LMFDB - Embedded newform 966.2.h.b.827.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(827,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("966.827");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			827.18
Character	$\chi$	$=$	966.827
Dual form			966.2.h.b.827.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.0866531 + 1.72988i) q^{3} -1.00000 q^{4} -0.713996 q^{5} +(-1.72988 - 0.0866531i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-2.98498 - 0.299799i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.0866531 + 1.72988i) q^{3} -1.00000 q^{4} -0.713996 q^{5} +(-1.72988 - 0.0866531i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-2.98498 - 0.299799i) q^{9} -0.713996i q^{10} -2.60291 q^{11} +(0.0866531 - 1.72988i) q^{12} -5.59277 q^{13} -1.00000 q^{14} +(0.0618700 - 1.23513i) q^{15} +1.00000 q^{16} +6.17695 q^{17} +(0.299799 - 2.98498i) q^{18} -3.14772i q^{19} +0.713996 q^{20} +(-1.72988 - 0.0866531i) q^{21} -2.60291i q^{22} +(4.47449 - 1.72597i) q^{23} +(1.72988 + 0.0866531i) q^{24} -4.49021 q^{25} -5.59277i q^{26} +(0.777275 - 5.13769i) q^{27} -1.00000i q^{28} -0.797080i q^{29} +(1.23513 + 0.0618700i) q^{30} -7.70109 q^{31} +1.00000i q^{32} +(0.225550 - 4.50272i) q^{33} +6.17695i q^{34} -0.713996i q^{35} +(2.98498 + 0.299799i) q^{36} -7.21190i q^{37} +3.14772 q^{38} +(0.484630 - 9.67482i) q^{39} +0.713996i q^{40} +3.84484i q^{41} +(0.0866531 - 1.72988i) q^{42} +4.89017i q^{43} +2.60291 q^{44} +(2.13127 + 0.214055i) q^{45} +(1.72597 + 4.47449i) q^{46} +4.60889i q^{47} +(-0.0866531 + 1.72988i) q^{48} -1.00000 q^{49} -4.49021i q^{50} +(-0.535252 + 10.6854i) q^{51} +5.59277 q^{52} -13.4827 q^{53} +(5.13769 + 0.777275i) q^{54} +1.85847 q^{55} +1.00000 q^{56} +(5.44518 + 0.272760i) q^{57} +0.797080 q^{58} -11.2753i q^{59} +(-0.0618700 + 1.23513i) q^{60} +1.01133i q^{61} -7.70109i q^{62} +(0.299799 - 2.98498i) q^{63} -1.00000 q^{64} +3.99321 q^{65} +(4.50272 + 0.225550i) q^{66} -13.9915i q^{67} -6.17695 q^{68} +(2.59799 + 7.88990i) q^{69} +0.713996 q^{70} +4.29100i q^{71} +(-0.299799 + 2.98498i) q^{72} +7.05414 q^{73} +7.21190 q^{74} +(0.389091 - 7.76753i) q^{75} +3.14772i q^{76} -2.60291i q^{77} +(9.67482 + 0.484630i) q^{78} -5.48457i q^{79} -0.713996 q^{80} +(8.82024 + 1.78979i) q^{81} -3.84484 q^{82} +10.1096 q^{83} +(1.72988 + 0.0866531i) q^{84} -4.41032 q^{85} -4.89017 q^{86} +(1.37885 + 0.0690694i) q^{87} +2.60291i q^{88} -8.77912 q^{89} +(-0.214055 + 2.13127i) q^{90} -5.59277i q^{91} +(-4.47449 + 1.72597i) q^{92} +(0.667323 - 13.3220i) q^{93} -4.60889 q^{94} +2.24746i q^{95} +(-1.72988 - 0.0866531i) q^{96} +14.9697i q^{97} -1.00000i q^{98} +(7.76963 + 0.780350i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9	$ 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 24 q^{14} + 4 q^{15} + 24 q^{16} - 32 q^{17} + 4 q^{18} - 4 q^{20} + 8 q^{23} - 12 q^{25} + 16 q^{27} + 4 q^{30} - 16 q^{31} - 20 q^{33} + 4 q^{36} - 8 q^{39} - 4 q^{42} - 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} - 24 q^{51} - 8 q^{52} - 24 q^{53} - 12 q^{54} + 16 q^{55} + 24 q^{56} - 4 q^{57} + 4 q^{58} - 4 q^{60} + 4 q^{63} - 24 q^{64} + 12 q^{66} + 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} + 16 q^{74} + 48 q^{75} + 12 q^{78} + 4 q^{80} - 8 q^{81} - 8 q^{82} - 16 q^{83} - 16 q^{85} - 16 q^{86} + 20 q^{87} - 24 q^{89} + 28 q^{90} - 8 q^{92} + 16 q^{93} + 8 q^{94} + 48 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 24 * q^14 + 4 * q^15 + 24 * q^16 - 32 * q^17 + 4 * q^18 - 4 * q^20 + 8 * q^23 - 12 * q^25 + 16 * q^27 + 4 * q^30 - 16 * q^31 - 20 * q^33 + 4 * q^36 - 8 * q^39 - 4 * q^42 - 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 - 24 * q^51 - 8 * q^52 - 24 * q^53 - 12 * q^54 + 16 * q^55 + 24 * q^56 - 4 * q^57 + 4 * q^58 - 4 * q^60 + 4 * q^63 - 24 * q^64 + 12 * q^66 + 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 + 16 * q^74 + 48 * q^75 + 12 * q^78 + 4 * q^80 - 8 * q^81 - 8 * q^82 - 16 * q^83 - 16 * q^85 - 16 * q^86 + 20 * q^87 - 24 * q^89 + 28 * q^90 - 8 * q^92 + 16 * q^93 + 8 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.0866531	+	1.72988i	−0.0500292	+	0.998748i
$3$	−0.0866531	+	1.72988i	−0.0500292	+	0.998748i
$4$	−1.00000			−0.500000
$5$	−0.713996			−0.319309			−0.159654	−	0.987173i	$-0.551038\pi$
$5$	−0.713996			−0.319309			−0.159654	+	0.987173i	$0.551038\pi$
$6$	−1.72988	−	0.0866531i	−0.706221	−	0.0353760i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	1.00000i		−	0.353553i
$9$	−2.98498	−	0.299799i	−0.994994	−	0.0999331i
$10$		−	0.713996i		−	0.225785i
$11$	−2.60291			−0.784806			−0.392403	−	0.919793i	$-0.628356\pi$
$11$	−2.60291			−0.784806			−0.392403	+	0.919793i	$0.628356\pi$
$12$	0.0866531	−	1.72988i	0.0250146	−	0.499374i
$13$	−5.59277			−1.55115			−0.775577	−	0.631253i	$-0.782541\pi$
$13$	−5.59277			−1.55115			−0.775577	+	0.631253i	$0.782541\pi$
$14$	−1.00000			−0.267261
$15$	0.0618700	−	1.23513i	0.0159748	−	0.318909i
$16$	1.00000			0.250000
$17$	6.17695			1.49813			0.749065	−	0.662496i	$-0.230503\pi$
$17$	6.17695			1.49813			0.749065	+	0.662496i	$0.230503\pi$
$18$	0.299799	−	2.98498i	0.0706633	−	0.703567i
$19$		−	3.14772i		−	0.722137i	−0.932539	−	0.361068i	$-0.882412\pi$
$19$		−	3.14772i		−	0.722137i	0.932539	−	0.361068i	$-0.117588\pi$
$20$	0.713996			0.159654
$21$	−1.72988	−	0.0866531i	−0.377491	−	0.0189093i
$22$		−	2.60291i		−	0.554942i
$23$	4.47449	−	1.72597i	0.932995	−	0.359889i
$23$	4.47449	−	1.72597i	0.932995	−	0.359889i
$24$	1.72988	+	0.0866531i	0.353111	+	0.0176880i
$25$	−4.49021			−0.898042
$26$		−	5.59277i		−	1.09683i
$27$	0.777275	−	5.13769i	0.149587	−	0.988749i
$28$		−	1.00000i		−	0.188982i
$29$		−	0.797080i		−	0.148014i	−0.997258	−	0.0740070i	$-0.976421\pi$
$29$		−	0.797080i		−	0.148014i	0.997258	−	0.0740070i	$-0.0235787\pi$
$30$	1.23513	+	0.0618700i	0.225503	+	0.0112959i
$31$	−7.70109			−1.38316			−0.691578	−	0.722302i	$-0.743084\pi$
$31$	−7.70109			−1.38316			−0.691578	+	0.722302i	$0.743084\pi$
$32$			1.00000i			0.176777i
$33$	0.225550	−	4.50272i	0.0392632	−	0.783823i
$34$			6.17695i			1.05934i
$35$		−	0.713996i		−	0.120687i
$36$	2.98498	+	0.299799i	0.497497	+	0.0499665i
$37$		−	7.21190i		−	1.18563i	−0.805339	−	0.592814i	$-0.798017\pi$
$37$		−	7.21190i		−	1.18563i	0.805339	−	0.592814i	$-0.201983\pi$
$38$	3.14772			0.510628
$39$	0.484630	−	9.67482i	0.0776030	−	1.54921i
$40$			0.713996i			0.112893i
$41$			3.84484i			0.600463i	0.953866	+	0.300232i	$0.0970640\pi$
$41$			3.84484i			0.600463i	−0.953866	+	0.300232i	$0.902936\pi$
$42$	0.0866531	−	1.72988i	0.0133709	−	0.266927i
$43$			4.89017i			0.745744i	0.927883	+	0.372872i	$0.121627\pi$
$43$			4.89017i			0.745744i	−0.927883	+	0.372872i	$0.878373\pi$
$44$	2.60291			0.392403
$45$	2.13127	+	0.214055i	0.317710	+	0.0319095i
$46$	1.72597	+	4.47449i	0.254480	+	0.659727i
$47$			4.60889i			0.672275i	0.941813	+	0.336138i	$0.109121\pi$
$47$			4.60889i			0.672275i	−0.941813	+	0.336138i	$0.890879\pi$
$48$	−0.0866531	+	1.72988i	−0.0125073	+	0.249687i
$49$	−1.00000			−0.142857
$50$		−	4.49021i		−	0.635012i
$51$	−0.535252	+	10.6854i	−0.0749502	+	1.49625i
$52$	5.59277			0.775577
$53$	−13.4827			−1.85200			−0.925998	−	0.377529i	$-0.876774\pi$
$53$	−13.4827			−1.85200			−0.925998	+	0.377529i	$0.876774\pi$
$54$	5.13769	+	0.777275i	0.699151	+	0.105774i
$55$	1.85847			0.250595
$56$	1.00000			0.133631
$57$	5.44518	+	0.272760i	0.721232	+	0.0361279i
$58$	0.797080			0.104662
$59$		−	11.2753i		−	1.46791i	−0.679196	−	0.733957i	$-0.737671\pi$
$59$		−	11.2753i		−	1.46791i	0.679196	−	0.733957i	$-0.262329\pi$
$60$	−0.0618700	+	1.23513i	−0.00798738	+	0.159454i
$61$			1.01133i			0.129487i	0.997902	+	0.0647436i	$0.0206229\pi$
