LMFDB - Embedded newform 966.2.q.d.841.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 10 x^{18} - 14 x^{17} + 77 x^{16} + 12 x^{15} - 226 x^{14} - 793 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 10x^18 - 14x^17 + 77x^16 + 12x^15 - 226x^14 - 793x^13 + 690x^12 + 6105x^11 + 13883x^10 + 24365x^9 + 36461x^8 + 41912x^7 + 45709x^6 + 33023x^5 + 25949x^4 + 12217x^3 + 2895x^2 - 172*x + 1849
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			841.2
Root			$-0.511167 - 1.11930i$ of defining polynomial
Character	$\chi$	$=$	966.841
Dual form			966.2.q.d.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.856306 - 1.87505i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.856306 - 1.87505i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-1.97783 + 0.580743i) q^{10} +(-1.11525 + 1.28707i) q^{11} +(0.654861 - 0.755750i) q^{12} +(5.23097 - 1.53595i) q^{13} +(0.415415 + 0.909632i) q^{14} +(-1.73410 + 1.11444i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(-0.173222 - 1.20479i) q^{17} +(0.415415 - 0.909632i) q^{18} +(1.09018 - 7.58236i) q^{19} +(1.73410 + 1.11444i) q^{20} +(0.654861 + 0.755750i) q^{21} +1.70303 q^{22} +(-4.60054 + 1.35464i) q^{23} -1.00000 q^{24} +(0.491753 + 0.567514i) q^{25} +(-4.58635 - 2.94747i) q^{26} +(0.142315 - 0.989821i) q^{27} +(0.415415 - 0.909632i) q^{28} +(-0.214710 - 1.49334i) q^{29} +(1.97783 + 0.580743i) q^{30} +(1.95530 - 1.25659i) q^{31} +(0.415415 + 0.909632i) q^{32} +(1.63405 - 0.479800i) q^{33} +(-0.797081 + 0.919880i) q^{34} +(-1.34988 + 1.55785i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.17357 - 2.56976i) q^{37} +(-6.44428 + 4.14149i) q^{38} +(-5.23097 - 1.53595i) q^{39} +(-0.293358 - 2.04035i) q^{40} +(1.70954 - 3.74337i) q^{41} +(0.142315 - 0.989821i) q^{42} +(-0.324224 - 0.208366i) q^{43} +(-1.11525 - 1.28707i) q^{44} +2.06133 q^{45} +(4.03648 + 2.58975i) q^{46} -8.97560 q^{47} +(0.654861 + 0.755750i) q^{48} +(0.841254 + 0.540641i) q^{49} +(0.106868 - 0.743285i) q^{50} +(-0.505633 + 1.10718i) q^{51} +(0.775873 + 5.39632i) q^{52} +(-1.60283 - 0.470633i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(1.45832 + 3.19327i) q^{55} +(-0.959493 + 0.281733i) q^{56} +(-5.01645 + 5.78930i) q^{57} +(-0.987987 + 1.14020i) q^{58} +(-1.14883 + 0.337326i) q^{59} +(-0.856306 - 1.87505i) q^{60} +(-1.91912 + 1.23334i) q^{61} +(-2.23012 - 0.654821i) q^{62} +(-0.142315 - 0.989821i) q^{63} +(0.415415 - 0.909632i) q^{64} +(1.59933 - 11.1236i) q^{65} +(-1.43268 - 0.920729i) q^{66} +(-5.33375 - 6.15547i) q^{67} +1.21718 q^{68} +(4.60259 + 1.34764i) q^{69} +2.06133 q^{70} +(-4.31220 - 4.97654i) q^{71} +(0.841254 + 0.540641i) q^{72} +(-0.319203 + 2.22010i) q^{73} +(-1.17357 + 2.56976i) q^{74} +(-0.106868 - 0.743285i) q^{75} +(7.35004 + 2.15817i) q^{76} +(1.43268 - 0.920729i) q^{77} +(2.26476 + 4.95914i) q^{78} +(0.365546 - 0.107334i) q^{79} +(-1.34988 + 1.55785i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-3.94856 + 1.15940i) q^{82} +(-4.47106 - 9.79025i) q^{83} +(-0.841254 + 0.540641i) q^{84} +(-2.40737 - 0.706866i) q^{85} +(0.0548490 + 0.381484i) q^{86} +(-0.626736 + 1.37236i) q^{87} +(-0.242367 + 1.68570i) q^{88} +(-7.68437 - 4.93845i) q^{89} +(-1.34988 - 1.55785i) q^{90} -5.45181 q^{91} +(-0.686130 - 4.74650i) q^{92} -2.32427 q^{93} +(5.87777 + 6.78331i) q^{94} +(-13.2838 - 8.53697i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-6.31621 + 13.8306i) q^{97} +(-0.142315 - 0.989821i) q^{98} +(-1.63405 - 0.479800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 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 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$2$	−0.654861	−	0.755750i	−0.463056	−	0.534396i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	0.856306	−	1.87505i	0.382952	−	0.838548i	−0.615766	−	0.787929i	$-0.711153\pi$
$5$	0.856306	−	1.87505i	0.382952	−	0.838548i	0.998718	−	0.0506187i	$-0.0161193\pi$
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−0.959493	−	0.281733i	−0.362654	−	0.106485i
$7$	−0.959493	−	0.281733i	−0.362654	−	0.106485i
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	−1.97783	+	0.580743i	−0.625445	+	0.183647i
$11$	−1.11525	+	1.28707i	−0.336260	+	0.388065i	−0.898547	−	0.438877i	$-0.855376\pi$
$11$	−1.11525	+	1.28707i	−0.336260	+	0.388065i	0.562287	+	0.826942i	$0.309922\pi$
$12$	0.654861	−	0.755750i	0.189042	−	0.218166i
$13$	5.23097	−	1.53595i	1.45081	−	0.425996i	0.541001	−	0.841022i	$-0.318046\pi$
$13$	5.23097	−	1.53595i	1.45081	−	0.425996i	0.909810	+	0.415026i	$0.136227\pi$
$14$	0.415415	+	0.909632i	0.111024	+	0.243109i
$15$	−1.73410	+	1.11444i	−0.447742	+	0.287747i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	−0.173222	−	1.20479i	−0.0420125	−	0.292204i	−0.999986	−	0.00534585i	$-0.998298\pi$
$17$	−0.173222	−	1.20479i	−0.0420125	−	0.292204i	0.957973	−	0.286858i	$-0.0926107\pi$
$18$	0.415415	−	0.909632i	0.0979143	−	0.214402i
$19$	1.09018	−	7.58236i	0.250104	−	1.73951i	−0.347462	−	0.937694i	$-0.612956\pi$
$19$	1.09018	−	7.58236i	0.250104	−	1.73951i	0.597566	−	0.801820i	$-0.296135\pi$
$20$	1.73410	+	1.11444i	0.387756	+	0.249196i
$21$	0.654861	+	0.755750i	0.142902	+	0.164918i
$22$	1.70303			0.363088
$23$	−4.60054	+	1.35464i	−0.959278	+	0.282463i
$23$	−4.60054	+	1.35464i	−0.959278	+	0.282463i
$24$	−1.00000			−0.204124
$25$	0.491753	+	0.567514i	0.0983507	+	0.113503i
$26$	−4.58635	−	2.94747i	−0.899458	−	0.578046i
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$	0.415415	−	0.909632i	0.0785061	−	0.171904i
$29$	−0.214710	−	1.49334i	−0.0398707	−	0.277307i	0.960127	−	0.279565i	$-0.0901902\pi$
$29$	−0.214710	−	1.49334i	−0.0398707	−	0.277307i	−0.999997	+	0.00225839i	$0.999281\pi$
$30$	1.97783	+	0.580743i	0.361101	+	0.106029i
$31$	1.95530	−	1.25659i	0.351182	−	0.225691i	−0.353142	−	0.935570i	$-0.614887\pi$
$31$	1.95530	−	1.25659i	0.351182	−	0.225691i	0.704324	+	0.709879i	$0.251250\pi$
$32$	0.415415	+	0.909632i	0.0734357	+	0.160802i
$33$	1.63405	−	0.479800i	0.284451	−	0.0835224i
$34$	−0.797081	+	0.919880i	−0.136698	+	0.157758i
$35$	−1.34988	+	1.55785i	−0.228172	+	0.263324i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−1.17357	−	2.56976i	−0.192934	−	0.422466i	0.788299	−	0.615292i	$-0.210962\pi$
$37$	−1.17357	−	2.56976i	−0.192934	−	0.422466i	−0.981233	+	0.192826i	$0.938235\pi$
$38$	−6.44428	+	4.14149i	−1.04540	+	0.671838i
$39$	−5.23097	−	1.53595i	−0.837626	−	0.245949i
$40$	−0.293358	−	2.04035i	−0.0463839	−	0.322607i
$41$	1.70954	−	3.74337i	0.266985	−	0.584616i	−0.727894	−	0.685690i	$-0.759501\pi$
$41$	1.70954	−	3.74337i	0.266985	−	0.584616i	0.994879	+	0.101074i	$0.0322278\pi$
$42$	0.142315	−	0.989821i	0.0219597	−	0.152733i
$43$	−0.324224	−	0.208366i	−0.0494438	−	0.0317756i	0.515685	−	0.856778i	$-0.327537\pi$
$43$	−0.324224	−	0.208366i	−0.0494438	−	0.0317756i	−0.565129	+	0.825002i	$0.691174\pi$
$44$	−1.11525	−	1.28707i	−0.168130	−	0.194032i
$45$	2.06133			0.307285
$46$	4.03648	+	2.58975i	0.595147	+	0.381838i
$47$	−8.97560			−1.30923			−0.654613	−	0.755964i	$-0.727168\pi$
$47$	−8.97560			−1.30923			−0.654613	+	0.755964i	$0.727168\pi$
$48$	0.654861	+	0.755750i	0.0945210	+	0.109083i
$49$	0.841254	+	0.540641i	0.120179	+	0.0772344i
$50$	0.106868	−	0.743285i	0.0151134	−	0.105116i
$51$	−0.505633	+	1.10718i	−0.0708028	+	0.155036i
$52$	0.775873	+	5.39632i	0.107594	+	0.748335i
$53$	−1.60283	−	0.470633i	−0.220165	−	0.0646464i	0.169789	−	0.985480i	$-0.445691\pi$
$53$	−1.60283	−	0.470633i	−0.220165	−	0.0646464i	−0.389955	+	0.920834i	$0.627509\pi$
$54$	−0.841254	+	0.540641i	−0.114480	+	0.0735719i
$55$	1.45832	+	3.19327i	0.196639	+	0.430580i
$56$	−0.959493	+	0.281733i	−0.128218	+	0.0376481i
$57$	−5.01645	+	5.78930i	−0.664445	+	0.766811i
$58$	−0.987987	+	1.14020i	−0.129729	+	0.149715i
$59$	−1.14883	+	0.337326i	−0.149564	+	0.0439161i	−0.355658	−	0.934616i	$-0.615743\pi$
$59$	−1.14883	+	0.337326i	−0.149564	+	0.0439161i	0.206093	+	0.978532i	$0.433925\pi$
$60$	−0.856306	−	1.87505i	−0.110549	−	0.242068i
$61$	−1.91912	+	1.23334i	−0.245718	+	0.157913i	−0.657703	−	0.753277i	$-0.728472\pi$
$61$	−1.91912	+	1.23334i	−0.245718	+	0.157913i	0.411985	+	0.911191i	$0.364836\pi$
$62$	−2.23012	−	0.654821i	−0.283225	−	0.0831624i
$63$	−0.142315	−	0.989821i	−0.0179300	−	0.124706i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	1.59933	−	11.1236i	0.198372	−	1.37971i
$66$	−1.43268	−	0.920729i	−0.176351	−	0.113334i
$67$	−5.33375	−	6.15547i	−0.651621	−	0.752010i	0.329764	−	0.944063i	$-0.393031\pi$
$67$	−5.33375	−	6.15547i	−0.651621	−	0.752010i	−0.981385	+	0.192053i	$0.938485\pi$
$68$	1.21718			0.147604
$69$	4.60259	+	1.34764i	0.554087	+	0.162237i
$70$	2.06133			0.246376
$71$	−4.31220	−	4.97654i	−0.511764	−	0.590607i	0.439786	−	0.898103i	$-0.355054\pi$
$71$	−4.31220	−	4.97654i	−0.511764	−	0.590607i	−0.951549	+	0.307496i	$0.900509\pi$
$72$	0.841254	+	0.540641i	0.0991427	+	0.0637151i
$73$	−0.319203	+	2.22010i	−0.0373599	+	0.259844i	−0.999938	−	0.0111618i	$-0.996447\pi$
$73$	−0.319203	+	2.22010i	−0.0373599	+	0.259844i	0.962578	+	0.271005i	$0.0873561\pi$
$74$	−1.17357	+	2.56976i	−0.136425	+	0.298728i
$75$	−0.106868	−	0.743285i	−0.0123401	−	0.0858271i
$76$	7.35004	+	2.15817i	0.843107	+	0.247559i
