LMFDB - Embedded newform 966.2.q.a.547.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			547.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	966.547
Dual form			966.2.q.a.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.0279611 + 0.194474i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.0279611 + 0.194474i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.0816181 - 0.178719i) q^{10} +(-0.219443 + 0.0644343i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(-1.17421 + 2.57115i) q^{13} +(0.142315 + 0.989821i) q^{14} +(-0.128663 - 0.148485i) q^{15} +(0.415415 + 0.909632i) q^{16} +(5.79111 - 3.72172i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(-2.47204 - 1.58868i) q^{19} +(-0.128663 + 0.148485i) q^{20} +(0.959493 + 0.281733i) q^{21} +0.228707 q^{22} +(-1.96755 - 4.37364i) q^{23} +1.00000 q^{24} +(4.76043 + 1.39779i) q^{25} +(1.85102 - 2.13619i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.142315 - 0.989821i) q^{28} +(-1.42849 + 0.918035i) q^{29} +(0.0816181 + 0.178719i) q^{30} +(0.220460 + 0.254424i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(0.0950085 - 0.208040i) q^{33} +(-6.60506 + 1.93942i) q^{34} +(0.188515 - 0.0553531i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.806342 + 5.60823i) q^{37} +(1.92432 + 2.22078i) q^{38} +(-1.17421 - 2.57115i) q^{39} +(0.165284 - 0.106222i) q^{40} +(1.78440 - 12.4108i) q^{41} +(-0.841254 - 0.540641i) q^{42} +(1.52644 - 1.76161i) q^{43} +(-0.219443 - 0.0644343i) q^{44} +0.196474 q^{45} +(0.655652 + 4.75080i) q^{46} +7.05688 q^{47} +(-0.959493 - 0.281733i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-4.17379 - 2.68233i) q^{50} +(-0.979683 + 6.81384i) q^{51} +(-2.37787 + 1.52817i) q^{52} +(0.831749 + 1.82128i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-0.00639492 - 0.0444776i) q^{55} +(-0.415415 + 0.909632i) q^{56} +(2.81949 - 0.827876i) q^{57} +(1.62927 - 0.478396i) q^{58} +(1.58190 - 3.46388i) q^{59} +(-0.0279611 - 0.194474i) q^{60} +(7.21774 + 8.32972i) q^{61} +(-0.139850 - 0.306229i) q^{62} +(-0.841254 + 0.540641i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.467190 - 0.300245i) q^{65} +(-0.149772 + 0.172846i) q^{66} +(7.19213 + 2.11180i) q^{67} +6.88391 q^{68} +(4.59385 + 1.37715i) q^{69} -0.196474 q^{70} +(13.2834 + 3.90035i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(4.82053 + 3.09797i) q^{73} +(0.806342 - 5.60823i) q^{74} +(-4.17379 + 2.68233i) q^{75} +(-1.22070 - 2.67297i) q^{76} +(0.149772 + 0.172846i) q^{77} +(0.402265 + 2.79781i) q^{78} +(2.61470 - 5.72539i) q^{79} +(-0.188515 + 0.0553531i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-5.20865 + 11.4054i) q^{82} +(-2.21761 - 15.4238i) q^{83} +(0.654861 + 0.755750i) q^{84} +(0.561852 + 1.23028i) q^{85} +(-1.96091 + 1.26020i) q^{86} +(0.241658 - 1.68077i) q^{87} +(0.192401 + 0.123649i) q^{88} +(-1.06607 + 1.23031i) q^{89} +(-0.188515 - 0.0553531i) q^{90} +2.82659 q^{91} +(0.709362 - 4.74308i) q^{92} -0.336651 q^{93} +(-6.77102 - 1.98815i) q^{94} +(0.378078 - 0.436326i) q^{95} +(0.841254 + 0.540641i) q^{96} +(2.60273 - 18.1024i) q^{97} +(0.841254 - 0.540641i) q^{98} +(0.0950085 + 0.208040i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) $ 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9} + 8 q^{10} - 4 q^{11} - q^{12} + 14 q^{13} + q^{14} - 3 q^{15} - q^{16} + 15 q^{17} - q^{18} - 11 q^{19} - 3 q^{20} + q^{21} - 26 q^{22} - q^{23} + 10 q^{24} + 7 q^{25} - 8 q^{26} - q^{27} + q^{28} + 19 q^{29} + 8 q^{30} - 5 q^{31} - q^{32} + 7 q^{33} - 18 q^{34} - 8 q^{35} - q^{36} - 2 q^{37} + 11 q^{38} + 14 q^{39} - 3 q^{40} + 2 q^{41} + q^{42} + 25 q^{43} - 4 q^{44} + 8 q^{45} - 23 q^{46} - 4 q^{47} - q^{48} - q^{49} - 15 q^{50} + 15 q^{51} - 8 q^{52} + 15 q^{53} - q^{54} + 54 q^{55} + q^{56} + 8 q^{58} - 17 q^{59} - 14 q^{60} + q^{61} - 16 q^{62} + q^{63} - q^{64} - 13 q^{65} - 4 q^{66} - 4 q^{67} + 26 q^{68} + 21 q^{69} - 8 q^{70} + 6 q^{71} - q^{72} - 25 q^{73} - 2 q^{74} - 15 q^{75} - 22 q^{76} + 4 q^{77} + 14 q^{78} + 3 q^{79} + 8 q^{80} - q^{81} + 2 q^{82} + 7 q^{83} + q^{84} + 12 q^{85} - 41 q^{86} + 8 q^{87} + 7 q^{88} - 41 q^{89} + 8 q^{90} + 30 q^{91} - q^{92} - 16 q^{93} - 15 q^{94} - 44 q^{95} - q^{96} - 4 q^{97} - q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9 + 8 * q^10 - 4 * q^11 - q^12 + 14 * q^13 + q^14 - 3 * q^15 - q^16 + 15 * q^17 - q^18 - 11 * q^19 - 3 * q^20 + q^21 - 26 * q^22 - q^23 + 10 * q^24 + 7 * q^25 - 8 * q^26 - q^27 + q^28 + 19 * q^29 + 8 * q^30 - 5 * q^31 - q^32 + 7 * q^33 - 18 * q^34 - 8 * q^35 - q^36 - 2 * q^37 + 11 * q^38 + 14 * q^39 - 3 * q^40 + 2 * q^41 + q^42 + 25 * q^43 - 4 * q^44 + 8 * q^45 - 23 * q^46 - 4 * q^47 - q^48 - q^49 - 15 * q^50 + 15 * q^51 - 8 * q^52 + 15 * q^53 - q^54 + 54 * q^55 + q^56 + 8 * q^58 - 17 * q^59 - 14 * q^60 + q^61 - 16 * q^62 + q^63 - q^64 - 13 * q^65 - 4 * q^66 - 4 * q^67 + 26 * q^68 + 21 * q^69 - 8 * q^70 + 6 * q^71 - q^72 - 25 * q^73 - 2 * q^74 - 15 * q^75 - 22 * q^76 + 4 * q^77 + 14 * q^78 + 3 * q^79 + 8 * q^80 - q^81 + 2 * q^82 + 7 * q^83 + q^84 + 12 * q^85 - 41 * q^86 + 8 * q^87 + 7 * q^88 - 41 * q^89 + 8 * q^90 + 30 * q^91 - q^92 - 16 * q^93 - 15 * q^94 - 44 * q^95 - q^96 - 4 * q^97 - q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

Coefficient data

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

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

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

$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$2$	−0.959493	−	0.281733i	−0.678464	−	0.199215i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$	0.841254	+	0.540641i	0.420627	+	0.270320i
$5$	−0.0279611	+	0.194474i	−0.0125046	+	0.0869714i	−0.995118	−	0.0986917i	$-0.968534\pi$
$5$	−0.0279611	+	0.194474i	−0.0125046	+	0.0869714i	0.982613	+	0.185663i	$0.0594433\pi$
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	−0.415415	−	0.909632i	−0.157012	−	0.343809i
$7$	−0.415415	−	0.909632i	−0.157012	−	0.343809i
$8$	−0.654861	−	0.755750i	−0.231528	−	0.267198i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	0.0816181	−	0.178719i	0.0258099	−	0.0565159i
$11$	−0.219443	+	0.0644343i	−0.0661646	+	0.0194277i	−0.314647	−	0.949209i	$-0.601886\pi$
$11$	−0.219443	+	0.0644343i	−0.0661646	+	0.0194277i	0.248483	+	0.968636i	$0.420068\pi$
$12$	−0.959493	+	0.281733i	−0.276982	+	0.0813292i
$13$	−1.17421	+	2.57115i	−0.325666	+	0.713109i	−0.999672	−	0.0256168i	$-0.991845\pi$
$13$	−1.17421	+	2.57115i	−0.325666	+	0.713109i	0.674006	+	0.738726i	$0.264572\pi$
$14$	0.142315	+	0.989821i	0.0380352	+	0.264541i
$15$	−0.128663	−	0.148485i	−0.0332206	−	0.0383387i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	5.79111	−	3.72172i	1.40455	−	0.902650i	0.404622	−	0.914484i	$-0.367403\pi$
$17$	5.79111	−	3.72172i	1.40455	−	0.902650i	0.999930	+	0.0118338i	$0.00376690\pi$
$18$	−0.142315	+	0.989821i	−0.0335439	+	0.233303i
$19$	−2.47204	−	1.58868i	−0.567125	−	0.364469i	0.225440	−	0.974257i	$-0.427618\pi$
$19$	−2.47204	−	1.58868i	−0.567125	−	0.364469i	−0.792564	+	0.609788i	$0.791254\pi$
$20$	−0.128663	+	0.148485i	−0.0287699	+	0.0332022i
$21$	0.959493	+	0.281733i	0.209379	+	0.0614791i
$22$	0.228707			0.0487606
$23$	−1.96755	−	4.37364i	−0.410262	−	0.911968i
$23$	−1.96755	−	4.37364i	−0.410262	−	0.911968i
$24$	1.00000			0.204124
$25$	4.76043	+	1.39779i	0.952085	+	0.279557i
$26$	1.85102	−	2.13619i	0.363015	−	0.418941i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	0.142315	−	0.989821i	0.0268950	−	0.187059i
$29$	−1.42849	+	0.918035i	−0.265264	+	0.170475i	−0.666511	−	0.745495i	$-0.732213\pi$
$29$	−1.42849	+	0.918035i	−0.265264	+	0.170475i	0.401247	+	0.915970i	$0.368577\pi$
$30$	0.0816181	+	0.178719i	0.0149014	+	0.0326294i
$31$	0.220460	+	0.254424i	0.0395957	+	0.0456959i	0.775202	−	0.631713i	$-0.217648\pi$
$31$	0.220460	+	0.254424i	0.0395957	+	0.0456959i	−0.735606	+	0.677409i	$0.763103\pi$
$32$	−0.142315	−	0.989821i	−0.0251579	−	0.174977i
$33$	0.0950085	−	0.208040i	0.0165389	−	0.0362150i
$34$	−6.60506	+	1.93942i	−1.13276	+	0.332608i
$35$	0.188515	−	0.0553531i	0.0318649	−	0.00935637i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	0.806342	+	5.60823i	0.132562	+	0.921988i	0.942198	+	0.335056i	$0.108755\pi$
$37$	0.806342	+	5.60823i	0.132562	+	0.921988i	−0.809636	+	0.586932i	$0.800336\pi$
$38$	1.92432	+	2.22078i	0.312166	+	0.360259i
$39$	−1.17421	−	2.57115i	−0.188023	−	0.411714i
$40$	0.165284	−	0.106222i	0.0261337	−	0.0167951i
$41$	1.78440	−	12.4108i	0.278677	−	1.93824i	−0.0620336	−	0.998074i	$-0.519759\pi$
$41$	1.78440	−	12.4108i	0.278677	−	1.93824i	0.340711	−	0.940168i	$-0.389332\pi$
$42$	−0.841254	−	0.540641i	−0.129808	−	0.0834227i
$43$	1.52644	−	1.76161i	0.232780	−	0.268643i	−0.627327	−	0.778756i	$-0.715851\pi$
$43$	1.52644	−	1.76161i	0.232780	−	0.268643i	0.860107	+	0.510113i	$0.170396\pi$
$44$	−0.219443	−	0.0644343i	−0.0330823	−	0.00971384i
$45$	0.196474			0.0292886
$46$	0.655652	+	4.75080i	0.0966706	+	0.700468i
$47$	7.05688			1.02935			0.514676	−	0.857385i	$-0.327912\pi$
$47$	7.05688			1.02935			0.514676	+	0.857385i	$0.327912\pi$
$48$	−0.959493	−	0.281733i	−0.138491	−	0.0406646i
$49$	−0.654861	+	0.755750i	−0.0935515	+	0.107964i
$50$	−4.17379	−	2.68233i	−0.590264	−	0.379339i
$51$	−0.979683	+	6.81384i	−0.137183	+	0.954129i
$52$	−2.37787	+	1.52817i	−0.329752	+	0.211919i
$53$	0.831749	+	1.82128i	0.114250	+	0.250172i	0.958115	−	0.286383i	$-0.0924529\pi$
$53$	0.831749	+	1.82128i	0.114250	+	0.250172i	−0.843866	+	0.536554i	$0.819726\pi$
$54$	−0.654861	−	0.755750i	−0.0891153	−	0.102844i
$55$	−0.00639492	−	0.0444776i	−0.000862291	−	0.00599736i
$56$	−0.415415	+	0.909632i	−0.0555122	+	0.121555i
$57$	2.81949	−	0.827876i	0.373450	−	0.109655i
$58$	1.62927	−	0.478396i	0.213933	−	0.0628165i
