LMFDB - Embedded newform 966.2.f.c.461.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(461,966)]

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, 1, 0]))

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

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

chi := DirichletCharacter("966.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.f (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:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.19
Character	$\chi$	$=$	966.461
Dual form			966.2.f.c.461.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.952183 - 1.44684i) q^{3} -1.00000 q^{4} +3.39470 q^{5} +(1.44684 - 0.952183i) q^{6} +(1.73823 + 1.99463i) q^{7} -1.00000i q^{8} +(-1.18670 + 2.75531i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.952183 - 1.44684i) q^{3} -1.00000 q^{4} +3.39470 q^{5} +(1.44684 - 0.952183i) q^{6} +(1.73823 + 1.99463i) q^{7} -1.00000i q^{8} +(-1.18670 + 2.75531i) q^{9} +3.39470i q^{10} -1.55701i q^{11} +(0.952183 + 1.44684i) q^{12} +6.18871i q^{13} +(-1.99463 + 1.73823i) q^{14} +(-3.23237 - 4.91159i) q^{15} +1.00000 q^{16} -2.89368 q^{17} +(-2.75531 - 1.18670i) q^{18} +6.93426i q^{19} -3.39470 q^{20} +(1.23079 - 4.41420i) q^{21} +1.55701 q^{22} +1.00000i q^{23} +(-1.44684 + 0.952183i) q^{24} +6.52399 q^{25} -6.18871 q^{26} +(5.11645 - 0.906601i) q^{27} +(-1.73823 - 1.99463i) q^{28} -1.06422i q^{29} +(4.91159 - 3.23237i) q^{30} -7.18822i q^{31} +1.00000i q^{32} +(-2.25274 + 1.48255i) q^{33} -2.89368i q^{34} +(5.90078 + 6.77116i) q^{35} +(1.18670 - 2.75531i) q^{36} -6.46015 q^{37} -6.93426 q^{38} +(8.95407 - 5.89278i) q^{39} -3.39470i q^{40} -4.43534 q^{41} +(4.41420 + 1.23079i) q^{42} +7.07753 q^{43} +1.55701i q^{44} +(-4.02848 + 9.35346i) q^{45} -1.00000 q^{46} +11.3183 q^{47} +(-0.952183 - 1.44684i) q^{48} +(-0.957082 + 6.93426i) q^{49} +6.52399i q^{50} +(2.75531 + 4.18670i) q^{51} -6.18871i q^{52} -2.78970i q^{53} +(0.906601 + 5.11645i) q^{54} -5.28557i q^{55} +(1.99463 - 1.73823i) q^{56} +(10.0328 - 6.60268i) q^{57} +1.06422 q^{58} -9.07749 q^{59} +(3.23237 + 4.91159i) q^{60} +13.7405i q^{61} +7.18822 q^{62} +(-7.55858 + 2.42236i) q^{63} -1.00000 q^{64} +21.0088i q^{65} +(-1.48255 - 2.25274i) q^{66} +10.9175 q^{67} +2.89368 q^{68} +(1.44684 - 0.952183i) q^{69} +(-6.77116 + 5.90078i) q^{70} -5.72662i q^{71} +(2.75531 + 1.18670i) q^{72} +11.2517i q^{73} -6.46015i q^{74} +(-6.21203 - 9.43917i) q^{75} -6.93426i q^{76} +(3.10565 - 2.70644i) q^{77} +(5.89278 + 8.95407i) q^{78} +0.738342 q^{79} +3.39470 q^{80} +(-6.18350 - 6.53944i) q^{81} -4.43534i q^{82} +2.20023 q^{83} +(-1.23079 + 4.41420i) q^{84} -9.82318 q^{85} +7.07753i q^{86} +(-1.53976 + 1.01333i) q^{87} -1.55701 q^{88} +3.01787 q^{89} +(-9.35346 - 4.02848i) q^{90} +(-12.3442 + 10.7574i) q^{91} -1.00000i q^{92} +(-10.4002 + 6.84450i) q^{93} +11.3183i q^{94} +23.5397i q^{95} +(1.44684 - 0.952183i) q^{96} -6.59867i q^{97} +(-6.93426 - 0.957082i) q^{98} +(4.29004 + 1.84769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9	$ 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9 + 16 * q^15 + 28 * q^16 - 16 * q^18 + 4 * q^21 + 80 * q^25 - 4 * q^28 + 12 * q^30 + 4 * q^36 + 20 * q^37 - 20 * q^39 + 28 * q^42 - 28 * q^43 - 28 * q^46 - 28 * q^49 + 16 * q^51 - 8 * q^57 - 36 * q^58 - 16 * q^60 + 36 * q^63 - 28 * q^64 - 8 * q^67 - 60 * q^70 + 16 * q^72 + 16 * q^78 - 76 * q^81 - 4 * q^84 - 24 * q^85 + 36 * q^91 + 48 * q^93 + 72 * 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
$3$	−0.952183	−	1.44684i	−0.549743	−	0.835334i
$3$	−0.952183	−	1.44684i	−0.549743	−	0.835334i
$4$	−1.00000			−0.500000
$5$	3.39470			1.51816			0.759078	−	0.651000i	$-0.225650\pi$
$5$	3.39470			1.51816			0.759078	+	0.651000i	$0.225650\pi$
$6$	1.44684	−	0.952183i	0.590670	−	0.388727i
$7$	1.73823	+	1.99463i	0.656991	+	0.753899i
$7$	1.73823	+	1.99463i	0.656991	+	0.753899i
$8$		−	1.00000i		−	0.353553i
$9$	−1.18670	+	2.75531i	−0.395565	+	0.918438i
$10$			3.39470i			1.07350i
$11$		−	1.55701i		−	0.469455i	−0.972061	−	0.234728i	$-0.924580\pi$
$11$		−	1.55701i		−	0.469455i	0.972061	−	0.234728i	$-0.0754198\pi$
$12$	0.952183	+	1.44684i	0.274871	+	0.417667i
$13$			6.18871i			1.71644i	0.513283	+	0.858219i	$0.328429\pi$
$13$			6.18871i			1.71644i	−0.513283	+	0.858219i	$0.671571\pi$
$14$	−1.99463	+	1.73823i	−0.533087	+	0.464563i
$15$	−3.23237	−	4.91159i	−0.834595	−	1.26817i
$16$	1.00000			0.250000
$17$	−2.89368			−0.701821			−0.350910	−	0.936409i	$-0.614128\pi$
$17$	−2.89368			−0.701821			−0.350910	+	0.936409i	$0.614128\pi$
$18$	−2.75531	−	1.18670i	−0.649434	−	0.279707i
$19$			6.93426i			1.59083i	0.606066	+	0.795414i	$0.292747\pi$
$19$			6.93426i			1.59083i	−0.606066	+	0.795414i	$0.707253\pi$
$20$	−3.39470			−0.759078
$21$	1.23079	−	4.41420i	0.268581	−	0.963257i
$22$	1.55701			0.331955
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	−1.44684	+	0.952183i	−0.295335	+	0.194363i
$25$	6.52399			1.30480
$26$	−6.18871			−1.21371
$27$	5.11645	−	0.906601i	0.984662	−	0.174475i
$28$	−1.73823	−	1.99463i	−0.328495	−	0.376949i
$29$		−	1.06422i		−	0.197620i	−0.995106	−	0.0988102i	$-0.968496\pi$
$29$		−	1.06422i		−	0.197620i	0.995106	−	0.0988102i	$-0.0315037\pi$
$30$	4.91159	−	3.23237i	0.896730	−	0.590148i
$31$		−	7.18822i		−	1.29104i	−0.763742	−	0.645521i	$-0.776640\pi$
$31$		−	7.18822i		−	1.29104i	0.763742	−	0.645521i	$-0.223360\pi$
$32$			1.00000i			0.176777i
$33$	−2.25274	+	1.48255i	−0.392152	+	0.258080i
$34$		−	2.89368i		−	0.496262i
$35$	5.90078	+	6.77116i	0.997415	+	1.14454i
$36$	1.18670	−	2.75531i	0.197783	−	0.459219i
$37$	−6.46015			−1.06204			−0.531021	−	0.847359i	$-0.678192\pi$
$37$	−6.46015			−1.06204			−0.531021	+	0.847359i	$0.678192\pi$
$38$	−6.93426			−1.12489
$39$	8.95407	−	5.89278i	1.43380	−	0.943600i
$40$		−	3.39470i		−	0.536749i
$41$	−4.43534			−0.692684			−0.346342	−	0.938108i	$-0.612576\pi$
$41$	−4.43534			−0.692684			−0.346342	+	0.938108i	$0.612576\pi$
$42$	4.41420	+	1.23079i	0.681126	+	0.189915i
$43$	7.07753			1.07931			0.539657	−	0.841885i	$-0.318554\pi$
$43$	7.07753			1.07931			0.539657	+	0.841885i	$0.318554\pi$
$44$			1.55701i			0.234728i
$45$	−4.02848	+	9.35346i	−0.600530	+	1.39433i
$46$	−1.00000			−0.147442
$47$	11.3183			1.65094			0.825470	−	0.564446i	$-0.190910\pi$
$47$	11.3183			1.65094			0.825470	+	0.564446i	$0.190910\pi$
$48$	−0.952183	−	1.44684i	−0.137436	−	0.208833i
$49$	−0.957082	+	6.93426i	−0.136726	+	0.990609i
$50$			6.52399i			0.922631i
$51$	2.75531	+	4.18670i	0.385821	+	0.586255i
$52$		−	6.18871i		−	0.858219i
$53$		−	2.78970i		−	0.383195i	−0.981474	−	0.191598i	$-0.938633\pi$
$53$		−	2.78970i		−	0.383195i	0.981474	−	0.191598i	$-0.0613669\pi$
$54$	0.906601	+	5.11645i	0.123373	+	0.696261i
$55$		−	5.28557i		−	0.712706i
$56$	1.99463	−	1.73823i	0.266543	−	0.232281i
$57$	10.0328	−	6.60268i	1.32887	−	0.874547i
$58$	1.06422			0.139739
$59$	−9.07749			−1.18179			−0.590894	−	0.806749i	$-0.701225\pi$
$59$	−9.07749			−1.18179			−0.590894	+	0.806749i	$0.701225\pi$
$60$	3.23237	+	4.91159i	0.417298	+	0.634084i
$61$			13.7405i			1.75929i	0.475634	+	0.879643i	$0.342219\pi$
$61$			13.7405i			1.75929i	−0.475634	+	0.879643i	$0.657781\pi$
$62$	7.18822			0.912905
$63$	−7.55858	+	2.42236i	−0.952292	+	0.305189i
$64$	−1.00000			−0.125000
$65$			21.0088i			2.60582i
$66$	−1.48255	−	2.25274i	−0.182490	−	0.277293i
$67$	10.9175			1.33378			0.666892	−	0.745154i	$-0.267624\pi$
$67$	10.9175			1.33378			0.666892	+	0.745154i	$0.267624\pi$
$68$	2.89368			0.350910
$69$	1.44684	−	0.952183i	0.174179	−	0.114629i
$70$	−6.77116	+	5.90078i	−0.809309	+	0.705279i