$77$	1.43268	−	0.920729i	0.163269	−	0.104927i
$78$	2.26476	+	4.95914i	0.256434	+	0.561512i
$79$	0.365546	−	0.107334i	0.0411271	−	0.0120760i	−0.261104	−	0.965311i	$-0.584087\pi$
$79$	0.365546	−	0.107334i	0.0411271	−	0.0120760i	0.302231	+	0.953235i	$0.402268\pi$
$80$	−1.34988	+	1.55785i	−0.150921	+	0.174173i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	−3.94856	+	1.15940i	−0.436046	+	0.128035i
$83$	−4.47106	−	9.79025i	−0.490762	−	1.07462i	−0.979362	−	0.202112i	$-0.935220\pi$
$83$	−4.47106	−	9.79025i	−0.490762	−	1.07462i	0.488600	−	0.872508i	$-0.337508\pi$
$84$	−0.841254	+	0.540641i	−0.0917883	+	0.0589887i
$85$	−2.40737	−	0.706866i	−0.261116	−	0.0766704i
$86$	0.0548490	+	0.381484i	0.00591453	+	0.0411364i
$87$	−0.626736	+	1.37236i	−0.0671931	+	0.147132i
$88$	−0.242367	+	1.68570i	−0.0258364	+	0.179696i
$89$	−7.68437	−	4.93845i	−0.814542	−	0.523474i	0.0657893	−	0.997834i	$-0.479043\pi$
$89$	−7.68437	−	4.93845i	−0.814542	−	0.523474i	−0.880331	+	0.474359i	$0.842680\pi$
$90$	−1.34988	−	1.55785i	−0.142290	−	0.164212i
$91$	−5.45181			−0.571505
$92$	−0.686130	−	4.74650i	−0.0715340	−	0.494856i
$93$	−2.32427			−0.241015
$94$	5.87777	+	6.78331i	0.606246	+	0.699645i
$95$	−13.2838	−	8.53697i	−1.36289	−	0.875875i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	−6.31621	+	13.8306i	−0.641314	+	1.40428i	0.257642	+	0.966241i	$0.417055\pi$
$97$	−6.31621	+	13.8306i	−0.641314	+	1.40428i	−0.898955	+	0.438040i	$0.855673\pi$
$98$	−0.142315	−	0.989821i	−0.0143760	−	0.0999871i
$99$	−1.63405	−	0.479800i	−0.164228	−	0.0482217i
$100$	−0.631721	+	0.405982i	−0.0631721	+	0.0405982i
$101$	1.01210	+	2.21619i	0.100708	+	0.220519i	0.953279	−	0.302092i	$-0.0976851\pi$
$101$	1.01210	+	2.21619i	0.100708	+	0.220519i	−0.852571	+	0.522612i	$0.824958\pi$
$102$	1.16787	−	0.342918i	0.115637	−	0.0339539i
$103$	−1.73072	+	1.99736i	−0.170533	+	0.196805i	−0.834582	−	0.550883i	$-0.814291\pi$
$103$	−1.73072	+	1.99736i	−0.170533	+	0.196805i	0.664049	+	0.747689i	$0.268836\pi$
$104$	3.57018	−	4.12020i	0.350084	−	0.404019i
$105$	1.97783	−	0.580743i	0.193016	−	0.0566747i
$106$	0.693949	+	1.51954i	0.0674023	+	0.147590i
$107$	2.18085	−	1.40155i	0.210831	−	0.135493i	−0.430964	−	0.902369i	$-0.641826\pi$
$107$	2.18085	−	1.40155i	0.210831	−	0.135493i	0.641795	+	0.766876i	$0.278190\pi$
$108$	0.959493	+	0.281733i	0.0923273	+	0.0271097i
$109$	−2.57419	−	17.9039i	−0.246563	−	1.71488i	−0.617792	−	0.786342i	$-0.711973\pi$
$109$	−2.57419	−	17.9039i	−0.246563	−	1.71488i	0.371229	−	0.928541i	$-0.378937\pi$
$110$	1.45832	−	3.19327i	0.139045	−	0.304466i
$111$	−0.402047	+	2.79630i	−0.0381606	+	0.265413i
$112$	0.841254	+	0.540641i	0.0794910	+	0.0510858i
$113$	−1.14959	−	1.32670i	−0.108144	−	0.124805i	0.699097	−	0.715027i	$-0.253586\pi$
$113$	−1.14959	−	1.32670i	−0.108144	−	0.124805i	−0.807241	+	0.590222i	$0.799040\pi$
$114$	7.66034			0.717456
$115$	−1.39945	+	9.78623i	−0.130499	+	0.912570i
$116$	1.50870			0.140079
$117$	3.57018	+	4.12020i	0.330063	+	0.380913i
$118$	1.00725	+	0.647323i	0.0927253	+	0.0595909i
$119$	−0.173222	+	1.20479i	−0.0158793	+	0.110443i
$120$	−0.856306	+	1.87505i	−0.0781697	+	0.171168i
$121$	1.15270	+	8.01724i	0.104791	+	0.728840i
$122$	2.18885	+	0.642705i	0.198170	+	0.0581878i
$123$	−3.46198	+	2.22488i	−0.312156	+	0.200610i
$124$	0.965535	+	2.11423i	0.0867076	+	0.189863i
$125$	11.3744	−	3.33981i	1.01735	−	0.298722i
$126$	−0.654861	+	0.755750i	−0.0583396	+	0.0673275i
$127$	−1.38679	+	1.60044i	−0.123058	+	0.142016i	−0.813935	−	0.580956i	$-0.802679\pi$
$127$	−1.38679	+	1.60044i	−0.123058	+	0.142016i	0.690877	+	0.722972i	$0.257224\pi$
$128$	−0.959493	+	0.281733i	−0.0848080	+	0.0249019i
$129$	0.160104	+	0.350578i	0.0140963	+	0.0308667i
$130$	−9.45398	+	6.07570i	−0.829169	+	0.532874i
$131$	1.14994	+	0.337652i	0.100470	+	0.0295008i	0.331581	−	0.943427i	$-0.392418\pi$
$131$	1.14994	+	0.337652i	0.100470	+	0.0295008i	−0.231111	+	0.972927i	$0.574236\pi$
$132$	0.242367	+	1.68570i	0.0210953	+	0.146721i
$133$	−3.18222	+	6.96809i	−0.275933	+	0.604210i
$134$	−1.15913	+	8.06195i	−0.100134	+	0.696447i
$135$	−1.73410	−	1.11444i	−0.149247	−	0.0959155i
$136$	−0.797081	−	0.919880i	−0.0683491	−	0.0788791i
$137$	−7.39409			−0.631720			−0.315860	−	0.948806i	$-0.602293\pi$
$137$	−7.39409			−0.631720			−0.315860	+	0.948806i	$0.602293\pi$
$138$	−1.99558	−	4.36092i	−0.169875	−	0.371227i
$139$	16.9708			1.43945			0.719723	−	0.694261i	$-0.244269\pi$
$139$	16.9708			1.43945			0.719723	+	0.694261i	$0.244269\pi$
$140$	−1.34988	−	1.55785i	−0.114086	−	0.131662i
$141$	7.55076	+	4.85258i	0.635889	+	0.408661i
$142$	−0.937130	+	6.51788i	−0.0786422	+	0.546968i
$143$	−3.85696	+	8.44557i	−0.322536	+	0.706254i
$144$	−0.142315	−	0.989821i	−0.0118596	−	0.0824851i
$145$	−2.98395	−	0.876166i	−0.247803	−	0.0727616i
$146$	1.88688	−	1.21262i	0.156159	−	0.100357i
$147$	−0.415415	−	0.909632i	−0.0342629	−	0.0750252i
$148$	2.71062	−	0.795910i	0.222812	−	0.0654234i
$149$	3.70837	−	4.27969i	0.303802	−	0.350606i	−0.583236	−	0.812303i	$-0.698214\pi$
$149$	3.70837	−	4.27969i	0.303802	−	0.350606i	0.887038	+	0.461697i	$0.152759\pi$
$150$	−0.491753	+	0.567514i	−0.0401515	+	0.0463373i
$151$	9.26296	−	2.71985i	0.753809	−	0.221338i	0.117818	−	0.993035i	$-0.462410\pi$
$151$	9.26296	−	2.71985i	0.753809	−	0.221338i	0.635990	+	0.771697i	$0.280592\pi$
$152$	−3.18222	−	6.96809i	−0.258112	−	0.565186i
$153$	1.02395	−	0.658055i	0.0827817	−	0.0532006i
$154$	−1.63405	−	0.479800i	−0.131675	−	0.0386634i
$155$	−0.681841	−	4.74231i	−0.0547668	−	0.380911i
$156$	2.26476	−	4.95914i	0.181326	−	0.397049i
$157$	2.12696	−	14.7933i	0.169750	−	1.18064i	−0.709650	−	0.704554i	$-0.751147\pi$
$157$	2.12696	−	14.7933i	0.169750	−	1.18064i	0.879400	−	0.476083i	$-0.157944\pi$
$158$	−0.320499	−	0.205972i	−0.0254975	−	0.0163863i
$159$	1.09394	+	1.26248i	0.0867552	+	0.100121i
$160$	2.06133			0.162962
$161$	4.79583	−	0.00364972i	0.377964	−	0.000287638i
$162$	1.00000			0.0785674
$163$	10.1629	+	11.7286i	0.796017	+	0.918653i	0.998156	−	0.0607040i	$-0.0193346\pi$
$163$	10.1629	+	11.7286i	0.796017	+	0.918653i	−0.202139	+	0.979357i	$0.564789\pi$
$164$	3.46198	+	2.22488i	0.270335	+	0.173734i
$165$	0.499597	−	3.47478i	0.0388936	−	0.270511i
$166$	−4.47106	+	9.79025i	−0.347021	+	0.759871i
$167$	0.0419965	+	0.292092i	0.00324978	+	0.0226027i	0.991382	−	0.131004i	$-0.0418201\pi$
$167$	0.0419965	+	0.292092i	0.00324978	+	0.0226027i	−0.988132	+	0.153607i	$0.950911\pi$
$168$	0.959493	+	0.281733i	0.0740265	+	0.0217361i
$169$	14.0676	−	9.04071i	1.08212	−	0.695439i
$170$	1.04228	+	2.28226i	0.0799389	+	0.175042i
$171$	7.35004	−	2.15817i	0.562072	−	0.165039i
$172$	0.252388	−	0.291271i	0.0192444	−	0.0222092i
$173$	−1.35155	+	1.55977i	−0.102756	+	0.118587i	−0.804798	−	0.593549i	$-0.797727\pi$
$173$	−1.35155	+	1.55977i	−0.102756	+	0.118587i	0.702042	+	0.712136i	$0.252272\pi$
$174$	1.44758	−	0.425049i	0.109741	−	0.0322229i
$175$	−0.311947	−	0.683068i	−0.0235810	−	0.0516351i
$176$	1.43268	−	0.920729i	0.107992	−	0.0694025i
$177$	1.14883	+	0.337326i	0.0863510	+	0.0253549i
$178$	1.29997	+	9.04146i	0.0974365	+	0.677686i
$179$	−4.30055	+	9.41689i	−0.321438	+	0.703851i	−0.999515	−	0.0311398i	$-0.990086\pi$
$179$	−4.30055	+	9.41689i	−0.321438	+	0.703851i	0.678077	+	0.734991i	$0.262814\pi$
$180$	−0.293358	+	2.04035i	−0.0218656	+	0.152078i
$181$	20.2634	+	13.0225i	1.50616	+	0.967952i	0.994037	+	0.109042i	$0.0347784\pi$
$181$	20.2634	+	13.0225i	1.50616	+	0.967952i	0.512126	+	0.858910i	$0.328858\pi$
$182$	3.57018	+	4.12020i	0.264639	+	0.305410i
$183$	2.28126			0.168636
$184$	−3.13784	+	3.62684i	−0.231325	+	0.267374i
$185$	−5.82336			−0.428142
$186$	1.52207	+	1.75656i	0.111604	+	0.128797i
$187$	1.74383	+	1.12069i	0.127521	+	0.0819529i
$188$	1.27736	−	8.88424i	0.0931612	−	0.647950i
$189$	−0.415415	+	0.909632i	−0.0302170	+	0.0661660i
$190$	2.24722	+	15.6297i	0.163030	+	1.13390i
$191$	16.0610	+	4.71593i	1.16213	+	0.341233i	0.805261	−	0.592921i	$-0.202025\pi$
$191$	16.0610	+	4.71593i	1.16213	+	0.341233i	0.356871	+	0.934154i	$0.383844\pi$
$192$	−0.841254	+	0.540641i	−0.0607122	+	0.0390174i
$193$	−6.24918	−	13.6838i	−0.449826	−	0.984981i	−0.989690	−	0.143228i	$-0.954252\pi$
$193$	−6.24918	−	13.6838i	−0.449826	−	0.984981i	0.539864	−	0.841752i	$-0.318476\pi$
$194$	14.5887	−	4.28362i	1.04741	−	0.307546i
$195$	−7.35930	+	8.49309i	−0.527010	+	0.608203i
$196$	−0.654861	+	0.755750i	−0.0467758	+	0.0539821i
$197$	21.7439	−	6.38458i	1.54919	−	0.454883i	0.608330	−	0.793684i	$-0.291840\pi$
$197$	21.7439	−	6.38458i	1.54919	−	0.454883i	0.940858	+	0.338801i	$0.110021\pi$
$198$	0.707465	+	1.54913i	0.0502774	+	0.110092i
$199$	7.44432	−	4.78417i	0.527714	−	0.339141i	−0.249503	−	0.968374i	$-0.580267\pi$
$199$	7.44432	−	4.78417i	0.527714	−	0.339141i	0.777217	+	0.629233i	$0.216631\pi$
$200$	0.720510	+	0.211561i	0.0509478	+	0.0149596i
$201$	1.15913	+	8.06195i	0.0817590	+	0.568646i
$202$	1.01210	−	2.21619i	0.0712111	−	0.155931i
$203$	−0.214710	+	1.49334i	−0.0150697	+	0.104812i
$204$	−1.02395	−	0.658055i	−0.0716911	−	0.0460731i
$205$	−5.55512	−	6.41095i	−0.387986	−	0.447760i
$206$	2.64288			0.184138
$207$	−3.14336	−	3.62206i	−0.218479	−	0.251750i
$208$	−5.45181			−0.378015
