LMFDB - Embedded newform 189.2.ba.a.5.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.20
Character	$\chi$	$=$	189.5
Dual form			189.2.ba.a.38.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.95754 - 0.345166i) q^{2} +(-1.39494 + 1.02672i) q^{3} +(1.83342 - 0.667310i) q^{4} +(-0.649669 + 3.68445i) q^{5} +(-2.37625 + 2.49133i) q^{6} +(2.58740 - 0.552593i) q^{7} +(-0.0842052 + 0.0486159i) q^{8} +(0.891690 - 2.86442i) q^{9} +O(q^{10})$	\(q+(1.95754 - 0.345166i) q^{2} +(-1.39494 + 1.02672i) q^{3} +(1.83342 - 0.667310i) q^{4} +(-0.649669 + 3.68445i) q^{5} +(-2.37625 + 2.49133i) q^{6} +(2.58740 - 0.552593i) q^{7} +(-0.0842052 + 0.0486159i) q^{8} +(0.891690 - 2.86442i) q^{9} +7.43669i q^{10} +(0.526860 - 0.0928996i) q^{11} +(-1.87236 + 2.81326i) q^{12} +(3.22666 - 3.84539i) q^{13} +(4.87419 - 1.97480i) q^{14} +(-2.87666 - 5.80660i) q^{15} +(-3.13729 + 2.63250i) q^{16} -4.53776 q^{17} +(0.756814 - 5.91498i) q^{18} -1.20759i q^{19} +(1.26756 + 7.18868i) q^{20} +(-3.04190 + 3.42737i) q^{21} +(0.999281 - 0.363709i) q^{22} +(5.35042 - 6.37638i) q^{23} +(0.0675459 - 0.154271i) q^{24} +(-8.45466 - 3.07725i) q^{25} +(4.98901 - 8.64122i) q^{26} +(1.69711 + 4.91119i) q^{27} +(4.37504 - 2.73973i) q^{28} +(2.30869 + 2.75138i) q^{29} +(-7.63540 - 10.3737i) q^{30} +(-0.0334941 - 0.0920242i) q^{31} +(-5.10770 + 6.08713i) q^{32} +(-0.639554 + 0.670527i) q^{33} +(-8.88283 + 1.56628i) q^{34} +(0.355050 + 9.89216i) q^{35} +(-0.276613 - 5.84671i) q^{36} +(-0.267738 - 0.463737i) q^{37} +(-0.416820 - 2.36390i) q^{38} +(-0.552849 + 8.67695i) q^{39} +(-0.124418 - 0.341834i) q^{40} +(-5.79016 - 4.85852i) q^{41} +(-4.77161 + 7.75916i) q^{42} +(-0.0316146 - 0.0115068i) q^{43} +(0.903962 - 0.521903i) q^{44} +(9.97451 + 5.14631i) q^{45} +(8.27273 - 14.3288i) q^{46} +(5.19200 + 1.88973i) q^{47} +(1.67348 - 6.89328i) q^{48} +(6.38928 - 2.85956i) q^{49} +(-17.6125 - 3.10555i) q^{50} +(6.32988 - 4.65901i) q^{51} +(3.34976 - 9.20340i) q^{52} +(-8.57774 + 4.95236i) q^{53} +(5.01732 + 9.02805i) q^{54} +2.00154i q^{55} +(-0.191008 + 0.172320i) q^{56} +(1.23986 + 1.68451i) q^{57} +(5.46902 + 4.58905i) q^{58} +(0.583744 + 0.489820i) q^{59} +(-9.14892 - 8.72631i) q^{60} +(2.21618 - 6.08890i) q^{61} +(-0.0973295 - 0.168580i) q^{62} +(0.724302 - 7.90414i) q^{63} +(-3.80200 + 6.58526i) q^{64} +(12.0719 + 14.3867i) q^{65} +(-1.02051 + 1.53333i) q^{66} +(-1.14393 + 6.48754i) q^{67} +(-8.31962 + 3.02809i) q^{68} +(-0.916728 + 14.3880i) q^{69} +(4.10946 + 19.2417i) q^{70} +(3.13261 + 1.80861i) q^{71} +(0.0641713 + 0.284549i) q^{72} +(-5.76249 - 3.32698i) q^{73} +(-0.684174 - 0.815366i) q^{74} +(14.9532 - 4.38802i) q^{75} +(-0.805838 - 2.21402i) q^{76} +(1.31186 - 0.531508i) q^{77} +(1.91277 + 17.1763i) q^{78} +(-0.909744 - 5.15941i) q^{79} +(-7.66112 - 13.2694i) q^{80} +(-7.40978 - 5.10834i) q^{81} +(-13.0114 - 7.51215i) q^{82} +(-1.39005 + 1.16639i) q^{83} +(-3.28996 + 8.31369i) q^{84} +(2.94804 - 16.7192i) q^{85} +(-0.0658585 - 0.0116126i) q^{86} +(-6.04537 - 1.46763i) q^{87} +(-0.0398480 + 0.0334364i) q^{88} -9.21301 q^{89} +(21.3018 + 6.63122i) q^{90} +(6.22374 - 11.7326i) q^{91} +(5.55454 - 15.2610i) q^{92} +(0.141205 + 0.0939788i) q^{93} +(10.8158 + 1.90712i) q^{94} +(4.44931 + 0.784534i) q^{95} +(0.875142 - 13.7353i) q^{96} +(-4.37434 + 12.0184i) q^{97} +(11.5202 - 7.80305i) q^{98} +(0.203692 - 1.59198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.95754	−	0.345166i	1.38419	−	0.244069i	0.568557	−	0.822644i	$-0.307502\pi$
$2$	1.95754	−	0.345166i	1.38419	−	0.244069i	0.815630	+	0.578575i	$0.196391\pi$
$3$	−1.39494	+	1.02672i	−0.805366	+	0.592777i
$3$	−1.39494	+	1.02672i	−0.805366	+	0.592777i
$4$	1.83342	−	0.667310i	0.916710	−	0.333655i
$5$	−0.649669	+	3.68445i	−0.290541	+	1.64774i	0.394254	+	0.919001i	$0.371003\pi$
$5$	−0.649669	+	3.68445i	−0.290541	+	1.64774i	−0.684795	+	0.728736i	$0.740108\pi$
$6$	−2.37625	+	2.49133i	−0.970098	+	1.01708i
$7$	2.58740	−	0.552593i	0.977945	−	0.208860i
$7$	2.58740	−	0.552593i	0.977945	−	0.208860i
$8$	−0.0842052	+	0.0486159i	−0.0297710	+	0.0171883i
$9$	0.891690	−	2.86442i	0.297230	−	0.954806i
$10$			7.43669i			2.35169i
$11$	0.526860	−	0.0928996i	0.158854	−	0.0280103i	−0.0936554	−	0.995605i	$-0.529855\pi$
$11$	0.526860	−	0.0928996i	0.158854	−	0.0280103i	0.252510	+	0.967594i	$0.418744\pi$
$12$	−1.87236	+	2.81326i	−0.540504	+	0.812119i
$13$	3.22666	−	3.84539i	0.894916	−	1.06652i	−0.102504	−	0.994733i	$-0.532686\pi$
$13$	3.22666	−	3.84539i	0.894916	−	1.06652i	0.997420	−	0.0717866i	$-0.0228700\pi$
$14$	4.87419	−	1.97480i	1.30268	−	0.527788i
$15$	−2.87666	−	5.80660i	−0.742750	−	1.49926i
$16$	−3.13729	+	2.63250i	−0.784322	+	0.658124i
$17$	−4.53776			−1.10057			−0.550284	−	0.834977i	$-0.685481\pi$
$17$	−4.53776			−1.10057			−0.550284	+	0.834977i	$0.685481\pi$
$18$	0.756814	−	5.91498i	0.178383	−	1.39417i
$19$		−	1.20759i		−	0.277041i	−0.990360	−	0.138520i	$-0.955765\pi$
$19$		−	1.20759i		−	0.277041i	0.990360	−	0.138520i	$-0.0442346\pi$
$20$	1.26756	+	7.18868i	0.283435	+	1.60744i
$21$	−3.04190	+	3.42737i	−0.663797	+	0.747913i
$22$	0.999281	−	0.363709i	0.213047	−	0.0775429i
$23$	5.35042	−	6.37638i	1.11564	−	1.32957i	0.177180	−	0.984178i	$-0.443302\pi$
$23$	5.35042	−	6.37638i	1.11564	−	1.32957i	0.938459	−	0.345389i	$-0.112253\pi$
$24$	0.0675459	−	0.154271i	0.0137878	−	0.0314905i
$25$	−8.45466	−	3.07725i	−1.69093	−	0.615449i
$26$	4.98901	−	8.64122i	0.978426	−	1.69468i
$27$	1.69711	+	4.91119i	0.326608	+	0.945160i
$28$	4.37504	−	2.73973i	0.826805	−	0.517761i
$29$	2.30869	+	2.75138i	0.428712	+	0.510919i	0.936550	−	0.350533i	$-0.114000\pi$
$29$	2.30869	+	2.75138i	0.428712	+	0.510919i	−0.507838	+	0.861452i	$0.669555\pi$
$30$	−7.63540	−	10.3737i	−1.39403	−	1.89397i
$31$	−0.0334941	−	0.0920242i	−0.00601571	−	0.0165280i	0.936648	−	0.350271i	$-0.113910\pi$
$31$	−0.0334941	−	0.0920242i	−0.00601571	−	0.0165280i	−0.942664	+	0.333743i	$0.891688\pi$
$32$	−5.10770	+	6.08713i	−0.902923	+	1.07606i
$33$	−0.639554	+	0.670527i	−0.111332	+	0.116724i
$34$	−8.88283	+	1.56628i	−1.52339	+	0.268615i
$35$	0.355050	+	9.89216i	0.0600144	+	1.67208i
$36$	−0.276613	−	5.84671i	−0.0461022	−	0.974452i
$37$	−0.267738	−	0.463737i	−0.0440159	−	0.0762378i	0.843178	−	0.537634i	$-0.180682\pi$
$37$	−0.267738	−	0.463737i	−0.0440159	−	0.0762378i	−0.887194	+	0.461397i	$0.847349\pi$
$38$	−0.416820	−	2.36390i	−0.0676171	−	0.383476i
$39$	−0.552849	+	8.67695i	−0.0885267	+	1.38942i
$40$	−0.124418	−	0.341834i	−0.0196721	−	0.0540488i
$41$	−5.79016	−	4.85852i	−0.904271	−	0.758773i	0.0667499	−	0.997770i	$-0.478737\pi$
$41$	−5.79016	−	4.85852i	−0.904271	−	0.758773i	−0.971020	+	0.238997i	$0.923181\pi$
$42$	−4.77161	+	7.75916i	−0.736276	+	1.19726i
$43$	−0.0316146	−	0.0115068i	−0.00482118	−	0.00175477i	0.339608	−	0.940567i	$-0.389705\pi$
$43$	−0.0316146	−	0.0115068i	−0.00482118	−	0.00175477i	−0.344430	+	0.938812i	$0.611928\pi$
$44$	0.903962	−	0.521903i	0.136277	−	0.0786798i
$45$	9.97451	+	5.14631i	1.48691	+	0.767167i
$46$	8.27273	−	14.3288i	1.21975	−	2.11266i
$47$	5.19200	+	1.88973i	0.757331	+	0.275646i	0.691687	−	0.722197i	$-0.256868\pi$
$47$	5.19200	+	1.88973i	0.757331	+	0.275646i	0.0656440	+	0.997843i	$0.479090\pi$
$48$	1.67348	−	6.89328i	0.241545	−	0.994960i
$49$	6.38928	−	2.85956i	0.912755	−	0.408508i
$50$	−17.6125	−	3.10555i	−2.49078	−	0.439191i
$51$	6.32988	−	4.65901i	0.886361	−	0.652392i
$52$	3.34976	−	9.20340i	0.464528	−	1.27628i
$53$	−8.57774	+	4.95236i	−1.17824	+	0.680259i	−0.955608	−	0.294642i	$-0.904799\pi$
$53$	−8.57774	+	4.95236i	−1.17824	+	0.680259i	−0.222636	+	0.974902i	$0.571466\pi$
$54$	5.01732	+	9.02805i	0.682771	+	1.22856i
$55$			2.00154i			0.269888i
$56$	−0.191008	+	0.172320i	−0.0255245	+	0.0230272i
$57$	1.23986	+	1.68451i	0.164223	+	0.223119i
$58$	5.46902	+	4.58905i	0.718117	+	0.602572i
$59$	0.583744	+	0.489820i	0.0759970	+	0.0637691i	0.679995	−	0.733217i	$-0.261982\pi$
$59$	0.583744	+	0.489820i	0.0759970	+	0.0637691i	−0.603998	+	0.796986i	$0.706426\pi$
$60$	−9.14892	−	8.72631i	−1.18112	−	1.12656i
$61$	2.21618	−	6.08890i	0.283753	−	0.779604i	−0.713154	−	0.701008i	$-0.752734\pi$
$61$	2.21618	−	6.08890i	0.283753	−	0.779604i	0.996906	−	0.0785967i	$-0.0250439\pi$
$62$	−0.0973295	−	0.168580i	−0.0123609	−	0.0214096i
$63$	0.724302	−	7.90414i	0.0912535	−	0.995828i
$64$	−3.80200	+	6.58526i	−0.475250	+	0.823158i
$65$	12.0719	+	14.3867i	1.49733	+	1.78445i
$66$	−1.02051	+	1.53333i	−0.125616	+	0.188740i
$67$	−1.14393	+	6.48754i	−0.139753	+	0.792579i	0.831678	+	0.555258i	$0.187380\pi$
$67$	−1.14393	+	6.48754i	−0.139753	+	0.792579i	−0.971431	+	0.237321i	$0.923731\pi$
$68$	−8.31962	+	3.02809i	−1.00890	+	0.367210i
$69$	−0.916728	+	14.3880i	−0.110361	+	1.73212i
$70$	4.10946	+	19.2417i	0.491175	+	2.29982i
$71$	3.13261	+	1.80861i	0.371772	+	0.214643i	0.674232	−	0.738519i	$-0.264475\pi$
$71$	3.13261	+	1.80861i	0.371772	+	0.214643i	−0.302460	+	0.953162i	$0.597808\pi$
$72$	0.0641713	+	0.284549i	0.00756266	+	0.0335345i
$73$	−5.76249	−	3.32698i	−0.674449	−	0.389393i	0.123312	−	0.992368i	$-0.460649\pi$
$73$	−5.76249	−	3.32698i	−0.674449	−	0.389393i	−0.797760	+	0.602975i	$0.793982\pi$
$74$	−0.684174	−	0.815366i	−0.0795336	−	0.0947844i
$75$	14.9532	−	4.38802i	1.72664	−	0.506685i
$76$	−0.805838	−	2.21402i	−0.0924360	−	0.253966i
$77$	1.31186	−	0.531508i	0.149501	−	0.0605709i
