LMFDB - Embedded newform 731.2.m.c.87.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.16
Character	$\chi$	$=$	731.87
Dual form			731.2.m.c.689.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0668491 - 0.0668491i) q^{2} +(-2.64125 + 1.09404i) q^{3} -1.99106i q^{4} +(-0.846330 - 2.04322i) q^{5} +(0.249701 + 0.103430i) q^{6} +(1.54141 - 3.72129i) q^{7} +(-0.266799 + 0.266799i) q^{8} +(3.65797 - 3.65797i) q^{9} +O(q^{10})$	\(q+(-0.0668491 - 0.0668491i) q^{2} +(-2.64125 + 1.09404i) q^{3} -1.99106i q^{4} +(-0.846330 - 2.04322i) q^{5} +(0.249701 + 0.103430i) q^{6} +(1.54141 - 3.72129i) q^{7} +(-0.266799 + 0.266799i) q^{8} +(3.65797 - 3.65797i) q^{9} +(-0.0800112 + 0.193164i) q^{10} +(2.21000 + 0.915411i) q^{11} +(2.17831 + 5.25890i) q^{12} -0.0553248i q^{13} +(-0.351807 + 0.145723i) q^{14} +(4.47075 + 4.47075i) q^{15} -3.94645 q^{16} +(3.88070 - 1.39291i) q^{17} -0.489065 q^{18} +(-4.14613 - 4.14613i) q^{19} +(-4.06818 + 1.68510i) q^{20} +11.5152i q^{21} +(-0.0865420 - 0.208931i) q^{22} +(-2.47475 - 1.02507i) q^{23} +(0.412794 - 0.996574i) q^{24} +(0.0770518 - 0.0770518i) q^{25} +(-0.00369841 + 0.00369841i) q^{26} +(-2.37752 + 5.73985i) q^{27} +(-7.40932 - 3.06904i) q^{28} +(1.65775 + 4.00216i) q^{29} -0.597731i q^{30} +(4.40220 - 1.82345i) q^{31} +(0.797415 + 0.797415i) q^{32} -6.83867 q^{33} +(-0.352536 - 0.166307i) q^{34} -8.90796 q^{35} +(-7.28325 - 7.28325i) q^{36} +(-7.74976 + 3.21006i) q^{37} +0.554330i q^{38} +(0.0605277 + 0.146127i) q^{39} +(0.770930 + 0.319330i) q^{40} +(0.0490939 - 0.118523i) q^{41} +(0.769784 - 0.769784i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(1.82264 - 4.40024i) q^{44} +(-10.5699 - 4.37820i) q^{45} +(0.0969094 + 0.233960i) q^{46} -5.01451i q^{47} +(10.4236 - 4.31759i) q^{48} +(-6.52231 - 6.52231i) q^{49} -0.0103017 q^{50} +(-8.72601 + 7.92467i) q^{51} -0.110155 q^{52} +(-3.29222 - 3.29222i) q^{53} +(0.542640 - 0.224769i) q^{54} -5.29026i q^{55} +(0.581590 + 1.40408i) q^{56} +(15.4870 + 6.41493i) q^{57} +(0.156722 - 0.378360i) q^{58} +(6.50024 - 6.50024i) q^{59} +(8.90154 - 8.90154i) q^{60} +(-2.12524 + 5.13079i) q^{61} +(-0.416179 - 0.172387i) q^{62} +(-7.97394 - 19.2508i) q^{63} +7.78630i q^{64} +(-0.113041 + 0.0468230i) q^{65} +(0.457159 + 0.457159i) q^{66} -14.7416 q^{67} +(-2.77336 - 7.72671i) q^{68} +7.65791 q^{69} +(0.595490 + 0.595490i) q^{70} +(-5.20984 + 2.15798i) q^{71} +1.95189i q^{72} +(1.57086 + 3.79238i) q^{73} +(0.732655 + 0.303476i) q^{74} +(-0.119215 + 0.287812i) q^{75} +(-8.25520 + 8.25520i) q^{76} +(6.81302 - 6.81302i) q^{77} +(0.00572223 - 0.0138147i) q^{78} +(8.63650 + 3.57735i) q^{79} +(3.34000 + 8.06348i) q^{80} -2.24206i q^{81} +(-0.0112051 + 0.00464129i) q^{82} +(-6.93634 - 6.93634i) q^{83} +22.9276 q^{84} +(-6.13037 - 6.75027i) q^{85} +0.0945390 q^{86} +(-8.75707 - 8.75707i) q^{87} +(-0.833856 + 0.345395i) q^{88} +16.0929i q^{89} +(0.413910 + 0.999268i) q^{90} +(-0.205879 - 0.0852781i) q^{91} +(-2.04099 + 4.92737i) q^{92} +(-9.63240 + 9.63240i) q^{93} +(-0.335216 + 0.335216i) q^{94} +(-4.96247 + 11.9805i) q^{95} +(-2.97858 - 1.23377i) q^{96} +(1.07576 + 2.59711i) q^{97} +0.872021i q^{98} +(11.4327 - 4.73556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−0.0668491	−	0.0668491i	−0.0472695	−	0.0472695i	0.683077	−	0.730346i	$-0.260641\pi$
$2$	−0.0668491	−	0.0668491i	−0.0472695	−	0.0472695i	−0.730346	+	0.683077i	$0.760641\pi$
$3$	−2.64125	+	1.09404i	−1.52493	+	0.631646i	−0.978572	−	0.205906i	$-0.933986\pi$
$3$	−2.64125	+	1.09404i	−1.52493	+	0.631646i	−0.546357	+	0.837552i	$0.683986\pi$
$4$		−	1.99106i		−	0.995531i
$5$	−0.846330	−	2.04322i	−0.378490	−	0.913757i	−0.992249	−	0.124263i	$-0.960343\pi$
$5$	−0.846330	−	2.04322i	−0.378490	−	0.913757i	0.613759	−	0.789494i	$-0.289657\pi$
$6$	0.249701	+	0.103430i	0.101940	+	0.0422250i
$7$	1.54141	−	3.72129i	0.582598	−	1.40652i	−0.307852	−	0.951434i	$-0.599610\pi$
$7$	1.54141	−	3.72129i	0.582598	−	1.40652i	0.890450	−	0.455081i	$-0.150390\pi$
$8$	−0.266799	+	0.266799i	−0.0943277	+	0.0943277i
$9$	3.65797	−	3.65797i	1.21932	−	1.21932i
$10$	−0.0800112	+	0.193164i	−0.0253018	+	0.0610839i
$11$	2.21000	+	0.915411i	0.666339	+	0.276007i	0.690103	−	0.723711i	$-0.257565\pi$
$11$	2.21000	+	0.915411i	0.666339	+	0.276007i	−0.0237640	+	0.999718i	$0.507565\pi$
$12$	2.17831	+	5.25890i	0.628823	+	1.51811i
$13$		−	0.0553248i		−	0.0153443i	−0.999971	−	0.00767217i	$-0.997558\pi$
$13$		−	0.0553248i		−	0.0153443i	0.999971	−	0.00767217i	$-0.00244215\pi$
$14$	−0.351807	+	0.145723i	−0.0940243	+	0.0389461i
$15$	4.47075	+	4.47075i	1.15434	+	1.15434i
$16$	−3.94645			−0.986614
$17$	3.88070	−	1.39291i	0.941207	−	0.337830i
$17$	3.88070	−	1.39291i	0.941207	−	0.337830i
$18$	−0.489065			−0.115274
$19$	−4.14613	−	4.14613i	−0.951187	−	0.951187i	0.0476761	−	0.998863i	$-0.484818\pi$
$19$	−4.14613	−	4.14613i	−0.951187	−	0.951187i	−0.998863	+	0.0476761i	$0.984818\pi$
$20$	−4.06818	+	1.68510i	−0.909673	+	0.376799i
$21$			11.5152i			2.51283i
$22$	−0.0865420	−	0.208931i	−0.0184508	−	0.0445442i
$23$	−2.47475	−	1.02507i	−0.516020	−	0.213743i	0.109448	−	0.993993i	$-0.465092\pi$
$23$	−2.47475	−	1.02507i	−0.516020	−	0.213743i	−0.625468	+	0.780250i	$0.715092\pi$
$24$	0.412794	−	0.996574i	0.0842613	−	0.203425i
$25$	0.0770518	−	0.0770518i	0.0154104	−	0.0154104i
$26$	−0.00369841	+	0.00369841i	−0.000725319	+	0.000725319i
$27$	−2.37752	+	5.73985i	−0.457555	+	1.10463i
$28$	−7.40932	−	3.06904i	−1.40023	−	0.579994i
$29$	1.65775	+	4.00216i	0.307836	+	0.743182i	0.999775	+	0.0212257i	$0.00675684\pi$
$29$	1.65775	+	4.00216i	0.307836	+	0.743182i	−0.691939	+	0.721956i	$0.743243\pi$
$30$		−	0.597731i		−	0.109130i
$31$	4.40220	−	1.82345i	0.790659	−	0.327501i	0.0494502	−	0.998777i	$-0.484253\pi$
$31$	4.40220	−	1.82345i	0.790659	−	0.327501i	0.741208	+	0.671275i	$0.234253\pi$
$32$	0.797415	+	0.797415i	0.140964	+	0.140964i
$33$	−6.83867			−1.19046
$34$	−0.352536	−	0.166307i	−0.0604594	−	0.0285214i
$35$	−8.90796			−1.50572
$36$	−7.28325	−	7.28325i	−1.21388	−	1.21388i
$37$	−7.74976	+	3.21006i	−1.27405	+	0.527730i	−0.914194	−	0.405276i	$-0.867175\pi$
$37$	−7.74976	+	3.21006i	−1.27405	+	0.527730i	−0.359859	+	0.933007i	$0.617175\pi$
$38$			0.554330i			0.0899242i
$39$	0.0605277	+	0.146127i	0.00969219	+	0.0233990i
$40$	0.770930	+	0.319330i	0.121895	+	0.0504905i
$41$	0.0490939	−	0.118523i	0.00766719	−	0.0185102i	−0.920000	−	0.391919i	$-0.871811\pi$
$41$	0.0490939	−	0.118523i	0.00766719	−	0.0185102i	0.927667	+	0.373409i	$0.121811\pi$
$42$	0.769784	−	0.769784i	0.118780	−	0.118780i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$44$	1.82264	−	4.40024i	0.274773	−	0.663362i
$45$	−10.5699	−	4.37820i	−1.57567	−	0.652663i
$46$	0.0969094	+	0.233960i	0.0142885	+	0.0344955i
$47$		−	5.01451i		−	0.731441i	−0.930725	−	0.365721i	$-0.880823\pi$
$47$		−	5.01451i		−	0.731441i	0.930725	−	0.365721i	$-0.119177\pi$
$48$	10.4236	−	4.31759i	1.50452	−	0.623191i
$49$	−6.52231	−	6.52231i	−0.931758	−	0.931758i
$50$	−0.0103017			−0.00145688
$51$	−8.72601	+	7.92467i	−1.22189	+	1.10968i
$52$	−0.110155			−0.0152758
$53$	−3.29222	−	3.29222i	−0.452221	−	0.452221i	0.443870	−	0.896091i	$-0.353605\pi$
$53$	−3.29222	−	3.29222i	−0.452221	−	0.452221i	−0.896091	+	0.443870i	$0.853605\pi$
$54$	0.542640	−	0.224769i	0.0738439	−	0.0305871i
$55$		−	5.29026i		−	0.713338i
$56$	0.581590	+	1.40408i	0.0777183	+	0.187628i
$57$	15.4870	+	6.41493i	2.05131	+	0.849679i
$58$	0.156722	−	0.378360i	0.0205786	−	0.0496811i
$59$	6.50024	−	6.50024i	0.846260	−	0.846260i	−0.143404	−	0.989664i	$-0.545805\pi$
$59$	6.50024	−	6.50024i	0.846260	−	0.846260i	0.989664	+	0.143404i	$0.0458050\pi$
$60$	8.90154	−	8.90154i	1.14918	−	1.14918i
$61$	−2.12524	+	5.13079i	−0.272109	+	0.656930i	−0.999573	−	0.0292159i	$-0.990699\pi$
$61$	−2.12524	+	5.13079i	−0.272109	+	0.656930i	0.727464	+	0.686146i	$0.240699\pi$
$62$	−0.416179	−	0.172387i	−0.0528548	−	0.0218932i
$63$	−7.97394	−	19.2508i	−1.00462	−	2.42537i
$64$			7.78630i			0.973287i
$65$	−0.113041	+	0.0468230i	−0.0140210	+	0.00580768i
$66$	0.457159	+	0.457159i	0.0562724	+	0.0562724i
$67$	−14.7416			−1.80098			−0.900489	−	0.434878i	$-0.856791\pi$
$67$	−14.7416			−1.80098			−0.900489	+	0.434878i	$0.856791\pi$
$68$	−2.77336	−	7.72671i	−0.336320	−	0.937001i
$69$	7.65791			0.921904
$70$	0.595490	+	0.595490i	0.0711746	+	0.0711746i
$71$	−5.20984	+	2.15798i	−0.618294	+	0.256106i	−0.669770	−	0.742569i	$-0.733607\pi$
$71$	−5.20984	+	2.15798i	−0.618294	+	0.256106i	0.0514763	+	0.998674i	$0.483607\pi$
$72$			1.95189i			0.230032i
$73$	1.57086	+	3.79238i	0.183855	+	0.443865i	0.988755	−	0.149546i	$-0.0477811\pi$
$73$	1.57086	+	3.79238i	0.183855	+	0.443865i	−0.804900	+	0.593410i	$0.797781\pi$
$74$	0.732655	+	0.303476i	0.0851694	+	0.0352783i
$75$	−0.119215	+	0.287812i	−0.0137658	+	0.0332336i
