LMFDB - Embedded newform 546.2.bz.b.73.9

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			73.9
Character	$\chi$	$=$	546.73
Dual form			546.2.bz.b.187.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.98554 + 0.799972i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.80183 + 1.93737i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.98554 + 0.799972i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.80183 + 1.93737i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.54543 - 2.67676i) q^{10} +(-0.659752 - 2.46223i) 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} +(0.965926 - 0.258819i) q^{18} +(5.76341 + 1.54430i) q^{19} +(-2.18556 - 2.18556i) q^{20} +(0.591740 + 2.57873i) q^{21} -2.54908 q^{22} +(-5.28314 + 3.05023i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(3.94335 + 2.27669i) q^{25} +(0.897093 + 3.49217i) q^{26} +1.00000i q^{27} +(-0.591740 - 2.57873i) q^{28} +1.72145 q^{29} +(2.67676 - 1.54543i) q^{30} +(-1.28115 - 4.78133i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.659752 - 2.46223i) q^{33} +(0.135979 + 0.135979i) q^{34} +(3.82957 + 7.22552i) q^{35} -1.00000i q^{36} +(-8.30660 - 2.22575i) q^{37} +(2.98336 - 5.16733i) q^{38} +(-3.60536 - 0.0373139i) q^{39} +(-2.67676 + 1.54543i) q^{40} +(6.08468 - 6.08468i) q^{41} +(2.64401 + 0.0958474i) q^{42} -8.17609i q^{43} +(-0.659752 + 2.46223i) q^{44} +(0.799972 + 2.98554i) q^{45} +(1.57891 + 5.89258i) q^{46} +(3.02709 - 11.2973i) q^{47} +1.00000i q^{48} +(-0.506844 + 6.98163i) q^{49} +(3.21973 - 3.21973i) q^{50} +(-0.166540 + 0.0961517i) q^{51} +(3.60536 + 0.0373139i) q^{52} +(2.33889 - 4.05108i) q^{53} +(0.965926 + 0.258819i) q^{54} -7.87885i q^{55} +(-2.64401 - 0.0958474i) q^{56} +(4.21911 + 4.21911i) q^{57} +(0.445545 - 1.66280i) q^{58} +(8.34882 - 2.23706i) q^{59} +(-0.799972 - 2.98554i) q^{60} +(-9.60184 + 5.54362i) q^{61} -4.95000 q^{62} +(-0.776903 + 2.52911i) q^{63} -1.00000i q^{64} +(-10.7938 + 2.77278i) q^{65} +(-2.20757 - 1.27454i) q^{66} +(-4.80864 + 1.28847i) q^{67} +(0.166540 - 0.0961517i) q^{68} -6.10045 q^{69} +(7.97048 - 1.82898i) q^{70} +(3.54963 + 3.54963i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(-9.47914 + 2.53993i) 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} +(0.799972 + 2.98554i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.30252 - 7.45218i) q^{82} +(0.125330 - 0.125330i) q^{83} +(0.776903 - 2.52911i) q^{84} +(-0.420292 + 0.420292i) q^{85} +(-7.89749 - 2.11613i) q^{86} +(1.49082 + 0.860727i) q^{87} +(2.20757 + 1.27454i) q^{88} +(-3.70373 + 13.8225i) q^{89} +3.09086 q^{90} +(-9.08938 - 2.89538i) q^{91} +6.10045 q^{92} +(1.28115 - 4.78133i) q^{93} +(-10.1288 - 5.84789i) q^{94} +(15.9715 + 9.22113i) q^{95} +(0.965926 + 0.258819i) q^{96} +(-7.26558 + 7.26558i) q^{97} +(6.61255 + 2.29655i) 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} + 16 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} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 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} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 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} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 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 + 16 * 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 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * 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 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * 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 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	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
$5$	2.98554	+	0.799972i	1.33517	+	0.357758i	0.854641	−	0.519219i	$-0.173777\pi$
$5$	2.98554	+	0.799972i	1.33517	+	0.357758i	0.480532	+	0.876977i	$0.340444\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	1.80183	+	1.93737i	0.681026	+	0.732259i
$7$	1.80183	+	1.93737i	0.681026	+	0.732259i
$8$	−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
$11$	−0.659752	−	2.46223i	−0.198923	−	0.742389i	−0.991216	−	0.132250i	$-0.957780\pi$
$11$	−0.659752	−	2.46223i	−0.198923	−	0.742389i	0.792294	−	0.610140i	$-0.208887\pi$
$12$	−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	−0.877450	−	0.479668i	$-0.840757\pi$
$17$	−0.0961517	+	0.166540i	−0.0233202	+	0.0403918i	0.854130	+	0.520060i	$0.174090\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	5.76341	+	1.54430i	1.32222	+	0.354287i	0.849808	−	0.527093i	$-0.176718\pi$
$19$	5.76341	+	1.54430i	1.32222	+	0.354287i	0.472409	+	0.881380i	$0.343385\pi$
$20$	−2.18556	−	2.18556i	−0.488707	−	0.488707i
$21$	0.591740	+	2.57873i	0.129128	+	0.562725i
$22$	−2.54908			−0.543467
$23$	−5.28314	+	3.05023i	−1.10161	+	0.636016i	−0.936644	−	0.350283i	$-0.886085\pi$
$23$	−5.28314	+	3.05023i	−1.10161	+	0.636016i	−0.164968	+	0.986299i	$0.552752\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	3.94335	+	2.27669i	0.788670	+	0.455339i
$26$	0.897093	+	3.49217i	0.175934	+	0.684870i
$27$			1.00000i			0.192450i
$28$	−0.591740	−	2.57873i	−0.111828	−	0.487334i
$29$	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
$31$	−1.28115	−	4.78133i	−0.230102	−	0.858752i	−0.980296	−	0.197534i	$-0.936707\pi$
$31$	−1.28115	−	4.78133i	−0.230102	−	0.858752i	0.750194	−	0.661218i	$-0.229960\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	0.659752	−	2.46223i	0.114848	−	0.428619i
$34$	0.135979	+	0.135979i	0.0233202	+	0.0233202i
$35$	3.82957	+	7.22552i	0.647316	+	1.22134i
$36$		−	1.00000i		−	0.166667i
$37$	−8.30660	−	2.22575i	−1.36560	−	0.365910i	−0.499728	−	0.866182i	$-0.666567\pi$
$37$	−8.30660	−	2.22575i	−1.36560	−	0.365910i	−0.865868	+	0.500272i	$0.833233\pi$
$38$	2.98336	−	5.16733i	0.483965	−	0.838252i
$39$	−3.60536	−	0.0373139i	−0.577319	−	0.00597501i
$40$	−2.67676	+	1.54543i	−0.423233	+	0.244354i
$41$	6.08468	−	6.08468i	0.950268	−	0.950268i	−0.0485529	−	0.998821i	$-0.515461\pi$
$41$	6.08468	−	6.08468i	0.950268	−	0.950268i	0.998821	+	0.0485529i	$0.0154609\pi$
$42$	2.64401	+	0.0958474i	0.407980	+	0.0147896i
$43$		−	8.17609i		−	1.24684i	−0.781887	−	0.623421i	$-0.785742\pi$
$43$		−	8.17609i		−	1.24684i	0.781887	−	0.623421i	$-0.214258\pi$
$44$	−0.659752	+	2.46223i	−0.0994613	+	0.371195i
$45$	0.799972	+	2.98554i	0.119253	+	0.445058i
$46$	1.57891	+	5.89258i	0.232798	+	0.868814i
$47$	3.02709	−	11.2973i	0.441546	−	1.64787i	−0.283350	−	0.959016i	$-0.591446\pi$
$47$	3.02709	−	11.2973i	0.441546	−	1.64787i	0.724897	−	0.688857i	$-0.241887\pi$
$48$			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
$52$	3.60536	+	0.0373139i	0.499973	+	0.00517451i
$53$	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	$0.0625565\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$		−	7.87885i		−	1.06238i
$56$	−2.64401	−	0.0958474i	−0.353321	−	0.0128081i
$57$	4.21911	+	4.21911i	0.558834	+	0.558834i
$58$	0.445545	−	1.66280i	0.0585029	−	0.218336i
$59$	8.34882	−	2.23706i	1.08692	−	0.291240i	0.329495	−	0.944157i	$-0.393122\pi$
$59$	8.34882	−	2.23706i	1.08692	−	0.291240i	0.757429	+	0.652917i	$0.226455\pi$
$60$	−0.799972	−	2.98554i	−0.103276	−	0.385431i
$61$	−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
$63$	−0.776903	+	2.52911i	−0.0978805	+	0.318639i
$64$		−	1.00000i		−	0.125000i
$65$	−10.7938	+	2.77278i	−1.33880	+	0.343922i
$66$	−2.20757	−	1.27454i	−0.271733	−	0.156885i
$67$	−4.80864	+	1.28847i	−0.587468	+	0.157412i	−0.540296	−	0.841475i	$-0.681688\pi$
