LMFDB - Embedded newform 966.2.q.e.883.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$20$
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			883.1
Root			$1.31816 + 2.88636i$ of defining polynomial
Character	$\chi$	$=$	966.883
Dual form			966.2.q.e.547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.959493 - 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.172611 - 1.20054i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.415415 - 0.909632i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.959493 - 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.172611 - 1.20054i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.415415 - 0.909632i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.503850 - 1.10328i) q^{10} +(-5.46503 - 1.60468i) q^{11} +(-0.959493 - 0.281733i) q^{12} +(-1.28324 - 2.80991i) q^{13} +(0.142315 - 0.989821i) q^{14} +(-0.794270 + 0.916636i) q^{15} +(0.415415 - 0.909632i) q^{16} +(2.80233 + 1.80095i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-4.03444 + 2.59278i) q^{19} +(-0.794270 - 0.916636i) q^{20} +(-0.959493 + 0.281733i) q^{21} -5.69574 q^{22} +(2.06031 - 4.33072i) q^{23} -1.00000 q^{24} +(3.38597 - 0.994210i) q^{25} +(-2.02291 - 2.33456i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.142315 - 0.989821i) q^{28} +(-7.51255 - 4.82802i) q^{29} +(-0.503850 + 1.10328i) q^{30} +(-6.26922 + 7.23507i) q^{31} +(0.142315 - 0.989821i) q^{32} +(2.36610 + 5.18103i) q^{33} +(3.19621 + 0.938491i) q^{34} +(-1.16375 - 0.341709i) q^{35} +(0.415415 + 0.909632i) q^{36} +(1.01397 - 7.05230i) q^{37} +(-3.14055 + 3.62439i) q^{38} +(-1.28324 + 2.80991i) q^{39} +(-1.02034 - 0.655734i) q^{40} +(-0.302398 - 2.10322i) q^{41} +(-0.841254 + 0.540641i) q^{42} +(5.69646 + 6.57407i) q^{43} +(-5.46503 + 1.60468i) q^{44} +1.21288 q^{45} +(0.756750 - 4.73575i) q^{46} +0.894736 q^{47} +(-0.959493 + 0.281733i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(2.96871 - 1.90787i) q^{50} +(-0.474071 - 3.29724i) q^{51} +(-2.59869 - 1.67008i) q^{52} +(1.27911 - 2.80086i) q^{53} +(0.654861 - 0.755750i) q^{54} +(-0.983150 + 6.83796i) q^{55} +(-0.415415 - 0.909632i) q^{56} +(4.60149 + 1.35112i) q^{57} +(-8.56845 - 2.51592i) q^{58} +(-1.79102 - 3.92180i) q^{59} +(-0.172611 + 1.20054i) q^{60} +(8.13382 - 9.38693i) q^{61} +(-3.97692 + 8.70824i) q^{62} +(0.841254 + 0.540641i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-3.15191 + 2.02561i) q^{65} +(3.72992 + 4.30456i) q^{66} +(11.6214 - 3.41236i) q^{67} +3.33114 q^{68} +(-4.62216 + 1.27894i) q^{69} -1.21288 q^{70} +(-9.30356 + 2.73177i) q^{71} +(0.654861 + 0.755750i) q^{72} +(-13.9001 + 8.93306i) q^{73} +(-1.01397 - 7.05230i) q^{74} +(-2.96871 - 1.90787i) q^{75} +(-1.99223 + 4.36237i) q^{76} +(-3.72992 + 4.30456i) q^{77} +(-0.439620 + 3.05762i) q^{78} +(-5.12769 - 11.2281i) q^{79} +(-1.16375 - 0.341709i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.882695 - 1.93283i) q^{82} +(-0.404655 + 2.81444i) q^{83} +(-0.654861 + 0.755750i) q^{84} +(1.67840 - 3.67517i) q^{85} +(7.31784 + 4.70289i) q^{86} +(1.27090 + 8.83929i) q^{87} +(-4.79157 + 3.07935i) q^{88} +(1.49434 + 1.72456i) q^{89} +(1.16375 - 0.341709i) q^{90} -3.08907 q^{91} +(-0.608119 - 4.75712i) q^{92} +9.57336 q^{93} +(0.858493 - 0.252076i) q^{94} +(3.80912 + 4.39596i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(0.736539 + 5.12274i) q^{97} +(-0.841254 - 0.540641i) q^{98} +(2.36610 - 5.18103i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$2$	0.959493	−	0.281733i	0.678464	−	0.199215i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	−0.172611	−	1.20054i	−0.0771941	−	0.536897i	−0.991320	−	0.131467i	$-0.958031\pi$
$5$	−0.172611	−	1.20054i	−0.0771941	−	0.536897i	0.914126	−	0.405429i	$-0.132878\pi$
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	0.415415	−	0.909632i	0.157012	−	0.343809i
$7$	0.415415	−	0.909632i	0.157012	−	0.343809i
$8$	0.654861	−	0.755750i	0.231528	−	0.267198i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	−0.503850	−	1.10328i	−0.159331	−	0.348887i
$11$	−5.46503	−	1.60468i	−1.64777	−	0.483828i	−0.679486	−	0.733689i	$-0.737797\pi$
$11$	−5.46503	−	1.60468i	−1.64777	−	0.483828i	−0.968282	+	0.249860i	$0.919615\pi$
$12$	−0.959493	−	0.281733i	−0.276982	−	0.0813292i
$13$	−1.28324	−	2.80991i	−0.355908	−	0.779330i	−0.999898	−	0.0142958i	$-0.995449\pi$
$13$	−1.28324	−	2.80991i	−0.355908	−	0.779330i	0.643990	−	0.765034i	$-0.277278\pi$
$14$	0.142315	−	0.989821i	0.0380352	−	0.264541i
$15$	−0.794270	+	0.916636i	−0.205080	+	0.236674i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	2.80233	+	1.80095i	0.679666	+	0.436795i	0.834399	−	0.551162i	$-0.185815\pi$
$17$	2.80233	+	1.80095i	0.679666	+	0.436795i	−0.154733	+	0.987956i	$0.549452\pi$
$18$	0.142315	+	0.989821i	0.0335439	+	0.233303i
$19$	−4.03444	+	2.59278i	−0.925564	+	0.594824i	−0.914267	−	0.405112i	$-0.867232\pi$
$19$	−4.03444	+	2.59278i	−0.925564	+	0.594824i	−0.0112972	+	0.999936i	$0.503596\pi$
$20$	−0.794270	−	0.916636i	−0.177604	−	0.204966i
$21$	−0.959493	+	0.281733i	−0.209379	+	0.0614791i
$22$	−5.69574			−1.21434
$23$	2.06031	−	4.33072i	0.429605	−	0.903017i
$23$	2.06031	−	4.33072i	0.429605	−	0.903017i
$24$	−1.00000			−0.204124
$25$	3.38597	−	0.994210i	0.677194	−	0.198842i
$26$	−2.02291	−	2.33456i	−0.396725	−	0.457845i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	−0.142315	−	0.989821i	−0.0268950	−	0.187059i
$29$	−7.51255	−	4.82802i	−1.39505	−	0.896541i	−0.395288	−	0.918557i	$-0.629355\pi$
$29$	−7.51255	−	4.82802i	−1.39505	−	0.896541i	−0.999758	+	0.0220162i	$0.992991\pi$
$30$	−0.503850	+	1.10328i	−0.0919900	+	0.201430i
$31$	−6.26922	+	7.23507i	−1.12599	+	1.29946i	−0.176973	+	0.984216i	$0.556631\pi$
$31$	−6.26922	+	7.23507i	−1.12599	+	1.29946i	−0.949012	+	0.315240i	$0.897915\pi$
$32$	0.142315	−	0.989821i	0.0251579	−	0.174977i
$33$	2.36610	+	5.18103i	0.411885	+	0.901902i
$34$	3.19621	+	0.938491i	0.548145	+	0.160950i
$35$	−1.16375	−	0.341709i	−0.196710	−	0.0577593i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	1.01397	−	7.05230i	0.166695	−	1.15939i	−0.718961	−	0.695050i	$-0.755382\pi$
$37$	1.01397	−	7.05230i	0.166695	−	1.15939i	0.885656	−	0.464341i	$-0.153709\pi$
$38$	−3.14055	+	3.62439i	−0.509464	+	0.587953i
$39$	−1.28324	+	2.80991i	−0.205484	+	0.449946i
$40$	−1.02034	−	0.655734i	−0.161330	−	0.103681i
$41$	−0.302398	−	2.10322i	−0.0472266	−	0.328468i	−0.999715	−	0.0238919i	$-0.992394\pi$
$41$	−0.302398	−	2.10322i	−0.0472266	−	0.328468i	0.952488	−	0.304576i	$-0.0985148\pi$
$42$	−0.841254	+	0.540641i	−0.129808	+	0.0834227i
$43$	5.69646	+	6.57407i	0.868702	+	1.00254i	0.999937	+	0.0111846i	$0.00356025\pi$
$43$	5.69646	+	6.57407i	0.868702	+	1.00254i	−0.131235	+	0.991351i	$0.541894\pi$
$44$	−5.46503	+	1.60468i	−0.823884	+	0.241914i
$45$	1.21288			0.180806
$46$	0.756750	−	4.73575i	0.111577	−	0.698248i
$47$	0.894736			0.130511			0.0652553	−	0.997869i	$-0.479214\pi$
$47$	0.894736			0.130511			0.0652553	+	0.997869i	$0.479214\pi$
$48$	−0.959493	+	0.281733i	−0.138491	+	0.0406646i
$49$	−0.654861	−	0.755750i	−0.0935515	−	0.107964i
$50$	2.96871	−	1.90787i	0.419839	−	0.269814i
$51$	−0.474071	−	3.29724i	−0.0663832	−	0.461705i
$52$	−2.59869	−	1.67008i	−0.360373	−	0.231598i
$53$	1.27911	−	2.80086i	0.175699	−	0.384728i	−0.801210	−	0.598384i	$-0.795810\pi$
$53$	1.27911	−	2.80086i	0.175699	−	0.384728i	0.976909	+	0.213656i	$0.0685371\pi$
$54$	0.654861	−	0.755750i	0.0891153	−	0.102844i
$55$	−0.983150	+	6.83796i	−0.132568	+	0.922030i
$56$	−0.415415	−	0.909632i	−0.0555122	−	0.121555i
$57$	4.60149	+	1.35112i	0.609482	+	0.178960i
$58$	−8.56845	−	2.51592i	−1.12509	−	0.330357i
$59$	−1.79102	−	3.92180i	−0.233171	−	0.510574i	0.756489	−	0.654007i	$-0.226913\pi$
$59$	−1.79102	−	3.92180i	−0.233171	−	0.510574i	−0.989660	+	0.143433i	$0.954186\pi$
$60$	−0.172611	+	1.20054i	−0.0222840	+	0.154989i
$61$	8.13382	−	9.38693i	1.04143	−	1.20187i	0.0624209	−	0.998050i	$-0.480118\pi$
$61$	8.13382	−	9.38693i	1.04143	−	1.20187i	0.979008	−	0.203823i	$-0.0653367\pi$
$62$	−3.97692	+	8.70824i	−0.505069	+	1.10595i
$63$	0.841254	+	0.540641i	0.105988	+	0.0681143i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−3.15191	+	2.02561i	−0.390946	+	0.251246i
$66$	3.72992	+	4.30456i	0.459121	+	0.529854i
$67$	11.6214	−	3.41236i	1.41978	−	0.416886i	0.520353	−	0.853951i	$-0.325800\pi$
$67$	11.6214	−	3.41236i	1.41978	−	0.416886i	0.899430	+	0.437065i	$0.143982\pi$
$68$	3.33114			0.403960
$69$	−4.62216	+	1.27894i	−0.556442	+	0.153966i
$70$	−1.21288			−0.144967
$71$	−9.30356	+	2.73177i	−1.10413	+	0.324202i	−0.782492	−	0.622661i	$-0.786052\pi$
$71$	−9.30356	+	2.73177i	−1.10413	+	0.324202i	−0.321638	+	0.946863i	$0.604233\pi$
$72$	0.654861	+	0.755750i	0.0771761	+	0.0890659i
$73$	−13.9001	+	8.93306i	−1.62688	+	1.04554i	−0.675578	+	0.737288i	$0.736106\pi$
$73$	−13.9001	+	8.93306i	−1.62688	+	1.04554i	−0.951306	+	0.308247i	$0.900258\pi$
$74$	−1.01397	−	7.05230i	−0.117871	−	0.819814i
$75$	−2.96871	−	1.90787i	−0.342797	−	0.220302i
$76$	−1.99223	+	4.36237i	−0.228524	+	0.500398i
$77$	−3.72992	+	4.30456i	−0.425064	+	0.490550i
$78$	−0.439620	+	3.05762i	−0.0497772	+	0.346208i
