LMFDB - Embedded newform 546.2.bz.a.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	546.31
Dual form			546.2.bz.a.229.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.799972 - 2.98554i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.93737 + 1.80183i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.799972 - 2.98554i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.93737 + 1.80183i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.54543 + 2.67676i) q^{10} +(2.46223 - 0.659752i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.14099 + 1.77036i) q^{13} +(2.33771 - 1.23900i) q^{14} +(2.18556 - 2.18556i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.0961517 - 0.166540i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(1.54430 - 5.76341i) q^{19} +(2.18556 - 2.18556i) q^{20} +(-2.57873 + 0.591740i) q^{21} -2.54908 q^{22} +(5.28314 - 3.05023i) q^{23} +(-0.258819 - 0.965926i) q^{24} +(-3.94335 - 2.27669i) q^{25} +(-2.57576 - 2.52299i) q^{26} +1.00000i q^{27} +(-2.57873 + 0.591740i) q^{28} +1.72145 q^{29} +(-2.67676 + 1.54543i) q^{30} +(-4.78133 + 1.28115i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.46223 + 0.659752i) q^{33} +(-0.135979 + 0.135979i) q^{34} +(3.82957 + 7.22552i) q^{35} +1.00000i q^{36} +(2.22575 - 8.30660i) q^{37} +(-2.98336 + 5.16733i) q^{38} +(1.83499 + 3.10367i) q^{39} +(-2.67676 + 1.54543i) q^{40} +(-6.08468 - 6.08468i) q^{41} +(2.64401 + 0.0958474i) q^{42} +8.17609i q^{43} +(2.46223 + 0.659752i) q^{44} +(2.98554 - 0.799972i) q^{45} +(-5.89258 + 1.57891i) q^{46} +(11.2973 + 3.02709i) q^{47} +1.00000i q^{48} +(0.506844 - 6.98163i) q^{49} +(3.21973 + 3.21973i) q^{50} +(0.166540 - 0.0961517i) q^{51} +(1.83499 + 3.10367i) q^{52} +(2.33889 - 4.05108i) q^{53} +(0.258819 - 0.965926i) q^{54} -7.87885i q^{55} +(2.64401 + 0.0958474i) q^{56} +(4.21911 - 4.21911i) q^{57} +(-1.66280 - 0.445545i) q^{58} +(2.23706 + 8.34882i) q^{59} +(2.98554 - 0.799972i) q^{60} +(-9.60184 + 5.54362i) q^{61} +4.95000 q^{62} +(-2.52911 - 0.776903i) q^{63} +1.00000i q^{64} +(7.79819 - 7.96130i) q^{65} +(-2.20757 - 1.27454i) q^{66} +(1.28847 + 4.80864i) q^{67} +(0.166540 - 0.0961517i) q^{68} +6.10045 q^{69} +(-1.82898 - 7.97048i) q^{70} +(3.54963 - 3.54963i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-2.53993 - 9.47914i) q^{73} +(-4.29981 + 7.44749i) q^{74} +(-2.27669 - 3.94335i) q^{75} +(4.21911 - 4.21911i) q^{76} +(-3.58150 + 5.71469i) q^{77} +(-0.969178 - 3.47285i) q^{78} +(3.52642 + 6.10793i) q^{79} +(2.98554 - 0.799972i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.30252 + 7.45218i) q^{82} +(-0.125330 - 0.125330i) q^{83} +(-2.52911 - 0.776903i) q^{84} +(-0.420292 - 0.420292i) q^{85} +(2.11613 - 7.89749i) q^{86} +(1.49082 + 0.860727i) q^{87} +(-2.20757 - 1.27454i) q^{88} +(-13.8225 - 3.70373i) q^{89} -3.09086 q^{90} +(-9.27516 + 2.22966i) q^{91} +6.10045 q^{92} +(-4.78133 - 1.28115i) q^{93} +(-10.1288 - 5.84789i) q^{94} +(-15.9715 - 9.22113i) q^{95} +(0.258819 - 0.965926i) q^{96} +(7.26558 + 7.26558i) q^{97} +(-2.29655 + 6.61255i) q^{98} +(1.80248 + 1.80248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 + 20 * q^9	$ 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.799972	−	2.98554i	0.357758	−	1.33517i	−0.519219	−	0.854641i	$-0.673777\pi$
$5$	0.799972	−	2.98554i	0.357758	−	1.33517i	0.876977	−	0.480532i	$-0.159556\pi$
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	−1.93737	+	1.80183i	−0.732259	+	0.681026i
$7$	−1.93737	+	1.80183i	−0.732259	+	0.681026i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.54543	+	2.67676i	−0.488707	+	0.846466i
$11$	2.46223	−	0.659752i	0.742389	−	0.198923i	0.132250	−	0.991216i	$-0.457780\pi$
$11$	2.46223	−	0.659752i	0.742389	−	0.198923i	0.610140	+	0.792294i	$0.291113\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	3.14099	+	1.77036i	0.871154	+	0.491011i
$13$	3.14099	+	1.77036i	0.871154	+	0.491011i
$14$	2.33771	−	1.23900i	0.624779	−	0.331137i
$15$	2.18556	−	2.18556i	0.564310	−	0.564310i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.0961517	−	0.166540i	0.0233202	−	0.0403918i	−0.854130	−	0.520060i	$-0.825910\pi$
$17$	0.0961517	−	0.166540i	0.0233202	−	0.0403918i	0.877450	+	0.479668i	$0.159243\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	1.54430	−	5.76341i	0.354287	−	1.32222i	−0.527093	−	0.849808i	$-0.676718\pi$
$19$	1.54430	−	5.76341i	0.354287	−	1.32222i	0.881380	−	0.472409i	$-0.156615\pi$
$20$	2.18556	−	2.18556i	0.488707	−	0.488707i
$21$	−2.57873	+	0.591740i	−0.562725	+	0.129128i
$22$	−2.54908			−0.543467
$23$	5.28314	−	3.05023i	1.10161	−	0.636016i	0.164968	−	0.986299i	$-0.447248\pi$
$23$	5.28314	−	3.05023i	1.10161	−	0.636016i	0.936644	+	0.350283i	$0.113915\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$	−3.94335	−	2.27669i	−0.788670	−	0.455339i
$26$	−2.57576	−	2.52299i	−0.505148	−	0.494799i
$27$			1.00000i			0.192450i
$28$	−2.57873	+	0.591740i	−0.487334	+	0.111828i
$29$	1.72145			0.319666			0.159833	−	0.987144i	$-0.448904\pi$
$29$	1.72145			0.319666			0.159833	+	0.987144i	$0.448904\pi$
$30$	−2.67676	+	1.54543i	−0.488707	+	0.282155i
$31$	−4.78133	+	1.28115i	−0.858752	+	0.230102i	−0.661218	−	0.750194i	$-0.729960\pi$
$31$	−4.78133	+	1.28115i	−0.858752	+	0.230102i	−0.197534	+	0.980296i	$0.563293\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	2.46223	+	0.659752i	0.428619	+	0.114848i
$34$	−0.135979	+	0.135979i	−0.0233202	+	0.0233202i
$35$	3.82957	+	7.22552i	0.647316	+	1.22134i
$36$			1.00000i			0.166667i
$37$	2.22575	−	8.30660i	0.365910	−	1.36560i	−0.500272	−	0.865868i	$-0.666767\pi$
$37$	2.22575	−	8.30660i	0.365910	−	1.36560i	0.866182	−	0.499728i	$-0.166567\pi$
$38$	−2.98336	+	5.16733i	−0.483965	+	0.838252i
$39$	1.83499	+	3.10367i	0.293834	+	0.496986i
$40$	−2.67676	+	1.54543i	−0.423233	+	0.244354i
$41$	−6.08468	−	6.08468i	−0.950268	−	0.950268i	0.0485529	−	0.998821i	$-0.484539\pi$
$41$	−6.08468	−	6.08468i	−0.950268	−	0.950268i	−0.998821	+	0.0485529i	$0.984539\pi$
$42$	2.64401	+	0.0958474i	0.407980	+	0.0147896i
$43$			8.17609i			1.24684i	0.781887	+	0.623421i	$0.214258\pi$
$43$			8.17609i			1.24684i	−0.781887	+	0.623421i	$0.785742\pi$
$44$	2.46223	+	0.659752i	0.371195	+	0.0994613i
$45$	2.98554	−	0.799972i	0.445058	−	0.119253i
$46$	−5.89258	+	1.57891i	−0.868814	+	0.232798i
$47$	11.2973	+	3.02709i	1.64787	+	0.441546i	0.959016	−	0.283350i	$-0.0914459\pi$
$47$	11.2973	+	3.02709i	1.64787	+	0.441546i	0.688857	+	0.724897i	$0.258113\pi$
$48$			1.00000i			0.144338i
$49$	0.506844	−	6.98163i	0.0724062	−	0.997375i
$50$	3.21973	+	3.21973i	0.455339	+	0.455339i
$51$	0.166540	−	0.0961517i	0.0233202	−	0.0134639i
$52$	1.83499	+	3.10367i	0.254468	+	0.430402i
$53$	2.33889	−	4.05108i	0.321271	−	0.556458i	−0.659479	−	0.751723i	$-0.729223\pi$
$53$	2.33889	−	4.05108i	0.321271	−	0.556458i	0.980751	+	0.195264i	$0.0625565\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$		−	7.87885i		−	1.06238i
$56$	2.64401	+	0.0958474i	0.353321	+	0.0128081i
$57$	4.21911	−	4.21911i	0.558834	−	0.558834i
$58$	−1.66280	−	0.445545i	−0.218336	−	0.0585029i
$59$	2.23706	+	8.34882i	0.291240	+	1.08692i	0.944157	+	0.329495i	$0.106878\pi$
$59$	2.23706	+	8.34882i	0.291240	+	1.08692i	−0.652917	+	0.757429i	$0.726455\pi$
$60$	2.98554	−	0.799972i	0.385431	−	0.103276i
$61$	−9.60184	+	5.54362i	−1.22939	+	0.709788i	−0.966902	−	0.255147i	$-0.917876\pi$
$61$	−9.60184	+	5.54362i	−1.22939	+	0.709788i	−0.262487	+	0.964935i	$0.584543\pi$
$62$	4.95000			0.628650
$63$	−2.52911	−	0.776903i	−0.318639	−	0.0978805i
$64$			1.00000i			0.125000i
$65$	7.79819	−	7.96130i	0.967247	−	0.987477i
$66$	−2.20757	−	1.27454i	−0.271733	−	0.156885i
$67$	1.28847	+	4.80864i	0.157412	+	0.587468i	0.998887	+	0.0471725i	$0.0150210\pi$
$67$	1.28847	+	4.80864i	0.157412	+	0.587468i	−0.841475	+	0.540296i	$0.818312\pi$
$68$	0.166540	−	0.0961517i	0.0201959	−	0.0116601i
$69$	6.10045			0.734408
$70$	−1.82898	−	7.97048i	−0.218605	−	0.952654i
$71$	3.54963	−	3.54963i	0.421264	−	0.421264i	−0.464375	−	0.885639i	$-0.653721\pi$
$71$	3.54963	−	3.54963i	0.421264	−	0.421264i	0.885639	+	0.464375i	$0.153721\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−2.53993	−	9.47914i	−0.297276	−	1.10945i	−0.939393	−	0.342843i	$-0.888610\pi$
$73$	−2.53993	−	9.47914i	−0.297276	−	1.10945i	0.642117	−	0.766607i	$-0.278056\pi$
$74$	−4.29981	+	7.44749i	−0.499843	+	0.865753i
$75$	−2.27669	−	3.94335i	−0.262890	−	0.455339i
$76$	4.21911	−	4.21911i	0.483965	−	0.483965i
$77$	−3.58150	+	5.71469i	−0.408150	+	0.651250i
$78$	−0.969178	−	3.47285i	−0.109738	−	0.393223i
$79$	3.52642	+	6.10793i	0.396753	+	0.687196i	0.993323	−	0.115365i	$-0.0368037\pi$
$79$	3.52642	+	6.10793i	0.396753	+	0.687196i	−0.596570	+	0.802561i	$0.703470\pi$
$80$	2.98554	−	0.799972i	0.333793	−	0.0894396i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.30252	+	7.45218i	0.475134	+	0.822956i
$83$	−0.125330	−	0.125330i	−0.0137567	−	0.0137567i	0.700195	−	0.713952i	$-0.253096\pi$
