LMFDB - Embedded newform 133.2.g.a.102.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(30,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("133.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.g (of order $3$, degree $2$, 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			102.8
Character	$\chi$	$=$	133.102
Dual form			133.2.g.a.30.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.433977 - 0.751669i) q^{2} -2.55943 q^{3} +(0.623329 + 1.07964i) q^{4} +(-1.78218 + 3.08682i) q^{5} +(-1.11073 + 1.92385i) q^{6} +(-2.63921 - 0.185998i) q^{7} +2.81795 q^{8} +3.55070 q^{9} +O(q^{10})$	\(q+(0.433977 - 0.751669i) q^{2} -2.55943 q^{3} +(0.623329 + 1.07964i) q^{4} +(-1.78218 + 3.08682i) q^{5} +(-1.11073 + 1.92385i) q^{6} +(-2.63921 - 0.185998i) q^{7} +2.81795 q^{8} +3.55070 q^{9} +(1.54685 + 2.67922i) q^{10} +(-1.71385 + 2.96848i) q^{11} +(-1.59537 - 2.76326i) q^{12} +(1.01753 - 1.76241i) q^{13} +(-1.28516 + 1.90309i) q^{14} +(4.56137 - 7.90052i) q^{15} +(-0.0237348 + 0.0411099i) q^{16} +5.19677 q^{17} +(1.54092 - 2.66895i) q^{18} +(-4.00476 + 1.72102i) q^{19} -4.44353 q^{20} +(6.75487 + 0.476049i) q^{21} +(1.48754 + 2.57650i) q^{22} -0.934166 q^{23} -7.21234 q^{24} +(-3.85232 - 6.67241i) q^{25} +(-0.883167 - 1.52969i) q^{26} -1.40947 q^{27} +(-1.44428 - 2.96532i) q^{28} +(-1.90513 + 3.29979i) q^{29} +(-3.95905 - 6.85728i) q^{30} +(0.776918 - 1.34566i) q^{31} +(2.83855 + 4.91651i) q^{32} +(4.38649 - 7.59762i) q^{33} +(2.25528 - 3.90625i) q^{34} +(5.27768 - 7.81528i) q^{35} +(2.21325 + 3.83346i) q^{36} +(-2.32338 - 4.02422i) q^{37} +(-0.444329 + 3.75714i) q^{38} +(-2.60429 + 4.51077i) q^{39} +(-5.02208 + 8.69850i) q^{40} +(5.71816 + 9.90415i) q^{41} +(3.28929 - 4.87083i) q^{42} +(1.90592 + 3.30114i) q^{43} -4.27317 q^{44} +(-6.32797 + 10.9604i) q^{45} +(-0.405406 + 0.702184i) q^{46} +10.4607 q^{47} +(0.0607476 - 0.105218i) q^{48} +(6.93081 + 0.981772i) q^{49} -6.68726 q^{50} -13.3008 q^{51} +2.53702 q^{52} +(-0.138988 - 0.240734i) q^{53} +(-0.611677 + 1.05946i) q^{54} +(-6.10878 - 10.5807i) q^{55} +(-7.43714 - 0.524132i) q^{56} +(10.2499 - 4.40485i) q^{57} +(1.65357 + 2.86406i) q^{58} +0.461843 q^{59} +11.3729 q^{60} +2.59395 q^{61} +(-0.674329 - 1.16797i) q^{62} +(-9.37102 - 0.660421i) q^{63} +4.83251 q^{64} +(3.62683 + 6.28186i) q^{65} +(-3.80727 - 6.59438i) q^{66} +(2.18080 + 3.77726i) q^{67} +(3.23929 + 5.61062i) q^{68} +2.39094 q^{69} +(-3.58412 - 7.35872i) q^{70} +(-1.39719 - 2.42000i) q^{71} +10.0057 q^{72} -13.2219 q^{73} -4.03317 q^{74} +(9.85975 + 17.0776i) q^{75} +(-4.35436 - 3.25092i) q^{76} +(5.07534 - 7.51565i) q^{77} +(2.26041 + 3.91514i) q^{78} +(2.69849 - 4.67392i) q^{79} +(-0.0845993 - 0.146530i) q^{80} -7.04464 q^{81} +9.92620 q^{82} -15.6183 q^{83} +(3.69654 + 7.58954i) q^{84} +(-9.26157 + 16.0415i) q^{85} +3.30849 q^{86} +(4.87606 - 8.44559i) q^{87} +(-4.82954 + 8.36502i) q^{88} -1.16469 q^{89} +(5.49238 + 9.51309i) q^{90} +(-3.01327 + 4.46210i) q^{91} +(-0.582293 - 1.00856i) q^{92} +(-1.98847 + 3.44413i) q^{93} +(4.53970 - 7.86299i) q^{94} +(1.82469 - 15.4291i) q^{95} +(-7.26507 - 12.5835i) q^{96} +(-1.27230 - 2.20368i) q^{97} +(3.74578 - 4.78361i) q^{98} +(-6.08537 + 10.5402i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.433977	−	0.751669i	0.306868	−	0.531511i	−0.670808	−	0.741631i	$-0.734052\pi$
$2$	0.433977	−	0.751669i	0.306868	−	0.531511i	0.977675	+	0.210121i	$0.0673857\pi$
$3$	−2.55943			−1.47769			−0.738845	−	0.673876i	$-0.764628\pi$
$3$	−2.55943			−1.47769			−0.738845	+	0.673876i	$0.764628\pi$
$4$	0.623329	+	1.07964i	0.311664	+	0.539819i
$5$	−1.78218	+	3.08682i	−0.797014	+	1.38047i	0.124538	+	0.992215i	$0.460255\pi$
$5$	−1.78218	+	3.08682i	−0.797014	+	1.38047i	−0.921552	+	0.388254i	$0.873078\pi$
$6$	−1.11073	+	1.92385i	−0.453455	+	0.785407i
$7$	−2.63921	−	0.185998i	−0.997526	−	0.0703005i
$7$	−2.63921	−	0.185998i	−0.997526	−	0.0703005i
$8$	2.81795			0.996294
$9$	3.55070			1.18357
$10$	1.54685	+	2.67922i	0.489156	+	0.847243i
$11$	−1.71385	+	2.96848i	−0.516746	+	0.895030i	0.483065	+	0.875584i	$0.339523\pi$
$11$	−1.71385	+	2.96848i	−0.516746	+	0.895030i	−0.999811	+	0.0194457i	$0.993810\pi$
$12$	−1.59537	−	2.76326i	−0.460543	−	0.797684i
$13$	1.01753	−	1.76241i	0.282211	−	0.488805i	−0.689718	−	0.724078i	$-0.742265\pi$
$13$	1.01753	−	1.76241i	0.282211	−	0.488805i	0.971929	+	0.235274i	$0.0755987\pi$
$14$	−1.28516	+	1.90309i	−0.343474	+	0.508623i
$15$	4.56137	−	7.90052i	1.17774	−	2.03990i
$16$	−0.0237348	+	0.0411099i	−0.00593370	+	0.0102775i
$17$	5.19677			1.26040			0.630201	−	0.776432i	$-0.282973\pi$
$17$	5.19677			1.26040			0.630201	+	0.776432i	$0.282973\pi$
$18$	1.54092	−	2.66895i	0.363198	−	0.629078i
$19$	−4.00476	+	1.72102i	−0.918754	+	0.394830i
$19$	−4.00476	+	1.72102i	−0.918754	+	0.394830i
$20$	−4.44353			−0.993604
$21$	6.75487	+	0.476049i	1.47403	+	0.103882i
$22$	1.48754	+	2.57650i	0.317145	+	0.549312i
$23$	−0.934166			−0.194787			−0.0973936	−	0.995246i	$-0.531051\pi$
$23$	−0.934166			−0.194787			−0.0973936	+	0.995246i	$0.531051\pi$
$24$	−7.21234			−1.47221
$25$	−3.85232	−	6.67241i	−0.770464	−	1.33448i
$26$	−0.883167	−	1.52969i	−0.173203	−	0.299997i
$27$	−1.40947			−0.271253
$28$	−1.44428	−	2.96532i	−0.272944	−	0.560393i
$29$	−1.90513	+	3.29979i	−0.353774	+	0.612755i	−0.986907	−	0.161288i	$-0.948435\pi$
$29$	−1.90513	+	3.29979i	−0.353774	+	0.612755i	0.633133	+	0.774043i	$0.281769\pi$
$30$	−3.95905	−	6.85728i	−0.722821	−	1.25196i
$31$	0.776918	−	1.34566i	0.139539	−	0.241688i	−0.787783	−	0.615952i	$-0.788771\pi$
$31$	0.776918	−	1.34566i	0.139539	−	0.241688i	0.927322	+	0.374264i	$0.122105\pi$
$32$	2.83855	+	4.91651i	0.501789	+	0.869124i
$33$	4.38649	−	7.59762i	0.763590	−	1.32258i
$34$	2.25528	−	3.90625i	0.386776	−	0.669917i
$35$	5.27768	−	7.81528i	0.892090	−	1.32102i
$36$	2.21325	+	3.83346i	0.368875	+	0.638911i
$37$	−2.32338	−	4.02422i	−0.381962	−	0.661577i	0.609381	−	0.792878i	$-0.291418\pi$
$37$	−2.32338	−	4.02422i	−0.381962	−	0.661577i	−0.991343	+	0.131300i	$0.958085\pi$
$38$	−0.444329	+	3.75714i	−0.0720797	+	0.609488i
$39$	−2.60429	+	4.51077i	−0.417021	+	0.722301i
$40$	−5.02208	+	8.69850i	−0.794061	+	1.37535i
$41$	5.71816	+	9.90415i	0.893027	+	1.54677i	0.836227	+	0.548383i	$0.184756\pi$
$41$	5.71816	+	9.90415i	0.893027	+	1.54677i	0.0567999	+	0.998386i	$0.481910\pi$
$42$	3.28929	−	4.87083i	0.507548	−	0.751586i
$43$	1.90592	+	3.30114i	0.290650	+	0.503420i	0.973963	−	0.226705i	$-0.0727953\pi$
$43$	1.90592	+	3.30114i	0.290650	+	0.503420i	−0.683314	+	0.730125i	$0.739462\pi$
$44$	−4.27317			−0.644205
$45$	−6.32797	+	10.9604i	−0.943319	+	1.63388i
$46$	−0.405406	+	0.702184i	−0.0597739	+	0.103531i
$47$	10.4607			1.52585			0.762925	−	0.646487i	$-0.223763\pi$
$47$	10.4607			1.52585			0.762925	+	0.646487i	$0.223763\pi$
$48$	0.0607476	−	0.105218i	0.00876816	−	0.0151869i
$49$	6.93081	+	0.981772i	0.990116	+	0.140253i
$50$	−6.68726			−0.945722
$51$	−13.3008			−1.86248
$52$	2.53702			0.351821
$53$	−0.138988	−	0.240734i	−0.0190915	−	0.0330674i	0.856322	−	0.516443i	$-0.172744\pi$
$53$	−0.138988	−	0.240734i	−0.0190915	−	0.0330674i	−0.875413	+	0.483375i	$0.839411\pi$
$54$	−0.611677	+	1.05946i	−0.0832387	+	0.144174i
$55$	−6.10878	−	10.5807i	−0.823708	−	1.42670i
$56$	−7.43714	−	0.524132i	−0.993830	−	0.0700400i
$57$	10.2499	−	4.40485i	1.35763	−	0.583436i
$58$	1.65357	+	2.86406i	0.217124	+	0.376070i
$59$	0.461843			0.0601268			0.0300634	−	0.999548i	$-0.490429\pi$
$59$	0.461843			0.0601268			0.0300634	+	0.999548i	$0.490429\pi$
$60$	11.3729			1.46824
$61$	2.59395			0.332121			0.166061	−	0.986116i	$-0.446895\pi$
$61$	2.59395			0.332121			0.166061	+	0.986116i	$0.446895\pi$
$62$	−0.674329	−	1.16797i	−0.0856398	−	0.148333i
$63$	−9.37102	−	0.660421i	−1.18064	−	0.0832053i
$64$	4.83251			0.604064
$65$	3.62683	+	6.28186i	0.449853	+	0.779169i
$66$	−3.80727	−	6.59438i	−0.468642	−	0.811712i
$67$	2.18080	+	3.77726i	0.266427	+	0.461466i	0.967937	−	0.251195i	$-0.0808234\pi$
$67$	2.18080	+	3.77726i	0.266427	+	0.461466i	−0.701509	+	0.712660i	$0.747490\pi$
$68$	3.23929	+	5.61062i	0.392822	+	0.680388i
$69$	2.39094			0.287835
$70$	−3.58412	−	7.35872i	−0.428384	−	0.879535i
$71$	−1.39719	−	2.42000i	−0.165816	−	0.287202i	0.771129	−	0.636679i	$-0.219692\pi$
$71$	−1.39719	−	2.42000i	−0.165816	−	0.287202i	−0.936945	+	0.349478i	$0.886359\pi$
$72$	10.0057			1.17918
$73$	−13.2219			−1.54751			−0.773753	−	0.633488i	$-0.781623\pi$
$73$	−13.2219			−1.54751			−0.773753	+	0.633488i	$0.781623\pi$
$74$	−4.03317			−0.468847
$75$	9.85975	+	17.0776i	1.13851	+	1.97195i
$76$	−4.35436	−	3.25092i	−0.499480	−	0.372906i