$79$	−5.12769	−	11.2281i	−0.576911	−	1.26326i	−0.943035	−	0.332692i	$-0.892043\pi$
$79$	−5.12769	−	11.2281i	−0.576911	−	1.26326i	0.366125	−	0.930566i	$-0.380684\pi$
$80$	−1.16375	−	0.341709i	−0.130112	−	0.0382042i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−0.882695	−	1.93283i	−0.0974773	−	0.213446i
$83$	−0.404655	+	2.81444i	−0.0444167	+	0.308925i	0.955487	+	0.295034i	$0.0953309\pi$
$83$	−0.404655	+	2.81444i	−0.0444167	+	0.308925i	−0.999904	+	0.0138910i	$0.995578\pi$
$84$	−0.654861	+	0.755750i	−0.0714512	+	0.0824590i
$85$	1.67840	−	3.67517i	0.182048	−	0.398629i
$86$	7.31784	+	4.70289i	0.789103	+	0.507126i
$87$	1.27090	+	8.83929i	0.136255	+	0.947671i
$88$	−4.79157	+	3.07935i	−0.510783	+	0.328260i
$89$	1.49434	+	1.72456i	0.158400	+	0.182803i	0.829402	−	0.558652i	$-0.188681\pi$
$89$	1.49434	+	1.72456i	0.158400	+	0.182803i	−0.671002	+	0.741455i	$0.734136\pi$
$90$	1.16375	−	0.341709i	0.122670	−	0.0360193i
$91$	−3.08907			−0.323822
$92$	−0.608119	−	4.75712i	−0.0634008	−	0.495964i
$93$	9.57336			0.992712
$94$	0.858493	−	0.252076i	0.0885468	−	0.0259997i
$95$	3.80912	+	4.39596i	0.390807	+	0.451016i
$96$	−0.841254	+	0.540641i	−0.0858601	+	0.0551789i
$97$	0.736539	+	5.12274i	0.0747842	+	0.520135i	0.992437	+	0.122753i	$0.0391723\pi$
$97$	0.736539	+	5.12274i	0.0747842	+	0.520135i	−0.917653	+	0.397382i	$0.869919\pi$
$98$	−0.841254	−	0.540641i	−0.0849794	−	0.0546130i
$99$	2.36610	−	5.18103i	0.237802	−	0.520713i
$100$	2.31095	−	2.66698i	0.231095	−	0.266698i
$101$	1.58303	−	11.0102i	0.157517	−	1.09556i	−0.745671	−	0.666314i	$-0.767871\pi$
$101$	1.58303	−	11.0102i	0.157517	−	1.09556i	0.903189	−	0.429244i	$-0.141220\pi$
$102$	−1.38381	−	3.03011i	−0.137017	−	0.300026i
$103$	−5.85536	−	1.71929i	−0.576945	−	0.169406i	−0.0197747	−	0.999804i	$-0.506295\pi$
$103$	−5.85536	−	1.71929i	−0.576945	−	0.169406i	−0.557171	+	0.830398i	$0.688113\pi$
$104$	−2.96394	−	0.870291i	−0.290638	−	0.0853390i
$105$	0.503850	+	1.10328i	0.0491707	+	0.107669i
$106$	0.438204	−	3.04777i	0.0425621	−	0.296026i
$107$	8.25816	−	9.53042i	0.798346	−	0.921341i	−0.199943	−	0.979808i	$-0.564076\pi$
$107$	8.25816	−	9.53042i	0.798346	−	0.921341i	0.998289	+	0.0584669i	$0.0186212\pi$
$108$	0.415415	−	0.909632i	0.0399733	−	0.0875294i
$109$	7.96545	+	5.11908i	0.762952	+	0.490319i	0.863336	−	0.504629i	$-0.168371\pi$
$109$	7.96545	+	5.11908i	0.762952	+	0.490319i	−0.100384	+	0.994949i	$0.532007\pi$
$110$	0.983150	+	6.83796i	0.0937397	+	0.651974i
$111$	−5.99378	+	3.85197i	−0.568905	+	0.365613i
$112$	−0.654861	−	0.755750i	−0.0618785	−	0.0714116i
$113$	10.4754	−	3.07585i	0.985442	−	0.289352i	0.250973	−	0.967994i	$-0.419249\pi$
$113$	10.4754	−	3.07585i	0.985442	−	0.289352i	0.734469	+	0.678642i	$0.237431\pi$
$114$	4.79575			0.449163
$115$	−5.55482	−	1.72595i	−0.517990	−	0.160946i
$116$	−8.93018			−0.829147
$117$	2.96394	−	0.870291i	0.274016	−	0.0804584i
$118$	−2.82337	−	3.25835i	−0.259912	−	0.299955i
$119$	2.80233	−	1.80095i	0.256890	−	0.165093i
$120$	0.172611	+	1.20054i	0.0157572	+	0.109594i
$121$	18.0377	+	11.5922i	1.63980	+	1.05383i
$122$	5.15974	−	11.2983i	0.467141	−	1.02290i
$123$	−1.39148	+	1.60585i	−0.125466	+	0.144795i
$124$	−1.36243	+	9.47592i	−0.122350	+	0.850963i
$125$	−4.29729	−	9.40976i	−0.384362	−	0.841634i
$126$	0.959493	+	0.281733i	0.0854784	+	0.0250987i
$127$	17.2631	+	5.06889i	1.53185	+	0.449791i	0.935616	−	0.353020i	$-0.114845\pi$
$127$	17.2631	+	5.06889i	1.53185	+	0.449791i	0.596233	+	0.802811i	$0.296663\pi$
$128$	−0.415415	−	0.909632i	−0.0367178	−	0.0804009i
$129$	1.23796	−	8.61020i	0.108996	−	0.758086i
$130$	−2.45355	+	2.83155i	−0.215191	+	0.248343i
$131$	4.05648	−	8.88244i	0.354416	−	0.776063i	−0.645508	−	0.763753i	$-0.723354\pi$
$131$	4.05648	−	8.88244i	0.354416	−	0.776063i	0.999924	−	0.0123094i	$-0.00391830\pi$
$132$	4.79157	+	3.07935i	0.417052	+	0.268023i
$133$	0.682506	+	4.74694i	0.0591808	+	0.411611i
$134$	10.1893	−	6.54827i	0.880222	−	0.565684i
$135$	−0.794270	−	0.916636i	−0.0683598	−	0.0788915i
$136$	3.19621	−	0.938491i	0.274073	−	0.0804749i
$137$	7.19599			0.614795			0.307397	−	0.951581i	$-0.400542\pi$
$137$	7.19599			0.614795			0.307397	+	0.951581i	$0.400542\pi$
$138$	−4.07461	+	2.52934i	−0.346854	+	0.215312i
$139$	18.9127			1.60416			0.802078	−	0.597219i	$-0.203728\pi$
$139$	18.9127			1.60416			0.802078	+	0.597219i	$0.203728\pi$
$140$	−1.16375	+	0.341709i	−0.0983551	+	0.0288797i
$141$	−0.585928	−	0.676196i	−0.0493440	−	0.0569460i
$142$	−8.15707	+	5.24223i	−0.684526	+	0.439918i
$143$	2.50396	+	17.4154i	0.209392	+	1.45635i
$144$	0.841254	+	0.540641i	0.0701045	+	0.0450534i
$145$	−4.49947	+	9.85247i	−0.373661	+	0.818203i
$146$	−10.8203	+	12.4873i	−0.895496	+	1.03346i
$147$	−0.142315	+	0.989821i	−0.0117379	+	0.0816391i
$148$	−2.95976	−	6.48097i	−0.243291	−	0.532732i
$149$	−1.76248	−	0.517510i	−0.144388	−	0.0423961i	0.208740	−	0.977971i	$-0.433064\pi$
$149$	−1.76248	−	0.517510i	−0.144388	−	0.0423961i	−0.353128	+	0.935575i	$0.614882\pi$
$150$	−3.38597	−	0.994210i	−0.276463	−	0.0811769i
$151$	3.49412	+	7.65107i	0.284348	+	0.622635i	0.996874	−	0.0790109i	$-0.0251762\pi$
$151$	3.49412	+	7.65107i	0.284348	+	0.622635i	−0.712526	+	0.701646i	$0.752449\pi$
$152$	−0.682506	+	4.74694i	−0.0553586	+	0.385027i
$153$	−2.18143	+	2.51751i	−0.176358	+	0.203529i
$154$	−2.36610	+	5.18103i	−0.190666	+	0.417499i
$155$	9.76811	+	6.27758i	0.784593	+	0.504228i
$156$	0.439620	+	3.05762i	0.0351978	+	0.244806i
$157$	1.68340	−	1.08186i	0.134350	−	0.0863414i	−0.471739	−	0.881738i	$-0.656374\pi$
$157$	1.68340	−	1.08186i	0.134350	−	0.0863414i	0.606089	+	0.795397i	$0.292737\pi$
$158$	−8.08330	−	9.32863i	−0.643073	−	0.742146i
$159$	−2.95439	+	0.867487i	−0.234298	+	0.0687962i
$160$	−1.21288			−0.0958868
$161$	−3.08348	−	3.67317i	−0.243012	−	0.289486i
$162$	−1.00000			−0.0785674
$163$	5.96853	−	1.75252i	0.467491	−	0.137268i	−0.0394990	−	0.999220i	$-0.512576\pi$
$163$	5.96853	−	1.75252i	0.467491	−	0.137268i	0.506990	+	0.861952i	$0.330758\pi$
$164$	−1.39148	−	1.60585i	−0.108656	−	0.125396i
$165$	5.81161	−	3.73489i	0.452433	−	0.290761i
$166$	0.404655	+	2.81444i	0.0314073	+	0.218443i
$167$	−3.94346	−	2.53431i	−0.305154	−	0.196111i	0.379097	−	0.925357i	$-0.376235\pi$
$167$	−3.94346	−	2.53431i	−0.305154	−	0.196111i	−0.684252	+	0.729246i	$0.739871\pi$
$168$	−0.415415	+	0.909632i	−0.0320500	+	0.0701796i
$169$	2.26429	−	2.61313i	0.174176	−	0.201010i
$170$	0.574993	−	3.99916i	0.0440999	−	0.306722i
$171$	−1.99223	−	4.36237i	−0.152349	−	0.333599i
$172$	8.34638	+	2.45072i	0.636405	+	0.186865i
$173$	0.217087	+	0.0637426i	0.0165048	+	0.00484626i	0.289975	−	0.957034i	$-0.406353\pi$
$173$	0.217087	+	0.0637426i	0.0165048	+	0.00484626i	−0.273470	+	0.961881i	$0.588171\pi$
$174$	3.70973	+	8.12318i	0.281234	+	0.615817i
$175$	0.502217	−	3.49299i	0.0379640	−	0.264046i
$176$	−3.72992	+	4.30456i	−0.281153	+	0.324468i
$177$	−1.79102	+	3.92180i	−0.134622	+	0.294780i
$178$	1.91967	+	1.23370i	0.143885	+	0.0924696i
$179$	0.708361	+	4.92676i	0.0529454	+	0.368243i	0.999019	+	0.0442907i	$0.0141028\pi$
$179$	0.708361	+	4.92676i	0.0529454	+	0.368243i	−0.946073	+	0.323953i	$0.894988\pi$
$180$	1.02034	−	0.655734i	0.0760518	−	0.0488755i
$181$	11.9454	+	13.7858i	0.887897	+	1.02469i	0.999521	+	0.0309370i	$0.00984914\pi$
$181$	11.9454	+	13.7858i	0.887897	+	1.02469i	−0.111625	+	0.993750i	$0.535605\pi$
$182$	−2.96394	+	0.870291i	−0.219702	+	0.0645102i
$183$	−12.4207			−0.918163
$184$	−1.92372	−	4.39310i	−0.141819	−	0.323863i
$185$	−8.64158			−0.635342
$186$	9.18558	−	2.69713i	0.673519	−	0.197763i
$187$	−12.4249	−	14.3391i	−0.908598	−	1.04858i
$188$	0.752700	−	0.483731i	0.0548963	−	0.0352797i
$189$	−0.142315	−	0.989821i	−0.0103519	−	0.0719989i
$190$	4.89331	+	3.14474i	0.354998	+	0.228143i
$191$	1.08857	−	2.38363i	0.0787660	−	0.172474i	−0.866152	−	0.499781i	$-0.833414\pi$
$191$	1.08857	−	2.38363i	0.0787660	−	0.172474i	0.944918	+	0.327307i	$0.106141\pi$
$192$	−0.654861	+	0.755750i	−0.0472605	+	0.0545415i
$193$	3.12298	−	21.7208i	0.224797	−	1.56350i	−0.494737	−	0.869043i	$-0.664736\pi$
$193$	3.12298	−	21.7208i	0.224797	−	1.56350i	0.719534	−	0.694457i	$-0.244355\pi$
$194$	2.14995	+	4.70773i	0.154357	+	0.337995i
$195$	3.59491	+	1.05556i	0.257437	+	0.0755903i
$196$	−0.959493	−	0.281733i	−0.0685352	−	0.0201238i
$197$	−6.70282	−	14.6771i	−0.477556	−	1.04570i	−0.983128	−	0.182918i	$-0.941446\pi$
$197$	−6.70282	−	14.6771i	−0.477556	−	1.04570i	0.505572	−	0.862784i	$-0.331281\pi$
$198$	0.810589	−	5.63777i	0.0576061	−	0.400659i
$199$	−10.3189	+	11.9087i	−0.731490	+	0.844185i	−0.992639	−	0.121114i	$-0.961353\pi$
$199$	−10.3189	+	11.9087i	−0.731490	+	0.844185i	0.261148	+	0.965299i	$0.415899\pi$
$200$	1.46596	−	3.21001i	0.103659	−	0.226982i
$201$	−10.1893	−	6.54827i	−0.718698	−	0.461879i
$202$	−1.58303	−	11.0102i	−0.111382	−	0.774676i
$203$	−7.51255	+	4.82802i	−0.527278	+	0.338861i
$204$	−2.18143	−	2.51751i	−0.152731	−	0.176261i
$205$	−2.47280	+	0.726080i	−0.172708	+	0.0507116i
$206$	−6.10255			−0.425185
$207$	3.99342	+	2.65567i	0.277562	+	0.184582i
$208$	−3.08907			−0.214188
$209$	26.2089	−	7.69563i	1.81291	−	0.532318i
$210$	0.794270	+	0.916636i	0.0548098	+	0.0632539i
