LMFDB - Embedded newform 966.2.q.a.883.1

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			883.1
Root			$0.654861 - 0.755750i$ of defining polynomial
Character	$\chi$	$=$	966.883
Dual form			966.2.q.a.547.1

$q$-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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

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	0.982613	−	0.185663i	$-0.0594433\pi$
$5$	−0.0279611	−	0.194474i	−0.0125046	−	0.0869714i	−0.995118	+	0.0986917i	$0.968534\pi$
$6$	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	0.248483	−	0.968636i	$-0.420068\pi$
$11$	−0.219443	−	0.0644343i	−0.0661646	−	0.0194277i	−0.314647	+	0.949209i	$0.601886\pi$
$12$	−0.959493	−	0.281733i	−0.276982	−	0.0813292i
$13$	−1.17421	−	2.57115i	−0.325666	−	0.713109i	0.674006	−	0.738726i	$-0.264572\pi$
$13$	−1.17421	−	2.57115i	−0.325666	−	0.713109i	−0.999672	+	0.0256168i	$0.991845\pi$
$14$	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	0.999930	−	0.0118338i	$-0.00376690\pi$
$17$	5.79111	+	3.72172i	1.40455	+	0.902650i	0.404622	+	0.914484i	$0.367403\pi$
$18$	−0.142315	−	0.989821i	−0.0335439	−	0.233303i
$19$	−2.47204	+	1.58868i	−0.567125	+	0.364469i	−0.792564	−	0.609788i	$-0.791254\pi$
$19$	−2.47204	+	1.58868i	−0.567125	+	0.364469i	0.225440	+	0.974257i	$0.427618\pi$
$20$	−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	0.401247	−	0.915970i	$-0.368577\pi$
$29$	−1.42849	−	0.918035i	−0.265264	−	0.170475i	−0.666511	+	0.745495i	$0.732213\pi$
$30$	0.0816181	−	0.178719i	0.0149014	−	0.0326294i
$31$	0.220460	−	0.254424i	0.0395957	−	0.0456959i	−0.735606	−	0.677409i	$-0.763103\pi$
$31$	0.220460	−	0.254424i	0.0395957	−	0.0456959i	0.775202	+	0.631713i	$0.217648\pi$
$32$	−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	−0.809636	−	0.586932i	$-0.800336\pi$
$37$	0.806342	−	5.60823i	0.132562	−	0.921988i	0.942198	−	0.335056i	$-0.108755\pi$
$38$	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	0.340711	+	0.940168i	$0.389332\pi$
$41$	1.78440	+	12.4108i	0.278677	+	1.93824i	−0.0620336	+	0.998074i	$0.519759\pi$
$42$	−0.841254	+	0.540641i	−0.129808	+	0.0834227i
$43$	1.52644	+	1.76161i	0.232780	+	0.268643i	0.860107	−	0.510113i	$-0.170396\pi$
$43$	1.52644	+	1.76161i	0.232780	+	0.268643i	−0.627327	+	0.778756i	$0.715851\pi$
$44$	−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	−0.843866	−	0.536554i	$-0.819726\pi$
$53$	0.831749	−	1.82128i	0.114250	−	0.250172i	0.958115	+	0.286383i	$0.0924529\pi$
$54$	−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	0.984216	−	0.176971i	$-0.0566297\pi$
$59$	1.58190	+	3.46388i	0.205946	+	0.450959i	−0.778270	+	0.627930i	$0.783902\pi$
$60$	−0.0279611	+	0.194474i	−0.00360977	+	0.0251065i
$61$	7.21774	−	8.32972i	0.924137	−	1.06651i	−0.0734645	−	0.997298i	$-0.523406\pi$
$61$	7.21774	−	8.32972i	0.924137	−	1.06651i	0.997602	−	0.0692136i	$-0.0220490\pi$
$62$	−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	0.188865	−	0.982003i	$-0.439519\pi$
$67$	7.19213	−	2.11180i	0.878659	−	0.257997i	0.689794	+	0.724006i	$0.257701\pi$
$68$	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	0.627578	−	0.778554i	$-0.284046\pi$
$71$	13.2834	−	3.90035i	1.57645	−	0.462887i	0.948870	+	0.315667i	$0.102228\pi$
$72$	−0.654861	−	0.755750i	−0.0771761	−	0.0890659i
$73$	4.82053	−	3.09797i	0.564201	−	0.362590i	−0.227237	−	0.973839i	$-0.572969\pi$
$73$	4.82053	−	3.09797i	0.564201	−	0.362590i	0.791438	+	0.611250i	$0.209333\pi$
$74$	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	0.997791	−	0.0664250i	$-0.0211593\pi$
$79$	2.61470	+	5.72539i	0.294176	+	0.644156i	−0.703615	+	0.710581i	$0.748432\pi$