$59$	1.58190	−	3.46388i	0.205946	−	0.450959i	−0.778270	−	0.627930i	$-0.783902\pi$
$59$	1.58190	−	3.46388i	0.205946	−	0.450959i	0.984216	+	0.176971i	$0.0566297\pi$
$60$	−0.0279611	−	0.194474i	−0.00360977	−	0.0251065i
$61$	7.21774	+	8.32972i	0.924137	+	1.06651i	0.997602	+	0.0692136i	$0.0220490\pi$
$61$	7.21774	+	8.32972i	0.924137	+	1.06651i	−0.0734645	+	0.997298i	$0.523406\pi$
$62$	−0.139850	−	0.306229i	−0.0177610	−	0.0388911i
$63$	−0.841254	+	0.540641i	−0.105988	+	0.0681143i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	−0.467190	−	0.300245i	−0.0579478	−	0.0372408i
$66$	−0.149772	+	0.172846i	−0.0184356	+	0.0212758i
$67$	7.19213	+	2.11180i	0.878659	+	0.257997i	0.689794	−	0.724006i	$-0.257701\pi$
$67$	7.19213	+	2.11180i	0.878659	+	0.257997i	0.188865	+	0.982003i	$0.439519\pi$
$68$	6.88391			0.834797
$69$	4.59385	+	1.37715i	0.553034	+	0.165790i
$70$	−0.196474			−0.0234831
$71$	13.2834	+	3.90035i	1.57645	+	0.462887i	0.948870	−	0.315667i	$-0.102228\pi$
$71$	13.2834	+	3.90035i	1.57645	+	0.462887i	0.627578	+	0.778554i	$0.284046\pi$
$72$	−0.654861	+	0.755750i	−0.0771761	+	0.0890659i
$73$	4.82053	+	3.09797i	0.564201	+	0.362590i	0.791438	−	0.611250i	$-0.209333\pi$
$73$	4.82053	+	3.09797i	0.564201	+	0.362590i	−0.227237	+	0.973839i	$0.572969\pi$
$74$	0.806342	−	5.60823i	0.0937354	−	0.651944i
$75$	−4.17379	+	2.68233i	−0.481948	+	0.309729i
$76$	−1.22070	−	2.67297i	−0.140024	−	0.306611i
$77$	0.149772	+	0.172846i	0.0170680	+	0.0196976i
$78$	0.402265	+	2.79781i	0.0455475	+	0.316790i
$79$	2.61470	−	5.72539i	0.294176	−	0.644156i	−0.703615	−	0.710581i	$-0.748432\pi$
$79$	2.61470	−	5.72539i	0.294176	−	0.644156i	0.997791	+	0.0664250i	$0.0211593\pi$
$80$	−0.188515	+	0.0553531i	−0.0210766	+	0.00618866i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−5.20865	+	11.4054i	−0.575199	+	1.25951i
$83$	−2.21761	−	15.4238i	−0.243414	−	1.69298i	−0.634735	−	0.772730i	$-0.718891\pi$
$83$	−2.21761	−	15.4238i	−0.243414	−	1.69298i	0.391321	−	0.920254i	$-0.372018\pi$
$84$	0.654861	+	0.755750i	0.0714512	+	0.0824590i
$85$	0.561852	+	1.23028i	0.0609414	+	0.133443i
$86$	−1.96091	+	1.26020i	−0.211451	+	0.135891i
$87$	0.241658	−	1.68077i	0.0259084	−	0.180197i
$88$	0.192401	+	0.123649i	0.0205100	+	0.0131810i
$89$	−1.06607	+	1.23031i	−0.113003	+	0.130413i	−0.809433	−	0.587212i	$-0.800225\pi$
$89$	−1.06607	+	1.23031i	−0.113003	+	0.130413i	0.696430	+	0.717625i	$0.254771\pi$
$90$	−0.188515	−	0.0553531i	−0.0198712	−	0.00583472i
$91$	2.82659			0.296307
$92$	0.709362	−	4.74308i	0.0739561	−	0.494500i
$93$	−0.336651			−0.0349091
$94$	−6.77102	−	1.98815i	−0.698378	−	0.205062i
$95$	0.378078	−	0.436326i	0.0387900	−	0.0447661i
$96$	0.841254	+	0.540641i	0.0858601	+	0.0551789i
$97$	2.60273	−	18.1024i	0.264268	−	1.83802i	−0.235515	−	0.971871i	$-0.575678\pi$
$97$	2.60273	−	18.1024i	0.264268	−	1.83802i	0.499782	−	0.866151i	$-0.333413\pi$
$98$	0.841254	−	0.540641i	0.0849794	−	0.0546130i
$99$	0.0950085	+	0.208040i	0.00954871	+	0.0209088i
$100$	3.24902	+	3.74957i	0.324902	+	0.374957i
$101$	0.688246	+	4.78685i	0.0684830	+	0.476310i	0.994985	+	0.100021i	$0.0318909\pi$
$101$	0.688246	+	4.78685i	0.0684830	+	0.476310i	−0.926502	+	0.376289i	$0.877200\pi$
$102$	2.85968	−	6.26183i	0.283150	−	0.620013i
$103$	12.5299	−	3.67912i	1.23461	−	0.362514i	0.401623	−	0.915805i	$-0.368446\pi$
$103$	12.5299	−	3.67912i	1.23461	−	0.362514i	0.832988	+	0.553291i	$0.186628\pi$
$104$	2.71209	−	0.796341i	0.265942	−	0.0780877i
$105$	−0.0816181	+	0.178719i	−0.00796512	+	0.0174412i
$106$	−0.284944	−	1.98183i	−0.0276763	−	0.192493i
$107$	−1.01912	−	1.17613i	−0.0985221	−	0.113701i	0.704347	−	0.709856i	$-0.251240\pi$
$107$	−1.01912	−	1.17613i	−0.0985221	−	0.113701i	−0.802869	+	0.596155i	$0.796694\pi$
$108$	0.415415	+	0.909632i	0.0399733	+	0.0875294i
$109$	7.65107	−	4.91705i	0.732840	−	0.470968i	−0.120242	−	0.992745i	$-0.538367\pi$
$109$	7.65107	−	4.91705i	0.732840	−	0.470968i	0.853082	+	0.521777i	$0.174731\pi$
$110$	−0.00639492	+	0.0444776i	−0.000609732	+	0.00424078i
$111$	−4.76646	−	3.06322i	−0.452413	−	0.290748i
$112$	0.654861	−	0.755750i	0.0618785	−	0.0714116i
$113$	−3.81057	−	1.11888i	−0.358468	−	0.105256i	0.0975395	−	0.995232i	$-0.468903\pi$
$113$	−3.81057	−	1.11888i	−0.358468	−	0.105256i	−0.456007	+	0.889976i	$0.650721\pi$
$114$	−2.93852			−0.275217
$115$	0.905574	−	0.260345i	0.0844452	−	0.0242773i
$116$	−1.69805			−0.157660
$117$	2.71209	+	0.796341i	0.250733	+	0.0736218i
$118$	−2.49371	+	2.87790i	−0.229565	+	0.264932i
$119$	−5.79111	−	3.72172i	−0.530871	−	0.341170i
$120$	−0.0279611	+	0.194474i	−0.00255249	+	0.0177530i
$121$	−9.20979	+	5.91877i	−0.837253	+	0.538070i
$122$	−4.57862	−	10.0258i	−0.414529	−	0.907692i
$123$	8.21092	+	9.47591i	0.740354	+	0.854414i
$124$	0.0479104	+	0.333224i	0.00430248	+	0.0299244i
$125$	−0.813031	+	1.78029i	−0.0727197	+	0.159234i
$126$	0.959493	−	0.281733i	0.0854784	−	0.0250987i
$127$	−2.33575	+	0.685837i	−0.207264	+	0.0608582i	−0.383716	−	0.923451i	$-0.625356\pi$
$127$	−2.33575	+	0.685837i	−0.207264	+	0.0608582i	0.176452	+	0.984309i	$0.443538\pi$
$128$	0.415415	−	0.909632i	0.0367178	−	0.0804009i
$129$	0.331728	+	2.30722i	0.0292070	+	0.203139i
$130$	0.363677	+	0.419705i	0.0318966	+	0.0368106i
$131$	−3.28809	−	7.19991i	−0.287282	−	0.629059i	0.709882	−	0.704320i	$-0.248748\pi$
$131$	−3.28809	−	7.19991i	−0.287282	−	0.629059i	−0.997164	+	0.0752613i	$0.976021\pi$
$132$	0.192401	−	0.123649i	0.0167464	−	0.0107622i
$133$	−0.418195	+	2.90861i	−0.0362621	+	0.252208i
$134$	−6.30584	−	4.05251i	−0.544741	−	0.350084i
$135$	−0.128663	+	0.148485i	−0.0110735	+	0.0127796i
$136$	−6.60506	−	1.93942i	−0.566380	−	0.166304i
$137$	21.8505			1.86681			0.933407	−	0.358820i	$-0.116821\pi$
$137$	21.8505			1.86681			0.933407	+	0.358820i	$0.116821\pi$
$138$	−4.01978	−	2.61561i	−0.342186	−	0.222655i
$139$	−21.6908			−1.83979			−0.919895	−	0.392165i	$-0.871726\pi$
$139$	−21.6908			−1.83979			−0.919895	+	0.392165i	$0.871726\pi$
$140$	0.188515	+	0.0553531i	0.0159324	+	0.00467819i
$141$	−4.62127	+	5.33323i	−0.389181	+	0.449139i
$142$	−11.6465	−	7.48473i	−0.977349	−	0.628104i
$143$	0.0920010	−	0.639881i	0.00769351	−	0.0535095i
$144$	0.841254	−	0.540641i	0.0701045	−	0.0450534i
$145$	−0.138592	−	0.303473i	−0.0115094	−	0.0252021i
$146$	−3.75247	−	4.33058i	−0.310556	−	0.358401i
$147$	−0.142315	−	0.989821i	−0.0117379	−	0.0816391i
$148$	−2.35370	+	5.15389i	−0.193473	+	0.423647i
$149$	−3.16037	+	0.927969i	−0.258908	+	0.0760222i	−0.408610	−	0.912709i	$-0.633987\pi$
$149$	−3.16037	+	0.927969i	−0.258908	+	0.0760222i	0.149703	+	0.988731i	$0.452168\pi$
$150$	4.76043	−	1.39779i	0.388687	−	0.114129i
$151$	−4.67179	+	10.2298i	−0.380184	+	0.832488i	0.618716	+	0.785614i	$0.287653\pi$
$151$	−4.67179	+	10.2298i	−0.380184	+	0.832488i	−0.998901	+	0.0468735i	$0.985074\pi$
$152$	0.418195	+	2.90861i	0.0339201	+	0.235919i
$153$	−4.50800	−	5.20251i	−0.364450	−	0.420598i
$154$	−0.0950085	−	0.208040i	−0.00765600	−	0.0167643i
$155$	−0.0556431	+	0.0357597i	−0.00446936	+	0.00287228i
$156$	0.402265	−	2.79781i	0.0322070	−	0.224004i
$157$	9.79036	+	6.29188i	0.781356	+	0.502147i	0.869483	−	0.493962i	$-0.164452\pi$
$157$	9.79036	+	6.29188i	0.781356	+	0.502147i	−0.0881276	+	0.996109i	$0.528088\pi$
$158$	−4.12181	+	4.75682i	−0.327914	+	0.378432i
$159$	−1.92111	−	0.564088i	−0.152354	−	0.0447351i
$160$	0.196474			0.0155326
$161$	−3.16106	+	3.60662i	−0.249126	+	0.284242i
$162$	1.00000			0.0785674
$163$	3.93371	+	1.15504i	0.308112	+	0.0904698i	0.432133	−	0.901810i	$-0.357761\pi$
$163$	3.93371	+	1.15504i	0.308112	+	0.0904698i	−0.124022	+	0.992280i	$0.539579\pi$
$164$	8.21092	−	9.47591i	0.641166	−	0.739944i
$165$	0.0378017	+	0.0242937i	0.00294286	+	0.00189126i
$166$	−2.21761	+	15.4238i	−0.172120	+	1.19712i
$167$	−12.6256	+	8.11399i	−0.976999	+	0.627879i	−0.928652	−	0.370951i	$-0.879032\pi$
$167$	−12.6256	+	8.11399i	−0.976999	+	0.627879i	−0.0483469	+	0.998831i	$0.515395\pi$
$168$	−0.415415	−	0.909632i	−0.0320500	−	0.0701796i
$169$	3.28112	+	3.78662i	0.252394	+	0.291278i
$170$	−0.192482	−	1.33874i	−0.0147627	−	0.102677i
$171$	−1.22070	+	2.67297i	−0.0933496	+	0.204407i
$172$	2.23652	−	0.656702i	0.170533	−	0.0500731i
$173$	21.1009	−	6.19577i	1.60427	−	0.471056i	0.647538	−	0.762033i	$-0.275799\pi$
$173$	21.1009	−	6.19577i	1.60427	−	0.471056i	0.956730	+	0.290977i	$0.0939804\pi$
$174$	−0.705395	+	1.54460i	−0.0534759	+	0.117096i
$175$	−0.706081	−	4.91090i	−0.0533747	−	0.371229i
$176$	−0.149772	−	0.172846i	−0.0112895	−	0.0130287i
$177$	1.58190	+	3.46388i	0.118903	+	0.260361i
$178$	1.36950	−	0.880127i	0.102649	−	0.0659683i
$179$	−1.47740	+	10.2755i	−0.110426	+	0.768029i	0.857080	+	0.515183i	$0.172276\pi$
$179$	−1.47740	+	10.2755i	−0.110426	+	0.768029i	−0.967506	+	0.252847i	$0.918633\pi$
$180$	0.165284	+	0.106222i	0.0123196	+	0.00791730i
$181$	−9.15861	+	10.5696i	−0.680754	+	0.785632i	−0.986019	−	0.166635i	$-0.946710\pi$
$181$	−9.15861	+	10.5696i	−0.680754	+	0.785632i	0.305264	+	0.952268i	$0.401255\pi$
$182$	−2.71209	−	0.796341i	−0.201033	−	0.0590287i
$183$	−11.0218			−0.814755
$184$	−2.01691	+	4.35110i	−0.148688	+	0.320767i
$185$	−1.11320			−0.0818442
$186$	0.323014	+	0.0948456i	0.0236846	+	0.00695441i
$187$	−1.03101	+	1.18985i	−0.0753952	+	0.0870107i
$188$	5.93662	+	3.81523i	0.432973	+	0.278255i
$189$	0.142315	−	0.989821i	0.0103519	−	0.0719989i
$190$	−0.485691	+	0.312134i	−0.0352357	+	0.0226446i
$191$	−8.17269	−	17.8957i	−0.591355	−	1.29489i	−0.934620	−	0.355648i	$-0.884260\pi$
$191$	−8.17269	−	17.8957i	−0.591355	−	1.29489i	0.343265	−	0.939239i	$-0.388467\pi$
$192$	−0.654861	−	0.755750i	−0.0472605	−	0.0545415i
$193$	1.02141	+	7.10408i	0.0735229	+	0.511363i	0.992990	+	0.118197i	$0.0377113\pi$
$193$	1.02141	+	7.10408i	0.0735229	+	0.511363i	−0.919467	+	0.393166i	$0.871380\pi$
$194$	−7.59735	+	16.6359i	−0.545458	+	1.19439i