$77$	5.07534	−	7.51565i	0.578388	−	0.856488i
$78$	2.26041	+	3.91514i	0.255941	+	0.443302i
$79$	2.69849	−	4.67392i	0.303604	−	0.525857i	−0.673346	−	0.739328i	$-0.735143\pi$
$79$	2.69849	−	4.67392i	0.303604	−	0.525857i	0.976949	+	0.213471i	$0.0684768\pi$
$80$	−0.0845993	−	0.146530i	−0.00945849	−	0.0163826i
$81$	−7.04464			−0.782738
$82$	9.92620			1.09617
$83$	−15.6183			−1.71433			−0.857163	−	0.515045i	$-0.827775\pi$
$83$	−15.6183			−1.71433			−0.857163	+	0.515045i	$0.827775\pi$
$84$	3.69654	+	7.58954i	0.403326	+	0.828087i
$85$	−9.26157	+	16.0415i	−1.00456	+	1.73995i
$86$	3.30849			0.356764
$87$	4.87606	−	8.44559i	0.522769	−	0.905462i
$88$	−4.82954	+	8.36502i	−0.514831	+	0.891714i
$89$	−1.16469			−0.123457			−0.0617287	−	0.998093i	$-0.519661\pi$
$89$	−1.16469			−0.123457			−0.0617287	+	0.998093i	$0.519661\pi$
$90$	5.49238	+	9.51309i	0.578948	+	1.00277i
$91$	−3.01327	+	4.46210i	−0.315876	+	0.467756i
$92$	−0.582293	−	1.00856i	−0.0607082	−	0.105150i
$93$	−1.98847	+	3.44413i	−0.206195	+	0.357140i
$94$	4.53970	−	7.86299i	0.468234	−	0.811005i
$95$	1.82469	−	15.4291i	0.187209	−	1.58300i
$96$	−7.26507	−	12.5835i	−0.741488	−	1.28430i
$97$	−1.27230	−	2.20368i	−0.129182	−	0.223750i	0.794178	−	0.607685i	$-0.207902\pi$
$97$	−1.27230	−	2.20368i	−0.129182	−	0.223750i	−0.923360	+	0.383936i	$0.874568\pi$
$98$	3.74578	−	4.78361i	0.378381	−	0.483218i
$99$	−6.08537	+	10.5402i	−0.611603	+	1.05933i
$100$	4.80252	−	8.31821i	0.480252	−	0.831821i
$101$	6.34412	+	10.9883i	0.631263	+	1.09338i	0.987294	+	0.158906i	$0.0507965\pi$
$101$	6.34412	+	10.9883i	0.631263	+	1.09338i	−0.356031	+	0.934474i	$0.615870\pi$
$102$	−5.77223	+	9.99779i	−0.571535	+	0.989928i
$103$	−1.78813	−	3.09713i	−0.176189	−	0.305169i	0.764383	−	0.644763i	$-0.223044\pi$
$103$	−1.78813	−	3.09713i	−0.176189	−	0.305169i	−0.940572	+	0.339594i	$0.889710\pi$
$104$	2.86734	−	4.96638i	0.281166	−	0.486993i
$105$	−13.5079	+	20.0027i	−1.31823	+	1.95206i
$106$	−0.241270			−0.0234342
$107$	3.51285	+	6.08443i	0.339600	+	0.588204i	0.984357	−	0.176183i	$-0.0563751\pi$
$107$	3.51285	+	6.08443i	0.339600	+	0.588204i	−0.644758	+	0.764387i	$0.723042\pi$
$108$	−0.878564	−	1.52172i	−0.0845398	−	0.146427i
$109$	16.0272			1.53513			0.767563	−	0.640974i	$-0.221469\pi$
$109$	16.0272			1.53513			0.767563	+	0.640974i	$0.221469\pi$
$110$	−10.6043			−1.01108
$111$	5.94654	+	10.2997i	0.564421	+	0.977606i
$112$	0.0702874	−	0.104083i	0.00664153	−	0.00983490i
$113$	−12.1186			−1.14002			−0.570009	−	0.821638i	$-0.693060\pi$
$113$	−12.1186			−1.14002			−0.570009	+	0.821638i	$0.693060\pi$
$114$	1.13723	−	9.61614i	0.106511	−	0.900634i
$115$	1.66485	−	2.88361i	0.155248	−	0.268898i
$116$	−4.75010			−0.441036
$117$	3.61293	−	6.25778i	0.334016	−	0.578532i
$118$	0.200429	−	0.347153i	0.0184510	−	0.0319580i
$119$	−13.7153	−	0.966587i	−1.25728	−	0.0886069i
$120$	12.8537	−	22.2632i	1.17338	−	2.03235i
$121$	−0.374579	−	0.648790i	−0.0340527	−	0.0589809i
$122$	1.12571	−	1.94979i	0.101917	−	0.176526i
$123$	−14.6353	−	25.3490i	−1.31962	−	2.28564i
$124$	1.93710			0.173957
$125$	9.64029			0.862254
$126$	−4.56322	+	6.75730i	−0.406524	+	0.601988i
$127$	8.87242	−	15.3675i	0.787300	−	1.36364i	−0.140315	−	0.990107i	$-0.544811\pi$
$127$	8.87242	−	15.3675i	0.787300	−	1.36364i	0.927615	−	0.373537i	$-0.121855\pi$
$128$	−3.57990	+	6.20056i	−0.316421	+	0.548058i
$129$	−4.87807	−	8.44906i	−0.429490	−	0.743898i
$130$	6.29584			0.552182
$131$	3.78036	−	6.54778i	0.330292	−	0.572082i	−0.652277	−	0.757980i	$-0.726186\pi$
$131$	3.78036	−	6.54778i	0.330292	−	0.572082i	0.982569	+	0.185898i	$0.0595195\pi$
$132$	10.9369			0.951935
$133$	10.8895	−	3.79726i	0.944238	−	0.329264i
$134$	3.78567			0.327032
$135$	2.51193	−	4.35079i	0.216192	−	0.374456i
$136$	14.6442			1.25573
$137$	−3.17940	−	5.50689i	−0.271635	−	0.470485i	0.697646	−	0.716443i	$-0.254231\pi$
$137$	−3.17940	−	5.50689i	−0.271635	−	0.470485i	−0.969281	+	0.245958i	$0.920898\pi$
$138$	1.03761	−	1.79719i	0.0883273	−	0.152987i
$139$	1.73871	−	3.01153i	0.147475	−	0.255435i	−0.782818	−	0.622250i	$-0.786219\pi$
$139$	1.73871	−	3.01153i	0.147475	−	0.255435i	0.930294	+	0.366816i	$0.119552\pi$
$140$	11.7274	+	0.826487i	0.991146	+	0.0698509i
$141$	−26.7734			−2.25473
$142$	−2.42539			−0.203534
$143$	3.48779	+	6.04102i	0.291663	+	0.505176i
$144$	−0.0842751	+	0.145969i	−0.00702292	+	0.0121641i
$145$	−6.79058	−	11.7616i	−0.563927	−	0.976750i
$146$	−5.73799	+	9.93849i	−0.474880	+	0.822515i
$147$	−17.7389	−	2.51278i	−1.46308	−	0.207251i
$148$	2.89646	−	5.01682i	0.238088	−	0.412380i
$149$	−0.725755	+	1.25705i	−0.0594562	+	0.102981i	−0.894221	−	0.447625i	$-0.852270\pi$
$149$	−0.725755	+	1.25705i	−0.0594562	+	0.102981i	0.834765	+	0.550606i	$0.185603\pi$
$150$	17.1156			1.39748
$151$	5.63839	−	9.76598i	0.458846	−	0.794745i	−0.540054	−	0.841630i	$-0.681596\pi$
$151$	5.63839	−	9.76598i	0.458846	−	0.794745i	0.998900	+	0.0468857i	$0.0149296\pi$
$152$	−11.2852	+	4.84975i	−0.915350	+	0.393367i
$153$	18.4521			1.49177
$154$	−3.44671	−	7.07659i	−0.277744	−	0.570248i
$155$	2.76921	+	4.79642i	0.222429	+	0.385258i
$156$	−6.49333			−0.519882
$157$	−5.15383			−0.411320			−0.205660	−	0.978623i	$-0.565934\pi$
$157$	−5.15383			−0.411320			−0.205660	+	0.978623i	$0.565934\pi$
$158$	−2.34216	−	4.05674i	−0.186332	−	0.322737i
$159$	0.355730	+	0.616143i	0.0282112	+	0.0488633i
$160$	−20.2352			−1.59973
$161$	2.46546	+	0.173753i	0.194305	+	0.0136936i
$162$	−3.05721	+	5.29524i	−0.240197	+	0.416034i
$163$	5.82594	+	10.0908i	0.456323	+	0.790375i	0.998763	−	0.0497197i	$-0.0158328\pi$
$163$	5.82594	+	10.0908i	0.456323	+	0.790375i	−0.542440	+	0.840094i	$0.682499\pi$
$164$	−7.12859	+	12.3471i	−0.556650	+	0.964145i
$165$	15.6350	+	27.0806i	1.21718	+	2.10822i
$166$	−6.77795	+	11.7398i	−0.526071	+	0.911182i
$167$	−4.23436	+	7.33413i	−0.327665	+	0.567532i	−0.982048	−	0.188631i	$-0.939595\pi$
$167$	−4.23436	+	7.33413i	−0.327665	+	0.567532i	0.654383	+	0.756163i	$0.272928\pi$
$168$	19.0349	+	1.34148i	1.46857	+	0.103497i
$169$	4.42927	+	7.67173i	0.340713	+	0.590133i
$170$	8.03860	+	13.9233i	0.616533	+	1.06787i
$171$	−14.2197	+	6.11084i	−1.08741	+	0.467307i
$172$	−2.37602	+	4.11540i	−0.181170	+	0.313796i
$173$	7.22273	−	12.5101i	0.549134	−	0.951128i	−0.449200	−	0.893431i	$-0.648291\pi$
$173$	7.22273	−	12.5101i	0.549134	−	0.951128i	0.998334	−	0.0576969i	$-0.0183757\pi$
$174$	−4.23219	−	7.33037i	−0.320842	−	0.555714i
$175$	8.92601	+	18.3264i	0.674743	+	1.38534i
$176$	−0.0813559	−	0.140913i	−0.00613243	−	0.0106217i
$177$	−1.18206			−0.0888487
$178$	−0.505450	+	0.875465i	−0.0378851	+	0.0656189i
$179$	3.56246	−	6.17037i	0.266271	−	0.461195i	−0.701625	−	0.712547i	$-0.747542\pi$
$179$	3.56246	−	6.17037i	0.266271	−	0.461195i	0.967896	+	0.251352i	$0.0808750\pi$
$180$	−15.7776			−1.17600
$181$	11.2731	−	19.5256i	0.837923	−	1.45133i	−0.0537050	−	0.998557i	$-0.517103\pi$
$181$	11.2731	−	19.5256i	0.837923	−	1.45133i	0.891628	−	0.452769i	$-0.149564\pi$
$182$	2.04634	+	4.20143i	0.151685	+	0.311431i
$183$	−6.63904			−0.490772
$184$	−2.63243			−0.194065
$185$	16.5627			1.21772
$186$	1.72590	+	2.98934i	0.126549	+	0.219189i
$187$	−8.90649	+	15.4265i	−0.651307	+	1.12810i
$188$	6.52045	+	11.2938i	0.475553	+	0.823682i
$189$	3.71988	+	0.262158i	0.270582	+	0.0190692i
$190$	−10.8057	−	8.06745i	−0.783931	−	0.585275i
$191$	4.06642	+	7.04325i	0.294236	+	0.509631i	0.974807	−	0.223051i	$-0.0716015\pi$
$191$	4.06642	+	7.04325i	0.294236	+	0.509631i	−0.680571	+	0.732682i	$0.738268\pi$
$192$	−12.3685			−0.892619
$193$	−20.9943			−1.51120			−0.755602	−	0.655031i	$-0.772656\pi$
$193$	−20.9943			−1.51120			−0.755602	+	0.655031i	$0.772656\pi$
$194$	−2.20859			−0.158567
$195$	−9.28263	−	16.0780i	−0.664743	−	1.15137i
$196$	3.26022	+	8.09473i	0.232873	+	0.578195i
$197$	7.60610			0.541912			0.270956	−	0.962592i	$-0.412660\pi$
$197$	7.60610			0.541912			0.270956	+	0.962592i	$0.412660\pi$
$198$	5.28182	+	9.14837i	0.375362	+	0.650147i
$199$	11.1991	+	19.3974i	0.793882	+	1.37504i	0.923547	+	0.383485i	$0.125276\pi$
$199$	11.1991	+	19.3974i	0.793882	+	1.37504i	−0.129665	+	0.991558i	$0.541390\pi$
$200$	−10.8556	−	18.8025i	−0.767609	−	1.32954i
$201$	−5.58162	−	9.66764i	−0.393697	−	0.681903i
$202$	11.0128			0.774857
$203$	5.64179	−	8.35447i	0.395976	−	0.586369i
$204$	−8.29076	−	14.3600i	−0.580469	−	1.00540i
$205$	−40.7631			−2.84702
$206$	−3.10402			−0.216267
$207$	−3.31694			−0.230543
$208$	0.0483016	+	0.0836609i	0.00334912	+	0.00580084i
$209$	1.75474	−	14.8376i	0.121378	−	1.02634i
$210$	9.17331	+	18.8341i	0.633019	+	1.29968i