$80$	−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	0.391321	+	0.920254i	$0.372018\pi$
$83$	−2.21761	+	15.4238i	−0.243414	+	1.69298i	−0.634735	+	0.772730i	$0.718891\pi$
$84$	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	0.696430	−	0.717625i	$-0.254771\pi$
$89$	−1.06607	−	1.23031i	−0.113003	−	0.130413i	−0.809433	+	0.587212i	$0.800225\pi$
$90$	−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	0.499782	+	0.866151i	$0.333413\pi$
$97$	2.60273	+	18.1024i	0.264268	+	1.83802i	−0.235515	+	0.971871i	$0.575678\pi$
$98$	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	−0.926502	−	0.376289i	$-0.877200\pi$
$101$	0.688246	−	4.78685i	0.0684830	−	0.476310i	0.994985	−	0.100021i	$-0.0318909\pi$
$102$	2.85968	+	6.26183i	0.283150	+	0.620013i
$103$	12.5299	+	3.67912i	1.23461	+	0.362514i	0.832988	−	0.553291i	$-0.186628\pi$
$103$	12.5299	+	3.67912i	1.23461	+	0.362514i	0.401623	+	0.915805i	$0.368446\pi$
$104$	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	−0.802869	−	0.596155i	$-0.796694\pi$
$107$	−1.01912	+	1.17613i	−0.0985221	+	0.113701i	0.704347	+	0.709856i	$0.251240\pi$
$108$	0.415415	−	0.909632i	0.0399733	−	0.0875294i
$109$	7.65107	+	4.91705i	0.732840	+	0.470968i	0.853082	−	0.521777i	$-0.174731\pi$
$109$	7.65107	+	4.91705i	0.732840	+	0.470968i	−0.120242	+	0.992745i	$0.538367\pi$
$110$	−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	−0.456007	−	0.889976i	$-0.650721\pi$
$113$	−3.81057	+	1.11888i	−0.358468	+	0.105256i	0.0975395	+	0.995232i	$0.468903\pi$
$114$	−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	0.176452	−	0.984309i	$-0.443538\pi$
$127$	−2.33575	−	0.685837i	−0.207264	−	0.0608582i	−0.383716	+	0.923451i	$0.625356\pi$
$128$	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	−0.997164	−	0.0752613i	$-0.976021\pi$
$131$	−3.28809	+	7.19991i	−0.287282	+	0.629059i	0.709882	+	0.704320i	$0.248748\pi$
$132$	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	0.149703	−	0.988731i	$-0.452168\pi$
$149$	−3.16037	−	0.927969i	−0.258908	−	0.0760222i	−0.408610	+	0.912709i	$0.633987\pi$
$150$	4.76043	+	1.39779i	0.388687	+	0.114129i
$151$	−4.67179	−	10.2298i	−0.380184	−	0.832488i	−0.998901	−	0.0468735i	$-0.985074\pi$
$151$	−4.67179	−	10.2298i	−0.380184	−	0.832488i	0.618716	−	0.785614i	$-0.287653\pi$
$152$	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	−0.0881276	−	0.996109i	$-0.528088\pi$
$157$	9.79036	−	6.29188i	0.781356	−	0.502147i	0.869483	+	0.493962i	$0.164452\pi$
$158$	−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	−0.124022	−	0.992280i	$-0.539579\pi$
$163$	3.93371	−	1.15504i	0.308112	−	0.0904698i	0.432133	+	0.901810i	$0.357761\pi$
$164$	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	−0.0483469	−	0.998831i	$-0.515395\pi$
$167$	−12.6256	−	8.11399i	−0.976999	−	0.627879i	−0.928652	+	0.370951i	$0.879032\pi$
$168$	−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	0.956730	−	0.290977i	$-0.0939804\pi$
$173$	21.1009	+	6.19577i	1.60427	+	0.471056i	0.647538	+	0.762033i	$0.275799\pi$
$174$	−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	−0.967506	−	0.252847i	$-0.918633\pi$
$179$	−1.47740	−	10.2755i	−0.110426	−	0.768029i	0.857080	−	0.515183i	$-0.172276\pi$
$180$	0.165284	−	0.106222i	0.0123196	−	0.00791730i
$181$	−9.15861	−	10.5696i	−0.680754	−	0.785632i	0.305264	−	0.952268i	$-0.401255\pi$
$181$	−9.15861	−	10.5696i	−0.680754	−	0.785632i	−0.986019	+	0.166635i	$0.946710\pi$
$182$	−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	0.343265	+	0.939239i	$0.388467\pi$
$191$	−8.17269	+	17.8957i	−0.591355	+	1.29489i	−0.934620	+	0.355648i	$0.884260\pi$
$192$	−0.654861	+	0.755750i	−0.0472605	+	0.0545415i