$71$		−	5.72662i		−	0.679625i	−0.940493	−	0.339812i	$-0.889636\pi$
$71$		−	5.72662i		−	0.679625i	0.940493	−	0.339812i	$-0.110364\pi$
$72$	2.75531	+	1.18670i	0.324717	+	0.139854i
$73$			11.2517i			1.31692i	0.752617	+	0.658459i	$0.228791\pi$
$73$			11.2517i			1.31692i	−0.752617	+	0.658459i	$0.771209\pi$
$74$		−	6.46015i		−	0.750977i
$75$	−6.21203	−	9.43917i	−0.717303	−	1.08994i
$76$		−	6.93426i		−	0.795414i
$77$	3.10565	−	2.70644i	0.353922	−	0.308428i
$78$	5.89278	+	8.95407i	0.667226	+	1.01385i
$79$	0.738342			0.0830700			0.0415350	−	0.999137i	$-0.486775\pi$
$79$	0.738342			0.0830700			0.0415350	+	0.999137i	$0.486775\pi$
$80$	3.39470			0.379539
$81$	−6.18350	−	6.53944i	−0.687056	−	0.726605i
$82$		−	4.43534i		−	0.489801i
$83$	2.20023			0.241506			0.120753	−	0.992683i	$-0.461469\pi$
$83$	2.20023			0.241506			0.120753	+	0.992683i	$0.461469\pi$
$84$	−1.23079	+	4.41420i	−0.134290	+	0.481629i
$85$	−9.82318			−1.06547
$86$			7.07753i			0.763190i
$87$	−1.53976	+	1.01333i	−0.165079	+	0.108640i
$88$	−1.55701			−0.165977
$89$	3.01787			0.319894			0.159947	−	0.987126i	$-0.448868\pi$
$89$	3.01787			0.319894			0.159947	+	0.987126i	$0.448868\pi$
$90$	−9.35346	−	4.02848i	−0.985941	−	0.424639i
$91$	−12.3442	+	10.7574i	−1.29402	+	1.12768i
$92$		−	1.00000i		−	0.104257i
$93$	−10.4002	+	6.84450i	−1.07845	+	0.709742i
$94$			11.3183i			1.16739i
$95$			23.5397i			2.41513i
$96$	1.44684	−	0.952183i	0.147668	−	0.0971817i
$97$		−	6.59867i		−	0.669994i	−0.942219	−	0.334997i	$-0.891265\pi$
$97$		−	6.59867i		−	0.669994i	0.942219	−	0.334997i	$-0.108735\pi$
$98$	−6.93426	−	0.957082i	−0.700466	−	0.0966798i
$99$	4.29004	+	1.84769i	0.431165	+	0.185700i
$100$	−6.52399			−0.652399
$101$	14.5366			1.44644			0.723222	−	0.690616i	$-0.242661\pi$
$101$	14.5366			1.44644			0.723222	+	0.690616i	$0.242661\pi$
$102$	−4.18670	+	2.75531i	−0.414545	+	0.272817i
$103$		−	8.33343i		−	0.821118i	−0.911834	−	0.410559i	$-0.865334\pi$
$103$		−	8.33343i		−	0.821118i	0.911834	−	0.410559i	$-0.134666\pi$
$104$	6.18871			0.606853
$105$	4.17817	−	14.9849i	0.407748	−	1.46237i
$106$	2.78970			0.270960
$107$		−	15.0016i		−	1.45026i	−0.688613	−	0.725129i	$-0.741780\pi$
$107$		−	15.0016i		−	1.45026i	0.688613	−	0.725129i	$-0.258220\pi$
$108$	−5.11645	+	0.906601i	−0.492331	+	0.0872377i
$109$	8.25400			0.790590			0.395295	−	0.918554i	$-0.370642\pi$
$109$	8.25400			0.790590			0.395295	+	0.918554i	$0.370642\pi$
$110$	5.28557			0.503959
$111$	6.15124	+	9.34681i	0.583850	+	0.887160i
$112$	1.73823	+	1.99463i	0.164248	+	0.188475i
$113$			3.23989i			0.304783i	0.988320	+	0.152392i	$0.0486975\pi$
$113$			3.23989i			0.304783i	−0.988320	+	0.152392i	$0.951302\pi$
$114$	6.60268	+	10.0328i	0.618398	+	0.939655i
$115$			3.39470i			0.316557i
$116$			1.06422i			0.0988102i
$117$	−17.0518	−	7.34412i	−1.57644	−	0.678964i
$118$		−	9.07749i		−	0.835651i
$119$	−5.02990	−	5.77182i	−0.461090	−	0.529102i
$120$	−4.91159	+	3.23237i	−0.448365	+	0.295074i
$121$	8.57573			0.779612
$122$	−13.7405			−1.24400
$123$	4.22325	+	6.41723i	0.380798	+	0.578622i
$124$			7.18822i			0.645521i
$125$	5.17347			0.462729
$126$	−2.42236	−	7.55858i	−0.215801	−	0.673372i
$127$	−7.00338			−0.621449			−0.310725	−	0.950500i	$-0.600572\pi$
$127$	−7.00338			−0.621449			−0.310725	+	0.950500i	$0.600572\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−6.73910	−	10.2401i	−0.593345	−	0.901587i
$130$	−21.0088			−1.84259
$131$	11.0660			0.966841			0.483421	−	0.875388i	$-0.339394\pi$
$131$	11.0660			0.966841			0.483421	+	0.875388i	$0.339394\pi$
$132$	2.25274	−	1.48255i	0.196076	−	0.129040i
$133$	−13.8313	+	12.0534i	−1.19932	+	1.04516i
$134$			10.9175i			0.943128i
$135$	17.3688	−	3.07764i	1.49487	−	0.264881i
$136$			2.89368i			0.248131i
$137$		−	17.0993i		−	1.46089i	−0.682971	−	0.730445i	$-0.739313\pi$
$137$		−	17.0993i		−	1.46089i	0.682971	−	0.730445i	$-0.260687\pi$
$138$	0.952183	+	1.44684i	0.0810552	+	0.123163i
$139$		−	17.0912i		−	1.44966i	−0.688929	−	0.724829i	$-0.741919\pi$
$139$		−	17.0912i		−	1.44966i	0.688929	−	0.724829i	$-0.258081\pi$
$140$	−5.90078	−	6.77116i	−0.498707	−	0.572268i
$141$	−10.7771	−	16.3757i	−0.907593	−	1.37909i
$142$	5.72662			0.480567
$143$	9.63586			0.805791
$144$	−1.18670	+	2.75531i	−0.0988914	+	0.229609i
$145$		−	3.61270i		−	0.300019i
$146$	−11.2517			−0.931201
$147$	10.9441	−	5.21794i	0.902653	−	0.430368i
$148$	6.46015			0.531021
$149$		−	2.18895i		−	0.179326i	−0.995972	−	0.0896628i	$-0.971421\pi$
$149$		−	2.18895i		−	0.179326i	0.995972	−	0.0896628i	$-0.0285789\pi$
$150$	9.43917	−	6.21203i	0.770705	−	0.507210i
$151$	−10.3233			−0.840100			−0.420050	−	0.907501i	$-0.637987\pi$
$151$	−10.3233			−0.840100			−0.420050	+	0.907501i	$0.637987\pi$
$152$	6.93426			0.562443
$153$	3.43392	−	7.97300i	0.277616	−	0.644579i
$154$	2.70644	+	3.10565i	0.218091	+	0.250260i
$155$		−	24.4019i		−	1.96000i
$156$	−8.95407	+	5.89278i	−0.716900	+	0.471800i
$157$		−	12.9450i		−	1.03312i	−0.856251	−	0.516560i	$-0.827212\pi$
$157$		−	12.9450i		−	1.03312i	0.856251	−	0.516560i	$-0.172788\pi$
$158$			0.738342i			0.0587394i
$159$	−4.03626	+	2.65631i	−0.320096	+	0.210659i
$160$			3.39470i			0.268375i
$161$	−1.99463	+	1.73823i	−0.157199	+	0.136992i
$162$	6.53944	−	6.18350i	0.513787	−	0.485822i
$163$	1.73236			0.135689			0.0678445	−	0.997696i	$-0.478388\pi$
$163$	1.73236			0.135689			0.0678445	+	0.997696i	$0.478388\pi$
$164$	4.43534			0.346342
$165$	−7.64738	+	5.03283i	−0.595348	+	0.391805i
$166$			2.20023i			0.170771i
$167$	1.67581			0.129678			0.0648391	−	0.997896i	$-0.479347\pi$
$167$	1.67581			0.129678			0.0648391	+	0.997896i	$0.479347\pi$
$168$	−4.41420	−	1.23079i	−0.340563	−	0.0949577i
$169$	−25.3001			−1.94616
$170$		−	9.82318i		−	0.753403i
$171$	−19.1061	−	8.22886i	−1.46108	−	0.629277i
$172$	−7.07753			−0.539657
$173$	−26.1692			−1.98961			−0.994804	−	0.101808i	$-0.967537\pi$
$173$	−26.1692			−1.98961			−0.994804	+	0.101808i	$0.967537\pi$
$174$	−1.01333	−	1.53976i	−0.0768204	−	0.116729i
$175$	11.3402	+	13.0129i	0.857240	+	0.983685i
$176$		−	1.55701i		−	0.117364i
$177$	8.64343	+	13.1337i	0.649680	+	0.987188i
$178$			3.01787i			0.226199i
$179$		−	10.9106i		−	0.815498i	−0.913094	−	0.407749i	$-0.866314\pi$
$179$		−	10.9106i		−	0.815498i	0.913094	−	0.407749i	$-0.133686\pi$
$180$	4.02848	−	9.35346i	0.300265	−	0.697166i
$181$		−	12.6502i		−	0.940282i	−0.882591	−	0.470141i	$-0.844203\pi$
$181$		−	12.6502i		−	0.940282i	0.882591	−	0.470141i	$-0.155797\pi$
$182$	−10.7574	−	12.3442i	−0.797393	−	0.915011i
$183$	19.8803	−	13.0834i	1.46959	−	0.967155i
$184$	1.00000			0.0737210
$185$	−21.9303			−1.61235
$186$	−6.84450	−	10.4002i	−0.501863	−	0.762581i
$187$			4.50548i			0.329473i
$188$	−11.3183			−0.825470
$189$	10.7019	+	8.62953i	0.778450	+	0.627706i
$190$	−23.5397			−1.70775
$191$		−	8.55112i		−	0.618737i	−0.950942	−	0.309369i	$-0.899882\pi$
$191$		−	8.55112i		−	0.618737i	0.950942	−	0.309369i	$-0.100118\pi$
$192$	0.952183	+	1.44684i	0.0687179	+	0.104417i
$193$	12.5635			0.904339			0.452169	−	0.891932i	$-0.350650\pi$
$193$	12.5635			0.904339			0.452169	+	0.891932i	$0.350650\pi$
$194$	6.59867			0.473757
$195$	30.3964	−	20.0042i	2.17673	−	1.43253i
$196$	0.957082	−	6.93426i	0.0683630	−	0.495304i
$197$			5.89370i			0.419909i	0.977711	+	0.209954i	$0.0673316\pi$
$197$			5.89370i			0.419909i	−0.977711	+	0.209954i	$0.932668\pi$
$198$	−1.84769	+	4.29004i	−0.131310	+	0.304880i
$199$			21.6731i			1.53637i	0.640230	+	0.768183i	$0.278839\pi$
$199$			21.6731i			1.53637i	−0.640230	+	0.768183i	$0.721161\pi$
$200$		−	6.52399i		−	0.461315i