$211$	12.6354	+	21.8852i	0.869859	+	1.50664i	0.862140	+	0.506670i	$0.169124\pi$
$211$	12.6354	+	21.8852i	0.869859	+	1.50664i	0.00771932	+	0.999970i	$0.497543\pi$
$212$	0.173270	−	0.300113i	0.0119003	−	0.0206118i
$213$	3.57601	+	6.19384i	0.245024	+	0.424395i
$214$	6.09797			0.416849
$215$	−13.5867			−0.926607
$216$	−3.97181			−0.270248
$217$	−2.30074	+	3.40697i	−0.156184	+	0.231280i
$218$	6.95542	−	12.0471i	0.471081	−	0.815936i
$219$	33.8405			2.28673
$220$	7.61556	−	13.1905i	0.513441	−	0.889305i
$221$	5.28786	−	9.15884i	0.355700	−	0.616090i
$222$	10.3226			0.692810
$223$	8.22523	+	14.2465i	0.550802	+	0.954018i	0.998217	+	0.0596911i	$0.0190116\pi$
$223$	8.22523	+	14.2465i	0.550802	+	0.954018i	−0.447414	+	0.894327i	$0.647655\pi$
$224$	−6.57705	−	13.5036i	−0.439448	−	0.902250i
$225$	−13.6784	−	23.6917i	−0.911894	−	1.57945i
$226$	−5.25917	+	9.10915i	−0.349835	+	0.605932i
$227$	7.80348	−	13.5160i	0.517935	−	0.897090i	−0.481848	−	0.876255i	$-0.660034\pi$
$227$	7.80348	−	13.5160i	0.517935	−	0.897090i	0.999783	−	0.0208353i	$-0.00663256\pi$
$228$	11.1447	+	8.32051i	0.738075	+	0.551039i
$229$	−2.61760	−	4.53382i	−0.172976	−	0.299603i	0.766483	−	0.642265i	$-0.222005\pi$
$229$	−2.61760	−	4.53382i	−0.172976	−	0.299603i	−0.939459	+	0.342661i	$0.888672\pi$
$230$	−1.44501	−	2.50284i	−0.0952813	−	0.165032i
$231$	−12.9900	+	19.2358i	−0.854678	+	1.26562i
$232$	−5.36856	+	9.29863i	−0.352464	+	0.610485i
$233$	8.02401	−	13.8980i	0.525670	−	0.910488i	−0.473883	−	0.880588i	$-0.657148\pi$
$233$	8.02401	−	13.8980i	0.525670	−	0.910488i	0.999553	−	0.0298996i	$-0.00951876\pi$
$234$	−3.13586	−	5.43146i	−0.204997	−	0.355066i
$235$	−18.6428	+	32.2903i	−1.21612	+	2.10639i
$236$	0.287880	+	0.498623i	0.0187394	+	0.0324576i
$237$	−6.90660	+	11.9626i	−0.448632	+	0.777053i
$238$	−6.67869	+	9.88992i	−0.432915	+	0.641068i
$239$	−5.13577			−0.332205			−0.166103	−	0.986108i	$-0.553118\pi$
$239$	−5.13577			−0.332205			−0.166103	+	0.986108i	$0.553118\pi$
$240$	0.216526	+	0.375034i	0.0139767	+	0.0242084i
$241$	−10.5355	−	18.2481i	−0.678654	−	1.17546i	−0.975386	−	0.220503i	$-0.929230\pi$
$241$	−10.5355	−	18.2481i	−0.678654	−	1.17546i	0.296732	−	0.954961i	$-0.404103\pi$
$242$	−0.650234			−0.0417986
$243$	22.2587			1.42790
$244$	1.61688	+	2.80052i	0.103510	+	0.179285i
$245$	−15.3825	+	19.6445i	−0.982752	+	1.25504i
$246$	−25.4054			−1.61979
$247$	−1.04180	+	8.80921i	−0.0662882	+	0.560517i
$248$	2.18931	−	3.79200i	0.139022	−	0.240792i
$249$	39.9739			2.53324
$250$	4.18366	−	7.24631i	0.264598	−	0.458297i
$251$	−1.95887	+	3.39285i	−0.123642	+	0.214155i	−0.921201	−	0.389086i	$-0.872791\pi$
$251$	−1.95887	+	3.39285i	−0.123642	+	0.214155i	0.797559	+	0.603241i	$0.206124\pi$
$252$	−5.12821	−	10.5290i	−0.323047	−	0.663262i
$253$	1.60102	−	2.77305i	0.100655	−	0.174340i
$254$	−7.70085	−	13.3383i	−0.483194	−	0.836917i
$255$	23.7044	−	41.0571i	1.48442	−	2.57110i
$256$	7.93969	+	13.7520i	0.496231	+	0.859497i
$257$	6.88236			0.429310			0.214655	−	0.976690i	$-0.431137\pi$
$257$	6.88236			0.429310			0.214655	+	0.976690i	$0.431137\pi$
$258$	−8.46786			−0.527186
$259$	5.38339	+	11.0529i	0.334508	+	0.686792i
$260$	−4.52142	+	7.83132i	−0.280406	+	0.485678i
$261$	−6.76455	+	11.7165i	−0.418715	+	0.725236i
$262$	−3.28118	−	5.68316i	−0.202712	−	0.351107i
$263$	9.75298			0.601394			0.300697	−	0.953720i	$-0.402781\pi$
$263$	9.75298			0.601394			0.300697	+	0.953720i	$0.402781\pi$
$264$	12.3609	−	21.4097i	0.760760	−	1.31768i
$265$	0.990805			0.0608646
$266$	1.87149	−	9.83321i	0.114749	−	0.602913i
$267$	2.98096			0.182432
$268$	−2.71871	+	4.70895i	−0.166072	+	0.287645i
$269$	−6.13142			−0.373839			−0.186920	−	0.982375i	$-0.559850\pi$
$269$	−6.13142			−0.373839			−0.186920	+	0.982375i	$0.559850\pi$
$270$	−2.18024	−	3.77628i	−0.132685	−	0.229817i
$271$	4.22577	−	7.31925i	0.256697	−	0.444613i	−0.708658	−	0.705552i	$-0.750699\pi$
$271$	4.22577	−	7.31925i	0.256697	−	0.444613i	0.965355	+	0.260940i	$0.0840323\pi$
$272$	−0.123344	+	0.213638i	−0.00747884	+	0.0129537i
$273$	7.71226	−	11.4205i	0.466767	−	0.691197i
$274$	−5.51915			−0.333424
$275$	26.4092			1.59254
$276$	1.49034	+	2.58134i	0.0897079	+	0.155379i
$277$	0.417799	−	0.723649i	0.0251031	−	0.0434799i	−0.853201	−	0.521582i	$-0.825342\pi$
$277$	0.417799	−	0.723649i	0.0251031	−	0.0434799i	0.878304	+	0.478102i	$0.158675\pi$
$278$	−1.50912	−	2.61387i	−0.0905108	−	0.156769i
$279$	2.75860	−	4.77804i	0.165153	−	0.286054i
$280$	14.8722	−	22.0230i	0.888784	−	1.31613i
$281$	−0.729726	+	1.26392i	−0.0435318	+	0.0753993i	−0.886970	−	0.461826i	$-0.847194\pi$
$281$	−0.729726	+	1.26392i	−0.0435318	+	0.0753993i	0.843439	+	0.537226i	$0.180528\pi$
$282$	−11.6190	+	20.1248i	−0.691904	+	1.19841i
$283$	−19.8528			−1.18012			−0.590062	−	0.807358i	$-0.700897\pi$
$283$	−19.8528			−1.18012			−0.590062	+	0.807358i	$0.700897\pi$
$284$	1.74182	−	3.01692i	0.103358	−	0.179021i
$285$	−4.67018	+	39.4899i	−0.276637	+	2.33918i
$286$	6.05447			0.358008
$287$	−13.2493	−	27.2027i	−0.782079	−	1.60572i
$288$	10.0788	+	17.4570i	0.593900	+	1.02867i
$289$	10.0064			0.588611
$290$	−11.7878			−0.692204
$291$	3.25636	+	5.64017i	0.190891	+	0.330633i
$292$	−8.24159	−	14.2748i	−0.482302	−	0.835372i
$293$	−5.29953			−0.309602			−0.154801	−	0.987946i	$-0.549474\pi$
$293$	−5.29953			−0.309602			−0.154801	+	0.987946i	$0.549474\pi$
$294$	−9.58706	+	12.2433i	−0.559129	+	0.714046i
$295$	−0.823086	+	1.42563i	−0.0479219	+	0.0830032i
$296$	−6.54717	−	11.3400i	−0.380546	−	0.659126i
$297$	2.41562	−	4.18399i	0.140169	−	0.242779i
$298$	0.629922	+	1.09106i	0.0364904	+	0.0632032i
$299$	−0.950540	+	1.64638i	−0.0549712	+	0.0952129i
$300$	−12.2917	+	21.2899i	−0.709663	+	1.22917i
$301$	−4.41610	−	9.06689i	−0.254540	−	0.522607i
$302$	−4.89386	−	8.47642i	−0.281610	−	0.487763i
$303$	−16.2373	−	28.1239i	−0.932811	−	1.61568i
$304$	0.0243010	−	0.205483i	0.00139376	−	0.0117853i
$305$	−4.62288	+	8.00706i	−0.264705	+	0.458483i
$306$	8.00780	−	13.8699i	0.457775	−	0.792890i
$307$	−0.542761	−	0.940090i	−0.0309770	−	0.0536538i	0.850121	−	0.526587i	$-0.176529\pi$
$307$	−0.542761	−	0.940090i	−0.0309770	−	0.0536538i	−0.881098	+	0.472933i	$0.843195\pi$
$308$	11.2778	+	0.794800i	0.642611	+	0.0452880i
$309$	4.57659	+	7.92689i	0.260353	+	0.450945i
$310$	4.80710			0.273025
$311$	12.5448	−	21.7283i	0.711353	−	1.23210i	−0.252997	−	0.967467i	$-0.581416\pi$
$311$	12.5448	−	21.7283i	0.711353	−	1.23210i	0.964349	−	0.264632i	$-0.0852505\pi$
$312$	−7.33876	+	12.7111i	−0.415476	+	0.719625i
$313$	25.8900			1.46339			0.731695	−	0.681633i	$-0.238730\pi$
$313$	25.8900			1.46339			0.731695	+	0.681633i	$0.238730\pi$
$314$	−2.23664	+	3.87398i	−0.126221	+	0.218621i
$315$	18.7394	−	27.7497i	1.05585	−	1.56352i
$316$	6.72818			0.378490
$317$	19.1031			1.07294			0.536469	−	0.843920i	$-0.319758\pi$
$317$	19.1031			1.07294			0.536469	+	0.843920i	$0.319758\pi$
$318$	0.617514			0.0346285
$319$	−6.53024	−	11.3107i	−0.365623	−	0.633278i
$320$	−8.61240	+	14.9171i	−0.481448	+	0.833892i
$321$	−8.99089	−	15.5727i	−0.501823	−	0.869182i
$322$	1.20056	−	1.77780i	0.0669043	−	0.0990731i
$323$	−20.8118	+	8.94376i	−1.15800	+	0.497644i
$324$	−4.39113	−	7.60566i	−0.243952	−	0.422537i
$325$	−15.6794			−0.869735
$326$	10.1133			0.560123
$327$	−41.0205			−2.26844
$328$	16.1135	+	27.9094i	0.889718	+	1.54104i
$329$	−27.6079	−	1.94567i	−1.52207	−	0.107268i
$330$	27.1409			1.49406
$331$	−4.93052	−	8.53990i	−0.271006	−	0.469396i	0.698114	−	0.715987i	$-0.254023\pi$
$331$	−4.93052	−	8.53990i	−0.271006	−	0.469396i	−0.969120	+	0.246591i	$0.920690\pi$
$332$	−9.73530	−	16.8620i	−0.534294	−	0.925425i
$333$	−8.24963	−	14.2888i	−0.452077	−	0.783020i
$334$	3.67523	+	6.36568i	0.201100	+	0.348315i
$335$	−15.5463			−0.849386
$336$	−0.179896	+	0.266393i	−0.00981412	+	0.0145329i
$337$	−2.08626	−	3.61351i	−0.113646	−	0.196840i	0.803592	−	0.595181i	$-0.202920\pi$
$337$	−2.08626	−	3.61351i	−0.113646	−	0.196840i	−0.917238	+	0.398341i	$0.869586\pi$
$338$	7.68880			0.418216
$339$	31.0167			1.68459
$340$	−23.0920			−1.25234
$341$	2.66305	+	4.61253i	0.144212	+	0.249783i
$342$	−1.57768	+	13.3405i	−0.0853110	+	0.721369i
$343$	−18.1092	−	3.88021i	−0.977806	−	0.209512i
$344$	5.37077	+	9.30245i	0.289573	+	0.501554i
$345$	−4.26107	+	7.38040i	−0.229409	+	0.397347i
$346$	−6.26899	−	10.8582i	−0.337023	−	0.583741i
$347$	3.84540			0.206432			0.103216	−	0.994659i	$-0.467087\pi$
$347$	3.84540			0.206432			0.103216	+	0.994659i	$0.467087\pi$
$348$	12.1576			0.651713
$349$	0.933598			0.0499744			0.0249872	−	0.999688i	$-0.492046\pi$
$349$	0.933598			0.0499744			0.0249872	+	0.999688i	$0.492046\pi$