$76$	−8.25520	+	8.25520i	−0.946936	+	0.946936i
$77$	6.81302	−	6.81302i	0.776416	−	0.776416i
$78$	0.00572223	−	0.0138147i	0.000647914	−	0.00156420i
$79$	8.63650	+	3.57735i	0.971682	+	0.402484i	0.811338	−	0.584577i	$-0.198740\pi$
$79$	8.63650	+	3.57735i	0.971682	+	0.402484i	0.160344	+	0.987061i	$0.448740\pi$
$80$	3.34000	+	8.06348i	0.373424	+	0.901525i
$81$		−	2.24206i		−	0.249118i
$82$	−0.0112051	+	0.00464129i	−0.00123739	+	0.000512545i
$83$	−6.93634	−	6.93634i	−0.761363	−	0.761363i	0.215206	−	0.976569i	$-0.430958\pi$
$83$	−6.93634	−	6.93634i	−0.761363	−	0.761363i	−0.976569	+	0.215206i	$0.930958\pi$
$84$	22.9276			2.50160
$85$	−6.13037	−	6.75027i	−0.664932	−	0.732169i
$86$	0.0945390			0.0101944
$87$	−8.75707	−	8.75707i	−0.938856	−	0.938856i
$88$	−0.833856	+	0.345395i	−0.0888894	+	0.0368192i
$89$			16.0929i			1.70585i	0.522037	+	0.852923i	$0.325172\pi$
$89$			16.0929i			1.70585i	−0.522037	+	0.852923i	$0.674828\pi$
$90$	0.413910	+	0.999268i	0.0436300	+	0.105332i
$91$	−0.205879	−	0.0852781i	−0.0215820	−	0.00893957i
$92$	−2.04099	+	4.92737i	−0.212787	+	0.513714i
$93$	−9.63240	+	9.63240i	−0.998833	+	0.998833i
$94$	−0.335216	+	0.335216i	−0.0345748	+	0.0345748i
$95$	−4.96247	+	11.9805i	−0.509138	+	1.22917i
$96$	−2.97858	−	1.23377i	−0.304000	−	0.125921i
$97$	1.07576	+	2.59711i	0.109227	+	0.263696i	0.969036	−	0.246918i	$-0.0794179\pi$
$97$	1.07576	+	2.59711i	0.109227	+	0.263696i	−0.859810	+	0.510615i	$0.829418\pi$
$98$			0.872021i			0.0880874i
$99$	11.4327	−	4.73556i	1.14903	−	0.475942i
$100$	−0.153415	−	0.153415i	−0.0153415	−	0.0153415i
$101$	16.9147			1.68308			0.841540	−	0.540195i	$-0.181649\pi$
$101$	16.9147			1.68308			0.841540	+	0.540195i	$0.181649\pi$
$102$	1.11308	+	0.0535686i	0.110212	+	0.00530408i
$103$	−12.4096			−1.22275			−0.611377	−	0.791339i	$-0.709384\pi$
$103$	−12.4096			−1.22275			−0.611377	+	0.791339i	$0.709384\pi$
$104$	0.0147606	+	0.0147606i	0.00144740	+	0.00144740i
$105$	23.5282	−	9.74570i	2.29612	−	0.951082i
$106$			0.440164i			0.0427525i
$107$	6.28677	+	15.1776i	0.607765	+	1.46728i	0.865424	+	0.501039i	$0.167049\pi$
$107$	6.28677	+	15.1776i	0.607765	+	1.46728i	−0.257659	+	0.966236i	$0.582951\pi$
$108$	11.4284	+	4.73380i	1.09970	+	0.455510i
$109$	−3.76112	+	9.08014i	−0.360250	+	0.869720i	0.635013	+	0.772501i	$0.280995\pi$
$109$	−3.76112	+	9.08014i	−0.360250	+	0.869720i	−0.995263	+	0.0972185i	$0.969005\pi$
$110$	−0.353649	+	0.353649i	−0.0337191	+	0.0337191i
$111$	16.9572	−	16.9572i	1.60950	−	1.60950i
$112$	−6.08310	+	14.6859i	−0.574799	+	1.38769i
$113$	6.29136	+	2.60597i	0.591841	+	0.245149i	0.658443	−	0.752631i	$-0.271216\pi$
$113$	6.29136	+	2.60597i	0.591841	+	0.245149i	−0.0666013	+	0.997780i	$0.521216\pi$
$114$	−0.606461	−	1.46413i	−0.0568003	−	0.137128i
$115$			5.92401i			0.552417i
$116$	7.96854	−	3.30068i	0.739861	−	0.306460i
$117$	−0.202376	−	0.202376i	−0.0187097	−	0.0187097i
$118$	−0.869072			−0.0800045
$119$	0.798330	−	16.5882i	0.0731828	−	1.52064i
$120$	−2.38558			−0.217773
$121$	−3.73206	−	3.73206i	−0.339278	−	0.339278i
$122$	0.485059	−	0.200918i	0.0439152	−	0.0181903i
$123$			0.366761i			0.0330697i
$124$	−3.63060	−	8.76506i	−0.326038	−	0.787125i
$125$	−10.4388	−	4.32387i	−0.933671	−	0.386739i
$126$	−0.753848	+	1.81995i	−0.0671581	+	0.162134i
$127$	10.3166	−	10.3166i	0.915449	−	0.915449i	−0.0812454	−	0.996694i	$-0.525890\pi$
$127$	10.3166	−	10.3166i	0.915449	−	0.915449i	0.996694	+	0.0812454i	$0.0258897\pi$
$128$	2.11534	−	2.11534i	0.186971	−	0.186971i
$129$	1.09404	−	2.64125i	0.0963251	−	0.232549i
$130$	0.0106868	+	0.00442660i	0.000937291	+	0.000388239i
$131$	−5.86095	−	14.1496i	−0.512074	−	1.23625i	−0.942675	−	0.333713i	$-0.891698\pi$
$131$	−5.86095	−	14.1496i	−0.512074	−	1.23625i	0.430601	−	0.902542i	$-0.358302\pi$
$132$			13.6162i			1.18514i
$133$	−21.8198	+	9.03806i	−1.89202	+	0.783699i
$134$	0.985466	+	0.985466i	0.0851313	+	0.0851313i
$135$	13.7400			1.18255
$136$	−0.663740	+	1.40699i	−0.0569153	+	0.120649i
$137$	10.5209			0.898859			0.449429	−	0.893316i	$-0.351627\pi$
$137$	10.5209			0.898859			0.449429	+	0.893316i	$0.351627\pi$
$138$	−0.511925	−	0.511925i	−0.0435779	−	0.0435779i
$139$	5.66300	−	2.34569i	0.480330	−	0.198959i	−0.129362	−	0.991597i	$-0.541293\pi$
$139$	5.66300	−	2.34569i	0.480330	−	0.198959i	0.609692	+	0.792638i	$0.291293\pi$
$140$			17.7363i			1.49899i
$141$	5.48609	+	13.2446i	0.462012	+	1.11540i
$142$	0.492532	+	0.204014i	0.0413324	+	0.0171204i
$143$	0.0506449	−	0.122268i	0.00423514	−	0.0102245i
$144$	−14.4360	+	14.4360i	−1.20300	+	1.20300i
$145$	6.77429	−	6.77429i	0.562575	−	0.562575i
$146$	0.148507	−	0.358528i	0.0122905	−	0.0296720i
$147$	24.3627	+	10.0914i	2.00941	+	0.832323i
$148$	6.39143	+	15.4303i	0.525372	+	1.26836i
$149$		−	9.63863i		−	0.789627i	−0.918761	−	0.394813i	$-0.870809\pi$
$149$		−	9.63863i		−	0.789627i	0.918761	−	0.394813i	$-0.129191\pi$
$150$	0.0272094	−	0.0112705i	0.00222164	−	0.000920233i
$151$	6.57985	+	6.57985i	0.535461	+	0.535461i	0.922192	−	0.386732i	$-0.126396\pi$
$151$	6.57985	+	6.57985i	0.535461	+	0.535461i	−0.386732	+	0.922192i	$0.626396\pi$
$152$	2.21237			0.179447
$153$	9.10027	−	19.2907i	0.735713	−	1.55956i
$154$	−0.910889			−0.0734015
$155$	−7.45143	−	7.45143i	−0.598513	−	0.598513i
$156$	0.290948	−	0.120514i	0.0232944	−	0.00964888i
$157$		−	12.2094i		−	0.974413i	−0.873287	−	0.487206i	$-0.838016\pi$
$157$		−	12.2094i		−	0.974413i	0.873287	−	0.487206i	$-0.161984\pi$
$158$	−0.338199	−	0.816486i	−0.0269057	−	0.0649561i
$159$	12.2974	+	5.09376i	0.975249	+	0.403961i
$160$	0.954420	−	2.30417i	0.0754535	−	0.182161i
$161$	−7.62919	+	7.62919i	−0.601264	+	0.601264i
$162$	−0.149880	+	0.149880i	−0.0117757	+	0.0117757i
$163$	−3.62941	+	8.76218i	−0.284277	+	0.686307i	−0.999926	−	0.0121539i	$-0.996131\pi$
$163$	−3.62941	+	8.76218i	−0.284277	+	0.686307i	0.715649	+	0.698460i	$0.246131\pi$
$164$	−0.235987	−	0.0977491i	−0.0184275	−	0.00763292i
$165$	5.78777	+	13.9729i	0.450577	+	1.08779i
$166$			0.927377i			0.0719784i
$167$	3.66770	−	1.51921i	0.283816	−	0.117560i	−0.236234	−	0.971696i	$-0.575913\pi$
$167$	3.66770	−	1.51921i	0.283816	−	0.117560i	0.520050	+	0.854136i	$0.325913\pi$
$168$	−3.07225	−	3.07225i	−0.237030	−	0.237030i
$169$	12.9969			0.999765
$170$	−0.0414396	+	0.861060i	−0.00317827	+	0.0660403i
$171$	−30.3328			−2.31961
$172$	1.40789	+	1.40789i	0.107351	+	0.107351i
$173$	−2.58192	+	1.06947i	−0.196300	+	0.0813101i	−0.478668	−	0.877996i	$-0.658880\pi$
$173$	−2.58192	+	1.06947i	−0.196300	+	0.0813101i	0.282368	+	0.959306i	$0.408880\pi$
$174$			1.17080i			0.0887585i
$175$	−0.167964	−	0.405501i	−0.0126969	−	0.0306530i
$176$	−8.72166	−	3.61263i	−0.657420	−	0.272312i
$177$	−10.0572	+	24.2803i	−0.755949	+	1.82502i
$178$	1.07580	−	1.07580i	0.0806344	−	0.0806344i
$179$	−7.10699	+	7.10699i	−0.531201	+	0.531201i	−0.920930	−	0.389728i	$-0.872569\pi$
$179$	−7.10699	+	7.10699i	−0.531201	+	0.531201i	0.389728	+	0.920930i	$0.372569\pi$
$180$	−8.71726	+	21.0453i	−0.649746	+	1.56863i
$181$	8.96332	+	3.71273i	0.666238	+	0.275965i	0.690061	−	0.723751i	$-0.257584\pi$
$181$	8.96332	+	3.71273i	0.666238	+	0.275965i	−0.0238228	+	0.999716i	$0.507584\pi$
$182$	0.00806210	+	0.0194636i	0.000597603	+	0.00144274i
$183$		−	15.8768i		−	1.17365i
$184$	0.933749	−	0.386771i	0.0688369	−	0.0285132i
$185$	13.1177	+	13.1177i	0.964434	+	0.964434i
$186$	1.28783			0.0944286
$187$	9.85141	+	0.474112i	0.720407	+	0.0346705i
$188$	−9.98420			−0.728172
$189$	17.6949	+	17.6949i	1.28712	+	1.28712i
$190$	1.13262	−	0.469146i	0.0821689	−	0.0340355i
$191$		−	13.5953i		−	0.983719i	−0.870674	−	0.491860i	$-0.836317\pi$
$191$		−	13.5953i		−	0.983719i	0.870674	−	0.491860i	$-0.163683\pi$
$192$	−8.51854	−	20.5656i	−0.614773	−	1.48419i
$193$	−9.91580	−	4.10726i	−0.713755	−	0.295647i	−0.00389741	−	0.999992i	$-0.501241\pi$
$193$	−9.91580	−	4.10726i	−0.713755	−	0.295647i	−0.709857	+	0.704346i	$0.751241\pi$
$194$	0.101701	−	0.245528i	0.00730171	−	0.0176279i
$195$	0.247343	−	0.247343i	0.0177126	−	0.0177126i
$196$	−12.9863	+	12.9863i	−0.927594	+	0.927594i
$197$	3.13615	−	7.57132i	0.223441	−	0.539435i	−0.771912	−	0.635730i	$-0.780699\pi$
$197$	3.13615	−	7.57132i	0.223441	−	0.539435i	0.995353	+	0.0962952i	$0.0306993\pi$
$198$	−1.08083	−	0.447695i	−0.0768114	−	0.0318163i
$199$	−3.95244	−	9.54204i	−0.280181	−	0.676417i	0.719658	−	0.694328i	$-0.244298\pi$
$199$	−3.95244	−	9.54204i	−0.280181	−	0.676417i	−0.999840	+	0.0179110i	$0.994298\pi$
$200$			0.0411147i			0.00290725i
$201$	38.9364	−	16.1280i	2.74636	−	1.13758i
$202$	−1.13074	−	1.13074i	−0.0795583	−	0.0795583i
$203$	17.4485			1.22464
$204$	15.7785	+	17.3740i	1.10472	+	1.21643i
$205$	−0.283719			−0.0198158
$206$	0.829571	+	0.829571i	0.0577989	+	0.0577989i
$207$	−12.8022	+	5.30286i	−0.889817	+	0.368574i
$208$			0.218337i			0.0151389i
$209$	−5.36752	−	12.9583i	−0.371279	−	0.896347i
