LMFDB - Embedded newform 966.2.q.d.715.1

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} - 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			715.1
Root			$3.56300 - 1.04619i$ of defining polynomial
Character	$\chi$	$=$	966.715
Dual form			966.2.q.d.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.72174 - 0.505549i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.72174 - 0.505549i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-1.17510 - 1.35614i) q^{10} +(-2.35671 + 1.51456i) q^{11} +(-0.841254 + 0.540641i) q^{12} +(-0.0968073 - 0.111722i) q^{13} +(-0.959493 + 0.281733i) q^{14} +(0.255374 - 1.77616i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-1.12468 + 2.46271i) q^{17} +(-0.959493 - 0.281733i) q^{18} +(-1.42645 - 3.12350i) q^{19} +(-0.255374 - 1.77616i) q^{20} +(-0.841254 - 0.540641i) q^{21} -2.80142 q^{22} +(-3.42760 + 3.35434i) q^{23} -1.00000 q^{24} +(-1.49745 - 0.962353i) q^{25} +(-0.0210382 - 0.146324i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-0.959493 - 0.281733i) q^{28} +(-0.588959 + 1.28964i) q^{29} +(1.17510 - 1.35614i) q^{30} +(0.296049 - 2.05906i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-1.83454 - 2.11717i) q^{33} +(-2.27758 + 1.46371i) q^{34} +(1.50957 - 0.970142i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-7.06583 + 2.07471i) q^{37} +(0.488682 - 3.39885i) q^{38} +(0.0968073 - 0.111722i) q^{39} +(0.745433 - 1.63227i) q^{40} +(0.863160 + 0.253447i) q^{41} +(-0.415415 - 0.909632i) q^{42} +(0.00386758 + 0.0268996i) q^{43} +(-2.35671 - 1.51456i) q^{44} +1.79443 q^{45} +(-4.69697 + 0.968747i) q^{46} +1.43124 q^{47} +(-0.841254 - 0.540641i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.739448 - 1.61917i) q^{50} +(-2.59770 - 0.762754i) q^{51} +(0.0614103 - 0.134470i) q^{52} +(-5.62329 + 6.48962i) q^{53} +(0.142315 - 0.989821i) q^{54} +(4.82333 - 1.41626i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(2.88870 - 1.85646i) q^{57} +(-1.19270 + 0.766499i) q^{58} +(4.94147 + 5.70276i) q^{59} +(1.72174 - 0.505549i) q^{60} +(0.620688 - 4.31698i) q^{61} +(1.36227 - 1.57214i) q^{62} +(0.415415 - 0.909632i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.110197 + 0.241297i) q^{65} +(-0.398684 - 2.77291i) q^{66} +(4.60866 + 2.96181i) q^{67} -2.70737 q^{68} +(-3.80799 - 2.91534i) q^{69} +1.79443 q^{70} +(5.51305 + 3.54302i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(0.364002 + 0.797053i) q^{73} +(-7.06583 - 2.07471i) q^{74} +(0.739448 - 1.61917i) q^{75} +(2.24866 - 2.59510i) q^{76} +(0.398684 - 2.77291i) q^{77} +(0.141841 - 0.0416482i) q^{78} +(1.94213 + 2.24134i) q^{79} +(1.50957 - 0.970142i) q^{80} +(0.841254 - 0.540641i) q^{81} +(0.589113 + 0.679872i) q^{82} +(-4.34998 + 1.27727i) q^{83} +(0.142315 - 0.989821i) q^{84} +(3.18143 - 3.67157i) q^{85} +(-0.0112894 + 0.0247204i) q^{86} +(-1.36033 - 0.399429i) q^{87} +(-1.16375 - 2.54826i) q^{88} +(0.345777 + 2.40493i) q^{89} +(1.50957 + 0.970142i) q^{90} +0.147829 q^{91} +(-4.47509 - 1.72441i) q^{92} +2.08024 q^{93} +(1.20403 + 0.773785i) q^{94} +(0.876905 + 6.09900i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(2.39358 + 0.702818i) q^{97} +(0.415415 - 0.909632i) q^{98} +(1.83454 - 2.11717i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$2$	0.841254	+	0.540641i	0.594856	+	0.382291i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	−1.72174	−	0.505549i	−0.769987	−	0.226088i	−0.126935	−	0.991911i	$-0.540514\pi$
$5$	−1.72174	−	0.505549i	−0.769987	−	0.226088i	−0.643052	+	0.765823i	$0.722332\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	−0.654861	+	0.755750i	−0.247514	+	0.285646i
$7$	−0.654861	+	0.755750i	−0.247514	+	0.285646i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$	−1.17510	−	1.35614i	−0.371600	−	0.428849i
$11$	−2.35671	+	1.51456i	−0.710574	+	0.456658i	−0.845347	−	0.534218i	$-0.820606\pi$
$11$	−2.35671	+	1.51456i	−0.710574	+	0.456658i	0.134772	+	0.990877i	$0.456970\pi$
$12$	−0.841254	+	0.540641i	−0.242849	+	0.156070i
$13$	−0.0968073	−	0.111722i	−0.0268495	−	0.0309860i	0.742166	−	0.670216i	$-0.233799\pi$
$13$	−0.0968073	−	0.111722i	−0.0268495	−	0.0309860i	−0.769016	+	0.639230i	$0.779253\pi$
$14$	−0.959493	+	0.281733i	−0.256435	+	0.0752962i
$15$	0.255374	−	1.77616i	0.0659373	−	0.458604i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−1.12468	+	2.46271i	−0.272775	+	0.597295i	−0.995597	−	0.0937402i	$-0.970118\pi$
$17$	−1.12468	+	2.46271i	−0.272775	+	0.597295i	0.722821	+	0.691035i	$0.242845\pi$
$18$	−0.959493	−	0.281733i	−0.226155	−	0.0664050i
$19$	−1.42645	−	3.12350i	−0.327251	−	0.716580i	0.672472	−	0.740123i	$-0.265233\pi$
$19$	−1.42645	−	3.12350i	−0.327251	−	0.716580i	−0.999723	+	0.0235428i	$0.992505\pi$
$20$	−0.255374	−	1.77616i	−0.0571033	−	0.397162i
$21$	−0.841254	−	0.540641i	−0.183577	−	0.117977i
$22$	−2.80142			−0.597266
$23$	−3.42760	+	3.35434i	−0.714704	+	0.699427i
$23$	−3.42760	+	3.35434i	−0.714704	+	0.699427i
$24$	−1.00000			−0.204124
$25$	−1.49745	−	0.962353i	−0.299490	−	0.192471i
$26$	−0.0210382	−	0.146324i	−0.00412594	−	0.0286965i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	−0.959493	−	0.281733i	−0.181327	−	0.0532424i
$29$	−0.588959	+	1.28964i	−0.109367	+	0.239480i	−0.956400	−	0.292060i	$-0.905659\pi$
$29$	−0.588959	+	1.28964i	−0.109367	+	0.239480i	0.847033	+	0.531540i	$0.178387\pi$
$30$	1.17510	−	1.35614i	0.214543	−	0.247596i
$31$	0.296049	−	2.05906i	0.0531719	−	0.369819i	−0.945811	−	0.324719i	$-0.894730\pi$
$31$	0.296049	−	2.05906i	0.0531719	−	0.369819i	0.998982	−	0.0450998i	$-0.0143606\pi$
$32$	−0.959493	+	0.281733i	−0.169616	+	0.0498038i
$33$	−1.83454	−	2.11717i	−0.319353	−	0.368553i
$34$	−2.27758	+	1.46371i	−0.390602	+	0.251025i
$35$	1.50957	−	0.970142i	0.255164	−	0.163984i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	−7.06583	+	2.07471i	−1.16161	+	0.341081i	−0.805060	−	0.593194i	$-0.797867\pi$
$37$	−7.06583	+	2.07471i	−1.16161	+	0.341081i	−0.356555	+	0.934274i	$0.616049\pi$
$38$	0.488682	−	3.39885i	0.0792746	−	0.551367i
$39$	0.0968073	−	0.111722i	0.0155016	−	0.0178898i
$40$	0.745433	−	1.63227i	0.117863	−	0.258085i
$41$	0.863160	+	0.253447i	0.134803	+	0.0395817i	0.348438	−	0.937332i	$-0.386712\pi$
$41$	0.863160	+	0.253447i	0.134803	+	0.0395817i	−0.213635	+	0.976914i	$0.568530\pi$
$42$	−0.415415	−	0.909632i	−0.0640999	−	0.140359i
$43$	0.00386758	+	0.0268996i	0.000589801	+	0.00410215i	0.990114	−	0.140263i	$-0.0447950\pi$
$43$	0.00386758	+	0.0268996i	0.000589801	+	0.00410215i	−0.989524	+	0.144366i	$0.953886\pi$
$44$	−2.35671	−	1.51456i	−0.355287	−	0.228329i
$45$	1.79443			0.267498
$46$	−4.69697	+	0.968747i	−0.692530	+	0.142834i
$47$	1.43124			0.208767			0.104384	−	0.994537i	$-0.466713\pi$
$47$	1.43124			0.208767			0.104384	+	0.994537i	$0.466713\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	−0.142315	−	0.989821i	−0.0203307	−	0.141403i
$50$	−0.739448	−	1.61917i	−0.104574	−	0.228985i
$51$	−2.59770	−	0.762754i	−0.363751	−	0.106807i
$52$	0.0614103	−	0.134470i	0.00851608	−	0.0186476i
$53$	−5.62329	+	6.48962i	−0.772418	+	0.891417i	−0.996538	−	0.0831441i	$-0.973504\pi$
$53$	−5.62329	+	6.48962i	−0.772418	+	0.891417i	0.224120	+	0.974562i	$0.428049\pi$
$54$	0.142315	−	0.989821i	0.0193666	−	0.134698i
$55$	4.82333	−	1.41626i	0.650378	−	0.190968i
$56$	−0.654861	−	0.755750i	−0.0875094	−	0.100991i
$57$	2.88870	−	1.85646i	0.382618	−	0.245894i
$58$	−1.19270	+	0.766499i	−0.156609	+	0.100646i
$59$	4.94147	+	5.70276i	0.643324	+	0.742436i	0.979959	−	0.199199i	$-0.0638341\pi$
$59$	4.94147	+	5.70276i	0.643324	+	0.742436i	−0.336635	+	0.941635i	$0.609289\pi$
$60$	1.72174	−	0.505549i	0.222276	−	0.0652661i
$61$	0.620688	−	4.31698i	0.0794710	−	0.552733i	−0.910721	−	0.413022i	$-0.864473\pi$
$61$	0.620688	−	4.31698i	0.0794710	−	0.552733i	0.990192	−	0.139711i	$-0.0446175\pi$
$62$	1.36227	−	1.57214i	0.173008	−	0.199662i
$63$	0.415415	−	0.909632i	0.0523374	−	0.114603i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	0.110197	+	0.241297i	0.0136682	+	0.0299292i
$66$	−0.398684	−	2.77291i	−0.0490746	−	0.341322i
$67$	4.60866	+	2.96181i	0.563037	+	0.361842i	0.790989	−	0.611830i	$-0.209566\pi$
$67$	4.60866	+	2.96181i	0.563037	+	0.361842i	−0.227952	+	0.973672i	$0.573203\pi$
$68$	−2.70737			−0.328317
$69$	−3.80799	−	2.91534i	−0.458428	−	0.350966i
$70$	1.79443			0.214475
$71$	5.51305	+	3.54302i	0.654279	+	0.420480i	0.825228	−	0.564800i	$-0.191047\pi$
$71$	5.51305	+	3.54302i	0.654279	+	0.420480i	−0.170949	+	0.985280i	$0.554683\pi$
$72$	−0.142315	−	0.989821i	−0.0167720	−	0.116652i
$73$	0.364002	+	0.797053i	0.0426032	+	0.0932880i	0.929737	−	0.368225i	$-0.120034\pi$
$73$	0.364002	+	0.797053i	0.0426032	+	0.0932880i	−0.887134	+	0.461512i	$0.847307\pi$
$74$	−7.06583	−	2.07471i	−0.821386	−	0.241181i
$75$	0.739448	−	1.61917i	0.0853841	−	0.186965i
$76$	2.24866	−	2.59510i	0.257940	−	0.297678i
$77$	0.398684	−	2.77291i	0.0454343	−	0.316002i
$78$	0.141841	−	0.0416482i	0.0160603	−	0.00471573i
$79$	1.94213	+	2.24134i	0.218507	+	0.252170i	0.854411	−	0.519598i	$-0.173918\pi$
$79$	1.94213	+	2.24134i	0.218507	+	0.252170i	−0.635904	+	0.771768i	$0.719373\pi$
$80$	1.50957	−	0.970142i	0.168775	−	0.108465i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	0.589113	+	0.679872i	0.0650566	+	0.0750793i