$211$	−17.7855	+	11.4301i	−1.22440	+	0.786877i	−0.983010	−	0.183550i	$-0.941241\pi$
$211$	−17.7855	+	11.4301i	−1.22440	+	0.786877i	−0.241394	+	0.970427i	$0.577605\pi$
$212$	−0.438204	−	3.04777i	−0.0300959	−	0.209322i
$213$	8.15707	+	5.24223i	0.558913	+	0.359192i
$214$	5.23861	−	11.4710i	0.358104	−	0.784139i
$215$	6.90914	−	7.97358i	0.471200	−	0.543793i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	3.97692	+	8.70824i	0.269971	+	0.591154i
$218$	9.08501	+	2.66760i	0.615314	+	0.180673i
$219$	15.8538	+	4.65509i	1.07130	+	0.314562i
$220$	2.86980	+	6.28399i	0.193482	+	0.423666i
$221$	1.46444	−	10.1854i	0.0985087	−	0.685143i
$222$	−4.66577	+	5.38458i	−0.313146	+	0.361390i
$223$	−6.02541	+	13.1938i	−0.403491	+	0.883523i	0.593413	+	0.804898i	$0.297780\pi$
$223$	−6.02541	+	13.1938i	−0.403491	+	0.883523i	−0.996904	+	0.0786248i	$0.974947\pi$
$224$	−0.841254	−	0.540641i	−0.0562086	−	0.0361231i
$225$	0.502217	+	3.49299i	0.0334811	+	0.232866i
$226$	9.18450	−	5.90252i	0.610944	−	0.392630i
$227$	0.706908	+	0.815815i	0.0469191	+	0.0541476i	0.778724	−	0.627367i	$-0.215867\pi$
$227$	0.706908	+	0.815815i	0.0469191	+	0.0541476i	−0.731805	+	0.681514i	$0.761322\pi$
$228$	4.60149	−	1.35112i	0.304741	−	0.0894800i
$229$	24.5265			1.62076			0.810380	−	0.585905i	$-0.199261\pi$
$229$	24.5265			1.62076			0.810380	+	0.585905i	$0.199261\pi$
$230$	−5.81607	−	0.0910627i	−0.383500	−	0.00600450i
$231$	5.69574			0.374752
$232$	−8.56845	+	2.51592i	−0.562546	+	0.165178i
$233$	7.94024	+	9.16353i	0.520183	+	0.600323i	0.953677	−	0.300834i	$-0.0972649\pi$
$233$	7.94024	+	9.16353i	0.520183	+	0.600323i	−0.433494	+	0.901156i	$0.642719\pi$
$234$	2.59869	−	1.67008i	0.169882	−	0.109176i
$235$	−0.154442	−	1.07416i	−0.0100747	−	0.0700708i
$236$	−3.62699	−	2.33092i	−0.236097	−	0.151730i
$237$	−5.12769	+	11.2281i	−0.333080	+	0.729342i
$238$	2.18143	−	2.51751i	0.141401	−	0.163186i
$239$	−2.94464	+	20.4804i	−0.190473	+	1.32477i	0.640286	+	0.768137i	$0.278816\pi$
$239$	−2.94464	+	20.4804i	−0.190473	+	1.32477i	−0.830759	+	0.556632i	$0.812093\pi$
$240$	0.503850	+	1.10328i	0.0325234	+	0.0712163i
$241$	19.0393	+	5.59044i	1.22643	+	0.360112i	0.829901	−	0.557911i	$-0.188397\pi$
$241$	19.0393	+	5.59044i	1.22643	+	0.360112i	0.396528	+	0.918023i	$0.370215\pi$
$242$	20.5730	+	6.04077i	1.32248	+	0.388315i
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$	1.76765	−	12.2943i	0.113162	−	0.787059i
$245$	−0.794270	+	0.916636i	−0.0507440	+	0.0585617i
$246$	−0.882695	+	1.93283i	−0.0562786	+	0.123233i
$247$	12.4627	+	8.00926i	0.792980	+	0.509617i
$248$	1.36243	+	9.47592i	0.0865145	+	0.601722i
$249$	2.39200	−	1.53725i	0.151587	−	0.0974191i
$250$	−6.77426	−	7.81791i	−0.428442	−	0.494448i
$251$	−6.10392	+	1.79227i	−0.385276	+	0.113127i	−0.468634	−	0.883392i	$-0.655254\pi$
$251$	−6.10392	+	1.79227i	−0.385276	+	0.113127i	0.0833579	+	0.996520i	$0.473436\pi$
$252$	1.00000			0.0629941
$253$	−18.2091	+	20.3614i	−1.14479	+	1.28011i
$254$	17.9919			1.12891
$255$	−3.87663	+	1.13828i	−0.242764	+	0.0712819i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	21.2061	−	13.6284i	1.32280	−	0.850114i	0.327307	−	0.944918i	$-0.393859\pi$
$257$	21.2061	−	13.6284i	1.32280	−	0.850114i	0.995496	+	0.0948045i	$0.0302226\pi$
$258$	−1.23796	−	8.61020i	−0.0770720	−	0.536047i
$259$	−5.99378	−	3.85197i	−0.372436	−	0.239350i
$260$	−1.55643	+	3.40810i	−0.0965254	+	0.211361i
$261$	5.84803	−	6.74898i	0.361984	−	0.417752i
$262$	1.38969	−	9.66548i	0.0858551	−	0.597136i
$263$	−9.13504	−	20.0030i	−0.563291	−	1.23343i	−0.950293	−	0.311356i	$-0.899217\pi$
$263$	−9.13504	−	20.0030i	−0.563291	−	1.23343i	0.387002	−	0.922079i	$-0.373511\pi$
$264$	5.46503	+	1.60468i	0.336349	+	0.0987610i
$265$	−3.58333	−	1.05216i	−0.220122	−	0.0646337i
$266$	1.99223	+	4.36237i	0.122151	+	0.267474i
$267$	0.324751	−	2.25869i	0.0198744	−	0.138230i
$268$	7.93170	−	9.15367i	0.484506	−	0.559150i
$269$	−12.9944	+	28.4538i	−0.792284	+	1.73486i	−0.122290	+	0.992494i	$0.539024\pi$
$269$	−12.9944	+	28.4538i	−0.792284	+	1.73486i	−0.669994	+	0.742366i	$0.733703\pi$
$270$	−1.02034	−	0.655734i	−0.0620961	−	0.0399067i
$271$	−2.15111	−	14.9613i	−0.130671	−	0.908835i	−0.944682	−	0.327987i	$-0.893630\pi$
$271$	−2.15111	−	14.9613i	−0.130671	−	0.908835i	0.814012	−	0.580849i	$-0.197279\pi$
$272$	2.80233	−	1.80095i	0.169917	−	0.109199i
$273$	2.02291	+	2.33456i	0.122432	+	0.141294i
$274$	6.90450	−	2.02734i	0.417116	−	0.122476i
$275$	−20.0998			−1.21206
$276$	−3.19696	+	3.57484i	−0.192434	+	0.215180i
$277$	−16.7386			−1.00572			−0.502862	−	0.864367i	$-0.667719\pi$
$277$	−16.7386			−1.00572			−0.502862	+	0.864367i	$0.667719\pi$
$278$	18.1466	−	5.32833i	1.08836	−	0.319572i
$279$	−6.26922	−	7.23507i	−0.375328	−	0.433152i
$280$	−1.02034	+	0.655734i	−0.0609771	+	0.0391876i
$281$	−3.08177	−	21.4342i	−0.183843	−	1.27865i	−0.847571	−	0.530681i	$-0.821936\pi$
$281$	−3.08177	−	21.4342i	−0.183843	−	1.27865i	0.663729	−	0.747973i	$-0.268973\pi$
$282$	−0.752700	−	0.483731i	−0.0448226	−	0.0288058i
$283$	0.104783	−	0.229442i	0.00622869	−	0.0136389i	−0.906492	−	0.422223i	$-0.861250\pi$
$283$	0.104783	−	0.229442i	0.00622869	−	0.0136389i	0.912721	+	0.408584i	$0.133977\pi$
$284$	−6.34975	+	7.32800i	−0.376788	+	0.434837i
$285$	0.827800	−	5.75748i	0.0490347	−	0.341044i
$286$	7.30903	+	16.0046i	0.432192	+	0.946369i
$287$	−2.03878	−	0.598639i	−0.120345	−	0.0353366i
$288$	0.959493	+	0.281733i	0.0565387	+	0.0166013i
$289$	−2.45240	−	5.37001i	−0.144259	−	0.315883i
$290$	−1.54145	+	10.7210i	−0.0905171	+	0.629560i
$291$	3.38918	−	3.91132i	0.198677	−	0.229286i
$292$	−6.86394	+	15.0299i	−0.401682	+	0.879560i
$293$	−5.86499	−	3.76920i	−0.342637	−	0.220199i	0.357993	−	0.933724i	$-0.383461\pi$
$293$	−5.86499	−	3.76920i	−0.342637	−	0.220199i	−0.700630	+	0.713525i	$0.747098\pi$
$294$	0.142315	+	0.989821i	0.00829997	+	0.0577276i
$295$	−4.39911	+	2.82714i	−0.256126	+	0.164602i
$296$	−4.66577	−	5.38458i	−0.271192	−	0.312973i
$297$	−5.46503	+	1.60468i	−0.317113	+	0.0931128i
$298$	−1.83689			−0.106408
$299$	−14.8128	−	0.231926i	−0.856648	−	0.0134126i
$300$	−3.52891			−0.203742
$301$	8.34638	−	2.45072i	0.481077	−	0.141257i
$302$	5.50814	+	6.35674i	0.316958	+	0.365789i
$303$	−9.35763	+	6.01379i	−0.537582	+	0.345483i
$304$	0.682506	+	4.74694i	0.0391444	+	0.272255i
$305$	−12.6733	−	8.14467i	−0.725674	−	0.466362i
$306$	−1.38381	+	3.03011i	−0.0791069	+	0.173220i
$307$	−2.38014	+	2.74682i	−0.135842	+	0.156770i	−0.819594	−	0.572944i	$-0.805801\pi$
$307$	−2.38014	+	2.74682i	−0.135842	+	0.156770i	0.683753	+	0.729714i	$0.260347\pi$
$308$	−0.810589	+	5.63777i	−0.0461876	+	0.321242i
$309$	2.53509	+	5.55108i	0.144216	+	0.315790i
$310$	11.1410	+	3.27130i	0.632768	+	0.185797i
$311$	−27.2643	−	8.00551i	−1.54601	−	0.453951i	−0.606108	−	0.795382i	$-0.707270\pi$
$311$	−27.2643	−	8.00551i	−1.54601	−	0.453951i	−0.939907	+	0.341431i	$0.889088\pi$
$312$	1.28324	+	2.80991i	0.0726494	+	0.159080i
$313$	1.62052	−	11.2710i	0.0915974	−	0.637074i	−0.891368	−	0.453281i	$-0.850253\pi$
$313$	1.62052	−	11.2710i	0.0915974	−	0.637074i	0.982965	−	0.183793i	$-0.0588375\pi$
$314$	1.31042	−	1.51230i	0.0739511	−	0.0853441i
$315$	0.503850	−	1.10328i	0.0283887	−	0.0621626i
$316$	−10.3841	−	6.67342i	−0.584149	−	0.375409i
$317$	−2.16566	−	15.0625i	−0.121635	−	0.845992i	−0.955704	−	0.294331i	$-0.904903\pi$
$317$	−2.16566	−	15.0625i	−0.121635	−	0.845992i	0.834068	−	0.551661i	$-0.186006\pi$
$318$	−2.59032	+	1.66469i	−0.145258	+	0.0933514i
$319$	33.3089	+	38.4405i	1.86494	+	2.15225i
$320$	−1.16375	+	0.341709i	−0.0650558	+	0.0191021i
$321$	−12.6106			−0.703853
$322$	−3.99342	−	2.65567i	−0.222545	−	0.147994i
$323$	−15.9753			−0.888891
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	−7.13867	−	8.23846i	−0.395982	−	0.456988i
$326$	5.23302	−	3.36306i	0.289830	−	0.186262i
$327$	−1.34752	−	9.37217i	−0.0745178	−	0.518282i
$328$	−1.78754	−	1.14878i	−0.0987002	−	0.0634308i
$329$	0.371687	−	0.813881i	0.0204918	−	0.0448707i
$330$	4.52396	−	5.22093i	0.249036	−	0.287402i
$331$	−3.13458	+	21.8015i	−0.172292	+	1.19832i	0.701734	+	0.712439i	$0.252409\pi$
$331$	−3.13458	+	21.8015i	−0.172292	+	1.19832i	−0.874026	+	0.485879i	$0.838500\pi$
$332$	1.18118	+	2.58643i	0.0648258	+	0.141949i
$333$	6.83622	+	2.00729i	0.374622	+	0.109999i
$334$	−4.49772	−	1.32065i	−0.246104	−	0.0722628i
$335$	−6.10265	−	13.3629i	−0.333424	−	0.730096i
$336$	−0.142315	+	0.989821i	−0.00776391	+	0.0539992i
$337$	−19.8143	+	22.8669i	−1.07935	+	1.24564i	−0.111594	+	0.993754i	$0.535596\pi$
$337$	−19.8143	+	22.8669i	−1.07935	+	1.24564i	−0.967757	+	0.251884i	$0.918950\pi$
$338$	1.43637	−	3.14520i	0.0781281	−	0.171077i
$339$	−9.18450	−	5.90252i	−0.498834	−	0.320581i
$340$	−0.574993	−	3.99916i	−0.0311834	−	0.216885i
$341$	45.8714	−	29.4798i	2.48408	−	1.59642i
$342$	−3.14055	−	3.62439i	−0.169821	−	0.195984i
$343$	−0.959493	+	0.281733i	−0.0518078	+	0.0152121i
$344$	8.69874			0.469005
$345$	2.33325	+	5.32831i	0.125618	+	0.286867i
$346$	0.226252			0.0121634
$347$	−9.19980	+	2.70131i	−0.493871	+	0.145014i	−0.519178	−	0.854666i	$-0.673762\pi$
$347$	−9.19980	+	2.70131i	−0.493871	+	0.145014i	0.0253069	+	0.999680i	$0.491944\pi$
$348$	5.84803	+	6.74898i	0.313487	+	0.361783i