$61$			1.01133i			0.129487i	−0.997902	+	0.0647436i	$0.979377\pi$
$62$		−	7.70109i		−	0.978039i
$63$	0.299799	−	2.98498i	0.0377711	−	0.376072i
$64$	−1.00000			−0.125000
$65$	3.99321			0.495297
$66$	4.50272	+	0.225550i	0.554247	+	0.0277633i
$67$		−	13.9915i		−	1.70933i	−0.519176	−	0.854667i	$-0.673761\pi$
$67$		−	13.9915i		−	1.70933i	0.519176	−	0.854667i	$-0.326239\pi$
$68$	−6.17695			−0.749065
$69$	2.59799	+	7.88990i	0.312761	+	0.949832i
$70$	0.713996			0.0853388
$71$			4.29100i			0.509247i	0.967040	+	0.254624i	$0.0819516\pi$
$71$			4.29100i			0.509247i	−0.967040	+	0.254624i	$0.918048\pi$
$72$	−0.299799	+	2.98498i	−0.0353317	+	0.351784i
$73$	7.05414			0.825625			0.412813	−	0.910816i	$-0.364546\pi$
$73$	7.05414			0.825625			0.412813	+	0.910816i	$0.364546\pi$
$74$	7.21190			0.838366
$75$	0.389091	−	7.76753i	0.0449283	−	0.896917i
$76$			3.14772i			0.361068i
$77$		−	2.60291i		−	0.296629i
$78$	9.67482	+	0.484630i	1.09546	+	0.0548736i
$79$		−	5.48457i		−	0.617062i	−0.951214	−	0.308531i	$-0.900163\pi$
$79$		−	5.48457i		−	0.617062i	0.951214	−	0.308531i	$-0.0998374\pi$
$80$	−0.713996			−0.0798272
$81$	8.82024	+	1.78979i	0.980027	+	0.198866i
$82$	−3.84484			−0.424592
$83$	10.1096			1.10967			0.554835	−	0.831960i	$-0.312781\pi$
$83$	10.1096			1.10967			0.554835	+	0.831960i	$0.312781\pi$
$84$	1.72988	+	0.0866531i	0.188746	+	0.00945463i
$85$	−4.41032			−0.478366
$86$	−4.89017			−0.527321
$87$	1.37885	+	0.0690694i	0.147829	+	0.00740502i
$88$			2.60291i			0.277471i
$89$	−8.77912			−0.930585			−0.465292	−	0.885157i	$-0.654051\pi$
$89$	−8.77912			−0.930585			−0.465292	+	0.885157i	$0.654051\pi$
$90$	−0.214055	+	2.13127i	−0.0225634	+	0.224655i
$91$		−	5.59277i		−	0.586281i
$92$	−4.47449	+	1.72597i	−0.466498	+	0.179944i
$93$	0.667323	−	13.3220i	0.0691982	−	1.38142i
$94$	−4.60889			−0.475370
$95$			2.24746i			0.230585i
$96$	−1.72988	−	0.0866531i	−0.176555	−	0.00884399i
$97$			14.9697i			1.51994i	0.649958	+	0.759970i	$0.274786\pi$
$97$			14.9697i			1.51994i	−0.649958	+	0.759970i	$0.725214\pi$
$98$		−	1.00000i		−	0.101015i
$99$	7.76963	+	0.780350i	0.780878	+	0.0784281i
$100$	4.49021			0.449021
$101$			14.4767i			1.44049i	0.693721	+	0.720244i	$0.255970\pi$
$101$			14.4767i			1.44049i	−0.693721	+	0.720244i	$0.744030\pi$
$102$	−10.6854	−	0.535252i	−1.05801	−	0.0529978i
$103$		−	5.40195i		−	0.532270i	−0.963936	−	0.266135i	$-0.914253\pi$
$103$		−	5.40195i		−	0.532270i	0.963936	−	0.266135i	$-0.0857467\pi$
$104$			5.59277i			0.548416i
$105$	1.23513	+	0.0618700i	0.120536	+	0.00603789i
$106$		−	13.4827i		−	1.30956i
$107$	−19.8819			−1.92206			−0.961028	−	0.276449i	$-0.910842\pi$
$107$	−19.8819			−1.92206			−0.961028	+	0.276449i	$0.910842\pi$
$108$	−0.777275	+	5.13769i	−0.0747933	+	0.494374i
$109$			16.2449i			1.55598i	0.628277	+	0.777990i	$0.283761\pi$
$109$			16.2449i			1.55598i	−0.628277	+	0.777990i	$0.716239\pi$
$110$			1.85847i			0.177198i
$111$	12.4757	+	0.624933i	1.18414	+	0.0593160i
$112$			1.00000i			0.0944911i
$113$	7.61914			0.716748			0.358374	−	0.933578i	$-0.383331\pi$
$113$	7.61914			0.716748			0.358374	+	0.933578i	$0.383331\pi$
$114$	−0.272760	+	5.44518i	−0.0255463	+	0.509988i
$115$	−3.19477	+	1.23233i	−0.297914	+	0.114916i
$116$			0.797080i			0.0740070i
$117$	16.6943	+	1.67671i	1.54339	+	0.155012i
$118$	11.2753			1.03797
$119$			6.17695i			0.566240i
$120$	−1.23513	−	0.0618700i	−0.112751	−	0.00564793i
$121$	−4.22487			−0.384079
$122$	−1.01133			−0.0915612
$123$	−6.65112	−	0.333167i	−0.599711	−	0.0300407i
$124$	7.70109			0.691578
$125$	6.77597			0.606061
$126$	2.98498	+	0.299799i	0.265923	+	0.0267082i
$127$	−16.5077			−1.46482			−0.732409	−	0.680865i	$-0.761604\pi$
$127$	−16.5077			−1.46482			−0.732409	+	0.680865i	$0.761604\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−8.45942	−	0.423749i	−0.744810	−	0.0373090i
$130$			3.99321i			0.350228i
$131$			1.27957i			0.111797i	0.998436	+	0.0558984i	$0.0178023\pi$
$131$			1.27957i			0.111797i	−0.998436	+	0.0558984i	$0.982198\pi$
$132$	−0.225550	+	4.50272i	−0.0196316	+	0.391912i
$133$	3.14772			0.272942
$134$	13.9915			1.20868
$135$	−0.554971	+	3.66829i	−0.0477643	+	0.315716i
$136$		−	6.17695i		−	0.529669i
$137$	−4.95606			−0.423425			−0.211713	−	0.977332i	$-0.567904\pi$
$137$	−4.95606			−0.423425			−0.211713	+	0.977332i	$0.567904\pi$
$138$	−7.88990	+	2.59799i	−0.671633	+	0.221156i
$139$	−15.4459			−1.31010			−0.655050	−	0.755585i	$-0.727353\pi$
$139$	−15.4459			−1.31010			−0.655050	+	0.755585i	$0.727353\pi$
$140$			0.713996i			0.0603437i
$141$	−7.97283	−	0.399374i	−0.671434	−	0.0336334i
$142$	−4.29100			−0.360092
$143$	14.5575			1.21736
$144$	−2.98498	−	0.299799i	−0.248749	−	0.0249833i
$145$			0.569112i			0.0472622i
$146$			7.05414i			0.583805i
$147$	0.0866531	−	1.72988i	0.00714703	−	0.142678i
$148$			7.21190i			0.592814i
$149$	−9.31147			−0.762825			−0.381413	−	0.924405i	$-0.624562\pi$
$149$	−9.31147			−0.762825			−0.381413	+	0.924405i	$0.624562\pi$
$150$	7.76753	+	0.389091i	0.634216	+	0.0317691i
$151$	−3.38946			−0.275830			−0.137915	−	0.990444i	$-0.544040\pi$
$151$	−3.38946			−0.275830			−0.137915	+	0.990444i	$0.544040\pi$
$152$	−3.14772			−0.255314
$153$	−18.4381	−	1.85184i	−1.49063	−	0.149713i
$154$	2.60291			0.209748
$155$	5.49855			0.441654
$156$	−0.484630	+	9.67482i	−0.0388015	+	0.774606i
$157$		−	20.2760i		−	1.61820i	−0.587670	−	0.809101i	$-0.699955\pi$
$157$		−	20.2760i		−	1.61820i	0.587670	−	0.809101i	$-0.300045\pi$
$158$	5.48457			0.436329
$159$	1.16832	−	23.3235i	0.0926538	−	1.84968i
$160$		−	0.713996i		−	0.0564463i
$161$	1.72597	+	4.47449i	0.136025	+	0.352639i
$162$	−1.78979	+	8.82024i	−0.140619	+	0.692984i
$163$	−17.2670			−1.35245			−0.676227	−	0.736693i	$-0.736386\pi$
$163$	−17.2670			−1.35245			−0.676227	+	0.736693i	$0.736386\pi$
$164$		−	3.84484i		−	0.300232i
$165$	−0.161042	+	3.21493i	−0.0125371	+	0.250282i
$166$			10.1096i			0.784656i
$167$			16.8328i			1.30256i	0.758837	+	0.651281i	$0.225768\pi$
$167$			16.8328i			1.30256i	−0.758837	+	0.651281i	$0.774232\pi$
$168$	−0.0866531	+	1.72988i	−0.00668543	+	0.133463i
$169$	18.2790			1.40608
$170$		−	4.41032i		−	0.338256i
$171$	−0.943684	+	9.39589i	−0.0721653	+	0.718522i
$172$		−	4.89017i		−	0.372872i
$173$		−	16.1662i		−	1.22909i	−0.788880	−	0.614547i	$-0.789339\pi$
$173$		−	16.1662i		−	1.22909i	0.788880	−	0.614547i	$-0.210661\pi$
$174$	−0.0690694	+	1.37885i	−0.00523614	+	0.104531i
$175$		−	4.49021i		−	0.339428i
$176$	−2.60291			−0.196202
$177$	19.5049	+	0.977036i	1.46608	+	0.0734385i
$178$		−	8.77912i		−	0.658023i
$179$		−	12.1351i		−	0.907018i	−0.891252	−	0.453509i	$-0.850172\pi$
$179$		−	12.1351i		−	0.907018i	0.891252	−	0.453509i	$-0.149828\pi$
$180$	−2.13127	−	0.214055i	−0.158855	−	0.0159547i
$181$		−	5.91848i		−	0.439917i	−0.975509	−	0.219959i	$-0.929408\pi$
$181$		−	5.91848i		−	0.439917i	0.975509	−	0.219959i	$-0.0705922\pi$
$182$	5.59277			0.414563
$183$	−1.74948	−	0.0876346i	−0.129325	−	0.00647813i
$184$	−1.72597	−	4.47449i	−0.127240	−	0.329864i
$185$			5.14927i			0.378582i
$186$	13.3220	+	0.667323i	0.976815	+	0.0489305i
$187$	−16.0780			−1.17574
$188$		−	4.60889i		−	0.336138i
$189$	5.13769	+	0.777275i	0.373712	+	0.0565384i
$190$	−2.24746			−0.163048
$191$	−22.3077			−1.61413			−0.807065	−	0.590463i	$-0.798945\pi$
$191$	−22.3077			−1.61413			−0.807065	+	0.590463i	$0.798945\pi$
$192$	0.0866531	−	1.72988i	0.00625365	−	0.124843i
$193$	−15.5365			−1.11834			−0.559171	−	0.829053i	$-0.688880\pi$
$193$	−15.5365			−1.11834			−0.559171	+	0.829053i	$0.688880\pi$
$194$	−14.9697			−1.07476
$195$	−0.346024	+	6.90778i	−0.0247793	+	0.494677i
$196$	1.00000			0.0714286
$197$			24.3381i			1.73402i	0.498291	+	0.867010i	$0.333961\pi$