$193$	1.02141	−	7.10408i	0.0735229	−	0.511363i	−0.919467	−	0.393166i	$-0.871380\pi$
$193$	1.02141	−	7.10408i	0.0735229	−	0.511363i	0.992990	−	0.118197i	$-0.0377113\pi$
$194$	−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	0.983751	+	0.179539i	$0.0574605\pi$
$197$	6.66999	+	14.6052i	0.475217	+	1.04058i	−0.508534	+	0.861042i	$0.669812\pi$
$198$	−0.0325485	+	0.226380i	−0.00231312	+	0.0160881i
$199$	−7.71366	+	8.90204i	−0.546807	+	0.631049i	−0.960136	−	0.279533i	$-0.909820\pi$
$199$	−7.71366	+	8.90204i	−0.546807	+	0.631049i	0.413329	+	0.910582i	$0.364366\pi$
$200$	−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	−0.981352	−	0.192217i	$-0.938432\pi$
$211$	−17.6369	+	11.3345i	−1.21417	+	0.780302i	−0.232821	+	0.972520i	$0.574796\pi$
$212$	−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	−0.988552	−	0.150882i	$-0.951789\pi$
$223$	−3.39221	+	7.42789i	−0.227159	+	0.497409i	0.761393	+	0.648291i	$0.224516\pi$
$224$	−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	0.220496	−	0.975388i	$-0.429232\pi$
$227$	−11.6968	−	13.4988i	−0.776344	−	0.895948i	−0.996840	+	0.0794395i	$0.974687\pi$
$228$	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	−0.997809	−	0.0661669i	$-0.978923\pi$
$233$	−14.0630	−	16.2296i	−0.921299	−	1.06324i	0.0765096	−	0.997069i	$-0.475622\pi$
$234$	−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	−0.986087	−	0.166231i	$-0.946840\pi$
$239$	0.106506	−	0.740765i	0.00688930	−	0.0479161i	0.992976	+	0.118315i	$0.0377493\pi$
$240$	0.0816181	+	0.178719i	0.00526843	+	0.0115362i
$241$	−4.88204	−	1.43350i	−0.314480	−	0.0923396i	0.120684	−	0.992691i	$-0.461491\pi$
$241$	−4.88204	−	1.43350i	−0.314480	−	0.0923396i	−0.435164	+	0.900351i	$0.643309\pi$
$242$	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	−0.826537	−	0.562883i	$-0.809692\pi$
$251$	−19.2896	+	5.66392i	−1.21755	+	0.357504i	−0.391009	+	0.920387i	$0.627874\pi$
$252$	−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	−0.507973	−	0.861373i	$-0.669605\pi$
$257$	1.03464	−	0.664921i	0.0645389	−	0.0414766i	0.572512	+	0.819896i	$0.305969\pi$
$258$	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	−0.968322	−	0.249705i	$-0.919666\pi$
$263$	−8.48035	−	18.5694i	−0.522921	−	1.14504i	0.445401	−	0.895331i	$-0.353061\pi$
$264$	−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	0.397365	+	0.917661i	$0.369925\pi$
$269$	−9.12524	+	19.9815i	−0.556376	+	1.21829i	−0.953740	+	0.300632i	$0.902802\pi$
$270$	0.165284	+	0.106222i	0.0100589	+	0.00646445i
$271$	1.64563	+	11.4456i	0.0999649	+	0.695271i	0.976749	+	0.214387i	$0.0687753\pi$
$271$	1.64563	+	11.4456i	0.0999649	+	0.695271i	−0.876784	+	0.480885i	$0.840316\pi$
$272$	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	−0.631601	−	0.775293i	$-0.717602\pi$
$281$	−4.09035	−	28.4490i	−0.244010	−	1.69712i	0.387592	−	0.921831i	$-0.373307\pi$
$282$	5.93662	+	3.81523i	0.353521	+	0.227194i
$283$	−9.84126	+	21.5494i	−0.585002	+	1.28098i	0.353413	+	0.935467i	$0.385021\pi$
$283$	−9.84126	+	21.5494i	−0.585002	+	1.28098i	−0.938415	+	0.345509i	$0.887706\pi$
$284$	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	0.945829	−	0.324665i	$-0.105251\pi$
$293$	17.8604	+	11.4782i	1.04342	+	0.670562i	0.0975861	+	0.995227i	$0.468888\pi$
$294$	−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	−0.364666	−	0.931138i	$-0.618817\pi$
$307$	10.6687	−	12.3123i	0.608892	−	0.702699i	0.973558	+	0.228439i	$0.0733623\pi$
$308$	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	0.480139	−	0.877193i	$-0.340586\pi$
$311$	7.22710	+	2.12207i	0.409811	+	0.120331i	−0.0703276	+	0.997524i	$0.522404\pi$
