LMFDB - Embedded newform 966.2.q.e.127.1

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:	$20$
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			127.1
Root			$-0.308405 + 0.355918i$ of defining polynomial
Character	$\chi$	$=$	966.127
Dual form			966.2.q.e.715.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.180741 + 0.0530703i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.180741 + 0.0530703i) 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} +(0.123357 - 0.142361i) q^{10} +(3.80560 + 2.44571i) q^{11} +(0.841254 + 0.540641i) q^{12} +(0.793507 - 0.915755i) q^{13} +(0.959493 + 0.281733i) q^{14} +(-0.0268080 - 0.186454i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.836884 - 1.83252i) q^{17} +(0.959493 - 0.281733i) q^{18} +(1.21560 - 2.66179i) q^{19} +(-0.0268080 + 0.186454i) q^{20} +(0.841254 - 0.540641i) q^{21} -4.52373 q^{22} +(3.83919 - 2.87413i) q^{23} -1.00000 q^{24} +(-4.17642 + 2.68402i) q^{25} +(-0.172445 + 1.19938i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(3.37837 + 7.39759i) q^{29} +(0.123357 + 0.142361i) q^{30} +(0.377787 + 2.62757i) q^{31} +(0.959493 + 0.281733i) q^{32} +(-2.96241 + 3.41880i) q^{33} +(1.69477 + 1.08916i) q^{34} +(0.158468 + 0.101841i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(5.09201 + 1.49515i) q^{37} +(0.416446 + 2.89644i) q^{38} +(0.793507 + 0.915755i) q^{39} +(-0.0782522 - 0.171348i) q^{40} +(9.86753 - 2.89737i) q^{41} +(-0.415415 + 0.909632i) q^{42} +(0.268034 - 1.86422i) q^{43} +(3.80560 - 2.44571i) q^{44} +0.188371 q^{45} +(-1.67586 + 4.49349i) q^{46} +1.78279 q^{47} +(0.841254 - 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(2.06233 - 4.51588i) q^{50} +(1.93297 - 0.567571i) q^{51} +(-0.503366 - 1.10222i) q^{52} +(4.22497 + 4.87587i) q^{53} +(0.142315 + 0.989821i) q^{54} +(-0.817622 - 0.240076i) q^{55} +(0.654861 - 0.755750i) q^{56} +(2.46170 + 1.58204i) q^{57} +(-6.84150 - 4.39677i) q^{58} +(-2.81063 + 3.24364i) q^{59} +(-0.180741 - 0.0530703i) q^{60} +(1.02134 + 7.10354i) q^{61} +(-1.73839 - 2.00620i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.0948197 + 0.207626i) q^{65} +(0.643793 - 4.47768i) q^{66} +(-11.6175 + 7.46614i) q^{67} -2.01457 q^{68} +(2.29850 + 4.20915i) q^{69} -0.188371 q^{70} +(-5.25766 + 3.37889i) q^{71} +(0.142315 - 0.989821i) q^{72} +(1.15662 - 2.53265i) q^{73} +(-5.09201 + 1.49515i) q^{74} +(-2.06233 - 4.51588i) q^{75} +(-1.91627 - 2.21149i) q^{76} +(-0.643793 - 4.47768i) q^{77} +(-1.16264 - 0.341380i) q^{78} +(-2.11981 + 2.44639i) q^{79} +(0.158468 + 0.101841i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-6.73466 + 7.77221i) q^{82} +(15.9876 + 4.69438i) q^{83} +(-0.142315 - 0.989821i) q^{84} +(0.248512 + 0.286798i) q^{85} +(0.782387 + 1.71319i) q^{86} +(-7.80309 + 2.29119i) q^{87} +(-1.87922 + 4.11493i) q^{88} +(0.116044 - 0.807102i) q^{89} +(-0.158468 + 0.101841i) q^{90} -1.21172 q^{91} +(-1.01954 - 4.68621i) q^{92} -2.65459 q^{93} +(-1.49978 + 0.963849i) q^{94} +(-0.0784464 + 0.545606i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(9.60021 - 2.81888i) q^{97} +(-0.415415 - 0.909632i) q^{98} +(-2.96241 - 3.41880i) 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
$5$	−0.180741	+	0.0530703i	−0.0808298	+	0.0237338i	−0.321897	−	0.946775i	$-0.604321\pi$
$5$	−0.180741	+	0.0530703i	−0.0808298	+	0.0237338i	0.241068	+	0.970508i	$0.422502\pi$
$6$	−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
$10$	0.123357	−	0.142361i	0.0390089	−	0.0450186i
$11$	3.80560	+	2.44571i	1.14743	+	0.737410i	0.969126	−	0.246566i	$-0.0793021\pi$
$11$	3.80560	+	2.44571i	1.14743	+	0.737410i	0.178306	+	0.983975i	$0.442938\pi$
$12$	0.841254	+	0.540641i	0.242849	+	0.156070i
$13$	0.793507	−	0.915755i	0.220079	−	0.253985i	−0.634964	−	0.772542i	$-0.718985\pi$
$13$	0.793507	−	0.915755i	0.220079	−	0.253985i	0.855043	+	0.518557i	$0.173531\pi$
$14$	0.959493	+	0.281733i	0.256435	+	0.0752962i
$15$	−0.0268080	−	0.186454i	−0.00692180	−	0.0481422i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−0.836884	−	1.83252i	−0.202974	−	0.444452i	0.780582	−	0.625053i	$-0.214923\pi$
$17$	−0.836884	−	1.83252i	−0.202974	−	0.444452i	−0.983556	+	0.180602i	$0.942196\pi$
$18$	0.959493	−	0.281733i	0.226155	−	0.0664050i
$19$	1.21560	−	2.66179i	0.278877	−	0.610656i	−0.717419	−	0.696642i	$-0.754677\pi$
$19$	1.21560	−	2.66179i	0.278877	−	0.610656i	0.996296	+	0.0859855i	$0.0274039\pi$
$20$	−0.0268080	+	0.186454i	−0.00599446	+	0.0416924i
$21$	0.841254	−	0.540641i	0.183577	−	0.117977i
$22$	−4.52373			−0.964462
$23$	3.83919	−	2.87413i	0.800527	−	0.599297i
$23$	3.83919	−	2.87413i	0.800527	−	0.599297i
$24$	−1.00000			−0.204124
$25$	−4.17642	+	2.68402i	−0.835283	+	0.536804i
$26$	−0.172445	+	1.19938i	−0.0338193	+	0.235219i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	−0.959493	+	0.281733i	−0.181327	+	0.0532424i
$29$	3.37837	+	7.39759i	0.627347	+	1.37370i	0.910053	+	0.414492i	$0.136041\pi$
$29$	3.37837	+	7.39759i	0.627347	+	1.37370i	−0.282706	+	0.959207i	$0.591232\pi$
$30$	0.123357	+	0.142361i	0.0225218	+	0.0259915i
$31$	0.377787	+	2.62757i	0.0678526	+	0.471925i	0.995211	+	0.0977508i	$0.0311648\pi$
$31$	0.377787	+	2.62757i	0.0678526	+	0.471925i	−0.927358	+	0.374175i	$0.877926\pi$
$32$	0.959493	+	0.281733i	0.169616	+	0.0498038i
$33$	−2.96241	+	3.41880i	−0.515690	+	0.595137i
$34$	1.69477	+	1.08916i	0.290650	+	0.186790i
$35$	0.158468	+	0.101841i	0.0267860	+	0.0172143i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	5.09201	+	1.49515i	0.837122	+	0.245801i	0.672073	−	0.740484i	$-0.265404\pi$
$37$	5.09201	+	1.49515i	0.837122	+	0.245801i	0.165048	+	0.986286i	$0.447222\pi$
$38$	0.416446	+	2.89644i	0.0675564	+	0.469865i
$39$	0.793507	+	0.915755i	0.127063	+	0.146638i
$40$	−0.0782522	−	0.171348i	−0.0123728	−	0.0270926i
$41$	9.86753	−	2.89737i	1.54105	−	0.452493i	0.602638	−	0.798014i	$-0.294116\pi$
$41$	9.86753	−	2.89737i	1.54105	−	0.452493i	0.938411	+	0.345521i	$0.112298\pi$
$42$	−0.415415	+	0.909632i	−0.0640999	+	0.140359i
$43$	0.268034	−	1.86422i	0.0408748	−	0.284290i	−0.959124	−	0.282985i	$-0.908675\pi$
$43$	0.268034	−	1.86422i	0.0408748	−	0.284290i	0.999999	−	0.00130542i	$-0.000415527\pi$
$44$	3.80560	−	2.44571i	0.573716	−	0.368705i
$45$	0.188371			0.0280807
$46$	−1.67586	+	4.49349i	−0.247093	+	0.662529i
$47$	1.78279			0.260047			0.130023	−	0.991511i	$-0.458495\pi$
$47$	1.78279			0.260047			0.130023	+	0.991511i	$0.458495\pi$
$48$	0.841254	−	0.540641i	0.121424	−	0.0780348i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	2.06233	−	4.51588i	0.291658	−	0.638642i
$51$	1.93297	−	0.567571i	0.270670	−	0.0794758i
$52$	−0.503366	−	1.10222i	−0.0698043	−	0.152850i
$53$	4.22497	+	4.87587i	0.580344	+	0.669752i	0.967679	−	0.252187i	$-0.0811497\pi$
$53$	4.22497	+	4.87587i	0.580344	+	0.669752i	−0.387335	+	0.921939i	$0.626604\pi$
$54$	0.142315	+	0.989821i	0.0193666	+	0.134698i
$55$	−0.817622	−	0.240076i	−0.110248	−	0.0323718i
$56$	0.654861	−	0.755750i	0.0875094	−	0.100991i
$57$	2.46170	+	1.58204i	0.326060	+	0.209546i
$58$	−6.84150	−	4.39677i	−0.898334	−	0.577324i
$59$	−2.81063	+	3.24364i	−0.365913	+	0.422286i	−0.908612	−	0.417641i	$-0.862857\pi$
$59$	−2.81063	+	3.24364i	−0.365913	+	0.422286i	0.542699	+	0.839927i	$0.317402\pi$
$60$	−0.180741	−	0.0530703i	−0.0233335	−	0.00685135i
$61$	1.02134	+	7.10354i	0.130769	+	0.909515i	0.944555	+	0.328352i	$0.106493\pi$
$61$	1.02134	+	7.10354i	0.130769	+	0.909515i	−0.813787	+	0.581163i	$0.802598\pi$
$62$	−1.73839	−	2.00620i	−0.220775	−	0.254788i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−0.0948197	+	0.207626i	−0.0117609	+	0.0257528i
$66$	0.643793	−	4.47768i	0.0792455	−	0.551164i
$67$	−11.6175	+	7.46614i	−1.41931	+	0.912134i	−0.419318	+	0.907839i	$0.637731\pi$
$67$	−11.6175	+	7.46614i	−1.41931	+	0.912134i	−0.999991	+	0.00429493i	$0.998633\pi$
$68$	−2.01457			−0.244303
$69$	2.29850	+	4.20915i	0.276707	+	0.506722i
$70$	−0.188371			−0.0225147
$71$	−5.25766	+	3.37889i	−0.623969	+	0.401001i	−0.814072	−	0.580764i	$-0.802754\pi$
$71$	−5.25766	+	3.37889i	−0.623969	+	0.401001i	0.190103	+	0.981764i	$0.439118\pi$
$72$	0.142315	−	0.989821i	0.0167720	−	0.116652i
$73$	1.15662	−	2.53265i	0.135372	−	0.296424i	−0.829790	−	0.558076i	$-0.811540\pi$
$73$	1.15662	−	2.53265i	0.135372	−	0.296424i	0.965162	+	0.261652i	$0.0842672\pi$
$74$	−5.09201	+	1.49515i	−0.591934	+	0.173808i
$75$	−2.06233	−	4.51588i	−0.238138	−	0.521449i
$76$	−1.91627	−	2.21149i	−0.219811	−	0.253676i
$77$	−0.643793	−	4.47768i	−0.0733671	−	0.510279i
$78$	−1.16264	−	0.341380i	−0.131642	−	0.0386537i
$79$	−2.11981	+	2.44639i	−0.238497	+	0.275240i	−0.862362	−	0.506292i	$-0.831016\pi$
$79$	−2.11981	+	2.44639i	−0.238497	+	0.275240i	0.623865	+	0.781532i	$0.285561\pi$
$80$	0.158468	+	0.101841i	0.0177173	+	0.0113862i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−6.73466	+	7.77221i	−0.743719	+	0.858297i
$83$	15.9876	+	4.69438i	1.75486	+	0.515275i	0.991433	−	0.130614i	$-0.0416949\pi$
$83$	15.9876	+	4.69438i	1.75486	+	0.515275i	0.763432	+	0.645889i	$0.223513\pi$
$84$	−0.142315	−	0.989821i	−0.0155278	−	0.107998i
$85$	0.248512	+	0.286798i	0.0269549	+	0.0311076i