$349$	−4.23700	+	2.72295i	−0.226801	+	0.145756i	−0.649107	−	0.760697i	$-0.724857\pi$
$349$	−4.23700	+	2.72295i	−0.226801	+	0.145756i	0.422306	+	0.906453i	$0.361221\pi$
$350$	−0.502217	−	3.49299i	−0.0268446	−	0.186708i
$351$	−2.59869	−	1.67008i	−0.138708	−	0.0891420i
$352$	−2.36610	+	5.18103i	−0.126113	+	0.276150i
$353$	5.03051	−	5.80552i	0.267747	−	0.308997i	−0.605915	−	0.795529i	$-0.707193\pi$
$353$	5.03051	−	5.80552i	0.267747	−	0.308997i	0.873662	+	0.486532i	$0.161738\pi$
$354$	−0.613577	+	4.26752i	−0.0326113	+	0.226816i
$355$	4.88550	+	10.6977i	0.259295	+	0.567777i
$356$	2.18948	+	0.642891i	0.116042	+	0.0340731i
$357$	−3.19621	−	0.938491i	−0.169161	−	0.0496702i
$358$	2.06770	+	4.52762i	0.109281	+	0.239292i
$359$	4.07685	−	28.3551i	0.215168	−	1.49653i	−0.540373	−	0.841426i	$-0.681717\pi$
$359$	4.07685	−	28.3551i	0.215168	−	1.49653i	0.755541	−	0.655102i	$-0.227374\pi$
$360$	0.794270	−	0.916636i	0.0418617	−	0.0483110i
$361$	1.66133	−	3.63781i	0.0874385	−	0.191464i
$362$	15.3455	+	9.86192i	0.806539	+	0.518331i
$363$	−3.05144	−	21.2233i	−0.160159	−	1.11393i
$364$	−2.59869	+	1.67008i	−0.136208	+	0.0875357i
$365$	13.1238	+	15.1457i	0.686931	+	0.792760i
$366$	−11.9176	+	3.49931i	−0.622941	+	0.182912i
$367$	22.7870			1.18947			0.594735	−	0.803921i	$-0.297257\pi$
$367$	22.7870			1.18947			0.594735	+	0.803921i	$0.297257\pi$
$368$	−3.08348	−	3.67317i	−0.160737	−	0.191477i
$369$	2.12485			0.110615
$370$	−8.29154	+	2.43461i	−0.431056	+	0.126570i
$371$	−2.01639	−	2.32704i	−0.104686	−	0.120814i
$372$	8.05363	−	5.17575i	0.417561	−	0.268350i
$373$	−3.48789	−	24.2588i	−0.180596	−	1.25607i	−0.855357	−	0.518039i	$-0.826662\pi$
$373$	−3.48789	−	24.2588i	−0.180596	−	1.25607i	0.674761	−	0.738036i	$-0.264247\pi$
$374$	−15.9614	−	10.2578i	−0.825344	−	0.530416i
$375$	−4.29729	+	9.40976i	−0.221911	+	0.485918i
$376$	0.585928	−	0.676196i	0.0302169	−	0.0348722i
$377$	−3.92589	+	27.3051i	−0.202194	+	1.40629i
$378$	−0.415415	−	0.909632i	−0.0213666	−	0.0467864i
$379$	−36.8306	−	10.8145i	−1.89186	−	0.555501i	−0.993132	−	0.117001i	$-0.962672\pi$
$379$	−36.8306	−	10.8145i	−1.89186	−	0.555501i	−0.898731	−	0.438500i	$-0.855510\pi$
$380$	5.58107	+	1.63875i	0.286303	+	0.0840661i
$381$	−7.47409	−	16.3660i	−0.382909	−	0.838454i
$382$	0.372927	−	2.59376i	0.0190806	−	0.132708i
$383$	−20.6798	+	23.8657i	−1.05669	+	1.21948i	−0.0818314	+	0.996646i	$0.526077\pi$
$383$	−20.6798	+	23.8657i	−1.05669	+	1.21948i	−0.974856	+	0.222836i	$0.928469\pi$
$384$	−0.415415	+	0.909632i	−0.0211991	+	0.0464195i
$385$	5.81161	+	3.73489i	0.296187	+	0.190348i
$386$	−3.12298	−	21.7208i	−0.158956	−	1.10556i
$387$	−7.31784	+	4.70289i	−0.371987	+	0.239061i
$388$	3.38918	+	3.91132i	0.172059	+	0.198567i
$389$	15.3888	−	4.51857i	0.780244	−	0.229100i	0.132729	−	0.991152i	$-0.457626\pi$
$389$	15.3888	−	4.51857i	0.780244	−	0.229100i	0.647516	+	0.762052i	$0.275808\pi$
$390$	3.74668			0.189720
$391$	13.5731	−	8.42560i	0.686421	−	0.426101i
$392$	−1.00000			−0.0505076
$393$	−9.36933	+	2.75108i	−0.472620	+	0.138774i
$394$	−10.5663	−	12.1942i	−0.532324	−	0.614335i
$395$	−12.5946	+	8.09409i	−0.633705	+	0.407258i
$396$	−0.810589	−	5.63777i	−0.0407336	−	0.283309i
$397$	−25.4942	−	16.3841i	−1.27951	−	0.822294i	−0.288687	−	0.957424i	$-0.593219\pi$
$397$	−25.4942	−	16.3841i	−1.27951	−	0.822294i	−0.990828	+	0.135129i	$0.956855\pi$
$398$	−6.54588	+	14.3335i	−0.328116	+	0.718473i
$399$	3.14055	−	3.62439i	0.157224	−	0.181446i
$400$	0.502217	−	3.49299i	0.0251108	−	0.174650i
$401$	1.27009	+	2.78111i	0.0634254	+	0.138882i	0.938690	−	0.344762i	$-0.112040\pi$
$401$	1.27009	+	2.78111i	0.0634254	+	0.138882i	−0.875265	+	0.483644i	$0.839313\pi$
$402$	−11.6214	−	3.41236i	−0.579624	−	0.170193i
$403$	28.3749	+	8.33161i	1.41345	+	0.415027i
$404$	−4.62084	−	10.1182i	−0.229896	−	0.503401i
$405$	−0.172611	+	1.20054i	−0.00857712	+	0.0596552i
$406$	−5.84803	+	6.74898i	−0.290233	+	0.334946i
$407$	−16.8580	+	36.9139i	−0.835622	+	1.82976i
$408$	−2.80233	−	1.80095i	−0.138736	−	0.0891604i
$409$	5.21430	+	36.2662i	0.257830	+	1.79325i	0.548213	+	0.836339i	$0.315308\pi$
$409$	5.21430	+	36.2662i	0.257830	+	1.79325i	−0.290382	+	0.956911i	$0.593783\pi$
$410$	−2.16807	+	1.39334i	−0.107074	+	0.0688120i
$411$	−4.71237	−	5.43837i	−0.232444	−	0.268255i
$412$	−5.85536	+	1.71929i	−0.288473	+	0.0847032i
$413$	−4.31141			−0.212151
$414$	4.57985	+	1.42301i	0.225087	+	0.0699374i
$415$	3.44869			0.169289
$416$	−2.96394	+	0.870291i	−0.145319	+	0.0426695i
$417$	−12.3852	−	14.2933i	−0.606506	−	0.699945i
$418$	22.9791	−	14.7678i	1.12395	−	0.722317i
$419$	−2.61148	−	18.1632i	−0.127579	−	0.887331i	−0.948610	−	0.316448i	$-0.897510\pi$
$419$	−2.61148	−	18.1632i	−0.127579	−	0.887331i	0.821031	−	0.570884i	$-0.193399\pi$
$420$	1.02034	+	0.655734i	0.0497876	+	0.0319966i
$421$	−8.38135	+	18.3526i	−0.408482	+	0.894451i	0.587857	+	0.808965i	$0.299972\pi$
$421$	−8.38135	+	18.3526i	−0.408482	+	0.894451i	−0.996339	+	0.0854864i	$0.972756\pi$
$422$	−13.8449	+	15.9778i	−0.673957	+	0.777788i
$423$	−0.127334	+	0.885629i	−0.00619120	+	0.0430608i
$424$	−1.27911	−	2.80086i	−0.0621191	−	0.136022i
$425$	11.2791	+	3.31185i	0.547119	+	0.160649i
$426$	9.30356	+	2.73177i	0.450759	+	0.132355i
$427$	−5.15974	−	11.2983i	−0.249697	−	0.546761i
$428$	1.79467	−	12.4822i	0.0867486	−	0.603350i
$429$	11.5220	−	13.2971i	0.556286	−	0.641988i
$430$	4.38286	−	9.59712i	0.211360	−	0.462814i
$431$	−9.37405	−	6.02434i	−0.451532	−	0.290182i	0.295042	−	0.955484i	$-0.404666\pi$
$431$	−9.37405	−	6.02434i	−0.451532	−	0.290182i	−0.746574	+	0.665302i	$0.768303\pi$
$432$	−0.142315	−	0.989821i	−0.00684713	−	0.0476228i
$433$	7.38289	−	4.74469i	0.354799	−	0.228015i	−0.351084	−	0.936344i	$-0.614187\pi$
$433$	7.38289	−	4.74469i	0.354799	−	0.228015i	0.705883	+	0.708329i	$0.250550\pi$
$434$	6.26922	+	7.23507i	0.300932	+	0.347294i
$435$	10.3925	−	3.05152i	0.498284	−	0.146309i
$436$	9.46855			0.453461
$437$	2.91639	+	22.8140i	0.139510	+	1.09134i
$438$	16.5231			0.789504
$439$	3.41355	−	1.00231i	0.162920	−	0.0478375i	−0.199256	−	0.979948i	$-0.563852\pi$
$439$	3.41355	−	1.00231i	0.162920	−	0.0478375i	0.362175	+	0.932110i	$0.382034\pi$
$440$	4.52396	+	5.22093i	0.215671	+	0.248898i
$441$	0.841254	−	0.540641i	0.0400597	−	0.0257448i
$442$	−1.46444	−	10.1854i	−0.0696561	−	0.484469i
$443$	18.1945	+	11.6929i	0.864447	+	0.555546i	0.896050	−	0.443954i	$-0.146425\pi$
$443$	18.1945	+	11.6929i	0.864447	+	0.555546i	−0.0316025	+	0.999501i	$0.510061\pi$
$444$	−2.95976	+	6.48097i	−0.140464	+	0.307573i
$445$	1.81246	−	2.09169i	0.0859188	−	0.0991555i
$446$	−2.06421	+	14.3569i	−0.0977434	+	0.679820i
$447$	0.763070	+	1.67089i	0.0360920	+	0.0790304i
$448$	−0.959493	−	0.281733i	−0.0453318	−	0.0133106i
$449$	33.2921	+	9.77543i	1.57115	+	0.461331i	0.947336	−	0.320242i	$-0.103764\pi$
$449$	33.2921	+	9.77543i	1.57115	+	0.461331i	0.623814	+	0.781573i	$0.285582\pi$
$450$	1.46596	+	3.21001i	0.0691062	+	0.151321i
$451$	−1.72238	+	11.9794i	−0.0811037	+	0.564089i
$452$	7.14953	−	8.25100i	0.336286	−	0.388094i
$453$	3.49412	−	7.65107i	0.164168	−	0.359478i
$454$	0.908115	+	0.583610i	0.0426199	+	0.0273902i
$455$	0.533208	+	3.70854i	0.0249972	+	0.173859i
$456$	4.03444	−	2.59278i	0.188930	−	0.121418i
$457$	−8.09805	−	9.34565i	−0.378811	−	0.437171i	0.534043	−	0.845457i	$-0.320672\pi$
$457$	−8.09805	−	9.34565i	−0.378811	−	0.437171i	−0.912854	+	0.408286i	$0.866127\pi$
$458$	23.5330	−	6.90992i	1.09963	−	0.322880i
$459$	3.33114			0.155484
$460$	−5.60613	+	1.55120i	−0.261387	+	0.0723252i
$461$	−24.4020			−1.13651			−0.568256	−	0.822852i	$-0.692382\pi$
$461$	−24.4020			−1.13651			−0.568256	+	0.822852i	$0.692382\pi$
$462$	5.46503	−	1.60468i	0.254256	−	0.0746563i
$463$	−10.1941	−	11.7647i	−0.473762	−	0.546750i	0.467692	−	0.883891i	$-0.345086\pi$
$463$	−10.1941	−	11.7647i	−0.473762	−	0.546750i	−0.941454	+	0.337141i	$0.890540\pi$
$464$	−7.51255	+	4.82802i	−0.348761	+	0.224135i
$465$	−1.65247	−	11.4932i	−0.0766315	−	0.532984i
$466$	10.2003	+	6.55532i	0.472518	+	0.303669i
$467$	−7.67061	+	16.7963i	−0.354953	+	0.777239i	0.644962	+	0.764215i	$0.276873\pi$
$467$	−7.67061	+	16.7963i	−0.354953	+	0.777239i	−0.999915	+	0.0130247i	$0.995854\pi$
$468$	2.02291	−	2.33456i	0.0935090	−	0.107915i
$469$	1.72372	−	11.9888i	0.0795942	−	0.553590i
$470$	−0.450813	−	0.987142i	−0.0207944	−	0.0455335i
$471$	−1.92000	−	0.563764i	−0.0884691	−	0.0259769i
$472$	−4.13677	−	1.21466i	−0.190410	−	0.0559094i
$473$	−20.5821	−	45.0684i	−0.946364	−	2.07225i
$474$	−1.75667	+	12.2179i	−0.0806865	+	0.561187i
$475$	−11.0827	+	12.7901i	−0.508510	+	0.586852i
$476$	1.38381	−	3.03011i	0.0634267	−	0.138885i
$477$	2.59032	+	1.66469i	0.118602	+	0.0762211i
$478$	2.94464	+	20.4804i	0.134685	+	0.936753i
$479$	24.8427	−	15.9654i	1.13509	−	0.729479i	0.168474	−	0.985706i	$-0.446116\pi$
$479$	24.8427	−	15.9654i	1.13509	−	0.729479i	0.966617	+	0.256227i	$0.0824796\pi$
$480$	0.794270	+	0.916636i	0.0362533	+	0.0418385i
$481$	−21.1175	+	6.20067i	−0.962877	+	0.282726i
$482$	19.8431			0.903827
$483$	−0.756750	+	4.73575i	−0.0344333	+	0.215484i
$484$	21.4415			0.974614
$485$	6.02291	−	1.76849i	0.273486	−	0.0803028i
$486$	0.654861	+	0.755750i	0.0297051	+	0.0342815i