$209$	8.54318	+	9.85936i	0.590944	+	0.681986i
$210$	−1.73410	−	1.11444i	−0.119664	−	0.0769035i
$211$	0.664457	−	4.62140i	0.0457431	−	0.318150i	−0.954084	−	0.299540i	$-0.903167\pi$
$211$	0.664457	−	4.62140i	0.0457431	−	0.318150i	0.999827	−	0.0186102i	$-0.00592416\pi$
$212$	0.693949	−	1.51954i	0.0476606	−	0.104362i
$213$	0.937130	+	6.51788i	0.0642111	+	0.446598i
$214$	−2.48737	−	0.730358i	−0.170033	−	0.0499262i
$215$	−0.668333	+	0.429511i	−0.0455799	+	0.0292924i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−2.23012	+	0.654821i	−0.151390	+	0.0444522i
$218$	−11.8451	+	13.6700i	−0.802253	+	0.925850i
$219$	1.46881	−	1.69510i	0.0992530	−	0.114544i
$220$	−3.36831	+	0.989024i	−0.227091	+	0.0666800i
$221$	−2.75661	−	6.03614i	−0.185430	−	0.406035i
$222$	2.37659	−	1.52734i	0.159506	−	0.102508i
$223$	−1.35991	−	0.399305i	−0.0910662	−	0.0267395i	0.235882	−	0.971782i	$-0.424202\pi$
$223$	−1.35991	−	0.399305i	−0.0910662	−	0.0267395i	−0.326948	+	0.945042i	$0.606020\pi$
$224$	−0.142315	−	0.989821i	−0.00950881	−	0.0661352i
$225$	−0.311947	+	0.683068i	−0.0207965	+	0.0455379i
$226$	−0.249830	+	1.73760i	−0.0166184	+	0.115584i
$227$	−15.9913	−	10.2770i	−1.06138	−	0.682108i	−0.111197	−	0.993798i	$-0.535468\pi$
$227$	−15.9913	−	10.2770i	−1.06138	−	0.682108i	−0.950184	+	0.311691i	$0.899105\pi$
$228$	−5.01645	−	5.78930i	−0.332223	−	0.383405i
$229$	−6.86202			−0.453455			−0.226727	−	0.973958i	$-0.572803\pi$
$229$	−6.86202			−0.453455			−0.226727	+	0.973958i	$0.572803\pi$
$230$	8.31238	−	5.35098i	0.548102	−	0.352833i
$231$	−1.70303			−0.112051
$232$	−0.987987	−	1.14020i	−0.0648645	−	0.0748576i
$233$	7.61549	+	4.89418i	0.498907	+	0.320628i	0.765779	−	0.643104i	$-0.222354\pi$
$233$	7.61549	+	4.89418i	0.498907	+	0.320628i	−0.266872	+	0.963732i	$0.585990\pi$
$234$	0.775873	−	5.39632i	0.0507204	−	0.352768i
$235$	−7.68587	+	16.8297i	−0.501371	+	1.09785i
$236$	−0.170397	−	1.18514i	−0.0110919	−	0.0771460i
$237$	−0.365546	−	0.107334i	−0.0237447	−	0.00697208i
$238$	1.02395	−	0.658055i	0.0663730	−	0.0426554i
$239$	2.08463	+	4.56471i	0.134844	+	0.295266i	0.964993	−	0.262274i	$-0.0844725\pi$
$239$	2.08463	+	4.56471i	0.134844	+	0.295266i	−0.830150	+	0.557540i	$0.811745\pi$
$240$	1.97783	−	0.580743i	0.127668	−	0.0374868i
$241$	19.6939	−	22.7280i	1.26860	−	1.46404i	0.446405	−	0.894831i	$-0.352704\pi$
$241$	19.6939	−	22.7280i	1.26860	−	1.46404i	0.822193	−	0.569209i	$-0.192750\pi$
$242$	5.30416	−	6.12133i	0.340965	−	0.393494i
$243$	0.959493	−	0.281733i	0.0615515	−	0.0180732i
$244$	−0.947670	−	2.07511i	−0.0606684	−	0.132845i
$245$	1.73410	−	1.11444i	0.110788	−	0.0711988i
$246$	3.94856	+	1.15940i	0.251751	+	0.0739208i
$247$	−5.94345	−	41.3376i	−0.378173	−	2.63025i
$248$	0.965535	−	2.11423i	0.0613115	−	0.134253i
$249$	−1.53172	+	10.6533i	−0.0970686	+	0.675127i
$250$	−9.97268	−	6.40905i	−0.630728	−	0.405344i
$251$	13.6505	+	15.7535i	0.861612	+	0.994354i	0.999992	+	0.00397439i	$0.00126509\pi$
$251$	13.6505	+	15.7535i	0.861612	+	0.994354i	−0.138380	+	0.990379i	$0.544189\pi$
$252$	1.00000			0.0629941
$253$	3.38723	−	7.43196i	0.212953	−	0.467243i
$254$	2.11769			0.132876
$255$	1.64304	+	1.89617i	0.102891	+	0.118743i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	3.45203	−	24.0094i	0.215332	−	1.49767i	−0.539632	−	0.841901i	$-0.681437\pi$
$257$	3.45203	−	24.0094i	0.215332	−	1.49767i	0.754964	−	0.655766i	$-0.227654\pi$
$258$	0.160104	−	0.350578i	0.00996761	−	0.0218260i
$259$	0.402047	+	2.79630i	0.0249820	+	0.173754i
$260$	10.7827	+	3.16610i	0.668718	+	0.196353i
$261$	1.26920	−	0.815664i	0.0785613	−	0.0504883i
$262$	−0.497868	−	1.09018i	−0.0307584	−	0.0673515i
$263$	1.60205	−	0.470404i	0.0987866	−	0.0290064i	−0.231966	−	0.972724i	$-0.574516\pi$
$263$	1.60205	−	0.470404i	0.0987866	−	0.0290064i	0.330752	+	0.943718i	$0.392698\pi$
$264$	1.11525	−	1.28707i	0.0686388	−	0.0792134i
$265$	−2.25497	+	2.60238i	−0.138522	+	0.159863i
$266$	7.35004	−	2.15817i	0.450660	−	0.132326i
$267$	3.79458	+	8.30897i	0.232225	+	0.508501i
$268$	6.85189	−	4.40344i	0.418546	−	0.268983i
$269$	12.2482	+	3.59641i	0.746788	+	0.219277i	0.632918	−	0.774219i	$-0.281857\pi$
$269$	12.2482	+	3.59641i	0.746788	+	0.219277i	0.113870	+	0.993496i	$0.463675\pi$
$270$	0.293358	+	2.04035i	0.0178532	+	0.124172i
$271$	−9.12842	+	19.9885i	−0.554512	+	1.21421i	0.400131	+	0.916458i	$0.368965\pi$
$271$	−9.12842	+	19.9885i	−0.554512	+	1.21421i	−0.954643	+	0.297754i	$0.903762\pi$
$272$	−0.173222	+	1.20479i	−0.0105031	+	0.0730509i
$273$	4.58635	+	2.94747i	0.277579	+	0.178389i
$274$	4.84210	+	5.58808i	0.292522	+	0.337588i
$275$	−1.27885			−0.0771178
$276$	−1.98894	+	4.36396i	−0.119720	+	0.262679i
$277$	13.2499			0.796108			0.398054	−	0.917362i	$-0.369686\pi$
$277$	13.2499			0.796108			0.398054	+	0.917362i	$0.369686\pi$
$278$	−11.1135	−	12.8257i	−0.666545	−	0.769234i
$279$	1.95530	+	1.25659i	0.117061	+	0.0752302i
$280$	−0.293358	+	2.04035i	−0.0175315	+	0.121934i
$281$	−5.73364	+	12.5549i	−0.342041	+	0.748964i	−0.999992	−	0.00409642i	$-0.998696\pi$
$281$	−5.73364	+	12.5549i	−0.342041	+	0.748964i	0.657951	+	0.753061i	$0.271423\pi$
$282$	−1.27736	−	8.88424i	−0.0760658	−	0.529049i
$283$	10.6638	+	3.13117i	0.633897	+	0.186129i	0.582866	−	0.812568i	$-0.301931\pi$
$283$	10.6638	+	3.13117i	0.633897	+	0.186129i	0.0510306	+	0.998697i	$0.483749\pi$
$284$	5.53958	−	3.56007i	0.328713	−	0.211251i
$285$	6.55960	+	14.3635i	0.388557	+	0.850821i
$286$	8.90851	−	2.61578i	0.526771	−	0.154674i
$287$	−2.69492	+	3.11011i	−0.159076	+	0.183584i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	14.8899	−	4.37206i	0.875875	−	0.257180i
$290$	1.29191	+	2.82888i	0.0758634	+	0.166118i
$291$	12.7909	−	8.22021i	0.749816	−	0.481877i
$292$	−2.15208	−	0.631908i	−0.125941	−	0.0369796i
$293$	0.975380	+	6.78392i	0.0569823	+	0.396321i	0.998274	+	0.0587266i	$0.0187040\pi$
$293$	0.975380	+	6.78392i	0.0569823	+	0.396321i	−0.941292	+	0.337594i	$0.890387\pi$
$294$	−0.415415	+	0.909632i	−0.0242275	+	0.0530508i
$295$	−0.351244	+	2.44296i	−0.0204502	+	0.142235i
$296$	−2.37659	−	1.52734i	−0.138136	−	0.0887748i
$297$	1.11525	+	1.28707i	0.0647133	+	0.0746831i
$298$	−5.66284			−0.328039
$299$	−21.9846	+	14.1523i	−1.27140	+	0.818449i
$300$	0.750928			0.0433549
$301$	0.252388	+	0.291271i	0.0145474	+	0.0167886i
$302$	−8.12147	−	5.21935i	−0.467338	−	0.300340i
$303$	0.346730	−	2.41156i	0.0199191	−	0.138541i
$304$	−3.18222	+	6.96809i	−0.182513	+	0.399647i
$305$	0.669225	+	4.65456i	0.0383197	+	0.266519i
$306$	−1.16787	−	0.342918i	−0.0667628	−	0.0196033i
$307$	−7.31774	+	4.70282i	−0.417645	+	0.268404i	−0.732542	−	0.680721i	$-0.761666\pi$
$307$	−7.31774	+	4.70282i	−0.417645	+	0.268404i	0.314897	+	0.949126i	$0.398030\pi$
$308$	0.707465	+	1.54913i	0.0403116	+	0.0882700i
$309$	2.53583	−	0.744586i	0.144258	−	0.0423580i
$310$	−3.13749	+	3.62085i	−0.178197	+	0.205651i
$311$	6.13051	−	7.07499i	0.347629	−	0.401186i	−0.554828	−	0.831965i	$-0.687216\pi$
$311$	6.13051	−	7.07499i	0.347629	−	0.401186i	0.902457	+	0.430780i	$0.141761\pi$
$312$	−5.23097	+	1.53595i	−0.296145	+	0.0869562i
$313$	2.63367	+	5.76694i	0.148864	+	0.325967i	0.969344	−	0.245709i	$-0.0790208\pi$
$313$	2.63367	+	5.76694i	0.148864	+	0.325967i	−0.820480	+	0.571676i	$0.806294\pi$
$314$	−12.5729	+	8.08013i	−0.709531	+	0.455988i
$315$	−1.97783	−	0.580743i	−0.111438	−	0.0327212i
$316$	0.0542188	+	0.377100i	0.00305005	+	0.0212135i
$317$	−6.03200	+	13.2082i	−0.338791	+	0.741848i	−0.999965	−	0.00838413i	$-0.997331\pi$
$317$	−6.03200	+	13.2082i	−0.338791	+	0.741848i	0.661174	+	0.750233i	$0.270058\pi$
$318$	0.237736	−	1.65349i	0.0133316	−	0.0927232i
$319$	2.16148	+	1.38910i	0.121020	+	0.0777747i
$320$	−1.34988	−	1.55785i	−0.0754607	−	0.0870863i
$321$	−2.59238			−0.144693
$322$	−3.14336	−	3.62206i	−0.175173	−	0.201849i
$323$	−9.32398			−0.518800
$324$	−0.654861	−	0.755750i	−0.0363812	−	0.0419861i
$325$	3.44402	+	2.21334i	0.191040	+	0.122774i
$326$	2.20860	−	15.3612i	0.122323	−	0.850776i
$327$	−7.51403	+	16.4534i	−0.415527	+	0.909877i
$328$	−0.585662	−	4.07337i	−0.0323378	−	0.224914i
$329$	8.61203	+	2.52872i	0.474797	+	0.139413i
$330$	−2.95323	+	1.89792i	−0.162570	+	0.104477i
$331$	−12.0003	−	26.2770i	−0.659597	−	1.44432i	−0.882897	−	0.469566i	$-0.844410\pi$
$331$	−12.0003	−	26.2770i	−0.659597	−	1.44432i	0.223301	−	0.974750i	$-0.428317\pi$
$332$	10.3269	−	3.03225i	0.566762	−	0.166416i
$333$	1.85002	−	2.13503i	0.101380	−	0.116999i
$334$	0.193246	−	0.223018i	0.0105740	−	0.0122030i
$335$	−16.1091	+	4.73007i	−0.880136	+	0.258431i
$336$	−0.415415	−	0.909632i	−0.0226627	−	0.0496245i
$337$	17.4568	−	11.2188i	0.950930	−	0.611126i	0.0294562	−	0.999566i	$-0.490622\pi$
$337$	17.4568	−	11.2188i	0.950930	−	0.611126i	0.921474	+	0.388440i	$0.126986\pi$
$338$	−16.0448	−	4.71119i	−0.872725	−	0.256255i
$339$	0.249830	+	1.73760i	0.0135689	+	0.0943736i
$340$	1.04228	−	2.28226i	0.0565253	−	0.123773i
$341$	−0.563325	+	3.91801i	−0.0305057	+	0.212172i
$342$	−6.44428	−	4.14149i	−0.348467	−	0.223946i
$343$	−0.654861	−	0.755750i	−0.0353592	−	0.0408066i
$344$	−0.385406			−0.0207797
$345$	6.46812	−	7.47610i	0.348232	−	0.402500i
$346$	2.06387			0.110955
$347$	−20.5541	−	23.7207i	−1.10340	−	1.27339i	−0.958855	−	0.283896i	$-0.908373\pi$