$86$	0.782387	+	1.71319i	0.0843669	+	0.184738i
$87$	−7.80309	+	2.29119i	−0.836579	+	0.245642i
$88$	−1.87922	+	4.11493i	−0.200326	+	0.438653i
$89$	0.116044	−	0.807102i	0.0123006	−	0.0855527i	−0.982746	−	0.184958i	$-0.940785\pi$
$89$	0.116044	−	0.807102i	0.0123006	−	0.0855527i	0.995047	+	0.0994055i	$0.0316941\pi$
$90$	−0.158468	+	0.101841i	−0.0167040	+	0.0107350i
$91$	−1.21172			−0.127023
$92$	−1.01954	−	4.68621i	−0.106294	−	0.488571i
$93$	−2.65459			−0.275268
$94$	−1.49978	+	0.963849i	−0.154690	+	0.0994134i
$95$	−0.0784464	+	0.545606i	−0.00804843	+	0.0559780i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	9.60021	−	2.81888i	0.974754	−	0.286214i	0.244697	−	0.969600i	$-0.421312\pi$
$97$	9.60021	−	2.81888i	0.974754	−	0.286214i	0.730057	+	0.683386i	$0.239493\pi$
$98$	−0.415415	−	0.909632i	−0.0419633	−	0.0918867i
$99$	−2.96241	−	3.41880i	−0.297733	−	0.343603i
$100$	0.706524	+	4.91398i	0.0706524	+	0.491398i
$101$	0.222133	+	0.0652242i	0.0221031	+	0.00649005i	0.292765	−	0.956184i	$-0.405425\pi$
$101$	0.222133	+	0.0652242i	0.0221031	+	0.00649005i	−0.270662	+	0.962674i	$0.587243\pi$
$102$	−1.31927	+	1.52251i	−0.130627	+	0.150751i
$103$	−3.47021	−	2.23017i	−0.341930	−	0.219745i	0.358394	−	0.933570i	$-0.383325\pi$
$103$	−3.47021	−	2.23017i	−0.341930	−	0.219745i	−0.700323	+	0.713826i	$0.746961\pi$
$104$	1.01936	+	0.655104i	0.0999567	+	0.0642383i
$105$	−0.123357	+	0.142361i	−0.0120384	+	0.0138931i
$106$	−6.19036	−	1.81765i	−0.601261	−	0.176546i
$107$	1.47183	+	10.2368i	0.142287	+	0.989626i	0.928410	+	0.371557i	$0.121176\pi$
$107$	1.47183	+	10.2368i	0.142287	+	0.989626i	−0.786124	+	0.618069i	$0.787915\pi$
$108$	−0.654861	−	0.755750i	−0.0630140	−	0.0727220i
$109$	1.90505	+	4.17148i	0.182471	+	0.399555i	0.978658	−	0.205495i	$-0.0658804\pi$
$109$	1.90505	+	4.17148i	0.182471	+	0.399555i	−0.796188	+	0.605050i	$0.793153\pi$
$110$	0.817622	−	0.240076i	0.0779572	−	0.0228903i
$111$	−2.20460	+	4.82740i	−0.209251	+	0.458197i
$112$	−0.142315	+	0.989821i	−0.0134475	+	0.0935293i
$113$	11.3353	−	7.28475i	1.06634	−	0.685292i	0.114974	−	0.993369i	$-0.463322\pi$
$113$	11.3353	−	7.28475i	1.06634	−	0.685292i	0.951362	+	0.308076i	$0.0996853\pi$
$114$	−2.92623			−0.274066
$115$	−0.541368	+	0.723219i	−0.0504828	+	0.0674405i
$116$	8.13251			0.755085
$117$	−1.01936	+	0.655104i	−0.0942401	+	0.0605644i
$118$	0.610808	−	4.24826i	0.0562294	−	0.391084i
$119$	−0.836884	+	1.83252i	−0.0767171	+	0.167987i
$120$	0.180741	−	0.0530703i	0.0164993	−	0.00484463i
$121$	3.93153	+	8.60885i	0.357412	+	0.782622i
$122$	−4.69967	−	5.42370i	−0.425488	−	0.491039i
$123$	1.46358	+	10.1794i	0.131967	+	0.917848i
$124$	2.54706	+	0.747884i	0.228733	+	0.0671620i
$125$	1.22919	−	1.41856i	0.109942	−	0.126880i
$126$	−0.841254	−	0.540641i	−0.0749448	−	0.0481641i
$127$	−13.8071	−	8.87327i	−1.22518	−	0.787375i	−0.242046	−	0.970265i	$-0.577819\pi$
$127$	−13.8071	−	8.87327i	−1.22518	−	0.787375i	−0.983133	+	0.182890i	$0.941455\pi$
$128$	0.654861	−	0.755750i	0.0578821	−	0.0667995i
$129$	1.80710	+	0.530611i	0.159106	+	0.0467177i
$130$	−0.0324838	−	0.225930i	−0.00284901	−	0.0198153i
$131$	14.4553	+	16.6823i	1.26297	+	1.45754i	0.831610	+	0.555360i	$0.187420\pi$
$131$	14.4553	+	16.6823i	1.26297	+	1.45754i	0.431357	+	0.902181i	$0.358035\pi$
$132$	1.87922	+	4.11493i	0.163565	+	0.358158i
$133$	−2.80769	+	0.824413i	−0.243458	+	0.0714857i
$134$	5.73680	−	12.5618i	0.495584	−	1.08518i
$135$	−0.0268080	+	0.186454i	−0.00230727	+	0.0160474i
$136$	1.69477	−	1.08916i	0.145325	−	0.0933948i
$137$	−10.4821			−0.895549			−0.447775	−	0.894146i	$-0.647783\pi$
$137$	−10.4821			−0.895549			−0.447775	+	0.894146i	$0.647783\pi$
$138$	−4.20926	−	2.29830i	−0.358316	−	0.195644i
$139$	−7.30510			−0.619610			−0.309805	−	0.950800i	$-0.600264\pi$
$139$	−7.30510			−0.619610			−0.309805	+	0.950800i	$0.600264\pi$
$140$	0.158468	−	0.101841i	0.0133930	−	0.00860715i
$141$	−0.253717	+	1.76464i	−0.0213669	+	0.148610i
$142$	2.59626	−	5.68501i	0.217873	−	0.477075i
$143$	5.25944	−	1.54431i	0.439817	−	0.129142i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	−1.00320	−	1.15776i	−0.0833114	−	0.0961464i
$146$	0.396241	+	2.75592i	0.0327931	+	0.228081i
$147$	−0.959493	−	0.281733i	−0.0791376	−	0.0232369i
$148$	3.47533	−	4.01075i	0.285671	−	0.329682i
$149$	−4.62916	−	2.97498i	−0.379235	−	0.243720i	0.337111	−	0.941465i	$-0.390550\pi$
$149$	−4.62916	−	2.97498i	−0.379235	−	0.243720i	−0.716346	+	0.697745i	$0.754187\pi$
$150$	4.17642	+	2.68402i	0.341003	+	0.219149i
$151$	1.61506	−	1.86388i	0.131432	−	0.151681i	−0.686219	−	0.727395i	$-0.740731\pi$
$151$	1.61506	−	1.86388i	0.131432	−	0.151681i	0.817651	+	0.575715i	$0.195276\pi$
$152$	2.80769	+	0.824413i	0.227734	+	0.0668688i
$153$	0.286704	+	1.99407i	0.0231786	+	0.161211i
$154$	2.96241	+	3.41880i	0.238718	+	0.275495i
$155$	−0.207727	−	0.454860i	−0.0166851	−	0.0365352i
$156$	1.16264	−	0.341380i	0.0930853	−	0.0273323i
$157$	9.06594	−	19.8516i	0.723541	−	1.58433i	−0.0853335	−	0.996352i	$-0.527196\pi$
$157$	9.06594	−	19.8516i	0.723541	−	1.58433i	0.808874	−	0.587981i	$-0.200077\pi$
$158$	0.460679	−	3.20409i	0.0366496	−	0.254904i
$159$	−5.42752	+	3.48805i	−0.430430	+	0.276621i
$160$	−0.188371			−0.0148921
$161$	−4.68626	−	1.01932i	−0.369329	−	0.0803333i
$162$	−1.00000			−0.0785674
$163$	15.1264	−	9.72116i	1.18479	−	0.761420i	0.208531	−	0.978016i	$-0.433132\pi$
$163$	15.1264	−	9.72116i	1.18479	−	0.761420i	0.976261	+	0.216596i	$0.0694953\pi$
$164$	1.46358	−	10.1794i	0.114287	−	0.794880i
$165$	0.353992	−	0.775134i	0.0275582	−	0.0603441i
$166$	−15.9876	+	4.69438i	−1.24088	+	0.364354i
$167$	−2.12690	−	4.65726i	−0.164584	−	0.360389i	0.809313	−	0.587377i	$-0.199839\pi$
$167$	−2.12690	−	4.65726i	−0.164584	−	0.360389i	−0.973898	+	0.226988i	$0.927112\pi$
$168$	0.654861	+	0.755750i	0.0505236	+	0.0583073i
$169$	1.64114	+	11.4144i	0.126241	+	0.878028i
$170$	−0.364116	−	0.106914i	−0.0279264	−	0.00819993i
$171$	−1.91627	+	2.21149i	−0.146541	+	0.169117i
$172$	−1.58441	−	1.01824i	−0.120810	−	0.0776397i
$173$	−3.32660	−	2.13788i	−0.252917	−	0.162540i	0.408039	−	0.912964i	$-0.366213\pi$
$173$	−3.32660	−	2.13788i	−0.252917	−	0.162540i	−0.660956	+	0.750425i	$0.729849\pi$
$174$	5.32566	−	6.14614i	0.403737	−	0.465938i
$175$	4.76342	+	1.39867i	0.360081	+	0.105729i
$176$	−0.643793	−	4.47768i	−0.0485278	−	0.337518i
$177$	−2.81063	−	3.24364i	−0.211260	−	0.243807i
$178$	0.338730	+	0.741716i	0.0253889	+	0.0555939i
$179$	−15.8393	+	4.65083i	−1.18388	+	0.347619i	−0.813669	−	0.581328i	$-0.802533\pi$
$179$	−15.8393	+	4.65083i	−1.18388	+	0.347619i	−0.370213	+	0.928947i	$0.620715\pi$
$180$	0.0782522	−	0.171348i	0.00583258	−	0.0127716i
$181$	2.97474	−	20.6897i	0.221110	−	1.53786i	−0.512739	−	0.858544i	$-0.671369\pi$
$181$	2.97474	−	20.6897i	0.221110	−	1.53786i	0.733850	−	0.679312i	$-0.237722\pi$
$182$	1.01936	−	0.655104i	0.0755602	−	0.0485596i
$183$	−7.17659			−0.530509
$184$	3.39125	+	3.39108i	0.250006	+	0.249994i
$185$	−0.999683			−0.0734981
$186$	2.23318	−	1.43518i	0.163745	−	0.105232i
$187$	1.29697	−	9.02062i	0.0948438	−	0.659653i
$188$	0.740597	−	1.62168i	0.0540136	−	0.118273i
$189$	−0.959493	+	0.281733i	−0.0697928	+	0.0204930i
$190$	−0.228984	−	0.501405i	−0.0166122	−	0.0363757i
$191$	−14.2491	−	16.4444i	−1.03103	−	1.18987i	−0.981571	−	0.191097i	$-0.938795\pi$
$191$	−14.2491	−	16.4444i	−1.03103	−	1.18987i	−0.0494599	−	0.998776i	$-0.515750\pi$
$192$	−0.142315	−	0.989821i	−0.0102707	−	0.0714342i
$193$	1.36463	+	0.400692i	0.0982283	+	0.0288424i	0.330477	−	0.943814i	$-0.392790\pi$
$193$	1.36463	+	0.400692i	0.0982283	+	0.0288424i	−0.232249	+	0.972656i	$0.574608\pi$
$194$	−6.55221	+	7.56166i	−0.470422	+	0.542895i
$195$	−0.192018	−	0.123403i	−0.0137507	−	0.00883706i
$196$	0.841254	+	0.540641i	0.0600895	+	0.0386172i
$197$	11.9406	−	13.7802i	0.850734	−	0.981799i	−0.149242	−	0.988801i	$-0.547683\pi$
$197$	11.9406	−	13.7802i	0.850734	−	0.981799i	0.999975	+	0.00700159i	$0.00222869\pi$
$198$	4.34048	+	1.27448i	0.308465	+	0.0905734i
$199$	−0.00172933	−	0.0120278i	−0.000122589	−	0.000852627i	0.989760	−	0.142741i	$-0.0455916\pi$
$199$	−0.00172933	−	0.0120278i	−0.000122589	−	0.000852627i	−0.989883	+	0.141889i	$0.954683\pi$
$200$	−3.25107	−	3.75193i	−0.229885	−	0.265302i
$201$	−5.73680	−	12.5618i	−0.404643	−	0.886044i
$202$	−0.222133	+	0.0652242i	−0.0156292	+	0.00458916i
$203$	3.37837	−	7.39759i	0.237115	−	0.519209i
$204$	0.286704	−	1.99407i	0.0200733	−	0.139613i
$205$	−1.62970	+	1.04735i	−0.113823	+	0.0731498i
$206$	4.12504			0.287405
$207$	−4.49341	+	1.67608i	−0.312314	+	0.116496i
$208$	−1.21172			−0.0840175
$209$	11.1361	−	7.15671i	0.770297	−	0.495040i
$210$	0.0268080	−	0.186454i	0.00184993	−	0.0128665i
$211$	−2.00438	+	4.38899i	−0.137987	+	0.302150i	−0.965992	−	0.258570i	$-0.916749\pi$
$211$	−2.00438	+	4.38899i	−0.137987	+	0.302150i	0.828005	+	0.560721i	$0.189476\pi$
$212$	6.19036	−	1.81765i	0.425156	−	0.124837i
$213$	−2.59626	−	5.68501i	−0.177893	−	0.389530i
$214$	−6.77259	−	7.81599i	−0.462965	−	0.534290i
$215$	0.0504899	+	0.351165i	0.00344338	+	0.0239492i
$216$	0.959493	+	0.281733i	0.0652852	+	0.0191695i
$217$	1.73839	−	2.00620i	0.118009	−	0.136190i