$487$	7.29923	−	4.69093i	0.330759	−	0.212566i	−0.364711	−	0.931121i	$-0.618832\pi$
$487$	7.29923	−	4.69093i	0.330759	−	0.212566i	0.695471	+	0.718554i	$0.255196\pi$
$488$	−1.76765	−	12.2943i	−0.0800176	−	0.556535i
$489$	−5.23302	−	3.36306i	−0.236645	−	0.152083i
$490$	−0.503850	+	1.10328i	−0.0227616	+	0.0498410i
$491$	−8.61638	+	9.94383i	−0.388852	+	0.448759i	−0.916098	−	0.400953i	$-0.868679\pi$
$491$	−8.61638	+	9.94383i	−0.388852	+	0.448759i	0.527247	+	0.849712i	$0.323224\pi$
$492$	−0.302398	+	2.10322i	−0.0136331	+	0.0948206i
$493$	−12.3576	−	27.0595i	−0.556560	−	1.21870i
$494$	14.2143	+	4.17370i	0.639532	+	0.187783i
$495$	−6.62844	−	1.94629i	−0.297926	−	0.0874790i
$496$	3.97692	+	8.70824i	0.178569	+	0.391011i
$497$	−1.37993	+	9.59764i	−0.0618984	+	0.430513i
$498$	1.86202	−	2.14888i	0.0834390	−	0.0962938i
$499$	−0.394801	+	0.864494i	−0.0176737	+	0.0387001i	−0.918263	−	0.395971i	$-0.870408\pi$
$499$	−0.394801	+	0.864494i	−0.0176737	+	0.0387001i	0.900589	+	0.434671i	$0.143135\pi$
$500$	−8.70241	−	5.59270i	−0.389184	−	0.250113i
$501$	0.667116	+	4.63989i	0.0298045	+	0.207295i
$502$	−5.35173	+	3.43935i	−0.238859	+	0.153506i
$503$	−1.93991	−	2.23877i	−0.0864963	−	0.0998220i	0.710852	−	0.703342i	$-0.248310\pi$
$503$	−1.93991	−	2.23877i	−0.0864963	−	0.0998220i	−0.797348	+	0.603520i	$0.793764\pi$
$504$	0.959493	−	0.281733i	0.0427392	−	0.0125494i
$505$	−13.4914			−0.600361
$506$	−11.7350	+	24.6667i	−0.521685	+	1.09657i
$507$	−3.45767			−0.153560
$508$	17.2631	−	5.06889i	0.765925	−	0.224896i
$509$	14.5167	+	16.7532i	0.643444	+	0.742574i	0.979980	−	0.199097i	$-0.0638009\pi$
$509$	14.5167	+	16.7532i	0.643444	+	0.742574i	−0.336536	+	0.941671i	$0.609255\pi$
$510$	−3.39891	+	2.18434i	−0.150506	+	0.0967244i
$511$	2.35148	+	16.3549i	0.104023	+	0.723499i
$512$	−0.841254	−	0.540641i	−0.0371785	−	0.0238932i
$513$	−1.99223	+	4.36237i	−0.0879589	+	0.192603i
$514$	16.5076	−	19.0508i	0.728119	−	0.840294i
$515$	−1.05337	+	7.32634i	−0.0464170	+	0.322837i
$516$	−3.61359	−	7.91265i	−0.159079	−	0.348335i
$517$	−4.88976	−	1.43576i	−0.215051	−	0.0631448i
$518$	−6.83622	−	2.00729i	−0.300366	−	0.0881955i
$519$	−0.0939885	−	0.205806i	−0.00412564	−	0.00903389i
$520$	−0.533208	+	3.70854i	−0.0233827	+	0.162630i
$521$	−26.7902	+	30.9176i	−1.17370	+	1.35452i	−0.251480	+	0.967862i	$0.580917\pi$
$521$	−26.7902	+	30.9176i	−1.17370	+	1.35452i	−0.922222	+	0.386662i	$0.873628\pi$
$522$	3.70973	−	8.12318i	0.162371	−	0.355542i
$523$	6.70092	+	4.30642i	0.293011	+	0.188307i	0.678885	−	0.734245i	$-0.262464\pi$
$523$	6.70092	+	4.30642i	0.293011	+	0.188307i	−0.385874	+	0.922552i	$0.626100\pi$
$524$	−1.38969	−	9.66548i	−0.0607087	−	0.422239i
$525$	−2.96871	+	1.90787i	−0.129565	+	0.0832665i
$526$	−14.4005	−	16.6191i	−0.627891	−	0.724625i
$527$	−30.5985	+	8.98452i	−1.33289	+	0.391372i
$528$	5.69574			0.247875
$529$	−14.5102	−	17.8453i	−0.630880	−	0.775881i
$530$	−3.73461			−0.162221
$531$	4.13677	−	1.21466i	0.179520	−	0.0527119i
$532$	3.14055	+	3.62439i	0.136160	+	0.157137i
$533$	−5.52182	+	3.54866i	−0.239177	+	0.153710i
$534$	−0.324751	−	2.25869i	−0.0140533	−	0.0977431i
$535$	−12.8671	−	8.26917i	−0.556293	−	0.357508i
$536$	5.03153	−	11.0175i	0.217329	−	0.475884i
$537$	3.25952	−	3.76169i	0.140659	−	0.162329i
$538$	−4.45169	+	30.9622i	−0.191926	+	1.33488i
$539$	2.36610	+	5.18103i	0.101915	+	0.223163i
$540$	−1.16375	−	0.341709i	−0.0500800	−	0.0147048i
$541$	−20.9460	−	6.15029i	−0.900537	−	0.264422i	−0.201484	−	0.979492i	$-0.564577\pi$
$541$	−20.9460	−	6.15029i	−0.900537	−	0.264422i	−0.699053	+	0.715070i	$0.746395\pi$
$542$	−6.27907	−	13.7492i	−0.269709	−	0.590581i
$543$	2.59599	−	18.0555i	0.111405	−	0.774836i
$544$	2.18143	−	2.51751i	0.0935282	−	0.107937i
$545$	4.77073	−	10.4464i	0.204356	−	0.447476i
$546$	2.59869	+	1.67008i	0.111214	+	0.0714726i
$547$	−0.421162	−	2.92925i	−0.0180076	−	0.125245i	0.978835	−	0.204652i	$-0.0656064\pi$
$547$	−0.421162	−	2.92925i	−0.0180076	−	0.125245i	−0.996842	+	0.0794070i	$0.974697\pi$
$548$	6.05365	−	3.89045i	0.258599	−	0.166192i
$549$	8.13382	+	9.38693i	0.347143	+	0.400624i
$550$	−19.2856	+	5.66277i	−0.822341	+	0.241461i
$551$	42.8269			1.82449
$552$	−2.06031	+	4.33072i	−0.0876927	+	0.184328i
$553$	−12.3435			−0.524901
$554$	−16.0605	+	4.71580i	−0.682347	+	0.200355i
$555$	5.65903	+	6.53087i	0.240213	+	0.277220i
$556$	15.9104	−	10.2250i	0.674751	−	0.433636i
$557$	2.63257	+	18.3099i	0.111545	+	0.775815i	0.966418	+	0.256977i	$0.0827264\pi$
$557$	2.63257	+	18.3099i	0.111545	+	0.775815i	−0.854872	+	0.518839i	$0.826365\pi$
$558$	−8.05363	−	5.17575i	−0.340937	−	0.219107i
$559$	11.1626	−	24.4427i	0.472128	−	1.03382i
$560$	−0.794270	+	0.916636i	−0.0335640	+	0.0387349i
$561$	−2.70019	+	18.7802i	−0.114002	+	0.792901i
$562$	−8.99563	−	19.6977i	−0.379458	−	0.830897i
$563$	−8.94054	−	2.62518i	−0.376799	−	0.110638i	0.0878487	−	0.996134i	$-0.472001\pi$
$563$	−8.94054	−	2.62518i	−0.376799	−	0.110638i	−0.464648	+	0.885496i	$0.653819\pi$
$564$	−0.858493	−	0.252076i	−0.0361491	−	0.0106143i
$565$	−5.50085	−	12.0452i	−0.231423	−	0.506745i
$566$	0.0358970	−	0.249669i	0.00150886	−	0.0104944i
$567$	−0.654861	+	0.755750i	−0.0275016	+	0.0317385i
$568$	−4.02800	+	8.82009i	−0.169011	+	0.370083i
$569$	24.9822	+	16.0551i	1.04731	+	0.673065i	0.946784	−	0.321870i	$-0.104311\pi$
$569$	24.9822	+	16.0551i	1.04731	+	0.673065i	0.100525	+	0.994935i	$0.467948\pi$
$570$	−0.827800	−	5.75748i	−0.0346727	−	0.241154i
$571$	13.0188	−	8.36667i	0.544820	−	0.350134i	−0.239102	−	0.970995i	$-0.576853\pi$
$571$	13.0188	−	8.36667i	0.544820	−	0.350134i	0.783921	+	0.620860i	$0.213217\pi$
$572$	11.5220	+	13.2971i	0.481758	+	0.555978i
$573$	−2.51429	+	0.738262i	−0.105036	+	0.0308413i
$574$	−2.12485			−0.0886895
$575$	2.67050	−	16.7121i	0.111368	−	0.696941i
$576$	1.00000			0.0416667
$577$	−17.8037	+	5.22765i	−0.741179	+	0.217630i	−0.630460	−	0.776222i	$-0.717134\pi$
$577$	−17.8037	+	5.22765i	−0.741179	+	0.217630i	−0.110719	+	0.993852i	$0.535315\pi$
$578$	−3.86597	−	4.46156i	−0.160803	−	0.185577i
$579$	−18.4606	+	11.8639i	−0.767198	+	0.493048i
$580$	1.54145	+	10.7210i	0.0640053	+	0.445166i
$581$	2.39200	+	1.53725i	0.0992370	+	0.0637758i
$582$	2.14995	−	4.70773i	0.0891182	−	0.195142i
$583$	−11.4848	+	13.2542i	−0.475654	+	0.548934i
$584$	−2.35148	+	16.3549i	−0.0973050	+	0.676771i
$585$	−1.55643	−	3.40810i	−0.0643503	−	0.140907i
$586$	−6.68933	−	1.96416i	−0.276334	−	0.0811389i
$587$	−13.5924	−	3.99108i	−0.561018	−	0.164730i	−0.0110849	−	0.999939i	$-0.503529\pi$
$587$	−13.5924	−	3.99108i	−0.561018	−	0.164730i	−0.549933	+	0.835209i	$0.685347\pi$
$588$	0.415415	+	0.909632i	0.0171314	+	0.0375126i
$589$	6.53388	−	45.4441i	0.269224	−	1.87249i
$590$	−3.42442	+	3.95199i	−0.140981	+	0.162701i
$591$	−6.70282	+	14.6771i	−0.275717	+	0.603736i
$592$	−5.99378	−	3.85197i	−0.246343	−	0.158315i
$593$	2.38952	+	16.6195i	0.0981257	+	0.682479i	0.978203	+	0.207649i	$0.0665813\pi$
$593$	2.38952	+	16.6195i	0.0981257	+	0.682479i	−0.880078	+	0.474830i	$0.842510\pi$
$594$	−4.79157	+	3.07935i	−0.196600	+	0.126347i
$595$	−2.64582	−	3.05344i	−0.108468	−	0.125179i
$596$	−1.76248	+	0.517510i	−0.0721939	+	0.0211981i
$597$	15.7575			0.644910
$598$	−14.2781	+	3.95072i	−0.583877	+	0.161557i
$599$	16.6268			0.679353			0.339677	−	0.940542i	$-0.389682\pi$
$599$	16.6268			0.679353			0.339677	+	0.940542i	$0.389682\pi$
$600$	−3.38597	+	0.994210i	−0.138232	+	0.0405885i
$601$	−21.8040	−	25.1631i	−0.889403	−	1.02643i	−0.999472	−	0.0325019i	$-0.989653\pi$
$601$	−21.8040	−	25.1631i	−0.889403	−	1.02643i	0.110069	−	0.993924i	$-0.464893\pi$
$602$	7.31784	−	4.70289i	0.298253	−	0.191676i
$603$	1.72372	+	11.9888i	0.0701955	+	0.488220i
$604$	7.07592	+	4.54742i	0.287915	+	0.185032i
$605$	10.8033	−	23.6559i	0.439217	−	0.961750i
$606$	−7.28430	+	8.40653i	−0.295905	+	0.341492i
$607$	5.80209	−	40.3544i	0.235500	−	1.63794i	−0.438162	−	0.898896i	$-0.644370\pi$
$607$	5.80209	−	40.3544i	0.235500	−	1.63794i	0.673661	−	0.739040i	$-0.264721\pi$
$608$	1.99223	+	4.36237i	0.0807954	+	0.176917i
$609$	8.56845	+	2.51592i	0.347211	+	0.101950i
$610$	−14.4546	−	4.24426i	−0.585250	−	0.171845i
$611$	−1.14817	−	2.51413i	−0.0464498	−	0.101711i
$612$	−0.474071	+	3.29724i	−0.0191632	+	0.133283i
$613$	12.6099	−	14.5526i	0.509310	−	0.587776i	−0.441611	−	0.897206i	$-0.645593\pi$
$613$	12.6099	−	14.5526i	0.509310	−	0.587776i	0.950922	+	0.309431i	$0.100138\pi$
$614$	−1.50985	+	3.30612i	−0.0609328	+	0.133424i
$615$	2.16807	+	1.39334i	0.0874252	+	0.0561848i
$616$	0.810589	+	5.63777i	0.0326596	+	0.227152i
$617$	−16.3341	+	10.4973i	−0.657585	+	0.422604i	−0.826431	−	0.563038i	$-0.809632\pi$
$617$	−16.3341	+	10.4973i	−0.657585	+	0.422604i	0.168846	+	0.985642i	$0.445996\pi$
$618$	3.99632	+	4.61200i	0.160756	+	0.185522i
$619$	11.3316	−	3.32725i	0.455454	−	0.133733i	−0.0459556	−	0.998943i	$-0.514633\pi$
$619$	11.3316	−	3.32725i	0.455454	−	0.133733i	0.501409	+	0.865210i	$0.332815\pi$
$620$	11.6114			0.466324
$621$	−0.608119	−	4.75712i	−0.0244030	−	0.190897i
$622$	−28.4153			−1.13935
$623$	2.18948	−	0.642891i	0.0877198	−	0.0257569i
$624$	2.02291	+	2.33456i	0.0809812	+	0.0934572i
$625$	4.28855	−	2.75608i	0.171542	−	0.110243i