$195$	0.532854	−	0.156460i	0.0381585	−	0.0112043i
$196$	−0.959493	+	0.281733i	−0.0685352	+	0.0201238i
$197$	6.66999	−	14.6052i	0.475217	−	1.04058i	−0.508534	−	0.861042i	$-0.669812\pi$
$197$	6.66999	−	14.6052i	0.475217	−	1.04058i	0.983751	−	0.179539i	$-0.0574605\pi$
$198$	−0.0325485	−	0.226380i	−0.00231312	−	0.0160881i
$199$	−7.71366	−	8.90204i	−0.546807	−	0.631049i	0.413329	−	0.910582i	$-0.364366\pi$
$199$	−7.71366	−	8.90204i	−0.546807	−	0.631049i	−0.960136	+	0.279533i	$0.909820\pi$
$200$	−2.06104	−	4.51305i	−0.145737	−	0.319121i
$201$	−6.30584	+	4.05251i	−0.444779	+	0.285842i
$202$	0.688246	−	4.78685i	0.0484248	−	0.336802i
$203$	1.42849	+	0.918035i	0.100260	+	0.0644334i
$204$	−4.50800	+	5.20251i	−0.315623	+	0.364249i
$205$	2.36368	+	0.694040i	0.165087	+	0.0484739i
$206$	−13.0589			−0.909857
$207$	−4.04911	+	2.56996i	−0.281433	+	0.178624i
$208$	−2.82659			−0.195988
$209$	0.644838	+	0.189341i	0.0446044	+	0.0130970i
$210$	0.128663	−	0.148485i	0.00887859	−	0.0102464i
$211$	−17.6369	−	11.3345i	−1.21417	−	0.780302i	−0.232821	−	0.972520i	$-0.574796\pi$
$211$	−17.6369	−	11.3345i	−1.21417	−	0.780302i	−0.981352	+	0.192217i	$0.938432\pi$
$212$	−0.284944	+	1.98183i	−0.0195701	+	0.136113i
$213$	−11.6465	+	7.48473i	−0.798002	+	0.512845i
$214$	0.646485	+	1.41561i	0.0441928	+	0.0967688i
$215$	0.299906	+	0.346110i	0.0204534	+	0.0236045i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	0.139850	−	0.306229i	0.00949363	−	0.0207881i
$218$	−8.72644	+	2.56231i	−0.591029	+	0.173542i
$219$	−5.49806	+	1.61438i	−0.371525	+	0.109090i
$220$	0.0186667	−	0.0408743i	0.00125851	−	0.00275575i
$221$	2.76916	+	19.2599i	0.186274	+	1.29556i
$222$	3.71038	+	4.28201i	0.249024	+	0.287389i
$223$	−3.39221	−	7.42789i	−0.227159	−	0.497409i	0.761393	−	0.648291i	$-0.224516\pi$
$223$	−3.39221	−	7.42789i	−0.227159	−	0.497409i	−0.988552	+	0.150882i	$0.951789\pi$
$224$	−0.841254	+	0.540641i	−0.0562086	+	0.0361231i
$225$	0.706081	−	4.91090i	0.0470720	−	0.327393i
$226$	3.34099	+	2.14712i	0.222239	+	0.142824i
$227$	−11.6968	+	13.4988i	−0.776344	+	0.895948i	−0.996840	−	0.0794395i	$-0.974687\pi$
$227$	−11.6968	+	13.4988i	−0.776344	+	0.895948i	0.220496	+	0.975388i	$0.429232\pi$
$228$	2.81949	+	0.827876i	0.186725	+	0.0548274i
$229$	−21.5824			−1.42621			−0.713103	−	0.701059i	$-0.752711\pi$
$229$	−21.5824			−1.42621			−0.713103	+	0.701059i	$0.752711\pi$
$230$	−0.942240	−	0.00533059i	−0.0621295	−	0.000351489i
$231$	−0.228707			−0.0150478
$232$	1.62927	+	0.478396i	0.106967	+	0.0314082i
$233$	−14.0630	+	16.2296i	−0.921299	+	1.06324i	0.0765096	+	0.997069i	$0.475622\pi$
$233$	−14.0630	+	16.2296i	−0.921299	+	1.06324i	−0.997809	+	0.0661669i	$0.978923\pi$
$234$	−2.37787	−	1.52817i	−0.155447	−	0.0998994i
$235$	−0.197318	+	1.37238i	−0.0128716	+	0.0895241i
$236$	3.20350	−	2.05876i	0.208530	−	0.134014i
$237$	2.61470	+	5.72539i	0.169843	+	0.371904i
$238$	4.50800	+	5.20251i	0.292210	+	0.337229i
$239$	0.106506	+	0.740765i	0.00688930	+	0.0479161i	0.992976	−	0.118315i	$-0.0377493\pi$
$239$	0.106506	+	0.740765i	0.00688930	+	0.0479161i	−0.986087	+	0.166231i	$0.946840\pi$
$240$	0.0816181	−	0.178719i	0.00526843	−	0.0115362i
$241$	−4.88204	+	1.43350i	−0.314480	+	0.0923396i	−0.435164	−	0.900351i	$-0.643309\pi$
$241$	−4.88204	+	1.43350i	−0.314480	+	0.0923396i	0.120684	+	0.992691i	$0.461491\pi$
$242$	10.5042	−	3.08432i	0.675238	−	0.198268i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	1.56857	+	10.9096i	0.100417	+	0.698416i
$245$	−0.128663	−	0.148485i	−0.00821997	−	0.00948636i
$246$	−5.20865	−	11.4054i	−0.332091	−	0.727179i
$247$	6.98743	−	4.49055i	0.444599	−	0.285727i
$248$	0.0479104	−	0.333224i	0.00304232	−	0.0211598i
$249$	13.1088	+	8.42449i	0.830734	+	0.533881i
$250$	1.28166	−	1.47912i	0.0810595	−	0.0935476i
$251$	−19.2896	−	5.66392i	−1.21755	−	0.357504i	−0.391009	−	0.920387i	$-0.627874\pi$
$251$	−19.2896	−	5.66392i	−1.21755	−	0.357504i	−0.826537	+	0.562883i	$0.809692\pi$
$252$	−1.00000			−0.0629941
$253$	0.713578	+	0.832988i	0.0448623	+	0.0523695i
$254$	2.43436			0.152745
$255$	−1.29772	−	0.381045i	−0.0812665	−	0.0238620i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	1.03464	+	0.664921i	0.0645389	+	0.0414766i	0.572512	−	0.819896i	$-0.305969\pi$
$257$	1.03464	+	0.664921i	0.0645389	+	0.0414766i	−0.507973	+	0.861373i	$0.669605\pi$
$258$	0.331728	−	2.30722i	0.0206525	−	0.143641i
$259$	4.76646	−	3.06322i	0.296174	−	0.190339i
$260$	−0.230701	−	0.505164i	−0.0143074	−	0.0313289i
$261$	1.11199	+	1.28330i	0.0688302	+	0.0794343i
$262$	1.12645	+	7.83463i	0.0695923	+	0.484025i
$263$	−8.48035	+	18.5694i	−0.522921	+	1.14504i	0.445401	+	0.895331i	$0.353061\pi$
$263$	−8.48035	+	18.5694i	−0.522921	+	1.14504i	−0.968322	+	0.249705i	$0.919666\pi$
$264$	−0.219443	+	0.0644343i	−0.0135058	+	0.00396566i
$265$	−0.377447	+	0.110829i	−0.0231864	+	0.00680814i
$266$	1.22070	−	2.67297i	0.0748462	−	0.163890i
$267$	−0.231679	−	1.61136i	−0.0141785	−	0.0986138i
$268$	4.90868	+	5.66492i	0.299845	+	0.346040i
$269$	−9.12524	−	19.9815i	−0.556376	−	1.21829i	−0.953740	−	0.300632i	$-0.902802\pi$
$269$	−9.12524	−	19.9815i	−0.556376	−	1.21829i	0.397365	−	0.917661i	$-0.369925\pi$
$270$	0.165284	−	0.106222i	0.0100589	−	0.00646445i
$271$	1.64563	−	11.4456i	0.0999649	−	0.695271i	−0.876784	−	0.480885i	$-0.840316\pi$
$271$	1.64563	−	11.4456i	0.0999649	−	0.695271i	0.976749	−	0.214387i	$-0.0687753\pi$
$272$	5.79111	+	3.72172i	0.351138	+	0.225663i
$273$	−1.85102	+	2.13619i	−0.112029	+	0.129288i
$274$	−20.9654	−	6.15599i	−1.26657	−	0.371897i
$275$	−1.13471			−0.0684255
$276$	3.12005	+	3.64216i	0.187805	+	0.219232i
$277$	0.885161			0.0531841			0.0265921	−	0.999646i	$-0.491534\pi$
$277$	0.885161			0.0531841			0.0265921	+	0.999646i	$0.491534\pi$
$278$	20.8122	+	6.11100i	1.24823	+	0.366514i
$279$	0.220460	−	0.254424i	0.0131986	−	0.0152320i
$280$	−0.165284	−	0.106222i	−0.00987762	−	0.00634796i
$281$	−4.09035	+	28.4490i	−0.244010	+	1.69712i	0.387592	+	0.921831i	$0.373307\pi$
$281$	−4.09035	+	28.4490i	−0.244010	+	1.69712i	−0.631601	+	0.775293i	$0.717602\pi$
$282$	5.93662	−	3.81523i	0.353521	−	0.227194i
$283$	−9.84126	−	21.5494i	−0.585002	−	1.28098i	−0.938415	−	0.345509i	$-0.887706\pi$
$283$	−9.84126	−	21.5494i	−0.585002	−	1.28098i	0.353413	−	0.935467i	$-0.385021\pi$
$284$	9.06601	+	10.4627i	0.537968	+	0.620849i
$285$	0.0821643	+	0.571465i	0.00486699	+	0.0338507i
$286$	−0.268550	+	0.588042i	−0.0158797	+	0.0347716i
$287$	−12.0305	+	3.53248i	−0.710140	+	0.208516i
$288$	−0.959493	+	0.281733i	−0.0565387	+	0.0166013i
$289$	12.6237	−	27.6421i	0.742572	−	1.62601i
$290$	0.0474794	+	0.330226i	0.00278809	+	0.0193916i
$291$	11.9765	+	13.8216i	0.702073	+	0.810235i
$292$	2.38040	+	5.21235i	0.139302	+	0.305030i
$293$	17.8604	−	11.4782i	1.04342	−	0.670562i	0.0975861	−	0.995227i	$-0.468888\pi$
$293$	17.8604	−	11.4782i	1.04342	−	0.670562i	0.945829	+	0.324665i	$0.105251\pi$
$294$	−0.142315	+	0.989821i	−0.00829997	+	0.0577276i
$295$	0.629403	+	0.404493i	0.0366453	+	0.0235505i
$296$	3.71038	−	4.28201i	0.215661	−	0.248886i
$297$	−0.219443	−	0.0644343i	−0.0127334	−	0.00373886i
$298$	3.29379			0.190804
$299$	13.5556	+	0.0766889i	0.783941	+	0.00443503i
$300$	−4.96140			−0.286446
$301$	−2.23652	−	0.656702i	−0.128911	−	0.0378517i
$302$	7.36461	−	8.49921i	0.423786	−	0.489075i
$303$	−4.06837	−	2.61458i	−0.233722	−	0.150204i
$304$	0.418195	−	2.90861i	0.0239851	−	0.166820i
$305$	−1.82173	+	1.17075i	−0.104312	+	0.0670372i
$306$	2.85968	+	6.26183i	0.163477	+	0.357965i
$307$	10.6687	+	12.3123i	0.608892	+	0.702699i	0.973558	−	0.228439i	$-0.0733623\pi$
$307$	10.6687	+	12.3123i	0.608892	+	0.702699i	−0.364666	+	0.931138i	$0.618817\pi$
$308$	0.0325485	+	0.226380i	0.00185462	+	0.0128992i
$309$	−5.42487	+	11.8788i	−0.308610	+	0.675761i
$310$	0.0634638	−	0.0186347i	0.00360450	−	0.00105838i
$311$	7.22710	−	2.12207i	0.409811	−	0.120331i	−0.0703276	−	0.997524i	$-0.522404\pi$
$311$	7.22710	−	2.12207i	0.409811	−	0.120331i	0.480139	+	0.877193i	$0.340586\pi$
$312$	−1.17421	+	2.57115i	−0.0664763	+	0.145563i
$313$	−0.443018	−	3.08126i	−0.0250409	−	0.174163i	0.973463	−	0.228845i	$-0.0734948\pi$
$313$	−0.443018	−	3.08126i	−0.0250409	−	0.174163i	−0.998504	+	0.0546814i	$0.982586\pi$
$314$	−7.62115	−	8.79528i	−0.430087	−	0.496346i
$315$	−0.0816181	−	0.178719i	−0.00459866	−	0.0100697i
$316$	5.29500	−	3.40289i	0.297867	−	0.191428i
$317$	−2.69343	+	18.7332i	−0.151278	+	1.05216i	0.762802	+	0.646632i	$0.223823\pi$
$317$	−2.69343	+	18.7332i	−0.151278	+	1.05216i	−0.914081	+	0.405532i	$0.867086\pi$
$318$	1.68437	+	1.08248i	0.0944547	+	0.0607023i
$319$	0.254320	−	0.293500i	0.0142392	−	0.0164329i
$320$	−0.188515	−	0.0553531i	−0.0105383	−	0.00309433i
$321$	1.55624			0.0868608
$322$	4.04911	−	2.56996i	0.225648	−	0.143218i
$323$	−20.2285			−1.12554
$324$	−0.959493	−	0.281733i	−0.0533052	−	0.0156518i
$325$	−9.18365	+	10.5985i	−0.509417	+	0.587899i
$326$	−3.44895	−	2.21651i	−0.191020	−	0.122761i
$327$	−1.29433	+	9.00227i	−0.0715767	+	0.497827i
$328$	−10.5480	+	6.77879i	−0.582416	+	0.374296i
$329$	−2.93153	−	6.41916i	−0.161621	−	0.353900i
$330$	−0.0294262	−	0.0339596i	−0.00161986	−	0.00186942i
$331$	2.03420	+	14.1482i	0.111810	+	0.777654i	0.966158	+	0.257952i	$0.0830477\pi$
$331$	2.03420	+	14.1482i	0.111810	+	0.777654i	−0.854348	+	0.519701i	$0.826043\pi$
$332$	6.47317	−	14.1743i	0.355262	−	0.777914i
$333$	5.43640	−	1.59627i	0.297913	−	0.0874750i
$334$	14.4002	−	4.22827i	0.787942	−	0.231361i
$335$	−0.611790	+	1.33963i	−0.0334257	+	0.0731920i
$336$	0.142315	+	0.989821i	0.00776391	+	0.0539992i
$337$	12.3686	+	14.2741i	0.673759	+	0.777560i	0.984960	−	0.172785i	$-0.0552764\pi$
$337$	12.3686	+	14.2741i	0.673759	+	0.777560i	−0.311200	+	0.950344i	$0.600731\pi$
$338$	−2.08140	−	4.55763i	−0.113213	−	0.247903i
$339$	3.34099	−	2.14712i	0.181457	−	0.116616i