$347$	−20.5541	−	23.7207i	−1.10340	−	1.27339i	−0.144547	−	0.989498i	$-0.546172\pi$
$348$	−1.26920	−	0.815664i	−0.0680361	−	0.0437242i
$349$	−3.39544	+	23.6158i	−0.181754	+	1.26412i	0.670861	+	0.741583i	$0.265925\pi$
$349$	−3.39544	+	23.6158i	−0.181754	+	1.26412i	−0.852615	+	0.522540i	$0.824984\pi$
$350$	−0.311947	+	0.683068i	−0.0166743	+	0.0365115i
$351$	−0.775873	−	5.39632i	−0.0414130	−	0.288034i
$352$	−1.63405	−	0.479800i	−0.0870950	−	0.0255734i
$353$	−25.9919	+	16.7040i	−1.38341	+	0.889065i	−0.999413	−	0.0342691i	$-0.989090\pi$
$353$	−25.9919	+	16.7040i	−1.38341	+	0.889065i	−0.383999	+	0.923334i	$0.625453\pi$
$354$	−0.497387	−	1.08913i	−0.0264358	−	0.0578864i
$355$	−13.0238	+	3.82414i	−0.691233	+	0.202964i
$356$	5.98178	−	6.90334i	0.317034	−	0.365877i
$357$	0.797081	−	0.919880i	0.0421860	−	0.0486852i
$358$	9.93307	−	2.91661i	0.524979	−	0.154148i
$359$	10.3712	+	22.7097i	0.547369	+	1.19857i	0.958000	+	0.286769i	$0.0925812\pi$
$359$	10.3712	+	22.7097i	0.547369	+	1.19857i	−0.410631	+	0.911802i	$0.634691\pi$
$360$	1.73410	−	1.11444i	0.0913951	−	0.0587360i
$361$	−38.0734	−	11.1794i	−2.00386	−	0.588387i
$362$	−3.42795	−	23.8419i	−0.180169	−	1.25310i
$363$	3.36473	−	7.36773i	0.176602	−	0.386706i
$364$	0.775873	−	5.39632i	0.0406668	−	0.282844i
$365$	3.88947	+	2.49961i	0.203584	+	0.130836i
$366$	−1.49391	−	1.72406i	−0.0780878	−	0.0901182i
$367$	15.2069			0.793795			0.396898	−	0.917863i	$-0.370087\pi$
$367$	15.2069			0.793795			0.396898	+	0.917863i	$0.370087\pi$
$368$	4.79583	−	0.00364972i	0.250000	−	0.000190255i
$369$	4.11526			0.214232
$370$	3.81349	+	4.40100i	0.198254	+	0.228797i
$371$	1.40531	+	0.903138i	0.0729601	+	0.0468886i
$372$	0.330777	−	2.30061i	0.0171500	−	0.119281i
$373$	−5.01971	+	10.9916i	−0.259911	+	0.569126i	−0.993931	−	0.110002i	$-0.964914\pi$
$373$	−5.01971	+	10.9916i	−0.259911	+	0.569126i	0.734020	+	0.679127i	$0.237642\pi$
$374$	−0.295003	−	2.05179i	−0.0152542	−	0.106096i
$375$	−11.3744	−	3.33981i	−0.587369	−	0.172467i
$376$	−7.55076	+	4.85258i	−0.389401	+	0.250253i
$377$	−3.41684	−	7.48184i	−0.175976	−	0.385334i
$378$	0.959493	−	0.281733i	0.0493510	−	0.0144908i
$379$	−23.7458	+	27.4041i	−1.21974	+	1.40765i	−0.334578	+	0.942368i	$0.608594\pi$
$379$	−23.7458	+	27.4041i	−1.21974	+	1.40765i	−0.885161	+	0.465286i	$0.845952\pi$
$380$	10.3406	−	11.9336i	0.530459	−	0.612183i
$381$	2.03191	−	0.596622i	0.104098	−	0.0305659i
$382$	−6.95364	−	15.2264i	−0.355779	−	0.779048i
$383$	19.6488	−	12.6275i	1.00401	−	0.645236i	0.0681715	−	0.997674i	$-0.478284\pi$
$383$	19.6488	−	12.6275i	1.00401	−	0.645236i	0.935835	+	0.352438i	$0.114647\pi$
$384$	0.959493	+	0.281733i	0.0489639	+	0.0143771i
$385$	−0.499597	−	3.47478i	−0.0254618	−	0.177091i
$386$	−6.24918	+	13.6838i	−0.318075	+	0.696487i
$387$	0.0548490	−	0.381484i	0.00278813	−	0.0193919i
$388$	−12.7909	−	8.22021i	−0.649359	−	0.417318i
$389$	−2.41693	−	2.78928i	−0.122543	−	0.141422i	0.691163	−	0.722699i	$-0.257099\pi$
$389$	−2.41693	−	2.78928i	−0.122543	−	0.141422i	−0.813706	+	0.581277i	$0.802553\pi$
$390$	11.2380			0.569056
$391$	2.42897	+	5.30801i	0.122838	+	0.268438i
$392$	1.00000			0.0505076
$393$	−0.784840	−	0.905753i	−0.0395899	−	0.0456892i
$394$	−19.0644	−	12.2519i	−0.960449	−	0.617243i
$395$	0.111763	−	0.777327i	0.00562339	−	0.0391115i
$396$	0.707465	−	1.54913i	0.0355515	−	0.0778468i
$397$	1.11893	+	7.78230i	0.0561573	+	0.390582i	0.998443	+	0.0557738i	$0.0177626\pi$
$397$	1.11893	+	7.78230i	0.0561573	+	0.390582i	−0.942286	+	0.334809i	$0.891328\pi$
$398$	−8.49063	−	2.49307i	−0.425597	−	0.124967i
$399$	6.44428	−	4.14149i	0.322618	−	0.207334i
$400$	−0.311947	−	0.683068i	−0.0155973	−	0.0341534i
$401$	−9.49252	+	2.78726i	−0.474034	+	0.139189i	−0.510019	−	0.860163i	$-0.670361\pi$
$401$	−9.49252	+	2.78726i	−0.474034	+	0.139189i	0.0359846	+	0.999352i	$0.488543\pi$
$402$	5.33375	−	6.15547i	0.266023	−	0.307007i
$403$	8.29803	−	9.57644i	0.413355	−	0.477037i
$404$	−2.33767	+	0.686402i	−0.116303	+	0.0341498i
$405$	0.856306	+	1.87505i	0.0425502	+	0.0931720i
$406$	1.26920	−	0.815664i	0.0629892	−	0.0404807i
$407$	4.61627	+	1.35546i	0.228820	+	0.0671876i
$408$	0.173222	+	1.20479i	0.00857578	+	0.0596458i
$409$	5.38948	−	11.8013i	0.266493	−	0.583537i	−0.728323	−	0.685234i	$-0.759700\pi$
$409$	5.38948	−	11.8013i	0.266493	−	0.583537i	0.994815	+	0.101697i	$0.0324271\pi$
$410$	−1.20724	+	8.39655i	−0.0596214	+	0.414676i
$411$	6.22030	+	3.99755i	0.306825	+	0.197184i
$412$	−1.73072	−	1.99736i	−0.0852664	−	0.0984027i
$413$	1.19733			0.0589165
$414$	−0.678905	+	4.74753i	−0.0333664	+	0.233329i
$415$	−22.1858			−1.08906
$416$	3.57018	+	4.12020i	0.175042	+	0.202010i
$417$	−14.2768	−	9.17512i	−0.699136	−	0.449308i
$418$	1.85661	−	12.9130i	0.0908098	−	0.631596i
$419$	−14.0777	+	30.8258i	−0.687739	+	1.50594i	0.166490	+	0.986043i	$0.446756\pi$
$419$	−14.0777	+	30.8258i	−0.687739	+	1.50594i	−0.854230	+	0.519896i	$0.825971\pi$
$420$	0.293358	+	2.04035i	0.0143144	+	0.0995587i
$421$	−5.98485	−	1.75731i	−0.291684	−	0.0856461i	0.132617	−	0.991167i	$-0.457662\pi$
$421$	−5.98485	−	1.75731i	−0.291684	−	0.0856461i	−0.424301	+	0.905521i	$0.639480\pi$
$422$	−3.92775	+	2.52421i	−0.191200	+	0.122877i
$423$	−3.72860	−	8.16450i	−0.181291	−	0.396971i
$424$	−1.60283	+	0.470633i	−0.0778402	+	0.0228560i
$425$	0.598550	−	0.690764i	0.0290340	−	0.0335070i
$426$	4.31220	−	4.97654i	0.208927	−	0.241114i
$427$	2.18885	−	0.642705i	0.105926	−	0.0311027i
$428$	1.07691	+	2.35811i	0.0520546	+	0.113984i
$429$	7.81071	−	5.01964i	0.377104	−	0.242350i
$430$	0.762268	+	0.223822i	0.0367598	+	0.0107937i
$431$	−3.47502	−	24.1693i	−0.167386	−	1.16419i	−0.884261	−	0.466993i	$-0.845337\pi$
$431$	−3.47502	−	24.1693i	−0.167386	−	1.16419i	0.716875	−	0.697202i	$-0.245572\pi$
$432$	−0.415415	+	0.909632i	−0.0199867	+	0.0437647i
$433$	−3.41681	+	23.7645i	−0.164202	+	1.14205i	0.726403	+	0.687269i	$0.241191\pi$
$433$	−3.41681	+	23.7645i	−0.164202	+	1.14205i	−0.890605	+	0.454778i	$0.849718\pi$
$434$	1.95530	+	1.25659i	0.0938572	+	0.0603184i
$435$	2.03656	+	2.35032i	0.0976458	+	0.112689i
$436$	18.0880			0.866259
$437$	5.25599	+	36.3598i	0.251428	+	1.73932i
$438$	−2.24293			−0.107172
$439$	24.9044	+	28.7412i	1.18862	+	1.37174i	0.911704	+	0.410849i	$0.134768\pi$
$439$	24.9044	+	28.7412i	1.18862	+	1.37174i	0.276918	+	0.960894i	$0.410687\pi$
$440$	2.95323	+	1.89792i	0.140790	+	0.0904800i
$441$	−0.142315	+	0.989821i	−0.00677690	+	0.0471344i
$442$	−2.75661	+	6.03614i	−0.131119	+	0.287110i
$443$	5.44837	+	37.8942i	0.258860	+	1.80041i	0.540987	+	0.841031i	$0.318051\pi$
$443$	5.44837	+	37.8942i	0.258860	+	1.80041i	−0.282127	+	0.959377i	$0.591040\pi$
$444$	−2.71062	−	0.795910i	−0.128640	−	0.0377722i
$445$	−15.8400	+	10.1798i	−0.750889	+	0.482567i
$446$	0.588776	+	1.28924i	0.0278794	+	0.0610473i
$447$	−5.43345	+	1.59541i	−0.256994	+	0.0754601i
$448$	−0.654861	+	0.755750i	−0.0309393	+	0.0357058i
$449$	16.7726	−	19.3566i	0.791549	−	0.913496i	−0.206337	−	0.978481i	$-0.566154\pi$
$449$	16.7726	−	19.3566i	0.791549	−	0.913496i	0.997886	+	0.0649847i	$0.0206998\pi$
$450$	0.720510	−	0.211561i	0.0339652	−	0.00997308i
$451$	2.91140	+	6.37508i	0.137093	+	0.300191i
$452$	1.47680	−	0.949079i	0.0694626	−	0.0446409i
$453$	−9.26296	−	2.71985i	−0.435212	−	0.127790i
$454$	2.70525	+	18.8154i	0.126964	+	0.883051i
$455$	−4.66842	+	10.2224i	−0.218859	+	0.479234i
$456$	−1.09018	+	7.58236i	−0.0510523	+	0.355077i
$457$	−15.6858	−	10.0807i	−0.733752	−	0.471554i	0.119644	−	0.992817i	$-0.461825\pi$
$457$	−15.6858	−	10.0807i	−0.733752	−	0.471554i	−0.853396	+	0.521263i	$0.825461\pi$
$458$	4.49367	+	5.18597i	0.209975	+	0.242324i
$459$	−1.21718			−0.0568129
$460$	−9.48745	−	2.77793i	−0.442355	−	0.129522i
$461$	31.6939			1.47613			0.738066	−	0.674728i	$-0.235739\pi$
$461$	31.6939			1.47613			0.738066	+	0.674728i	$0.235739\pi$
$462$	1.11525	+	1.28707i	0.0518861	+	0.0598797i
$463$	−17.4037	−	11.1847i	−0.808817	−	0.519795i	0.0696652	−	0.997570i	$-0.477807\pi$
$463$	−17.4037	−	11.1847i	−0.808817	−	0.519795i	−0.878482	+	0.477775i	$0.841443\pi$
$464$	−0.214710	+	1.49334i	−0.00996767	+	0.0693266i
$465$	−1.99028	+	4.35811i	−0.0922972	+	0.202103i
$466$	−1.28831	−	8.96041i	−0.0596799	−	0.415083i
$467$	−0.692207	−	0.203250i	−0.0320315	−	0.00940530i	0.265678	−	0.964062i	$-0.414404\pi$
$467$	−0.692207	−	0.203250i	−0.0320315	−	0.00940530i	−0.297709	+	0.954657i	$0.596223\pi$
$468$	−4.58635	+	2.94747i	−0.212004	+	0.136247i
$469$	3.38349	+	7.40882i	0.156235	+	0.342108i
$470$	17.7522	−	5.21252i	0.818849	−	0.240436i
$471$	−9.78720	+	11.2950i	−0.450970	+	0.520448i
$472$	−0.784082	+	0.904878i	−0.0360903	+	0.0416504i
$473$	0.629772	−	0.184918i	0.0289570	−	0.00850253i
$474$	0.158264	+	0.346550i	0.00726930	+	0.0159176i
$475$	4.83919	−	3.10996i	0.222037	−	0.142695i
$476$	−1.16787	−	0.342918i	−0.0535293	−	0.0157176i
$477$	−0.237736	−	1.65349i	−0.0108852	−	0.0757082i
$478$	2.08463	−	4.56471i	0.0953488	−	0.208785i
$479$	−2.60980	+	18.1515i	−0.119245	+	0.829364i	0.839146	+	0.543906i	$0.183055\pi$
$479$	−2.60980	+	18.1515i	−0.119245	+	0.829364i	−0.958391	+	0.285459i	$0.907854\pi$
$480$	−1.73410	−	1.11444i	−0.0791504	−	0.0508669i
$481$	−10.0859	−	11.6398i	−0.459879	−	0.530729i