$78$	1.91277	+	17.1763i	0.216579	+	1.94483i
$79$	−0.909744	−	5.15941i	−0.102354	−	0.580480i	−0.992244	−	0.124304i	$-0.960330\pi$
$79$	−0.909744	−	5.15941i	−0.102354	−	0.580480i	0.889890	−	0.456175i	$-0.150781\pi$
$80$	−7.66112	−	13.2694i	−0.856539	−	1.48357i
$81$	−7.40978	−	5.10834i	−0.823309	−	0.567594i
$82$	−13.0114	−	7.51215i	−1.43687	−	0.829579i
$83$	−1.39005	+	1.16639i	−0.152578	+	0.128028i	−0.715881	−	0.698222i	$-0.753975\pi$
$83$	−1.39005	+	1.16639i	−0.152578	+	0.128028i	0.563303	+	0.826250i	$0.309530\pi$
$84$	−3.28996	+	8.31369i	−0.358964	+	0.907098i
$85$	2.94804	−	16.7192i	0.319760	−	1.81345i
$86$	−0.0658585	−	0.0116126i	−0.00710170	−	0.00125222i
$87$	−6.04537	−	1.46763i	−0.648132	−	0.157346i
$88$	−0.0398480	+	0.0334364i	−0.00424781	+	0.00356433i
$89$	−9.21301			−0.976577			−0.488289	−	0.872682i	$-0.662379\pi$
$89$	−9.21301			−0.976577			−0.488289	+	0.872682i	$0.662379\pi$
$90$	21.3018	+	6.63122i	2.24541	+	0.698992i
$91$	6.22374	−	11.7326i	0.652425	−	1.22991i
$92$	5.55454	−	15.2610i	0.579101	−	1.59107i
$93$	0.141205	+	0.0939788i	0.0146423	+	0.00974515i
$94$	10.8158	+	1.90712i	1.11556	+	0.196704i
$95$	4.44931	+	0.784534i	0.456490	+	0.0804915i
$96$	0.875142	−	13.7353i	0.0893188	−	1.40186i
$97$	−4.37434	+	12.0184i	−0.444147	+	1.22028i	0.492593	+	0.870260i	$0.336049\pi$
$97$	−4.37434	+	12.0184i	−0.444147	+	1.22028i	−0.936741	+	0.350025i	$0.886173\pi$
$98$	11.5202	−	7.80305i	1.16372	−	0.788227i
$99$	0.203692	−	1.59198i	0.0204719	−	0.160000i
$100$	−17.5544			−1.75544
$101$	−1.63246	+	1.36979i	−0.162436	+	0.136300i	−0.720383	−	0.693577i	$-0.756034\pi$
$101$	−1.63246	+	1.36979i	−0.162436	+	0.136300i	0.557947	+	0.829877i	$0.311589\pi$
$102$	10.7828	−	11.3050i	1.06766	−	1.11937i
$103$	−11.7534	−	2.07244i	−1.15810	−	0.204204i	−0.438588	−	0.898688i	$-0.644521\pi$
$103$	−11.7534	−	2.07244i	−1.15810	−	0.204204i	−0.719508	+	0.694485i	$0.755632\pi$
$104$	−0.0847549	+	0.480669i	−0.00831091	+	0.0471335i
$105$	−10.6518	−	13.4344i	−1.03950	−	1.31106i
$106$	−15.0818	+	12.6552i	−1.46488	+	1.22918i
$107$	13.4523	+	7.76670i	1.30048	+	0.750835i	0.980487	−	0.196583i	$-0.0629845\pi$
$107$	13.4523	+	7.76670i	1.30048	+	0.750835i	0.319998	+	0.947418i	$0.396318\pi$
$108$	6.38880	+	7.87178i	0.614762	+	0.757463i
$109$	−1.01428	−	1.75678i	−0.0971503	−	0.168269i	0.813354	−	0.581770i	$-0.197639\pi$
$109$	−1.01428	−	1.75678i	−0.0971503	−	0.168269i	−0.910504	+	0.413500i	$0.864306\pi$
$110$	0.690866	+	3.91809i	0.0658715	+	0.373576i
$111$	0.849606	+	0.371990i	0.0806410	+	0.0353077i
$112$	−6.66272	+	8.54497i	−0.629568	+	0.807424i
$113$	−2.57486	−	7.07437i	−0.242222	−	0.665501i	−0.999917	−	0.0128913i	$-0.995896\pi$
$113$	−2.57486	−	7.07437i	−0.242222	−	0.665501i	0.757694	−	0.652610i	$-0.226326\pi$
$114$	3.00850	+	2.86953i	0.281772	+	0.268757i
$115$	20.0175	+	23.8559i	1.86664	+	2.22458i
$116$	6.06881	+	3.50383i	0.563475	+	0.325323i
$117$	−8.13762	−	12.6714i	−0.752323	−	1.17147i
$118$	1.31177	+	0.757350i	0.120758	+	0.0697197i
$119$	−11.7410	+	2.50753i	−1.07630	+	0.229865i
$120$	0.524523	+	0.349095i	0.0478822	+	0.0318679i
$121$	−10.0677	+	3.66433i	−0.915243	+	0.333121i
$122$	2.23657	−	12.6842i	0.202489	−	1.14837i
$123$	13.0652	+	0.832447i	1.17805	+	0.0750592i
$124$	−0.122817	−	0.146368i	−0.0110293	−	0.0131442i
$125$	7.47747	−	12.9514i	0.668805	−	1.15840i
$126$	−1.31040	−	15.7226i	−0.116739	−	1.40068i
$127$	9.23798	+	16.0006i	0.819738	+	1.41983i	0.905875	+	0.423545i	$0.139214\pi$
$127$	9.23798	+	16.0006i	0.819738	+	1.41983i	−0.0861371	+	0.996283i	$0.527452\pi$
$128$	0.265962	−	0.730726i	0.0235080	−	0.0645876i
$129$	0.0559146	−	0.0164082i	0.00492301	−	0.00144466i
$130$	28.5970	+	23.9957i	2.50812	+	2.10456i
$131$	0.439975	+	0.369183i	0.0384408	+	0.0322556i	0.661806	−	0.749675i	$-0.269790\pi$
$131$	0.439975	+	0.369183i	0.0384408	+	0.0322556i	−0.623365	+	0.781931i	$0.714235\pi$
$132$	−0.725121	+	1.65614i	−0.0631137	+	0.144148i
$133$	−0.667307	−	3.12452i	−0.0578628	−	0.270931i
$134$			13.0944i			1.13119i
$135$	−19.1976	+	3.06226i	−1.65227	+	0.263558i
$136$	0.382103	−	0.220607i	0.0327651	−	0.0189169i
$137$	−0.799505	+	2.19662i	−0.0683063	+	0.187670i	−0.969149	−	0.246476i	$-0.920727\pi$
$137$	−0.799505	+	2.19662i	−0.0683063	+	0.187670i	0.900843	+	0.434146i	$0.142950\pi$
$138$	3.17174	+	28.4815i	0.269996	+	2.42451i
$139$	0.461702	+	0.0814105i	0.0391610	+	0.00690515i	0.193194	−	0.981161i	$-0.438115\pi$
$139$	0.461702	+	0.0814105i	0.0391610	+	0.00690515i	−0.154033	+	0.988066i	$0.549226\pi$
$140$	7.25209	+	17.8995i	0.612914	+	1.51279i
$141$	−9.18274	+	2.69468i	−0.773326	+	0.226933i
$142$	6.75646	+	2.45915i	0.566989	+	0.206367i
$143$	1.34277	−	2.32574i	0.112288	−	0.194488i
$144$	4.74308	+	11.3339i	0.395257	+	0.944490i
$145$	−11.6372	+	6.71875i	−0.966419	+	0.557962i
$146$	−12.4286	−	4.52365i	−1.02860	−	0.374380i
$147$	−5.97667	+	10.5489i	−0.492947	+	0.870059i
$148$	−0.800333	−	0.671559i	−0.0657870	−	0.0552018i
$149$	−3.51315	−	9.65231i	−0.287809	−	0.790748i	−0.996372	−	0.0851012i	$-0.972879\pi$
$149$	−3.51315	−	9.65231i	−0.287809	−	0.790748i	0.708564	−	0.705647i	$-0.249344\pi$
$150$	27.7568	−	13.7510i	2.26633	−	1.12277i
$151$	0.0992784	+	0.563036i	0.00807916	+	0.0458192i	0.988581	−	0.150692i	$-0.0481500\pi$
$151$	0.0992784	+	0.563036i	0.00807916	+	0.0458192i	−0.980502	+	0.196511i	$0.937039\pi$
$152$	0.0587082	+	0.101686i	0.00476186	+	0.00824779i
$153$	−4.04628	+	12.9980i	−0.327122	+	1.05083i
$154$	2.38456	−	1.49326i	0.192153	−	0.120330i
$155$	0.360819	−	0.0636221i	0.0289817	−	0.00511025i
$156$	4.77661	+	16.2774i	0.382435	+	1.30324i
$157$	−5.09539	+	6.07244i	−0.406656	+	0.484634i	−0.930037	−	0.367465i	$-0.880226\pi$
$157$	−5.09539	+	6.07244i	−0.406656	+	0.484634i	0.523381	+	0.852099i	$0.324670\pi$
$158$	−3.56171	−	9.78572i	−0.283355	−	0.778510i
$159$	6.88071	−	15.7152i	0.545675	−	1.24629i
$160$	−19.1094	−	22.7737i	−1.51073	−	1.80042i
$161$	10.3201	−	19.4549i	0.813341	−	1.53326i
$162$	−16.2681	−	7.44216i	−1.27815	−	0.584711i
$163$	−2.96576	+	5.13684i	−0.232296	+	0.402349i	−0.958483	−	0.285148i	$-0.907957\pi$
$163$	−2.96576	+	5.13684i	−0.232296	+	0.402349i	0.726187	+	0.687497i	$0.241290\pi$
$164$	−13.8579	−	5.04387i	−1.08212	−	0.393860i
$165$	−2.05503	−	2.79203i	−0.159984	−	0.217359i
$166$	−2.31847	+	2.76305i	−0.179948	+	0.214454i
$167$	10.6282	−	3.86836i	0.822438	−	0.299343i	0.103687	−	0.994610i	$-0.466936\pi$
$167$	10.6282	−	3.86836i	0.822438	−	0.299343i	0.718752	+	0.695267i	$0.244714\pi$
$168$	0.0895191	−	0.436487i	0.00690655	−	0.0336757i
$169$	−2.11823	−	12.0131i	−0.162941	−	0.924082i
$170$		−	33.7459i		−	2.58819i
$171$	−3.45905	−	1.07680i	−0.264520	−	0.0823447i
$172$	−0.0656414			−0.00500511
$173$	−7.90197	+	6.63054i	−0.600776	+	0.504111i	−0.891695	−	0.452637i	$-0.850483\pi$
$173$	−7.90197	+	6.63054i	−0.600776	+	0.504111i	0.290919	+	0.956748i	$0.406039\pi$
$174$	−12.3406	−	0.786277i	−0.935538	−	0.0596075i
$175$	−23.5761	−	3.29008i	−1.78218	−	0.248707i
$176$	−1.40835	+	1.67841i	−0.106159	+	0.126515i
$177$	−1.31719	−	0.0839245i	−0.0990063	−	0.00630815i
$178$	−18.0348	+	3.18002i	−1.35177	+	0.238353i
$179$		−	7.50492i		−	0.560944i	−0.959862	−	0.280472i	$-0.909509\pi$
$179$		−	7.50492i		−	0.560944i	0.959862	−	0.280472i	$-0.0904910\pi$
$180$	21.7216	+	2.77926i	1.61904	+	0.207154i
$181$	15.7096	−	9.06992i	1.16768	−	0.674162i	0.214549	−	0.976713i	$-0.431172\pi$
$181$	15.7096	−	9.06992i	1.16768	−	0.674162i	0.953133	+	0.302552i	$0.0978385\pi$
$182$	8.13349	−	25.1152i	0.602895	−	1.86166i
$183$	3.16018	+	10.7690i	0.233607	+	0.796069i
$184$	−0.140540	+	0.797040i	−0.0103607	+	0.0587586i
$185$	1.88256	−	0.685195i	0.138408	−	0.0503765i
$186$	0.308853	+	0.135228i	0.0226462	+	0.00991536i
$187$	−2.39076	+	0.421556i	−0.174830	+	0.0308272i
$188$	10.7802			0.786224
$189$	7.10499	+	11.7694i	0.516812	+	0.856099i
$190$	8.98049			0.651513
$191$	−11.7224	+	2.06698i	−0.848203	+	0.149561i	−0.580823	−	0.814030i	$-0.697269\pi$
$191$	−11.7224	+	2.06698i	−0.848203	+	0.149561i	−0.267380	+	0.963591i	$0.586158\pi$
$192$	−1.45767	−	13.0896i	−0.105199	−	0.944661i
$193$	6.92404	−	2.52014i	0.498403	−	0.181404i	−0.0805725	−	0.996749i	$-0.525675\pi$
$193$	6.92404	−	2.52014i	0.498403	−	0.181404i	0.578976	+	0.815345i	$0.303453\pi$
$194$	−4.41458	+	25.0363i	−0.316948	+	1.79750i
$195$	−31.6107	−	7.67409i	−2.26369	−	0.549553i
$196$	9.80602	−	9.50640i	0.700430	−	0.679029i
$197$	7.81959	−	4.51464i	0.557123	−	0.321655i	−0.194867	−	0.980830i	$-0.562428\pi$
$197$	7.81959	−	4.51464i	0.557123	−	0.321655i	0.751990	+	0.659175i	$0.229094\pi$
$198$	−0.150764	−	3.18667i	−0.0107144	−	0.226467i
$199$		−	27.0924i		−	1.92053i	−0.279093	−	0.960264i	$-0.590034\pi$
$199$		−	27.0924i		−	1.92053i	0.279093	−	0.960264i	$-0.409966\pi$
$200$	0.861530	−	0.151911i	0.0609194	−	0.0107417i
$201$	−5.06518	−	10.2242i	−0.357270	−	0.721159i
$202$	−2.72279	+	3.24489i	−0.191575	+	0.228310i
$203$	7.49389	+	5.84317i	0.525968	+	0.410110i
$204$	8.49633	−	12.7659i	0.594862	−	0.893793i
$205$	21.6627	−	18.1771i	1.51299	−	1.26955i
$206$	−23.7230			−1.65286
$207$	−13.4937	−	21.0116i	−0.937878	−	1.46041i
$208$			20.5583i			1.42546i
$209$	−0.112185	−	0.636232i	−0.00775998	−	0.0440091i
$210$	−25.4883	−	22.6217i	−1.75886	−	1.56104i
$211$	4.05592	−	1.47623i	0.279221	−	0.101628i	−0.198614	−	0.980078i	$-0.563644\pi$