$626$	−1.62052	−	11.2710i	−0.0647691	−	0.450479i
$627$	−22.9791	−	14.7678i	−0.917699	−	0.589769i
$628$	0.831271	−	1.82023i	0.0331713	−	0.0726350i
$629$	15.5423	−	17.9368i	0.619713	−	0.715187i
$630$	0.172611	−	1.20054i	0.00687700	−	0.0478306i
$631$	0.277256	+	0.607106i	0.0110374	+	0.0241685i	0.915070	−	0.403294i	$-0.132135\pi$
$631$	0.277256	+	0.607106i	0.0110374	+	0.0241685i	−0.904033	+	0.427463i	$0.859408\pi$
$632$	−11.8435	−	3.47758i	−0.471111	−	0.138331i
$633$	20.2853	+	5.95630i	0.806268	+	0.236742i
$634$	−6.32152	−	13.8422i	−0.251059	−	0.549744i
$635$	3.10560	−	21.5999i	0.123242	−	0.857166i
$636$	−2.01639	+	2.32704i	−0.0799551	+	0.0922731i
$637$	−1.28324	+	2.80991i	−0.0508440	+	0.111333i
$638$	42.7896	+	27.4992i	1.69406	+	1.08870i
$639$	−1.37993	−	9.59764i	−0.0545893	−	0.379677i
$640$	−1.02034	+	0.655734i	−0.0403326	+	0.0259202i
$641$	5.60060	+	6.46344i	0.221210	+	0.255290i	0.855497	−	0.517807i	$-0.173252\pi$
$641$	5.60060	+	6.46344i	0.221210	+	0.255290i	−0.634287	+	0.773098i	$0.718706\pi$
$642$	−12.0997	+	3.55280i	−0.477539	+	0.140218i
$643$	6.25822			0.246800			0.123400	−	0.992357i	$-0.460620\pi$
$643$	6.25822			0.246800			0.123400	+	0.992357i	$0.460620\pi$
$644$	−4.57985	−	1.42301i	−0.180471	−	0.0560746i
$645$	−10.5506			−0.415428
$646$	−15.3282	+	4.50077i	−0.603080	+	0.177080i
$647$	−21.3488	−	24.6378i	−0.839307	−	0.968611i	0.160524	−	0.987032i	$-0.448682\pi$
$647$	−21.3488	−	24.6378i	−0.839307	−	0.968611i	−0.999830	+	0.0184205i	$0.994136\pi$
$648$	−0.841254	+	0.540641i	−0.0330476	+	0.0212384i
$649$	3.49478	+	24.3067i	0.137182	+	0.954123i
$650$	−9.17055	−	5.89355i	−0.359698	−	0.231164i
$651$	3.97692	−	8.70824i	0.155868	−	0.341303i
$652$	4.07356	−	4.70114i	0.159533	−	0.184111i
$653$	−4.11557	+	28.6244i	−0.161055	+	1.12016i	0.735596	+	0.677421i	$0.236902\pi$
$653$	−4.11557	+	28.6244i	−0.161055	+	1.12016i	−0.896651	+	0.442739i	$0.854007\pi$
$654$	−3.93338	−	8.61290i	−0.153807	−	0.336791i
$655$	−11.3639	−	3.33674i	−0.444024	−	0.130377i
$656$	−2.03878	−	0.598639i	−0.0796009	−	0.0233729i
$657$	−6.86394	−	15.0299i	−0.267788	−	0.586373i
$658$	0.127334	−	0.885629i	0.00496401	−	0.0345254i
$659$	15.1525	−	17.4869i	0.590258	−	0.681194i	−0.379520	−	0.925184i	$-0.623911\pi$
$659$	15.1525	−	17.4869i	0.590258	−	0.681194i	0.969778	+	0.243989i	$0.0784562\pi$
$660$	2.86980	−	6.28399i	0.111707	−	0.244604i
$661$	−9.63602	−	6.19270i	−0.374798	−	0.240868i	0.339657	−	0.940549i	$-0.389689\pi$
$661$	−9.63602	−	6.19270i	−0.374798	−	0.240868i	−0.714455	+	0.699681i	$0.753325\pi$
$662$	3.13458	+	21.8015i	0.121829	+	0.847339i
$663$	−8.65660	+	5.56326i	−0.336194	+	0.216059i
$664$	1.86202	+	2.14888i	0.0722603	+	0.0833928i
$665$	5.58107	−	1.63875i	0.216425	−	0.0635480i
$666$	7.12482			0.276081
$667$	−36.3870	+	22.5875i	−1.40891	+	0.874592i
$668$	−4.68760			−0.181369
$669$	13.9170	−	4.08641i	0.538063	−	0.157990i
$670$	−9.62023	−	11.1023i	−0.371662	−	0.428921i
$671$	−59.5145	+	38.2477i	−2.29753	+	1.47653i
$672$	0.142315	+	0.989821i	0.00548991	+	0.0381832i
$673$	25.7920	+	16.5755i	0.994210	+	0.638940i	0.933260	−	0.359201i	$-0.116951\pi$
$673$	25.7920	+	16.5755i	0.994210	+	0.638940i	0.0609495	+	0.998141i	$0.480587\pi$
$674$	−12.5693	+	27.5229i	−0.484151	+	1.06014i
$675$	2.31095	−	2.66698i	0.0889484	−	0.102652i
$676$	0.492077	−	3.42247i	0.0189261	−	0.131634i
$677$	18.9583	+	41.5129i	0.728627	+	1.59547i	0.801405	+	0.598122i	$0.204086\pi$
$677$	18.9583	+	41.5129i	0.728627	+	1.59547i	−0.0727785	+	0.997348i	$0.523187\pi$
$678$	−10.4754	−	3.07585i	−0.402305	−	0.118127i
$679$	4.96578	+	1.45808i	0.190569	+	0.0559561i
$680$	−1.67840	−	3.67517i	−0.0643635	−	0.140936i
$681$	0.153626	−	1.06849i	0.00588695	−	0.0409446i
$682$	35.7079	−	41.2091i	1.36733	−	1.57798i
$683$	−15.7145	+	34.4099i	−0.601298	+	1.31666i	0.327072	+	0.944999i	$0.393938\pi$
$683$	−15.7145	+	34.4099i	−0.601298	+	1.31666i	−0.928370	+	0.371659i	$0.878789\pi$
$684$	−4.03444	−	2.59278i	−0.154261	−	0.0991373i
$685$	−1.24211	−	8.63906i	−0.0474585	−	0.330081i
$686$	−0.841254	+	0.540641i	−0.0321192	+	0.0206418i
$687$	−16.0615	−	18.5359i	−0.612783	−	0.707190i
$688$	8.34638	−	2.45072i	0.318203	−	0.0934327i
$689$	−9.51159			−0.362363
$690$	3.73990	+	4.45513i	0.142375	+	0.169604i
$691$	−0.0610331			−0.00232181			−0.00116090	−	0.999999i	$-0.500370\pi$
$691$	−0.0610331			−0.00232181			−0.00116090	+	0.999999i	$0.500370\pi$
$692$	0.217087	−	0.0637426i	0.00825242	−	0.00242313i
$693$	−3.72992	−	4.30456i	−0.141688	−	0.163517i
$694$	−8.06610	+	5.18377i	−0.306185	+	0.196773i
$695$	−3.26455	−	22.7054i	−0.123831	−	0.861266i
$696$	7.51255	+	4.82802i	0.284762	+	0.183006i
$697$	2.94038	−	6.43854i	0.111375	−	0.243877i
$698$	−3.29822	+	3.80635i	−0.124840	+	0.144073i
$699$	1.72558	−	12.0017i	0.0652674	−	0.453945i
$700$	−1.46596	−	3.21001i	−0.0554082	−	0.121327i
$701$	9.35214	+	2.74603i	0.353225	+	0.103716i	0.453531	−	0.891240i	$-0.350164\pi$
$701$	9.35214	+	2.74603i	0.353225	+	0.103716i	−0.100306	+	0.994957i	$0.531982\pi$
$702$	−2.96394	−	0.870291i	−0.111867	−	0.0328470i
$703$	14.1943	+	31.0811i	0.535347	+	1.17225i
$704$	−0.810589	+	5.63777i	−0.0305502	+	0.212481i
$705$	−0.710662	+	0.820147i	−0.0267651	+	0.0308885i
$706$	3.19114	−	6.98761i	0.120100	−	0.262982i
$707$	−9.35763	−	6.01379i	−0.351930	−	0.226172i
$708$	0.613577	+	4.26752i	0.0230597	+	0.160383i
$709$	19.8378	−	12.7490i	0.745026	−	0.478799i	−0.112235	−	0.993682i	$-0.535801\pi$
$709$	19.8378	−	12.7490i	0.745026	−	0.478799i	0.857261	+	0.514883i	$0.172164\pi$
$710$	7.70150	+	8.88801i	0.289032	+	0.333561i
$711$	11.8435	−	3.47758i	0.444168	−	0.130419i
$712$	2.28192			0.0855185
$713$	18.4165	+	42.0567i	0.689703	+	1.57504i
$714$	−3.33114			−0.124665
$715$	20.4757	−	6.01221i	0.765748	−	0.224844i
$716$	3.25952	+	3.76169i	0.121814	+	0.140581i
$717$	17.4064	−	11.1864i	0.650054	−	0.417765i
$718$	−4.07685	−	28.3551i	−0.152147	−	1.05820i
$719$	21.7999	+	14.0100i	0.813000	+	0.522484i	0.879834	−	0.475280i	$-0.157653\pi$
$719$	21.7999	+	14.0100i	0.813000	+	0.522484i	−0.0668339	+	0.997764i	$0.521290\pi$
$720$	0.503850	−	1.10328i	0.0187774	−	0.0411167i
$721$	−3.99632	+	4.61200i	−0.148831	+	0.171760i
$722$	0.569147	−	3.95850i	0.0211814	−	0.147320i
$723$	−8.24311	−	18.0499i	−0.306565	−	0.671283i
$724$	17.5023	+	5.13913i	0.650467	+	0.190994i
$725$	−30.2373	−	8.87848i	−1.12299	−	0.329738i
$726$	−8.90712	−	19.5039i	−0.330574	−	0.723857i
$727$	3.49544	−	24.3113i	0.129639	−	0.901656i	−0.816374	−	0.577524i	$-0.804019\pi$
$727$	3.49544	−	24.3113i	0.129639	−	0.901656i	0.946012	−	0.324131i	$-0.105072\pi$
$728$	−2.02291	+	2.33456i	−0.0749740	+	0.0865246i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	16.8592	+	10.8348i	0.623987	+	0.401012i
$731$	4.12382	+	28.6818i	0.152525	+	1.06083i
$732$	−10.4489	+	6.71513i	−0.386204	+	0.248198i
$733$	−5.63180	−	6.49944i	−0.208015	−	0.240062i	0.642149	−	0.766580i	$-0.278043\pi$
$733$	−5.63180	−	6.49944i	−0.208015	−	0.240062i	−0.850164	+	0.526517i	$0.823498\pi$
$734$	21.8640	−	6.41984i	0.807013	−	0.236960i
$735$	1.21288			0.0447379
$736$	−3.99342	−	2.65567i	−0.147200	−	0.0978891i
$737$	−68.9871			−2.54117
$738$	2.03878	−	0.598639i	0.0750485	−	0.0220362i
$739$	−18.2075	−	21.0126i	−0.669773	−	0.772959i	0.314568	−	0.949235i	$-0.398140\pi$
$739$	−18.2075	−	21.0126i	−0.669773	−	0.772959i	−0.984341	+	0.176276i	$0.943595\pi$
$740$	−7.26976	+	4.67199i	−0.267242	+	0.171746i
$741$	−2.10831	−	14.6636i	−0.0774506	−	0.538681i
$742$	−2.59032	−	1.66469i	−0.0950935	−	0.0611129i
$743$	1.83475	−	4.01755i	0.0673105	−	0.147389i	−0.872987	−	0.487744i	$-0.837820\pi$
$743$	1.83475	−	4.01755i	0.0673105	−	0.147389i	0.940297	+	0.340355i	$0.110547\pi$
$744$	6.26922	−	7.23507i	0.229841	−	0.265250i
$745$	−0.317067	+	2.20525i	−0.0116164	+	0.0807941i
$746$	−10.1811	−	22.2935i	−0.372757	−	0.816224i
$747$	−2.72820	−	0.801073i	−0.0998197	−	0.0293097i
$748$	−18.2048	−	5.34541i	−0.665633	−	0.195447i
$749$	−5.23861	−	11.4710i	−0.191415	−	0.419140i
$750$	−1.47219	+	10.2393i	−0.0537567	+	0.373886i
$751$	0.00851161	−	0.00982292i	0.000310593	−	0.000358443i	−0.755594	−	0.655040i	$-0.772652\pi$
$751$	0.00851161	−	0.00982292i	0.000310593	−	0.000358443i	0.755905	+	0.654681i	$0.227197\pi$
$752$	0.371687	−	0.813881i	0.0135540	−	0.0296792i
$753$	5.35173	+	3.43935i	0.195028	+	0.125337i
$754$	3.92589	+	27.3051i	0.142972	+	0.994395i
$755$	8.58227	−	5.51549i	0.312341	−	0.200729i
$756$	−0.654861	−	0.755750i	−0.0238171	−	0.0274863i
$757$	−3.58064	+	1.05137i	−0.130141	+	0.0382128i	−0.346154	−	0.938178i	$-0.612513\pi$
$757$	−3.58064	+	1.05137i	−0.130141	+	0.0382128i	0.216014	+	0.976390i	$0.430694\pi$
$758$	−38.3855			−1.39422
$759$	27.3125	+	0.427634i	0.991380	+	0.0155221i
$760$	5.81668			0.210993
$761$	10.7846	−	3.16664i	0.390941	−	0.114791i	−0.0803537	−	0.996766i	$-0.525605\pi$
$761$	10.7846	−	3.16664i	0.390941	−	0.114791i	0.471295	+	0.881976i	$0.343787\pi$
$762$	−11.7822	−	13.5973i	−0.426823	−	0.492580i
$763$	7.96545	−	5.11908i	0.288369	−	0.185323i
$764$	−0.372927	−	2.59376i	−0.0134920	−	0.0938391i
$765$	3.39891	+	2.18434i	0.122888	+	0.0789751i
$766$	−13.1183	+	28.7252i	−0.473985	+	1.03788i
$767$	−8.72158	+	10.0652i	−0.314918	+	0.363435i