$197$			24.3381i			1.73402i	−0.498291	+	0.867010i	$0.666039\pi$
$198$	−0.780350	+	7.76963i	−0.0554570	+	0.552164i
$199$			9.11474i			0.646127i	0.946377	+	0.323063i	$0.104713\pi$
$199$			9.11474i			0.646127i	−0.946377	+	0.323063i	$0.895287\pi$
$200$			4.49021i			0.317506i
$201$	24.2036	+	1.21241i	1.70719	+	0.0855166i
$202$	−14.4767			−1.01858
$203$	0.797080			0.0559440
$204$	0.535252	−	10.6854i	0.0374751	−	0.748127i
$205$		−	2.74520i		−	0.191733i
$206$	5.40195			0.376372
$207$	−13.8737	+	3.81053i	−0.964290	+	0.264850i
$208$	−5.59277			−0.387788
$209$			8.19323i			0.566737i
$210$	−0.0618700	+	1.23513i	−0.00426943	+	0.0852320i
$211$	4.54697			0.313026			0.156513	−	0.987676i	$-0.449975\pi$
$211$	4.54697			0.313026			0.156513	+	0.987676i	$0.449975\pi$
$212$	13.4827			0.925998
$213$	−7.42292	−	0.371828i	−0.508610	−	0.0254772i
$214$		−	19.8819i		−	1.35910i
$215$		−	3.49156i		−	0.238123i
$216$	−5.13769	−	0.777275i	−0.349575	−	0.0528869i
$217$		−	7.70109i		−	0.522784i
$218$	−16.2449			−1.10024
$219$	−0.611263	+	12.2028i	−0.0413053	+	0.824591i
$220$	−1.85847			−0.125298
$221$	−34.5462			−2.32383
$222$	−0.624933	+	12.4757i	−0.0419428	+	0.837316i
$223$	−17.5209			−1.17329			−0.586644	−	0.809845i	$-0.699551\pi$
$223$	−17.5209			−1.17329			−0.586644	+	0.809845i	$0.699551\pi$
$224$	−1.00000			−0.0668153
$225$	13.4032	+	1.34616i	0.893546	+	0.0897441i
$226$			7.61914i			0.506817i
$227$	10.8036			0.717060			0.358530	−	0.933518i	$-0.383278\pi$
$227$	10.8036			0.717060			0.358530	+	0.933518i	$0.383278\pi$
$228$	−5.44518	−	0.272760i	−0.360616	−	0.0180640i
$229$		−	3.03657i		−	0.200662i	−0.994954	−	0.100331i	$-0.968010\pi$
$229$		−	3.03657i		−	0.200662i	0.994954	−	0.100331i	$-0.0319902\pi$
$230$	−1.23233	−	3.19477i	−0.0812576	−	0.210657i
$231$	4.50272	+	0.225550i	0.296257	+	0.0148401i
$232$	−0.797080			−0.0523309
$233$			2.34523i			0.153641i	0.997045	+	0.0768205i	$0.0244768\pi$
$233$			2.34523i			0.153641i	−0.997045	+	0.0768205i	$0.975523\pi$
$234$	−1.67671	+	16.6943i	−0.109610	+	1.09134i
$235$		−	3.29073i		−	0.214663i
$236$			11.2753i			0.733957i
$237$	9.48766	+	0.475255i	0.616290	+	0.0308711i
$238$	−6.17695			−0.400392
$239$		−	10.7409i		−	0.694770i	−0.937723	−	0.347385i	$-0.887070\pi$
$239$		−	10.7409i		−	0.694770i	0.937723	−	0.347385i	$-0.112930\pi$
$240$	0.0618700	−	1.23513i	0.00399369	−	0.0797272i
$241$			1.76807i			0.113891i	0.998377	+	0.0569456i	$0.0181362\pi$
$241$			1.76807i			0.113891i	−0.998377	+	0.0569456i	$0.981864\pi$
$242$		−	4.22487i		−	0.271585i
$243$	−3.86043	+	15.1029i	−0.247647	+	0.968850i
$244$		−	1.01133i		−	0.0647436i
$245$	0.713996			0.0456155
$246$	0.333167	−	6.65112i	0.0212420	−	0.424060i
$247$			17.6045i			1.12015i
$248$			7.70109i			0.489020i
$249$	−0.876027	+	17.4884i	−0.0555159	+	1.10828i
$250$			6.77597i			0.428550i
$251$	13.1890			0.832482			0.416241	−	0.909254i	$-0.363347\pi$
$251$	13.1890			0.832482			0.416241	+	0.909254i	$0.363347\pi$
$252$	−0.299799	+	2.98498i	−0.0188856	+	0.188036i
$253$	−11.6467	+	4.49253i	−0.732220	+	0.282443i
$254$		−	16.5077i		−	1.03578i
$255$	0.382168	−	7.62933i	0.0239323	−	0.477767i
$256$	1.00000			0.0625000
$257$			8.51302i			0.531028i	0.964107	+	0.265514i	$0.0855416\pi$
$257$			8.51302i			0.531028i	−0.964107	+	0.265514i	$0.914458\pi$
$258$	0.423749	−	8.45942i	0.0263814	−	0.526661i
$259$	7.21190			0.448126
$260$	−3.99321			−0.247648
$261$	−0.238964	+	2.37927i	−0.0147915	+	0.147273i
$262$	−1.27957			−0.0790522
$263$	2.78124			0.171498			0.0857492	−	0.996317i	$-0.472672\pi$
$263$	2.78124			0.171498			0.0857492	+	0.996317i	$0.472672\pi$
$264$	−4.50272	−	0.225550i	−0.277123	−	0.0138816i
$265$	9.62662			0.591358
$266$			3.14772i			0.192999i
$267$	0.760738	−	15.1868i	0.0465564	−	0.929419i
$268$			13.9915i			0.854667i
$269$			6.48999i			0.395701i	0.980232	+	0.197851i	$0.0633961\pi$
$269$			6.48999i			0.395701i	−0.980232	+	0.197851i	$0.936604\pi$
$270$	−3.66829	−	0.554971i	−0.223245	−	0.0337745i
$271$	16.1511			0.981112			0.490556	−	0.871410i	$-0.336794\pi$
$271$	16.1511			0.981112			0.490556	+	0.871410i	$0.336794\pi$
$272$	6.17695			0.374533
$273$	9.67482	+	0.484630i	0.585547	+	0.0293312i
$274$		−	4.95606i		−	0.299407i
$275$	11.6876			0.704789
$276$	−2.59799	−	7.88990i	−0.156381	−	0.474916i
$277$	10.4013			0.624955			0.312477	−	0.949925i	$-0.398841\pi$
$277$	10.4013			0.624955			0.312477	+	0.949925i	$0.398841\pi$
$278$		−	15.4459i		−	0.926381i
$279$	22.9876	+	2.30878i	1.37623	+	0.138223i
$280$	−0.713996			−0.0426694
$281$	0.00513086			0.000306082			0.000153041	−	1.00000i	$-0.499951\pi$
$281$	0.00513086			0.000306082			0.000153041		1.00000i	$0.499951\pi$
$282$	0.399374	−	7.97283i	0.0237824	−	0.474775i
$283$		−	18.3442i		−	1.09045i	−0.838289	−	0.545226i	$-0.816444\pi$
$283$		−	18.3442i		−	1.09045i	0.838289	−	0.545226i	$-0.183556\pi$
$284$		−	4.29100i		−	0.254624i
$285$	−3.88784	−	0.194749i	−0.230296	−	0.0115360i
$286$			14.5575i			0.860800i
$287$	−3.84484			−0.226954
$288$	0.299799	−	2.98498i	0.0176658	−	0.175892i
$289$	21.1547			1.24439
$290$	−0.569112			−0.0334194
$291$	−25.8958	−	1.29717i	−1.51804	−	0.0760413i
$292$	−7.05414			−0.412813
$293$	21.9697			1.28348			0.641742	−	0.766921i	$-0.278212\pi$
$293$	21.9697			1.28348			0.641742	+	0.766921i	$0.278212\pi$
$294$	1.72988	+	0.0866531i	0.100889	+	0.00505371i
$295$			8.05049i			0.468718i
$296$	−7.21190			−0.419183
$297$	−2.02318	+	13.3729i	−0.117397	+	0.775976i
$298$		−	9.31147i		−	0.539399i
$299$	−25.0248	+	9.65292i	−1.44722	+	0.558243i
$300$	−0.389091	+	7.76753i	−0.0224642	+	0.448459i
$301$	−4.89017			−0.281865
$302$		−	3.38946i		−	0.195041i
$303$	−25.0430	−	1.25445i	−1.43868	−	0.0720665i
$304$		−	3.14772i		−	0.180534i
$305$		−	0.722083i		−	0.0413464i
$306$	1.85184	−	18.4381i	0.105863	−	1.05404i
$307$	−20.1170			−1.14814			−0.574070	−	0.818806i	$-0.694636\pi$
$307$	−20.1170			−1.14814			−0.574070	+	0.818806i	$0.694636\pi$
$308$			2.60291i			0.148314i
$309$	9.34474	+	0.468096i	0.531604	+	0.0266290i
$310$			5.49855i			0.312296i
$311$			15.3928i			0.872847i	0.899741	+	0.436424i	$0.143755\pi$
$311$			15.3928i			0.872847i	−0.899741	+	0.436424i	$0.856245\pi$
$312$	−9.67482	−	0.484630i	−0.547729	−	0.0274368i
$313$		−	8.80771i		−	0.497841i	−0.968524	−	0.248921i	$-0.919924\pi$
$313$		−	8.80771i		−	0.497841i	0.968524	−	0.248921i	$-0.0800759\pi$
$314$	20.2760			1.14424
$315$	−0.214055	+	2.13127i	−0.0120607	+	0.120083i
$316$			5.48457i			0.308531i
$317$			14.7125i			0.826334i	0.910655	+	0.413167i	$0.135577\pi$
$317$			14.7125i			0.826334i	−0.910655	+	0.413167i	$0.864423\pi$
$318$	23.3235	+	1.16832i	1.30792	+	0.0655161i
$319$			2.07473i			0.116162i
$320$	0.713996			0.0399136
$321$	1.72283	−	34.3934i	0.0961589	−	1.91965i
$322$	−4.47449	+	1.72597i	−0.249353	+	0.0961843i
$323$		−	19.4433i		−	1.08185i
$324$	−8.82024	−	1.78979i	−0.490013	−	0.0994328i
$325$	25.1127			1.39300
$326$		−	17.2670i		−	0.956329i
$327$	−28.1018	−	1.40767i	−1.55403	−	0.0778444i
$328$	3.84484			0.212296
$329$	−4.60889			−0.254096
$330$	−3.21493	−	0.161042i	−0.176976	−	0.00886506i
$331$	15.2366			0.837480			0.418740	−	0.908106i	$-0.362472\pi$
$331$	15.2366			0.837480			0.418740	+	0.908106i	$0.362472\pi$
$332$	−10.1096			−0.554835
$333$	−2.16212	+	21.5274i	−0.118484	+	1.17969i
$334$	−16.8328			−0.921050
$335$			9.98988i			0.545805i
$336$	−1.72988	−	0.0866531i	−0.0943728	−	0.00472731i
$337$			35.6683i			1.94298i	0.237088	+	0.971488i	$0.423807\pi$
$337$			35.6683i			1.94298i	−0.237088	+	0.971488i	$0.576193\pi$
$338$			18.2790i			0.994248i
$339$	−0.660222	+	13.1802i	−0.0358583	+	0.715850i
$340$	4.41032			0.239183
$341$	20.0452			1.08551
