−0.0127958	−	0.00816469i
$931$	543.638	+	394.976i	0.583929	+	0.424249i
$932$	240.273	+	330.708i	0.257804	+	0.354837i
$933$	1322.73	−	519.948i	1.41772	−	0.557286i
$934$	701.251			0.750804
$935$		0			0
$936$	1316.20	+	257.795i	1.40620	+	0.275422i
$937$	222.292	−	684.144i	0.237238	−	0.730143i	−0.759579	−	0.650415i	$-0.774595\pi$
$937$	222.292	−	684.144i	0.237238	−	0.730143i	0.996817	−	0.0797279i	$-0.0254051\pi$
$938$	196.524	+	270.492i	0.209514	+	0.288372i
$939$	89.7587	−	5.42552i	0.0955896	−	0.00577797i
$940$	−19.9258	−	61.3253i	−0.0211977	−	0.0652397i
$941$	1115.86	−	362.566i	1.18583	−	0.385298i	0.351298	−	0.936264i	$-0.385740\pi$
$941$	1115.86	−	362.566i	1.18583	−	0.385298i	0.834528	+	0.550965i	$0.185740\pi$
$942$	−19.6104	−	324.430i	−0.0208178	−	0.344406i
$943$	−1261.90	+	916.826i	−1.33818	+	0.972244i
$944$	257.852	+	83.7810i	0.273148	+	0.0887511i
$945$	−43.2940	+	23.3867i	−0.0458137	+	0.0247478i
$946$		0			0
$947$		−	266.119i		−	0.281013i	−0.990080	−	0.140506i	$-0.955127\pi$
$947$		−	266.119i		−	0.281013i	0.990080	−	0.140506i	$-0.0448730\pi$
$948$	−69.8921	−	177.804i	−0.0737258	−	0.187557i
$949$	786.185	−	571.197i	0.828435	−	0.601894i
$950$	−380.488	+	523.697i	−0.400514	+	0.551261i
$951$	−257.026	+	402.814i	−0.270269	+	0.423569i
$952$	113.101	+	348.089i	0.118804	+	0.365640i
$953$	75.3267	−	103.678i	0.0790417	−	0.108792i	−0.767665	−	0.640851i	$-0.778582\pi$
$953$	75.3267	−	103.678i	0.0790417	−	0.108792i	0.846707	+	0.532059i	$0.178582\pi$
$954$	269.430	+	579.957i	0.282422	+	0.607922i
$955$	12.1314	−	37.3365i	0.0127030	−	0.0390958i
$956$			116.864i			0.122242i
$957$		0			0
$958$	894.933			0.934168
$959$	507.132	+	164.777i	0.528814	+	0.171822i
$960$	141.059	+	36.5879i	0.146937	+	0.0381124i
$961$	764.113	+	555.160i	0.795123	+	0.577690i
$962$	−1714.93	+	557.214i	−1.78267	+	0.579224i
$963$	30.7946	+	253.800i	0.0319778	+	0.263551i
$964$	209.182	+	151.979i	0.216993	+	0.157655i
$965$	61.9846	+	85.3145i	0.0642328	+	0.0884088i
$966$	−109.823	−	279.386i	−0.113688	−	0.289220i
$967$	−1324.17			−1.36936			−0.684682	−	0.728842i	$-0.740059\pi$
$967$	−1324.17			−1.36936			−0.684682	+	0.728842i	$0.740059\pi$
$968$		0			0
$969$	−489.255	−	594.379i	−0.504907	−	0.613394i
$970$	5.83126	−	17.9468i	0.00601161	−	0.0185018i
$971$	−343.782	−	473.176i	−0.354050	−	0.487308i	0.594429	−	0.804148i	$-0.297378\pi$
$971$	−343.782	−	473.176i	−0.354050	−	0.487308i	−0.948479	+	0.316840i	$0.897378\pi$
$972$	287.824	+	97.4491i	0.296115	+	0.100256i
$973$	−40.5076	−	124.669i	−0.0416316	−	0.128129i
$974$	962.991	−	312.895i	0.988697	−	0.321247i
$975$	1256.42	−	75.9452i	1.28864	−	0.0778925i
$976$	353.391	−	256.754i	0.362081	−	0.263068i
$977$	−657.510	−	213.638i	−0.672988	−	0.218667i	−0.0474654	−	0.998873i	$-0.515114\pi$
$977$	−657.510	−	213.638i	−0.672988	−	0.218667i	−0.625523	+	0.780206i	$0.715114\pi$
$978$	48.8073	+	59.2943i	0.0499052	+	0.0606281i
$979$		0			0
$980$		−	36.8545i		−	0.0376066i
$981$	−324.476	−	180.467i	−0.330761	−	0.183962i
$982$	−76.2955	+	55.4319i	−0.0776939	+	0.0564480i
$983$	385.287	−	530.302i	0.391950	−	0.539473i	−0.566751	−	0.823889i	$-0.691800\pi$