$482$	−30.0735			−1.36981
$483$	−4.03648	−	2.58975i	−0.183666	−	0.117838i
$484$	−8.09968			−0.368167
$485$	20.5244	+	23.6864i	0.931964	+	1.07554i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	3.72492	−	25.9074i	0.168792	−	1.17398i	−0.712593	−	0.701578i	$-0.752479\pi$
$487$	3.72492	−	25.9074i	0.168792	−	1.17398i	0.881385	−	0.472398i	$-0.156612\pi$
$488$	−0.947670	+	2.07511i	−0.0428990	+	0.0939357i
$489$	−2.20860	−	15.3612i	−0.0998765	−	0.694656i
$490$	−1.97783	−	0.580743i	−0.0893492	−	0.0262353i
$491$	22.3654	−	14.3733i	1.00933	−	0.648660i	0.0721140	−	0.997396i	$-0.477025\pi$
$491$	22.3654	−	14.3733i	1.00933	−	0.648660i	0.937221	+	0.348736i	$0.113389\pi$
$492$	−1.70954	−	3.74337i	−0.0770720	−	0.168764i
$493$	−1.76197	+	0.517360i	−0.0793549	+	0.0233007i
$494$	−27.3487	+	31.5621i	−1.23048	+	1.42005i
$495$	−2.29889	+	2.65306i	−0.103328	+	0.119246i
$496$	−2.23012	+	0.654821i	−0.100135	+	0.0294023i
$497$	2.73547	+	5.98984i	0.122703	+	0.268681i
$498$	9.05430	−	5.81885i	0.405733	−	0.260749i
$499$	−29.4673	−	8.65238i	−1.31914	−	0.387334i	−0.454956	−	0.890514i	$-0.650345\pi$
$499$	−29.4673	−	8.65238i	−1.31914	−	0.387334i	−0.864181	+	0.503181i	$0.832163\pi$
$500$	1.68708	+	11.7339i	0.0754484	+	0.524755i
$501$	0.122587	−	0.268428i	0.00547679	−	0.0119925i
$502$	2.96654	−	20.6327i	0.132403	−	0.920884i
$503$	−2.43112	−	1.56239i	−0.108398	−	0.0696633i	0.485318	−	0.874337i	$-0.338704\pi$
$503$	−2.43112	−	1.56239i	−0.108398	−	0.0696633i	−0.593717	+	0.804674i	$0.702340\pi$
$504$	−0.654861	−	0.755750i	−0.0291698	−	0.0336638i
$505$	5.02214			0.223482
$506$	−7.83486	+	2.30700i	−0.348302	+	0.102559i
$507$	−16.7222			−0.742660
$508$	−1.38679	−	1.60044i	−0.0615289	−	0.0710081i
$509$	−34.3197	−	22.0559i	−1.52119	−	0.977612i	−0.991598	−	0.129361i	$-0.958707\pi$
$509$	−34.3197	−	22.0559i	−1.52119	−	0.977612i	−0.529596	−	0.848250i	$-0.677656\pi$
$510$	0.357068	−	2.48346i	0.0158112	−	0.109969i
$511$	0.931749	−	2.04025i	0.0412181	−	0.0902551i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	−7.35004	−	2.15817i	−0.324512	−	0.0952854i
$514$	−20.4057	+	13.1140i	−0.900058	+	0.578432i
$515$	2.26312	+	4.95553i	0.0997248	+	0.218367i
$516$	−0.369795	+	0.108582i	−0.0162793	+	0.00478004i
$517$	10.0100	−	11.5522i	0.440241	−	0.508065i
$518$	1.85002	−	2.13503i	0.0812851	−	0.0938080i
$519$	1.98027	−	0.581460i	0.0869243	−	0.0255233i
$520$	−4.66842	−	10.2224i	−0.204724	−	0.448282i
$521$	24.2754	−	15.6009i	1.06352	−	0.683486i	0.112830	−	0.993614i	$-0.464008\pi$
$521$	24.2754	−	15.6009i	1.06352	−	0.683486i	0.950695	+	0.310128i	$0.100372\pi$
$522$	−1.44758	−	0.425049i	−0.0633591	−	0.0186039i
$523$	−2.60380	−	18.1098i	−0.113856	−	0.791888i	−0.964108	−	0.265511i	$-0.914459\pi$
$523$	−2.60380	−	18.1098i	−0.113856	−	0.791888i	0.850251	−	0.526377i	$-0.176450\pi$
$524$	−0.497868	+	1.09018i	−0.0217495	+	0.0476247i
$525$	−0.106868	+	0.743285i	−0.00466411	+	0.0324396i
$526$	−1.40463	−	0.902699i	−0.0612446	−	0.0393595i
$527$	−1.85263	−	2.13805i	−0.0807017	−	0.0931347i
$528$	−1.70303			−0.0741150
$529$	19.3299	−	12.4642i	0.840430	−	0.541921i
$530$	3.44344			0.149573
$531$	−0.784082	−	0.904878i	−0.0340262	−	0.0392684i
$532$	−6.44428	−	4.14149i	−0.279395	−	0.179556i
$533$	3.19292	−	22.2072i	0.138301	−	0.961902i
$534$	3.79458	−	8.30897i	0.164208	−	0.359564i
$535$	−0.760494	−	5.28935i	−0.0328790	−	0.228679i
$536$	−7.81493	−	2.29467i	−0.337554	−	0.0991147i
$537$	8.70900	−	5.59694i	0.375821	−	0.241526i
$538$	−5.30290	−	11.6117i	−0.228624	−	0.500618i
$539$	−1.63405	+	0.479800i	−0.0703834	+	0.0206664i
$540$	1.34988	−	1.55785i	0.0580897	−	0.0670391i
$541$	−11.4195	+	13.1787i	−0.490961	+	0.566599i	−0.946122	−	0.323810i	$-0.895036\pi$
$541$	−11.4195	+	13.1787i	−0.490961	+	0.566599i	0.455161	+	0.890409i	$0.349582\pi$
$542$	21.0841	−	6.19085i	0.905640	−	0.265920i
$543$	−10.0061	−	21.9104i	−0.429405	−	0.940265i
$544$	1.02395	−	0.658055i	0.0439016	−	0.0282139i
$545$	−35.7750	−	10.5045i	−1.53243	−	0.449963i
$546$	−0.775873	−	5.39632i	−0.0332043	−	0.230941i
$547$	4.02288	−	8.80888i	0.172006	−	0.376640i	−0.803922	−	0.594735i	$-0.797257\pi$
$547$	4.02288	−	8.80888i	0.172006	−	0.376640i	0.975928	+	0.218095i	$0.0699842\pi$
$548$	1.05229	−	7.31883i	0.0449515	−	0.312645i
$549$	−1.91912	−	1.23334i	−0.0819060	−	0.0526378i
$550$	0.837472	+	0.966494i	0.0357099	+	0.0412114i
$551$	−11.5571			−0.492350
$552$	4.60054	−	1.35464i	0.195812	−	0.0576575i
$553$	−0.380978			−0.0162008
$554$	−8.67682	−	10.0136i	−0.368643	−	0.425437i
$555$	4.89892	+	3.14835i	0.207948	+	0.133640i
$556$	−2.41520	+	16.7981i	−0.102427	+	0.712398i
$557$	−6.23122	+	13.6445i	−0.264025	+	0.578134i	−0.994492	−	0.104814i	$-0.966575\pi$
$557$	−6.23122	+	13.6445i	−0.264025	+	0.578134i	0.730467	+	0.682948i	$0.239303\pi$
$558$	−0.330777	−	2.30061i	−0.0140029	−	0.0973925i
$559$	−2.01605	−	0.591966i	−0.0852698	−	0.0250375i
$560$	1.73410	−	1.11444i	0.0732791	−	0.0470936i
$561$	−0.861109	−	1.88557i	−0.0363561	−	0.0796087i
$562$	13.2431	−	3.88853i	0.558627	−	0.164028i
$563$	−9.09243	+	10.4932i	−0.383200	+	0.442236i	−0.914278	−	0.405086i	$-0.867241\pi$
$563$	−9.09243	+	10.4932i	−0.383200	+	0.442236i	0.531078	+	0.847323i	$0.321787\pi$
$564$	−5.87777	+	6.78331i	−0.247499	+	0.285629i
$565$	−3.47202	+	1.01948i	−0.146069	+	0.0428897i
$566$	−4.61692	−	10.1096i	−0.194064	−	0.424940i
$567$	0.841254	−	0.540641i	0.0353293	−	0.0227048i
$568$	−6.31817	−	1.85518i	−0.265105	−	0.0778417i
$569$	3.68145	+	25.6050i	0.154334	+	1.07342i	0.908846	+	0.417132i	$0.136965\pi$
$569$	3.68145	+	25.6050i	0.154334	+	1.07342i	−0.754511	+	0.656287i	$0.772126\pi$
$570$	6.55960	−	14.3635i	0.274751	−	0.601621i
$571$	1.15741	−	8.04993i	0.0484359	−	0.336879i	−0.951166	−	0.308679i	$-0.900113\pi$
$571$	1.15741	−	8.04993i	0.0484359	−	0.336879i	0.999602	−	0.0282005i	$-0.00897770\pi$
$572$	−7.81071	−	5.01964i	−0.326582	−	0.209882i
$573$	−10.9617	−	12.6505i	−0.457933	−	0.528483i
$574$	4.11526			0.171768
$575$	−3.03111	−	1.94472i	−0.126406	−	0.0811003i
$576$	1.00000			0.0416667
$577$	−10.0832	−	11.6367i	−0.419770	−	0.484441i	0.505997	−	0.862535i	$-0.331125\pi$
$577$	−10.0832	−	11.6367i	−0.419770	−	0.484441i	−0.925767	+	0.378095i	$0.876579\pi$
$578$	−13.0550	−	8.38993i	−0.543016	−	0.348975i
$579$	−2.14087	+	14.8901i	−0.0889716	+	0.618811i
$580$	1.29191	−	2.82888i	0.0536435	−	0.117463i
$581$	1.53172	+	10.6533i	0.0635463	+	0.441974i
$582$	−14.5887	−	4.28362i	−0.604720	−	0.177562i
$583$	2.39329	−	1.53807i	0.0991199	−	0.0637005i
$584$	0.931749	+	2.04025i	0.0385560	+	0.0844259i
$585$	10.7827	−	3.16610i	0.445812	−	0.130902i
$586$	4.48821	−	5.17967i	0.185406	−	0.213970i
$587$	9.16011	−	10.5713i	0.378078	−	0.436326i	−0.534537	−	0.845145i	$-0.679514\pi$
$587$	9.16011	−	10.5713i	0.378078	−	0.436326i	0.912615	+	0.408820i	$0.134059\pi$
$588$	0.959493	−	0.281733i	0.0395688	−	0.0116185i
$589$	−7.39632	−	16.1957i	−0.304760	−	0.667331i
$590$	2.07628	−	1.33435i	0.0854792	−	0.0549341i
$591$	−21.7439	−	6.38458i	−0.894424	−	0.262627i
$592$	0.402047	+	2.79630i	0.0165240	+	0.114927i
$593$	19.8654	−	43.4991i	0.815772	−	1.78629i	0.235489	−	0.971877i	$-0.424331\pi$
$593$	19.8654	−	43.4991i	0.815772	−	1.78629i	0.580283	−	0.814415i	$-0.302942\pi$
$594$	0.242367	−	1.68570i	0.00994443	−	0.0691650i
$595$	2.11070	+	1.35647i	0.0865304	+	0.0556097i
$596$	3.70837	+	4.27969i	0.151901	+	0.175303i
$597$	−8.84908			−0.362169
$598$	25.0925	+	7.34707i	1.02611	+	0.300444i
$599$	25.1176			1.02628			0.513139	−	0.858305i	$-0.328483\pi$
$599$	25.1176			1.02628			0.513139	+	0.858305i	$0.328483\pi$
$600$	−0.491753	−	0.567514i	−0.0200757	−	0.0231686i
$601$	−31.2876	−	20.1073i	−1.27625	−	0.820194i	−0.285827	−	0.958281i	$-0.592268\pi$
$601$	−31.2876	−	20.1073i	−1.27625	−	0.820194i	−0.990420	+	0.138087i	$0.955905\pi$
$602$	0.0548490	−	0.381484i	0.00223548	−	0.0155481i
$603$	3.38349	−	7.40882i	0.137787	−	0.301710i
$604$	1.37391	+	9.55575i	0.0559036	+	0.388818i
$605$	16.0198	+	4.70383i	0.651297	+	0.191238i
$606$	−2.04960	+	1.31720i	−0.0832592	+	0.0535074i
$607$	9.19144	+	20.1265i	0.373069	+	0.816908i	0.999305	+	0.0372739i	$0.0118674\pi$
$607$	9.19144	+	20.1265i	0.373069	+	0.816908i	−0.626236	+	0.779634i	$0.715405\pi$
$608$	7.35004	−	2.15817i	0.298083	−	0.0875252i
$609$	0.987987	−	1.14020i	0.0400353	−	0.0462031i
$610$	3.07943	−	3.55386i	0.124683	−	0.143891i
$611$	−46.9511	+	13.7861i	−1.89944	+	0.557726i
$612$	0.505633	+	1.10718i	0.0204390	+	0.0447552i
$613$	−34.2095	+	21.9851i	−1.38171	+	0.887971i	−0.999350	−	0.0360431i	$-0.988525\pi$
$613$	−34.2095	+	21.9851i	−1.38171	+	0.887971i	−0.382359	+	0.924014i	$0.624888\pi$
$614$	8.34626	+	2.45068i	0.336828	+	0.0989015i
$615$	1.20724	+	8.39655i	0.0486807	+	0.338582i
$616$	0.707465	−	1.54913i	0.0285046	−	0.0624163i
$617$	1.28950	−	8.96867i	0.0519133	−	0.361065i	−0.947262	−	0.320460i	$-0.896162\pi$
$617$	1.28950	−	8.96867i	0.0519133	−	0.361065i	0.999175	−	0.0406047i	$-0.0129284\pi$
$618$	−2.22333	−	1.42885i	−0.0894356	−	0.0574768i
$619$	12.3291	+	14.2286i	0.495549	+	0.571895i	0.947340	−	0.320230i	$-0.103760\pi$
$619$	12.3291	+	14.2286i	0.495549	+	0.571895i	−0.451791	+	0.892124i	$0.649215\pi$
$620$	4.79107			0.192414