$67$	−4.80864	+	1.28847i	−0.587468	+	0.157412i	−0.0471725	+	0.998887i	$0.515021\pi$
$68$	0.166540	−	0.0961517i	0.0201959	−	0.0116601i
$69$	−6.10045			−0.734408
$70$	7.97048	−	1.82898i	0.952654	−	0.218605i
$71$	3.54963	+	3.54963i	0.421264	+	0.421264i	0.885639	−	0.464375i	$-0.153721\pi$
$71$	3.54963	+	3.54963i	0.421264	+	0.421264i	−0.464375	+	0.885639i	$0.653721\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	−9.47914	+	2.53993i	−1.10945	+	0.297276i	−0.766607	−	0.642117i	$-0.778056\pi$
$73$	−9.47914	+	2.53993i	−1.10945	+	0.297276i	−0.342843	+	0.939393i	$0.611390\pi$
$74$	−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	$0.703470\pi$
$80$	0.799972	+	2.98554i	0.0894396	+	0.333793i
$81$	−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	$-0.746904\pi$
$83$	0.125330	−	0.125330i	0.0137567	−	0.0137567i	0.713952	+	0.700195i	$0.246904\pi$
$84$	0.776903	−	2.52911i	0.0847670	−	0.275949i
$85$	−0.420292	+	0.420292i	−0.0455870	+	0.0455870i
$86$	−7.89749	−	2.11613i	−0.851608	−	0.228188i
$87$	1.49082	+	0.860727i	0.159833	+	0.0922796i
$88$	2.20757	+	1.27454i	0.235328	+	0.135867i
$89$	−3.70373	+	13.8225i	−0.392594	+	1.46518i	0.433245	+	0.901276i	$0.357368\pi$
$89$	−3.70373	+	13.8225i	−0.392594	+	1.46518i	−0.825839	+	0.563905i	$0.809298\pi$
$90$	3.09086			0.325805
$91$	−9.08938	−	2.89538i	−0.952825	−	0.303519i
$92$	6.10045			0.636016
$93$	1.28115	−	4.78133i	0.132849	−	0.495801i
$94$	−10.1288	−	5.84789i	−1.04471	−	0.603164i
$95$	15.9715	+	9.22113i	1.63864	+	0.946068i
$96$	0.965926	+	0.258819i	0.0985844	+	0.0264156i
$97$	−7.26558	+	7.26558i	−0.737708	+	0.737708i	−0.972134	−	0.234426i	$-0.924679\pi$
$97$	−7.26558	+	7.26558i	−0.737708	+	0.737708i	0.234426	+	0.972134i	$0.424679\pi$
$98$	6.61255	+	2.29655i	0.667969	+	0.231987i
$99$	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	$-0.581587\pi$
$101$	7.14522	−	12.3759i	0.710976	−	1.23145i	0.964491	−	0.264115i	$-0.0850799\pi$
$102$	0.0497718	+	0.185751i	0.00492814	+	0.0183921i
$103$	−4.68944	−	8.12235i	−0.462065	−	0.800319i	0.536999	−	0.843583i	$-0.319558\pi$
$103$	−4.68944	−	8.12235i	−0.462065	−	0.800319i	−0.999064	+	0.0432635i	$0.986225\pi$
$104$	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
$109$	−10.0242	+	2.68597i	−0.960141	+	0.257269i	−0.704660	−	0.709545i	$-0.748900\pi$
$109$	−10.0242	+	2.68597i	−0.960141	+	0.257269i	−0.255481	+	0.966814i	$0.582234\pi$
$110$	−7.61039	−	2.03920i	−0.725622	−	0.194430i
$111$	−6.08085	−	6.08085i	−0.577169	−	0.577169i
$112$	−0.776903	+	2.52911i	−0.0734104	+	0.238979i
$113$	−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
$115$	−18.2131	+	4.88019i	−1.69838	+	0.455080i
$116$	−1.49082	−	0.860727i	−0.138419	−	0.0799165i
$117$	−3.10367	−	1.83499i	−0.286935	−	0.169645i
$118$		−	8.64334i		−	0.795684i
$119$	−0.495898	+	0.113794i	−0.0454589	+	0.0104314i
$120$	−3.09086			−0.282155
$121$	3.89899	−	2.25108i	0.354454	−	0.204644i
$122$	2.86959	+	10.7095i	0.259801	+	0.969589i
$123$	8.31183	−	2.22715i	0.749453	−	0.200815i
$124$	−1.28115	+	4.78133i	−0.115051	+	0.429376i
$125$	−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	$-0.802234\pi$
$127$		−	13.1197i		−	1.16419i	0.813122	−	0.582093i	$-0.197766\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	4.08804	−	7.08070i	0.359932	−	0.623421i
$130$	−0.115332	+	11.1436i	−0.0101153	+	0.977362i
$131$	−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
$135$	−0.799972	+	2.98554i	−0.0688506	+	0.256954i
$136$	−0.0497718	−	0.185751i	−0.00426790	−	0.0159280i
$137$	3.82257	+	14.2660i	0.326584	+	1.21883i	0.912710	+	0.408608i	$0.133986\pi$
$137$	3.82257	+	14.2660i	0.326584	+	1.21883i	−0.586126	+	0.810220i	$0.699348\pi$
$138$	−1.57891	+	5.89258i	−0.134406	+	0.501610i
$139$			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
$143$	6.43131	+	6.56583i	0.537813	+	0.549062i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	5.13946	+	1.37712i	0.426809	+	0.114363i
$146$			9.81353i			0.812174i
$147$	−3.92975	+	5.79284i	−0.324121	+	0.477786i
$148$	6.08085	+	6.08085i	0.499843	+	0.499843i
$149$	−1.72921	+	6.45351i	−0.141663	+	0.528692i	0.858219	+	0.513284i	$0.171571\pi$
$149$	−1.72921	+	6.45351i	−0.141663	+	0.528692i	−0.999881	+	0.0154078i	$0.995095\pi$
$150$	4.39823	−	1.17850i	0.359114	−	0.0962244i
$151$	3.05577	+	11.4043i	0.248675	+	0.928067i	0.971501	+	0.237037i	$0.0761763\pi$
$151$	3.05577	+	11.4043i	0.248675	+	0.928067i	−0.722826	+	0.691030i	$0.757157\pi$
$152$	−5.16733	+	2.98336i	−0.419126	+	0.241982i
$153$	−0.192303			−0.0155468
$154$	−4.59301	−	4.93853i	−0.370115	−	0.397958i
$155$		−	15.2997i		−	1.22890i
$156$	3.10367	+	1.83499i	0.248493	+	0.146917i
$157$	−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	$0.833209\pi$
$158$	6.81251	−	1.82541i	0.541974	−	0.145222i
$159$	4.05108	−	2.33889i	0.321271	−	0.185486i
$160$	3.09086			0.244354
$161$	−15.4287	−	4.73946i	−1.21596	−	0.373522i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	18.9313	+	5.07262i	1.48281	+	0.397318i	0.907303	−	0.420478i	$-0.138138\pi$
$163$	18.9313	+	5.07262i	1.48281	+	0.397318i	0.575508	+	0.817796i	$0.304804\pi$
$164$	−8.31183	+	2.22715i	−0.649045	+	0.173911i
$165$	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	−0.999909	−	0.0135245i	$-0.995695\pi$
$167$	−13.0964	−	13.0964i	−1.01343	−	1.01343i	−0.0135245	−	0.999909i	$-0.504305\pi$
$168$	−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
$171$	1.54430	+	5.76341i	0.118096	+	0.440739i
$172$	−4.08804	+	7.08070i	−0.311710	+	0.539898i
$173$	8.38540	+	14.5239i	0.637530	+	1.10423i	0.985973	+	0.166904i	$0.0533770\pi$
$173$	8.38540	+	14.5239i	0.637530	+	1.10423i	−0.348443	+	0.937330i	$0.613290\pi$
$174$	1.21725	−	1.21725i	0.0922796	−	0.0922796i
$175$	2.69442	+	11.7420i	0.203679	+	0.887608i
$176$	1.80248	−	1.80248i	0.135867	−	0.135867i
$177$	8.34882	+	2.23706i	0.627536	+	0.168148i
$178$	12.3929	+	7.15505i	0.928888	+	0.536294i
$179$	7.66247	+	4.42393i	0.572720	+	0.330660i	0.758235	−	0.651981i	$-0.226062\pi$
$179$	7.66247	+	4.42393i	0.572720	+	0.330660i	−0.185515	+	0.982641i	$0.559395\pi$
$180$	0.799972	−	2.98554i	0.0596264	−	0.222529i
$181$	−9.29817			−0.691128			−0.345564	−	0.938395i	$-0.612312\pi$
$181$	−9.29817			−0.691128			−0.345564	+	0.938395i	$0.612312\pi$
$182$	−5.14923	+	8.03028i	−0.381686	+	0.595244i
$183$	−11.0872			−0.819593
$184$	1.57891	−	5.89258i	0.116399	−	0.434407i
$185$	−23.0191	−	13.2901i	−1.69240	−	0.977107i
$186$	−4.28682	−	2.47500i	−0.314325	−	0.181476i
$187$	0.473495	+	0.126873i	0.0346254	+	0.00927784i
$188$	−8.27016	+	8.27016i	−0.603164	+	0.603164i
$189$	−1.93737	+	1.80183i	−0.140923	+	0.131064i
$190$	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
$193$	2.85208	+	10.6441i	0.205298	+	0.766181i	0.989359	+	0.145497i	$0.0464782\pi$
$193$	2.85208	+	10.6441i	0.205298	+	0.766181i	−0.784061	+	0.620684i	$0.786855\pi$
$194$	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	0.591829	−	0.806064i	$-0.298406\pi$
$197$	−3.00693	−	3.00693i	−0.214235	−	0.214235i	−0.806064	+	0.591829i	$0.798406\pi$
$198$	−1.27454	−	2.20757i	−0.0905778	−	0.156885i
$199$	−8.33229	+	14.4319i	−0.590660	+	1.02305i	0.403484	+	0.914987i	$0.367799\pi$
$199$	−8.33229	+	14.4319i	−0.590660	+	1.02305i	−0.994144	+	0.108066i	$0.965534\pi$
$200$	−4.39823	+	1.17850i	−0.311002	+	0.0833328i
$201$	−4.80864	−	1.28847i	−0.339175	−	0.0908817i
$202$	−10.1049	−	10.1049i	−0.710976	−	0.710976i
$203$	3.10176	+	3.33510i	0.217701	+	0.234078i