$983$	385.287	−	530.302i	0.391950	−	0.539473i	0.958701	+	0.284416i	$0.0917998\pi$
$984$	1484.85	+	947.447i	1.50900	+	0.962853i
$985$	−4.82151	−	14.8391i	−0.00489493	−	0.0150650i
$986$	84.2662	−	115.982i	0.0854626	−	0.117629i
$987$	559.312	+	145.074i	0.566679	+	0.146985i
$988$	−105.344	+	324.216i	−0.106624	+	0.328154i
$989$		−	524.164i		−	0.529994i
$990$		0			0
$991$	95.0559			0.0959192			0.0479596	−	0.998849i	$-0.484728\pi$
$991$	95.0559			0.0959192			0.0479596	+	0.998849i	$0.484728\pi$
$992$	74.1119	+	24.0804i	0.0747095	+	0.0242746i
$993$	−250.601	+	966.156i	−0.252368	+	0.972967i
$994$	144.423	+	104.929i	0.145295	+	0.105563i
$995$	100.265	−	32.5782i	0.100769	−	0.0327419i
$996$	−119.482	+	187.254i	−0.119962	+	0.188006i
$997$	−632.168	−	459.297i	−0.634070	−	0.460679i	0.223738	−	0.974649i	$-0.428174\pi$
$997$	−632.168	−	459.297i	−0.634070	−	0.460679i	−0.857808	+	0.513970i	$0.828174\pi$
$998$	456.988	+	628.990i	0.457904	+	0.630251i
$999$	−1687.28	+	308.981i	−1.68897	+	0.309290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.h.n.251.2		16
3.2	odd	2	inner	363.3.h.n.251.3		16
11.2	odd	10		33.3.h.b.14.2	✓	16
11.3	even	5		363.3.h.j.323.2		16
11.4	even	5		363.3.b.l.122.4		8
11.5	even	5	inner	363.3.h.n.269.3		16
11.6	odd	10		363.3.h.o.269.2		16
11.7	odd	10		363.3.b.m.122.5		8
11.8	odd	10		33.3.h.b.26.3	yes	16
11.9	even	5		363.3.h.j.245.3		16
11.10	odd	2		363.3.h.o.251.3		16
33.2	even	10		33.3.h.b.14.3	yes	16
33.5	odd	10	inner	363.3.h.n.269.2		16
33.8	even	10		33.3.h.b.26.2	yes	16
33.14	odd	10		363.3.h.j.323.3		16
33.17	even	10		363.3.h.o.269.3		16
33.20	odd	10		363.3.h.j.245.2		16
33.26	odd	10		363.3.b.l.122.5		8
33.29	even	10		363.3.b.m.122.4		8
33.32	even	2		363.3.h.o.251.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.b.14.2	✓	16	11.2	odd	10
33.3.h.b.14.3	yes	16	33.2	even	10
33.3.h.b.26.2	yes	16	33.8	even	10
33.3.h.b.26.3	yes	16	11.8	odd	10
363.3.b.l.122.4		8	11.4	even	5
363.3.b.l.122.5		8	33.26	odd	10
363.3.b.m.122.4		8	33.29	even	10
363.3.b.m.122.5		8	11.7	odd	10
363.3.h.j.245.2		16	33.20	odd	10
363.3.h.j.245.3		16	11.9	even	5
363.3.h.j.323.2		16	11.3	even	5
363.3.h.j.323.3		16	33.14	odd	10
363.3.h.n.251.2		16	1.1	even	1	trivial
363.3.h.n.251.3		16	3.2	odd	2	inner
363.3.h.n.269.2		16	33.5	odd	10	inner
363.3.h.n.269.3		16	11.5	even	5	inner
363.3.h.o.251.2		16	33.32	even	2
363.3.h.o.251.3		16	11.10	odd	2
363.3.h.o.269.2		16	11.6	odd	10
363.3.h.o.269.3		16	33.17	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.57700 - 0.512399i) q^{2} +(-0.753215 + 2.90391i) q^{3} +(-1.01168 - 0.735029i) q^{4} +(-0.664316 + 0.215849i) q^{5} +(2.67578 - 4.19352i) q^{6} +(2.11081 + 1.53360i) q^{7} +(5.11736 + 7.04345i) q^{8} +(-7.86534 - 4.37453i) q^{9} +1.15823 q^{10} +(2.89647 - 2.38419i) q^{12} +(-5.28943 + 16.2792i) q^{13} +(-2.54295 - 3.50007i) q^{14} +(-0.126434 - 2.09169i) q^{15} +(-2.91533 - 8.97246i) q^{16} +(15.3239 - 4.97905i) q^{17} +(10.1622 + 10.9288i) q^{18} +(-12.8847 + 9.36127i) q^{19} +(0.830732 + 0.269921i) q^{20} +(-6.04332 + 4.97448i) q^{21} -23.1295i