LMFDB - Embedded newform 966.2.q.e.127.2

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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 9 x^{19} + 42 x^{18} - 126 x^{17} + 277 x^{16} - 538 x^{15} + 1046 x^{14} - 1170 x^{13} + \cdots + 529 $ x^20 - 9x^19 + 42x^18 - 126x^17 + 277x^16 - 538x^15 + 1046x^14 - 1170x^13 - 619x^12 + 2218x^11 + 1660x^10 - 3225x^9 + 2719x^8 + 8761x^7 + 14705x^6 + 21691x^5 + 21163x^4 + 14656x^3 + 7846x^2 + 2622*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.2
Root			$1.16609 - 1.34574i$ of defining polynomial
Character	$\chi$	$=$	966.127
Dual form			966.2.q.e.715.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(3.96506 - 1.16425i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(3.96506 - 1.16425i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-2.70618 + 3.12310i) q^{10} +(-1.40305 - 0.901683i) q^{11} +(0.841254 + 0.540641i) q^{12} +(3.62304 - 4.18121i) q^{13} +(0.959493 + 0.281733i) q^{14} +(0.588109 + 4.09039i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.00309 + 2.19646i) q^{17} +(0.959493 - 0.281733i) q^{18} +(-1.65897 + 3.63265i) q^{19} +(0.588109 - 4.09039i) q^{20} +(0.841254 - 0.540641i) q^{21} +1.66780 q^{22} +(4.27431 + 2.17493i) q^{23} -1.00000 q^{24} +(10.1599 - 6.52939i) q^{25} +(-0.787362 + 5.47623i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(-3.56623 - 7.80894i) q^{29} +(-2.70618 - 3.12310i) q^{30} +(-0.401622 - 2.79335i) q^{31} +(0.959493 + 0.281733i) q^{32} +(1.09218 - 1.26044i) q^{33} +(-2.03134 - 1.30547i) q^{34} +(-3.47644 - 2.23417i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-6.20414 - 1.82170i) q^{37} +(-0.568339 - 3.95289i) q^{38} +(3.62304 + 4.18121i) q^{39} +(1.71668 + 3.75901i) q^{40} +(8.79154 - 2.58143i) q^{41} +(-0.415415 + 0.909632i) q^{42} +(-0.491048 + 3.41531i) q^{43} +(-1.40305 + 0.901683i) q^{44} -4.13245 q^{45} +(-4.77163 + 0.481201i) q^{46} +7.27423 q^{47} +(0.841254 - 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-5.01702 + 10.9857i) q^{50} +(-2.31685 + 0.680289i) q^{51} +(-2.29830 - 5.03257i) q^{52} +(-8.31645 - 9.59769i) q^{53} +(0.142315 + 0.989821i) q^{54} +(-6.61294 - 1.94173i) q^{55} +(0.654861 - 0.755750i) q^{56} +(-3.35958 - 2.15907i) q^{57} +(7.22193 + 4.64126i) q^{58} +(1.52562 - 1.76066i) q^{59} +(3.96506 + 1.16425i) q^{60} +(2.01051 + 13.9834i) q^{61} +(1.84806 + 2.13278i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(9.49761 - 20.7969i) q^{65} +(-0.237353 + 1.65083i) q^{66} +(4.77448 - 3.06837i) q^{67} +2.41466 q^{68} +(-2.76109 + 3.92128i) q^{69} +4.13245 q^{70} +(4.83501 - 3.10727i) q^{71} +(0.142315 - 0.989821i) q^{72} +(0.546484 - 1.19663i) q^{73} +(6.20414 - 1.82170i) q^{74} +(5.01702 + 10.9857i) q^{75} +(2.61521 + 3.01811i) q^{76} +(0.237353 + 1.65083i) q^{77} +(-5.30843 - 1.55870i) q^{78} +(-6.38684 + 7.37081i) q^{79} +(-3.47644 - 2.23417i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-6.00029 + 6.92470i) q^{82} +(1.25615 + 0.368837i) q^{83} +(-0.142315 - 0.989821i) q^{84} +(6.53451 + 7.54123i) q^{85} +(-1.43336 - 3.13862i) q^{86} +(8.23699 - 2.41860i) q^{87} +(0.692831 - 1.51709i) q^{88} +(-0.692975 + 4.81974i) q^{89} +(3.47644 - 2.23417i) q^{90} -5.53254 q^{91} +(3.75399 - 2.98455i) q^{92} +2.82207 q^{93} +(-6.11947 + 3.93274i) q^{94} +(-2.34863 + 16.3351i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(-10.8563 + 3.18769i) q^{97} +(-0.415415 - 0.909632i) q^{98} +(1.09218 + 1.26044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{10} - 3 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} - 12 q^{15} - 2 q^{16} + 14 q^{17} + 2 q^{18} - 13 q^{19} - 12 q^{20} - 2 q^{21} - 8 q^{22} - 2 q^{23} - 20 q^{24} + 22 q^{25} - 28 q^{26} - 2 q^{27} - 2 q^{28} + 26 q^{29} - 10 q^{30} + 15 q^{31} + 2 q^{32} - 14 q^{33} - 3 q^{34} - q^{35} - 2 q^{36} - 26 q^{37} + 2 q^{38} + 6 q^{39} + q^{40} + 40 q^{41} + 2 q^{42} + 8 q^{43} - 3 q^{44} - 12 q^{45} - 20 q^{46} + 36 q^{47} - 2 q^{48} - 2 q^{49} + 11 q^{50} + 3 q^{51} - 27 q^{52} - 5 q^{53} + 2 q^{54} - 7 q^{55} + 2 q^{56} + 9 q^{57} - 15 q^{58} + 13 q^{59} + 10 q^{60} + 59 q^{61} - 4 q^{62} - 2 q^{63} - 2 q^{64} - q^{65} - 8 q^{66} - 26 q^{67} - 8 q^{68} - 35 q^{69} + 12 q^{70} + 13 q^{71} + 2 q^{72} - 34 q^{73} + 26 q^{74} - 11 q^{75} - 2 q^{76} + 8 q^{77} - 6 q^{78} - 27 q^{79} - q^{80} - 2 q^{81} - 40 q^{82} + 41 q^{83} - 2 q^{84} + 51 q^{85} + 14 q^{86} - 7 q^{87} - 8 q^{88} + 43 q^{89} + q^{90} - 16 q^{91} + 9 q^{92} + 4 q^{93} - 3 q^{94} - 26 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{98} - 14 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 10 * q^10 - 3 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^14 - 12 * q^15 - 2 * q^16 + 14 * q^17 + 2 * q^18 - 13 * q^19 - 12 * q^20 - 2 * q^21 - 8 * q^22 - 2 * q^23 - 20 * q^24 + 22 * q^25 - 28 * q^26 - 2 * q^27 - 2 * q^28 + 26 * q^29 - 10 * q^30 + 15 * q^31 + 2 * q^32 - 14 * q^33 - 3 * q^34 - q^35 - 2 * q^36 - 26 * q^37 + 2 * q^38 + 6 * q^39 + q^40 + 40 * q^41 + 2 * q^42 + 8 * q^43 - 3 * q^44 - 12 * q^45 - 20 * q^46 + 36 * q^47 - 2 * q^48 - 2 * q^49 + 11 * q^50 + 3 * q^51 - 27 * q^52 - 5 * q^53 + 2 * q^54 - 7 * q^55 + 2 * q^56 + 9 * q^57 - 15 * q^58 + 13 * q^59 + 10 * q^60 + 59 * q^61 - 4 * q^62 - 2 * q^63 - 2 * q^64 - q^65 - 8 * q^66 - 26 * q^67 - 8 * q^68 - 35 * q^69 + 12 * q^70 + 13 * q^71 + 2 * q^72 - 34 * q^73 + 26 * q^74 - 11 * q^75 - 2 * q^76 + 8 * q^77 - 6 * q^78 - 27 * q^79 - q^80 - 2 * q^81 - 40 * q^82 + 41 * q^83 - 2 * q^84 + 51 * q^85 + 14 * q^86 - 7 * q^87 - 8 * q^88 + 43 * q^89 + q^90 - 16 * q^91 + 9 * q^92 + 4 * q^93 - 3 * q^94 - 26 * q^95 + 2 * q^96 - 8 * q^97 + 2 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−0.841254	+	0.540641i	−0.594856	+	0.382291i
$2$	−0.841254	+	0.540641i	−0.594856	+	0.382291i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	3.96506	−	1.16425i	1.77323	−	0.520666i	0.778911	−	0.627135i	$-0.215772\pi$
$5$	3.96506	−	1.16425i	1.77323	−	0.520666i	0.994316	+	0.106468i	$0.0339543\pi$
$6$	−0.415415	−	0.909632i	−0.169592	−	0.371356i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	0.142315	+	0.989821i	0.0503159	+	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	−2.70618	+	3.12310i	−0.855769	+	0.987610i
$11$	−1.40305	−	0.901683i	−0.423034	−	0.271868i	0.311756	−	0.950162i	$-0.399083\pi$
$11$	−1.40305	−	0.901683i	−0.423034	−	0.271868i	−0.734790	+	0.678295i	$0.762719\pi$
$12$	0.841254	+	0.540641i	0.242849	+	0.156070i
$13$	3.62304	−	4.18121i	1.00485	−	1.15966i	0.0177044	−	0.999843i	$-0.494364\pi$
$13$	3.62304	−	4.18121i	1.00485	−	1.15966i	0.987147	−	0.159817i	$-0.0510903\pi$
$14$	0.959493	+	0.281733i	0.256435	+	0.0752962i
$15$	0.588109	+	4.09039i	0.151849	+	1.05613i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	1.00309	+	2.19646i	0.243284	+	0.532719i	0.991403	−	0.130847i	$-0.0417697\pi$
$17$	1.00309	+	2.19646i	0.243284	+	0.532719i	−0.748118	+	0.663566i	$0.769042\pi$
$18$	0.959493	−	0.281733i	0.226155	−	0.0664050i
$19$	−1.65897	+	3.63265i	−0.380595	+	0.833387i	0.618280	+	0.785958i	$0.287830\pi$
$19$	−1.65897	+	3.63265i	−0.380595	+	0.833387i	−0.998875	+	0.0474285i	$0.984897\pi$
$20$	0.588109	−	4.09039i	0.131505	−	0.914638i
$21$	0.841254	−	0.540641i	0.183577	−	0.117977i
$22$	1.66780			0.355577
$23$	4.27431	+	2.17493i	0.891255	+	0.453503i
$23$	4.27431	+	2.17493i	0.891255	+	0.453503i
$24$	−1.00000			−0.204124
$25$	10.1599	−	6.52939i	2.03199	−	1.30588i
$26$	−0.787362	+	5.47623i	−0.154414	+	1.07398i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	−0.959493	+	0.281733i	−0.181327	+	0.0532424i
$29$	−3.56623	−	7.80894i	−0.662231	−	1.45008i	−0.880428	−	0.474180i	$-0.842745\pi$
$29$	−3.56623	−	7.80894i	−0.662231	−	1.45008i	0.218197	−	0.975905i	$-0.429983\pi$
$30$	−2.70618	−	3.12310i	−0.494078	−	0.570197i
$31$	−0.401622	−	2.79335i	−0.0721335	−	0.501700i	−0.993574	−	0.113181i	$-0.963896\pi$
$31$	−0.401622	−	2.79335i	−0.0721335	−	0.501700i	0.921441	−	0.388519i	$-0.127013\pi$
$32$	0.959493	+	0.281733i	0.169616	+	0.0498038i
$33$	1.09218	−	1.26044i	0.190124	−	0.219415i
$34$	−2.03134	−	1.30547i	−0.348373	−	0.223885i
$35$	−3.47644	−	2.23417i	−0.587625	−	0.377644i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	−6.20414	−	1.82170i	−1.01995	−	0.299486i	−0.271335	−	0.962485i	$-0.587465\pi$
$37$	−6.20414	−	1.82170i	−1.01995	−	0.299486i	−0.748620	+	0.662999i	$0.769283\pi$
$38$	−0.568339	−	3.95289i	−0.0921968	−	0.641243i
$39$	3.62304	+	4.18121i	0.580151	+	0.669530i
$40$	1.71668	+	3.75901i	0.271431	+	0.594351i
$41$	8.79154	−	2.58143i	1.37301	−	0.403151i	0.489678	−	0.871903i	$-0.337114\pi$
$41$	8.79154	−	2.58143i	1.37301	−	0.403151i	0.883330	+	0.468752i	$0.155296\pi$
$42$	−0.415415	+	0.909632i	−0.0640999	+	0.140359i
$43$	−0.491048	+	3.41531i	−0.0748841	+	0.520830i	0.917508	+	0.397716i	$0.130197\pi$
$43$	−0.491048	+	3.41531i	−0.0748841	+	0.520830i	−0.992393	+	0.123114i	$0.960712\pi$
$44$	−1.40305	+	0.901683i	−0.211517	+	0.135934i
$45$	−4.13245			−0.616029
$46$	−4.77163	+	0.481201i	−0.703538	+	0.0709492i
$47$	7.27423			1.06105			0.530527	−	0.847668i	$-0.321994\pi$
$47$	7.27423			1.06105			0.530527	+	0.847668i	$0.321994\pi$
$48$	0.841254	−	0.540641i	0.121424	−	0.0780348i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	−5.01702	+	10.9857i	−0.709514	+	1.55362i
$51$	−2.31685	+	0.680289i	−0.324424	+	0.0952596i
$52$	−2.29830	−	5.03257i	−0.318717	−	0.697892i
$53$	−8.31645	−	9.59769i	−1.14235	−	1.31834i	−0.940837	−	0.338859i	$-0.889959\pi$
$53$	−8.31645	−	9.59769i	−1.14235	−	1.31834i	−0.201515	−	0.979485i	$-0.564586\pi$
$54$	0.142315	+	0.989821i	0.0193666	+	0.134698i
$55$	−6.61294	−	1.94173i	−0.891688	−	0.261823i