$204$	0.192303			0.0134639
$205$	23.0336	−	13.2985i	1.60874	−	0.928805i
$206$	−9.05931	+	2.42743i	−0.631192	+	0.169127i
$207$	−5.28314	−	3.05023i	−0.367204	−	0.212005i
$208$	−3.10367	−	1.83499i	−0.215201	−	0.127234i
$209$		−	15.2097i		−	1.05208i
$210$	7.81713	+	2.40129i	0.539433	+	0.165705i
$211$	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
$213$	1.29926	+	4.84889i	0.0890235	+	0.332240i
$214$	−4.62329	+	1.23881i	−0.316042	+	0.0846831i
$215$	6.54064	−	24.4100i	0.446068	−	1.66475i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	6.95481	−	11.0972i	0.472123	−	0.753327i
$218$			10.3778i			0.702872i
$219$	−9.47914	−	2.53993i	−0.640541	−	0.171632i
$220$	−3.93943	+	6.82329i	−0.265596	+	0.460026i
$221$	0.00717560	−	0.693323i	0.000482683	−	0.0466379i
$222$	−7.44749	+	4.29981i	−0.499843	+	0.288584i
$223$	13.5086	−	13.5086i	0.904604	−	0.904604i	−0.0912259	−	0.995830i	$-0.529079\pi$
$223$	13.5086	−	13.5086i	0.904604	−	0.904604i	0.995830	+	0.0912259i	$0.0290785\pi$
$224$	2.24186	+	1.40501i	0.149791	+	0.0938764i
$225$			4.55339i			0.303559i
$226$	−0.859804	+	3.20883i	−0.0571933	+	0.213448i
$227$	−1.75395	−	6.54583i	−0.116414	−	0.434462i	0.882975	−	0.469420i	$-0.155537\pi$
$227$	−1.75395	−	6.54583i	−0.116414	−	0.434462i	−0.999389	+	0.0349578i	$0.988870\pi$
$228$	−1.54430	−	5.76341i	−0.102274	−	0.381691i
$229$	−3.67462	+	13.7139i	−0.242826	+	0.906239i	0.731638	+	0.681694i	$0.238756\pi$
$229$	−3.67462	+	13.7139i	−0.242826	+	0.906239i	−0.974464	+	0.224545i	$0.927910\pi$
$230$			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	−0.292046	−	0.956404i	$-0.594336\pi$
$233$	5.95618	−	3.43880i	0.390202	−	0.225283i	0.682248	+	0.731121i	$0.261003\pi$
$234$	−2.57576	+	2.52299i	−0.168383	+	0.164933i
$235$	18.0750	−	31.3068i	1.17908	−	2.04223i
$236$	−8.34882	−	2.23706i	−0.543462	−	0.145620i
$237$			7.05283i			0.458131i
$238$	−0.0184318	+	0.508453i	−0.00119475	+	0.0329581i
$239$	−3.10382	−	3.10382i	−0.200770	−	0.200770i	0.599560	−	0.800330i	$-0.295342\pi$
$239$	−3.10382	−	3.10382i	−0.200770	−	0.200770i	−0.800330	+	0.599560i	$0.795342\pi$
$240$	−0.799972	+	2.98554i	−0.0516380	+	0.192716i
$241$	−9.25180	+	2.47901i	−0.595961	+	0.159687i	−0.544176	−	0.838971i	$-0.683158\pi$
$241$	−9.25180	+	2.47901i	−0.595961	+	0.159687i	−0.0517849	+	0.998658i	$0.516491\pi$
$242$	−1.16525	−	4.34876i	−0.0749049	−	0.279549i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	11.0872			0.709788
$245$	−7.09831	+	20.4384i	−0.453494	+	1.30576i
$246$		−	8.60504i		−	0.548637i
$247$	−20.8368	+	5.35270i	−1.32581	+	0.340584i
$248$	4.28682	+	2.47500i	0.272214	+	0.157163i
$249$	0.171204	−	0.0458739i	0.0108496	−	0.00290714i
$250$	−1.19548	+	0.690208i	−0.0756085	+	0.0436526i
$251$	26.5647			1.67675			0.838375	−	0.545095i	$-0.183506\pi$
$251$	26.5647			1.67675			0.838375	+	0.545095i	$0.183506\pi$
$252$	1.93737	−	1.80183i	0.122043	−	0.113504i
$253$	10.9959	+	10.9959i	0.691307	+	0.691307i
$254$	−12.6727	−	3.39563i	−0.795154	−	0.213061i
$255$	−0.574129	+	0.153837i	−0.0359534	+	0.00963367i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.16190	+	7.20862i	0.259612	+	0.449661i	0.966138	−	0.258026i	$-0.0830720\pi$
$257$	4.16190	+	7.20862i	0.259612	+	0.449661i	−0.706526	+	0.707687i	$0.749739\pi$
$258$	−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
$262$	4.18266	+	15.6099i	0.258406	+	0.964383i
$263$	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
$266$	15.3866	−	3.53075i	0.943410	−	0.216484i
$267$	−10.1188	+	10.1188i	−0.619259	+	0.619259i
$268$	4.80864	+	1.28847i	0.293734	+	0.0787058i
$269$	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
$271$	0.0581928	−	0.217179i	0.00353496	−	0.0131927i	−0.964136	−	0.265409i	$-0.914493\pi$
$271$	0.0581928	−	0.217179i	0.00353496	−	0.0131927i	0.967671	+	0.252217i	$0.0811596\pi$
$272$	−0.192303			−0.0116601
$273$	−6.42394	−	7.05216i	−0.388794	−	0.426816i
$274$	14.7693			0.892244
$275$	3.00410	−	11.2115i	0.181154	−	0.676077i
$276$	5.28314	+	3.05023i	0.318008	+	0.183602i
$277$	−27.7764	−	16.0367i	−1.66892	−	0.963554i	−0.968219	−	0.250103i	$-0.919535\pi$
$277$	−27.7764	−	16.0367i	−1.66892	−	0.963554i	−0.700705	−	0.713451i	$-0.747131\pi$
$278$	0.924807	+	0.247801i	0.0554662	+	0.0148621i
$279$	3.50018	−	3.50018i	0.209550	−	0.209550i
$280$	−7.81713	−	2.40129i	−0.467163	−	0.143505i
$281$	4.90671	−	4.90671i	0.292710	−	0.292710i	−0.545440	−	0.838150i	$-0.683638\pi$
$281$	4.90671	−	4.90671i	0.292710	−	0.292710i	0.838150	+	0.545440i	$0.183638\pi$
$282$	−5.84789	−	10.1288i	−0.348237	−	0.603164i
$283$	9.61696	−	16.6571i	0.571669	−	0.990159i	−0.424726	−	0.905322i	$-0.639630\pi$
$283$	9.61696	−	16.6571i	0.571669	−	0.990159i	0.996395	−	0.0848375i	$-0.0270371\pi$
$284$	−1.29926	−	4.84889i	−0.0770966	−	0.287728i
$285$	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
$291$	−9.92497	+	2.65939i	−0.581812	+	0.155896i
$292$	9.47914	+	2.53993i	0.554725	+	0.148638i
$293$	−12.2790	−	12.2790i	−0.717348	−	0.717348i	0.250714	−	0.968061i	$-0.419335\pi$
$293$	−12.2790	−	12.2790i	−0.717348	−	0.717348i	−0.968061	+	0.250714i	$0.919335\pi$
$294$	4.57836	+	5.29515i	0.267016	+	0.308819i
$295$	26.7153			1.55543
$296$	7.44749	−	4.29981i	0.432877	−	0.249921i
$297$	2.46223	−	0.659752i	0.142873	−	0.0382827i
$298$	5.78606	+	3.34058i	0.335177	+	0.193515i
$299$	11.1943	−	18.9338i	0.647382	−	1.09497i
$300$		−	4.55339i		−	0.262890i
$301$	15.8401	−	14.7319i	0.913011	−	0.849132i
$302$	11.8066			0.679393
$303$	12.3759	−	7.14522i	0.710976	−	0.410482i
$304$	1.54430	+	5.76341i	0.0885717	+	0.330554i
$305$	−33.1014	+	8.86949i	−1.89538	+	0.507866i
$306$	−0.0497718	+	0.185751i	−0.00284526	+	0.0106187i
$307$	9.35808	+	9.35808i	0.534094	+	0.534094i	0.921788	−	0.387694i	$-0.126728\pi$
$307$	9.35808	+	9.35808i	0.534094	+	0.534094i	−0.387694	+	0.921788i	$0.626728\pi$
$308$	−5.95901	+	3.15832i	−0.339546	+	0.179962i
$309$		−	9.37889i		−	0.533546i
$310$	−14.7784	−	3.95986i	−0.839357	−	0.224905i
$311$	−1.67332	+	2.89828i	−0.0948855	+	0.164346i	−0.909561	−	0.415571i	$-0.863582\pi$
$311$	−1.67332	+	2.89828i	−0.0948855	+	0.164346i	0.814675	+	0.579917i	$0.196915\pi$
$312$	2.57576	−	2.52299i	0.145824	−	0.142836i
$313$	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
$317$	−6.36280	+	23.7463i	−0.357370	+	1.33372i	0.520105	+	0.854103i	$0.325893\pi$
$317$	−6.36280	+	23.7463i	−0.357370	+	1.33372i	−0.877475	+	0.479622i	$0.840774\pi$
$318$	−1.21070	−	4.51839i	−0.0678926	−	0.253379i
$319$	−1.13573	−	4.23861i	−0.0635888	−	0.237317i
$320$	0.799972	−	2.98554i	0.0447198	−	0.166897i
$321$		−	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
$325$	−16.4166	−	0.169905i	−0.910629	−	0.00942462i
$326$	9.79954	−	16.9733i	0.542746	−	0.940064i
$327$	−10.0242	−	2.68597i	−0.554338	−	0.148534i
$328$			8.60504i			0.475134i
$329$	27.3413	−	14.4911i	1.50738	−	0.798919i
$330$	−5.57119	−	5.57119i	−0.306684	−	0.306684i
$331$	−6.39933	+	23.8826i	−0.351739	+	1.31271i	0.532800	+	0.846241i	$0.321140\pi$
$331$	−6.39933	+	23.8826i	−0.351739	+	1.31271i	−0.884539	+	0.466466i	$0.845527\pi$
$332$	−0.171204	+	0.0458739i	−0.00939602	+	0.00251766i
$333$	−2.22575	−	8.30660i	−0.121970	−	0.455199i
$334$	−16.0398	+	9.26058i	−0.877659	+	0.506717i
$335$	−15.3871			−0.840687
$336$	−1.93737	+	1.80183i	−0.105692	+	0.0982977i
$337$			5.02373i			0.273660i	0.990595	+	0.136830i	$0.0436914\pi$
$337$			5.02373i			0.273660i	−0.990595	+	0.136830i	$0.956309\pi$