$210$	−2.22433	−	0.921348i	−0.153493	−	0.0635790i
$211$	−1.66040	+	4.00857i	−0.114307	+	0.275961i	−0.970671	−	0.240411i	$-0.922718\pi$
$211$	−1.66040	+	4.00857i	−0.114307	+	0.275961i	0.856364	+	0.516372i	$0.172718\pi$
$212$	−6.55502	+	6.55502i	−0.450200	+	0.450200i
$213$	11.3996	−	11.3996i	0.781086	−	0.781086i
$214$	0.594345	−	1.43488i	0.0406286	−	0.0980861i
$215$	2.04322	+	0.846330i	0.139347	+	0.0577193i
$216$	−0.897066	−	2.16571i	−0.0610376	−	0.147358i
$217$		−	19.1925i		−	1.30287i
$218$	0.858427	−	0.355572i	0.0581400	−	0.0240824i
$219$	−8.29806	−	8.29806i	−0.560731	−	0.560731i
$220$	−10.5332			−0.710150
$221$	−0.0770623	−	0.214699i	−0.00518377	−	0.0144422i
$222$	−2.26714			−0.152161
$223$	−14.1820	−	14.1820i	−0.949697	−	0.949697i	0.0490974	−	0.998794i	$-0.484366\pi$
$223$	−14.1820	−	14.1820i	−0.949697	−	0.949697i	−0.998794	+	0.0490974i	$0.984366\pi$
$224$	4.19656	−	1.73827i	0.280394	−	0.116143i
$225$		−	0.563707i		−	0.0375805i
$226$	−0.246365	−	0.594778i	−0.0163880	−	0.0395641i
$227$	−0.467058	−	0.193462i	−0.0309998	−	0.0128405i	0.367130	−	0.930170i	$-0.380341\pi$
$227$	−0.467058	−	0.193462i	−0.0309998	−	0.0128405i	−0.398129	+	0.917329i	$0.630341\pi$
$228$	12.7725	−	30.8356i	0.845881	−	2.04214i
$229$	11.9981	−	11.9981i	0.792858	−	0.792858i	−0.189099	−	0.981958i	$-0.560557\pi$
$229$	11.9981	−	11.9981i	0.792858	−	0.792858i	0.981958	+	0.189099i	$0.0605569\pi$
$230$	0.396015	−	0.396015i	0.0261124	−	0.0261124i
$231$	−10.5412	+	25.4487i	−0.693558	+	1.67440i
$232$	−1.51006	−	0.625486i	−0.0991401	−	0.0410652i
$233$	−2.13754	−	5.16049i	−0.140035	−	0.338075i	0.838266	−	0.545261i	$-0.183569\pi$
$233$	−2.13754	−	5.16049i	−0.140035	−	0.338075i	−0.978302	+	0.207186i	$0.933569\pi$
$234$			0.0270574i			0.00176880i
$235$	−10.2458	+	4.24393i	−0.668359	+	0.276843i
$236$	−12.9424	−	12.9424i	−0.842478	−	0.842478i
$237$	−26.7250			−1.73597
$238$	−1.16228	+	1.05554i	−0.0753392	+	0.0684206i
$239$	−1.55071			−0.100307			−0.0501534	−	0.998742i	$-0.515971\pi$
$239$	−1.55071			−0.100307			−0.0501534	+	0.998742i	$0.515971\pi$
$240$	−17.6436	−	17.6436i	−1.13889	−	1.13889i
$241$	14.3165	−	5.93008i	0.922205	−	0.381990i	0.129489	−	0.991581i	$-0.458666\pi$
$241$	14.3165	−	5.93008i	0.922205	−	0.381990i	0.792716	+	0.609591i	$0.208666\pi$
$242$			0.498970i			0.0320750i
$243$	−4.67966	−	11.2977i	−0.300201	−	0.724748i
$244$	10.2157	+	4.23149i	0.653995	+	0.270893i
$245$	−7.80649	+	18.8465i	−0.498739	+	1.20406i
$246$	0.0245177	−	0.0245177i	0.00156319	−	0.00156319i
$247$	−0.229384	+	0.229384i	−0.0145953	+	0.0145953i
$248$	−0.688008	+	1.66100i	−0.0436885	+	0.105473i
$249$	25.9093	+	10.7320i	1.64194	+	0.680112i
$250$	0.408775	+	0.986869i	0.0258532	+	0.0624151i
$251$		−	27.1618i		−	1.71444i	−0.514950	−	0.857220i	$-0.672190\pi$
$251$		−	27.1618i		−	1.71444i	0.514950	−	0.857220i	$-0.327810\pi$
$252$	−38.3295	+	15.8766i	−2.41453	+	1.00013i
$253$	−4.53082	−	4.53082i	−0.284850	−	0.284850i
$254$	−1.37931			−0.0865456
$255$	23.5769	+	11.1223i	1.47645	+	0.696504i
$256$	15.2898			0.955611
$257$	−14.3360	−	14.3360i	−0.894253	−	0.894253i	0.100667	−	0.994920i	$-0.467902\pi$
$257$	−14.3360	−	14.3360i	−0.894253	−	0.894253i	−0.994920	+	0.100667i	$0.967902\pi$
$258$	−0.249701	+	0.103430i	−0.0155457	+	0.00643925i
$259$			33.7871i			2.09943i
$260$	0.0932276	+	0.225071i	0.00578173	+	0.0139583i
$261$	20.7038	+	8.57578i	1.28153	+	0.530828i
$262$	−0.554088	+	1.33769i	−0.0342317	+	0.0826426i
$263$	−3.64361	+	3.64361i	−0.224674	+	0.224674i	−0.810464	−	0.585789i	$-0.800785\pi$
$263$	−3.64361	+	3.64361i	−0.224674	+	0.224674i	0.585789	+	0.810464i	$0.300785\pi$
$264$	1.82455	−	1.82455i	0.112293	−	0.112293i
$265$	−3.94043	+	9.51304i	−0.242059	+	0.584382i
$266$	2.06282	+	0.854449i	0.126480	+	0.0523896i
$267$	−17.6063	−	42.5055i	−1.07749	−	2.60129i
$268$			29.3515i			1.79293i
$269$	24.3054	−	10.0676i	1.48193	−	0.613835i	0.512385	−	0.858756i	$-0.328762\pi$
$269$	24.3054	−	10.0676i	1.48193	−	0.613835i	0.969543	+	0.244921i	$0.0787620\pi$
$270$	−0.918505	−	0.918505i	−0.0558984	−	0.0558984i
$271$	−30.6474			−1.86170			−0.930848	−	0.365406i	$-0.880930\pi$
$271$	−30.6474			−1.86170			−0.930848	+	0.365406i	$0.880930\pi$
$272$	−15.3150	+	5.49704i	−0.928608	+	0.333307i
$273$	0.637078			0.0385577
$274$	−0.703311	−	0.703311i	−0.0424886	−	0.0424886i
$275$	0.240819	−	0.0997503i	0.0145219	−	0.00601517i
$276$		−	15.2474i		−	0.917784i
$277$	5.06869	+	12.2369i	0.304548	+	0.735244i	0.999863	+	0.0165393i	$0.00526488\pi$
$277$	5.06869	+	12.2369i	0.304548	+	0.735244i	−0.695315	+	0.718705i	$0.744735\pi$
$278$	−0.535374	−	0.221759i	−0.0321096	−	0.0133002i
$279$	9.43299	−	22.7733i	0.564739	−	1.36340i
$280$	2.37664	−	2.37664i	0.142031	−	0.142031i
$281$	9.63229	−	9.63229i	0.574614	−	0.574614i	−0.358800	−	0.933414i	$-0.616814\pi$
$281$	9.63229	−	9.63229i	0.574614	−	0.574614i	0.933414	+	0.358800i	$0.116814\pi$
$282$	0.518649	−	1.25213i	0.0308851	−	0.0745632i
$283$	23.1858	+	9.60386i	1.37825	+	0.570890i	0.944013	−	0.329908i	$-0.107018\pi$
$283$	23.1858	+	9.60386i	1.37825	+	0.570890i	0.434238	+	0.900798i	$0.357018\pi$
$284$	4.29668	+	10.3731i	0.254961	+	0.615531i
$285$		−	37.0726i		−	2.19599i
$286$	−0.0115591	+	0.00478792i	−0.000683501	+	0.000283115i
$287$	−0.365386	−	0.365386i	−0.0215680	−	0.0215680i
$288$	5.83385			0.343763
$289$	13.1196	−	10.8109i	0.771742	−	0.635935i
$290$	−0.905711			−0.0531852
$291$	−5.68270	−	5.68270i	−0.333126	−	0.333126i
$292$	7.55087	−	3.12767i	0.441881	−	0.183033i
$293$			23.2782i			1.35993i	0.733246	+	0.679964i	$0.238004\pi$
$293$			23.2782i			1.35993i	−0.733246	+	0.679964i	$0.761996\pi$
$294$	−0.954029	−	2.30323i	−0.0556401	−	0.134327i
$295$	−18.7828	−	7.78009i	−1.09358	−	0.452974i
$296$	1.21119	−	2.92407i	0.0703990	−	0.169958i
$297$	−10.5086	+	10.5086i	−0.609774	+	0.609774i
$298$	−0.644334	+	0.644334i	−0.0373253	+	0.0373253i
$299$	−0.0567120	+	0.136915i	−0.00327974	+	0.00791799i
$300$	0.573051	+	0.237365i	0.0330851	+	0.0137043i
$301$	1.54141	+	3.72129i	0.0888453	+	0.214492i
$302$		−	0.879715i		−	0.0506219i
$303$	−44.6761	+	18.5055i	−2.56658	+	1.06311i
$304$	16.3625	+	16.3625i	0.938454	+	0.938454i
$305$	12.2820			0.703265
$306$	−1.89791	+	0.681221i	−0.108496	+	0.0389428i
$307$	−11.6558			−0.665232			−0.332616	−	0.943062i	$-0.607931\pi$
$307$	−11.6558			−0.665232			−0.332616	+	0.943062i	$0.607931\pi$
$308$	−13.5651	−	13.5651i	−0.772946	−	0.772946i
$309$	32.7769	−	13.5766i	1.86461	−	0.772348i
$310$			0.996244i			0.0565828i
$311$	10.1781	+	24.5722i	0.577150	+	1.39336i	0.895360	+	0.445343i	$0.146918\pi$
$311$	10.1781	+	24.5722i	0.577150	+	1.39336i	−0.318211	+	0.948020i	$0.603082\pi$
$312$	−0.0551352	−	0.0228378i	−0.00312142	−	0.00129293i
$313$	7.27000	−	17.5513i	0.410925	−	0.992060i	−0.573965	−	0.818879i	$-0.694596\pi$
$313$	7.27000	−	17.5513i	0.410925	−	0.992060i	0.984890	−	0.173180i	$-0.0554043\pi$
$314$	−0.816185	+	0.816185i	−0.0460600	+	0.0460600i
$315$	−32.5851	+	32.5851i	−1.83596	+	1.83596i
$316$	7.12274	−	17.1958i	0.400685	−	0.967340i
$317$	24.7423	+	10.2486i	1.38966	+	0.575618i	0.947048	−	0.321093i	$-0.104050\pi$
$317$	24.7423	+	10.2486i	1.38966	+	0.575618i	0.442617	+	0.896711i	$0.354050\pi$
$318$	−0.481559	−	1.16259i	−0.0270045	−	0.0651946i
$319$			10.3623i			0.580176i
$320$	15.9091	−	6.58978i	0.889348	−	0.368380i
$321$	−33.2099	−	33.2099i	−1.85360	−	1.85360i
$322$	1.02001			0.0568429
$323$	−21.8650	−	10.3147i	−1.21660	−	0.573925i
$324$	−4.46408			−0.248004
$325$	−0.00426288	−	0.00426288i	−0.000236462	−	0.000236462i
$326$	0.828367	−	0.343121i	0.0458790	−	0.0190037i
$327$		−	28.0978i		−	1.55381i
$328$	0.0185237	+	0.0447201i	0.00102280	+	0.00246926i
$329$	−18.6604	−	7.72940i	−1.02878	−	0.426136i
$330$	0.547170	−	1.32098i	0.0301207	−	0.0727178i
$331$	−0.300269	+	0.300269i	−0.0165043	+	0.0165043i	−0.715311	−	0.698806i	$-0.753715\pi$
$331$	−0.300269	+	0.300269i	−0.0165043	+	0.0165043i	0.698806	+	0.715311i	$0.253715\pi$
$332$	−13.8107	+	13.8107i	−0.757960	+	0.757960i
$333$	−16.6061	+	40.0907i	−0.910010	+	2.19696i
$334$	−0.346741	−	0.143625i	−0.0189728	−	0.00785880i
$335$	12.4763	+	30.1205i	0.681653	+	1.64566i
$336$		−	45.4444i		−	2.47919i
$337$	−27.9871	+	11.5926i	−1.52455	+	0.631491i	−0.978498	−	0.206258i	$-0.933872\pi$
$337$	−27.9871	+	11.5926i	−1.52455	+	0.631491i	−0.546056	+	0.837748i	$0.683872\pi$
$338$	−0.868834	−	0.868834i	−0.0472583	−	0.0472583i
$339$	−19.4681			−1.05736
$340$	−13.4402	+	12.2059i	−0.728897	+	0.661961i
$341$	11.3981			0.617240
$342$	2.02772	+	2.02772i	0.109647	+	0.109647i
$343$	−8.27589	+	3.42799i	−0.446856	+	0.185094i
$344$		−	0.377311i		−	0.0203432i
$345$	−6.48112	−	15.6468i	−0.348932	−	0.842396i
$346$	0.244092	+	0.101106i	0.0131225	+	0.00543551i
$347$	1.32392	−	3.19623i	0.0710719	−	0.171583i	−0.884352	−	0.466821i	$-0.845399\pi$