$211$	4.05592	−	1.47623i	0.279221	−	0.101628i	0.477835	+	0.878450i	$0.341422\pi$
$212$	−12.4218	+	14.8038i	−0.853135	+	1.01673i
$213$	−6.22672	+	0.693415i	−0.426648	+	0.0475120i
$214$	29.0142	+	10.5603i	1.98337	+	0.721887i
$215$	0.0629352	−	0.109007i	0.00429215	−	0.00743421i
$216$	−0.381667	−	0.331042i	−0.0259692	−	0.0225245i
$217$	−0.137515	−	0.219595i	−0.00933509	−	0.0149071i
$218$	−2.59187	−	3.08887i	−0.175544	−	0.209205i
$219$	11.4542	−	1.27555i	0.774002	−	0.0861938i
$220$	1.33565	+	3.66967i	0.0900496	+	0.247409i
$221$	−14.6418	+	17.4495i	−0.984916	+	1.17378i
$222$	1.79153	+	0.434928i	0.120240	+	0.0291905i
$223$	1.40482	−	0.247708i	0.0940737	−	0.0165877i	−0.126413	−	0.991978i	$-0.540347\pi$
$223$	1.40482	−	0.247708i	0.0940737	−	0.0165877i	0.220487	+	0.975390i	$0.429235\pi$
$224$	−9.85197	+	18.5723i	−0.658263	+	1.24091i
$225$	−16.3535	+	21.4737i	−1.09023	+	1.43158i
$226$	−7.48221	−	12.9596i	−0.497709	−	0.862058i
$227$	−3.36736	−	19.0973i	−0.223500	−	1.26753i	−0.865533	−	0.500853i	$-0.833020\pi$
$227$	−3.36736	−	19.0973i	−0.223500	−	1.26753i	0.642033	−	0.766677i	$-0.278091\pi$
$228$	3.39727	+	2.26105i	0.224990	+	0.149741i
$229$	0.882943	+	2.42587i	0.0583465	+	0.160306i	0.965441	−	0.260621i	$-0.0839272\pi$
$229$	0.882943	+	2.42587i	0.0583465	+	0.160306i	−0.907095	+	0.420927i	$0.861705\pi$
$230$	47.4192	+	39.7894i	3.12673	+	2.62364i
$231$	−1.28425	+	2.08833i	−0.0844976	+	0.137402i
$232$	−0.328164	−	0.119442i	−0.0215450	−	0.00784176i
$233$	−21.1555	+	12.2141i	−1.38594	+	0.800173i	−0.992855	−	0.119329i	$-0.961926\pi$
$233$	−21.1555	+	12.2141i	−1.38594	+	0.800173i	−0.393085	+	0.919502i	$0.628592\pi$
$234$	−20.3034	−	21.9959i	−1.32728	−	1.43792i
$235$	−10.3357	+	17.9020i	−0.674228	+	1.16780i
$236$	1.39711	+	0.508506i	0.0909441	+	0.0331009i
$237$	6.56631	+	6.26300i	0.426528	+	0.406825i
$238$	−22.1179	+	8.96119i	−1.43369	+	0.580867i
$239$	−23.2178	−	4.09392i	−1.50183	−	0.264813i	−0.638568	−	0.769566i	$-0.720473\pi$
$239$	−23.2178	−	4.09392i	−1.50183	−	0.264813i	−0.863264	+	0.504752i	$0.831584\pi$
$240$	24.3108	+	10.6442i	1.56925	+	0.687080i
$241$	−3.27955	+	9.01050i	−0.211255	+	0.580418i	−0.999384	−	0.0350921i	$-0.988828\pi$
$241$	−3.27955	+	9.01050i	−0.211255	+	0.580418i	0.788129	+	0.615510i	$0.211050\pi$
$242$	−18.4430	+	10.6481i	−1.18556	+	0.684484i
$243$	15.5810	−	0.481960i	0.999522	−	0.0309178i
$244$		−	12.6424i		−	0.809346i
$245$	6.38499	+	25.3988i	0.407922	+	1.62267i
$246$	25.8630	−	2.88013i	1.64896	−	0.183631i
$247$	−4.64366	−	3.89649i	−0.295469	−	0.247928i
$248$	0.00729422	+	0.00612058i	0.000463183	+	0.000388657i
$249$	0.741473	−	3.05423i	0.0469889	−	0.193554i
$250$	10.1670	−	27.9337i	0.643020	−	1.76668i
$251$	−6.84105	−	11.8491i	−0.431803	−	0.747906i	0.565225	−	0.824937i	$-0.308789\pi$
$251$	−6.84105	−	11.8491i	−0.431803	−	0.747906i	−0.997029	+	0.0770311i	$0.975456\pi$
$252$	−3.94656	−	14.9749i	−0.248610	−	0.943332i
$253$	2.22656	−	3.85651i	0.139983	−	0.242457i
$254$	23.6066	+	28.1332i	1.48121	+	1.76523i
$255$	13.0536	+	26.3490i	0.817447	+	1.65004i
$256$	2.90925	−	16.4992i	0.181828	−	1.03120i
$257$	28.7802	−	10.4751i	1.79526	−	0.653421i	0.796446	−	0.604710i	$-0.206711\pi$
$257$	28.7802	−	10.4751i	1.79526	−	0.653421i	0.998813	−	0.0487109i	$-0.0155113\pi$
$258$	0.103791	−	0.0514194i	0.00646176	−	0.00320123i
$259$	−0.949004	−	1.05192i	−0.0589682	−	0.0653632i
$260$	31.7333	+	18.3212i	1.96801	+	1.13623i
$261$	9.93974	−	4.15966i	0.615255	−	0.257476i
$262$	0.988696	+	0.570824i	0.0610818	+	0.0352656i
$263$	2.34116	+	2.79009i	0.144362	+	0.172044i	0.833380	−	0.552700i	$-0.186402\pi$
$263$	2.34116	+	2.79009i	0.144362	+	0.172044i	−0.689018	+	0.724744i	$0.741958\pi$
$264$	0.0212555	−	0.0875544i	0.00130818	−	0.00538860i
$265$	−12.6741	−	34.8217i	−0.778561	−	2.13908i
$266$	−2.38476	−	5.88603i	−0.146219	−	0.360896i
$267$	12.8516	−	9.45919i	0.786503	−	0.578893i
$268$	2.23190	+	12.6577i	0.136335	+	0.773194i
$269$	16.1461	+	27.9659i	0.984446	+	1.70511i	0.644374	+	0.764710i	$0.277118\pi$
$269$	16.1461	+	27.9659i	0.984446	+	1.70511i	0.340071	+	0.940400i	$0.389549\pi$
$270$	−36.5230	+	12.6209i	−2.22272	+	0.768081i
$271$	21.4767	+	12.3996i	1.30462	+	0.753220i	0.981192	−	0.193034i	$-0.0618328\pi$
$271$	21.4767	+	12.3996i	1.30462	+	0.753220i	0.323424	+	0.946254i	$0.395166\pi$
$272$	14.2363	−	11.9456i	0.863200	−	0.724311i
$273$	3.36438	+	22.7563i	0.203622	+	1.37727i
$274$	−0.806859	+	4.57593i	−0.0487441	+	0.276442i
$275$	−4.74030	−	0.835842i	−0.285851	−	0.0504032i
$276$	7.92053	+	26.9910i	0.476760	+	1.62467i
$277$	−12.0197	+	10.0857i	−0.722191	+	0.605990i	−0.927990	−	0.372604i	$-0.878465\pi$
$277$	−12.0197	+	10.0857i	−0.722191	+	0.605990i	0.205799	+	0.978594i	$0.434021\pi$
$278$	0.931898			0.0558915
$279$	−0.293462	+	0.0138840i	−0.0175691	+	0.000831211i
$280$	−0.510813	−	0.815710i	−0.0305269	−	0.0487480i
$281$	4.41595	−	12.1327i	0.263433	−	0.723777i	−0.735497	−	0.677528i	$-0.763051\pi$
$281$	4.41595	−	12.1327i	0.263433	−	0.723777i	0.998930	−	0.0462486i	$-0.0147266\pi$
$282$	−17.0454	+	8.44450i	−1.01504	+	0.502863i
$283$	22.4248	+	3.95410i	1.33302	+	0.235047i	0.794344	−	0.607469i	$-0.207815\pi$
$283$	22.4248	+	3.95410i	1.33302	+	0.235047i	0.538672	+	0.842515i	$0.318926\pi$
$284$	6.95028	+	1.22552i	0.412423	+	0.0727214i
$285$	−7.01200	+	3.47383i	−0.415355	+	0.205772i
$286$	1.82574	−	5.01619i	0.107959	−	0.296614i
$287$	−17.6662	−	9.37133i	−1.04280	−	0.553172i
$288$	12.8816	+	20.0584i	0.759054	+	1.18195i
$289$	3.59128			0.211252
$290$	−20.4612	+	17.1690i	−1.20152	+	1.00820i
$291$	−6.23762	−	21.2561i	−0.365656	−	1.24606i
$292$	−12.7852	−	2.25437i	−0.748196	−	0.131927i
$293$	0.0377838	−	0.214282i	0.00220735	−	0.0125185i	−0.983684	−	0.179904i	$-0.942421\pi$
$293$	0.0377838	−	0.214282i	0.00220735	−	0.0125185i	0.985892	+	0.167385i	$0.0535324\pi$
$294$	−8.05841	+	22.7128i	−0.469976	+	1.32464i
$295$	−2.18396	+	1.83256i	−0.127155	+	0.106696i
$296$	0.0450900	+	0.0260327i	0.00262080	+	0.00151312i
$297$	1.35039	+	2.42985i	0.0783573	+	0.140994i
$298$	−10.2088	−	17.6821i	−0.591379	−	1.02430i
$299$	−7.25566	−	41.1489i	−0.419606	−	2.37970i
$300$	24.4873	−	18.0235i	1.41377	−	1.04059i
$301$	−0.0881582	−	0.0123026i	−0.00508136	−	0.000709112i
$302$	0.388682	+	1.06789i	0.0223661	+	0.0614504i
$303$	0.870777	−	3.58685i	0.0500248	−	0.206059i
$304$	3.17898	+	3.78856i	0.182327	+	0.217289i
$305$	20.9945	+	12.1212i	1.20214	+	0.694057i
$306$	−3.43424	+	26.8408i	−0.196322	+	1.53438i
$307$	17.3825	+	10.0358i	0.992072	+	0.572773i	0.905893	−	0.423506i	$-0.139201\pi$
$307$	17.3825	+	10.0358i	0.992072	+	0.572773i	0.0861792	+	0.996280i	$0.472534\pi$
$308$	2.05051	−	1.84989i	0.116839	−	0.105408i
$309$	18.5230	−	9.17653i	1.05374	−	0.522034i
$310$	0.684356	−	0.249085i	0.0388688	−	0.0141471i
$311$	−0.0344600	+	0.195432i	−0.00195405	+	0.0110820i	−0.985769	−	0.168104i	$-0.946235\pi$
$311$	−0.0344600	+	0.195432i	−0.00195405	+	0.0110820i	0.983815	+	0.179186i	$0.0573465\pi$
$312$	−0.375285	−	0.757522i	−0.0212463	−	0.0428862i
$313$	10.5334	+	12.5532i	0.595385	+	0.709552i	0.976631	−	0.214922i	$-0.0689496\pi$
$313$	10.5334	+	12.5532i	0.595385	+	0.709552i	−0.381247	+	0.924473i	$0.624505\pi$
$314$	−7.87839	+	13.6458i	−0.444604	+	0.770076i
$315$	28.6519	+	7.80373i	1.61435	+	0.439690i
$316$	−5.11087	−	8.85229i	−0.287509	−	0.497980i
$317$	−4.79018	+	13.1609i	−0.269043	+	0.739190i	0.729436	+	0.684050i	$0.239783\pi$
$317$	−4.79018	+	13.1609i	−0.269043	+	0.739190i	−0.998479	+	0.0551403i	$0.982439\pi$
$318$	8.04488	−	33.1380i	0.451134	−	1.85829i
$319$	1.47196	+	1.23512i	0.0824137	+	0.0691533i
$320$	−21.7930	−	18.2865i	−1.21827	−	1.02225i
$321$	−26.7394	+	2.97773i	−1.49245	+	0.166201i
$322$	13.4869	−	41.6457i	0.751594	−	2.32083i
$323$			5.47976i			0.304902i
$324$	−16.9941	−	4.42112i	−0.944116	−	0.245618i
$325$	−39.1136	+	22.5822i	−2.16963	+	1.25264i
$326$	−4.03251	+	11.0792i	−0.223340	+	0.613622i
$327$	3.21858	+	1.40922i	0.177988	+	0.0779299i
$328$	0.723763	+	0.127619i	0.0399631	+	0.00704658i
$329$	14.4780	+	2.02044i	0.798200	+	0.111390i
$330$	−4.98650	−	4.75616i	−0.274498	−	0.261818i
$331$	13.7531	+	5.00572i	0.755939	+	0.275139i	0.691102	−	0.722757i	$-0.257125\pi$
$331$	13.7531	+	5.00572i	0.755939	+	0.275139i	0.0648361	+	0.997896i	$0.479348\pi$
$332$	−1.77020	+	3.06608i	−0.0971524	+	0.168273i
$333$	−1.56707	+	0.353406i	−0.0858752	+	0.0193665i
$334$	19.4699	−	11.2410i	1.06535	−	0.615079i
$335$	−23.1598	−	8.42950i	−1.26536	−	0.460553i
$336$	0.520773	−	18.7604i	0.0284105	−	1.02347i
$337$	15.3298	+	12.8633i	0.835070	+	0.700707i	0.956449	−	0.291899i	$-0.0942873\pi$
$337$	15.3298	+	12.8633i	0.835070	+	0.700707i	−0.121379	+	0.992606i	$0.538732\pi$
$338$	−8.29301	−	22.7849i	−0.451080	−	1.23933i
$339$	10.8552	+	7.22463i	0.589572	+	0.392388i
$340$	−5.75187	−	32.6205i	−0.311939	−	1.76910i
$341$	−0.0261957	−	0.0453723i	−0.00141858	−	0.00245705i
$342$	−7.14288	−	0.913922i	−0.386243	−	0.0494193i
$343$	14.9515	−	10.9295i	0.807303	−	0.590137i
$344$	0.00322153		0.000568042i	0.000173693		3.06268e-5i
$345$	−52.4165	−	12.7251i	−2.82201	−	0.685096i
$346$	−13.1797	+	15.7070i	−0.708547	+	0.844414i
$347$	−3.69757	−	10.1590i	−0.198496	−	0.545363i	0.800011	−	0.599985i	$-0.204827\pi$
$347$	−3.69757	−	10.1590i	−0.198496	−	0.545363i	−0.998507	+	0.0546221i	$0.982605\pi$