$621$	0.686130	+	4.74650i	0.0275335	+	0.190470i
$622$	−9.36155			−0.375364
$623$	5.98178	+	6.90334i	0.239655	+	0.276577i
$624$	4.58635	+	2.94747i	0.183601	+	0.117993i
$625$	2.94328	−	20.4710i	0.117731	−	0.818838i
$626$	2.63367	−	5.76694i	0.105263	−	0.230493i
$627$	−1.85661	−	12.9130i	−0.0741459	−	0.515696i
$628$	14.3401	+	4.21062i	0.572231	+	0.168022i
$629$	−2.89272	+	1.85904i	−0.115340	+	0.0741248i
$630$	0.856306	+	1.87505i	0.0341161	+	0.0747038i
$631$	−28.9647	+	8.50479i	−1.15307	+	0.338571i	−0.801734	−	0.597681i	$-0.796089\pi$
$631$	−28.9647	+	8.50479i	−1.15307	+	0.338571i	−0.351331	+	0.936251i	$0.614271\pi$
$632$	0.249487	−	0.287924i	0.00992408	−	0.0114530i
$633$	−3.05750	+	3.52854i	−0.121525	+	0.140247i
$634$	13.9322	−	4.09087i	0.553320	−	0.162469i
$635$	1.81339	+	3.97077i	0.0719622	+	0.157575i
$636$	−1.40531	+	0.903138i	−0.0557242	+	0.0358117i
$637$	5.23097	+	1.53595i	0.207259	+	0.0608566i
$638$	−0.365658	−	2.54321i	−0.0144765	−	0.100687i
$639$	2.73547	−	5.98984i	0.108213	−	0.236954i
$640$	−0.293358	+	2.04035i	−0.0115960	+	0.0806518i
$641$	12.2869	+	7.89630i	0.485303	+	0.311885i	0.760314	−	0.649556i	$-0.225045\pi$
$641$	12.2869	+	7.89630i	0.485303	+	0.311885i	−0.275011	+	0.961441i	$0.588682\pi$
$642$	1.69765	+	1.95919i	0.0670008	+	0.0773231i
$643$	37.0361			1.46056			0.730281	−	0.683147i	$-0.239389\pi$
$643$	37.0361			1.46056			0.730281	+	0.683147i	$0.239389\pi$
$644$	−0.678905	+	4.74753i	−0.0267526	+	0.187079i
$645$	0.794449			0.0312814
$646$	6.10591	+	7.04659i	0.240234	+	0.277244i
$647$	−37.3006	−	23.9717i	−1.46644	−	0.942423i	−0.998271	−	0.0587841i	$-0.981278\pi$
$647$	−37.3006	−	23.9717i	−1.46644	−	0.942423i	−0.468169	−	0.883639i	$-0.655086\pi$
$648$	−0.142315	+	0.989821i	−0.00559065	+	0.0388839i
$649$	0.847066	−	1.85482i	0.0332503	−	0.0728079i
$650$	−0.582625	−	4.05225i	−0.0228524	−	0.158942i
$651$	2.23012	+	0.654821i	0.0874051	+	0.0256645i
$652$	−13.0555	+	8.39027i	−0.511294	+	0.328589i
$653$	10.8101	+	23.6708i	0.423032	+	0.926310i	0.994406	+	0.105621i	$0.0336830\pi$
$653$	10.8101	+	23.6708i	0.423032	+	0.926310i	−0.571375	+	0.820689i	$0.693590\pi$
$654$	17.3553	−	5.09598i	0.678647	−	0.199269i
$655$	1.61781	−	1.86705i	0.0632132	−	0.0729519i
$656$	−2.69492	+	3.11011i	−0.105219	+	0.121429i
$657$	−2.15208	+	0.631908i	−0.0839606	+	0.0246531i
$658$	−3.72860	−	8.16450i	−0.145356	−	0.318285i
$659$	42.1420	−	27.0830i	1.64162	−	1.05501i	0.702347	−	0.711835i	$-0.252136\pi$
$659$	42.1420	−	27.0830i	1.64162	−	1.05501i	0.939273	−	0.343170i	$-0.111501\pi$
$660$	3.36831	+	0.989024i	0.131111	+	0.0384977i
$661$	−2.36347	−	16.4383i	−0.0919283	−	0.639376i	−0.982739	−	0.185000i	$-0.940772\pi$
$661$	−2.36347	−	16.4383i	−0.0919283	−	0.639376i	0.890810	−	0.454376i	$-0.150138\pi$
$662$	−12.0003	+	26.2770i	−0.466405	+	1.02129i
$663$	−0.944374	+	6.56827i	−0.0366764	+	0.255090i
$664$	−9.05430	−	5.81885i	−0.351375	−	0.225815i
$665$	10.3406	+	11.9336i	0.400989	+	0.462767i
$666$	−2.82505			−0.109469
$667$	3.01073	+	6.57932i	0.116576	+	0.254752i
$668$	−0.295095			−0.0114176
$669$	0.928147	+	1.07114i	0.0358842	+	0.0414126i
$670$	14.1240	+	9.07693i	0.545657	+	0.350673i
$671$	0.552902	−	3.84552i	0.0213445	−	0.148454i
$672$	−0.415415	+	0.909632i	−0.0160250	+	0.0350898i
$673$	2.97741	+	20.7084i	0.114771	+	0.798249i	0.963170	+	0.268892i	$0.0866576\pi$
$673$	2.97741	+	20.7084i	0.114771	+	0.798249i	−0.848399	+	0.529357i	$0.822433\pi$
$674$	−19.9103	−	5.84620i	−0.766917	−	0.225187i
$675$	0.631721	−	0.405982i	0.0243150	−	0.0156263i
$676$	6.94666	+	15.2111i	0.267179	+	0.585041i
$677$	−12.6510	+	3.71466i	−0.486217	+	0.142766i	−0.515648	−	0.856801i	$-0.672449\pi$
$677$	−12.6510	+	3.71466i	−0.486217	+	0.142766i	0.0294311	+	0.999567i	$0.490630\pi$
$678$	1.14959	−	1.32670i	0.0441497	−	0.0509515i
$679$	9.95687	−	11.4908i	0.382110	−	0.440978i
$680$	−2.40737	+	0.706866i	−0.0923183	+	0.0271071i
$681$	7.89658	+	17.2911i	0.302598	+	0.662597i
$682$	3.32993	−	2.14002i	0.127510	−	0.0819455i
$683$	42.3085	+	12.4229i	1.61889	+	0.475349i	0.960720	−	0.277519i	$-0.0895120\pi$
$683$	42.3085	+	12.4229i	1.61889	+	0.475349i	0.658171	+	0.752868i	$0.271330\pi$
$684$	1.09018	+	7.58236i	0.0416841	+	0.289919i
$685$	−6.33161	+	13.8643i	−0.241918	+	0.529727i
$686$	−0.142315	+	0.989821i	−0.00543361	+	0.0377916i
$687$	5.77270	+	3.70989i	0.220242	+	0.141541i
$688$	0.252388	+	0.291271i	0.00962218	+	0.0111046i
$689$	−9.10722			−0.346957
$690$	−9.88578	+	0.00752327i	−0.376345	+	0.000286406i
$691$	32.3580			1.23096			0.615478	−	0.788154i	$-0.288963\pi$
$691$	32.3580			1.23096			0.615478	+	0.788154i	$0.288963\pi$
$692$	−1.35155	−	1.55977i	−0.0513782	−	0.0592936i
$693$	1.43268	+	0.920729i	0.0544231	+	0.0349756i
$694$	−4.46683	+	31.0675i	−0.169559	+	1.17931i
$695$	14.5322	−	31.8211i	0.551239	−	1.20704i
$696$	0.214710	+	1.49334i	0.00813856	+	0.0566050i
$697$	−4.80609	−	1.41120i	−0.182044	−	0.0534529i
$698$	20.0711	−	12.8989i	0.759704	−	0.488232i
$699$	−3.76056	−	8.23449i	−0.142238	−	0.311457i
$700$	0.720510	−	0.211561i	0.0272327	−	0.00799625i
$701$	1.40944	−	1.62658i	0.0532338	−	0.0614351i	−0.728508	−	0.685037i	$-0.759786\pi$
$701$	1.40944	−	1.62658i	0.0532338	−	0.0614351i	0.781742	+	0.623602i	$0.214331\pi$
$702$	−3.57018	+	4.12020i	−0.134748	+	0.155507i
$703$	−20.7643	+	6.09694i	−0.783139	+	0.229950i
$704$	0.707465	+	1.54913i	0.0266636	+	0.0583851i
$705$	15.5646	−	10.0028i	0.586196	−	0.376725i
$706$	29.6451	+	8.70460i	1.11571	+	0.327602i
$707$	−0.346730	−	2.41156i	−0.0130401	−	0.0906961i
$708$	−0.497387	+	1.08913i	−0.0186930	+	0.0409319i
$709$	−3.00464	+	20.8977i	−0.112842	+	0.784831i	0.852291	+	0.523069i	$0.175213\pi$
$709$	−3.00464	+	20.8977i	−0.112842	+	0.784831i	−0.965132	+	0.261763i	$0.915696\pi$
$710$	11.4189	+	7.33847i	0.428543	+	0.275408i
$711$	0.249487	+	0.287924i	0.00935651	+	0.0107980i
$712$	−9.13443			−0.342327
$713$	−7.29318	+	8.42973i	−0.273132	+	0.315696i
$714$	−1.21718			−0.0455517
$715$	12.5331	+	14.4640i	0.468712	+	0.540923i
$716$	−8.70900	−	5.59694i	−0.325471	−	0.209167i
$717$	0.714163	−	4.96711i	0.0266709	−	0.185500i
$718$	10.3712	−	22.7097i	0.387048	−	0.847518i
$719$	2.81436	+	19.5743i	0.104958	+	0.729999i	0.972545	+	0.232714i	$0.0747606\pi$
$719$	2.81436	+	19.5743i	0.104958	+	0.729999i	−0.867587	+	0.497285i	$0.834330\pi$
$720$	−1.97783	−	0.580743i	−0.0737094	−	0.0216430i
$721$	2.22333	−	1.42885i	0.0828013	−	0.0532131i
$722$	16.4840	+	36.0949i	0.613470	+	1.34331i
$723$	−28.8553	+	8.47267i	−1.07314	+	0.315102i
$724$	−15.7737	+	18.2038i	−0.586225	+	0.676539i
$725$	0.741907	−	0.856207i	0.0275537	−	0.0317987i
$726$	−7.77159	+	2.28194i	−0.288431	+	0.0846909i
$727$	−21.3898	−	46.8371i	−0.793303	−	1.73709i	−0.666946	−	0.745106i	$-0.732399\pi$
$727$	−21.3898	−	46.8371i	−0.793303	−	1.73709i	−0.126357	−	0.991985i	$-0.540328\pi$
$728$	−4.58635	+	2.94747i	−0.169982	+	0.109241i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−0.657982	−	4.57636i	−0.0243530	−	0.169379i
$731$	−0.194874	+	0.426715i	−0.00720768	+	0.0157826i
$732$	−0.324657	+	2.25804i	−0.0119997	+	0.0834596i
$733$	−3.79890	−	2.44140i	−0.140315	−	0.0901753i	0.468600	−	0.883411i	$-0.344759\pi$
$733$	−3.79890	−	2.44140i	−0.140315	−	0.0901753i	−0.608915	+	0.793235i	$0.708395\pi$
$734$	−9.95842	−	11.4926i	−0.367572	−	0.424201i
$735$	−2.06133			−0.0760332
$736$	−3.14336	−	3.62206i	−0.115866	−	0.133511i
$737$	13.8709			0.510943
$738$	−2.69492	−	3.11011i	−0.0992014	−	0.114485i
$739$	15.2565	+	9.80478i	0.561221	+	0.360675i	0.790288	−	0.612736i	$-0.209931\pi$
$739$	15.2565	+	9.80478i	0.561221	+	0.360675i	−0.229067	+	0.973411i	$0.573568\pi$
$740$	0.828751	−	5.76409i	0.0304655	−	0.211892i
$741$	−17.3488	+	37.9887i	−0.637326	+	1.39555i
$742$	−0.237736	−	1.65349i	−0.00872757	−	0.0607016i
$743$	6.52189	+	1.91500i	0.239265	+	0.0702546i	0.399167	−	0.916878i	$-0.369299\pi$
$743$	6.52189	+	1.91500i	0.239265	+	0.0702546i	−0.159902	+	0.987133i	$0.551118\pi$
$744$	−1.95530	+	1.25659i	−0.0716846	+	0.0460689i
$745$	−4.84913	−	10.6181i	−0.177658	−	0.389017i
$746$	11.5941	−	3.40435i	0.424492	−	0.124642i
$747$	7.04818	−	8.13403i	0.257879	−	0.297609i
$748$	−1.35745	+	1.56659i	−0.0496334	+	0.0572800i
$749$	−2.48737	+	0.730358i	−0.0908865	+	0.0266867i
$750$	4.92456	+	10.7833i	0.179819	+	0.393750i
$751$	6.35823	−	4.08619i	0.232015	−	0.149107i	−0.419468	−	0.907770i	$-0.637783\pi$
$751$	6.35823	−	4.08619i	0.232015	−	0.149107i	0.651483	+	0.758663i	$0.274147\pi$
$752$	8.61203	+	2.52872i	0.314048	+	0.0922129i
$753$	−2.96654	−	20.6327i	−0.108107	−	0.751898i
$754$	−3.41684	+	7.48184i	−0.124434	+	0.272473i
$755$	2.83208	−	19.6975i	0.103070	−	0.716866i
$756$	−0.841254	−	0.540641i	−0.0305961	−	0.0196629i
$757$	−11.6052	−	13.3931i	−0.421798	−	0.486781i	0.504586	−	0.863362i	$-0.331645\pi$
$757$	−11.6052	−	13.3931i	−0.421798	−	0.486781i	−0.926384	+	0.376580i	$0.877100\pi$
$758$	36.2608			1.31705
$759$	−6.86754	+	4.42089i	−0.249276	+	0.160468i
$760$	−15.7905			−0.572780
$761$	18.0390	+	20.8182i	0.653914	+	0.754657i	0.981771	−	0.190070i	$-0.0608716\pi$
$761$	18.0390	+	20.8182i	0.653914	+	0.754657i	−0.327856	+	0.944728i	$0.606326\pi$
$762$	−1.78151	−	1.14491i	−0.0645374	−	0.0414757i
$763$	−2.57419	+	17.9039i	−0.0931920	+	0.648165i