$347$	1.32392	−	3.19623i	0.0710719	−	0.171583i	0.955424	+	0.295239i	$0.0953991\pi$
$348$	−17.4359	+	17.4359i	−0.934660	+	0.934660i
$349$	3.43627	−	3.43627i	0.183939	−	0.183939i	−0.609131	−	0.793070i	$-0.708482\pi$
$349$	3.43627	−	3.43627i	0.183939	−	0.183939i	0.793070	+	0.609131i	$0.208482\pi$
$350$	−0.0158791	+	0.0383356i	−0.000848775	+	0.00204912i
$351$	0.317556	+	0.131536i	0.0169499	+	0.00702087i
$352$	1.03232	+	2.49225i	0.0550230	+	0.132837i
$353$			24.6396i			1.31143i	0.755008	+	0.655716i	$0.227633\pi$
$353$			24.6396i			1.31143i	−0.755008	+	0.655716i	$0.772367\pi$
$354$	2.29544	−	0.950802i	0.122001	−	0.0505345i
$355$	8.81848	+	8.81848i	0.468037	+	0.468037i
$356$	32.0420			1.69822
$357$	16.0397	+	44.6871i	0.848908	+	2.36509i
$358$	0.950192			0.0502192
$359$	−4.63102	−	4.63102i	−0.244416	−	0.244416i	0.574258	−	0.818674i	$-0.305291\pi$
$359$	−4.63102	−	4.63102i	−0.244416	−	0.244416i	−0.818674	+	0.574258i	$0.805291\pi$
$360$	3.98814	−	1.65194i	0.210193	−	0.0870650i
$361$			15.3807i			0.809512i
$362$	−0.350997	−	0.847383i	−0.0184480	−	0.0445374i
$363$	13.9404	+	5.77429i	0.731679	+	0.303071i
$364$	−0.169794	+	0.409919i	−0.00889962	+	0.0214856i
$365$	6.41922	−	6.41922i	0.335997	−	0.335997i
$366$	−1.06135	+	1.06135i	−0.0554778	+	0.0554778i
$367$	3.31928	−	8.01345i	0.173265	−	0.418299i	−0.813262	−	0.581898i	$-0.802310\pi$
$367$	3.31928	−	8.01345i	0.173265	−	0.418299i	0.986527	+	0.163599i	$0.0523103\pi$
$368$	9.76647	+	4.04541i	0.509113	+	0.210881i
$369$	−0.253971	−	0.613139i	−0.0132212	−	0.0319187i
$370$		−	1.75382i		−	0.0911766i
$371$	−17.3260	+	7.17665i	−0.899519	+	0.372593i
$372$	19.1787	+	19.1787i	0.994369	+	0.994369i
$373$	−13.0426			−0.675321			−0.337661	−	0.941268i	$-0.609636\pi$
$373$	−13.0426			−0.675321			−0.337661	+	0.941268i	$0.609636\pi$
$374$	−0.626865	−	0.690253i	−0.0324144	−	0.0356921i
$375$	32.3019			1.66806
$376$	1.33787	+	1.33787i	0.0689952	+	0.0689952i
$377$	0.221418	−	0.0917145i	0.0114036	−	0.00472354i
$378$		−	2.36578i		−	0.121683i
$379$	−9.66872	−	23.3424i	−0.496649	−	1.19902i	−0.951278	−	0.308336i	$-0.900228\pi$
$379$	−9.66872	−	23.3424i	−0.496649	−	1.19902i	0.454629	−	0.890681i	$-0.349772\pi$
$380$	23.8538	+	9.88058i	1.22368	+	0.506863i
$381$	−15.9619	+	38.5355i	−0.817754	+	1.97423i
$382$	−0.908832	+	0.908832i	−0.0464999	+	0.0464999i
$383$	13.2646	−	13.2646i	0.677791	−	0.677791i	−0.281709	−	0.959500i	$-0.590901\pi$
$383$	13.2646	−	13.2646i	0.677791	−	0.677791i	0.959500	+	0.281709i	$0.0909014\pi$
$384$	−3.27287	+	7.90141i	−0.167018	+	0.403217i
$385$	−19.6866	−	8.15445i	−1.00332	−	0.415589i
$386$	0.388296	+	0.937429i	0.0197637	+	0.0477139i
$387$			5.17315i			0.262966i
$388$	5.17101	−	2.14190i	0.262518	−	0.108739i
$389$	20.3841	+	20.3841i	1.03351	+	1.03351i	0.999419	+	0.0340953i	$0.0108550\pi$
$389$	20.3841	+	20.3841i	1.03351	+	1.03351i	0.0340953	+	0.999419i	$0.489145\pi$
$390$	−0.0330693			−0.00167453
$391$	−11.0316	−	0.530909i	−0.557891	−	0.0268492i
$392$	3.48029			0.175781
$393$	30.9605	+	30.9605i	1.56175	+	1.56175i
$394$	−0.715785	+	0.296488i	−0.0360607	+	0.0149368i
$395$		−	20.6739i		−	1.04022i
$396$	−9.42880	−	22.7631i	−0.473815	−	1.14389i
$397$	−34.9856	−	14.4915i	−1.75588	−	0.727308i	−0.997112	−	0.0759428i	$-0.975803\pi$
$397$	−34.9856	−	14.4915i	−1.75588	−	0.727308i	−0.758764	−	0.651365i	$-0.774197\pi$
$398$	−0.373660	+	0.902095i	−0.0187299	+	0.0452179i
$399$	47.7436	−	47.7436i	2.39017	−	2.39017i
$400$	−0.304082	+	0.304082i	−0.0152041	+	0.0152041i
$401$	−12.6048	+	30.4307i	−0.629455	+	1.51964i	0.210847	+	0.977519i	$0.432378\pi$
$401$	−12.6048	+	30.4307i	−0.629455	+	1.51964i	−0.840302	+	0.542119i	$0.817622\pi$
$402$	−3.68101	−	1.52472i	−0.183592	−	0.0760463i
$403$	−0.100882	−	0.243551i	−0.00502529	−	0.0121321i
$404$		−	33.6783i		−	1.67556i
$405$	−4.58102	+	1.89752i	−0.227633	+	0.0942886i
$406$	−1.16641	−	1.16641i	−0.0578881	−	0.0578881i
$407$	−20.0655			−0.994609
$408$	0.213796	−	4.44239i	0.0105845	−	0.219931i
$409$	−24.8125			−1.22690			−0.613450	−	0.789734i	$-0.710219\pi$
$409$	−24.8125			−1.22690			−0.613450	+	0.789734i	$0.710219\pi$
$410$	0.0189664	+	0.0189664i	0.000936683	+	0.000936683i
$411$	−27.7883	+	11.5103i	−1.37070	+	0.567761i
$412$			24.7083i			1.21729i
$413$	−14.1698	−	34.2088i	−0.697248	−	1.68331i
$414$	1.21031	+	0.501327i	0.0594835	+	0.0246389i
$415$	−8.30205	+	20.0429i	−0.407532	+	0.983869i
$416$	0.0441168	−	0.0441168i	0.00216300	−	0.00216300i
$417$	−12.3911	+	12.3911i	−0.606797	+	0.606797i
$418$	−0.507440	+	1.22507i	−0.0248197	+	0.0599200i
$419$	−9.50922	−	3.93885i	−0.464556	−	0.192425i	0.138113	−	0.990416i	$-0.455896\pi$
$419$	−9.50922	−	3.93885i	−0.464556	−	0.192425i	−0.602669	+	0.797991i	$0.705896\pi$
$420$	−19.4043	−	46.8461i	−0.946832	−	2.28586i
$421$		−	13.3151i		−	0.648940i	−0.945896	−	0.324470i	$-0.894814\pi$
$421$		−	13.3151i		−	0.648940i	0.945896	−	0.324470i	$-0.105186\pi$
$422$	0.378966	−	0.156973i	0.0184478	−	0.00764132i
$423$	−18.3429	−	18.3429i	−0.891864	−	0.891864i
$424$	1.75672			0.0853140
$425$	0.191689	−	0.406341i	0.00929827	−	0.0197104i
$426$	−1.52410			−0.0738430
$427$	15.8173	+	15.8173i	0.765452	+	0.765452i
$428$	30.2196	−	12.5174i	1.46072	−	0.605049i
$429$			0.378348i			0.0182668i
$430$	−0.0800112	−	0.193164i	−0.00385848	−	0.00931520i
$431$	22.4897	+	9.31555i	1.08329	+	0.448714i	0.851663	−	0.524090i	$-0.175594\pi$
$431$	22.4897	+	9.31555i	1.08329	+	0.448714i	0.231629	+	0.972804i	$0.425594\pi$
$432$	9.38279	−	22.6521i	0.451430	−	1.08985i
$433$	7.05812	−	7.05812i	0.339192	−	0.339192i	−0.516871	−	0.856063i	$-0.672904\pi$
$433$	7.05812	−	7.05812i	0.339192	−	0.339192i	0.856063	+	0.516871i	$0.172904\pi$
$434$	−1.28301	+	1.28301i	−0.0615862	+	0.0615862i
$435$	−10.4813	+	25.3040i	−0.502538	+	1.21323i
$436$	18.0791	+	7.48862i	0.865833	+	0.358640i
$437$	6.01053	+	14.5107i	0.287523	+	0.694141i
$438$			1.10944i			0.0530109i
$439$	31.6453	−	13.1079i	1.51035	−	0.625607i	0.534718	−	0.845030i	$-0.320418\pi$
$439$	31.6453	−	13.1079i	1.51035	−	0.625607i	0.975630	+	0.219424i	$0.0704177\pi$
$440$	1.41144	+	1.41144i	0.0672876	+	0.0672876i
$441$	−47.7168			−2.27223
$442$	−0.00920088	+	0.0195040i	−0.000437641	+	0.000927709i
$443$	−29.2614			−1.39025			−0.695127	−	0.718887i	$-0.744652\pi$
$443$	−29.2614			−1.39025			−0.695127	+	0.718887i	$0.744652\pi$
$444$	−33.7628	−	33.7628i	−1.60231	−	1.60231i
$445$	32.8814	−	13.6199i	1.55873	−	0.645646i
$446$			1.89611i			0.0897833i
$447$	10.5451	+	25.4581i	0.498765	+	1.20412i
$448$	28.9751	+	12.0019i	1.36894	+	0.567035i
$449$	10.3290	−	24.9365i	0.487458	−	1.17683i	−0.468537	−	0.883444i	$-0.655219\pi$
$449$	10.3290	−	24.9365i	0.487458	−	1.17683i	0.955995	−	0.293383i	$-0.0947812\pi$
$450$	−0.0376833	+	0.0376833i	−0.00177641	+	0.00177641i
$451$	0.216995	−	0.216995i	0.0102179	−	0.0102179i
$452$	5.18864	−	12.5265i	0.244053	−	0.589196i
$453$	−24.5777	−	10.1804i	−1.15476	−	0.478318i
$454$	0.0182897	+	0.0441552i	0.000858378	+	0.00207231i
$455$			0.492831i			0.0231043i
$456$	−5.84342	+	2.42042i	−0.273643	+	0.113347i
$457$	−12.7428	−	12.7428i	−0.596085	−	0.596085i	0.343183	−	0.939268i	$-0.388495\pi$
$457$	−12.7428	−	12.7428i	−0.596085	−	0.596085i	−0.939268	+	0.343183i	$0.888495\pi$
$458$	−1.60413			−0.0749560
$459$	−1.23137	+	25.5863i	−0.0574756	+	1.19427i
$460$	11.7951			0.549948
$461$	20.0369	+	20.0369i	0.933213	+	0.933213i	0.997905	−	0.0646918i	$-0.0206064\pi$
$461$	20.0369	+	20.0369i	0.933213	+	0.933213i	−0.0646918	+	0.997905i	$0.520606\pi$
$462$	2.40589	−	0.996552i	0.111932	−	0.0463638i
$463$			14.7905i			0.687373i	0.939084	+	0.343687i	$0.111676\pi$
$463$			14.7905i			0.687373i	−0.939084	+	0.343687i	$0.888324\pi$
$464$	−6.54223	−	15.7943i	−0.303715	−	0.733233i
$465$	27.8333	+	11.5289i	1.29074	+	0.534642i
$466$	−0.202081	+	0.487867i	−0.00936123	+	0.0226000i
$467$	8.75175	−	8.75175i	0.404982	−	0.404982i	−0.475002	−	0.879985i	$-0.657553\pi$
$467$	8.75175	−	8.75175i	0.404982	−	0.404982i	0.879985	+	0.475002i	$0.157553\pi$
$468$	−0.402944	+	0.402944i	−0.0186261	+	0.0186261i
$469$	−22.7229	+	54.8579i	−1.04925	+	2.53310i
$470$	0.968623	+	0.401217i	0.0446792	+	0.0185067i
$471$	13.3576	+	32.2480i	0.615484	+	1.48591i
$472$			3.46852i			0.159652i
$473$	−2.21000	+	0.915411i	−0.101616	+	0.0420906i
$474$	1.78654	+	1.78654i	0.0820585	+	0.0820585i
$475$	−0.638933			−0.0293163
$476$	−33.0282	−	1.58953i	−1.51385	−	0.0728558i
$477$	−24.0857			−1.10281
$478$	0.103663	+	0.103663i	0.00474145	+	0.00474145i
$479$	−2.52671	+	1.04660i	−0.115448	+	0.0478203i	−0.439660	−	0.898164i	$-0.644901\pi$
$479$	−2.52671	+	1.04660i	−0.115448	+	0.0478203i	0.324212	+	0.945985i	$0.394901\pi$
$480$			7.13008i			0.325442i
$481$	0.177596	+	0.428754i	0.00809767	+	0.0195495i
$482$	−1.35346	−	0.560623i	−0.0616486	−	0.0255357i
$483$	11.8040	−	28.4973i	0.537099	−	1.29667i