$56$	0.654861	−	0.755750i	0.0875094	−	0.100991i
$57$	−3.35958	−	2.15907i	−0.444987	−	0.285976i
$58$	7.22193	+	4.64126i	0.948286	+	0.609427i
$59$	1.52562	−	1.76066i	0.198619	−	0.229218i	−0.647699	−	0.761896i	$-0.724269\pi$
$59$	1.52562	−	1.76066i	0.198619	−	0.229218i	0.846318	+	0.532678i	$0.178814\pi$
$60$	3.96506	+	1.16425i	0.511886	+	0.150303i
$61$	2.01051	+	13.9834i	0.257420	+	1.79039i	0.551048	+	0.834473i	$0.314228\pi$
$61$	2.01051	+	13.9834i	0.257420	+	1.79039i	−0.293629	+	0.955920i	$0.594863\pi$
$62$	1.84806	+	2.13278i	0.234704	+	0.270863i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	9.49761	−	20.7969i	1.17803	−	2.57953i
$66$	−0.237353	+	1.65083i	−0.0292162	+	0.203203i
$67$	4.77448	−	3.06837i	0.583296	−	0.374861i	−0.215464	−	0.976512i	$-0.569126\pi$
$67$	4.77448	−	3.06837i	0.583296	−	0.374861i	0.798760	+	0.601650i	$0.205490\pi$
$68$	2.41466			0.292821
$69$	−2.76109	+	3.92128i	−0.332396	+	0.472066i
$70$	4.13245			0.493922
$71$	4.83501	−	3.10727i	0.573810	−	0.368765i	−0.221323	−	0.975201i	$-0.571037\pi$
$71$	4.83501	−	3.10727i	0.573810	−	0.368765i	0.795133	+	0.606435i	$0.207401\pi$
$72$	0.142315	−	0.989821i	0.0167720	−	0.116652i
$73$	0.546484	−	1.19663i	0.0639611	−	0.140055i	−0.874952	−	0.484210i	$-0.839107\pi$
$73$	0.546484	−	1.19663i	0.0639611	−	0.140055i	0.938913	+	0.344155i	$0.111834\pi$
$74$	6.20414	−	1.82170i	0.721217	−	0.211768i
$75$	5.01702	+	10.9857i	0.579316	+	1.26852i
$76$	2.61521	+	3.01811i	0.299985	+	0.346201i
$77$	0.237353	+	1.65083i	0.0270489	+	0.188129i
$78$	−5.30843	−	1.55870i	−0.601062	−	0.176488i
$79$	−6.38684	+	7.37081i	−0.718576	+	0.829281i	−0.991135	−	0.132858i	$-0.957585\pi$
$79$	−6.38684	+	7.37081i	−0.718576	+	0.829281i	0.272559	+	0.962139i	$0.412130\pi$
$80$	−3.47644	−	2.23417i	−0.388678	−	0.249788i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−6.00029	+	6.92470i	−0.662621	+	0.764705i
$83$	1.25615	+	0.368837i	0.137880	+	0.0404852i	0.349944	−	0.936771i	$-0.386201\pi$
$83$	1.25615	+	0.368837i	0.137880	+	0.0404852i	−0.212064	+	0.977256i	$0.568019\pi$
$84$	−0.142315	−	0.989821i	−0.0155278	−	0.107998i
$85$	6.53451	+	7.54123i	0.708767	+	0.817961i
$86$	−1.43336	−	3.13862i	−0.154563	−	0.338447i
$87$	8.23699	−	2.41860i	0.883098	−	0.259301i
$88$	0.692831	−	1.51709i	0.0738560	−	0.161722i
$89$	−0.692975	+	4.81974i	−0.0734552	+	0.510892i	0.919564	+	0.392940i	$0.128542\pi$
$89$	−0.692975	+	4.81974i	−0.0734552	+	0.510892i	−0.993019	+	0.117952i	$0.962367\pi$
$90$	3.47644	−	2.23417i	0.366449	−	0.235502i
$91$	−5.53254			−0.579968
$92$	3.75399	−	2.98455i	0.391381	−	0.311161i
$93$	2.82207			0.292635
$94$	−6.11947	+	3.93274i	−0.631175	+	0.405631i
$95$	−2.34863	+	16.3351i	−0.240965	+	1.67595i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	−10.8563	+	3.18769i	−1.10229	+	0.323661i	−0.781761	−	0.623578i	$-0.785678\pi$
$97$	−10.8563	+	3.18769i	−1.10229	+	0.323661i	−0.320527	+	0.947239i	$0.603860\pi$
$98$	−0.415415	−	0.909632i	−0.0419633	−	0.0918867i
$99$	1.09218	+	1.26044i	0.109768	+	0.126679i
$100$	−1.71876	−	11.9542i	−0.171876	−	1.19542i
$101$	18.1732	+	5.33613i	1.80830	+	0.530964i	0.998449	−	0.0556727i	$-0.0177304\pi$
$101$	18.1732	+	5.33613i	1.80830	+	0.530964i	0.809850	+	0.586637i	$0.199549\pi$
$102$	1.58127	−	1.82488i	0.156569	−	0.180690i
$103$	12.9273	+	8.30788i	1.27377	+	0.818599i	0.990105	−	0.140326i	$-0.0448150\pi$
$103$	12.9273	+	8.30788i	1.27377	+	0.818599i	0.283660	+	0.958925i	$0.408451\pi$
$104$	4.65427	+	2.99112i	0.456388	+	0.293303i
$105$	2.70618	−	3.12310i	0.264096	−	0.304783i
$106$	12.1851	+	3.57788i	1.18353	+	0.347515i
$107$	0.0706169	+	0.491151i	0.00682679	+	0.0474814i	0.992950	−	0.118533i	$-0.0378192\pi$
$107$	0.0706169	+	0.491151i	0.00682679	+	0.0474814i	−0.986123	+	0.166015i	$0.946910\pi$
$108$	−0.654861	−	0.755750i	−0.0630140	−	0.0727220i
$109$	8.39806	+	18.3892i	0.804388	+	1.76136i	0.629854	+	0.776713i	$0.283115\pi$
$109$	8.39806	+	18.3892i	0.804388	+	1.76136i	0.174534	+	0.984651i	$0.444158\pi$
$110$	6.61294	−	1.94173i	0.630519	−	0.185137i
$111$	2.68610	−	5.88174i	0.254953	−	0.558270i
$112$	−0.142315	+	0.989821i	−0.0134475	+	0.0935293i
$113$	−0.0285898	+	0.0183735i	−0.00268950	+	0.00172844i	−0.541985	−	0.840388i	$-0.682327\pi$
$113$	−0.0285898	+	0.0183735i	−0.00268950	+	0.00172844i	0.539295	+	0.842117i	$0.318691\pi$
$114$	3.99354			0.374029
$115$	19.4800	+	3.64736i	1.81652	+	0.340118i
$116$	−8.58473			−0.797072
$117$	−4.65427	+	2.99112i	−0.430287	+	0.276529i
$118$	−0.331549	+	2.30597i	−0.0305216	+	0.212282i
$119$	1.00309	−	2.19646i	0.0919529	−	0.201349i
$120$	−3.96506	+	1.16425i	−0.361958	+	0.106281i
$121$	−3.41406	−	7.47575i	−0.310369	−	0.679613i
$122$	−9.25136	−	10.6766i	−0.837578	−	0.966617i
$123$	1.30399	+	9.06943i	0.117577	+	0.817763i
$124$	−2.70776	−	0.795069i	−0.243164	−	0.0713993i
$125$	19.1520	−	22.1026i	1.71301	−	1.97691i
$126$	−0.841254	−	0.540641i	−0.0749448	−	0.0481641i
$127$	6.56990	+	4.22222i	0.582985	+	0.374661i	0.798641	−	0.601808i	$-0.205553\pi$
$127$	6.56990	+	4.22222i	0.582985	+	0.374661i	−0.215656	+	0.976469i	$0.569189\pi$
$128$	0.654861	−	0.755750i	0.0578821	−	0.0667995i
$129$	−3.31067	−	0.972099i	−0.291488	−	0.0855886i
$130$	3.25373	+	22.6302i	0.285371	+	1.98480i
$131$	−5.61110	−	6.47556i	−0.490244	−	0.565772i	0.455687	−	0.890140i	$-0.349394\pi$
$131$	−5.61110	−	6.47556i	−0.490244	−	0.565772i	−0.945931	+	0.324368i	$0.894848\pi$
$132$	−0.692831	−	1.51709i	−0.0603032	−	0.132046i
$133$	3.83177	−	1.12511i	0.332257	−	0.0975593i
$134$	−2.35766	+	5.16256i	−0.203671	+	0.445977i
$135$	0.588109	−	4.09039i	0.0506163	−	0.352044i
$136$	−2.03134	+	1.30547i	−0.174186	+	0.111943i
$137$	−9.72033			−0.830463			−0.415232	−	0.909716i	$-0.636300\pi$
$137$	−9.72033			−0.830463			−0.415232	+	0.909716i	$0.636300\pi$
$138$	0.202771	−	4.79154i	0.0172610	−	0.407883i
$139$	−22.6634			−1.92229			−0.961144	−	0.276049i	$-0.910975\pi$
$139$	−22.6634			−1.92229			−0.961144	+	0.276049i	$0.910975\pi$
$140$	−3.47644	+	2.23417i	−0.293813	+	0.188822i
$141$	−1.03523	+	7.20018i	−0.0871821	+	0.606365i
$142$	−2.38755	+	5.22801i	−0.200359	+	0.438725i
$143$	−8.85343	+	2.59960i	−0.740361	+	0.217390i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	−23.2318	−	26.8109i	−1.92930	−	2.22653i
$146$	0.187217	+	1.30212i	0.0154942	+	0.107764i
$147$	−0.959493	−	0.281733i	−0.0791376	−	0.0232369i
$148$	−4.23437	+	4.88672i	−0.348063	+	0.401686i
$149$	5.66449	+	3.64035i	0.464053	+	0.298229i	0.751697	−	0.659508i	$-0.229236\pi$
$149$	5.66449	+	3.64035i	0.464053	+	0.298229i	−0.287644	+	0.957737i	$0.592872\pi$
$150$	−10.1599	−	6.52939i	−0.829555	−	0.533123i
$151$	−11.2146	+	12.9423i	−0.912629	+	1.05323i	0.0857503	+	0.996317i	$0.472671\pi$
$151$	−11.2146	+	12.9423i	−0.912629	+	1.05323i	−0.998379	+	0.0569131i	$0.981874\pi$
$152$	−3.83177	−	1.12511i	−0.310798	−	0.0912584i
$153$	−0.343642	−	2.39009i	−0.0277818	−	0.193227i
$154$	−1.09218	−	1.26044i	−0.0880103	−	0.101569i
$155$	−4.84459	−	10.6082i	−0.389127	−	0.852070i
$156$	5.30843	−	1.55870i	0.425015	−	0.124796i
$157$	−2.23282	+	4.88919i	−0.178198	+	0.390200i	−0.977562	−	0.210647i	$-0.932443\pi$
$157$	−2.23282	+	4.88919i	−0.178198	+	0.390200i	0.799364	+	0.600847i	$0.205170\pi$
$158$	1.38799	−	9.65371i	0.110423	−	0.768008i
$159$	10.6836	−	6.86590i	0.847261	−	0.544502i
$160$	4.13245			0.326699
$161$	−1.15538	−	4.65458i	−0.0910564	−	0.366832i
$162$	−1.00000			−0.0785674
$163$	−14.6523	+	9.41644i	−1.14765	+	0.737552i	−0.969171	−	0.246391i	$-0.920755\pi$
$163$	−14.6523	+	9.41644i	−1.14765	+	0.737552i	−0.178483	+	0.983943i	$0.557119\pi$
$164$	1.30399	−	9.06943i	0.101824	−	0.708203i
$165$	2.86309	−	6.26929i	0.222891	−	0.488064i
$166$	−1.25615	+	0.368837i	−0.0974958	+	0.0286273i
$167$	−7.26226	−	15.9021i	−0.561970	−	1.23054i	−0.950964	−	0.309303i	$-0.899904\pi$
$167$	−7.26226	−	15.9021i	−0.561970	−	1.23054i	0.388993	−	0.921241i	$-0.372823\pi$
$168$	0.654861	+	0.755750i	0.0505236	+	0.0583073i
$169$	−2.50602	−	17.4297i	−0.192771	−	1.34075i
$170$	−9.57427	−	2.81126i	−0.734313	−	0.215614i
$171$	2.61521	−	3.01811i	0.199990	−	0.230801i
$172$	2.90269	+	1.86545i	0.221328	+	0.142239i
$173$	−2.51874	−	1.61870i	−0.191496	−	0.123067i	0.441379	−	0.897321i	$-0.354489\pi$
$173$	−2.51874	−	1.61870i	−0.191496	−	0.123067i	−0.632876	+	0.774253i	$0.718126\pi$
$174$	−5.62180	+	6.48791i	−0.426188	+	0.491847i
$175$	−11.5879	−	3.40252i	−0.875965	−	0.257206i
$176$	0.237353	+	1.65083i	0.0178912	+	0.124436i
$177$	1.52562	+	1.76066i	0.114673	+	0.132339i
$178$	−2.02278	−	4.42928i	−0.151614	−	0.331988i
$179$	1.03654	−	0.304355i	0.0774744	−	0.0227485i	−0.242766	−	0.970085i	$-0.578055\pi$
$179$	1.03654	−	0.304355i	0.0774744	−	0.0227485i	0.320240	+	0.947336i	$0.396236\pi$
$180$	−1.71668	+	3.75901i	−0.127954	+	0.280180i
$181$	0.841324	−	5.85154i	0.0625351	−	0.434941i	−0.934368	−	0.356308i	$-0.884035\pi$
$181$	0.841324	−	5.85154i	0.0625351	−	0.434941i	0.996904	−	0.0786332i	$-0.0250556\pi$
$182$	4.65427	−	2.99112i	0.344997	−	0.221716i
$183$	−14.1272			−1.04431
$184$	−1.54449	+	4.54032i	−0.113861	+	0.334717i
$185$	−26.7207			−1.96454
$186$	−2.37408	+	1.52573i	−0.174076	+	0.111872i
$187$	0.573128	−	3.98620i	0.0419113	−	0.291499i
$188$	3.02182	−	6.61687i	0.220389	−	0.482585i
$189$	−0.959493	+	0.281733i	−0.0697928	+	0.0204930i
$190$	−6.85563	−	15.0117i	−0.497360	−	1.08907i
$191$	−2.53563	−	2.92627i	−0.183472	−	0.211737i	0.656562	−	0.754272i	$-0.272010\pi$
$191$	−2.53563	−	2.92627i	−0.183472	−	0.211737i	−0.840033	+	0.542535i	$0.817465\pi$
$192$	−0.142315	−	0.989821i	−0.0102707	−	0.0714342i
$193$	6.12399	+	1.79816i	0.440814	+	0.129435i	0.494606	−	0.869117i	$-0.335312\pi$
$193$	6.12399	+	1.79816i	0.440814	+	0.129435i	−0.0537916	+	0.998552i	$0.517131\pi$