$83$	−0.125330	−	0.125330i	−0.0137567	−	0.0137567i	−0.713952	+	0.700195i	$0.753096\pi$
$84$	−2.52911	−	0.776903i	−0.275949	−	0.0847670i
$85$	−0.420292	−	0.420292i	−0.0455870	−	0.0455870i
$86$	2.11613	−	7.89749i	0.228188	−	0.851608i
$87$	1.49082	+	0.860727i	0.159833	+	0.0922796i
$88$	−2.20757	−	1.27454i	−0.235328	−	0.135867i
$89$	−13.8225	−	3.70373i	−1.46518	−	0.392594i	−0.563905	−	0.825839i	$-0.690702\pi$
$89$	−13.8225	−	3.70373i	−1.46518	−	0.392594i	−0.901276	+	0.433245i	$0.857368\pi$
$90$	−3.09086			−0.325805
$91$	−9.27516	+	2.22966i	−0.972301	+	0.233732i
$92$	6.10045			0.636016
$93$	−4.78133	−	1.28115i	−0.495801	−	0.132849i
$94$	−10.1288	−	5.84789i	−1.04471	−	0.603164i
$95$	−15.9715	−	9.22113i	−1.63864	−	0.946068i
$96$	0.258819	−	0.965926i	0.0264156	−	0.0985844i
$97$	7.26558	+	7.26558i	0.737708	+	0.737708i	0.972134	−	0.234426i	$-0.0753210\pi$
$97$	7.26558	+	7.26558i	0.737708	+	0.737708i	−0.234426	+	0.972134i	$0.575321\pi$
$98$	−2.29655	+	6.61255i	−0.231987	+	0.667969i
$99$	1.80248	+	1.80248i	0.181156	+	0.181156i
$100$	−2.27669	−	3.94335i	−0.227669	−	0.394335i
$101$	−7.14522	+	12.3759i	−0.710976	+	1.23145i	0.253515	+	0.967331i	$0.418413\pi$
$101$	−7.14522	+	12.3759i	−0.710976	+	1.23145i	−0.964491	+	0.264115i	$0.914920\pi$
$102$	−0.185751	+	0.0497718i	−0.0183921	+	0.00492814i
$103$	4.68944	+	8.12235i	0.462065	+	0.800319i	0.999064	−	0.0432635i	$-0.0137755\pi$
$103$	4.68944	+	8.12235i	0.462065	+	0.800319i	−0.536999	+	0.843583i	$0.680442\pi$
$104$	−0.969178	−	3.47285i	−0.0950357	−	0.340541i
$105$	−0.296250	+	8.17227i	−0.0289111	+	0.797532i
$106$	−3.30769	+	3.30769i	−0.321271	+	0.321271i
$107$	−2.39319	−	4.14513i	−0.231359	−	0.400725i	0.726850	−	0.686797i	$-0.240984\pi$
$107$	−2.39319	−	4.14513i	−0.231359	−	0.400725i	−0.958208	+	0.286072i	$0.907650\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	2.68597	+	10.0242i	0.257269	+	0.960141i	0.966814	+	0.255481i	$0.0822338\pi$
$109$	2.68597	+	10.0242i	0.257269	+	0.960141i	−0.709545	+	0.704660i	$0.751100\pi$
$110$	−2.03920	+	7.61039i	−0.194430	+	0.725622i
$111$	6.08085	−	6.08085i	0.577169	−	0.577169i
$112$	−2.52911	−	0.776903i	−0.238979	−	0.0734104i
$113$	−3.32203			−0.312510			−0.156255	−	0.987717i	$-0.549942\pi$
$113$	−3.32203			−0.312510			−0.156255	+	0.987717i	$0.549942\pi$
$114$	−5.16733	+	2.98336i	−0.483965	+	0.279417i
$115$	−4.88019	−	18.2131i	−0.455080	−	1.69838i
$116$	1.49082	+	0.860727i	0.138419	+	0.0799165i
$117$	0.0373139	+	3.60536i	0.00344967	+	0.333315i
$118$		−	8.64334i		−	0.795684i
$119$	0.113794	+	0.495898i	0.0104314	+	0.0454589i
$120$	−3.09086			−0.282155
$121$	−3.89899	+	2.25108i	−0.354454	+	0.204644i
$122$	10.7095	−	2.86959i	0.969589	−	0.259801i
$123$	−2.22715	−	8.31183i	−0.200815	−	0.749453i
$124$	−4.78133	−	1.28115i	−0.429376	−	0.115051i
$125$	0.976102	−	0.976102i	0.0873052	−	0.0873052i
$126$	2.24186	+	1.40501i	0.199721	+	0.125169i
$127$			13.1197i			1.16419i	0.813122	+	0.582093i	$0.197766\pi$
$127$			13.1197i			1.16419i	−0.813122	+	0.582093i	$0.802234\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−4.08804	+	7.08070i	−0.359932	+	0.623421i
$130$	−9.59301	+	5.67170i	−0.841363	+	0.497441i
$131$	−13.9955	+	8.08028i	−1.22279	+	0.705978i	−0.965512	−	0.260360i	$-0.916159\pi$
$131$	−13.9955	+	8.08028i	−1.22279	+	0.705978i	−0.257277	+	0.966338i	$0.582825\pi$
$132$	1.80248	+	1.80248i	0.156885	+	0.156885i
$133$	7.39277	+	13.9484i	0.641035	+	1.20948i
$134$		−	4.97827i		−	0.430057i
$135$	2.98554	+	0.799972i	0.256954	+	0.0688506i
$136$	−0.185751	+	0.0497718i	−0.0159280	+	0.00426790i
$137$	−14.2660	+	3.82257i	−1.21883	+	0.326584i	−0.810220	−	0.586126i	$-0.800652\pi$
$137$	−14.2660	+	3.82257i	−1.21883	+	0.326584i	−0.408608	+	0.912710i	$0.633986\pi$
$138$	−5.89258	−	1.57891i	−0.501610	−	0.134406i
$139$			0.957430i			0.0812082i	0.999175	+	0.0406041i	$0.0129282\pi$
$139$			0.957430i			0.0812082i	−0.999175	+	0.0406041i	$0.987072\pi$
$140$	−0.296250	+	8.17227i	−0.0250377	+	0.690683i
$141$	8.27016	+	8.27016i	0.696473	+	0.696473i
$142$	−4.34739	+	2.50997i	−0.364825	+	0.210632i
$143$	8.90183	+	2.28677i	0.744408	+	0.191229i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.37712	−	5.13946i	0.114363	−	0.426809i
$146$			9.81353i			0.812174i
$147$	3.92975	−	5.79284i	0.324121	−	0.477786i
$148$	6.08085	−	6.08085i	0.499843	−	0.499843i
$149$	6.45351	+	1.72921i	0.528692	+	0.141663i	0.513284	−	0.858219i	$-0.328429\pi$
$149$	6.45351	+	1.72921i	0.528692	+	0.141663i	0.0154078	+	0.999881i	$0.495095\pi$
$150$	1.17850	+	4.39823i	0.0962244	+	0.359114i
$151$	−11.4043	+	3.05577i	−0.928067	+	0.248675i	−0.691030	−	0.722826i	$-0.742843\pi$
$151$	−11.4043	+	3.05577i	−0.928067	+	0.248675i	−0.237037	+	0.971501i	$0.576176\pi$
$152$	−5.16733	+	2.98336i	−0.419126	+	0.241982i
$153$	0.192303			0.0155468
$154$	4.93853	−	4.59301i	0.397958	−	0.370115i
$155$			15.2997i			1.22890i
$156$	0.0373139	+	3.60536i	0.00298751	+	0.288660i
$157$	−10.8439	−	6.26073i	−0.865437	−	0.499661i	0.000391926	−	1.00000i	$-0.499875\pi$
$157$	−10.8439	−	6.26073i	−0.865437	−	0.499661i	−0.865829	+	0.500339i	$0.833209\pi$
$158$	−1.82541	−	6.81251i	−0.145222	−	0.541974i
$159$	4.05108	−	2.33889i	0.321271	−	0.185486i
$160$	−3.09086			−0.244354
$161$	−4.73946	+	15.4287i	−0.373522	+	1.21596i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−5.07262	+	18.9313i	−0.397318	+	1.48281i	0.420478	+	0.907303i	$0.361862\pi$
$163$	−5.07262	+	18.9313i	−0.397318	+	1.48281i	−0.817796	+	0.575508i	$0.804804\pi$
$164$	−2.22715	−	8.31183i	−0.173911	−	0.649045i
$165$	3.93943	−	6.82329i	0.306684	−	0.531192i
$166$	0.0886215	+	0.153497i	0.00687837	+	0.0119137i
$167$	13.0964	−	13.0964i	1.01343	−	1.01343i	0.0135245	−	0.999909i	$-0.495695\pi$
$167$	13.0964	−	13.0964i	1.01343	−	1.01343i	0.999909	−	0.0135245i	$-0.00430512\pi$
$168$	2.24186	+	1.40501i	0.172963	+	0.108399i
$169$	6.73162	+	11.1214i	0.517817	+	0.855491i
$170$	0.297191	+	0.514750i	0.0227935	+	0.0394795i
$171$	5.76341	−	1.54430i	0.440739	−	0.118096i
$172$	−4.08804	+	7.08070i	−0.311710	+	0.539898i
$173$	−8.38540	−	14.5239i	−0.637530	−	1.10423i	−0.985973	−	0.166904i	$-0.946623\pi$
$173$	−8.38540	−	14.5239i	−0.637530	−	1.10423i	0.348443	−	0.937330i	$-0.386710\pi$
$174$	−1.21725	−	1.21725i	−0.0922796	−	0.0922796i
$175$	11.7420	−	2.69442i	0.887608	−	0.203679i
$176$	1.80248	+	1.80248i	0.135867	+	0.135867i
$177$	−2.23706	+	8.34882i	−0.168148	+	0.627536i
$178$	12.3929	+	7.15505i	0.928888	+	0.536294i
$179$	−7.66247	−	4.42393i	−0.572720	−	0.330660i	0.185515	−	0.982641i	$-0.440605\pi$
$179$	−7.66247	−	4.42393i	−0.572720	−	0.330660i	−0.758235	+	0.651981i	$0.773938\pi$
$180$	2.98554	+	0.799972i	0.222529	+	0.0596264i
$181$	9.29817			0.691128			0.345564	−	0.938395i	$-0.387688\pi$
$181$	9.29817			0.691128			0.345564	+	0.938395i	$0.387688\pi$
$182$	9.53620	+	0.246905i	0.706870	+	0.0183019i
$183$	−11.0872			−0.819593
$184$	−5.89258	−	1.57891i	−0.434407	−	0.116399i
$185$	−23.0191	−	13.2901i	−1.69240	−	0.977107i
$186$	4.28682	+	2.47500i	0.314325	+	0.181476i
$187$	0.126873	−	0.473495i	0.00927784	−	0.0346254i
$188$	8.27016	+	8.27016i	0.603164	+	0.603164i
$189$	−1.80183	−	1.93737i	−0.131064	−	0.140923i
$190$	13.0407	+	13.0407i	0.946068	+	0.946068i
$191$	−2.60280	−	4.50819i	−0.188332	−	0.326201i	0.756362	−	0.654153i	$-0.226975\pi$
$191$	−2.60280	−	4.50819i	−0.188332	−	0.326201i	−0.944694	+	0.327952i	$0.893642\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−10.6441	+	2.85208i	−0.766181	+	0.205298i	−0.620684	−	0.784061i	$-0.713145\pi$
$193$	−10.6441	+	2.85208i	−0.766181	+	0.205298i	−0.145497	+	0.989359i	$0.546478\pi$
$194$	−5.13754	−	8.89848i	−0.368854	−	0.638874i
$195$	10.7341	−	2.99559i	0.768683	−	0.214519i
$196$	3.92975	−	5.79284i	0.280697	−	0.413775i
$197$	−3.00693	+	3.00693i	−0.214235	+	0.214235i	−0.806064	−	0.591829i	$-0.798406\pi$
$197$	−3.00693	+	3.00693i	−0.214235	+	0.214235i	0.591829	+	0.806064i	$0.298406\pi$
$198$	−1.27454	−	2.20757i	−0.0905778	−	0.156885i
$199$	8.33229	−	14.4319i	0.590660	−	1.02305i	−0.403484	−	0.914987i	$-0.632201\pi$
$199$	8.33229	−	14.4319i	0.590660	−	1.02305i	0.994144	−	0.108066i	$-0.0344659\pi$
$200$	1.17850	+	4.39823i	0.0833328	+	0.311002i
$201$	−1.28847	+	4.80864i	−0.0908817	+	0.339175i
$202$	10.1049	−	10.1049i	0.710976	−	0.710976i
$203$	−3.33510	+	3.10176i	−0.234078	+	0.217701i
$204$	0.192303			0.0134639
$205$	−23.0336	+	13.2985i	−1.60874	+	0.928805i
$206$	−2.42743	−	9.05931i	−0.169127	−	0.631192i
$207$	5.28314	+	3.05023i	0.367204	+	0.212005i
$208$	0.0373139	+	3.60536i	0.00258726	+	0.249987i
$209$		−	15.2097i		−	1.05208i
$210$	2.40129	−	7.81713i	0.165705	−	0.539433i
$211$	6.55651			0.451369			0.225684	−	0.974200i	$-0.427538\pi$
$211$	6.55651			0.451369			0.225684	+	0.974200i	$0.427538\pi$
$212$	4.05108	−	2.33889i	0.278229	−	0.160636i
$213$	4.84889	−	1.29926i	0.332240	−	0.0890235i
$214$	1.23881	+	4.62329i	0.0846831	+	0.316042i
$215$	24.4100	+	6.54064i	1.66475	+	0.446068i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	6.95481	−	11.0972i	0.472123	−	0.753327i