$484$	−7.43077	+	7.43077i	−0.337762	+	0.337762i
$485$	4.39602	−	4.39602i	0.199613	−	0.199613i
$486$	−0.442411	+	1.06807i	−0.0200681	+	0.0484488i
$487$	−32.7826	−	13.5790i	−1.48552	−	0.615324i	−0.515186	−	0.857079i	$-0.672277\pi$
$487$	−32.7826	−	13.5790i	−1.48552	−	0.615324i	−0.970337	+	0.241755i	$0.922277\pi$
$488$	−0.801877	−	1.93590i	−0.0362993	−	0.0876342i
$489$		−	27.1139i		−	1.22613i
$490$	1.78173	−	0.738018i	0.0804905	−	0.0333402i
$491$	15.5584	+	15.5584i	0.702142	+	0.702142i	0.964870	−	0.262728i	$-0.0846221\pi$
$491$	15.5584	+	15.5584i	0.702142	+	0.702142i	−0.262728	+	0.964870i	$0.584622\pi$
$492$	0.730244			0.0329219
$493$	12.0078	+	13.2221i	0.540806	+	0.595492i
$494$	0.0306682			0.00137983
$495$	−19.3516	−	19.3516i	−0.869790	−	0.869790i
$496$	−17.3731	+	7.19617i	−0.780074	+	0.323117i
$497$			22.7136i			1.01885i
$498$	−1.01459	−	2.44944i	−0.0454649	−	0.109762i
$499$	−37.0432	−	15.3438i	−1.65828	−	0.686882i	−0.660336	−	0.750971i	$-0.729586\pi$
$499$	−37.0432	−	15.3438i	−1.65828	−	0.686882i	−0.997944	+	0.0640885i	$0.979586\pi$
$500$	−8.60910	+	20.7842i	−0.385011	+	0.929498i
$501$	−8.02526	+	8.02526i	−0.358542	+	0.358542i
$502$	−1.81575	+	1.81575i	−0.0810407	+	0.0810407i
$503$	11.7016	−	28.2502i	0.521750	−	1.25962i	−0.415066	−	0.909791i	$-0.636241\pi$
$503$	11.7016	−	28.2502i	0.521750	−	1.25962i	0.936815	−	0.349824i	$-0.113759\pi$
$504$	7.26354	+	3.00866i	0.323544	+	0.134016i
$505$	−14.3155	−	34.5606i	−0.637030	−	1.53793i
$506$			0.605763i			0.0269294i
$507$	−34.3282	+	14.2192i	−1.52457	+	0.631497i
$508$	−20.5410	−	20.5410i	−0.911358	−	0.911358i
$509$	23.4192			1.03804			0.519018	−	0.854763i	$-0.326298\pi$
$509$	23.4192			1.03804			0.519018	+	0.854763i	$0.326298\pi$
$510$	−0.832584	−	2.31961i	−0.0368674	−	0.102714i
$511$	16.5339			0.731416
$512$	−5.25278	−	5.25278i	−0.232142	−	0.232142i
$513$	33.6557	−	13.9406i	1.48593	−	0.615494i
$514$			1.91669i			0.0845418i
$515$	10.5026	+	25.3556i	0.462801	+	1.11730i
$516$	−5.25890	−	2.17831i	−0.231510	−	0.0958947i
$517$	4.59034	−	11.0821i	0.201883	−	0.487388i
$518$	2.25864	−	2.25864i	0.0992390	−	0.0992390i
$519$	5.64947	−	5.64947i	0.247984	−	0.247984i
$520$	0.0176668	−	0.0426515i	0.000774742	−	0.00187039i
$521$	−15.8085	−	6.54807i	−0.692581	−	0.286876i	0.00849418	−	0.999964i	$-0.497296\pi$
$521$	−15.8085	−	6.54807i	−0.692581	−	0.286876i	−0.701075	+	0.713088i	$0.747296\pi$
$522$	−0.810746	−	1.95731i	−0.0354854	−	0.0856693i
$523$			1.86620i			0.0816031i	0.999167	+	0.0408015i	$0.0129911\pi$
$523$			1.86620i			0.0816031i	−0.999167	+	0.0408015i	$0.987009\pi$
$524$	−28.1727	+	11.6695i	−1.23073	+	0.509785i
$525$	0.887270	+	0.887270i	0.0387236	+	0.0387236i
$526$	0.487144			0.0212405
$527$	14.5437	−	13.2081i	0.633534	−	0.575355i
$528$	26.9885			1.17452
$529$	−11.1899	−	11.1899i	−0.486516	−	0.486516i
$530$	0.899353	−	0.372524i	0.0390654	−	0.0161814i
$531$		−	47.5554i		−	2.06373i
$532$	17.9953	+	43.4446i	0.780197	+	1.88356i
$533$	−0.00655727	−	0.00271611i	−0.000284027	−	0.000117648i
$534$	−1.66449	+	4.01842i	−0.0720293	+	0.173894i
$535$	25.6906	−	25.6906i	1.11070	−	1.11070i
$536$	3.93306	−	3.93306i	0.169882	−	0.169882i
$537$	10.9960	−	26.5467i	0.474513	−	1.14558i
$538$	−2.29781	−	0.951784i	−0.0990656	−	0.0410343i
$539$	−8.44369	−	20.3849i	−0.363695	−	0.878039i
$540$		−	27.3571i		−	1.17726i
$541$	−0.0550784	+	0.0228142i	−0.00236801	+	0.000980860i	−0.383867	−	0.923388i	$-0.625408\pi$
$541$	−0.0550784	+	0.0228142i	−0.00236801	+	0.000980860i	0.381499	+	0.924369i	$0.375408\pi$
$542$	2.04875	+	2.04875i	0.0880014	+	0.0880014i
$543$	−27.7363			−1.19028
$544$	4.20525	+	1.98380i	0.180299	+	0.0850548i
$545$	21.7359			0.931063
$546$	−0.0425881	−	0.0425881i	−0.00182260	−	0.00182260i
$547$	−14.1059	+	5.84287i	−0.603127	+	0.249823i	−0.663287	−	0.748366i	$-0.730839\pi$
$547$	−14.1059	+	5.84287i	−0.603127	+	0.249823i	0.0601600	+	0.998189i	$0.480839\pi$
$548$		−	20.9477i		−	0.894842i
$549$	10.9942	+	26.5424i	0.469221	+	1.13280i
$550$	−0.0227667	−	0.00943029i	−0.000970777	−	0.000402109i
$551$	9.72022	−	23.4667i	0.414095	−	0.999714i
$552$	−2.04312	+	2.04312i	−0.0869611	+	0.0869611i
$553$	26.6247	−	26.6247i	1.13220	−	1.13220i
$554$	0.479189	−	1.15686i	0.0203588	−	0.0491505i
$555$	−48.9986	−	20.2959i	−2.07987	−	0.861512i
$556$	−4.67042	−	11.2754i	−0.198070	−	0.478183i
$557$		−	10.1024i		−	0.428053i	−0.976828	−	0.214026i	$-0.931342\pi$
$557$		−	10.1024i		−	0.428053i	0.976828	−	0.214026i	$-0.0686578\pi$
$558$	−2.15296	+	0.891785i	−0.0911421	+	0.0377523i
$559$	0.0391205	+	0.0391205i	0.00165462	+	0.00165462i
$560$	35.1549			1.48556
$561$	−26.5388	+	9.52562i	−1.12047	+	0.402172i
$562$	−1.28782			−0.0543234
$563$	2.29689	+	2.29689i	0.0968022	+	0.0968022i	0.753849	−	0.657047i	$-0.228195\pi$
$563$	2.29689	+	2.29689i	0.0968022	+	0.0968022i	−0.657047	+	0.753849i	$0.728195\pi$
$564$	26.3708	−	10.9231i	1.11041	−	0.459947i
$565$		−	15.0602i		−	0.633585i
$566$	−0.907939	−	2.19196i	−0.0381635	−	0.0921349i
$567$	−8.34335	−	3.45593i	−0.350388	−	0.145135i
$568$	0.814231	−	1.96573i	0.0341644	−	0.0824801i
$569$	8.03530	−	8.03530i	0.336857	−	0.336857i	−0.518326	−	0.855183i	$-0.673445\pi$
$569$	8.03530	−	8.03530i	0.336857	−	0.336857i	0.855183	+	0.518326i	$0.173445\pi$
$570$	−2.47827	+	2.47827i	−0.103803	+	0.103803i
$571$	−3.45244	+	8.33493i	−0.144480	+	0.348806i	−0.979509	−	0.201400i	$-0.935451\pi$
$571$	−3.45244	+	8.33493i	−0.144480	+	0.348806i	0.835029	+	0.550206i	$0.185451\pi$
$572$	−0.243442	−	0.100837i	−0.0101788	−	0.00421621i
$573$	14.8738	+	35.9086i	0.621363	+	1.50010i
$574$			0.0488514i			0.00203902i
$575$	−0.269668	+	0.111700i	−0.0112459	+	0.00465821i
$576$	28.4821	+	28.4821i	1.18675	+	1.18675i
$577$	−23.1592			−0.964131			−0.482065	−	0.876135i	$-0.660113\pi$
$577$	−23.1592			−0.964131			−0.482065	+	0.876135i	$0.660113\pi$
$578$	−1.59973	−	0.154336i	−0.0665402	−	0.00641954i
$579$	30.6837			1.27517
$580$	−13.4880	−	13.4880i	−0.560060	−	0.560060i
$581$	−36.5039	+	15.1204i	−1.51444	+	0.627300i
$582$			0.759767i			0.0314934i
$583$	−4.26206	−	10.2895i	−0.176517	−	0.426149i
$584$	−1.43091	−	0.592701i	−0.0592114	−	0.0245261i
$585$	−0.242223	+	0.584777i	−0.0100147	+	0.0241776i
$586$	1.55613	−	1.55613i	0.0642831	−	0.0642831i
$587$	25.8558	−	25.8558i	1.06718	−	1.06718i	0.0696089	−	0.997574i	$-0.477825\pi$
$587$	25.8558	−	25.8558i	1.06718	−	1.06718i	0.997574	−	0.0696089i	$-0.0221751\pi$
$588$	20.0926	−	48.5078i	0.828604	−	2.00043i
$589$	−25.8123	−	10.6918i	−1.06358	−	0.440549i
$590$	0.735522	+	1.77571i	0.0302809	+	0.0731047i
$591$			23.4289i			0.963735i
$592$	30.5841	−	12.6683i	1.25700	−	0.520666i
$593$	1.48459	+	1.48459i	0.0609649	+	0.0609649i	0.736932	−	0.675967i	$-0.236274\pi$
$593$	1.48459	+	1.48459i	0.0609649	+	0.0609649i	−0.675967	+	0.736932i	$0.736274\pi$
$594$	1.40499			0.0576474
$595$	−34.5691	+	12.4080i	−1.41719	+	0.508677i
$596$	−19.1911			−0.786098
$597$	20.8788	+	20.8788i	0.854513	+	0.854513i
$598$	0.0129438	−	0.00536149i	0.000529311	−	0.000219248i
$599$		−	8.01874i		−	0.327637i	−0.986491	−	0.163818i	$-0.947619\pi$
$599$		−	8.01874i		−	0.327637i	0.986491	−	0.163818i	$-0.0523811\pi$
$600$	−0.0449813	−	0.108594i	−0.00183635	−	0.00443335i
$601$	20.7931	+	8.61278i	0.848168	+	0.351323i	0.764069	−	0.645135i	$-0.223199\pi$
$601$	20.7931	+	8.61278i	0.848168	+	0.351323i	0.0840993	+	0.996457i	$0.473199\pi$
$602$	0.145723	−	0.351807i	0.00593923	−	0.0143386i
$603$	−53.9245	+	53.9245i	−2.19598	+	2.19598i
$604$	13.1009	−	13.1009i	0.533068	−	0.533068i
$605$	−4.46687	+	10.7840i	−0.181604	+	0.438431i
$606$	4.22364	+	1.74949i	0.171573	+	0.0710681i
$607$	6.07343	+	14.6625i	0.246513	+	0.595134i	0.997903	−	0.0647234i	$-0.0206165\pi$
$607$	6.07343	+	14.6625i	0.246513	+	0.595134i	−0.751390	+	0.659858i	$0.770617\pi$
$608$		−	6.61237i		−	0.268167i
$609$	−46.0858	+	19.0894i	−1.86749	+	0.773540i
$610$	−0.821041	−	0.821041i	−0.0332430	−	0.0332430i
$611$	−0.277426			−0.0112235
$612$	−38.4090	−	18.1192i	−1.55259	−	0.732425i
$613$	48.6876			1.96647			0.983237	−	0.182334i	$-0.0583654\pi$
$613$	48.6876			1.96647			0.983237	+	0.182334i	$0.0583654\pi$
$614$	0.779181	+	0.779181i	0.0314452	+	0.0314452i
$615$	0.749374	−	0.310401i	0.0302177	−	0.0125166i
$616$			3.63541i			0.146475i
$617$	5.95187	+	14.3691i	0.239613	+	0.578477i	0.997243	−	0.0742073i	$-0.0236426\pi$
$617$	5.95187	+	14.3691i	0.239613	+	0.578477i	−0.757630	+	0.652685i	$0.773643\pi$
$618$	−3.09869	−	1.28352i	−0.124648	−	0.0516308i
$619$	−9.58962	+	23.1514i	−0.385439	+	0.930533i	0.605454	+	0.795881i	$0.292992\pi$
$619$	−9.58962	+	23.1514i	−0.385439	+	0.930533i	−0.990893	+	0.134652i	$0.957008\pi$
$620$	−14.8363	+	14.8363i	−0.595839	+	0.595839i
$621$	11.7675	−	11.7675i	0.472215	−	0.472215i
$622$	0.962231	−	2.32303i	0.0385820	−	0.0931451i