$348$	−12.0631	+	1.34336i	−0.646648	+	0.0720115i
$349$	18.8455	+	22.4591i	1.00877	+	1.20221i	0.979252	+	0.202646i	$0.0649541\pi$
$349$	18.8455	+	22.4591i	1.00877	+	1.20221i	0.0295221	+	0.999564i	$0.490601\pi$
$350$	−47.2866	+	1.69721i	−2.52758	+	0.0907199i
$351$	24.3614	+	9.32074i	1.30032	+	0.497504i
$352$	−2.12555	+	3.68157i	−0.113292	+	0.196228i
$353$	18.9495	+	6.89706i	1.00858	+	0.367094i	0.792888	−	0.609368i	$-0.208577\pi$
$353$	18.9495	+	6.89706i	1.00858	+	0.367094i	0.215693	+	0.976461i	$0.430799\pi$
$354$	−2.60742	+	0.290366i	−0.138583	+	0.0154328i
$355$	−8.69890	+	10.3669i	−0.461689	+	0.550220i
$356$	−16.8913	+	6.14794i	−0.895238	+	0.325840i
$357$	13.8034	−	15.5526i	0.730554	−	0.823130i
$358$	−2.59045	−	14.6911i	−0.136909	−	0.776451i
$359$			16.7354i			0.883260i	0.897197	+	0.441630i	$0.145600\pi$
$359$			16.7354i			0.883260i	−0.897197	+	0.441630i	$0.854400\pi$
$360$	−1.09010	+	0.0515736i	−0.0574532	+	0.00271817i
$361$	17.5417			0.923249
$362$	27.6214	−	23.1771i	1.45175	−	1.21816i
$363$	10.2815	−	15.4482i	0.539639	−	0.810820i
$364$	3.58145	−	25.6639i	0.187719	−	1.34516i
$365$	16.0018	−	19.0702i	0.837572	−	0.998180i
$366$	9.90326	+	19.9900i	0.517652	+	1.04489i
$367$	−8.10506	+	1.42914i	−0.423081	+	0.0746005i	−0.381135	−	0.924519i	$-0.624467\pi$
$367$	−8.10506	+	1.42914i	−0.423081	+	0.0746005i	−0.0419455	+	0.999120i	$0.513356\pi$
$368$			34.0895i			1.77704i
$369$	−19.0798	+	12.2531i	−0.993257	+	0.637873i
$370$	3.44867	−	1.99109i	0.179288	−	0.103512i
$371$	−19.4574	+	17.5537i	−1.01018	+	0.911345i
$372$	0.321601	+	0.0780749i	0.0166743	+	0.00404799i
$373$	2.60691	−	14.7845i	0.134981	−	0.765513i	−0.839892	−	0.542753i	$-0.817382\pi$
$373$	2.60691	−	14.7845i	0.134981	−	0.765513i	0.974873	−	0.222761i	$-0.0715068\pi$
$374$	−4.53450	+	1.65042i	−0.234473	+	0.0853413i
$375$	2.86684	+	25.7436i	0.148043	+	1.32939i
$376$	−0.529065	+	0.0932884i	−0.0272844	+	0.00481098i
$377$	18.0295			0.928566
$378$	17.9707	+	20.5866i	0.924311	+	1.05886i
$379$	−23.6638			−1.21553			−0.607763	−	0.794118i	$-0.707933\pi$
$379$	−23.6638			−1.21553			−0.607763	+	0.794118i	$0.707933\pi$
$380$	8.68099	−	1.53069i	0.445325	−	0.0785229i
$381$	−29.3146	−	12.8351i	−1.50183	−	0.657560i
$382$	−22.2336	+	8.09235i	−1.13757	+	0.414041i
$383$	0.334399	−	1.89647i	0.0170870	−	0.0969052i	−0.975072	−	0.221890i	$-0.928777\pi$
$383$	0.334399	−	1.89647i	0.0170870	−	0.0969052i	0.992159	+	0.124985i	$0.0398884\pi$
$384$	0.379251	+	1.29238i	0.0193536	+	0.0659517i
$385$	1.10604	+	5.17880i	0.0563690	+	0.263936i
$386$	12.6842	−	7.32321i	0.645608	−	0.372742i
$387$	−0.0611507	+	0.0802970i	−0.00310846	+	0.00408173i
$388$			24.9538i			1.26684i
$389$	−28.0414	+	4.94446i	−1.42176	+	0.250694i	−0.831053	−	0.556193i	$-0.812261\pi$
$389$	−28.0414	+	4.94446i	−1.42176	+	0.250694i	−0.590705	+	0.806888i	$0.701150\pi$
$390$	−64.5278	−	4.11137i	−3.26749	−	0.208187i
$391$	−24.2789	+	28.9345i	−1.22784	+	1.46328i
$392$	−0.398991	+	0.551411i	−0.0201521	+	0.0278504i
$393$	−0.992784	−	0.0632549i	−0.0500793	−	0.00319079i
$394$	13.7488	−	11.5366i	0.692656	−	0.581207i
$395$	19.6007			0.986216
$396$	−0.688894	−	3.05470i	−0.0346182	−	0.153505i
$397$			17.7545i			0.891073i	0.895264	+	0.445536i	$0.146987\pi$
$397$			17.7545i			0.891073i	−0.895264	+	0.445536i	$0.853013\pi$
$398$	−9.35138	−	53.0343i	−0.468742	−	2.65837i
$399$	4.13886	+	3.67337i	0.207202	+	0.183899i
$400$	34.6256	−	12.6027i	1.73128	−	0.630134i
$401$	15.5181	−	18.4938i	0.774939	−	0.923536i	−0.223754	−	0.974646i	$-0.571831\pi$
$401$	15.5181	−	18.4938i	0.774939	−	0.923536i	0.998693	+	0.0511095i	$0.0162758\pi$
$402$	−13.4443	−	18.2659i	−0.670542	−	0.911019i
$403$	−0.461943	−	0.168134i	−0.0230110	−	0.00837533i
$404$	−2.07890	+	3.60076i	−0.103429	+	0.179145i
$405$	23.6354	−	23.9823i	1.17445	−	1.19169i
$406$	16.6864	+	8.85157i	0.828133	+	0.439296i
$407$	−0.184142	−	0.219451i	−0.00912756	−	0.0108778i
$408$	−0.306507	+	0.700046i	−0.0151744	+	0.0346575i
$409$	−6.50514	−	17.8727i	−0.321659	−	0.883750i	−0.990148	−	0.140028i	$-0.955281\pi$
$409$	−6.50514	−	17.8727i	−0.321659	−	0.883750i	0.668489	−	0.743722i	$-0.266941\pi$
$410$	36.1313	−	43.0596i	1.78440	−	2.12656i
$411$	−1.14006	−	3.88501i	−0.0562349	−	0.191634i
$412$	−22.9319	+	4.04350i	−1.12977	+	0.199209i
$413$	1.78105	+	0.944787i	0.0876398	+	0.0464899i
$414$	−33.6669	−	36.4734i	−1.65464	−	1.79257i
$415$	−3.39444	−	5.87934i	−0.166626	−	0.288605i
$416$	6.92652	+	39.2822i	0.339600	+	1.92597i
$417$	−0.727630	+	0.360476i	−0.0356322	+	0.0176526i
$418$	−0.439211	−	1.20672i	−0.0214825	−	0.0590228i
$419$	−24.5217	−	20.5762i	−1.19796	−	1.00521i	−0.999686	−	0.0250662i	$-0.992020\pi$
$419$	−24.5217	−	20.5762i	−1.19796	−	1.00521i	−0.198279	−	0.980146i	$-0.563535\pi$
$420$	−28.4940	−	17.5228i	−1.39037	−	0.855027i
$421$	−11.0428	−	4.01925i	−0.538193	−	0.195886i	0.0585997	−	0.998282i	$-0.481336\pi$
$421$	−11.0428	−	4.01925i	−0.538193	−	0.195886i	−0.596793	+	0.802395i	$0.703559\pi$
$422$	7.43006	−	4.28975i	0.361689	−	0.208822i
$423$	10.0426	−	13.1870i	0.488290	−	0.641174i
$424$	0.481527	−	0.834030i	0.0233850	−	0.0405041i
$425$	38.3652	+	13.9638i	1.86099	+	0.677344i
$426$	−11.9497	+	3.50664i	−0.578964	+	0.169897i
$427$	2.36946	−	16.9791i	0.114666	−	0.821675i
$428$	29.8465	+	5.26275i	1.44269	+	0.254385i
$429$	0.514812	+	4.62290i	0.0248553	+	0.223196i
$430$	0.0855724	−	0.235108i	0.00412667	−	0.0113379i
$431$	−8.85449	+	5.11214i	−0.426506	+	0.246243i	−0.697857	−	0.716237i	$-0.745863\pi$
$431$	−8.85449	+	5.11214i	−0.426506	+	0.246243i	0.271351	+	0.962480i	$0.412530\pi$
$432$	−18.2530	−	10.9402i	−0.878199	−	0.526361i
$433$			2.62462i			0.126131i	0.998009	+	0.0630656i	$0.0200877\pi$
$433$			2.62462i			0.126131i	−0.998009	+	0.0630656i	$0.979912\pi$
$434$	−0.344986	−	0.382399i	−0.0165599	−	0.0183558i
$435$	9.33489	−	21.3204i	0.447574	−	1.02224i
$436$	−3.03192	−	2.54408i	−0.145203	−	0.121839i
$437$	−7.70007	−	6.46112i	−0.368344	−	0.309077i
$438$	21.9817	−	6.45053i	1.05033	−	0.308218i
$439$	−0.310662	+	0.853536i	−0.0148271	+	0.0407371i	−0.946885	−	0.321571i	$-0.895789\pi$
$439$	−0.310662	+	0.853536i	−0.0148271	+	0.0407371i	0.932058	+	0.362308i	$0.118011\pi$
$440$	−0.0973069	−	0.168541i	−0.00463893	−	0.00803486i
$441$	−2.49371	−	20.8514i	−0.118748	−	0.992924i
$442$	−22.6389	+	39.2118i	−1.07682	+	1.86512i
$443$	−7.50939	−	8.94934i	−0.356782	−	0.425196i	0.557562	−	0.830136i	$-0.311737\pi$
$443$	−7.50939	−	8.94934i	−0.356782	−	0.425196i	−0.914344	+	0.404939i	$0.867293\pi$
$444$	1.80592	+	0.115063i	0.0857050	+	0.00546066i
$445$	5.98540	−	33.9449i	0.283735	−	1.60914i
$446$	2.66448	−	0.969793i	0.126167	−	0.0459210i
$447$	14.8109	+	9.85732i	0.700529	+	0.466235i
$448$	−6.19833	+	19.1397i	−0.292844	+	0.904264i
$449$	8.77509	+	5.06630i	0.414122	+	0.239094i	0.692559	−	0.721361i	$-0.256483\pi$
$449$	8.77509	+	5.06630i	0.414122	+	0.239094i	−0.278437	+	0.960454i	$0.589816\pi$
$450$	−24.6005	+	47.6803i	−1.15968	+	2.24767i
$451$	−3.50196	−	2.02186i	−0.164901	−	0.0952054i
$452$	−9.44160	−	11.2521i	−0.444095	−	0.529252i
$453$	−0.716567	−	0.683467i	−0.0336673	−	0.0321121i
$454$	−13.1835	−	36.2213i	−0.618731	−	1.69995i
$455$	39.1848	+	30.5534i	1.83701	+	1.43236i
$456$	−0.186297	−	0.0815679i	−0.00872414	−	0.00381977i
$457$	4.79126	+	27.1726i	0.224126	+	1.27108i	0.864349	+	0.502892i	$0.167731\pi$
$457$	4.79126	+	27.1726i	0.224126	+	1.27108i	−0.640223	+	0.768189i	$0.721158\pi$
$458$	2.56572	+	4.44395i	0.119888	+	0.207652i
$459$	−7.70106	−	22.2858i	−0.359455	−	1.04021i
$460$	52.6197	+	30.3800i	2.45341	+	1.41648i
$461$	14.3944	−	12.0783i	0.670413	−	0.562543i	−0.242775	−	0.970083i	$-0.578058\pi$
$461$	14.3944	−	12.0783i	0.670413	−	0.562543i	0.913188	+	0.407540i	$0.133613\pi$
$462$	−1.79315	+	4.53127i	−0.0834248	+	0.210814i
$463$	0.164111	−	0.930721i	0.00762690	−	0.0432543i	−0.980757	−	0.195233i	$-0.937454\pi$
$463$	0.164111	−	0.930721i	0.00762690	−	0.0432543i	0.988384	+	0.151979i	$0.0485647\pi$
$464$	−14.4860	−	2.55428i	−0.672497	−	0.118579i
$465$	−0.437997	+	0.459209i	−0.0203116	+	0.0212953i
$466$	−37.1966	+	31.2117i	−1.72310	+	1.44585i
$467$	−10.5286			−0.487204			−0.243602	−	0.969875i	$-0.578329\pi$
$467$	−10.5286			−0.487204			−0.243602	+	0.969875i	$0.578329\pi$
$468$	−23.3754	−	17.8017i	−1.08053	−	0.822884i
$469$	0.625167	+	17.4180i	0.0288675	+	0.804288i
$470$	−14.0534	+	38.6113i	−0.648234	+	1.78101i
$471$	0.873031	−	13.7022i	0.0402271	−	0.631364i
$472$	−0.0729674	−	0.0128661i	−0.00335859	−	0.000592211i
$473$	−0.0177254	−	0.00312548i	−0.000815017	−	0.000143709i
$474$	15.0156	+	9.99357i	0.689688	+	0.459020i
$475$	−3.71606	+	10.2098i	−0.170504	+	0.468457i
$476$	−19.8529	+	12.4323i	−0.909955	+	0.569831i
$477$	6.53695	+	28.9862i	0.299306	+	1.32719i
$478$	−46.8627			−2.14345
$479$	−3.38457	+	2.83999i	−0.154645	+	0.129763i	−0.716827	−	0.697251i	$-0.754406\pi$
$479$	−3.38457	+	2.83999i	−0.154645	+	0.129763i	0.562182	+	0.827013i	$0.309962\pi$
$480$	50.0386	+	12.1478i	2.28394	+	0.554470i
$481$	−2.64715	−	0.466764i	−0.120700	−	0.0212826i
$482$	−3.30972	+	18.7704i	−0.150754	+	0.854967i
$483$	5.57878	+	37.7342i	0.253843	+	1.71696i
$484$	−16.0130	+	13.4365i	−0.727864	+	0.610751i
$485$	−41.4394	−	23.9250i	−1.88167	−	1.08638i
$486$	30.3340	−	6.32149i	1.37598	−	0.286749i
$487$	17.8504	+	30.9178i	0.808879	+	1.40102i	0.913641	+	0.406523i	$0.133259\pi$