$764$	−6.95364	+	15.2264i	−0.251574	+	0.550870i
$765$	−0.357068	−	2.48346i	−0.0129098	−	0.0897897i
$766$	−22.4105	−	6.58031i	−0.809723	−	0.237756i
$767$	−5.49136	+	3.52908i	−0.198281	+	0.127428i
$768$	−0.415415	−	0.909632i	−0.0149900	−	0.0328235i
$769$	33.2510	−	9.76338i	1.19906	−	0.352076i	0.379568	−	0.925164i	$-0.376073\pi$
$769$	33.2510	−	9.76338i	1.19906	−	0.352076i	0.819494	+	0.573087i	$0.194254\pi$
$770$	−2.29889	+	2.65306i	−0.0828464	+	0.0956098i
$771$	−15.8845	+	18.3317i	−0.572067	+	0.660200i
$772$	14.4339	−	4.23816i	0.519486	−	0.152535i
$773$	18.1799	+	39.8084i	0.653886	+	1.43181i	0.888112	+	0.459627i	$0.152017\pi$
$773$	18.1799	+	39.8084i	0.653886	+	1.43181i	−0.234226	+	0.972182i	$0.575256\pi$
$774$	−0.324224	+	0.208366i	−0.0116540	+	0.00748958i
$775$	1.67466	+	0.491724i	0.0601555	+	0.0176632i
$776$	2.16384	+	15.0498i	0.0776772	+	0.540257i
$777$	1.17357	−	2.56976i	0.0421016	−	0.0921896i
$778$	−0.525248	+	3.65318i	−0.0188311	+	0.130973i
$779$	−26.5199	−	17.0433i	−0.950174	−	0.610640i
$780$	−7.35930	−	8.49309i	−0.263505	−	0.304101i
$781$	11.2143			0.401279
$782$	2.42089	−	5.31170i	0.0865708	−	0.189946i
$783$	−1.50870			−0.0539165
$784$	−0.654861	−	0.755750i	−0.0233879	−	0.0269911i
$785$	−25.9169	−	16.6558i	−0.925015	−	0.594471i
$786$	−0.170562	+	1.18628i	−0.00608375	+	0.0423134i
$787$	22.6784	−	49.6587i	0.808396	−	1.77014i	0.194245	−	0.980953i	$-0.437774\pi$
$787$	22.6784	−	49.6587i	0.808396	−	1.77014i	0.614151	−	0.789188i	$-0.289498\pi$
$788$	3.22512	+	22.4312i	0.114890	+	0.799078i
$789$	−1.60205	−	0.470404i	−0.0570345	−	0.0167468i
$790$	−0.660653	+	0.424576i	−0.0235050	+	0.0151057i
$791$	0.729249	+	1.59683i	0.0259291	+	0.0567768i
$792$	−1.63405	+	0.479800i	−0.0580633	+	0.0170489i
$793$	−8.14450	+	9.39926i	−0.289220	+	0.333777i
$794$	5.14873	−	5.94195i	0.182722	−	0.210872i
$795$	3.30395	−	0.970129i	0.117179	−	0.0344069i
$796$	3.67604	+	8.04941i	0.130294	+	0.285304i
$797$	18.9915	−	12.2051i	0.672714	−	0.432327i	−0.159189	−	0.987248i	$-0.550888\pi$
$797$	18.9915	−	12.2051i	0.672714	−	0.432327i	0.831903	+	0.554921i	$0.187252\pi$
$798$	−7.35004	−	2.15817i	−0.260189	−	0.0763983i
$799$	1.55477	+	10.8137i	0.0550039	+	0.382561i
$800$	−0.311947	+	0.683068i	−0.0110290	+	0.0241501i
$801$	1.29997	−	9.04146i	0.0459320	−	0.319464i
$802$	8.32275	+	5.34871i	0.293886	+	0.188869i
$803$	−2.50143	−	2.88680i	−0.0882736	−	0.101873i
$804$	−8.14485			−0.287247
$805$	4.09986	−	8.99554i	0.144501	−	0.317051i
$806$	−12.6714			−0.446333
$807$	−8.35951	−	9.64738i	−0.294269	−	0.339604i
$808$	2.04960	+	1.31720i	0.0721045	+	0.0463388i
$809$	−5.94370	+	41.3394i	−0.208970	+	1.45341i	0.567559	+	0.823333i	$0.307888\pi$
$809$	−5.94370	+	41.3394i	−0.208970	+	1.45341i	−0.776528	+	0.630082i	$0.783021\pi$
$810$	0.856306	−	1.87505i	0.0300875	−	0.0658825i
$811$	4.74218	+	32.9826i	0.166520	+	1.15817i	0.886008	+	0.463670i	$0.153468\pi$
$811$	4.74218	+	32.9826i	0.166520	+	1.15817i	−0.719488	+	0.694505i	$0.755623\pi$
$812$	−1.44758	−	0.425049i	−0.0508003	−	0.0149163i
$813$	18.4859	−	11.8802i	0.648328	−	0.416655i
$814$	−1.99863	−	4.37638i	−0.0700518	−	0.153392i
$815$	30.6942	−	9.01263i	1.07517	−	0.315699i
$816$	0.797081	−	0.919880i	0.0279034	−	0.0322022i
$817$	−1.93337	+	2.23123i	−0.0676402	+	0.0780609i
$818$	−12.4482	+	3.65512i	−0.435241	+	0.127798i
$819$	−2.26476	−	4.95914i	−0.0791372	−	0.173286i
$820$	7.13627	−	4.58620i	0.249209	−	0.160157i
$821$	−8.26013	−	2.42539i	−0.288281	−	0.0846468i	0.134395	−	0.990928i	$-0.457091\pi$
$821$	−8.26013	−	2.42539i	−0.288281	−	0.0846468i	−0.422676	+	0.906281i	$0.638909\pi$
$822$	−1.05229	−	7.31883i	−0.0367028	−	0.255273i
$823$	−17.2852	+	37.8493i	−0.602524	+	1.31934i	0.325047	+	0.945698i	$0.394620\pi$
$823$	−17.2852	+	37.8493i	−0.602524	+	1.31934i	−0.927571	+	0.373646i	$0.878107\pi$
$824$	−0.376121	+	2.61598i	−0.0131028	+	0.0911320i
$825$	1.07584	+	0.691401i	0.0374560	+	0.0240715i
$826$	−0.784082	−	0.904878i	−0.0272817	−	0.0314847i
$827$	−27.5623			−0.958435			−0.479218	−	0.877696i	$-0.659079\pi$
$827$	−27.5623			−0.958435			−0.479218	+	0.877696i	$0.659079\pi$
$828$	4.03254	−	2.59589i	0.140140	−	0.0902135i
$829$	8.93770			0.310419			0.155210	−	0.987882i	$-0.450395\pi$
$829$	8.93770			0.310419			0.155210	+	0.987882i	$0.450395\pi$
$830$	14.5286	+	16.7669i	0.504295	+	0.581988i
$831$	−11.1465	−	7.16342i	−0.386668	−	0.248496i
$832$	0.775873	−	5.39632i	0.0268986	−	0.187084i
$833$	0.505633	−	1.10718i	0.0175191	−	0.0383616i
$834$	2.41520	+	16.7981i	0.0836316	+	0.581670i
$835$	0.583648	+	0.171375i	0.0201980	+	0.00593066i
$836$	−10.9748	+	7.05309i	−0.379572	+	0.243936i
$837$	−0.965535	−	2.11423i	−0.0333738	−	0.0730783i
$838$	32.5155	−	9.54741i	1.12323	−	0.329810i
$839$	−15.8988	+	18.3482i	−0.548887	+	0.633450i	−0.960624	−	0.277853i	$-0.910377\pi$
$839$	−15.8988	+	18.3482i	−0.548887	+	0.633450i	0.411736	+	0.911303i	$0.364923\pi$
$840$	1.34988	−	1.55785i	0.0465754	−	0.0537508i
$841$	25.6413	−	7.52897i	0.884184	−	0.259620i
$842$	2.59116	+	5.67384i	0.0892972	+	0.195534i
$843$	11.6112	−	7.46204i	0.399909	−	0.257006i
$844$	4.47980	+	1.31539i	0.154201	+	0.0452775i
$845$	−4.90559	−	34.1191i	−0.168757	−	1.17373i
$846$	−3.72860	+	8.16450i	−0.128192	+	0.280701i
$847$	1.15270	−	8.01724i	0.0396074	−	0.275476i
$848$	1.40531	+	0.903138i	0.0482585	+	0.0310139i
$849$	−7.27811	−	8.39939i	−0.249784	−	0.288266i
$850$	−0.914012			−0.0313503
$851$	8.88016	+	10.2325i	0.304408	+	0.350766i
$852$	−6.58491			−0.225595
$853$	29.8951	+	34.5008i	1.02359	+	1.18128i	0.983281	+	0.182096i	$0.0582881\pi$
$853$	29.8951	+	34.5008i	1.02359	+	1.18128i	0.0403070	+	0.999187i	$0.487166\pi$
$854$	−1.91912	−	1.23334i	−0.0656709	−	0.0422041i
$855$	2.24722	−	15.6297i	0.0768532	−	0.534526i
$856$	1.07691	−	2.35811i	0.0368081	−	0.0805986i
$857$	6.14978	+	42.7727i	0.210073	+	1.46109i	0.772908	+	0.634518i	$0.218801\pi$
$857$	6.14978	+	42.7727i	0.210073	+	1.46109i	−0.562836	+	0.826569i	$0.690290\pi$
$858$	−8.90851	−	2.61578i	−0.304132	−	0.0893011i
$859$	15.4972	−	9.95943i	0.528757	−	0.339811i	−0.248871	−	0.968537i	$-0.580059\pi$
$859$	15.4972	−	9.95943i	0.528757	−	0.339811i	0.777627	+	0.628725i	$0.216423\pi$
$860$	−0.330026	−	0.722656i	−0.0112538	−	0.0246424i
$861$	3.94856	−	1.15940i	0.134567	−	0.0395123i
$862$	−15.9903	+	18.4538i	−0.544631	+	0.628538i
$863$	−4.26281	+	4.91954i	−0.145108	+	0.167463i	−0.823651	−	0.567098i	$-0.808066\pi$
$863$	−4.26281	+	4.91954i	−0.145108	+	0.167463i	0.678543	+	0.734561i	$0.262612\pi$
$864$	0.959493	−	0.281733i	0.0326426	−	0.00958474i
$865$	1.76731	+	3.86987i	0.0600903	+	0.131579i
$866$	20.1975	−	12.9802i	0.686340	−	0.441084i
$867$	−14.8899	−	4.37206i	−0.505687	−	0.148483i
$868$	−0.330777	−	2.30061i	−0.0112273	−	0.0780877i
$869$	−0.269528	+	0.590185i	−0.00914313	+	0.0200207i
$870$	0.442588	−	3.07827i	0.0150051	−	0.104363i
$871$	−37.3552	−	24.0067i	−1.26573	−	0.813437i
$872$	−11.8451	−	13.6700i	−0.401127	−	0.462925i
$873$	−15.2046			−0.514597
$874$	24.0369	−	27.7828i	0.813061	−	0.939767i
$875$	−11.8545			−0.400757
$876$	1.46881	+	1.69510i	0.0496265	+	0.0572720i
$877$	0.857538	+	0.551106i	0.0289570	+	0.0186095i	0.555039	−	0.831824i	$-0.312703\pi$
$877$	0.857538	+	0.551106i	0.0289570	+	0.0186095i	−0.526082	+	0.850434i	$0.676340\pi$
$878$	5.41224	−	37.6430i	0.182654	−	1.27039i
$879$	2.84712	−	6.23433i	0.0960310	−	0.210279i
$880$	−0.499597	−	3.47478i	−0.0168414	−	0.117135i
$881$	41.1660	+	12.0874i	1.38692	+	0.407235i	0.888171	−	0.459513i	$-0.151976\pi$
$881$	41.1660	+	12.0874i	1.38692	+	0.407235i	0.498745	+	0.866749i	$0.333794\pi$
$882$	0.841254	−	0.540641i	0.0283265	−	0.0182043i
$883$	2.16003	+	4.72981i	0.0726908	+	0.159171i	0.942489	−	0.334237i	$-0.108478\pi$
$883$	2.16003	+	4.72981i	0.0726908	+	0.159171i	−0.869798	+	0.493407i	$0.835751\pi$
$884$	6.36701	−	1.86952i	0.214146	−	0.0628789i
$885$	1.61625	−	1.86525i	0.0543296	−	0.0626997i
$886$	25.0706	−	28.9330i	0.842264	−	0.972024i
$887$	−34.4150	+	10.1051i	−1.15554	+	0.339297i	−0.802698	−	0.596385i	$-0.796603\pi$
$887$	−34.4150	+	10.1051i	−1.15554	+	0.339297i	−0.352843	+	0.935683i	$0.614785\pi$
$888$	1.17357	+	2.56976i	0.0393824	+	0.0862355i
$889$	1.78151	−	1.14491i	0.0597500	−	0.0383990i
$890$	18.0664	+	5.30476i	0.605586	+	0.177816i
$891$	−0.242367	−	1.68570i	−0.00811959	−	0.0564730i
$892$	0.588776	−	1.28924i	0.0197137	−	0.0431669i
$893$	−9.78502	+	68.0563i	−0.327443	+	2.27742i
$894$	4.76388	+	3.06156i	0.159328	+	0.102394i
$895$	13.9745	+	16.1275i	0.467117	+	0.539082i
$896$	1.00000			0.0334077
$897$	26.1459	−	0.0198976i	0.872988	−	0.000664361i
$898$	−25.6125			−0.854700
$899$	−2.29634	−	2.65012i	−0.0765874	−	0.0883865i
$900$	−0.631721	−	0.405982i	−0.0210574	−	0.0135327i
$901$	−0.289367	+	2.01259i	−0.00964021	+	0.0670491i
$902$	2.91140	−	6.37508i	0.0969391	−	0.212267i
$903$	−0.0548490	−	0.381484i	−0.00182526	−	0.0126950i
$904$	−1.68436	−	0.494573i	−0.0560210	−	0.0164493i
$905$	41.7694	−	26.8436i	1.38846	−	0.892311i
$906$	4.01042	+	8.78160i	0.133237	+	0.291749i
$907$	46.7229	−	13.7191i	1.55141	−	0.455535i	0.609887	−	0.792488i	$-0.291215\pi$
$907$	46.7229	−	13.7191i	1.55141	−	0.455535i	0.941521	+	0.336953i	$0.109396\pi$
$908$	12.4482	−	14.3660i	0.413108	−	0.476751i