$342$	−9.39589	−	0.943684i	−0.508072	−	0.0510286i
$343$		−	1.00000i		−	0.0539949i
$344$	4.89017			0.263660
$345$	−1.85495	−	5.63335i	−0.0998674	−	0.303290i
$346$	16.1662			0.869101
$347$		−	20.7559i		−	1.11424i	−0.830433	−	0.557119i	$-0.811907\pi$
$347$		−	20.7559i		−	1.11424i	0.830433	−	0.557119i	$-0.188093\pi$
$348$	−1.37885	−	0.0690694i	−0.0739143	−	0.00370251i
$349$	30.0671			1.60945			0.804727	−	0.593645i	$-0.202312\pi$
$349$	30.0671			1.60945			0.804727	+	0.593645i	$0.202312\pi$
$350$	4.49021			0.240012
$351$	−4.34712	+	28.7339i	−0.232032	+	1.53370i
$352$		−	2.60291i		−	0.138735i
$353$			2.95341i			0.157194i	0.996906	+	0.0785971i	$0.0250441\pi$
$353$			2.95341i			0.157194i	−0.996906	+	0.0785971i	$0.974956\pi$
$354$	−0.977036	+	19.5049i	−0.0519289	+	1.03667i
$355$		−	3.06375i		−	0.162607i
$356$	8.77912			0.465292
$357$	−10.6854	−	0.535252i	−0.565531	−	0.0283285i
$358$	12.1351			0.641359
$359$	1.60633			0.0847790			0.0423895	−	0.999101i	$-0.486503\pi$
$359$	1.60633			0.0847790			0.0423895	+	0.999101i	$0.486503\pi$
$360$	0.214055	−	2.13127i	0.0112817	−	0.112328i
$361$	9.09185			0.478519
$362$	5.91848			0.311068
$363$	0.366098	−	7.30853i	0.0192152	−	0.383598i
$364$			5.59277i			0.293141i
$365$	−5.03663			−0.263629
$366$	0.0876346	−	1.74948i	0.00458073	−	0.0914466i
$367$			9.08620i			0.474296i	0.971474	+	0.237148i	$0.0762126\pi$
$367$			9.08620i			0.474296i	−0.971474	+	0.237148i	$0.923787\pi$
$368$	4.47449	−	1.72597i	0.233249	−	0.0899722i
$369$	1.15268	−	11.4768i	0.0600061	−	0.597457i
$370$	−5.14927			−0.267698
$371$		−	13.4827i		−	0.699989i
$372$	−0.667323	+	13.3220i	−0.0345991	+	0.690712i
$373$		−	18.9335i		−	0.980337i	−0.871628	−	0.490169i	$-0.836935\pi$
$373$		−	18.9335i		−	0.980337i	0.871628	−	0.490169i	$-0.163065\pi$
$374$		−	16.0780i		−	0.831375i
$375$	−0.587159	+	11.7216i	−0.0303208	+	0.605302i
$376$	4.60889			0.237685
$377$			4.45788i			0.229593i
$378$	−0.777275	+	5.13769i	−0.0399787	+	0.264254i
$379$			28.3631i			1.45691i	0.685091	+	0.728457i	$0.259762\pi$
$379$			28.3631i			1.45691i	−0.685091	+	0.728457i	$0.740238\pi$
$380$		−	2.24746i		−	0.115292i
$381$	1.43044	−	28.5563i	0.0732837	−	1.46298i
$382$		−	22.3077i		−	1.14136i
$383$	−5.40212			−0.276035			−0.138018	−	0.990430i	$-0.544073\pi$
$383$	−5.40212			−0.276035			−0.138018	+	0.990430i	$0.544073\pi$
$384$	1.72988	+	0.0866531i	0.0882777	+	0.00442200i
$385$			1.85847i			0.0947162i
$386$		−	15.5365i		−	0.790787i
$387$	1.46607	−	14.5971i	0.0745245	−	0.742011i
$388$		−	14.9697i		−	0.759970i
$389$	−15.5715			−0.789505			−0.394752	−	0.918788i	$-0.629170\pi$
$389$	−15.5715			−0.789505			−0.394752	+	0.918788i	$0.629170\pi$
$390$	−6.90778	−	0.346024i	−0.349789	−	0.0175216i
$391$	27.6387	−	10.6612i	1.39775	−	0.539160i
$392$			1.00000i			0.0505076i
$393$	−2.21351	−	0.110879i	−0.111657	−	0.00559310i
$394$	−24.3381			−1.22614
$395$			3.91596i			0.197033i
$396$	−7.76963	−	0.780350i	−0.390439	−	0.0392140i
$397$	−0.247683			−0.0124309			−0.00621543	−	0.999981i	$-0.501978\pi$
$397$	−0.247683			−0.0124309			−0.00621543	+	0.999981i	$0.501978\pi$
$398$	−9.11474			−0.456880
$399$	−0.272760	+	5.44518i	−0.0136551	+	0.272600i
$400$	−4.49021			−0.224510
$401$	9.95514			0.497136			0.248568	−	0.968614i	$-0.420040\pi$
$401$	9.95514			0.497136			0.248568	+	0.968614i	$0.420040\pi$
$402$	−1.21241	+	24.2036i	−0.0604694	+	1.20717i
$403$	43.0704			2.14549
$404$		−	14.4767i		−	0.720244i
$405$	−6.29762	−	1.27790i	−0.312931	−	0.0634995i
$406$			0.797080i			0.0395584i
$407$			18.7719i			0.930489i
$408$	10.6854	+	0.535252i	0.529006	+	0.0264989i
$409$	−11.4996			−0.568621			−0.284311	−	0.958732i	$-0.591765\pi$
$409$	−11.4996			−0.568621			−0.284311	+	0.958732i	$0.591765\pi$
$410$	2.74520			0.135576
$411$	0.429458	−	8.57341i	0.0211836	−	0.422895i
$412$			5.40195i			0.266135i
$413$	11.2753			0.554819
$414$	−3.81053	−	13.8737i	−0.187277	−	0.681856i
$415$	−7.21820			−0.354328
$416$		−	5.59277i		−	0.274208i
$417$	1.33843	−	26.7195i	0.0655433	−	1.30846i
$418$	−8.19323			−0.400744
$419$	28.7429			1.40418			0.702092	−	0.712086i	$-0.252250\pi$
$419$	28.7429			1.40418			0.702092	+	0.712086i	$0.252250\pi$
$420$	−1.23513	−	0.0618700i	−0.0602681	−	0.00301894i
$421$			15.3490i			0.748065i	0.927416	+	0.374033i	$0.122025\pi$
$421$			15.3490i			0.748065i	−0.927416	+	0.374033i	$0.877975\pi$
$422$			4.54697i			0.221343i
$423$	1.38174	−	13.7574i	0.0671825	−	0.668910i
$424$			13.4827i			0.654779i
$425$	−27.7358			−1.34538
$426$	0.371828	−	7.42292i	0.0180151	−	0.359641i
$427$	−1.01133			−0.0489415
$428$	19.8819			0.961028
$429$	−1.26145	+	25.1827i	−0.0609033	+	1.21583i
$430$	3.49156			0.168378
$431$	−19.2983			−0.929568			−0.464784	−	0.885424i	$-0.653868\pi$
$431$	−19.2983			−0.929568			−0.464784	+	0.885424i	$0.653868\pi$
$432$	0.777275	−	5.13769i	0.0373967	−	0.247187i
$433$		−	26.4517i		−	1.27119i	−0.772024	−	0.635593i	$-0.780756\pi$
$433$		−	26.4517i		−	1.27119i	0.772024	−	0.635593i	$-0.219244\pi$
$434$	7.70109			0.369664
$435$	−0.984496	−	0.0493153i	−0.0472030	−	0.00236449i
$436$		−	16.2449i		−	0.777990i
$437$	−5.43286	−	14.0844i	−0.259889	−	0.673750i
$438$	−12.2028	−	0.611263i	−0.583074	−	0.0292073i
$439$	4.94670			0.236093			0.118047	−	0.993008i	$-0.462337\pi$
$439$	4.94670			0.236093			0.118047	+	0.993008i	$0.462337\pi$
$440$		−	1.85847i		−	0.0885989i
$441$	2.98498	+	0.299799i	0.142142	+	0.0142762i
$442$		−	34.5462i		−	1.64320i
$443$		−	26.9543i		−	1.28064i	−0.768110	−	0.640318i	$-0.778802\pi$
$443$		−	26.9543i		−	1.28064i	0.768110	−	0.640318i	$-0.221198\pi$
$444$	−12.4757	−	0.624933i	−0.592072	−	0.0296580i
$445$	6.26825			0.297144
$446$		−	17.5209i		−	0.829640i
$447$	0.806867	−	16.1077i	0.0381635	−	0.761870i
$448$		−	1.00000i		−	0.0472456i
$449$			9.06238i			0.427680i	0.976869	+	0.213840i	$0.0685972\pi$
$449$			9.06238i			0.427680i	−0.976869	+	0.213840i	$0.931403\pi$
$450$	−1.34616	+	13.4032i	−0.0634587	+	0.631833i
$451$		−	10.0078i		−	0.471247i
$452$	−7.61914			−0.358374
$453$	0.293707	−	5.86336i	0.0137996	−	0.275485i
$454$			10.8036i			0.507038i
$455$			3.99321i			0.187205i
$456$	0.272760	−	5.44518i	0.0127731	−	0.254994i
$457$			8.08036i			0.377983i	0.981979	+	0.188992i	$0.0605219\pi$
$457$			8.08036i			0.377983i	−0.981979	+	0.188992i	$0.939478\pi$
$458$	3.03657			0.141890
$459$	4.80119	−	31.7352i	0.224100	−	1.48127i
$460$	3.19477	−	1.23233i	0.148957	−	0.0574578i
$461$			5.82827i			0.271450i	0.990747	+	0.135725i	$0.0433363\pi$
$461$			5.82827i			0.271450i	−0.990747	+	0.135725i	$0.956664\pi$
$462$	−0.225550	+	4.50272i	−0.0104935	+	0.209486i
$463$	−30.5512			−1.41983			−0.709917	−	0.704285i	$-0.751268\pi$
$463$	−30.5512			−1.41983			−0.709917	+	0.704285i	$0.751268\pi$
$464$		−	0.797080i		−	0.0370035i
$465$	−0.476466	+	9.51184i	−0.0220956	+	0.441101i
$466$	−2.34523			−0.108641
$467$	32.2099			1.49050			0.745249	−	0.666786i	$-0.232331\pi$
$467$	32.2099			1.49050			0.745249	+	0.666786i	$0.232331\pi$
$468$	−16.6943	−	1.67671i	−0.771695	−	0.0775058i
$469$	13.9915			0.646068
$470$	3.29073			0.151790
$471$	35.0751	+	1.75698i	1.61618	+	0.0809573i
$472$	−11.2753			−0.518986
$473$		−	12.7287i		−	0.585265i
$474$	−0.475255	+	9.48766i	−0.0218292	+	0.435783i
$475$			14.1339i			0.648509i
$476$		−	6.17695i		−	0.283120i
$477$	40.2457	+	4.04211i	1.84272	+	0.185076i
$478$	10.7409			0.491276
$479$	10.9190			0.498902			0.249451	−	0.968387i	$-0.419750\pi$
$479$	10.9190			0.498902			0.249451	+	0.968387i	$0.419750\pi$
$480$	1.23513	+	0.0618700i	0.0563757	+	0.00282396i
$481$			40.3345i			1.83909i
$482$	−1.76807			−0.0805333
$483$	−7.88990	+	2.59799i	−0.359003	+	0.118213i
$484$	4.22487			0.192040
$485$		−	10.6883i		−	0.485330i