$201$	−10.3954	−	15.7959i	−0.733238	−	1.11416i
$202$			14.5366i			1.02279i
$203$	2.12272	−	1.84986i	0.148986	−	0.129835i
$204$	−2.75531	−	4.18670i	−0.192911	−	0.293127i
$205$	−15.0566			−1.05160
$206$	8.33343			0.580618
$207$	−2.75531	−	1.18670i	−0.191508	−	0.0824811i
$208$			6.18871i			0.429110i
$209$	10.7967			0.746823
$210$	14.9849	+	4.17817i	1.03405	+	0.288321i
$211$	−7.97787			−0.549219			−0.274610	−	0.961556i	$-0.588549\pi$
$211$	−7.97787			−0.549219			−0.274610	+	0.961556i	$0.588549\pi$
$212$			2.78970i			0.191598i
$213$	−8.28551	+	5.45279i	−0.567714	+	0.373619i
$214$	15.0016			1.02549
$215$	24.0261			1.63857
$216$	−0.906601	−	5.11645i	−0.0616864	−	0.348130i
$217$	14.3378	−	12.4948i	0.973315	−	0.848203i
$218$			8.25400i			0.559031i
$219$	16.2795	−	10.7137i	1.10007	−	0.723966i
$220$			5.28557i			0.356353i
$221$		−	17.9081i		−	1.20463i
$222$	−9.34681	+	6.15124i	−0.627317	+	0.412844i
$223$			2.86053i			0.191556i	0.995403	+	0.0957778i	$0.0305338\pi$
$223$			2.86053i			0.191556i	−0.995403	+	0.0957778i	$0.969466\pi$
$224$	−1.99463	+	1.73823i	−0.133272	+	0.116141i
$225$	−7.74199	+	17.9756i	−0.516133	+	1.19837i
$226$	−3.23989			−0.215514
$227$	−3.48995			−0.231636			−0.115818	−	0.993270i	$-0.536949\pi$
$227$	−3.48995			−0.231636			−0.115818	+	0.993270i	$0.536949\pi$
$228$	−10.0328	+	6.60268i	−0.664437	+	0.437273i
$229$		−	0.242367i		−	0.0160161i	−0.999968	−	0.00800805i	$-0.997451\pi$
$229$		−	0.242367i		−	0.0160161i	0.999968	−	0.00800805i	$-0.00254907\pi$
$230$	−3.39470			−0.223840
$231$	−6.87294	−	1.91635i	−0.452206	−	0.126087i
$232$	−1.06422			−0.0698694
$233$			10.3374i			0.677226i	0.940926	+	0.338613i	$0.109958\pi$
$233$			10.3374i			0.677226i	−0.940926	+	0.338613i	$0.890042\pi$
$234$	7.34412	−	17.0518i	0.480100	−	1.11471i
$235$	38.4222			2.50639
$236$	9.07749			0.590894
$237$	−0.703037	−	1.06826i	−0.0456672	−	0.0693912i
$238$	5.77182	−	5.02990i	0.374131	−	0.326040i
$239$			18.1395i			1.17335i	0.809824	+	0.586673i	$0.199562\pi$
$239$			18.1395i			1.17335i	−0.809824	+	0.586673i	$0.800438\pi$
$240$	−3.23237	−	4.91159i	−0.208649	−	0.317042i
$241$			0.758241i			0.0488426i	0.999702	+	0.0244213i	$0.00777431\pi$
$241$			0.758241i			0.0488426i	−0.999702	+	0.0244213i	$0.992226\pi$
$242$			8.57573i			0.551269i
$243$	−3.57370	+	15.1733i	−0.229253	+	0.973367i
$244$		−	13.7405i		−	0.879643i
$245$	−3.24900	+	23.5397i	−0.207571	+	1.50390i
$246$	−6.41723	+	4.22325i	−0.409148	+	0.269265i
$247$	−42.9141			−2.73056
$248$	−7.18822			−0.456453
$249$	−2.09502	−	3.18338i	−0.132766	−	0.201738i
$250$			5.17347i			0.327199i
$251$	−4.73975			−0.299170			−0.149585	−	0.988749i	$-0.547794\pi$
$251$	−4.73975			−0.299170			−0.149585	+	0.988749i	$0.547794\pi$
$252$	7.55858	−	2.42236i	0.476146	−	0.152595i
$253$	1.55701			0.0978882
$254$		−	7.00338i		−	0.439431i
$255$	9.35346	+	14.2126i	0.585736	+	0.890026i
$256$	1.00000			0.0625000
$257$	25.2375			1.57427			0.787135	−	0.616781i	$-0.211564\pi$
$257$	25.2375			1.57427			0.787135	+	0.616781i	$0.211564\pi$
$258$	10.2401	−	6.73910i	0.637518	−	0.419558i
$259$	−11.2293	−	12.8856i	−0.697752	−	0.800672i
$260$		−	21.0088i		−	1.30291i
$261$	2.93226	+	1.26290i	0.181502	+	0.0781718i
$262$			11.0660i			0.683660i
$263$			14.4468i			0.890827i	0.895325	+	0.445413i	$0.146943\pi$
$263$			14.4468i			0.890827i	−0.895325	+	0.445413i	$0.853057\pi$
$264$	1.48255	+	2.25274i	0.0912449	+	0.138647i
$265$		−	9.47021i		−	0.581750i
$266$	−12.0534	−	13.8313i	−0.739040	−	0.848050i
$267$	−2.87357	−	4.36638i	−0.175859	−	0.267218i
$268$	−10.9175			−0.666892
$269$	21.5181			1.31198			0.655991	−	0.754769i	$-0.272251\pi$
$269$	21.5181			1.31198			0.655991	+	0.754769i	$0.272251\pi$
$270$	3.07764	+	17.3688i	0.187299	+	1.05703i
$271$			10.8069i			0.656475i	0.944595	+	0.328238i	$0.106455\pi$
$271$			10.8069i			0.656475i	−0.944595	+	0.328238i	$0.893545\pi$
$272$	−2.89368			−0.175455
$273$	27.3182	+	7.61701i	1.65337	+	0.461003i
$274$	17.0993			1.03301
$275$		−	10.1579i		−	0.612544i
$276$	−1.44684	+	0.952183i	−0.0870896	+	0.0573147i
$277$	−26.4435			−1.58884			−0.794419	−	0.607370i	$-0.792224\pi$
$277$	−26.4435			−1.58884			−0.794419	+	0.607370i	$0.792224\pi$
$278$	17.0912			1.02506
$279$	19.8058	+	8.53024i	1.18574	+	0.510692i
$280$	6.77116	−	5.90078i	0.404654	−	0.352639i
$281$			9.30680i			0.555197i	0.960697	+	0.277599i	$0.0895385\pi$
$281$			9.30680i			0.555197i	−0.960697	+	0.277599i	$0.910461\pi$
$282$	16.3757	−	10.7771i	0.975161	−	0.641765i
$283$		−	25.3286i		−	1.50563i	−0.658234	−	0.752814i	$-0.728696\pi$
$283$		−	25.3286i		−	1.50563i	0.658234	−	0.752814i	$-0.271304\pi$
$284$			5.72662i			0.339812i
$285$	34.0583	−	22.4141i	2.01744	−	1.32770i
$286$			9.63586i			0.569780i
$287$	−7.70966	−	8.84685i	−0.455087	−	0.522213i
$288$	−2.75531	−	1.18670i	−0.162358	−	0.0699268i
$289$	−8.62661			−0.507447
$290$	3.61270			0.212145
$291$	−9.54723	+	6.28314i	−0.559669	+	0.368324i
$292$		−	11.2517i		−	0.658459i
$293$	0.668104			0.0390311			0.0195155	−	0.999810i	$-0.493788\pi$
$293$	0.668104			0.0390311			0.0195155	+	0.999810i	$0.493788\pi$
$294$	5.21794	+	10.9441i	0.304316	+	0.638272i
$295$	−30.8154			−1.79414
$296$			6.46015i			0.375489i
$297$	−1.41158	−	7.96635i	−0.0819084	−	0.462254i
$298$	2.18895			0.126802
$299$	−6.18871			−0.357902
$300$	6.21203	+	9.43917i	0.358651	+	0.544971i
$301$	12.3024	+	14.1170i	0.709099	+	0.813693i
$302$		−	10.3233i		−	0.594041i
$303$	−13.8415	−	21.0321i	−0.795172	−	1.20826i
$304$			6.93426i			0.397707i
$305$			46.6448i			2.67087i
$306$	7.97300	+	3.43392i	0.455786	+	0.196304i
$307$		−	4.92353i		−	0.281000i	−0.990081	−	0.140500i	$-0.955129\pi$
$307$		−	4.92353i		−	0.281000i	0.990081	−	0.140500i	$-0.0448711\pi$
$308$	−3.10565	+	2.70644i	−0.176961	+	0.154214i
$309$	−12.0572	+	7.93495i	−0.685907	+	0.451404i
$310$	24.4019			1.38593
$311$	−29.5130			−1.67353			−0.836764	−	0.547564i	$-0.815555\pi$
$311$	−29.5130			−1.67353			−0.836764	+	0.547564i	$0.815555\pi$
$312$	−5.89278	−	8.95407i	−0.333613	−	0.506925i
$313$		−	10.3786i		−	0.586636i	−0.956015	−	0.293318i	$-0.905241\pi$
$313$		−	10.3786i		−	0.586636i	0.956015	−	0.293318i	$-0.0947594\pi$
$314$	12.9450			0.730527
$315$	−25.6591	+	8.22319i	−1.44573	+	0.463325i
$316$	−0.738342			−0.0415350
$317$		−	14.6819i		−	0.824620i	−0.911044	−	0.412310i	$-0.864722\pi$
$317$		−	14.6819i		−	0.824620i	0.911044	−	0.412310i	$-0.135278\pi$
$318$	−2.65631	−	4.03626i	−0.148958	−	0.226342i
$319$	−1.65700			−0.0927739
$320$	−3.39470			−0.189769
$321$	−21.7049	+	14.2843i	−1.21145	+	0.797269i
$322$	−1.73823	−	1.99463i	−0.0968680	−	0.111156i
$323$		−	20.0655i		−	1.11648i
$324$	6.18350	+	6.53944i	0.343528	+	0.363302i
$325$			40.3750i			2.23960i
$326$			1.73236i			0.0959466i
$327$	−7.85931	−	11.9422i	−0.434621	−	0.660406i
$328$			4.43534i			0.244901i
$329$	19.6738	+	22.5758i	1.08465	+	1.24464i
$330$	−5.03283	−	7.64738i	−0.277048	−	0.420974i
$331$	8.46086			0.465051			0.232525	−	0.972590i	$-0.425301\pi$
$331$	8.46086			0.465051			0.232525	+	0.972590i	$0.425301\pi$
$332$	−2.20023			−0.120753
$333$	7.66624	−	17.7997i	0.420107	−	0.975420i
$334$			1.67581i			0.0916963i
$335$	37.0616			2.02489
$336$	1.23079	−	4.41420i	0.0671452	−	0.240814i
$337$	7.27378			0.396228			0.198114	−	0.980179i	$-0.436518\pi$
$337$	7.27378			0.396228			0.198114	+	0.980179i	$0.436518\pi$
$338$		−	25.3001i		−	1.37614i
$339$	4.68761	−	3.08497i	0.254596	−	0.167552i
$340$	9.82318			0.532737
$341$	−11.1921			−0.606087
$342$	8.22886	−	19.1061i	0.444966	−	1.03314i
$343$	−15.4949	+	10.1444i	−0.836646	+	0.547744i
$344$		−	7.07753i		−	0.381595i