$218$		−	10.3778i		−	0.702872i
$219$	2.53993	−	9.47914i	0.171632	−	0.640541i
$220$	3.93943	−	6.82329i	0.265596	−	0.460026i
$221$	0.596847	−	0.352876i	0.0401483	−	0.0237370i
$222$	−7.44749	+	4.29981i	−0.499843	+	0.288584i
$223$	−13.5086	−	13.5086i	−0.904604	−	0.904604i	0.0912259	−	0.995830i	$-0.470921\pi$
$223$	−13.5086	−	13.5086i	−0.904604	−	0.904604i	−0.995830	+	0.0912259i	$0.970921\pi$
$224$	2.24186	+	1.40501i	0.149791	+	0.0938764i
$225$		−	4.55339i		−	0.303559i
$226$	3.20883	+	0.859804i	0.213448	+	0.0571933i
$227$	−6.54583	+	1.75395i	−0.434462	+	0.116414i	−0.469420	−	0.882975i	$-0.655537\pi$
$227$	−6.54583	+	1.75395i	−0.434462	+	0.116414i	0.0349578	+	0.999389i	$0.488870\pi$
$228$	5.76341	−	1.54430i	0.381691	−	0.102274i
$229$	−13.7139	−	3.67462i	−0.906239	−	0.242826i	−0.224545	−	0.974464i	$-0.572090\pi$
$229$	−13.7139	−	3.67462i	−0.906239	−	0.242826i	−0.681694	+	0.731638i	$0.738756\pi$
$230$			18.8556i			1.24330i
$231$	−5.95901	+	3.15832i	−0.392074	+	0.207802i
$232$	−1.21725	−	1.21725i	−0.0799165	−	0.0799165i
$233$	−5.95618	+	3.43880i	−0.390202	+	0.225283i	−0.682248	−	0.731121i	$-0.738997\pi$
$233$	−5.95618	+	3.43880i	−0.390202	+	0.225283i	0.292046	+	0.956404i	$0.405664\pi$
$234$	0.897093	−	3.49217i	0.0586448	−	0.228290i
$235$	18.0750	−	31.3068i	1.17908	−	2.04223i
$236$	−2.23706	+	8.34882i	−0.145620	+	0.543462i
$237$			7.05283i			0.458131i
$238$	0.0184318	−	0.508453i	0.00119475	−	0.0329581i
$239$	−3.10382	+	3.10382i	−0.200770	+	0.200770i	−0.800330	−	0.599560i	$-0.795342\pi$
$239$	−3.10382	+	3.10382i	−0.200770	+	0.200770i	0.599560	+	0.800330i	$0.295342\pi$
$240$	2.98554	+	0.799972i	0.192716	+	0.0516380i
$241$	−2.47901	−	9.25180i	−0.159687	−	0.595961i	−0.998658	−	0.0517849i	$-0.983509\pi$
$241$	−2.47901	−	9.25180i	−0.159687	−	0.595961i	0.838971	−	0.544176i	$-0.183158\pi$
$242$	4.34876	−	1.16525i	0.279549	−	0.0749049i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−11.0872			−0.709788
$245$	−20.4384	−	7.09831i	−1.30576	−	0.453494i
$246$			8.60504i			0.548637i
$247$	15.0540	−	15.3688i	0.957861	−	0.977895i
$248$	4.28682	+	2.47500i	0.272214	+	0.157163i
$249$	−0.0458739	−	0.171204i	−0.00290714	−	0.0108496i
$250$	−1.19548	+	0.690208i	−0.0756085	+	0.0436526i
$251$	−26.5647			−1.67675			−0.838375	−	0.545095i	$-0.816494\pi$
$251$	−26.5647			−1.67675			−0.838375	+	0.545095i	$0.816494\pi$
$252$	−1.80183	−	1.93737i	−0.113504	−	0.122043i
$253$	10.9959	−	10.9959i	0.691307	−	0.691307i
$254$	3.39563	−	12.6727i	0.213061	−	0.795154i
$255$	−0.153837	−	0.574129i	−0.00963367	−	0.0359534i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.16190	−	7.20862i	−0.259612	−	0.449661i	0.706526	−	0.707687i	$-0.250261\pi$
$257$	−4.16190	−	7.20862i	−0.259612	−	0.449661i	−0.966138	+	0.258026i	$0.916928\pi$
$258$	5.78137	−	5.78137i	0.359932	−	0.359932i
$259$	10.6549	+	20.1034i	0.662066	+	1.24916i
$260$	10.7341	−	2.99559i	0.665699	−	0.185779i
$261$	0.860727	+	1.49082i	0.0532777	+	0.0922796i
$262$	15.6099	−	4.18266i	0.964383	−	0.258406i
$263$	8.27191	−	14.3274i	0.510068	−	0.883464i	−0.489864	−	0.871799i	$-0.662954\pi$
$263$	8.27191	−	14.3274i	0.510068	−	0.883464i	0.999932	−	0.0116649i	$-0.00371315\pi$
$264$	−1.27454	−	2.20757i	−0.0784427	−	0.135867i
$265$	−10.2236	−	10.2236i	−0.628030	−	0.628030i
$266$	−3.53075	−	15.3866i	−0.216484	−	0.943410i
$267$	−10.1188	−	10.1188i	−0.619259	−	0.619259i
$268$	−1.28847	+	4.80864i	−0.0787058	+	0.293734i
$269$	21.5406	+	12.4365i	1.31335	+	0.758264i	0.982650	−	0.185470i	$-0.0593809\pi$
$269$	21.5406	+	12.4365i	1.31335	+	0.758264i	0.330703	+	0.943735i	$0.392714\pi$
$270$	−2.67676	−	1.54543i	−0.162902	−	0.0940517i
$271$	0.217179	+	0.0581928i	0.0131927	+	0.00353496i	0.265409	−	0.964136i	$-0.414493\pi$
$271$	0.217179	+	0.0581928i	0.0131927	+	0.00353496i	−0.252217	+	0.967671i	$0.581160\pi$
$272$	0.192303			0.0116601
$273$	−9.14735	−	2.70664i	−0.553623	−	0.163813i
$274$	14.7693			0.892244
$275$	−11.2115	−	3.00410i	−0.676077	−	0.181154i
$276$	5.28314	+	3.05023i	0.318008	+	0.183602i
$277$	27.7764	+	16.0367i	1.66892	+	0.963554i	0.968219	+	0.250103i	$0.0804645\pi$
$277$	27.7764	+	16.0367i	1.66892	+	0.963554i	0.700705	+	0.713451i	$0.252869\pi$
$278$	0.247801	−	0.924807i	0.0148621	−	0.0554662i
$279$	−3.50018	−	3.50018i	−0.209550	−	0.209550i
$280$	2.40129	−	7.81713i	0.143505	−	0.467163i
$281$	4.90671	+	4.90671i	0.292710	+	0.292710i	0.838150	−	0.545440i	$-0.183638\pi$
$281$	4.90671	+	4.90671i	0.292710	+	0.292710i	−0.545440	+	0.838150i	$0.683638\pi$
$282$	−5.84789	−	10.1288i	−0.348237	−	0.603164i
$283$	−9.61696	+	16.6571i	−0.571669	+	0.990159i	0.424726	+	0.905322i	$0.360370\pi$
$283$	−9.61696	+	16.6571i	−0.571669	+	0.990159i	−0.996395	+	0.0848375i	$0.972963\pi$
$284$	4.84889	−	1.29926i	0.287728	−	0.0770966i
$285$	−9.22113	−	15.9715i	−0.546213	−	0.946068i
$286$	−8.00665	−	4.51281i	−0.473443	−	0.266848i
$287$	22.7519	+	0.824770i	1.34300	+	0.0486847i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	8.48151	+	14.6904i	0.498912	+	0.864142i
$290$	−2.66038	+	4.60792i	−0.156223	+	0.270586i
$291$	2.65939	+	9.92497i	0.155896	+	0.581812i
$292$	2.53993	−	9.47914i	0.148638	−	0.554725i
$293$	12.2790	−	12.2790i	0.717348	−	0.717348i	−0.250714	−	0.968061i	$-0.580665\pi$
$293$	12.2790	−	12.2790i	0.717348	−	0.717348i	0.968061	+	0.250714i	$0.0806653\pi$
$294$	−5.29515	+	4.57836i	−0.308819	+	0.267016i
$295$	26.7153			1.55543
$296$	−7.44749	+	4.29981i	−0.432877	+	0.249921i
$297$	0.659752	+	2.46223i	0.0382827	+	0.142873i
$298$	−5.78606	−	3.34058i	−0.335177	−	0.193515i
$299$	21.9943	−	0.227632i	1.27196	−	0.0131643i
$300$		−	4.55339i		−	0.262890i
$301$	−14.7319	−	15.8401i	−0.849132	−	0.913011i
$302$	11.8066			0.679393
$303$	−12.3759	+	7.14522i	−0.710976	+	0.410482i
$304$	5.76341	−	1.54430i	0.330554	−	0.0885717i
$305$	8.86949	+	33.1014i	0.507866	+	1.89538i
$306$	−0.185751	−	0.0497718i	−0.0106187	−	0.00284526i
$307$	−9.35808	+	9.35808i	−0.534094	+	0.534094i	−0.921788	−	0.387694i	$-0.873272\pi$
$307$	−9.35808	+	9.35808i	−0.534094	+	0.534094i	0.387694	+	0.921788i	$0.373272\pi$
$308$	−5.95901	+	3.15832i	−0.339546	+	0.179962i
$309$			9.37889i			0.533546i
$310$	3.95986	−	14.7784i	0.224905	−	0.839357i
$311$	1.67332	−	2.89828i	0.0948855	−	0.164346i	−0.814675	−	0.579917i	$-0.803085\pi$
$311$	1.67332	−	2.89828i	0.0948855	−	0.164346i	0.909561	+	0.415571i	$0.136418\pi$
$312$	0.897093	−	3.49217i	0.0507879	−	0.197705i
$313$	23.6762	−	13.6695i	1.33826	−	0.772643i	0.351708	−	0.936110i	$-0.385601\pi$
$313$	23.6762	−	13.6695i	1.33826	−	0.772643i	0.986549	+	0.163467i	$0.0522676\pi$
$314$	8.85401	+	8.85401i	0.499661	+	0.499661i
$315$	−4.34269	+	6.92927i	−0.244683	+	0.390420i
$316$			7.05283i			0.396753i
$317$	23.7463	+	6.36280i	1.33372	+	0.357370i	0.854103	−	0.520105i	$-0.174107\pi$
$317$	23.7463	+	6.36280i	1.33372	+	0.357370i	0.479622	+	0.877475i	$0.340774\pi$
$318$	−4.51839	+	1.21070i	−0.253379	+	0.0678926i
$319$	4.23861	−	1.13573i	0.237317	−	0.0635888i
$320$	2.98554	+	0.799972i	0.166897	+	0.0447198i
$321$		−	4.78638i		−	0.267150i
$322$	8.57122	−	13.6764i	0.477655	−	0.762154i
$323$	−0.811349	−	0.811349i	−0.0451447	−	0.0451447i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−8.35544	−	14.1322i	−0.463476	−	0.783915i
$326$	9.79954	−	16.9733i	0.542746	−	0.940064i
$327$	−2.68597	+	10.0242i	−0.148534	+	0.554338i
$328$			8.60504i			0.475134i
$329$	−27.3413	+	14.4911i	−1.50738	+	0.798919i
$330$	−5.57119	+	5.57119i	−0.306684	+	0.306684i
$331$	23.8826	+	6.39933i	1.31271	+	0.351739i	0.846241	−	0.532800i	$-0.178860\pi$
$331$	23.8826	+	6.39933i	1.31271	+	0.351739i	0.466466	+	0.884539i	$0.345527\pi$
$332$	−0.0458739	−	0.171204i	−0.00251766	−	0.00939602i
$333$	8.30660	−	2.22575i	0.455199	−	0.121970i
$334$	−16.0398	+	9.26058i	−0.877659	+	0.506717i
$335$	15.3871			0.840687
$336$	−1.80183	−	1.93737i	−0.0982977	−	0.105692i
$337$		−	5.02373i		−	0.273660i	−0.990595	−	0.136830i	$-0.956309\pi$
$337$		−	5.02373i		−	0.273660i	0.990595	−	0.136830i	$-0.0436914\pi$
$338$	−3.62382	−	12.4847i	−0.197110	−	0.679079i
$339$	−2.87696	−	1.66101i	−0.156255	−	0.0902139i
$340$	−0.153837	−	0.574129i	−0.00834301	−	0.0311365i
$341$	−10.9275	+	6.30898i	−0.591756	+	0.341650i
$342$	−5.96672			−0.322643
$343$	11.5977	+	14.4393i	0.626219	+	0.779647i
$344$	5.78137	−	5.78137i	0.311710	−	0.311710i
$345$	4.88019	−	18.2131i	0.262741	−	0.980561i
$346$	4.34060	+	16.1993i	0.233352	+	0.870882i
$347$	7.56173	−	13.0973i	0.405935	−	0.703100i	−0.588495	−	0.808501i	$-0.700279\pi$
$347$	7.56173	−	13.0973i	0.405935	−	0.703100i	0.994430	+	0.105401i	$0.0336125\pi$
$348$	0.860727	+	1.49082i	0.0461398	+	0.0799165i
$349$	8.09220	−	8.09220i	0.433166	−	0.433166i	−0.456538	−	0.889704i	$-0.650911\pi$
$349$	8.09220	−	8.09220i	0.433166	−	0.433166i	0.889704	+	0.456538i	$0.150911\pi$
$350$	−12.0392	−	0.436430i	−0.643523	−	0.0233282i
$351$	−1.77036	+	3.14099i	−0.0944951	+	0.167654i