$350$	17.6491	+	1.24382i	0.943382	+	0.0664847i
$351$	−1.43418	+	2.48407i	−0.0765507	+	0.132590i
$352$	−19.4594			−1.03719
$353$	−12.5382	+	21.7167i	−0.667339	+	1.15586i	0.311307	+	0.950309i	$0.399233\pi$
$353$	−12.5382	+	21.7167i	−0.667339	+	1.15586i	−0.978646	+	0.205555i	$0.934100\pi$
$354$	−0.512984	+	0.888515i	−0.0272648	+	0.0472240i
$355$	9.96017			0.528631
$356$	−0.725987	−	1.25745i	−0.0384772	−	0.0666445i
$357$	35.1035	+	2.47391i	1.85787	+	0.130933i
$358$	−3.09205	−	5.35559i	−0.163420	−	0.283052i
$359$	−3.79456	+	6.57237i	−0.200269	+	0.346876i	−0.948615	−	0.316432i	$-0.897515\pi$
$359$	−3.79456	+	6.57237i	−0.200269	+	0.346876i	0.748346	+	0.663309i	$0.230848\pi$
$360$	−17.8319	+	30.8857i	−0.939823	+	1.62782i
$361$	13.0762	−	13.7846i	0.688218	−	0.725504i
$362$	−9.78452	−	16.9473i	−0.514263	−	0.890730i
$363$	0.958710	+	1.66053i	0.0503192	+	0.0871555i
$364$	−6.69571	−	0.471879i	−0.350951	−	0.0247332i
$365$	23.5638	−	40.8136i	1.23338	−	2.13628i
$366$	−2.88119	+	4.99036i	−0.150602	+	0.260850i
$367$	16.8798	+	29.2366i	0.881116	+	1.52614i	0.850102	+	0.526619i	$0.176540\pi$
$367$	16.8798	+	29.2366i	0.881116	+	1.52614i	0.0310143	+	0.999519i	$0.490126\pi$
$368$	0.0221723	−	0.0384035i	0.00115581	−	0.00200192i
$369$	20.3035	+	35.1666i	1.05696	+	1.83070i
$370$	7.18784	−	12.4497i	0.373678	−	0.647229i
$371$	0.322042	+	0.661198i	0.0167196	+	0.0343277i
$372$	−4.95788			−0.257054
$373$	−6.45964	−	11.1884i	−0.334467	−	0.579314i	0.648915	−	0.760861i	$-0.275223\pi$
$373$	−6.45964	−	11.1884i	−0.334467	−	0.579314i	−0.983382	+	0.181547i	$0.941890\pi$
$374$	7.73042	+	13.3895i	0.399730	+	0.692353i
$375$	−24.6737			−1.27414
$376$	29.4777			1.52020
$377$	3.87705	+	6.71525i	0.199678	+	0.345853i
$378$	1.81140	−	2.68235i	0.0931683	−	0.137965i
$379$	−4.55540			−0.233995			−0.116998	−	0.993132i	$-0.537327\pi$
$379$	−4.55540			−0.233995			−0.116998	+	0.993132i	$0.537327\pi$
$380$	17.7953	−	7.64743i	0.912878	−	0.392305i
$381$	−22.7084	+	39.3321i	−1.16339	+	2.01504i
$382$	7.05892			0.361166
$383$	0.653175	−	1.13133i	0.0333757	−	0.0578084i	−0.848855	−	0.528626i	$-0.822708\pi$
$383$	0.653175	−	1.13133i	0.0333757	−	0.0578084i	0.882231	+	0.470817i	$0.156041\pi$
$384$	9.16251	−	15.8699i	0.467572	−	0.809859i
$385$	14.1543	+	29.0609i	0.721372	+	1.48108i
$386$	−9.11104	+	15.7808i	−0.463740	+	0.803221i
$387$	6.76733	+	11.7214i	0.344003	+	0.595830i
$388$	1.58612	−	2.74724i	0.0805229	−	0.139470i
$389$	−8.52576	−	14.7671i	−0.432273	−	0.748720i	0.564795	−	0.825231i	$-0.308955\pi$
$389$	−8.52576	−	14.7671i	−0.432273	−	0.748720i	−0.997069	+	0.0765115i	$0.975622\pi$
$390$	−16.1138			−0.815953
$391$	−4.85465			−0.245510
$392$	19.5306	+	2.76658i	0.986447	+	0.139733i
$393$	−9.67558	+	16.7586i	−0.488069	+	0.845359i
$394$	3.30087	−	5.71727i	0.166295	−	0.288032i
$395$	9.61837	+	16.6595i	0.483953	+	0.838231i
$396$	−15.1727			−0.762459
$397$	2.33618	−	4.04638i	0.117249	−	0.203082i	−0.801427	−	0.598092i	$-0.795926\pi$
$397$	2.33618	−	4.04638i	0.117249	−	0.203082i	0.918677	+	0.395010i	$0.129259\pi$
$398$	19.4405			0.974467
$399$	−27.8709	+	9.71884i	−1.39529	+	0.486550i
$400$	0.365736			0.0182868
$401$	−16.1139	+	27.9100i	−0.804688	+	1.39376i	0.111814	+	0.993729i	$0.464334\pi$
$401$	−16.1139	+	27.9100i	−0.804688	+	1.39376i	−0.916502	+	0.400031i	$0.868999\pi$
$402$	−9.68916			−0.483252
$403$	−1.58107	−	2.73850i	−0.0787588	−	0.136414i
$404$	−7.90894	+	13.6987i	−0.393484	+	0.681535i
$405$	12.5548	−	21.7456i	0.623854	−	1.08055i
$406$	−3.83139	−	7.86641i	−0.190149	−	0.390403i
$407$	15.9277			0.789509
$408$	−37.4809			−1.85558
$409$	4.17605	+	7.23313i	0.206492	+	0.357655i	0.950607	−	0.310396i	$-0.100462\pi$
$409$	4.17605	+	7.23313i	0.206492	+	0.357655i	−0.744115	+	0.668052i	$0.767128\pi$
$410$	−17.6903	+	30.6404i	−0.873659	+	1.51322i
$411$	8.13747	+	14.0945i	0.401392	+	0.695231i
$412$	2.22918	−	3.86106i	0.109824	−	0.190221i
$413$	−1.21890	−	0.0859017i	−0.0599780	−	0.00422695i
$414$	−1.43947	+	2.49324i	−0.0707463	+	0.122536i
$415$	27.8345	−	48.2108i	1.36634	−	2.36657i
$416$	11.5532			0.566442
$417$	−4.45011	+	7.70781i	−0.217923	+	0.377453i
$418$	−10.3915	−	7.75816i	−0.508263	−	0.379464i
$419$	−8.01684			−0.391648			−0.195824	−	0.980639i	$-0.562738\pi$
$419$	−8.01684			−0.391648			−0.195824	+	0.980639i	$0.562738\pi$
$420$	−30.0155	−	2.11534i	−1.46461	−	0.103218i
$421$	−0.785684	−	1.36084i	−0.0382919	−	0.0663235i	0.846244	−	0.532795i	$-0.178858\pi$
$421$	−0.785684	−	1.36084i	−0.0382919	−	0.0663235i	−0.884536	+	0.466472i	$0.845525\pi$
$422$	21.9339			1.06773
$423$	37.1428			1.80594
$424$	−0.391660	−	0.678376i	−0.0190207	−	0.0329448i
$425$	−20.0196	−	34.6750i	−0.971093	−	1.68198i
$426$	6.20763			0.300760
$427$	−6.84596	−	0.482469i	−0.331299	−	0.0233483i
$428$	−4.37932	+	7.58520i	−0.211682	+	0.366644i
$429$	−8.92675	−	15.4616i	−0.430988	−	0.746493i
$430$	−5.89632	+	10.2127i	−0.284346	+	0.492502i
$431$	−0.335354	−	0.580851i	−0.0161534	−	0.0279786i	0.857836	−	0.513924i	$-0.171809\pi$
$431$	−0.335354	−	0.580851i	−0.0161534	−	0.0279786i	−0.873989	+	0.485945i	$0.838475\pi$
$432$	0.0334535	−	0.0579432i	0.00160953	−	0.00278779i
$433$	0.201011	−	0.348161i	0.00965997	−	0.0167316i	−0.861155	−	0.508342i	$-0.830258\pi$
$433$	0.201011	−	0.348161i	0.00965997	−	0.0167316i	0.870815	+	0.491611i	$0.163592\pi$
$434$	1.56245	+	3.20794i	0.0750001	+	0.153986i
$435$	17.3800	+	30.1031i	0.833308	+	1.44333i
$436$	9.99021	+	17.3035i	0.478444	+	0.828689i
$437$	3.74111	−	1.60772i	0.178962	−	0.0769078i
$438$	14.6860	−	25.4369i	0.701724	−	1.21542i
$439$	−9.82015	+	17.0090i	−0.468690	+	0.811795i	−0.999360	−	0.0357836i	$-0.988607\pi$
$439$	−9.82015	+	17.0090i	−0.468690	+	0.811795i	0.530669	+	0.847579i	$0.321941\pi$
$440$	−17.2142	−	29.8159i	−0.820656	−	1.42142i
$441$	24.6092	+	3.48598i	1.17187	+	0.165999i
$442$	−4.58961	−	7.94944i	−0.218306	−	0.378116i
$443$	−2.02235			−0.0960848			−0.0480424	−	0.998845i	$-0.515298\pi$
$443$	−2.02235			−0.0960848			−0.0480424	+	0.998845i	$0.515298\pi$
$444$	−7.41330	+	12.8402i	−0.351820	+	0.609370i
$445$	2.07569	−	3.59520i	0.0983973	−	0.170429i
$446$	14.2782			0.676094
$447$	1.85752	−	3.21732i	0.0878578	−	0.152174i
$448$	−12.7540	−	0.898836i	−0.602569	−	0.0424660i
$449$	29.8869			1.41045			0.705225	−	0.708983i	$-0.250846\pi$
$449$	29.8869			1.41045			0.705225	+	0.708983i	$0.250846\pi$
$450$	−23.7444			−1.11932
$451$	−39.2004			−1.84587
$452$	−7.55385	−	13.0837i	−0.355303	−	0.615403i
$453$	−14.4311	+	24.9954i	−0.678032	+	1.17439i
$454$	−6.77306	−	11.7313i	−0.317875	−	0.550576i
$455$	−8.40354	−	17.2537i	−0.393964	−	0.808866i
$456$	28.8837	−	12.4126i	1.35260	−	0.581274i
$457$	−4.48131	−	7.76186i	−0.209627	−	0.363085i	0.741970	−	0.670433i	$-0.233892\pi$
$457$	−4.48131	−	7.76186i	−0.209627	−	0.363085i	−0.951597	+	0.307348i	$0.900558\pi$
$458$	−4.54391			−0.212323
$459$	−7.32469			−0.341887
$460$	4.15100			0.193541
$461$	−6.09103	−	10.5500i	−0.283688	−	0.491361i	0.688602	−	0.725139i	$-0.258225\pi$
$461$	−6.09103	−	10.5500i	−0.283688	−	0.491361i	−0.972290	+	0.233778i	$0.924891\pi$
$462$	8.82162	+	18.1121i	0.410419	+	0.842650i
$463$	25.3270			1.17705			0.588523	−	0.808480i	$-0.299710\pi$
$463$	25.3270			1.17705			0.588523	+	0.808480i	$0.299710\pi$
$464$	−0.0904359	−	0.156640i	−0.00419838	−	0.00727181i
$465$	−7.08762	−	12.2761i	−0.328680	−	0.569291i
$466$	−6.96446	−	12.0628i	−0.322623	−	0.558799i
$467$	1.30670	+	2.26327i	0.0604668	+	0.104731i	0.894674	−	0.446719i	$-0.147408\pi$
$467$	1.30670	+	2.26327i	0.0604668	+	0.104731i	−0.834207	+	0.551451i	$0.814074\pi$
$468$	9.00818			0.416403
$469$	−5.05302	−	10.3746i	−0.233327	−	0.479054i
$470$	16.1811	+	28.0265i	0.746378	+	1.29277i
$471$	13.1909			0.607804
$472$	1.30145			0.0599040
$473$	−13.0658			−0.600768
$474$	5.99460	+	10.3830i	0.275341	+	0.476905i
$475$	26.9110	+	20.0914i	1.23476	+	0.921859i
$476$	−7.50560	−	15.4101i	−0.344019	−	0.706320i
$477$	−0.493504	−	0.854774i	−0.0225960	−	0.0391374i
$478$	−2.22880	+	3.86040i	−0.101943	+	0.176571i
$479$	4.05591	+	7.02504i	0.185319	+	0.320982i	0.943684	−	0.330848i	$-0.107335\pi$
$479$	4.05591	+	7.02504i	0.185319	+	0.320982i	−0.758365	+	0.651830i	$0.774001\pi$
$480$	51.7906			2.36391
$481$	−9.45643			−0.431176
$482$	−18.2887			−0.833028
$483$	−6.31017	−	0.444709i	−0.287123	−	0.0202349i
$484$	0.466972	−	0.808819i	0.0212260	−	0.0367645i
$485$	9.06983			0.411840
$486$	9.65976	−	16.7312i	0.438175	−	0.758942i
$487$	11.2636	−	19.5092i	0.510405	−	0.884047i	−0.489523	−	0.871991i	$-0.662829\pi$
$487$	11.2636	−	19.5092i	0.510405	−	0.884047i	0.999927	−	0.0120562i	$-0.00383771\pi$