$83$	−4.34998	+	1.27727i	−0.477472	+	0.140198i	−0.511608	−	0.859219i	$-0.670950\pi$
$83$	−4.34998	+	1.27727i	−0.477472	+	0.140198i	0.0341365	+	0.999417i	$0.489132\pi$
$84$	0.142315	−	0.989821i	0.0155278	−	0.107998i
$85$	3.18143	−	3.67157i	0.345075	−	0.398238i
$86$	−0.0112894	+	0.0247204i	−0.00121737	+	0.00266567i
$87$	−1.36033	−	0.399429i	−0.145843	−	0.0428233i
$88$	−1.16375	−	2.54826i	−0.124057	−	0.271646i
$89$	0.345777	+	2.40493i	0.0366523	+	0.254922i	0.999907	−	0.0136687i	$-0.00435103\pi$
$89$	0.345777	+	2.40493i	0.0366523	+	0.254922i	−0.963254	+	0.268591i	$0.913442\pi$
$90$	1.50957	+	0.970142i	0.159123	+	0.102262i
$91$	0.147829			0.0154967
$92$	−4.47509	−	1.72441i	−0.466560	−	0.179782i
$93$	2.08024			0.215711
$94$	1.20403	+	0.773785i	0.124187	+	0.0798098i
$95$	0.876905	+	6.09900i	0.0899685	+	0.625745i
$96$	−0.415415	−	0.909632i	−0.0423981	−	0.0928389i
$97$	2.39358	+	0.702818i	0.243031	+	0.0713604i	0.400980	−	0.916087i	$-0.368670\pi$
$97$	2.39358	+	0.702818i	0.243031	+	0.0713604i	−0.157948	+	0.987447i	$0.550488\pi$
$98$	0.415415	−	0.909632i	0.0419633	−	0.0918867i
$99$	1.83454	−	2.11717i	0.184378	−	0.212784i
$100$	0.253324	−	1.76191i	0.0253324	−	0.176191i
$101$	4.81907	−	1.41501i	0.479515	−	0.140798i	−0.0330375	−	0.999454i	$-0.510518\pi$
$101$	4.81907	−	1.41501i	0.479515	−	0.140798i	0.512553	+	0.858656i	$0.328700\pi$
$102$	−1.77295	−	2.04609i	−0.175548	−	0.202593i
$103$	5.32823	−	3.42425i	0.525006	−	0.337401i	−0.251143	−	0.967950i	$-0.580806\pi$
$103$	5.32823	−	3.42425i	0.525006	−	0.337401i	0.776150	+	0.630549i	$0.217170\pi$
$104$	0.124362	−	0.0799223i	0.0121947	−	0.00783703i
$105$	1.17510	+	1.35614i	0.114678	+	0.132346i
$106$	−8.23916	+	2.41924i	−0.800258	+	0.234977i
$107$	−0.915132	+	6.36488i	−0.0884691	+	0.615316i	0.896559	+	0.442924i	$0.146059\pi$
$107$	−0.915132	+	6.36488i	−0.0884691	+	0.615316i	−0.985028	+	0.172392i	$0.944850\pi$
$108$	0.654861	−	0.755750i	0.0630140	−	0.0727220i
$109$	−2.58028	+	5.65003i	−0.247146	+	0.541175i	−0.992027	−	0.126022i	$-0.959779\pi$
$109$	−2.58028	+	5.65003i	−0.247146	+	0.541175i	0.744881	+	0.667197i	$0.232506\pi$
$110$	4.82333	+	1.41626i	0.459886	+	0.135035i
$111$	−3.05917	−	6.69864i	−0.290363	−	0.635807i
$112$	−0.142315	−	0.989821i	−0.0134475	−	0.0935293i
$113$	0.144409	+	0.0928063i	0.0135849	+	0.00873048i	0.547416	−	0.836861i	$-0.315612\pi$
$113$	0.144409	+	0.0928063i	0.0135849	+	0.00873048i	−0.533831	+	0.845591i	$0.679248\pi$
$114$	3.43381			0.321605
$115$	7.59722	−	4.04248i	0.708445	−	0.376963i
$116$	−1.41776			−0.131636
$117$	0.124362	+	0.0799223i	0.0114972	+	0.00738882i
$118$	1.07388	+	7.46903i	0.0988590	+	0.687580i
$119$	−1.12468	−	2.46271i	−0.103099	−	0.225756i
$120$	1.72174	+	0.505549i	0.157173	+	0.0461501i
$121$	−1.30940	+	2.86718i	−0.119036	+	0.260653i
$122$	2.85609	−	3.29611i	0.258579	−	0.298416i
$123$	−0.128026	+	0.890443i	−0.0115438	+	0.0802886i
$124$	1.99597	−	0.586070i	0.179244	−	0.0526307i
$125$	7.96721	+	9.19466i	0.712609	+	0.822395i
$126$	0.841254	−	0.540641i	0.0749448	−	0.0481641i
$127$	1.02357	−	0.657807i	0.0908270	−	0.0583710i	−0.494439	−	0.869212i	$-0.664626\pi$
$127$	1.02357	−	0.657807i	0.0908270	−	0.0583710i	0.585266	+	0.810841i	$0.300990\pi$
$128$	−0.654861	−	0.755750i	−0.0578821	−	0.0667995i
$129$	−0.0260754	+	0.00765643i	−0.00229581	+	0.000674111i
$130$	−0.0377516	+	0.262568i	−0.00331104	+	0.0230288i
$131$	2.93518	−	3.38738i	0.256448	−	0.295956i	−0.612897	−	0.790163i	$-0.709996\pi$
$131$	2.93518	−	3.38738i	0.256448	−	0.295956i	0.869345	+	0.494207i	$0.164541\pi$
$132$	1.16375	−	2.54826i	0.101292	−	0.221798i
$133$	3.29471	+	0.967415i	0.285688	+	0.0838855i
$134$	2.27578	+	4.98326i	0.196597	+	0.430488i
$135$	0.255374	+	1.77616i	0.0219791	+	0.152868i
$136$	−2.27758	−	1.46371i	−0.195301	−	0.125512i
$137$	−7.61063			−0.650220			−0.325110	−	0.945676i	$-0.605401\pi$
$137$	−7.61063			−0.650220			−0.325110	+	0.945676i	$0.605401\pi$
$138$	−1.62734	−	4.51129i	−0.138528	−	0.384027i
$139$	20.9038			1.77304			0.886519	−	0.462692i	$-0.153117\pi$
$139$	20.9038			1.77304			0.886519	+	0.462692i	$0.153117\pi$
$140$	1.50957	+	0.970142i	0.127582	+	0.0819919i
$141$	0.203686	+	1.41667i	0.0171535	+	0.119305i
$142$	2.72237	+	5.96116i	0.228456	+	0.500250i
$143$	0.397356	+	0.116674i	0.0332286	+	0.00975679i
$144$	0.415415	−	0.909632i	0.0346179	−	0.0758027i
$145$	1.66601	−	1.92268i	0.138355	−	0.159670i
$146$	−0.124701	+	0.867318i	−0.0103204	+	0.0717797i
$147$	0.959493	−	0.281733i	0.0791376	−	0.0232369i
$148$	−4.82248	−	5.56543i	−0.396405	−	0.457476i
$149$	−9.14161	+	5.87495i	−0.748910	+	0.481295i	−0.858584	−	0.512673i	$-0.828655\pi$
$149$	−9.14161	+	5.87495i	−0.748910	+	0.481295i	0.109675	+	0.993968i	$0.465019\pi$
$150$	1.49745	−	0.962353i	0.122266	−	0.0785758i
$151$	13.2335	+	15.2722i	1.07692	+	1.24284i	0.968575	+	0.248723i	$0.0800109\pi$
$151$	13.2335	+	15.2722i	1.07692	+	1.24284i	0.108349	+	0.994113i	$0.465444\pi$
$152$	3.29471	−	0.967415i	0.267236	−	0.0784677i
$153$	0.385299	−	2.67981i	0.0311496	−	0.216650i
$154$	1.83454	−	2.11717i	0.147832	−	0.170607i
$155$	−1.55068	+	3.39551i	−0.124553	+	0.272734i
$156$	0.141841	+	0.0416482i	0.0113563	+	0.00333453i
$157$	−5.07731	−	11.1178i	−0.405214	−	0.887294i	−0.996715	−	0.0809899i	$-0.974192\pi$
$157$	−5.07731	−	11.1178i	−0.405214	−	0.887294i	0.591501	−	0.806304i	$-0.298535\pi$
$158$	0.422066	+	2.93553i	0.0335777	+	0.233538i
$159$	−7.22384	−	4.64248i	−0.572888	−	0.368173i
$160$	1.79443			0.141862
$161$	−0.290438	−	4.78703i	−0.0228897	−	0.377271i
$162$	1.00000			0.0785674
$163$	−4.51403	−	2.90099i	−0.353566	−	0.227223i	0.351786	−	0.936081i	$-0.385575\pi$
$163$	−4.51403	−	2.90099i	−0.353566	−	0.227223i	−0.705352	+	0.708857i	$0.749211\pi$
$164$	0.128026	+	0.890443i	0.00999718	+	0.0695319i
$165$	2.08827	+	4.57268i	0.162572	+	0.355983i
$166$	−4.34998	−	1.27727i	−0.337624	−	0.0991352i
$167$	−4.44375	+	9.73044i	−0.343867	+	0.752964i	−0.999999	−	0.00168236i	$-0.999464\pi$
$167$	−4.44375	+	9.73044i	−0.343867	+	0.752964i	0.656131	+	0.754647i	$0.272192\pi$
$168$	0.654861	−	0.755750i	0.0505236	−	0.0583073i
$169$	1.84698	−	12.8460i	0.142076	−	0.988158i
$170$	4.66139	−	1.36871i	0.357512	−	0.104975i
$171$	2.24866	+	2.59510i	0.171960	+	0.198452i
$172$	−0.0228621	+	0.0146926i	−0.00174322	+	0.00112030i
$173$	−13.4837	+	8.66546i	−1.02515	+	0.658823i	−0.941271	−	0.337653i	$-0.890367\pi$
$173$	−13.4837	+	8.66546i	−1.02515	+	0.658823i	−0.0838778	+	0.996476i	$0.526731\pi$
$174$	−0.928435	−	1.07147i	−0.0703845	−	0.0812280i
$175$	1.70792	−	0.501490i	0.129107	−	0.0379091i
$176$	0.398684	−	2.77291i	0.0300520	−	0.209016i
$177$	−4.94147	+	5.70276i	−0.371424	+	0.428646i
$178$	−1.00932	+	2.21010i	−0.0756516	+	0.165654i
$179$	−16.3781	−	4.80905i	−1.22416	−	0.359445i	−0.395116	−	0.918631i	$-0.629296\pi$
$179$	−16.3781	−	4.80905i	−1.22416	−	0.359445i	−0.829042	+	0.559186i	$0.811114\pi$
$180$	0.745433	+	1.63227i	0.0555613	+	0.121662i
$181$	3.15231	+	21.9248i	0.234309	+	1.62966i	0.679116	+	0.734031i	$0.262364\pi$
$181$	3.15231	+	21.9248i	0.234309	+	1.62966i	−0.444806	+	0.895627i	$0.646727\pi$
$182$	0.124362	+	0.0799223i	0.00921829	+	0.00592424i
$183$	4.36138			0.322402
$184$	−2.83240	−	3.87008i	−0.208807	−	0.285306i
$185$	13.2144			0.971542
$186$	1.75001	+	1.12466i	0.128317	+	0.0824641i
$187$	−1.07939	−	7.50729i	−0.0789325	−	0.548987i
$188$	0.594557	+	1.30190i	0.0433625	+	0.0949507i
$189$	0.959493	+	0.281733i	0.0697928	+	0.0204930i
$190$	−2.55967	+	5.60490i	−0.185698	+	0.406622i
$191$	−1.69369	+	1.95462i	−0.122551	+	0.141431i	−0.813709	−	0.581272i	$-0.802555\pi$
$191$	−1.69369	+	1.95462i	−0.122551	+	0.141431i	0.691158	+	0.722703i	$0.257101\pi$
$192$	0.142315	−	0.989821i	0.0102707	−	0.0714342i
$193$	−3.10632	+	0.912097i	−0.223598	+	0.0656542i	−0.391612	−	0.920130i	$-0.628083\pi$
$193$	−3.10632	+	0.912097i	−0.223598	+	0.0656542i	0.168015	+	0.985784i	$0.446264\pi$
$194$	1.63363	+	1.88532i	0.117288	+	0.135358i
$195$	−0.223158	+	0.143415i	−0.0159807	+	0.0102702i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	13.4489	+	15.5209i	0.958195	+	1.10582i	0.994316	+	0.106468i	$0.0339542\pi$
$197$	13.4489	+	15.5209i	0.958195	+	1.10582i	−0.0361215	+	0.999347i	$0.511500\pi$
$198$	2.68795	−	0.789252i	0.191024	−	0.0560897i
$199$	−0.117663	+	0.818365i	−0.00834092	+	0.0580124i	−0.993567	−	0.113248i	$-0.963875\pi$
$199$	−0.117663	+	0.818365i	−0.00834092	+	0.0580124i	0.985226	+	0.171260i	$0.0547838\pi$
$200$	1.16567	−	1.34525i	0.0824251	−	0.0951237i
$201$	−2.27578	+	4.98326i	−0.160521	+	0.351492i
$202$	4.81907	+	1.41501i	0.339069	+	0.0995595i
$203$	−0.588959	−	1.28964i	−0.0413368	−	0.0905149i
$204$	−0.385299	−	2.67981i	−0.0269763	−	0.187624i
$205$	−1.35801	−	0.872739i	−0.0948475	−	0.0609548i
$206$	6.33368			0.441289
$207$	2.34373	−	4.18413i	0.162901	−	0.290817i
$208$	0.147829			0.0102501
$209$	8.09248	+	5.20072i	0.559768	+	0.359741i
$210$	0.255374	+	1.77616i	0.0176225	+	0.122567i
$211$	0.126154	+	0.276239i	0.00868482	+	0.0190171i	0.913925	−	0.405884i	$-0.133036\pi$
$211$	0.126154	+	0.276239i	0.00868482	+	0.0190171i	−0.905240	+	0.424901i	$0.860309\pi$
$212$	−8.23916	−	2.41924i	−0.565868	−	0.166154i