$194$	7.40949	−	8.55100i	0.531970	−	0.613926i
$195$	19.2335	+	12.3606i	1.37734	+	0.885163i
$196$	0.841254	+	0.540641i	0.0600895	+	0.0386172i
$197$	−6.11437	+	7.05636i	−0.435631	+	0.502745i	−0.930535	−	0.366203i	$-0.880658\pi$
$197$	−6.11437	+	7.05636i	−0.435631	+	0.502745i	0.494904	+	0.868947i	$0.335203\pi$
$198$	−1.60025	−	0.469875i	−0.113725	−	0.0333925i
$199$	1.69179	+	11.7667i	0.119928	+	0.834116i	0.957633	+	0.287993i	$0.0929879\pi$
$199$	1.69179	+	11.7667i	0.119928	+	0.834116i	−0.837705	+	0.546123i	$0.816103\pi$
$200$	7.90884	+	9.12729i	0.559240	+	0.645397i
$201$	2.35766	+	5.16256i	0.166297	+	0.364139i
$202$	−18.1732	+	5.33613i	−1.27866	+	0.375449i
$203$	−3.56623	+	7.80894i	−0.250300	+	0.548080i
$204$	−0.343642	+	2.39009i	−0.0240598	+	0.167339i
$205$	31.8535	−	20.4710i	2.22475	−	1.42976i
$206$	−15.3667			−1.07065
$207$	−3.48842	−	3.29104i	−0.242462	−	0.228743i
$208$	−5.53254			−0.383613
$209$	5.60312	−	3.60090i	0.387576	−	0.249080i
$210$	−0.588109	+	4.09039i	−0.0405834	+	0.282263i
$211$	10.9372	−	23.9492i	0.752949	−	1.64873i	−0.00804324	−	0.999968i	$-0.502560\pi$
$211$	10.9372	−	23.9492i	0.752949	−	1.64873i	0.760992	−	0.648761i	$-0.224712\pi$
$212$	−12.1851	+	3.57788i	−0.836879	+	0.245730i
$213$	2.38755	+	5.22801i	0.163592	+	0.358217i
$214$	−0.324943	−	0.375004i	−0.0222127	−	0.0256348i
$215$	2.02923	+	14.1136i	0.138392	+	0.962540i
$216$	0.959493	+	0.281733i	0.0652852	+	0.0191695i
$217$	−1.84806	+	2.13278i	−0.125455	+	0.144782i
$218$	−17.0068	−	10.9296i	−1.15185	−	0.740248i
$219$	1.10668	+	0.711220i	0.0747825	+	0.0480598i
$220$	−4.51338	+	5.20871i	−0.304292	+	0.351171i
$221$	12.8181	+	3.76373i	0.862237	+	0.253176i
$222$	0.920217	+	6.40025i	0.0617609	+	0.429556i
$223$	−17.8680	−	20.6208i	−1.19653	−	1.38087i	−0.905603	−	0.424127i	$-0.860581\pi$
$223$	−17.8680	−	20.6208i	−1.19653	−	1.38087i	−0.290929	−	0.956745i	$-0.593964\pi$
$224$	−0.415415	−	0.909632i	−0.0277561	−	0.0607773i
$225$	−11.5879	+	3.40252i	−0.772528	+	0.226835i
$226$	0.0141178	−	0.0309136i	0.000939100	−	0.00205634i
$227$	−1.73148	+	12.0427i	−0.114923	+	0.799304i	0.848091	+	0.529851i	$0.177752\pi$
$227$	−1.73148	+	12.0427i	−0.114923	+	0.799304i	−0.963013	+	0.269453i	$0.913157\pi$
$228$	−3.35958	+	2.15907i	−0.222493	+	0.142988i
$229$	−8.58127			−0.567066			−0.283533	−	0.958962i	$-0.591507\pi$
$229$	−8.58127			−0.567066			−0.283533	+	0.958962i	$0.591507\pi$
$230$	−18.3595	+	7.46333i	−1.21059	+	0.492118i
$231$	−1.66780			−0.109733
$232$	7.22193	−	4.64126i	0.474143	−	0.304713i
$233$	−2.60414	+	18.1122i	−0.170603	+	1.18657i	0.707011	+	0.707203i	$0.250043\pi$
$233$	−2.60414	+	18.1122i	−0.170603	+	1.18657i	−0.877614	+	0.479368i	$0.840866\pi$
$234$	2.29830	−	5.03257i	0.150245	−	0.328990i
$235$	28.8427	−	8.46898i	1.88149	−	0.552456i
$236$	−0.967787	−	2.11916i	−0.0629976	−	0.137945i
$237$	−6.38684	−	7.37081i	−0.414870	−	0.478785i
$238$	0.343642	+	2.39009i	0.0222750	+	0.154926i
$239$	−10.0536	−	2.95201i	−0.650315	−	0.190950i	−0.0600955	−	0.998193i	$-0.519141\pi$
$239$	−10.0536	−	2.95201i	−0.650315	−	0.190950i	−0.590219	+	0.807243i	$0.700959\pi$
$240$	2.70618	−	3.12310i	0.174683	−	0.201595i
$241$	3.00147	+	1.92893i	0.193341	+	0.124253i	0.633730	−	0.773554i	$-0.281523\pi$
$241$	3.00147	+	1.92893i	0.193341	+	0.124253i	−0.440389	+	0.897807i	$0.645159\pi$
$242$	6.91378	+	4.44322i	0.444435	+	0.285621i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	13.5550	+	3.98010i	0.867767	+	0.254799i
$245$	0.588109	+	4.09039i	0.0375729	+	0.261325i
$246$	−6.00029	−	6.92470i	−0.382564	−	0.441503i
$247$	9.17834	+	20.0978i	0.584004	+	1.27879i
$248$	2.70776	−	0.795069i	0.171943	−	0.0504869i
$249$	−0.543851	+	1.19087i	−0.0344652	+	0.0754682i
$250$	−4.16213	+	28.9482i	−0.263236	+	1.83085i
$251$	−14.5858	+	9.37370i	−0.920645	+	0.591662i	−0.912845	−	0.408307i	$-0.866119\pi$
$251$	−14.5858	+	9.37370i	−0.920645	+	0.591662i	−0.00780010	+	0.999970i	$0.502483\pi$
$252$	1.00000			0.0629941
$253$	−4.03596	−	6.90559i	−0.253738	−	0.434151i
$254$	−7.80966			−0.490022
$255$	−8.39443	+	5.39477i	−0.525679	+	0.337834i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	0.144154	−	0.315654i	0.00899209	−	0.0196899i	−0.905083	−	0.425236i	$-0.860191\pi$
$257$	0.144154	−	0.315654i	0.00899209	−	0.0196899i	0.914075	+	0.405546i	$0.132918\pi$
$258$	3.31067	−	0.972099i	0.206113	−	0.0605203i
$259$	2.68610	+	5.88174i	0.166906	+	0.365473i
$260$	−14.9720	−	17.2787i	−0.928526	−	1.07158i
$261$	1.22173	+	8.49735i	0.0756235	+	0.525973i
$262$	8.22131	+	2.41399i	0.507914	+	0.149137i
$263$	−2.16722	+	2.50111i	−0.133637	+	0.154225i	−0.818624	−	0.574330i	$-0.805262\pi$
$263$	−2.16722	+	2.50111i	−0.133637	+	0.154225i	0.684987	+	0.728555i	$0.259808\pi$
$264$	1.40305	+	0.901683i	0.0863515	+	0.0554948i
$265$	−44.1493	−	28.3730i	−2.71207	−	1.74294i
$266$	−2.61521	+	3.01811i	−0.160349	+	0.185052i
$267$	−4.67207	−	1.37184i	−0.285926	−	0.0839554i
$268$	−0.807699	−	5.61767i	−0.0493381	−	0.343154i
$269$	10.5469	+	12.1718i	0.643058	+	0.742129i	0.979913	−	0.199428i	$-0.0639084\pi$
$269$	10.5469	+	12.1718i	0.643058	+	0.742129i	−0.336854	+	0.941557i	$0.609363\pi$
$270$	1.71668	+	3.75901i	0.104474	+	0.228766i
$271$	−2.63024	+	0.772308i	−0.159776	+	0.0469144i	−0.360642	−	0.932704i	$-0.617442\pi$
$271$	−2.63024	+	0.772308i	−0.159776	+	0.0469144i	0.200867	+	0.979619i	$0.435624\pi$
$272$	1.00309	−	2.19646i	0.0608211	−	0.133180i
$273$	0.787362	−	5.47623i	0.0476533	−	0.331436i
$274$	8.17726	−	5.25520i	0.494006	−	0.317479i
$275$	−20.1423			−1.21463
$276$	2.41992	+	4.14053i	0.145662	+	0.249231i
$277$	−11.0349			−0.663020			−0.331510	−	0.943452i	$-0.607558\pi$
$277$	−11.0349			−0.663020			−0.331510	+	0.943452i	$0.607558\pi$
$278$	19.0657	−	12.2528i	1.14348	−	0.734873i
$279$	−0.401622	+	2.79335i	−0.0240445	+	0.167233i
$280$	1.71668	−	3.75901i	0.102591	−	0.224644i
$281$	25.5655	−	7.50669i	1.52511	−	0.447812i	0.591558	−	0.806262i	$-0.298513\pi$
$281$	25.5655	−	7.50669i	1.52511	−	0.447812i	0.933549	+	0.358450i	$0.116695\pi$
$282$	−3.02182	−	6.61687i	−0.179947	−	0.394029i
$283$	−13.6864	−	15.7950i	−0.813573	−	0.938914i	0.185470	−	0.982650i	$-0.440619\pi$
$283$	−13.6864	−	15.7950i	−0.813573	−	0.938914i	−0.999043	+	0.0437362i	$0.986074\pi$
$284$	−0.817938	−	5.68889i	−0.0485357	−	0.337573i
$285$	−15.8346	−	4.64946i	−0.937960	−	0.275410i
$286$	6.04253	−	6.97345i	0.357302	−	0.412349i
$287$	−7.70815	−	4.95373i	−0.454998	−	0.292409i
$288$	−0.841254	−	0.540641i	−0.0495713	−	0.0318576i
$289$	7.31440	−	8.44127i	0.430259	−	0.496545i
$290$	34.0389	+	9.99473i	1.99883	+	0.586911i
$291$	−1.61024	−	11.1994i	−0.0943937	−	0.656522i
$292$	−0.861477	−	0.994198i	−0.0504141	−	0.0581810i
$293$	0.0623222	+	0.136467i	0.00364090	+	0.00797246i	0.911444	−	0.411425i	$-0.134969\pi$
$293$	0.0623222	+	0.136467i	0.00364090	+	0.00797246i	−0.907803	+	0.419397i	$0.862241\pi$
$294$	0.959493	−	0.281733i	0.0559588	−	0.0164310i
$295$	3.99933	−	8.75731i	0.232850	−	0.509870i
$296$	0.920217	−	6.40025i	0.0534865	−	0.372007i
$297$	−1.40305	+	0.901683i	−0.0814130	+	0.0523210i
$298$	−6.73340			−0.390055
$299$	24.5798	−	9.99194i	1.42149	−	0.577849i
$300$	12.0771			0.697274
$301$	2.90269	−	1.86545i	0.167308	−	0.107522i
$302$	2.43716	−	16.9508i	0.140243	−	0.975410i
$303$	−7.86813	+	17.2288i	−0.452012	+	0.989768i
$304$	3.83177	−	1.12511i	0.219767	−	0.0645294i
$305$	24.2519	+	53.1043i	1.38866	+	3.04074i
$306$	1.58127	+	1.82488i	0.0903951	+	0.104321i
$307$	0.151878	+	1.05634i	0.00866815	+	0.0602883i	0.993696	−	0.112105i	$-0.0357592\pi$
$307$	0.151878	+	1.05634i	0.00866815	+	0.0602883i	−0.985028	+	0.172393i	$0.944850\pi$
$308$	1.60025	+	0.469875i	0.0911825	+	0.0267736i
$309$	−10.0631	+	11.6134i	−0.572468	+	0.660663i
$310$	9.81075	+	6.30499i	0.557213	+	0.358099i
$311$	2.57740	+	1.65640i	0.146151	+	0.0939257i	0.611673	−	0.791111i	$-0.290497\pi$
$311$	2.57740	+	1.65640i	0.146151	+	0.0939257i	−0.465522	+	0.885037i	$0.654133\pi$
$312$	−3.62304	+	4.18121i	−0.205114	+	0.236715i
$313$	−11.0236	−	3.23682i	−0.623091	−	0.182956i	−0.0450779	−	0.998983i	$-0.514354\pi$
$313$	−11.0236	−	3.23682i	−0.623091	−	0.182956i	−0.578013	+	0.816027i	$0.696172\pi$
$314$	−0.764930	−	5.32020i	−0.0431675	−	0.300237i
$315$	2.70618	+	3.12310i	0.152476	+	0.175967i
$316$	4.05153	+	8.87162i	0.227917	+	0.499068i
$317$	−22.8575	+	6.71156i	−1.28380	+	0.376959i	−0.851303	−	0.524675i	$-0.824187\pi$
$317$	−22.8575	+	6.71156i	−1.28380	+	0.376959i	−0.432501	+	0.901634i	$0.642369\pi$
$318$	−5.27559	+	11.5519i	−0.295840	+	0.647800i
$319$	−2.03761	+	14.1719i	−0.114084	+	0.793475i
$320$	−3.47644	+	2.23417i	−0.194339	+	0.124894i
$321$	−0.496202			−0.0276953
$322$	3.48842	+	3.29104i	0.194402	+	0.183402i
$323$	−9.64305			−0.536553
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	9.50908	−	66.1371i	0.527469	−	3.66863i
$326$	7.23536	−	15.8432i	0.400729	−	0.877475i
$327$	−19.3972	+	5.69553i	−1.07267	+	0.314963i
$328$	3.80632	+	8.33468i	0.210169	+	0.460206i
$329$	−4.76360	−	5.49749i	−0.262626	−	0.303087i
$330$	0.980850	+	6.82196i	0.0539940	+	0.375537i
$331$	0.466709	+	0.137038i	0.0256526	+	0.00753229i	0.294534	−	0.955641i	$-0.404836\pi$
$331$	0.466709	+	0.137038i	0.0256526	+	0.00753229i	−0.268881	+	0.963173i	$0.586654\pi$
$332$	0.857328	−	0.989409i	0.0470520	−	0.0543009i
$333$	5.43960	+	3.49582i	0.298088	+	0.191570i
$334$	14.7067	+	9.45145i	0.804717	+	0.517160i
$335$	15.3587	−	17.7249i	0.839138	−	0.968417i
$336$	−0.959493	−	0.281733i	−0.0523446	−	0.0153698i
$337$	2.66647	+	18.5457i	0.145252	+	1.01025i	0.923857	+	0.382737i	$0.125018\pi$
$337$	2.66647	+	18.5457i	0.145252	+	1.01025i	−0.778605	+	0.627514i	$0.784073\pi$