$487$	17.8504	+	30.9178i	0.808879	+	1.40102i	−0.104761	+	0.994497i	$0.533408\pi$
$488$	0.109404	+	0.620459i	0.00495247	+	0.0280869i
$489$	−1.13706	−	10.2106i	−0.0514197	−	0.461738i
$490$	21.2656	+	47.5151i	0.960684	+	2.14651i
$491$	7.59387	+	20.8640i	0.342707	+	0.941579i	0.984606	+	0.174790i	$0.0559246\pi$
$491$	7.59387	+	20.8640i	0.342707	+	0.941579i	−0.641899	+	0.766789i	$0.721853\pi$
$492$	24.5096	−	7.19234i	1.10498	−	0.324256i
$493$	−10.4763	−	12.4851i	−0.471827	−	0.562302i
$494$	−10.4351	−	6.02469i	−0.469496	−	0.271064i
$495$	5.73326	+	1.78476i	0.257691	+	0.0802189i
$496$	0.347334	+	0.200533i	0.0155958	+	0.00900422i
$497$	9.10473	+	2.94854i	0.408403	+	0.132260i
$498$	0.397242	−	6.23470i	0.0178008	−	0.279383i
$499$	34.0726	−	12.4014i	1.52530	−	0.555164i	0.562835	−	0.826569i	$-0.309710\pi$
$499$	34.0726	−	12.4014i	1.52530	−	0.555164i	0.962465	+	0.271405i	$0.0874882\pi$
$500$	5.06676	−	28.7351i	0.226593	−	1.28507i
$501$	−10.8540	+	16.3084i	−0.484920	+	0.728604i
$502$	−17.4815	−	20.8336i	−0.780237	−	0.929851i
$503$	−1.90297	+	3.29604i	−0.0848491	+	0.146963i	−0.905327	−	0.424715i	$-0.860374\pi$
$503$	−1.90297	+	3.29604i	−0.0848491	+	0.146963i	0.820478	+	0.571678i	$0.193708\pi$
$504$	0.323277	+	0.700782i	0.0143999	+	0.0312153i
$505$	−3.98639	−	6.90463i	−0.177392	−	0.307252i
$506$	3.02743	−	8.31779i	0.134586	−	0.369771i
$507$	15.2889	+	14.5826i	0.679002	+	0.647637i
$508$	27.6145	+	23.1713i	1.22519	+	1.02806i
$509$	−8.19879	−	6.87960i	−0.363405	−	0.304933i	0.442741	−	0.896649i	$-0.354006\pi$
$509$	−8.19879	−	6.87960i	−0.363405	−	0.304933i	−0.806146	+	0.591717i	$0.798450\pi$
$510$	34.6476	+	47.0734i	1.53422	+	2.08444i
$511$	−16.7483	−	5.42391i	−0.740903	−	0.239940i
$512$		−	31.7467i		−	1.40302i
$513$	5.93072	−	2.04941i	0.261848	−	0.0904837i
$514$	52.7226	−	30.4394i	2.32549	−	1.34262i
$515$	15.2716	−	41.9584i	0.672948	−	1.84891i
$516$	0.0915656	−	0.0673954i	0.00403095	−	0.00296692i
$517$	2.91101	+	0.513290i	0.128026	+	0.0225745i
$518$	−2.22080	−	1.73161i	−0.0975762	−	0.0760826i
$519$	4.21503	−	17.3623i	0.185019	−	0.762120i
$520$	−1.71594	−	0.624551i	−0.0752490	−	0.0273884i
$521$	20.5421	−	35.5799i	0.899965	−	1.55878i	0.0724277	−	0.997374i	$-0.476925\pi$
$521$	20.5421	−	35.5799i	0.899965	−	1.55878i	0.827537	−	0.561411i	$-0.189741\pi$
$522$	18.0216	−	11.5735i	0.788785	−	0.506560i
$523$	−31.7383	+	18.3241i	−1.38782	+	0.801258i	−0.993069	−	0.117530i	$-0.962502\pi$
$523$	−31.7383	+	18.3241i	−1.38782	+	0.801258i	−0.394751	+	0.918788i	$0.629169\pi$
$524$	1.05302	+	0.383267i	0.0460013	+	0.0167431i
$525$	36.2651	−	19.6166i	1.58274	−	0.856138i
$526$	5.54595	+	4.65360i	0.241815	+	0.202907i
$527$	0.151988	+	0.417584i	0.00662071	+	0.0181902i
$528$	0.241304	−	3.78726i	0.0105014	−	0.164819i
$529$	−8.03735	−	45.5821i	−0.349450	−	1.98183i
$530$	−36.8292	−	63.7900i	−1.59976	−	2.77086i
$531$	1.92357	−	1.23532i	0.0834757	−	0.0536083i
$532$	−3.30848	−	5.28326i	−0.143441	−	0.229058i
$533$	−37.3658	+	6.58860i	−1.61849	+	0.285384i
$534$	21.8924	−	22.9526i	0.947376	−	0.993257i
$535$	−37.3556	+	44.5187i	−1.61502	+	1.92471i
$536$	−0.219073	−	0.601898i	−0.00946250	−	0.0259980i
$537$	7.70546	+	10.4689i	0.332515	+	0.451765i
$538$	41.2595	+	49.1711i	1.77882	+	2.11992i
$539$	3.10060	−	2.10015i	0.133553	−	0.0904598i
$540$	−33.1538	+	18.4252i	−1.42671	+	0.792893i
$541$	−17.5845	+	30.4573i	−0.756018	+	1.30946i	0.188849	+	0.982006i	$0.439524\pi$
$541$	−17.5845	+	30.4573i	−0.756018	+	1.30946i	−0.944867	+	0.327455i	$0.893809\pi$
$542$	46.3213	+	16.8596i	1.98967	+	0.724180i
$543$	−12.6015	+	28.7813i	−0.540784	+	1.23512i
$544$	23.1775	−	27.6219i	0.993729	−	1.18428i
$545$	7.13173	−	2.59574i	0.305490	−	0.111189i
$546$	14.4406	+	43.3849i	0.618000	+	1.85670i
$547$	−5.94589	−	33.7208i	−0.254228	−	1.44180i	−0.798046	−	0.602596i	$-0.794133\pi$
$547$	−5.94589	−	33.7208i	−0.254228	−	1.44180i	0.543818	−	0.839203i	$-0.316978\pi$
$548$			4.56085i			0.194830i
$549$	−15.4650	−	11.7775i	−0.660031	−	0.502651i
$550$	−9.56781			−0.407973
$551$	3.32255	−	2.78795i	0.141545	−	0.118771i
$552$	−0.622294	−	1.25612i	−0.0264866	−	0.0534638i
$553$	−5.20493	−	12.8468i	−0.221336	−	0.546300i
$554$	−20.0477	+	23.8919i	−0.851743	+	1.01507i
$555$	−1.92254	+	2.88866i	−0.0816074	+	0.122617i
$556$	0.900819	−	0.158839i	0.0382032	−	0.00673626i
$557$			34.3108i			1.45379i	0.686746	+	0.726897i	$0.259038\pi$
$557$			34.3108i			1.45379i	−0.686746	+	0.726897i	$0.740962\pi$
$558$	−0.569670	+	0.128472i	−0.0241161	+	0.00543864i
$559$	−0.146258	+	0.0844420i	−0.00618605	+	0.00357152i
$560$	−27.1550	−	30.0999i	−1.14751	−	1.27195i
$561$	2.90214	−	3.04269i	0.122529	−	0.128462i
$562$	4.45657	−	25.2744i	0.187989	−	1.06614i
$563$	−12.0895	+	4.40022i	−0.509512	+	0.185447i	−0.583967	−	0.811777i	$-0.698500\pi$
$563$	−12.0895	+	4.40022i	−0.509512	+	0.185447i	0.0744555	+	0.997224i	$0.476278\pi$
$564$	−15.0376	+	11.0682i	−0.633198	+	0.466056i
$565$	27.7380	−	4.89096i	1.16695	−	0.205764i
$566$	45.2622			1.90251
$567$	−21.9949	−	9.12274i	−0.923699	−	0.383119i
$568$	−0.351709			−0.0147574
$569$	−2.71061	+	0.477954i	−0.113635	+	0.0200369i	−0.230176	−	0.973149i	$-0.573930\pi$
$569$	−2.71061	+	0.477954i	−0.113635	+	0.0200369i	0.116542	+	0.993186i	$0.462819\pi$
$570$	−12.5272	+	9.22045i	−0.524707	+	0.386202i
$571$	−25.9325	+	9.43866i	−1.08524	+	0.394996i	−0.821856	−	0.569695i	$-0.807061\pi$
$571$	−25.9325	+	9.43866i	−1.08524	+	0.394996i	−0.263386	+	0.964691i	$0.584839\pi$
$572$	0.909864	−	5.16009i	0.0380433	−	0.215754i
$573$	14.2298	−	14.9189i	0.594458	−	0.623247i
$574$	−37.8169	−	12.2469i	−1.57845	−	0.511177i
$575$	−64.8577	+	37.4456i	−2.70475	+	1.56159i
$576$	15.4727	+	16.7625i	0.644697	+	0.698439i
$577$			8.16361i			0.339856i	0.985457	+	0.169928i	$0.0543535\pi$
$577$			8.16361i			0.339856i	−0.985457	+	0.169928i	$0.945647\pi$
$578$	7.03005	−	1.23959i	0.292412	−	0.0515600i
$579$	−7.07110	+	10.6245i	−0.293865	+	0.441539i
$580$	−16.8524	+	20.0839i	−0.699759	+	0.833940i
$581$	−2.95208	+	3.78605i	−0.122473	+	0.157072i
$582$	−19.5473	−	39.4566i	−0.810260	−	1.63553i
$583$	−4.05920	+	3.40607i	−0.168115	+	0.141065i
$584$	0.646976			0.0267721
$585$	51.9740	−	21.7505i	2.14886	−	0.899271i
$586$		−	0.432507i		−	0.0178667i
$587$	4.51916	+	25.6294i	0.186526	+	1.05784i	0.923979	+	0.382442i	$0.124917\pi$
$587$	4.51916	+	25.6294i	0.186526	+	1.05784i	−0.737454	+	0.675398i	$0.763972\pi$
$588$	−3.91835	+	23.3289i	−0.161590	+	0.962066i
$589$	−0.111128	+	0.0404472i	−0.00457894	+	0.00166660i
$590$	−3.64264	+	4.34113i	−0.149965	+	0.178721i
$591$	−6.27255	+	14.3262i	−0.258018	+	0.589300i
$592$	2.06076	+	0.750055i	0.0846966	+	0.0308271i
$593$	−11.0942	+	19.2157i	−0.455584	+	0.789095i	−0.998722	−	0.0505489i	$-0.983903\pi$
$593$	−11.0942	+	19.2157i	−0.455584	+	0.789095i	0.543137	+	0.839644i	$0.317236\pi$
$594$	3.48213	+	4.29041i	0.142874	+	0.176038i
$595$	−1.61113	−	44.8883i	−0.0660500	−	1.84024i
$596$	−12.8822	−	15.3524i	−0.527674	−	0.628858i
$597$	27.8163	+	37.7921i	1.13845	+	1.54673i
$598$	−28.4064	−	78.0460i	−1.16163	−	3.19154i
$599$	10.5607	−	12.5858i	0.431500	−	0.514242i	−0.505854	−	0.862619i	$-0.668823\pi$
$599$	10.5607	−	12.5858i	0.431500	−	0.514242i	0.937354	+	0.348377i	$0.113267\pi$
$600$	−1.04581	+	1.09646i	−0.0426950	+	0.0447627i
$601$	−23.4204	+	4.12965i	−0.955338	+	0.168452i	−0.629523	−	0.776982i	$-0.716750\pi$
$601$	−23.4204	+	4.12965i	−0.955338	+	0.168452i	−0.325815	+	0.945434i	$0.605639\pi$
$602$	−0.176819	+	0.00634641i	−0.00720662	+	0.000258660i
$603$	17.5630	+	9.06156i	0.715220	+	0.369015i
$604$	0.557738	+	0.966031i	0.0226940	+	0.0393072i
$605$	−6.96041	−	39.4745i	−0.282981	−	1.60486i
$606$	0.466516	−	7.32196i	0.0189509	−	0.297434i
$607$	7.02430	+	19.2991i	0.285108	+	0.783327i	0.996733	+	0.0807677i	$0.0257372\pi$
$607$	7.02430	+	19.2991i	0.285108	+	0.783327i	−0.711625	+	0.702559i	$0.752041\pi$
$608$	7.35076	+	6.16802i	0.298113	+	0.250146i
$609$	−16.4528	−	0.456715i	−0.666701	−	0.0185070i
$610$	45.2813	+	16.4810i	1.83339	+	0.667298i
$611$	24.0196	−	13.8677i	0.971730	−	0.561028i
$612$	1.25521	+	26.5310i	0.0507387	+	1.07245i
$613$	3.78576	−	6.55712i	0.152905	−	0.264840i	−0.779389	−	0.626540i	$-0.784470\pi$
$613$	3.78576	−	6.55712i	0.152905	−	0.264840i	0.932294	+	0.361701i	$0.117804\pi$
$614$	37.4909	+	13.6456i	1.51301	+	0.550690i
$615$	−11.5552	+	47.5974i	−0.465950	+	1.91931i
$616$	−0.0846259	+	0.108533i	−0.00340968	+	0.00437292i
$617$	−20.9804	−	3.69941i	−0.844639	−	0.148933i	−0.265448	−	0.964125i	$-0.585520\pi$
$617$	−20.9804	−	3.69941i	−0.844639	−	0.148933i	−0.579190	+	0.815192i	$0.696631\pi$
$618$	33.0921	−	24.3569i	1.33116	−	0.979778i
$619$	14.3321	−	39.3772i	0.576057	−	1.58270i	−0.218712	−	0.975789i	$-0.570185\pi$
$619$	14.3321	−	39.3772i	0.576057	−	1.58270i	0.794768	−	0.606913i	$-0.207592\pi$
$620$	0.619077	−	0.357424i	0.0248627	−	0.0143545i
$621$	40.3959	+	15.4556i	1.62103	+	0.620210i
$622$			0.394460i			0.0158164i
$623$	−23.8378	+	5.09104i	−0.955039	+	0.203968i
$624$	−21.1076	−	28.6775i	−0.844981	−	1.14802i
$625$	8.39926	+	7.04781i	0.335970	+	0.281913i
$626$	24.9525	+	20.9376i	0.997303	+	0.836837i
$627$	0.809723	+	0.772320i	0.0323372	+	0.0308435i
$628$	−5.28978	+	14.5335i	−0.211085	+	0.579951i
$629$	1.21493	+	2.10433i	0.0484426	+	0.0839050i
$630$	58.7806	+	5.38641i	2.34188	+	0.214600i