$338$	−9.00016	−	9.38067i	−0.489544	−	0.510241i
$339$	−2.87696	−	1.66101i	−0.156255	−	0.0902139i
$340$	0.574129	−	0.153837i	0.0311365	−	0.00834301i
$341$	−10.9275	+	6.30898i	−0.591756	+	0.341650i
$342$	5.96672			0.322643
$343$	−14.4393	+	11.5977i	−0.779647	+	0.626219i
$344$	5.78137	+	5.78137i	0.311710	+	0.311710i
$345$	−18.2131	−	4.88019i	−0.980561	−	0.262741i
$346$	16.1993	−	4.34060i	0.870882	−	0.233352i
$347$	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	$-0.349089\pi$
$349$	−8.09220	−	8.09220i	−0.433166	−	0.433166i	−0.889704	+	0.456538i	$0.849089\pi$
$350$	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
$353$	−4.04703	−	15.1037i	−0.215402	−	0.803890i	−0.986025	−	0.166599i	$-0.946721\pi$
$353$	−4.04703	−	15.1037i	−0.215402	−	0.803890i	0.770623	−	0.637291i	$-0.219945\pi$
$354$	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
$357$	−0.486358	−	0.149401i	−0.0257408	−	0.00790714i
$358$	6.25638	−	6.25638i	0.330660	−	0.330660i
$359$	28.7496	+	7.70342i	1.51734	+	0.406571i	0.918866	−	0.394569i	$-0.129106\pi$
$359$	28.7496	+	7.70342i	1.51734	+	0.406571i	0.598477	+	0.801140i	$0.295773\pi$
$360$	−2.67676	−	1.54543i	−0.141078	−	0.0814512i
$361$	14.3775	+	8.30087i	0.756712	+	0.436888i
$362$	−2.40654	+	8.98135i	−0.126485	+	0.472049i
$363$	4.50217			0.236302
$364$	6.42394	+	7.05216i	0.336706	+	0.369634i
$365$	−30.3322			−1.58766
$366$	−2.86959	+	10.7095i	−0.149996	+	0.559792i
$367$	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
$369$	8.31183	+	2.22715i	0.432697	+	0.115941i
$370$	−18.7950	+	18.7950i	−0.977107	+	0.977107i
$371$	12.0627	−	2.76803i	0.626266	−	0.143709i
$372$	−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
$375$	−0.357278	−	1.33338i	−0.0184498	−	0.0688554i
$376$	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	0.829412	−	0.558638i	$-0.188676\pi$
$379$	5.27141	+	5.27141i	0.270774	+	0.270774i	−0.558638	+	0.829412i	$0.688676\pi$
$380$	−9.22113	−	15.9715i	−0.473034	−	0.819319i
$381$	6.55986	−	11.3620i	0.336072	−	0.582093i
$382$	−5.02823	+	1.34731i	−0.257267	+	0.0689344i
$383$	−32.0667	−	8.59224i	−1.63853	−	0.439043i	−0.682161	−	0.731202i	$-0.738960\pi$
$383$	−32.0667	−	8.59224i	−1.63853	−	0.439043i	−0.956370	+	0.292159i	$0.905626\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	15.2643	−	14.1963i	0.777940	−	0.723512i
$386$	11.0196			0.560883
$387$	7.08070	−	4.08804i	0.359932	−	0.207807i
$388$	9.92497	−	2.65939i	0.503864	−	0.135010i
$389$	10.4389	+	6.02690i	0.529273	+	0.305576i	0.740720	−	0.671813i	$-0.234484\pi$
$389$	10.4389	+	6.02690i	0.529273	+	0.305576i	−0.211447	+	0.977389i	$0.567818\pi$
$390$	−5.67170	+	9.59301i	−0.287198	+	0.485761i
$391$		−	1.17314i		−	0.0593281i
$392$	−4.57836	−	5.29515i	−0.231242	−	0.267445i
$393$	−16.1606			−0.815193
$394$	−3.68273	+	2.12622i	−0.185533	+	0.107118i
$395$	5.64207	+	21.0565i	0.283883	+	1.05947i
$396$	−2.46223	+	0.659752i	−0.123732	+	0.0331538i
$397$	−5.34143	+	19.9345i	−0.268079	+	1.00048i	0.692260	+	0.721648i	$0.256615\pi$
$397$	−5.34143	+	19.9345i	−0.268079	+	1.00048i	−0.960339	+	0.278836i	$0.910052\pi$
$398$	11.7836	+	11.7836i	0.590660	+	0.590660i
$399$	−0.571894	+	15.7761i	−0.0286305	+	0.789793i
$400$			4.55339i			0.227669i
$401$	−3.91604	−	1.04930i	−0.195557	−	0.0523995i	0.159711	−	0.987164i	$-0.448944\pi$
$401$	−3.91604	−	1.04930i	−0.195557	−	0.0523995i	−0.355268	+	0.934764i	$0.615610\pi$
$402$	−2.48913	+	4.31131i	−0.124147	+	0.215028i
$403$	12.4888	+	12.7500i	0.622111	+	0.635122i
$404$	−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
$408$	0.0497718	−	0.185751i	0.00246407	−	0.00919604i
$409$	−2.33814	−	8.72606i	−0.115614	−	0.431476i	0.883718	−	0.468019i	$-0.155032\pi$
$409$	−2.33814	−	8.72606i	−0.115614	−	0.431476i	−0.999332	+	0.0365430i	$0.988365\pi$
$410$	−6.88379	−	25.6907i	−0.339966	−	1.26877i
$411$	−3.82257	+	14.2660i	−0.188553	+	0.703690i
$412$			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
$416$	−2.57576	+	2.52299i	−0.126287	+	0.123700i
$417$	−0.478715	+	0.829159i	−0.0234428	+	0.0406041i
$418$	−14.6914	−	3.93655i	−0.718581	−	0.192543i
$419$		−	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	0.831548	−	0.555453i	$-0.187455\pi$
$421$	5.66498	+	5.66498i	0.276094	+	0.276094i	−0.555453	+	0.831548i	$0.687455\pi$
$422$	1.69695	−	6.33310i	0.0826062	−	0.308291i
$423$	11.2973	−	3.02709i	0.549291	−	0.147182i
$424$	1.21070	+	4.51839i	0.0587967	+	0.219432i
$425$	−0.758320	+	0.437816i	−0.0367839	+	0.0212372i
$426$	5.01994			0.243217
$427$	−28.0409	−	8.61371i	−1.35700	−	0.416847i
$428$			4.78638i			0.231359i
$429$	2.28677	+	8.90183i	0.110406	+	0.429784i
$430$	−21.8854	−	12.6355i	−1.05541	−	0.609340i
$431$	−18.0413	+	4.83415i	−0.869019	+	0.232853i	−0.665663	−	0.746252i	$-0.731851\pi$
$431$	−18.0413	+	4.83415i	−0.869019	+	0.232853i	−0.203355	+	0.979105i	$0.565185\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	3.49283			0.167855			0.0839273	−	0.996472i	$-0.473254\pi$
$433$	3.49283			0.167855			0.0839273	+	0.996472i	$0.473254\pi$
$434$	−8.91903	−	9.59000i	−0.428127	−	0.460335i
$435$	3.76235	+	3.76235i	0.180391	+	0.180391i
$436$	10.0242	+	2.68597i	0.480071	+	0.128635i
$437$	−35.1594	+	9.42093i	−1.68190	+	0.450664i
$438$	−4.90677	+	8.49877i	−0.234454	+	0.406087i
$439$	−0.131695	−	0.228102i	−0.00628546	−	0.0108867i	0.862866	−	0.505433i	$-0.168667\pi$
$439$	−0.131695	−	0.228102i	−0.00628546	−	0.0108867i	−0.869151	+	0.494547i	$0.835334\pi$
$440$	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	$0.768704\pi$
$444$	2.22575	+	8.30660i	0.105629	+	0.394214i
$445$	−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
$448$	1.93737	−	1.80183i	0.0915324	−	0.0851283i
$449$	−22.2036	+	22.2036i	−1.04785	+	1.04785i	−0.0490587	+	0.998796i	$0.515622\pi$
$449$	−22.2036	+	22.2036i	−1.04785	+	1.04785i	−0.998796	+	0.0490587i	$0.984378\pi$
$450$	4.39823	+	1.17850i	0.207335	+	0.0555552i
$451$	−18.9962	−	10.9675i	−0.894498	−	0.516439i
$452$	2.87696	+	1.66101i	0.135321	+	0.0781275i
$453$	−3.05577	+	11.4043i	−0.143573	+	0.535820i
$454$	−6.77675			−0.318048
$455$	−24.8204	−	15.9155i	−1.16360	−	0.746131i
$456$	−5.96672			−0.279417
$457$	−1.25123	+	4.66966i	−0.0585301	+	0.218437i	−0.988996	−	0.147941i	$-0.952736\pi$
$457$	−1.25123	+	4.66966i	−0.0585301	+	0.218437i	0.930466	+	0.366378i	$0.119402\pi$
$458$	12.2955	+	7.09883i	0.574532	+	0.331706i
$459$	−0.166540	−	0.0961517i	−0.00777341	−	0.00448798i
$460$	18.2131	+	4.88019i	0.849191	+	0.227540i
$461$	19.1638	−	19.1638i	0.892547	−	0.892547i	−0.102215	−	0.994762i	$-0.532593\pi$
$461$	19.1638	−	19.1638i	0.892547	−	0.892547i	0.994762	+	0.102215i	$0.0325930\pi$
$462$	−1.50840	−	6.57340i	−0.0701769	−	0.305822i
$463$	−5.75634	+	5.75634i	−0.267520	+	0.267520i	−0.828100	−	0.560580i	$-0.810578\pi$
$463$	−5.75634	+	5.75634i	−0.267520	+	0.267520i	0.560580	+	0.828100i	$0.310578\pi$
$464$	0.860727	+	1.49082i	0.0399582	+	0.0692097i
$465$	7.64986	−	13.2499i	0.354754	−	0.614452i
$466$	−1.78005	−	6.64325i	−0.0824594	−	0.307743i
$467$	−3.04421	−	5.27272i	−0.140869	−	0.243992i	0.786955	−	0.617010i	$-0.211656\pi$
$467$	−3.04421	−	5.27272i	−0.140869	−	0.243992i	−0.927824	+	0.373018i	$0.878323\pi$
$468$	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
$473$	−20.1314	+	5.39419i	−0.925642	+	0.248025i
$474$	6.81251	+	1.82541i	0.312909	+	0.0838437i
$475$	19.2112	+	19.2112i	0.881472	+	0.881472i
$476$	0.486358	+	0.149401i	0.0222922	+	0.00684779i
$477$	4.67778			0.214181