$488$	7.30961			0.330890
$489$	−14.9111	−	25.8268i	−0.674304	−	1.16793i
$490$	8.09052	+	20.0878i	0.365492	+	0.907474i
$491$	−15.8743	−	27.4952i	−0.716399	−	1.24084i	−0.962417	−	0.271575i	$-0.912456\pi$
$491$	−15.8743	−	27.4952i	−0.716399	−	1.24084i	0.246018	−	0.969265i	$-0.420878\pi$
$492$	18.2452	−	31.6015i	0.822555	−	1.42471i
$493$	−9.90054	+	17.1482i	−0.445898	+	0.772318i
$494$	6.16950	+	4.60608i	0.277579	+	0.207237i
$495$	−21.6904	−	37.5689i	−0.974912	−	1.68860i
$496$	0.0368800	+	0.0638780i	0.00165596	+	0.00286821i
$497$	3.23736	+	6.64676i	0.145215	+	0.298148i
$498$	17.3477	−	30.0471i	0.777370	−	1.34644i
$499$	−11.0419	+	19.1252i	−0.494305	+	0.856162i	−0.999978	−	0.00656316i	$-0.997911\pi$
$499$	−11.0419	+	19.1252i	−0.494305	+	0.856162i	0.505673	+	0.862725i	$0.331244\pi$
$500$	6.00907	+	10.4080i	0.268734	+	0.465460i
$501$	10.8376	−	18.7712i	0.484187	−	0.838636i
$502$	1.70020	+	2.94484i	0.0758838	+	0.131435i
$503$	−11.8787	+	20.5746i	−0.529647	+	0.917375i	0.469755	+	0.882797i	$0.344342\pi$
$503$	−11.8787	+	20.5746i	−0.529647	+	0.917375i	−0.999402	+	0.0345781i	$0.988991\pi$
$504$	−26.4070	−	1.86103i	−1.17626	−	0.0828970i
$505$	−45.2254			−2.01250
$506$	−1.38961	−	2.40688i	−0.0617758	−	0.106999i
$507$	−11.3364	−	19.6353i	−0.503468	−	0.872033i
$508$	22.1217			0.981494
$509$	−28.7699			−1.27520			−0.637602	−	0.770366i	$-0.720074\pi$
$509$	−28.7699			−1.27520			−0.637602	+	0.770366i	$0.720074\pi$
$510$	−20.5743	−	35.6357i	−0.911044	−	1.57797i
$511$	34.8953	+	2.45924i	1.54368	+	0.108790i
$512$	−0.537023			−0.0237333
$513$	5.64459	−	2.42573i	0.249215	−	0.107099i
$514$	2.98678	−	5.17326i	0.131741	−	0.228183i
$515$	12.7470			0.561702
$516$	6.08128	−	10.5331i	0.267713	−	0.463693i
$517$	−17.9281	+	31.0524i	−0.788476	+	1.36568i
$518$	10.6444	+	0.750161i	0.467687	+	0.0329602i
$519$	−18.4861	+	32.0189i	−0.811449	+	1.40547i
$520$	10.2202	+	17.7019i	0.448186	+	0.776281i
$521$	−7.86181	+	13.6171i	−0.344432	+	0.596574i	−0.985250	−	0.171119i	$-0.945262\pi$
$521$	−7.86181	+	13.6171i	−0.344432	+	0.596574i	0.640818	+	0.767693i	$0.278595\pi$
$522$	5.87131	+	10.1694i	0.256980	+	0.445103i
$523$	−16.5986			−0.725805			−0.362903	−	0.931827i	$-0.618214\pi$
$523$	−16.5986			−0.725805			−0.362903	+	0.931827i	$0.618214\pi$
$524$	9.42563			0.411761
$525$	−22.8455	−	46.9052i	−0.997060	−	2.04711i
$526$	4.23256	−	7.33101i	0.184549	−	0.319647i
$527$	4.03746	−	6.99309i	0.175875	−	0.304624i
$528$	0.208225	+	0.360656i	0.00906183	+	0.0156955i
$529$	−22.1273			−0.962058
$530$	0.429986	−	0.744758i	0.0186774	−	0.0323502i
$531$	1.63986			0.0711640
$532$	10.8874	+	9.38975i	0.472028	+	0.407097i
$533$	23.2736			1.00809
$534$	1.29367	−	2.24069i	0.0559824	−	0.0969643i
$535$	−25.0421			−1.08266
$536$	6.14538	+	10.6441i	0.265440	+	0.459756i
$537$	−9.11789	+	15.7926i	−0.393466	+	0.681503i
$538$	−2.66089	+	4.60880i	−0.114719	+	0.198700i
$539$	−14.7928	+	18.8914i	−0.637169	+	0.813708i
$540$	6.26303			0.269518
$541$	−14.4146			−0.619734			−0.309867	−	0.950780i	$-0.600285\pi$
$541$	−14.4146			−0.619734			−0.309867	+	0.950780i	$0.600285\pi$
$542$	−3.66777	−	6.35276i	−0.157544	−	0.272875i
$543$	−28.8527	+	49.9744i	−1.23819	+	2.14461i
$544$	14.7513	+	25.5499i	0.632455	+	1.09544i
$545$	−28.5633	+	49.4731i	−1.22352	+	2.11919i
$546$	−5.23747	−	10.7533i	−0.224143	−	0.460198i
$547$	19.4811	−	33.7423i	0.832952	−	1.44272i	−0.0627349	−	0.998030i	$-0.519982\pi$
$547$	19.4811	−	33.7423i	0.832952	−	1.44272i	0.895687	−	0.444685i	$-0.146684\pi$
$548$	3.96363	−	6.86520i	0.169318	−	0.293267i
$549$	9.21033			0.393087
$550$	11.4610	−	19.8510i	0.488698	−	0.846450i
$551$	1.95058	−	16.4936i	0.0830975	−	0.702652i
$552$	6.73753			0.286768
$553$	−7.99120	+	11.8335i	−0.339820	+	0.503212i
$554$	−0.362630	−	0.628094i	−0.0154067	−	0.0266851i
$555$	−42.3912			−1.79941
$556$	4.33515			0.183851
$557$	7.17391	+	12.4256i	0.303968	+	0.526489i	0.977031	−	0.213097i	$-0.0683549\pi$
$557$	7.17391	+	12.4256i	0.303968	+	0.526489i	−0.673063	+	0.739585i	$0.735022\pi$
$558$	−2.39434	−	4.14711i	−0.101360	−	0.175561i
$559$	7.75729			0.328099
$560$	0.196021	+	0.402459i	0.00828338	+	0.0170070i
$561$	22.7956	−	39.4831i	0.962430	−	1.66698i
$562$	0.633368	+	1.09702i	0.0267170	+	0.0462752i
$563$	1.86373	−	3.22807i	0.0785467	−	0.136047i	−0.824076	−	0.566479i	$-0.808305\pi$
$563$	1.86373	−	3.22807i	0.0785467	−	0.136047i	0.902623	+	0.430432i	$0.141639\pi$
$564$	−16.6887	−	28.9056i	−0.702719	−	1.21715i
$565$	21.5974	−	37.4079i	0.908611	−	1.57376i
$566$	−8.61563	+	14.9227i	−0.362142	+	0.627248i
$567$	18.5923	+	1.31029i	0.780802	+	0.0550269i
$568$	−3.93721	−	6.81944i	−0.165202	−	0.286137i
$569$	16.0548	+	27.8077i	0.673051	+	1.16576i	0.977035	+	0.213081i	$0.0683498\pi$
$569$	16.0548	+	27.8077i	0.673051	+	1.16576i	−0.303984	+	0.952677i	$0.598317\pi$
$570$	27.6566	+	20.6481i	1.15841	+	0.864854i
$571$	−10.8008	+	18.7076i	−0.452000	+	0.782887i	−0.998510	−	0.0545656i	$-0.982623\pi$
$571$	−10.8008	+	18.7076i	−0.452000	+	0.782887i	0.546510	+	0.837452i	$0.315956\pi$
$572$	−4.34807	+	7.53108i	−0.181802	+	0.314890i
$573$	−10.4077	−	18.0267i	−0.434789	−	0.753077i
$574$	−26.1973	−	1.84625i	−1.09345	−	0.0770610i
$575$	3.59871	+	6.23314i	0.150076	+	0.259940i
$576$	17.1588			0.714949
$577$	10.6395	−	18.4282i	0.442930	−	0.767177i	−0.554975	−	0.831867i	$-0.687272\pi$
$577$	10.6395	−	18.4282i	0.442930	−	0.767177i	0.997905	+	0.0646895i	$0.0206057\pi$
$578$	4.34254	−	7.52150i	0.180626	−	0.312853i
$579$	53.7335			2.23309
$580$	8.46552	−	14.6627i	0.351512	−	0.608836i
$581$	41.2198	+	2.90496i	1.71008	+	0.120518i
$582$	5.65273			0.234313
$583$	0.952819			0.0394617
$584$	−37.2586			−1.54177
$585$	12.8778	+	22.3050i	0.532431	+	0.922197i
$586$	−2.29987	+	3.98349i	−0.0950068	+	0.164557i
$587$	19.6688	+	34.0674i	0.811818	+	1.40611i	0.911590	+	0.411100i	$0.134855\pi$
$587$	19.6688	+	34.0674i	0.811818	+	1.40611i	−0.0997720	+	0.995010i	$0.531811\pi$
$588$	−8.34430	−	20.7179i	−0.344113	−	0.854392i
$589$	−0.795452	+	6.72614i	−0.0327760	+	0.277146i
$590$	0.714400	+	1.23738i	0.0294114	+	0.0509420i
$591$	−19.4673			−0.800777
$592$	0.220580			0.00906579
$593$	7.48953			0.307558			0.153779	−	0.988105i	$-0.450856\pi$
$593$	7.48953			0.307558			0.153779	+	0.988105i	$0.450856\pi$
$594$	−2.09665	−	3.63150i	−0.0860266	−	0.149002i
$595$	27.4269	−	40.6142i	1.12439	−	1.66502i
$596$	−1.80954			−0.0741215
$597$	−28.6633	−	49.6463i	−1.17311	−	2.03189i
$598$	0.825025	+	1.42898i	0.0337378	+	0.0584355i
$599$	−8.09040	−	14.0130i	−0.330565	−	0.572555i	0.652058	−	0.758169i	$-0.273906\pi$
$599$	−8.09040	−	14.0130i	−0.330565	−	0.572555i	−0.982623	+	0.185614i	$0.940573\pi$
$600$	27.7842	+	48.1237i	1.13429	+	1.96464i
$601$	−14.0496			−0.573094			−0.286547	−	0.958066i	$-0.592507\pi$
$601$	−14.0496			−0.573094			−0.286547	+	0.958066i	$0.592507\pi$
$602$	−8.73179	−	0.615372i	−0.355881	−	0.0250807i
$603$	7.74337	+	13.4119i	0.315334	+	0.546175i
$604$	14.0583			0.572024
$605$	2.67027			0.108562
$606$	−28.1865			−1.14500
$607$	−10.6075	−	18.3727i	−0.430545	−	0.745726i	0.566375	−	0.824148i	$-0.308345\pi$
$607$	−10.6075	−	18.3727i	−0.430545	−	0.745726i	−0.996920	+	0.0784215i	$0.975012\pi$
$608$	−19.8291	−	14.8042i	−0.804177	−	0.600390i
$609$	−14.4398	+	21.3827i	−0.585130	+	0.866471i
$610$	4.01244	+	6.94975i	0.162459	+	0.281387i
$611$	10.6441	−	18.4360i	0.430612	−	0.745842i
$612$	11.5018	+	19.9216i	0.464931	+	0.805284i
$613$	−19.8383			−0.801260			−0.400630	−	0.916240i	$-0.631209\pi$
$613$	−19.8383			−0.801260			−0.400630	+	0.916240i	$0.631209\pi$
$614$	−0.942183			−0.0380234
$615$	104.331			4.20701
$616$	14.3020	−	21.1787i	0.576245	−	0.853314i
$617$	−21.5569	+	37.3376i	−0.867847	+	1.50315i	−0.00365444	+	0.999993i	$0.501163\pi$
$617$	−21.5569	+	37.3376i	−0.867847	+	1.50315i	−0.864192	+	0.503161i	$0.832170\pi$
$618$	7.94453			0.319576
$619$	16.6037	−	28.7585i	0.667360	−	1.15590i	−0.311280	−	0.950318i	$-0.600758\pi$
$619$	16.6037	−	28.7585i	0.667360	−	1.15590i	0.978640	−	0.205582i	$-0.0659089\pi$
$620$	−3.45226	+	5.97949i	−0.138646	+	0.240142i
$621$	1.31668			0.0528366
$622$	−10.8883	−	18.8592i	−0.436583	−	0.756183i
$623$	3.07387	+	0.216630i	0.123152	+	0.00867911i
$624$	−0.123625	−	0.214124i	−0.00494895	−	0.00857184i
$625$	2.08088	−	3.60419i	0.0832352	−	0.144168i
$626$	11.2357	−	19.4607i	0.449067	−	0.777807i
$627$	−4.49113	+	37.9759i	−0.179358	+	1.51661i
$628$	−3.21253	−	5.56426i	−0.128194	−	0.222038i
$629$	−12.0741	−	20.9129i	−0.481425	−	0.833853i
$630$	−12.7261	−	26.1286i	−0.507021	−	1.04099i
$631$	4.39966	−	7.62044i	0.175148	−	0.303365i	−0.765065	−	0.643954i	$-0.777293\pi$