$213$	−2.72237	+	5.96116i	−0.186534	+	0.408452i
$214$	−4.21097	+	4.85972i	−0.287856	+	0.332204i
$215$	0.00694010	−	0.0482695i	0.000473311	−	0.00329195i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	1.36227	+	1.57214i	0.0924766	+	0.106724i
$218$	−5.22531	+	3.35810i	−0.353903	+	0.227439i
$219$	−0.737137	+	0.473729i	−0.0498111	+	0.0320117i
$220$	3.29196	+	3.79912i	0.221944	+	0.256137i
$221$	0.384015	−	0.112757i	0.0258317	−	0.00758486i
$222$	1.04802	−	7.28917i	0.0703388	−	0.489217i
$223$	7.46883	−	8.61949i	0.500150	−	0.577204i	−0.448399	−	0.893833i	$-0.648006\pi$
$223$	7.46883	−	8.61949i	0.500150	−	0.577204i	0.948549	+	0.316630i	$0.102551\pi$
$224$	0.415415	−	0.909632i	0.0277561	−	0.0607773i
$225$	1.70792	+	0.501490i	0.113861	+	0.0334327i
$226$	0.0713100	+	0.156147i	0.00474347	+	0.0103868i
$227$	−2.55167	−	17.7473i	−0.169360	−	1.17793i	−0.880210	−	0.474583i	$-0.842599\pi$
$227$	−2.55167	−	17.7473i	−0.169360	−	1.17793i	0.710850	−	0.703343i	$-0.248310\pi$
$228$	2.88870	+	1.85646i	0.191309	+	0.122947i
$229$	−22.7884			−1.50590			−0.752951	−	0.658076i	$-0.771370\pi$
$229$	−22.7884			−1.50590			−0.752951	+	0.658076i	$0.771370\pi$
$230$	8.57672	+	0.706616i	0.565532	+	0.0465929i
$231$	2.80142			0.184320
$232$	−1.19270	−	0.766499i	−0.0783043	−	0.0503231i
$233$	1.15624	+	8.04182i	0.0757477	+	0.526837i	0.992000	+	0.126236i	$0.0402896\pi$
$233$	1.15624	+	8.04182i	0.0757477	+	0.526837i	−0.916253	+	0.400601i	$0.868801\pi$
$234$	0.0614103	+	0.134470i	0.00401452	+	0.00879057i
$235$	−2.46422	−	0.723561i	−0.160748	−	0.0471999i
$236$	−3.13465	+	6.86393i	−0.204048	+	0.446804i
$237$	−1.94213	+	2.24134i	−0.126155	+	0.145591i
$238$	0.385299	−	2.67981i	0.0249752	−	0.173706i
$239$	19.3294	−	5.67562i	1.25031	−	0.367125i	0.411433	−	0.911440i	$-0.365029\pi$
$239$	19.3294	−	5.67562i	1.25031	−	0.367125i	0.838881	+	0.544315i	$0.183210\pi$
$240$	1.17510	+	1.35614i	0.0758525	+	0.0875384i
$241$	6.02823	−	3.87411i	0.388313	−	0.249553i	−0.331889	−	0.943319i	$-0.607686\pi$
$241$	6.02823	−	3.87411i	0.388313	−	0.249553i	0.720201	+	0.693765i	$0.244049\pi$
$242$	−2.65165	+	1.70411i	−0.170455	+	0.109545i
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$	4.18471	−	1.22874i	0.267899	−	0.0786621i
$245$	−0.255374	+	1.77616i	−0.0163152	+	0.113475i
$246$	−0.589113	+	0.679872i	−0.0375604	+	0.0433471i
$247$	−0.210871	+	0.461743i	−0.0134174	+	0.0293800i
$248$	1.99597	+	0.586070i	0.126744	+	0.0372155i
$249$	−1.88333	−	4.12392i	−0.119351	−	0.261343i
$250$	1.73144	+	12.0424i	0.109506	+	0.761631i
$251$	−11.0138	−	7.07814i	−0.695185	−	0.446768i	0.144741	−	0.989470i	$-0.453765\pi$
$251$	−11.0138	−	7.07814i	−0.695185	−	0.446768i	−0.839926	+	0.542701i	$0.817402\pi$
$252$	1.00000			0.0629941
$253$	2.99749	−	13.0965i	0.188451	−	0.823370i
$254$	1.21672			0.0763437
$255$	4.08696	+	2.62653i	0.255936	+	0.164480i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	8.21966	+	17.9985i	0.512728	+	1.12272i	0.972120	+	0.234485i	$0.0753403\pi$
$257$	8.21966	+	17.9985i	0.512728	+	1.12272i	−0.459391	+	0.888234i	$0.651932\pi$
$258$	−0.0260754	−	0.00765643i	−0.00162338	−	0.000476669i
$259$	3.05917	−	6.69864i	0.190087	−	0.416233i
$260$	−0.173714	+	0.200477i	−0.0107733	+	0.0124330i
$261$	0.201768	−	1.40333i	0.0124891	−	0.0868639i
$262$	4.30058	−	1.26276i	0.265691	−	0.0780139i
$263$	−3.88830	−	4.48734i	−0.239763	−	0.276701i	0.623097	−	0.782145i	$-0.285874\pi$
$263$	−3.88830	−	4.48734i	−0.239763	−	0.276701i	−0.862860	+	0.505444i	$0.831329\pi$
$264$	2.35671	−	1.51456i	0.145045	−	0.0932150i
$265$	12.9627	−	8.33060i	0.796290	−	0.511745i
$266$	2.24866	+	2.59510i	0.137874	+	0.159116i
$267$	−2.33125	+	0.684515i	−0.142670	+	0.0418917i
$268$	−0.779647	+	5.42256i	−0.0476245	+	0.331236i
$269$	6.03799	−	6.96821i	0.368143	−	0.424859i	−0.541209	−	0.840888i	$-0.682033\pi$
$269$	6.03799	−	6.96821i	0.368143	−	0.424859i	0.909351	+	0.416029i	$0.136579\pi$
$270$	−0.745433	+	1.63227i	−0.0453656	+	0.0993368i
$271$	−11.0067	−	3.23186i	−0.668609	−	0.196321i	−0.0702256	−	0.997531i	$-0.522372\pi$
$271$	−11.0067	−	3.23186i	−0.668609	−	0.196321i	−0.598384	+	0.801210i	$0.704190\pi$
$272$	−1.12468	−	2.46271i	−0.0681938	−	0.149324i
$273$	0.0210382	+	0.146324i	0.00127329	+	0.00885594i
$274$	−6.40247	−	4.11462i	−0.386787	−	0.248573i
$275$	4.98660			0.300703
$276$	1.06999	−	4.67495i	0.0644057	−	0.281399i
$277$	−13.1550			−0.790405			−0.395203	−	0.918594i	$-0.629326\pi$
$277$	−13.1550			−0.790405			−0.395203	+	0.918594i	$0.629326\pi$
$278$	17.5854	+	11.3015i	1.05470	+	0.677816i
$279$	0.296049	+	2.05906i	0.0177240	+	0.123273i
$280$	0.745433	+	1.63227i	0.0445481	+	0.0975468i
$281$	15.5981	+	4.58002i	0.930505	+	0.273221i	0.711648	−	0.702536i	$-0.247949\pi$
$281$	15.5981	+	4.58002i	0.930505	+	0.273221i	0.218857	+	0.975757i	$0.429767\pi$
$282$	−0.594557	+	1.30190i	−0.0354054	+	0.0775269i
$283$	15.8159	−	18.2525i	0.940156	−	1.08500i	−0.0560899	−	0.998426i	$-0.517863\pi$
$283$	15.8159	−	18.2525i	0.940156	−	1.08500i	0.996246	−	0.0865718i	$-0.0275912\pi$
$284$	−0.932643	+	6.48667i	−0.0553422	+	0.384913i
$285$	−5.91213	+	1.73596i	−0.350204	+	0.102829i
$286$	0.271198	+	0.312980i	0.0160363	+	0.0185069i
$287$	−0.756792	+	0.486360i	−0.0446720	+	0.0287089i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	6.33260	+	7.30821i	0.372506	+	0.429895i
$290$	2.44102	−	0.716747i	0.143341	−	0.0420888i
$291$	−0.355023	+	2.46924i	−0.0208118	+	0.144749i
$292$	−0.573813	+	0.662215i	−0.0335799	+	0.0387532i
$293$	−4.01405	+	8.78955i	−0.234504	+	0.513491i	−0.989898	−	0.141779i	$-0.954718\pi$
$293$	−4.01405	+	8.78955i	−0.234504	+	0.513491i	0.755395	+	0.655270i	$0.227445\pi$
$294$	0.959493	+	0.281733i	0.0559588	+	0.0164310i
$295$	−5.62491	−	12.3168i	−0.327495	−	0.717114i
$296$	−1.04802	−	7.28917i	−0.0609152	−	0.423674i
$297$	2.35671	+	1.51456i	0.136750	+	0.0878839i
$298$	−10.8666			−0.629488
$299$	0.706568	+	0.0582125i	0.0408619	+	0.00336652i
$300$	1.78002			0.102770
$301$	−0.0228621	−	0.0146926i	−0.00131775	−	0.000846866i
$302$	2.87591	+	20.0024i	0.165490	+	1.15101i
$303$	2.08643	+	4.56864i	0.119862	+	0.262462i
$304$	3.29471	+	0.967415i	0.188965	+	0.0554851i
$305$	−3.25111	+	7.11894i	−0.186158	+	0.407630i
$306$	1.77295	−	2.04609i	0.101353	−	0.116967i
$307$	3.26066	−	22.6784i	0.186096	−	1.29432i	−0.655903	−	0.754845i	$-0.727712\pi$
$307$	3.26066	−	22.6784i	0.186096	−	1.29432i	0.841999	−	0.539480i	$-0.181379\pi$
$308$	2.68795	−	0.789252i	0.153160	−	0.0449718i
$309$	4.14768	+	4.78668i	0.235953	+	0.272305i
$310$	−3.14026	+	2.01812i	−0.178355	+	0.114622i
$311$	−5.81405	+	3.73647i	−0.329685	+	0.211876i	−0.695002	−	0.719007i	$-0.744597\pi$
$311$	−5.81405	+	3.73647i	−0.329685	+	0.211876i	0.365318	+	0.930883i	$0.380960\pi$
$312$	0.0968073	+	0.111722i	0.00548064	+	0.00632499i
$313$	0.303209	−	0.0890302i	0.0171384	−	0.00503229i	−0.273152	−	0.961971i	$-0.588066\pi$
$313$	0.303209	−	0.0890302i	0.0171384	−	0.00503229i	0.290291	+	0.956939i	$0.406248\pi$
$314$	1.73941	−	12.0979i	0.0981605	−	0.682722i
$315$	−1.17510	+	1.35614i	−0.0662095	+	0.0764098i
$316$	−1.23200	+	2.69771i	−0.0693056	+	0.151758i
$317$	−9.39892	−	2.75977i	−0.527896	−	0.155004i	0.00691480	−	0.999976i	$-0.497799\pi$
$317$	−9.39892	−	2.75977i	−0.527896	−	0.155004i	−0.534811	+	0.844972i	$0.679617\pi$
$318$	−3.56717	−	7.81100i	−0.200037	−	0.438019i
$319$	−0.565238	−	3.93132i	−0.0316473	−	0.220112i
$320$	1.50957	+	0.970142i	0.0843875	+	0.0542326i
$321$	−6.43033			−0.358906
$322$	2.34373	−	4.18413i	0.130611	−	0.233172i
$323$	9.29658			0.517276
$324$	0.841254	+	0.540641i	0.0467363	+	0.0300356i
$325$	0.0374486	+	0.260460i	0.00207727	+	0.0144477i
$326$	−2.22905	−	4.88094i	−0.123456	−	0.270330i
$327$	−5.95974	−	1.74994i	−0.329574	−	0.0967717i
$328$	−0.373707	+	0.818305i	−0.0206345	+	0.0451833i
$329$	−0.937261	+	1.08166i	−0.0516729	+	0.0596337i
$330$	−0.715411	+	4.97579i	−0.0393821	+	0.273908i
$331$	−3.08065	+	0.904560i	−0.169328	+	0.0497191i	−0.365298	−	0.930891i	$-0.619033\pi$
$331$	−3.08065	+	0.904560i	−0.169328	+	0.0497191i	0.195970	+	0.980610i	$0.437215\pi$
$332$	−2.96889	−	3.42628i	−0.162939	−	0.188042i
$333$	6.19510	−	3.98135i	0.339489	−	0.218176i
$334$	−8.99899	+	5.78330i	−0.492403	+	0.316448i
$335$	−6.43759	−	7.42937i	−0.351723	−	0.405910i
$336$	0.959493	−	0.281733i	0.0523446	−	0.0153698i
$337$	0.319062	−	2.21912i	0.0173804	−	0.120883i	−0.979284	−	0.202491i	$-0.935096\pi$
$337$	0.319062	−	2.21912i	0.0173804	−	0.120883i	0.996665	+	0.0816076i	$0.0260054\pi$
$338$	8.49888	−	9.80823i	0.462278	−	0.533497i
$339$	−0.0713100	+	0.156147i	−0.00387303	+	0.00848075i
$340$	4.66139	+	1.36871i	0.252799	+	0.0742286i
$341$	2.42088	+	5.30099i	0.131098	+	0.287065i
$342$	0.488682	+	3.39885i	0.0264249	+	0.183789i
$343$	0.841254	+	0.540641i	0.0454234	+	0.0291919i
$344$	−0.0271762			−0.00146524
$345$	5.08253	+	6.94459i	0.273634	+	0.373884i
$346$	−16.0281			−0.861678
$347$	5.08569	+	3.26837i	0.273014	+	0.175455i	0.669983	−	0.742377i	$-0.266301\pi$
$347$	5.08569	+	3.26837i	0.273014	+	0.175455i	−0.396969	+	0.917832i	$0.629938\pi$
$348$	−0.201768	−	1.40333i	−0.0108159	−	0.0752263i
$349$	−6.47798	−	14.1848i	−0.346758	−	0.759294i	−0.999998	−	0.00214314i	$-0.999318\pi$