$338$	11.5314	+	13.3080i	0.627227	+	0.723859i
$339$	−0.0141178	−	0.0309136i	−0.000766772	−	0.00167900i
$340$	9.57427	−	2.81126i	0.519238	−	0.152462i
$341$	−1.95522	+	4.28133i	−0.105881	+	0.231847i
$342$	−0.568339	+	3.95289i	−0.0307323	+	0.213748i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	−3.45043			−0.186035
$345$	−6.38253	+	18.7627i	−0.343624	+	1.01015i
$346$	2.99403			0.160960
$347$	−22.5971	+	14.5223i	−1.21308	+	0.779597i	−0.981171	−	0.193141i	$-0.938132\pi$
$347$	−22.5971	+	14.5223i	−1.21308	+	0.779597i	−0.231906	+	0.972738i	$0.574496\pi$
$348$	1.22173	−	8.49735i	0.0654918	−	0.455506i
$349$	−11.2223	+	24.5735i	−0.600718	+	1.31539i	0.328027	+	0.944669i	$0.393616\pi$
$349$	−11.2223	+	24.5735i	−0.600718	+	1.31539i	−0.928745	+	0.370720i	$0.879111\pi$
$350$	11.5879	−	3.40252i	0.619401	−	0.181872i
$351$	−2.29830	−	5.03257i	−0.122674	−	0.268619i
$352$	−1.09218	−	1.26044i	−0.0582134	−	0.0671818i
$353$	−1.18952	−	8.27328i	−0.0633117	−	0.440342i	−0.996680	−	0.0814217i	$-0.974054\pi$
$353$	−1.18952	−	8.27328i	−0.0633117	−	0.440342i	0.933368	−	0.358921i	$-0.116855\pi$
$354$	−2.23532	−	0.656349i	−0.118806	−	0.0348845i
$355$	15.5535	−	17.9496i	0.825492	−	0.952668i
$356$	4.09632	+	2.63255i	0.217105	+	0.139525i
$357$	2.03134	+	1.30547i	0.107510	+	0.0690926i
$358$	−0.707443	+	0.816433i	−0.0373895	+	0.0431498i
$359$	33.6854	+	9.89092i	1.77785	+	0.522023i	0.994972	−	0.100156i	$-0.0319342\pi$
$359$	33.6854	+	9.89092i	1.77785	+	0.522023i	0.782875	+	0.622179i	$0.213752\pi$
$360$	−0.588109	−	4.09039i	−0.0309961	−	0.215582i
$361$	1.99842	+	2.30630i	0.105180	+	0.121384i
$362$	2.45581	+	5.37748i	0.129075	+	0.282634i
$363$	7.88552	−	2.31540i	0.413883	−	0.121527i
$364$	−2.29830	+	5.03257i	−0.120464	+	0.263779i
$365$	0.773664	−	5.38095i	0.0404954	−	0.281652i
$366$	11.8846	−	7.63775i	0.621216	−	0.399231i
$367$	−19.1939			−1.00191			−0.500956	−	0.865473i	$-0.667018\pi$
$367$	−19.1939			−1.00191			−0.500956	+	0.865473i	$0.667018\pi$
$368$	−1.15538	−	4.65458i	−0.0602282	−	0.242637i
$369$	−9.16269			−0.476991
$370$	22.4789	−	14.4463i	1.16862	−	0.751027i
$371$	−1.80734	+	12.5703i	−0.0938323	+	0.652618i
$372$	1.17233	−	2.56704i	0.0607825	−	0.133095i
$373$	−1.84120	+	0.540626i	−0.0953339	+	0.0279926i	−0.329052	−	0.944312i	$-0.606729\pi$
$373$	−1.84120	+	0.540626i	−0.0953339	+	0.0279926i	0.233718	+	0.972304i	$0.424911\pi$
$374$	1.67295	+	3.66326i	0.0865064	+	0.189423i
$375$	19.1520	+	22.1026i	0.989004	+	1.14137i
$376$	1.03523	+	7.20018i	0.0533879	+	0.371321i
$377$	−45.5715	−	13.3810i	−2.34705	−	0.689156i
$378$	0.654861	−	0.755750i	0.0336824	−	0.0388716i
$379$	13.6118	+	8.74778i	0.699192	+	0.449343i	0.841343	−	0.540502i	$-0.181766\pi$
$379$	13.6118	+	8.74778i	0.699192	+	0.449343i	−0.142151	+	0.989845i	$0.545402\pi$
$380$	13.8833	+	8.92224i	0.712197	+	0.457701i
$381$	−5.11424	+	5.90215i	−0.262010	+	0.302376i
$382$	3.71517	+	1.09087i	0.190084	+	0.0558138i
$383$	−2.95580	−	20.5580i	−0.151034	−	1.05047i	−0.914491	−	0.404606i	$-0.867409\pi$
$383$	−2.95580	−	20.5580i	−0.151034	−	1.05047i	0.763457	−	0.645859i	$-0.223501\pi$
$384$	0.654861	+	0.755750i	0.0334182	+	0.0385667i
$385$	2.86309	+	6.26929i	0.145917	+	0.319513i
$386$	−6.12399	+	1.79816i	−0.311703	+	0.0915242i
$387$	1.43336	−	3.13862i	0.0728619	−	0.159545i
$388$	−1.61024	+	11.1994i	−0.0817473	+	0.568565i
$389$	−2.27239	+	1.46037i	−0.115215	+	0.0740439i	−0.596979	−	0.802257i	$-0.703632\pi$
$389$	−2.27239	+	1.46037i	−0.115215	+	0.0740439i	0.481764	+	0.876301i	$0.339996\pi$
$390$	−22.8629			−1.15771
$391$	−0.489624	+	11.5700i	−0.0247613	+	0.585118i
$392$	−1.00000			−0.0505076
$393$	7.20819	−	4.63242i	0.363605	−	0.233675i
$394$	1.32878	−	9.24186i	0.0669429	−	0.465598i
$395$	−16.7428	+	36.6615i	−0.842419	+	1.84464i
$396$	1.60025	−	0.469875i	0.0804154	−	0.0236121i
$397$	9.32828	+	20.4261i	0.468173	+	1.02516i	0.985548	+	0.169397i	$0.0541821\pi$
$397$	9.32828	+	20.4261i	0.468173	+	1.02516i	−0.517375	+	0.855759i	$0.673091\pi$
$398$	−7.78476	−	8.98409i	−0.390215	−	0.450332i
$399$	0.568339	+	3.95289i	0.0284526	+	0.197892i
$400$	−11.5879	−	3.40252i	−0.579396	−	0.170126i
$401$	9.62846	−	11.1118i	0.480822	−	0.554898i	−0.462568	−	0.886584i	$-0.653072\pi$
$401$	9.62846	−	11.1118i	0.480822	−	0.554898i	0.943390	+	0.331686i	$0.107617\pi$
$402$	−4.77448	−	3.06837i	−0.238130	−	0.153037i
$403$	−13.1347	−	8.44114i	−0.654284	−	0.420483i
$404$	12.4033	−	14.3142i	0.617088	−	0.712158i
$405$	3.96506	+	1.16425i	0.197025	+	0.0578518i
$406$	−1.22173	−	8.49735i	−0.0606337	−	0.421716i
$407$	7.06210	+	8.15010i	0.350055	+	0.403985i
$408$	−1.00309	−	2.19646i	−0.0496602	−	0.108741i
$409$	22.1101	−	6.49210i	1.09327	−	0.321014i	0.315096	−	0.949060i	$-0.397963\pi$
$409$	22.1101	−	6.49210i	1.09327	−	0.321014i	0.778176	+	0.628046i	$0.216145\pi$
$410$	−15.7294	+	34.4426i	−0.776821	+	1.70100i
$411$	1.38335	−	9.62139i	0.0682355	−	0.474588i
$412$	12.9273	−	8.30788i	0.636883	−	0.409300i
$413$	−2.32969			−0.114636
$414$	4.71391	+	0.882615i	0.231676	+	0.0433781i
$415$	5.41010			0.265572
$416$	4.65427	−	2.99112i	0.228194	−	0.146652i
$417$	3.22534	−	22.4327i	0.157946	−	1.09854i
$418$	−2.76685	+	6.05855i	−0.135331	+	0.296333i
$419$	13.0191	−	3.82274i	0.636023	−	0.186753i	0.0522030	−	0.998636i	$-0.483376\pi$
$419$	13.0191	−	3.82274i	0.636023	−	0.186753i	0.583820	+	0.811883i	$0.301558\pi$
$420$	−1.71668	−	3.75901i	−0.0837655	−	0.183421i
$421$	−0.152200	−	0.175648i	−0.00741777	−	0.00856056i	0.752029	−	0.659131i	$-0.229076\pi$
$421$	−0.152200	−	0.175648i	−0.00741777	−	0.00856056i	−0.759446	+	0.650570i	$0.774530\pi$
$422$	3.74692	+	26.0604i	0.182397	+	1.26860i
$423$	−6.97957	−	2.04939i	−0.339358	−	0.0996446i
$424$	8.31645	−	9.59769i	0.403882	−	0.466105i
$425$	24.5328	+	15.7663i	1.19002	+	0.764777i
$426$	−4.83501	−	3.10727i	−0.234257	−	0.150548i
$427$	9.25136	−	10.6766i	0.447704	−	0.516679i
$428$	0.476102	+	0.139796i	0.0230133	+	0.00675731i
$429$	−1.31317	−	9.13327i	−0.0634003	−	0.440959i
$430$	−9.33749	−	10.7760i	−0.450294	−	0.519667i
$431$	7.16603	+	15.6914i	0.345175	+	0.755828i	1.00000		4.76847e-5i	$1.51785e-5\pi$
$431$	7.16603	+	15.6914i	0.345175	+	0.755828i	−0.654825	+	0.755781i	$0.727258\pi$
$432$	−0.959493	+	0.281733i	−0.0461636	+	0.0135549i
$433$	8.24075	−	18.0447i	0.396025	−	0.867175i	−0.601632	−	0.798773i	$-0.705483\pi$
$433$	8.24075	−	18.0447i	0.396025	−	0.867175i	0.997658	−	0.0684016i	$-0.0217899\pi$
$434$	0.401622	−	2.79335i	0.0192785	−	0.134085i
$435$	29.8443	−	19.1798i	1.43092	−	0.919599i
$436$	20.2161			0.968174
$437$	−14.9917	+	11.9189i	−0.717151	+	0.570159i
$438$	−1.31551			−0.0628576
$439$	−3.32720	+	2.13826i	−0.158798	+	0.102054i	−0.617627	−	0.786471i	$-0.711906\pi$
$439$	−3.32720	+	2.13826i	−0.158798	+	0.102054i	0.458828	+	0.888525i	$0.348269\pi$
$440$	0.980850	−	6.82196i	0.0467602	−	0.325224i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	−12.8181	+	3.76373i	−0.609694	+	0.179022i
$443$	−13.2572	−	29.0293i	−0.629871	−	1.37922i	−0.908118	−	0.418715i	$-0.862481\pi$
$443$	−13.2572	−	29.0293i	−0.629871	−	1.37922i	0.278247	−	0.960510i	$-0.410247\pi$
$444$	−4.23437	−	4.88672i	−0.200954	−	0.231914i
$445$	2.86368	+	19.9173i	0.135752	+	0.944173i
$446$	26.1800	+	7.68714i	1.23966	+	0.363997i
$447$	−4.40944	+	5.08876i	−0.208559	+	0.240690i
$448$	0.841254	+	0.540641i	0.0397455	+	0.0255429i
$449$	−19.6422	−	12.6232i	−0.926971	−	0.595728i	−0.0122986	−	0.999924i	$-0.503915\pi$
$449$	−19.6422	−	12.6232i	−0.926971	−	0.595728i	−0.914672	+	0.404196i	$0.867551\pi$
$450$	7.90884	−	9.12729i	0.372826	−	0.430265i
$451$	−14.6626	−	4.30532i	−0.690433	−	0.202730i
$452$	0.00483653	+	0.0336388i	0.000227491	+	0.00158224i
$453$	−11.2146	−	12.9423i	−0.526906	−	0.608082i
$454$	−5.05418	−	11.0671i	−0.237204	−	0.519405i
$455$	−21.9368	+	6.44123i	−1.02841	+	0.301970i
$456$	1.65897	−	3.63265i	0.0776886	−	0.170114i
$457$	−2.23827	+	15.5675i	−0.104702	+	0.728216i	0.868069	+	0.496444i	$0.165361\pi$
$457$	−2.23827	+	15.5675i	−0.104702	+	0.728216i	−0.972770	+	0.231772i	$0.925548\pi$
$458$	7.21902	−	4.63939i	0.337323	−	0.216784i
$459$	2.41466			0.112707
$460$	11.4100	−	16.2045i	0.531996	−	0.755537i
$461$	−31.8065			−1.48138			−0.740688	−	0.671849i	$-0.765500\pi$
$461$	−31.8065			−1.48138			−0.740688	+	0.671849i	$0.765500\pi$
$462$	1.40305	−	0.901683i	0.0652756	−	0.0419501i
$463$	0.402619	−	2.80028i	0.0187113	−	0.130140i	−0.978325	−	0.207077i	$-0.933605\pi$
$463$	0.402619	−	2.80028i	0.0187113	−	0.130140i	0.997036	+	0.0769370i	$0.0245140\pi$
$464$	−3.56623	+	7.80894i	−0.165558	+	0.362521i
$465$	11.1897	−	3.28558i	0.518908	−	0.152365i
$466$	−7.60146	−	16.6449i	−0.352131	−	0.771059i
$467$	−12.0866	−	13.9486i	−0.559300	−	0.645466i	0.403725	−	0.914881i	$-0.367715\pi$
$467$	−12.0866	−	13.9486i	−0.559300	−	0.645466i	−0.963024	+	0.269414i	$0.913170\pi$
$468$	0.787362	+	5.47623i	0.0363958	+	0.253139i
$469$	−5.44554	−	1.59896i	−0.251452	−	0.0738329i
$470$	−19.6854	+	22.7181i	−0.908018	+	1.04791i
$471$	−4.52166	−	2.90590i	−0.208347	−	0.133897i
$472$	1.95986	+	1.25952i	0.0902097	+	0.0579743i
$473$	3.76849	−	4.34907i	0.173276	−	0.199971i
$474$	9.35791	+	2.74773i	0.429823	+	0.126207i
$475$	6.86391	+	47.7396i	0.314938	+	2.19044i
$476$	−1.58127	−	1.82488i	−0.0724773	−	0.0836433i
$477$	5.27559	+	11.5519i	0.241553	+	0.528927i
$478$	10.0536	−	2.95201i	0.459842	−	0.135022i
$479$	10.6810	−	23.3882i	0.488030	−	1.06864i	−0.492147	−	0.870512i	$-0.663788\pi$
$479$	10.6810	−	23.3882i	0.488030	−	1.06864i	0.980177	−	0.198124i	$-0.0634848\pi$
$480$	−0.588109	+	4.09039i	−0.0268434	+	0.186700i
$481$	−30.0948	+	19.3407i	−1.37220	+	0.881862i
$482$	−3.56785			−0.162511
$483$	4.77163	−	0.481201i	0.217117	−	0.0218954i