$623$	59.8864	+	24.8058i	2.39930	+	0.993822i
$624$	−0.238870	−	0.576683i	−0.00956244	−	0.0230858i
$625$			24.4433i			0.977731i
$626$	−1.65928	+	0.687298i	−0.0663183	+	0.0274700i
$627$	28.3540	+	28.3540i	1.13235	+	1.13235i
$628$	−24.3096			−0.970058
$629$	−25.6032	+	23.2520i	−1.02087	+	0.927116i
$630$	4.35657			0.173570
$631$	28.8505	+	28.8505i	1.14852	+	1.14852i	0.986844	+	0.161676i	$0.0516901\pi$
$631$	28.8505	+	28.8505i	1.14852	+	1.14852i	0.161676	+	0.986844i	$0.448310\pi$
$632$	−3.25864	+	1.34977i	−0.129622	+	0.0536912i
$633$		−	12.4042i		−	0.493023i
$634$	−0.968890	−	2.33911i	−0.0384796	−	0.0928979i
$635$	−29.8103	−	12.3478i	−1.18299	−	0.490009i
$636$	10.1420	−	24.4849i	0.402156	−	0.970891i
$637$	−0.360845	+	0.360845i	−0.0142972	+	0.0142972i
$638$	0.692709	−	0.692709i	0.0274246	−	0.0274246i
$639$	−11.1636	+	26.9513i	−0.441625	+	1.06618i
$640$	−6.11238	−	2.53183i	−0.241613	−	0.100079i
$641$	−16.0868	−	38.8371i	−0.635392	−	1.53397i	−0.832755	−	0.553641i	$-0.813238\pi$
$641$	−16.0868	−	38.8371i	−0.635392	−	1.53397i	0.197363	−	0.980330i	$-0.436762\pi$
$642$			4.44011i			0.175237i
$643$	6.01619	−	2.49199i	0.237255	−	0.0982744i	−0.260888	−	0.965369i	$-0.584015\pi$
$643$	6.01619	−	2.49199i	0.237255	−	0.0982744i	0.498143	+	0.867095i	$0.334015\pi$
$644$	15.1902	+	15.1902i	0.598577	+	0.598577i
$645$	−6.32259			−0.248952
$646$	0.772130	+	2.15119i	0.0303791	+	0.0846373i
$647$	11.7937			0.463659			0.231830	−	0.972756i	$-0.425529\pi$
$647$	11.7937			0.463659			0.231830	+	0.972756i	$0.425529\pi$
$648$	0.598179	+	0.598179i	0.0234987	+	0.0234987i
$649$	20.3159	−	8.41513i	0.797470	−	0.330323i
$650$		0	0.000569939i		0	2.23549e-5i
$651$	20.9975	+	50.6924i	0.822956	+	1.98679i
$652$	17.4460	+	7.22639i	0.683240	+	0.283007i
$653$	−15.3181	+	36.9812i	−0.599444	+	1.44719i	0.274706	+	0.961528i	$0.411420\pi$
$653$	−15.3181	+	36.9812i	−0.599444	+	1.44719i	−0.874150	+	0.485657i	$0.838580\pi$
$654$	−1.87831	+	1.87831i	−0.0734478	+	0.0734478i
$655$	−23.9504	+	23.9504i	−0.935821	+	0.935821i
$656$	−0.193747	+	0.467747i	−0.00756455	+	0.0182624i
$657$	19.6186	+	8.12628i	0.765394	+	0.317036i
$658$	0.730730	+	1.76414i	0.0284868	+	0.0687733i
$659$			0.349527i			0.0136157i	0.999977	+	0.00680783i	$0.00216702\pi$
$659$			0.349527i			0.0136157i	−0.999977	+	0.00680783i	$0.997833\pi$
$660$	27.8209	−	11.5238i	1.08293	−	0.448564i
$661$	−23.6387	−	23.6387i	−0.919439	−	0.919439i	0.0775499	−	0.996988i	$-0.475290\pi$
$661$	−23.6387	−	23.6387i	−0.919439	−	0.919439i	−0.996988	+	0.0775499i	$0.975290\pi$
$662$	0.0401454			0.00156030
$663$	0.438431	+	0.482764i	0.0170272	+	0.0187490i
$664$	3.70122			0.143635
$665$	36.9335	+	36.9335i	1.43222	+	1.43222i
$666$	3.79014	−	1.56993i	0.146865	−	0.0608334i
$667$		−	11.6036i		−	0.449295i
$668$	−3.02485	−	7.30263i	−0.117035	−	0.282547i
$669$	52.9740	+	21.9425i	2.04809	+	0.848347i
$670$	1.17950	−	2.84756i	0.0455679	−	0.110011i
$671$	−9.39356	+	9.39356i	−0.362634	+	0.362634i
$672$	−9.18243	+	9.18243i	−0.354220	+	0.354220i
$673$	10.8812	−	26.2694i	0.419438	−	1.01261i	−0.563073	−	0.826407i	$-0.690381\pi$
$673$	10.8812	−	26.2694i	0.419438	−	1.01261i	0.982511	−	0.186205i	$-0.0596190\pi$
$674$	2.64587	+	1.09596i	0.101915	+	0.0422146i
$675$	0.259073	+	0.625459i	0.00997174	+	0.0240739i
$676$		−	25.8777i		−	0.995297i
$677$	−14.9752	+	6.20291i	−0.575542	+	0.238397i	−0.651417	−	0.758720i	$-0.725825\pi$
$677$	−14.9752	+	6.20291i	−0.575542	+	0.238397i	0.0758748	+	0.997117i	$0.475825\pi$
$678$	1.30143	+	1.30143i	0.0499810	+	0.0499810i
$679$	11.3228			0.434528
$680$	3.43654	+	0.165388i	0.131785	+	0.00634234i
$681$	1.44528			0.0553831
$682$	−0.761951	−	0.761951i	−0.0291766	−	0.0291766i
$683$	−10.9987	+	4.55580i	−0.420853	+	0.174323i	−0.583052	−	0.812435i	$-0.698141\pi$
$683$	−10.9987	+	4.55580i	−0.420853	+	0.174323i	0.162199	+	0.986758i	$0.448141\pi$
$684$			60.3946i			2.30924i
$685$	−8.90413	−	21.4965i	−0.340209	−	0.821338i
$686$	0.782394	+	0.324078i	0.0298720	+	0.0123734i
$687$	−18.5636	+	44.8166i	−0.708247	+	1.70986i
$688$	2.79056	−	2.79056i	0.106389	−	0.106389i
$689$	−0.182141	+	0.182141i	−0.00693903	+	0.00693903i
$690$	−0.612718	+	1.47923i	−0.0233258	+	0.0563134i
$691$	30.8530	+	12.7797i	1.17370	+	0.486163i	0.882415	−	0.470472i	$-0.155916\pi$
$691$	30.8530	+	12.7797i	1.17370	+	0.486163i	0.291287	+	0.956636i	$0.405916\pi$
$692$	2.12938	+	5.14077i	0.0809468	+	0.195423i
$693$		−	49.8437i		−	1.89340i
$694$	−0.302169	+	0.125162i	−0.0114702	+	0.00475110i
$695$	−9.58554	−	9.58554i	−0.363600	−	0.363600i
$696$	4.67275			0.177120
$697$	0.0254269	−	0.528336i	0.000963111	−	0.0200122i
$698$	−0.459423			−0.0173894
$699$	11.2916	+	11.2916i	0.427087	+	0.427087i
$700$	−0.807377	+	0.334426i	−0.0305160	+	0.0126401i
$701$		−	25.4242i		−	0.960259i	−0.877198	−	0.480129i	$-0.840590\pi$
$701$		−	25.4242i		−	0.960259i	0.877198	−	0.480129i	$-0.159410\pi$
$702$	−0.0124353	−	0.0300214i	−0.000469339	−	0.00113309i
$703$	45.4408	+	18.8222i	1.71383	+	0.709893i
$704$	−7.12766	+	17.2077i	−0.268634	+	0.648539i
$705$	22.4186	−	22.4186i	0.844333	−	0.844333i
$706$	1.64713	−	1.64713i	0.0619907	−	0.0619907i
$707$	26.0725	−	62.9446i	0.980558	−	2.36728i
$708$	48.3437	+	20.0246i	1.81687	+	0.752571i
$709$	3.17781	+	7.67192i	0.119345	+	0.288125i	0.972251	−	0.233940i	$-0.0751619\pi$
$709$	3.17781	+	7.67192i	0.119345	+	0.288125i	−0.852906	+	0.522065i	$0.825162\pi$
$710$		−	1.17902i		−	0.0442477i
$711$	44.6779	−	18.5062i	1.67555	−	0.694037i
$712$	−4.29358	−	4.29358i	−0.160909	−	0.160909i
$713$	−12.7635			−0.477997
$714$	1.91506	−	4.05953i	0.0716693	−	0.151924i
$715$	−0.292682			−0.0109457
$716$	14.1505	+	14.1505i	0.528828	+	0.528828i
$717$	4.09581	−	1.69654i	0.152961	−	0.0633584i
$718$			0.619159i			0.0231068i
$719$	−4.65914	−	11.2482i	−0.173757	−	0.419486i	0.812878	−	0.582434i	$-0.197900\pi$
$719$	−4.65914	−	11.2482i	−0.173757	−	0.419486i	−0.986635	+	0.162948i	$0.947900\pi$
$720$	41.7136	+	17.2784i	1.55458	+	0.643926i
$721$	−19.1283	+	46.1797i	−0.712374	+	1.71982i
$722$	1.02819	−	1.02819i	0.0382652	−	0.0382652i
$723$	−31.3257	+	31.3257i	−1.16501	+	1.16501i
$724$	7.39227	−	17.8465i	0.274732	−	0.663261i
$725$	0.436106	+	0.180641i	0.0161966	+	0.00670884i
$726$	−0.545895	−	1.31791i	−0.0202601	−	0.0489121i
$727$		−	8.82992i		−	0.327484i	−0.986503	−	0.163742i	$-0.947644\pi$
$727$		−	8.82992i		−	0.327484i	0.986503	−	0.163742i	$-0.0523564\pi$
$728$	0.0776806	−	0.0321763i	0.00287903	−	0.00119253i
$729$	29.4765	+	29.4765i	1.09172	+	1.09172i
$730$	−0.858238			−0.0317648
$731$	−1.75913	+	3.72900i	−0.0650639	+	0.137922i
$732$	−31.6117			−1.16840
$733$	26.2091	+	26.2091i	0.968055	+	0.968055i	0.999505	−	0.0314499i	$-0.0100125\pi$
$733$	26.2091	+	26.2091i	0.968055	+	0.968055i	−0.0314499	+	0.999505i	$0.510012\pi$
$734$	−0.757584	+	0.313801i	−0.0279629	+	0.0115826i
$735$		−	58.3192i		−	2.15113i
$736$	−1.15599	−	2.79081i	−0.0426104	−	0.102871i
$737$	−32.5790	−	13.4947i	−1.20006	−	0.497082i
$738$	−0.0240101	+	0.0579655i	−0.000883824	+	0.00213374i
$739$	−11.3299	+	11.3299i	−0.416779	+	0.416779i	−0.884092	−	0.467313i	$-0.845222\pi$
$739$	−11.3299	+	11.3299i	−0.416779	+	0.416779i	0.467313	+	0.884092i	$0.345222\pi$
$740$	26.1182	−	26.1182i	0.960124	−	0.960124i
$741$	0.354905	−	0.856816i	0.0130377	−	0.0314759i
$742$	1.63798	+	0.678473i	0.0601321	+	0.0249075i
$743$	12.3645	+	29.8506i	0.453610	+	1.09511i	0.970939	+	0.239326i	$0.0769264\pi$
$743$	12.3645	+	29.8506i	0.453610	+	1.09511i	−0.517329	+	0.855787i	$0.673074\pi$
$744$		−	5.13983i		−	0.188435i
$745$	−19.6939	+	8.15746i	−0.721527	+	0.298866i
$746$	0.871888	+	0.871888i	0.0319221	+	0.0319221i
$747$	−50.7459			−1.85670
$748$	0.943987	−	19.6148i	0.0345156	−	0.717187i
$749$	66.1708			2.41783
$750$	−2.15936	−	2.15936i	−0.0788485	−	0.0788485i
$751$	16.3709	−	6.78107i	0.597384	−	0.247445i	−0.0634396	−	0.997986i	$-0.520207\pi$
$751$	16.3709	−	6.78107i	0.597384	−	0.247445i	0.660824	+	0.750541i	$0.270207\pi$
$752$			19.7895i			0.721650i
$753$	29.7162	+	71.7413i	1.08292	+	2.61440i
$754$	−0.0209327	−	0.00867060i	−0.000762323	−	0.000315764i
$755$	7.87537	−	19.0128i	0.286614	−	0.691947i
$756$	35.2317	−	35.2317i	1.28136	−	1.28136i
$757$	32.7225	−	32.7225i	1.18932	−	1.18932i	0.212064	−	0.977256i	$-0.431981\pi$
$757$	32.7225	−	32.7225i	1.18932	−	1.18932i	0.977256	−	0.212064i	$-0.0680186\pi$
$758$	−0.914071	+	2.20676i	−0.0332006	+	0.0801532i
$759$	16.9240	+	7.01013i	0.614301	+	0.254452i
$760$	−1.87239	−	4.52035i	−0.0679188	−	0.163971i
$761$			30.2330i			1.09594i	0.836497	+	0.547972i	$0.184600\pi$
$761$			30.2330i			1.09594i	−0.836497	+	0.547972i	$0.815400\pi$
$762$	3.64311	−	1.50902i	0.131976	−	0.0546662i
$763$	27.9924	+	27.9924i	1.01339	+	1.01339i
$764$	−27.0690			−0.979323
$765$	−47.1170	−	2.26757i	−1.70352	−	0.0819841i
$766$	−1.77346			−0.0640776