$312$	−1.17421	−	2.57115i	−0.0664763	−	0.145563i
$313$	−0.443018	+	3.08126i	−0.0250409	+	0.174163i	−0.998504	−	0.0546814i	$-0.982586\pi$
$313$	−0.443018	+	3.08126i	−0.0250409	+	0.174163i	0.973463	+	0.228845i	$0.0734948\pi$
$314$	−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	−0.914081	−	0.405532i	$-0.867086\pi$
$317$	−2.69343	−	18.7332i	−0.151278	−	1.05216i	0.762802	−	0.646632i	$-0.223823\pi$
$318$	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	−0.854348	−	0.519701i	$-0.826043\pi$
$331$	2.03420	−	14.1482i	0.111810	−	0.777654i	0.966158	−	0.257952i	$-0.0830477\pi$
$332$	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	−0.311200	−	0.950344i	$-0.600731\pi$
$337$	12.3686	−	14.2741i	0.673759	−	0.777560i	0.984960	+	0.172785i	$0.0552764\pi$
$338$	−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	−0.797144	−	0.603789i	$-0.793657\pi$
$347$	−21.2603	+	6.24258i	−1.14131	+	0.335119i	−0.344167	+	0.938908i	$0.611839\pi$
$348$	1.11199	+	1.28330i	0.0596087	+	0.0687921i
$349$	−14.2343	+	9.14783i	−0.761944	+	0.489672i	−0.862997	−	0.505209i	$-0.831415\pi$
$349$	−14.2343	+	9.14783i	−0.761944	+	0.489672i	0.101053	+	0.994881i	$0.467779\pi$
$350$	−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	−0.995147	−	0.0984004i	$-0.968627\pi$
$353$	−14.2063	+	16.3949i	−0.756124	+	0.872614i	0.239023	+	0.971014i	$0.423173\pi$
$354$	−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	0.928617	+	0.371039i	$0.120998\pi$
$359$	−1.26792	+	8.81858i	−0.0669183	+	0.465427i	−0.995536	+	0.0943877i	$0.969911\pi$
$360$	−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	0.991240	+	0.132076i	$0.0421644\pi$
$373$	1.49411	+	10.3918i	0.0773623	+	0.538067i	−0.913877	+	0.405991i	$0.866927\pi$
$374$	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	0.595617	−	0.803269i	$-0.296908\pi$
$379$	12.8956	+	3.78648i	0.662401	+	0.194498i	0.0667845	+	0.997767i	$0.478726\pi$
$380$	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	−0.703966	−	0.710234i	$-0.748589\pi$
$383$	1.94184	−	2.24100i	0.0992233	−	0.114510i	0.803189	+	0.595724i	$0.203135\pi$
$384$	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	0.227343	−	0.973815i	$-0.426996\pi$
$389$	18.6399	−	5.47317i	0.945080	−	0.277501i	0.717737	+	0.696314i	$0.245178\pi$
$390$	−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	0.830580	−	0.556899i	$-0.188009\pi$
$397$	13.3306	+	8.56704i	0.669042	+	0.429967i	−0.161538	+	0.986867i	$0.551645\pi$
$398$	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	0.816273	−	0.577666i	$-0.196036\pi$
$401$	−3.10073	−	6.78965i	−0.154843	−	0.339059i	−0.971116	+	0.238607i	$0.923309\pi$
$402$	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	−0.975629	−	0.219424i	$-0.929582\pi$
$409$	−2.04945	−	14.2542i	−0.101339	−	0.704827i	0.874291	−	0.485403i	$-0.161327\pi$
$410$	−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	−0.950776	−	0.309880i	$-0.899711\pi$
$419$	−2.57540	−	17.9123i	−0.125816	−	0.875072i	0.824959	−	0.565192i	$-0.191198\pi$
$420$	−0.165284	−	0.106222i	−0.00806505	−	0.00518309i
$421$	−7.29017	+	15.9632i	−0.355301	+	0.778000i	0.644608	+	0.764513i	$0.277021\pi$
$421$	−7.29017	+	15.9632i	−0.355301	+	0.778000i	−0.999909	+	0.0134873i	$0.995707\pi$
$422$	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	0.653885	−	0.756594i	$-0.273138\pi$
$431$	4.92638	+	3.16599i	0.237296	+	0.152501i	−0.416589	+	0.909095i	$0.636775\pi$
$432$	−0.142315	−	0.989821i	−0.00684713	−	0.0476228i
$433$	−10.0265	+	6.44365i	−0.481844	+	0.309662i	−0.758918	−	0.651186i	$-0.774272\pi$
$433$	−10.0265	+	6.44365i	−0.481844	+	0.309662i	0.277074	+	0.960849i	$0.410635\pi$