$484$	−8.21843			−0.373565
$485$	−39.3345	+	25.2787i	−1.78609	+	1.14785i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	−0.154000	+	0.337214i	−0.00697843	+	0.0152806i	−0.913089	−	0.407760i	$-0.866310\pi$
$487$	−0.154000	+	0.337214i	−0.00697843	+	0.0152806i	0.906111	+	0.423041i	$0.139037\pi$
$488$	−13.5550	+	3.98010i	−0.613604	+	0.180170i
$489$	−7.23536	−	15.8432i	−0.327194	−	0.716455i
$490$	−2.70618	−	3.12310i	−0.122253	−	0.141087i
$491$	2.68420	+	18.6690i	0.121136	+	0.842521i	0.956272	+	0.292478i	$0.0944797\pi$
$491$	2.68420	+	18.6690i	0.121136	+	0.842521i	−0.835136	+	0.550043i	$0.814611\pi$
$492$	8.79154	+	2.58143i	0.396353	+	0.116380i
$493$	13.5748	−	15.6661i	0.611376	−	0.705566i
$494$	−18.5870	−	11.9451i	−0.836268	−	0.537437i
$495$	5.79802	+	3.72616i	0.260602	+	0.167478i
$496$	−1.84806	+	2.13278i	−0.0829805	+	0.0957646i
$497$	−5.51458	−	1.61923i	−0.247363	−	0.0726322i
$498$	−0.186315	−	1.29585i	−0.00834898	−	0.0580684i
$499$	−1.32618	−	1.53049i	−0.0593680	−	0.0685143i	0.725289	−	0.688445i	$-0.241706\pi$
$499$	−1.32618	−	1.53049i	−0.0593680	−	0.0685143i	−0.784657	+	0.619930i	$0.787161\pi$
$500$	−12.1492	−	26.6030i	−0.543328	−	1.18972i
$501$	16.7738	−	4.92523i	0.749398	−	0.220043i
$502$	7.20252	−	15.7713i	0.321464	−	0.703908i
$503$	−0.291362	+	2.02647i	−0.0129912	+	0.0903559i	−0.995285	−	0.0969886i	$-0.969079\pi$
$503$	−0.291362	+	2.02647i	−0.0129912	+	0.0903559i	0.982294	+	0.187344i	$0.0599881\pi$
$504$	−0.841254	+	0.540641i	−0.0374724	+	0.0240821i
$505$	78.2702			3.48298
$506$	7.12871	+	3.62735i	0.316910	+	0.161255i
$507$	17.6090			0.782042
$508$	6.56990	−	4.22222i	0.291492	−	0.187331i
$509$	−2.92309	+	20.3305i	−0.129564	+	0.901135i	0.816544	+	0.577283i	$0.195887\pi$
$509$	−2.92309	+	20.3305i	−0.129564	+	0.901135i	−0.946108	+	0.323852i	$0.895022\pi$
$510$	4.14521	−	9.07674i	0.183553	−	0.401925i
$511$	−1.26222	+	0.370623i	−0.0558375	+	0.0163954i
$512$	−0.415415	−	0.909632i	−0.0183589	−	0.0402004i
$513$	2.61521	+	3.01811i	0.115464	+	0.133253i
$514$	0.0493850	+	0.343480i	0.00217828	+	0.0151503i
$515$	60.9299	+	17.8906i	2.68489	+	0.788355i
$516$	−2.25955	+	2.60766i	−0.0994713	+	0.114796i
$517$	−10.2061	−	6.55905i	−0.448863	−	0.288467i
$518$	−5.43960	−	3.49582i	−0.239002	−	0.153597i
$519$	1.96068	−	2.26274i	0.0860641	−	0.0993233i
$520$	21.9368	+	6.44123i	0.961993	+	0.282467i
$521$	−2.05632	−	14.3020i	−0.0900888	−	0.626582i	−0.983978	−	0.178293i	$-0.942943\pi$
$521$	−2.05632	−	14.3020i	−0.0900888	−	0.626582i	0.893889	−	0.448289i	$-0.147966\pi$
$522$	−5.62180	−	6.48791i	−0.246060	−	0.283968i
$523$	−11.2709	−	24.6798i	−0.492841	−	1.07917i	−0.978730	−	0.205151i	$-0.934231\pi$
$523$	−11.2709	−	24.6798i	−0.492841	−	1.07917i	0.485889	−	0.874020i	$-0.338496\pi$
$524$	−8.22131	+	2.41399i	−0.359149	+	0.105456i
$525$	5.01702	−	10.9857i	0.218961	−	0.479457i
$526$	0.470983	−	3.27576i	0.0205358	−	0.142830i
$527$	5.73259	−	3.68411i	0.249716	−	0.160483i
$528$	−1.66780			−0.0725819
$529$	13.5394	+	18.5926i	0.588669	+	0.808374i
$530$	52.4803			2.27960
$531$	−1.95986	+	1.25952i	−0.0850506	+	0.0546587i
$532$	0.568339	−	3.95289i	0.0246406	−	0.171379i
$533$	21.0586	−	46.1119i	0.912150	−	1.99733i
$534$	4.67207	−	1.37184i	0.202180	−	0.0593654i
$535$	0.851821	+	1.86523i	0.0368274	+	0.0806408i
$536$	3.71662	+	4.28921i	0.160534	+	0.185266i
$537$	0.153742	+	1.06930i	0.00663446	+	0.0461437i
$538$	−15.4532	−	4.53748i	−0.666236	−	0.195625i
$539$	1.09218	−	1.26044i	0.0470435	−	0.0542911i
$540$	−3.47644	−	2.23417i	−0.149602	−	0.0961434i
$541$	−14.7672	−	9.49030i	−0.634891	−	0.408020i	0.183227	−	0.983071i	$-0.441346\pi$
$541$	−14.7672	−	9.49030i	−0.634891	−	0.408020i	−0.818118	+	0.575051i	$0.804982\pi$
$542$	1.79516	−	2.07172i	0.0771086	−	0.0889881i
$543$	5.67225	+	1.66552i	0.243419	+	0.0714744i
$544$	0.343642	+	2.39009i	0.0147335	+	0.102474i
$545$	54.7083	+	63.1367i	2.34345	+	2.70448i
$546$	2.29830	+	5.03257i	0.0983581	+	0.215374i
$547$	−35.8091	+	10.5145i	−1.53109	+	0.449568i	−0.935383	−	0.353636i	$-0.884945\pi$
$547$	−35.8091	+	10.5145i	−1.53109	+	0.449568i	−0.595705	+	0.803204i	$0.703127\pi$
$548$	−4.03797	+	8.84192i	−0.172493	+	0.377708i
$549$	2.01051	−	13.9834i	0.0858066	−	0.596798i
$550$	16.9448	−	10.8897i	0.722528	−	0.464340i
$551$	34.2834			1.46052
$552$	−4.27431	−	2.17493i	−0.181927	−	0.0925710i
$553$	9.75298			0.414739
$554$	9.28311	−	5.96589i	0.394402	−	0.253466i
$555$	3.80275	−	26.4487i	0.161418	−	1.12268i
$556$	−9.41473	+	20.6154i	−0.399273	+	0.874287i
$557$	11.7344	−	3.44553i	0.497202	−	0.145992i	−0.0235110	−	0.999724i	$-0.507484\pi$
$557$	11.7344	−	3.44553i	0.497202	−	0.145992i	0.520713	+	0.853732i	$0.325666\pi$
$558$	−1.17233	−	2.56704i	−0.0496287	−	0.108672i
$559$	12.5011	+	14.4270i	0.528739	+	0.610197i
$560$	0.588109	+	4.09039i	0.0248521	+	0.172850i
$561$	3.86406	+	1.13459i	0.163141	+	0.0479024i
$562$	−17.4486	+	20.1368i	−0.736025	+	0.849418i
$563$	20.3545	+	13.0810i	0.857839	+	0.551300i	0.894011	−	0.448046i	$-0.147880\pi$
$563$	20.3545	+	13.0810i	0.857839	+	0.551300i	−0.0361714	+	0.999346i	$0.511516\pi$
$564$	6.11947	+	3.93274i	0.257676	+	0.165598i
$565$	−0.0919687	+	0.106138i	−0.00386915	+	0.00446524i
$566$	20.0532	+	5.88814i	0.842897	+	0.247497i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	3.76374	+	4.34359i	0.157923	+	0.182253i
$569$	−0.161273	−	0.353139i	−0.00676092	−	0.0148044i	0.906221	−	0.422803i	$-0.138954\pi$
$569$	−0.161273	−	0.353139i	−0.00676092	−	0.0148044i	−0.912982	+	0.407999i	$0.866227\pi$
$570$	15.8346	−	4.64946i	0.663238	−	0.194744i
$571$	−3.20189	+	7.01117i	−0.133995	+	0.293408i	−0.964721	−	0.263273i	$-0.915198\pi$
$571$	−3.20189	+	7.01117i	−0.133995	+	0.293408i	0.830726	+	0.556681i	$0.187925\pi$
$572$	−1.31317	+	9.13327i	−0.0549062	+	0.381881i
$573$	3.25734	−	2.09337i	0.136077	−	0.0874517i
$574$	9.16269			0.382443
$575$	57.6276	−	5.81152i	2.40324	−	0.242357i
$576$	1.00000			0.0416667
$577$	−14.2382	+	9.15035i	−0.592745	+	0.380934i	−0.802352	−	0.596852i	$-0.796418\pi$
$577$	−14.2382	+	9.15035i	−0.592745	+	0.380934i	0.209606	+	0.977786i	$0.432782\pi$
$578$	−1.58957	+	11.0557i	−0.0661175	+	0.459857i
$579$	−2.65140	+	5.80575i	−0.110188	+	0.241279i
$580$	−34.0389	+	9.99473i	−1.41339	+	0.415009i
$581$	−0.543851	−	1.19087i	−0.0225628	−	0.0494055i
$582$	7.40949	+	8.55100i	0.307133	+	0.354451i
$583$	3.01428	+	20.9648i	0.124839	+	0.868274i
$584$	1.26222	+	0.370623i	0.0522312	+	0.0153365i
$585$	−14.9720	+	17.2787i	−0.619018	+	0.714384i
$586$	−0.126208	−	0.0811090i	−0.00521361	−	0.00335058i
$587$	−3.23493	−	2.07896i	−0.133520	−	0.0858079i	0.472176	−	0.881504i	$-0.343469\pi$
$587$	−3.23493	−	2.07896i	−0.133520	−	0.0858079i	−0.605696	+	0.795696i	$0.707105\pi$
$588$	−0.654861	+	0.755750i	−0.0270060	+	0.0311666i
$589$	10.8135	+	3.17514i	0.445563	+	0.130829i
$590$	1.37011	+	9.52932i	0.0564065	+	0.392316i
$591$	−6.11437	−	7.05636i	−0.251511	−	0.290260i
$592$	2.68610	+	5.88174i	0.110398	+	0.241738i
$593$	−22.5630	+	6.62511i	−0.926553	+	0.272061i	−0.709993	−	0.704209i	$-0.751302\pi$
$593$	−22.5630	+	6.62511i	−0.926553	+	0.272061i	−0.216560	+	0.976269i	$0.569484\pi$
$594$	0.692831	−	1.51709i	0.0284272	−	0.0622469i
$595$	1.42008	−	9.87691i	0.0582178	−	0.404914i
$596$	5.66449	−	3.64035i	0.232027	−	0.149114i
$597$	−11.8876			−0.486529
$598$	−15.2758	+	21.6946i	−0.624674	+	0.887159i
$599$	−13.0669			−0.533900			−0.266950	−	0.963710i	$-0.586016\pi$
$599$	−13.0669			−0.533900			−0.266950	+	0.963710i	$0.586016\pi$
$600$	−10.1599	+	6.52939i	−0.414777	+	0.266561i
$601$	−2.91763	+	20.2926i	−0.119013	+	0.827751i	0.839634	+	0.543152i	$0.182769\pi$
$601$	−2.91763	+	20.2926i	−0.119013	+	0.827751i	−0.958647	+	0.284598i	$0.908140\pi$
$602$	−1.43336	+	3.13862i	−0.0584195	+	0.127921i
$603$	−5.44554	+	1.59896i	−0.221760	+	0.0651145i
$604$	7.11403	+	15.5776i	0.289466	+	0.633842i
$605$	−22.2405	−	25.6669i	−0.904206	−	1.04351i
$606$	−2.69550	−	18.7476i	−0.109497	−	0.761570i
$607$	11.2528	+	3.30413i	0.456738	+	0.134111i	0.502006	−	0.864864i	$-0.332596\pi$
$607$	11.2528	+	3.30413i	0.456738	+	0.134111i	−0.0452671	+	0.998975i	$0.514414\pi$
$608$	−2.61521	+	3.01811i	−0.106061	+	0.122401i
$609$	−7.22193	−	4.64126i	−0.292648	−	0.188073i
$610$	−49.1124	−	31.5626i	−1.98850	−	1.27793i
$611$	26.3548	−	30.4151i	1.06620	−	1.23046i
$612$	−2.31685	−	0.680289i	−0.0936532	−	0.0274991i
$613$	−4.40692	−	30.6508i	−0.177994	−	1.23797i	−0.861397	−	0.507933i	$-0.830410\pi$
$613$	−4.40692	−	30.6508i	−0.177994	−	1.23797i	0.683403	−	0.730042i	$-0.260499\pi$
$614$	−0.698867	−	0.806535i	−0.0282040	−	0.0325491i
$615$	15.7294	+	34.4426i	0.634272	+	1.38886i
$616$	−1.60025	+	0.469875i	−0.0644758	+	0.0189318i
$617$	3.62489	−	7.93741i	0.145933	−	0.319548i	−0.822524	−	0.568731i	$-0.807435\pi$
$617$	3.62489	−	7.93741i	0.145933	−	0.319548i	0.968456	+	0.249183i	$0.0801620\pi$
$618$	2.18691	−	15.2103i	0.0879705	−	0.611848i
$619$	−3.11866	+	2.00424i	−0.125350	+	0.0805573i	−0.601813	−	0.798637i	$-0.705555\pi$
$619$	−3.11866	+	2.00424i	−0.125350	+	0.0805573i	0.476464	+	0.879194i	$0.341918\pi$
$620$	−11.6621			−0.468360
$621$	3.75399	−	2.98455i	0.150643	−	0.119766i
$622$	−3.06377			−0.122846
$623$	4.09632	−	2.63255i	0.164116	−	0.105471i
$624$	0.787362	−	5.47623i	0.0315197	−	0.219224i
$625$	25.1208	−	55.0068i	1.00483	−	2.20027i
$626$	11.0236	−	3.23682i	0.440592	−	0.129369i
$627$	2.76685	+	6.05855i	0.110497	+	0.241955i
$628$	3.51982	+	4.06209i	0.140456	+	0.162095i
$629$	−2.22201	−	15.4544i	−0.0885975	−	0.616209i
$630$	−3.96506	−	1.16425i	−0.157972	−	0.0463846i
$631$	−19.4827	+	22.4842i	−0.775593	+	0.895082i	−0.996783	−	0.0801489i	$-0.974460\pi$