$345$	4.91159	−	3.23237i	0.264431	−	0.174025i
$346$		−	26.1692i		−	1.40687i
$347$		−	3.86179i		−	0.207312i	−0.994613	−	0.103656i	$-0.966946\pi$
$347$		−	3.86179i		−	0.207312i	0.994613	−	0.103656i	$-0.0330540\pi$
$348$	1.53976	−	1.01333i	0.0825395	−	0.0543202i
$349$			0.221907i			0.0118784i	0.999982	+	0.00593920i	$0.00189052\pi$
$349$			0.221907i			0.0118784i	−0.999982	+	0.00593920i	$0.998109\pi$
$350$	−13.0129	+	11.3402i	−0.695570	+	0.606160i
$351$	5.61069	+	31.6642i	0.299476	+	1.69011i
$352$	1.55701			0.0829887
$353$	−29.8769			−1.59019			−0.795093	−	0.606487i	$-0.792578\pi$
$353$	−29.8769			−1.59019			−0.795093	+	0.606487i	$0.792578\pi$
$354$	−13.1337	+	8.64343i	−0.698048	+	0.459393i
$355$		−	19.4402i		−	1.03178i
$356$	−3.01787			−0.159947
$357$	−3.56152	+	12.7733i	−0.188496	+	0.676034i
$358$	10.9106			0.576644
$359$		−	25.5746i		−	1.34978i	−0.737920	−	0.674888i	$-0.764192\pi$
$359$		−	25.5746i		−	1.34978i	0.737920	−	0.674888i	$-0.235808\pi$
$360$	9.35346	+	4.02848i	0.492971	+	0.212319i
$361$	−29.0840			−1.53074
$362$	12.6502			0.664880
$363$	−8.16566	−	12.4077i	−0.428586	−	0.651236i
$364$	12.3442	−	10.7574i	0.647010	−	0.563842i
$365$			38.1963i			1.99929i
$366$	13.0834	+	19.8803i	0.683882	+	1.03916i
$367$		−	10.7813i		−	0.562781i	−0.959593	−	0.281390i	$-0.909204\pi$
$367$		−	10.7813i		−	0.562781i	0.959593	−	0.281390i	$-0.0907956\pi$
$368$			1.00000i			0.0521286i
$369$	5.26340	−	12.2208i	0.274002	−	0.636187i
$370$		−	21.9303i		−	1.14010i
$371$	5.56442	−	4.84916i	0.288890	−	0.251756i
$372$	10.4002	−	6.84450i	0.539226	−	0.354871i
$373$	5.23913			0.271272			0.135636	−	0.990759i	$-0.456692\pi$
$373$	5.23913			0.271272			0.135636	+	0.990759i	$0.456692\pi$
$374$	−4.50548			−0.232973
$375$	−4.92609	−	7.48519i	−0.254382	−	0.386534i
$376$		−	11.3183i		−	0.583696i
$377$	6.58614			0.339203
$378$	−8.62953	+	10.7019i	−0.443855	+	0.550448i
$379$	36.1729			1.85808			0.929039	−	0.369983i	$-0.120636\pi$
$379$	36.1729			1.85808			0.929039	+	0.369983i	$0.120636\pi$
$380$		−	23.5397i		−	1.20756i
$381$	6.66850	+	10.1328i	0.341637	+	0.519118i
$382$	8.55112			0.437513
$383$	−16.7488			−0.855825			−0.427912	−	0.903820i	$-0.640751\pi$
$383$	−16.7488			−0.855825			−0.427912	+	0.903820i	$0.640751\pi$
$384$	−1.44684	+	0.952183i	−0.0738338	+	0.0485909i
$385$	10.5427	−	9.18756i	0.537308	−	0.468241i
$386$			12.5635i			0.639464i
$387$	−8.39888	+	19.5008i	−0.426939	+	0.991282i
$388$			6.59867i			0.334997i
$389$			20.2976i			1.02913i	0.857452	+	0.514564i	$0.172046\pi$
$389$			20.2976i			1.02913i	−0.857452	+	0.514564i	$0.827954\pi$
$390$	20.0042	+	30.3964i	1.01295	+	1.53918i
$391$		−	2.89368i		−	0.146340i
$392$	6.93426	+	0.957082i	0.350233	+	0.0483399i
$393$	−10.5369	−	16.0107i	−0.531514	−	0.807635i
$394$	−5.89370			−0.296920
$395$	2.50645			0.126113
$396$	−4.29004	−	1.84769i	−0.215583	−	0.0928501i
$397$		−	12.7869i		−	0.641757i	−0.947120	−	0.320879i	$-0.896022\pi$
$397$		−	12.7869i		−	0.641757i	0.947120	−	0.320879i	$-0.103978\pi$
$398$	−21.6731			−1.08638
$399$	30.6092	+	8.53464i	1.53238	+	0.427266i
$400$	6.52399			0.326199
$401$			9.20540i			0.459696i	0.973227	+	0.229848i	$0.0738229\pi$
$401$			9.20540i			0.459696i	−0.973227	+	0.229848i	$0.926177\pi$
$402$	15.7959	−	10.3954i	0.787827	−	0.518478i
$403$	44.4858			2.21600
$404$	−14.5366			−0.723222
$405$	−20.9911	−	22.1994i	−1.04306	−	1.10310i
$406$	1.84986	+	2.12272i	0.0918071	+	0.105349i
$407$			10.0585i			0.498581i
$408$	4.18670	−	2.75531i	0.207272	−	0.136408i
$409$		−	7.16384i		−	0.354229i	−0.984190	−	0.177115i	$-0.943324\pi$
$409$		−	7.16384i		−	0.354229i	0.984190	−	0.177115i	$-0.0566763\pi$
$410$		−	15.0566i		−	0.743595i
$411$	−24.7399	+	16.2816i	−1.22033	+	0.803114i
$412$			8.33343i			0.410559i
$413$	−15.7788	−	18.1062i	−0.776425	−	0.890949i
$414$	1.18670	−	2.75531i	0.0583229	−	0.135416i
$415$	7.46911			0.366644
$416$	−6.18871			−0.303426
$417$	−24.7283	+	16.2740i	−1.21095	+	0.796939i
$418$			10.7967i			0.528084i
$419$	−27.1004			−1.32394			−0.661970	−	0.749530i	$-0.730279\pi$
$419$	−27.1004			−1.32394			−0.661970	+	0.749530i	$0.730279\pi$
$420$	−4.17817	+	14.9849i	−0.203874	+	0.731187i
$421$	20.9392			1.02051			0.510257	−	0.860022i	$-0.329550\pi$
$421$	20.9392			1.02051			0.510257	+	0.860022i	$0.329550\pi$
$422$		−	7.97787i		−	0.388357i
$423$	−13.4314	+	31.1854i	−0.653055	+	1.51629i
$424$	−2.78970			−0.135480
$425$	−18.8783			−0.915734
$426$	−5.45279	−	8.28551i	−0.264189	−	0.401434i
$427$	−27.4071	+	23.8842i	−1.32632	+	1.15584i
$428$			15.0016i			0.725129i
$429$	−9.17510	−	13.9416i	−0.442978	−	0.673105i
$430$			24.0261i			1.15864i
$431$		−	1.03688i		−	0.0499446i	−0.999688	−	0.0249723i	$-0.992050\pi$
$431$		−	1.03688i		−	0.0499446i	0.999688	−	0.0249723i	$-0.00794976\pi$
$432$	5.11645	−	0.906601i	0.246165	−	0.0436189i
$433$		−	27.5813i		−	1.32547i	−0.748854	−	0.662735i	$-0.769395\pi$
$433$		−	27.5813i		−	1.32547i	0.748854	−	0.662735i	$-0.230605\pi$
$434$	12.4948	+	14.3378i	0.599770	+	0.688238i
$435$	−5.22701	+	3.43995i	−0.250616	+	0.164933i
$436$	−8.25400			−0.395295
$437$	−6.93426			−0.331711
$438$	10.7137	+	16.2795i	0.511921	+	0.777864i
$439$		−	24.9190i		−	1.18932i	−0.803977	−	0.594660i	$-0.797286\pi$
$439$		−	24.9190i		−	1.18932i	0.803977	−	0.594660i	$-0.202714\pi$
$440$	−5.28557			−0.251980
$441$	−17.9703	−	10.8659i	−0.855729	−	0.517425i
$442$	17.9081			0.851804
$443$		−	32.6089i		−	1.54930i	−0.632392	−	0.774649i	$-0.717927\pi$
$443$		−	32.6089i		−	1.54930i	0.632392	−	0.774649i	$-0.282073\pi$
$444$	−6.15124	−	9.34681i	−0.291925	−	0.443580i
$445$	10.2448			0.485649
$446$	−2.86053			−0.135450
$447$	−3.16706	+	2.08428i	−0.149797	+	0.0985830i
$448$	−1.73823	−	1.99463i	−0.0821239	−	0.0942373i
$449$			36.1231i			1.70475i	0.522928	+	0.852377i	$0.324840\pi$
$449$			36.1231i			1.70475i	−0.522928	+	0.852377i	$0.675160\pi$
$450$	−17.9756	−	7.74199i	−0.847379	−	0.364961i
$451$			6.90586i			0.325184i
$452$		−	3.23989i		−	0.152392i
$453$	9.82969	+	14.9362i	0.461839	+	0.701764i
$454$		−	3.48995i		−	0.163791i
$455$	−41.9047	+	36.5182i	−1.96452	+	1.71200i
$456$	−6.60268	−	10.0328i	−0.309199	−	0.469828i
$457$	−13.0502			−0.610463			−0.305232	−	0.952278i	$-0.598734\pi$
$457$	−13.0502			−0.610463			−0.305232	+	0.952278i	$0.598734\pi$
$458$	0.242367			0.0113251
$459$	−14.8054	+	2.62341i	−0.691056	+	0.122450i
$460$		−	3.39470i		−	0.158279i
$461$	−16.8476			−0.784672			−0.392336	−	0.919822i	$-0.628333\pi$
$461$	−16.8476			−0.784672			−0.392336	+	0.919822i	$0.628333\pi$
$462$	1.91635	−	6.87294i	0.0891568	−	0.319758i
$463$	10.9250			0.507728			0.253864	−	0.967240i	$-0.418298\pi$
$463$	10.9250			0.507728			0.253864	+	0.967240i	$0.418298\pi$
$464$		−	1.06422i		−	0.0494051i
$465$	−35.3056	+	23.2350i	−1.63726	+	1.07750i
$466$	−10.3374			−0.478871
$467$	14.2934			0.661419			0.330709	−	0.943733i	$-0.392712\pi$
$467$	14.2934			0.661419			0.330709	+	0.943733i	$0.392712\pi$
$468$	17.0518	+	7.34412i	0.788221	+	0.339482i
$469$	18.9772	+	21.7763i	0.876284	+	1.00554i
$470$			38.4222i			1.77228i
$471$	−18.7293	+	12.3260i	−0.863001	+	0.567951i
$472$			9.07749i			0.417826i
$473$		−	11.0198i		−	0.506689i
$474$	1.06826	−	0.703037i	0.0490670	−	0.0322916i
$475$			45.2390i			2.07571i
$476$	5.02990	+	5.77182i	0.230545	+	0.264551i
$477$	7.68651	+	3.31053i	0.351941	+	0.151579i
$478$	−18.1395			−0.829680
$479$	−24.5346			−1.12101			−0.560507	−	0.828150i	$-0.689394\pi$
$479$	−24.5346			−1.12101			−0.560507	+	0.828150i	$0.689394\pi$
$480$	4.91159	−	3.23237i	0.224182	−	0.147537i
$481$		−	39.9800i		−	1.82293i