$767$	−0.359625	−	0.359625i	−0.0129853	−	0.0129853i
$768$	−40.3842	+	16.7277i	−1.45724	+	0.603608i
$769$			21.4812i			0.774633i	0.921947	+	0.387317i	$0.126598\pi$
$769$			21.4812i			0.774633i	−0.921947	+	0.387317i	$0.873402\pi$
$770$	0.770913	+	1.86115i	0.0277818	+	0.0670711i
$771$	53.5491	+	22.1808i	1.92852	+	0.798821i
$772$	−8.17781	+	19.7430i	−0.294326	+	0.710565i
$773$	−15.1627	+	15.1627i	−0.545365	+	0.545365i	−0.925097	−	0.379731i	$-0.876016\pi$
$773$	−15.1627	+	15.1627i	−0.545365	+	0.545365i	0.379731	+	0.925097i	$0.376016\pi$
$774$	0.345821	−	0.345821i	0.0124303	−	0.0124303i
$775$	0.198697	−	0.479698i	0.00713742	−	0.0172313i
$776$	−0.979917	−	0.405895i	−0.0351770	−	0.0145708i
$777$	−36.9646	−	89.2404i	−1.32610	−	3.20148i
$778$		−	2.72532i		−	0.0977073i
$779$	−0.694962	+	0.287863i	−0.0248996	+	0.0103138i
$780$	−0.492475	−	0.492475i	−0.0176335	−	0.0176335i
$781$	−13.4892			−0.482680
$782$	0.701960	+	0.772942i	0.0251021	+	0.0276403i
$783$	−26.9131			−0.961797
$784$	25.7400	+	25.7400i	0.919285	+	0.919285i
$785$	−24.9464	+	10.3332i	−0.890376	+	0.368806i
$786$		−	4.13937i		−	0.147646i
$787$	−18.0856	−	43.6624i	−0.644681	−	1.55640i	−0.820296	−	0.571939i	$-0.806191\pi$
$787$	−18.0856	−	43.6624i	−0.644681	−	1.55640i	0.175615	−	0.984459i	$-0.443809\pi$
$788$	−15.0750	−	6.24426i	−0.537024	−	0.222443i
$789$	5.63743	−	13.6100i	0.200698	−	0.484527i
$790$	−1.38203	+	1.38203i	−0.0491705	+	0.0491705i
$791$	19.3951	−	19.3951i	0.689610	−	0.689610i
$792$	−1.78678	+	4.31367i	−0.0634904	+	0.153279i
$793$	0.283860	+	0.117579i	0.0100802	+	0.00417534i
$794$	1.37001	+	3.30750i	0.0486199	+	0.117379i
$795$		−	29.4374i		−	1.04404i
$796$	−18.9988	+	7.86956i	−0.673395	+	0.278929i
$797$	−24.5339	−	24.5339i	−0.869036	−	0.869036i	0.123330	−	0.992366i	$-0.460643\pi$
$797$	−24.5339	−	24.5339i	−0.869036	−	0.869036i	−0.992366	+	0.123330i	$0.960643\pi$
$798$	−6.38324			−0.225964
$799$	−6.98474	−	19.4598i	−0.247102	−	0.688438i
$800$	0.122885			0.00434463
$801$	58.8674	+	58.8674i	2.07998	+	2.07998i
$802$	2.87689	−	1.19165i	0.101587	−	0.0420785i
$803$			9.81914i			0.346510i
$804$	−32.1118	−	77.5249i	−1.13250	−	2.73409i
$805$	22.0449	+	9.13132i	0.776982	+	0.321837i
$806$	−0.00953728	+	0.0230250i	−0.000335936	+	0.000811022i
$807$	−53.1824	+	53.1824i	−1.87211	+	1.87211i
$808$	−4.51284	+	4.51284i	−0.158761	+	0.158761i
$809$	12.2017	−	29.4576i	0.428990	−	1.03567i	−0.550619	−	0.834757i	$-0.685608\pi$
$809$	12.2017	−	29.4576i	0.428990	−	1.03567i	0.979608	−	0.200916i	$-0.0643918\pi$
$810$	0.433085	+	0.179390i	0.0152171	+	0.00630311i
$811$	12.3384	+	29.7875i	0.433259	+	1.04598i	0.978230	+	0.207525i	$0.0665408\pi$
$811$	12.3384	+	29.7875i	0.433259	+	1.04598i	−0.544971	+	0.838455i	$0.683459\pi$
$812$		−	34.7410i		−	1.21917i
$813$	80.9476	−	33.5296i	2.83895	−	1.17593i
$814$	1.34136	+	1.34136i	0.0470147	+	0.0470147i
$815$	20.9748			0.734714
$816$	34.4368	−	31.2744i	1.20553	−	1.09482i
$817$	5.86351			0.205138
$818$	1.65869	+	1.65869i	0.0579949	+	0.0579949i
$819$	−1.06505	+	0.441157i	−0.0372157	+	0.0154153i
$820$			0.564902i			0.0197272i
$821$	4.81939	+	11.6350i	0.168198	+	0.406065i	0.985393	−	0.170296i	$-0.0544723\pi$
$821$	4.81939	+	11.6350i	0.168198	+	0.406065i	−0.817195	+	0.576361i	$0.804472\pi$
$822$	2.62708	+	1.08817i	0.0916298	+	0.0379543i
$823$	9.08595	−	21.9354i	0.316716	−	0.764621i	−0.682708	−	0.730691i	$-0.739198\pi$
$823$	9.08595	−	21.9354i	0.316716	−	0.764621i	0.999424	−	0.0339296i	$-0.0108022\pi$
$824$	3.31087	−	3.31087i	0.115340	−	0.115340i
$825$	−0.526932	+	0.526932i	−0.0183454	+	0.0183454i
$826$	−1.33959	+	3.23407i	−0.0466104	+	0.112528i
$827$	29.2536	+	12.1172i	1.01725	+	0.421358i	0.828094	−	0.560589i	$-0.189425\pi$
$827$	29.2536	+	12.1172i	1.01725	+	0.421358i	0.189154	+	0.981947i	$0.439425\pi$
$828$	10.5583	+	25.4901i	0.366927	+	0.885841i
$829$			14.9390i			0.518852i	0.965763	+	0.259426i	$0.0835334\pi$
$829$			14.9390i			0.518852i	−0.965763	+	0.259426i	$0.916467\pi$
$830$	1.89484	−	0.784867i	0.0657708	−	0.0272431i
$831$	−26.7754	−	26.7754i	−0.928829	−	0.928829i
$832$	0.430775			0.0149344
$833$	−34.3961	−	16.2261i	−1.19175	−	0.562202i
$834$	1.65667			0.0573659
$835$	−6.20818	−	6.20818i	−0.214843	−	0.214843i
$836$	−25.8009	+	10.6871i	−0.892342	+	0.369620i
$837$			29.6033i			1.02324i
$838$	0.372375	+	0.898992i	0.0128635	+	0.0310552i
$839$	−40.3344	−	16.7071i	−1.39250	−	0.576792i	−0.444705	−	0.895677i	$-0.646692\pi$
$839$	−40.3344	−	16.7071i	−1.39250	−	0.576792i	−0.947793	+	0.318885i	$0.896692\pi$
$840$	−3.67716	+	8.87744i	−0.126874	+	0.306301i
$841$	7.23696	−	7.23696i	0.249550	−	0.249550i
$842$	−0.890105	+	0.890105i	−0.0306750	+	0.0306750i
$843$	−14.9032	+	35.9795i	−0.513293	+	1.23920i
$844$	7.98131	+	3.30597i	0.274728	+	0.113796i
$845$	−10.9997	−	26.5556i	−0.378401	−	0.913542i
$846$			2.45242i			0.0843159i
$847$	−19.6407	+	8.13545i	−0.674863	+	0.279537i
$848$	12.9926	+	12.9926i	0.446168	+	0.446168i
$849$	−71.7465			−2.46233
$850$	−0.0399778	+	0.0143493i	−0.00137123	+	0.000492177i
$851$	22.4692			0.770236
$852$	−22.6973	−	22.6973i	−0.777595	−	0.777595i
$853$	39.9752	−	16.5583i	1.36872	−	0.566944i	0.427282	−	0.904118i	$-0.359471\pi$
$853$	39.9752	−	16.5583i	1.36872	−	0.566944i	0.941442	+	0.337174i	$0.109471\pi$
$854$		−	2.11474i		−	0.0723650i
$855$	25.6716	+	61.9767i	0.877950	+	2.11956i
$856$	−5.72668	−	2.37207i	−0.195734	−	0.0810756i
$857$	16.0139	−	38.6609i	0.547024	−	1.32063i	−0.372659	−	0.927969i	$-0.621554\pi$
$857$	16.0139	−	38.6609i	0.547024	−	1.32063i	0.919682	−	0.392663i	$-0.128446\pi$
$858$	0.0252922	−	0.0252922i	0.000863462	−	0.000863462i
$859$	9.57905	−	9.57905i	0.326833	−	0.326833i	−0.524548	−	0.851381i	$-0.675766\pi$
$859$	9.57905	−	9.57905i	0.326833	−	0.326833i	0.851381	+	0.524548i	$0.175766\pi$
$860$	1.68510	−	4.06818i	0.0574613	−	0.138724i
$861$	1.36482	+	0.565328i	0.0465131	+	0.0192663i
$862$	−0.880683	−	2.12616i	−0.0299962	−	0.0724172i
$863$		−	11.1428i		−	0.379306i	−0.981851	−	0.189653i	$-0.939264\pi$
$863$		−	11.1428i		−	0.379306i	0.981851	−	0.189653i	$-0.0607363\pi$
$864$	−6.47292	+	2.68117i	−0.220213	+	0.0912153i
$865$	4.37032	+	4.37032i	0.148595	+	0.148595i
$866$	−0.943658			−0.0320668
$867$	−22.8247	+	42.9078i	−0.775166	+	1.45722i
$868$	−38.2136			−1.29705
$869$	15.8119	+	15.8119i	0.536382	+	0.536382i
$870$	2.39221	−	0.990888i	0.0811037	−	0.0335942i
$871$			0.815578i			0.0276348i
$872$	−1.41911	−	3.42604i	−0.0480571	−	0.116020i
$873$	13.4352	+	5.56506i	0.454714	+	0.188349i
$874$	0.568229	−	1.37183i	0.0192206	−	0.0464027i
$875$	−32.1808	+	32.1808i	−1.08791	+	1.08791i
$876$	−16.5220	+	16.5220i	−0.558225	+	0.558225i
$877$	16.2230	−	39.1658i	0.547811	−	1.32253i	−0.371292	−	0.928516i	$-0.621085\pi$
$877$	16.2230	−	39.1658i	0.547811	−	1.32253i	0.919103	−	0.394017i	$-0.128915\pi$
$878$	−2.99171	−	1.23921i	−0.100965	−	0.0418213i
$879$	−25.4674	−	61.4837i	−0.858993	−	2.07379i
$880$			20.8778i			0.703789i
$881$	−26.3508	+	10.9149i	−0.887781	+	0.367731i	−0.779509	−	0.626391i	$-0.784532\pi$
$881$	−26.3508	+	10.9149i	−0.887781	+	0.367731i	−0.108271	+	0.994121i	$0.534532\pi$
$882$	3.18983	+	3.18983i	0.107407	+	0.107407i
$883$	−34.2528			−1.15270			−0.576350	−	0.817203i	$-0.695523\pi$
$883$	−34.2528			−1.15270			−0.576350	+	0.817203i	$0.695523\pi$
$884$	−0.427478	+	0.153436i	−0.0143777	+	0.00516060i
$885$	58.1219			1.95375
$886$	1.95610	+	1.95610i	0.0657165	+	0.0657165i
$887$	19.8205	−	8.20992i	0.665507	−	0.275662i	−0.0242468	−	0.999706i	$-0.507719\pi$
$887$	19.8205	−	8.20992i	0.665507	−	0.275662i	0.689754	+	0.724044i	$0.257719\pi$
$888$			9.04831i			0.303641i
$889$	−22.4889	−	54.2931i	−0.754254	−	1.82093i
$890$	−3.10857	−	1.28761i	−0.104200	−	0.0431609i
$891$	2.05240	−	4.95494i	0.0687582	−	0.165997i
$892$	−28.2372	+	28.2372i	−0.945453	+	0.945453i
$893$	−20.7908	+	20.7908i	−0.695737	+	0.695737i
$894$	0.996920	−	2.40678i	0.0333420	−	0.0804947i
$895$	20.5360	+	8.50630i	0.686444	+	0.284334i
$896$	−4.61118	−	11.1324i	−0.154049	−	0.371907i
$897$		−	0.423672i		−	0.0141460i
$898$	−2.35747	+	0.976497i	−0.0786699	+	0.0325861i
$899$	14.5955	+	14.5955i	0.486786	+	0.486786i
$900$	−1.12238			−0.0374125
$901$	−17.3619	−	8.19035i	−0.578408	−	0.272860i
$902$	−0.0290119			−0.000965989
$903$	−8.14250	−	8.14250i	−0.270966	−	0.270966i
$904$	−2.37380	+	0.983259i	−0.0789513	+	0.0327027i
$905$		−	21.4562i		−	0.713230i
$906$	0.962446	+	2.32355i	0.0319751	+	0.0771948i
$907$	−22.8979	−	9.48460i	−0.760311	−	0.314931i	−0.0313700	−	0.999508i	$-0.509987\pi$
$907$	−22.8979	−	9.48460i	−0.760311	−	0.314931i	−0.728941	+	0.684577i	$0.759987\pi$
$908$	−0.385195	+	0.929942i	−0.0127831	+	0.0308612i
$909$	61.8737	−	61.8737i	2.05222	−	2.05222i
$910$	0.0329453	−	0.0329453i	0.00109213	−	0.00109213i
$911$	−0.192766	+	0.465377i	−0.00638661	+	0.0154186i	−0.927041	−	0.374961i	$-0.877656\pi$