$631$	−19.4827	+	22.4842i	−0.775593	+	0.895082i	0.221190	+	0.975231i	$0.429006\pi$
$632$	−8.20473	−	5.27286i	−0.326367	−	0.209743i
$633$	22.1489	+	14.2342i	0.880339	+	0.565759i
$634$	15.6004	−	18.0038i	0.619570	−	0.715022i
$635$	30.9657	+	9.09236i	1.22884	+	0.360819i
$636$	−1.80734	−	12.5703i	−0.0716656	−	0.498445i
$637$	3.62304	+	4.18121i	0.143550	+	0.165666i
$638$	−5.94777	−	13.0238i	−0.235474	−	0.515617i
$639$	−5.51458	+	1.61923i	−0.218153	+	0.0640556i
$640$	1.71668	−	3.75901i	0.0678578	−	0.148588i
$641$	0.608871	−	4.23479i	0.0240490	−	0.167264i	−0.974258	−	0.225438i	$-0.927619\pi$
$641$	0.608871	−	4.23479i	0.0240490	−	0.167264i	0.998306	+	0.0581739i	$0.0185278\pi$
$642$	0.417432	−	0.268267i	0.0164747	−	0.0105877i
$643$	−2.12433			−0.0837754			−0.0418877	−	0.999122i	$-0.513337\pi$
$643$	−2.12433			−0.0837754			−0.0418877	+	0.999122i	$0.513337\pi$
$644$	−4.71391	−	0.882615i	−0.185754	−	0.0347799i
$645$	−14.2587			−0.561437
$646$	8.11225	−	5.21342i	0.319172	−	0.205119i
$647$	−1.88556	+	13.1144i	−0.0741291	+	0.515579i	0.918598	+	0.395193i	$0.129322\pi$
$647$	−1.88556	+	13.1144i	−0.0741291	+	0.515579i	−0.992727	+	0.120386i	$0.961587\pi$
$648$	−0.415415	+	0.909632i	−0.0163190	+	0.0357337i
$649$	−3.72807	+	1.09466i	−0.146340	+	0.0429692i
$650$	27.7569	+	60.7791i	1.08871	+	2.38395i
$651$	−1.84806	−	2.13278i	−0.0724313	−	0.0835902i
$652$	2.47872	+	17.2399i	0.0970743	+	0.675166i
$653$	19.5715	+	5.74670i	0.765891	+	0.224886i	0.641267	−	0.767318i	$-0.278409\pi$
$653$	19.5715	+	5.74670i	0.765891	+	0.224886i	0.124624	+	0.992204i	$0.460227\pi$
$654$	13.2387	−	15.2783i	0.517675	−	0.597428i
$655$	−29.7875	−	19.1432i	−1.16389	−	0.747988i
$656$	−7.70815	−	4.95373i	−0.300953	−	0.193410i
$657$	−0.861477	+	0.994198i	−0.0336094	+	0.0387874i
$658$	6.97957	+	2.04939i	0.272092	+	0.0798934i
$659$	5.04109	+	35.0615i	0.196373	+	1.36580i	0.814700	+	0.579882i	$0.196901\pi$
$659$	5.04109	+	35.0615i	0.196373	+	1.36580i	−0.618328	+	0.785921i	$0.712189\pi$
$660$	−4.51338	−	5.20871i	−0.175683	−	0.202749i
$661$	−11.8121	−	25.8648i	−0.459436	−	1.00602i	−0.987616	−	0.156891i	$-0.949853\pi$
$661$	−11.8121	−	25.8648i	−0.459436	−	1.00602i	0.528180	−	0.849132i	$-0.322875\pi$
$662$	−0.466709	+	0.137038i	−0.0181391	+	0.00532613i
$663$	−5.54962	+	12.1520i	−0.215529	+	0.471943i
$664$	−0.186315	+	1.29585i	−0.00723043	+	0.0502888i
$665$	13.8833	−	8.92224i	0.538370	−	0.345990i
$666$	−6.46606			−0.250555
$667$	1.74073	−	41.1341i	0.0674015	−	1.59272i
$668$	−17.4819			−0.676396
$669$	22.9538	−	14.7515i	0.887445	−	0.570327i
$670$	−3.33777	+	23.2147i	−0.128949	+	0.896863i
$671$	9.78777	−	21.4322i	0.377853	−	0.827382i
$672$	0.959493	−	0.281733i	0.0370132	−	0.0108681i
$673$	14.3480	+	31.4177i	0.553074	+	1.21106i	0.955332	+	0.295536i	$0.0954982\pi$
$673$	14.3480	+	31.4177i	0.553074	+	1.21106i	−0.402258	+	0.915526i	$0.631775\pi$
$674$	−12.2698	−	14.1601i	−0.472614	−	0.545425i
$675$	−1.71876	−	11.9542i	−0.0661549	−	0.460118i
$676$	−16.8957	−	4.96102i	−0.649834	−	0.190809i
$677$	−7.79697	+	8.99818i	−0.299662	+	0.345828i	−0.885533	−	0.464576i	$-0.846207\pi$
$677$	−7.79697	+	8.99818i	−0.299662	+	0.345828i	0.585872	+	0.810404i	$0.300752\pi$
$678$	0.0285898	+	0.0183735i	0.00109798	+	0.000705631i
$679$	9.51845	+	6.11713i	0.365284	+	0.234754i
$680$	−6.53451	+	7.54123i	−0.250587	+	0.289193i
$681$	−11.6737	−	3.42772i	−0.447339	−	0.131350i
$682$	−0.669828	−	4.65875i	−0.0256490	−	0.178393i
$683$	24.4555	+	28.2231i	0.935762	+	1.07993i	0.996650	+	0.0817821i	$0.0260612\pi$
$683$	24.4555	+	28.2231i	0.935762	+	1.07993i	−0.0608884	+	0.998145i	$0.519393\pi$
$684$	−1.65897	−	3.63265i	−0.0634325	−	0.138898i
$685$	−38.5416	+	11.3168i	−1.47260	+	0.432394i
$686$	−0.415415	+	0.909632i	−0.0158606	+	0.0347299i
$687$	1.22124	−	8.49393i	0.0465933	−	0.324063i
$688$	2.90269	−	1.86545i	0.110664	−	0.0711194i
$689$	−70.2608			−2.67673
$690$	−4.77453	−	19.2348i	−0.181763	−	0.732257i
$691$	23.8002			0.905400			0.452700	−	0.891663i	$-0.350461\pi$
$691$	23.8002			0.905400			0.452700	+	0.891663i	$0.350461\pi$
$692$	−2.51874	+	1.61870i	−0.0957482	+	0.0615336i
$693$	0.237353	−	1.65083i	0.00901631	−	0.0627098i
$694$	11.1586	−	24.4338i	0.423573	−	0.927496i
$695$	−89.8618	+	26.3858i	−3.40865	+	1.00087i
$696$	3.56623	+	7.80894i	0.135177	+	0.295997i
$697$	14.4887	+	16.7208i	0.548798	+	0.633346i
$698$	−3.84460	−	26.7398i	−0.145520	−	1.01212i
$699$	−17.5573	−	5.15528i	−0.664077	−	0.194990i
$700$	−7.90884	+	9.12729i	−0.298926	+	0.344979i
$701$	8.82274	+	5.67003i	0.333230	+	0.214154i	0.696546	−	0.717512i	$-0.254719\pi$
$701$	8.82274	+	5.67003i	0.333230	+	0.214154i	−0.363316	+	0.931666i	$0.618355\pi$
$702$	4.65427	+	2.99112i	0.175664	+	0.112892i
$703$	16.9101	−	19.5153i	0.637777	−	0.736034i
$704$	1.60025	+	0.469875i	0.0603116	+	0.0177091i
$705$	4.27804	+	29.7544i	0.161120	+	1.12062i
$706$	5.47356	+	6.31683i	0.206000	+	0.237737i
$707$	−7.86813	−	17.2288i	−0.295911	−	0.647955i
$708$	2.23532	−	0.656349i	0.0840084	−	0.0246671i
$709$	−9.25044	+	20.2556i	−0.347408	+	0.760717i	0.652588	+	0.757713i	$0.273683\pi$
$709$	−9.25044	+	20.2556i	−0.347408	+	0.760717i	−0.999995	+	0.00300352i	$0.999044\pi$
$710$	−3.38009	+	23.5090i	−0.126852	+	0.882278i
$711$	8.20473	−	5.27286i	0.307701	−	0.197748i
$712$	−4.86931			−0.182485
$713$	4.35866	−	12.8131i	0.163233	−	0.479855i
$714$	−2.41466			−0.0903665
$715$	−32.0778	+	20.6151i	−1.19964	+	0.770962i
$716$	0.153742	−	1.06930i	0.00574561	−	0.0399616i
$717$	4.35274	−	9.53117i	0.162556	−	0.355948i
$718$	−33.6854	+	9.89092i	−1.25713	+	0.369126i
$719$	−8.61762	−	18.8700i	−0.321383	−	0.703731i	0.678130	−	0.734942i	$-0.262791\pi$
$719$	−8.61762	−	18.8700i	−0.321383	−	0.703731i	−0.999513	+	0.0312116i	$0.990063\pi$
$720$	2.70618	+	3.12310i	0.100853	+	0.116391i
$721$	−2.18691	−	15.2103i	−0.0814449	−	0.566461i
$722$	−2.92806	−	0.859755i	−0.108971	−	0.0319968i
$723$	−2.33644	+	2.69640i	−0.0868933	+	0.100280i
$724$	−4.97325	−	3.19611i	−0.184829	−	0.118783i
$725$	−87.2203	−	56.0531i	−3.23928	−	2.08176i
$726$	−5.38193	+	6.21107i	−0.199742	+	0.230515i
$727$	2.48714	+	0.730289i	0.0922427	+	0.0270849i	0.327528	−	0.944841i	$-0.393784\pi$
$727$	2.48714	+	0.730289i	0.0922427	+	0.0270849i	−0.235286	+	0.971926i	$0.575603\pi$
$728$	−0.787362	−	5.47623i	−0.0291816	−	0.202962i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	2.25832	+	4.94502i	0.0835840	+	0.183023i
$731$	−7.99415	+	2.34729i	−0.295674	+	0.0868178i
$732$	−5.86866	+	12.8506i	−0.216912	+	0.474970i
$733$	−3.43016	+	23.8573i	−0.126696	+	0.881190i	0.823006	+	0.568033i	$0.192296\pi$
$733$	−3.43016	+	23.8573i	−0.126696	+	0.881190i	−0.949701	+	0.313157i	$0.898614\pi$
$734$	16.1469	−	10.3770i	0.595993	−	0.383022i
$735$	−4.13245			−0.152428
$736$	3.48842	+	3.29104i	0.128585	+	0.121309i
$737$	−9.46552			−0.348667
$738$	7.70815	−	4.95373i	0.283741	−	0.182349i
$739$	3.93739	−	27.3852i	0.144839	−	1.00738i	−0.779662	−	0.626201i	$-0.784609\pi$
$739$	3.93739	−	27.3852i	0.144839	−	1.00738i	0.924501	−	0.381179i	$-0.124482\pi$
$740$	−11.1002	+	24.3060i	−0.408050	+	0.893505i
$741$	−21.1994	+	6.22471i	−0.778780	+	0.228670i
$742$	−5.27559	−	11.5519i	−0.193673	−	0.424085i
$743$	16.8487	+	19.4445i	0.618121	+	0.713349i	0.975349	−	0.220668i	$-0.0708237\pi$
$743$	16.8487	+	19.4445i	0.618121	+	0.713349i	−0.357228	+	0.934017i	$0.616278\pi$
$744$	0.401622	+	2.79335i	0.0147242	+	0.102409i
$745$	26.6983	+	7.83933i	0.978150	+	0.287211i
$746$	1.25663	−	1.45023i	0.0460087	−	0.0530968i
$747$	−1.10135	−	0.707794i	−0.0402962	−	0.0258968i
$748$	−3.38788	−	2.17726i	−0.123873	−	0.0796086i
$749$	0.324943	−	0.375004i	0.0118732	−	0.0137024i
$750$	−28.0612	−	8.23952i	−1.02465	−	0.300865i
$751$	3.71981	+	25.8718i	0.135738	+	0.944077i	0.937884	+	0.346949i	$0.112782\pi$
$751$	3.71981	+	25.8718i	0.135738	+	0.944077i	−0.802146	+	0.597128i	$0.796309\pi$
$752$	−4.76360	−	5.49749i	−0.173711	−	0.200473i
$753$	−7.20252	−	15.7713i	−0.262474	−	0.574738i
$754$	45.5715	−	13.3810i	1.65961	−	0.487307i
$755$	−29.3984	+	64.3735i	−1.06992	+	2.34279i
$756$	−0.142315	+	0.989821i	−0.00517594	+	0.0359995i
$757$	−16.8219	+	10.8108i	−0.611404	+	0.392926i	−0.809383	−	0.587281i	$-0.800198\pi$
$757$	−16.8219	+	10.8108i	−0.611404	+	0.392926i	0.197979	+	0.980206i	$0.436562\pi$
$758$	−16.1804			−0.587698
$759$	7.40968	−	3.01211i	0.268954	−	0.109333i
$760$	−16.5031			−0.598630
$761$	1.14625	−	0.736649i	0.0415515	−	0.0267035i	−0.519700	−	0.854349i	$-0.673956\pi$
$761$	1.14625	−	0.736649i	0.0415515	−	0.0267035i	0.561252	+	0.827645i	$0.310320\pi$
$762$	1.11143	−	7.73017i	0.0402629	−	0.280034i
$763$	8.39806	−	18.3892i	0.304030	−	0.665733i
$764$	−3.71517	+	1.09087i	−0.134410	+	0.0394663i
$765$	−4.14521	−	9.07674i	−0.149870	−	0.328170i
$766$	13.6011	+	15.6965i	0.491427	+	0.567137i
$767$	−1.83431	−	12.7579i	−0.0662330	−	0.460661i
$768$	−0.959493	−	0.281733i	−0.0346227	−	0.0101661i
$769$	26.9825	−	31.1395i	0.973015	−	1.12292i	−0.0193780	−	0.999812i	$-0.506169\pi$
$769$	26.9825	−	31.1395i	0.973015	−	1.12292i	0.992393	−	0.123107i	$-0.0392859\pi$
$770$	−5.79802	−	3.72616i	−0.208946	−	0.134281i
$771$	0.291925	+	0.187609i	0.0105134	+	0.00675657i
$772$	4.17966	−	4.82359i	0.150429	−	0.173605i
$773$	21.0666	+	6.18572i	0.757713	+	0.222485i	0.637697	−	0.770287i	$-0.279887\pi$
$773$	21.0666	+	6.18572i	0.757713	+	0.222485i	0.120016	+	0.992772i	$0.461705\pi$
$774$	0.491048	+	3.41531i	0.0176504	+	0.122761i
$775$	−22.3193	−	25.7578i	−0.801733	−	0.925249i
$776$	−4.70025	−	10.2921i	−0.168729	−	0.369466i
$777$	−6.20414	+	1.82170i	−0.222572	+	0.0653531i
$778$	1.12211	−	2.45709i	0.0402298	−	0.0880909i
$779$	−5.20752	+	36.2191i	−0.186579	+	1.29768i
$780$	19.2335	−	12.3606i	0.688671	−	0.442582i