$352$	−1.27454	−	2.20757i	−0.0679333	−	0.117664i
$353$	−15.1037	+	4.04703i	−0.803890	+	0.215402i	−0.637291	−	0.770623i	$-0.719945\pi$
$353$	−15.1037	+	4.04703i	−0.803890	+	0.215402i	−0.166599	+	0.986025i	$0.553279\pi$
$354$	4.32167	−	7.48535i	0.229694	−	0.397842i
$355$	−7.75795	−	13.4372i	−0.411749	−	0.713171i
$356$	−10.1188	−	10.1188i	−0.536294	−	0.536294i
$357$	−0.149401	+	0.486358i	−0.00790714	+	0.0257408i
$358$	6.25638	+	6.25638i	0.330660	+	0.330660i
$359$	−7.70342	+	28.7496i	−0.406571	+	1.51734i	0.394569	+	0.918866i	$0.370894\pi$
$359$	−7.70342	+	28.7496i	−0.406571	+	1.51734i	−0.801140	+	0.598477i	$0.795773\pi$
$360$	−2.67676	−	1.54543i	−0.141078	−	0.0814512i
$361$	−14.3775	−	8.30087i	−0.756712	−	0.436888i
$362$	−8.98135	−	2.40654i	−0.472049	−	0.126485i
$363$	−4.50217			−0.236302
$364$	−9.14735	−	2.70664i	−0.479452	−	0.141867i
$365$	−30.3322			−1.58766
$366$	10.7095	+	2.86959i	0.559792	+	0.149996i
$367$	8.41442	+	4.85807i	0.439229	+	0.253589i	0.703271	−	0.710922i	$-0.251722\pi$
$367$	8.41442	+	4.85807i	0.439229	+	0.253589i	−0.264041	+	0.964511i	$0.585056\pi$
$368$	5.28314	+	3.05023i	0.275403	+	0.159004i
$369$	2.22715	−	8.31183i	0.115941	−	0.432697i
$370$	18.7950	+	18.7950i	0.977107	+	0.977107i
$371$	2.76803	+	12.0627i	0.143709	+	0.626266i
$372$	−3.50018	−	3.50018i	−0.181476	−	0.181476i
$373$	7.97540	+	13.8138i	0.412950	+	0.715251i	0.995211	−	0.0977512i	$-0.0311649\pi$
$373$	7.97540	+	13.8138i	0.412950	+	0.715251i	−0.582260	+	0.813002i	$0.697832\pi$
$374$	−0.245099	+	0.424524i	−0.0126738	+	0.0219516i
$375$	1.33338	−	0.357278i	0.0688554	−	0.0184498i
$376$	−5.84789	−	10.1288i	−0.301582	−	0.522355i
$377$	5.40707	+	3.04760i	0.278478	+	0.156959i
$378$	1.23900	+	2.33771i	0.0637273	+	0.120239i
$379$	5.27141	−	5.27141i	0.270774	−	0.270774i	−0.558638	−	0.829412i	$-0.688676\pi$
$379$	5.27141	−	5.27141i	0.270774	−	0.270774i	0.829412	+	0.558638i	$0.188676\pi$
$380$	−9.22113	−	15.9715i	−0.473034	−	0.819319i
$381$	−6.55986	+	11.3620i	−0.336072	+	0.582093i
$382$	1.34731	+	5.02823i	0.0689344	+	0.257267i
$383$	−8.59224	+	32.0667i	−0.439043	+	1.63853i	0.292159	+	0.956370i	$0.405626\pi$
$383$	−8.59224	+	32.0667i	−0.439043	+	1.63853i	−0.731202	+	0.682161i	$0.761040\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	14.1963	+	15.2643i	0.723512	+	0.777940i
$386$	11.0196			0.560883
$387$	−7.08070	+	4.08804i	−0.359932	+	0.207807i
$388$	2.65939	+	9.92497i	0.135010	+	0.503864i
$389$	−10.4389	−	6.02690i	−0.529273	−	0.305576i	0.211447	−	0.977389i	$-0.432182\pi$
$389$	−10.4389	−	6.02690i	−0.529273	−	0.305576i	−0.740720	+	0.671813i	$0.765516\pi$
$390$	−11.1436	+	0.115332i	−0.564280	+	0.00584006i
$391$		−	1.17314i		−	0.0593281i
$392$	−5.29515	+	4.57836i	−0.267445	+	0.231242i
$393$	−16.1606			−0.815193
$394$	3.68273	−	2.12622i	0.185533	−	0.107118i
$395$	21.0565	−	5.64207i	1.05947	−	0.283883i
$396$	0.659752	+	2.46223i	0.0331538	+	0.123732i
$397$	−19.9345	−	5.34143i	−1.00048	−	0.268079i	−0.278836	−	0.960339i	$-0.589948\pi$
$397$	−19.9345	−	5.34143i	−1.00048	−	0.268079i	−0.721648	+	0.692260i	$0.756615\pi$
$398$	−11.7836	+	11.7836i	−0.590660	+	0.590660i
$399$	−0.571894	+	15.7761i	−0.0286305	+	0.789793i
$400$		−	4.55339i		−	0.227669i
$401$	1.04930	−	3.91604i	0.0523995	−	0.195557i	−0.934764	−	0.355268i	$-0.884390\pi$
$401$	1.04930	−	3.91604i	0.0523995	−	0.195557i	0.987164	+	0.159711i	$0.0510562\pi$
$402$	2.48913	−	4.31131i	0.124147	−	0.215028i
$403$	−17.2862	−	4.44061i	−0.861087	−	0.221202i
$404$	−12.3759	+	7.14522i	−0.615723	+	0.355488i
$405$	2.18556	+	2.18556i	0.108602	+	0.108602i
$406$	4.02426	−	2.13288i	0.199720	−	0.105853i
$407$		−	21.9212i		−	1.08659i
$408$	−0.185751	−	0.0497718i	−0.00919604	−	0.00246407i
$409$	−8.72606	+	2.33814i	−0.431476	+	0.115614i	−0.468019	−	0.883718i	$-0.655032\pi$
$409$	−8.72606	+	2.33814i	−0.431476	+	0.115614i	0.0365430	+	0.999332i	$0.488365\pi$
$410$	25.6907	−	6.88379i	1.26877	−	0.339966i
$411$	−14.2660	−	3.82257i	−0.703690	−	0.188553i
$412$			9.37889i			0.462065i
$413$	−19.3772	−	12.1440i	−0.953487	−	0.597568i
$414$	−4.31367	−	4.31367i	−0.212005	−	0.212005i
$415$	−0.474437	+	0.273916i	−0.0232892	+	0.0134460i
$416$	0.897093	−	3.49217i	0.0439836	−	0.171218i
$417$	−0.478715	+	0.829159i	−0.0234428	+	0.0406041i
$418$	−3.93655	+	14.6914i	−0.192543	+	0.718581i
$419$		−	35.1145i		−	1.71545i	−0.514106	−	0.857727i	$-0.671876\pi$
$419$		−	35.1145i		−	1.71545i	0.514106	−	0.857727i	$-0.328124\pi$
$420$	−4.34269	+	6.92927i	−0.211902	+	0.338114i
$421$	5.66498	−	5.66498i	0.276094	−	0.276094i	−0.555453	−	0.831548i	$-0.687455\pi$
$421$	5.66498	−	5.66498i	0.276094	−	0.276094i	0.831548	+	0.555453i	$0.187455\pi$
$422$	−6.33310	−	1.69695i	−0.308291	−	0.0826062i
$423$	3.02709	+	11.2973i	0.147182	+	0.549291i
$424$	−4.51839	+	1.21070i	−0.219432	+	0.0587967i
$425$	−0.758320	+	0.437816i	−0.0367839	+	0.0212372i
$426$	−5.01994			−0.243217
$427$	8.61371	−	28.0409i	0.416847	−	1.35700i
$428$		−	4.78638i		−	0.231359i
$429$	6.56583	+	6.43131i	0.317001	+	0.310507i
$430$	−21.8854	−	12.6355i	−1.05541	−	0.609340i
$431$	4.83415	+	18.0413i	0.232853	+	0.869019i	0.979105	+	0.203355i	$0.0651847\pi$
$431$	4.83415	+	18.0413i	0.232853	+	0.869019i	−0.746252	+	0.665663i	$0.768149\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−3.49283			−0.167855			−0.0839273	−	0.996472i	$-0.526746\pi$
$433$	−3.49283			−0.167855			−0.0839273	+	0.996472i	$0.526746\pi$
$434$	−9.59000	+	8.91903i	−0.460335	+	0.428127i
$435$	3.76235	−	3.76235i	0.180391	−	0.180391i
$436$	−2.68597	+	10.0242i	−0.128635	+	0.480071i
$437$	−9.42093	−	35.1594i	−0.450664	−	1.68190i
$438$	−4.90677	+	8.49877i	−0.234454	+	0.406087i
$439$	0.131695	+	0.228102i	0.00628546	+	0.0108867i	0.869151	−	0.494547i	$-0.164666\pi$
$439$	0.131695	+	0.228102i	0.00628546	+	0.0108867i	−0.862866	+	0.505433i	$0.831333\pi$
$440$	−5.57119	+	5.57119i	−0.265596	+	0.265596i
$441$	6.29969	−	3.05187i	0.299985	−	0.145327i
$442$	−0.667841	+	0.186376i	−0.0317660	+	0.00886501i
$443$	4.24419	+	7.35116i	0.201648	+	0.349264i	0.949059	−	0.315097i	$-0.102037\pi$
$443$	4.24419	+	7.35116i	0.201648	+	0.349264i	−0.747412	+	0.664361i	$0.768704\pi$
$444$	8.30660	−	2.22575i	0.394214	−	0.105629i
$445$	−22.1152	+	38.3047i	−1.04836	+	1.81582i
$446$	9.55204	+	16.5446i	0.452302	+	0.783410i
$447$	4.72430	+	4.72430i	0.223452	+	0.223452i
$448$	−1.80183	−	1.93737i	−0.0851283	−	0.0915324i
$449$	−22.2036	−	22.2036i	−1.04785	−	1.04785i	−0.998796	−	0.0490587i	$-0.984378\pi$
$449$	−22.2036	−	22.2036i	−1.04785	−	1.04785i	−0.0490587	−	0.998796i	$-0.515622\pi$
$450$	−1.17850	+	4.39823i	−0.0555552	+	0.207335i
$451$	−18.9962	−	10.9675i	−0.894498	−	0.516439i
$452$	−2.87696	−	1.66101i	−0.135321	−	0.0781275i
$453$	−11.4043	−	3.05577i	−0.535820	−	0.143573i
$454$	6.77675			0.318048
$455$	−0.763149	+	29.4750i	−0.0357770	+	1.38181i
$456$	−5.96672			−0.279417
$457$	4.66966	+	1.25123i	0.218437	+	0.0585301i	0.366378	−	0.930466i	$-0.380598\pi$
$457$	4.66966	+	1.25123i	0.218437	+	0.0585301i	−0.147941	+	0.988996i	$0.547264\pi$
$458$	12.2955	+	7.09883i	0.574532	+	0.331706i
$459$	0.166540	+	0.0961517i	0.00777341	+	0.00448798i
$460$	4.88019	−	18.2131i	0.227540	−	0.849191i
$461$	−19.1638	−	19.1638i	−0.892547	−	0.892547i	0.102215	−	0.994762i	$-0.467407\pi$
$461$	−19.1638	−	19.1638i	−0.892547	−	0.892547i	−0.994762	+	0.102215i	$0.967407\pi$
$462$	6.57340	−	1.50840i	0.305822	−	0.0701769i
$463$	−5.75634	−	5.75634i	−0.267520	−	0.267520i	0.560580	−	0.828100i	$-0.310578\pi$
$463$	−5.75634	−	5.75634i	−0.267520	−	0.267520i	−0.828100	+	0.560580i	$0.810578\pi$
$464$	0.860727	+	1.49082i	0.0399582	+	0.0692097i
$465$	−7.64986	+	13.2499i	−0.354754	+	0.614452i
$466$	6.64325	−	1.78005i	0.307743	−	0.0824594i
$467$	3.04421	+	5.27272i	0.140869	+	0.243992i	0.927824	−	0.373018i	$-0.121677\pi$
$467$	3.04421	+	5.27272i	0.140869	+	0.243992i	−0.786955	+	0.617010i	$0.788344\pi$
$468$	−1.77036	+	3.14099i	−0.0818351	+	0.145192i
$469$	−11.1606	−	6.99453i	−0.515348	−	0.322977i
$470$	−25.5619	+	25.5619i	−1.17908	+	1.17908i
$471$	−6.26073	−	10.8439i	−0.288479	−	0.499661i
$472$	4.32167	−	7.48535i	0.198921	−	0.344541i
$473$	5.39419	+	20.1314i	0.248025	+	0.925642i
$474$	1.82541	−	6.81251i	0.0838437	−	0.312909i
$475$	−19.2112	+	19.2112i	−0.881472	+	0.881472i
$476$	−0.149401	+	0.486358i	−0.00684779	+	0.0222922i
$477$	4.67778			0.214181
$478$	3.80139	−	2.19473i	0.173872	−	0.100385i
$479$	−0.892919	−	3.33242i	−0.0407985	−	0.152262i	0.942522	−	0.334145i	$-0.108447\pi$
$479$	−0.892919	−	3.33242i	−0.0407985	−	0.152262i	−0.983320	+	0.181883i	$0.941781\pi$
$480$	−2.67676	−	1.54543i	−0.122177	−	0.0705388i
$481$	21.6967	−	22.1506i	0.989287	−	1.00998i
$482$			9.57817i			0.436274i
$483$	−11.8189	+	10.9920i	−0.537777	+	0.500151i
$484$	−4.50217			−0.204644
$485$	27.5039	−	15.8794i	1.24889	−	0.721046i
$486$	0.965926	−	0.258819i	0.0438153	−	0.0117403i
$487$	4.58146	+	17.0982i	0.207606	+	0.774795i	0.988639	+	0.150306i	$0.0480260\pi$