$340$	−0.192482	+	1.33874i	−0.0104388	+	0.0726034i
$341$	−0.0647720	−	0.0416264i	−0.00350760	−	0.00225420i
$342$	1.92432	−	2.22078i	0.104055	−	0.120086i
$343$	0.959493	+	0.281733i	0.0518078	+	0.0152121i
$344$	−2.33094			−0.125676
$345$	−0.396269	+	0.854877i	−0.0213344	+	0.0460250i
$346$	−21.9917			−1.18228
$347$	−21.2603	−	6.24258i	−1.14131	−	0.335119i	−0.344167	−	0.938908i	$-0.611839\pi$
$347$	−21.2603	−	6.24258i	−1.14131	−	0.335119i	−0.797144	+	0.603789i	$0.793657\pi$
$348$	1.11199	−	1.28330i	0.0596087	−	0.0687921i
$349$	−14.2343	−	9.14783i	−0.761944	−	0.489672i	0.101053	−	0.994881i	$-0.467779\pi$
$349$	−14.2343	−	9.14783i	−0.761944	−	0.489672i	−0.862997	+	0.505209i	$0.831415\pi$
$350$	−0.706081	+	4.91090i	−0.0377416	+	0.262499i
$351$	−2.37787	+	1.52817i	−0.126922	+	0.0815675i
$352$	0.0950085	+	0.208040i	0.00506397	+	0.0110885i
$353$	−14.2063	−	16.3949i	−0.756124	−	0.872614i	0.239023	−	0.971014i	$-0.423173\pi$
$353$	−14.2063	−	16.3949i	−0.756124	−	0.872614i	−0.995147	+	0.0984004i	$0.968627\pi$
$354$	−0.541936	−	3.76925i	−0.0288036	−	0.200333i
$355$	−1.12994	+	2.47421i	−0.0599708	+	0.131318i
$356$	−1.56199	+	0.458642i	−0.0827853	+	0.0243080i
$357$	6.60506	−	1.93942i	0.349577	−	0.102645i
$358$	4.31251	−	9.44307i	0.227923	−	0.499082i
$359$	−1.26792	−	8.81858i	−0.0669183	−	0.465427i	−0.995536	−	0.0943877i	$-0.969911\pi$
$359$	−1.26792	−	8.81858i	−0.0669183	−	0.465427i	0.928617	−	0.371039i	$-0.120998\pi$
$360$	−0.128663	−	0.148485i	−0.00678113	−	0.00782584i
$361$	−4.30582	−	9.42844i	−0.226622	−	0.496233i
$362$	11.7654	−	7.56118i	0.618377	−	0.397407i
$363$	1.55802	−	10.8363i	0.0817748	−	0.568756i
$364$	2.37787	+	1.52817i	0.124635	+	0.0800977i
$365$	−0.737261	+	0.850845i	−0.0385900	+	0.0445353i
$366$	10.5753	+	3.10520i	0.552782	+	0.162311i
$367$	32.9332			1.71910			0.859551	−	0.511050i	$-0.170743\pi$
$367$	32.9332			1.71910			0.859551	+	0.511050i	$0.170743\pi$
$368$	3.16106	−	3.60662i	0.164781	−	0.188008i
$369$	−12.5384			−0.652725
$370$	1.06811	+	0.313625i	0.0555283	+	0.0163046i
$371$	1.31117	−	1.51317i	0.0680726	−	0.0785599i
$372$	−0.283209	−	0.182007i	−0.0146837	−	0.00943664i
$373$	1.49411	−	10.3918i	0.0773623	−	0.538067i	−0.913877	−	0.405991i	$-0.866927\pi$
$373$	1.49411	−	10.3918i	0.0773623	−	0.538067i	0.991240	−	0.132076i	$-0.0421644\pi$
$374$	1.32447	−	0.851186i	0.0684868	−	0.0440138i
$375$	−0.813031	−	1.78029i	−0.0419847	−	0.0919337i
$376$	−4.62127	−	5.33323i	−0.238324	−	0.275040i
$377$	−0.683066	−	4.75083i	−0.0351797	−	0.244680i
$378$	−0.415415	+	0.909632i	−0.0213666	+	0.0467864i
$379$	12.8956	−	3.78648i	0.662401	−	0.194498i	0.0667845	−	0.997767i	$-0.478726\pi$
$379$	12.8956	−	3.78648i	0.662401	−	0.194498i	0.595617	+	0.803269i	$0.296908\pi$
$380$	0.553955	−	0.162656i	0.0284173	−	0.00834407i
$381$	1.01127	−	2.21437i	0.0518088	−	0.113446i
$382$	2.79984	+	19.4733i	0.143252	+	0.996341i
$383$	1.94184	+	2.24100i	0.0992233	+	0.114510i	0.803189	−	0.595724i	$-0.203135\pi$
$383$	1.94184	+	2.24100i	0.0992233	+	0.114510i	−0.703966	+	0.710234i	$0.748589\pi$
$384$	0.415415	+	0.909632i	0.0211991	+	0.0464195i
$385$	−0.0378017	+	0.0242937i	−0.00192655	+	0.00123812i
$386$	1.02141	−	7.10408i	0.0519886	−	0.361588i
$387$	−1.96091	−	1.26020i	−0.0996788	−	0.0640597i
$388$	11.9765	−	13.8216i	0.608013	−	0.701684i
$389$	18.6399	+	5.47317i	0.945080	+	0.277501i	0.717737	−	0.696314i	$-0.245178\pi$
$389$	18.6399	+	5.47317i	0.945080	+	0.277501i	0.227343	+	0.973815i	$0.426996\pi$
$390$	−0.555350			−0.0281212
$391$	−27.6718	−	18.0056i	−1.39942	−	0.910582i
$392$	1.00000			0.0505076
$393$	7.59457	+	2.22997i	0.383095	+	0.112487i
$394$	−10.5146	+	12.1345i	−0.529717	+	0.611326i
$395$	1.04033	+	0.668579i	0.0523446	+	0.0336398i
$396$	−0.0325485	+	0.226380i	−0.00163562	+	0.0113760i
$397$	13.3306	−	8.56704i	0.669042	−	0.429967i	−0.161538	−	0.986867i	$-0.551645\pi$
$397$	13.3306	−	8.56704i	0.669042	−	0.429967i	0.830580	+	0.556899i	$0.188009\pi$
$398$	4.89321	+	10.7146i	0.245274	+	0.537076i
$399$	−1.92432	−	2.22078i	−0.0963365	−	0.111178i
$400$	0.706081	+	4.91090i	0.0353040	+	0.245545i
$401$	−3.10073	+	6.78965i	−0.154843	+	0.339059i	−0.971116	−	0.238607i	$-0.923309\pi$
$401$	−3.10073	+	6.78965i	−0.154843	+	0.339059i	0.816273	+	0.577666i	$0.196036\pi$
$402$	7.19213	−	2.11180i	0.358711	−	0.105327i
$403$	−0.913027	+	0.268089i	−0.0454811	+	0.0133545i
$404$	−2.00898	+	4.39905i	−0.0999505	+	0.218861i
$405$	−0.0279611	−	0.194474i	−0.00138940	−	0.00966349i
$406$	−1.11199	−	1.28330i	−0.0551870	−	0.0636891i
$407$	−0.538309	−	1.17873i	−0.0266830	−	0.0584276i
$408$	5.79111	−	3.72172i	0.286703	−	0.184253i
$409$	−2.04945	+	14.2542i	−0.101339	+	0.704827i	0.874291	+	0.485403i	$0.161327\pi$
$409$	−2.04945	+	14.2542i	−0.101339	+	0.704827i	−0.975629	+	0.219424i	$0.929582\pi$
$410$	−2.07240	−	1.33185i	−0.102349	−	0.0657756i
$411$	−14.3090	+	16.5135i	−0.705812	+	0.814551i
$412$	12.5299	+	3.67912i	0.617305	+	0.181257i
$413$	−3.80801			−0.187380
$414$	4.60914	−	1.32509i	0.226527	−	0.0651245i
$415$	3.06154			0.150285
$416$	2.71209	+	0.796341i	0.132971	+	0.0390438i
$417$	14.2045	−	16.3928i	0.695595	−	0.802759i
$418$	−0.565374	−	0.363344i	−0.0276533	−	0.0177717i
$419$	−2.57540	+	17.9123i	−0.125816	+	0.875072i	0.824959	+	0.565192i	$0.191198\pi$
$419$	−2.57540	+	17.9123i	−0.125816	+	0.875072i	−0.950776	+	0.309880i	$0.899711\pi$
$420$	−0.165284	+	0.106222i	−0.00806505	+	0.00518309i
$421$	−7.29017	−	15.9632i	−0.355301	−	0.778000i	−0.999909	−	0.0134873i	$-0.995707\pi$
$421$	−7.29017	−	15.9632i	−0.355301	−	0.778000i	0.644608	−	0.764513i	$-0.277021\pi$
$422$	13.7292	+	15.8443i	0.668325	+	0.771288i
$423$	−1.00430	−	6.98505i	−0.0488306	−	0.339625i
$424$	0.831749	−	1.82128i	0.0403933	−	0.0884490i
$425$	32.7704	−	9.62224i	1.58960	−	0.466747i
$426$	13.2834	−	3.90035i	0.643582	−	0.188973i
$427$	4.57862	−	10.0258i	0.221575	−	0.485182i
$428$	−0.221476	−	1.54040i	−0.0107054	−	0.0744580i
$429$	0.423342	+	0.488563i	0.0204391	+	0.0235880i
$430$	−0.190247	−	0.416583i	−0.00917454	−	0.0200894i
$431$	4.92638	−	3.16599i	0.237296	−	0.152501i	−0.416589	−	0.909095i	$-0.636775\pi$
$431$	4.92638	−	3.16599i	0.237296	−	0.152501i	0.653885	+	0.756594i	$0.273138\pi$
$432$	−0.142315	+	0.989821i	−0.00684713	+	0.0476228i
$433$	−10.0265	−	6.44365i	−0.481844	−	0.309662i	0.277074	−	0.960849i	$-0.410635\pi$
$433$	−10.0265	−	6.44365i	−0.481844	−	0.309662i	−0.758918	+	0.651186i	$0.774272\pi$
$434$	−0.220460	+	0.254424i	−0.0105824	+	0.0122127i
$435$	0.320108	+	0.0939923i	0.0153480	+	0.00450658i
$436$	9.09485			0.435564
$437$	−2.08447	+	13.9376i	−0.0997139	+	0.666727i
$438$	5.73018			0.273798
$439$	16.9510	+	4.97727i	0.809028	+	0.237552i	0.659985	−	0.751279i	$-0.270563\pi$
$439$	16.9510	+	4.97727i	0.809028	+	0.237552i	0.149043	+	0.988831i	$0.452381\pi$
$440$	−0.0294262	+	0.0339596i	−0.00140284	+	0.00161896i
$441$	0.841254	+	0.540641i	0.0400597	+	0.0257448i
$442$	2.76916	−	19.2599i	0.131715	−	0.916100i
$443$	−11.3350	+	7.28458i	−0.538544	+	0.346101i	−0.781469	−	0.623944i	$-0.785529\pi$
$443$	−11.3350	+	7.28458i	−0.538544	+	0.346101i	0.242926	+	0.970045i	$0.421893\pi$
$444$	−2.35370	−	5.15389i	−0.111702	−	0.244593i
$445$	−0.209455	−	0.241723i	−0.00992910	−	0.0114588i
$446$	1.16212	+	8.08271i	0.0550279	+	0.382727i
$447$	1.36829	−	2.99614i	0.0647180	−	0.141713i
$448$	0.959493	−	0.281733i	0.0453318	−	0.0133106i
$449$	1.34617	−	0.395272i	0.0635298	−	0.0186540i	−0.249813	−	0.968294i	$-0.580369\pi$
$449$	1.34617	−	0.395272i	0.0635298	−	0.0186540i	0.313343	+	0.949640i	$0.398551\pi$
$450$	−2.06104	+	4.51305i	−0.0971583	+	0.212747i
$451$	0.408107	+	2.83844i	0.0192170	+	0.133657i
$452$	−2.60074	−	3.00141i	−0.122328	−	0.141175i
$453$	−4.67179	−	10.2298i	−0.219500	−	0.480637i
$454$	15.0261	−	9.65666i	0.705208	−	0.453209i
$455$	−0.0790345	+	0.549697i	−0.00370520	+	0.0257702i
$456$	−2.47204	−	1.58868i	−0.115764	−	0.0743969i
$457$	13.0648	−	15.0776i	0.611146	−	0.705300i	−0.362855	−	0.931846i	$-0.618198\pi$
$457$	13.0648	−	15.0776i	0.611146	−	0.705300i	0.974000	+	0.226546i	$0.0727433\pi$
$458$	20.7082	+	6.08047i	0.967630	+	0.284122i
$459$	6.88391			0.321313
$460$	0.902571	+	0.270574i	0.0420826	+	0.0126156i
$461$	12.9451			0.602916			0.301458	−	0.953480i	$-0.402527\pi$
$461$	12.9451			0.602916			0.301458	+	0.953480i	$0.402527\pi$
$462$	0.219443	+	0.0644343i	0.0102094	+	0.00299776i
$463$	7.25012	−	8.36708i	0.336942	−	0.388851i	−0.561842	−	0.827245i	$-0.689907\pi$
$463$	7.25012	−	8.36708i	0.336942	−	0.388851i	0.898783	+	0.438394i	$0.144452\pi$
$464$	−1.42849	−	0.918035i	−0.0663160	−	0.0426187i
$465$	0.00941314	−	0.0654699i	0.000436524	−	0.00303609i
$466$	18.0658	−	11.6102i	0.836881	−	0.537831i
$467$	2.46186	+	5.39073i	0.113921	+	0.249453i	0.958001	−	0.286765i	$-0.0925798\pi$
$467$	2.46186	+	5.39073i	0.113921	+	0.249453i	−0.844080	+	0.536218i	$0.819853\pi$
$468$	1.85102	+	2.13619i	0.0855634	+	0.0987454i
$469$	−1.06676	−	7.41947i	−0.0492583	−	0.342599i
$470$	0.575969	−	1.26120i	0.0265675	−	0.0581746i
$471$	−11.1664	+	3.27875i	−0.514521	+	0.151077i
$472$	−3.65375	+	1.07284i	−0.168178	+	0.0493814i
$473$	−0.221459	+	0.484928i	−0.0101827	+	0.0222970i
$474$	−0.895755	−	6.23011i	−0.0411434	−	0.286159i
$475$	−9.54732	−	11.0182i	−0.438061	−	0.505549i
$476$	−2.85968	−	6.26183i	−0.131073	−	0.287010i
$477$	1.68437	−	1.08248i	0.0771219	−	0.0495632i
$478$	0.106506	−	0.740765i	0.00487147	−	0.0338818i
$479$	−15.4028	−	9.89880i	−0.703773	−	0.452288i	0.139185	−	0.990266i	$-0.455552\pi$
$479$	−15.4028	−	9.89880i	−0.703773	−	0.452288i	−0.842958	+	0.537979i	$0.819188\pi$
$480$	−0.128663	+	0.148485i	−0.00587263	+	0.00677738i
$481$	−15.3664	−	4.51199i	−0.700649	−	0.205729i
$482$	5.08815			0.231759
$483$	−0.655652	−	4.75080i	−0.0298332	−	0.216169i
$484$	−10.9477			−0.497622
$485$	3.44767	+	1.01233i	0.156551	+	0.0459675i