$349$	−6.47798	−	14.1848i	−0.346758	−	0.759294i	0.653240	−	0.757151i	$-0.273409\pi$
$350$	1.70792	+	0.501490i	0.0912922	+	0.0268058i
$351$	−0.0614103	+	0.134470i	−0.00327784	+	0.00717747i
$352$	1.83454	−	2.11717i	0.0977814	−	0.112846i
$353$	1.84840	−	12.8559i	0.0983803	−	0.684250i	−0.879625	−	0.475668i	$-0.842206\pi$
$353$	1.84840	−	12.8559i	0.0983803	−	0.684250i	0.978005	−	0.208582i	$-0.0668847\pi$
$354$	−7.24017	+	2.12591i	−0.384811	+	0.112991i
$355$	−7.70088	−	8.88729i	−0.408720	−	0.471689i
$356$	−2.04396	+	1.31358i	−0.108330	+	0.0696194i
$357$	2.27758	−	1.46371i	0.120543	−	0.0774680i
$358$	−11.1782	−	12.9003i	−0.590785	−	0.681803i
$359$	−4.24187	+	1.24553i	−0.223878	+	0.0657364i	−0.391748	−	0.920073i	$-0.628129\pi$
$359$	−4.24187	+	1.24553i	−0.223878	+	0.0657364i	0.167870	+	0.985809i	$0.446311\pi$
$360$	−0.255374	+	1.77616i	−0.0134594	+	0.0936121i
$361$	4.72088	−	5.44818i	0.248467	−	0.286746i
$362$	−9.20155	+	20.1486i	−0.483623	+	1.05899i
$363$	−3.02435	−	0.888028i	−0.158737	−	0.0466094i
$364$	0.0614103	+	0.134470i	0.00321878	+	0.00704814i
$365$	−0.223768	−	1.55634i	−0.0117125	−	0.0814626i
$366$	3.66902	+	2.35794i	0.191783	+	0.123251i
$367$	12.8852			0.672603			0.336301	−	0.941754i	$-0.390824\pi$
$367$	12.8852			0.672603			0.336301	+	0.941754i	$0.390824\pi$
$368$	−0.290438	−	4.78703i	−0.0151401	−	0.249541i
$369$	−0.899600			−0.0468313
$370$	11.1167	+	7.14424i	0.577928	+	0.371412i
$371$	−1.22206	−	8.49959i	−0.0634460	−	0.441277i
$372$	0.864162	+	1.89225i	0.0448047	+	0.0981086i
$373$	−34.3530	−	10.0869i	−1.77873	−	0.522282i	−0.783636	−	0.621220i	$-0.786637\pi$
$373$	−34.3530	−	10.0869i	−1.77873	−	0.522282i	−0.995094	+	0.0989376i	$0.968456\pi$
$374$	3.15071	−	6.89909i	0.162919	−	0.356744i
$375$	−7.96721	+	9.19466i	−0.411425	+	0.474810i
$376$	−0.203686	+	1.41667i	−0.0105043	+	0.0730591i
$377$	0.201096	−	0.0590471i	0.0103570	−	0.00304108i
$378$	0.654861	+	0.755750i	0.0336824	+	0.0388716i
$379$	13.3528	−	8.58131i	0.685886	−	0.440792i	−0.150735	−	0.988574i	$-0.548164\pi$
$379$	13.3528	−	8.58131i	0.685886	−	0.440792i	0.836621	+	0.547782i	$0.184528\pi$
$380$	−5.18357	+	3.33128i	−0.265912	+	0.170891i
$381$	0.796781	+	0.919534i	0.0408203	+	0.0471091i
$382$	−2.48157	+	0.728653i	−0.126968	+	0.0372811i
$383$	−2.39233	+	16.6390i	−0.122242	+	0.850215i	0.832764	+	0.553629i	$0.186757\pi$
$383$	−2.39233	+	16.6390i	−0.122242	+	0.850215i	−0.955006	+	0.296586i	$0.904152\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	−2.08827	+	4.57268i	−0.106428	+	0.233045i
$386$	−3.10632	−	0.912097i	−0.158107	−	0.0464245i
$387$	−0.0112894	−	0.0247204i	−0.000573873	−	0.00125661i
$388$	0.355023	+	2.46924i	0.0180236	+	0.125357i
$389$	−25.2888	−	16.2521i	−1.28219	−	0.824015i	−0.291036	−	0.956712i	$-0.594000\pi$
$389$	−25.2888	−	16.2521i	−1.28219	−	0.824015i	−0.991157	+	0.132697i	$0.957636\pi$
$390$	−0.265268			−0.0134324
$391$	−4.40580	−	12.2137i	−0.222811	−	0.617675i
$392$	1.00000			0.0505076
$393$	3.77062	+	2.42323i	0.190202	+	0.122236i
$394$	2.92273	+	20.3280i	0.147245	+	1.02411i
$395$	−2.21074	−	4.84085i	−0.111235	−	0.243570i
$396$	2.68795	+	0.789252i	0.135074	+	0.0396614i
$397$	−13.5685	+	29.7108i	−0.680983	+	1.49114i	0.180616	+	0.983554i	$0.442191\pi$
$397$	−13.5685	+	29.7108i	−0.680983	+	1.49114i	−0.861598	+	0.507590i	$0.830536\pi$
$398$	−0.541426	+	0.624839i	−0.0271392	+	0.0313204i
$399$	−0.488682	+	3.39885i	−0.0244647	+	0.170156i
$400$	1.70792	−	0.501490i	0.0853960	−	0.0250745i
$401$	9.42918	+	10.8819i	0.470871	+	0.543414i	0.940654	−	0.339368i	$-0.110213\pi$
$401$	9.42918	+	10.8819i	0.470871	+	0.543414i	−0.469783	+	0.882782i	$0.655668\pi$
$402$	−4.60866	+	2.96181i	−0.229859	+	0.147721i
$403$	−0.258702	+	0.166257i	−0.0128868	+	0.00828187i
$404$	3.28905	+	3.79576i	0.163636	+	0.188846i
$405$	−1.72174	+	0.505549i	−0.0855541	+	0.0251209i
$406$	0.201768	−	1.40333i	0.0100136	−	0.0696460i
$407$	13.5098	−	15.5911i	0.669656	−	0.772824i
$408$	1.12468	−	2.46271i	0.0556800	−	0.121922i
$409$	−5.07861	−	1.49122i	−0.251121	−	0.0737359i	0.153749	−	0.988110i	$-0.450865\pi$
$409$	−5.07861	−	1.49122i	−0.251121	−	0.0737359i	−0.404870	+	0.914374i	$0.632683\pi$
$410$	−0.670591	−	1.46839i	−0.0331181	−	0.0725186i
$411$	−1.08311	−	7.53317i	−0.0534257	−	0.371584i
$412$	5.32823	+	3.42425i	0.262503	+	0.168701i
$413$	−7.54583			−0.371306
$414$	4.23378	−	2.25280i	0.208079	−	0.110719i
$415$	8.13526			0.399344
$416$	0.124362	+	0.0799223i	0.00609733	+	0.00391851i
$417$	2.97492	+	20.6910i	0.145683	+	1.01324i
$418$	3.99610	+	8.75025i	0.195456	+	0.427989i
$419$	−16.9714	−	4.98327i	−0.829109	−	0.243448i	−0.160475	−	0.987040i	$-0.551303\pi$
$419$	−16.9714	−	4.98327i	−0.829109	−	0.243448i	−0.668634	+	0.743591i	$0.733121\pi$
$420$	−0.745433	+	1.63227i	−0.0363734	+	0.0796466i
$421$	−7.20001	+	8.30925i	−0.350907	+	0.404968i	−0.903573	−	0.428435i	$-0.859065\pi$
$421$	−7.20001	+	8.30925i	−0.350907	+	0.404968i	0.552666	+	0.833403i	$0.313611\pi$
$422$	−0.0432185	+	0.300592i	−0.00210385	+	0.0146326i
$423$	−1.37326	+	0.403226i	−0.0667703	+	0.0196055i
$424$	−5.62329	−	6.48962i	−0.273091	−	0.315164i
$425$	4.05415	−	2.60545i	0.196655	−	0.126383i
$426$	−5.51305	+	3.54302i	−0.267108	+	0.171660i
$427$	2.85609	+	3.29611i	0.138216	+	0.159510i
$428$	−6.16986	+	1.81163i	−0.298231	+	0.0875687i
$429$	−0.0589370	+	0.409916i	−0.00284551	+	0.0197909i
$430$	0.0319348	−	0.0368548i	0.00154003	−	0.00177729i
$431$	−4.22369	+	9.24860i	−0.203448	+	0.445489i	−0.983662	−	0.180023i	$-0.942383\pi$
$431$	−4.22369	+	9.24860i	−0.203448	+	0.445489i	0.780214	+	0.625512i	$0.215110\pi$
$432$	0.959493	+	0.281733i	0.0461636	+	0.0135549i
$433$	−3.19042	−	6.98605i	−0.153322	−	0.335728i	0.817348	−	0.576144i	$-0.195443\pi$
$433$	−3.19042	−	6.98605i	−0.153322	−	0.335728i	−0.970670	+	0.240416i	$0.922716\pi$
$434$	0.296049	+	2.05906i	0.0142108	+	0.0988382i
$435$	2.14021	+	1.37543i	0.102615	+	0.0659467i
$436$	−6.21134			−0.297469
$437$	15.3666	+	5.92130i	0.735083	+	0.283254i
$438$	−0.876236			−0.0418682
$439$	−14.4688	−	9.29856i	−0.690560	−	0.443796i	0.147725	−	0.989029i	$-0.452805\pi$
$439$	−14.4688	−	9.29856i	−0.690560	−	0.443796i	−0.838285	+	0.545233i	$0.816441\pi$
$440$	0.715411	+	4.97579i	0.0341059	+	0.237211i
$441$	0.415415	+	0.909632i	0.0197817	+	0.0433158i
$442$	0.384015	+	0.112757i	0.0182657	+	0.00536331i
$443$	7.56519	−	16.5655i	0.359433	−	0.787049i	−0.640386	−	0.768053i	$-0.721226\pi$
$443$	7.56519	−	16.5655i	0.359433	−	0.787049i	0.999820	−	0.0189959i	$-0.00604696\pi$
$444$	4.82248	−	5.56543i	0.228865	−	0.264124i
$445$	0.620473	−	4.31548i	0.0294132	−	0.204574i
$446$	10.9432	−	3.21322i	0.518177	−	0.152150i
$447$	−7.11614	−	8.21246i	−0.336582	−	0.388436i
$448$	0.841254	−	0.540641i	0.0397455	−	0.0255429i
$449$	−23.2550	+	14.9451i	−1.09747	+	0.705302i	−0.958528	−	0.284998i	$-0.908007\pi$
$449$	−23.2550	+	14.9451i	−1.09747	+	0.705302i	−0.138944	+	0.990300i	$0.544371\pi$
$450$	1.16567	+	1.34525i	0.0549501	+	0.0634158i
$451$	−2.41808	+	0.710011i	−0.113863	+	0.0334331i
$452$	−0.0244297	+	0.169913i	−0.00114908	+	0.00799201i
$453$	−13.2335	+	15.2722i	−0.621762	+	0.717552i
$454$	7.44829	−	16.3095i	0.349566	−	0.765442i
$455$	−0.254523	−	0.0747348i	−0.0119322	−	0.00350362i
$456$	1.42645	+	3.12350i	0.0667999	+	0.146271i
$457$	2.30342	+	16.0206i	0.107749	+	0.749412i	0.970031	+	0.242983i	$0.0781259\pi$
$457$	2.30342	+	16.0206i	0.107749	+	0.749412i	−0.862281	+	0.506430i	$0.830965\pi$
$458$	−19.1709	−	12.3204i	−0.895795	−	0.575693i
$459$	2.70737			0.126369
$460$	6.83317	+	5.23137i	0.318598	+	0.243914i
$461$	9.49809			0.442370			0.221185	−	0.975232i	$-0.429008\pi$
$461$	9.49809			0.442370			0.221185	+	0.975232i	$0.429008\pi$
$462$	2.35671	+	1.51456i	0.109644	+	0.0704639i
$463$	1.90660	+	13.2607i	0.0886072	+	0.616277i	0.984940	+	0.172895i	$0.0553122\pi$
$463$	1.90660	+	13.2607i	0.0886072	+	0.616277i	−0.896333	+	0.443382i	$0.853779\pi$
$464$	−0.588959	−	1.28964i	−0.0273417	−	0.0598700i
$465$	−3.58163	−	1.05166i	−0.166094	−	0.0487697i
$466$	−3.37504	+	7.39032i	−0.156346	+	0.342350i
$467$	−8.74909	+	10.0970i	−0.404860	+	0.467233i	−0.921165	−	0.389172i	$-0.872761\pi$
$467$	−8.74909	+	10.0970i	−0.404860	+	0.467233i	0.516306	+	0.856404i	$0.327307\pi$
$468$	−0.0210382	+	0.146324i	−0.000972493	+	0.00676384i
$469$	−5.25641	+	1.54342i	−0.242719	+	0.0712686i
$470$	−1.68185	−	1.94096i	−0.0775779	−	0.0895296i
$471$	10.2820	−	6.60785i	0.473771	−	0.304474i
$472$	−6.34796	+	4.07958i	−0.292188	+	0.187778i
$473$	−0.0498560	−	0.0575368i	−0.00229238	−	0.00264555i
$474$	−2.84559	+	0.835539i	−0.130702	+	0.0383776i
$475$	−0.869864	+	6.05004i	−0.0399121	+	0.277595i
$476$	1.77295	−	2.04609i	0.0812630	−	0.0937825i
$477$	3.56717	−	7.81100i	0.163329	−	0.357641i
$478$	19.3294	+	5.67562i	0.884105	+	0.259597i
$479$	−17.2384	−	37.7468i	−0.787641	−	1.72469i	−0.683282	−	0.730154i	$-0.739448\pi$
$479$	−17.2384	−	37.7468i	−0.787641	−	1.72469i	−0.104359	−	0.994540i	$-0.533279\pi$
$480$	0.255374	+	1.77616i	0.0116562	+	0.0810705i
$481$	0.915814	+	0.588558i	0.0417575	+	0.0268359i
$482$	7.16578			0.326392
$483$	4.69697	−	0.968747i	0.213720	−	0.0440795i
$484$	−3.15202			−0.143274
$485$	−3.76582	−	2.42014i	−0.170997	−	0.109893i