$434$	−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	0.149043	−	0.988831i	$-0.452381\pi$
$439$	16.9510	−	4.97727i	0.809028	−	0.237552i	0.659985	+	0.751279i	$0.270563\pi$
$440$	−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	0.242926	−	0.970045i	$-0.421893\pi$
$443$	−11.3350	−	7.28458i	−0.538544	−	0.346101i	−0.781469	+	0.623944i	$0.785529\pi$
$444$	−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	0.313343	−	0.949640i	$-0.398551\pi$
$449$	1.34617	+	0.395272i	0.0635298	+	0.0186540i	−0.249813	+	0.968294i	$0.580369\pi$
$450$	−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	0.974000	−	0.226546i	$-0.0727433\pi$
$457$	13.0648	+	15.0776i	0.611146	+	0.705300i	−0.362855	+	0.931846i	$0.618198\pi$
$458$	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	0.898783	−	0.438394i	$-0.144452\pi$
$463$	7.25012	+	8.36708i	0.336942	+	0.388851i	−0.561842	+	0.827245i	$0.689907\pi$
$464$	−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	−0.844080	−	0.536218i	$-0.819853\pi$
$467$	2.46186	−	5.39073i	0.113921	−	0.249453i	0.958001	+	0.286765i	$0.0925798\pi$
$468$	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	−0.842958	−	0.537979i	$-0.819188\pi$
$479$	−15.4028	+	9.89880i	−0.703773	+	0.452288i	0.139185	+	0.990266i	$0.455552\pi$
$480$	−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	0.428526	−	0.903529i	$-0.359033\pi$
$487$	31.5225	−	20.2583i	1.42842	−	0.917991i	0.999895	−	0.0144616i	$-0.00460344\pi$
$488$	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	−0.879906	−	0.475148i	$-0.842395\pi$
$491$	−6.30123	+	7.27201i	−0.284370	+	0.328181i	0.595535	+	0.803329i	$0.296940\pi$
$492$	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	−0.991352	−	0.131228i	$-0.958108\pi$
$499$	−5.42774	+	11.8851i	−0.242979	+	0.532050i	0.748373	+	0.663278i	$0.230835\pi$
$500$	−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	0.866029	−	0.499994i	$-0.166665\pi$
$503$	5.55925	+	6.41571i	0.247875	+	0.286063i	−0.618154	+	0.786057i	$0.712119\pi$
$504$	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	0.523367	−	0.852107i	$-0.324676\pi$
$509$	−8.90146	−	10.2728i	−0.394550	−	0.455335i	−0.917917	+	0.396772i	$0.870130\pi$
$510$	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	−0.576649	−	0.816992i	$-0.695640\pi$
$521$	7.16929	−	8.27380i	0.314092	−	0.362482i	0.890742	+	0.454510i	$0.150186\pi$
$522$	−0.705395	+	1.54460i	−0.0308743	+	0.0676053i
$523$	2.68290	+	1.72420i	0.117315	+	0.0753939i	0.597983	−	0.801509i	$-0.295969\pi$
$523$	2.68290	+	1.72420i	0.117315	+	0.0753939i	−0.480667	+	0.876903i	$0.659606\pi$
$524$	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	0.931847	−	0.362851i	$-0.118197\pi$
$541$	35.3449	+	10.3782i	1.51959	+	0.446193i	0.587748	+	0.809044i	$0.300015\pi$
$542$	−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	0.881612	+	0.471974i	$0.156458\pi$
$547$	3.94514	+	27.4390i	0.168682	+	1.17321i	−0.712930	+	0.701235i	$0.752632\pi$
$548$	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	0.996193	−	0.0871808i	$-0.0277858\pi$
$557$	0.372684	+	2.59207i	0.0157911	+	0.109830i	−0.980401	+	0.197010i	$0.936877\pi$
$558$	−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	−0.340666	−	0.940185i	$-0.610652\pi$
$563$	−26.9440	−	7.91147i	−1.13555	−	0.333429i	−0.794888	+	0.606756i	$0.792471\pi$
$564$	−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	0.632433	−	0.774615i	$-0.282057\pi$
$569$	4.54508	+	2.92095i	0.190540	+	0.122452i	−0.441893	+	0.897068i	$0.645693\pi$
$570$	0.0821643	+	0.571465i	0.00344148	+	0.0239360i
$571$	33.2528	−	21.3703i	1.39159	−	0.894318i	0.391915	−	0.920001i	$-0.371813\pi$