$218$	−3.85790	−	2.47932i	−0.261290	−	0.167921i
$219$	2.34226	+	1.50528i	0.158276	+	0.101718i
$220$	−0.558033	+	0.644004i	−0.0376226	+	0.0434188i
$221$	−2.34221	−	0.687736i	−0.157554	−	0.0462621i
$222$	−0.755262	−	5.25296i	−0.0506899	−	0.352556i
$223$	−10.2998	−	11.8866i	−0.689724	−	0.795984i	0.297602	−	0.954690i	$-0.403813\pi$
$223$	−10.2998	−	11.8866i	−0.689724	−	0.795984i	−0.987326	+	0.158706i	$0.949268\pi$
$224$	−0.415415	−	0.909632i	−0.0277561	−	0.0607773i
$225$	4.76342	−	1.39867i	0.317561	−	0.0932444i
$226$	−5.59742	+	12.2567i	−0.372335	+	0.815300i
$227$	−0.989723	+	6.88367i	−0.0656902	+	0.456886i	0.930254	+	0.366916i	$0.119586\pi$
$227$	−0.989723	+	6.88367i	−0.0656902	+	0.456886i	−0.995944	+	0.0899700i	$0.971323\pi$
$228$	2.46170	−	1.58204i	0.163030	−	0.104773i
$229$	−9.09623			−0.601096			−0.300548	−	0.953767i	$-0.597170\pi$
$229$	−9.09623			−0.601096			−0.300548	+	0.953767i	$0.597170\pi$
$230$	0.0644260	−	0.901096i	0.00424813	−	0.0594165i
$231$	4.52373			0.297639
$232$	−6.84150	+	4.39677i	−0.449167	+	0.288662i
$233$	1.09675	−	7.62806i	0.0718505	−	0.499731i	−0.921840	−	0.387571i	$-0.873314\pi$
$233$	1.09675	−	7.62806i	0.0718505	−	0.499731i	0.993690	−	0.112160i	$-0.0357768\pi$
$234$	0.503366	−	1.10222i	0.0329061	−	0.0720542i
$235$	−0.322223	+	0.0946132i	−0.0210195	+	0.00617188i
$236$	1.78294	+	3.90409i	0.116060	+	0.254135i
$237$	−2.11981	−	2.44639i	−0.137696	−	0.158910i
$238$	−0.286704	−	1.99407i	−0.0185842	−	0.129256i
$239$	2.14976	+	0.631226i	0.139056	+	0.0408306i	0.350520	−	0.936555i	$-0.386005\pi$
$239$	2.14976	+	0.631226i	0.139056	+	0.0408306i	−0.211464	+	0.977386i	$0.567823\pi$
$240$	−0.123357	+	0.142361i	−0.00796265	+	0.00918939i
$241$	15.1635	+	9.74501i	0.976769	+	0.627732i	0.928590	−	0.371107i	$-0.121022\pi$
$241$	15.1635	+	9.74501i	0.976769	+	0.627732i	0.0481793	+	0.998839i	$0.484658\pi$
$242$	−7.96171	−	5.11668i	−0.511798	−	0.328913i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	6.88589	+	2.02188i	0.440824	+	0.129438i
$245$	−0.0268080	−	0.186454i	−0.00171270	−	0.0119121i
$246$	−6.73466	−	7.77221i	−0.429386	−	0.495538i
$247$	−1.47296	−	3.22534i	−0.0937224	−	0.205223i
$248$	−2.54706	+	0.747884i	−0.161738	+	0.0474907i
$249$	−6.92186	+	15.1568i	−0.438655	+	0.960521i
$250$	−0.267129	+	1.85792i	−0.0168947	+	0.117505i
$251$	19.9384	−	12.8136i	1.25850	−	0.808788i	0.270421	−	0.962742i	$-0.412837\pi$
$251$	19.9384	−	12.8136i	1.25850	−	0.808788i	0.988078	+	0.153954i	$0.0492009\pi$
$252$	1.00000			0.0629941
$253$	21.6397	−	1.54822i	1.36048	−	0.0973359i
$254$	16.4125			1.02981
$255$	−0.319245	+	0.205167i	−0.0199919	+	0.0128480i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−3.62777	+	7.94370i	−0.226294	+	0.495514i	−0.988388	−	0.151952i	$-0.951444\pi$
$257$	−3.62777	+	7.94370i	−0.226294	+	0.495514i	0.762094	+	0.647466i	$0.224171\pi$
$258$	−1.80710	+	0.530611i	−0.112505	+	0.0330344i
$259$	−2.20460	−	4.82740i	−0.136987	−	0.299960i
$260$	0.149474	+	0.172502i	0.00926997	+	0.0106981i
$261$	−1.15738	−	8.04974i	−0.0716398	−	0.498266i
$262$	−21.1797	−	6.21893i	−1.30849	−	0.384207i
$263$	2.78394	−	3.21284i	0.171665	−	0.198112i	−0.663397	−	0.748267i	$-0.730886\pi$
$263$	2.78394	−	3.21284i	0.171665	−	0.198112i	0.835062	+	0.550155i	$0.185431\pi$
$264$	−3.80560	−	2.44571i	−0.234219	−	0.150523i
$265$	−1.02239	−	0.657049i	−0.0628048	−	0.0403622i
$266$	1.91627	−	2.21149i	0.117494	−	0.135595i
$267$	0.782373	+	0.229725i	0.0478804	+	0.0140590i
$268$	1.96534	+	13.6692i	0.120052	+	0.834981i
$269$	12.9318	+	14.9241i	0.788466	+	0.909938i	0.997690	−	0.0679293i	$-0.0216392\pi$
$269$	12.9318	+	14.9241i	0.788466	+	0.909938i	−0.209224	+	0.977868i	$0.567094\pi$
$270$	−0.0782522	−	0.171348i	−0.00476228	−	0.0104279i
$271$	−7.65896	+	2.24887i	−0.465249	+	0.136609i	−0.505952	−	0.862562i	$-0.668859\pi$
$271$	−7.65896	+	2.24887i	−0.465249	+	0.136609i	0.0407026	+	0.999171i	$0.487040\pi$
$272$	−0.836884	+	1.83252i	−0.0507436	+	0.111113i
$273$	0.172445	−	1.19938i	0.0104369	−	0.0725901i
$274$	8.81814	−	5.66707i	0.532723	−	0.342360i
$275$	−22.4581			−1.35428
$276$	4.78360	−	0.342245i	0.287939	−	0.0206007i
$277$	−11.5013			−0.691044			−0.345522	−	0.938411i	$-0.612298\pi$
$277$	−11.5013			−0.691044			−0.345522	+	0.938411i	$0.612298\pi$
$278$	6.14544	−	3.94943i	0.368579	−	0.236871i
$279$	0.377787	−	2.62757i	0.0226175	−	0.157308i
$280$	−0.0782522	+	0.171348i	−0.00467647	+	0.0102400i
$281$	0.662932	−	0.194655i	0.0395472	−	0.0116121i	−0.261899	−	0.965095i	$-0.584349\pi$
$281$	0.662932	−	0.194655i	0.0395472	−	0.0116121i	0.301446	+	0.953483i	$0.402531\pi$
$282$	−0.740597	−	1.62168i	−0.0441019	−	0.0965698i
$283$	−14.6252	−	16.8784i	−0.869378	−	1.00332i	−0.999930	−	0.0118739i	$-0.996220\pi$
$283$	−14.6252	−	16.8784i	−0.869378	−	1.00332i	0.130552	−	0.991441i	$-0.458325\pi$
$284$	0.889438	+	6.18617i	0.0527784	+	0.367082i
$285$	−0.528889	−	0.155296i	−0.0313287	−	0.00919893i
$286$	−3.58961	+	4.14263i	−0.212258	+	0.244959i
$287$	−8.65154	−	5.56001i	−0.510684	−	0.328197i
$288$	−0.841254	−	0.540641i	−0.0495713	−	0.0318576i
$289$	8.47487	−	9.78053i	0.498522	−	0.575325i
$290$	1.46988	+	0.431595i	0.0863142	+	0.0253441i
$291$	1.42393	+	9.90367i	0.0834724	+	0.580563i
$292$	−1.82330	−	2.10420i	−0.106701	−	0.123139i
$293$	−10.3161	−	22.5890i	−0.602671	−	1.31967i	−0.927475	−	0.373885i	$-0.878026\pi$
$293$	−10.3161	−	22.5890i	−0.602671	−	1.31967i	0.324804	−	0.945781i	$-0.394702\pi$
$294$	0.959493	−	0.281733i	0.0559588	−	0.0164310i
$295$	0.335855	−	0.735419i	0.0195542	−	0.0428178i
$296$	−0.755262	+	5.25296i	−0.0438987	+	0.305322i
$297$	3.80560	−	2.44571i	0.220823	−	0.141915i
$298$	5.50269			0.318762
$299$	0.414427	−	5.79640i	0.0239670	−	0.335214i
$300$	−4.96452			−0.286626
$301$	−1.58441	+	1.01824i	−0.0913236	+	0.0586901i
$302$	−0.350987	+	2.44117i	−0.0201970	+	0.140473i
$303$	−0.0961732	+	0.210590i	−0.00552501	+	0.0120981i
$304$	−2.80769	+	0.824413i	−0.161032	+	0.0472834i
$305$	−0.561584	−	1.22970i	−0.0321562	−	0.0704123i
$306$	−1.31927	−	1.52251i	−0.0754174	−	0.0870363i
$307$	−4.59705	−	31.9732i	−0.262368	−	1.82481i	−0.514936	−	0.857229i	$-0.672184\pi$
$307$	−4.59705	−	31.9732i	−0.262368	−	1.82481i	0.252568	−	0.967579i	$-0.418725\pi$
$308$	−4.34048	−	1.27448i	−0.247322	−	0.0726203i
$309$	2.70133	−	3.11750i	0.153673	−	0.177348i
$310$	0.420667	+	0.270346i	0.0238923	+	0.0153546i
$311$	−22.9774	−	14.7667i	−1.30293	−	0.837342i	−0.309402	−	0.950931i	$-0.600129\pi$
$311$	−22.9774	−	14.7667i	−1.30293	−	0.837342i	−0.993528	+	0.113589i	$0.963765\pi$
$312$	−0.793507	+	0.915755i	−0.0449235	+	0.0518444i
$313$	15.1392	+	4.44526i	0.855716	+	0.251261i	0.680029	−	0.733185i	$-0.261967\pi$
$313$	15.1392	+	4.44526i	0.855716	+	0.251261i	0.175687	+	0.984446i	$0.443785\pi$
$314$	3.10585	+	21.6017i	0.175273	+	1.21905i
$315$	−0.123357	−	0.142361i	−0.00695037	−	0.00802116i
$316$	1.34471	+	2.94451i	0.0756461	+	0.165642i
$317$	15.3548	−	4.50859i	0.862414	−	0.253228i	0.179528	−	0.983753i	$-0.442543\pi$
$317$	15.3548	−	4.50859i	0.862414	−	0.253228i	0.682886	+	0.730525i	$0.260725\pi$
$318$	2.68013	−	5.86868i	0.150294	−	0.329099i
$319$	−5.23566	+	36.4148i	−0.293141	+	2.03884i
$320$	0.158468	−	0.101841i	0.00885863	−	0.00569309i
$321$	−10.3420			−0.577236
$322$	4.49341	−	1.67608i	0.250408	−	0.0934042i
$323$	−5.89510			−0.328012
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	−0.856108	+	5.95436i	−0.0474883	+	0.330289i
$326$	−7.46950	+	16.3559i	−0.413697	+	0.905871i
$327$	−4.40013	+	1.29200i	−0.243328	+	0.0714475i
$328$	4.27217	+	9.35475i	0.235891	+	0.516530i
$329$	−1.16748	−	1.34734i	−0.0643652	−	0.0742814i
$330$	0.121272	+	0.843466i	0.00667581	+	0.0464313i
$331$	7.28485	+	2.13902i	0.400411	+	0.117571i	0.475737	−	0.879588i	$-0.342181\pi$
$331$	7.28485	+	2.13902i	0.400411	+	0.117571i	−0.0753256	+	0.997159i	$0.524000\pi$
$332$	10.9116	−	12.5927i	0.598854	−	0.691114i
$333$	−4.46452	−	2.86917i	−0.244654	−	0.157230i
$334$	4.30716	+	2.76805i	0.235677	+	0.151461i
$335$	1.70353	−	1.96598i	0.0930740	−	0.107413i
$336$	−0.959493	−	0.281733i	−0.0523446	−	0.0153698i
$337$	1.07366	+	7.46750i	0.0584862	+	0.406781i	0.997943	+	0.0641123i	$0.0204216\pi$
$337$	1.07366	+	7.46750i	0.0584862	+	0.406781i	−0.939456	+	0.342668i	$0.888669\pi$
$338$	−7.55168	−	8.71511i	−0.410757	−	0.474039i
$339$	5.59742	+	12.2567i	0.304010	+	0.665690i
$340$	0.364116	−	0.106914i	0.0197470	−	0.00579823i
$341$	−4.98857	+	10.9234i	−0.270146	+	0.591537i
$342$	0.416446	−	2.89644i	0.0225188	−	0.156622i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	1.88339			0.101545
$345$	−0.638813	−	0.638783i	−0.0343925	−	0.0343909i
$346$	3.95434			0.212587
$347$	−16.2018	+	10.4122i	−0.869756	+	0.558959i	−0.897678	−	0.440652i	$-0.854747\pi$
$347$	−16.2018	+	10.4122i	−0.869756	+	0.558959i	0.0279218	+	0.999610i	$0.491111\pi$
$348$	−1.15738	+	8.04974i	−0.0620419	+	0.431511i
$349$	10.4214	−	22.8196i	0.557843	−	1.22151i	−0.395179	−	0.918604i	$-0.629317\pi$
$349$	10.4214	−	22.8196i	0.557843	−	1.22151i	0.953022	−	0.302902i	$-0.0979554\pi$
$350$	−4.76342	+	1.39867i	−0.254615	+	0.0747618i
$351$	−0.503366	−	1.10222i	−0.0268677	−	0.0588320i