$486$	0.142315	+	0.989821i	0.00645553	+	0.0448992i
$487$	9.46832	+	20.7327i	0.429051	+	0.939490i	0.993480	+	0.114008i	$0.0363691\pi$
$487$	9.46832	+	20.7327i	0.429051	+	0.939490i	−0.564429	+	0.825482i	$0.690904\pi$
$488$	4.18471	+	1.22874i	0.189433	+	0.0556225i
$489$	2.22905	−	4.88094i	0.100801	−	0.220724i
$490$	−1.17510	+	1.35614i	−0.0530857	+	0.0612641i
$491$	4.81769	−	33.5078i	0.217419	−	1.51218i	−0.530095	−	0.847939i	$-0.677844\pi$
$491$	4.81769	−	33.5078i	0.217419	−	1.51218i	0.747514	−	0.664246i	$-0.231247\pi$
$492$	−0.863160	+	0.253447i	−0.0389142	+	0.0114263i
$493$	−2.51362	−	2.90087i	−0.113208	−	0.130649i
$494$	−0.427033	+	0.274438i	−0.0192131	+	0.0123475i
$495$	−4.22895	+	2.71778i	−0.190077	+	0.122155i
$496$	1.36227	+	1.57214i	0.0611675	+	0.0705911i
$497$	−6.28792	+	1.84630i	−0.282052	+	0.0828179i
$498$	0.645201	−	4.48747i	0.0289122	−	0.201088i
$499$	14.5559	−	16.7984i	0.651611	−	0.751999i	−0.329772	−	0.944061i	$-0.606972\pi$
$499$	14.5559	−	16.7984i	0.651611	−	0.751999i	0.981383	+	0.192062i	$0.0615174\pi$
$500$	−5.05405	+	11.0668i	−0.226024	+	0.494924i
$501$	−10.2638	−	3.01373i	−0.458553	−	0.134643i
$502$	−5.43867	−	11.9090i	−0.242740	−	0.531526i
$503$	−4.85273	−	33.7515i	−0.216373	−	1.50491i	−0.751274	−	0.659991i	$-0.770560\pi$
$503$	−4.85273	−	33.7515i	−0.216373	−	1.50491i	0.534901	−	0.844915i	$-0.320349\pi$
$504$	0.841254	+	0.540641i	0.0374724	+	0.0240821i
$505$	−9.01255			−0.401053
$506$	9.60216	−	9.39692i	0.426868	−	0.417744i
$507$	12.9781			0.576380
$508$	1.02357	+	0.657807i	0.0454135	+	0.0291855i
$509$	−4.89912	−	34.0741i	−0.217150	−	1.51031i	−0.748487	−	0.663149i	$-0.769220\pi$
$509$	−4.89912	−	34.0741i	−0.217150	−	1.51031i	0.531338	−	0.847160i	$-0.321690\pi$
$510$	2.01816	+	4.41916i	0.0893657	+	0.195684i
$511$	−0.840743	−	0.246864i	−0.0371923	−	0.0109206i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	−2.24866	+	2.59510i	−0.0992810	+	0.114576i
$514$	−2.81593	+	19.5852i	−0.124205	+	0.863867i
$515$	−10.9050	+	3.20199i	−0.480530	+	0.141096i
$516$	−0.0177966	−	0.0205384i	−0.000783454	−	0.000904154i
$517$	−3.37301	+	2.16770i	−0.148345	+	0.0953353i
$518$	6.19510	−	3.98135i	0.272197	−	0.174930i
$519$	−10.4962	−	12.1133i	−0.460732	−	0.531713i
$520$	−0.254523	+	0.0747348i	−0.0111616	+	0.00327734i
$521$	−3.14648	+	21.8842i	−0.137850	+	0.958766i	0.797065	+	0.603894i	$0.206385\pi$
$521$	−3.14648	+	21.8842i	−0.137850	+	0.958766i	−0.934915	+	0.354873i	$0.884524\pi$
$522$	0.928435	−	1.07147i	0.0406365	−	0.0468970i
$523$	−2.10317	+	4.60529i	−0.0919650	+	0.201375i	−0.950025	−	0.312175i	$-0.898943\pi$
$523$	−2.10317	+	4.60529i	−0.0919650	+	0.201375i	0.858060	+	0.513550i	$0.171670\pi$
$524$	4.30058	+	1.26276i	0.187872	+	0.0551641i
$525$	0.739448	+	1.61917i	0.0322722	+	0.0706662i
$526$	−0.845009	−	5.87717i	−0.0368441	−	0.256257i
$527$	4.73791	+	3.04487i	0.206387	+	0.132637i
$528$	2.80142			0.121916
$529$	0.496862	−	22.9946i	0.0216027	−	0.999767i
$530$	15.4088			0.669314
$531$	−6.34796	−	4.07958i	−0.275478	−	0.177039i
$532$	0.488682	+	3.39885i	0.0211870	+	0.147359i
$533$	−0.0552447	−	0.120969i	−0.00239291	−	0.00523975i
$534$	−2.33125	−	0.684515i	−0.100883	−	0.0296219i
$535$	4.79338	−	10.4960i	0.207236	−	0.453784i
$536$	−3.58754	+	4.14024i	−0.154958	+	0.178831i
$537$	2.42925	−	16.8958i	0.104830	−	0.729108i
$538$	8.84677	−	2.59765i	0.381412	−	0.111993i
$539$	1.83454	+	2.11717i	0.0790193	+	0.0911932i
$540$	−1.50957	+	0.970142i	−0.0649616	+	0.0417483i
$541$	−29.3578	+	18.8671i	−1.26219	+	0.811161i	−0.988582	−	0.150681i	$-0.951853\pi$
$541$	−29.3578	+	18.8671i	−1.26219	+	0.811161i	−0.273608	+	0.961841i	$0.588217\pi$
$542$	−7.51215	−	8.66948i	−0.322674	−	0.372386i
$543$	−21.2530	+	6.24045i	−0.912055	+	0.267803i
$544$	0.385299	−	2.67981i	0.0165195	−	0.114896i
$545$	7.29895	−	8.42344i	0.312653	−	0.360820i
$546$	−0.0614103	+	0.134470i	−0.00262812	+	0.00575478i
$547$	−6.79028	−	1.99381i	−0.290331	−	0.0852490i	0.133324	−	0.991073i	$-0.457435\pi$
$547$	−6.79028	−	1.99381i	−0.290331	−	0.0852490i	−0.423655	+	0.905824i	$0.639253\pi$
$548$	−3.16157	−	6.92288i	−0.135056	−	0.295731i
$549$	0.620688	+	4.31698i	0.0264903	+	0.184244i
$550$	4.19499	+	2.69596i	0.178875	+	0.114956i
$551$	4.86831			0.207397
$552$	3.42760	−	3.35434i	0.145888	−	0.142770i
$553$	−2.96572			−0.126115
$554$	−11.0667	−	7.11211i	−0.470177	−	0.302165i
$555$	1.88061	+	13.0799i	0.0798273	+	0.555211i
$556$	8.68376	+	19.0148i	0.368273	+	0.806406i
$557$	−27.1618	−	7.97542i	−1.15088	−	0.337929i	−0.349999	−	0.936750i	$-0.613818\pi$
$557$	−27.1618	−	7.97542i	−1.15088	−	0.337929i	−0.800883	+	0.598821i	$0.795636\pi$
$558$	−0.864162	+	1.89225i	−0.0365829	+	0.0801053i
$559$	0.00263086	−	0.00303617i	0.000111273	−	0.000128416i
$560$	−0.255374	+	1.77616i	−0.0107915	+	0.0750567i
$561$	7.27726	−	2.13680i	0.307246	−	0.0902156i
$562$	10.6458	+	12.2859i	0.449067	+	0.518250i
$563$	−13.8567	+	8.90514i	−0.583989	+	0.375307i	−0.799024	−	0.601299i	$-0.794650\pi$
$563$	−13.8567	+	8.90514i	−0.583989	+	0.375307i	0.215035	+	0.976606i	$0.431014\pi$
$564$	−1.20403	+	0.773785i	−0.0506989	+	0.0325822i
$565$	−0.201718	−	0.232795i	−0.00848632	−	0.00979374i
$566$	23.1732	−	6.80426i	0.974042	−	0.286005i
$567$	−0.142315	+	0.989821i	−0.00597666	+	0.0415686i
$568$	−4.29155	+	4.95271i	−0.180069	+	0.207811i
$569$	11.1836	−	24.4887i	0.468841	−	1.02662i	−0.516541	−	0.856262i	$-0.672781\pi$
$569$	11.1836	−	24.4887i	0.468841	−	1.02662i	0.985382	−	0.170357i	$-0.0544919\pi$
$570$	−5.91213	−	1.73596i	−0.247632	−	0.0727113i
$571$	5.57408	+	12.2055i	0.233268	+	0.510786i	0.989677	−	0.143313i	$-0.0457754\pi$
$571$	5.57408	+	12.2055i	0.233268	+	0.510786i	−0.756409	+	0.654099i	$0.773048\pi$
$572$	0.0589370	+	0.409916i	0.00246428	+	0.0171395i
$573$	−2.17576	−	1.39828i	−0.0908936	−	0.0584138i
$574$	−0.899600			−0.0375486
$575$	8.36072	−	1.72439i	0.348666	−	0.0719121i
$576$	1.00000			0.0416667
$577$	18.7064	+	12.0219i	0.778757	+	0.500477i	0.868621	−	0.495477i	$-0.165007\pi$
$577$	18.7064	+	12.0219i	0.778757	+	0.500477i	−0.0898636	+	0.995954i	$0.528643\pi$
$578$	1.37621	+	9.57172i	0.0572426	+	0.398131i
$579$	−1.34489	−	2.94489i	−0.0558916	−	0.122386i
$580$	2.44102	+	0.716747i	0.101358	+	0.0297613i
$581$	1.88333	−	4.12392i	0.0781338	−	0.171089i
$582$	−1.63363	+	1.88532i	−0.0677163	+	0.0781488i
$583$	3.42350	−	23.8110i	0.141787	−	0.986149i
$584$	−0.840743	+	0.246864i	−0.0347902	+	0.0102153i
$585$	−0.173714	−	0.200477i	−0.00718219	−	0.00828868i
$586$	−8.12883	+	5.22408i	−0.335799	+	0.215805i
$587$	−13.6054	+	8.74364i	−0.561554	+	0.360889i	−0.790416	−	0.612570i	$-0.790136\pi$
$587$	−13.6054	+	8.74364i	−0.561554	+	0.360889i	0.228863	+	0.973459i	$0.426499\pi$
$588$	0.654861	+	0.755750i	0.0270060	+	0.0311666i
$589$	−6.85378	+	2.01245i	−0.282405	+	0.0829217i
$590$	1.92701	−	13.4026i	0.0793337	−	0.551778i
$591$	−13.4489	+	15.5209i	−0.553214	+	0.638443i
$592$	3.05917	−	6.69864i	0.125731	−	0.275313i
$593$	23.4067	+	6.87282i	0.961196	+	0.282233i	0.724441	−	0.689337i	$-0.242098\pi$
$593$	23.4067	+	6.87282i	0.961196	+	0.282233i	0.236755	+	0.971569i	$0.423916\pi$
$594$	1.16375	+	2.54826i	0.0477494	+	0.104557i
$595$	0.691391	+	4.80873i	0.0283443	+	0.197139i
$596$	−9.14161	−	5.87495i	−0.374455	−	0.240647i
$597$	−0.826781			−0.0338379
$598$	0.562931	+	0.430971i	0.0230200	+	0.0176237i
$599$	−9.17564			−0.374907			−0.187453	−	0.982274i	$-0.560023\pi$
$599$	−9.17564			−0.374907			−0.187453	+	0.982274i	$0.560023\pi$
$600$	1.49745	+	0.962353i	0.0611332	+	0.0392879i
$601$	2.88469	+	20.0635i	0.117669	+	0.818407i	0.960111	+	0.279619i	$0.0902083\pi$
$601$	2.88469	+	20.0635i	0.117669	+	0.818407i	−0.842442	+	0.538787i	$0.818883\pi$
$602$	−0.0112894	−	0.0247204i	−0.000460122	−	0.00100753i
$603$	−5.25641	−	1.54342i	−0.214058	−	0.0628530i
$604$	−8.39473	+	18.3819i	−0.341577	+	0.747948i
$605$	3.70395	−	4.27458i	0.150587	−	0.173787i
$606$	−0.714779	+	4.97139i	−0.0290359	+	0.201949i
$607$	−26.4803	+	7.77532i	−1.07480	+	0.315590i	−0.770797	−	0.637080i	$-0.780142\pi$
$607$	−26.4803	+	7.77532i	−1.07480	+	0.315590i	−0.304004	+	0.952671i	$0.598324\pi$
$608$	2.24866	+	2.59510i	0.0911954	+	0.105245i
$609$	1.19270	−	0.766499i	0.0483304	−	0.0310601i
$610$	−6.58380	+	4.23115i	−0.266570	+	0.171314i
$611$	−0.138554	−	0.159900i	−0.00560530	−	0.00646886i
$612$	2.59770	−	0.762754i	0.105006	−	0.0308325i
$613$	−6.44353	+	44.8157i	−0.260252	+	1.81009i	0.270674	+	0.962671i	$0.412753\pi$
$613$	−6.44353	+	44.8157i	−0.260252	+	1.81009i	−0.530926	+	0.847418i	$0.678156\pi$
$614$	15.0039	−	17.3154i	0.605509	−	0.698794i
$615$	0.670591	−	1.46839i	0.0270409	−	0.0592112i
$616$	2.68795	+	0.789252i	0.108300	+	0.0317999i
$617$	10.3498	+	22.6629i	0.416668	+	0.912375i	0.995305	+	0.0967897i	$0.0308574\pi$
$617$	10.3498	+	22.6629i	0.416668	+	0.912375i	−0.578637	+	0.815585i	$0.696415\pi$
$618$	0.901377	+	6.26922i	0.0362587	+	0.252185i
$619$	29.2159	+	18.7759i	1.17428	+	0.754667i	0.974327	−	0.225137i	$-0.0722831\pi$
$619$	29.2159	+	18.7759i	1.17428	+	0.754667i	0.199958	+	0.979805i	$0.435919\pi$
$620$	−3.73284			−0.149914
$621$	4.47509	+	1.72441i	0.179579	+	0.0691983i
$622$	−6.91118			−0.277113
$623$	−2.04396	−	1.31358i	−0.0818897	−	0.0526273i
$624$	0.0210382	+	0.146324i	0.000842204	+	0.00585766i