$487$	4.58146	+	17.0982i	0.207606	+	0.774795i	−0.781034	+	0.624489i	$0.785307\pi$
$488$	10.7095	+	2.86959i	0.484794	+	0.129900i
$489$	−13.8586	+	13.8586i	−0.626709	+	0.626709i
$490$	17.9048	+	12.1463i	0.808858	+	0.548714i
$491$			4.05304i			0.182911i	0.995809	+	0.0914555i	$0.0291519\pi$
$491$			4.05304i			0.182911i	−0.995809	+	0.0914555i	$0.970848\pi$
$492$	2.22715	−	8.31183i	0.100408	−	0.374726i
$493$	0.165521	−	0.286690i	0.00745468	−	0.0129119i
$494$	−18.5188	+	10.9489i	−0.833198	+	0.492614i
$495$	6.82329	−	3.93943i	0.306684	−	0.177064i
$496$	−3.50018	−	3.50018i	−0.157163	−	0.157163i
$497$	−0.481148	+	13.2728i	−0.0215824	+	0.595366i
$498$			0.177243i			0.00794245i
$499$	−14.2135	−	3.80849i	−0.636283	−	0.170491i	−0.0737636	−	0.997276i	$-0.523501\pi$
$499$	−14.2135	−	3.80849i	−0.636283	−	0.170491i	−0.562519	+	0.826784i	$0.690168\pi$
$500$	1.33338	−	0.357278i	0.0596306	−	0.0159780i
$501$	17.8901	−	4.79363i	0.799269	−	0.214164i
$502$	25.6595	+	6.87545i	1.14524	+	0.306866i
$503$			19.7497i			0.880596i	0.897852	+	0.440298i	$0.145127\pi$
$503$			19.7497i			0.880596i	−0.897852	+	0.440298i	$0.854873\pi$
$504$	1.23900	+	2.33771i	0.0551895	+	0.104130i
$505$	31.2327	+	31.2327i	1.38984	+	1.38984i
$506$	−13.4672	+	7.77528i	−0.598689	+	0.345653i
$507$	0.269060	+	12.9972i	0.0119494	+	0.577227i
$508$	−6.55986	+	11.3620i	−0.291047	+	0.504108i
$509$	7.81272	−	29.1575i	0.346293	−	1.29238i	−0.544802	−	0.838565i	$-0.683395\pi$
$509$	7.81272	−	29.1575i	0.346293	−	1.29238i	0.891095	−	0.453817i	$-0.149938\pi$
$510$			0.594382i			0.0263197i
$511$	22.0006	+	13.7881i	0.973248	+	0.609952i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	5.76341	+	1.54430i	0.254461	+	0.0681825i
$514$	2.15436	+	8.04017i	0.0950246	+	0.354637i
$515$	28.0010	−	7.50285i	1.23387	−	0.330615i
$516$	−7.08070	+	4.08804i	−0.311710	+	0.179966i
$517$	29.8135			1.31120
$518$	−5.08874	−	22.1761i	−0.223586	−	0.974362i
$519$		−	16.7708i		−	0.736156i
$520$	−11.1436	+	0.115332i	−0.488681	+	0.00505764i
$521$	6.78569	+	3.91772i	0.297286	+	0.171638i	0.641223	−	0.767354i	$-0.278427\pi$
$521$	6.78569	+	3.91772i	0.297286	+	0.171638i	−0.343937	+	0.938993i	$0.611761\pi$
$522$	−0.445545	−	1.66280i	−0.0195010	−	0.0727786i
$523$	19.4339	−	11.2202i	0.849785	−	0.490624i	−0.0107931	−	0.999942i	$-0.503436\pi$
$523$	19.4339	−	11.2202i	0.849785	−	0.490624i	0.860578	+	0.509318i	$0.170102\pi$
$524$	−16.1606			−0.705978
$525$	11.5160	+	3.53754i	0.502601	+	0.154391i
$526$	−11.6983	+	11.6983i	−0.510068	+	0.510068i
$527$	−0.246370	+	0.919466i	−0.0107321	+	0.0400526i
$528$	0.659752	+	2.46223i	0.0287120	+	0.107155i
$529$	7.10775	−	12.3110i	0.309032	−	0.535260i
$530$	7.22917	+	12.5213i	0.314015	+	0.543890i
$531$	−6.11176	+	6.11176i	−0.265228	+	0.265228i
$532$	−0.571894	+	15.7761i	−0.0247948	+	0.683980i
$533$	−8.33981	−	29.8840i	−0.361237	−	1.29442i
$534$	7.15505	+	12.3929i	0.309629	+	0.536294i
$535$	−14.2899	+	3.82897i	−0.617807	+	0.165541i
$536$	2.48913	−	4.31131i	0.107514	−	0.186220i
$537$	−4.42393	−	7.66247i	−0.190907	−	0.330660i
$538$	−17.5878	−	17.5878i	−0.758264	−	0.758264i
$539$	−3.35818	−	17.5247i	−0.144647	−	0.754844i
$540$	2.18556	+	2.18556i	0.0940517	+	0.0940517i
$541$	−11.5078	+	42.9477i	−0.494759	+	1.84647i	0.0366160	+	0.999329i	$0.488342\pi$
$541$	−11.5078	+	42.9477i	−0.494759	+	1.84647i	−0.531375	+	0.847137i	$0.678325\pi$
$542$	−0.194717	−	0.112420i	−0.00836381	−	0.00482885i
$543$	8.05245	+	4.64909i	0.345564	+	0.199511i
$544$	−0.185751	−	0.0497718i	−0.00796400	−	0.00213395i
$545$	32.0762			1.37399
$546$	8.13514	+	4.98192i	0.348152	+	0.213207i
$547$	−14.0813			−0.602073			−0.301037	−	0.953613i	$-0.597333\pi$
$547$	−14.0813			−0.602073			−0.301037	+	0.953613i	$0.597333\pi$
$548$	−14.2660	−	3.82257i	−0.609414	−	0.163292i
$549$	−9.60184	−	5.54362i	−0.409797	−	0.236596i
$550$	10.0519	+	5.80348i	0.428616	+	0.247461i
$551$	2.65844	−	9.92144i	0.113253	−	0.422668i
$552$	−4.31367	−	4.31367i	−0.183602	−	0.183602i
$553$	−17.8374	−	5.47937i	−0.758524	−	0.233006i
$554$	−22.6794	−	22.6794i	−0.963554	−	0.963554i
$555$	−13.2901	−	23.0191i	−0.564133	−	0.977107i
$556$	−0.478715	+	0.829159i	−0.0203020	+	0.0351642i
$557$	25.2460	−	6.76465i	1.06971	−	0.286627i	0.319335	−	0.947642i	$-0.396541\pi$
$557$	25.2460	−	6.76465i	1.06971	−	0.286627i	0.750373	+	0.661015i	$0.229874\pi$
$558$	2.47500	+	4.28682i	0.104775	+	0.181476i
$559$	−14.4746	+	25.6810i	−0.612212	+	1.08619i
$560$	−4.34269	+	6.92927i	−0.183512	+	0.292815i
$561$	0.346622	−	0.346622i	0.0146344	−	0.0146344i
$562$	−3.46956	−	6.00946i	−0.146355	−	0.253494i
$563$	−7.43428	+	12.8766i	−0.313318	+	0.542682i	−0.979078	−	0.203483i	$-0.934774\pi$
$563$	−7.43428	+	12.8766i	−0.313318	+	0.542682i	0.665761	+	0.746165i	$0.268107\pi$
$564$	3.02709	+	11.2973i	0.127463	+	0.475700i
$565$	−2.65753	+	9.91803i	−0.111803	+	0.417255i
$566$	13.6004	−	13.6004i	0.571669	−	0.571669i
$567$	−0.591740	−	2.57873i	−0.0248507	−	0.108296i
$568$	−5.01994			−0.210632
$569$	7.47184	−	4.31387i	0.313236	−	0.180847i	−0.335138	−	0.942169i	$-0.608783\pi$
$569$	7.47184	−	4.31387i	0.313236	−	0.180847i	0.648373	+	0.761322i	$0.275450\pi$
$570$	4.77321	+	17.8139i	0.199928	+	0.746141i
$571$	−38.3123	−	22.1196i	−1.60332	−	0.925677i	−0.990817	−	0.135208i	$-0.956830\pi$
$571$	−38.3123	−	22.1196i	−1.60332	−	0.925677i	−0.612502	−	0.790469i	$-0.709837\pi$
$572$	6.56583	+	6.43131i	0.274531	+	0.268907i
$573$		−	5.20561i		−	0.217467i
$574$	−21.7631	−	6.68528i	−0.908376	−	0.279038i
$575$	−27.7777			−1.15841
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	27.0612	−	7.25101i	1.12657	−	0.301864i	0.353031	−	0.935612i	$-0.385151\pi$
$577$	27.0612	−	7.25101i	1.12657	−	0.301864i	0.773540	+	0.633748i	$0.218484\pi$
$578$	−4.39035	−	16.3850i	−0.182615	−	0.681527i
$579$	−10.6441	−	2.85208i	−0.442355	−	0.118529i
$580$	3.76235	−	3.76235i	0.156223	−	0.156223i
$581$	0.468633	+	0.0169883i	0.0194422	+	0.000704793i
$582$		−	10.2751i		−	0.425916i
$583$	3.08617	−	11.5178i	0.127816	−	0.477017i
$584$	−4.90677	+	8.49877i	−0.203043	+	0.351681i
$585$	10.7938	+	2.77278i	0.446268	+	0.114641i
$586$	−15.0387	+	8.68257i	−0.621241	+	0.358674i
$587$	−17.4506	−	17.4506i	−0.720265	−	0.720265i	0.248394	−	0.968659i	$-0.420097\pi$
$587$	−17.4506	−	17.4506i	−0.720265	−	0.720265i	−0.968659	+	0.248394i	$0.920097\pi$
$588$	6.29969	−	3.05187i	0.259795	−	0.125857i
$589$			29.5352i			1.21698i
$590$	−25.8050	−	6.91443i	−1.06238	−	0.284663i
$591$	−4.10755	+	1.10061i	−0.168962	+	0.0452732i
$592$	8.30660	−	2.22575i	0.341399	−	0.0914776i
$593$	−3.58434	−	0.960420i	−0.147191	−	0.0394397i	0.184471	−	0.982838i	$-0.440943\pi$
$593$	−3.58434	−	0.960420i	−0.147191	−	0.0394397i	−0.331662	+	0.943398i	$0.607609\pi$
$594$		−	2.54908i		−	0.104590i
$595$	1.57156	+	0.0569700i	0.0644275	+	0.00233554i
$596$	4.72430	+	4.72430i	0.193515	+	0.193515i
$597$	14.4319	−	8.33229i	0.590660	−	0.341018i
$598$	−21.3038	−	5.47267i	−0.871177	−	0.223794i
$599$	−4.51066	+	7.81269i	−0.184300	+	0.319218i	−0.943341	−	0.331826i	$-0.892335\pi$
$599$	−4.51066	+	7.81269i	−0.184300	+	0.319218i	0.759040	+	0.651044i	$0.225669\pi$
$600$	−1.17850	+	4.39823i	−0.0481122	+	0.179557i
$601$			25.6560i			1.04653i	0.852170	+	0.523265i	$0.175286\pi$
$601$			25.6560i			1.04653i	−0.852170	+	0.523265i	$0.824714\pi$
$602$	10.1302	+	19.1133i	0.412875	+	0.779000i
$603$	−3.52017	+	3.52017i	−0.143352	+	0.143352i
$604$	−11.4043	−	3.05577i	−0.464034	−	0.124337i
$605$	3.60161	+	13.4414i	0.146426	+	0.546470i
$606$	13.8035	−	3.69864i	0.560729	−	0.150247i
$607$	16.5741	−	9.56906i	0.672722	−	0.388396i	−0.124385	−	0.992234i	$-0.539696\pi$
$607$	16.5741	−	9.56906i	0.672722	−	0.388396i	0.797107	+	0.603838i	$0.206363\pi$
$608$	−5.96672			−0.241982
$609$	−4.43916	+	1.01865i	−0.179884	+	0.0412779i
$610$		−	34.2691i		−	1.38751i
$611$	30.1255	+	29.5083i	1.21875	+	1.19378i
$612$	0.166540	+	0.0961517i	0.00673197	+	0.00388670i
$613$	−11.6508	−	43.4816i	−0.470573	−	1.75620i	−0.637717	−	0.770271i	$-0.720121\pi$
$613$	−11.6508	−	43.4816i	−0.470573	−	1.75620i	0.167143	−	0.985933i	$-0.446546\pi$
$614$	11.4613	−	6.61716i	0.462539	−	0.267047i
$615$	−26.5969			−1.07249
$616$	6.57340	−	1.50840i	0.264850	−	0.0607750i
$617$	−9.55565	+	9.55565i	−0.384696	+	0.384696i	−0.872791	−	0.488095i	$-0.837692\pi$
$617$	−9.55565	+	9.55565i	−0.384696	+	0.384696i	0.488095	+	0.872791i	$0.337692\pi$
$618$	2.42743	−	9.05931i	0.0976457	−	0.364419i
$619$	−11.5042	−	42.9344i	−0.462395	−	1.72568i	−0.665385	−	0.746500i	$-0.731733\pi$
$619$	−11.5042	−	42.9344i	−0.462395	−	1.72568i	0.202991	−	0.979181i	$-0.434934\pi$
$620$	−7.64986	+	13.2499i	−0.307226	+	0.532131i
$621$	3.05023	+	5.28314i	0.122401	+	0.212005i
$622$	−2.36644	+	2.36644i	−0.0948855	+	0.0948855i
$623$	33.4528	−	17.7302i	1.34026	−	0.710347i
$624$	−1.77036	+	3.14099i	−0.0708713	+	0.125740i
$625$	−13.5168	−	23.4118i	−0.540672	−	0.936471i
$626$	−26.4074	+	7.07583i	−1.05545	+	0.282807i
$627$	7.60484	−	13.1720i	0.303708	−	0.526038i