$631$	4.39966	−	7.62044i	0.175148	−	0.303365i	0.940212	+	0.340589i	$0.110626\pi$
$632$	7.60419	−	13.1708i	0.302479	−	0.523908i
$633$	−32.3395	−	56.0137i	−1.28538	−	2.22635i
$634$	8.29030	−	14.3592i	0.329250	−	0.570277i
$635$	31.6245	+	54.7752i	1.25498	+	2.17369i
$636$	−0.443474	+	0.768119i	−0.0175849	+	0.0304579i
$637$	8.78258	−	11.2159i	0.347978	−	0.444392i
$638$	−11.3359			−0.448792
$639$	−4.96100	−	8.59270i	−0.196254	−	0.339922i
$640$	−12.7600	−	22.1010i	−0.504384	−	0.873619i
$641$	13.2256			0.522381			0.261190	−	0.965287i	$-0.415885\pi$
$641$	13.2256			0.522381			0.261190	+	0.965287i	$0.415885\pi$
$642$	−15.6073			−0.615973
$643$	19.6913	+	34.1063i	0.776548	+	1.34502i	0.933920	+	0.357481i	$0.116364\pi$
$643$	19.6913	+	34.1063i	0.776548	+	1.34502i	−0.157372	+	0.987539i	$0.550302\pi$
$644$	1.34920	+	2.77010i	0.0531659	+	0.109157i
$645$	34.7743			1.36924
$646$	−2.30907	+	19.5250i	−0.0908493	+	0.768200i
$647$	−20.4294	+	35.3848i	−0.803164	+	1.39112i	0.114360	+	0.993439i	$0.463518\pi$
$647$	−20.4294	+	35.3848i	−0.803164	+	1.39112i	−0.917524	+	0.397681i	$0.869815\pi$
$648$	−19.8514			−0.779838
$649$	−0.791530	+	1.37097i	−0.0310703	+	0.0538153i
$650$	−6.80448	+	11.7857i	−0.266894	+	0.462273i
$651$	5.88858	−	8.71992i	0.230792	−	0.341761i
$652$	−7.26296	+	12.5798i	−0.284439	+	0.492663i
$653$	−10.8988	−	18.8772i	−0.426502	−	0.738722i	0.570058	−	0.821605i	$-0.306921\pi$
$653$	−10.8988	−	18.8772i	−0.426502	−	0.738722i	−0.996559	+	0.0828822i	$0.973587\pi$
$654$	−17.8019	+	30.8339i	−0.696111	+	1.20570i
$655$	13.4746	+	23.3386i	0.526494	+	0.911915i
$656$	−0.542878			−0.0211958
$657$	−46.9469			−1.83157
$658$	−13.4437	+	19.9077i	−0.524090	+	0.776081i
$659$	−20.7028	+	35.8583i	−0.806467	+	1.39684i	0.108830	+	0.994060i	$0.465290\pi$
$659$	−20.7028	+	35.8583i	−0.806467	+	1.39684i	−0.915296	+	0.402781i	$0.868044\pi$
$660$	−19.4915	+	33.7603i	−0.758706	+	1.31412i
$661$	2.64354	+	4.57875i	0.102822	+	0.178093i	0.912846	−	0.408304i	$-0.133880\pi$
$661$	2.64354	+	4.57875i	0.102822	+	0.178093i	−0.810024	+	0.586396i	$0.800546\pi$
$662$	−8.55891			−0.332652
$663$	−13.5339	+	23.4414i	−0.525614	+	0.910389i
$664$	−44.0114			−1.70797
$665$	−7.68552	+	40.3813i	−0.298032	+	1.56592i
$666$	−14.3206			−0.554911
$667$	1.77971	−	3.08255i	0.0689107	−	0.119357i
$668$	−10.5576			−0.408486
$669$	−21.0519	−	36.4630i	−0.813915	−	1.40974i
$670$	−6.74674	+	11.6857i	−0.260649	+	0.451458i
$671$	−4.44565	+	7.70008i	−0.171622	+	0.297258i
$672$	16.8335	+	34.5617i	0.649367	+	1.33324i
$673$	27.4259			1.05719			0.528595	−	0.848874i	$-0.322719\pi$
$673$	27.4259			1.05719			0.528595	+	0.848874i	$0.322719\pi$
$674$	−3.62155			−0.139497
$675$	5.42973	+	9.40457i	0.208990	+	0.361982i
$676$	−5.52179	+	9.56402i	−0.212376	+	0.367847i
$677$	−16.3284	−	28.2816i	−0.627551	−	1.08695i	−0.988042	−	0.154187i	$-0.950724\pi$
$677$	−16.3284	−	28.2816i	−0.627551	−	1.08695i	0.360491	−	0.932763i	$-0.382609\pi$
$678$	13.4605	−	23.3143i	0.516947	−	0.895379i
$679$	2.94797	+	6.05261i	0.113133	+	0.232278i
$680$	−26.0986	+	45.2041i	−1.00084	+	1.73350i
$681$	−19.9725	+	34.5934i	−0.765348	+	1.32562i
$682$	4.62280			0.177016
$683$	−9.23232	+	15.9908i	−0.353265	+	0.611873i	−0.986819	−	0.161825i	$-0.948262\pi$
$683$	−9.23232	+	15.9908i	−0.353265	+	0.611873i	0.633555	+	0.773698i	$0.281595\pi$
$684$	−15.4610	−	11.5430i	−0.591167	−	0.441359i
$685$	22.6651			0.865987
$686$	−10.7756	+	11.9282i	−0.411415	+	0.455422i
$687$	6.69958	+	11.6040i	0.255605	+	0.442721i
$688$	−0.180946			−0.00689851
$689$	−0.565696			−0.0215513
$690$	3.69841	+	6.40584i	0.140796	+	0.243866i
$691$	−5.70621	−	9.88344i	−0.217074	−	0.375984i	0.736838	−	0.676069i	$-0.236318\pi$
$691$	−5.70621	−	9.88344i	−0.217074	−	0.375984i	−0.953912	+	0.300086i	$0.902985\pi$
$692$	18.0085			0.684582
$693$	18.0210	−	26.6858i	0.684561	−	1.01371i
$694$	1.66882	−	2.89047i	0.0633474	−	0.109721i
$695$	6.19737	+	10.7342i	0.235080	+	0.407170i
$696$	13.7405	−	23.7992i	0.520832	−	0.902107i
$697$	29.7160	+	51.4696i	1.12557	+	1.94955i
$698$	0.405160	−	0.701757i	0.0153355	−	0.0265619i
$699$	−20.5369	+	35.5710i	−0.776777	+	1.34542i
$700$	−14.2220	+	21.0602i	−0.537541	+	0.796001i
$701$	−16.8999	−	29.2714i	−0.638300	−	1.10557i	−0.985806	−	0.167890i	$-0.946305\pi$
$701$	−16.8999	−	29.2714i	−0.638300	−	1.10557i	0.347506	−	0.937678i	$-0.387029\pi$
$702$	1.24480	+	2.15605i	0.0469819	+	0.0813750i
$703$	16.2304	+	12.1174i	0.612140	+	0.457017i
$704$	−8.28221	+	14.3452i	−0.312148	+	0.540656i
$705$	47.7151	−	82.6449i	1.79705	−	3.11259i
$706$	10.8825	+	18.8491i	0.409569	+	0.709395i
$707$	−14.6996	−	30.1805i	−0.552836	−	1.13505i
$708$	−0.736809	−	1.27619i	−0.0276910	−	0.0479622i
$709$	21.2030			0.796295			0.398147	−	0.917321i	$-0.369653\pi$
$709$	21.2030			0.796295			0.398147	+	0.917321i	$0.369653\pi$
$710$	4.32248	−	7.48675i	0.162220	−	0.280973i
$711$	9.58151	−	16.5957i	0.359335	−	0.622386i
$712$	−3.28205			−0.123000
$713$	−0.725771	+	1.25707i	−0.0271803	+	0.0470777i
$714$	17.0937	−	25.3126i	0.639714	−	0.947300i
$715$	−24.8634			−0.929839
$716$	8.88235			0.331949
$717$	13.1447			0.490896
$718$	3.29350	+	5.70451i	0.122912	+	0.212890i
$719$	7.42044	−	12.8526i	0.276736	−	0.479321i	−0.693836	−	0.720133i	$-0.744081\pi$
$719$	7.42044	−	12.8526i	0.276736	−	0.479321i	0.970572	+	0.240813i	$0.0774140\pi$
$720$	−0.300386	−	0.520284i	−0.0111947	−	0.0193899i
$721$	4.14318	+	8.50654i	0.154300	+	0.316800i
$722$	−4.68670	−	15.8111i	−0.174421	−	0.588429i
$723$	26.9650	+	46.7048i	1.00284	+	1.73697i
$724$	28.1074			1.04460
$725$	29.3567			1.09028
$726$	1.66423			0.0617654
$727$	−16.9634	−	29.3814i	−0.629137	−	1.08970i	−0.987725	−	0.156201i	$-0.950075\pi$
$727$	−16.9634	−	29.3814i	−0.629137	−	1.08970i	0.358588	−	0.933496i	$-0.383258\pi$
$728$	−8.49123	+	12.5740i	−0.314706	+	0.466022i
$729$	−35.8357			−1.32725
$730$	−20.4522	−	35.4243i	−0.756972	−	1.31111i
$731$	9.90460	+	17.1553i	0.366335	+	0.634511i
$732$	−4.13830	−	7.16775i	−0.152956	−	0.264928i
$733$	23.7385	+	41.1163i	0.876801	+	1.51866i	0.854832	+	0.518905i	$0.173660\pi$
$733$	23.7385	+	41.1163i	0.876801	+	1.51866i	0.0219694	+	0.999759i	$0.493006\pi$
$734$	29.3017			1.08154
$735$	39.3705	−	50.2788i	1.45220	−	1.85456i
$736$	−2.65168	−	4.59284i	−0.0977421	−	0.169294i
$737$	−14.9503			−0.550701
$738$	35.2449			1.29738
$739$	33.9814			1.25003			0.625013	−	0.780614i	$-0.285094\pi$
$739$	33.9814			1.25003			0.625013	+	0.780614i	$0.285094\pi$
$740$	10.3240	+	17.8817i	0.379519	+	0.657346i
$741$	2.66642	−	22.5466i	0.0979534	−	0.828270i
$742$	0.636761	+	0.0448756i	0.0233762	+	0.00164744i
$743$	−26.4141	−	45.7506i	−0.969039	−	1.67843i	−0.698347	−	0.715759i	$-0.746081\pi$
$743$	−26.4141	−	45.7506i	−0.969039	−	1.67843i	−0.270692	−	0.962666i	$-0.587253\pi$
$744$	−5.60340	+	9.70538i	−0.205431	+	0.355816i
$745$	−2.58685	−	4.48056i	−0.0947749	−	0.164155i
$746$	−11.2133			−0.410549
$747$	−55.4557			−2.02902
$748$	−22.2067			−0.811957
$749$	−8.13943	−	16.7114i	−0.297408	−	0.610623i
$750$	−10.7078	+	18.5464i	−0.390993	+	0.677220i
$751$	−5.51428			−0.201219			−0.100609	−	0.994926i	$-0.532079\pi$
$751$	−5.51428			−0.201219			−0.100609	+	0.994926i	$0.532079\pi$
$752$	−0.248283	+	0.430038i	−0.00905393	+	0.0156819i
$753$	5.01358	−	8.68378i	0.182705	−	0.316455i
$754$	6.73020			0.245099
$755$	20.0972	+	34.8094i	0.731414	+	1.26685i
$756$	2.03567	+	4.17953i	0.0740368	+	0.152008i
$757$	−6.78869	−	11.7584i	−0.246739	−	0.427365i	0.715880	−	0.698223i	$-0.246026\pi$
$757$	−6.78869	−	11.7584i	−0.246739	−	0.427365i	−0.962619	+	0.270858i	$0.912692\pi$
$758$	−1.97694	+	3.42415i	−0.0718055	+	0.124371i
$759$	−4.09771	+	7.09744i	−0.148738	+	0.257621i
$760$	5.14188	−	43.4785i	0.186516	−	1.57713i
$761$	21.5535	+	37.3317i	0.781313	+	1.35327i	0.931177	+	0.364567i	$0.118783\pi$
$761$	21.5535	+	37.3317i	0.781313	+	1.35327i	−0.149864	+	0.988707i	$0.547884\pi$
$762$	19.7098	+	34.1384i	0.714011	+	1.23670i
$763$	−42.2990	−	2.98102i	−1.53133	−	0.107920i
$764$	−5.06943	+	8.78052i	−0.183406	+	0.317668i
$765$	−32.8850	+	56.9585i	−1.18896	+	2.05934i
$766$	−0.566925	−	0.981943i	−0.0204838	−	0.0354791i
$767$	0.469938	−	0.813956i	0.0169685	−	0.0293903i
$768$	−20.3211	−	35.1972i	−0.733275	−	1.27007i
$769$	16.7051	−	28.9341i	0.602403	−	1.04339i	−0.390054	−	0.920792i	$-0.627544\pi$
$769$	16.7051	−	28.9341i	0.602403	−	1.04339i	0.992456	−	0.122600i	$-0.0391231\pi$
$770$	27.9868	+	1.97237i	1.00858	+	0.0710793i
$771$	−17.6149			−0.634386
$772$	−13.0864	−	22.6662i	−0.470988	−	0.815776i
$773$	−13.1751	−	22.8200i	−0.473877	−	0.820779i	0.525676	−	0.850685i	$-0.323812\pi$