$486$	−0.654861	+	0.755750i	−0.0297051	+	0.0342815i
$487$	31.5225	+	20.2583i	1.42842	+	0.917991i	0.999895	+	0.0144616i	$0.00460344\pi$
$487$	31.5225	+	20.2583i	1.42842	+	0.917991i	0.428526	+	0.903529i	$0.359033\pi$
$488$	1.56857	−	10.9096i	0.0710056	−	0.493855i
$489$	−3.44895	+	2.21651i	−0.155967	+	0.100234i
$490$	0.0816181	+	0.178719i	0.00368713	+	0.00807369i
$491$	−6.30123	−	7.27201i	−0.284370	−	0.328181i	0.595535	−	0.803329i	$-0.296940\pi$
$491$	−6.30123	−	7.27201i	−0.284370	−	0.328181i	−0.879906	+	0.475148i	$0.842395\pi$
$492$	1.78440	+	12.4108i	0.0804472	+	0.559522i
$493$	−4.85588	+	10.6329i	−0.218698	+	0.478881i
$494$	−7.96952	+	2.34006i	−0.358566	+	0.105284i
$495$	−0.0431148	+	0.0126597i	−0.00193787	+	0.000569009i
$496$	−0.139850	+	0.306229i	−0.00627945	+	0.0137501i
$497$	−1.97023	−	13.7033i	−0.0883770	−	0.614675i
$498$	−10.2043	−	11.7764i	−0.457266	−	0.527714i
$499$	−5.42774	−	11.8851i	−0.242979	−	0.532050i	0.748373	−	0.663278i	$-0.230835\pi$
$499$	−5.42774	−	11.8851i	−0.242979	−	0.532050i	−0.991352	+	0.131228i	$0.958108\pi$
$500$	−1.64646	+	1.05812i	−0.0736320	+	0.0473204i
$501$	2.13587	−	14.8553i	0.0954238	−	0.663687i
$502$	16.9125	+	10.8690i	0.754841	+	0.485107i
$503$	5.55925	−	6.41571i	0.247875	−	0.286063i	−0.618154	−	0.786057i	$-0.712119\pi$
$503$	5.55925	−	6.41571i	0.247875	−	0.286063i	0.866029	+	0.499994i	$0.166665\pi$
$504$	0.959493	+	0.281733i	0.0427392	+	0.0125494i
$505$	−0.950163			−0.0422817
$506$	−0.449993	−	1.00028i	−0.0200046	−	0.0444681i
$507$	−5.01042			−0.222520
$508$	−2.33575	−	0.685837i	−0.103632	−	0.0304291i
$509$	−8.90146	+	10.2728i	−0.394550	+	0.455335i	−0.917917	−	0.396772i	$-0.870130\pi$
$509$	−8.90146	+	10.2728i	−0.394550	+	0.455335i	0.523367	+	0.852107i	$0.324676\pi$
$510$	1.13780	+	0.731221i	0.0503827	+	0.0323790i
$511$	0.815489	−	5.67185i	0.0360751	−	0.250908i
$512$	0.841254	−	0.540641i	0.0371785	−	0.0238932i
$513$	−1.22070	−	2.67297i	−0.0538954	−	0.118015i
$514$	−0.805397	−	0.929478i	−0.0355246	−	0.0409975i
$515$	0.365142	+	2.53962i	0.0160901	+	0.111909i
$516$	−0.968309	+	2.12030i	−0.0426274	+	0.0933410i
$517$	−1.54858	+	0.454705i	−0.0681066	+	0.0199979i
$518$	−5.43640	+	1.59627i	−0.238862	+	0.0701361i
$519$	−9.13567	+	20.0043i	−0.401011	+	0.878093i
$520$	0.0790345	+	0.549697i	0.00346589	+	0.0241058i
$521$	7.16929	+	8.27380i	0.314092	+	0.362482i	0.890742	−	0.454510i	$-0.150186\pi$
$521$	7.16929	+	8.27380i	0.314092	+	0.362482i	−0.576649	+	0.816992i	$0.695640\pi$
$522$	−0.705395	−	1.54460i	−0.0308743	−	0.0676053i
$523$	2.68290	−	1.72420i	0.117315	−	0.0753939i	−0.480667	−	0.876903i	$-0.659606\pi$
$523$	2.68290	−	1.72420i	0.117315	−	0.0753939i	0.597983	+	0.801509i	$0.295969\pi$
$524$	1.12645	−	7.83463i	0.0492092	−	0.342257i
$525$	4.17379	+	2.68233i	0.182159	+	0.117067i
$526$	13.3684	−	15.4280i	0.582891	−	0.672692i
$527$	2.22360	+	0.652908i	0.0968616	+	0.0284411i
$528$	0.228707			0.00995321
$529$	−15.2575	+	17.2107i	−0.663370	+	0.748292i
$530$	0.393382			0.0170874
$531$	−3.65375	−	1.07284i	−0.158559	−	0.0465573i
$532$	−1.92432	+	2.22078i	−0.0834299	+	0.0962832i
$533$	29.8148	+	19.1608i	1.29142	+	0.829947i
$534$	−0.231679	+	1.61136i	−0.0100257	+	0.0697305i
$535$	0.257222	−	0.165306i	0.0111207	−	0.00714682i
$536$	−3.11385	−	6.81838i	−0.134498	−	0.294509i
$537$	−6.79824	−	7.84559i	−0.293366	−	0.338562i
$538$	3.12617	+	21.7430i	0.134779	+	0.937406i
$539$	0.0950085	−	0.208040i	0.00409231	−	0.00896090i
$540$	−0.188515	+	0.0553531i	−0.00811240	+	0.00238202i
$541$	35.3449	−	10.3782i	1.51959	−	0.446193i	0.587748	−	0.809044i	$-0.300015\pi$
$541$	35.3449	−	10.3782i	1.51959	−	0.446193i	0.931847	+	0.362851i	$0.118197\pi$
$542$	−4.80357	+	10.5184i	−0.206331	+	0.451802i
$543$	−1.99036	−	13.8432i	−0.0854144	−	0.594070i
$544$	−4.50800	−	5.20251i	−0.193279	−	0.223056i
$545$	0.742305	+	1.62542i	0.0317968	+	0.0696254i
$546$	2.37787	−	1.52817i	0.101764	−	0.0653995i
$547$	3.94514	−	27.4390i	0.168682	−	1.17321i	−0.712930	−	0.701235i	$-0.752632\pi$
$547$	3.94514	−	27.4390i	0.168682	−	1.17321i	0.881612	−	0.471974i	$-0.156458\pi$
$548$	18.3818	+	11.8133i	0.785232	+	0.504638i
$549$	7.21774	−	8.32972i	0.308046	−	0.355504i
$550$	1.08874	+	0.319684i	0.0464242	+	0.0136314i
$551$	4.98975			0.212571
$552$	−1.96755	−	4.37364i	−0.0837444	−	0.186155i
$553$	−6.29418			−0.267656
$554$	−0.849305	−	0.249379i	−0.0360835	−	0.0105951i
$555$	0.728992	−	0.841302i	0.0309440	−	0.0357113i
$556$	−18.2475	−	11.7269i	−0.773865	−	0.497333i
$557$	0.372684	−	2.59207i	0.0157911	−	0.109830i	−0.980401	−	0.197010i	$-0.936877\pi$
$557$	0.372684	−	2.59207i	0.0157911	−	0.109830i	0.996193	+	0.0871808i	$0.0277858\pi$
$558$	−0.283209	+	0.182007i	−0.0119892	+	0.00770498i
$559$	2.73701	+	5.99321i	0.115763	+	0.253486i
$560$	0.128663	+	0.148485i	0.00543700	+	0.00627463i
$561$	−0.224061	−	1.55838i	−0.00945985	−	0.0657947i
$562$	11.9397	−	26.1442i	0.503644	−	1.10283i
$563$	−26.9440	+	7.91147i	−1.13555	+	0.333429i	−0.794888	−	0.606756i	$-0.792471\pi$
$563$	−26.9440	+	7.91147i	−1.13555	+	0.333429i	−0.340666	+	0.940185i	$0.610652\pi$
$564$	−6.77102	+	1.98815i	−0.285111	+	0.0837163i
$565$	0.324141	−	0.709771i	0.0136367	−	0.0298603i
$566$	3.37147	+	23.4491i	0.141713	+	0.985638i
$567$	0.654861	+	0.755750i	0.0275016	+	0.0317385i
$568$	−5.75108	−	12.5931i	−0.241310	−	0.528395i
$569$	4.54508	−	2.92095i	0.190540	−	0.122452i	−0.441893	−	0.897068i	$-0.645693\pi$
$569$	4.54508	−	2.92095i	0.190540	−	0.122452i	0.632433	+	0.774615i	$0.282057\pi$
$570$	0.0821643	−	0.571465i	0.00344148	−	0.0239360i
$571$	33.2528	+	21.3703i	1.39159	+	0.894318i	0.999670	−	0.0256837i	$-0.00817627\pi$
$571$	33.2528	+	21.3703i	1.39159	+	0.894318i	0.391915	+	0.920001i	$0.371813\pi$
$572$	0.423342	−	0.488563i	0.0177008	−	0.0204278i
$573$	18.8766	+	5.54268i	0.788583	+	0.231549i
$574$	12.5384			0.523344
$575$	−3.25295	−	23.5706i	−0.135657	−	0.982963i
$576$	1.00000			0.0416667
$577$	2.88473	+	0.847034i	0.120093	+	0.0352625i	0.341227	−	0.939981i	$-0.389158\pi$
$577$	2.88473	+	0.847034i	0.120093	+	0.0352625i	−0.221134	+	0.975243i	$0.570976\pi$
$578$	−19.9001	+	22.9659i	−0.827733	+	0.955255i
$579$	−6.03779	−	3.88025i	−0.250922	−	0.161258i
$580$	0.0474794	−	0.330226i	0.00197147	−	0.0137119i
$581$	−13.1088	+	8.42449i	−0.543843	+	0.349507i
$582$	−7.59735	−	16.6359i	−0.314920	−	0.689579i
$583$	−0.299874	−	0.346073i	−0.0124195	−	0.0143329i
$584$	−0.815489	−	5.67185i	−0.0337452	−	0.234703i
$585$	−0.230701	+	0.505164i	−0.00953830	+	0.0208860i
$586$	−20.3707	+	5.98138i	−0.841506	+	0.247088i
$587$	33.9750	−	9.97597i	1.40230	−	0.411752i	0.508827	−	0.860869i	$-0.330079\pi$
$587$	33.9750	−	9.97597i	1.40230	−	0.411752i	0.893473	+	0.449116i	$0.148261\pi$
$588$	0.415415	−	0.909632i	0.0171314	−	0.0375126i
$589$	−0.140786	−	0.979186i	−0.00580097	−	0.0403467i
$590$	−0.489949	−	0.565432i	−0.0201709	−	0.0232784i
$591$	6.66999	+	14.6052i	0.274367	+	0.600780i
$592$	−4.76646	+	3.06322i	−0.195900	+	0.125898i
$593$	2.59999	−	18.0833i	0.106769	−	0.742592i	−0.864159	−	0.503219i	$-0.832149\pi$
$593$	2.59999	−	18.0833i	0.106769	−	0.742592i	0.970928	−	0.239373i	$-0.0769419\pi$
$594$	0.192401	+	0.123649i	0.00789431	+	0.00507336i
$595$	0.885704	−	1.02216i	0.0363103	−	0.0419044i
$596$	−3.16037	−	0.927969i	−0.129454	−	0.0380111i
$597$	11.7791			0.482086
$598$	−12.9849	−	3.89264i	−0.530992	−	0.159182i
$599$	−34.3704			−1.40434			−0.702169	−	0.712011i	$-0.747785\pi$
$599$	−34.3704			−1.40434			−0.702169	+	0.712011i	$0.747785\pi$
$600$	4.76043	+	1.39779i	0.194344	+	0.0570644i
$601$	−15.7077	+	18.1277i	−0.640732	+	0.739444i	−0.979504	−	0.201425i	$-0.935443\pi$
$601$	−15.7077	+	18.1277i	−0.640732	+	0.739444i	0.338772	+	0.940868i	$0.389988\pi$
$602$	1.96091	+	1.26020i	0.0799209	+	0.0513620i
$603$	1.06676	−	7.41947i	0.0434417	−	0.302144i
$604$	−9.46079	+	6.08008i	−0.384954	+	0.247395i
$605$	−0.893530	−	1.95656i	−0.0363272	−	0.0795454i
$606$	3.16696	+	3.65486i	0.128649	+	0.148469i
$607$	−2.66760	−	18.5535i	−0.108274	−	0.753065i	−0.969544	−	0.244917i	$-0.921239\pi$
$607$	−2.66760	−	18.5535i	−0.108274	−	0.753065i	0.861270	−	0.508148i	$-0.169670\pi$
$608$	−1.22070	+	2.67297i	−0.0495061	+	0.108403i
$609$	−1.62927	+	0.478396i	−0.0660212	+	0.0193856i
$610$	2.07778	−	0.610090i	0.0841267	−	0.0247018i
$611$	−8.28622	+	18.1443i	−0.335225	+	0.734040i
$612$	−0.979683	−	6.81384i	−0.0396013	−	0.275433i
$613$	21.5841	+	24.9094i	0.871775	+	1.00608i	0.999897	+	0.0143237i	$0.00455953\pi$
$613$	21.5841	+	24.9094i	0.871775	+	1.00608i	−0.128122	+	0.991758i	$0.540895\pi$
$614$	−6.76773	−	14.8193i	−0.273123	−	0.598056i
$615$	−2.07240	+	1.33185i	−0.0835674	+	0.0537055i
$616$	0.0325485	−	0.226380i	0.00131141	−	0.00912109i
$617$	−4.86986	−	3.12967i	−0.196053	−	0.125996i	0.438931	−	0.898521i	$-0.355357\pi$
$617$	−4.86986	−	3.12967i	−0.196053	−	0.125996i	−0.634984	+	0.772525i	$0.718993\pi$
$618$	8.55177	−	9.86926i	0.344002	−	0.397000i
$619$	−5.49369	−	1.61309i	−0.220810	−	0.0648356i	0.169456	−	0.985538i	$-0.445799\pi$
$619$	−5.49369	−	1.61309i	−0.220810	−	0.0648356i	−0.390266	+	0.920702i	$0.627617\pi$
$620$	−0.0661431			−0.00265637
$621$	0.709362	−	4.74308i	0.0284657	−	0.190333i
$622$	−7.53221			−0.302014
$623$	1.56199	+	0.458642i	0.0625798	+	0.0183751i
$624$	1.85102	−	2.13619i	0.0741001	−	0.0855161i
$625$	20.5455	+	13.2038i	0.821819	+	0.528151i
$626$	−0.443018	+	3.08126i	−0.0177066	+	0.123152i
$627$	−0.565374	+	0.363344i	−0.0225788	+	0.0145105i
$628$	4.83453	+	10.5861i	0.192919	+	0.422433i
$629$	25.5419	+	29.4769i	1.01842	+	1.17532i
$630$	0.0279611	+	0.194474i	0.00111400	+	0.00774803i
$631$	−11.5403	+	25.2698i	−0.459414	+	1.00598i	0.528207	+	0.849115i	$0.322864\pi$
$631$	−11.5403	+	25.2698i	−0.459414	+	1.00598i	−0.987621	+	0.156860i	$0.949863\pi$
$632$	−6.03922	+	1.77328i	−0.240227	+	0.0705371i
$633$	20.1158	−	5.90653i	0.799531	−	0.234763i