$628$	−6.26073	−	10.8439i	−0.249830	−	0.432719i
$629$	−1.16937	−	1.16937i	−0.0466258	−	0.0466258i
$630$	5.98815	−	5.56918i	0.238573	−	0.221882i
$631$	−30.3285	−	30.3285i	−1.20736	−	1.20736i	−0.971879	−	0.235482i	$-0.924333\pi$
$631$	−30.3285	−	30.3285i	−1.20736	−	1.20736i	−0.235482	−	0.971879i	$-0.575667\pi$
$632$	1.82541	−	6.81251i	0.0726108	−	0.270987i
$633$	5.67810	+	3.27825i	0.225684	+	0.130299i
$634$	−21.2903	−	12.2920i	−0.845548	−	0.488177i
$635$	39.1694	+	10.4954i	1.55439	+	0.416498i
$636$	4.67778			0.185486
$637$	13.9520	−	21.0319i	0.552799	−	0.833315i
$638$	−4.38813			−0.173728
$639$	4.84889	+	1.29926i	0.191819	+	0.0513977i
$640$	−2.67676	−	1.54543i	−0.105808	−	0.0610884i
$641$	17.1177	+	9.88291i	0.676109	+	0.390352i	0.798387	−	0.602144i	$-0.205687\pi$
$641$	17.1177	+	9.88291i	0.676109	+	0.390352i	−0.122278	+	0.992496i	$0.539020\pi$
$642$	−1.23881	+	4.62329i	−0.0488918	+	0.182467i
$643$	21.8195	+	21.8195i	0.860475	+	0.860475i	0.991393	−	0.130918i	$-0.0417924\pi$
$643$	21.8195	+	21.8195i	0.860475	+	0.860475i	−0.130918	+	0.991393i	$0.541792\pi$
$644$	−11.8189	+	10.9920i	−0.465728	+	0.433144i
$645$	17.8694	+	17.8694i	0.703606	+	0.703606i
$646$	0.573710	+	0.993695i	0.0225723	+	0.0390964i
$647$	9.39268	−	16.2686i	0.369265	−	0.639585i	−0.620186	−	0.784455i	$-0.712943\pi$
$647$	9.39268	−	16.2686i	0.369265	−	0.639585i	0.989451	+	0.144870i	$0.0462763\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	11.0163	+	19.0808i	0.432428	+	0.748987i
$650$	4.41304	+	15.8132i	0.173094	+	0.620246i
$651$	11.5716	−	6.13305i	0.453528	−	0.240373i
$652$	−13.8586	+	13.8586i	−0.542746	+	0.542746i
$653$	4.34430	+	7.52455i	0.170006	+	0.294459i	0.938422	−	0.345492i	$-0.112288\pi$
$653$	4.34430	+	7.52455i	0.170006	+	0.294459i	−0.768416	+	0.639951i	$0.778955\pi$
$654$	5.18889	−	8.98742i	0.202902	−	0.351436i
$655$	12.9280	+	48.2480i	0.505139	+	1.88520i
$656$	2.22715	−	8.31183i	0.0869555	−	0.324522i
$657$	6.93921	−	6.93921i	0.270725	−	0.270725i
$658$	30.1602	−	6.92086i	1.17577	−	0.269803i
$659$	19.3439			0.753532			0.376766	−	0.926308i	$-0.377036\pi$
$659$	19.3439			0.753532			0.376766	+	0.926308i	$0.377036\pi$
$660$	6.82329	−	3.93943i	0.265596	−	0.153342i
$661$	−0.815022	−	3.04170i	−0.0317007	−	0.118309i	0.948262	−	0.317488i	$-0.102839\pi$
$661$	−0.815022	−	3.04170i	−0.0317007	−	0.118309i	−0.979963	+	0.199179i	$0.936172\pi$
$662$	−21.4126	−	12.3626i	−0.832223	−	0.480484i
$663$	0.693323	−	0.00717560i	0.0269264	−	0.000278677i
$664$			0.177243i			0.00687837i
$665$	47.5576	−	10.9130i	1.84421	−	0.423189i
$666$	−8.59962			−0.333229
$667$	9.09469	−	5.25082i	0.352148	−	0.203313i
$668$	17.8901	−	4.79363i	0.692188	−	0.185471i
$669$	−4.94450	−	18.4531i	−0.191165	−	0.713439i
$670$	−14.8628	−	3.98247i	−0.574200	−	0.153856i
$671$	−19.9845	+	19.9845i	−0.771493	+	0.771493i
$672$	1.23900	+	2.33771i	0.0477955	+	0.0901790i
$673$			18.7681i			0.723455i	0.932284	+	0.361728i	$0.117813\pi$
$673$			18.7681i			0.723455i	−0.932284	+	0.361728i	$0.882187\pi$
$674$	−1.30024	+	4.85255i	−0.0500832	+	0.186913i
$675$	2.27669	−	3.94335i	0.0876300	−	0.151780i
$676$	0.269060	+	12.9972i	0.0103485	+	0.499893i
$677$	−11.3439	+	6.54939i	−0.435981	+	0.251714i	−0.701891	−	0.712284i	$-0.747661\pi$
$677$	−11.3439	+	6.54939i	−0.435981	+	0.251714i	0.265910	+	0.963998i	$0.414327\pi$
$678$	2.34903	+	2.34903i	0.0902139	+	0.0902139i
$679$	−27.1675	−	0.984840i	−1.04259	−	0.0377947i
$680$			0.594382i			0.0227935i
$681$	−6.54583	−	1.75395i	−0.250837	−	0.0672115i
$682$	12.1880	−	3.26577i	0.466703	−	0.125053i
$683$	−17.6381	+	4.72612i	−0.674903	+	0.180840i	−0.579963	−	0.814643i	$-0.696933\pi$
$683$	−17.6381	+	4.72612i	−0.674903	+	0.180840i	−0.0949408	+	0.995483i	$0.530266\pi$
$684$	5.76341	+	1.54430i	0.220369	+	0.0590478i
$685$			45.6496i			1.74418i
$686$	−7.46539	−	16.9490i	−0.285030	−	0.647115i
$687$	−10.0393	−	10.0393i	−0.383021	−	0.383021i
$688$	−7.08070	+	4.08804i	−0.269949	+	0.155855i
$689$	14.5183	−	8.58370i	0.553104	−	0.327013i
$690$	−9.42780	+	16.3294i	−0.358910	+	0.621651i
$691$	2.54737	−	9.50693i	0.0969067	−	0.361661i	−0.900395	−	0.435073i	$-0.856722\pi$
$691$	2.54737	−	9.50693i	0.0969067	−	0.361661i	0.997302	+	0.0734128i	$0.0233891\pi$
$692$		−	16.7708i		−	0.637530i
$693$	−6.73982	−	0.244323i	−0.256024	−	0.00928106i
$694$	−10.6939	+	10.6939i	−0.405935	+	0.405935i
$695$	2.85844	+	0.765918i	0.108427	+	0.0290529i
$696$	−0.445545	−	1.66280i	−0.0168883	−	0.0630282i
$697$	−1.59839	+	0.428288i	−0.0605435	+	0.0162226i
$698$	−9.91089	+	5.72205i	−0.375133	+	0.216583i
$699$	−6.87760			−0.260135
$700$	11.5160	+	3.53754i	0.435265	+	0.133706i
$701$		−	0.764820i		−	0.0288869i	−0.999896	−	0.0144434i	$-0.995402\pi$
$701$		−	0.764820i		−	0.0288869i	0.999896	−	0.0144434i	$-0.00459765\pi$
$702$	2.52299	−	2.57576i	0.0952241	−	0.0972157i
$703$	−44.4371	−	25.6558i	−1.67598	−	0.967626i
$704$	0.659752	+	2.46223i	0.0248653	+	0.0927987i
$705$	31.3068	−	18.0750i	1.17908	−	0.680743i
$706$	15.6365			0.588488
$707$	−8.45622	−	36.8512i	−0.318029	−	1.38593i
$708$	−6.11176	+	6.11176i	−0.229694	+	0.229694i
$709$	−3.56678	+	13.3114i	−0.133953	+	0.499920i	−1.00000		4.29989e-5i	$-0.999986\pi$
$709$	−3.56678	+	13.3114i	−0.133953	+	0.499920i	0.866047	+	0.499963i	$0.166653\pi$
$710$	4.01581	+	14.9872i	0.150711	+	0.562460i
$711$	−3.52642	+	6.10793i	−0.132251	+	0.229065i
$712$	7.15505	+	12.3929i	0.268147	+	0.464444i
$713$	−21.3527	+	21.3527i	−0.799663	+	0.799663i
$714$	0.270189	−	0.431117i	0.0101116	−	0.0161342i
$715$	13.9484	−	24.7474i	0.521642	−	0.925500i
$716$	−4.42393	−	7.66247i	−0.165330	−	0.286360i
$717$	−4.23990	+	1.13608i	−0.158342	+	0.0424276i
$718$	14.8819	−	25.7761i	0.555386	−	0.961957i
$719$	11.8270	+	20.4850i	0.441074	+	0.763962i	0.997769	−	0.0667542i	$-0.0212643\pi$
$719$	11.8270	+	20.4850i	0.441074	+	0.763962i	−0.556696	+	0.830717i	$0.687931\pi$
$720$	2.18556	+	2.18556i	0.0814512	+	0.0814512i
$721$	−23.7203	−	7.28648i	−0.883389	−	0.271363i
$722$	11.7392	+	11.7392i	0.436888	+	0.436888i
$723$	2.47901	−	9.25180i	0.0921955	−	0.344078i
$724$	8.05245	+	4.64909i	0.299267	+	0.172782i
$725$	−6.78829	−	3.91922i	−0.252111	−	0.145556i
$726$	4.34876	+	1.16525i	0.161398	+	0.0432464i
$727$	8.17936			0.303356			0.151678	−	0.988430i	$-0.451532\pi$
$727$	8.17936			0.303356			0.151678	+	0.988430i	$0.451532\pi$
$728$	8.13514	+	4.98192i	0.301508	+	0.184642i
$729$	−1.00000			−0.0370370
$730$	29.2987	+	7.85055i	1.08439	+	0.290562i
$731$	1.36164	+	0.786145i	0.0503622	+	0.0290766i
$732$	−9.60184	−	5.54362i	−0.354894	−	0.204898i
$733$	−7.25552	+	27.0780i	−0.267989	+	1.00015i	0.692407	+	0.721507i	$0.256550\pi$
$733$	−7.25552	+	27.0780i	−0.267989	+	1.00015i	−0.960396	+	0.278640i	$0.910116\pi$
$734$	−6.87035	−	6.87035i	−0.253589	−	0.253589i
$735$	−14.1511	−	16.3665i	−0.521970	−	0.603689i
$736$	−4.31367	−	4.31367i	−0.159004	−	0.159004i
$737$	6.34501	+	10.9899i	0.233721	+	0.404818i
$738$	−4.30252	+	7.45218i	−0.158378	+	0.274319i
$739$	−41.2564	+	11.0546i	−1.51764	+	0.406651i	−0.918965	−	0.394340i	$-0.870973\pi$
$739$	−41.2564	+	11.0546i	−1.51764	+	0.406651i	−0.598677	+	0.800991i	$0.704307\pi$
$740$	−13.2901	−	23.0191i	−0.488554	−	0.846200i
$741$	20.7215	−	5.78281i	0.761224	−	0.212437i
$742$	0.448353	−	12.3681i	0.0164596	−	0.454048i
$743$	−0.290617	+	0.290617i	−0.0106617	+	0.0106617i	−0.712418	−	0.701756i	$-0.752400\pi$
$743$	−0.290617	+	0.290617i	−0.0106617	+	0.0106617i	0.701756	+	0.712418i	$0.252400\pi$
$744$	2.47500	+	4.28682i	0.0907378	+	0.157163i
$745$	10.3253	−	17.8839i	0.378288	−	0.655214i
$746$	−4.12837	−	15.4073i	−0.151150	−	0.564101i
$747$	0.0458739	−	0.171204i	0.00167844	−	0.00626401i
$748$	0.346622	−	0.346622i	0.0126738	−	0.0126738i
$749$	12.1053	+	3.71855i	0.442319	+	0.135873i
$750$	−1.38042			−0.0504057
$751$	33.4252	−	19.2980i	1.21970	−	0.704195i	0.254848	−	0.966981i	$-0.417975\pi$
$751$	33.4252	−	19.2980i	1.21970	−	0.704195i	0.964854	+	0.262786i	$0.0846413\pi$
$752$	3.02709	+	11.2973i	0.110387	+	0.411968i
$753$	−23.0057	−	13.2824i	−0.838375	−	0.484036i
$754$	−4.43405	−	4.34321i	−0.161479	−	0.158170i
$755$			36.4924i			1.32810i
$756$	−0.591740	−	2.57873i	−0.0215214	−	0.0937875i
$757$	47.4480			1.72453			0.862264	−	0.506459i	$-0.169046\pi$
$757$	47.4480			1.72453			0.862264	+	0.506459i	$0.169046\pi$
$758$	−6.45614	+	3.72745i	−0.234498	+	0.135387i
$759$	15.0207	−	4.02478i	0.545217	−	0.146090i
$760$	4.77321	+	17.8139i	0.173143	+	0.646177i
$761$	14.8204	+	3.97112i	0.537239	+	0.143953i	0.517229	−	0.855847i	$-0.326964\pi$
$761$	14.8204	+	3.97112i	0.537239	+	0.143953i	0.0200101	+	0.999800i	$0.493630\pi$
$762$	9.27704	−	9.27704i	0.336072	−	0.336072i
$763$	−23.2655	−	14.5809i	−0.842269	−	0.527865i
$764$		−	5.20561i		−	0.188332i
$765$	0.153837	−	0.574129i	0.00556200	−	0.0207577i
$766$	16.5989	−	28.7502i	0.599744	−	1.03879i
$767$	−7.75388	+	30.1840i	−0.279976	+	1.08988i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−7.59086	−	7.59086i	−0.273734	−	0.273734i	0.556868	−	0.830601i	$-0.312003\pi$