$773$	−13.1751	−	22.8200i	−0.473877	−	0.820779i	−0.999553	+	0.0299063i	$0.990479\pi$
$774$	11.7475			0.422253
$775$	−11.9717			−0.430038
$776$	−3.58526	−	6.20985i	−0.128703	−	0.222921i
$777$	−13.7784	−	28.2891i	−0.494298	−	1.01487i
$778$	−14.7999			−0.530603
$779$	−39.9451	−	29.8226i	−1.43118	−	1.06851i
$780$	11.5723	−	20.0438i	0.414354	−	0.717681i
$781$	9.57831			0.342739
$782$	−2.10680	+	3.64909i	−0.0753391	+	0.130491i
$783$	2.68523	−	4.65096i	0.0959623	−	0.166212i
$784$	−0.204862	+	0.261623i	−0.00731650	+	0.00934366i
$785$	9.18504	−	15.9090i	0.327828	−	0.567815i
$786$	8.39795	+	14.5457i	0.299545	+	0.518827i
$787$	7.76012	−	13.4409i	0.276618	−	0.479117i	−0.693924	−	0.720049i	$-0.744120\pi$
$787$	7.76012	−	13.4409i	0.276618	−	0.479117i	0.970542	+	0.240931i	$0.0774529\pi$
$788$	4.74110	+	8.21182i	0.168895	+	0.292534i
$789$	−24.9621			−0.888674
$790$	16.6966			0.594038
$791$	31.9834	+	2.25403i	1.13720	+	0.0801439i
$792$	−17.1482	+	29.7016i	−0.609336	+	1.05540i
$793$	2.63942	−	4.57160i	0.0937284	−	0.162342i
$794$	−2.02769	−	3.51207i	−0.0719601	−	0.124639i
$795$	−2.53590			−0.0899390
$796$	−13.9614	+	24.1819i	−0.494849	+	0.857104i
$797$	−3.10087			−0.109838			−0.0549192	−	0.998491i	$-0.517490\pi$
$797$	−3.10087			−0.109838			−0.0549192	+	0.998491i	$0.517490\pi$
$798$	−4.78996	+	25.1674i	−0.169563	+	0.890918i
$799$	54.3618			1.92318
$800$	21.8700	−	37.8799i	0.773220	−	1.33926i
$801$	−4.13548			−0.146120
$802$	13.9861	+	24.2246i	0.493866	+	0.855400i
$803$	22.6604	−	39.2489i	0.799667	−	1.38506i
$804$	6.95836	−	12.0522i	0.245403	−	0.425050i
$805$	−4.93023	+	7.30077i	−0.173768	+	0.257318i
$806$	−2.74459			−0.0966742
$807$	15.6930			0.552419
$808$	17.8774	+	30.9645i	0.628924	+	1.08933i
$809$	22.8267	−	39.5370i	0.802544	−	1.39005i	−0.115393	−	0.993320i	$-0.536813\pi$
$809$	22.8267	−	39.5370i	0.802544	−	1.39005i	0.917937	−	0.396727i	$-0.129854\pi$
$810$	−10.8970	−	18.8741i	−0.382881	−	0.663169i
$811$	13.4552	−	23.3051i	0.472477	−	0.818354i	−0.527027	−	0.849849i	$-0.676693\pi$
$811$	13.4552	−	23.3051i	0.472477	−	0.818354i	0.999504	+	0.0314943i	$0.0100266\pi$
$812$	12.5365	+	0.883507i	0.439944	+	0.0310050i
$813$	−10.8156	+	18.7331i	−0.379319	+	0.656999i
$814$	6.91227	−	11.9724i	0.242275	−	0.419632i
$815$	−41.5315			−1.45478
$816$	0.315691	−	0.546793i	0.0110514	−	0.0191416i
$817$	−13.3141	−	9.94015i	−0.465801	−	0.347762i
$818$	7.24923			0.253463
$819$	−10.6992	+	15.8436i	−0.373861	+	0.553619i
$820$	−25.4088	−	44.0094i	−0.887315	−	1.53688i
$821$	10.5836			0.369369			0.184684	−	0.982798i	$-0.440874\pi$
$821$	10.5836			0.369369			0.184684	+	0.982798i	$0.440874\pi$
$822$	14.1259			0.492697
$823$	−22.3617	−	38.7316i	−0.779479	−	1.35010i	−0.932242	−	0.361834i	$-0.882151\pi$
$823$	−22.3617	−	38.7316i	−0.779479	−	1.35010i	0.152763	−	0.988263i	$-0.451183\pi$
$824$	−5.03885	−	8.72754i	−0.175536	−	0.304038i
$825$	−67.5926			−2.35327
$826$	−0.593543	+	0.878929i	−0.0206520	+	0.0305819i
$827$	22.1495	−	38.3640i	0.770213	−	1.33405i	−0.167233	−	0.985917i	$-0.553483\pi$
$827$	22.1495	−	38.3640i	0.770213	−	1.33405i	0.937446	−	0.348130i	$-0.113183\pi$
$828$	−2.06754	−	3.58109i	−0.0718522	−	0.124452i
$829$	23.8642	−	41.3339i	0.828837	−	1.43559i	−0.0701146	−	0.997539i	$-0.522337\pi$
$829$	23.8642	−	41.3339i	0.828837	−	1.43559i	0.898951	−	0.438048i	$-0.144330\pi$
$830$	−24.1590	−	41.8447i	−0.838573	−	1.45245i
$831$	−1.06933	+	1.85213i	−0.0370946	+	0.0642497i
$832$	4.91722	−	8.51687i	0.170474	−	0.295269i
$833$	36.0178	+	5.10204i	1.24794	+	0.176775i
$834$	3.86248	+	6.69002i	0.133747	+	0.231656i
$835$	−15.0928	−	26.1415i	−0.522307	−	0.904662i
$836$	17.1130	−	7.35424i	0.591866	−	0.254352i
$837$	−1.09504	+	1.89667i	−0.0378503	+	0.0655586i
$838$	−3.47912	+	6.02601i	−0.120184	+	0.208165i
$839$	6.50139	+	11.2607i	0.224453	+	0.388764i	0.956155	−	0.292860i	$-0.0946071\pi$
$839$	6.50139	+	11.2607i	0.224453	+	0.388764i	−0.731702	+	0.681625i	$0.761274\pi$
$840$	−38.0644	+	56.3665i	−1.31335	+	1.94483i
$841$	7.24093	+	12.5417i	0.249687	+	0.432471i
$842$	−1.36387			−0.0470022
$843$	1.86768	−	3.23492i	0.0643264	−	0.111417i
$844$	−15.7521	+	27.2834i	−0.542208	+	0.939132i
$845$	−31.5750			−1.08621
$846$	16.1191	−	27.9191i	0.554186	−	0.959878i
$847$	0.867918	+	1.78196i	0.0298220	+	0.0612289i
$848$	0.0131954			0.000453132
$849$	50.8118			1.74386
$850$	−34.7521			−1.19199
$851$	2.17043	+	3.75929i	0.0744013	+	0.128867i
$852$	−4.45807	+	7.72160i	−0.152731	+	0.264538i
$853$	−19.9714	−	34.5914i	−0.683807	−	1.18439i	−0.973810	−	0.227362i	$-0.926990\pi$
$853$	−19.9714	−	34.5914i	−0.683807	−	1.18439i	0.290004	−	0.957026i	$-0.406343\pi$
$854$	−3.33364	+	4.93652i	−0.114075	+	0.168924i
$855$	6.47893	−	54.7842i	0.221575	−	1.87358i
$856$	9.89901	+	17.1456i	0.338341	+	0.586024i
$857$	−7.50160			−0.256250			−0.128125	−	0.991758i	$-0.540896\pi$
$857$	−7.50160			−0.256250			−0.128125	+	0.991758i	$0.540896\pi$
$858$	−15.4960			−0.529025
$859$	−1.29221			−0.0440898			−0.0220449	−	0.999757i	$-0.507018\pi$
$859$	−1.29221			−0.0440898			−0.0220449	+	0.999757i	$0.507018\pi$
$860$	−8.46900	−	14.6687i	−0.288790	−	0.500200i
$861$	33.9106	+	69.6234i	1.15567	+	2.37276i
$862$	−0.582143			−0.0198279
$863$	−5.86394	−	10.1566i	−0.199611	−	0.345736i	0.748791	−	0.662806i	$-0.230634\pi$
$863$	−5.86394	−	10.1566i	−0.199611	−	0.345736i	−0.948402	+	0.317070i	$0.897301\pi$
$864$	−4.00085	−	6.92967i	−0.136112	−	0.235752i
$865$	25.7444	+	44.5906i	0.875335	+	1.51613i
$866$	−0.174468	−	0.302188i	−0.00592867	−	0.0102688i
$867$	−25.6107			−0.869784
$868$	−5.11241	−	0.360297i	−0.173527	−	0.0122293i
$869$	9.24962	+	16.0208i	0.313772	+	0.543469i
$870$	30.1701			1.02286
$871$	8.87611			0.300755
$872$	45.1637			1.52944
$873$	−4.51754	−	7.82460i	−0.152895	−	0.264823i
$874$	0.415077	−	3.50979i	0.0140402	−	0.118720i
$875$	−25.4427	−	1.79307i	−0.860120	−	0.0606169i
$876$	21.0938	+	36.5355i	0.712693	+	1.23442i
$877$	−16.9011	+	29.2735i	−0.570708	+	0.988496i	0.425785	+	0.904824i	$0.359998\pi$
$877$	−16.9011	+	29.2735i	−0.570708	+	0.988496i	−0.996493	+	0.0836713i	$0.973335\pi$
$878$	8.52343	+	14.7630i	0.287652	+	0.498228i
$879$	13.5638			0.457495
$880$	0.579963			0.0195505
$881$	37.5390			1.26472			0.632360	−	0.774675i	$-0.282086\pi$
$881$	37.5390			1.26472			0.632360	+	0.774675i	$0.282086\pi$
$882$	13.3001	−	16.9852i	0.447838	−	0.571920i
$883$	13.4151	−	23.2356i	0.451454	−	0.781941i	−0.547023	−	0.837118i	$-0.684239\pi$
$883$	13.4151	−	23.2356i	0.451454	−	0.781941i	0.998477	+	0.0551766i	$0.0175722\pi$
$884$	13.1843			0.443436
$885$	2.10663	−	3.64880i	0.0708137	−	0.122653i
$886$	−0.877653	+	1.52014i	−0.0294853	+	0.0510701i
$887$	−29.5641			−0.992664			−0.496332	−	0.868133i	$-0.665320\pi$
$887$	−29.5641			−0.992664			−0.496332	+	0.868133i	$0.665320\pi$
$888$	16.7570	+	29.0240i	0.562329	+	0.973983i
$889$	−26.2745	+	38.9077i	−0.881217	+	1.30492i
$890$	−1.80160	−	3.12047i	−0.0603899	−	0.104598i
$891$	12.0735	−	20.9119i	0.404477	−	0.700574i
$892$	−10.2540	+	17.7605i	−0.343331	+	0.594667i
$893$	−41.8925	+	18.0031i	−1.40188	+	0.602451i
$894$	−1.61224	−	2.79249i	−0.0539214	−	0.0933947i
$895$	12.6979	+	21.9934i	0.424444	+	0.735158i
$896$	10.6014	−	15.6987i	0.354167	−	0.524457i
$897$	2.43284	−	4.21381i	0.0812303	−	0.140695i
$898$	12.9702	−	22.4651i	0.432822	−	0.749669i
$899$	2.96027	+	5.12733i	0.0987304	+	0.171006i
$900$	17.0523	−	29.5354i	0.568410	−	0.984515i
$901$	−0.722288	−	1.25104i	−0.0240629	−	0.0416781i
$902$	−17.0120	+	29.4657i	−0.566439	+	0.981101i
$903$	11.3027	+	23.2061i	0.376131	+	0.772251i
$904$	−34.1495			−1.13579
$905$	40.1814	+	69.5961i	1.33567	+	2.31345i
$906$	12.5255	+	21.6948i	0.416132	+	0.720762i
$907$	−35.9515			−1.19375			−0.596875	−	0.802334i	$-0.703591\pi$
$907$	−35.9515			−1.19375			−0.596875	+	0.802334i	$0.703591\pi$
$908$	19.4565			0.645688
$909$	22.5260	+	39.0162i	0.747141	+	1.29409i
$910$	−16.6160	−	1.17101i	−0.550816	−	0.0388187i
$911$	18.4427			0.611034			0.305517	−	0.952187i	$-0.401171\pi$
$911$	18.4427			0.611034			0.305517	+	0.952187i	$0.401171\pi$
$912$	−0.0621968	+	0.525921i	−0.00205954	+	0.0174150i
$913$	26.7674	−	46.3625i	0.885871	−	1.53437i
$914$	−7.77914			−0.257311
$915$	11.8319	−	20.4935i	0.391152	−	0.677495i
$916$	3.26325	−	5.65212i	0.107821	−	0.186751i
$917$	−11.1950	+	16.5778i	−0.369692	+	0.547447i
$918$	−3.17874	+	5.50575i	−0.104914	+	0.181717i
$919$	14.8142	+	25.6590i	0.488677	+	0.846413i	0.999915	−	0.0130260i	$-0.00414644\pi$
$919$	14.8142	+	25.6590i	0.488677	+	0.846413i	−0.511238	+	0.859439i	$0.670813\pi$
$920$	4.69146	−	8.12585i	0.154673	−	0.267901i