$768$	−0.142315	+	0.989821i	−0.00513534	+	0.0357171i
$769$	1.76947	+	3.87460i	0.0638088	+	0.139722i	0.938850	−	0.344327i	$-0.111893\pi$
$769$	1.76947	+	3.87460i	0.0638088	+	0.139722i	−0.875041	+	0.484049i	$0.839166\pi$
$770$	6.62844	+	1.94629i	0.238872	+	0.0701393i
$771$	−24.1867	−	7.10185i	−0.871063	−	0.255767i
$772$	−9.11595	−	19.9611i	−0.328090	−	0.718417i
$773$	−2.62623	+	18.2658i	−0.0944590	+	0.656977i	0.886495	+	0.462738i	$0.153133\pi$
$773$	−2.62623	+	18.2658i	−0.0944590	+	0.656977i	−0.980954	+	0.194239i	$0.937776\pi$
$774$	−5.69646	+	6.57407i	−0.204755	+	0.236300i
$775$	−14.0342	+	30.7306i	−0.504124	+	1.10388i
$776$	4.35384	+	2.79804i	0.156294	+	0.100444i
$777$	1.01397	+	7.05230i	0.0363759	+	0.253000i
$778$	13.4924	−	8.67107i	0.483728	−	0.310873i
$779$	6.67319	+	7.70127i	0.239092	+	0.275927i
$780$	3.59491	−	1.05556i	0.128718	−	0.0377951i
$781$	55.2278			1.97621
$782$	10.6495	−	11.9083i	0.380826	−	0.425840i
$783$	−8.93018			−0.319139
$784$	−0.959493	+	0.281733i	−0.0342676	+	0.0100619i
$785$	−1.58938	−	1.83424i	−0.0567275	−	0.0654670i
$786$	−8.21474	+	5.27929i	−0.293010	+	0.188306i
$787$	0.0234779	+	0.163292i	0.000836896	+	0.00582074i	0.990236	−	0.139404i	$-0.0445186\pi$
$787$	0.0234779	+	0.163292i	0.000836896	+	0.00582074i	−0.989399	+	0.145225i	$0.953610\pi$
$788$	−13.5738	−	8.72337i	−0.483548	−	0.310757i
$789$	−9.13504	+	20.0030i	−0.325216	+	0.712124i
$790$	−9.80410	+	11.3145i	−0.348814	+	0.402553i
$791$	1.55374	−	10.8065i	0.0552447	−	0.384235i
$792$	−2.36610	−	5.18103i	−0.0840756	−	0.184100i
$793$	−36.8141	−	10.8096i	−1.30731	−	0.383860i
$794$	−29.0774	−	8.53789i	−1.03192	−	0.302999i
$795$	1.55141	+	3.39712i	0.0550229	+	0.120483i
$796$	−2.24252	+	15.5971i	−0.0794840	+	0.552824i
$797$	21.8844	−	25.2559i	0.775185	−	0.894612i	−0.221567	−	0.975145i	$-0.571117\pi$
$797$	21.8844	−	25.2559i	0.775185	−	0.894612i	0.996752	+	0.0805337i	$0.0256625\pi$
$798$	1.99223	−	4.36237i	0.0705240	−	0.154426i
$799$	2.50735	+	1.61138i	0.0887037	+	0.0570064i
$800$	−0.502217	−	3.49299i	−0.0177560	−	0.123496i
$801$	−1.91967	+	1.23370i	−0.0678283	+	0.0435906i
$802$	2.00217	+	2.31063i	0.0706992	+	0.0815913i
$803$	90.2991	−	26.5142i	3.18659	−	0.935666i
$804$	−12.1120			−0.427159
$805$	−3.87754	+	4.33586i	−0.136665	+	0.152819i
$806$	29.5728			1.04166
$807$	30.0135	−	8.81276i	1.05653	−	0.310224i
$808$	−7.28430	−	8.40653i	−0.256261	−	0.295741i
$809$	−26.5225	+	17.0450i	−0.932482	+	0.599270i	−0.916254	−	0.400599i	$-0.868802\pi$
$809$	−26.5225	+	17.0450i	−0.932482	+	0.599270i	−0.0162281	+	0.999868i	$0.505166\pi$
$810$	0.172611	+	1.20054i	0.00606494	+	0.0421826i
$811$	12.2502	+	7.87270i	0.430161	+	0.276448i	0.737753	−	0.675071i	$-0.235887\pi$
$811$	12.2502	+	7.87270i	0.430161	+	0.276448i	−0.307592	+	0.951518i	$0.599523\pi$
$812$	−3.70973	+	8.12318i	−0.130186	+	0.285068i
$813$	−9.89833	+	11.4233i	−0.347150	+	0.400632i
$814$	−5.77530	+	40.1681i	−0.202424	+	1.40789i
$815$	−3.13420	−	6.86294i	−0.109786	−	0.240398i
$816$	−3.19621	−	0.938491i	−0.111890	−	0.0328538i
$817$	−40.0271	−	11.7530i	−1.40037	−	0.411186i
$818$	15.2205	+	33.3282i	0.532171	+	1.16529i
$819$	0.439620	−	3.05762i	0.0153616	−	0.106842i
$820$	−1.68770	+	1.94771i	−0.0589372	+	0.0680171i
$821$	8.39294	−	18.3780i	0.292916	−	0.641396i	−0.704767	−	0.709439i	$-0.748948\pi$
$821$	8.39294	−	18.3780i	0.292916	−	0.641396i	0.997682	+	0.0680433i	$0.0216756\pi$
$822$	−6.05365	−	3.89045i	−0.211145	−	0.135695i
$823$	−1.55372	−	10.8064i	−0.0541594	−	0.376687i	−0.998817	−	0.0486288i	$-0.984515\pi$
$823$	−1.55372	−	10.8064i	−0.0541594	−	0.376687i	0.944657	−	0.328058i	$-0.106394\pi$
$824$	−5.13379	+	3.29929i	−0.178844	+	0.114936i
$825$	13.1626	+	15.1904i	0.458262	+	0.528862i
$826$	−4.13677	+	1.21466i	−0.143937	+	0.0422636i
$827$	3.51774			0.122324			0.0611619	−	0.998128i	$-0.480519\pi$
$827$	3.51774			0.122324			0.0611619	+	0.998128i	$0.480519\pi$
$828$	4.79524	+	0.0750795i	0.166646	+	0.00260919i
$829$	1.36541			0.0474228			0.0237114	−	0.999719i	$-0.492452\pi$
$829$	1.36541			0.0474228			0.0237114	+	0.999719i	$0.492452\pi$
$830$	3.30899	−	0.971608i	0.114857	−	0.0337250i
$831$	10.9614	+	12.6502i	0.380248	+	0.438830i
$832$	−2.59869	+	1.67008i	−0.0900933	+	0.0578995i
$833$	−0.474071	−	3.29724i	−0.0164256	−	0.114242i
$834$	−15.9104	−	10.2250i	−0.550932	−	0.354062i
$835$	−2.36185	+	5.17173i	−0.0817352	+	0.178975i
$836$	17.8878	−	20.6436i	0.618661	−	0.713973i
$837$	−1.36243	+	9.47592i	−0.0470925	+	0.327536i
$838$	−7.62286	−	16.6917i	−0.263327	−	0.576607i
$839$	46.7175	+	13.7175i	1.61287	+	0.473581i	0.959089	−	0.283105i	$-0.0913644\pi$
$839$	46.7175	+	13.7175i	1.61287	+	0.473581i	0.653779	+	0.756685i	$0.273183\pi$
$840$	1.16375	+	0.341709i	0.0401533	+	0.0117901i
$841$	21.0816	+	46.1622i	0.726950	+	1.59180i
$842$	−2.87132	+	19.9705i	−0.0989523	+	0.688229i
$843$	−14.1807	+	16.3654i	−0.488410	+	0.563655i
$844$	−8.78257	+	19.2311i	−0.302308	+	0.661963i
$845$	−3.52800	−	2.26731i	−0.121367	−	0.0779979i
$846$	0.127334	+	0.885629i	0.00437784	+	0.0304486i
$847$	18.0377	−	11.5922i	0.619784	−	0.398311i
$848$	−2.01639	−	2.32704i	−0.0692431	−	0.0799108i
$849$	−0.242019	+	0.0710632i	−0.00830607	+	0.00243888i
$850$	11.7553			0.403204
$851$	−28.4524	−	18.9211i	−0.975337	−	0.648609i
$852$	9.69633			0.332191
$853$	15.3414	−	4.50463i	0.525278	−	0.154236i	−0.00833342	−	0.999965i	$-0.502653\pi$
$853$	15.3414	−	4.50463i	0.525278	−	0.154236i	0.533612	+	0.845730i	$0.320834\pi$
$854$	−8.13382	−	9.38693i	−0.278334	−	0.321214i
$855$	−4.89331	+	3.14474i	−0.167348	+	0.107548i
$856$	−1.79467	−	12.4822i	−0.0613405	−	0.426633i
$857$	18.1684	+	11.6761i	0.620620	+	0.398848i	0.812826	−	0.582506i	$-0.197928\pi$
$857$	18.1684	+	11.6761i	0.620620	+	0.398848i	−0.192206	+	0.981355i	$0.561564\pi$
$858$	7.30903	−	16.0046i	0.249526	−	0.546386i
$859$	14.3467	−	16.5570i	0.489503	−	0.564916i	−0.456230	−	0.889862i	$-0.650801\pi$
$859$	14.3467	−	16.5570i	0.489503	−	0.564916i	0.945733	+	0.324946i	$0.105346\pi$
$860$	1.50150	−	10.4432i	0.0512007	−	0.356109i
$861$	0.882695	+	1.93283i	0.0300822	+	0.0658707i
$862$	−10.6916	−	3.13933i	−0.364157	−	0.106926i
$863$	−13.0810	−	3.84092i	−0.445281	−	0.130746i	0.0514026	−	0.998678i	$-0.483631\pi$
$863$	−13.0810	−	3.84092i	−0.445281	−	0.130746i	−0.496684	+	0.867932i	$0.665449\pi$
$864$	−0.415415	−	0.909632i	−0.0141327	−	0.0309463i
$865$	0.0390537	−	0.271624i	0.00132786	−	0.00923550i
$866$	5.74709	−	6.63250i	0.195294	−	0.225382i
$867$	−2.45240	+	5.37001i	−0.0832879	+	0.182375i
$868$	8.05363	+	5.17575i	0.273358	+	0.175676i
$869$	10.0055	+	69.5901i	0.339415	+	2.36068i
$870$	9.11185	−	5.85583i	0.308920	−	0.198531i
$871$	−24.5016	−	28.2763i	−0.830204	−	0.958106i
$872$	9.08501	−	2.66760i	0.307657	−	0.0903363i
$873$	−5.17542			−0.175161
$874$	9.22569	+	21.0682i	0.312063	+	0.712642i
$875$	−10.3446			−0.349711
$876$	15.8538	−	4.65509i	0.535650	−	0.157281i
$877$	31.2895	+	36.1100i	1.05657	+	1.21935i	0.974889	+	0.222691i	$0.0714840\pi$
$877$	31.2895	+	36.1100i	1.05657	+	1.21935i	0.0816829	+	0.996658i	$0.473971\pi$
$878$	2.99289	−	1.92341i	0.101005	−	0.0649121i
$879$	0.992181	+	6.90077i	0.0334654	+	0.232757i
$880$	5.81161	+	3.73489i	0.195909	+	0.125903i
$881$	−20.1592	+	44.1426i	−0.679182	+	1.48720i	0.184326	+	0.982865i	$0.440990\pi$
$881$	−20.1592	+	44.1426i	−0.679182	+	1.48720i	−0.863508	+	0.504336i	$0.831737\pi$
$882$	0.654861	−	0.755750i	0.0220503	−	0.0254474i
$883$	6.55386	−	45.5831i	0.220555	−	1.53399i	−0.515392	−	0.856955i	$-0.672354\pi$
$883$	6.55386	−	45.5831i	0.220555	−	1.53399i	0.735947	−	0.677040i	$-0.236737\pi$
$884$	−4.27467	−	9.36022i	−0.143773	−	0.314818i
$885$	5.01741	+	1.47325i	0.168659	+	0.0495226i
$886$	20.7518	+	6.09327i	0.697169	+	0.204707i
$887$	−5.26405	−	11.5267i	−0.176749	−	0.387027i	0.800435	−	0.599419i	$-0.204602\pi$
$887$	−5.26405	−	11.5267i	−0.176749	−	0.387027i	−0.977184	+	0.212392i	$0.931875\pi$
$888$	−1.01397	+	7.05230i	−0.0340265	+	0.236660i
$889$	11.7822	−	13.5973i	0.395161	−	0.456040i
$890$	1.14974	−	2.51759i	0.0385395	−	0.0843898i
$891$	4.79157	+	3.07935i	0.160523	+	0.103162i
$892$	2.06421	+	14.3569i	0.0691150	+	0.480705i
$893$	−3.60976	+	2.31985i	−0.120796	+	0.0776309i
$894$	1.20290	+	1.38823i	0.0402311	+	0.0464292i
$895$	5.79249	−	1.70083i	0.193622	−	0.0568525i
$896$	−1.00000			−0.0334077
$897$	9.52506	+	11.3467i	0.318033	+	0.378854i
$898$	34.6976			1.15787
$899$	82.0289	−	24.0859i	2.73582	−	0.803308i
$900$	2.31095	+	2.66698i	0.0770316	+	0.0888992i
$901$	8.62871	−	5.54533i	0.287464	−	0.184742i
$902$	1.72238	+	11.9794i	0.0573490	+	0.398871i
$903$	−7.31784	−	4.70289i	−0.243523	−	0.156502i
$904$	4.53535	−	9.93103i	0.150844	−	0.330301i
$905$	14.4884	−	16.7205i	0.481611	−	0.555809i
$906$	1.19703	−	8.32555i	0.0397688	−	0.276598i
$907$	7.61674	+	16.6783i	0.252910	+	0.553795i	0.992918	−	0.118803i	$-0.0379057\pi$
$907$	7.61674	+	16.6783i	0.252910	+	0.553795i	−0.740008	+	0.672598i	$0.765178\pi$
$908$	1.03575	+	0.304124i	0.0343726	+	0.0100927i
$909$	10.6729	+	3.13384i	0.353996	+	0.103943i
$910$	1.55643	+	3.40810i	0.0515950	+	0.112977i
$911$	−5.74666	+	39.9689i	−0.190395	+	1.32423i	0.640568	+	0.767901i	$0.278699\pi$