$781$	−9.58552			−0.342997
$782$	−5.84330	−	9.99798i	−0.208956	−	0.357527i
$783$	−8.58473			−0.306793
$784$	0.841254	−	0.540641i	0.0300448	−	0.0193086i
$785$	−3.16103	+	21.9855i	−0.112822	+	0.784695i
$786$	−3.55944	+	7.79408i	−0.126961	+	0.278006i
$787$	−42.7168	+	12.5428i	−1.52269	+	0.447102i	−0.932804	−	0.360385i	$-0.882645\pi$
$787$	−42.7168	+	12.5428i	−1.52269	+	0.447102i	−0.589885	+	0.807487i	$0.700827\pi$
$788$	3.87869	+	8.49314i	0.138173	+	0.302556i
$789$	−2.16722	−	2.50111i	−0.0771552	−	0.0890419i
$790$	−5.73581	−	39.8935i	−0.204071	−	1.41935i
$791$	0.0326081	+	0.00957460i	0.00115941	+	0.000340434i
$792$	−1.09218	+	1.26044i	−0.0388089	+	0.0447879i
$793$	65.7518	+	42.2561i	2.33492	+	1.50056i
$794$	−18.8906	−	12.1403i	−0.670403	−	0.430842i
$795$	34.3673	−	39.6620i	1.21888	−	1.40667i
$796$	11.4061	+	3.34914i	0.404279	+	0.118707i
$797$	−2.08028	−	14.4687i	−0.0736873	−	0.512506i	−0.992919	−	0.118790i	$-0.962098\pi$
$797$	−2.08028	−	14.4687i	−0.0736873	−	0.512506i	0.919232	−	0.393716i	$-0.128811\pi$
$798$	−2.61521	−	3.01811i	−0.0925774	−	0.106840i
$799$	7.29668	+	15.9775i	0.258138	+	0.565244i
$800$	11.5879	−	3.40252i	0.409695	−	0.120297i
$801$	2.02278	−	4.42928i	0.0714715	−	0.156501i
$802$	−2.09246	+	14.5534i	−0.0738875	+	0.513899i
$803$	−1.84572	+	1.18618i	−0.0651342	+	0.0418592i
$804$	5.67544			0.200157
$805$	−10.0002	−	17.1105i	−0.352461	−	0.603067i
$806$	15.6132			0.549952
$807$	−13.5489	+	8.70736i	−0.476944	+	0.306514i
$808$	−2.69550	+	18.7476i	−0.0948273	+	0.659539i
$809$	2.21938	−	4.85977i	0.0780293	−	0.170860i	−0.866597	−	0.499009i	$-0.833697\pi$
$809$	2.21938	−	4.85977i	0.0780293	−	0.170860i	0.944626	+	0.328149i	$0.106425\pi$
$810$	−3.96506	+	1.16425i	−0.139318	+	0.0409074i
$811$	11.5392	+	25.2672i	0.405194	+	0.887252i	0.996717	+	0.0809636i	$0.0257998\pi$
$811$	11.5392	+	25.2672i	0.405194	+	0.887252i	−0.591523	+	0.806288i	$0.701473\pi$
$812$	5.62180	+	6.48791i	0.197287	+	0.227681i
$813$	−0.390125	−	2.71338i	−0.0136823	−	0.0951623i
$814$	−10.3473	−	3.03824i	−0.362672	−	0.106490i
$815$	−47.1340	+	54.3955i	−1.65103	+	1.90539i
$816$	2.03134	+	1.30547i	0.0711113	+	0.0457004i
$817$	−11.5920	−	7.44972i	−0.405553	−	0.260633i
$818$	−15.0903	+	17.4151i	−0.527619	+	0.608905i
$819$	5.30843	+	1.55870i	0.185492	+	0.0544653i
$820$	−5.38866	−	37.4790i	−0.188180	−	1.30882i
$821$	11.5181	+	13.2926i	0.401985	+	0.463915i	0.920265	−	0.391296i	$-0.127973\pi$
$821$	11.5181	+	13.2926i	0.401985	+	0.463915i	−0.518280	+	0.855211i	$0.673428\pi$
$822$	4.03797	+	8.84192i	0.140840	+	0.308397i
$823$	−38.9740	+	11.4438i	−1.35855	+	0.398906i	−0.878251	−	0.478200i	$-0.841289\pi$
$823$	−38.9740	+	11.4438i	−1.35855	+	0.398906i	−0.480298	+	0.877106i	$0.659471\pi$
$824$	−6.38357	+	13.9781i	−0.222382	+	0.486949i
$825$	2.86655	−	19.9373i	0.0998004	−	0.694127i
$826$	1.95986	−	1.25952i	0.0681922	−	0.0438244i
$827$	26.5015			0.921548			0.460774	−	0.887517i	$-0.347572\pi$
$827$	26.5015			0.921548			0.460774	+	0.887517i	$0.347572\pi$
$828$	−4.44277	+	1.80603i	−0.154397	+	0.0627639i
$829$	36.9284			1.28258			0.641289	−	0.767300i	$-0.278400\pi$
$829$	36.9284			1.28258			0.641289	+	0.767300i	$0.278400\pi$
$830$	−4.55127	+	2.92492i	−0.157977	+	0.101526i
$831$	1.57042	−	10.9225i	0.0544774	−	0.378898i
$832$	−2.29830	+	5.03257i	−0.0796792	+	0.174473i
$833$	−2.31685	+	0.680289i	−0.0802742	+	0.0235706i
$834$	9.41473	+	20.6154i	0.326005	+	0.713852i
$835$	−47.3092	−	54.5978i	−1.63720	−	1.88943i
$836$	−0.947879	−	6.59264i	−0.0327831	−	0.228011i
$837$	−2.70776	−	0.795069i	−0.0935937	−	0.0274816i
$838$	−8.88560	+	10.2545i	−0.306948	+	0.354237i
$839$	−18.5948	−	11.9502i	−0.641965	−	0.412566i	0.178758	−	0.983893i	$-0.442792\pi$
$839$	−18.5948	−	11.9502i	−0.641965	−	0.412566i	−0.820722	+	0.571328i	$0.806429\pi$
$840$	3.47644	+	2.23417i	0.119948	+	0.0770862i
$841$	−29.2707	+	33.7802i	−1.00933	+	1.16483i
$842$	0.223001	+	0.0654790i	0.00768513	+	0.00225656i
$843$	3.79194	+	26.3735i	0.130601	+	0.908353i
$844$	−17.2414	−	19.8977i	−0.593475	−	0.684907i
$845$	−30.2290	−	66.1923i	−1.03991	−	2.27708i
$846$	6.97957	−	2.04939i	0.239962	−	0.0704593i
$847$	−3.41406	+	7.47575i	−0.117308	+	0.256870i
$848$	−1.80734	+	12.5703i	−0.0620642	+	0.431666i
$849$	17.5820	−	11.2993i	0.603412	−	0.387789i
$850$	−29.1622			−1.00026
$851$	−22.5563	−	21.2801i	−0.773221	−	0.729471i
$852$	5.74739			0.196902
$853$	30.7080	−	19.7349i	1.05142	−	0.675709i	0.103637	−	0.994615i	$-0.466952\pi$
$853$	30.7080	−	19.7349i	1.05142	−	0.675709i	0.947786	+	0.318907i	$0.103316\pi$
$854$	−2.01051	+	13.9834i	−0.0687983	+	0.478503i
$855$	6.85563	−	15.0117i	0.234458	−	0.513390i
$856$	−0.476102	+	0.139796i	−0.0162728	+	0.00477814i
$857$	−17.1248	−	37.4981i	−0.584972	−	1.28091i	−0.938433	−	0.345461i	$-0.887723\pi$
$857$	−17.1248	−	37.4981i	−0.584972	−	1.28091i	0.353461	−	0.935449i	$-0.385005\pi$
$858$	6.04253	+	6.97345i	0.206288	+	0.238070i
$859$	1.23770	+	8.60840i	0.0422298	+	0.293715i	0.999981	+	0.00611760i	$0.00194731\pi$
$859$	1.23770	+	8.60840i	0.0422298	+	0.293715i	−0.957751	+	0.287597i	$0.907144\pi$
$860$	13.6812	+	4.01715i	0.466524	+	0.136984i
$861$	6.00029	−	6.92470i	0.204489	−	0.235993i
$862$	−14.5119	−	9.32621i	−0.494276	−	0.317652i
$863$	38.8029	+	24.9371i	1.32087	+	0.848870i	0.995318	−	0.0966551i	$-0.0308144\pi$
$863$	38.8029	+	24.9371i	1.32087	+	0.848870i	0.325549	+	0.945525i	$0.394451\pi$
$864$	0.654861	−	0.755750i	0.0222788	−	0.0257111i
$865$	−11.8715	−	3.48579i	−0.403644	−	0.118520i
$866$	2.82316	+	19.6355i	0.0959348	+	0.667241i
$867$	7.31440	+	8.44127i	0.248410	+	0.286681i
$868$	1.17233	+	2.56704i	0.0397915	+	0.0871312i
$869$	15.6072	−	4.58268i	0.529437	−	0.155457i
$870$	−14.7372	+	32.2701i	−0.499639	+	1.09406i
$871$	4.46863	−	31.0800i	0.151414	−	1.05310i
$872$	−17.0068	+	10.9296i	−0.575924	+	0.370124i
$873$	11.3146			0.382941
$874$	6.16798	−	18.1320i	0.208635	−	0.613322i
$875$	−29.2459			−0.988692
$876$	1.10668	−	0.711220i	0.0373912	−	0.0240299i
$877$	3.22866	−	22.4558i	0.109024	−	0.758280i	−0.859818	−	0.510601i	$-0.829423\pi$
$877$	3.22866	−	22.4558i	0.109024	−	0.758280i	0.968842	−	0.247679i	$-0.0796679\pi$
$878$	1.64299	−	3.59764i	0.0554481	−	0.121414i
$879$	−0.143947	+	0.0422666i	−0.00485521	+	0.00142562i
$880$	2.86309	+	6.26929i	0.0965147	+	0.211338i
$881$	15.7196	+	18.1414i	0.529608	+	0.611200i	0.956010	−	0.293334i	$-0.0947647\pi$
$881$	15.7196	+	18.1414i	0.529608	+	0.611200i	−0.426403	+	0.904534i	$0.640219\pi$
$882$	0.142315	+	0.989821i	0.00479199	+	0.0333290i
$883$	4.91563	+	1.44336i	0.165424	+	0.0485729i	0.363396	−	0.931635i	$-0.381617\pi$
$883$	4.91563	+	1.44336i	0.165424	+	0.0485729i	−0.197972	+	0.980208i	$0.563435\pi$
$884$	8.74843	−	10.0962i	0.294241	−	0.339573i
$885$	8.09901	+	5.20492i	0.272245	+	0.174961i
$886$	26.8471	+	17.2536i	0.901947	+	0.579646i
$887$	−14.4060	+	16.6254i	−0.483707	+	0.558228i	−0.944173	−	0.329449i	$-0.893137\pi$
$887$	−14.4060	+	16.6254i	−0.483707	+	0.558228i	0.460466	+	0.887677i	$0.347682\pi$
$888$	6.20414	+	1.82170i	0.208197	+	0.0611323i
$889$	−1.11143	−	7.73017i	−0.0372762	−	0.259262i
$890$	−13.1772	−	15.2073i	−0.441701	−	0.509750i
$891$	−0.692831	−	1.51709i	−0.0232107	−	0.0508244i
$892$	−26.1800	+	7.68714i	−0.876571	+	0.257385i
$893$	−12.0678	+	26.4247i	−0.403832	+	0.884269i
$894$	0.958262	−	6.66486i	0.0320491	−	0.222906i
$895$	3.75558	−	2.41357i	0.125535	−	0.0806766i
$896$	−1.00000			−0.0334077
$897$	6.39216	+	25.7516i	0.213428	+	0.859822i
$898$	23.3487			0.779156
$899$	−20.3808	+	13.0979i	−0.679738	+	0.436841i
$900$	−1.71876	+	11.9542i	−0.0572918	+	0.398474i
$901$	12.7388	−	27.8940i	0.424390	−	0.929285i
$902$	14.6626	−	4.30532i	0.488210	−	0.143351i
$903$	1.43336	+	3.13862i	0.0476993	+	0.104447i
$904$	−0.0222553	−	0.0256839i	−0.000740199	−	0.000854235i
$905$	−3.47673	−	24.1812i	−0.115570	−	0.803810i
$906$	16.4314	+	4.82470i	0.545898	+	0.160290i
$907$	11.2352	−	12.9661i	0.373060	−	0.430534i	−0.537913	−	0.843000i	$-0.680787\pi$
$907$	11.2352	−	12.9661i	0.373060	−	0.430534i	0.910973	+	0.412466i	$0.135333\pi$
$908$	10.2352	+	6.57774i	0.339666	+	0.218290i
$909$	−15.9337	−	10.2400i	−0.528487	−	0.339638i
$910$	14.9720	−	17.2787i	0.496318	−	0.572782i
$911$	32.1334	+	9.43521i	1.06463	+	0.312602i	0.766713	−	0.641990i	$-0.221891\pi$
$911$	32.1334	+	9.43521i	1.06463	+	0.312602i	0.297914	+	0.954593i	$0.403709\pi$
$912$	0.568339	+	3.95289i	0.0188196	+	0.130893i
$913$	−1.42986	−	1.65014i	−0.0473213	−	0.0546117i
$914$	−6.53347	−	14.3063i	−0.216108	−	0.473210i
$915$	−56.0152	+	16.4475i	−1.85180	+	0.543739i
$916$	−3.56479	+	7.80580i	−0.117784	+	0.257911i
$917$	−1.21941	+	8.48117i	−0.0402684	+	0.280073i
$918$	−2.03134	+	1.30547i	−0.0670443	+	0.0430868i
$919$	−50.3589			−1.66119			−0.830593	−	0.556880i	$-0.811998\pi$
$919$	−50.3589			−1.66119			−0.830593	+	0.556880i	$0.811998\pi$
$920$	−0.837941	+	19.8008i	−0.0276261	+	0.652813i
$921$	−1.06720			−0.0351654
$922$	26.7573	−	17.1959i	0.881205	−	0.566316i
$923$	4.52528	−	31.4740i	0.148951	−	1.03598i
$924$	−0.692831	+	1.51709i	−0.0227925	+	0.0499085i
$925$	−74.9282	+	22.0009i	−2.46363	+	0.723386i
$926$	1.17524	+	2.57341i	0.0386208	+	0.0845677i
$927$	−10.0631	−	11.6134i	−0.330514	−	0.381434i
$928$	−1.22173	−	8.49735i	−0.0401054	−	0.278939i
$929$	44.5736	+	13.0880i	1.46241	+	0.429403i	0.913625	−	0.406558i	$-0.133271\pi$
$929$	44.5736	+	13.0880i	1.46241	+	0.429403i	0.548788	+	0.835961i	$0.315089\pi$
$930$	−7.63702	+	8.81360i	−0.250428	+	0.289009i
$931$	−3.35958	−	2.15907i	−0.110106	−	0.0707606i
$932$	15.3937	+	9.89290i	0.504236	+	0.324053i
$933$	−2.00634	+	2.31544i	−0.0656846	+	0.0758041i
$934$	17.7091	+	5.19986i	0.579459	+	0.170144i