$571$	33.2528	−	21.3703i	1.39159	−	0.894318i	0.999670	+	0.0256837i	$0.00817627\pi$
$572$	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	−0.221134	−	0.975243i	$-0.570976\pi$
$577$	2.88473	−	0.847034i	0.120093	−	0.0352625i	0.341227	+	0.939981i	$0.389158\pi$
$578$	−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	0.893473	−	0.449116i	$-0.148261\pi$
$587$	33.9750	+	9.97597i	1.40230	+	0.411752i	0.508827	+	0.860869i	$0.330079\pi$
$588$	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	0.970928	+	0.239373i	$0.0769419\pi$
$593$	2.59999	+	18.0833i	0.106769	+	0.742592i	−0.864159	+	0.503219i	$0.832149\pi$
$594$	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	0.338772	−	0.940868i	$-0.389988\pi$
$601$	−15.7077	−	18.1277i	−0.640732	−	0.739444i	−0.979504	+	0.201425i	$0.935443\pi$
$602$	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	0.861270	+	0.508148i	$0.169670\pi$
$607$	−2.66760	+	18.5535i	−0.108274	+	0.753065i	−0.969544	+	0.244917i	$0.921239\pi$
$608$	−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	−0.128122	−	0.991758i	$-0.540895\pi$
$613$	21.5841	−	24.9094i	0.871775	−	1.00608i	0.999897	−	0.0143237i	$-0.00455953\pi$
$614$	−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	−0.634984	−	0.772525i	$-0.718993\pi$
$617$	−4.86986	+	3.12967i	−0.196053	+	0.125996i	0.438931	+	0.898521i	$0.355357\pi$
$618$	8.55177	+	9.86926i	0.344002	+	0.397000i
$619$	−5.49369	+	1.61309i	−0.220810	+	0.0648356i	−0.390266	−	0.920702i	$-0.627617\pi$
$619$	−5.49369	+	1.61309i	−0.220810	+	0.0648356i	0.169456	+	0.985538i	$0.445799\pi$
$620$	−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	−0.987621	−	0.156860i	$-0.949863\pi$
$631$	−11.5403	−	25.2698i	−0.459414	−	1.00598i	0.528207	−	0.849115i	$-0.322864\pi$
$632$	−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	0.456817	−	0.889561i	$-0.348990\pi$
$641$	−12.3729	−	14.2791i	−0.488702	−	0.563992i	−0.945518	+	0.325569i	$0.894444\pi$
$642$	−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	−0.989066	−	0.147471i	$-0.952887\pi$
$647$	−25.2906	−	29.1870i	−0.994278	−	1.14746i	−0.00521124	−	0.999986i	$-0.501659\pi$
$648$	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	0.885967	+	0.463749i	$0.153496\pi$
$653$	−2.42162	+	16.8427i	−0.0947652	+	0.659106i	−0.980732	+	0.195358i	$0.937413\pi$
$654$	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	0.251452	−	0.967870i	$-0.419092\pi$
$659$	30.1297	−	34.7715i	1.17368	−	1.35450i	0.922233	−	0.386634i	$-0.126362\pi$
$660$	0.0186667	−	0.0408743i	0.000726599	−	0.00159103i
$661$	23.9870	+	15.4155i	0.932985	+	0.599593i	0.916398	−	0.400269i	$-0.131083\pi$
$661$	23.9870	+	15.4155i	0.932985	+	0.599593i	0.0165878	+	0.999862i	$0.494720\pi$
$662$	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	−0.162171	−	0.986763i	$-0.551850\pi$
$673$	−29.2403	−	18.7916i	−1.12713	−	0.724363i	−0.964959	+	0.262400i	$0.915486\pi$
$674$	−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	−0.931126	−	0.364696i	$-0.881173\pi$
$677$	−15.5332	−	34.0129i	−0.596987	−	1.30722i	0.334139	−	0.942524i	$-0.391554\pi$
$678$	−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	−0.574179	−	0.818730i	$-0.694679\pi$
$683$	10.9916	−	24.0683i	0.420583	−	0.920949i	0.994762	−	0.102219i	$-0.0325942\pi$
$684$	−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	0.384366	−	0.923181i	$-0.374420\pi$
$701$	5.52312	+	1.62173i	0.208605	+	0.0612520i	−0.175760	+	0.984433i	$0.556238\pi$
$702$	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	−0.288872	−	0.957368i	$-0.593280\pi$
$709$	12.3011	−	7.90546i	0.461979	−	0.296896i	0.750851	+	0.660472i	$0.229644\pi$
$710$	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	0.648243	−	0.761434i	$-0.275504\pi$