$911$	−0.192766	+	0.465377i	−0.00638661	+	0.0154186i	0.920654	+	0.390379i	$0.127656\pi$
$912$	−61.1188	−	25.3162i	−2.02385	−	0.838304i
$913$	−8.97970	−	21.6789i	−0.297185	−	0.717467i
$914$			1.70370i			0.0563533i
$915$	−32.4399	+	13.4370i	−1.07243	+	0.444215i
$916$	−23.8890	−	23.8890i	−0.789315	−	0.789315i
$917$	−61.6888			−2.03714
$918$	1.79274	−	1.62811i	0.0591692	−	0.0537355i
$919$	2.55631			0.0843248			0.0421624	−	0.999111i	$-0.486575\pi$
$919$	2.55631			0.0843248			0.0421624	+	0.999111i	$0.486575\pi$
$920$	−1.58052	−	1.58052i	−0.0521082	−	0.0521082i
$921$	30.7859	−	12.7520i	1.01443	−	0.420191i
$922$		−	2.67890i		−	0.0882250i
$923$	0.119390	+	0.288233i	0.00392977	+	0.00948730i
$924$	50.6699	+	20.9881i	1.66692	+	0.690459i
$925$	−0.349793	+	0.844474i	−0.0115011	+	0.0277661i
$926$	0.988733	−	0.988733i	0.0324918	−	0.0324918i
$927$	−45.3940	+	45.3940i	−1.49093	+	1.49093i
$928$	−1.86947	+	4.51329i	−0.0613683	+	0.148156i
$929$	9.17142	+	3.79892i	0.300904	+	0.124639i	0.528027	−	0.849227i	$-0.322932\pi$
$929$	9.17142	+	3.79892i	0.300904	+	0.124639i	−0.227123	+	0.973866i	$0.572932\pi$
$930$	−1.08993	−	2.63133i	−0.0357403	−	0.0862848i
$931$			54.0846i			1.77255i
$932$	−10.2749	+	4.25599i	−0.336564	+	0.139409i
$933$	−53.7661	−	53.7661i	−1.76022	−	1.76022i
$934$	−1.17009			−0.0382866
$935$	−7.36884	−	20.5299i	−0.240987	−	0.671399i
$936$	0.107988			0.00352969
$937$	−35.6785	−	35.6785i	−1.16557	−	1.16557i	−0.983238	−	0.182327i	$-0.941637\pi$
$937$	−35.6785	−	35.6785i	−1.16557	−	1.16557i	−0.182327	−	0.983238i	$-0.558363\pi$
$938$	5.18621	−	2.14820i	0.169336	−	0.0701412i
$939$			54.3112i			1.77238i
$940$	8.44993	+	20.3999i	0.275606	+	0.665372i
$941$	−26.3457	−	10.9127i	−0.858845	−	0.355745i	−0.0905893	−	0.995888i	$-0.528875\pi$
$941$	−26.3457	−	10.9127i	−0.858845	−	0.355745i	−0.768256	+	0.640143i	$0.778875\pi$
$942$	1.26281	−	3.04869i	0.0411446	−	0.0993318i
$943$	−0.242990	+	0.242990i	−0.00791285	+	0.00791285i
$944$	−25.6529	+	25.6529i	−0.834931	+	0.834931i
$945$	21.1789	−	51.1304i	0.688949	−	1.66327i
$946$	0.208931	+	0.0865420i	0.00679293	+	0.00281372i
$947$	−2.54844	−	6.15248i	−0.0828133	−	0.199929i	0.877049	−	0.480401i	$-0.159509\pi$
$947$	−2.54844	−	6.15248i	−0.0828133	−	0.199929i	−0.959862	+	0.280472i	$0.909509\pi$
$948$			53.2111i			1.72822i
$949$	0.209813	−	0.0869073i	0.00681081	−	0.00282113i
$950$	0.0427121	+	0.0427121i	0.00138577	+	0.00138577i
$951$	−76.5630			−2.48273
$952$	4.21273	+	4.63872i	0.136535	+	0.150342i
$953$	21.7354			0.704077			0.352039	−	0.935985i	$-0.385489\pi$
$953$	21.7354			0.704077			0.352039	+	0.935985i	$0.385489\pi$
$954$	1.61011	+	1.61011i	0.0521292	+	0.0521292i
$955$	−27.7782	+	11.5061i	−0.898880	+	0.372328i
$956$			3.08755i			0.0998585i
$957$	−11.3368	−	27.3694i	−0.366466	−	0.884727i
$958$	0.238873	+	0.0989442i	0.00771762	+	0.00319674i
$959$	16.2170	−	39.1512i	0.523673	−	1.26426i
$960$	−34.8106	+	34.8106i	−1.12351	+	1.12351i
$961$	−5.86592	+	5.86592i	−0.189223	+	0.189223i
$962$	0.0167897	−	0.0405340i	0.000541322	−	0.00130687i
$963$	78.5161	+	32.5224i	2.53015	+	1.04802i
$964$	−11.8072	−	28.5050i	−0.380283	−	0.918084i
$965$			23.7363i			0.764098i
$966$	−2.69410	+	1.11593i	−0.0866814	+	0.0359046i
$967$	34.5001	+	34.5001i	1.10945	+	1.10945i	0.993223	+	0.116227i	$0.0370799\pi$
$967$	34.5001	+	34.5001i	1.10945	+	1.10945i	0.116227	+	0.993223i	$0.462920\pi$
$968$	1.99142			0.0640067
$969$	69.0358	+	3.32244i	2.21775	+	0.106732i
$970$	−0.587741			−0.0188712
$971$	−17.3468	−	17.3468i	−0.556687	−	0.556687i	0.371676	−	0.928363i	$-0.378783\pi$
$971$	−17.3468	−	17.3468i	−0.556687	−	0.556687i	−0.928363	+	0.371676i	$0.878783\pi$
$972$	−22.4944	+	9.31750i	−0.721510	+	0.298859i
$973$		−	24.6893i		−	0.791504i
$974$	1.28375	+	3.09924i	0.0411339	+	0.0993059i
$975$	0.0159231	+	0.00659557i	0.000509948	+	0.000211227i
$976$	8.38717	−	20.2484i	0.268467	−	0.648136i
$977$	−3.05063	+	3.05063i	−0.0975982	+	0.0975982i	−0.754220	−	0.656622i	$-0.771985\pi$
$977$	−3.05063	+	3.05063i	−0.0975982	+	0.0975982i	0.656622	+	0.754220i	$0.271985\pi$
$978$	−1.81254	+	1.81254i	−0.0579586	+	0.0579586i
$979$	−14.7316	+	35.5653i	−0.470825	+	1.13667i
$980$	37.5246	+	15.5432i	1.19868	+	0.496510i
$981$	19.4568	+	46.9730i	0.621209	+	1.49973i
$982$		−	2.08014i		−	0.0663798i
$983$	−9.58136	+	3.96873i	−0.305598	+	0.126583i	−0.530212	−	0.847865i	$-0.677888\pi$
$983$	−9.58136	+	3.96873i	−0.305598	+	0.126583i	0.224614	+	0.974448i	$0.427888\pi$
$984$	−0.0978515	−	0.0978515i	−0.00311939	−	0.00311939i
$985$	−18.1241			−0.577482
$986$	0.0811698	−	1.68660i	0.00258497	−	0.0537122i
$987$	57.7432			1.83799
$988$	0.456717	+	0.456717i	0.0145301	+	0.0145301i
$989$	2.47475	−	1.02507i	0.0786924	−	0.0325954i
$990$			2.58728i			0.0822291i
$991$	−4.86012	−	11.7334i	−0.154387	−	0.372723i	0.827695	−	0.561178i	$-0.189652\pi$
$991$	−4.86012	−	11.7334i	−0.154387	−	0.372723i	−0.982082	+	0.188455i	$0.939652\pi$
$992$	4.96443	+	2.05633i	0.157621	+	0.0652887i
$993$	0.464579	−	1.12159i	0.0147430	−	0.0355927i
$994$	1.51839	−	1.51839i	0.0481603	−	0.0481603i
$995$	−16.1514	+	16.1514i	−0.512035	+	0.512035i
$996$	21.3681	−	51.5870i	0.677073	−	1.63460i
$997$	−40.1391	−	16.6262i	−1.27122	−	0.526556i	−0.357884	−	0.933766i	$-0.616502\pi$
$997$	−40.1391	−	16.6262i	−1.27122	−	0.526556i	−0.913334	+	0.407211i	$0.866502\pi$
$998$	1.45059	+	3.50202i	0.0459175	+	0.110855i
$999$		−	52.1145i		−	1.64883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.87.16	✓	128
17.9	even	8	inner	731.2.m.c.689.16	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.16	✓	128	1.1	even	1	trivial
731.2.m.c.689.16	yes	128	17.9	even	8	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0668491 - 0.0668491i) q^{2} +(-2.64125 + 1.09404i) q^{3} -1.99106i q^{4} +(-0.846330 - 2.04322i) q^{5} +(0.249701 + 0.103430i) q^{6} +(1.54141 - 3.72129i) q^{7} +(-0.266799 + 0.266799i) q^{8} +(3.65797 - 3.65797i) q^{9} +O(q^{10})\)	\(q+(-0.0668491 - 0.0668491i) q^{2} +(-2.64125 + 1.09404i) q^{3} -1.99106i q^{4} +(-0.846330 - 2.04322i) q^{5} +(0.249701 + 0.103430i) q^{6} +(1.54141 - 3.72129i) q^{7} +(-0.266799 + 0.266799i) q^{8} +(3.65797 - 3.65797i) q^{9} +(-0.0800112 + 0.193164i) q^{10} +(2.21000 + 0.915411i) q^{11} +(2.17831 + 5.25890i) q^{12} -0.0553248i q^{13} +(-0.351807 + 0.145723i) q^{14} +(4.47075 + 4.47075i) q^{15} -3.94645 q^{16} +(3.88070 - 1.39291i) q^{17} -0.489065 q^{18} +(-4.14613 - 4.14613i) q^{19} +(-4.06818 + 1.68510i) q^{20} +11.5152i q^{21} +(-0.0865420 - 0.208931i) q^{22} +(-2.47475 - 1.02507i) q^{23} +(0.412794 - 0.996574i) q^{24} +(0.0770518 - 0.0770518i) q^{25} +(-0.00369841 + 0.00369841i) q^{26} +(-2.37752 + 5.73985i) q^{27} +(-7.40932 - 3.06904i) q^{28} +(1.65775 + 4.00216i) q^{29} -0.597731i q^{30} +(4.40220 - 1.82345i) q^{31} +(0.797415 + 0.797415i) q^{32} -6.83867 q^{33} +(-0.352536 - 0.166307i) q^{34} -8.90796 q^{35} +(-7.28325 - 7.28325i) q^{36} +(-7.74976 + 3.21006i) q^{37} +0.554330i q^{38} +(0.0605277 + 0.146127i) q^{39} +(0.770930 + 0.319330i) q^{40} +(0.0490939 - 0.118523i) q^{41} +(0.769784 - 0.769784i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(1.82264 - 4.40024i) q^{44} +(-10.5699 - 4.37820i) q^{45} +(0.0969094 + 0.233960i) q^{46} -5.01451i q^{47} +(10.4236 - 4.31759i) q^{48} +(-6.52231 - 6.52231i) q^{49} -0.0103017 q^{50} +(-8.72601 + 7.92467i) q^{51} -0.110155 q^{52} +(-3.29222 - 3.29222i) q^{53} +(0.542640 - 0.224769i) q^{54} -5.29026i q^{55} +(0.581590 + 1.40408i) q^{56} +(15.4870 + 6.41493i) q^{57} +(0.156722 - 0.378360i) q^{58} +(6.50024 - 6.50024i) q^{59} +(8.90154 - 8.90154i) q^{60} +(-2.12524 + 5.13079i) q^{61} +(-0.416179 - 0.172387i) q^{62} +(-7.97394 - 19.2508i) q^{63} +7.78630i q^{64} +(-0.113041 + 0.0468230i) q^{65} +(0.457159 + 0.457159i) q^{66} -14.7416 q^{67} +(-2.77336 - 7.72671i) q^{68} +7.65791 q^{69} +(0.595490 + 0.595490i) q^{70} +(-5.20984 + 2.15798i) q^{71} +1.95189i q^{72} +(1.57086 + 3.79238i) q^{73} +(0.732655 + 0.303476i) q^{74} +(-0.119215 + 0.287812i) q^{75} +(-8.25520 + 8.25520i) q^{76} +(6.81302 - 6.81302i) q^{77} +(0.00572223 - 0.0138147i) q^{78} +(8.63650 + 3.57735i) q^{79} +(3.34000 + 8.06348i) q^{80} -2.24206i q^{81} +(-0.0112051 + 0.00464129i) q^{82} +(-6.93634 - 6.93634i) q^{83} +22.9276 q^{84} +(-6.13037 - 6.75027i) q^{85} +0.0945390 q^{86} +(-8.75707 - 8.75707i) q^{87} +(-0.833856 + 0.345395i) q^{88} +16.0929i q^{89} +(0.413910 + 0.999268i) q^{90} +(-0.205879 - 0.0852781i) q^{91} +(-2.04099 + 4.92737i) q^{92} +(-9.63240 + 9.63240i) q^{93} +(-0.335216 + 0.335216i) q^{94} +(-4.96247 + 11.9805i) q^{95} +(-2.97858 - 1.23377i) q^{96} +(1.07576 + 2.59711i) q^{97} +0.872021i q^{98} +(11.4327 - 4.73556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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