$921$	1.38916	+	2.40610i	0.0457744	+	0.0792836i
$922$	−10.5735			−0.348218
$923$	−5.68672			−0.187181
$924$	−28.8647	−	2.03424i	−0.949580	−	0.0669215i
$925$	−17.9008	+	31.0051i	−0.588575	+	1.01944i
$926$	10.9913	−	19.0375i	0.361198	−	0.625613i
$927$	−6.34910	−	10.9970i	−0.208532	−	0.361187i
$928$	−21.6312			−0.710080
$929$	1.62734	−	2.81864i	0.0533914	−	0.0924766i	−0.838094	−	0.545525i	$-0.816330\pi$
$929$	1.62734	−	2.81864i	0.0533914	−	0.0924766i	0.891486	+	0.453049i	$0.149664\pi$
$930$	−12.3034			−0.403446
$931$	−29.4459	+	7.99633i	−0.965049	+	0.262069i
$932$	20.0064			0.655331
$933$	−32.1077	+	55.6121i	−1.05116	+	1.82066i
$934$	2.26830			0.0742212
$935$	−31.7459	−	54.9855i	−1.03820	−	1.79822i
$936$	10.1811	−	17.6341i	0.332778	−	0.576389i
$937$	−14.3369	+	24.8322i	−0.468366	+	0.811234i	−0.999346	−	0.0361504i	$-0.988490\pi$
$937$	−14.3369	+	24.8322i	−0.468366	+	0.811234i	0.530980	+	0.847384i	$0.321824\pi$
$938$	−9.99116	−	0.704126i	−0.326223	−	0.0229905i
$939$	−66.2637			−2.16243
$940$	−46.4824			−1.51609
$941$	10.9466	+	18.9601i	0.356849	+	0.618081i	0.987433	−	0.158041i	$-0.0505177\pi$
$941$	10.9466	+	18.9601i	0.356849	+	0.618081i	−0.630584	+	0.776121i	$0.717184\pi$
$942$	5.72453	−	9.91518i	0.186515	−	0.323054i
$943$	−5.34172	−	9.25213i	−0.173950	−	0.301291i
$944$	−0.0109617	+	0.0189863i	−0.000356774	+	0.000617951i
$945$	−7.43873	+	11.0154i	−0.241982	+	0.358331i
$946$	−5.67027	+	9.82119i	−0.184356	+	0.319314i
$947$	−9.32989	+	16.1598i	−0.303181	+	0.525124i	−0.976855	−	0.213904i	$-0.931382\pi$
$947$	−9.32989	+	16.1598i	−0.303181	+	0.525124i	0.673674	+	0.739029i	$0.264715\pi$
$948$	−17.2203			−0.559290
$949$	−13.4536	+	23.3024i	−0.436724	+	0.756428i
$950$	26.7809	−	11.5089i	0.868886	−	0.373399i
$951$	−48.8931			−1.58547
$952$	−38.6491	−	2.72379i	−1.25262	−	0.0882785i
$953$	3.25923	+	5.64515i	0.105577	+	0.182864i	0.913974	−	0.405773i	$-0.132998\pi$
$953$	3.25923	+	5.64515i	0.105577	+	0.182864i	−0.808397	+	0.588638i	$0.799664\pi$
$954$	−0.856676			−0.0277359
$955$	−28.9883			−0.938041
$956$	−3.20127	−	5.54477i	−0.103537	−	0.179331i
$957$	16.7137	+	28.9490i	0.540277	+	0.935788i
$958$	7.04067			0.227474
$959$	7.36683	+	15.1252i	0.237887	+	0.488417i
$960$	22.0429	−	38.1793i	0.711430	−	1.23223i
$961$	14.2928	+	24.7558i	0.461058	+	0.798576i
$962$	−4.10387	+	7.10811i	−0.132314	+	0.229175i
$963$	12.4730	+	21.6040i	0.401938	+	0.696178i
$964$	13.1342	−	22.7491i	0.423025	−	0.732700i
$965$	37.4156	−	64.8057i	1.20445	−	2.08617i
$966$	−3.07274	+	4.55017i	−0.0988638	+	0.146399i
$967$	−1.46787	−	2.54242i	−0.0472034	−	0.0817587i	0.841458	−	0.540322i	$-0.181698\pi$
$967$	−1.46787	−	2.54242i	−0.0472034	−	0.0817587i	−0.888662	+	0.458563i	$0.848364\pi$
$968$	−1.05554	−	1.82826i	−0.0339265	−	0.0587624i
$969$	53.2664	−	22.8910i	1.71116	−	0.735364i
$970$	3.93609	−	6.81751i	0.126380	−	0.218897i
$971$	25.0357	−	43.3631i	0.803434	−	1.39159i	−0.113909	−	0.993491i	$-0.536337\pi$
$971$	25.0357	−	43.3631i	0.803434	−	1.39159i	0.917343	−	0.398098i	$-0.130329\pi$
$972$	13.8745	+	24.0313i	0.445024	+	0.770805i
$973$	−5.14894	+	7.62465i	−0.165068	+	0.244435i
$974$	−9.77632	−	16.9331i	−0.313253	−	0.542571i
$975$	40.1303			1.28520
$976$	−0.0615669	+	0.106637i	−0.00197071	+	0.00341337i
$977$	−16.8145	+	29.1235i	−0.537942	+	0.931743i	0.461072	+	0.887362i	$0.347465\pi$
$977$	−16.8145	+	29.1235i	−0.537942	+	0.931743i	−0.999015	+	0.0443807i	$0.985869\pi$
$978$	−25.8843			−0.827688
$979$	1.99611	−	3.45737i	0.0637961	−	0.110498i
$980$	−30.7973	−	4.36254i	−0.983783	−	0.139356i
$981$	56.9077			1.81692
$982$	−27.5564			−0.879359
$983$	−1.61336			−0.0514583			−0.0257292	−	0.999669i	$-0.508191\pi$
$983$	−1.61336			−0.0514583			−0.0257292	+	0.999669i	$0.508191\pi$
$984$	−41.2414	−	71.4321i	−1.31473	−	2.27717i
$985$	−13.5554	+	23.4787i	−0.431912	+	0.748093i
$986$	8.59320	+	14.8839i	0.273663	+	0.473999i
$987$	70.6606	+	4.97980i	2.24915	+	0.158509i
$988$	−10.1601	+	4.36627i	−0.323237	+	0.138910i
$989$	−1.78044	−	3.08382i	−0.0566148	−	0.0980597i
$990$	−37.6525			−1.19668
$991$	27.5272			0.874430			0.437215	−	0.899357i	$-0.355965\pi$
$991$	27.5272			0.874430			0.437215	+	0.899357i	$0.355965\pi$
$992$	8.82128			0.280076
$993$	12.6193	+	21.8573i	0.400462	+	0.693621i
$994$	6.40111	+	0.451117i	0.203031	+	0.0143086i
$995$	−79.8350			−2.53094
$996$	24.9169	+	43.1573i	0.789521	+	1.36749i
$997$	−0.549237	−	0.951307i	−0.0173945	−	0.0301282i	0.857197	−	0.514988i	$-0.172204\pi$
$997$	−0.549237	−	0.951307i	−0.0173945	−	0.0301282i	−0.874592	+	0.484860i	$0.838870\pi$
$998$	9.58389	+	16.5998i	0.303373	+	0.525457i
$999$	3.27474	+	5.67202i	0.103608	+	0.179455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.g.a.102.8	yes	24
7.2	even	3		133.2.h.a.121.5	yes	24
7.3	odd	6		931.2.e.e.197.8		24
7.4	even	3		931.2.e.f.197.8		24
7.5	odd	6		931.2.h.h.520.5		24
7.6	odd	2		931.2.g.h.900.8		24
19.11	even	3		133.2.h.a.11.5	yes	24
133.11	even	3		931.2.e.f.638.8		24
133.30	even	3	inner	133.2.g.a.30.8	✓	24
133.68	odd	6		931.2.g.h.30.8		24
133.87	odd	6		931.2.e.e.638.8		24
133.125	odd	6		931.2.h.h.410.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.g.a.30.8	✓	24	133.30	even	3	inner
133.2.g.a.102.8	yes	24	1.1	even	1	trivial
133.2.h.a.11.5	yes	24	19.11	even	3
133.2.h.a.121.5	yes	24	7.2	even	3
931.2.e.e.197.8		24	7.3	odd	6
931.2.e.e.638.8		24	133.87	odd	6
931.2.e.f.197.8		24	7.4	even	3
931.2.e.f.638.8		24	133.11	even	3
931.2.g.h.30.8		24	133.68	odd	6
931.2.g.h.900.8		24	7.6	odd	2
931.2.h.h.410.5		24	133.125	odd	6
931.2.h.h.520.5		24	7.5	odd	6

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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.433977 - 0.751669i) q^{2} -2.55943 q^{3} +(0.623329 + 1.07964i) q^{4} +(-1.78218 + 3.08682i) q^{5} +(-1.11073 + 1.92385i) q^{6} +(-2.63921 - 0.185998i) q^{7} +2.81795 q^{8} +3.55070 q^{9} +O(q^{10})\)	\(q+(0.433977 - 0.751669i) q^{2} -2.55943 q^{3} +(0.623329 + 1.07964i) q^{4} +(-1.78218 + 3.08682i) q^{5} +(-1.11073 + 1.92385i) q^{6} +(-2.63921 - 0.185998i) q^{7} +2.81795 q^{8} +3.55070 q^{9} +(1.54685 + 2.67922i) q^{10} +(-1.71385 + 2.96848i) q^{11} +(-1.59537 - 2.76326i) q^{12} +(1.01753 - 1.76241i) q^{13} +(-1.28516 + 1.90309i) q^{14} +(4.56137 - 7.90052i) q^{15} +(-0.0237348 + 0.0411099i) q^{16} +5.19677 q^{17} +(1.54092 - 2.66895i) q^{18} +(-4.00476 + 1.72102i) q^{19} -4.44353 q^{20} +(6.75487 + 0.476049i) q^{21} +(1.48754 + 2.57650i) q^{22} -0.934166 q^{23} -7.21234 q^{24} +(-3.85232 - 6.67241i) q^{25} +(-0.883167 - 1.52969i) q^{26} -1.40947 q^{27} +(-1.44428 - 2.96532i) q^{28} +(-1.90513 + 3.29979i) q^{29} +(-3.95905 - 6.85728i) q^{30} +(0.776918 - 1.34566i) q^{31} +(2.83855 + 4.91651i) q^{32} +(4.38649 - 7.59762i) q^{33} +(2.25528 - 3.90625i) q^{34} +(5.27768 - 7.81528i) q^{35} +(2.21325 + 3.83346i) q^{36} +(-2.32338 - 4.02422i) q^{37} +(-0.444329 + 3.75714i) q^{38} +(-2.60429 + 4.51077i) q^{39} +(-5.02208 + 8.69850i) q^{40} +(5.71816 + 9.90415i) q^{41} +(3.28929 - 4.87083i) q^{42} +(1.90592 + 3.30114i) q^{43} -4.27317 q^{44} +(-6.32797 + 10.9604i) q^{45} +(-0.405406 + 0.702184i) q^{46} +10.4607 q^{47} +(0.0607476 - 0.105218i) q^{48} +(6.93081 + 0.981772i) q^{49} -6.68726 q^{50} -13.3008 q^{51} +2.53702 q^{52} +(-0.138988 - 0.240734i) q^{53} +(-0.611677 + 1.05946i) q^{54} +(-6.10878 - 10.5807i) q^{55} +(-7.43714 - 0.524132i) q^{56} +(10.2499 - 4.40485i) q^{57} +(1.65357 + 2.86406i) q^{58} +0.461843 q^{59} +11.3729 q^{60} +2.59395 q^{61} +(-0.674329 - 1.16797i) q^{62} +(-9.37102 - 0.660421i) q^{63} +4.83251 q^{64} +(3.62683 + 6.28186i) q^{65} +(-3.80727 - 6.59438i) q^{66} +(2.18080 + 3.77726i) q^{67} +(3.23929 + 5.61062i) q^{68} +2.39094 q^{69} +(-3.58412 - 7.35872i) q^{70} +(-1.39719 - 2.42000i) q^{71} +10.0057 q^{72} -13.2219 q^{73} -4.03317 q^{74} +(9.85975 + 17.0776i) q^{75} +(-4.35436 - 3.25092i) q^{76} +(5.07534 - 7.51565i) q^{77} +(2.26041 + 3.91514i) q^{78} +(2.69849 - 4.67392i) q^{79} +(-0.0845993 - 0.146530i) q^{80} -7.04464 q^{81} +9.92620 q^{82} -15.6183 q^{83} +(3.69654 + 7.58954i) q^{84} +(-9.26157 + 16.0415i) q^{85} +3.30849 q^{86} +(4.87606 - 8.44559i) q^{87} +(-4.82954 + 8.36502i) q^{88} -1.16469 q^{89} +(5.49238 + 9.51309i) q^{90} +(-3.01327 + 4.46210i) q^{91} +(-0.582293 - 1.00856i) q^{92} +(-1.98847 + 3.44413i) q^{93} +(4.53970 - 7.86299i) q^{94} +(1.82469 - 15.4291i) q^{95} +(-7.26507 - 12.5835i) q^{96} +(-1.27230 - 2.20368i) q^{97} +(3.74578 - 4.78361i) q^{98} +(-6.08537 + 10.5402i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

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