$478$	−3.80139	+	2.19473i	−0.173872	+	0.100385i
$479$	−3.33242	+	0.892919i	−0.152262	+	0.0407985i	−0.334145	−	0.942522i	$-0.608447\pi$
$479$	−3.33242	+	0.892919i	−0.152262	+	0.0407985i	0.181883	+	0.983320i	$0.441781\pi$
$480$	2.67676	+	1.54543i	0.122177	+	0.0705388i
$481$	30.0313	−	7.71466i	1.36931	−	0.351758i
$482$			9.57817i			0.436274i
$483$	−10.9920	−	11.8189i	−0.500151	−	0.537777i
$484$	−4.50217			−0.204644
$485$	−27.5039	+	15.8794i	−1.24889	+	0.721046i
$486$	0.258819	+	0.965926i	0.0117403	+	0.0438153i
$487$	−17.0982	+	4.58146i	−0.774795	+	0.207606i	−0.624489	−	0.781034i	$-0.714693\pi$
$487$	−17.0982	+	4.58146i	−0.774795	+	0.207606i	−0.150306	+	0.988639i	$0.548026\pi$
$488$	2.86959	−	10.7095i	0.129900	−	0.484794i
$489$	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	$-0.970848\pi$
$491$		−	4.05304i		−	0.182911i	0.995809	−	0.0914555i	$-0.0291519\pi$
$492$	−8.31183	−	2.22715i	−0.374726	−	0.100408i
$493$	−0.165521	+	0.286690i	−0.00745468	+	0.0129119i
$494$	−0.222642	+	21.5122i	−0.0100171	+	0.967878i
$495$	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
$499$	3.80849	−	14.2135i	0.170491	−	0.636283i	−0.826784	−	0.562519i	$-0.809832\pi$
$499$	3.80849	−	14.2135i	0.170491	−	0.636283i	0.997276	−	0.0737636i	$-0.0235010\pi$
$500$	0.357278	+	1.33338i	0.0159780	+	0.0596306i
$501$	−4.79363	−	17.8901i	−0.214164	−	0.799269i
$502$	6.87545	−	25.6595i	0.306866	−	1.14524i
$503$			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
$507$	11.3904	−	6.26559i	0.505868	−	0.278265i
$508$	−6.55986	+	11.3620i	−0.291047	+	0.504108i
$509$	29.1575	+	7.81272i	1.29238	+	0.346293i	0.838565	−	0.544802i	$-0.183395\pi$
$509$	29.1575	+	7.81272i	1.29238	+	0.346293i	0.453817	+	0.891095i	$0.350062\pi$
$510$			0.594382i			0.0263197i
$511$	−22.0006	−	13.7881i	−0.973248	−	0.609952i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.54430	+	5.76341i	−0.0681825	+	0.254461i
$514$	8.04017	−	2.15436i	0.354637	−	0.0950246i
$515$	−7.50285	−	28.0010i	−0.330615	−	1.23387i
$516$	−7.08070	+	4.08804i	−0.311710	+	0.179966i
$517$	−29.8135			−1.31120
$518$	−22.1761	+	5.08874i	−0.974362	+	0.223586i
$519$			16.7708i			0.736156i
$520$	5.67170	−	9.59301i	0.248721	−	0.420681i
$521$	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	$0.611761\pi$
$522$	1.66280	−	0.445545i	0.0727786	−	0.0195010i
$523$	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
$525$	−3.53754	+	11.5160i	−0.154391	+	0.502601i
$526$	−11.6983	−	11.6983i	−0.510068	−	0.510068i
$527$	0.919466	+	0.246370i	0.0400526	+	0.0107321i
$528$	2.46223	−	0.659752i	0.107155	−	0.0287120i
$529$	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
$535$	−3.82897	−	14.2899i	−0.165541	−	0.617807i
$536$	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
$539$	17.5247	−	3.35818i	0.754844	−	0.144647i
$540$	2.18556	−	2.18556i	0.0940517	−	0.0940517i
$541$	42.9477	+	11.5078i	1.84647	+	0.494759i	0.999329	−	0.0366160i	$-0.0116578\pi$
$541$	42.9477	+	11.5078i	1.84647	+	0.494759i	0.847137	+	0.531375i	$0.178325\pi$
$542$	−0.194717	−	0.112420i	−0.00836381	−	0.00482885i
$543$	−8.05245	−	4.64909i	−0.345564	−	0.199511i
$544$	−0.0497718	+	0.185751i	−0.00213395	+	0.00796400i
$545$	−32.0762			−1.37399
$546$	−8.47450	+	4.37981i	−0.362675	+	0.187439i
$547$	−14.0813			−0.602073			−0.301037	−	0.953613i	$-0.597333\pi$
$547$	−14.0813			−0.602073			−0.301037	+	0.953613i	$0.597333\pi$
$548$	3.82257	−	14.2660i	0.163292	−	0.609414i
$549$	−9.60184	−	5.54362i	−0.409797	−	0.236596i
$550$	−10.0519	−	5.80348i	−0.428616	−	0.247461i
$551$	9.92144	+	2.65844i	0.422668	+	0.113253i
$552$	4.31367	−	4.31367i	0.183602	−	0.183602i
$553$	−5.47937	+	17.8374i	−0.233006	+	0.758524i
$554$	−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
$557$	−6.76465	−	25.2460i	−0.286627	−	1.06971i	−0.947642	−	0.319335i	$-0.896541\pi$
$557$	−6.76465	−	25.2460i	−0.286627	−	1.06971i	0.661015	−	0.750373i	$-0.270126\pi$
$558$	−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	−0.665761	−	0.746165i	$-0.731893\pi$
$563$	7.43428	−	12.8766i	0.313318	−	0.542682i	0.979078	+	0.203483i	$0.0652262\pi$
$564$	−11.2973	+	3.02709i	−0.475700	+	0.127463i
$565$	−9.91803	−	2.65753i	−0.417255	−	0.111803i
$566$	−13.6004	−	13.6004i	−0.571669	−	0.571669i
$567$	−2.57873	+	0.591740i	−0.108296	+	0.0248507i
$568$	−5.01994			−0.210632
$569$	−7.47184	+	4.31387i	−0.313236	+	0.180847i	−0.648373	−	0.761322i	$-0.724550\pi$
$569$	−7.47184	+	4.31387i	−0.313236	+	0.180847i	0.335138	+	0.942169i	$0.391217\pi$
$570$	17.8139	−	4.77321i	0.746141	−	0.199928i
$571$	38.3123	+	22.1196i	1.60332	+	0.925677i	0.990817	+	0.135208i	$0.0431702\pi$
$571$	38.3123	+	22.1196i	1.60332	+	0.925677i	0.612502	+	0.790469i	$0.290163\pi$
$572$	−2.28677	−	8.90183i	−0.0956145	−	0.372204i
$573$		−	5.20561i		−	0.217467i
$574$	6.68528	−	21.7631i	0.279038	−	0.908376i
$575$	−27.7777			−1.15841
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	7.25101	+	27.0612i	0.301864	+	1.12657i	0.935612	+	0.353031i	$0.114849\pi$
$577$	7.25101	+	27.0612i	0.301864	+	1.12657i	−0.633748	+	0.773540i	$0.718484\pi$
$578$	16.3850	−	4.39035i	0.681527	−	0.182615i
$579$	−2.85208	+	10.6441i	−0.118529	+	0.442355i
$580$	−3.76235	−	3.76235i	−0.156223	−	0.156223i
$581$	0.468633	+	0.0169883i	0.0194422	+	0.000704793i
$582$			10.2751i			0.425916i
$583$	−11.5178	−	3.08617i	−0.477017	−	0.127816i
$584$	4.90677	−	8.49877i	0.203043	−	0.351681i
$585$	−7.79819	−	7.96130i	−0.322416	−	0.329159i
$586$	−15.0387	+	8.68257i	−0.621241	+	0.358674i
$587$	17.4506	−	17.4506i	0.720265	−	0.720265i	−0.248394	−	0.968659i	$-0.579903\pi$
$587$	17.4506	−	17.4506i	0.720265	−	0.720265i	0.968659	+	0.248394i	$0.0799028\pi$
$588$	6.29969	−	3.05187i	0.259795	−	0.125857i
$589$		−	29.5352i		−	1.21698i
$590$	6.91443	−	25.8050i	0.284663	−	1.06238i
$591$	−1.10061	−	4.10755i	−0.0452732	−	0.168962i
$592$	−2.22575	−	8.30660i	−0.0914776	−	0.341399i
$593$	−0.960420	+	3.58434i	−0.0394397	+	0.147191i	−0.982838	−	0.184471i	$-0.940943\pi$
$593$	−0.960420	+	3.58434i	−0.0394397	+	0.147191i	0.943398	+	0.331662i	$0.107609\pi$
$594$		−	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
$598$	−15.3914	−	15.7133i	−0.629400	−	0.642564i
$599$	−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	$0.225669\pi$
$600$	−4.39823	−	1.17850i	−0.179557	−	0.0481122i
$601$			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
$604$	3.05577	−	11.4043i	0.124337	−	0.464034i
$605$	13.4414	−	3.60161i	0.546470	−	0.146426i
$606$	−3.69864	−	13.8035i	−0.150247	−	0.560729i
$607$	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
$609$	1.01865	+	4.43916i	0.0412779	+	0.179884i
$610$			34.2691i			1.38751i
$611$	10.4922	+	40.8436i	0.424469	+	1.65236i
$612$	0.166540	+	0.0961517i	0.00673197	+	0.00388670i
$613$	43.4816	−	11.6508i	1.75620	−	0.470573i	0.770271	−	0.637717i	$-0.220121\pi$
$613$	43.4816	−	11.6508i	1.75620	−	0.470573i	0.985933	+	0.167143i	$0.0534543\pi$
$614$	11.4613	−	6.61716i	0.462539	−	0.267047i
$615$	26.5969			1.07249
$616$	1.50840	+	6.57340i	0.0607750	+	0.264850i
$617$	−9.55565	−	9.55565i	−0.384696	−	0.384696i	0.488095	−	0.872791i	$-0.337692\pi$
$617$	−9.55565	−	9.55565i	−0.384696	−	0.384696i	−0.872791	+	0.488095i	$0.837692\pi$
$618$	−9.05931	−	2.42743i	−0.364419	−	0.0976457i
$619$	−42.9344	+	11.5042i	−1.72568	+	0.462395i	−0.979181	−	0.202991i	$-0.934934\pi$
$619$	−42.9344	+	11.5042i	−1.72568	+	0.462395i	−0.746500	+	0.665385i	$0.768267\pi$