$631$	15.3609	−	26.6058i	0.611507	−	1.05916i	−0.379479	−	0.925200i	$-0.623897\pi$
$631$	15.3609	−	26.6058i	0.611507	−	1.05916i	0.990987	−	0.133961i	$-0.0427698\pi$
$632$	0.327435	+	0.390222i	0.0130247	+	0.0155222i
$633$	−4.14206	+	6.22354i	−0.164632	+	0.247364i
$634$	−4.83424	+	27.4163i	−0.191992	+	1.08884i
$635$	−64.9553	+	23.6418i	−2.57767	+	0.938196i
$636$	2.12833	−	33.4041i	0.0843937	−	1.32456i
$637$	9.61996	−	33.7961i	0.381157	−	1.33905i
$638$	3.30773	+	1.90972i	0.130954	+	0.0756064i
$639$	7.97393	−	7.36037i	0.315444	−	0.291172i
$640$	2.51954	+	1.45466i	0.0995935	+	0.0575003i
$641$	−6.04399	−	7.20295i	−0.238723	−	0.284499i	0.633359	−	0.773858i	$-0.281675\pi$
$641$	−6.04399	−	7.20295i	−0.238723	−	0.284499i	−0.872083	+	0.489358i	$0.837231\pi$
$642$	−51.3154	+	15.0585i	−2.02526	+	0.594313i
$643$	11.5765	+	31.8061i	0.456531	+	1.25431i	0.928051	+	0.372454i	$0.121484\pi$
$643$	11.5765	+	31.8061i	0.456531	+	1.25431i	−0.471519	+	0.881856i	$0.656294\pi$
$644$	5.93871	−	42.5557i	0.234018	−	1.67693i
$645$	0.0241292	+	0.216675i	0.000950084	+	0.00853155i
$646$	1.89143	+	10.7268i	0.0744173	+	0.422041i
$647$	−13.4560	−	23.3065i	−0.529011	−	0.916274i	−0.999428	−	0.0338292i	$-0.989230\pi$
$647$	−13.4560	−	23.3065i	−0.529011	−	0.916274i	0.470417	−	0.882444i	$-0.344104\pi$
$648$	0.872289	+	0.0699162i	0.0342667	+	0.00274657i
$649$	0.353055	+	0.203837i	0.0138586	+	0.00800129i
$650$	−68.7716	+	57.7062i	−2.69744	+	2.26342i
$651$	0.417286	+	0.165132i	0.0163547	+	0.00647202i
$652$	−2.00961	+	11.3971i	−0.0787024	+	0.446344i
$653$	−38.0056	−	6.70141i	−1.48727	−	0.262247i	−0.629793	−	0.776763i	$-0.716860\pi$
$653$	−38.0056	−	6.70141i	−1.48727	−	0.262247i	−0.857481	+	0.514516i	$0.827972\pi$
$654$	6.78690	+	1.64765i	0.265389	+	0.0644282i
$655$	−1.64607	+	1.38122i	−0.0643175	+	0.0539688i
$656$	30.9554			1.20861
$657$	−14.6682	+	13.5396i	−0.572261	+	0.528228i
$658$	29.0387	−	1.04226i	1.13205	−	0.0406314i
$659$	−4.48755	+	12.3294i	−0.174810	+	0.480287i	−0.995895	−	0.0905197i	$-0.971147\pi$
$659$	−4.48755	+	12.3294i	−0.174810	+	0.480287i	0.821085	+	0.570807i	$0.193369\pi$
$660$	−5.63087	−	3.74761i	−0.219181	−	0.145876i
$661$	−44.5728	−	7.85938i	−1.73368	−	0.305695i	−0.784430	−	0.620217i	$-0.787044\pi$
$661$	−44.5728	−	7.85938i	−1.73368	−	0.305695i	−0.949250	+	0.314523i	$0.898156\pi$
$662$	28.6500	+	5.05176i	1.11351	+	0.196342i
$663$	2.50870	−	39.3739i	0.0974297	−	1.52916i
$664$	0.0603443	−	0.165795i	0.00234181	−	0.00643408i
$665$	11.9457	−	0.428755i	0.463234	−	0.0166264i
$666$	−2.94562	+	1.23271i	−0.114140	+	0.0477664i
$667$	29.8963			1.15759
$668$	16.9046	−	14.1847i	0.654060	−	0.548821i
$669$	−1.70531	+	1.78789i	−0.0659310	+	0.0691240i
$670$	−48.2458	−	8.50704i	−1.86390	−	0.328655i
$671$	0.601960	−	3.41388i	0.0232384	−	0.131791i
$672$	−5.32570	−	36.0224i	−0.205444	−	1.38959i
$673$	13.0981	−	10.9906i	0.504895	−	0.423657i	−0.354434	−	0.935081i	$-0.615326\pi$
$673$	13.0981	−	10.9906i	0.504895	−	0.423657i	0.859328	+	0.511424i	$0.170882\pi$
$674$	34.4487	+	19.8890i	1.32691	+	0.766094i
$675$	0.764486	−	46.7449i	0.0294251	−	1.79921i
$676$	−11.9000	−	20.6115i	−0.457694	−	0.792749i
$677$	2.82362	+	16.0135i	0.108520	+	0.615450i	0.989756	+	0.142772i	$0.0456016\pi$
$677$	2.82362	+	16.0135i	0.108520	+	0.615450i	−0.881235	+	0.472678i	$0.843287\pi$
$678$	23.7431	+	10.3956i	0.911847	+	0.399242i
$679$	−4.67689	+	33.5137i	−0.179483	+	1.28614i
$680$	0.564577	+	1.55116i	0.0216505	+	0.0594844i
$681$	24.3048	+	23.1821i	0.931362	+	0.888340i
$682$	−0.0669400	−	0.0797760i	−0.00256326	−	0.00305478i
$683$	15.1999	+	8.77566i	0.581608	+	0.335791i	0.761772	−	0.647845i	$-0.224330\pi$
$683$	15.1999	+	8.77566i	0.581608	+	0.335791i	−0.180164	+	0.983637i	$0.557663\pi$
$684$	−7.06044	+	0.334036i	−0.269963	+	0.0127722i
$685$	−7.57394	−	4.37281i	−0.289385	−	0.167077i
$686$	25.4955	−	26.5556i	0.973423	−	1.01390i
$687$	−3.72233	−	2.47739i	−0.142016	−	0.0945183i
$688$	0.129476	−	0.0471253i	0.00493622	−	0.00179664i
$689$	−8.63374	+	48.9644i	−0.328919	+	1.86539i
$690$	−106.999	−	6.81742i	−4.07339	−	0.259535i
$691$	−9.66628	−	11.5198i	−0.367723	−	0.438235i	0.550177	−	0.835048i	$-0.314560\pi$
$691$	−9.66628	−	11.5198i	−0.367723	−	0.438235i	−0.917899	+	0.396814i	$0.870116\pi$
$692$	−10.0630	+	17.4296i	−0.382538	+	0.662575i
$693$	−0.352686	−	4.23166i	−0.0133974	−	0.160747i
$694$	−10.7447	−	18.6103i	−0.407862	−	0.706437i
$695$	−0.599906	+	1.64823i	−0.0227557	+	0.0625209i
$696$	0.580402	−	0.170319i	0.0220001	−	0.00645593i
$697$	26.2743	+	22.0468i	0.995212	+	0.835082i
$698$	44.6428	+	37.4597i	1.68975	+	1.41787i
$699$	16.9700	−	38.7586i	0.641865	−	1.46599i
$700$	−45.4203	+	9.70045i	−1.71673	+	0.366642i
$701$		−	29.7179i		−	1.12243i	−0.827670	−	0.561215i	$-0.810334\pi$
$701$		−	29.7179i		−	1.12243i	0.827670	−	0.561215i	$-0.189666\pi$
$702$	50.9056	+	9.83693i	1.92131	+	0.371271i
$703$	−0.560004	+	0.323319i	−0.0211210	+	0.0121942i
$704$	−1.39135	+	3.82271i	−0.0524386	+	0.144074i
$705$	−3.96268	−	35.5840i	−0.149243	−	1.34017i
$706$	39.4750	+	6.96051i	1.48566	+	0.261962i
$707$	−3.46688	+	4.44629i	−0.130386	+	0.167220i
$708$	−2.47097	+	0.725108i	−0.0928648	+	0.0272512i
$709$	12.7351	+	4.63518i	0.478275	+	0.174078i	0.569897	−	0.821716i	$-0.306983\pi$
$709$	12.7351	+	4.63518i	0.478275	+	0.174078i	−0.0916221	+	0.995794i	$0.529205\pi$
$710$	−13.4501	+	23.2962i	−0.504772	+	0.874292i
$711$	−15.5899	−	1.99471i	−0.584668	−	0.0748075i
$712$	0.775784	−	0.447899i	0.0290737	−	0.0167857i
$713$	−0.765989	−	0.278797i	−0.0286865	−	0.0104410i
$714$	21.6524	−	35.2092i	0.810322	−	1.31767i
$715$	7.69672	+	6.45831i	0.287841	+	0.241527i
$716$	−5.00811	−	13.7597i	−0.187162	−	0.514223i
$717$	36.5906	−	18.1274i	1.36650	−	0.676980i
$718$	5.77649	+	32.7601i	0.215577	+	1.22260i
$719$	−6.04872	−	10.4767i	−0.225579	−	0.390714i	0.730914	−	0.682470i	$-0.239094\pi$
$719$	−6.04872	−	10.4767i	−0.225579	−	0.390714i	−0.956493	+	0.291755i	$0.905761\pi$
$720$	−44.8406	+	10.1124i	−1.67111	+	0.376867i
$721$	−31.5559	+	1.13261i	−1.17520	+	0.0421805i
$722$	34.3385	−	6.05481i	1.27795	−	0.225337i
$723$	−4.67650	−	15.9363i	−0.173921	−	0.592676i
$724$	22.7498	−	27.1121i	0.845488	−	1.00761i
$725$	−11.0525	−	30.3664i	−0.410478	−	1.12778i
$726$	14.7942	−	33.7892i	0.549065	−	1.25403i
$727$	−12.2167	−	14.5592i	−0.453091	−	0.539973i	0.490345	−	0.871529i	$-0.336871\pi$
$727$	−12.2167	−	14.5592i	−0.453091	−	0.539973i	−0.943436	+	0.331556i	$0.892426\pi$
$728$	0.0463194	+	1.29052i	0.00171671	+	0.0478298i
$729$	−21.2397	+	16.6696i	−0.786654	+	0.617394i
$730$	24.7417	−	42.8539i	0.915731	−	1.58609i
$731$	0.143460	+	0.0522150i	0.00530604	+	0.00193124i
$732$	12.9802	+	17.6353i	0.479762	+	0.651820i
$733$	−0.281308	+	0.335249i	−0.0103903	+	0.0123827i	−0.771215	−	0.636575i	$-0.780350\pi$
$733$	−0.281308	+	0.335249i	−0.0103903	+	0.0123827i	0.760824	+	0.648958i	$0.224795\pi$
$734$	−15.3726	+	5.59518i	−0.567415	+	0.206522i
$735$	−34.9841	−	28.8741i	−1.29041	−	1.06504i
$736$	11.4855	+	65.1374i	0.423360	+	2.40100i
$737$			3.52429i			0.129819i
$738$	−33.1201	+	30.5717i	−1.21917	+	1.12536i
$739$	−23.5322			−0.865644			−0.432822	−	0.901479i	$-0.642482\pi$
$739$	−23.5322			−0.865644			−0.432822	+	0.901479i	$0.642482\pi$
$740$	2.99428	−	2.51250i	0.110072	−	0.0923613i
$741$	10.4782	+	0.667616i	0.384927	+	0.0245255i
$742$	−32.0296	+	41.0781i	−1.17584	+	1.50803i
$743$	24.1698	−	28.8045i	0.886705	−	1.05673i	−0.111312	−	0.993786i	$-0.535505\pi$
$743$	24.1698	−	28.8045i	0.886705	−	1.05673i	0.998017	−	0.0629481i	$-0.0200503\pi$
$744$	−0.0164591	−	0.00104868i	−0.000603419	−	3.84466e-5i
$745$	37.8459	−	6.67325i	1.38657	−	0.244489i
$746$		−	29.8410i		−	1.09256i
$747$	2.10154	+	5.02174i	0.0768912	+	0.183736i
$748$	−4.10196	+	2.36827i	−0.149983	+	0.0865925i
$749$	39.0984	+	12.6619i	1.42862	+	0.462656i
$750$	14.4977	+	49.4044i	0.529383	+	1.80399i
$751$	7.27989	−	41.2863i	0.265647	−	1.50656i	−0.501540	−	0.865134i	$-0.667233\pi$
$751$	7.27989	−	41.2863i	0.265647	−	1.50656i	0.767187	−	0.641424i	$-0.221656\pi$
$752$	−21.2635	+	7.73929i	−0.775401	+	0.282223i
$753$	21.7085	+	9.50481i	0.791101	+	0.346375i
$754$	35.2934	−	6.22317i	1.28531	−	0.226635i
$755$	−2.13898			−0.0778453
$756$	20.8803	+	16.8370i	0.759408	+	0.612358i
$757$	−48.7358			−1.77133			−0.885667	−	0.464321i	$-0.846298\pi$
$757$	−48.7358			−1.77133			−0.885667	+	0.464321i	$0.846298\pi$
$758$	−46.3227	+	8.16794i	−1.68252	+	0.296673i
$759$	0.853655	+	7.66564i	0.0309857	+	0.278245i
$760$	−0.412796	+	0.150246i	−0.0149737	+	0.00544998i
$761$	−3.97930	+	22.5677i	−0.144250	+	0.818080i	0.823717	+	0.567001i	$0.191896\pi$
$761$	−3.97930	+	22.5677i	−0.144250	+	0.818080i	−0.967967	+	0.251079i	$0.919215\pi$
$762$	−61.8146	−	15.0067i	−2.23930	−	0.543634i
$763$	−3.59513	−	3.98502i	−0.130153	−	0.144267i
$764$	−20.1128	+	11.6121i	−0.727654	+	0.420111i
$765$	−45.2619	−	23.3527i	−1.63645	−	0.844320i
$766$		−	3.82783i		−	0.138305i
$767$	3.76709	−	0.664240i	0.136022	−	0.0239843i
$768$	12.8818	+	26.0023i	0.464833	+	0.938277i
$769$	6.82411	−	8.13266i	0.246084	−	0.293271i	−0.628837	−	0.777537i	$-0.716469\pi$
$769$	6.82411	−	8.13266i	0.246084	−	0.293271i	0.874921	+	0.484266i	$0.160913\pi$
$770$	3.95266	+	9.75591i	0.142444	+	0.351579i
$771$	−29.3915	+	44.1613i	−1.05851	+	1.59043i