$909$	−1.59548	+	1.84128i	−0.0529186	+	0.0610713i
$910$	10.7827	−	3.16610i	0.357445	−	0.104955i
$911$	−7.11189	−	15.5729i	−0.235627	−	0.515952i	0.754470	−	0.656335i	$-0.227894\pi$
$911$	−7.11189	−	15.5729i	−0.235627	−	0.515952i	−0.990097	+	0.140383i	$0.955167\pi$
$912$	6.44428	−	4.14149i	0.213392	−	0.137138i
$913$	17.5870	+	5.16402i	0.582046	+	0.170904i
$914$	2.65357	+	18.4560i	0.0877723	+	0.610470i
$915$	1.95346	−	4.27748i	0.0645793	−	0.141409i
$916$	0.976567	−	6.79217i	0.0322667	−	0.224420i
$917$	−1.00823	−	0.647949i	−0.0332946	−	0.0213972i
$918$	0.797081	+	0.919880i	0.0263076	+	0.0303606i
$919$	28.0363			0.924833			0.462417	−	0.886663i	$-0.346982\pi$
$919$	28.0363			0.924833			0.462417	+	0.886663i	$0.346982\pi$
$920$	4.11354	+	8.98929i	0.135620	+	0.296368i
$921$	8.69861			0.286629
$922$	−20.7551	−	23.9527i	−0.683533	−	0.788839i
$923$	−30.2007	−	19.4088i	−0.994068	−	0.638849i
$924$	0.242367	−	1.68570i	0.00797328	−	0.0554554i
$925$	0.881267	−	1.92970i	0.0289759	−	0.0634483i
$926$	2.94418	+	20.4772i	0.0967517	+	0.672923i
$927$	−2.53583	−	0.744586i	−0.0832875	−	0.0244554i
$928$	1.26920	−	0.815664i	0.0416634	−	0.0267755i
$929$	−0.817753	−	1.79063i	−0.0268296	−	0.0587487i	0.895743	−	0.444573i	$-0.146644\pi$
$929$	−0.817753	−	1.79063i	−0.0268296	−	0.0587487i	−0.922572	+	0.385824i	$0.873917\pi$
$930$	4.59700	−	1.34980i	0.150742	−	0.0442617i
$931$	5.01645	−	5.78930i	0.164408	−	0.189737i
$932$	−5.92816	+	6.84146i	−0.194183	+	0.224099i
$933$	−8.98234	+	2.63745i	−0.294069	+	0.0863463i
$934$	0.299693	+	0.656235i	0.00980624	+	0.0214727i
$935$	3.59460	−	2.31011i	0.117556	−	0.0755486i
$936$	5.23097	+	1.53595i	0.170980	+	0.0502042i
$937$	−2.85438	−	19.8526i	−0.0932485	−	0.648558i	−0.981819	−	0.189818i	$-0.939210\pi$
$937$	−2.85438	−	19.8526i	−0.0932485	−	0.648558i	0.888571	−	0.458740i	$-0.151699\pi$
$938$	3.38349	−	7.40882i	0.110475	−	0.241907i
$939$	0.902256	−	6.27533i	0.0294440	−	0.204788i
$940$	−15.5646	−	10.0028i	−0.507661	−	0.326254i
$941$	32.5747	+	37.5932i	1.06190	+	1.22550i	0.973324	+	0.229433i	$0.0736872\pi$
$941$	32.5747	+	37.5932i	1.06190	+	1.22550i	0.0885791	+	0.996069i	$0.471767\pi$
$942$	14.9455			0.486950
$943$	−2.79387	+	19.5373i	−0.0909809	+	0.636223i
$944$	1.19733			0.0389696
$945$	1.34988	+	1.55785i	0.0439117	+	0.0506768i
$946$	−0.552165	−	0.354855i	−0.0179524	−	0.0115373i
$947$	−5.97802	+	41.5780i	−0.194259	+	1.35110i	0.626317	+	0.779568i	$0.284561\pi$
$947$	−5.97802	+	41.5780i	−0.194259	+	1.35110i	−0.820577	+	0.571536i	$0.806348\pi$
$948$	0.158264	−	0.346550i	0.00514017	−	0.0112554i
$949$	1.74023	+	12.1036i	0.0564904	+	0.392899i
$950$	−5.51935	−	1.62063i	−0.179071	−	0.0525801i
$951$	12.2154	−	7.85033i	0.396110	−	0.254564i
$952$	0.505633	+	1.10718i	0.0163877	+	0.0358840i
$953$	−37.6705	+	11.0611i	−1.22027	+	0.358303i	−0.827569	−	0.561365i	$-0.810277\pi$
$953$	−37.6705	+	11.0611i	−1.22027	+	0.358303i	−0.392698	+	0.919667i	$0.628458\pi$
$954$	−1.09394	+	1.26248i	−0.0354177	+	0.0408742i
$955$	22.5957	−	26.0768i	0.731180	−	0.843827i
$956$	−4.81492	+	1.41379i	−0.155726	+	0.0457252i
$957$	−1.06735	−	2.33717i	−0.0345026	−	0.0755501i
$958$	15.4271	−	9.91437i	0.498426	−	0.320319i
$959$	7.09458	+	2.08316i	0.229096	+	0.0672686i
$960$	0.293358	+	2.04035i	0.00946807	+	0.0658519i
$961$	−10.6337	+	23.2846i	−0.343023	+	0.751115i
$962$	−2.19188	+	15.2449i	−0.0706692	+	0.491515i
$963$	2.18085	+	1.40155i	0.0702769	+	0.0451642i
$964$	19.6939	+	22.7280i	0.634299	+	0.732020i
$965$	−31.0090			−0.998215
$966$	0.686130	+	4.74650i	0.0220759	+	0.152716i
$967$	7.10221			0.228392			0.114196	−	0.993458i	$-0.463571\pi$
$967$	7.10221			0.228392			0.114196	+	0.993458i	$0.463571\pi$
$968$	5.30416	+	6.12133i	0.170482	+	0.196747i
$969$	7.84383	+	5.04092i	0.251980	+	0.161938i
$970$	4.46037	−	31.0226i	0.143214	−	0.996075i
$971$	25.5543	−	55.9561i	0.820076	−	1.79572i	0.264156	−	0.964480i	$-0.414907\pi$
$971$	25.5543	−	55.9561i	0.820076	−	1.79572i	0.555920	−	0.831236i	$-0.312366\pi$
$972$	0.142315	+	0.989821i	0.00456475	+	0.0317485i
$973$	−16.2834	−	4.78123i	−0.522022	−	0.153279i
$974$	−22.0188	+	14.1506i	−0.705528	+	0.453415i
$975$	−1.70067	−	3.72396i	−0.0544652	−	0.119262i
$976$	2.18885	−	0.642705i	0.0700635	−	0.0205725i
$977$	23.7283	−	27.3839i	0.759134	−	0.876088i	−0.236286	−	0.971684i	$-0.575930\pi$
$977$	23.7283	−	27.3839i	0.759134	−	0.876088i	0.995420	+	0.0955958i	$0.0304756\pi$
$978$	−10.1629	+	11.7286i	−0.324973	+	0.375038i
$979$	14.9261	−	4.38270i	0.477040	−	0.140072i
$980$	0.856306	+	1.87505i	0.0273537	+	0.0598963i
$981$	15.2166	−	9.77912i	0.485829	−	0.312223i
$982$	−25.5089	−	7.49008i	−0.814020	−	0.239018i
$983$	−4.34503	−	30.2204i	−0.138585	−	0.963880i	−0.933862	−	0.357633i	$-0.883584\pi$
$983$	−4.34503	−	30.2204i	−0.138585	−	0.963880i	0.795277	−	0.606246i	$-0.207325\pi$
$984$	−1.70954	+	3.74337i	−0.0544982	+	0.119334i
$985$	6.64803	−	46.2380i	0.211824	−	1.47327i
$986$	1.54484	+	0.992806i	0.0491976	+	0.0316174i
$987$	−5.87777	−	6.78331i	−0.187091	−	0.215915i
$988$	41.7627			1.32865
$989$	1.77387	+	0.519389i	0.0564058	+	0.0165156i
$990$	3.51051			0.111571
$991$	25.6939	+	29.6523i	0.816193	+	0.941937i	0.999152	−	0.0411838i	$-0.0131129\pi$
$991$	25.6939	+	29.6523i	0.816193	+	0.941937i	−0.182959	+	0.983121i	$0.558567\pi$
$992$	1.95530	+	1.25659i	0.0620807	+	0.0398969i
$993$	−4.11112	+	28.5935i	−0.130463	+	0.907387i
$994$	2.73547	−	5.98984i	0.0867638	−	0.189986i
$995$	−2.59594	−	18.0552i	−0.0822970	−	0.572388i
$996$	−10.3269	−	3.03225i	−0.327220	−	0.0960805i
$997$	−29.0757	+	18.6858i	−0.920835	+	0.591785i	−0.912900	−	0.408184i	$-0.866162\pi$
$997$	−29.0757	+	18.6858i	−0.920835	+	0.591785i	−0.00793530	+	0.999969i	$0.502526\pi$
$998$	12.7579	+	27.9360i	0.403845	+	0.884298i
$999$	−2.71062	+	0.795910i	−0.0857602	+	0.0251815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.d.841.2	yes	20
23.16	even	11	inner	966.2.q.d.85.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.d.85.2	✓	20	23.16	even	11	inner
966.2.q.d.841.2	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)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.856306 - 1.87505i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{2} +(-0.841254 - 0.540641i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.856306 - 1.87505i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-1.97783 + 0.580743i) q^{10} +(-1.11525 + 1.28707i) q^{11} +(0.654861 - 0.755750i) q^{12} +(5.23097 - 1.53595i) q^{13} +(0.415415 + 0.909632i) q^{14} +(-1.73410 + 1.11444i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(-0.173222 - 1.20479i) q^{17} +(0.415415 - 0.909632i) q^{18} +(1.09018 - 7.58236i) q^{19} +(1.73410 + 1.11444i) q^{20} +(0.654861 + 0.755750i) q^{21} +1.70303 q^{22} +(-4.60054 + 1.35464i) q^{23} -1.00000 q^{24} +(0.491753 + 0.567514i) q^{25} +(-4.58635 - 2.94747i) q^{26} +(0.142315 - 0.989821i) q^{27} +(0.415415 - 0.909632i) q^{28} +(-0.214710 - 1.49334i) q^{29} +(1.97783 + 0.580743i) q^{30} +(1.95530 - 1.25659i) q^{31} +(0.415415 + 0.909632i) q^{32} +(1.63405 - 0.479800i) q^{33} +(-0.797081 + 0.919880i) q^{34} +(-1.34988 + 1.55785i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.17357 - 2.56976i) q^{37} +(-6.44428 + 4.14149i) q^{38} +(-5.23097 - 1.53595i) q^{39} +(-0.293358 - 2.04035i) q^{40} +(1.70954 - 3.74337i) q^{41} +(0.142315 - 0.989821i) q^{42} +(-0.324224 - 0.208366i) q^{43} +(-1.11525 - 1.28707i) q^{44} +2.06133 q^{45} +(4.03648 + 2.58975i) q^{46} -8.97560 q^{47} +(0.654861 + 0.755750i) q^{48} +(0.841254 + 0.540641i) q^{49} +(0.106868 - 0.743285i) q^{50} +(-0.505633 + 1.10718i) q^{51} +(0.775873 + 5.39632i) q^{52} +(-1.60283 - 0.470633i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(1.45832 + 3.19327i) q^{55} +(-0.959493 + 0.281733i) q^{56} +(-5.01645 + 5.78930i) q^{57} +(-0.987987 + 1.14020i) q^{58} +(-1.14883 + 0.337326i) q^{59} +(-0.856306 - 1.87505i) q^{60} +(-1.91912 + 1.23334i) q^{61} +(-2.23012 - 0.654821i) q^{62} +(-0.142315 - 0.989821i) q^{63} +(0.415415 - 0.909632i) q^{64} +(1.59933 - 11.1236i) q^{65} +(-1.43268 - 0.920729i) q^{66} +(-5.33375 - 6.15547i) q^{67} +1.21718 q^{68} +(4.60259 + 1.34764i) q^{69} +2.06133 q^{70} +(-4.31220 - 4.97654i) q^{71} +(0.841254 + 0.540641i) q^{72} +(-0.319203 + 2.22010i) q^{73} +(-1.17357 + 2.56976i) q^{74} +(-0.106868 - 0.743285i) q^{75} +(7.35004 + 2.15817i) q^{76} +(1.43268 - 0.920729i) q^{77} +(2.26476 + 4.95914i) q^{78} +(0.365546 - 0.107334i) q^{79} +(-1.34988 + 1.55785i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-3.94856 + 1.15940i) q^{82} +(-4.47106 - 9.79025i) q^{83} +(-0.841254 + 0.540641i) q^{84} +(-2.40737 - 0.706866i) q^{85} +(0.0548490 + 0.381484i) q^{86} +(-0.626736 + 1.37236i) q^{87} +(-0.242367 + 1.68570i) q^{88} +(-7.68437 - 4.93845i) q^{89} +(-1.34988 - 1.55785i) q^{90} -5.45181 q^{91} +(-0.686130 - 4.74650i) q^{92} -2.32427 q^{93} +(5.87777 + 6.78331i) q^{94} +(-13.2838 - 8.53697i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-6.31621 + 13.8306i) q^{97} +(-0.142315 - 0.989821i) q^{98} +(-1.63405 - 0.479800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Introduction

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