$482$	−0.758241			−0.0345369
$483$	4.41420	+	1.23079i	0.200853	+	0.0560030i
$484$	−8.57573			−0.389806
$485$		−	22.4005i		−	1.01716i
$486$	−15.1733	−	3.57370i	−0.688274	−	0.162107i
$487$	−5.87039			−0.266013			−0.133006	−	0.991115i	$-0.542463\pi$
$487$	−5.87039			−0.266013			−0.133006	+	0.991115i	$0.542463\pi$
$488$	13.7405			0.622002
$489$	−1.64952	−	2.50645i	−0.0745941	−	0.113346i
$490$	−23.5397	−	3.24900i	−1.06342	−	0.146775i
$491$		−	13.4519i		−	0.607075i	−0.952820	−	0.303537i	$-0.901832\pi$
$491$		−	13.4519i		−	0.607075i	0.952820	−	0.303537i	$-0.0981677\pi$
$492$	−4.22325	−	6.41723i	−0.190399	−	0.289311i
$493$			3.07951i			0.138694i
$494$		−	42.9141i		−	1.93080i
$495$	14.5634	+	6.27237i	0.654576	+	0.281922i
$496$		−	7.18822i		−	0.322761i
$497$	11.4225	−	9.95421i	0.512368	−	0.446507i
$498$	3.18338	−	2.09502i	0.142651	−	0.0938800i
$499$	4.40063			0.196999			0.0984997	−	0.995137i	$-0.468596\pi$
$499$	4.40063			0.196999			0.0984997	+	0.995137i	$0.468596\pi$
$500$	−5.17347			−0.231365
$501$	−1.59568	−	2.42463i	−0.0712896	−	0.108325i
$502$		−	4.73975i		−	0.211545i
$503$	28.3962			1.26612			0.633062	−	0.774101i	$-0.281798\pi$
$503$	28.3962			1.26612			0.633062	+	0.774101i	$0.281798\pi$
$504$	2.42236	+	7.55858i	0.107901	+	0.336686i
$505$	49.3473			2.19593
$506$			1.55701i			0.0692174i
$507$	24.0903	+	36.6052i	1.06989	+	1.62569i
$508$	7.00338			0.310725
$509$	−30.3408			−1.34483			−0.672415	−	0.740174i	$-0.734743\pi$
$509$	−30.3408			−1.34483			−0.672415	+	0.740174i	$0.734743\pi$
$510$	−14.2126	+	9.35346i	−0.629343	+	0.414178i
$511$	−22.4430	+	19.5582i	−0.992822	+	0.865203i
$512$			1.00000i			0.0441942i
$513$	6.28661	+	35.4788i	0.277561	+	1.56643i
$514$			25.2375i			1.11318i
$515$		−	28.2895i		−	1.24658i
$516$	6.73910	+	10.2401i	0.296672	+	0.450793i
$517$		−	17.6226i		−	0.775043i
$518$	12.8856	−	11.2293i	0.566161	−	0.493385i
$519$	24.9179	+	37.8627i	1.09377	+	1.66199i
$520$	21.0088			0.921297
$521$	31.4827			1.37928			0.689642	−	0.724151i	$-0.257768\pi$
$521$	31.4827			1.37928			0.689642	+	0.724151i	$0.257768\pi$
$522$	−1.26290	+	2.93226i	−0.0552758	+	0.128341i
$523$		−	1.46045i		−	0.0638609i	−0.999490	−	0.0319305i	$-0.989834\pi$
$523$		−	1.46045i		−	0.0638609i	0.999490	−	0.0319305i	$-0.0101655\pi$
$524$	−11.0660			−0.483421
$525$	8.02967	−	28.7982i	0.350444	−	1.25686i
$526$	−14.4468			−0.629910
$527$			20.8004i			0.906081i
$528$	−2.25274	+	1.48255i	−0.0980380	+	0.0645199i
$529$	−1.00000			−0.0434783
$530$	9.47021			0.411359
$531$	10.7722	−	25.0113i	0.467475	−	1.08540i
$532$	13.8313	−	12.0534i	0.599662	−	0.522580i
$533$		−	27.4490i		−	1.18895i
$534$	4.36638	−	2.87357i	0.188952	−	0.124351i
$535$		−	50.9259i		−	2.20172i
$536$		−	10.9175i		−	0.471564i
$537$	−15.7859	+	10.3889i	−0.681213	+	0.448314i
$538$			21.5181i			0.927711i
$539$	10.7967	+	1.49018i	0.465046	+	0.0641867i
$540$	−17.3688	+	3.07764i	−0.747435	+	0.132440i
$541$	14.1462			0.608194			0.304097	−	0.952641i	$-0.401645\pi$
$541$	14.1462			0.608194			0.304097	+	0.952641i	$0.401645\pi$
$542$	−10.8069			−0.464198
$543$	−18.3028	+	12.0453i	−0.785449	+	0.516913i
$544$		−	2.89368i		−	0.124066i
$545$	28.0198			1.20024
$546$	−7.61701	+	27.3182i	−0.325978	+	1.16911i
$547$	−11.8389			−0.506194			−0.253097	−	0.967441i	$-0.581449\pi$
$547$	−11.8389			−0.506194			−0.253097	+	0.967441i	$0.581449\pi$
$548$			17.0993i			0.730445i
$549$	−37.8593	−	16.3058i	−1.61580	−	0.695913i
$550$	10.1579			0.433134
$551$	7.37957			0.314380
$552$	−0.952183	−	1.44684i	−0.0405276	−	0.0615816i
$553$	1.28341	+	1.47272i	0.0545762	+	0.0626264i
$554$		−	26.4435i		−	1.12348i
$555$	20.8816	+	31.7296i	0.886375	+	1.34685i
$556$			17.0912i			0.724829i
$557$		−	12.8125i		−	0.542882i	−0.962455	−	0.271441i	$-0.912500\pi$
$557$		−	12.8125i		−	0.542882i	0.962455	−	0.271441i	$-0.0875003\pi$
$558$	−8.53024	+	19.8058i	−0.361114	+	0.838447i
$559$			43.8008i			1.85258i
$560$	5.90078	+	6.77116i	0.249354	+	0.286134i
$561$	6.51871	−	4.29004i	0.275220	−	0.181126i
$562$	−9.30680			−0.392584
$563$	−8.19464			−0.345363			−0.172682	−	0.984978i	$-0.555243\pi$
$563$	−8.19464			−0.345363			−0.172682	+	0.984978i	$0.555243\pi$
$564$	10.7771	+	16.3757i	0.453796	+	0.689543i
$565$			10.9985i			0.462709i
$566$	25.3286			1.06464
$567$	2.29537	−	23.7009i	0.0963966	−	0.995343i
$568$	−5.72662			−0.240284
$569$			42.9496i			1.80054i	0.435333	+	0.900269i	$0.356631\pi$
$569$			42.9496i			1.80054i	−0.435333	+	0.900269i	$0.643369\pi$
$570$	22.4141	+	34.0583i	0.938825	+	1.42654i
$571$	−8.86738			−0.371088			−0.185544	−	0.982636i	$-0.559405\pi$
$571$	−8.86738			−0.371088			−0.185544	+	0.982636i	$0.559405\pi$
$572$	−9.63586			−0.402896
$573$	−12.3721	+	8.14223i	−0.516852	+	0.340147i
$574$	8.84685	−	7.70966i	0.369261	−	0.321795i
$575$			6.52399i			0.272069i
$576$	1.18670	−	2.75531i	0.0494457	−	0.114805i
$577$		−	2.64204i		−	0.109990i	−0.998487	−	0.0549948i	$-0.982486\pi$
$577$		−	2.64204i		−	0.109990i	0.998487	−	0.0549948i	$-0.0175142\pi$
$578$		−	8.62661i		−	0.358820i
$579$	−11.9627	−	18.1774i	−0.497154	−	0.755425i
$580$			3.61270i			0.150009i
$581$	3.82451	+	4.38863i	0.158667	+	0.182071i
$582$	−6.28314	−	9.54723i	−0.260445	−	0.395745i
$583$	−4.34359			−0.179893
$584$	11.2517			0.465601
$585$	−57.8858	−	24.9311i	−2.39328	−	1.03077i
$586$			0.668104i			0.0275991i
$587$	31.9288			1.31784			0.658922	−	0.752211i	$-0.271013\pi$
$587$	31.9288			1.31784			0.658922	+	0.752211i	$0.271013\pi$
$588$	−10.9441	+	5.21794i	−0.451327	+	0.215184i
$589$	49.8450			2.05383
$590$		−	30.8154i		−	1.26865i
$591$	8.52725	−	5.61188i	0.350764	−	0.230842i
$592$	−6.46015			−0.265511
$593$	−12.3178			−0.505831			−0.252916	−	0.967488i	$-0.581390\pi$
$593$	−12.3178			−0.505831			−0.252916	+	0.967488i	$0.581390\pi$
$594$	7.96635	−	1.41158i	0.326863	−	0.0579180i
$595$	−17.0750	−	19.5936i	−0.700006	−	0.803259i
$596$			2.18895i			0.0896628i
$597$	31.3576	−	20.6368i	1.28338	−	0.844607i
$598$		−	6.18871i		−	0.253075i
$599$			30.6695i			1.25312i	0.779373	+	0.626560i	$0.215538\pi$
$599$			30.6695i			1.25312i	−0.779373	+	0.626560i	$0.784462\pi$
$600$	−9.43917	+	6.21203i	−0.385352	+	0.253605i
$601$		−	10.1305i		−	0.413230i	−0.978422	−	0.206615i	$-0.933755\pi$
$601$		−	10.1305i		−	0.413230i	0.978422	−	0.206615i	$-0.0662448\pi$
$602$	−14.1170	+	12.3024i	−0.575368	+	0.501409i
$603$	−12.9558	+	30.0811i	−0.527599	+	1.22500i
$604$	10.3233			0.420050
$605$	29.1120			1.18357
$606$	21.0321	−	13.8415i	0.854371	−	0.562271i
$607$			23.0184i			0.934286i	0.884182	+	0.467143i	$0.154717\pi$
$607$			23.0184i			0.934286i	−0.884182	+	0.467143i	$0.845283\pi$
$608$	−6.93426			−0.281221
$609$	−4.69767	−	1.30983i	−0.190359	−	0.0530771i
$610$	−46.6448			−1.88859
$611$			70.0455i			2.83374i
$612$	−3.43392	+	7.97300i	−0.138808	+	0.322289i
$613$	32.3023			1.30468			0.652338	−	0.757928i	$-0.273788\pi$
$613$	32.3023			1.30468			0.652338	+	0.757928i	$0.273788\pi$
$614$	4.92353			0.198697
$615$	14.3367	+	21.7846i	0.578111	+	0.878439i
$616$	−2.70644	−	3.10565i	−0.109046	−	0.125130i
$617$		−	16.3098i		−	0.656608i	−0.944572	−	0.328304i	$-0.893523\pi$
$617$		−	16.3098i		−	0.656608i	0.944572	−	0.328304i	$-0.106477\pi$
$618$	−7.93495	−	12.0572i	−0.319191	−	0.485010i
$619$			23.8209i			0.957442i	0.877967	+	0.478721i	$0.158899\pi$
$619$			23.8209i			0.957442i	−0.877967	+	0.478721i	$0.841101\pi$
$620$			24.4019i			0.980002i
$621$	0.906601	+	5.11645i	0.0363806	+	0.205316i
$622$		−	29.5130i		−	1.18336i
$623$	5.24577	+	6.01954i	0.210167	+	0.241168i
$624$	8.95407	−	5.89278i	0.358450	−	0.235900i
$625$	−15.0575			−0.602302