$620$	−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
$626$	−7.07583	−	26.4074i	−0.282807	−	1.05545i
$627$	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
$630$	5.56918	+	5.98815i	0.221882	+	0.238573i
$631$	−30.3285	+	30.3285i	−1.20736	+	1.20736i	−0.235482	+	0.971879i	$0.575667\pi$
$631$	−30.3285	+	30.3285i	−1.20736	+	1.20736i	−0.971879	+	0.235482i	$0.924333\pi$
$632$	−6.81251	−	1.82541i	−0.270987	−	0.0726108i
$633$	5.67810	+	3.27825i	0.225684	+	0.130299i
$634$	21.2903	+	12.2920i	0.845548	+	0.488177i
$635$	10.4954	−	39.1694i	0.416498	−	1.55439i
$636$	−4.67778			−0.185486
$637$	−10.7680	−	22.8265i	−0.426645	−	0.904419i
$638$	−4.38813			−0.173728
$639$	−1.29926	+	4.84889i	−0.0513977	+	0.191819i
$640$	−2.67676	−	1.54543i	−0.105808	−	0.0610884i
$641$	−17.1177	−	9.88291i	−0.676109	−	0.390352i	0.122278	−	0.992496i	$-0.460980\pi$
$641$	−17.1177	−	9.88291i	−0.676109	−	0.390352i	−0.798387	+	0.602144i	$0.794313\pi$
$642$	−4.62329	−	1.23881i	−0.182467	−	0.0488918i
$643$	−21.8195	+	21.8195i	−0.860475	+	0.860475i	−0.991393	−	0.130918i	$-0.958208\pi$
$643$	−21.8195	+	21.8195i	−0.860475	+	0.860475i	0.130918	+	0.991393i	$0.458208\pi$
$644$	10.9920	+	11.8189i	0.433144	+	0.465728i
$645$	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	−0.989451	−	0.144870i	$-0.953724\pi$
$647$	−9.39268	+	16.2686i	−0.369265	+	0.639585i	0.620186	+	0.784455i	$0.287057\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	−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
$655$	−48.2480	+	12.9280i	−1.88520	+	0.505139i
$656$	8.31183	+	2.22715i	0.324522	+	0.0869555i
$657$	−6.93921	−	6.93921i	−0.270725	−	0.270725i
$658$	−6.92086	−	30.1602i	−0.269803	−	1.17577i
$659$	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
$661$	−3.04170	+	0.815022i	−0.118309	+	0.0317007i	−0.317488	−	0.948262i	$-0.602839\pi$
$661$	−3.04170	+	0.815022i	−0.118309	+	0.0317007i	0.199179	+	0.979963i	$0.436172\pi$
$662$	21.4126	+	12.3626i	0.832223	+	0.480484i
$663$	0.352876	−	0.596847i	0.0137046	−	0.0231796i
$664$			0.177243i			0.00687837i
$665$	10.9130	+	47.5576i	0.423189	+	1.84421i
$666$	−8.59962			−0.333229
$667$	−9.09469	+	5.25082i	−0.352148	+	0.203313i
$668$	4.79363	+	17.8901i	0.185471	+	0.692188i
$669$	18.4531	−	4.94450i	0.713439	−	0.191165i
$670$	−3.98247	+	14.8628i	−0.153856	+	0.574200i
$671$	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	$-0.882187\pi$
$673$		−	18.7681i		−	0.723455i	0.932284	−	0.361728i	$-0.117813\pi$
$674$	4.85255	+	1.30024i	0.186913	+	0.0500832i
$675$	−2.27669	+	3.94335i	−0.0876300	+	0.151780i
$676$	−11.3904	+	6.26559i	−0.438094	+	0.240984i
$677$	−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
$681$	1.75395	−	6.54583i	0.0672115	−	0.250837i
$682$	3.26577	+	12.1880i	0.125053	+	0.466703i
$683$	4.72612	+	17.6381i	0.180840	+	0.674903i	0.995483	+	0.0949408i	$0.0302662\pi$
$683$	4.72612	+	17.6381i	0.180840	+	0.674903i	−0.814643	+	0.579963i	$0.803067\pi$
$684$	1.54430	−	5.76341i	0.0590478	−	0.220369i
$685$			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
$689$	−0.174546	+	16.8651i	−0.00664969	+	0.642508i
$690$	−9.42780	+	16.3294i	−0.358910	+	0.621651i
$691$	9.50693	+	2.54737i	0.361661	+	0.0969067i	0.435073	−	0.900395i	$-0.356722\pi$
$691$	9.50693	+	2.54737i	0.361661	+	0.0969067i	−0.0734128	+	0.997302i	$0.523389\pi$
$692$		−	16.7708i		−	0.637530i
$693$	6.73982	+	0.244323i	0.256024	+	0.00928106i
$694$	−10.6939	−	10.6939i	−0.405935	−	0.405935i
$695$	−0.765918	+	2.85844i	−0.0290529	+	0.108427i
$696$	−1.66280	+	0.445545i	−0.0630282	+	0.0168883i
$697$	0.428288	+	1.59839i	0.0162226	+	0.0605435i
$698$	−9.91089	+	5.72205i	−0.375133	+	0.216583i
$699$	6.87760			0.260135
$700$	3.53754	−	11.5160i	0.133706	−	0.435265i
$701$			0.764820i			0.0288869i	0.999896	+	0.0144434i	$0.00459765\pi$
$701$			0.764820i			0.0288869i	−0.999896	+	0.0144434i	$0.995402\pi$
$702$	−3.49217	+	0.897093i	−0.131803	+	0.0338586i
$703$	−44.4371	−	25.6558i	−1.67598	−	0.967626i
$704$	−2.46223	+	0.659752i	−0.0927987	+	0.0248653i
$705$	31.3068	−	18.0750i	1.17908	−	0.680743i
$706$	−15.6365			−0.588488
$707$	36.8512	−	8.45622i	1.38593	−	0.318029i
$708$	−6.11176	−	6.11176i	−0.229694	−	0.229694i
$709$	13.3114	+	3.56678i	0.499920	+	0.133953i	0.499963	−	0.866047i	$-0.333347\pi$
$709$	13.3114	+	3.56678i	0.499920	+	0.133953i	−4.29989e−5		1.00000i	$0.500014\pi$
$710$	14.9872	−	4.01581i	0.562460	−	0.150711i
$711$	−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
$717$	−1.13608	−	4.23990i	−0.0424276	−	0.158342i
$718$	14.8819	−	25.7761i	0.555386	−	0.961957i
$719$	−11.8270	−	20.4850i	−0.441074	−	0.763962i	0.556696	−	0.830717i	$-0.312069\pi$
$719$	−11.8270	−	20.4850i	−0.441074	−	0.763962i	−0.997769	+	0.0667542i	$0.978736\pi$
$720$	−2.18556	+	2.18556i	−0.0814512	+	0.0814512i
$721$	7.28648	−	23.7203i	0.271363	−	0.883389i
$722$	11.7392	−	11.7392i	0.436888	−	0.436888i
$723$	−9.25180	−	2.47901i	−0.344078	−	0.0921955i
$724$	8.05245	+	4.64909i	0.299267	+	0.172782i
$725$	6.78829	+	3.91922i	0.252111	+	0.145556i
$726$	1.16525	−	4.34876i	0.0432464	−	0.161398i
$727$	−8.17936			−0.303356			−0.151678	−	0.988430i	$-0.548468\pi$
$727$	−8.17936			−0.303356			−0.151678	+	0.988430i	$0.548468\pi$
$728$	8.47450	−	4.37981i	0.314086	−	0.162327i
$729$	−1.00000			−0.0370370
$730$	−7.85055	+	29.2987i	−0.290562	+	1.08439i
$731$	1.36164	+	0.786145i	0.0503622	+	0.0290766i
$732$	9.60184	+	5.54362i	0.354894	+	0.204898i
$733$	−27.0780	−	7.25552i	−1.00015	−	0.267989i	−0.278640	−	0.960396i	$-0.589884\pi$
$733$	−27.0780	−	7.25552i	−1.00015	−	0.267989i	−0.721507	+	0.692407i	$0.756550\pi$
$734$	6.87035	−	6.87035i	0.253589	−	0.253589i
$735$	−16.3665	+	14.1511i	−0.603689	+	0.521970i
$736$	−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
$739$	11.0546	+	41.2564i	0.406651	+	1.51764i	0.800991	+	0.598677i	$0.204307\pi$
$739$	11.0546	+	41.2564i	0.406651	+	1.51764i	−0.394340	+	0.918965i	$0.629027\pi$
$740$	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	0.701756	−	0.712418i	$-0.252400\pi$
$743$	−0.290617	−	0.290617i	−0.0106617	−	0.0106617i	−0.712418	+	0.701756i	$0.752400\pi$
$744$	2.47500	+	4.28682i	0.0907378	+	0.157163i
$745$	−10.3253	+	17.8839i	−0.378288	+	0.655214i
$746$	15.4073	−	4.12837i	0.564101	−	0.151150i
$747$	0.171204	+	0.0458739i	0.00626401	+	0.00167844i
$748$	−0.346622	−	0.346622i	−0.0126738	−	0.0126738i
$749$	3.71855	−	12.1053i	0.135873	−	0.442319i
$750$	−1.38042			−0.0504057
$751$	−33.4252	+	19.2980i	−1.21970	+	0.704195i	−0.964854	−	0.262786i	$-0.915359\pi$
$751$	−33.4252	+	19.2980i	−1.21970	+	0.704195i	−0.254848	+	0.966981i	$0.582025\pi$
$752$	11.2973	−	3.02709i	0.411968	−	0.110387i
$753$	23.0057	+	13.2824i	0.838375	+	0.484036i
$754$	1.54430	+	6.01160i	0.0562402	+	0.218930i
$755$			36.4924i			1.32810i
$756$	2.57873	−	0.591740i	0.0937875	−	0.0215214i
$757$	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
$759$	4.02478	+	15.0207i	0.146090	+	0.545217i
$760$	−17.8139	+	4.77321i	−0.646177	+	0.173143i
$761$	3.97112	−	14.8204i	0.143953	−	0.537239i	−0.855847	−	0.517229i	$-0.826964\pi$
$761$	3.97112	−	14.8204i	0.143953	−	0.537239i	0.999800	−	0.0200101i	$-0.00636983\pi$
$762$	−9.27704	−	9.27704i	−0.336072	−	0.336072i
$763$	−23.2655	−	14.5809i	−0.842269	−	0.527865i
$764$			5.20561i			0.188332i
$765$	−0.574129	−	0.153837i	−0.0207577	−	0.00556200i
$766$	−16.5989	+	28.7502i	−0.599744	+	1.03879i