$486$	−15.1029	−	3.86043i	−0.685081	−	0.175113i
$487$	−31.2013			−1.41386			−0.706932	−	0.707281i	$-0.749921\pi$
$487$	−31.2013			−1.41386			−0.706932	+	0.707281i	$0.749921\pi$
$488$	1.01133			0.0457806
$489$	1.49624	−	29.8698i	0.0676621	−	1.35076i
$490$			0.713996i			0.0322551i
$491$		−	36.2759i		−	1.63711i	−0.574428	−	0.818555i	$-0.694776\pi$
$491$		−	36.2759i		−	1.63711i	0.574428	−	0.818555i	$-0.305224\pi$
$492$	6.65112	+	0.333167i	0.299856	+	0.0150203i
$493$		−	4.92352i		−	0.221744i
$494$	−17.6045			−0.792062
$495$	−5.54749	−	0.557166i	−0.249341	−	0.0250428i
$496$	−7.70109			−0.345789
$497$	−4.29100			−0.192477
$498$	−17.4884	−	0.876027i	−0.783673	−	0.0392557i
$499$	12.1997			0.546135			0.273067	−	0.961995i	$-0.411962\pi$
$499$	12.1997			0.546135			0.273067	+	0.961995i	$0.411962\pi$
$500$	−6.77597			−0.303031
$501$	−29.1188	−	1.45862i	−1.30093	−	0.0651661i
$502$			13.1890i			0.588654i
$503$	7.74030			0.345123			0.172562	−	0.984999i	$-0.444796\pi$
$503$	7.74030			0.345123			0.172562	+	0.984999i	$0.444796\pi$
$504$	−2.98498	−	0.299799i	−0.132962	−	0.0133541i
$505$		−	10.3363i		−	0.459961i
$506$	−4.49253	−	11.6467i	−0.199717	−	0.517758i
$507$	−1.58393	+	31.6205i	−0.0703450	+	1.40432i
$508$	16.5077			0.732409
$509$			23.1000i			1.02389i	0.859018	+	0.511945i	$0.171075\pi$
$509$			23.1000i			1.02389i	−0.859018	+	0.511945i	$0.828925\pi$
$510$	7.62933	+	0.382168i	0.337832	+	0.0169227i
$511$			7.05414i			0.312057i
$512$			1.00000i			0.0441942i
$513$	−16.1720	−	2.44664i	−0.714012	−	0.108022i
$514$	−8.51302			−0.375493
$515$			3.85697i			0.169959i
$516$	8.45942	+	0.423749i	0.372405	+	0.0186545i
$517$		−	11.9965i		−	0.527606i
$518$			7.21190i			0.316873i
$519$	27.9656	+	1.40085i	1.22756	+	0.0614906i
$520$		−	3.99321i		−	0.175114i
$521$	−0.0178429			−0.000781710			−0.000390855	−	1.00000i	$-0.500124\pi$
$521$	−0.0178429			−0.000781710			−0.000390855		1.00000i	$0.500124\pi$
$522$	−2.37927	−	0.238964i	−0.104138	−	0.0104592i
$523$			36.6039i			1.60058i	0.599615	+	0.800289i	$0.295321\pi$
$523$			36.6039i			1.60058i	−0.599615	+	0.800289i	$0.704679\pi$
$524$		−	1.27957i		−	0.0558984i
$525$	7.76753	+	0.389091i	0.339003	+	0.0169813i
$526$			2.78124i			0.121268i
$527$	−47.5692			−2.07215
$528$	0.225550	−	4.50272i	0.00981580	−	0.195956i
$529$	17.0421	−	15.4456i	0.740960	−	0.671549i
$530$			9.62662i			0.418153i
$531$	−3.38031	+	33.6564i	−0.146693	+	1.46057i
$532$	−3.14772			−0.136471
$533$		−	21.5033i		−	0.931411i
$534$	15.1868	+	0.760738i	0.657199	+	0.0329203i
$535$	14.1956			0.613730
$536$	−13.9915			−0.604341
$537$	20.9922	+	1.05154i	0.905882	+	0.0453774i
$538$	−6.48999			−0.279803
$539$	2.60291			0.112115
$540$	0.554971	−	3.66829i	0.0238822	−	0.157858i
$541$	−21.1972			−0.911340			−0.455670	−	0.890149i	$-0.650600\pi$
$541$	−21.1972			−0.911340			−0.455670	+	0.890149i	$0.650600\pi$
$542$			16.1511i			0.693751i
$543$	10.2383	+	0.512855i	0.439366	+	0.0220087i
$544$			6.17695i			0.264834i
$545$		−	11.5988i		−	0.496838i
$546$	−0.484630	+	9.67482i	−0.0207403	+	0.414044i
$547$	−20.5347			−0.877999			−0.439000	−	0.898487i	$-0.644667\pi$
$547$	−20.5347			−0.877999			−0.439000	+	0.898487i	$0.644667\pi$
$548$	4.95606			0.211713
$549$	0.303195	−	3.01879i	0.0129400	−	0.128839i
$550$			11.6876i			0.498361i
$551$	−2.50898			−0.106886
$552$	7.88990	−	2.59799i	0.335816	−	0.110578i
$553$	5.48457			0.233228
$554$			10.4013i			0.441910i
$555$	−8.90762	−	0.446200i	−0.378108	−	0.0189401i
$556$	15.4459			0.655050
$557$	24.0277			1.01809			0.509044	−	0.860741i	$-0.329999\pi$
$557$	24.0277			1.01809			0.509044	+	0.860741i	$0.329999\pi$
$558$	−2.30878	+	22.9876i	−0.0977385	+	0.973143i
$559$		−	27.3496i		−	1.15676i
$560$		−	0.713996i		−	0.0301718i
$561$	1.39321	−	27.8131i	0.0588214	−	1.17427i
$562$			0.00513086i			0.000216432i
$563$	7.50512			0.316303			0.158152	−	0.987415i	$-0.449447\pi$
$563$	7.50512			0.316303			0.158152	+	0.987415i	$0.449447\pi$
$564$	7.97283	+	0.399374i	0.335717	+	0.0168167i
$565$	−5.44003			−0.228864
$566$	18.3442			0.771066
$567$	−1.78979	+	8.82024i	−0.0751641	+	0.370415i
$568$	4.29100			0.180046
$569$	34.7841			1.45823			0.729114	−	0.684393i	$-0.239933\pi$
$569$	34.7841			1.45823			0.729114	+	0.684393i	$0.239933\pi$
$570$	0.194749	−	3.88784i	0.00815715	−	0.162844i
$571$		−	39.3279i		−	1.64582i	−0.568171	−	0.822910i	$-0.692349\pi$
$571$		−	39.3279i		−	1.64582i	0.568171	−	0.822910i	$-0.307651\pi$
$572$	−14.5575			−0.608678
$573$	1.93303	−	38.5897i	0.0807536	−	1.61211i
$574$		−	3.84484i		−	0.160481i
$575$	−20.0914	+	7.74995i	−0.837869	+	0.323195i
$576$	2.98498	+	0.299799i	0.124374	+	0.0124916i
$577$	11.7431			0.488871			0.244435	−	0.969666i	$-0.421397\pi$
$577$	11.7431			0.488871			0.244435	+	0.969666i	$0.421397\pi$
$578$			21.1547i			0.879919i
$579$	1.34628	−	26.8763i	0.0559497	−	1.11694i
$580$		−	0.569112i		−	0.0236311i
$581$			10.1096i			0.419416i
$582$	1.29717	−	25.8958i	0.0537693	−	1.07341i
$583$	35.0943			1.45346
$584$		−	7.05414i		−	0.291903i
$585$	−11.9197	−	1.19716i	−0.492818	−	0.0494965i
$586$			21.9697i			0.907560i
$587$		−	0.591106i		−	0.0243976i	−0.999926	−	0.0121988i	$-0.996117\pi$
$587$		−	0.591106i		−	0.0243976i	0.999926	−	0.0121988i	$-0.00388309\pi$
$588$	−0.0866531	+	1.72988i	−0.00357351	+	0.0713391i
$589$			24.2409i			0.998828i
$590$	−8.05049			−0.331433
$591$	−42.1021	−	2.10897i	−1.73185	−	0.0867516i
$592$		−	7.21190i		−	0.296407i
$593$		−	46.9429i		−	1.92772i	−0.266417	−	0.963858i	$-0.585840\pi$
$593$		−	46.9429i		−	1.92772i	0.266417	−	0.963858i	$-0.414160\pi$
$594$	−13.3729	−	2.02318i	−0.548698	−	0.0830119i
$595$		−	4.41032i		−	0.180805i
$596$	9.31147			0.381413
$597$	−15.7674	−	0.789820i	−0.645317	−	0.0323252i
$598$	−9.65292	−	25.0248i	−0.394737	−	1.02334i
$599$			0.252873i			0.0103321i	0.999987	+	0.00516606i	$0.00164442\pi$
$599$			0.252873i			0.0103321i	−0.999987	+	0.00516606i	$0.998356\pi$
$600$	−7.76753	−	0.389091i	−0.317108	−	0.0158846i
$601$	48.4817			1.97761			0.988806	−	0.149207i	$-0.0476722\pi$
$601$	48.4817			1.97761			0.988806	+	0.149207i	$0.0476722\pi$
$602$		−	4.89017i		−	0.199309i
$603$	−4.19464	+	41.7644i	−0.170819	+	1.70078i
$604$	3.38946			0.137915
$605$	3.01654			0.122640
$606$	1.25445	−	25.0430i	0.0509587	−	1.01730i
$607$	−12.7850			−0.518926			−0.259463	−	0.965753i	$-0.583546\pi$
$607$	−12.7850			−0.518926			−0.259463	+	0.965753i	$0.583546\pi$
$608$	3.14772			0.127657
$609$	−0.0690694	+	1.37885i	−0.00279883	+	0.0558740i
$610$	0.722083			0.0292363
$611$		−	25.7764i		−	1.04280i
$612$	18.4381	+	1.85184i	0.745315	+	0.0748564i
$613$			15.2913i			0.617608i	0.951126	+	0.308804i	$0.0999288\pi$
$613$			15.2913i			0.617608i	−0.951126	+	0.308804i	$0.900071\pi$
$614$		−	20.1170i		−	0.811858i
$615$	4.74887	+	0.237880i	0.191493	+	0.00959225i
$616$	−2.60291			−0.104874
$617$	−10.8625			−0.437307			−0.218653	−	0.975803i	$-0.570166\pi$
$617$	−10.8625			−0.437307			−0.218653	+	0.975803i	$0.570166\pi$
$618$	−0.468096	+	9.34474i	−0.0188296	+	0.375901i
$619$		−	1.87758i		−	0.0754664i	−0.999288	−	0.0377332i	$-0.987986\pi$
$619$		−	1.87758i		−	0.0754664i	0.999288	−	0.0377332i	$-0.0120137\pi$
$620$	−5.49855			−0.220827
$621$	−5.38957	−	24.3301i	−0.216276	−	0.976332i
$622$	−15.3928			−0.617196
$623$		−	8.77912i		−	0.351728i
$624$	0.484630	−	9.67482i	0.0194007	−	0.387303i
$625$	17.6130			0.704521
$626$	8.80771			0.352027
$627$	−14.1733	−	0.709968i	−0.566028	−	0.0283534i
$628$			20.2760i			0.809101i
$629$		−	44.5475i		−	1.77623i
$630$	−2.13127	−	0.214055i	−0.0849117	−	0.00852817i
$631$			9.31314i			0.370750i	0.982668	+	0.185375i	$0.0593500\pi$
$631$			9.31314i			0.370750i	−0.982668	+	0.185375i	$0.940650\pi$
$632$	−5.48457			−0.218165