$626$	10.3786			0.414814
$627$	−10.2804	−	15.6211i	−0.410561	−	0.623846i
$628$			12.9450i			0.516560i
$629$	18.6936			0.745363
$630$	−8.22319	−	25.6591i	−0.327620	−	1.02228i
$631$	11.1650			0.444471			0.222236	−	0.974993i	$-0.428665\pi$
$631$	11.1650			0.444471			0.222236	+	0.974993i	$0.428665\pi$
$632$		−	0.738342i		−	0.0293697i
$633$	7.59639	+	11.5427i	0.301929	+	0.458781i
$634$	14.6819			0.583095
$635$	−23.7744			−0.943457
$636$	4.03626	−	2.65631i	0.160048	−	0.105329i
$637$	−42.9141	−	5.92310i	−1.70032	−	0.234682i
$638$		−	1.65700i		−	0.0656011i
$639$	15.7786	+	6.79576i	0.624193	+	0.268836i
$640$		−	3.39470i		−	0.134187i
$641$			8.64773i			0.341565i	0.985309	+	0.170782i	$0.0546295\pi$
$641$			8.64773i			0.341565i	−0.985309	+	0.170782i	$0.945370\pi$
$642$	−14.2843	−	21.7049i	−0.563755	−	0.856625i
$643$			32.7956i			1.29333i	0.762774	+	0.646665i	$0.223837\pi$
$643$			32.7956i			1.29333i	−0.762774	+	0.646665i	$0.776163\pi$
$644$	1.99463	−	1.73823i	0.0785994	−	0.0684960i
$645$	−22.8772	−	34.7619i	−0.900790	−	1.36875i
$646$	20.0655			0.789468
$647$	36.7024			1.44292			0.721460	−	0.692456i	$-0.243471\pi$
$647$	36.7024			1.44292			0.721460	+	0.692456i	$0.243471\pi$
$648$	−6.53944	+	6.18350i	−0.256893	+	0.242911i
$649$			14.1337i			0.554797i
$650$	−40.3750			−1.58364
$651$	−31.7302	−	8.84721i	−1.24361	−	0.346749i
$652$	−1.73236			−0.0678445
$653$		−	7.53645i		−	0.294924i	−0.989068	−	0.147462i	$-0.952890\pi$
$653$		−	7.53645i		−	0.294924i	0.989068	−	0.147462i	$-0.0471104\pi$
$654$	11.9422	−	7.85931i	0.466978	−	0.307323i
$655$	37.5658			1.46782
$656$	−4.43534			−0.173171
$657$	−31.0021	−	13.3524i	−1.20951	−	0.520927i
$658$	−22.5758	+	19.6738i	−0.880095	+	0.766965i
$659$			15.8111i			0.615912i	0.951401	+	0.307956i	$0.0996449\pi$
$659$			15.8111i			0.615912i	−0.951401	+	0.307956i	$0.900355\pi$
$660$	7.64738	−	5.03283i	0.297674	−	0.195903i
$661$		−	9.17489i		−	0.356862i	−0.983952	−	0.178431i	$-0.942898\pi$
$661$		−	9.17489i		−	0.356862i	0.983952	−	0.178431i	$-0.0571021\pi$
$662$			8.46086i			0.328841i
$663$	−25.9102	+	17.0518i	−1.00627	+	0.662238i
$664$		−	2.20023i		−	0.0853854i
$665$	−46.9530	+	40.9176i	−1.82076	+	1.58672i
$666$	17.7997	+	7.66624i	0.689726	+	0.297061i
$667$	1.06422			0.0412067
$668$	−1.67581			−0.0648391
$669$	4.13874	−	2.72375i	0.160013	−	0.105306i
$670$			37.0616i			1.43182i
$671$	21.3940			0.825906
$672$	4.41420	+	1.23079i	0.170281	+	0.0474788i
$673$	5.01612			0.193357			0.0966786	−	0.995316i	$-0.469178\pi$
$673$	5.01612			0.193357			0.0966786	+	0.995316i	$0.469178\pi$
$674$			7.27378i			0.280175i
$675$	33.3797	−	5.91465i	1.28478	−	0.227655i
$676$	25.3001			0.973081
$677$	−32.8047			−1.26079			−0.630393	−	0.776276i	$-0.717106\pi$
$677$	−32.8047			−1.26079			−0.630393	+	0.776276i	$0.717106\pi$
$678$	3.08497	+	4.68761i	0.118477	+	0.180026i
$679$	13.1619	−	11.4700i	0.505107	−	0.440180i
$680$			9.82318i			0.376702i
$681$	3.32307	+	5.04940i	0.127340	+	0.193494i
$682$		−	11.1921i		−	0.428568i
$683$		−	35.8671i		−	1.37242i	−0.727405	−	0.686209i	$-0.759274\pi$
$683$		−	35.8671i		−	1.37242i	0.727405	−	0.686209i	$-0.240726\pi$
$684$	19.1061	+	8.22886i	0.730539	+	0.314638i
$685$		−	58.0469i		−	2.21786i
$686$	−10.1444	−	15.4949i	−0.387313	−	0.591598i
$687$	−0.350667	+	0.230778i	−0.0133788	+	0.00880473i
$688$	7.07753			0.269828
$689$	17.2647			0.657731
$690$	3.23237	+	4.91159i	0.123054	+	0.186981i
$691$		−	20.1106i		−	0.765044i	−0.923946	−	0.382522i	$-0.875056\pi$
$691$		−	20.1106i		−	0.765044i	0.923946	−	0.382522i	$-0.124944\pi$
$692$	26.1692			0.994804
$693$	3.77164	+	11.7688i	0.143273	+	0.447058i
$694$	3.86179			0.146591
$695$		−	58.0195i		−	2.20081i
$696$	1.01333	+	1.53976i	0.0384102	+	0.0583643i
$697$	12.8345			0.486140
$698$	−0.221907			−0.00839930
$699$	14.9566	−	9.84309i	0.565710	−	0.372300i
$700$	−11.3402	−	13.0129i	−0.428620	−	0.491842i
$701$			9.07530i			0.342769i	0.985204	+	0.171385i	$0.0548241\pi$
$701$			9.07530i			0.342769i	−0.985204	+	0.171385i	$0.945176\pi$
$702$	−31.6642	+	5.61069i	−1.19509	+	0.211762i
$703$		−	44.7964i		−	1.68953i
$704$			1.55701i			0.0586819i
$705$	−36.5849	−	55.5907i	−1.37787	−	2.09367i
$706$		−	29.8769i		−	1.12443i
$707$	25.2680	+	28.9951i	0.950300	+	1.09047i
$708$	−8.64343	−	13.1337i	−0.324840	−	0.493594i
$709$	−19.0152			−0.714131			−0.357066	−	0.934079i	$-0.616223\pi$
$709$	−19.0152			−0.714131			−0.357066	+	0.934079i	$0.616223\pi$
$710$	19.4402			0.729576
$711$	−0.876188	+	2.03436i	−0.0328596	+	0.0762946i
$712$		−	3.01787i		−	0.113100i
$713$	7.18822			0.269201
$714$	−12.7733	−	3.56152i	−0.478028	−	0.133287i
$715$	32.7108			1.22332
$716$			10.9106i			0.407749i
$717$	26.2449	−	17.2721i	0.980135	−	0.645038i
$718$	25.5746			0.954436
$719$	−14.7368			−0.549592			−0.274796	−	0.961503i	$-0.588610\pi$
$719$	−14.7368			−0.549592			−0.274796	+	0.961503i	$0.588610\pi$
$720$	−4.02848	+	9.35346i	−0.150133	+	0.348583i
$721$	16.6221	−	14.4855i	0.619039	−	0.539467i
$722$		−	29.0840i		−	1.08239i
$723$	1.09705	−	0.721984i	0.0407999	−	0.0268509i
$724$			12.6502i			0.470141i
$725$		−	6.94295i		−	0.257855i
$726$	12.4077	−	8.16566i	0.460494	−	0.303056i
$727$			29.1096i			1.07962i	0.841788	+	0.539808i	$0.181503\pi$
$727$			29.1096i			1.07962i	−0.841788	+	0.539808i	$0.818497\pi$
$728$	10.7574	+	12.3442i	0.398697	+	0.457505i
$729$	25.3561	−	9.27716i	0.939117	−	0.343598i
$730$	−38.1963			−1.41371
$731$	−20.4801			−0.757485
$732$	−19.8803	+	13.0834i	−0.734796	+	0.483578i
$733$		−	11.3726i		−	0.420057i	−0.977695	−	0.210029i	$-0.932644\pi$
$733$		−	11.3726i		−	0.420057i	0.977695	−	0.210029i	$-0.0673558\pi$
$734$	10.7813			0.397946
$735$	37.1519	−	17.7133i	1.37037	−	0.653366i
$736$	−1.00000			−0.0368605
$737$		−	16.9986i		−	0.626152i
$738$	12.2208	+	5.26340i	0.449852	+	0.193749i
$739$	49.8787			1.83482			0.917409	−	0.397945i	$-0.130276\pi$
$739$	49.8787			1.83482			0.917409	+	0.397945i	$0.130276\pi$
$740$	21.9303			0.806173
$741$	40.8621	+	62.0899i	1.50111	+	2.28093i
$742$	4.84916	+	5.56442i	0.178018	+	0.204276i
$743$		−	39.6098i		−	1.45314i	−0.687090	−	0.726572i	$-0.741112\pi$
$743$		−	39.6098i		−	1.45314i	0.687090	−	0.726572i	$-0.258888\pi$
$744$	6.84450	+	10.4002i	0.250932	+	0.381290i
$745$		−	7.43082i		−	0.272244i
$746$			5.23913i			0.191818i
$747$	−2.61100	+	6.06231i	−0.0955315	+	0.221808i
$748$		−	4.50548i		−	0.164737i
$749$	29.9226	−	26.0763i	1.09335	−	0.952807i
$750$	7.48519	−	4.92609i	0.273321	−	0.179875i
$751$	44.1819			1.61222			0.806110	−	0.591766i	$-0.201569\pi$
$751$	44.1819			1.61222			0.806110	+	0.591766i	$0.201569\pi$
$752$	11.3183			0.412735
$753$	4.51310	+	6.85766i	0.164467	+	0.249907i
$754$			6.58614i			0.239853i
$755$	−35.0446			−1.27540
$756$	−10.7019	−	8.62953i	−0.389225	−	0.313853i
$757$	−15.3592			−0.558241			−0.279121	−	0.960256i	$-0.590043\pi$
$757$	−15.3592			−0.558241			−0.279121	+	0.960256i	$0.590043\pi$
$758$			36.1729i			1.31386i
$759$	−1.48255	−	2.25274i	−0.0538133	−	0.0817693i
$760$	23.5397			0.853876
$761$	38.0684			1.37998			0.689989	−	0.723819i	$-0.257615\pi$
$761$	38.0684			1.37998			0.689989	+	0.723819i	$0.257615\pi$
$762$	−10.1328	+	6.66850i	−0.367072	+	0.241574i
$763$	14.3474	+	16.4637i	0.519410	+	0.596024i
$764$			8.55112i			0.309369i
$765$	11.6571	−	27.0659i	0.421464	−	0.978571i
$766$		−	16.7488i		−	0.605160i
$767$		−	56.1780i		−	2.02847i
$768$	−0.952183	−	1.44684i	−0.0343589	−	0.0522084i
$769$			24.3857i			0.879372i	0.898152	+	0.439686i	$0.144910\pi$
$769$			24.3857i			0.879372i	−0.898152	+	0.439686i	$0.855090\pi$
$770$	9.18756	+	10.5427i	0.331097	+	0.379934i