$352$	2.96241	+	3.41880i	0.157897	+	0.182223i
$353$	0.880870	+	6.12658i	0.0468840	+	0.326085i	0.999743	+	0.0226717i	$0.00721724\pi$
$353$	0.880870	+	6.12658i	0.0468840	+	0.326085i	−0.952859	+	0.303413i	$0.901874\pi$
$354$	4.11810	+	1.20918i	0.218874	+	0.0642673i
$355$	0.770955	−	0.889729i	0.0409180	−	0.0472219i
$356$	−0.685960	−	0.440840i	−0.0363558	−	0.0233645i
$357$	−1.69477	−	1.08916i	−0.0896966	−	0.0576445i
$358$	10.8104	−	12.4759i	0.571348	−	0.659371i
$359$	−30.6759	−	9.00726i	−1.61901	−	0.475385i	−0.658259	−	0.752791i	$-0.728707\pi$
$359$	−30.6759	−	9.00726i	−1.61901	−	0.475385i	−0.960753	+	0.277406i	$0.910525\pi$
$360$	0.0268080	+	0.186454i	0.00141291	+	0.00982698i
$361$	6.83491	+	7.88791i	0.359732	+	0.415153i
$362$	8.68321	+	19.0136i	0.456379	+	0.999332i
$363$	−9.08074	+	2.66634i	−0.476615	+	0.139947i
$364$	−0.503366	+	1.10222i	−0.0263835	+	0.0577719i
$365$	−0.0746404	+	0.519135i	−0.00390686	+	0.0271728i
$366$	6.03733	−	3.87996i	0.315576	−	0.202809i
$367$	4.13687			0.215943			0.107971	−	0.994154i	$-0.465565\pi$
$367$	4.13687			0.215943			0.107971	+	0.994154i	$0.465565\pi$
$368$	−4.68626	−	1.01932i	−0.244288	−	0.0531355i
$369$	−10.2841			−0.535369
$370$	0.840987	−	0.540469i	0.0437208	−	0.0280977i
$371$	0.918173	−	6.38603i	0.0476692	−	0.331546i
$372$	−1.10276	+	2.41470i	−0.0571752	+	0.125196i
$373$	−6.61109	+	1.94119i	−0.342309	+	0.100511i	−0.448369	−	0.893849i	$-0.647995\pi$
$373$	−6.61109	+	1.94119i	−0.342309	+	0.100511i	0.106059	+	0.994360i	$0.466177\pi$
$374$	3.78584	+	8.28982i	0.195761	+	0.428657i
$375$	1.22919	+	1.41856i	0.0634752	+	0.0732543i
$376$	0.253717	+	1.76464i	0.0130845	+	0.0910045i
$377$	9.45514	+	2.77628i	0.486965	+	0.142986i
$378$	0.654861	−	0.755750i	0.0336824	−	0.0388716i
$379$	25.0034	+	16.0687i	1.28434	+	0.825393i	0.991416	−	0.130744i	$-0.0417366\pi$
$379$	25.0034	+	16.0687i	1.28434	+	0.825393i	0.292920	+	0.956137i	$0.405373\pi$
$380$	0.463713	+	0.298010i	0.0237880	+	0.0152876i
$381$	10.7479	−	12.4037i	0.550632	−	0.635463i
$382$	20.8776	+	6.13023i	1.06819	+	0.313650i
$383$	3.03704	+	21.1231i	0.155186	+	1.07934i	0.907354	+	0.420368i	$0.138099\pi$
$383$	3.03704	+	21.1231i	0.155186	+	1.07934i	−0.752168	+	0.658971i	$0.770992\pi$
$384$	0.654861	+	0.755750i	0.0334182	+	0.0385667i
$385$	0.353992	+	0.775134i	0.0180411	+	0.0395045i
$386$	−1.36463	+	0.400692i	−0.0694579	+	0.0203947i
$387$	−0.782387	+	1.71319i	−0.0397710	+	0.0870863i
$388$	1.42393	−	9.90367i	0.0722892	−	0.502782i
$389$	−6.20687	+	3.98891i	−0.314701	+	0.202246i	−0.688450	−	0.725284i	$-0.741708\pi$
$389$	−6.20687	+	3.98891i	−0.314701	+	0.202246i	0.373749	+	0.927530i	$0.378072\pi$
$390$	0.228253			0.0115580
$391$	−8.47986	−	4.63009i	−0.428845	−	0.234154i
$392$	−1.00000			−0.0505076
$393$	−18.5697	+	11.9340i	−0.936719	+	0.601993i
$394$	−2.59494	+	18.0482i	−0.130731	+	0.909257i
$395$	0.253305	−	0.554662i	0.0127452	−	0.0279081i
$396$	−4.34048	+	1.27448i	−0.218118	+	0.0640451i
$397$	−6.93089	−	15.1765i	−0.347852	−	0.761689i	−0.999994	−	0.00359177i	$-0.998857\pi$
$397$	−6.93089	−	15.1765i	−0.347852	−	0.761689i	0.652142	−	0.758097i	$-0.273871\pi$
$398$	0.00795752	+	0.00918347i	0.000398874	+	0.000460326i
$399$	−0.416446	−	2.89644i	−0.0208484	−	0.145003i
$400$	4.76342	+	1.39867i	0.238171	+	0.0699333i
$401$	−3.40415	+	3.92860i	−0.169995	+	0.196185i	−0.834354	−	0.551229i	$-0.814159\pi$
$401$	−3.40415	+	3.92860i	−0.169995	+	0.196185i	0.664359	+	0.747414i	$0.268705\pi$
$402$	11.6175	+	7.46614i	0.579430	+	0.372377i
$403$	2.70599	+	1.73903i	0.134795	+	0.0866274i
$404$	0.151608	−	0.174964i	0.00754276	−	0.00870481i
$405$	−0.180741	−	0.0530703i	−0.00898109	−	0.00263708i
$406$	1.15738	+	8.04974i	0.0574397	+	0.399502i
$407$	15.7215	+	18.1435i	0.779284	+	0.899341i
$408$	0.836884	+	1.83252i	0.0414319	+	0.0907233i
$409$	−25.5757	+	7.50971i	−1.26464	+	0.371331i	−0.844219	−	0.535999i	$-0.819935\pi$
$409$	−25.5757	+	7.50971i	−1.26464	+	0.371331i	−0.420419	+	0.907330i	$0.638117\pi$
$410$	0.804755	−	1.76217i	0.0397440	−	0.0870272i
$411$	1.49176	−	10.3754i	0.0735833	−	0.511783i
$412$	−3.47021	+	2.23017i	−0.170965	+	0.109872i
$413$	4.29195			0.211193
$414$	2.87394	−	3.83933i	0.141247	−	0.188693i
$415$	−3.13874			−0.154075
$416$	1.01936	−	0.655104i	0.0499783	−	0.0321191i
$417$	1.03962	−	7.23074i	0.0509106	−	0.354091i
$418$	−5.49904	+	12.0412i	−0.268967	+	0.588955i
$419$	−21.2613	+	6.24289i	−1.03868	+	0.304985i	−0.756237	−	0.654298i	$-0.772964\pi$
$419$	−21.2613	+	6.24289i	−1.03868	+	0.304985i	−0.282447	+	0.959283i	$0.591146\pi$
$420$	0.0782522	+	0.171348i	0.00381832	+	0.00836095i
$421$	−0.891902	−	1.02931i	−0.0434686	−	0.0501655i	0.733599	−	0.679583i	$-0.237839\pi$
$421$	−0.891902	−	1.02931i	−0.0434686	−	0.0501655i	−0.777068	+	0.629417i	$0.783294\pi$
$422$	−0.686671	−	4.77590i	−0.0334266	−	0.232487i
$423$	−1.71057	−	0.502270i	−0.0831709	−	0.0244212i
$424$	−4.22497	+	4.87587i	−0.205183	+	0.236793i
$425$	8.41370	+	5.40716i	0.408124	+	0.262286i
$426$	5.25766	+	3.37889i	0.254734	+	0.163708i
$427$	4.69967	−	5.42370i	0.227433	−	0.262471i
$428$	9.92311	+	2.91369i	0.479652	+	0.140838i
$429$	0.780096	+	5.42569i	0.0376634	+	0.261955i
$430$	−0.232329	−	0.268122i	−0.0112039	−	0.0129300i
$431$	13.1072	+	28.7007i	0.631350	+	1.38246i	0.906969	+	0.421198i	$0.138390\pi$
$431$	13.1072	+	28.7007i	0.631350	+	1.38246i	−0.275618	+	0.961267i	$0.588883\pi$
$432$	−0.959493	+	0.281733i	−0.0461636	+	0.0135549i
$433$	−5.07394	+	11.1104i	−0.243838	+	0.533931i	−0.991494	−	0.130156i	$-0.958452\pi$
$433$	−5.07394	+	11.1104i	−0.243838	+	0.533931i	0.747655	+	0.664087i	$0.231179\pi$
$434$	−0.377787	+	2.62757i	−0.0181344	+	0.126127i
$435$	1.28874	−	0.828225i	0.0617905	−	0.0397103i
$436$	4.58589			0.219624
$437$	−2.98340	−	13.7129i	−0.142716	−	0.655977i
$438$	−2.78426			−0.133037
$439$	−1.58072	+	1.01587i	−0.0754437	+	0.0484847i	−0.577819	−	0.816165i	$-0.696096\pi$
$439$	−1.58072	+	1.01587i	−0.0754437	+	0.0484847i	0.502375	+	0.864650i	$0.332460\pi$
$440$	0.121272	−	0.843466i	0.00578142	−	0.0402107i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	2.34221	−	0.687736i	0.111408	−	0.0327123i
$443$	13.7866	+	30.1884i	0.655020	+	1.43429i	0.887091	+	0.461595i	$0.152722\pi$
$443$	13.7866	+	30.1884i	0.655020	+	1.43429i	−0.232071	+	0.972699i	$0.574550\pi$
$444$	3.47533	+	4.01075i	0.164932	+	0.190342i
$445$	0.0218593	+	0.152035i	0.00103623	+	0.00720714i
$446$	15.0911	+	4.43114i	0.714584	+	0.209821i
$447$	3.60349	−	4.15865i	0.170439	−	0.196698i
$448$	0.841254	+	0.540641i	0.0397455	+	0.0255429i
$449$	−1.56461	−	1.00551i	−0.0738385	−	0.0474531i	0.503201	−	0.864170i	$-0.332156\pi$
$449$	−1.56461	−	1.00551i	−0.0738385	−	0.0474531i	−0.577039	+	0.816716i	$0.695792\pi$
$450$	−3.25107	+	3.75193i	−0.153257	+	0.176868i
$451$	44.6380	+	13.1069i	2.10192	+	0.617180i
$452$	−1.91759	−	13.3371i	−0.0901960	−	0.627327i
$453$	1.61506	+	1.86388i	0.0758823	+	0.0875729i
$454$	−2.88899	−	6.32600i	−0.135587	−	0.296894i
$455$	0.219007	−	0.0643063i	0.0102672	−	0.00301472i
$456$	−1.21560	+	2.66179i	−0.0569256	+	0.124650i
$457$	−3.75023	+	26.0834i	−0.175428	+	1.22013i	0.691752	+	0.722135i	$0.256839\pi$
$457$	−3.75023	+	26.0834i	−0.175428	+	1.22013i	−0.867180	+	0.497994i	$0.834070\pi$
$458$	7.65224	−	4.91779i	0.357566	−	0.229793i
$459$	−2.01457			−0.0940323
$460$	0.432971	+	0.792882i	0.0201874	+	0.0369683i
$461$	−30.1172			−1.40270			−0.701348	−	0.712819i	$-0.747418\pi$
$461$	−30.1172			−1.40270			−0.701348	+	0.712819i	$0.747418\pi$
$462$	−3.80560	+	2.44571i	−0.177053	+	0.113785i
$463$	3.53476	−	24.5848i	0.164274	−	1.14255i	−0.726188	−	0.687497i	$-0.758710\pi$
$463$	3.53476	−	24.5848i	0.164274	−	1.14255i	0.890462	−	0.455057i	$-0.150381\pi$
$464$	3.37837	−	7.39759i	0.156837	−	0.343425i
$465$	0.479793	−	0.140880i	0.0222499	−	0.00653315i
$466$	3.20140	+	7.01008i	0.148302	+	0.324736i
$467$	−21.3727	−	24.6654i	−0.989008	−	1.14138i	−0.989956	−	0.141377i	$-0.954847\pi$
$467$	−21.3727	−	24.6654i	−0.989008	−	1.14138i	0.000947411	−	1.00000i	$-0.499698\pi$
$468$	0.172445	+	1.19938i	0.00797129	+	0.0554416i
$469$	13.2504	+	3.89067i	0.611847	+	0.179654i
$470$	0.219919	−	0.253800i	0.0101441	−	0.0117069i
$471$	18.3594	+	11.7988i	0.845955	+	0.543662i
$472$	−3.61062	−	2.32040i	−0.166192	−	0.106805i
$473$	5.57936	−	6.43893i	0.256539	−	0.296062i
$474$	3.10592	+	0.911979i	0.142659	+	0.0418886i
$475$	2.06745	+	14.3794i	0.0948611	+	0.659774i
$476$	1.31927	+	1.52251i	0.0604684	+	0.0697843i
$477$	−2.68013	−	5.86868i	−0.122715	−	0.268708i
$478$	−2.14976	+	0.631226i	−0.0983276	+	0.0288716i
$479$	−4.43400	+	9.70911i	−0.202595	+	0.443620i	−0.983471	−	0.181065i	$-0.942046\pi$
$479$	−4.43400	+	9.70911i	−0.202595	+	0.443620i	0.780876	+	0.624685i	$0.214773\pi$
$480$	0.0268080	−	0.186454i	0.00122361	−	0.00851042i
$481$	5.40974	−	3.47663i	0.246663	−	0.158521i
$482$	−18.0249			−0.821013
$483$	1.67586	−	4.49349i	0.0762544	−	0.204461i
$484$	9.46410			0.430186
$485$	−1.58555	+	1.01897i	−0.0719962	+	0.0462692i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	6.47377	−	14.1756i	0.293355	−	0.642357i	−0.704366	−	0.709837i	$-0.748769\pi$
$487$	6.47377	−	14.1756i	0.293355	−	0.642357i	0.997721	+	0.0674798i	$0.0214958\pi$
