LMFDB - Embedded newform 115.2.g.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			81.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	115.81
Dual form			115.2.g.a.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30075 + 0.835939i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.162317 - 0.355426i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.642315 + 1.40647i) q^{6} +(1.57028 + 1.81219i) q^{7} +(-0.354114 - 2.46292i) q^{8} +(1.91899 + 0.563465i) q^{9} +O(q^{10})$	\(q+(-1.30075 + 0.835939i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.162317 - 0.355426i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.642315 + 1.40647i) q^{6} +(1.57028 + 1.81219i) q^{7} +(-0.354114 - 2.46292i) q^{8} +(1.91899 + 0.563465i) q^{9} +(-1.01255 + 1.16854i) q^{10} +(3.19505 + 2.05334i) q^{11} +(-0.328708 - 0.211248i) q^{12} +(-1.07028 + 1.23516i) q^{13} +(-3.55742 - 1.04455i) q^{14} +(-0.142315 - 0.989821i) q^{15} +(3.03122 + 3.49821i) q^{16} +(-1.19028 - 2.60635i) q^{17} +(-2.96714 + 0.871230i) q^{18} +(-0.754359 + 1.65182i) q^{19} +(0.0556075 - 0.386758i) q^{20} +(2.01722 - 1.29639i) q^{21} -5.87242 q^{22} +(-3.50654 - 3.27173i) q^{23} -2.48825 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.359636 - 2.50132i) q^{26} +(2.07708 - 4.54816i) q^{27} +(0.898983 - 0.263965i) q^{28} +(-3.57631 - 7.83103i) q^{29} +(1.01255 + 1.16854i) q^{30} +(0.185062 + 1.28713i) q^{31} +(-2.09223 - 0.614334i) q^{32} +(2.48714 - 2.87031i) q^{33} +(3.72700 + 2.39520i) q^{34} +(2.01722 + 1.29639i) q^{35} +(0.511755 - 0.590596i) q^{36} +(-6.58052 - 1.93221i) q^{37} +(-0.399587 - 2.77919i) q^{38} +(1.07028 + 1.23516i) q^{39} +(-1.03365 - 2.26339i) q^{40} +(-6.01710 + 1.76678i) q^{41} +(-1.54019 + 3.37255i) q^{42} +(-1.72084 + 11.9687i) q^{43} +(1.24842 - 0.802311i) q^{44} +2.00000 q^{45} +(7.29608 + 1.32443i) q^{46} +4.66817 q^{47} +(3.89399 - 2.50252i) q^{48} +(0.177920 - 1.23746i) q^{49} +(-0.642315 + 1.40647i) q^{50} +(-2.74921 + 0.807241i) q^{51} +(0.265284 + 0.580892i) q^{52} +(3.35061 + 3.86681i) q^{53} +(1.10024 + 7.65231i) q^{54} +(3.64412 + 1.07001i) q^{55} +(3.90723 - 4.50919i) q^{56} +(1.52765 + 0.981759i) q^{57} +(11.1981 + 7.19661i) q^{58} +(-4.75399 + 5.48639i) q^{59} +(-0.374908 - 0.110083i) q^{60} +(-1.23344 - 8.57875i) q^{61} +(-1.31668 - 1.51953i) q^{62} +(1.99223 + 4.36237i) q^{63} +(-5.64759 + 1.65828i) q^{64} +(-0.678936 + 1.48666i) q^{65} +(-0.835732 + 5.81264i) q^{66} +(4.36550 - 2.80554i) q^{67} -1.11956 q^{68} +(-3.73746 + 3.00523i) q^{69} -3.70760 q^{70} +(-2.38202 + 1.53083i) q^{71} +(0.708228 - 4.92584i) q^{72} +(-0.872226 + 1.90991i) q^{73} +(10.1748 - 2.98759i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(0.464652 + 0.536237i) q^{76} +(1.29607 + 9.01436i) q^{77} +(-2.42468 - 0.711950i) q^{78} +(8.09638 - 9.34373i) q^{79} +(3.89399 + 2.50252i) q^{80} +(0.841254 + 0.540641i) q^{81} +(6.34980 - 7.32806i) q^{82} +(-13.1023 - 3.84719i) q^{83} +(-0.133340 - 0.927399i) q^{84} +(-1.87636 - 2.16543i) q^{85} +(-7.76672 - 17.0068i) q^{86} +(-8.26028 + 2.42544i) q^{87} +(3.92579 - 8.59627i) q^{88} +(1.65356 - 11.5007i) q^{89} +(-2.60149 + 1.67188i) q^{90} -3.91899 q^{91} +(-1.73203 + 0.715255i) q^{92} +1.30037 q^{93} +(-6.07211 + 3.90231i) q^{94} +(-0.258432 + 1.79743i) q^{95} +(-0.905836 + 1.98350i) q^{96} +(5.95288 - 1.74792i) q^{97} +(0.803012 + 1.75835i) q^{98} +(4.97428 + 5.74062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9 - 5 * q^10 + 8 * q^11 + q^12 - 3 * q^14 - q^15 + 5 * q^16 - 23 * q^17 - 10 * q^18 - 13 * q^19 + q^20 + 6 * q^21 + 4 * q^22 - 21 * q^23 - 6 * q^24 - q^25 + 11 * q^26 - 5 * q^27 - 6 * q^28 + 2 * q^29 + 5 * q^30 - 20 * q^31 - 15 * q^32 + 3 * q^33 + 16 * q^34 + 6 * q^35 + 24 * q^36 + 13 * q^37 + 21 * q^38 - 6 * q^40 - 5 * q^41 + 3 * q^42 + 15 * q^43 + 19 * q^44 + 20 * q^45 - 16 * q^46 - 52 * q^47 + 6 * q^48 + 4 * q^49 - 6 * q^50 - 10 * q^51 + 22 * q^52 + 6 * q^53 - 30 * q^54 + 3 * q^55 + 3 * q^56 + 2 * q^57 + 45 * q^58 + 5 * q^59 + 10 * q^60 - 3 * q^61 - 54 * q^62 - 10 * q^63 - 34 * q^64 - 4 * q^66 + 20 * q^67 + 32 * q^68 - q^69 - 8 * q^70 - 22 * q^71 + 32 * q^72 + 43 * q^73 + q^74 + q^75 - 2 * q^76 + 4 * q^77 + 11 * q^78 + 51 * q^79 + 6 * q^80 - q^81 + 58 * q^82 - 17 * q^83 + 6 * q^84 + q^85 - 9 * q^86 - 2 * q^87 + 7 * q^88 + 57 * q^89 + 10 * q^90 - 22 * q^91 - 43 * q^92 + 20 * q^93 - 81 * q^94 - 9 * q^95 - 7 * q^96 + 52 * q^97 + 24 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	−1.30075	+	0.835939i	−0.919767	+	0.591098i	−0.912590	−	0.408876i	$-0.865921\pi$
$2$	−1.30075	+	0.835939i	−0.919767	+	0.591098i	−0.00717677	+	0.999974i	$0.502284\pi$
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i	−0.906599	−	0.421993i	$-0.861331\pi$
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i	0.988765	−	0.149481i	$-0.0477602\pi$
$4$	0.162317	−	0.355426i	0.0811587	−	0.177713i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$6$	0.642315	+	1.40647i	0.262224	+	0.574190i
$7$	1.57028	+	1.81219i	0.593508	+	0.684945i	0.970453	−	0.241291i	$-0.0775707\pi$
$7$	1.57028	+	1.81219i	0.593508	+	0.684945i	−0.376944	+	0.926236i	$0.623025\pi$
$8$	−0.354114	−	2.46292i	−0.125198	−	0.870773i
$9$	1.91899	+	0.563465i	0.639662	+	0.187822i
$10$	−1.01255	+	1.16854i	−0.320195	+	0.369525i
$11$	3.19505	+	2.05334i	0.963345	+	0.619104i	0.924922	−	0.380158i	$-0.124130\pi$
$11$	3.19505	+	2.05334i	0.963345	+	0.619104i	0.0384230	+	0.999262i	$0.487767\pi$