$625$	−5.37190	−	11.7628i	−0.214876	−	0.470513i
$626$	0.303209	+	0.0890302i	0.0121187	+	0.00355836i
$627$	−3.99610	+	8.75025i	−0.159589	+	0.349451i
$628$	8.00388	−	9.23697i	0.319390	−	0.368595i
$629$	2.83739	−	19.7345i	0.113134	−	0.786865i
$630$	−1.72174	+	0.505549i	−0.0685959	+	0.0201416i
$631$	7.72964	+	8.92048i	0.307712	+	0.355119i	0.888451	−	0.458971i	$-0.151782\pi$
$631$	7.72964	+	8.92048i	0.307712	+	0.355119i	−0.580739	+	0.814090i	$0.697236\pi$
$632$	−2.49492	+	1.60339i	−0.0992426	+	0.0637794i
$633$	−0.255474	+	0.164183i	−0.0101542	+	0.00652570i
$634$	−6.41483	−	7.40311i	−0.254765	−	0.294015i
$635$	−2.09487	+	0.615111i	−0.0831326	+	0.0244099i
$636$	1.22206	−	8.49959i	0.0484577	−	0.337031i
$637$	−0.0968073	+	0.111722i	−0.00383565	+	0.00442657i
$638$	1.64992	−	3.61283i	0.0653211	−	0.143033i
$639$	−6.28792	−	1.84630i	−0.248746	−	0.0730385i
$640$	0.745433	+	1.63227i	0.0294658	+	0.0645212i
$641$	−5.81339	−	40.4330i	−0.229615	−	1.59701i	−0.699733	−	0.714405i	$-0.746698\pi$
$641$	−5.81339	−	40.4330i	−0.229615	−	1.59701i	0.470118	−	0.882604i	$-0.344211\pi$
$642$	−5.40954	−	3.47650i	−0.213498	−	0.137207i
$643$	−30.8941			−1.21834			−0.609172	−	0.793038i	$-0.708498\pi$
$643$	−30.8941			−1.21834			−0.609172	+	0.793038i	$0.708498\pi$
$644$	4.23378	−	2.25280i	0.166834	−	0.0887726i
$645$	0.0487658			0.00192015
$646$	7.82078	+	5.02611i	0.307705	+	0.197750i
$647$	−3.00107	−	20.8729i	−0.117984	−	0.820599i	−0.959770	−	0.280787i	$-0.909405\pi$
$647$	−3.00107	−	20.8729i	−0.117984	−	0.820599i	0.841786	−	0.539812i	$-0.181505\pi$
$648$	0.415415	+	0.909632i	0.0163190	+	0.0357337i
$649$	−20.2828	−	5.95557i	−0.796169	−	0.233776i
$650$	−0.109312	+	0.239359i	−0.00428756	+	0.00938845i
$651$	−1.36227	+	1.57214i	−0.0533914	+	0.0616170i
$652$	0.763639	−	5.31122i	0.0299064	−	0.208004i
$653$	−28.7362	+	8.43772i	−1.12454	+	0.330193i	−0.790558	−	0.612387i	$-0.790209\pi$
$653$	−28.7362	+	8.43772i	−1.12454	+	0.330193i	−0.333978	+	0.942581i	$0.608391\pi$
$654$	−4.06756	−	4.69422i	−0.159054	−	0.183558i
$655$	−6.76611	+	4.34831i	−0.264374	+	0.169903i
$656$	−0.756792	+	0.486360i	−0.0295477	+	0.0189892i
$657$	−0.573813	−	0.662215i	−0.0223866	−	0.0258355i
$658$	−1.37326	+	0.403226i	−0.0535353	+	0.0157194i
$659$	4.55106	−	31.6533i	0.177284	−	1.23304i	−0.685729	−	0.727857i	$-0.740516\pi$
$659$	4.55106	−	31.6533i	0.177284	−	1.23304i	0.863013	−	0.505182i	$-0.168574\pi$
$660$	−3.29196	+	3.79912i	−0.128139	+	0.147881i
$661$	2.74863	−	6.01867i	0.106909	−	0.234099i	−0.848615	−	0.529011i	$-0.822563\pi$
$661$	2.74863	−	6.01867i	0.106909	−	0.234099i	0.955524	+	0.294912i	$0.0952903\pi$
$662$	−3.08065	−	0.904560i	−0.119733	−	0.0351567i
$663$	0.166260	+	0.364060i	0.00645702	+	0.0141389i
$664$	−0.645201	−	4.48747i	−0.0250387	−	0.174148i
$665$	−5.18357	−	3.33128i	−0.201010	−	0.129181i
$666$	7.36412			0.285354
$667$	−2.30717	−	6.39593i	−0.0893340	−	0.247651i
$668$	−10.6971			−0.413884
$669$	9.59468	+	6.16613i	0.370952	+	0.238396i
$670$	−1.39902	−	9.73041i	−0.0540489	−	0.375918i
$671$	5.07557	+	11.1139i	0.195940	+	0.429049i
$672$	0.959493	+	0.281733i	0.0370132	+	0.0108681i
$673$	−1.09429	+	2.39617i	−0.0421820	+	0.0923656i	−0.929550	−	0.368696i	$-0.879804\pi$
$673$	−1.09429	+	2.39617i	−0.0421820	+	0.0923656i	0.887368	+	0.461062i	$0.152531\pi$
$674$	1.46816	−	1.69435i	0.0565514	−	0.0652638i
$675$	−0.253324	+	1.76191i	−0.00975043	+	0.0678158i
$676$	12.4524	−	3.65637i	0.478940	−	0.140629i
$677$	16.1484	+	18.6363i	0.620635	+	0.716251i	0.975828	−	0.218542i	$-0.0701301\pi$
$677$	16.1484	+	18.6363i	0.620635	+	0.716251i	−0.355192	+	0.934793i	$0.615585\pi$
$678$	−0.144409	+	0.0928063i	−0.00554601	+	0.00356420i
$679$	−2.09862	+	1.34870i	−0.0805375	+	0.0517583i
$680$	3.18143	+	3.67157i	0.122002	+	0.140798i
$681$	17.2035	−	5.05140i	0.659239	−	0.193570i
$682$	−0.829358	+	5.76831i	−0.0317577	+	0.220880i
$683$	1.43422	−	1.65517i	0.0548788	−	0.0633335i	−0.727646	−	0.685952i	$-0.759386\pi$
$683$	1.43422	−	1.65517i	0.0548788	−	0.0633335i	0.782525	+	0.622619i	$0.213931\pi$
$684$	−1.42645	+	3.12350i	−0.0545419	+	0.119430i
$685$	13.1035	+	3.84755i	0.500661	+	0.147007i
$686$	0.415415	+	0.909632i	0.0158606	+	0.0347299i
$687$	−3.24313	−	22.5565i	−0.123733	−	0.860584i
$688$	−0.0228621	−	0.0146926i	−0.000871610	−	0.000560149i
$689$	1.26941			0.0483605
$690$	0.521171	+	8.58999i	0.0198406	+	0.327015i
$691$	15.2876			0.581568			0.290784	−	0.956789i	$-0.406084\pi$
$691$	15.2876			0.581568			0.290784	+	0.956789i	$0.406084\pi$
$692$	−13.4837	−	8.66546i	−0.512574	−	0.329411i
$693$	0.398684	+	2.77291i	0.0151448	+	0.105334i
$694$	2.51134	+	5.49906i	0.0953290	+	0.208741i
$695$	−35.9910	−	10.5679i	−1.36522	−	0.400863i
$696$	0.588959	−	1.28964i	0.0223244	−	0.0488837i
$697$	−1.59495	+	1.84066i	−0.0604129	+	0.0697202i
$698$	2.21926	−	15.4353i	0.0840001	−	0.584233i
$699$	−7.79541	+	2.28894i	−0.294850	+	0.0865756i
$700$	1.16567	+	1.34525i	0.0440581	+	0.0508457i
$701$	14.4572	−	9.29108i	0.546041	−	0.350919i	−0.238357	−	0.971178i	$-0.576609\pi$
$701$	14.4572	−	9.29108i	0.546041	−	0.350919i	0.784397	+	0.620259i	$0.212972\pi$
$702$	−0.124362	+	0.0799223i	−0.00469372	+	0.00301647i
$703$	16.5594	+	19.1106i	0.624551	+	0.720771i
$704$	2.68795	−	0.789252i	0.101306	−	0.0297461i
$705$	0.365501	−	2.54211i	0.0137655	−	0.0957415i
$706$	8.50539	−	9.81574i	0.320105	−	0.369420i
$707$	−2.08643	+	4.56864i	−0.0784682	+	0.171821i
$708$	−7.24017	−	2.12591i	−0.272102	−	0.0798965i
$709$	−13.1737	−	28.8464i	−0.494749	−	1.08335i	−0.978140	−	0.207945i	$-0.933322\pi$
$709$	−13.1737	−	28.8464i	−0.494749	−	1.08335i	0.483391	−	0.875404i	$-0.339405\pi$
$710$	−1.67356	−	11.6399i	−0.0628077	−	0.436837i
$711$	−2.49492	−	1.60339i	−0.0935668	−	0.0601318i
$712$	−2.42966			−0.0910555
$713$	5.89205	+	8.05069i	0.220659	+	0.301501i
$714$	2.70737			0.101321
$715$	−0.625160	−	0.401766i	−0.0233797	−	0.0150252i
$716$	−2.42925	−	16.8958i	−0.0907854	−	0.631426i
$717$	8.36870	+	18.3249i	0.312535	+	0.684356i
$718$	−4.24187	−	1.24553i	−0.158305	−	0.0464826i
$719$	−9.53863	+	20.8867i	−0.355731	+	0.778942i	0.644170	+	0.764882i	$0.277203\pi$
$719$	−9.53863	+	20.8867i	−0.355731	+	0.778942i	−0.999901	+	0.0140600i	$0.995524\pi$
$720$	−1.17510	+	1.35614i	−0.0437934	+	0.0505403i
$721$	−0.901377	+	6.26922i	−0.0335690	+	0.233478i
$722$	6.91696	−	2.03100i	0.257423	−	0.0755861i
$723$	4.69259	+	5.41553i	0.174519	+	0.201406i
$724$	−18.6340	+	11.9753i	−0.692527	+	0.445060i
$725$	2.12303	−	1.36439i	0.0788472	−	0.0506720i
$726$	−2.06414	−	2.38214i	−0.0766073	−	0.0884096i
$727$	−10.7692	+	3.16213i	−0.399408	+	0.117277i	−0.475267	−	0.879842i	$-0.657648\pi$
$727$	−10.7692	+	3.16213i	−0.399408	+	0.117277i	0.0758584	+	0.997119i	$0.475830\pi$
$728$	−0.0210382	+	0.146324i	−0.000779729	+	0.00542314i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	0.653176	−	1.43025i	0.0241751	−	0.0529361i
$731$	−0.0705957	−	0.0207288i	−0.00261108	−	0.000766682i
$732$	1.81178	+	3.96725i	0.0669653	+	0.146634i
$733$	−2.21030	−	15.3730i	−0.0816394	−	0.567814i	−0.989051	−	0.147572i	$-0.952854\pi$
$733$	−2.21030	−	15.3730i	−0.0816394	−	0.567814i	0.907412	−	0.420242i	$-0.138055\pi$
$734$	10.8397	+	6.96627i	0.400102	+	0.257130i
$735$	−1.79443			−0.0661885
$736$	2.34373	−	4.18413i	0.0863911	−	0.154229i
$737$	−15.3471			−0.565318
$738$	−0.756792	−	0.486360i	−0.0278579	−	0.0179032i
$739$	4.92099	+	34.2262i	0.181021	+	1.25903i	0.854354	+	0.519692i	$0.173953\pi$
$739$	4.92099	+	34.2262i	0.181021	+	1.25903i	−0.673332	+	0.739340i	$0.735138\pi$
$740$	5.48946	+	12.0202i	0.201797	+	0.441873i
$741$	−0.487054	−	0.143012i	−0.0178924	−	0.00525367i
$742$	3.56717	−	7.81100i	0.130955	−	0.286751i
$743$	−32.2984	+	37.2743i	−1.18491	+	1.36746i	−0.270481	+	0.962725i	$0.587183\pi$
$743$	−32.2984	+	37.2743i	−1.18491	+	1.36746i	−0.914433	+	0.404738i	$0.867363\pi$
$744$	−0.296049	+	2.05906i	−0.0108537	+	0.0754889i
$745$	18.7096	−	5.49362i	0.685466	−	0.201271i
$746$	−23.4462	−	27.0583i	−0.858425	−	0.990675i
$747$	3.81392	−	2.45106i	0.139544	−	0.0896796i
$748$	6.38048	−	4.10048i	0.233293	−	0.149929i
$749$	−4.21097	−	4.85972i	−0.153866	−	0.177570i
$750$	−11.6735	+	3.42764i	−0.426254	+	0.125160i
$751$	−1.14145	+	7.93894i	−0.0416520	+	0.289696i	0.958340	+	0.285631i	$0.0922031\pi$
$751$	−1.14145	+	7.93894i	−0.0416520	+	0.289696i	−0.999992	+	0.00406532i	$0.998706\pi$
$752$	−0.937261	+	1.08166i	−0.0341784	+	0.0394440i
$753$	5.43867	−	11.9090i	0.198196	−	0.433989i
$754$	0.201096	+	0.0590471i	0.00732349	+	0.00215037i
$755$	−15.0637	−	32.9850i	−0.548226	−	1.20045i
$756$	0.142315	+	0.989821i	0.00517594	+	0.0359995i
$757$	41.1032	+	26.4154i	1.49392	+	0.960084i	0.995661	+	0.0930567i	$0.0296638\pi$
$757$	41.1032	+	26.4154i	1.49392	+	0.960084i	0.498260	+	0.867028i	$0.333973\pi$
$758$	15.8725			0.576515
$759$	13.3898	+	1.10315i	0.486019	+	0.0400419i
$760$	−6.16172			−0.223509
$761$	39.4914	+	25.3796i	1.43156	+	0.920010i	0.999838	+	0.0180047i	$0.00573139\pi$
$761$	39.4914	+	25.3796i	1.43156	+	0.920010i	0.431725	+	0.902005i	$0.357905\pi$
$762$	0.173157	+	1.20433i	0.00627282	+	0.0436284i
$763$	−2.58028	−	5.65003i	−0.0934125	−	0.204545i
$764$	−2.48157	−	0.728653i	−0.0897799	−	0.0263618i