$767$	−22.2631	+	21.8070i	−0.803876	+	0.787407i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	7.59086	−	7.59086i	0.273734	−	0.273734i	−0.556868	−	0.830601i	$-0.687997\pi$
$769$	7.59086	−	7.59086i	0.273734	−	0.273734i	0.830601	+	0.556868i	$0.187997\pi$
$770$	−9.76191	−	18.4185i	−0.351795	−	0.663755i
$771$			8.32379i			0.299774i
$772$	2.85208	−	10.6441i	0.102649	−	0.383090i
$773$	4.44264	+	16.5801i	0.159790	+	0.596346i	0.998647	+	0.0519942i	$0.0165577\pi$
$773$	4.44264	+	16.5801i	0.159790	+	0.596346i	−0.838857	+	0.544352i	$0.816776\pi$
$774$	−2.11613	−	7.89749i	−0.0760626	−	0.283869i
$775$	5.83359	−	21.7712i	0.209549	−	0.782046i
$776$		−	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
$780$	7.79819	+	7.96130i	0.279220	+	0.285060i
$781$	6.39812	−	11.0819i	0.228943	−	0.396541i
$782$	−1.13316	−	0.303630i	−0.0405219	−	0.0108578i
$783$			1.72145i			0.0615197i
$784$	−6.29969	+	3.05187i	−0.224989	+	0.108995i
$785$	−27.3665	−	27.3665i	−0.976751	−	0.976751i
$786$	−4.18266	+	15.6099i	−0.149191	+	0.556787i
$787$	52.5495	−	14.0806i	1.87319	−	0.501919i	0.873295	−	0.487191i	$-0.161978\pi$
$787$	52.5495	−	14.0806i	1.87319	−	0.501919i	0.999892	−	0.0147279i	$-0.00468821\pi$
$788$	1.10061	+	4.10755i	0.0392078	+	0.146325i
$789$	14.3274	−	8.27191i	0.510068	−	0.294488i
$790$	21.7993			0.775584
$791$	−5.98571	−	6.43601i	−0.212828	−	0.228838i
$792$			2.54908i			0.0905778i
$793$	20.3450	−	34.4112i	0.722473	−	1.22198i
$794$	17.8728	+	10.3189i	0.634281	+	0.366203i
$795$	13.9657	−	3.74210i	0.495312	−	0.132718i
$796$	14.4319	−	8.33229i	0.511527	−	0.295330i
$797$	19.3651			0.685946			0.342973	−	0.939345i	$-0.388566\pi$
$797$	19.3651			0.685946			0.342973	+	0.939345i	$0.388566\pi$
$798$	15.0905	+	4.63556i	0.534199	+	0.164097i
$799$	1.59038	+	1.59038i	0.0562636	+	0.0562636i
$800$	4.39823	+	1.17850i	0.155501	+	0.0416664i
$801$	−13.8225	+	3.70373i	−0.488394	+	0.130865i
$802$	−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
$808$	3.69864	+	13.8035i	0.130118	+	0.485606i
$809$	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	0.465092	−	0.885262i	$-0.346021\pi$
$811$	38.4555	−	38.4555i	1.35035	−	1.35035i	0.885262	−	0.465092i	$-0.153979\pi$
$812$	−1.01865	−	4.43916i	−0.0357477	−	0.155784i
$813$	0.158986	−	0.158986i	0.00557587	−	0.00557587i
$814$	21.1742	+	5.67362i	0.742156	+	0.198860i
$815$	52.4620	+	30.2890i	1.83766	+	1.06098i
$816$	−0.166540	−	0.0961517i	−0.00583005	−	0.00336598i
$817$	12.6263	−	47.1221i	0.441739	−	1.64859i
$818$	−9.03388			−0.315862
$819$	−2.03721	−	9.31932i	−0.0711859	−	0.325643i
$820$	−26.5969			−0.928805
$821$	12.7667	−	47.6458i	0.445560	−	1.66285i	−0.268895	−	0.963169i	$-0.586659\pi$
$821$	12.7667	−	47.6458i	0.445560	−	1.66285i	0.714455	−	0.699682i	$-0.246675\pi$
$822$	12.7906	+	7.38463i	0.446122	+	0.257569i
$823$	29.4007	+	16.9745i	1.02484	+	0.591694i	0.915504	−	0.402310i	$-0.131793\pi$
$823$	29.4007	+	16.9745i	1.02484	+	0.591694i	0.109341	+	0.994004i	$0.465126\pi$
$824$	9.05931	+	2.42743i	0.315596	+	0.0845637i
$825$	8.20737	−	8.20737i	0.285744	−	0.285744i
$826$	16.7454	−	15.5738i	0.582647	−	0.541882i
$827$	−13.9459	+	13.9459i	−0.484948	+	0.484948i	−0.906708	−	0.421760i	$-0.861412\pi$
$827$	−13.9459	+	13.9459i	−0.484948	+	0.484948i	0.421760	+	0.906708i	$0.361412\pi$
$828$	3.05023	+	5.28314i	0.106003	+	0.183602i
$829$	16.8805	−	29.2379i	0.586284	−	1.01547i	−0.408430	−	0.912790i	$-0.633924\pi$
$829$	16.8805	−	29.2379i	0.586284	−	1.01547i	0.994714	−	0.102684i	$-0.0327430\pi$
$830$	−0.141790	−	0.529166i	−0.00492159	−	0.0183676i
$831$	−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
$837$	4.78133	−	1.28115i	0.165267	−	0.0442831i
$838$	−33.9180	−	9.08829i	−1.17168	−	0.313950i
$839$	28.9271	+	28.9271i	0.998673	+	0.998673i	0.999999	−	0.00132603i	$-0.000422087\pi$
$839$	28.9271	+	28.9271i	0.998673	+	0.998673i	−0.00132603	+	0.999999i	$0.500422\pi$
$840$	−5.56918	−	5.98815i	−0.192155	−	0.206611i
$841$	−26.0366			−0.897814
$842$	6.93815	−	4.00575i	0.239105	−	0.138047i
$843$	6.70268	−	1.79598i	0.230853	−	0.0618568i
$844$	−5.67810	−	3.27825i	−0.195448	−	0.112842i
$845$	28.9943	−	27.8182i	0.997434	−	0.956975i
$846$		−	11.6958i		−	0.402109i
$847$	11.3865	+	3.49775i	0.391245	+	0.120184i
$848$	4.67778			0.160636
$849$	16.6571	−	9.61696i	0.571669	−	0.330053i
$850$	0.226630	+	0.845796i	0.00777335	+	0.0290105i
$851$	50.6740	−	13.5781i	1.73708	−	0.465450i
$852$	1.29926	−	4.84889i	0.0445118	−	0.166120i
$853$	−23.3837	−	23.3837i	−0.800643	−	0.800643i	0.182553	−	0.983196i	$-0.441564\pi$
$853$	−23.3837	−	23.3837i	−0.800643	−	0.800643i	−0.983196	+	0.182553i	$0.941564\pi$
$854$	−15.5777	+	24.8561i	−0.533059	+	0.850557i
$855$			18.4423i			0.630712i
$856$	4.62329	+	1.23881i	0.158021	+	0.0423416i
$857$	−10.4269	+	18.0599i	−0.356175	+	0.616913i	−0.987318	−	0.158753i	$-0.949253\pi$
$857$	−10.4269	+	18.0599i	−0.356175	+	0.616913i	0.631143	+	0.775666i	$0.282586\pi$
$858$	9.19036	+	0.0951164i	0.313754	+	0.00324722i
$859$	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
$863$	−10.9121	+	40.7246i	−0.371453	+	1.38628i	0.487005	+	0.873399i	$0.338089\pi$
$863$	−10.9121	+	40.7246i	−0.371453	+	1.38628i	−0.858458	+	0.512884i	$0.828577\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	13.4162	+	50.0698i	0.456163	+	1.70242i
$866$	0.904010	−	3.37381i	0.0307195	−	0.114647i
$867$			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
$871$	12.8228	−	12.5601i	0.434484	−	0.425583i
$872$	5.18889	−	8.98742i	0.175718	−	0.304353i
$873$	−9.92497	−	2.65939i	−0.335909	−	0.0900066i
$874$			36.3997i			1.23124i
$875$	0.132309	−	3.64984i	0.00447287	−	0.123387i
$876$	6.93921	+	6.93921i	0.234454	+	0.234454i
$877$	−4.45463	+	16.6249i	−0.150422	+	0.561383i	0.849032	+	0.528342i	$0.177186\pi$
$877$	−4.45463	+	16.6249i	−0.150422	+	0.561383i	−0.999454	+	0.0330415i	$0.989481\pi$
$878$	−0.254415	+	0.0681703i	−0.00858610	+	0.00230064i
$879$	−4.49443	−	16.7734i	−0.151593	−	0.565754i
$880$	6.82329	−	3.93943i	0.230013	−	0.132798i
$881$	−54.6900			−1.84255			−0.921277	−	0.388907i	$-0.872853\pi$
$881$	−54.6900			−1.84255			−0.921277	+	0.388907i	$0.872853\pi$
$882$	1.31740	+	6.87491i	0.0443593	+	0.231490i
$883$			33.5777i			1.12998i	0.825098	+	0.564990i	$0.191120\pi$
$883$			33.5777i			1.12998i	−0.825098	+	0.564990i	$0.808880\pi$
$884$	−0.352876	+	0.596847i	−0.0118685	+	0.0200741i
$885$	23.1361	+	13.3577i	0.777713	+	0.449013i
$886$	8.19915	−	2.19696i	0.275456	−	0.0738082i
$887$	−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
$889$	25.4178	−	23.6394i	0.852486	−	0.792842i
$890$	31.2756	+	31.2756i	1.04836	+	1.04836i
$891$	2.46223	+	0.659752i	0.0824877	+	0.0221025i
$892$	−18.4531	+	4.94450i	−0.617856	+	0.165554i
$893$	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
$899$	−2.20545	−	8.23084i	−0.0735558	−	0.274514i
$900$	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
$903$	21.0839	−	4.83812i	0.701629	−	0.161002i
$904$	2.34903	−	2.34903i	0.0781275	−	0.0781275i
$905$	−27.7600	−	7.43828i	−0.922775	−	0.247257i
$906$	10.2248	+	5.90329i	0.339696	+	0.196124i
$907$	−52.1007	−	30.0804i	−1.72998	−	0.998802i	−0.889458	−	0.457016i	$-0.848918\pi$
$907$	−52.1007	−	30.0804i	−1.72998	−	0.998802i	−0.840517	−	0.541785i	$-0.817749\pi$
$908$	−1.75395	+	6.54583i	−0.0582069	+	0.217231i
$909$	14.2904			0.473984
$910$	−21.7972	+	19.8555i	−0.722571	+	0.658202i
$911$	−22.9257			−0.759561			−0.379780	−	0.925077i	$-0.624000\pi$
$911$	−22.9257			−0.759561			−0.379780	+	0.925077i	$0.624000\pi$