$488$	−6.88589	+	2.02188i	−0.311709	+	0.0915262i
$489$	7.46950	+	16.3559i	0.337782	+	0.739640i
$490$	0.123357	+	0.142361i	0.00557270	+	0.00643124i
$491$	3.13442	+	21.8004i	0.141454	+	0.983837i	0.929658	+	0.368423i	$0.120102\pi$
$491$	3.13442	+	21.8004i	0.141454	+	0.983837i	−0.788204	+	0.615414i	$0.788989\pi$
$492$	9.86753	+	2.89737i	0.444863	+	0.130623i
$493$	10.7289	−	12.3819i	0.483207	−	0.557651i
$494$	2.98289	+	1.91698i	0.134206	+	0.0862492i
$495$	0.716866	+	0.460702i	0.0322207	+	0.0207070i
$496$	1.73839	−	2.00620i	0.0780558	−	0.0900812i
$497$	5.99663	+	1.76077i	0.268986	+	0.0789813i
$498$	−2.37133	−	16.4929i	−0.106262	−	0.739066i
$499$	−19.4435	−	22.4390i	−0.870411	−	1.00451i	−0.999916	−	0.0129287i	$-0.995885\pi$
$499$	−19.4435	−	22.4390i	−0.870411	−	1.00451i	0.129506	−	0.991579i	$-0.458661\pi$
$500$	−0.779746	−	1.70740i	−0.0348713	−	0.0763575i
$501$	4.91254	−	1.44245i	0.219476	−	0.0644440i
$502$	−9.84566	+	21.5590i	−0.439433	+	0.962225i
$503$	−4.21878	+	29.3423i	−0.188106	+	1.30831i	0.648800	+	0.760959i	$0.275271\pi$
$503$	−4.21878	+	29.3423i	−0.188106	+	1.30831i	−0.836906	+	0.547347i	$0.815638\pi$
$504$	−0.841254	+	0.540641i	−0.0374724	+	0.0240821i
$505$	−0.0436100			−0.00194062
$506$	−17.3675	+	13.0018i	−0.772078	+	0.577999i
$507$	−11.5317			−0.512143
$508$	−13.8071	+	8.87327i	−0.612590	+	0.393688i
$509$	−1.01711	+	7.07416i	−0.0450827	+	0.313557i	0.954785	+	0.297297i	$0.0960851\pi$
$509$	−1.01711	+	7.07416i	−0.0450827	+	0.313557i	−0.999868	+	0.0162601i	$0.994824\pi$
$510$	0.157645	−	0.345194i	0.00698063	−	0.0152855i
$511$	−2.67147	+	0.784415i	−0.118179	+	0.0347005i
$512$	−0.415415	−	0.909632i	−0.0183589	−	0.0402004i
$513$	−1.91627	−	2.21149i	−0.0846054	−	0.0976399i
$514$	−1.24282	−	8.64399i	−0.0548183	−	0.381270i
$515$	0.745564	+	0.218917i	0.0328535	+	0.00964665i
$516$	1.23336	−	1.42337i	0.0542955	−	0.0626603i
$517$	6.78458	+	4.36019i	0.298386	+	0.191761i
$518$	4.46452	+	2.86917i	0.196160	+	0.126064i
$519$	2.58954	−	2.98849i	0.113668	−	0.131180i
$520$	−0.219007	−	0.0643063i	−0.00960409	−	0.00282002i
$521$	2.14123	+	14.8926i	0.0938091	+	0.652457i	0.981421	+	0.191865i	$0.0614536\pi$
$521$	2.14123	+	14.8926i	0.0938091	+	0.652457i	−0.887612	+	0.460592i	$0.847637\pi$
$522$	5.32566	+	6.14614i	0.233098	+	0.269009i
$523$	9.16331	+	20.0648i	0.400683	+	0.877374i	0.997201	+	0.0747738i	$0.0238235\pi$
$523$	9.16331	+	20.0648i	0.400683	+	0.877374i	−0.596517	+	0.802600i	$0.703449\pi$
$524$	21.1797	−	6.21893i	0.925241	−	0.271675i
$525$	−2.06233	+	4.51588i	−0.0900077	+	0.197089i
$526$	−0.605008	+	4.20793i	−0.0263796	+	0.183474i
$527$	4.49891	−	2.89127i	0.195976	−	0.125946i
$528$	4.52373			0.196870
$529$	6.47879	−	22.0686i	0.281687	−	0.959506i
$530$	1.21532			0.0527899
$531$	3.61062	−	2.32040i	0.156687	−	0.100697i
$532$	−0.416446	+	2.89644i	−0.0180552	+	0.125577i
$533$	5.17667	−	11.3353i	0.224226	−	0.490987i
$534$	−0.782373	+	0.229725i	−0.0338566	+	0.00994119i
$535$	−0.809288	−	1.77209i	−0.0349886	−	0.0766142i
$536$	−9.04350	−	10.4368i	−0.390620	−	0.450799i
$537$	−2.34933	−	16.3399i	−0.101381	−	0.705120i
$538$	−18.9475	−	5.56349i	−0.816885	−	0.239859i
$539$	−2.96241	+	3.41880i	−0.127600	+	0.147258i
$540$	0.158468	+	0.101841i	0.00681937	+	0.00438255i
$541$	10.6496	+	6.84405i	0.457860	+	0.294249i	0.749167	−	0.662381i	$-0.230454\pi$
$541$	10.6496	+	6.84405i	0.457860	+	0.294249i	−0.291307	+	0.956630i	$0.594090\pi$
$542$	5.22730	−	6.03262i	0.224532	−	0.259123i
$543$	20.0558	+	5.88891i	0.860677	+	0.252718i
$544$	−0.286704	−	1.99407i	−0.0122923	−	0.0854950i
$545$	−0.565702	−	0.652855i	−0.0242320	−	0.0279652i
$546$	0.503366	+	1.10222i	0.0215421	+	0.0471706i
$547$	−31.1093	+	9.13451i	−1.33014	+	0.390563i	−0.868140	−	0.496319i	$-0.834685\pi$
$547$	−31.1093	+	9.13451i	−1.33014	+	0.390563i	−0.461996	+	0.886882i	$0.652867\pi$
$548$	−4.35444	+	9.53489i	−0.186012	+	0.407310i
$549$	1.02134	−	7.10354i	0.0435895	−	0.303172i
$550$	18.8930	−	12.1418i	0.805599	−	0.517727i
$551$	23.7976			1.01381
$552$	−3.83919	+	2.87413i	−0.163407	+	0.122331i
$553$	3.23704			0.137653
$554$	9.67547	−	6.21805i	0.411071	−	0.264180i
$555$	0.142270	−	0.989507i	0.00603901	−	0.0420022i
$556$	−3.03465	+	6.64495i	−0.128698	+	0.281809i
$557$	−33.7756	+	9.91740i	−1.43112	+	0.420214i	−0.903250	−	0.429114i	$-0.858826\pi$
$557$	−33.7756	+	9.91740i	−1.43112	+	0.420214i	−0.527866	+	0.849328i	$0.677008\pi$
$558$	1.10276	+	2.41470i	0.0466834	+	0.102222i
$559$	−1.49448	−	1.72472i	−0.0632097	−	0.0729479i
$560$	−0.0268080	−	0.186454i	−0.00113285	−	0.00787911i
$561$	8.74423	+	2.56754i	0.369181	+	0.108401i
$562$	−0.452456	+	0.522162i	−0.0190857	+	0.0220261i
$563$	−32.9797	−	21.1948i	−1.38993	−	0.893254i	−0.390306	−	0.920685i	$-0.627631\pi$
$563$	−32.9797	−	21.1948i	−1.38993	−	0.893254i	−0.999624	+	0.0274317i	$0.991267\pi$
$564$	1.49978	+	0.963849i	0.0631520	+	0.0405853i
$565$	−1.66215	+	1.91822i	−0.0699271	+	0.0807001i
$566$	21.4286	+	6.29202i	0.900713	+	0.264473i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	−4.09274	−	4.72327i	−0.171728	−	0.198184i
$569$	1.09565	+	2.39914i	0.0459321	+	0.100577i	0.931207	−	0.364491i	$-0.118757\pi$
$569$	1.09565	+	2.39914i	0.0459321	+	0.100577i	−0.885275	+	0.465068i	$0.846030\pi$
$570$	0.528889	−	0.155296i	0.0221527	−	0.00650462i
$571$	−2.74314	+	6.00664i	−0.114797	+	0.251370i	−0.958306	−	0.285745i	$-0.907759\pi$
$571$	−2.74314	+	6.00664i	−0.114797	+	0.251370i	0.843509	+	0.537116i	$0.180486\pi$
$572$	0.780096	−	5.42569i	0.0326175	−	0.226859i
$573$	18.3049	−	11.7638i	0.764696	−	0.491441i
$574$	10.2841			0.429250
$575$	−8.31985	+	22.3080i	−0.346962	+	0.930309i
$576$	1.00000			0.0416667
$577$	6.97551	−	4.48289i	0.290394	−	0.186625i	−0.387330	−	0.921941i	$-0.626603\pi$
$577$	6.97551	−	4.48289i	0.290394	−	0.186625i	0.677724	+	0.735316i	$0.262966\pi$
$578$	−1.84177	+	12.8098i	−0.0766074	+	0.532816i
$579$	−0.590821	+	1.29372i	−0.0245537	+	0.0537651i
$580$	−1.46988	+	0.431595i	−0.0610333	+	0.0179210i
$581$	−6.92186	−	15.1568i	−0.287167	−	0.628809i
$582$	−6.55221	−	7.56166i	−0.271598	−	0.313441i
$583$	4.15356	+	28.8887i	0.172023	+	1.19645i
$584$	2.67147	+	0.784415i	0.110546	+	0.0324593i
$585$	0.149474	−	0.172502i	0.00617998	−	0.00713208i
$586$	20.8910	+	13.4258i	0.862999	+	0.554616i
$587$	−15.9380	−	10.2428i	−0.657833	−	0.422764i	0.168688	−	0.985670i	$-0.446047\pi$
$587$	−15.9380	−	10.2428i	−0.657833	−	0.422764i	−0.826521	+	0.562906i	$0.809683\pi$
$588$	−0.654861	+	0.755750i	−0.0270060	+	0.0311666i
$589$	7.45327	+	2.18848i	0.307107	+	0.0901747i
$590$	0.115059	+	0.800251i	0.00473689	+	0.0329458i
$591$	11.9406	+	13.7802i	0.491171	+	0.566842i
$592$	−2.20460	−	4.82740i	−0.0906085	−	0.198405i
$593$	21.2752	−	6.24696i	0.873667	−	0.256532i	0.185993	−	0.982551i	$-0.440450\pi$
$593$	21.2752	−	6.24696i	0.873667	−	0.256532i	0.687674	+	0.726019i	$0.258632\pi$
$594$	−1.87922	+	4.11493i	−0.0771055	+	0.168837i
$595$	0.0540067	−	0.375625i	0.00221406	−	0.0153991i
$596$	−4.62916	+	2.97498i	−0.189618	+	0.121860i
$597$	0.0121515			0.000497326
$598$	2.78513	+	5.10030i	0.113893	+	0.208567i
$599$	−28.0680			−1.14683			−0.573413	−	0.819267i	$-0.694381\pi$
$599$	−28.0680			−1.14683			−0.573413	+	0.819267i	$0.694381\pi$
$600$	4.17642	−	2.68402i	0.170502	−	0.109575i
$601$	4.24162	−	29.5011i	0.173019	−	1.20338i	−0.699441	−	0.714690i	$-0.746568\pi$
$601$	4.24162	−	29.5011i	0.173019	−	1.20338i	0.872460	−	0.488685i	$-0.162523\pi$
$602$	0.782387	−	1.71319i	0.0318877	−	0.0698243i
$603$	13.2504	−	3.89067i	0.539598	−	0.158440i
$604$	−1.02453	−	2.24340i	−0.0416874	−	0.0912826i
$605$	−1.16746	−	1.34732i	−0.0474641	−	0.0547765i
$606$	−0.0329475	−	0.229155i	−0.00133840	−	0.00930877i
$607$	−8.84058	−	2.59583i	−0.358828	−	0.105361i	0.0973493	−	0.995250i	$-0.468964\pi$
$607$	−8.84058	−	2.59583i	−0.358828	−	0.105361i	−0.456177	+	0.889889i	$0.650782\pi$
$608$	1.91627	−	2.21149i	0.0777151	−	0.0896880i
$609$	6.84150	+	4.39677i	0.277232	+	0.178166i
$610$	1.13726	+	0.730872i	0.0460463	+	0.0295922i
$611$	1.41465	−	1.63260i	0.0572308	−	0.0660479i
$612$	1.93297	+	0.567571i	0.0781357	+	0.0229427i
$613$	5.74425	+	39.9522i	0.232008	+	1.61365i	0.689396	+	0.724385i	$0.257876\pi$
$613$	5.74425	+	39.9522i	0.232008	+	1.61365i	−0.457387	+	0.889268i	$0.651215\pi$
$614$	21.1533	+	24.4122i	0.853678	+	0.985197i
$615$	−0.804755	−	1.76217i	−0.0324508	−	0.0710574i
$616$	4.34048	−	1.27448i	0.174883	−	0.0513503i
$617$	−5.90187	+	12.9233i	−0.237600	+	0.520272i	−0.990442	−	0.137930i	$-0.955955\pi$
$617$	−5.90187	+	12.9233i	−0.237600	+	0.520272i	0.752842	+	0.658201i	$0.228682\pi$
$618$	−0.587055	+	4.08305i	−0.0236148	+	0.164245i
$619$	15.2582	−	9.80585i	0.613279	−	0.394131i	−0.196806	−	0.980442i	$-0.563057\pi$
$619$	15.2582	−	9.80585i	0.613279	−	0.394131i	0.810085	+	0.586312i	$0.199421\pi$
$620$	−0.500048			−0.0200824
$621$	−1.01954	−	4.68621i	−0.0409127	−	0.188051i
$622$	27.3133			1.09516
$623$	−0.685960	+	0.440840i	−0.0274824	+	0.0176619i
$624$	0.172445	−	1.19938i	0.00690334	−	0.0480138i
$625$	10.1648	−	22.2578i	0.406592	−	0.890312i
$626$	−15.1392	+	4.44526i	−0.605083	+	0.177668i
$627$	5.49904	+	12.0412i	0.219610	+	0.480880i