$719$	6.03072	+	3.87571i	0.224908	+	0.144540i	−0.423335	+	0.905973i	$0.639141\pi$
$720$	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	0.634278	+	0.773105i	$0.281297\pi$
$727$	−5.18001	+	36.0278i	−0.192116	+	1.33620i	−0.826394	+	0.563092i	$0.809612\pi$
$728$	−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	0.823286	−	0.567627i	$-0.192139\pi$
$733$	3.90596	+	4.50772i	0.144270	+	0.166496i	−0.679016	+	0.734124i	$0.737593\pi$
$734$	−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	0.264910	−	0.964273i	$-0.414658\pi$
$739$	−19.7699	−	22.8157i	−0.727248	−	0.839289i	−0.992159	+	0.124984i	$0.960112\pi$
$740$	−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	−0.669117	−	0.743157i	$-0.733327\pi$
$743$	9.01429	−	19.7385i	0.330702	−	0.724137i	0.999819	+	0.0190204i	$0.00605476\pi$
$744$	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	0.545607	−	0.838041i	$-0.316299\pi$
$751$	35.5564	−	41.0342i	1.29747	−	1.49736i	0.751863	−	0.659319i	$-0.229155\pi$
$752$	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	−0.0493438	−	0.998782i	$-0.515713\pi$
$757$	12.3571	−	3.62838i	0.449128	−	0.131876i	0.498472	+	0.866906i	$0.333895\pi$
$758$	−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	0.210297	−	0.977638i	$-0.432557\pi$
$761$	25.2624	−	7.41770i	0.915761	−	0.268892i	0.705464	+	0.708746i	$0.250739\pi$
$762$	−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	−0.859972	−	0.510342i	$-0.829519\pi$
$769$	−18.9263	−	41.4429i	−0.682501	−	1.49447i	0.177471	−	0.984126i	$-0.443208\pi$
$770$	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	−0.342493	−	0.939520i	$-0.611271\pi$
$773$	6.97352	−	48.5019i	0.250820	−	1.74449i	0.593313	−	0.804972i	$-0.297820\pi$
$774$	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	0.986002	−	0.166734i	$-0.0533222\pi$
$787$	−0.197341	−	1.37253i	−0.00703443	−	0.0489256i	−0.993036	+	0.117809i	$0.962413\pi$
$788$	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	−0.921858	−	0.387528i	$-0.873329\pi$
$797$	−11.4924	+	13.2629i	−0.407081	+	0.469796i	0.514777	+	0.857324i	$0.327875\pi$
$798$	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	−0.958810	−	0.284049i	$-0.908322\pi$
$809$	−31.2512	+	20.0839i	−1.09873	+	0.706113i	−0.139923	+	0.990162i	$0.544686\pi$
$810$	−0.0279611	−	0.194474i	−0.000982454	−	0.00683312i
$811$	32.3880	+	20.8145i	1.13730	+	0.730897i	0.967071	−	0.254508i	$-0.0819136\pi$
$811$	32.3880	+	20.8145i	1.13730	+	0.730897i	0.170227	+	0.985405i	$0.445550\pi$
$812$	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	0.318660	+	0.947869i	$0.396767\pi$
$821$	−17.3744	+	38.0445i	−0.606369	+	1.32776i	−0.925030	+	0.379895i	$0.875960\pi$
$822$	18.3818	+	11.8133i	0.641139	+	0.412035i
$823$	−0.672179	−	4.67511i	−0.0234307	−	0.162964i	0.974747	−	0.223314i	$-0.0716875\pi$
$823$	−0.672179	−	4.67511i	−0.0234307	−	0.162964i	−0.998177	+	0.0603498i	$0.980778\pi$
$824$	−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	0.454675	−	0.890657i	$-0.349755\pi$
$839$	10.3015	+	3.02479i	0.355646	+	0.104427i	−0.0990287	+	0.995085i	$0.531574\pi$
$840$	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	−0.487240	−	0.873268i	$-0.661996\pi$
$853$	−12.4129	+	3.64475i	−0.425009	+	0.124794i	0.0622314	+	0.998062i	$0.480178\pi$
$854$	−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	0.345675	−	0.938354i	$-0.387650\pi$
$857$	−10.6642	−	6.85349i	−0.364283	−	0.234111i	−0.709958	+	0.704244i	$0.751286\pi$
$858$	−0.268550	+	0.588042i	−0.00916813	+	0.0200754i
$859$	−23.1393	+	26.7041i	−0.789502	+	0.911133i	−0.997757	−	0.0669411i	$-0.978676\pi$