$769$	−7.59086	−	7.59086i	−0.273734	−	0.273734i	−0.830601	+	0.556868i	$0.812003\pi$
$770$	−9.76191	−	18.4185i	−0.351795	−	0.663755i
$771$		−	8.32379i		−	0.299774i
$772$	−10.6441	−	2.85208i	−0.383090	−	0.102649i
$773$	16.5801	−	4.44264i	0.596346	−	0.159790i	0.0519942	−	0.998647i	$-0.483442\pi$
$773$	16.5801	−	4.44264i	0.596346	−	0.159790i	0.544352	+	0.838857i	$0.316776\pi$
$774$	7.89749	−	2.11613i	0.283869	−	0.0760626i
$775$	21.7712	+	5.83359i	0.782046	+	0.209549i
$776$		−	10.2751i		−	0.368854i
$777$	−0.824251	+	22.7375i	−0.0295698	+	0.815704i
$778$	8.52332	+	8.52332i	0.305576	+	0.305576i
$779$	−44.4651	+	25.6719i	−1.59313	+	0.919792i
$780$	10.7938	+	2.77278i	0.386479	+	0.0992816i
$781$	6.39812	−	11.0819i	0.228943	−	0.396541i
$782$	−0.303630	+	1.13316i	−0.0108578	+	0.0405219i
$783$			1.72145i			0.0615197i
$784$	6.29969	−	3.05187i	0.224989	−	0.108995i
$785$	−27.3665	+	27.3665i	−0.976751	+	0.976751i
$786$	15.6099	+	4.18266i	0.556787	+	0.149191i
$787$	14.0806	+	52.5495i	0.501919	+	1.87319i	0.487191	+	0.873295i	$0.338022\pi$
$787$	14.0806	+	52.5495i	0.501919	+	1.87319i	0.0147279	+	0.999892i	$0.495312\pi$
$788$	−4.10755	+	1.10061i	−0.146325	+	0.0392078i
$789$	14.3274	−	8.27191i	0.510068	−	0.294488i
$790$	−21.7993			−0.775584
$791$	6.43601	−	5.98571i	0.228838	−	0.212828i
$792$		−	2.54908i		−	0.0905778i
$793$	−39.9735	+	0.413709i	−1.41950	+	0.0146912i
$794$	17.8728	+	10.3189i	0.634281	+	0.366203i
$795$	−3.74210	−	13.9657i	−0.132718	−	0.495312i
$796$	14.4319	−	8.33229i	0.511527	−	0.295330i
$797$	−19.3651			−0.685946			−0.342973	−	0.939345i	$-0.611434\pi$
$797$	−19.3651			−0.685946			−0.342973	+	0.939345i	$0.611434\pi$
$798$	4.63556	−	15.0905i	0.164097	−	0.534199i
$799$	1.59038	−	1.59038i	0.0562636	−	0.0562636i
$800$	−1.17850	+	4.39823i	−0.0416664	+	0.155501i
$801$	−3.70373	−	13.8225i	−0.130865	−	0.488394i
$802$	−2.02709	+	3.51102i	−0.0715790	+	0.123978i
$803$	−12.5078	−	21.6641i	−0.441389	−	0.764509i
$804$	−3.52017	+	3.52017i	−0.124147	+	0.124147i
$805$	42.2716	+	26.4924i	1.48988	+	0.933734i
$806$	15.5479	+	8.76330i	0.547651	+	0.308674i
$807$	12.4365	+	21.5406i	0.437784	+	0.758264i
$808$	13.8035	−	3.69864i	0.485606	−	0.130118i
$809$	9.28273	−	16.0782i	0.326363	−	0.565278i	−0.655424	−	0.755261i	$-0.727510\pi$
$809$	9.28273	−	16.0782i	0.326363	−	0.565278i	0.981787	+	0.189983i	$0.0608433\pi$
$810$	−1.54543	−	2.67676i	−0.0543008	−	0.0940517i
$811$	−38.4555	−	38.4555i	−1.35035	−	1.35035i	−0.885262	−	0.465092i	$-0.846021\pi$
$811$	−38.4555	−	38.4555i	−1.35035	−	1.35035i	−0.465092	−	0.885262i	$-0.653979\pi$
$812$	−4.43916	+	1.01865i	−0.155784	+	0.0357477i
$813$	0.158986	+	0.158986i	0.00557587	+	0.00557587i
$814$	−5.67362	+	21.1742i	−0.198860	+	0.742156i
$815$	52.4620	+	30.2890i	1.83766	+	1.06098i
$816$	0.166540	+	0.0961517i	0.00583005	+	0.00336598i
$817$	47.1221	+	12.6263i	1.64859	+	0.441739i
$818$	9.03388			0.315862
$819$	−6.56852	−	6.91770i	−0.229523	−	0.241724i
$820$	−26.5969			−0.928805
$821$	−47.6458	−	12.7667i	−1.66285	−	0.445560i	−0.699682	−	0.714455i	$-0.746675\pi$
$821$	−47.6458	−	12.7667i	−1.66285	−	0.445560i	−0.963169	+	0.268895i	$0.913341\pi$
$822$	12.7906	+	7.38463i	0.446122	+	0.257569i
$823$	−29.4007	−	16.9745i	−1.02484	−	0.591694i	−0.109341	−	0.994004i	$-0.534874\pi$
$823$	−29.4007	−	16.9745i	−1.02484	−	0.591694i	−0.915504	+	0.402310i	$0.868207\pi$
$824$	2.42743	−	9.05931i	0.0845637	−	0.315596i
$825$	−8.20737	−	8.20737i	−0.285744	−	0.285744i
$826$	15.5738	+	16.7454i	0.541882	+	0.582647i
$827$	−13.9459	−	13.9459i	−0.484948	−	0.484948i	0.421760	−	0.906708i	$-0.361412\pi$
$827$	−13.9459	−	13.9459i	−0.484948	−	0.484948i	−0.906708	+	0.421760i	$0.861412\pi$
$828$	3.05023	+	5.28314i	0.106003	+	0.183602i
$829$	−16.8805	+	29.2379i	−0.586284	+	1.01547i	0.408430	+	0.912790i	$0.366076\pi$
$829$	−16.8805	+	29.2379i	−0.586284	+	1.01547i	−0.994714	+	0.102684i	$0.967257\pi$
$830$	0.529166	−	0.141790i	0.0183676	−	0.00492159i
$831$	16.0367	+	27.7764i	0.556308	+	0.963554i
$832$	−1.77036	+	3.14099i	−0.0613763	+	0.108894i
$833$	−1.11398	−	0.755705i	−0.0385973	−	0.0261836i
$834$	0.677006	−	0.677006i	0.0234428	−	0.0234428i
$835$	−28.6231	−	49.5767i	−0.990544	−	1.71567i
$836$	7.60484	−	13.1720i	0.263019	−	0.455562i
$837$	−1.28115	−	4.78133i	−0.0442831	−	0.165267i
$838$	−9.08829	+	33.9180i	−0.313950	+	1.17168i
$839$	−28.9271	+	28.9271i	−0.998673	+	0.998673i	−0.999999	−	0.00132603i	$-0.999578\pi$
$839$	−28.9271	+	28.9271i	−0.998673	+	0.998673i	0.00132603	+	0.999999i	$0.499578\pi$
$840$	5.98815	−	5.56918i	0.206611	−	0.192155i
$841$	−26.0366			−0.897814
$842$	−6.93815	+	4.00575i	−0.239105	+	0.138047i
$843$	1.79598	+	6.70268i	0.0618568	+	0.230853i
$844$	5.67810	+	3.27825i	0.195448	+	0.112842i
$845$	38.5884	−	11.2007i	1.32748	−	0.385316i
$846$		−	11.6958i		−	0.402109i
$847$	3.49775	−	11.3865i	0.120184	−	0.391245i
$848$	4.67778			0.160636
$849$	−16.6571	+	9.61696i	−0.571669	+	0.330053i
$850$	0.845796	−	0.226630i	0.0290105	−	0.00777335i
$851$	−13.5781	−	50.6740i	−0.465450	−	1.73708i
$852$	4.84889	+	1.29926i	0.166120	+	0.0445118i
$853$	23.3837	−	23.3837i	0.800643	−	0.800643i	−0.182553	−	0.983196i	$-0.558436\pi$
$853$	23.3837	−	23.3837i	0.800643	−	0.800643i	0.983196	+	0.182553i	$0.0584362\pi$
$854$	−15.5777	+	24.8561i	−0.533059	+	0.850557i
$855$		−	18.4423i		−	0.630712i
$856$	−1.23881	+	4.62329i	−0.0423416	+	0.158021i
$857$	10.4269	−	18.0599i	0.356175	−	0.616913i	−0.631143	−	0.775666i	$-0.717414\pi$
$857$	10.4269	−	18.0599i	0.356175	−	0.616913i	0.987318	+	0.158753i	$0.0507474\pi$
$858$	−4.67755	−	7.91153i	−0.159689	−	0.270095i
$859$	29.2467	−	16.8856i	0.997884	−	0.576129i	0.0902628	−	0.995918i	$-0.471229\pi$
$859$	29.2467	−	16.8856i	0.997884	−	0.576129i	0.907622	+	0.419789i	$0.137896\pi$
$860$	17.8694	+	17.8694i	0.609340	+	0.609340i
$861$	19.2913	+	12.0902i	0.657446	+	0.412033i
$862$		−	18.6777i		−	0.636166i
$863$	40.7246	+	10.9121i	1.38628	+	0.371453i	0.873399	−	0.487005i	$-0.161911\pi$
$863$	40.7246	+	10.9121i	1.38628	+	0.371453i	0.512884	+	0.858458i	$0.328577\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−50.0698	+	13.4162i	−1.70242	+	0.456163i
$866$	3.37381	+	0.904010i	0.114647	+	0.0307195i
$867$			16.9630i			0.576094i
$868$	11.5716	−	6.13305i	0.392767	−	0.208169i
$869$	12.7126	+	12.7126i	0.431244	+	0.431244i
$870$	−4.60792	+	2.66038i	−0.156223	+	0.0901954i
$871$	−4.46597	+	17.3849i	−0.151324	+	0.589066i
$872$	5.18889	−	8.98742i	0.175718	−	0.304353i
$873$	−2.65939	+	9.92497i	−0.0900066	+	0.335909i
$874$			36.3997i			1.23124i
$875$	−0.132309	+	3.64984i	−0.00447287	+	0.123387i
$876$	6.93921	−	6.93921i	0.234454	−	0.234454i
$877$	16.6249	+	4.45463i	0.561383	+	0.150422i	0.528342	−	0.849032i	$-0.322814\pi$
$877$	16.6249	+	4.45463i	0.561383	+	0.150422i	0.0330415	+	0.999454i	$0.489481\pi$
$878$	−0.0681703	−	0.254415i	−0.00230064	−	0.00858610i
$879$	16.7734	−	4.49443i	0.565754	−	0.151593i
$880$	6.82329	−	3.93943i	0.230013	−	0.132798i
$881$	54.6900			1.84255			0.921277	−	0.388907i	$-0.127147\pi$
$881$	54.6900			1.84255			0.921277	+	0.388907i	$0.127147\pi$
$882$	−6.87491	+	1.31740i	−0.231490	+	0.0443593i
$883$		−	33.5777i		−	1.12998i	−0.825098	−	0.564990i	$-0.808880\pi$
$883$		−	33.5777i		−	1.12998i	0.825098	−	0.564990i	$-0.191120\pi$
$884$	0.693323	−	0.00717560i	0.0233190	−	0.000241341i
$885$	23.1361	+	13.3577i	0.777713	+	0.449013i
$886$	−2.19696	−	8.19915i	−0.0738082	−	0.275456i
$887$	−44.4852	+	25.6835i	−1.49367	+	0.862369i	−0.999974	−	0.00726789i	$-0.997687\pi$
$887$	−44.4852	+	25.6835i	−1.49367	+	0.862369i	−0.493693	+	0.869636i	$0.664353\pi$
$888$	−8.59962			−0.288584
$889$	−23.6394	−	25.4178i	−0.792842	−	0.852486i
$890$	31.2756	−	31.2756i	1.04836	−	1.04836i
$891$	−0.659752	+	2.46223i	−0.0221025	+	0.0824877i
$892$	−4.94450	−	18.4531i	−0.165554	−	0.617856i
$893$	34.8927	−	60.4360i	1.16764	−	2.02241i
$894$	−3.34058	−	5.78606i	−0.111726	−	0.193515i
$895$	−19.3376	+	19.3376i	−0.646384	+	0.646384i
$896$	1.23900	+	2.33771i	0.0413921	+	0.0780973i
$897$	19.1614	+	10.8000i	0.639782	+	0.360602i
$898$	15.7003	+	27.1938i	0.523927	+	0.907469i
$899$	−8.23084	+	2.20545i	−0.274514	+	0.0735558i
$900$	2.27669	−	3.94335i	0.0758898	−	0.131445i
$901$	−0.449777	−	0.779036i	−0.0149842	−	0.0259535i
$902$	15.5104	+	15.5104i	0.516439	+	0.516439i
$903$	−4.83812	−	21.0839i	−0.161002	−	0.701629i
$904$	2.34903	+	2.34903i	0.0781275	+	0.0781275i
$905$	7.43828	−	27.7600i	0.247257	−	0.922775i
$906$	10.2248	+	5.90329i	0.339696	+	0.196124i
$907$	52.1007	+	30.0804i	1.72998	+	0.998802i	0.889458	+	0.457016i	$0.151082\pi$
$907$	52.1007	+	30.0804i	1.72998	+	0.998802i	0.840517	+	0.541785i	$0.182251\pi$
$908$	−6.54583	−	1.75395i	−0.217231	−	0.0582069i
$909$	−14.2904			−0.473984
$910$	8.36584	−	28.2731i	0.277325	−	0.937246i
$911$	−22.9257			−0.759561			−0.379780	−	0.925077i	$-0.624000\pi$
$911$	−22.9257			−0.759561			−0.379780	+	0.925077i	$0.624000\pi$
$912$	5.76341	+	1.54430i	0.190846	+	0.0511369i