$628$	−14.2916	−	16.4933i	−0.570295	−	0.658156i
$629$	−1.52153	−	10.5825i	−0.0606674	−	0.421951i
$630$	0.180741	+	0.0530703i	0.00720089	+	0.00211437i
$631$	−22.7460	+	26.2503i	−0.905503	+	1.04501i	0.0932774	+	0.995640i	$0.470266\pi$
$631$	−22.7460	+	26.2503i	−0.905503	+	1.04501i	−0.998781	+	0.0493664i	$0.984280\pi$
$632$	−2.72317	−	1.75008i	−0.108322	−	0.0696143i
$633$	−4.05906	−	2.60860i	−0.161333	−	0.103683i
$634$	−10.4798	+	12.0943i	−0.416206	+	0.480327i
$635$	2.96641	+	0.871016i	0.117718	+	0.0345652i
$636$	0.918173	+	6.38603i	0.0364079	+	0.253223i
$637$	0.793507	+	0.915755i	0.0314399	+	0.0362836i
$638$	−15.2828	−	33.4647i	−0.605052	−	1.32488i
$639$	5.99663	−	1.76077i	0.237223	−	0.0696549i
$640$	−0.0782522	+	0.171348i	−0.00309319	+	0.00677314i
$641$	−1.04655	+	7.27892i	−0.0413363	+	0.287500i	0.958659	+	0.284556i	$0.0918462\pi$
$641$	−1.04655	+	7.27892i	−0.0413363	+	0.287500i	−0.999996	+	0.00294401i	$0.999063\pi$
$642$	8.70028	−	5.59133i	0.343372	−	0.220672i
$643$	−2.42892			−0.0957874			−0.0478937	−	0.998852i	$-0.515251\pi$
$643$	−2.42892			−0.0957874			−0.0478937	+	0.998852i	$0.515251\pi$
$644$	−2.87394	+	3.83933i	−0.113249	+	0.151291i
$645$	−0.354776			−0.0139693
$646$	4.95927	−	3.18713i	0.195120	−	0.125396i
$647$	2.55136	−	17.7451i	0.100304	−	0.697631i	−0.876171	−	0.482001i	$-0.839910\pi$
$647$	2.55136	−	17.7451i	0.100304	−	0.697631i	0.976475	−	0.215631i	$-0.0691807\pi$
$648$	−0.415415	+	0.909632i	−0.0163190	+	0.0357337i
$649$	−18.6291	+	5.47001i	−0.731258	+	0.214717i
$650$	−2.49897	−	5.47198i	−0.0980176	−	0.214629i
$651$	1.73839	+	2.00620i	0.0681327	+	0.0786293i
$652$	−2.55894	−	17.7978i	−0.100216	−	0.697015i
$653$	−19.8500	−	5.82850i	−0.776792	−	0.228087i	−0.130777	−	0.991412i	$-0.541747\pi$
$653$	−19.8500	−	5.82850i	−0.776792	−	0.228087i	−0.646015	+	0.763325i	$0.723566\pi$
$654$	3.00312	−	3.46579i	0.117431	−	0.135523i
$655$	−3.49800	−	2.24803i	−0.136678	−	0.0878378i
$656$	−8.65154	−	5.56001i	−0.337786	−	0.217082i
$657$	−1.82330	+	2.10420i	−0.0711337	+	0.0820927i
$658$	1.71057	+	0.502270i	0.0666851	+	0.0195805i
$659$	−2.65572	−	18.4710i	−0.103452	−	0.719527i	−0.973852	−	0.227182i	$-0.927049\pi$
$659$	−2.65572	−	18.4710i	−0.103452	−	0.719527i	0.870400	−	0.492345i	$-0.163860\pi$
$660$	−0.558033	−	0.644004i	−0.0217214	−	0.0250678i
$661$	−4.92044	−	10.7743i	−0.191383	−	0.419070i	0.789478	−	0.613779i	$-0.210351\pi$
$661$	−4.92044	−	10.7743i	−0.191383	−	0.419070i	−0.980861	+	0.194708i	$0.937624\pi$
$662$	−7.28485	+	2.13902i	−0.283134	+	0.0831355i
$663$	1.01407	−	2.22050i	0.0393831	−	0.0862370i
$664$	−2.37133	+	16.4929i	−0.0920253	+	0.640050i
$665$	0.463713	−	0.298010i	0.0179820	−	0.0115563i
$666$	5.30698			0.205641
$667$	34.2318	+	18.6909i	1.32546	+	0.723716i
$668$	−5.11993			−0.198096
$669$	13.2314	−	8.50330i	0.511555	−	0.328757i
$670$	−0.370213	+	2.57489i	−0.0143026	+	0.0994767i
$671$	−13.4864	+	29.5311i	−0.520637	+	1.14004i
$672$	0.959493	−	0.281733i	0.0370132	−	0.0108681i
$673$	8.01161	+	17.5430i	0.308825	+	0.676232i	0.998870	−	0.0475344i	$-0.0151364\pi$
$673$	8.01161	+	17.5430i	0.308825	+	0.676232i	−0.690045	+	0.723767i	$0.742409\pi$
$674$	−4.94046	−	5.70159i	−0.190299	−	0.219617i
$675$	0.706524	+	4.91398i	0.0271941	+	0.189139i
$676$	11.0646	+	3.24887i	0.425562	+	0.124956i
$677$	22.0938	−	25.4976i	0.849134	−	0.979953i	−0.150829	−	0.988560i	$-0.548194\pi$
$677$	22.0938	−	25.4976i	0.849134	−	0.979953i	0.999963	+	0.00860707i	$0.00273975\pi$
$678$	−11.3353	−	7.28475i	−0.435330	−	0.279769i
$679$	−8.41717	−	5.40939i	−0.323021	−	0.207593i
$680$	−0.248512	+	0.286798i	−0.00952999	+	0.0109982i
$681$	−6.67276	−	1.95930i	−0.255701	−	0.0750805i
$682$	−1.70901	−	11.8864i	−0.0654412	−	0.455154i
$683$	7.66514	+	8.84605i	0.293298	+	0.338485i	0.883205	−	0.468987i	$-0.155381\pi$
$683$	7.66514	+	8.84605i	0.293298	+	0.338485i	−0.589907	+	0.807472i	$0.700835\pi$
$684$	1.21560	+	2.66179i	0.0464796	+	0.101776i
$685$	1.89455	−	0.556290i	0.0723871	−	0.0212548i
$686$	−0.415415	+	0.909632i	−0.0158606	+	0.0347299i
$687$	1.29453	−	9.00365i	0.0493894	−	0.343510i
$688$	−1.58441	+	1.01824i	−0.0604049	+	0.0388199i
$689$	7.81765			0.297829
$690$	0.882756	+	0.192010i	0.0336059	+	0.00730968i
$691$	−27.0998			−1.03092			−0.515462	−	0.856912i	$-0.672380\pi$
$691$	−27.0998			−1.03092			−0.515462	+	0.856912i	$0.672380\pi$
$692$	−3.32660	+	2.13788i	−0.126458	+	0.0812699i
$693$	−0.643793	+	4.47768i	−0.0244557	+	0.170093i
$694$	8.00051	−	17.5187i	0.303695	−	0.665000i
$695$	1.32033	−	0.387684i	0.0500830	−	0.0147057i
$696$	−3.37837	−	7.39759i	−0.128057	−	0.280405i
$697$	−13.5675	−	15.6577i	−0.513905	−	0.593077i
$698$	3.57020	+	24.8313i	0.135134	+	0.939879i
$699$	7.39434	+	2.17117i	0.279679	+	0.0821213i
$700$	3.25107	−	3.75193i	0.122879	−	0.141810i
$701$	26.0399	+	16.7348i	0.983512	+	0.632065i	0.930408	−	0.366524i	$-0.119452\pi$
$701$	26.0399	+	16.7348i	0.983512	+	0.632065i	0.0531034	+	0.998589i	$0.483089\pi$
$702$	1.01936	+	0.655104i	0.0384733	+	0.0247253i
$703$	10.1696	−	11.7364i	0.383554	−	0.442645i
$704$	−4.34048	−	1.27448i	−0.163588	−	0.0480338i
$705$	−0.0477930	−	0.332408i	−0.00179999	−	0.0125192i
$706$	−4.05332	−	4.67778i	−0.152549	−	0.176050i
$707$	−0.0961732	−	0.210590i	−0.00361697	−	0.00792005i
$708$	−4.11810	+	1.20918i	−0.154767	+	0.0454438i
$709$	−5.56152	+	12.1780i	−0.208867	+	0.457355i	−0.984852	−	0.173396i	$-0.944526\pi$
$709$	−5.56152	+	12.1780i	−0.208867	+	0.457355i	0.775985	+	0.630751i	$0.217253\pi$
$710$	−0.167544	+	1.16530i	−0.00628783	+	0.0437328i
$711$	2.72317	−	1.75008i	0.102127	−	0.0656329i
$712$	0.815402			0.0305585
$713$	9.00236	+	9.00193i	0.337141	+	0.337125i
$714$	2.01457			0.0753935
$715$	−0.868639	+	0.558240i	−0.0324853	+	0.0208770i
$716$	−2.34933	+	16.3399i	−0.0877984	+	0.610652i
$717$	−0.930743	+	2.03804i	−0.0347593	+	0.0761121i
$718$	30.6759	−	9.00726i	1.14481	−	0.336148i
$719$	15.8867	+	34.7870i	0.592474	+	1.29734i	0.933935	+	0.357442i	$0.116351\pi$
$719$	15.8867	+	34.7870i	0.592474	+	1.29734i	−0.341461	+	0.939896i	$0.610922\pi$
$720$	−0.123357	−	0.142361i	−0.00459724	−	0.00530550i
$721$	0.587055	+	4.08305i	0.0218631	+	0.152061i
$722$	−10.0144	−	2.94050i	−0.372698	−	0.109434i
$723$	−11.8038	+	13.6223i	−0.438989	+	0.506620i
$724$	−17.5843	−	11.3007i	−0.653515	−	0.419989i
$725$	−33.9648	−	21.8278i	−1.26142	−	0.810665i
$726$	6.19767	−	7.15249i	0.230017	−	0.265454i
$727$	−46.6971	−	13.7115i	−1.73190	−	0.508532i	−0.744615	−	0.667494i	$-0.767367\pi$
$727$	−46.6971	−	13.7115i	−1.73190	−	0.508532i	−0.987285	+	0.158962i	$0.949185\pi$
$728$	−0.172445	−	1.19938i	−0.00639125	−	0.0444522i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	−0.217874	−	0.477078i	−0.00806389	−	0.0176574i
$731$	−3.64053	+	1.06896i	−0.134650	+	0.0395367i
$732$	−2.98126	+	6.52805i	−0.110191	+	0.241284i
$733$	4.68819	−	32.6071i	0.173162	−	1.20437i	−0.698989	−	0.715132i	$-0.746366\pi$
$733$	4.68819	−	32.6071i	0.173162	−	1.20437i	0.872151	−	0.489237i	$-0.162725\pi$
$734$	−3.48015	+	2.23656i	−0.128455	+	0.0825529i
$735$	0.188371			0.00694818
$736$	4.49341	−	1.67608i	0.165629	−	0.0617811i
$737$	−62.4718			−2.30118
$738$	8.65154	−	5.56001i	0.318468	−	0.204667i
$739$	5.89143	−	40.9758i	0.216720	−	1.50732i	−0.533314	−	0.845918i	$-0.679053\pi$
$739$	5.89143	−	40.9758i	0.216720	−	1.50732i	0.750033	−	0.661400i	$-0.230037\pi$
$740$	−0.415283	+	0.909343i	−0.0152661	+	0.0334281i
$741$	3.40213	−	0.998957i	0.124981	−	0.0366976i
$742$	2.68013	+	5.86868i	0.0983908	+	0.215446i
$743$	7.66769	+	8.84899i	0.281300	+	0.324638i	0.878763	−	0.477259i	$-0.158370\pi$
$743$	7.66769	+	8.84899i	0.281300	+	0.324638i	−0.597462	+	0.801897i	$0.703824\pi$
$744$	−0.377787	−	2.62757i	−0.0138504	−	0.0963313i
$745$	0.994561	+	0.292029i	0.0364379	+	0.0106991i
$746$	4.51211	−	5.20726i	0.165200	−	0.190651i
$747$	−14.0174	−	9.00844i	−0.512870	−	0.329602i
$748$	−7.66666	−	4.92707i	−0.280321	−	0.180151i
$749$	6.77259	−	7.81599i	0.247465	−	0.285590i
$750$	−1.80100	−	0.528820i	−0.0657630	−	0.0193098i
$751$	1.29485	+	9.00588i	0.0472497	+	0.328629i	0.999713	+	0.0239743i	$0.00763200\pi$
$751$	1.29485	+	9.00588i	0.0472497	+	0.328629i	−0.952463	+	0.304655i	$0.901459\pi$
$752$	−1.16748	−	1.34734i	−0.0425736	−	0.0491325i
$753$	9.84566	+	21.5590i	0.358796	+	0.785653i
$754$	−9.45514	+	2.77628i	−0.344336	+	0.101106i
$755$	−0.192991	+	0.422592i	−0.00702367	+	0.0153797i
$756$	−0.142315	+	0.989821i	−0.00517594	+	0.0359995i
$757$	8.87738	−	5.70514i	0.322654	−	0.207357i	−0.369280	−	0.929318i	$-0.620396\pi$
$757$	8.87738	−	5.70514i	0.322654	−	0.207357i	0.691933	+	0.721961i	$0.256759\pi$
$758$	−29.7216			−1.07954
$759$	−1.54719	+	21.6398i	−0.0561594	+	0.785475i
$760$	−0.551217			−0.0199947
$761$	−10.6514	+	6.84524i	−0.386113	+	0.248140i	−0.719268	−	0.694732i	$-0.755523\pi$
$761$	−10.6514	+	6.84524i	−0.386113	+	0.248140i	0.333156	+	0.942872i	$0.391887\pi$
$762$	−2.33574	+	16.2454i	−0.0846150	+	0.588510i
$763$	1.90505	−	4.17148i	0.0689674	−	0.151018i
$764$	−20.8776	+	6.13023i	−0.755326	+	0.221784i
$765$	−0.157645	−	0.345194i	−0.00569966	−	0.0124805i
$766$	−13.9749	−	16.1279i	−0.504934	−	0.582725i