$634$	7.86210	−	17.2156i	0.312244	−	0.683718i
$635$	−0.0680673	−	0.473419i	−0.00270117	−	0.0187871i
$636$	−1.31117	−	1.51317i	−0.0519913	−	0.0600011i
$637$	−1.17421	−	2.57115i	−0.0465237	−	0.101873i
$638$	−0.326706	+	0.209961i	−0.0129344	+	0.00831245i
$639$	1.97023	−	13.7033i	0.0779411	−	0.542093i
$640$	0.165284	+	0.106222i	0.00653343	+	0.00419878i
$641$	−12.3729	+	14.2791i	−0.488702	+	0.563992i	−0.945518	−	0.325569i	$-0.894444\pi$
$641$	−12.3729	+	14.2791i	−0.488702	+	0.563992i	0.456817	+	0.889561i	$0.348990\pi$
$642$	−1.49320	−	0.438443i	−0.0589319	−	0.0173040i
$643$	−17.2829			−0.681570			−0.340785	−	0.940141i	$-0.610693\pi$
$643$	−17.2829			−0.681570			−0.340785	+	0.940141i	$0.610693\pi$
$644$	−4.60914	+	1.32509i	−0.181625	+	0.0522158i
$645$	−0.457969			−0.0180325
$646$	19.4091	+	5.69903i	0.763641	+	0.224225i
$647$	−25.2906	+	29.1870i	−0.994278	+	1.14746i	−0.00521124	+	0.999986i	$0.501659\pi$
$647$	−25.2906	+	29.1870i	−0.994278	+	1.14746i	−0.989066	+	0.147471i	$0.952887\pi$
$648$	0.841254	+	0.540641i	0.0330476	+	0.0212384i
$649$	−0.123945	+	0.862054i	−0.00486526	+	0.0338386i
$650$	11.7976	−	7.58185i	0.462739	−	0.297384i
$651$	0.139850	+	0.306229i	0.00548115	+	0.0120020i
$652$	2.68478	+	3.09840i	0.105144	+	0.121343i
$653$	−2.42162	−	16.8427i	−0.0947652	−	0.659106i	−0.980732	−	0.195358i	$-0.937413\pi$
$653$	−2.42162	−	16.8427i	−0.0947652	−	0.659106i	0.885967	−	0.463749i	$-0.153496\pi$
$654$	3.77814	−	8.27296i	0.147737	−	0.323498i
$655$	1.49213	−	0.438130i	0.0583025	−	0.0171192i
$656$	12.0305	−	3.53248i	0.469713	−	0.137920i
$657$	2.38040	−	5.21235i	0.0928683	−	0.203353i
$658$	1.00430	+	6.98505i	0.0391516	+	0.272305i
$659$	30.1297	+	34.7715i	1.17368	+	1.35450i	0.922233	+	0.386634i	$0.126362\pi$
$659$	30.1297	+	34.7715i	1.17368	+	1.35450i	0.251452	+	0.967870i	$0.419092\pi$
$660$	0.0186667	+	0.0408743i	0.000726599	+	0.00159103i
$661$	23.9870	−	15.4155i	0.932985	−	0.599593i	0.0165878	−	0.999862i	$-0.494720\pi$
$661$	23.9870	−	15.4155i	0.932985	−	0.599593i	0.916398	+	0.400269i	$0.131083\pi$
$662$	2.03420	−	14.1482i	0.0790614	−	0.549884i
$663$	−16.3691	−	10.5198i	−0.635722	−	0.408554i
$664$	−10.2043	+	11.7764i	−0.396004	+	0.457013i
$665$	−0.553955	−	0.162656i	−0.0214815	−	0.00630753i
$666$	−5.66590			−0.219549
$667$	6.82578	+	4.44143i	0.264295	+	0.171973i
$668$	−15.0081			−0.580681
$669$	7.83505	+	2.30058i	0.302921	+	0.0889455i
$670$	0.964427	−	1.11301i	0.0372591	−	0.0429992i
$671$	−2.12060	−	1.36283i	−0.0818650	−	0.0526115i
$672$	0.142315	−	0.989821i	0.00548991	−	0.0381832i
$673$	−29.2403	+	18.7916i	−1.12713	+	0.724363i	−0.964959	−	0.262400i	$-0.915486\pi$
$673$	−29.2403	+	18.7916i	−1.12713	+	0.724363i	−0.162171	+	0.986763i	$0.551850\pi$
$674$	−7.84609	−	17.1805i	−0.302220	−	0.661769i
$675$	3.24902	+	3.74957i	0.125055	+	0.144321i
$676$	0.713057	+	4.95942i	0.0274253	+	0.190747i
$677$	−15.5332	+	34.0129i	−0.596987	+	1.30722i	0.334139	+	0.942524i	$0.391554\pi$
$677$	−15.5332	+	34.0129i	−0.596987	+	1.30722i	−0.931126	+	0.364696i	$0.881173\pi$
$678$	−3.81057	+	1.11888i	−0.146344	+	0.0429704i
$679$	−17.5478	+	5.15249i	−0.673421	+	0.197734i
$680$	0.561852	−	1.23028i	0.0215460	−	0.0471793i
$681$	−2.54196	−	17.6797i	−0.0974080	−	0.677488i
$682$	0.0504207	+	0.0581886i	0.00193071	+	0.00222816i
$683$	10.9916	+	24.0683i	0.420583	+	0.920949i	0.994762	+	0.102219i	$0.0325942\pi$
$683$	10.9916	+	24.0683i	0.420583	+	0.920949i	−0.574179	+	0.818730i	$0.694679\pi$
$684$	−2.47204	+	1.58868i	−0.0945208	+	0.0607448i
$685$	−0.610964	+	4.24935i	−0.0233438	+	0.162359i
$686$	−0.841254	−	0.540641i	−0.0321192	−	0.0206418i
$687$	14.1335	−	16.3109i	0.539226	−	0.622300i
$688$	2.23652	+	0.656702i	0.0852666	+	0.0250365i
$689$	−5.65942			−0.215607
$690$	0.621065	−	0.708607i	0.0236435	−	0.0269762i
$691$	−32.6292			−1.24127			−0.620636	−	0.784099i	$-0.713125\pi$
$691$	−32.6292			−1.24127			−0.620636	+	0.784099i	$0.713125\pi$
$692$	21.1009	+	6.19577i	0.802134	+	0.235528i
$693$	0.149772	−	0.172846i	0.00568935	−	0.00656586i
$694$	18.6403	+	11.9794i	0.707578	+	0.454733i
$695$	0.606499	−	4.21829i	0.0230058	−	0.160009i
$696$	−1.42849	+	0.918035i	−0.0541468	+	0.0347980i
$697$	−35.8559	−	78.5135i	−1.35814	−	2.97391i
$698$	11.0805	+	12.7875i	0.419402	+	0.484015i
$699$	−3.05619	−	21.2562i	−0.115596	−	0.803985i
$700$	2.06104	−	4.51305i	0.0779000	−	0.170577i
$701$	5.52312	−	1.62173i	0.208605	−	0.0612520i	−0.175760	−	0.984433i	$-0.556238\pi$
$701$	5.52312	−	1.62173i	0.208605	−	0.0612520i	0.384366	+	0.923181i	$0.374420\pi$
$702$	2.71209	−	0.796341i	0.102361	−	0.0300560i
$703$	6.91640	−	15.1448i	0.260857	−	0.571197i
$704$	−0.0325485	−	0.226380i	−0.00122672	−	0.00853200i
$705$	−0.907958	−	1.04784i	−0.0341957	−	0.0394639i
$706$	9.01184	+	19.7332i	0.339165	+	0.742668i
$707$	4.06837	−	2.61458i	0.153007	−	0.0983315i
$708$	−0.541936	+	3.76925i	−0.0203672	+	0.141657i
$709$	12.3011	+	7.90546i	0.461979	+	0.296896i	0.750851	−	0.660472i	$-0.229644\pi$
$709$	12.3011	+	7.90546i	0.461979	+	0.296896i	−0.288872	+	0.957368i	$0.593280\pi$
$710$	1.78123	−	2.05565i	0.0668485	−	0.0771472i
$711$	−6.03922	−	1.77328i	−0.226488	−	0.0665030i
$712$	1.62793			0.0610093
$713$	0.678994	−	1.46480i	0.0254285	−	0.0548573i
$714$	−6.88391			−0.257624
$715$	0.121868	+	0.0357836i	0.00455759	+	0.00133823i
$716$	−6.79824	+	7.84559i	−0.254062	+	0.293203i
$717$	−0.629579	−	0.404606i	−0.0235121	−	0.0151103i
$718$	−1.26792	+	8.81858i	−0.0473184	+	0.329106i
$719$	6.03072	−	3.87571i	0.224908	−	0.144540i	−0.423335	−	0.905973i	$-0.639141\pi$
$719$	6.03072	−	3.87571i	0.224908	−	0.144540i	0.648243	+	0.761434i	$0.275504\pi$
$720$	0.0816181	+	0.178719i	0.00304173	+	0.00666046i
$721$	−8.55177	−	9.86926i	−0.318484	−	0.367551i
$722$	1.47511	+	10.2596i	0.0548979	+	0.381823i
$723$	2.11369	−	4.62834i	0.0786091	−	0.172130i
$724$	−13.4191	+	3.94020i	−0.498716	+	0.146436i
$725$	−8.08344	+	2.37351i	−0.300212	+	0.0881501i
$726$	−4.54784	+	9.95837i	−0.168786	+	0.369590i
$727$	−5.18001	−	36.0278i	−0.192116	−	1.33620i	−0.826394	−	0.563092i	$-0.809612\pi$
$727$	−5.18001	−	36.0278i	−0.192116	−	1.33620i	0.634278	−	0.773105i	$-0.281297\pi$
$728$	−1.85102	−	2.13619i	−0.0686034	−	0.0791725i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	0.947108	−	0.608669i	0.0350540	−	0.0225279i
$731$	2.28358	−	15.8827i	0.0844614	−	0.587442i
$732$	−9.27213	−	5.95883i	−0.342708	−	0.220245i
$733$	3.90596	−	4.50772i	0.144270	−	0.166496i	−0.679016	−	0.734124i	$-0.737593\pi$
$733$	3.90596	−	4.50772i	0.144270	−	0.166496i	0.823286	+	0.567627i	$0.192139\pi$
$734$	−31.5992	−	9.27837i	−1.16635	−	0.342471i
$735$	0.196474			0.00724704
$736$	−4.04911	+	2.56996i	−0.149252	+	0.0947299i
$737$	−1.71434			−0.0631484
$738$	12.0305	+	3.53248i	0.442850	+	0.130033i
$739$	−19.7699	+	22.8157i	−0.727248	+	0.839289i	−0.992159	−	0.124984i	$-0.960112\pi$
$739$	−19.7699	+	22.8157i	−0.727248	+	0.839289i	0.264910	+	0.964273i	$0.414658\pi$
$740$	−0.936485	−	0.601842i	−0.0344259	−	0.0221242i
$741$	−1.18206	+	8.22143i	−0.0434242	+	0.302022i
$742$	−1.68437	+	1.08248i	−0.0618351	+	0.0397390i
$743$	9.01429	+	19.7385i	0.330702	+	0.724137i	0.999819	−	0.0190204i	$-0.00605476\pi$
$743$	9.01429	+	19.7385i	0.330702	+	0.724137i	−0.669117	+	0.743157i	$0.733327\pi$
$744$	0.220460	+	0.254424i	0.00808244	+	0.00932763i
$745$	−0.0920982	−	0.640557i	−0.00337422	−	0.0234682i
$746$	−4.36130	+	9.54992i	−0.159679	+	0.349647i
$747$	−14.9512	+	4.39008i	−0.547037	+	0.160624i
$748$	−1.51063	+	0.443560i	−0.0552340	+	0.0162182i
$749$	−0.646485	+	1.41561i	−0.0236221	+	0.0517251i
$750$	0.278532	+	1.93723i	0.0101705	+	0.0707377i
$751$	35.5564	+	41.0342i	1.29747	+	1.49736i	0.751863	+	0.659319i	$0.229155\pi$
$751$	35.5564	+	41.0342i	1.29747	+	1.49736i	0.545607	+	0.838041i	$0.316299\pi$
$752$	2.93153	+	6.41916i	0.106902	+	0.234083i
$753$	16.9125	−	10.8690i	0.616325	−	0.396088i
$754$	−0.683066	+	4.75083i	−0.0248758	+	0.173015i
$755$	−1.85880	−	1.19458i	−0.0676486	−	0.0434751i
$756$	0.654861	−	0.755750i	0.0238171	−	0.0274863i
$757$	12.3571	+	3.62838i	0.449128	+	0.131876i	0.498472	−	0.866906i	$-0.333895\pi$
$757$	12.3571	+	3.62838i	0.449128	+	0.131876i	−0.0493438	+	0.998782i	$0.515713\pi$
$758$	−13.4400			−0.488162
$759$	−1.09682	−	0.00620513i	−0.0398122	−	0.000225232i
$760$	−0.577342			−0.0209424
$761$	25.2624	+	7.41770i	0.915761	+	0.268892i	0.705464	−	0.708746i	$-0.250739\pi$
$761$	25.2624	+	7.41770i	0.915761	+	0.268892i	0.210297	+	0.977638i	$0.432557\pi$
$762$	−1.59416	+	1.83976i	−0.0577505	+	0.0666476i
$763$	−7.65107	−	4.91705i	−0.276987	−	0.178009i
$764$	2.79984	−	19.4733i	0.101295	−	0.704519i
$765$	1.13780	−	0.731221i	0.0411373	−	0.0264373i
$766$	−1.23182	−	2.69730i	−0.0445074	−	0.0974575i
$767$	7.04869	+	8.13463i	0.254514	+	0.293724i
$768$	−0.142315	−	0.989821i	−0.00513534	−	0.0357171i
$769$	−18.9263	+	41.4429i	−0.682501	+	1.49447i	0.177471	+	0.984126i	$0.443208\pi$
$769$	−18.9263	+	41.4429i	−0.682501	+	1.49447i	−0.859972	+	0.510342i	$0.829519\pi$
$770$	0.0431148	−	0.0126597i	0.00155375	−	0.000456222i
$771$	−1.18006	+	0.346496i	−0.0424987	+	0.0124788i
$772$	−2.98149	+	6.52855i	−0.107306	+	0.234968i
$773$	6.97352	+	48.5019i	0.250820	+	1.74449i	0.593313	+	0.804972i	$0.297820\pi$
$773$	6.97352	+	48.5019i	0.250820	+	1.74449i	−0.342493	+	0.939520i	$0.611271\pi$
$774$	1.52644	+	1.76161i	0.0548669	+	0.0633197i
$775$	0.693851	+	1.51932i	0.0249239	+	0.0545757i
$776$	−15.3853	+	9.88755i	−0.552301	+	0.354942i
$777$	−0.806342	+	5.60823i	−0.0289274	+	0.201194i
$778$	−16.3429	−	10.5029i	−0.585921	−	0.376548i
$779$	−24.1280	+	27.8451i	−0.864474	+	0.997656i
$780$	0.532854	+	0.156460i	0.0190792	+	0.00560217i
$781$	−3.16627			−0.113298
$782$	21.4781	+	25.0723i	0.768056	+	0.896583i
$783$	−1.69805			−0.0606834
$784$	−0.959493	−	0.281733i	−0.0342676	−	0.0100619i