$12$	−0.328708	−	0.211248i	−0.0948897	−	0.0609819i
$13$	−1.07028	+	1.23516i	−0.296841	+	0.342573i	−0.884504	−	0.466533i	$-0.845503\pi$
$13$	−1.07028	+	1.23516i	−0.296841	+	0.342573i	0.587663	+	0.809106i	$0.300048\pi$
$14$	−3.55742	−	1.04455i	−0.950759	−	0.279168i
$15$	−0.142315	−	0.989821i	−0.0367455	−	0.255571i
$16$	3.03122	+	3.49821i	0.757804	+	0.874553i
$17$	−1.19028	−	2.60635i	−0.288685	−	0.632132i	0.708613	−	0.705598i	$-0.249321\pi$
$17$	−1.19028	−	2.60635i	−0.288685	−	0.632132i	−0.997298	+	0.0734657i	$0.976594\pi$
$18$	−2.96714	+	0.871230i	−0.699361	+	0.205351i
$19$	−0.754359	+	1.65182i	−0.173062	+	0.378953i	−0.976210	−	0.216827i	$-0.930429\pi$
$19$	−0.754359	+	1.65182i	−0.173062	+	0.378953i	0.803148	+	0.595779i	$0.203157\pi$
$20$	0.0556075	−	0.386758i	0.0124342	−	0.0864818i
$21$	2.01722	−	1.29639i	0.440194	−	0.282896i
$22$	−5.87242			−1.25200
$23$	−3.50654	−	3.27173i	−0.731164	−	0.682202i
$23$	−3.50654	−	3.27173i	−0.731164	−	0.682202i
$24$	−2.48825			−0.507911
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.359636	−	2.50132i	0.0705303	−	0.490549i
$27$	2.07708	−	4.54816i	0.399733	−	0.875294i
$28$	0.898983	−	0.263965i	0.169892	−	0.0498848i
$29$	−3.57631	−	7.83103i	−0.664104	−	1.45419i	−0.878647	−	0.477471i	$-0.841553\pi$
$29$	−3.57631	−	7.83103i	−0.664104	−	1.45419i	0.214543	−	0.976715i	$-0.431174\pi$
$30$	1.01255	+	1.16854i	0.184865	+	0.213345i
$31$	0.185062	+	1.28713i	0.0332380	+	0.231176i	0.999668	−	0.0257533i	$-0.00819844\pi$
$31$	0.185062	+	1.28713i	0.0332380	+	0.231176i	−0.966430	+	0.256929i	$0.917289\pi$
$32$	−2.09223	−	0.614334i	−0.369857	−	0.108600i
$33$	2.48714	−	2.87031i	0.432955	−	0.499657i
$34$	3.72700	+	2.39520i	0.639175	+	0.410773i
$35$	2.01722	+	1.29639i	0.340973	+	0.219130i
$36$	0.511755	−	0.590596i	0.0852924	−	0.0984327i
$37$	−6.58052	−	1.93221i	−1.08183	−	0.317654i	−0.308220	−	0.951315i	$-0.599733\pi$
$37$	−6.58052	−	1.93221i	−1.08183	−	0.317654i	−0.773611	+	0.633661i	$0.781551\pi$
$38$	−0.399587	−	2.77919i	−0.0648216	−	0.450844i
$39$	1.07028	+	1.23516i	0.171381	+	0.197785i
$40$	−1.03365	−	2.26339i	−0.163435	−	0.357873i
$41$	−6.01710	+	1.76678i	−0.939712	+	0.275924i	−0.715498	−	0.698615i	$-0.753800\pi$
$41$	−6.01710	+	1.76678i	−0.939712	+	0.275924i	−0.224215	+	0.974540i	$0.571982\pi$
$42$	−1.54019	+	3.37255i	−0.237657	+	0.520396i
$43$	−1.72084	+	11.9687i	−0.262425	+	1.82521i	0.252062	+	0.967711i	$0.418891\pi$
$43$	−1.72084	+	11.9687i	−0.262425	+	1.82521i	−0.514488	+	0.857498i	$0.672018\pi$
$44$	1.24842	−	0.802311i	0.188206	−	0.120953i
$45$	2.00000			0.298142
$46$	7.29608	+	1.32443i	1.07575	+	0.195277i
$47$	4.66817			0.680923			0.340461	−	0.940258i	$-0.389417\pi$