$765$	−2.01816	+	4.41916i	−0.0729668	+	0.159775i
$766$	−11.0083	+	12.7042i	−0.397746	+	0.459023i
$767$	0.158751	−	1.10414i	0.00573217	−	0.0398681i
$768$	0.959493	−	0.281733i	0.0346227	−	0.0101661i
$769$	7.29861	+	8.42305i	0.263195	+	0.303743i	0.871930	−	0.489630i	$-0.162868\pi$
$769$	7.29861	+	8.42305i	0.263195	+	0.303743i	−0.608735	+	0.793373i	$0.708323\pi$
$770$	−4.22895	+	2.71778i	−0.152401	+	0.0979419i
$771$	−16.6456	+	10.6975i	−0.599476	+	0.385260i
$772$	−2.12008	−	2.44671i	−0.0763034	−	0.0880589i
$773$	−6.82154	+	2.00298i	−0.245354	+	0.0720424i	−0.402097	−	0.915597i	$-0.631719\pi$
$773$	−6.82154	+	2.00298i	−0.245354	+	0.0720424i	0.156743	+	0.987639i	$0.449900\pi$
$774$	0.00386758	−	0.0268996i	0.000139017	−	0.000966887i
$775$	−2.42486	+	2.79844i	−0.0871037	+	0.100523i
$776$	−1.03631	+	2.26919i	−0.0372012	+	0.0814593i
$777$	7.06583	+	2.07471i	0.253485	+	0.0744299i
$778$	−12.4877	−	27.3443i	−0.447707	−	0.980341i
$779$	−0.439618	−	3.05761i	−0.0157509	−	0.109550i
$780$	−0.223158	−	0.143415i	−0.00799034	−	0.00513508i
$781$	−18.3588			−0.656929
$782$	2.89685	−	12.6568i	0.103591	−	0.452606i
$783$	1.41776			0.0506666
$784$	0.841254	+	0.540641i	0.0300448	+	0.0193086i
$785$	3.12125	+	21.7088i	0.111402	+	0.774819i
$786$	1.86195	+	4.07710i	0.0664135	+	0.145425i
$787$	8.59359	+	2.52331i	0.306328	+	0.0899461i	0.431284	−	0.902216i	$-0.358061\pi$
$787$	8.59359	+	2.52331i	0.306328	+	0.0899461i	−0.124956	+	0.992162i	$0.539879\pi$
$788$	−8.53140	+	18.6812i	−0.303918	+	0.665488i
$789$	3.88830	−	4.48734i	0.138427	−	0.159754i
$790$	0.757367	−	5.26760i	0.0269459	−	0.187413i
$791$	−0.164706	+	0.0483621i	−0.00585628	+	0.00171956i
$792$	1.83454	+	2.11717i	0.0651876	+	0.0752305i
$793$	−0.542387	+	0.348571i	−0.0192607	+	0.0123781i
$794$	−27.4774	+	17.6587i	−0.975137	+	0.626683i
$795$	10.0906	+	11.6452i	0.357876	+	0.413011i
$796$	−0.793290	+	0.232931i	−0.0281174	+	0.00825602i
$797$	1.60992	−	11.1973i	0.0570264	−	0.396628i	−0.941238	−	0.337743i	$-0.890337\pi$
$797$	1.60992	−	11.1973i	0.0570264	−	0.396628i	0.998265	−	0.0588846i	$-0.0187544\pi$
$798$	−2.24866	+	2.59510i	−0.0796019	+	0.0918655i
$799$	−1.60969	+	3.52472i	−0.0569466	+	0.124696i
$800$	1.70792	+	0.501490i	0.0603841	+	0.0177304i
$801$	−1.00932	−	2.21010i	−0.0356625	−	0.0780900i
$802$	2.04916	+	14.2522i	0.0723582	+	0.503262i
$803$	−2.06503	−	1.32712i	−0.0728734	−	0.0468329i
$804$	−5.47832			−0.193206
$805$	−1.92002	+	8.38886i	−0.0676718	+	0.295669i
$806$	−0.307519			−0.0108319
$807$	7.75658	+	4.98485i	0.273044	+	0.175475i
$808$	0.714779	+	4.97139i	0.0251458	+	0.174893i
$809$	−16.1155	−	35.2881i	−0.566592	−	1.24066i	−0.948592	−	0.316501i	$-0.897492\pi$
$809$	−16.1155	−	35.2881i	−0.566592	−	1.24066i	0.382001	−	0.924162i	$-0.375235\pi$
$810$	−1.72174	−	0.505549i	−0.0604959	−	0.0177632i
$811$	−13.1658	+	28.8291i	−0.462314	+	1.01233i	0.524640	+	0.851324i	$0.324200\pi$
$811$	−13.1658	+	28.8291i	−0.462314	+	1.01233i	−0.986954	+	0.161002i	$0.948527\pi$
$812$	0.928435	−	1.07147i	0.0325817	−	0.0376013i
$813$	1.63255	−	11.3546i	0.0572559	−	0.398223i
$814$	19.7944	−	5.81215i	0.693792	−	0.203716i
$815$	6.30540	+	7.27682i	0.220869	+	0.254896i
$816$	2.27758	−	1.46371i	0.0797314	−	0.0512402i
$817$	0.0785040	−	0.0504515i	0.00274651	−	0.00176507i
$818$	−3.46619	−	4.00020i	−0.121192	−	0.139864i
$819$	−0.141841	+	0.0416482i	−0.00495632	+	0.00145531i
$820$	0.229734	−	1.59784i	0.00802267	−	0.0557989i
$821$	16.0761	−	18.5528i	0.561061	−	0.647499i	−0.402363	−	0.915480i	$-0.631811\pi$
$821$	16.0761	−	18.5528i	0.561061	−	0.647499i	0.963424	+	0.267981i	$0.0863566\pi$
$822$	3.16157	−	6.92288i	0.110272	−	0.241463i
$823$	25.5358	+	7.49799i	0.890122	+	0.261363i	0.694652	−	0.719346i	$-0.255558\pi$
$823$	25.5358	+	7.49799i	0.890122	+	0.261363i	0.195470	+	0.980710i	$0.437377\pi$
$824$	2.63111	+	5.76132i	0.0916590	+	0.200705i
$825$	0.709667	+	4.93584i	0.0247074	+	0.171844i
$826$	−6.34796	−	4.07958i	−0.220874	−	0.141947i
$827$	46.6348			1.62165			0.810826	−	0.585287i	$-0.199018\pi$
$827$	46.6348			1.62165			0.810826	+	0.585287i	$0.199018\pi$
$828$	4.77964	+	0.393783i	0.166104	+	0.0136849i
$829$	−47.9161			−1.66420			−0.832098	−	0.554628i	$-0.812860\pi$
$829$	−47.9161			−1.66420			−0.832098	+	0.554628i	$0.812860\pi$
$830$	6.84381	+	4.39825i	0.237552	+	0.152666i
$831$	−1.87215	−	13.0211i	−0.0649441	−	0.451696i
$832$	0.0614103	+	0.134470i	0.00212902	+	0.00466190i
$833$	2.59770	+	0.762754i	0.0900050	+	0.0264279i
$834$	−8.68376	+	19.0148i	−0.300694	+	0.658428i
$835$	12.5702	−	14.5068i	0.435010	−	0.502028i
$836$	−1.36900	+	9.52163i	−0.0473480	+	0.329313i
$837$	−1.99597	+	0.586070i	−0.0689909	+	0.0202576i
$838$	−11.5831	−	13.3676i	−0.400133	−	0.461778i
$839$	12.6884	−	8.15433i	0.438052	−	0.281519i	−0.302970	−	0.953000i	$-0.597978\pi$
$839$	12.6884	−	8.15433i	0.438052	−	0.281519i	0.741021	+	0.671481i	$0.234342\pi$
$840$	−1.50957	+	0.970142i	−0.0520851	+	0.0334731i
$841$	17.6747	+	20.3976i	0.609471	+	0.703367i
$842$	−10.5494	+	3.09757i	−0.363555	+	0.106749i
$843$	−2.31356	+	16.0911i	−0.0796831	+	0.554208i
$844$	−0.198870	+	0.229508i	−0.00684538	+	0.00789999i
$845$	−9.67434	+	21.1838i	−0.332807	+	0.728746i
$846$	−1.37326	−	0.403226i	−0.0472137	−	0.0138632i
$847$	−1.30940	−	2.86718i	−0.0449915	−	0.0985176i
$848$	−1.22206	−	8.49959i	−0.0419656	−	0.291877i
$849$	20.3175	+	13.0573i	0.697296	+	0.448125i
$850$	4.81918			0.165297
$851$	17.2595	−	30.8124i	0.591649	−	1.05624i
$852$	−6.55338			−0.224515
$853$	24.0687	+	15.4680i	0.824098	+	0.529615i	0.883397	−	0.468625i	$-0.155250\pi$
$853$	24.0687	+	15.4680i	0.824098	+	0.529615i	−0.0592996	+	0.998240i	$0.518887\pi$
$854$	0.620688	+	4.31698i	0.0212395	+	0.147724i
$855$	−2.55967	−	5.60490i	−0.0875389	−	0.191684i
$856$	−6.16986	−	1.81163i	−0.210881	−	0.0619204i
$857$	−1.36871	+	2.99706i	−0.0467543	+	0.102378i	−0.931568	−	0.363568i	$-0.881558\pi$
$857$	−1.36871	+	2.99706i	−0.0467543	+	0.102378i	0.884813	+	0.465946i	$0.154286\pi$
$858$	−0.271198	+	0.312980i	−0.00925856	+	0.0106849i
$859$	1.77142	−	12.3205i	0.0604402	−	0.420371i	−0.937028	−	0.349255i	$-0.886435\pi$
$859$	1.77142	−	12.3205i	0.0604402	−	0.420371i	0.997468	−	0.0711161i	$-0.0226561\pi$
$860$	0.0467905	−	0.0137389i	0.00159554	−	0.000468493i
$861$	−0.589113	−	0.679872i	−0.0200769	−	0.0231700i
$862$	−8.55336	+	5.49691i	−0.291329	+	0.187226i
$863$	12.2307	−	7.86017i	0.416337	−	0.267563i	−0.315659	−	0.948873i	$-0.602226\pi$
$863$	12.2307	−	7.86017i	0.416337	−	0.267563i	0.731996	+	0.681309i	$0.238589\pi$
$864$	0.654861	+	0.755750i	0.0222788	+	0.0257111i
$865$	27.5963	−	8.10301i	0.938303	−	0.275511i
$866$	1.09299	−	7.60191i	0.0371413	−	0.258323i
$867$	−6.33260	+	7.30821i	−0.215066	+	0.248200i
$868$	−0.864162	+	1.89225i	−0.0293316	+	0.0642272i
$869$	−7.97169	−	2.34070i	−0.270421	−	0.0794028i
$870$	1.05684	+	2.31417i	0.0358304	+	0.0784576i
$871$	−0.115254	−	0.801611i	−0.00390524	−	0.0271616i
$872$	−5.22531	−	3.35810i	−0.176951	−	0.113720i
$873$	−2.49463			−0.0844304
$874$	9.72590	+	13.2891i	0.328983	+	0.449511i
$875$	−12.1663			−0.411295
$876$	−0.737137	−	0.473729i	−0.0249056	−	0.0160058i
$877$	0.231366	+	1.60919i	0.00781269	+	0.0543384i	0.993355	−	0.115092i	$-0.0367163\pi$
$877$	0.231366	+	1.60919i	0.00781269	+	0.0543384i	−0.985542	+	0.169430i	$0.945807\pi$
$878$	−7.14478	−	15.6449i	−0.241125	−	0.527989i
$879$	−9.27135	−	2.72231i	−0.312715	−	0.0918214i
$880$	−2.08827	+	4.57268i	−0.0703957	+	0.154145i
$881$	−4.34552	+	5.01500i	−0.146404	+	0.168960i	−0.824215	−	0.566277i	$-0.808383\pi$
$881$	−4.34552	+	5.01500i	−0.146404	+	0.168960i	0.677811	+	0.735236i	$0.262929\pi$
$882$	−0.142315	+	0.989821i	−0.00479199	+	0.0333290i
$883$	19.4337	−	5.70624i	0.653995	−	0.192030i	0.0621308	−	0.998068i	$-0.480210\pi$
$883$	19.4337	−	5.70624i	0.653995	−	0.192030i	0.591864	+	0.806038i	$0.298392\pi$
$884$	0.262093	+	0.302472i	0.00881515	+	0.0101732i
$885$	11.3910	−	7.32053i	0.382903	−	0.246077i
$886$	15.3202	−	9.84570i	0.514693	−	0.330773i
$887$	25.0272	+	28.8829i	0.840330	+	0.969793i	0.999849	−	0.0174023i	$-0.00553961\pi$
$887$	25.0272	+	28.8829i	0.840330	+	0.969793i	−0.159518	+	0.987195i	$0.550994\pi$
$888$	7.06583	−	2.07471i	0.237114	−	0.0696228i
$889$	−0.173157	+	1.20433i	−0.00580750	+	0.0403920i
$890$	2.85510	−	3.29496i	0.0957032	−	0.110447i
$891$	−1.16375	+	2.54826i	−0.0389872	+	0.0853701i
$892$	10.9432	+	3.21322i	0.366406	+	0.107587i
$893$	−2.04159	−	4.47047i	−0.0683193	−	0.149598i
$894$	−1.54649	−	10.7560i	−0.0517222	−	0.359736i
$895$	25.7677	+	16.5599i	0.861319	+	0.553536i
$896$	1.00000			0.0334077
$897$	0.0429352	+	0.707661i	0.00143356	+	0.0236281i
$898$	−27.6433			−0.922468
$899$	2.48109	+	1.59450i	0.0827489	+	0.0531795i
$900$	0.253324	+	1.76191i	0.00844412	+	0.0587302i
$901$	−9.65764	−	21.1473i	−0.321742	−	0.704518i
$902$	−2.41808	−	0.710011i	−0.0805131	−	0.0236408i
$903$	0.0112894	−	0.0247204i	0.000375688	−	0.000822642i
$904$	−0.112413	+	0.129732i	−0.00373881	+	0.00431482i
$905$	5.65660	−	39.3425i	0.188032	−	1.30779i
$906$	−19.3895	+	5.69327i	−0.644172	+	0.189146i
$907$	13.8406	+	15.9729i	0.459570	+	0.530373i	0.937481	−	0.348036i	$-0.113151\pi$
$907$	13.8406	+	15.9729i	0.459570	+	0.530373i	−0.477911	+	0.878408i	$0.658606\pi$