$935$	−2.36842	−	16.4727i	−0.0774557	−	0.538716i
$936$	−3.62304	−	4.18121i	−0.118423	−	0.136667i
$937$	−17.4223	−	38.1495i	−0.569162	−	1.24629i	−0.947243	−	0.320518i	$-0.896143\pi$
$937$	−17.4223	−	38.1495i	−0.569162	−	1.24629i	0.378081	−	0.925773i	$-0.376584\pi$
$938$	5.44554	−	1.59896i	0.177803	−	0.0522077i
$939$	4.77270	−	10.4508i	0.155751	−	0.341047i
$940$	4.27804	−	29.7544i	0.139534	−	0.970481i
$941$	11.3119	−	7.26973i	0.368758	−	0.236986i	−0.343117	−	0.939293i	$-0.611483\pi$
$941$	11.3119	−	7.26973i	0.368758	−	0.236986i	0.711875	+	0.702306i	$0.247846\pi$
$942$	5.37491			0.175124
$943$	43.1922	+	8.08713i	1.40653	+	0.263353i
$944$	−2.32969			−0.0758249
$945$	−3.47644	+	2.23417i	−0.113089	+	0.0726776i
$946$	−0.818972	+	5.69607i	−0.0266271	+	0.185195i
$947$	1.02505	−	2.24454i	0.0333095	−	0.0729377i	−0.892246	−	0.451550i	$-0.850871\pi$
$947$	1.02505	−	2.24454i	0.0333095	−	0.0729377i	0.925555	+	0.378612i	$0.123599\pi$
$948$	−9.35791	+	2.74773i	−0.303931	+	0.0892422i
$949$	−3.02344	−	6.62041i	−0.0981451	−	0.214908i
$950$	−31.5842	−	36.4502i	−1.02473	−	1.18260i
$951$	−3.39029	−	23.5800i	−0.109938	−	0.764633i
$952$	2.31685	+	0.680289i	0.0750896	+	0.0220483i
$953$	27.3268	−	31.5368i	0.885202	−	1.02158i	−0.114402	−	0.993435i	$-0.536495\pi$
$953$	27.3268	−	31.5368i	0.885202	−	1.02158i	0.999604	−	0.0281427i	$-0.00895927\pi$
$954$	−10.6836	−	6.86590i	−0.345893	−	0.222292i
$955$	−13.4608	−	8.65073i	−0.435581	−	0.279931i
$956$	−6.86167	+	7.91879i	−0.221922	+	0.256112i
$957$	−13.7377	−	4.03375i	−0.444076	−	0.130393i
$958$	3.65916	+	25.4500i	0.118222	+	0.822254i
$959$	6.36546	+	7.34613i	0.205551	+	0.237219i
$960$	−1.71668	−	3.75901i	−0.0554057	−	0.121321i
$961$	22.1028	−	6.48997i	0.712994	−	0.209354i
$962$	14.8609	−	32.5409i	0.479136	−	1.04916i
$963$	0.0706169	−	0.491151i	0.00227560	−	0.0158271i
$964$	3.00147	−	1.92893i	0.0966707	−	0.0621265i
$965$	26.3754			0.849056
$966$	−3.75399	+	2.98455i	−0.120783	+	0.0960263i
$967$	−26.9694			−0.867277			−0.433638	−	0.901087i	$-0.642770\pi$
$967$	−26.9694			−0.867277			−0.433638	+	0.901087i	$0.642770\pi$
$968$	6.91378	−	4.44322i	0.222217	−	0.142810i
$969$	1.37235	−	9.54489i	0.0440862	−	0.306626i
$970$	19.4236	−	42.5317i	0.623653	−	1.36561i
$971$	−30.9019	+	9.07361i	−0.991689	+	0.291186i	−0.737041	−	0.675848i	$-0.763778\pi$
$971$	−30.9019	+	9.07361i	−0.991689	+	0.291186i	−0.254648	+	0.967034i	$0.581959\pi$
$972$	0.415415	+	0.909632i	0.0133244	+	0.0291765i
$973$	14.8414	+	17.1279i	0.475793	+	0.549095i
$974$	−0.0527582	−	0.366941i	−0.00169048	−	0.0117576i
$975$	64.1106	+	18.8246i	2.05318	+	0.602869i
$976$	9.25136	−	10.6766i	0.296129	−	0.341751i
$977$	−42.9226	−	27.5847i	−1.37322	−	0.882512i	−0.374221	−	0.927340i	$-0.622090\pi$
$977$	−42.9226	−	27.5847i	−1.37322	−	0.882512i	−0.998995	+	0.0448278i	$0.985726\pi$
$978$	14.6523	+	9.41644i	0.468528	+	0.301104i
$979$	5.31816	−	6.13748i	0.169969	−	0.196155i
$980$	3.96506	+	1.16425i	0.126659	+	0.0371905i
$981$	−2.87705	−	20.0103i	−0.0918570	−	0.638880i
$982$	−12.3513	−	14.2542i	−0.394147	−	0.454869i
$983$	−1.95638	−	4.28388i	−0.0623989	−	0.136635i	0.875863	−	0.482559i	$-0.160293\pi$
$983$	−1.95638	−	4.28388i	−0.0623989	−	0.136635i	−0.938262	+	0.345924i	$0.887565\pi$
$984$	−8.79154	+	2.58143i	−0.280264	+	0.0822929i
$985$	−16.0285	+	35.0975i	−0.510710	+	1.11830i
$986$	−2.95008	+	20.5182i	−0.0939496	+	0.653434i
$987$	6.11947	−	3.93274i	0.194785	−	0.125181i
$988$	22.0944			0.702916
$989$	−9.52694	+	13.5301i	−0.302939	+	0.430232i
$990$	−6.89212			−0.219046
$991$	48.2344	−	30.9984i	1.53222	−	0.984696i	0.542758	−	0.839889i	$-0.317380\pi$
$991$	48.2344	−	30.9984i	1.53222	−	0.984696i	0.989460	−	0.144807i	$-0.0462561\pi$
$992$	0.401622	−	2.79335i	0.0127515	−	0.0886888i
$993$	−0.202063	+	0.442456i	−0.00641227	+	0.0140409i
$994$	5.51458	−	1.61923i	0.174912	−	0.0513587i
$995$	20.4073	+	44.6858i	0.646955	+	1.41663i
$996$	0.857328	+	0.989409i	0.0271655	+	0.0313506i
$997$	3.68554	+	25.6335i	0.116722	+	0.811821i	0.961125	+	0.276112i	$0.0890462\pi$
$997$	3.68554	+	25.6335i	0.116722	+	0.811821i	−0.844403	+	0.535708i	$0.820045\pi$
$998$	1.94310	+	0.570546i	0.0615078	+	0.0180603i
$999$	−4.23437	+	4.88672i	−0.133970	+	0.154609i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.e.127.2	✓	20
23.2	even	11	inner	966.2.q.e.715.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.e.127.2	✓	20	1.1	even	1	trivial
966.2.q.e.715.2	yes	20	23.2	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)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(3.96506 - 1.16425i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(3.96506 - 1.16425i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-2.70618 + 3.12310i) q^{10} +(-1.40305 - 0.901683i) q^{11} +(0.841254 + 0.540641i) q^{12} +(3.62304 - 4.18121i) q^{13} +(0.959493 + 0.281733i) q^{14} +(0.588109 + 4.09039i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(1.00309 + 2.19646i) q^{17} +(0.959493 - 0.281733i) q^{18} +(-1.65897 + 3.63265i) q^{19} +(0.588109 - 4.09039i) q^{20} +(0.841254 - 0.540641i) q^{21} +1.66780 q^{22} +(4.27431 + 2.17493i) q^{23} -1.00000 q^{24} +(10.1599 - 6.52939i) q^{25} +(-0.787362 + 5.47623i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(-3.56623 - 7.80894i) q^{29} +(-2.70618 - 3.12310i) q^{30} +(-0.401622 - 2.79335i) q^{31} +(0.959493 + 0.281733i) q^{32} +(1.09218 - 1.26044i) q^{33} +(-2.03134 - 1.30547i) q^{34} +(-3.47644 - 2.23417i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-6.20414 - 1.82170i) q^{37} +(-0.568339 - 3.95289i) q^{38} +(3.62304 + 4.18121i) q^{39} +(1.71668 + 3.75901i) q^{40} +(8.79154 - 2.58143i) q^{41} +(-0.415415 + 0.909632i) q^{42} +(-0.491048 + 3.41531i) q^{43} +(-1.40305 + 0.901683i) q^{44} -4.13245 q^{45} +(-4.77163 + 0.481201i) q^{46} +7.27423 q^{47} +(0.841254 - 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(-5.01702 + 10.9857i) q^{50} +(-2.31685 + 0.680289i) q^{51} +(-2.29830 - 5.03257i) q^{52} +(-8.31645 - 9.59769i) q^{53} +(0.142315 + 0.989821i) q^{54} +(-6.61294 - 1.94173i) q^{55} +(0.654861 - 0.755750i) q^{56} +(-3.35958 - 2.15907i) q^{57} +(7.22193 + 4.64126i) q^{58} +(1.52562 - 1.76066i) q^{59} +(3.96506 + 1.16425i) q^{60} +(2.01051 + 13.9834i) q^{61} +(1.84806 + 2.13278i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(9.49761 - 20.7969i) q^{65} +(-0.237353 + 1.65083i) q^{66} +(4.77448 - 3.06837i) q^{67} +2.41466 q^{68} +(-2.76109 + 3.92128i) q^{69} +4.13245 q^{70} +(4.83501 - 3.10727i) q^{71} +(0.142315 - 0.989821i) q^{72} +(0.546484 - 1.19663i) q^{73} +(6.20414 - 1.82170i) q^{74} +(5.01702 + 10.9857i) q^{75} +(2.61521 + 3.01811i) q^{76} +(0.237353 + 1.65083i) q^{77} +(-5.30843 - 1.55870i) q^{78} +(-6.38684 + 7.37081i) q^{79} +(-3.47644 - 2.23417i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-6.00029 + 6.92470i) q^{82} +(1.25615 + 0.368837i) q^{83} +(-0.142315 - 0.989821i) q^{84} +(6.53451 + 7.54123i) q^{85} +(-1.43336 - 3.13862i) q^{86} +(8.23699 - 2.41860i) q^{87} +(0.692831 - 1.51709i) q^{88} +(-0.692975 + 4.81974i) q^{89} +(3.47644 - 2.23417i) q^{90} -5.53254 q^{91} +(3.75399 - 2.98455i) q^{92} +2.82207 q^{93} +(-6.11947 + 3.93274i) q^{94} +(-2.34863 + 16.3351i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(-10.8563 + 3.18769i) q^{97} +(-0.415415 - 0.909632i) q^{98} +(1.09218 + 1.26044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 10 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{10} - 3 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{14} - 12 q^{15} - 2 q^{16} + 14 q^{17} + 2 q^{18} - 13 q^{19} - 12 q^{20} - 2 q^{21} - 8 q^{22} - 2 q^{23} - 20 q^{24} + 22 q^{25} - 28 q^{26} - 2 q^{27} - 2 q^{28} + 26 q^{29} - 10 q^{30} + 15 q^{31} + 2 q^{32} - 14 q^{33} - 3 q^{34} - q^{35} - 2 q^{36} - 26 q^{37} + 2 q^{38} + 6 q^{39} + q^{40} + 40 q^{41} + 2 q^{42} + 8 q^{43} - 3 q^{44} - 12 q^{45} - 20 q^{46} + 36 q^{47} - 2 q^{48} - 2 q^{49} + 11 q^{50} + 3 q^{51} - 27 q^{52} - 5 q^{53} + 2 q^{54} - 7 q^{55} + 2 q^{56} + 9 q^{57} - 15 q^{58} + 13 q^{59} + 10 q^{60} + 59 q^{61} - 4 q^{62} - 2 q^{63} - 2 q^{64} - q^{65} - 8 q^{66} - 26 q^{67} - 8 q^{68} - 35 q^{69} + 12 q^{70} + 13 q^{71} + 2 q^{72} - 34 q^{73} + 26 q^{74} - 11 q^{75} - 2 q^{76} + 8 q^{77} - 6 q^{78} - 27 q^{79} - q^{80} - 2 q^{81} - 40 q^{82} + 41 q^{83} - 2 q^{84} + 51 q^{85} + 14 q^{86} - 7 q^{87} - 8 q^{88} + 43 q^{89} + q^{90} - 16 q^{91} + 9 q^{92} + 4 q^{93} - 3 q^{94} - 26 q^{95} + 2 q^{96} - 8 q^{97} + 2 q^{98} - 14 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 10 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 10 * q^10 - 3 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^14 - 12 * q^15 - 2 * q^16 + 14 * q^17 + 2 * q^18 - 13 * q^19 - 12 * q^20 - 2 * q^21 - 8 * q^22 - 2 * q^23 - 20 * q^24 + 22 * q^25 - 28 * q^26 - 2 * q^27 - 2 * q^28 + 26 * q^29 - 10 * q^30 + 15 * q^31 + 2 * q^32 - 14 * q^33 - 3 * q^34 - q^35 - 2 * q^36 - 26 * q^37 + 2 * q^38 + 6 * q^39 + q^40 + 40 * q^41 + 2 * q^42 + 8 * q^43 - 3 * q^44 - 12 * q^45 - 20 * q^46 + 36 * q^47 - 2 * q^48 - 2 * q^49 + 11 * q^50 + 3 * q^51 - 27 * q^52 - 5 * q^53 + 2 * q^54 - 7 * q^55 + 2 * q^56 + 9 * q^57 - 15 * q^58 + 13 * q^59 + 10 * q^60 + 59 * q^61 - 4 * q^62 - 2 * q^63 - 2 * q^64 - q^65 - 8 * q^66 - 26 * q^67 - 8 * q^68 - 35 * q^69 + 12 * q^70 + 13 * q^71 + 2 * q^72 - 34 * q^73 + 26 * q^74 - 11 * q^75 - 2 * q^76 + 8 * q^77 - 6 * q^78 - 27 * q^79 - q^80 - 2 * q^81 - 40 * q^82 + 41 * q^83 - 2 * q^84 + 51 * q^85 + 14 * q^86 - 7 * q^87 - 8 * q^88 + 43 * q^89 + q^90 - 16 * q^91 + 9 * q^92 + 4 * q^93 - 3 * q^94 - 26 * q^95 + 2 * q^96 - 8 * q^97 + 2 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more