$767$	0.740127	+	5.14770i	0.0267244	+	0.185873i
$768$	−0.959493	−	0.281733i	−0.0346227	−	0.0101661i
$769$	−12.3531	+	14.2563i	−0.445465	+	0.514094i	−0.933425	−	0.358772i	$-0.883196\pi$
$769$	−12.3531	+	14.2563i	−0.445465	+	0.514094i	0.487960	+	0.872866i	$0.337741\pi$
$770$	−0.716866	−	0.460702i	−0.0258340	−	0.0166025i
$771$	−7.34656	−	4.72135i	−0.264580	−	0.170035i
$772$	0.931371	−	1.07486i	0.0335208	−	0.0386850i
$773$	−15.6456	−	4.59397i	−0.562734	−	0.165234i	−0.0120202	−	0.999928i	$-0.503826\pi$
$773$	−15.6456	−	4.59397i	−0.562734	−	0.165234i	−0.550714	+	0.834694i	$0.685644\pi$
$774$	−0.268034	−	1.86422i	−0.00963428	−	0.0670079i
$775$	−8.63024	−	9.95983i	−0.310008	−	0.357768i
$776$	4.15644	+	9.10133i	0.149207	+	0.326719i
$777$	5.09201	−	1.49515i	0.182675	−	0.0536382i
$778$	3.06498	−	6.71137i	0.109885	−	0.240614i
$779$	4.28277	−	29.7873i	0.153446	−	1.06724i
$780$	−0.192018	+	0.123403i	−0.00687537	+	0.00441853i
$781$	−28.2723			−1.01166
$782$	9.63692	−	0.689478i	0.344616	−	0.0246557i
$783$	8.13251			0.290632
$784$	0.841254	−	0.540641i	0.0300448	−	0.0193086i
$785$	−0.585053	+	4.06914i	−0.0208815	+	0.145234i
$786$	9.16982	−	20.0791i	0.327077	−	0.716198i
$787$	−12.6955	+	3.72773i	−0.452545	+	0.132879i	−0.500059	−	0.865991i	$-0.666688\pi$
$787$	−12.6955	+	3.72773i	−0.452545	+	0.132879i	0.0475142	+	0.998871i	$0.484870\pi$
$788$	−7.57461	−	16.5861i	−0.269834	−	0.590854i
$789$	2.78394	+	3.21284i	0.0991109	+	0.114380i
$790$	0.0867786	+	0.603558i	0.00308744	+	0.0214736i
$791$	−12.9285	−	3.79615i	−0.459684	−	0.134975i
$792$	2.96241	−	3.41880i	0.105265	−	0.121482i
$793$	7.31554	+	4.70141i	0.259783	+	0.166952i
$794$	14.0357	+	9.02019i	0.498108	+	0.320115i
$795$	0.795862	−	0.918474i	0.0282263	−	0.0325749i
$796$	−0.0116592	−	0.00342346i	−0.000413251	−	0.000121341i
$797$	−1.60951	−	11.1944i	−0.0570118	−	0.396526i	−0.998268	−	0.0588322i	$-0.981262\pi$
$797$	−1.60951	−	11.1944i	−0.0570118	−	0.396526i	0.941256	−	0.337694i	$-0.109647\pi$
$798$	1.91627	+	2.21149i	0.0678353	+	0.0782861i
$799$	−1.49199	−	3.26700i	−0.0527827	−	0.115578i
$800$	−4.76342	+	1.39867i	−0.168412	+	0.0494503i
$801$	−0.338730	+	0.741716i	−0.0119684	+	0.0262072i
$802$	0.739792	−	5.14537i	0.0261230	−	0.181689i
$803$	10.5958	−	6.80948i	0.373916	−	0.240301i
$804$	−13.8098			−0.487034
$805$	0.901093	−	0.0644691i	0.0317594	−	0.00227224i
$806$	−3.21661			−0.113300
$807$	−16.6126	+	10.6763i	−0.584791	+	0.375822i
$808$	−0.0329475	+	0.229155i	−0.00115909	+	0.00806163i
$809$	20.9316	−	45.8339i	0.735917	−	1.61143i	−0.0542400	−	0.998528i	$-0.517274\pi$
$809$	20.9316	−	45.8339i	0.735917	−	1.61143i	0.790157	−	0.612905i	$-0.209999\pi$
$810$	0.180741	−	0.0530703i	0.00635059	−	0.00186470i
$811$	−9.87022	−	21.6128i	−0.346590	−	0.758927i	−0.999998	−	0.00192085i	$-0.999389\pi$
$811$	−9.87022	−	21.6128i	−0.346590	−	0.758927i	0.653408	−	0.757006i	$-0.273339\pi$
$812$	−5.32566	−	6.14614i	−0.186894	−	0.215687i
$813$	−1.13600	−	7.90105i	−0.0398413	−	0.277102i
$814$	−23.0349	−	6.76365i	−0.807372	−	0.237066i
$815$	−2.21806	+	2.55978i	−0.0776952	+	0.0896650i
$816$	−1.69477	−	1.08916i	−0.0593287	−	0.0381283i
$817$	−4.63633	−	2.97959i	−0.162205	−	0.104243i
$818$	17.4556	−	20.1448i	0.610321	−	0.704348i
$819$	1.16264	+	0.341380i	0.0406258	+	0.0119288i
$820$	0.275697	+	1.91751i	0.00962774	+	0.0669624i
$821$	−13.8028	−	15.9292i	−0.481719	−	0.555934i	0.461915	−	0.886924i	$-0.347163\pi$
$821$	−13.8028	−	15.9292i	−0.481719	−	0.555934i	−0.943634	+	0.330990i	$0.892617\pi$
$822$	4.35444	+	9.53489i	0.151878	+	0.332567i
$823$	5.60132	−	1.64470i	0.195250	−	0.0573305i	−0.182646	−	0.983179i	$-0.558466\pi$
$823$	5.60132	−	1.64470i	0.195250	−	0.0573305i	0.377895	+	0.925848i	$0.376648\pi$
$824$	1.71360	−	3.75227i	0.0596962	−	0.130717i
$825$	3.19612	−	22.2295i	0.111275	−	0.773933i
$826$	−3.61062	+	2.32040i	−0.125629	+	0.0807371i
$827$	8.66416			0.301282			0.150641	−	0.988588i	$-0.451866\pi$
$827$	8.66416			0.301282			0.150641	+	0.988588i	$0.451866\pi$
$828$	−0.342016	+	4.78362i	−0.0118859	+	0.166242i
$829$	38.2553			1.32866			0.664330	−	0.747439i	$-0.268717\pi$
$829$	38.2553			1.32866			0.664330	+	0.747439i	$0.268717\pi$
$830$	2.64048	−	1.69693i	0.0916523	−	0.0589013i
$831$	1.63680	−	11.3842i	0.0567800	−	0.394913i
$832$	−0.503366	+	1.10222i	−0.0174511	+	0.0382125i
$833$	1.93297	−	0.567571i	0.0669734	−	0.0196652i
$834$	3.03465	+	6.64495i	0.105081	+	0.230096i
$835$	0.631579	+	0.728881i	0.0218567	+	0.0252240i
$836$	−1.88389	−	13.1027i	−0.0651555	−	0.453167i
$837$	2.54706	+	0.747884i	0.0880392	+	0.0258507i
$838$	14.5110	−	16.7466i	0.501275	−	0.578502i
$839$	25.6396	+	16.4776i	0.885177	+	0.568869i	0.902360	−	0.430984i	$-0.141833\pi$
$839$	25.6396	+	16.4776i	0.885177	+	0.568869i	−0.0171827	+	0.999852i	$0.505470\pi$
$840$	−0.158468	−	0.101841i	−0.00546766	−	0.00351385i
$841$	−24.3201	+	28.0668i	−0.838623	+	0.967822i
$842$	1.30680	+	0.383712i	0.0450354	+	0.0132236i
$843$	0.0983281	+	0.683887i	0.00338660	+	0.0235543i
$844$	3.15971	+	3.64650i	0.108762	+	0.125518i
$845$	−0.902384	−	1.97595i	−0.0310430	−	0.0679746i
$846$	1.71057	−	0.502270i	0.0588107	−	0.0172684i
$847$	3.93153	−	8.60885i	0.135089	−	0.295803i
$848$	0.918173	−	6.38603i	0.0315302	−	0.219297i
$849$	18.7880	−	12.0743i	0.644801	−	0.414389i
$850$	−10.0014			−0.343045
$851$	23.8465	−	8.89492i	0.817446	−	0.304914i
$852$	−6.24979			−0.214114
$853$	27.9000	−	17.9302i	0.955276	−	0.613919i	0.0325895	−	0.999469i	$-0.489625\pi$
$853$	27.9000	−	17.9302i	0.955276	−	0.613919i	0.922687	+	0.385550i	$0.125988\pi$
$854$	−1.02134	+	7.10354i	−0.0349494	+	0.243078i
$855$	0.228984	−	0.501405i	0.00783108	−	0.0171477i
$856$	−9.92311	+	2.91369i	−0.339165	+	0.0995878i
$857$	−12.9577	−	28.3734i	−0.442626	−	0.969216i	−0.991109	−	0.133054i	$-0.957522\pi$
$857$	−12.9577	−	28.3734i	−0.442626	−	0.969216i	0.548482	−	0.836162i	$-0.315206\pi$
$858$	−3.58961	−	4.14263i	−0.122547	−	0.141427i
$859$	−0.993972	−	6.91323i	−0.0339139	−	0.235876i	0.965813	−	0.259239i	$-0.0834718\pi$
$859$	−0.993972	−	6.91323i	−0.0339139	−	0.235876i	−0.999727	+	0.0233629i	$0.992563\pi$
$860$	0.340405	+	0.0999519i	0.0116077	+	0.00340833i
$861$	6.73466	−	7.77221i	0.229517	−	0.264876i
$862$	−26.5432	−	17.0583i	−0.904066	−	0.581008i
$863$	−24.8591	−	15.9760i	−0.846215	−	0.543829i	0.0441772	−	0.999024i	$-0.485933\pi$
$863$	−24.8591	−	15.9760i	−0.846215	−	0.543829i	−0.890392	+	0.455194i	$0.849570\pi$
$864$	0.654861	−	0.755750i	0.0222788	−	0.0257111i
$865$	0.714711	+	0.209858i	0.0243009	+	0.00713539i
$866$	−1.73826	−	12.0898i	−0.0590683	−	0.410829i
$867$	8.47487	+	9.78053i	0.287822	+	0.332164i
$868$	−1.10276	−	2.41470i	−0.0374300	−	0.0819602i
$869$	−14.0503	+	4.12554i	−0.476624	+	0.139949i
$870$	−0.636387	+	1.39349i	−0.0215755	+	0.0472439i
$871$	−2.38144	+	16.5633i	−0.0806919	+	0.561225i
$872$	−3.85790	+	2.47932i	−0.130645	+	0.0839604i
$873$	−10.0055			−0.338635
$874$	9.92356	+	9.92308i	0.335669	+	0.335653i
$875$	−1.87703			−0.0634551
$876$	2.34226	−	1.50528i	0.0791378	−	0.0508588i
$877$	−2.58105	+	17.9516i	−0.0871559	+	0.606182i	0.898697	+	0.438570i	$0.144515\pi$
$877$	−2.58105	+	17.9516i	−0.0871559	+	0.606182i	−0.985853	+	0.167613i	$0.946394\pi$
$878$	0.780567	−	1.70920i	0.0263429	−	0.0576828i
$879$	23.8273	−	6.99631i	0.803673	−	0.235980i
$880$	0.353992	+	0.775134i	0.0119331	+	0.0261298i
$881$	36.1143	+	41.6781i	1.21672	+	1.40417i	0.888062	+	0.459723i	$0.152051\pi$
$881$	36.1143	+	41.6781i	1.21672	+	1.40417i	0.328660	+	0.944448i	$0.393403\pi$
$882$	0.142315	+	0.989821i	0.00479199	+	0.0333290i
$883$	3.80093	+	1.11605i	0.127912	+	0.0375582i	0.345062	−	0.938580i	$-0.387858\pi$
$883$	3.80093	+	1.11605i	0.127912	+	0.0375582i	−0.217150	+	0.976138i	$0.569676\pi$
$884$	−1.59858	+	1.84486i	−0.0537660	+	0.0620493i
$885$	0.680136	+	0.437097i	0.0228625	+	0.0146929i
$886$	−27.9191	−	17.9425i	−0.937960	−	0.602790i
$887$	28.7341	−	33.1609i	0.964795	−	1.11343i	−0.0287033	−	0.999588i	$-0.509138\pi$
$887$	28.7341	−	33.1609i	0.964795	−	1.11343i	0.993499	−	0.113845i	$-0.0363168\pi$
$888$	−5.09201	−	1.49515i	−0.170877	−	0.0501739i
$889$	2.33574	+	16.2454i	0.0783383	+	0.544855i
$890$	−0.100585	−	0.116082i	−0.00337163	−	0.00389107i
$891$	1.87922	+	4.11493i	0.0629564	+	0.137855i
$892$	−15.0911	+	4.43114i	−0.505287	+	0.148366i
$893$	2.16716	−	4.74541i	0.0725211	−	0.158799i
$894$	−0.783114	+	5.44668i	−0.0261913	+	0.182164i
$895$	2.61598	−	1.68119i	0.0874426	−	0.0561959i
$896$	−1.00000			−0.0334077
$897$	5.67842	+	1.23512i	0.189597	+	0.0412396i
$898$	1.85986			0.0620642
$899$	−18.1614	+	11.6716i	−0.605716	+	0.389270i
$900$	0.706524	−	4.91398i	0.0235508	−	0.163799i
$901$	5.39933	−	11.8229i	0.179878	−	0.393877i
$902$	−44.6380	+	13.1069i	−1.48628	+	0.436412i
$903$	−0.782387	−	1.71319i	−0.0260362	−	0.0570113i
$904$	8.82379	+	10.1832i	0.293475	+	0.338688i
$905$	0.560355	+	3.89735i	0.0186268	+	0.129552i
$906$	−2.36637	−	0.694829i	−0.0786174	−	0.0230841i
$907$	18.9113	−	21.8248i	0.627939	−	0.724680i	−0.349255	−	0.937028i	$-0.613565\pi$
$907$	18.9113	−	21.8248i	0.627939	−	0.724680i	0.977194	+	0.212348i	$0.0681109\pi$
$908$	5.85046	+	3.75987i	0.194154	+	0.124776i