$911$	−5.74666	+	39.9689i	−0.190395	+	1.32423i	−0.830963	+	0.556327i	$0.812210\pi$
$912$	3.14055	−	3.62439i	0.103994	−	0.120015i
$913$	6.72772	−	14.7316i	0.222655	−	0.487546i
$914$	−10.4030	−	6.68560i	−0.344101	−	0.221140i
$915$	2.14395	+	14.9115i	0.0708768	+	0.492959i
$916$	20.6330	−	13.2600i	0.681735	−	0.438124i
$917$	−6.39463	−	7.37980i	−0.211169	−	0.243702i
$918$	3.19621	−	0.938491i	0.105491	−	0.0309748i
$919$	21.8632			0.721199			0.360600	−	0.932721i	$-0.382572\pi$
$919$	21.8632			0.721199			0.360600	+	0.932721i	$0.382572\pi$
$920$	−4.94202	+	3.06780i	−0.162934	+	0.101142i
$921$	3.63457			0.119763
$922$	−23.4135	+	6.87483i	−0.771083	+	0.226410i
$923$	19.6148	+	22.6367i	0.645629	+	0.745095i
$924$	4.79157	−	3.07935i	0.157631	−	0.101303i
$925$	−3.57821	−	24.8870i	−0.117651	−	0.818279i
$926$	−13.0957	−	8.41609i	−0.430351	−	0.276570i
$927$	2.53509	−	5.55108i	0.0832633	−	0.182321i
$928$	−5.84803	+	6.74898i	−0.191971	+	0.221546i
$929$	2.91653	−	20.2849i	0.0956883	−	0.665527i	−0.884366	−	0.466795i	$-0.845409\pi$
$929$	2.91653	−	20.2849i	0.0956883	−	0.665527i	0.980054	−	0.198732i	$-0.0636823\pi$
$930$	−4.82354	−	10.5621i	−0.158170	−	0.346344i
$931$	4.60149	+	1.35112i	0.150808	+	0.0442811i
$932$	11.6339	+	3.41603i	0.381082	+	0.111896i
$933$	11.8041	+	25.8475i	0.386450	+	0.846208i
$934$	−2.62783	+	18.2770i	−0.0859853	+	0.598041i
$935$	−15.0699	+	17.3916i	−0.492840	+	0.568768i
$936$	1.28324	−	2.80991i	0.0419442	−	0.0918449i
$937$	38.4434	+	24.7061i	1.25589	+	0.807113i	0.987716	−	0.156258i	$-0.0499430\pi$
$937$	38.4434	+	24.7061i	1.25589	+	0.807113i	0.268175	+	0.963370i	$0.413579\pi$
$938$	−1.72372	−	11.9888i	−0.0562816	−	0.391447i
$939$	−9.57926	+	6.15622i	−0.312607	+	0.200901i
$940$	−0.710662	−	0.820147i	−0.0231792	−	0.0267503i
$941$	−3.34162	+	0.981189i	−0.108934	+	0.0319858i	−0.335745	−	0.941953i	$-0.608988\pi$
$941$	−3.34162	+	0.981189i	−0.108934	+	0.0319858i	0.226811	+	0.973939i	$0.427170\pi$
$942$	−2.00106			−0.0651981
$943$	−9.73149	−	3.02369i	−0.316901	−	0.0984650i
$944$	−4.31141			−0.140324
$945$	−1.16375	+	0.341709i	−0.0378569	+	0.0111158i
$946$	−32.4456	−	37.4442i	−1.05490	−	1.21742i
$947$	−2.27695	+	1.46331i	−0.0739910	+	0.0475511i	−0.577113	−	0.816664i	$-0.695821\pi$
$947$	−2.27695	+	1.46331i	−0.0739910	+	0.0475511i	0.503122	+	0.864215i	$0.332185\pi$
$948$	1.75667	+	12.2179i	0.0570540	+	0.396819i
$949$	42.9384	+	27.5948i	1.39384	+	0.895765i
$950$	−7.03039	+	15.3944i	−0.228096	+	0.499461i
$951$	−9.96525	+	11.5005i	−0.323145	+	0.372930i
$952$	0.474071	−	3.29724i	0.0153647	−	0.106864i
$953$	10.3427	+	22.6473i	0.335032	+	0.733617i	0.999911	−	0.0133337i	$-0.00424437\pi$
$953$	10.3427	+	22.6473i	0.335032	+	0.733617i	−0.664879	+	0.746951i	$0.731517\pi$
$954$	2.95439	+	0.867487i	0.0956518	+	0.0280859i
$955$	−3.04954	−	0.895426i	−0.0986808	−	0.0289753i
$956$	8.59537	+	18.8212i	0.277994	+	0.608722i
$957$	7.23871	−	50.3463i	0.233994	−	1.62747i
$958$	19.3384	−	22.3177i	0.624795	−	0.721052i
$959$	2.98932	−	6.54570i	0.0965302	−	0.211372i
$960$	1.02034	+	0.655734i	0.0329314	+	0.0211637i
$961$	−8.63129	−	60.0320i	−0.278429	−	1.93652i
$962$	−18.5152	+	11.8990i	−0.596954	+	0.383639i
$963$	8.25816	+	9.53042i	0.266115	+	0.307114i
$964$	19.0393	−	5.59044i	0.613214	−	0.180056i
$965$	−26.6158			−0.856791
$966$	0.608119	+	4.75712i	0.0195659	+	0.153058i
$967$	37.7530			1.21405			0.607027	−	0.794681i	$-0.292362\pi$
$967$	37.7530			1.21405			0.607027	+	0.794681i	$0.292362\pi$
$968$	20.5730	−	6.04077i	0.661241	−	0.194158i
$969$	10.4616	+	12.0733i	0.336075	+	0.387852i
$970$	5.28070	−	3.39370i	0.169553	−	0.108965i
$971$	−5.91393	−	41.1323i	−0.189787	−	1.32000i	−0.832557	−	0.553939i	$-0.813124\pi$
$971$	−5.91393	−	41.1323i	−0.189787	−	1.32000i	0.642770	−	0.766059i	$-0.277785\pi$
$972$	0.841254	+	0.540641i	0.0269832	+	0.0173411i
$973$	7.85663	−	17.2036i	0.251872	−	0.551522i
$974$	5.68197	−	6.55734i	0.182062	−	0.210111i
$975$	−1.55138	+	10.7901i	−0.0496840	+	0.345560i
$976$	−5.15974	−	11.2983i	−0.165159	−	0.361648i
$977$	0.213534	+	0.0626991i	0.00683155	+	0.00200592i	0.285147	−	0.958484i	$-0.407958\pi$
$977$	0.213534	+	0.0626991i	0.00683155	+	0.00200592i	−0.278315	+	0.960490i	$0.589776\pi$
$978$	−5.96853	−	1.75252i	−0.190852	−	0.0560393i
$979$	−5.39924	−	11.8227i	−0.172561	−	0.377855i
$980$	−0.172611	+	1.20054i	−0.00551387	+	0.0383498i
$981$	−6.20058	+	7.15585i	−0.197969	+	0.228469i
$982$	−5.46585	+	11.9686i	−0.174422	+	0.381932i
$983$	23.4738	+	15.0857i	0.748699	+	0.481160i	0.858513	−	0.512793i	$-0.171389\pi$
$983$	23.4738	+	15.0857i	0.748699	+	0.481160i	−0.109814	+	0.993952i	$0.535025\pi$
$984$	0.302398	+	2.10322i	0.00964009	+	0.0670483i
$985$	−16.4635	+	10.5804i	−0.524570	+	0.337120i
$986$	−19.4806	−	22.4818i	−0.620389	−	0.715967i
$987$	−0.858493	+	0.252076i	−0.0273261	+	0.00802368i
$988$	14.8144			0.471308
$989$	40.2069	−	11.1251i	1.27851	−	0.353759i
$990$	−6.90827			−0.219559
$991$	−15.4183	+	4.52723i	−0.489780	+	0.143812i	−0.517292	−	0.855809i	$-0.673060\pi$
$991$	−15.4183	+	4.52723i	−0.489780	+	0.143812i	0.0275119	+	0.999621i	$0.491242\pi$
$992$	6.26922	+	7.23507i	0.199048	+	0.229714i
$993$	18.5292	−	11.9080i	0.588006	−	0.377888i
$994$	1.37993	+	9.59764i	0.0437688	+	0.304419i
$995$	16.0780	+	10.3327i	0.509707	+	0.327569i
$996$	1.18118	−	2.58643i	0.0374272	−	0.0819542i
$997$	−12.9585	+	14.9549i	−0.410399	+	0.473626i	−0.922888	−	0.385068i	$-0.874178\pi$
$997$	−12.9585	+	14.9549i	−0.410399	+	0.473626i	0.512489	+	0.858694i	$0.328723\pi$
$998$	−0.135253	+	0.940705i	−0.00428136	+	0.0297775i
$999$	−2.95976	−	6.48097i	−0.0936426	−	0.205049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.e.883.1	yes	20
23.18	even	11	inner	966.2.q.e.547.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.e.547.1	✓	20	23.18	even	11	inner
966.2.q.e.883.1	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959493 - 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.172611 - 1.20054i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.415415 - 0.909632i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.959493 - 0.281733i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.841254 - 0.540641i) q^{4} +(-0.172611 - 1.20054i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(0.415415 - 0.909632i) q^{7} +(0.654861 - 0.755750i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.503850 - 1.10328i) q^{10} +(-5.46503 - 1.60468i) q^{11} +(-0.959493 - 0.281733i) q^{12} +(-1.28324 - 2.80991i) q^{13} +(0.142315 - 0.989821i) q^{14} +(-0.794270 + 0.916636i) q^{15} +(0.415415 - 0.909632i) q^{16} +(2.80233 + 1.80095i) q^{17} +(0.142315 + 0.989821i) q^{18} +(-4.03444 + 2.59278i) q^{19} +(-0.794270 - 0.916636i) q^{20} +(-0.959493 + 0.281733i) q^{21} -5.69574 q^{22} +(2.06031 - 4.33072i) q^{23} -1.00000 q^{24} +(3.38597 - 0.994210i) q^{25} +(-2.02291 - 2.33456i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.142315 - 0.989821i) q^{28} +(-7.51255 - 4.82802i) q^{29} +(-0.503850 + 1.10328i) q^{30} +(-6.26922 + 7.23507i) q^{31} +(0.142315 - 0.989821i) q^{32} +(2.36610 + 5.18103i) q^{33} +(3.19621 + 0.938491i) q^{34} +(-1.16375 - 0.341709i) q^{35} +(0.415415 + 0.909632i) q^{36} +(1.01397 - 7.05230i) q^{37} +(-3.14055 + 3.62439i) q^{38} +(-1.28324 + 2.80991i) q^{39} +(-1.02034 - 0.655734i) q^{40} +(-0.302398 - 2.10322i) q^{41} +(-0.841254 + 0.540641i) q^{42} +(5.69646 + 6.57407i) q^{43} +(-5.46503 + 1.60468i) q^{44} +1.21288 q^{45} +(0.756750 - 4.73575i) q^{46} +0.894736 q^{47} +(-0.959493 + 0.281733i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(2.96871 - 1.90787i) q^{50} +(-0.474071 - 3.29724i) q^{51} +(-2.59869 - 1.67008i) q^{52} +(1.27911 - 2.80086i) q^{53} +(0.654861 - 0.755750i) q^{54} +(-0.983150 + 6.83796i) q^{55} +(-0.415415 - 0.909632i) q^{56} +(4.60149 + 1.35112i) q^{57} +(-8.56845 - 2.51592i) q^{58} +(-1.79102 - 3.92180i) q^{59} +(-0.172611 + 1.20054i) q^{60} +(8.13382 - 9.38693i) q^{61} +(-3.97692 + 8.70824i) q^{62} +(0.841254 + 0.540641i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-3.15191 + 2.02561i) q^{65} +(3.72992 + 4.30456i) q^{66} +(11.6214 - 3.41236i) q^{67} +3.33114 q^{68} +(-4.62216 + 1.27894i) q^{69} -1.21288 q^{70} +(-9.30356 + 2.73177i) q^{71} +(0.654861 + 0.755750i) q^{72} +(-13.9001 + 8.93306i) q^{73} +(-1.01397 - 7.05230i) q^{74} +(-2.96871 - 1.90787i) q^{75} +(-1.99223 + 4.36237i) q^{76} +(-3.72992 + 4.30456i) q^{77} +(-0.439620 + 3.05762i) q^{78} +(-5.12769 - 11.2281i) q^{79} +(-1.16375 - 0.341709i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.882695 - 1.93283i) q^{82} +(-0.404655 + 2.81444i) q^{83} +(-0.654861 + 0.755750i) q^{84} +(1.67840 - 3.67517i) q^{85} +(7.31784 + 4.70289i) q^{86} +(1.27090 + 8.83929i) q^{87} +(-4.79157 + 3.07935i) q^{88} +(1.49434 + 1.72456i) q^{89} +(1.16375 - 0.341709i) q^{90} -3.08907 q^{91} +(-0.608119 - 4.75712i) q^{92} +9.57336 q^{93} +(0.858493 - 0.252076i) q^{94} +(3.80912 + 4.39596i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(0.736539 + 5.12274i) q^{97} +(-0.841254 - 0.540641i) q^{98} +(2.36610 - 5.18103i) 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

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