$771$	−24.0307	−	36.5146i	−0.865443	−	1.31504i
$772$	−12.5635			−0.452169
$773$	13.0454			0.469211			0.234605	−	0.972091i	$-0.424620\pi$
$773$	13.0454			0.469211			0.234605	+	0.972091i	$0.424620\pi$
$774$	−19.5008	−	8.39888i	−0.700942	−	0.301892i
$775$		−	46.8959i		−	1.68455i
$776$	−6.59867			−0.236879
$777$	−7.95110	+	28.5164i	−0.285244	+	1.02302i
$778$	−20.2976			−0.727703
$779$		−	30.7558i		−	1.10194i
$780$	−30.3964	+	20.0042i	−1.08837	+	0.716266i
$781$	−8.91639			−0.319053
$782$	2.89368			0.103478
$783$	−0.964822	−	5.44502i	−0.0344799	−	0.194589i
$784$	−0.957082	+	6.93426i	−0.0341815	+	0.247652i
$785$		−	43.9443i		−	1.56844i
$786$	16.0107	−	10.5369i	0.571085	−	0.375837i
$787$		−	2.44434i		−	0.0871313i	−0.999051	−	0.0435657i	$-0.986128\pi$
$787$		−	2.44434i		−	0.0871313i	0.999051	−	0.0435657i	$-0.0138718\pi$
$788$		−	5.89370i		−	0.209954i
$789$	20.9022	−	13.7560i	0.744138	−	0.489726i
$790$			2.50645i			0.0891755i
$791$	−6.46238	+	5.63169i	−0.229776	+	0.200240i
$792$	1.84769	−	4.29004i	0.0656550	−	0.152440i
$793$	−85.0357			−3.01971
$794$	12.7869			0.453791
$795$	−13.7019	+	9.01737i	−0.485956	+	0.319813i
$796$		−	21.6731i		−	0.768183i
$797$	36.9888			1.31021			0.655105	−	0.755538i	$-0.272624\pi$
$797$	36.9888			1.31021			0.655105	+	0.755538i	$0.272624\pi$
$798$	−8.53464	+	30.6092i	−0.302123	+	1.08355i
$799$	−32.7515			−1.15866
$800$			6.52399i			0.230658i
$801$	−3.58130	+	8.31519i	−0.126539	+	0.293803i
$802$	−9.20540			−0.325054
$803$	17.5190			0.618234
$804$	10.3954	+	15.7959i	0.366619	+	0.557078i
$805$	−6.77116	+	5.90078i	−0.238652	+	0.207975i
$806$			44.4858i			1.56695i
$807$	−20.4892	−	31.1333i	−0.721252	−	1.09594i
$808$		−	14.5366i		−	0.511395i
$809$			25.6182i			0.900686i	0.892856	+	0.450343i	$0.148698\pi$
$809$			25.6182i			0.900686i	−0.892856	+	0.450343i	$0.851302\pi$
$810$	22.1994	−	20.9911i	0.780009	−	0.737553i
$811$		−	29.8021i		−	1.04649i	−0.852181	−	0.523247i	$-0.824720\pi$
$811$		−	29.8021i		−	1.04649i	0.852181	−	0.523247i	$-0.175280\pi$
$812$	−2.12272	+	1.84986i	−0.0744929	+	0.0649174i
$813$	15.6359	−	10.2902i	0.548376	−	0.360893i
$814$	−10.0585			−0.352550
$815$	5.88085			0.205997
$816$	2.75531	+	4.18670i	0.0964553	+	0.146564i
$817$			49.0775i			1.71700i
$818$	7.16384			0.250478
$819$	−14.9913	−	46.7779i	−0.523838	−	1.63455i
$820$	15.0566			0.525801
$821$			20.3703i			0.710929i	0.934690	+	0.355465i	$0.115677\pi$
$821$			20.3703i			0.710929i	−0.934690	+	0.355465i	$0.884323\pi$
$822$	−16.2816	−	24.7399i	−0.567888	−	0.862905i
$823$	30.1791			1.05198			0.525989	−	0.850491i	$-0.323695\pi$
$823$	30.1791			1.05198			0.525989	+	0.850491i	$0.323695\pi$
$824$	−8.33343			−0.290309
$825$	−14.6968	+	9.67217i	−0.511679	+	0.336742i
$826$	18.1062	−	15.7788i	0.629996	−	0.549015i
$827$			12.7879i			0.444678i	0.974969	+	0.222339i	$0.0713691\pi$
$827$			12.7879i			0.444678i	−0.974969	+	0.222339i	$0.928631\pi$
$828$	2.75531	+	1.18670i	0.0957538	+	0.0412405i
$829$			26.0987i			0.906444i	0.891398	+	0.453222i	$0.149726\pi$
$829$			26.0987i			0.906444i	−0.891398	+	0.453222i	$0.850274\pi$
$830$			7.46911i			0.259257i
$831$	25.1791	+	38.2596i	0.873452	+	1.32721i
$832$		−	6.18871i		−	0.214555i
$833$	2.76949	−	20.0655i	0.0959571	−	0.695230i
$834$	−16.2740	−	24.7283i	−0.563521	−	0.856270i
$835$	5.68888			0.196872
$836$	−10.7967			−0.373411
$837$	−6.51685	−	36.7782i	−0.225255	−	1.27124i
$838$		−	27.1004i		−	0.936167i
$839$	−48.0301			−1.65818			−0.829091	−	0.559113i	$-0.811142\pi$
$839$	−48.0301			−1.65818			−0.829091	+	0.559113i	$0.811142\pi$
$840$	−14.9849	−	4.17817i	−0.517027	−	0.144161i
$841$	27.8674			0.960946
$842$			20.9392i			0.721613i
$843$	13.4655	−	8.86178i	0.463775	−	0.305216i
$844$	7.97787			0.274610
$845$	−85.8863			−2.95458
$846$	−31.1854	−	13.4314i	−1.07218	−	0.461780i
$847$	14.9066	+	17.1054i	0.512198	+	0.587748i
$848$		−	2.78970i		−	0.0957988i
$849$	−36.6464	+	24.1174i	−1.25770	+	0.827708i
$850$		−	18.8783i		−	0.647522i
$851$		−	6.46015i		−	0.221451i
$852$	8.28551	−	5.45279i	0.283857	−	0.186810i
$853$			10.8492i			0.371470i	0.982600	+	0.185735i	$0.0594666\pi$
$853$			10.8492i			0.371470i	−0.982600	+	0.185735i	$0.940533\pi$
$854$	−23.8842	−	27.4071i	−0.817299	−	0.937852i
$855$	−64.8594	−	27.9345i	−2.21814	−	0.955340i
$856$	−15.0016			−0.512744
$857$	5.49805			0.187810			0.0939049	−	0.995581i	$-0.470065\pi$
$857$	5.49805			0.187810			0.0939049	+	0.995581i	$0.470065\pi$
$858$	13.9416	−	9.17510i	0.475957	−	0.313233i
$859$			11.4982i			0.392315i	0.980572	+	0.196158i	$0.0628464\pi$
$859$			11.4982i			0.392315i	−0.980572	+	0.196158i	$0.937154\pi$
$860$	−24.0261			−0.819283
$861$	−5.45898	+	19.5785i	−0.186042	+	0.667233i
$862$	1.03688			0.0353162
$863$		−	42.0443i		−	1.43121i	−0.698508	−	0.715603i	$-0.746152\pi$
$863$		−	42.0443i		−	1.43121i	0.698508	−	0.715603i	$-0.253848\pi$
$864$	0.906601	+	5.11645i	0.0308432	+	0.174065i
$865$	−88.8366			−3.02054
$866$	27.5813			0.937249
$867$	8.21411	+	12.4813i	0.278966	+	0.423888i
$868$	−14.3378	+	12.4948i	−0.486658	+	0.424102i
$869$		−	1.14960i		−	0.0389977i
$870$	−3.43995	−	5.22701i	−0.116625	−	0.177212i
$871$			67.5652i			2.28936i
$872$		−	8.25400i		−	0.279516i
$873$	18.1814	+	7.83062i	0.615348	+	0.265026i
$874$		−	6.93426i		−	0.234555i
$875$	8.99271	+	10.3192i	0.304009	+	0.348851i
$876$	−16.2795	+	10.7137i	−0.550033	+	0.361983i
$877$	41.9913			1.41795			0.708973	−	0.705236i	$-0.249159\pi$
$877$	41.9913			1.41795			0.708973	+	0.705236i	$0.249159\pi$
$878$	24.9190			0.840977
$879$	−0.636157	−	0.966640i	−0.0214570	−	0.0326040i
$880$		−	5.28557i		−	0.178177i
$881$	−6.82042			−0.229786			−0.114893	−	0.993378i	$-0.536652\pi$
$881$	−6.82042			−0.229786			−0.114893	+	0.993378i	$0.536652\pi$
$882$	10.8659	−	17.9703i	0.365875	−	0.605091i
$883$	−23.3772			−0.786707			−0.393353	−	0.919387i	$-0.628685\pi$
$883$	−23.3772			−0.786707			−0.393353	+	0.919387i	$0.628685\pi$
$884$			17.9081i			0.602316i
$885$	29.3419	+	44.5849i	0.986316	+	1.49871i
$886$	32.6089			1.09552
$887$	−33.8300			−1.13590			−0.567950	−	0.823063i	$-0.692263\pi$
$887$	−33.8300			−1.13590			−0.567950	+	0.823063i	$0.692263\pi$
$888$	9.34681	−	6.15124i	0.313658	−	0.206422i
$889$	−12.1735	−	13.9691i	−0.408287	−	0.468510i
$890$			10.2448i			0.343406i
$891$	−10.1820	+	9.62776i	−0.341108	+	0.322542i
$892$		−	2.86053i		−	0.0957778i
$893$			78.4839i			2.62636i
$894$	−2.08428	−	3.16706i	−0.0697087	−	0.105922i
$895$		−	37.0383i		−	1.23805i
$896$	1.99463	−	1.73823i	0.0666358	−	0.0580703i
$897$	5.89278	+	8.95407i	0.196754	+	0.298968i
$898$	−36.1231			−1.20544
$899$	−7.64984			−0.255137
$900$	7.74199	−	17.9756i	0.258066	−	0.599187i
$901$			8.07251i			0.268934i
$902$	−6.90586			−0.229940
$903$	8.71097	−	31.2416i	0.289883	−	1.03966i
$904$	3.23989			0.107757
$905$		−	42.9436i		−	1.42749i
$906$	−14.9362	+	9.82969i	−0.496222	+	0.326570i
$907$	−24.5753			−0.816011			−0.408005	−	0.912979i	$-0.633776\pi$
$907$	−24.5753			−0.816011			−0.408005	+	0.912979i	$0.633776\pi$
$908$	3.48995			0.115818
$909$	−17.2505	+	40.0528i	−0.572163	+	1.32847i
$910$	−36.5182	−	41.9047i	−1.21057	−	1.38913i
$911$			34.7124i			1.15007i	0.818127	+	0.575037i	$0.195012\pi$
$911$			34.7124i			1.15007i	−0.818127	+	0.575037i	$0.804988\pi$
$912$	10.0328	−	6.60268i	0.332218	−	0.218637i
$913$		−	3.42577i		−	0.113376i
$914$		−	13.0502i		−	0.431663i
$915$	67.4875	−	44.4143i	2.23107	−	1.46829i
$916$			0.242367i			0.00800805i
$917$	19.2353	+	22.0726i	0.635206	+	0.728900i
$918$	−2.62341	−	14.8054i	−0.0865856	−	0.488650i