$912$	−1.54430	+	5.76341i	−0.0511369	+	0.190846i
$913$	−0.391277	−	0.225904i	−0.0129494	−	0.00747632i
$914$	4.18670	+	2.41719i	0.138484	+	0.0799536i
$915$	−33.1014	−	8.86949i	−1.09430	−	0.293216i
$916$	10.0393	−	10.0393i	0.331706	−	0.331706i
$917$	−40.8719	−	12.5552i	−1.34971	−	0.414609i
$918$	−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
$921$	3.42530	+	12.7834i	0.112867	+	0.421227i
$922$	−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
$928$	1.66280	−	0.445545i	0.0545840	−	0.0146257i
$929$	12.5427	+	3.36080i	0.411512	+	0.110264i	0.458635	−	0.888625i	$-0.348339\pi$
$929$	12.5427	+	3.36080i	0.411512	+	0.110264i	−0.0471227	+	0.998889i	$0.515005\pi$
$930$	−10.8185	−	10.8185i	−0.354754	−	0.354754i
$931$	−13.7029	+	39.4552i	−0.449094	+	1.29309i
$932$	−6.87760			−0.225283
$933$	−2.89828	+	1.67332i	−0.0948855	+	0.0547822i
$934$	−5.88096	+	1.57580i	−0.192431	+	0.0515617i
$935$	1.31214	+	0.757565i	0.0429116	+	0.0247750i
$936$	3.49217	−	0.897093i	0.114145	−	0.0293224i
$937$		−	35.8464i		−	1.17105i	−0.810654	−	0.585526i	$-0.800888\pi$
$937$		−	35.8464i		−	1.17105i	0.810654	−	0.585526i	$-0.199112\pi$
$938$	−9.64477	+	8.96997i	−0.314913	+	0.292880i
$939$	27.3389			0.892171
$940$	−31.3068	+	18.0750i	−1.02111	+	0.589541i
$941$	−11.0520	−	41.2468i	−0.360286	−	1.34461i	−0.873700	−	0.486466i	$-0.838286\pi$
$941$	−11.0520	−	41.2468i	−0.360286	−	1.34461i	0.513413	−	0.858142i	$-0.328381\pi$
$942$	−12.0948	+	3.24079i	−0.394070	+	0.105591i
$943$	−13.5866	+	50.7059i	−0.442441	+	1.65121i
$944$	6.11176	+	6.11176i	0.198921	+	0.198921i
$945$	−7.22552	+	3.82957i	−0.235046	+	0.124576i
$946$			20.8415i			0.677617i
$947$	−14.3264	−	3.83874i	−0.465544	−	0.124742i	0.0184193	−	0.999830i	$-0.494137\pi$
$947$	−14.3264	−	3.83874i	−0.465544	−	0.124742i	−0.483964	+	0.875088i	$0.660803\pi$
$948$	3.52642	−	6.10793i	0.114533	−	0.198376i
$949$	25.2773	−	24.7594i	0.820535	−	0.803725i
$950$	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	$-0.968785\pi$
$953$		−	6.04490i		−	0.195814i	0.995196	−	0.0979068i	$-0.0312147\pi$
$954$	1.21070	−	4.51839i	0.0391978	−	0.146288i
$955$	−4.16434	−	15.5415i	−0.134755	−	0.502912i
$956$	1.13608	+	4.23990i	0.0367434	+	0.137128i
$957$	1.13573	−	4.23861i	0.0367130	−	0.137015i
$958$			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
$962$	0.320886	−	31.0047i	0.0103458	−	0.999632i
$963$	2.39319	−	4.14513i	0.0771195	−	0.133575i
$964$	9.25180	+	2.47901i	0.297980	+	0.0798436i
$965$			34.0600i			1.09643i
$966$	−14.2611	+	7.55846i	−0.458842	+	0.243190i
$967$	−3.98042	−	3.98042i	−0.128002	−	0.128002i	0.640204	−	0.768205i	$-0.278850\pi$
$967$	−3.98042	−	3.98042i	−0.128002	−	0.128002i	−0.768205	+	0.640204i	$0.778850\pi$
$968$	−1.16525	+	4.34876i	−0.0374524	+	0.139774i
$969$	−1.10832	+	0.296974i	−0.0356045	+	0.00954019i
$970$	8.21978	+	30.6766i	0.263921	+	0.984968i
$971$	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
$973$	−1.85490	+	1.72512i	−0.0594654	+	0.0553049i
$974$			17.7014i			0.567190i
$975$	−14.1322	−	8.35544i	−0.452594	−	0.267588i
$976$	−9.60184	−	5.54362i	−0.307347	−	0.177447i
$977$	0.595513	−	0.159567i	0.0190521	−	0.00510500i	−0.249280	−	0.968431i	$-0.580194\pi$
$977$	0.595513	−	0.159567i	0.0190521	−	0.00510500i	0.268333	+	0.963326i	$0.413527\pi$
$978$	16.9733	−	9.79954i	0.542746	−	0.313355i
$979$	36.4777			1.16583
$980$	16.3665	−	14.1511i	0.522810	−	0.452039i
$981$	−7.33820	−	7.33820i	−0.234291	−	0.234291i
$982$	−3.91494	−	1.04900i	−0.124931	−	0.0334751i
$983$	21.2803	−	5.70203i	0.678736	−	0.181867i	0.0970489	−	0.995280i	$-0.469060\pi$
$983$	21.2803	−	5.70203i	0.678736	−	0.181867i	0.581687	+	0.813413i	$0.302393\pi$
$984$	−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
$990$	−2.03920	−	7.61039i	−0.0648099	−	0.241874i
$991$	−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
$994$	12.6960	+	3.90000i	0.402693	+	0.123701i
$995$	−36.4215	+	36.4215i	−1.15464	+	1.15464i
$996$	−0.171204	−	0.0458739i	−0.00542480	−	0.00145357i
$997$	−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
$999$	2.22575	−	8.30660i	0.0704195	−	0.262809i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.31.4	✓	40	13.5	odd	4
546.2.bz.a.229.4	yes	40	7.5	odd	6
546.2.bz.b.73.9	yes	40	1.1	even	1	trivial
546.2.bz.b.187.9	yes	40	91.5	even	12	inner

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.98554 + 0.799972i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.80183 + 1.93737i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.98554 + 0.799972i) q^{5} +(0.707107 - 0.707107i) q^{6} +(1.80183 + 1.93737i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.54543 - 2.67676i) q^{10} +(-0.659752 - 2.46223i) 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} +(0.965926 - 0.258819i) q^{18} +(5.76341 + 1.54430i) q^{19} +(-2.18556 - 2.18556i) q^{20} +(0.591740 + 2.57873i) q^{21} -2.54908 q^{22} +(-5.28314 + 3.05023i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(3.94335 + 2.27669i) q^{25} +(0.897093 + 3.49217i) q^{26} +1.00000i q^{27} +(-0.591740 - 2.57873i) q^{28} +1.72145 q^{29} +(2.67676 - 1.54543i) q^{30} +(-1.28115 - 4.78133i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.659752 - 2.46223i) q^{33} +(0.135979 + 0.135979i) q^{34} +(3.82957 + 7.22552i) q^{35} -1.00000i q^{36} +(-8.30660 - 2.22575i) q^{37} +(2.98336 - 5.16733i) q^{38} +(-3.60536 - 0.0373139i) q^{39} +(-2.67676 + 1.54543i) q^{40} +(6.08468 - 6.08468i) q^{41} +(2.64401 + 0.0958474i) q^{42} -8.17609i q^{43} +(-0.659752 + 2.46223i) q^{44} +(0.799972 + 2.98554i) q^{45} +(1.57891 + 5.89258i) q^{46} +(3.02709 - 11.2973i) q^{47} +1.00000i q^{48} +(-0.506844 + 6.98163i) q^{49} +(3.21973 - 3.21973i) q^{50} +(-0.166540 + 0.0961517i) q^{51} +(3.60536 + 0.0373139i) q^{52} +(2.33889 - 4.05108i) q^{53} +(0.965926 + 0.258819i) q^{54} -7.87885i q^{55} +(-2.64401 - 0.0958474i) q^{56} +(4.21911 + 4.21911i) q^{57} +(0.445545 - 1.66280i) q^{58} +(8.34882 - 2.23706i) q^{59} +(-0.799972 - 2.98554i) q^{60} +(-9.60184 + 5.54362i) q^{61} -4.95000 q^{62} +(-0.776903 + 2.52911i) q^{63} -1.00000i q^{64} +(-10.7938 + 2.77278i) q^{65} +(-2.20757 - 1.27454i) q^{66} +(-4.80864 + 1.28847i) q^{67} +(0.166540 - 0.0961517i) q^{68} -6.10045 q^{69} +(7.97048 - 1.82898i) q^{70} +(3.54963 + 3.54963i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(-9.47914 + 2.53993i) 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} +(0.799972 + 2.98554i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.30252 - 7.45218i) q^{82} +(0.125330 - 0.125330i) q^{83} +(0.776903 - 2.52911i) q^{84} +(-0.420292 + 0.420292i) q^{85} +(-7.89749 - 2.11613i) q^{86} +(1.49082 + 0.860727i) q^{87} +(2.20757 + 1.27454i) q^{88} +(-3.70373 + 13.8225i) q^{89} +3.09086 q^{90} +(-9.08938 - 2.89538i) q^{91} +6.10045 q^{92} +(1.28115 - 4.78133i) q^{93} +(-10.1288 - 5.84789i) q^{94} +(15.9715 + 9.22113i) q^{95} +(0.965926 + 0.258819i) q^{96} +(-7.26558 + 7.26558i) q^{97} +(6.61255 + 2.29655i) 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	\( 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * 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 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * 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 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * 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 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

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