$633$	−0.394009	+	7.86571i	−0.0156604	+	0.312634i
$634$	−14.7125			−0.584306
$635$	11.7864			0.467729
$636$	−1.16832	+	23.3235i	−0.0463269	+	0.924838i
$637$	5.59277			0.221593
$638$	−2.07473			−0.0821392
$639$	1.28644	−	12.8085i	0.0508907	−	0.506698i
$640$			0.713996i			0.0282232i
$641$	−1.12391			−0.0443918			−0.0221959	−	0.999754i	$-0.507066\pi$
$641$	−1.12391			−0.0443918			−0.0221959	+	0.999754i	$0.507066\pi$
$642$	34.3934	+	1.72283i	1.35740	+	0.0679946i
$643$			18.8246i			0.742372i	0.928559	+	0.371186i	$0.121049\pi$
$643$			18.8246i			0.742372i	−0.928559	+	0.371186i	$0.878951\pi$
$644$	−1.72597	−	4.47449i	−0.0680126	−	0.176320i
$645$	6.03999	+	0.302555i	0.237824	+	0.0119131i
$646$	19.4433			0.764987
$647$			0.584405i			0.0229753i	0.999934	+	0.0114877i	$0.00365672\pi$
$647$			0.584405i			0.0229753i	−0.999934	+	0.0114877i	$0.996343\pi$
$648$	1.78979	−	8.82024i	0.0703096	−	0.346492i
$649$			29.3485i			1.15203i
$650$			25.1127i			0.985001i
$651$	13.3220	+	0.667323i	0.522129	+	0.0261545i
$652$	17.2670			0.676227
$653$			23.3867i			0.915191i	0.889161	+	0.457595i	$0.151289\pi$
$653$			23.3867i			0.915191i	−0.889161	+	0.457595i	$0.848711\pi$
$654$	1.40767	−	28.1018i	0.0550443	−	1.09887i
$655$		−	0.913609i		−	0.0356977i
$656$			3.84484i			0.150116i
$657$	−21.0565	−	2.11483i	−0.821492	−	0.0825072i
$658$		−	4.60889i		−	0.179673i
$659$	−9.57615			−0.373034			−0.186517	−	0.982452i	$-0.559720\pi$
$659$	−9.57615			−0.373034			−0.186517	+	0.982452i	$0.559720\pi$
$660$	0.161042	−	3.21493i	0.00626854	−	0.125141i
$661$			50.7172i			1.97267i	0.164746	+	0.986336i	$0.447320\pi$
$661$			50.7172i			1.97267i	−0.164746	+	0.986336i	$0.552680\pi$
$662$			15.2366i			0.592188i
$663$	2.99354	−	59.7609i	0.116259	−	2.32092i
$664$		−	10.1096i		−	0.392328i
$665$	−2.24746			−0.0871528
$666$	−21.5274	−	2.16212i	−0.834169	−	0.0837805i
$667$	−1.37573	−	3.56652i	−0.0532686	−	0.138096i
$668$		−	16.8328i		−	0.651281i
$669$	1.51824	−	30.3091i	0.0586986	−	1.17182i
$670$	−9.98988			−0.385943
$671$		−	2.63239i		−	0.101622i
$672$	0.0866531	−	1.72988i	0.00334272	−	0.0667316i
$673$	−3.40150			−0.131118			−0.0655590	−	0.997849i	$-0.520883\pi$
$673$	−3.40150			−0.131118			−0.0655590	+	0.997849i	$0.520883\pi$
$674$	−35.6683			−1.37389
$675$	−3.49013	+	23.0693i	−0.134335	+	0.887938i
$676$	−18.2790			−0.703039
$677$	−7.00373			−0.269175			−0.134588	−	0.990902i	$-0.542971\pi$
$677$	−7.00373			−0.269175			−0.134588	+	0.990902i	$0.542971\pi$
$678$	−13.1802	−	0.660222i	−0.506183	−	0.0253557i
$679$	−14.9697			−0.574483
$680$			4.41032i			0.169128i
$681$	−0.936165	+	18.6889i	−0.0358739	+	0.716162i
$682$			20.0452i			0.767571i
$683$			2.40940i			0.0921932i	0.998937	+	0.0460966i	$0.0146782\pi$
$683$			2.40940i			0.0921932i	−0.998937	+	0.0460966i	$0.985322\pi$
$684$	0.943684	−	9.39589i	0.0360827	−	0.359261i
$685$	3.53861			0.135203
$686$	1.00000			0.0381802
$687$	5.25291	+	0.263128i	0.200411	+	0.0100390i
$688$			4.89017i			0.186436i
$689$	75.4058			2.87273
$690$	5.63335	−	1.85495i	0.214458	−	0.0706169i
$691$	37.6772			1.43331			0.716654	−	0.697429i	$-0.245673\pi$
$691$	37.6772			1.43331			0.716654	+	0.697429i	$0.245673\pi$
$692$			16.1662i			0.614547i
$693$	−0.780350	+	7.76963i	−0.0296430	+	0.295144i
$694$	20.7559			0.787885
$695$	11.0283			0.418327
$696$	0.0690694	−	1.37885i	0.00261807	−	0.0522653i
$697$			23.7494i			0.899572i
$698$			30.0671i			1.13806i
$699$	−4.05697	−	0.203221i	−0.153449	−	0.00768653i
$700$			4.49021i			0.169714i
$701$	6.19795			0.234093			0.117047	−	0.993126i	$-0.462657\pi$
$701$	6.19795			0.234093			0.117047	+	0.993126i	$0.462657\pi$
$702$	−28.7339	−	4.34712i	−1.08449	−	0.164071i
$703$	−22.7010			−0.856186
$704$	2.60291			0.0981008
$705$	5.69257	+	0.285152i	0.214395	+	0.0107394i
$706$	−2.95341			−0.111153
$707$	−14.4767			−0.544454
$708$	−19.5049	−	0.977036i	−0.733038	−	0.0367193i
$709$		−	50.5724i		−	1.89929i	−0.313331	−	0.949644i	$-0.601445\pi$
$709$		−	50.5724i		−	1.89929i	0.313331	−	0.949644i	$-0.398555\pi$
$710$	3.06375			0.114981
$711$	−1.64427	+	16.3713i	−0.0616649	+	0.613974i
$712$			8.77912i			0.329011i
$713$	−34.4584	+	13.2918i	−1.29048	+	0.497783i
$714$	0.535252	−	10.6854i	0.0200313	−	0.399891i
$715$	−10.3940			−0.388712
$716$			12.1351i			0.453509i
$717$	18.5805	+	0.930730i	0.693900	+	0.0347588i
$718$			1.60633i			0.0599478i
$719$		−	3.49958i		−	0.130512i	−0.997869	−	0.0652561i	$-0.979214\pi$
$719$		−	3.49958i		−	0.130512i	0.997869	−	0.0652561i	$-0.0207864\pi$
$720$	2.13127	+	0.214055i	0.0794276	+	0.00797737i
$721$	5.40195			0.201179
$722$			9.09185i			0.338364i
$723$	−3.05855	−	0.153209i	−0.113749	−	0.00569789i
$724$			5.91848i			0.219959i
$725$			3.57906i			0.132923i
$726$	7.30853	+	0.366098i	0.271245	+	0.0135872i
$727$		−	22.8490i		−	0.847423i	−0.905797	−	0.423712i	$-0.860727\pi$
$727$		−	22.8490i		−	0.847423i	0.905797	−	0.423712i	$-0.139273\pi$
$728$	−5.59277			−0.207282
$729$	−25.7917	−	7.98680i	−0.955248	−	0.295807i
$730$		−	5.03663i		−	0.186414i
$731$			30.2063i			1.11722i
$732$	1.74948	+	0.0876346i	0.0646625	+	0.00323907i
$733$			8.46635i			0.312712i	0.987701	+	0.156356i	$0.0499747\pi$
$733$			8.46635i			0.312712i	−0.987701	+	0.156356i	$0.950025\pi$
$734$	−9.08620			−0.335378
$735$	−0.0618700	+	1.23513i	−0.00228211	+	0.0455584i
$736$	1.72597	+	4.47449i	0.0636200	+	0.164932i
$737$			36.4186i			1.34150i
$738$	11.4768	+	1.15268i	0.422466	+	0.0424307i
$739$	−9.85076			−0.362366			−0.181183	−	0.983449i	$-0.557993\pi$
$739$	−9.85076			−0.362366			−0.181183	+	0.983449i	$0.557993\pi$
$740$		−	5.14927i		−	0.189291i
$741$	−30.4536	−	1.52548i	−1.11874	−	0.0560399i
$742$	13.4827			0.494967
$743$	−3.83501			−0.140693			−0.0703464	−	0.997523i	$-0.522410\pi$
$743$	−3.83501			−0.140693			−0.0703464	+	0.997523i	$0.522410\pi$
$744$	−13.3220	−	0.667323i	−0.488407	−	0.0244653i
$745$	6.64835			0.243577
$746$	18.9335			0.693203
$747$	−30.1769	−	3.03084i	−1.10412	−	0.110893i
$748$	16.0780			0.587871
$749$		−	19.8819i		−	0.726469i
$750$	−11.7216	−	0.587159i	−0.428013	−	0.0214400i
$751$		−	34.5852i		−	1.26203i	−0.775769	−	0.631016i	$-0.782638\pi$
$751$		−	34.5852i		−	1.26203i	0.775769	−	0.631016i	$-0.217362\pi$
$752$			4.60889i			0.168069i
$753$	−1.14287	+	22.8154i	−0.0416484	+	0.831439i
$754$	−4.45788			−0.162346
$755$	2.42006			0.0880750
$756$	−5.13769	−	0.777275i	−0.186856	−	0.0282692i
$757$		−	41.0381i		−	1.49156i	−0.666194	−	0.745778i	$-0.732078\pi$
$757$		−	41.0381i		−	1.49156i	0.666194	−	0.745778i	$-0.267922\pi$
$758$	−28.3631			−1.03019
$759$	−6.76233	−	20.5367i	−0.245457	−	0.745434i
$760$	2.24746			0.0815239
$761$			49.3500i			1.78894i	0.447132	+	0.894468i	$0.352445\pi$
$761$			49.3500i			1.78894i	−0.447132	+	0.894468i	$0.647555\pi$
$762$	28.5563	+	1.43044i	1.03449	+	0.0518194i
$763$	−16.2449			−0.588105
$764$	22.3077			0.807065
$765$	13.1647	+	1.32221i	0.475971	+	0.0478046i
$766$		−	5.40212i		−	0.195187i
$767$			63.0599i			2.27696i
$768$	−0.0866531	+	1.72988i	−0.00312682	+	0.0624217i
$769$		−	24.5992i		−	0.887070i	−0.896257	−	0.443535i	$-0.853724\pi$
$769$		−	24.5992i		−	0.887070i	0.896257	−	0.443535i	$-0.146276\pi$
$770$	−1.85847			−0.0669744
$771$	−14.7265	−	0.737680i	−0.530363	−	0.0265669i
$772$	15.5365			0.559171
$773$	−29.6725			−1.06725			−0.533623	−	0.845723i	$-0.679170\pi$
$773$	−29.6725			−1.06725			−0.533623	+	0.845723i	$0.679170\pi$
$774$	14.5971	+	1.46607i	0.524681	+	0.0526968i
$775$	34.5795			1.24213
$776$	14.9697			0.537380
$777$	−0.624933	+	12.4757i	−0.0224194	+	0.447564i
$778$		−	15.5715i		−	0.558264i
$779$	12.1025			0.433617
$780$	0.346024	−	6.90778i	0.0123897	−	0.247338i
$781$		−	11.1691i		−	0.399661i