$859$	−23.1393	+	26.7041i	−0.789502	+	0.911133i	0.208255	+	0.978074i	$0.433222\pi$
$860$	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	−0.308622	−	0.951185i	$-0.599868\pi$
$863$	−31.8005	−	9.33746i	−1.08250	−	0.317851i	−0.773879	+	0.633334i	$0.781686\pi$
$864$	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	−0.999935	−	0.0113610i	$-0.996384\pi$
$877$	−25.7310	−	29.6952i	−0.868875	−	1.00274i	0.131060	−	0.991374i	$-0.458162\pi$
$878$	−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	0.360661	+	0.932697i	$0.382551\pi$
$881$	−17.2274	+	37.7228i	−0.580407	+	1.27091i	−0.941068	+	0.338218i	$0.890176\pi$
$882$	−0.654861	+	0.755750i	−0.0220503	+	0.0254474i
$883$	5.98263	−	41.6101i	0.201331	−	1.40029i	−0.599008	−	0.800743i	$-0.704438\pi$
$883$	5.98263	−	41.6101i	0.201331	−	1.40029i	0.800339	−	0.599547i	$-0.204653\pi$
$884$	−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	0.969477	−	0.245184i	$-0.0788484\pi$
$887$	4.44673	+	9.73699i	0.149307	+	0.326936i	−0.820170	+	0.572120i	$0.806121\pi$
$888$	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	0.791370	−	0.611337i	$-0.209368\pi$
$907$	−5.68855	−	12.4562i	−0.188885	−	0.413601i	−0.980255	+	0.197737i	$0.936641\pi$
$908$	−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	−0.820474	−	0.571684i	$-0.806290\pi$
$911$	3.85818	−	26.8342i	0.127827	−	0.889057i	0.948301	−	0.317373i	$-0.102801\pi$
$912$	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	0.390263	+	0.920703i	$0.372384\pi$
$929$	−7.42431	+	51.6372i	−0.243584	+	1.69416i	−0.633847	+	0.773459i	$0.718525\pi$
$930$	−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	0.847602	−	0.530632i	$-0.178045\pi$
$937$	21.9486	+	14.1055i	0.717029	+	0.460807i	−0.130573	+	0.991439i	$0.541682\pi$
$938$	−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	−0.589672	−	0.807643i	$-0.700743\pi$
$941$	−19.9113	+	5.84649i	−0.649090	+	0.190590i	−0.0594184	+	0.998233i	$0.518925\pi$
$942$	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	−0.111116	−	0.993807i	$-0.535442\pi$
$947$	22.9792	−	14.7678i	0.746724	−	0.479891i	0.857840	+	0.513917i	$0.171806\pi$
$948$	−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	0.995634	+	0.0933399i	$0.0297543\pi$
$953$	12.7858	+	27.9971i	0.414174	+	0.906915i	−0.581460	+	0.813575i	$0.697518\pi$
$954$	−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	−0.960299	−	0.278972i	$-0.910006\pi$
$971$	−3.66123	−	25.4644i	−0.117494	−	0.817191i	0.842805	−	0.538219i	$-0.180903\pi$
$972$	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	0.715830	−	0.698275i	$-0.246049\pi$
$977$	29.3975	+	8.63187i	0.940508	+	0.276158i	0.224678	+	0.974433i	$0.427867\pi$
$978$	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	0.824815	−	0.565403i	$-0.191279\pi$
$983$	20.4780	+	13.1604i	0.653146	+	0.419752i	−0.171668	+	0.985155i	$0.554916\pi$
$984$	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	−0.717355	−	0.696708i	$-0.754647\pi$
$991$	−29.7224	+	8.72728i	−0.944163	+	0.277231i	−0.226808	+	0.973939i	$0.572829\pi$
$992$	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	−0.472198	−	0.881493i	$-0.656539\pi$
$997$	14.7622	−	17.0365i	0.467524	−	0.539551i	0.939721	+	0.341942i	$0.111085\pi$
$998$	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.883.1	yes	10
23.18	even	11	inner	966.2.q.a.547.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.a.547.1	✓	10	23.18	even	11	inner
966.2.q.a.883.1	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.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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Database

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