$785$	−1.49736	+	1.72804i	−0.0534429	+	0.0616764i
$786$	−6.65868	−	4.27928i	−0.237507	−	0.152637i
$787$	−0.197341	+	1.37253i	−0.00703443	+	0.0489256i	−0.993036	−	0.117809i	$-0.962413\pi$
$787$	−0.197341	+	1.37253i	−0.00703443	+	0.0489256i	0.986002	+	0.166734i	$0.0533222\pi$
$788$	13.5073	−	8.68065i	0.481179	−	0.309235i
$789$	−8.48035	−	18.5694i	−0.301908	−	0.661087i
$790$	−0.809828	−	0.934591i	−0.0288124	−	0.0332512i
$791$	0.565194	+	3.93101i	0.0200960	+	0.139771i
$792$	0.0950085	−	0.208040i	0.00337598	−	0.00739236i
$793$	−29.8921	+	8.77711i	−1.06150	+	0.311684i
$794$	−15.2042	+	4.46436i	−0.539577	+	0.158434i
$795$	0.163417	−	0.357833i	0.00579580	−	0.0126910i
$796$	−1.67634	−	11.6592i	−0.0594162	−	0.413249i
$797$	−11.4924	−	13.2629i	−0.407081	−	0.469796i	0.514777	−	0.857324i	$-0.327875\pi$
$797$	−11.4924	−	13.2629i	−0.407081	−	0.469796i	−0.921858	+	0.387528i	$0.873329\pi$
$798$	1.22070	+	2.67297i	0.0432125	+	0.0946221i
$799$	40.8672	−	26.2637i	1.44578	−	0.929144i
$800$	0.706081	−	4.91090i	0.0249637	−	0.173626i
$801$	1.36950	+	0.880127i	0.0483890	+	0.0310977i
$802$	4.88799	−	5.64105i	0.172601	−	0.199192i
$803$	−1.25745	−	0.369220i	−0.0443744	−	0.0130295i
$804$	−7.49576			−0.264355
$805$	−0.613007	−	0.715588i	−0.0216057	−	0.0252212i
$806$	0.951573			0.0335177
$807$	21.0768	+	6.18870i	0.741937	+	0.217852i
$808$	3.16696	−	3.65486i	0.111413	−	0.128578i
$809$	−31.2512	−	20.0839i	−1.09873	−	0.706113i	−0.139923	−	0.990162i	$-0.544686\pi$
$809$	−31.2512	−	20.0839i	−1.09873	−	0.706113i	−0.958810	+	0.284049i	$0.908322\pi$
$810$	−0.0279611	+	0.194474i	−0.000982454	+	0.00683312i
$811$	32.3880	−	20.8145i	1.13730	−	0.730897i	0.170227	−	0.985405i	$-0.445550\pi$
$811$	32.3880	−	20.8145i	1.13730	−	0.730897i	0.967071	+	0.254508i	$0.0819136\pi$
$812$	0.705395	+	1.54460i	0.0247545	+	0.0542049i
$813$	7.57236	+	8.73896i	0.265574	+	0.306489i
$814$	0.184416	+	1.28264i	0.00646379	+	0.0449567i
$815$	−0.334616	+	0.732707i	−0.0117211	+	0.0256656i
$816$	−6.60506	+	1.93942i	−0.231223	+	0.0678933i
$817$	−6.57206	+	1.92973i	−0.229927	+	0.0675128i
$818$	5.98232	−	13.0995i	0.209167	−	0.458012i
$819$	−0.402265	−	2.79781i	−0.0140563	−	0.0977636i
$820$	1.61323	+	1.86177i	0.0563365	+	0.0650158i
$821$	−17.3744	−	38.0445i	−0.606369	−	1.32776i	−0.925030	−	0.379895i	$-0.875960\pi$
$821$	−17.3744	−	38.0445i	−0.606369	−	1.32776i	0.318660	−	0.947869i	$-0.396767\pi$
$822$	18.3818	−	11.8133i	0.641139	−	0.412035i
$823$	−0.672179	+	4.67511i	−0.0234307	+	0.162964i	−0.998177	−	0.0603498i	$-0.980778\pi$
$823$	−0.672179	+	4.67511i	−0.0234307	+	0.162964i	0.974747	+	0.223314i	$0.0716875\pi$
$824$	−10.9859	−	7.06018i	−0.382710	−	0.245953i
$825$	0.743076	−	0.857555i	0.0258706	−	0.0298562i
$826$	3.65375	+	1.07284i	0.127130	+	0.0373288i
$827$	19.9532			0.693840			0.346920	−	0.937895i	$-0.387228\pi$
$827$	19.9532			0.693840			0.346920	+	0.937895i	$0.387228\pi$
$828$	−4.79575	−	0.0271313i	−0.166664	−	0.000942878i
$829$	23.2253			0.806650			0.403325	−	0.915057i	$-0.367854\pi$
$829$	23.2253			0.806650			0.403325	+	0.915057i	$0.367854\pi$
$830$	−2.93752	−	0.862535i	−0.101963	−	0.0299390i
$831$	−0.579657	+	0.668960i	−0.0201081	+	0.0232060i
$832$	−2.37787	−	1.52817i	−0.0824380	−	0.0529797i
$833$	−0.979683	+	6.81384i	−0.0339440	+	0.236086i
$834$	−18.2475	+	11.7269i	−0.631858	+	0.406070i
$835$	−1.22493	−	2.68223i	−0.0423906	−	0.0928224i
$836$	0.440106	+	0.507910i	0.0152214	+	0.0175664i
$837$	0.0479104	+	0.333224i	0.00165603	+	0.0115179i
$838$	7.51755	−	16.4611i	0.259689	−	0.568641i
$839$	10.3015	−	3.02479i	0.355646	−	0.104427i	−0.0990287	−	0.995085i	$-0.531574\pi$
$839$	10.3015	−	3.02479i	0.355646	−	0.104427i	0.454675	+	0.890657i	$0.349755\pi$
$840$	0.188515	−	0.0553531i	0.00650439	−	0.00190986i
$841$	−10.8492	+	23.7565i	−0.374112	+	0.819190i
$842$	2.49750	+	17.3705i	0.0860695	+	0.598627i
$843$	−18.8217	−	21.7214i	−0.648254	−	0.748125i
$844$	−8.70918	−	19.0704i	−0.299782	−	0.656432i
$845$	−0.828143	+	0.532215i	−0.0284890	+	0.0183088i
$846$	−1.00430	+	6.98505i	−0.0345285	+	0.240151i
$847$	9.20979	+	5.91877i	0.316452	+	0.203371i
$848$	−1.31117	+	1.51317i	−0.0450258	+	0.0519625i
$849$	22.7306	+	6.67430i	0.780112	+	0.229061i
$850$	−34.1538			−1.17147
$851$	22.9419	−	14.5611i	0.786438	−	0.499149i
$852$	−13.8442			−0.474294
$853$	−12.4129	−	3.64475i	−0.425009	−	0.124794i	0.0622314	−	0.998062i	$-0.480178\pi$
$853$	−12.4129	−	3.64475i	−0.425009	−	0.124794i	−0.487240	+	0.873268i	$0.661996\pi$
$854$	−7.21774	+	8.32972i	−0.246986	+	0.285037i
$855$	−0.485691	−	0.312134i	−0.0166103	−	0.0106748i
$856$	−0.221476	+	1.54040i	−0.00756989	+	0.0526498i
$857$	−10.6642	+	6.85349i	−0.364283	+	0.234111i	−0.709958	−	0.704244i	$-0.751286\pi$
$857$	−10.6642	+	6.85349i	−0.364283	+	0.234111i	0.345675	+	0.938354i	$0.387650\pi$
$858$	−0.268550	−	0.588042i	−0.00916813	−	0.0200754i
$859$	−23.1393	−	26.7041i	−0.789502	−	0.911133i	0.208255	−	0.978074i	$-0.433222\pi$
$859$	−23.1393	−	26.7041i	−0.789502	−	0.911133i	−0.997757	+	0.0669411i	$0.978676\pi$
$860$	0.0651758	+	0.453308i	0.00222248	+	0.0154577i
$861$	5.20865	−	11.4054i	0.177510	−	0.388693i
$862$	−5.61879	+	1.64983i	−0.191377	+	0.0561933i
$863$	−31.8005	+	9.33746i	−1.08250	+	0.317851i	−0.773879	−	0.633334i	$-0.781686\pi$
$863$	−31.8005	+	9.33746i	−1.08250	+	0.317851i	−0.308622	+	0.951185i	$0.599868\pi$
$864$	0.415415	−	0.909632i	0.0141327	−	0.0309463i
$865$	0.614912	+	4.27681i	0.0209076	+	0.145416i
$866$	7.80499	+	9.00743i	0.265224	+	0.306085i
$867$	12.6237	+	27.6421i	0.428724	+	0.938775i
$868$	0.283209	−	0.182007i	0.00961274	−	0.00617773i
$869$	−0.204866	+	1.42487i	−0.00694960	+	0.0483355i
$870$	−0.280661	−	0.180370i	−0.00951530	−	0.00611511i
$871$	−13.8748	+	16.0124i	−0.470130	+	0.542559i
$872$	−8.72644	−	2.56231i	−0.295515	−	0.0867709i
$873$	−18.2886			−0.618974
$874$	5.92672	−	12.7858i	0.200474	−	0.432486i
$875$	1.95715			0.0661639
$876$	−5.49806	−	1.61438i	−0.185762	−	0.0545448i
$877$	−25.7310	+	29.6952i	−0.868875	+	1.00274i	0.131060	+	0.991374i	$0.458162\pi$
$877$	−25.7310	+	29.6952i	−0.868875	+	1.00274i	−0.999935	+	0.0113610i	$0.996384\pi$
$878$	−14.8621	−	9.55131i	−0.501572	−	0.322341i
$879$	−3.02144	+	21.0146i	−0.101911	+	0.708805i
$880$	0.0378017	−	0.0242937i	0.00127430	−	0.000818940i
$881$	−17.2274	−	37.7228i	−0.580407	−	1.27091i	−0.941068	−	0.338218i	$-0.890176\pi$
$881$	−17.2274	−	37.7228i	−0.580407	−	1.27091i	0.360661	−	0.932697i	$-0.382551\pi$
$882$	−0.654861	−	0.755750i	−0.0220503	−	0.0254474i
$883$	5.98263	+	41.6101i	0.201331	+	1.40029i	0.800339	+	0.599547i	$0.204653\pi$
$883$	5.98263	+	41.6101i	0.201331	+	1.40029i	−0.599008	+	0.800743i	$0.704438\pi$
$884$	−8.08313	+	17.6996i	−0.271865	+	0.595301i
$885$	−0.717867	+	0.210785i	−0.0241308	+	0.00708545i
$886$	12.9282	−	3.79606i	0.434331	−	0.127531i
$887$	4.44673	−	9.73699i	0.149307	−	0.326936i	−0.820170	−	0.572120i	$-0.806121\pi$
$887$	4.44673	−	9.73699i	0.149307	−	0.326936i	0.969477	+	0.245184i	$0.0788484\pi$
$888$	0.806342	+	5.60823i	0.0270591	+	0.188200i
$889$	1.59416	+	1.83976i	0.0534665	+	0.0617037i
$890$	0.132869	+	0.290942i	0.00445377	+	0.00975240i
$891$	0.192401	−	0.123649i	0.00644567	−	0.00414238i
$892$	1.16212	−	8.08271i	0.0389106	−	0.270629i
$893$	−17.4449	−	11.2111i	−0.583770	−	0.375166i
$894$	−2.15698	+	2.48928i	−0.0721401	+	0.0832541i
$895$	−1.95701	−	0.574631i	−0.0654158	−	0.0192078i
$896$	−1.00000			−0.0334077
$897$	−8.93499	+	10.1944i	−0.298331	+	0.340382i
$898$	−1.40300			−0.0468188
$899$	−0.548494	−	0.161053i	−0.0182933	−	0.00537140i
$900$	3.24902	−	3.74957i	0.108301	−	0.124986i
$901$	11.5950	+	7.45168i	0.386287	+	0.248251i
$902$	0.408107	−	2.83844i	0.0135885	−	0.0945098i
$903$	1.96091	−	1.26020i	0.0652551	−	0.0419369i
$904$	1.64979	+	3.61255i	0.0548714	+	0.120151i
$905$	−1.79943	−	2.07665i	−0.0598150	−	0.0690302i
$906$	1.60048	+	11.1316i	0.0531725	+	0.369823i
$907$	−5.68855	+	12.4562i	−0.188885	+	0.413601i	−0.980255	−	0.197737i	$-0.936641\pi$
$907$	−5.68855	+	12.4562i	−0.188885	+	0.413601i	0.791370	+	0.611337i	$0.209368\pi$
$908$	−17.1380	+	5.03217i	−0.568744	+	0.166998i
$909$	4.64018	−	1.36248i	0.153905	−	0.0451906i
$910$	0.230701	−	0.505164i	0.00764765	−	0.0167460i
$911$	3.85818	+	26.8342i	0.127827	+	0.889057i	0.948301	+	0.317373i	$0.102801\pi$
$911$	3.85818	+	26.8342i	0.127827	+	0.889057i	−0.820474	+	0.571684i	$0.806290\pi$
$912$	1.92432	+	2.22078i	0.0637206	+	0.0735375i
$913$	1.48046	+	3.24176i	0.0489962	+	0.107287i
$914$	−16.7834	+	10.7861i	−0.555147	+	0.356771i
$915$	0.308182	−	2.14345i	0.0101882	−	0.0708604i
$916$	−18.1563	−	11.6683i	−0.599901	−	0.385533i
$917$	−5.18335	+	5.98190i	−0.171169	+	0.197540i
$918$	−6.60506	−	1.93942i	−0.218000	−	0.0640105i
$919$	28.8679			0.952263			0.476131	−	0.879374i	$-0.342039\pi$
$919$	28.8679			0.952263			0.476131	+	0.879374i	$0.342039\pi$
$920$	−0.789781	−	0.513898i	−0.0260383	−	0.0169427i
$921$	−16.2915			−0.536823
$922$	−12.4208	−	3.64707i	−0.409057	−	0.120110i
$923$	−25.6258	+	29.5738i	−0.843485	+	0.973433i
$924$	−0.192401	−	0.123649i	−0.00632953	−	0.00406774i
$925$	−4.00059	+	27.8247i	−0.131538	+	0.914870i
$926$	−9.31372	+	5.98556i	−0.306068	+	0.196698i
$927$	−5.42487	−	11.8788i	−0.178176	−	0.390151i
$928$	1.11199	+	1.28330i	0.0365027	+	0.0421264i
$929$	−7.42431	−	51.6372i	−0.243584	−	1.69416i	−0.633847	−	0.773459i	$-0.718525\pi$
$929$	−7.42431	−	51.6372i	−0.243584	−	1.69416i	0.390263	−	0.920703i	$-0.372384\pi$
$930$	−0.0274768	+	0.0601659i	−0.000901001	+	0.00197292i
$931$	2.81949	−	0.827876i	0.0924050	−	0.0271325i
$932$	−20.6049	+	6.05016i	−0.674937	+	0.198179i
$933$	−3.12899	+	6.85154i	−0.102439	+	0.224309i
$934$	−0.843397	−	5.86595i	−0.0275968	−	0.191940i
$935$	−0.202567	−	0.233775i	−0.00662465	−	0.00764526i
$936$	−1.17421	−	2.57115i	−0.0383801	−	0.0840407i