$782$	10.6612	+	27.6387i	0.381244	+	0.988357i
$783$	−4.09515	−	0.619550i	−0.146349	−	0.0221409i
$784$	−1.00000			−0.0357143
$785$			14.4770i			0.516706i
$786$	0.110879	−	2.21351i	0.00395492	−	0.0789532i
$787$		−	19.1824i		−	0.683780i	−0.939740	−	0.341890i	$-0.888933\pi$
$787$		−	19.1824i		−	0.683780i	0.939740	−	0.341890i	$-0.111067\pi$
$788$		−	24.3381i		−	0.867010i
$789$	−0.241003	+	4.81121i	−0.00857992	+	0.171284i
$790$	−3.91596			−0.139324
$791$			7.61914i			0.270905i
$792$	0.780350	−	7.76963i	0.0277285	−	0.276082i
$793$		−	5.65611i		−	0.200854i
$794$		−	0.247683i		−	0.00878994i
$795$	−0.834176	+	16.6529i	−0.0295852	+	0.590618i
$796$		−	9.11474i		−	0.323063i
$797$	−43.2583			−1.53229			−0.766143	−	0.642670i	$-0.777827\pi$
$797$	−43.2583			−1.53229			−0.766143	+	0.642670i	$0.777827\pi$
$798$	−5.44518	−	0.272760i	−0.192757	−	0.00965559i
$799$			28.4689i			1.00716i
$800$		−	4.49021i		−	0.158753i
$801$	26.2055	+	2.63197i	0.925926	+	0.0929962i
$802$			9.95514i			0.351528i
$803$	−18.3613			−0.647956
$804$	−24.2036	−	1.21241i	−0.853597	−	0.0427583i
$805$	−1.23233	−	3.19477i	−0.0434340	−	0.112601i
$806$			43.0704i			1.51709i
$807$	−11.2269	−	0.562377i	−0.395206	−	0.0197966i
$808$	14.4767			0.509290
$809$			18.3392i			0.644773i	0.946608	+	0.322386i	$0.104485\pi$
$809$			18.3392i			0.644773i	−0.946608	+	0.322386i	$0.895515\pi$
$810$	1.27790	−	6.29762i	0.0449009	−	0.221276i
$811$	−2.94379			−0.103370			−0.0516851	−	0.998663i	$-0.516459\pi$
$811$	−2.94379			−0.103370			−0.0516851	+	0.998663i	$0.516459\pi$
$812$	−0.797080			−0.0279720
$813$	−1.39955	+	27.9396i	−0.0490842	+	0.979884i
$814$	−18.7719			−0.657955
$815$	12.3285			0.431850
$816$	−0.535252	+	10.6854i	−0.0187376	+	0.374063i
$817$	15.3929			0.538529
$818$		−	11.4996i		−	0.402076i
$819$	−1.67671	+	16.6943i	−0.0585889	+	0.583346i
$820$			2.74520i			0.0958666i
$821$		−	19.2686i		−	0.672480i	−0.941776	−	0.336240i	$-0.890845\pi$
$821$		−	19.2686i		−	0.672480i	0.941776	−	0.336240i	$-0.109155\pi$
$822$	8.57341	+	0.429458i	0.299032	+	0.0149791i
$823$	9.56170			0.333300			0.166650	−	0.986016i	$-0.446705\pi$
$823$	9.56170			0.333300			0.166650	+	0.986016i	$0.446705\pi$
$824$	−5.40195			−0.188186
$825$	−1.01277	+	20.2182i	−0.0352600	+	0.703906i
$826$			11.2753i			0.392316i
$827$	−16.5002			−0.573769			−0.286884	−	0.957965i	$-0.592620\pi$
$827$	−16.5002			−0.573769			−0.286884	+	0.957965i	$0.592620\pi$
$828$	13.8737	−	3.81053i	0.482145	−	0.132425i
$829$	−32.4643			−1.12753			−0.563766	−	0.825935i	$-0.690648\pi$
$829$	−32.4643			−1.12753			−0.563766	+	0.825935i	$0.690648\pi$
$830$		−	7.21820i		−	0.250547i
$831$	−0.901307	+	17.9931i	−0.0312660	+	0.624172i
$832$	5.59277			0.193894
$833$	−6.17695			−0.214019
$834$	26.7195	+	1.33843i	0.925221	+	0.0463461i
$835$		−	12.0186i		−	0.415919i
$836$		−	8.19323i		−	0.283369i
$837$	−5.98587	+	39.5658i	−0.206902	+	1.36759i
$838$			28.7429i			0.992908i
$839$	−0.0390290			−0.00134743			−0.000673716	−	1.00000i	$-0.500214\pi$
$839$	−0.0390290			−0.00134743			−0.000673716		1.00000i	$0.500214\pi$
$840$	0.0618700	−	1.23513i	0.00213472	−	0.0426160i
$841$	28.3647			0.978092
$842$	−15.3490			−0.528962
$843$	−0.000444605		0.00887579i	−1.53130e−5		0.000305698i
$844$	−4.54697			−0.156513
$845$	−13.0511			−0.448973
$846$	13.7574	+	1.38174i	0.472991	+	0.0475052i
$847$		−	4.22487i		−	0.145168i
$848$	−13.4827			−0.462999
$849$	31.7334	+	1.58959i	1.08909	+	0.0545544i
$850$		−	27.7358i		−	0.951330i
$851$	−12.4475	−	32.2696i	−0.426695	−	1.10619i
$852$	7.42292	+	0.371828i	0.254305	+	0.0127386i
$853$	−17.9003			−0.612894			−0.306447	−	0.951888i	$-0.599140\pi$
$853$	−17.9003			−0.612894			−0.306447	+	0.951888i	$0.599140\pi$
$854$		−	1.01133i		−	0.0346069i
$855$	0.673787	−	6.70863i	0.0230430	−	0.229430i
$856$			19.8819i			0.679550i
$857$			32.4643i			1.10896i	0.832197	+	0.554480i	$0.187083\pi$
$857$			32.4643i			1.10896i	−0.832197	+	0.554480i	$0.812917\pi$
$858$	−25.1827	−	1.26145i	−0.859722	−	0.0430651i
$859$	−49.0225			−1.67263			−0.836314	−	0.548251i	$-0.815294\pi$
$859$	−49.0225			−1.67263			−0.836314	+	0.548251i	$0.815294\pi$
$860$			3.49156i			0.119061i
$861$	0.333167	−	6.65112i	0.0113543	−	0.226670i
$862$		−	19.2983i		−	0.657304i
$863$		−	13.8981i		−	0.473098i	−0.971620	−	0.236549i	$-0.923984\pi$
$863$		−	13.8981i		−	0.473098i	0.971620	−	0.236549i	$-0.0760164\pi$
$864$	5.13769	+	0.777275i	0.174788	+	0.0264434i
$865$			11.5426i			0.392461i
$866$	26.4517			0.898865
$867$	−1.83312	+	36.5951i	−0.0622560	+	1.24284i
$868$			7.70109i			0.261392i
$869$			14.2758i			0.484274i
$870$	0.0493153	−	0.984496i	0.00167195	−	0.0333775i
$871$			78.2512i			2.65144i
$872$	16.2449			0.550122
$873$	4.48789	−	44.6842i	0.151892	−	1.51233i
$874$	14.0844	−	5.43286i	0.476413	−	0.183769i
$875$			6.77597i			0.229070i
$876$	0.611263	−	12.2028i	0.0206527	−	0.412296i
$877$	−35.0584			−1.18384			−0.591919	−	0.805997i	$-0.701630\pi$
$877$	−35.0584			−1.18384			−0.591919	+	0.805997i	$0.701630\pi$
$878$			4.94670i			0.166943i
$879$	−1.90374	+	38.0050i	−0.0642116	+	1.28188i
$880$	1.85847			0.0626489
$881$	−17.6711			−0.595354			−0.297677	−	0.954667i	$-0.596212\pi$
$881$	−17.6711			−0.595354			−0.297677	+	0.954667i	$0.596212\pi$
$882$	−0.299799	+	2.98498i	−0.0100948	+	0.100510i
$883$	16.8553			0.567226			0.283613	−	0.958939i	$-0.408467\pi$
$883$	16.8553			0.567226			0.283613	+	0.958939i	$0.408467\pi$
$884$	34.5462			1.16192
$885$	−13.9264	−	0.697600i	−0.468131	−	0.0234496i
$886$	26.9543			0.905547
$887$			19.0502i			0.639644i	0.947478	+	0.319822i	$0.103623\pi$
$887$			19.0502i			0.639644i	−0.947478	+	0.319822i	$0.896377\pi$
$888$	0.624933	−	12.4757i	0.0209714	−	0.418658i
$889$		−	16.5077i		−	0.553649i
$890$			6.26825i			0.210112i
$891$	−22.9583	−	4.65866i	−0.769131	−	0.156071i
$892$	17.5209			0.586644
$893$	14.5075			0.485475
$894$	16.1077	+	0.806867i	0.538723	+	0.0269857i
$895$			8.66440i			0.289619i
$896$	1.00000			0.0334077
$897$	−14.5299	−	44.1263i	−0.485141	−	1.47334i
$898$	−9.06238			−0.302416
$899$			6.13838i			0.204727i
$900$	−13.4032	−	1.34616i	−0.446773	−	0.0448720i
$901$	−83.2821			−2.77453
$902$	10.0078			0.333222
$903$	0.423749	−	8.45942i	0.0141015	−	0.281512i
$904$		−	7.61914i		−	0.253409i
$905$			4.22577i			0.140469i
$906$	5.86336	+	0.293707i	0.194797	+	0.00975776i
$907$		−	30.0466i		−	0.997682i	−0.866693	−	0.498841i	$-0.833759\pi$
$907$		−	30.0466i		−	0.997682i	0.866693	−	0.498841i	$-0.166241\pi$
$908$	−10.8036			−0.358530
$909$	4.34011	−	43.2128i	0.143952	−	1.43328i
$910$	−3.99321			−0.132374
$911$	11.9614			0.396300			0.198150	−	0.980172i	$-0.436507\pi$
$911$	11.9614			0.396300			0.198150	+	0.980172i	$0.436507\pi$
$912$	5.44518	+	0.272760i	0.180308	+	0.00903198i
$913$	−26.3143			−0.870877
$914$	−8.08036			−0.267275
$915$	1.24912	+	0.0625707i	0.0412946	+	0.00206852i
$916$			3.03657i			0.100331i
$917$	−1.27957			−0.0422552
$918$	31.7352	+	4.80119i	1.04742	+	0.158463i
$919$		−	54.4913i		−	1.79750i	−0.438460	−	0.898751i	$-0.644476\pi$
$919$		−	54.4913i		−	1.79750i	0.438460	−	0.898751i	$-0.355524\pi$
$920$	1.23233	+	3.19477i	0.0406288	+	0.105328i
$921$	1.74320	−	34.8001i	0.0574405	−	1.14670i
$922$	−5.82827			−0.191944
$923$		−	23.9985i		−	0.789921i
$924$	−4.50272	−	0.225550i	−0.148129	−	0.00742005i
$925$			32.3829i			1.06474i
$926$		−	30.5512i		−	1.00397i
$927$	−1.61950	+	16.1247i	−0.0531914	+	0.529606i
$928$	0.797080			0.0261654
$929$		−	46.9843i		−	1.54150i	−0.637136	−	0.770752i	$-0.719881\pi$
$929$		−	46.9843i		−	1.54150i	0.637136	−	0.770752i	$-0.280119\pi$
$930$	−9.51184	−	0.476466i	−0.311905	−	0.0156239i
$931$			3.14772i			0.103162i
$932$		−	2.34523i		−	0.0768205i
$933$	−26.6278	−	1.33384i	−0.871754	−	0.0436678i