$908$	15.0835	−	9.69356i	0.500563	−	0.321692i
$909$	−4.22521	+	2.71538i	−0.140141	+	0.0900634i
$910$	−0.173714	−	0.200477i	−0.00575856	−	0.00664573i
$911$	43.5574	−	12.7896i	1.44312	−	0.423738i	0.535859	−	0.844307i	$-0.319988\pi$
$911$	43.5574	−	12.7896i	1.44312	−	0.423738i	0.907260	+	0.420569i	$0.138170\pi$
$912$	−0.488682	+	3.39885i	−0.0161819	+	0.112547i
$913$	8.31712	−	9.59846i	0.275256	−	0.317663i
$914$	−6.72364	+	14.7227i	−0.222398	+	0.486984i
$915$	−7.50916	−	2.20489i	−0.248245	−	0.0728914i
$916$	−9.46666	−	20.7291i	−0.312787	−	0.684908i
$917$	0.637875	+	4.43652i	0.0210645	+	0.146507i
$918$	2.27758	+	1.46371i	0.0751715	+	0.0483098i
$919$	46.0654			1.51956			0.759779	−	0.650181i	$-0.225307\pi$
$919$	46.0654			1.51956			0.759779	+	0.650181i	$0.225307\pi$
$920$	2.92014	+	8.09520i	0.0962741	+	0.266891i
$921$	22.9116			0.754963
$922$	7.99030	+	5.13505i	0.263146	+	0.169114i
$923$	−0.137872	−	0.958918i	−0.00453810	−	0.0315632i
$924$	1.16375	+	2.54826i	0.0382847	+	0.0838318i
$925$	12.5773	+	3.69304i	0.413540	+	0.121426i
$926$	−5.56534	+	12.1864i	−0.182888	+	0.400470i
$927$	−4.14768	+	4.78668i	−0.136228	+	0.157215i
$928$	0.201768	−	1.40333i	0.00662337	−	0.0460665i
$929$	−22.5722	+	6.62779i	−0.740569	+	0.217451i	−0.630192	−	0.776439i	$-0.717024\pi$
$929$	−22.5722	+	6.62779i	−0.740569	+	0.217451i	−0.110377	+	0.993890i	$0.535206\pi$
$930$	−2.44449	−	2.82109i	−0.0801580	−	0.0925072i
$931$	−2.88870	+	1.85646i	−0.0946734	+	0.0608429i
$932$	−6.83477	+	4.39244i	−0.223880	+	0.143879i
$933$	−4.52586	−	5.22312i	−0.148170	−	0.170997i
$934$	−12.8190	+	3.76401i	−0.419452	+	0.123162i
$935$	−1.93688	+	13.4713i	−0.0633428	+	0.440559i
$936$	−0.0968073	+	0.111722i	−0.00316425	+	0.00365173i
$937$	1.27292	−	2.78730i	0.0415844	−	0.0910571i	−0.887700	−	0.460423i	$-0.847698\pi$
$937$	1.27292	−	2.78730i	0.0415844	−	0.0910571i	0.929284	+	0.369366i	$0.120425\pi$
$938$	−5.25641	−	1.54342i	−0.171628	−	0.0503945i
$939$	0.131275	+	0.287453i	0.00428400	+	0.00938066i
$940$	−0.365501	−	2.54211i	−0.0119213	−	0.0829146i
$941$	28.7094	+	18.4504i	0.935900	+	0.601466i	0.917229	−	0.398359i	$-0.130420\pi$
$941$	28.7094	+	18.4504i	0.935900	+	0.601466i	0.0186703	+	0.999826i	$0.494057\pi$
$942$	12.2223			0.398223
$943$	−3.80871	+	2.02661i	−0.124029	+	0.0659957i
$944$	−7.54583			−0.245596
$945$	−1.50957	−	0.970142i	−0.0491063	−	0.0315587i
$946$	−0.0108347	−	0.0753572i	−0.000352268	−	0.00245008i
$947$	14.3550	+	31.4330i	0.466474	+	1.02144i	0.985964	+	0.166959i	$0.0533948\pi$
$947$	14.3550	+	31.4330i	0.466474	+	1.02144i	−0.519490	+	0.854477i	$0.673878\pi$
$948$	−2.84559	−	0.835539i	−0.0924203	−	0.0271371i
$949$	0.0538100	−	0.117827i	0.00174675	−	0.00382484i
$950$	−4.00268	+	4.61933i	−0.129864	+	0.149871i
$951$	1.39408	−	9.69601i	0.0452060	−	0.314415i
$952$	2.59770	−	0.762754i	0.0841920	−	0.0247210i
$953$	22.8785	+	26.4032i	0.741108	+	0.855284i	0.993675	−	0.112296i	$-0.0358203\pi$
$953$	22.8785	+	26.4032i	0.741108	+	0.855284i	−0.252567	+	0.967579i	$0.581275\pi$
$954$	7.22384	−	4.64248i	0.233880	−	0.150306i
$955$	3.90425	−	2.50911i	0.126338	−	0.0811928i
$956$	13.1924	+	15.2249i	0.426674	+	0.492408i
$957$	3.81086	−	1.11897i	0.123188	−	0.0361712i
$958$	5.90560	−	41.0744i	0.190801	−	1.32705i
$959$	4.98390	−	5.75173i	0.160939	−	0.185733i
$960$	−0.745433	+	1.63227i	−0.0240587	+	0.0526813i
$961$	25.5922	+	7.51454i	0.825554	+	0.242405i
$962$	0.452233	+	0.990253i	0.0145806	+	0.0319270i
$963$	−0.915132	−	6.36488i	−0.0294897	−	0.205105i
$964$	6.02823	+	3.87411i	0.194156	+	0.124777i
$965$	5.80939			0.187011
$966$	4.47509	+	1.72441i	0.143984	+	0.0554820i
$967$	26.4836			0.851655			0.425828	−	0.904804i	$-0.359983\pi$
$967$	26.4836			0.851655			0.425828	+	0.904804i	$0.359983\pi$
$968$	−2.65165	−	1.70411i	−0.0852273	−	0.0547723i
$969$	1.32304	+	9.20195i	0.0425022	+	0.295609i
$970$	−1.85958	−	4.07191i	−0.0597075	−	0.130741i
$971$	36.5820	+	10.7414i	1.17397	+	0.344709i	0.809847	−	0.586641i	$-0.199550\pi$
$971$	36.5820	+	10.7414i	1.17397	+	0.344709i	0.364125	+	0.931350i	$0.381368\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	−13.6891	+	15.7980i	−0.438852	+	0.506462i
$974$	−3.24370	+	22.5605i	−0.103935	+	0.722883i
$975$	−0.252480	+	0.0741348i	−0.00808583	+	0.00237421i
$976$	2.85609	+	3.29611i	0.0914213	+	0.105506i
$977$	21.5677	−	13.8607i	0.690010	−	0.443443i	−0.148079	−	0.988976i	$-0.547309\pi$
$977$	21.5677	−	13.8607i	0.690010	−	0.443443i	0.838089	+	0.545533i	$0.183673\pi$
$978$	4.51403	−	2.90099i	0.144343	−	0.0927635i
$979$	−4.45732	−	5.14402i	−0.142457	−	0.164404i
$980$	−1.72174	+	0.505549i	−0.0549990	+	0.0161492i
$981$	0.883966	−	6.14812i	0.0282228	−	0.196294i
$982$	22.1686	−	25.5839i	0.707427	−	0.816415i
$983$	−7.58214	+	16.6026i	−0.241833	+	0.529540i	−0.991162	−	0.132658i	$-0.957649\pi$
$983$	−7.58214	+	16.6026i	−0.241833	+	0.529540i	0.749329	+	0.662198i	$0.230376\pi$
$984$	−0.863160	−	0.253447i	−0.0275165	−	0.00807958i
$985$	−15.3090	−	33.5220i	−0.487785	−	1.06810i
$986$	−0.546261	−	3.79933i	−0.0173965	−	0.120995i
$987$	−1.20403	−	0.773785i	−0.0383248	−	0.0246298i
$988$	−0.507616			−0.0161494
$989$	−0.103487	−	0.0792279i	−0.00329069	−	0.00251930i
$990$	−5.02696			−0.159767
$991$	36.1576	+	23.2371i	1.14858	+	0.738150i	0.969357	−	0.245658i	$-0.0790039\pi$
$991$	36.1576	+	23.2371i	1.14858	+	0.738150i	0.179227	+	0.983808i	$0.442640\pi$
$992$	0.296049	+	2.05906i	0.00939955	+	0.0653753i
$993$	−1.33378	−	2.92056i	−0.0423261	−	0.0926812i
$994$	−6.28792	−	1.84630i	−0.199441	−	0.0585611i
$995$	0.616310	−	1.34953i	0.0195383	−	0.0427830i
$996$	2.96889	−	3.42628i	0.0940728	−	0.108566i
$997$	−1.75451	+	12.2029i	−0.0555658	+	0.386469i	0.942994	+	0.332811i	$0.107997\pi$
$997$	−1.75451	+	12.2029i	−0.0555658	+	0.386469i	−0.998559	+	0.0536577i	$0.982912\pi$
$998$	21.3271	−	6.26219i	0.675097	−	0.198226i
$999$	4.82248	+	5.56543i	0.152576	+	0.176083i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.d.127.1	✓	20	23.12	even	11	inner
966.2.q.d.715.1	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)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.72174 - 0.505549i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-1.72174 - 0.505549i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-0.654861 + 0.755750i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-1.17510 - 1.35614i) q^{10} +(-2.35671 + 1.51456i) q^{11} +(-0.841254 + 0.540641i) q^{12} +(-0.0968073 - 0.111722i) q^{13} +(-0.959493 + 0.281733i) q^{14} +(0.255374 - 1.77616i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-1.12468 + 2.46271i) q^{17} +(-0.959493 - 0.281733i) q^{18} +(-1.42645 - 3.12350i) q^{19} +(-0.255374 - 1.77616i) q^{20} +(-0.841254 - 0.540641i) q^{21} -2.80142 q^{22} +(-3.42760 + 3.35434i) q^{23} -1.00000 q^{24} +(-1.49745 - 0.962353i) q^{25} +(-0.0210382 - 0.146324i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-0.959493 - 0.281733i) q^{28} +(-0.588959 + 1.28964i) q^{29} +(1.17510 - 1.35614i) q^{30} +(0.296049 - 2.05906i) q^{31} +(-0.959493 + 0.281733i) q^{32} +(-1.83454 - 2.11717i) q^{33} +(-2.27758 + 1.46371i) q^{34} +(1.50957 - 0.970142i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-7.06583 + 2.07471i) q^{37} +(0.488682 - 3.39885i) q^{38} +(0.0968073 - 0.111722i) q^{39} +(0.745433 - 1.63227i) q^{40} +(0.863160 + 0.253447i) q^{41} +(-0.415415 - 0.909632i) q^{42} +(0.00386758 + 0.0268996i) q^{43} +(-2.35671 - 1.51456i) q^{44} +1.79443 q^{45} +(-4.69697 + 0.968747i) q^{46} +1.43124 q^{47} +(-0.841254 - 0.540641i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.739448 - 1.61917i) q^{50} +(-2.59770 - 0.762754i) q^{51} +(0.0614103 - 0.134470i) q^{52} +(-5.62329 + 6.48962i) q^{53} +(0.142315 - 0.989821i) q^{54} +(4.82333 - 1.41626i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(2.88870 - 1.85646i) q^{57} +(-1.19270 + 0.766499i) q^{58} +(4.94147 + 5.70276i) q^{59} +(1.72174 - 0.505549i) q^{60} +(0.620688 - 4.31698i) q^{61} +(1.36227 - 1.57214i) q^{62} +(0.415415 - 0.909632i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.110197 + 0.241297i) q^{65} +(-0.398684 - 2.77291i) q^{66} +(4.60866 + 2.96181i) q^{67} -2.70737 q^{68} +(-3.80799 - 2.91534i) q^{69} +1.79443 q^{70} +(5.51305 + 3.54302i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(0.364002 + 0.797053i) q^{73} +(-7.06583 - 2.07471i) q^{74} +(0.739448 - 1.61917i) q^{75} +(2.24866 - 2.59510i) q^{76} +(0.398684 - 2.77291i) q^{77} +(0.141841 - 0.0416482i) q^{78} +(1.94213 + 2.24134i) q^{79} +(1.50957 - 0.970142i) q^{80} +(0.841254 - 0.540641i) q^{81} +(0.589113 + 0.679872i) q^{82} +(-4.34998 + 1.27727i) q^{83} +(0.142315 - 0.989821i) q^{84} +(3.18143 - 3.67157i) q^{85} +(-0.0112894 + 0.0247204i) q^{86} +(-1.36033 - 0.399429i) q^{87} +(-1.16375 - 2.54826i) q^{88} +(0.345777 + 2.40493i) q^{89} +(1.50957 + 0.970142i) q^{90} +0.147829 q^{91} +(-4.47509 - 1.72441i) q^{92} +2.08024 q^{93} +(1.20403 + 0.773785i) q^{94} +(0.876905 + 6.09900i) q^{95} +(-0.415415 - 0.909632i) q^{96} +(2.39358 + 0.702818i) q^{97} +(0.415415 - 0.909632i) q^{98} +(1.83454 - 2.11717i) 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

L-functions

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