$937$	21.9486	−	14.1055i	0.717029	−	0.460807i	−0.130573	−	0.991439i	$-0.541682\pi$
$937$	21.9486	−	14.1055i	0.717029	−	0.460807i	0.847602	+	0.530632i	$0.178045\pi$
$938$	−1.06676	+	7.41947i	−0.0348309	+	0.242254i
$939$	2.61878	+	1.68299i	0.0854606	+	0.0549222i
$940$	−0.907958	+	1.04784i	−0.0296143	+	0.0341768i
$941$	−19.9113	−	5.84649i	−0.649090	−	0.190590i	−0.0594184	−	0.998233i	$-0.518925\pi$
$941$	−19.9113	−	5.84649i	−0.649090	−	0.190590i	−0.589672	+	0.807643i	$0.700743\pi$
$942$	11.6378			0.379181
$943$	−57.7913	+	16.6145i	−1.88194	+	0.541043i
$944$	3.80801			0.123940
$945$	0.188515	+	0.0553531i	0.00613240	+	0.00180063i
$946$	0.349109	−	0.402893i	0.0113505	−	0.0130992i
$947$	22.9792	+	14.7678i	0.746724	+	0.479891i	0.857840	−	0.513917i	$-0.171806\pi$
$947$	22.9792	+	14.7678i	0.746724	+	0.479891i	−0.111116	+	0.993807i	$0.535442\pi$
$948$	−0.895755	+	6.23011i	−0.0290928	+	0.202345i
$949$	−13.6256	+	8.75667i	−0.442307	+	0.284254i
$950$	6.05640	+	13.2617i	0.196496	+	0.430265i
$951$	−12.3938	−	14.3032i	−0.401897	−	0.463814i
$952$	0.979683	+	6.81384i	0.0317517	+	0.220838i
$953$	12.7858	−	27.9971i	0.414174	−	0.906915i	−0.581460	−	0.813575i	$-0.697518\pi$
$953$	12.7858	−	27.9971i	0.414174	−	0.906915i	0.995634	−	0.0933399i	$-0.0297543\pi$
$954$	−1.92111	+	0.564088i	−0.0621982	+	0.0182630i
$955$	3.70876	−	1.08899i	0.120013	−	0.0352389i
$956$	−0.310889	+	0.680753i	−0.0100549	+	0.0220171i
$957$	0.0552689	+	0.384404i	0.00178659	+	0.0124260i
$958$	11.9901	+	13.8373i	0.387382	+	0.447063i
$959$	−9.07702	−	19.8759i	−0.293112	−	0.641826i
$960$	0.165284	−	0.106222i	0.00533453	−	0.00342829i
$961$	4.39563	−	30.5723i	0.141795	−	0.986203i
$962$	13.4728	+	8.65845i	0.434381	+	0.279160i
$963$	−1.01912	+	1.17613i	−0.0328407	+	0.0379002i
$964$	−4.88204	−	1.43350i	−0.157240	−	0.0461698i
$965$	−1.41012			−0.0453933
$966$	−0.709362	+	4.74308i	−0.0228234	+	0.152606i
$967$	−44.4266			−1.42866			−0.714332	−	0.699807i	$-0.753269\pi$
$967$	−44.4266			−1.42866			−0.714332	+	0.699807i	$0.753269\pi$
$968$	10.5042	+	3.08432i	0.337619	+	0.0991338i
$969$	13.2468	−	15.2877i	0.425550	−	0.491111i
$970$	−3.02281	−	1.94264i	−0.0970566	−	0.0623745i
$971$	−3.66123	+	25.4644i	−0.117494	+	0.817191i	0.842805	+	0.538219i	$0.180903\pi$
$971$	−3.66123	+	25.4644i	−0.117494	+	0.817191i	−0.960299	+	0.278972i	$0.910006\pi$
$972$	0.841254	−	0.540641i	0.0269832	−	0.0173411i
$973$	9.01068	+	19.7306i	0.288869	+	0.632535i
$974$	−24.5382	−	28.3186i	−0.786255	−	0.907387i
$975$	−1.99580	−	13.8811i	−0.0639167	−	0.444550i
$976$	−4.57862	+	10.0258i	−0.146558	+	0.320917i
$977$	29.3975	−	8.63187i	0.940508	−	0.276158i	0.224678	−	0.974433i	$-0.427867\pi$
$977$	29.3975	−	8.63187i	0.940508	−	0.276158i	0.715830	+	0.698275i	$0.246049\pi$
$978$	3.93371	−	1.15504i	0.125786	−	0.0369341i
$979$	0.154667	−	0.338674i	0.00494319	−	0.0108241i
$980$	−0.0279611	−	0.194474i	−0.000893186	−	0.00621224i
$981$	−5.95586	−	6.87343i	−0.190156	−	0.219452i
$982$	3.99722	+	8.75270i	0.127557	+	0.279310i
$983$	20.4780	−	13.1604i	0.653146	−	0.419752i	−0.171668	−	0.985155i	$-0.554916\pi$
$983$	20.4780	−	13.1604i	0.653146	−	0.419752i	0.824815	+	0.565403i	$0.191279\pi$
$984$	1.78440	−	12.4108i	0.0568847	−	0.395642i
$985$	2.65384	+	1.70552i	0.0845584	+	0.0543424i
$986$	7.65481	−	8.83413i	0.243779	−	0.281336i
$987$	6.77102	+	1.98815i	0.215524	+	0.0632836i
$988$	8.30597			0.264248
$989$	−10.7080	−	3.21006i	−0.340495	−	0.102074i
$990$	0.0449350			0.00142813
$991$	−29.7224	−	8.72728i	−0.944163	−	0.277231i	−0.226808	−	0.973939i	$-0.572829\pi$
$991$	−29.7224	−	8.72728i	−0.944163	−	0.277231i	−0.717355	+	0.696708i	$0.754647\pi$
$992$	0.220460	−	0.254424i	0.00699960	−	0.00807797i
$993$	−12.0246	−	7.72773i	−0.381589	−	0.245232i
$994$	−1.97023	+	13.7033i	−0.0624919	+	0.434641i
$995$	1.94690	−	1.25119i	0.0617208	−	0.0396655i
$996$	6.47317	+	14.1743i	0.205110	+	0.449129i
$997$	14.7622	+	17.0365i	0.467524	+	0.539551i	0.939721	−	0.341942i	$-0.111085\pi$
$997$	14.7622	+	17.0365i	0.467524	+	0.539551i	−0.472198	+	0.881493i	$0.656539\pi$
$998$	1.85946	+	12.9328i	0.0588603	+	0.409382i
$999$	−2.35370	+	5.15389i	−0.0744678	+	0.163062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.a.547.1	✓	10
23.9	even	11	inner	966.2.q.a.883.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.a.547.1	✓	10	1.1	even	1	trivial
966.2.q.a.883.1	yes	10	23.9	even	11	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.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.0279611 + 0.194474i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.0279611 + 0.194474i) q^{5} +(0.841254 - 0.540641i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(-0.654861 - 0.755750i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(0.0816181 - 0.178719i) q^{10} +(-0.219443 + 0.0644343i) q^{11} +(-0.959493 + 0.281733i) q^{12} +(-1.17421 + 2.57115i) q^{13} +(0.142315 + 0.989821i) q^{14} +(-0.128663 - 0.148485i) q^{15} +(0.415415 + 0.909632i) q^{16} +(5.79111 - 3.72172i) q^{17} +(-0.142315 + 0.989821i) q^{18} +(-2.47204 - 1.58868i) q^{19} +(-0.128663 + 0.148485i) q^{20} +(0.959493 + 0.281733i) q^{21} +0.228707 q^{22} +(-1.96755 - 4.37364i) q^{23} +1.00000 q^{24} +(4.76043 + 1.39779i) q^{25} +(1.85102 - 2.13619i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.142315 - 0.989821i) q^{28} +(-1.42849 + 0.918035i) q^{29} +(0.0816181 + 0.178719i) q^{30} +(0.220460 + 0.254424i) q^{31} +(-0.142315 - 0.989821i) q^{32} +(0.0950085 - 0.208040i) q^{33} +(-6.60506 + 1.93942i) q^{34} +(0.188515 - 0.0553531i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.806342 + 5.60823i) q^{37} +(1.92432 + 2.22078i) q^{38} +(-1.17421 - 2.57115i) q^{39} +(0.165284 - 0.106222i) q^{40} +(1.78440 - 12.4108i) q^{41} +(-0.841254 - 0.540641i) q^{42} +(1.52644 - 1.76161i) q^{43} +(-0.219443 - 0.0644343i) q^{44} +0.196474 q^{45} +(0.655652 + 4.75080i) q^{46} +7.05688 q^{47} +(-0.959493 - 0.281733i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-4.17379 - 2.68233i) q^{50} +(-0.979683 + 6.81384i) q^{51} +(-2.37787 + 1.52817i) q^{52} +(0.831749 + 1.82128i) q^{53} +(-0.654861 - 0.755750i) q^{54} +(-0.00639492 - 0.0444776i) q^{55} +(-0.415415 + 0.909632i) q^{56} +(2.81949 - 0.827876i) q^{57} +(1.62927 - 0.478396i) q^{58} +(1.58190 - 3.46388i) q^{59} +(-0.0279611 - 0.194474i) q^{60} +(7.21774 + 8.32972i) q^{61} +(-0.139850 - 0.306229i) q^{62} +(-0.841254 + 0.540641i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.467190 - 0.300245i) q^{65} +(-0.149772 + 0.172846i) q^{66} +(7.19213 + 2.11180i) q^{67} +6.88391 q^{68} +(4.59385 + 1.37715i) q^{69} -0.196474 q^{70} +(13.2834 + 3.90035i) q^{71} +(-0.654861 + 0.755750i) q^{72} +(4.82053 + 3.09797i) q^{73} +(0.806342 - 5.60823i) q^{74} +(-4.17379 + 2.68233i) q^{75} +(-1.22070 - 2.67297i) q^{76} +(0.149772 + 0.172846i) q^{77} +(0.402265 + 2.79781i) q^{78} +(2.61470 - 5.72539i) q^{79} +(-0.188515 + 0.0553531i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-5.20865 + 11.4054i) q^{82} +(-2.21761 - 15.4238i) q^{83} +(0.654861 + 0.755750i) q^{84} +(0.561852 + 1.23028i) q^{85} +(-1.96091 + 1.26020i) q^{86} +(0.241658 - 1.68077i) q^{87} +(0.192401 + 0.123649i) q^{88} +(-1.06607 + 1.23031i) q^{89} +(-0.188515 - 0.0553531i) q^{90} +2.82659 q^{91} +(0.709362 - 4.74308i) q^{92} -0.336651 q^{93} +(-6.77102 - 1.98815i) q^{94} +(0.378078 - 0.436326i) q^{95} +(0.841254 + 0.540641i) q^{96} +(2.60273 - 18.1024i) q^{97} +(0.841254 - 0.540641i) q^{98} +(0.0950085 + 0.208040i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) \) 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9	\( 10 q - q^{2} - q^{3} - q^{4} - 14 q^{5} - q^{6} + q^{7} - q^{8} - q^{9} + 8 q^{10} - 4 q^{11} - q^{12} + 14 q^{13} + q^{14} - 3 q^{15} - q^{16} + 15 q^{17} - q^{18} - 11 q^{19} - 3 q^{20} + q^{21} - 26 q^{22} - q^{23} + 10 q^{24} + 7 q^{25} - 8 q^{26} - q^{27} + q^{28} + 19 q^{29} + 8 q^{30} - 5 q^{31} - q^{32} + 7 q^{33} - 18 q^{34} - 8 q^{35} - q^{36} - 2 q^{37} + 11 q^{38} + 14 q^{39} - 3 q^{40} + 2 q^{41} + q^{42} + 25 q^{43} - 4 q^{44} + 8 q^{45} - 23 q^{46} - 4 q^{47} - q^{48} - q^{49} - 15 q^{50} + 15 q^{51} - 8 q^{52} + 15 q^{53} - q^{54} + 54 q^{55} + q^{56} + 8 q^{58} - 17 q^{59} - 14 q^{60} + q^{61} - 16 q^{62} + q^{63} - q^{64} - 13 q^{65} - 4 q^{66} - 4 q^{67} + 26 q^{68} + 21 q^{69} - 8 q^{70} + 6 q^{71} - q^{72} - 25 q^{73} - 2 q^{74} - 15 q^{75} - 22 q^{76} + 4 q^{77} + 14 q^{78} + 3 q^{79} + 8 q^{80} - q^{81} + 2 q^{82} + 7 q^{83} + q^{84} + 12 q^{85} - 41 q^{86} + 8 q^{87} + 7 q^{88} - 41 q^{89} + 8 q^{90} + 30 q^{91} - q^{92} - 16 q^{93} - 15 q^{94} - 44 q^{95} - q^{96} - 4 q^{97} - q^{98} + 7 q^{99}+O(q^{100}) \) 10 * q - q^2 - q^3 - q^4 - 14 * q^5 - q^6 + q^7 - q^8 - q^9 + 8 * q^10 - 4 * q^11 - q^12 + 14 * q^13 + q^14 - 3 * q^15 - q^16 + 15 * q^17 - q^18 - 11 * q^19 - 3 * q^20 + q^21 - 26 * q^22 - q^23 + 10 * q^24 + 7 * q^25 - 8 * q^26 - q^27 + q^28 + 19 * q^29 + 8 * q^30 - 5 * q^31 - q^32 + 7 * q^33 - 18 * q^34 - 8 * q^35 - q^36 - 2 * q^37 + 11 * q^38 + 14 * q^39 - 3 * q^40 + 2 * q^41 + q^42 + 25 * q^43 - 4 * q^44 + 8 * q^45 - 23 * q^46 - 4 * q^47 - q^48 - q^49 - 15 * q^50 + 15 * q^51 - 8 * q^52 + 15 * q^53 - q^54 + 54 * q^55 + q^56 + 8 * q^58 - 17 * q^59 - 14 * q^60 + q^61 - 16 * q^62 + q^63 - q^64 - 13 * q^65 - 4 * q^66 - 4 * q^67 + 26 * q^68 + 21 * q^69 - 8 * q^70 + 6 * q^71 - q^72 - 25 * q^73 - 2 * q^74 - 15 * q^75 - 22 * q^76 + 4 * q^77 + 14 * q^78 + 3 * q^79 + 8 * q^80 - q^81 + 2 * q^82 + 7 * q^83 + q^84 + 12 * q^85 - 41 * q^86 + 8 * q^87 + 7 * q^88 - 41 * q^89 + 8 * q^90 + 30 * q^91 - q^92 - 16 * q^93 - 15 * q^94 - 44 * q^95 - q^96 - 4 * q^97 - q^98 + 7 * q^99

Introduction

L-functions

Modular forms

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Groups

Database

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