$934$			32.2099i			1.05394i
$935$	11.4796			0.375425
$936$	1.67671	−	16.6943i	0.0548049	−	0.545670i
$937$			44.5772i			1.45627i	0.685432	+	0.728137i	$0.259614\pi$
$937$			44.5772i			1.45627i	−0.685432	+	0.728137i	$0.740386\pi$
$938$			13.9915i			0.456839i
$939$	15.2363	+	0.763216i	0.497218	+	0.0249066i
$940$			3.29073i			0.107332i
$941$	−33.2954			−1.08540			−0.542699	−	0.839927i	$-0.682598\pi$
$941$	−33.2954			−1.08540			−0.542699	+	0.839927i	$0.682598\pi$
$942$	−1.75698	+	35.0751i	−0.0572455	+	1.14281i
$943$	6.63607	+	17.2037i	0.216100	+	0.560229i
$944$		−	11.2753i		−	0.366978i
$945$	−3.66829	−	0.554971i	−0.119329	−	0.0180532i
$946$	12.7287			0.413845
$947$			46.2085i			1.50158i	0.660543	+	0.750788i	$0.270326\pi$
$947$			46.2085i			1.50158i	−0.660543	+	0.750788i	$0.729674\pi$
$948$	−9.48766	−	0.475255i	−0.308145	−	0.0154356i
$949$	−39.4522			−1.28067
$950$	−14.1339			−0.458565
$951$	−25.4508	−	1.27488i	−0.825299	−	0.0413408i
$952$	6.17695			0.200196
$953$	7.12715			0.230871			0.115436	−	0.993315i	$-0.463174\pi$
$953$	7.12715			0.230871			0.115436	+	0.993315i	$0.463174\pi$
$954$	−4.04211	+	40.2457i	−0.130868	+	1.30300i
$955$	15.9276			0.515406
$956$			10.7409i			0.347385i
$957$	−3.58903	−	0.179781i	−0.116017	−	0.00581151i
$958$			10.9190i			0.352777i
$959$		−	4.95606i		−	0.160040i
$960$	−0.0618700	+	1.23513i	−0.00199684	+	0.0398636i
$961$	28.3068			0.913122
$962$	−40.3345			−1.30043
$963$	59.3472	+	5.96058i	1.91244	+	0.192077i
$964$		−	1.76807i		−	0.0569456i
$965$	11.0930			0.357096
$966$	−2.59799	−	7.88990i	−0.0835889	−	0.253853i
$967$	1.80407			0.0580151			0.0290076	−	0.999579i	$-0.490765\pi$
$967$	1.80407			0.0580151			0.0290076	+	0.999579i	$0.490765\pi$
$968$			4.22487i			0.135793i
$969$	33.6346	+	1.68482i	1.08050	+	0.0541243i
$970$	10.6883			0.343180
$971$	7.25522			0.232831			0.116416	−	0.993201i	$-0.462860\pi$
$971$	7.25522			0.232831			0.116416	+	0.993201i	$0.462860\pi$
$972$	3.86043	−	15.1029i	0.123823	−	0.484425i
$973$		−	15.4459i		−	0.495172i
$974$		−	31.2013i		−	0.999753i
$975$	−2.17609	+	43.4420i	−0.0696907	+	1.39126i
$976$			1.01133i			0.0323718i
$977$	−4.20709			−0.134597			−0.0672984	−	0.997733i	$-0.521438\pi$
$977$	−4.20709			−0.134597			−0.0672984	+	0.997733i	$0.521438\pi$
$978$	29.8698	+	1.49624i	0.955132	+	0.0478444i
$979$	22.8512			0.730329
$980$	−0.713996			−0.0228078
$981$	4.87021	−	48.4908i	0.155494	−	1.54819i
$982$	36.2759			1.15761
$983$	25.6221			0.817219			0.408609	−	0.912709i	$-0.366014\pi$
$983$	25.6221			0.817219			0.408609	+	0.912709i	$0.366014\pi$
$984$	−0.333167	+	6.65112i	−0.0106210	+	0.212030i
$985$		−	17.3773i		−	0.553688i
$986$	4.92352			0.156797
$987$	0.399374	−	7.97283i	0.0127122	−	0.253778i
$988$		−	17.6045i		−	0.560073i
$989$	8.44027	+	21.8810i	0.268385	+	0.695776i
$990$	0.557166	−	5.54749i	0.0177079	−	0.176311i
$991$	42.7537			1.35812			0.679058	−	0.734085i	$-0.262389\pi$
$991$	42.7537			1.35812			0.679058	+	0.734085i	$0.262389\pi$
$992$		−	7.70109i		−	0.244510i
$993$	−1.32030	+	26.3576i	−0.0418985	+	0.836432i
$994$		−	4.29100i		−	0.136102i
$995$		−	6.50789i		−	0.206314i
$996$	0.876027	−	17.4884i	0.0277580	−	0.554141i
$997$	2.60235			0.0824172			0.0412086	−	0.999151i	$-0.486879\pi$
$997$	2.60235			0.0824172			0.0412086	+	0.999151i	$0.486879\pi$
$998$			12.1997i			0.386176i
$999$	−37.0525	−	5.60563i	−1.17229	−	0.177354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.h.b.827.18	yes	24
3.2	odd	2		966.2.h.a.827.6	✓	24
23.22	odd	2		966.2.h.a.827.18	yes	24
69.68	even	2	inner	966.2.h.b.827.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.h.a.827.6	✓	24	3.2	odd	2
966.2.h.a.827.18	yes	24	23.22	odd	2
966.2.h.b.827.6	yes	24	69.68	even	2	inner
966.2.h.b.827.18	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.0866531 + 1.72988i) q^{3} -1.00000 q^{4} -0.713996 q^{5} +(-1.72988 - 0.0866531i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-2.98498 - 0.299799i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.0866531 + 1.72988i) q^{3} -1.00000 q^{4} -0.713996 q^{5} +(-1.72988 - 0.0866531i) q^{6} +1.00000i q^{7} -1.00000i q^{8} +(-2.98498 - 0.299799i) q^{9} -0.713996i q^{10} -2.60291 q^{11} +(0.0866531 - 1.72988i) q^{12} -5.59277 q^{13} -1.00000 q^{14} +(0.0618700 - 1.23513i) q^{15} +1.00000 q^{16} +6.17695 q^{17} +(0.299799 - 2.98498i) q^{18} -3.14772i q^{19} +0.713996 q^{20} +(-1.72988 - 0.0866531i) q^{21} -2.60291i q^{22} +(4.47449 - 1.72597i) q^{23} +(1.72988 + 0.0866531i) q^{24} -4.49021 q^{25} -5.59277i q^{26} +(0.777275 - 5.13769i) q^{27} -1.00000i q^{28} -0.797080i q^{29} +(1.23513 + 0.0618700i) q^{30} -7.70109 q^{31} +1.00000i q^{32} +(0.225550 - 4.50272i) q^{33} +6.17695i q^{34} -0.713996i q^{35} +(2.98498 + 0.299799i) q^{36} -7.21190i q^{37} +3.14772 q^{38} +(0.484630 - 9.67482i) q^{39} +0.713996i q^{40} +3.84484i q^{41} +(0.0866531 - 1.72988i) q^{42} +4.89017i q^{43} +2.60291 q^{44} +(2.13127 + 0.214055i) q^{45} +(1.72597 + 4.47449i) q^{46} +4.60889i q^{47} +(-0.0866531 + 1.72988i) q^{48} -1.00000 q^{49} -4.49021i q^{50} +(-0.535252 + 10.6854i) q^{51} +5.59277 q^{52} -13.4827 q^{53} +(5.13769 + 0.777275i) q^{54} +1.85847 q^{55} +1.00000 q^{56} +(5.44518 + 0.272760i) q^{57} +0.797080 q^{58} -11.2753i q^{59} +(-0.0618700 + 1.23513i) q^{60} +1.01133i q^{61} -7.70109i q^{62} +(0.299799 - 2.98498i) q^{63} -1.00000 q^{64} +3.99321 q^{65} +(4.50272 + 0.225550i) q^{66} -13.9915i q^{67} -6.17695 q^{68} +(2.59799 + 7.88990i) q^{69} +0.713996 q^{70} +4.29100i q^{71} +(-0.299799 + 2.98498i) q^{72} +7.05414 q^{73} +7.21190 q^{74} +(0.389091 - 7.76753i) q^{75} +3.14772i q^{76} -2.60291i q^{77} +(9.67482 + 0.484630i) q^{78} -5.48457i q^{79} -0.713996 q^{80} +(8.82024 + 1.78979i) q^{81} -3.84484 q^{82} +10.1096 q^{83} +(1.72988 + 0.0866531i) q^{84} -4.41032 q^{85} -4.89017 q^{86} +(1.37885 + 0.0690694i) q^{87} +2.60291i q^{88} -8.77912 q^{89} +(-0.214055 + 2.13127i) q^{90} -5.59277i q^{91} +(-4.47449 + 1.72597i) q^{92} +(0.667323 - 13.3220i) q^{93} -4.60889 q^{94} +2.24746i q^{95} +(-1.72988 - 0.0866531i) q^{96} +14.9697i q^{97} -1.00000i q^{98} +(7.76963 + 0.780350i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9	\( 24 q + 4 q^{3} - 24 q^{4} + 4 q^{5} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 24 q^{14} + 4 q^{15} + 24 q^{16} - 32 q^{17} + 4 q^{18} - 4 q^{20} + 8 q^{23} - 12 q^{25} + 16 q^{27} + 4 q^{30} - 16 q^{31} - 20 q^{33} + 4 q^{36} - 8 q^{39} - 4 q^{42} - 24 q^{45} - 4 q^{46} + 4 q^{48} - 24 q^{49} - 24 q^{51} - 8 q^{52} - 24 q^{53} - 12 q^{54} + 16 q^{55} + 24 q^{56} - 4 q^{57} + 4 q^{58} - 4 q^{60} + 4 q^{63} - 24 q^{64} + 12 q^{66} + 32 q^{68} - 24 q^{69} - 4 q^{70} - 4 q^{72} - 32 q^{73} + 16 q^{74} + 48 q^{75} + 12 q^{78} + 4 q^{80} - 8 q^{81} - 8 q^{82} - 16 q^{83} - 16 q^{85} - 16 q^{86} + 20 q^{87} - 24 q^{89} + 28 q^{90} - 8 q^{92} + 16 q^{93} + 8 q^{94} + 48 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^4 + 4 * q^5 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 24 * q^14 + 4 * q^15 + 24 * q^16 - 32 * q^17 + 4 * q^18 - 4 * q^20 + 8 * q^23 - 12 * q^25 + 16 * q^27 + 4 * q^30 - 16 * q^31 - 20 * q^33 + 4 * q^36 - 8 * q^39 - 4 * q^42 - 24 * q^45 - 4 * q^46 + 4 * q^48 - 24 * q^49 - 24 * q^51 - 8 * q^52 - 24 * q^53 - 12 * q^54 + 16 * q^55 + 24 * q^56 - 4 * q^57 + 4 * q^58 - 4 * q^60 + 4 * q^63 - 24 * q^64 + 12 * q^66 + 32 * q^68 - 24 * q^69 - 4 * q^70 - 4 * q^72 - 32 * q^73 + 16 * q^74 + 48 * q^75 + 12 * q^78 + 4 * q^80 - 8 * q^81 - 8 * q^82 - 16 * q^83 - 16 * q^85 - 16 * q^86 + 20 * q^87 - 24 * q^89 + 28 * q^90 - 8 * q^92 + 16 * q^93 + 8 * q^94 + 48 * q^99

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