$772$	11.0129	−	9.24096i	0.396365	−	0.332589i
$773$	36.5000			1.31281			0.656406	−	0.754408i	$-0.272076\pi$
$773$	36.5000			1.31281			0.656406	+	0.754408i	$0.272076\pi$
$774$	−0.0919888	+	0.178291i	−0.00330647	+	0.00640855i
$775$			0.881103i			0.0316502i
$776$	−0.215943	−	1.22468i	−0.00775191	−	0.0439633i
$777$	2.40383	+	0.493001i	0.0862369	+	0.0176863i
$778$	−53.1855	+	19.3579i	−1.90679	+	0.694015i
$779$	−5.86711	+	6.99214i	−0.210211	+	0.250520i
$780$	−63.0766	+	7.02429i	−2.25850	+	0.251510i
$781$	1.81846	+	0.661867i	0.0650697	+	0.0236834i
$782$	−37.5397	+	65.0206i	−1.34242	+	2.32513i
$783$	−9.59450	+	16.0078i	−0.342879	+	0.572072i
$784$	−12.5172	+	25.7910i	−0.447044	+	0.921108i
$785$	−19.0633	−	22.7188i	−0.680399	−	0.810868i
$786$	−1.96524	+	0.218852i	−0.0700979	+	0.00780619i
$787$	7.83500	+	21.5265i	0.279287	+	0.767336i	0.997444	+	0.0714543i	$0.0227640\pi$
$787$	7.83500	+	21.5265i	0.279287	+	0.767336i	−0.718156	+	0.695882i	$0.755014\pi$
$788$	11.3239	−	13.4953i	0.403398	−	0.480751i
$789$	−6.13040	−	1.48827i	−0.218248	−	0.0529839i
$790$	38.3690	−	6.76549i	1.36511	−	0.240705i
$791$	−10.5714	−	16.8814i	−0.375877	−	0.600233i
$792$	0.0602438	+	0.143956i	0.00214067	+	0.00511526i
$793$	−16.2633	−	28.1689i	−0.577528	−	1.00031i
$794$	6.12825	+	34.7551i	0.217484	+	1.23341i
$795$	53.4316	+	35.5613i	1.89502	+	1.26123i
$796$	−18.0790	−	49.6717i	−0.640794	−	1.76057i
$797$	−9.18486	−	7.70701i	−0.325344	−	0.272996i	0.465455	−	0.885071i	$-0.345891\pi$
$797$	−9.18486	−	7.70701i	−0.325344	−	0.272996i	−0.790800	+	0.612075i	$0.790335\pi$
$798$	9.36989	+	5.76216i	0.331691	+	0.203978i
$799$	−23.5601	−	8.57516i	−0.833495	−	0.303367i
$800$	61.9155	−	35.7469i	2.18904	−	1.26384i
$801$	−8.21515	+	26.3899i	−0.290268	+	0.932442i
$802$	23.9939	−	41.5586i	0.847253	−	1.46748i
$803$	−3.34510	−	1.21752i	−0.118046	−	0.0429652i
$804$	−16.1093	−	15.3652i	−0.568131	−	0.541888i
$805$	64.9759	+	50.6633i	2.29010	+	1.78565i
$806$	−0.962304	−	0.169680i	−0.0338957	−	0.00597673i
$807$	−51.2359	−	22.4331i	−1.80359	−	0.789681i
$808$	0.0708677	−	0.194707i	0.00249312	−	0.00684978i
$809$	40.1666	−	23.1902i	1.41218	−	0.815324i	0.416588	−	0.909095i	$-0.363226\pi$
$809$	40.1666	−	23.1902i	1.41218	−	0.815324i	0.995594	+	0.0937717i	$0.0298924\pi$
$810$	37.9892	−	55.1042i	1.33480	−	1.93617i
$811$		−	11.1740i		−	0.392373i	−0.980567	−	0.196187i	$-0.937144\pi$
$811$		−	11.1740i		−	0.392373i	0.980567	−	0.196187i	$-0.0628558\pi$
$812$	17.6386	+	5.71223i	0.618995	+	0.200460i
$813$	−42.6895	+	4.75395i	−1.49719	+	0.166728i
$814$	−0.436211	−	0.366024i	−0.0152892	−	0.0128291i
$815$	−16.9997	−	14.2644i	−0.595473	−	0.499661i
$816$	−7.59383	+	31.2801i	−0.265837	+	1.09502i
$817$	−0.0138955	+	0.0381775i	−0.000486142	+	0.00133566i
$818$	−18.9031	−	32.7411i	−0.660932	−	1.14477i
$819$	−28.0574	−	28.2892i	−0.980405	−	0.988506i
$820$	27.5870	−	47.7820i	0.963379	−	1.66862i
$821$	10.6251	+	12.6626i	0.370820	+	0.441926i	0.918894	−	0.394503i	$-0.129083\pi$
$821$	10.6251	+	12.6626i	0.370820	+	0.441926i	−0.548074	+	0.836430i	$0.684639\pi$
$822$	−3.57268	−	7.21154i	−0.124612	−	0.251531i
$823$	7.91541	−	44.8905i	0.275914	−	1.56479i	−0.460130	−	0.887851i	$-0.652197\pi$
$823$	7.91541	−	44.8905i	0.275914	−	1.56479i	0.736044	−	0.676934i	$-0.236692\pi$
$824$	1.09045	−	0.396892i	0.0379876	−	0.0138264i
$825$	7.47059	−	3.70102i	0.260092	−	0.128853i
$826$	3.81258	+	1.23469i	0.132657	+	0.0429605i
$827$	39.6502	+	22.8921i	1.37877	+	0.796035i	0.992012	−	0.126145i	$-0.0402604\pi$
$827$	39.6502	+	22.8921i	1.37877	+	0.796035i	0.386761	+	0.922180i	$0.373594\pi$
$828$	−38.7609	−	29.5186i	−1.34703	−	1.02584i
$829$	15.0730	+	8.70243i	0.523508	+	0.302248i	0.738369	−	0.674397i	$-0.235596\pi$
$829$	15.0730	+	8.70243i	0.523508	+	0.302248i	−0.214860	+	0.976645i	$0.568930\pi$
$830$	−8.67408	−	10.3374i	−0.301082	−	0.358815i
$831$	6.41146	−	26.4097i	0.222411	−	0.916143i
$832$	13.0551	+	35.8686i	0.452604	+	1.24352i
$833$	−28.9930	+	12.9760i	−1.00455	+	0.449591i
$834$	−1.29994	+	0.956798i	−0.0450131	+	0.0331312i
$835$	7.34797	+	41.6724i	0.254287	+	1.44213i
$836$	−0.630245	−	1.09162i	−0.0217975	−	0.0377544i
$837$	0.395106	−	0.320671i	0.0136569	−	0.0110840i
$838$	−55.1043	−	31.8145i	−1.90355	−	1.09901i
$839$	−3.94033	+	3.30633i	−0.136035	+	0.114147i	−0.708266	−	0.705945i	$-0.750522\pi$
$839$	−3.94033	+	3.30633i	−0.136035	+	0.114147i	0.572231	+	0.820092i	$0.306078\pi$
$840$	1.55006	+	0.613401i	0.0534821	+	0.0211643i
$841$	2.79571	−	15.8553i	0.0964038	−	0.546733i
$842$	−23.0040	−	4.05622i	−0.792770	−	0.139787i
$843$	6.29694	+	21.4583i	0.216878	+	0.739063i
$844$	6.45109	−	5.41311i	0.222056	−	0.186327i
$845$	45.6377			1.56999
$846$	15.1071	−	29.2804i	0.519394	−	1.00668i
$847$	−24.0242	+	15.0444i	−0.825481	+	0.516932i
$848$	13.8738	−	38.1179i	0.476427	−	1.30897i
$849$	−35.3409	+	17.5083i	−1.21290	+	0.600883i
$850$	79.9212	+	14.0923i	2.74127	+	0.483360i
$851$	−4.38948	−	0.773983i	−0.150469	−	0.0265318i
$852$	−10.9535	+	5.42647i	−0.375260	+	0.185908i
$853$	1.43875	−	3.95294i	0.0492620	−	0.135346i	−0.912622	−	0.408805i	$-0.865946\pi$
$853$	1.43875	−	3.95294i	0.0492620	−	0.135346i	0.961884	+	0.273459i	$0.0881678\pi$
$854$	−1.22230	−	34.0550i	−0.0418264	−	1.16534i
$855$	6.21464	−	12.0451i	0.212536	−	0.411935i
$856$	−1.51034			−0.0516224
$857$	14.8371	−	12.4498i	0.506826	−	0.425277i	−0.353185	−	0.935554i	$-0.614901\pi$
$857$	14.8371	−	12.4498i	0.506826	−	0.425277i	0.860011	+	0.510276i	$0.170457\pi$
$858$	2.60343	+	8.87179i	0.0888797	+	0.302878i
$859$	2.03705	+	0.359186i	0.0695031	+	0.0122553i	0.208292	−	0.978067i	$-0.433210\pi$
$859$	2.03705	+	0.359186i	0.0695031	+	0.0122553i	−0.138788	+	0.990322i	$0.544321\pi$
$860$	0.0426452	−	0.241853i	0.00145419	−	0.00824711i
$861$	34.2650	−	5.06588i	1.16775	−	0.172645i
$862$	−15.5684	+	13.0635i	−0.530263	+	0.444944i
$863$	−5.67206	−	3.27476i	−0.193079	−	0.111474i	0.400344	−	0.916365i	$-0.368891\pi$
$863$	−5.67206	−	3.27476i	−0.193079	−	0.111474i	−0.593423	+	0.804891i	$0.702224\pi$
$864$	−38.5634	−	14.7544i	−1.31195	−	0.501956i
$865$	−19.2962	−	33.4221i	−0.656092	−	1.13638i
$866$	0.905930	+	5.13778i	0.0307848	+	0.174589i
$867$	−5.00960	+	3.68724i	−0.170135	+	0.125225i
$868$	−0.398660	−	0.310845i	−0.0135314	−	0.0105508i
$869$	−0.958615	−	2.63377i	−0.0325188	−	0.0893447i
$870$	10.9143	−	44.9575i	0.370029	−	1.52420i
$871$	21.2560	+	25.3320i	0.720233	+	0.858340i
$872$	0.170815	+	0.0986202i	0.00578453	+	0.00333970i
$873$	30.5252	+	23.2466i	1.03312	+	0.786779i
$874$	−17.3033	−	9.99007i	−0.585293	−	0.337919i
$875$	12.1904	−	37.6423i	0.412110	−	1.27254i
$876$	20.1491	−	9.98211i	0.680776	−	0.337264i
$877$	−27.8396	+	10.1328i	−0.940078	+	0.342160i	−0.766197	−	0.642606i	$-0.777853\pi$
$877$	−27.8396	+	10.1328i	−0.940078	+	0.342160i	−0.173881	+	0.984767i	$0.555631\pi$
$878$	−0.313519	+	1.77806i	−0.0105808	+	0.0600065i
$879$	0.167302	+	0.337703i	0.00564296	+	0.0113905i
$880$	−5.26906	−	6.27942i	−0.177620	−	0.211679i
$881$	−15.7274	+	27.2407i	−0.529870	+	0.917762i	0.469522	+	0.882921i	$0.344426\pi$
$881$	−15.7274	+	27.2407i	−0.529870	+	0.917762i	−0.999393	+	0.0348419i	$0.988907\pi$
$882$	−12.0787	−	39.9566i	−0.406712	−	1.34541i
$883$	−5.78793	−	10.0250i	−0.194779	−	0.337368i	0.752049	−	0.659107i	$-0.229066\pi$
$883$	−5.78793	−	10.0250i	−0.194779	−	0.337368i	−0.946828	+	0.321740i	$0.895732\pi$
$884$	−15.2004	+	41.7628i	−0.511246	+	1.40464i
$885$	1.16495	−	4.79861i	0.0391595	−	0.161304i
$886$	−17.7889	−	14.9267i	−0.597630	−	0.501471i
$887$	1.02348	+	0.858799i	0.0343650	+	0.0288356i	0.659808	−	0.751434i	$-0.270637\pi$
$887$	1.02348	+	0.858799i	0.0343650	+	0.0288356i	−0.625443	+	0.780270i	$0.715082\pi$
$888$	−0.0896259	+	0.00998085i	−0.00300765	+	0.000334935i
$889$	32.7442	+	36.2952i	1.09821	+	1.21730i
$890$		−	68.5143i		−	2.29661i
$891$	−4.37848	−	2.00302i	−0.146685	−	0.0671036i
$892$	2.41033	−	1.39160i	0.0807037	−	0.0465943i
$893$	2.28203	−	6.26982i	0.0763651	−	0.209811i
$894$	32.3952	+	14.1839i	1.08346	+	0.474379i
$895$	27.6515	+	4.87571i	0.924289	+	0.162977i
$896$	0.284357	−	2.03765i	0.00949971	−	0.0680731i
$897$	52.3696	+	49.9505i	1.74857	+	1.66780i
$898$	18.9263	+	6.88860i	0.631578	+	0.229876i
$899$	0.175867	−	0.304610i	0.00586548	−	0.0101593i
$900$	−15.6531	+	50.2832i	−0.521770	+	1.67611i
$901$	38.9237	−	22.4726i	1.29674	−	0.748672i
$902$	−7.55308	−	2.74910i	−0.251490	−	0.0915349i
$903$	0.135606	−	0.0733525i	0.00451270	−	0.00244102i
$904$	0.560744	+	0.470520i	0.0186501	+	0.0156493i
$905$	23.2117	+	63.7736i	0.771582	+	2.11991i
$906$	−1.63862	−	1.09058i	−0.0544393	−	0.0362320i
$907$	8.02332	+	45.5025i	0.266410	+	1.51089i	0.764990	+	0.644042i	$0.222744\pi$
$907$	8.02332	+	45.5025i	0.266410	+	1.51089i	−0.498580	+	0.866844i	$0.666145\pi$
$908$	−18.9176	−	32.7662i	−0.627802	−	1.08738i
$909$	2.46802	+	5.89747i	0.0818590	+	0.195607i
$910$	87.2517	+	46.2840i	2.89236	+	1.53430i
$911$	−4.92566	+	0.868526i	−0.163194	+	0.0287756i	−0.254648	−	0.967034i	$-0.581960\pi$
$911$	−4.92566	+	0.868526i	−0.163194	+	0.0287756i	0.0914540	+	0.995809i	$0.470849\pi$
$912$	−8.32427	−	2.02087i	−0.275644	−	0.0669179i
$913$	−0.624004	+	0.743659i	−0.0206515	+	0.0246115i
$914$	18.7581	+	51.5376i	0.620464	+	1.70471i
$915$	−41.7310	+	4.64722i	−1.37959	+	0.153632i
$916$	3.23761	+	3.85843i	0.106974	+	0.127486i