$913$	−0.391277	−	0.225904i	−0.0129494	−	0.00747632i
$914$	−4.18670	−	2.41719i	−0.138484	−	0.0799536i
$915$	−8.86949	+	33.1014i	−0.293216	+	1.09430i
$916$	−10.0393	−	10.0393i	−0.331706	−	0.331706i
$917$	12.5552	−	40.8719i	0.414609	−	1.34971i
$918$	−0.135979	−	0.135979i	−0.00448798	−	0.00448798i
$919$	−5.70486	−	9.88111i	−0.188186	−	0.325948i	0.756460	−	0.654041i	$-0.226927\pi$
$919$	−5.70486	−	9.88111i	−0.188186	−	0.325948i	−0.944645	+	0.328093i	$0.893594\pi$
$920$	−9.42780	+	16.3294i	−0.310826	+	0.538366i
$921$	−12.7834	+	3.42530i	−0.421227	+	0.112867i
$922$	13.5509	+	23.4708i	0.446274	+	0.772969i
$923$	17.4335	−	4.86521i	0.573830	−	0.160140i
$924$	−6.73982	−	0.244323i	−0.221724	−	0.00803764i
$925$	−27.6885	+	27.6885i	−0.910391	+	0.910391i
$926$	4.07035	+	7.05005i	0.133760	+	0.231679i
$927$	−4.68944	+	8.12235i	−0.154022	+	0.266773i
$928$	−0.445545	−	1.66280i	−0.0146257	−	0.0545840i
$929$	3.36080	−	12.5427i	0.110264	−	0.411512i	−0.888625	−	0.458635i	$-0.848339\pi$
$929$	3.36080	−	12.5427i	0.110264	−	0.411512i	0.998889	+	0.0471227i	$0.0150052\pi$
$930$	10.8185	−	10.8185i	0.354754	−	0.354754i
$931$	−39.4552	−	13.7029i	−1.29309	−	0.449094i
$932$	−6.87760			−0.225283
$933$	2.89828	−	1.67332i	0.0948855	−	0.0547822i
$934$	−1.57580	−	5.88096i	−0.0515617	−	0.192431i
$935$	−1.31214	−	0.757565i	−0.0429116	−	0.0247750i
$936$	2.52299	−	2.57576i	0.0824665	−	0.0841913i
$937$		−	35.8464i		−	1.17105i	−0.810654	−	0.585526i	$-0.800888\pi$
$937$		−	35.8464i		−	1.17105i	0.810654	−	0.585526i	$-0.199112\pi$
$938$	8.96997	+	9.64477i	0.292880	+	0.314913i
$939$	27.3389			0.892171
$940$	31.3068	−	18.0750i	1.02111	−	0.589541i
$941$	−41.2468	+	11.0520i	−1.34461	+	0.360286i	−0.858142	−	0.513413i	$-0.828381\pi$
$941$	−41.2468	+	11.0520i	−1.34461	+	0.360286i	−0.486466	+	0.873700i	$0.661714\pi$
$942$	3.24079	+	12.0948i	0.105591	+	0.394070i
$943$	−50.7059	−	13.5866i	−1.65121	−	0.442441i
$944$	−6.11176	+	6.11176i	−0.198921	+	0.198921i
$945$	−7.22552	+	3.82957i	−0.235046	+	0.124576i
$946$		−	20.8415i		−	0.677617i
$947$	3.83874	−	14.3264i	0.124742	−	0.465544i	−0.875088	−	0.483964i	$-0.839197\pi$
$947$	3.83874	−	14.3264i	0.124742	−	0.465544i	0.999830	+	0.0184193i	$0.00586338\pi$
$948$	−3.52642	+	6.10793i	−0.114533	+	0.198376i
$949$	8.80365	−	34.2705i	0.285779	−	1.11247i
$950$	23.5289	−	13.5844i	0.763377	−	0.440736i
$951$	17.3835	+	17.3835i	0.563698	+	0.563698i
$952$	0.270189	−	0.431117i	0.00875687	−	0.0139726i
$953$			6.04490i			0.195814i	0.995196	+	0.0979068i	$0.0312147\pi$
$953$			6.04490i			0.195814i	−0.995196	+	0.0979068i	$0.968785\pi$
$954$	−4.51839	−	1.21070i	−0.146288	−	0.0391978i
$955$	−15.5415	+	4.16434i	−0.502912	+	0.134755i
$956$	−4.23990	+	1.13608i	−0.137128	+	0.0367434i
$957$	4.23861	+	1.13573i	0.137015	+	0.0367130i
$958$			3.44997i			0.111464i
$959$	20.7510	−	33.1106i	0.670085	−	1.06920i
$960$	2.18556	+	2.18556i	0.0705388	+	0.0705388i
$961$	−5.62703	+	3.24877i	−0.181517	+	0.104799i
$962$	−26.6904	+	15.7803i	−0.860534	+	0.508776i
$963$	2.39319	−	4.14513i	0.0771195	−	0.133575i
$964$	2.47901	−	9.25180i	0.0798436	−	0.297980i
$965$			34.0600i			1.09643i
$966$	14.2611	−	7.55846i	0.458842	−	0.243190i
$967$	−3.98042	+	3.98042i	−0.128002	+	0.128002i	−0.768205	−	0.640204i	$-0.778850\pi$
$967$	−3.98042	+	3.98042i	−0.128002	+	0.128002i	0.640204	+	0.768205i	$0.278850\pi$
$968$	4.34876	+	1.16525i	0.139774	+	0.0374524i
$969$	−0.296974	−	1.10832i	−0.00954019	−	0.0356045i
$970$	−30.6766	+	8.21978i	−0.984968	+	0.263921i
$971$	17.4091	−	10.0512i	0.558685	−	0.322557i	−0.193933	−	0.981015i	$-0.562124\pi$
$971$	17.4091	−	10.0512i	0.558685	−	0.322557i	0.752617	+	0.658458i	$0.228791\pi$
$972$	−1.00000			−0.0320750
$973$	−1.72512	−	1.85490i	−0.0553049	−	0.0594654i
$974$		−	17.7014i		−	0.567190i
$975$	−0.169905	−	16.4166i	−0.00544131	−	0.525752i
$976$	−9.60184	−	5.54362i	−0.307347	−	0.177447i
$977$	−0.159567	−	0.595513i	−0.00510500	−	0.0190521i	0.963326	−	0.268333i	$-0.0864726\pi$
$977$	−0.159567	−	0.595513i	−0.00510500	−	0.0190521i	−0.968431	+	0.249280i	$0.919806\pi$
$978$	16.9733	−	9.79954i	0.542746	−	0.313355i
$979$	−36.4777			−1.16583
$980$	−14.1511	−	16.3665i	−0.452039	−	0.522810i
$981$	−7.33820	+	7.33820i	−0.234291	+	0.234291i
$982$	1.04900	−	3.91494i	0.0334751	−	0.124931i
$983$	5.70203	+	21.2803i	0.181867	+	0.678736i	0.995280	+	0.0970489i	$0.0309403\pi$
$983$	5.70203	+	21.2803i	0.181867	+	0.678736i	−0.813413	+	0.581687i	$0.802393\pi$
$984$	−4.30252	+	7.45218i	−0.137159	+	0.237567i
$985$	6.57185	+	11.3828i	0.209397	+	0.362685i
$986$	−0.234082	+	0.234082i	−0.00745468	+	0.00745468i
$987$	−30.9238	−	1.12101i	−0.984316	−	0.0356821i
$988$	20.7215	−	5.78281i	0.659240	−	0.183976i
$989$	24.9389	+	43.1954i	0.793011	+	1.37354i
$990$	−7.61039	+	2.03920i	−0.241874	+	0.0648099i
$991$	−12.2355	+	21.1925i	−0.388673	+	0.673201i	−0.992271	−	0.124087i	$-0.960400\pi$
$991$	−12.2355	+	21.1925i	−0.388673	+	0.673201i	0.603598	+	0.797289i	$0.293733\pi$
$992$	2.47500	+	4.28682i	0.0785813	+	0.136107i
$993$	17.4833	+	17.4833i	0.554815	+	0.554815i
$994$	3.90000	−	12.6960i	0.123701	−	0.402693i
$995$	−36.4215	−	36.4215i	−1.15464	−	1.15464i
$996$	0.0458739	−	0.171204i	0.00145357	−	0.00542480i
$997$	−19.0699	−	11.0100i	−0.603948	−	0.348690i	0.166645	−	0.986017i	$-0.446707\pi$
$997$	−19.0699	−	11.0100i	−0.603948	−	0.348690i	−0.770593	+	0.637327i	$0.780040\pi$
$998$	12.7435	+	7.35744i	0.403387	+	0.232896i
$999$	8.30660	+	2.22575i	0.262809	+	0.0704195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.a.31.4	✓	40
7.5	odd	6		546.2.bz.b.187.9	yes	40
13.8	odd	4		546.2.bz.b.73.9	yes	40
91.47	even	12	inner	546.2.bz.a.229.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.31.4	✓	40	1.1	even	1	trivial
546.2.bz.a.229.4	yes	40	91.47	even	12	inner
546.2.bz.b.73.9	yes	40	13.8	odd	4
546.2.bz.b.187.9	yes	40	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.799972 - 2.98554i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.93737 + 1.80183i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.799972 - 2.98554i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.93737 + 1.80183i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.54543 + 2.67676i) q^{10} +(2.46223 - 0.659752i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.14099 + 1.77036i) q^{13} +(2.33771 - 1.23900i) q^{14} +(2.18556 - 2.18556i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.0961517 - 0.166540i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(1.54430 - 5.76341i) q^{19} +(2.18556 - 2.18556i) q^{20} +(-2.57873 + 0.591740i) q^{21} -2.54908 q^{22} +(5.28314 - 3.05023i) q^{23} +(-0.258819 - 0.965926i) q^{24} +(-3.94335 - 2.27669i) q^{25} +(-2.57576 - 2.52299i) q^{26} +1.00000i q^{27} +(-2.57873 + 0.591740i) q^{28} +1.72145 q^{29} +(-2.67676 + 1.54543i) q^{30} +(-4.78133 + 1.28115i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.46223 + 0.659752i) q^{33} +(-0.135979 + 0.135979i) q^{34} +(3.82957 + 7.22552i) q^{35} +1.00000i q^{36} +(2.22575 - 8.30660i) q^{37} +(-2.98336 + 5.16733i) q^{38} +(1.83499 + 3.10367i) q^{39} +(-2.67676 + 1.54543i) q^{40} +(-6.08468 - 6.08468i) q^{41} +(2.64401 + 0.0958474i) q^{42} +8.17609i q^{43} +(2.46223 + 0.659752i) q^{44} +(2.98554 - 0.799972i) q^{45} +(-5.89258 + 1.57891i) q^{46} +(11.2973 + 3.02709i) q^{47} +1.00000i q^{48} +(0.506844 - 6.98163i) q^{49} +(3.21973 + 3.21973i) q^{50} +(0.166540 - 0.0961517i) q^{51} +(1.83499 + 3.10367i) q^{52} +(2.33889 - 4.05108i) q^{53} +(0.258819 - 0.965926i) q^{54} -7.87885i q^{55} +(2.64401 + 0.0958474i) q^{56} +(4.21911 - 4.21911i) q^{57} +(-1.66280 - 0.445545i) q^{58} +(2.23706 + 8.34882i) q^{59} +(2.98554 - 0.799972i) q^{60} +(-9.60184 + 5.54362i) q^{61} +4.95000 q^{62} +(-2.52911 - 0.776903i) q^{63} +1.00000i q^{64} +(7.79819 - 7.96130i) q^{65} +(-2.20757 - 1.27454i) q^{66} +(1.28847 + 4.80864i) q^{67} +(0.166540 - 0.0961517i) q^{68} +6.10045 q^{69} +(-1.82898 - 7.97048i) q^{70} +(3.54963 - 3.54963i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-2.53993 - 9.47914i) q^{73} +(-4.29981 + 7.44749i) q^{74} +(-2.27669 - 3.94335i) q^{75} +(4.21911 - 4.21911i) q^{76} +(-3.58150 + 5.71469i) q^{77} +(-0.969178 - 3.47285i) q^{78} +(3.52642 + 6.10793i) q^{79} +(2.98554 - 0.799972i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.30252 + 7.45218i) q^{82} +(-0.125330 - 0.125330i) q^{83} +(-2.52911 - 0.776903i) q^{84} +(-0.420292 - 0.420292i) q^{85} +(2.11613 - 7.89749i) q^{86} +(1.49082 + 0.860727i) q^{87} +(-2.20757 - 1.27454i) q^{88} +(-13.8225 - 3.70373i) q^{89} -3.09086 q^{90} +(-9.27516 + 2.22966i) q^{91} +6.10045 q^{92} +(-4.78133 - 1.28115i) q^{93} +(-10.1288 - 5.84789i) q^{94} +(-15.9715 - 9.22113i) q^{95} +(0.258819 - 0.965926i) q^{96} +(7.26558 + 7.26558i) q^{97} +(-2.29655 + 6.61255i) q^{98} +(1.80248 + 1.80248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 + 20 * q^9	\( 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more