$909$	−0.194760	−	0.125164i	−0.00645977	−	0.00415144i
$910$	−0.149474	+	0.172502i	−0.00495501	+	0.00571838i
$911$	38.4482	+	11.2894i	1.27385	+	0.374035i	0.847631	−	0.530586i	$-0.178028\pi$
$911$	38.4482	+	11.2894i	1.27385	+	0.374035i	0.426216	+	0.904621i	$0.359846\pi$
$912$	−0.416446	−	2.89644i	−0.0137899	−	0.0959108i
$913$	49.3613	+	56.9659i	1.63362	+	1.88530i
$914$	−10.9469	−	23.9703i	−0.362090	−	0.792866i
$915$	1.29710	−	0.380864i	0.0428809	−	0.0125910i
$916$	−3.77871	+	8.27422i	−0.124852	+	0.273388i
$917$	3.14144	−	21.8492i	0.103740	−	0.721524i
$918$	1.69477	−	1.08916i	0.0559357	−	0.0359477i
$919$	−7.05020			−0.232565			−0.116282	−	0.993216i	$-0.537098\pi$
$919$	−7.05020			−0.232565			−0.116282	+	0.993216i	$0.537098\pi$
$920$	−0.792903	−	0.432933i	−0.0261412	−	0.0142734i
$921$	32.3020			1.06439
$922$	25.3362	−	16.2826i	0.834403	−	0.536238i
$923$	−1.07775	+	7.49590i	−0.0354745	+	0.246731i
$924$	1.87922	−	4.11493i	0.0618219	−	0.135371i
$925$	−25.2794	+	7.42269i	−0.831181	+	0.244057i
$926$	10.3179	+	22.5931i	0.339068	+	0.742456i
$927$	2.70133	+	3.11750i	0.0887233	+	0.102392i
$928$	1.15738	+	8.04974i	0.0379928	+	0.264245i
$929$	33.9140	+	9.95804i	1.11268	+	0.326713i	0.785879	−	0.618380i	$-0.212211\pi$
$929$	33.9140	+	9.95804i	1.11268	+	0.326713i	0.326802	+	0.945093i	$0.394029\pi$
$930$	−0.327462	+	0.377911i	−0.0107379	+	0.0123922i
$931$	2.46170	+	1.58204i	0.0806789	+	0.0518492i
$932$	−6.48312	−	4.16645i	−0.212362	−	0.136477i
$933$	17.8864	−	20.6420i	0.585575	−	0.675789i
$934$	31.3149	+	9.19489i	1.02466	+	0.300866i
$935$	0.244312	+	1.69923i	0.00798985	+	0.0555706i
$936$	−0.793507	−	0.915755i	−0.0259366	−	0.0299324i
$937$	−6.50097	−	14.2351i	−0.212378	−	0.465042i	0.773223	−	0.634135i	$-0.218644\pi$
$937$	−6.50097	−	14.2351i	−0.212378	−	0.465042i	−0.985600	+	0.169093i	$0.945916\pi$
$938$	−13.2504	+	3.89067i	−0.432641	+	0.127035i
$939$	−6.55454	+	14.3524i	−0.213899	+	0.468374i
$940$	−0.0477930	+	0.332408i	−0.00155884	+	0.0108420i
$941$	12.8765	−	8.27524i	0.419763	−	0.269765i	−0.313664	−	0.949534i	$-0.601556\pi$
$941$	12.8765	−	8.27524i	0.419763	−	0.269765i	0.733426	+	0.679769i	$0.237920\pi$
$942$	−21.8238			−0.711058
$943$	29.5559	−	39.4841i	0.962474	−	1.28578i
$944$	4.29195			0.139691
$945$	0.158468	−	0.101841i	0.00515496	−	0.00331289i
$946$	−1.21251	+	8.43320i	−0.0394221	+	0.274187i
$947$	22.4361	−	49.1281i	0.729074	−	1.59645i	−0.0716588	−	0.997429i	$-0.522829\pi$
$947$	22.4361	−	49.1281i	0.729074	−	1.59645i	0.800733	−	0.599021i	$-0.204443\pi$
$948$	−3.10592	+	0.911979i	−0.100875	+	0.0296197i
$949$	−1.40150	−	3.06886i	−0.0454946	−	0.0996193i
$950$	−9.51336	−	10.9790i	−0.308654	−	0.356206i
$951$	2.27748	+	15.8402i	0.0738522	+	0.513653i
$952$	−1.93297	−	0.567571i	−0.0626479	−	0.0183951i
$953$	−22.5942	+	26.0751i	−0.731898	+	0.844655i	−0.992684	−	0.120741i	$-0.961473\pi$
$953$	−22.5942	+	26.0751i	−0.731898	+	0.844655i	0.260786	+	0.965397i	$0.416018\pi$
$954$	5.42752	+	3.48805i	0.175722	+	0.112930i
$955$	3.44811	+	2.21596i	0.111578	+	0.0717069i
$956$	1.46723	−	1.69327i	0.0474535	−	0.0547642i
$957$	−35.2990	−	10.3647i	−1.14106	−	0.335044i
$958$	−1.51902	−	10.5650i	−0.0490773	−	0.341340i
$959$	6.86434	+	7.92187i	0.221661	+	0.255811i
$960$	0.0782522	+	0.171348i	0.00252558	+	0.00553025i
$961$	22.9829	−	6.74838i	0.741383	−	0.217690i
$962$	−2.67135	+	5.84945i	−0.0861279	+	0.188594i
$963$	1.47183	−	10.2368i	0.0474289	−	0.329875i
$964$	15.1635	−	9.74501i	0.488385	−	0.313866i
$965$	−0.267910			−0.00862431
$966$	1.01954	+	4.68621i	0.0328031	+	0.150776i
$967$	−41.5737			−1.33692			−0.668460	−	0.743748i	$-0.733046\pi$
$967$	−41.5737			−1.33692			−0.668460	+	0.743748i	$0.733046\pi$
$968$	−7.96171	+	5.11668i	−0.255899	+	0.164456i
$969$	0.838960	−	5.83510i	0.0269513	−	0.187450i
$970$	0.782953	−	1.71443i	0.0251391	−	0.0550470i
$971$	−24.9003	+	7.31140i	−0.799090	+	0.234634i	−0.655689	−	0.755031i	$-0.727622\pi$
$971$	−24.9003	+	7.31140i	−0.799090	+	0.234634i	−0.143400	+	0.989665i	$0.545804\pi$
$972$	0.415415	+	0.909632i	0.0133244	+	0.0291765i
$973$	4.78382	+	5.52082i	0.153362	+	0.176990i
$974$	2.21782	+	15.4253i	0.0710634	+	0.494257i
$975$	−5.77192	−	1.69479i	−0.184849	−	0.0542767i
$976$	4.69967	−	5.42370i	0.150433	−	0.173609i
$977$	−37.2041	−	23.9096i	−1.19026	−	0.764937i	−0.213019	−	0.977048i	$-0.568330\pi$
$977$	−37.2041	−	23.9096i	−1.19026	−	0.764937i	−0.977245	+	0.212111i	$0.931966\pi$
$978$	−15.1264	−	9.72116i	−0.483690	−	0.310848i
$979$	2.41556	−	2.78770i	0.0772015	−	0.0890953i
$980$	−0.180741	−	0.0530703i	−0.00577356	−	0.00169527i
$981$	−0.652641	−	4.53922i	−0.0208372	−	0.144926i
$982$	−14.4230	−	16.6450i	−0.460257	−	0.531165i
$983$	−7.29527	−	15.9744i	−0.232683	−	0.509504i	0.756889	−	0.653543i	$-0.226718\pi$
$983$	−7.29527	−	15.9744i	−0.232683	−	0.509504i	−0.989572	+	0.144039i	$0.953991\pi$
$984$	−9.86753	+	2.89737i	−0.314565	+	0.0923647i
$985$	−1.42684	+	3.12434i	−0.0454628	+	0.0995497i
$986$	−2.33162	+	16.2168i	−0.0742540	+	0.516448i
$987$	1.49978	−	0.963849i	0.0477384	−	0.0306796i
$988$	−3.54576			−0.112806
$989$	−4.32896	−	7.92745i	−0.137653	−	0.252078i
$990$	−0.852140			−0.0270828
$991$	29.0618	−	18.6769i	0.923179	−	0.593291i	0.00960038	−	0.999954i	$-0.496944\pi$
$991$	29.0618	−	18.6769i	0.923179	−	0.593291i	0.913578	+	0.406663i	$0.133308\pi$
$992$	−0.377787	+	2.62757i	−0.0119948	+	0.0834254i
$993$	−3.15399	+	6.90628i	−0.100089	+	0.219164i
$994$	−5.99663	+	1.76077i	−0.190201	+	0.0558482i
$995$	0.000950879		0.00208214i	3.01449e−5		6.60081e-5i
$996$	10.9116	+	12.5927i	0.345748	+	0.399015i
$997$	5.94470	+	41.3463i	0.188270	+	1.30945i	0.836484	+	0.547991i	$0.184607\pi$
$997$	5.94470	+	41.3463i	0.188270	+	1.30945i	−0.648214	+	0.761459i	$0.724484\pi$
$998$	28.4884	+	8.36493i	0.901783	+	0.264787i
$999$	3.47533	−	4.01075i	0.109955	−	0.126894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.e.127.1	✓	20
23.2	even	11	inner	966.2.q.e.715.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.e.127.1	✓	20	1.1	even	1	trivial
966.2.q.e.715.1	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)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.180741 + 0.0530703i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.841254 + 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.180741 + 0.0530703i) 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} +(0.123357 - 0.142361i) q^{10} +(3.80560 + 2.44571i) q^{11} +(0.841254 + 0.540641i) q^{12} +(0.793507 - 0.915755i) q^{13} +(0.959493 + 0.281733i) q^{14} +(-0.0268080 - 0.186454i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.836884 - 1.83252i) q^{17} +(0.959493 - 0.281733i) q^{18} +(1.21560 - 2.66179i) q^{19} +(-0.0268080 + 0.186454i) q^{20} +(0.841254 - 0.540641i) q^{21} -4.52373 q^{22} +(3.83919 - 2.87413i) q^{23} -1.00000 q^{24} +(-4.17642 + 2.68402i) q^{25} +(-0.172445 + 1.19938i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(3.37837 + 7.39759i) q^{29} +(0.123357 + 0.142361i) q^{30} +(0.377787 + 2.62757i) q^{31} +(0.959493 + 0.281733i) q^{32} +(-2.96241 + 3.41880i) q^{33} +(1.69477 + 1.08916i) q^{34} +(0.158468 + 0.101841i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(5.09201 + 1.49515i) q^{37} +(0.416446 + 2.89644i) q^{38} +(0.793507 + 0.915755i) q^{39} +(-0.0782522 - 0.171348i) q^{40} +(9.86753 - 2.89737i) q^{41} +(-0.415415 + 0.909632i) q^{42} +(0.268034 - 1.86422i) q^{43} +(3.80560 - 2.44571i) q^{44} +0.188371 q^{45} +(-1.67586 + 4.49349i) q^{46} +1.78279 q^{47} +(0.841254 - 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(2.06233 - 4.51588i) q^{50} +(1.93297 - 0.567571i) q^{51} +(-0.503366 - 1.10222i) q^{52} +(4.22497 + 4.87587i) q^{53} +(0.142315 + 0.989821i) q^{54} +(-0.817622 - 0.240076i) q^{55} +(0.654861 - 0.755750i) q^{56} +(2.46170 + 1.58204i) q^{57} +(-6.84150 - 4.39677i) q^{58} +(-2.81063 + 3.24364i) q^{59} +(-0.180741 - 0.0530703i) q^{60} +(1.02134 + 7.10354i) q^{61} +(-1.73839 - 2.00620i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-0.0948197 + 0.207626i) q^{65} +(0.643793 - 4.47768i) q^{66} +(-11.6175 + 7.46614i) q^{67} -2.01457 q^{68} +(2.29850 + 4.20915i) q^{69} -0.188371 q^{70} +(-5.25766 + 3.37889i) q^{71} +(0.142315 - 0.989821i) q^{72} +(1.15662 - 2.53265i) q^{73} +(-5.09201 + 1.49515i) q^{74} +(-2.06233 - 4.51588i) q^{75} +(-1.91627 - 2.21149i) q^{76} +(-0.643793 - 4.47768i) q^{77} +(-1.16264 - 0.341380i) q^{78} +(-2.11981 + 2.44639i) q^{79} +(0.158468 + 0.101841i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-6.73466 + 7.77221i) q^{82} +(15.9876 + 4.69438i) q^{83} +(-0.142315 - 0.989821i) q^{84} +(0.248512 + 0.286798i) q^{85} +(0.782387 + 1.71319i) q^{86} +(-7.80309 + 2.29119i) q^{87} +(-1.87922 + 4.11493i) q^{88} +(0.116044 - 0.807102i) q^{89} +(-0.158468 + 0.101841i) q^{90} -1.21172 q^{91} +(-1.01954 - 4.68621i) q^{92} -2.65459 q^{93} +(-1.49978 + 0.963849i) q^{94} +(-0.0784464 + 0.545606i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(9.60021 - 2.81888i) q^{97} +(-0.415415 - 0.909632i) q^{98} +(-2.96241 - 3.41880i) 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

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