$917$	1.34240	+	0.712097i	0.0443299	+	0.0235155i
$918$	−22.7674	−	40.9671i	−0.751437	−	1.35212i
$919$	−20.9077	+	36.2133i	−0.689683	+	1.19457i	0.282258	+	0.959339i	$0.408917\pi$
$919$	−20.9077	+	36.2133i	−0.689683	+	1.19457i	−0.971940	+	0.235227i	$0.924417\pi$
$920$	−2.84535	−	1.03562i	−0.0938085	−	0.0341435i
$921$	−34.5514	+	3.84769i	−1.13851	+	0.126786i
$922$	24.0085	−	28.6122i	0.790677	−	0.942292i
$923$	17.0627	−	6.21031i	0.561625	−	0.204415i
$924$	−0.961008	+	4.68579i	−0.0316148	+	0.154151i
$925$	0.836607	+	4.74463i	0.0275075	+	0.156003i
$926$		−	1.87857i		−	0.0617335i
$927$	−16.4167	+	31.8186i	−0.539196	+	1.04506i
$928$	−28.5401			−0.936875
$929$	−37.9713	+	31.8617i	−1.24580	+	1.04535i	−0.248748	+	0.968568i	$0.580019\pi$
$929$	−37.9713	+	31.8617i	−1.24580	+	1.04535i	−0.997048	+	0.0767791i	$0.975536\pi$
$930$	−0.698891	+	1.05010i	−0.0229175	+	0.0344341i
$931$	−3.45318	−	7.71564i	−0.113173	−	0.252870i
$932$	−30.6362	+	36.5108i	−1.00352	+	1.19595i
$933$	−0.152585	−	0.307996i	−0.00499541	−	0.0100834i
$934$	−20.6100	+	3.63411i	−0.674381	+	0.118912i
$935$		−	9.08253i		−	0.297031i
$936$	1.30126	+	0.671381i	0.0425331	+	0.0219448i
$937$	22.5053	−	12.9934i	0.735215	−	0.424477i	−0.0851120	−	0.996371i	$-0.527125\pi$
$937$	22.5053	−	12.9934i	0.735215	−	0.424477i	0.820327	+	0.571895i	$0.193791\pi$
$938$	7.23589	+	33.8805i	0.236260	+	1.10624i
$939$	−27.5821	−	6.69609i	−0.900109	−	0.218519i
$940$	−7.00353	+	39.7190i	−0.228430	+	1.29549i
$941$	8.45962	−	3.07905i	0.275776	−	0.100374i	−0.200430	−	0.979708i	$-0.564234\pi$
$941$	8.45962	−	3.07905i	0.275776	−	0.100374i	0.476206	+	0.879334i	$0.342012\pi$
$942$	−3.02055	−	27.1239i	−0.0984148	−	0.883744i
$943$	−61.9595	+	10.9251i	−2.01768	+	0.355772i
$944$	−3.12082			−0.101574
$945$	−47.9798	+	18.5318i	−1.56078	+	0.602838i
$946$	−0.0357770			−0.00116321
$947$	30.5085	−	5.37947i	0.991392	−	0.174809i	0.345649	−	0.938364i	$-0.387659\pi$
$947$	30.5085	−	5.37947i	0.991392	−	0.174809i	0.645743	+	0.763555i	$0.276548\pi$
$948$	16.2182	+	7.10094i	0.526741	+	0.230628i
$949$	−31.3871	+	11.4240i	−1.01887	+	0.370838i
$950$	−3.75024	+	21.2687i	−0.121674	+	0.690047i
$951$	−6.83058	−	23.2768i	−0.221497	−	0.754801i
$952$	0.866748	−	0.781947i	0.0280915	−	0.0253431i
$953$	26.4646	−	15.2793i	0.857272	−	0.494946i	−0.00582605	−	0.999983i	$-0.501854\pi$
$953$	26.4646	−	15.2793i	0.857272	−	0.494946i	0.863098	+	0.505037i	$0.168521\pi$
$954$	22.8014	+	54.4852i	0.738222	+	1.76402i
$955$		−	44.5335i		−	1.44107i
$956$	−45.2998	+	7.98758i	−1.46510	+	0.258337i
$957$	−3.32140	−	0.211622i	−0.107366	−	0.00684077i
$958$	−5.64515	+	6.72762i	−0.182386	+	0.217360i
$959$	−0.854802	+	6.12534i	−0.0276030	+	0.197798i
$960$	49.1751	+	3.13317i	1.58712	+	0.101123i
$961$	23.7400	−	19.9203i	0.765807	−	0.642589i
$962$	−5.34300			−0.172265
$963$	34.2424	−	31.6076i	1.10345	−	1.01854i
$964$			18.7085i			0.602561i
$965$	4.78702	+	27.1486i	0.154100	+	0.873943i
$966$	23.9452	+	71.9404i	0.770425	+	2.31464i
$967$	36.5940	−	13.3191i	1.17678	−	0.428314i	0.321719	−	0.946835i	$-0.395739\pi$
$967$	36.5940	−	13.3191i	1.17678	−	0.428314i	0.855065	+	0.518521i	$0.173517\pi$
$968$	0.669606	−	0.798005i	0.0215219	−	0.0256488i
$969$	−5.62618	−	7.64391i	−0.180739	−	0.245558i
$970$	−89.3772	−	32.5306i	−2.86973	−	1.04450i
$971$	1.63236	−	2.82733i	0.0523849	−	0.0907333i	−0.838644	−	0.544680i	$-0.816651\pi$
$971$	1.63236	−	2.82733i	0.0523849	−	0.0907333i	0.891029	+	0.453947i	$0.149984\pi$
$972$	28.2449	−	11.2810i	0.905956	−	0.361838i
$973$	1.23959	−	0.0444916i	0.0397396	−	0.00142634i
$974$	45.6146	+	54.3614i	1.46159	+	1.74185i
$975$	31.3753	−	71.6595i	1.00481	−	2.29494i
$976$	9.07623	+	24.9367i	0.290523	+	0.798206i
$977$	24.7248	−	29.4659i	0.791018	−	0.942698i	−0.208357	−	0.978053i	$-0.566812\pi$
$977$	24.7248	−	29.4659i	0.791018	−	0.942698i	0.999375	+	0.0353548i	$0.0112561\pi$
$978$	−5.75018	−	19.5951i	−0.183871	−	0.626581i
$979$	−4.85397	+	0.855885i	−0.155133	+	0.0273542i
$980$	28.6552	+	42.3058i	0.915358	+	1.35141i
$981$	−5.93658	+	1.33881i	−0.189541	+	0.0427450i
$982$	22.0668	+	38.2209i	0.704181	+	1.21968i
$983$	−2.16548	−	12.2810i	−0.0690681	−	0.391704i	−0.999670	−	0.0256726i	$-0.991827\pi$
$983$	−2.16548	−	12.2810i	−0.0690681	−	0.391704i	0.930602	−	0.366032i	$-0.119284\pi$
$984$	−1.14063	+	0.565082i	−0.0363620	+	0.0180142i
$985$	11.5539	+	31.7439i	0.368136	+	1.01145i
$986$	−24.8171	−	20.8240i	−0.790337	−	0.663172i
$987$	−22.2704	+	12.0465i	−0.708873	+	0.383445i
$988$	−11.1139	−	4.04515i	−0.353582	−	0.128693i
$989$	−0.242523	+	0.140021i	−0.00771179	+	0.00445240i
$990$	11.8391	+	1.51480i	0.376271	+	0.0481434i
$991$	−14.3275	+	24.8160i	−0.455129	+	0.788306i	−0.998696	−	0.0510596i	$-0.983740\pi$
$991$	−14.3275	+	24.8160i	−0.455129	+	0.788306i	0.543567	+	0.839366i	$0.317073\pi$
$992$	0.731241	+	0.266150i	0.0232169	+	0.00845027i
$993$	−24.3242	+	7.13793i	−0.771904	+	0.226515i
$994$	18.8406	+	2.62923i	0.597587	+	0.0833942i
$995$	99.8206	+	17.6011i	3.16453	+	0.557991i
$996$	−0.678689	−	6.09448i	−0.0215051	−	0.193111i
$997$	1.96853	−	5.40850i	0.0623440	−	0.171289i	−0.904610	−	0.426241i	$-0.859838\pi$
$997$	1.96853	−	5.40850i	0.0623440	−	0.171289i	0.966954	+	0.254952i	$0.0820598\pi$
$998$	62.4178	−	36.0370i	1.97580	−	1.14073i
$999$	1.82312	−	2.10193i	0.0576810	−	0.0665020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.5.20	✓	132
3.2	odd	2		567.2.ba.a.530.3		132
7.3	odd	6		189.2.bd.a.59.3	yes	132
21.17	even	6		567.2.bd.a.206.20		132
27.11	odd	18		189.2.bd.a.173.3	yes	132
27.16	even	9		567.2.bd.a.278.20		132
189.38	even	18	inner	189.2.ba.a.38.20	yes	132
189.178	odd	18		567.2.ba.a.521.3		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.20	✓	132	1.1	even	1	trivial
189.2.ba.a.38.20	yes	132	189.38	even	18	inner
189.2.bd.a.59.3	yes	132	7.3	odd	6
189.2.bd.a.173.3	yes	132	27.11	odd	18
567.2.ba.a.521.3		132	189.178	odd	18
567.2.ba.a.530.3		132	3.2	odd	2
567.2.bd.a.206.20		132	21.17	even	6
567.2.bd.a.278.20		132	27.16	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.95754 - 0.345166i) q^{2} +(-1.39494 + 1.02672i) q^{3} +(1.83342 - 0.667310i) q^{4} +(-0.649669 + 3.68445i) q^{5} +(-2.37625 + 2.49133i) q^{6} +(2.58740 - 0.552593i) q^{7} +(-0.0842052 + 0.0486159i) q^{8} +(0.891690 - 2.86442i) q^{9} +O(q^{10})\)	\(q+(1.95754 - 0.345166i) q^{2} +(-1.39494 + 1.02672i) q^{3} +(1.83342 - 0.667310i) q^{4} +(-0.649669 + 3.68445i) q^{5} +(-2.37625 + 2.49133i) q^{6} +(2.58740 - 0.552593i) q^{7} +(-0.0842052 + 0.0486159i) q^{8} +(0.891690 - 2.86442i) q^{9} +7.43669i q^{10} +(0.526860 - 0.0928996i) q^{11} +(-1.87236 + 2.81326i) q^{12} +(3.22666 - 3.84539i) q^{13} +(4.87419 - 1.97480i) q^{14} +(-2.87666 - 5.80660i) q^{15} +(-3.13729 + 2.63250i) q^{16} -4.53776 q^{17} +(0.756814 - 5.91498i) q^{18} -1.20759i q^{19} +(1.26756 + 7.18868i) q^{20} +(-3.04190 + 3.42737i) q^{21} +(0.999281 - 0.363709i) q^{22} +(5.35042 - 6.37638i) q^{23} +(0.0675459 - 0.154271i) q^{24} +(-8.45466 - 3.07725i) q^{25} +(4.98901 - 8.64122i) q^{26} +(1.69711 + 4.91119i) q^{27} +(4.37504 - 2.73973i) q^{28} +(2.30869 + 2.75138i) q^{29} +(-7.63540 - 10.3737i) q^{30} +(-0.0334941 - 0.0920242i) q^{31} +(-5.10770 + 6.08713i) q^{32} +(-0.639554 + 0.670527i) q^{33} +(-8.88283 + 1.56628i) q^{34} +(0.355050 + 9.89216i) q^{35} +(-0.276613 - 5.84671i) q^{36} +(-0.267738 - 0.463737i) q^{37} +(-0.416820 - 2.36390i) q^{38} +(-0.552849 + 8.67695i) q^{39} +(-0.124418 - 0.341834i) q^{40} +(-5.79016 - 4.85852i) q^{41} +(-4.77161 + 7.75916i) q^{42} +(-0.0316146 - 0.0115068i) q^{43} +(0.903962 - 0.521903i) q^{44} +(9.97451 + 5.14631i) q^{45} +(8.27273 - 14.3288i) q^{46} +(5.19200 + 1.88973i) q^{47} +(1.67348 - 6.89328i) q^{48} +(6.38928 - 2.85956i) q^{49} +(-17.6125 - 3.10555i) q^{50} +(6.32988 - 4.65901i) q^{51} +(3.34976 - 9.20340i) q^{52} +(-8.57774 + 4.95236i) q^{53} +(5.01732 + 9.02805i) q^{54} +2.00154i q^{55} +(-0.191008 + 0.172320i) q^{56} +(1.23986 + 1.68451i) q^{57} +(5.46902 + 4.58905i) q^{58} +(0.583744 + 0.489820i) q^{59} +(-9.14892 - 8.72631i) q^{60} +(2.21618 - 6.08890i) q^{61} +(-0.0973295 - 0.168580i) q^{62} +(0.724302 - 7.90414i) q^{63} +(-3.80200 + 6.58526i) q^{64} +(12.0719 + 14.3867i) q^{65} +(-1.02051 + 1.53333i) q^{66} +(-1.14393 + 6.48754i) q^{67} +(-8.31962 + 3.02809i) q^{68} +(-0.916728 + 14.3880i) q^{69} +(4.10946 + 19.2417i) q^{70} +(3.13261 + 1.80861i) q^{71} +(0.0641713 + 0.284549i) q^{72} +(-5.76249 - 3.32698i) q^{73} +(-0.684174 - 0.815366i) q^{74} +(14.9532 - 4.38802i) q^{75} +(-0.805838 - 2.21402i) q^{76} +(1.31186 - 0.531508i) q^{77} +(1.91277 + 17.1763i) q^{78} +(-0.909744 - 5.15941i) q^{79} +(-7.66112 - 13.2694i) q^{80} +(-7.40978 - 5.10834i) q^{81} +(-13.0114 - 7.51215i) q^{82} +(-1.39005 + 1.16639i) q^{83} +(-3.28996 + 8.31369i) q^{84} +(2.94804 - 16.7192i) q^{85} +(-0.0658585 - 0.0116126i) q^{86} +(-6.04537 - 1.46763i) q^{87} +(-0.0398480 + 0.0334364i) q^{88} -9.21301 q^{89} +(21.3018 + 6.63122i) q^{90} +(6.22374 - 11.7326i) q^{91} +(5.55454 - 15.2610i) q^{92} +(0.141205 + 0.0939788i) q^{93} +(10.8158 + 1.90712i) q^{94} +(4.44931 + 0.784534i) q^{95} +(0.875142 - 13.7353i) q^{96} +(-4.37434 + 12.0184i) q^{97} +(11.5202 - 7.80305i) q^{98} +(0.203692 - 1.59198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

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