$919$	−13.2441			−0.436881			−0.218441	−	0.975850i	$-0.570097\pi$
$919$	−13.2441			−0.436881			−0.218441	+	0.975850i	$0.570097\pi$
$920$	3.39470			0.111920
$921$	−7.12356	+	4.68810i	−0.234729	+	0.154478i
$922$		−	16.8476i		−	0.554847i
$923$	35.4404			1.16653
$924$	6.87294	+	1.91635i	0.226103	+	0.0630433i
$925$	−42.1459			−1.38575
$926$			10.9250i			0.359018i
$927$	22.9612	+	9.88925i	0.754145	+	0.324806i
$928$	1.06422			0.0349347
$929$	−8.55490			−0.280677			−0.140339	−	0.990104i	$-0.544819\pi$
$929$	−8.55490			−0.280677			−0.140339	+	0.990104i	$0.544819\pi$
$930$	−23.2350	−	35.3056i	−0.761907	−	1.15772i
$931$	−48.0840	−	6.63665i	−1.57589	−	0.217508i
$932$		−	10.3374i		−	0.338613i
$933$	28.1018	+	42.7006i	0.920010	+	1.39795i
$934$			14.2934i			0.467694i
$935$			15.2948i			0.500192i
$936$	−7.34412	+	17.0518i	−0.240050	+	0.557356i
$937$		−	25.1455i		−	0.821468i	−0.911755	−	0.410734i	$-0.865272\pi$
$937$		−	25.1455i		−	0.821468i	0.911755	−	0.410734i	$-0.134728\pi$
$938$	−21.7763	+	18.9772i	−0.711023	+	0.619626i
$939$	−15.0162	+	9.88237i	−0.490037	+	0.322499i
$940$	−38.4222			−1.25319
$941$	−2.63281			−0.0858272			−0.0429136	−	0.999079i	$-0.513664\pi$
$941$	−2.63281			−0.0858272			−0.0429136	+	0.999079i	$0.513664\pi$
$942$	−12.3260	−	18.7293i	−0.401602	−	0.610234i
$943$		−	4.43534i		−	0.144435i
$944$	−9.07749			−0.295447
$945$	36.3298	+	29.2947i	1.18181	+	0.952956i
$946$	11.0198			0.358283
$947$			42.4248i			1.37862i	0.724466	+	0.689311i	$0.242087\pi$
$947$			42.4248i			1.37862i	−0.724466	+	0.689311i	$0.757913\pi$
$948$	0.703037	+	1.06826i	0.0228336	+	0.0346956i
$949$	−69.6338			−2.26041
$950$	−45.2390			−1.46775
$951$	−21.2424	+	13.9799i	−0.688833	+	0.453329i
$952$	−5.77182	+	5.02990i	−0.187066	+	0.163020i
$953$		−	0.663916i		−	0.0215063i	−0.999942	−	0.0107532i	$-0.996577\pi$
$953$		−	0.663916i		−	0.0215063i	0.999942	−	0.0107532i	$-0.00342291\pi$
$954$	−3.31053	+	7.68651i	−0.107182	+	0.248860i
$955$		−	29.0285i		−	0.939340i
$956$		−	18.1395i		−	0.586673i
$957$	1.57776	+	2.39741i	0.0510018	+	0.0774972i
$958$		−	24.5346i		−	0.792676i
$959$	34.1067	−	29.7226i	1.10136	−	0.959792i
$960$	3.23237	+	4.91159i	0.104324	+	0.158521i
$961$	−20.6705			−0.666792
$962$	39.9800			1.28901
$963$	41.3341	+	17.8023i	1.33197	+	0.573672i
$964$		−	0.758241i		−	0.0244213i
$965$	42.6492			1.37293
$966$	−1.23079	+	4.41420i	−0.0396001	+	0.142025i
$967$	−18.8641			−0.606629			−0.303314	−	0.952891i	$-0.598093\pi$
$967$	−18.8641			−0.606629			−0.303314	+	0.952891i	$0.598093\pi$
$968$		−	8.57573i		−	0.275634i
$969$	−29.0317	+	19.1061i	−0.932631	+	0.613775i
$970$	22.4005			0.719237
$971$	−52.7364			−1.69239			−0.846196	−	0.532872i	$-0.821113\pi$
$971$	−52.7364			−1.69239			−0.846196	+	0.532872i	$0.821113\pi$
$972$	3.57370	−	15.1733i	0.114627	−	0.486683i
$973$	34.0906	−	29.7085i	1.09289	−	0.952412i
$974$		−	5.87039i		−	0.188099i
$975$	58.4163	−	38.4444i	1.87082	−	1.23121i
$976$			13.7405i			0.439822i
$977$		−	54.6382i		−	1.74803i	−0.485898	−	0.874016i	$-0.661507\pi$
$977$		−	54.6382i		−	1.74803i	0.485898	−	0.874016i	$-0.338493\pi$
$978$	2.50645	−	1.64952i	0.0801475	−	0.0527460i
$979$		−	4.69885i		−	0.150176i
$980$	3.24900	−	23.5397i	0.103786	−	0.751949i
$981$	−9.79499	+	22.7423i	−0.312730	+	0.726107i
$982$	13.4519			0.429267
$983$	−50.8213			−1.62095			−0.810474	−	0.585774i	$-0.800791\pi$
$983$	−50.8213			−1.62095			−0.810474	+	0.585774i	$0.800791\pi$
$984$	6.41723	−	4.22325i	0.204574	−	0.134632i
$985$			20.0073i			0.637487i
$986$	−3.07951			−0.0980716
$987$	13.9304	−	49.9611i	0.443411	−	1.59028i
$988$	42.9141			1.36528
$989$			7.07753i			0.225052i
$990$	−6.27237	+	14.5634i	−0.199349	+	0.462855i
$991$	32.0621			1.01849			0.509243	−	0.860623i	$-0.329925\pi$
$991$	32.0621			1.01849			0.509243	+	0.860623i	$0.329925\pi$
$992$	7.18822			0.228226
$993$	−8.05628	−	12.2415i	−0.255658	−	0.388473i
$994$	9.95421	+	11.4225i	0.315728	+	0.362299i
$995$			73.5737i			2.33244i
$996$	2.09502	+	3.18338i	0.0663832	+	0.100869i
$997$		−	56.2228i		−	1.78059i	−0.455379	−	0.890297i	$-0.650496\pi$
$997$		−	56.2228i		−	1.78059i	0.455379	−	0.890297i	$-0.349504\pi$
$998$			4.40063i			0.139300i
$999$	−33.0530	+	5.85678i	−1.04575	+	0.185300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.c.461.19	yes	28
3.2	odd	2	inner	966.2.f.c.461.10	yes	28
7.6	odd	2	inner	966.2.f.c.461.24	yes	28
21.20	even	2	inner	966.2.f.c.461.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.c.461.5	✓	28	21.20	even	2	inner
966.2.f.c.461.10	yes	28	3.2	odd	2	inner
966.2.f.c.461.19	yes	28	1.1	even	1	trivial
966.2.f.c.461.24	yes	28	7.6	odd	2	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.952183 - 1.44684i) q^{3} -1.00000 q^{4} +3.39470 q^{5} +(1.44684 - 0.952183i) q^{6} +(1.73823 + 1.99463i) q^{7} -1.00000i q^{8} +(-1.18670 + 2.75531i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.952183 - 1.44684i) q^{3} -1.00000 q^{4} +3.39470 q^{5} +(1.44684 - 0.952183i) q^{6} +(1.73823 + 1.99463i) q^{7} -1.00000i q^{8} +(-1.18670 + 2.75531i) q^{9} +3.39470i q^{10} -1.55701i q^{11} +(0.952183 + 1.44684i) q^{12} +6.18871i q^{13} +(-1.99463 + 1.73823i) q^{14} +(-3.23237 - 4.91159i) q^{15} +1.00000 q^{16} -2.89368 q^{17} +(-2.75531 - 1.18670i) q^{18} +6.93426i q^{19} -3.39470 q^{20} +(1.23079 - 4.41420i) q^{21} +1.55701 q^{22} +1.00000i q^{23} +(-1.44684 + 0.952183i) q^{24} +6.52399 q^{25} -6.18871 q^{26} +(5.11645 - 0.906601i) q^{27} +(-1.73823 - 1.99463i) q^{28} -1.06422i q^{29} +(4.91159 - 3.23237i) q^{30} -7.18822i q^{31} +1.00000i q^{32} +(-2.25274 + 1.48255i) q^{33} -2.89368i q^{34} +(5.90078 + 6.77116i) q^{35} +(1.18670 - 2.75531i) q^{36} -6.46015 q^{37} -6.93426 q^{38} +(8.95407 - 5.89278i) q^{39} -3.39470i q^{40} -4.43534 q^{41} +(4.41420 + 1.23079i) q^{42} +7.07753 q^{43} +1.55701i q^{44} +(-4.02848 + 9.35346i) q^{45} -1.00000 q^{46} +11.3183 q^{47} +(-0.952183 - 1.44684i) q^{48} +(-0.957082 + 6.93426i) q^{49} +6.52399i q^{50} +(2.75531 + 4.18670i) q^{51} -6.18871i q^{52} -2.78970i q^{53} +(0.906601 + 5.11645i) q^{54} -5.28557i q^{55} +(1.99463 - 1.73823i) q^{56} +(10.0328 - 6.60268i) q^{57} +1.06422 q^{58} -9.07749 q^{59} +(3.23237 + 4.91159i) q^{60} +13.7405i q^{61} +7.18822 q^{62} +(-7.55858 + 2.42236i) q^{63} -1.00000 q^{64} +21.0088i q^{65} +(-1.48255 - 2.25274i) q^{66} +10.9175 q^{67} +2.89368 q^{68} +(1.44684 - 0.952183i) q^{69} +(-6.77116 + 5.90078i) q^{70} -5.72662i q^{71} +(2.75531 + 1.18670i) q^{72} +11.2517i q^{73} -6.46015i q^{74} +(-6.21203 - 9.43917i) q^{75} -6.93426i q^{76} +(3.10565 - 2.70644i) q^{77} +(5.89278 + 8.95407i) q^{78} +0.738342 q^{79} +3.39470 q^{80} +(-6.18350 - 6.53944i) q^{81} -4.43534i q^{82} +2.20023 q^{83} +(-1.23079 + 4.41420i) q^{84} -9.82318 q^{85} +7.07753i q^{86} +(-1.53976 + 1.01333i) q^{87} -1.55701 q^{88} +3.01787 q^{89} +(-9.35346 - 4.02848i) q^{90} +(-12.3442 + 10.7574i) q^{91} -1.00000i q^{92} +(-10.4002 + 6.84450i) q^{93} +11.3183i q^{94} +23.5397i q^{95} +(1.44684 - 0.952183i) q^{96} -6.59867i q^{97} +(-6.93426 - 0.957082i) q^{98} +(4.29004 + 1.84769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9	\( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9 + 16 * q^15 + 28 * q^16 - 16 * q^18 + 4 * q^21 + 80 * q^25 - 4 * q^28 + 12 * q^30 + 4 * q^36 + 20 * q^37 - 20 * q^39 + 28 * q^42 - 28 * q^43 - 28 * q^46 - 28 * q^49 + 16 * q^51 - 8 * q^57 - 36 * q^58 - 16 * q^60 + 36 * q^63 - 28 * q^64 - 8 * q^67 - 60 * q^70 + 16 * q^72 + 16 * q^78 - 76 * q^81 - 4 * q^84 - 24 * q^85 + 36 * q^91 + 48 * q^93 + 72 * q^99

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