q^{23} +(-24.3080 + 9.55511i) q^{24} +(-19.8307 + 14.4078i) q^{25} +(16.6829 - 22.9620i) q^{26} +(18.6275 - 19.5452i) q^{27} +(-1.00823 - 3.10302i) q^{28} +(-3.15401 + 4.34112i) q^{29} +(-0.872396 + 3.36339i) q^{30} +(-1.25541 + 3.86376i) q^{31} -19.1813i q^{32} -26.7172 q^{34} +(-1.73327 - 0.563175i) q^{35} +(4.74180 + 10.2069i) q^{36} +(-51.3978 - 37.3427i) q^{37} +(25.1159 - 8.16065i) q^{38} +(-43.2891 - 27.6217i) q^{39} +(-4.91987 - 3.57450i) q^{40} +(-39.6389 - 54.5583i) q^{41} +(12.0793 - 4.74818i) q^{42} +22.6622 q^{43} +(6.16931 + 1.20834i) q^{45} +(-11.8515 + 36.4752i) q^{46} +(-43.3908 - 59.7223i) q^{47} +(28.2511 - 1.70765i) q^{48} +(-13.0382 - 40.1275i) q^{49} +(38.6557 - 12.5600i) q^{50} +(2.91647 + 48.2496i) q^{51} +(17.3169 - 12.5815i) q^{52} +(40.7539 + 13.2417i) q^{53} +(-39.3906 + 21.2782i) q^{54} +22.7154i q^{56} +(-17.4793 - 44.4670i) q^{57} +(7.19827 - 5.22985i) q^{58} +(-16.8918 + 23.2496i) q^{59} +(-1.40955 + 2.20906i) q^{60} +(14.3079 + 44.0351i) q^{61} +(3.95957 - 5.44989i) q^{62} +(-9.89350 - 21.2961i) q^{63} +(-21.4898 + 66.1388i) q^{64} -11.9562i q^{65} -77.2821 q^{67} +(-19.1627 - 6.22634i) q^{68} +(67.1657 + 17.4214i) q^{69} +(2.44481 + 1.77626i) q^{70} +(-39.2433 + 12.7509i) q^{71} +(-9.43802 - 77.7851i) q^{72} +(-45.9302 - 33.3703i) q^{73} +(61.9201 + 85.2257i) q^{74} +(-26.9023 - 68.4387i) q^{75} +19.9160 q^{76} +(54.1137 + 65.7409i) q^{78} +(15.7368 - 48.4329i) q^{79} +(3.87340 + 5.33128i) q^{80} +(42.7270 + 68.8143i) q^{81} +(34.5551 + 106.350i) q^{82} +(-56.3118 + 18.2968i) q^{83} +(9.77030 - 0.590571i) q^{84} +(-9.10522 + 6.61533i) q^{85} +(-35.7384 - 11.6121i) q^{86} +(-10.2306 - 12.4287i) q^{87} +38.1909i q^{89} +(-9.10987 - 5.06671i) q^{90} +(-36.1307 + 26.2505i) q^{91} +(-17.0008 + 23.3996i) q^{92} +(-10.2744 - 6.55583i) q^{93} +(37.8258 + 116.416i) q^{94} +(6.53888 - 9.00000i) q^{95} +(55.7007 + 14.4476i) q^{96} +(5.03463 - 15.4950i) q^{97} +69.9620i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} + 18 q^{4} - 32 q^{6} + 34 q^{7} + 17 q^{9} + 12 q^{10} + 106 q^{12} + 2 q^{13} - 28 q^{15} + 102 q^{16} - 42 q^{18} - 66 q^{19} + 12 q^{21} + 74 q^{24} - 176 q^{25} - 55 q^{27} + 146 q^{28}+ \cdots + 252 q^{97}+O(q^{100}) \) 16 * q + 5 * q^3 + 18 * q^4 - 32 * q^6 + 34 * q^7 + 17 * q^9 + 12 * q^10 + 106 * q^12 + 2 * q^13 - 28 * q^15 + 102 * q^16 - 42 * q^18 - 66 * q^19 + 12 * q^21 + 74 * q^24 - 176 * q^25 - 55 * q^27 + 146 * q^28 - 110 * q^30 - 126 * q^31 - 132 * q^34 + 226 * q^36 - 230 * q^37 - 136 * q^39 - 226 * q^40 - 72 * q^42 + 156 * q^43 - 72 * q^45 - 308 * q^46 + 255 * q^48 + 170 * q^49 + 169 * q^51 + 224 * q^52 - 1046 * q^54 + 259 * q^57 + 184 * q^58 - 316 * q^60 - 104 * q^61 + 108 * q^63 - 184 * q^64 + 368 * q^67 - 22 * q^69 - 52 * q^70 - 73 * q^72 - 354 * q^73 + 54 * q^75 + 900 * q^76 - 492 * q^78 - 566 * q^79 + 377 * q^81 + 200 * q^82 + 720 * q^84 + 162 * q^85 - 132 * q^87 + 774 * q^90 - 226 * q^91 - 370 * q^93 + 530 * q^94 + 67 * q^96 + 252 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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