$47$	4.66817			0.680923			0.340461	+	0.940258i	$0.389417\pi$
$48$	3.89399	−	2.50252i	0.562049	−	0.361207i
$49$	0.177920	−	1.23746i	0.0254171	−	0.176780i
$50$	−0.642315	+	1.40647i	−0.0908370	+	0.198905i
$51$	−2.74921	+	0.807241i	−0.384967	+	0.113036i
$52$	0.265284	+	0.580892i	0.0367883	+	0.0805552i
$53$	3.35061	+	3.86681i	0.460241	+	0.531147i	0.937671	−	0.347523i	$-0.112977\pi$
$53$	3.35061	+	3.86681i	0.460241	+	0.531147i	−0.477430	+	0.878670i	$0.658432\pi$
$54$	1.10024	+	7.65231i	0.149723	+	1.04135i
$55$	3.64412	+	1.07001i	0.491373	+	0.144280i
$56$	3.90723	−	4.50919i	0.522126	−	0.602565i
$57$	1.52765	+	0.981759i	0.202342	+	0.130037i
$58$	11.1981	+	7.19661i	1.47039	+	0.944961i
$59$	−4.75399	+	5.48639i	−0.618916	+	0.714267i	−0.975501	−	0.219996i	$-0.929396\pi$
$59$	−4.75399	+	5.48639i	−0.618916	+	0.714267i	0.356585	+	0.934263i	$0.383941\pi$
$60$	−0.374908	−	0.110083i	−0.0484004	−	0.0142116i
$61$	−1.23344	−	8.57875i	−0.157926	−	1.09840i	−0.902448	−	0.430799i	$-0.858232\pi$
$61$	−1.23344	−	8.57875i	−0.157926	−	1.09840i	0.744523	−	0.667597i	$-0.232677\pi$
$62$	−1.31668	−	1.51953i	−0.167219	−	0.192981i
$63$	1.99223	+	4.36237i	0.250997	+	0.549607i
$64$	−5.64759	+	1.65828i	−0.705949	+	0.207285i
$65$	−0.678936	+	1.48666i	−0.0842117	+	0.184398i
$66$	−0.835732	+	5.81264i	−0.102872	+	0.715487i
$67$	4.36550	−	2.80554i	0.533331	−	0.342751i	−0.246095	−	0.969246i	$-0.579147\pi$
$67$	4.36550	−	2.80554i	0.533331	−	0.342751i	0.779426	+	0.626495i	$0.215511\pi$
$68$	−1.11956			−0.135767
$69$	−3.73746	+	3.00523i	−0.449937	+	0.361787i
$70$	−3.70760			−0.443143
$71$	−2.38202	+	1.53083i	−0.282694	+	0.181676i	−0.674302	−	0.738456i	$-0.735555\pi$
$71$	−2.38202	+	1.53083i	−0.282694	+	0.181676i	0.391608	+	0.920132i	$0.371919\pi$
$72$	0.708228	−	4.92584i	0.0834655	−	0.580515i
$73$	−0.872226	+	1.90991i	−0.102086	+	0.223538i	−0.953782	−	0.300498i	$-0.902847\pi$
$73$	−0.872226	+	1.90991i	−0.102086	+	0.223538i	0.851696	+	0.524036i	$0.175574\pi$
$74$	10.1748	−	2.98759i	1.18280	−	0.347300i
$75$	−0.415415	−	0.909632i	−0.0479680	−	0.105035i
$76$	0.464652	+	0.536237i	0.0532992	+	0.0615106i
$77$	1.29607	+	9.01436i	0.147701	+	1.02728i
$78$	−2.42468	−	0.711950i	−0.274541	−	0.0806125i
$79$	8.09638	−	9.34373i	0.910914	−	1.05125i	−0.0875669	−	0.996159i	$-0.527909\pi$
$79$	8.09638	−	9.34373i	0.910914	−	1.05125i	0.998481	−	0.0550926i	$-0.0175454\pi$
$80$	3.89399	+	2.50252i	0.435362	+	0.279790i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	6.34980	−	7.32806i	0.701218	−	0.809248i
$83$	−13.1023	−	3.84719i	−1.43817	−	0.422284i	−0.532557	−	0.846394i	$-0.678769\pi$
$83$	−13.1023	−	3.84719i	−1.43817	−	0.422284i	−0.905611	+	0.424110i	$0.860587\pi$
$84$	−0.133340	−	0.927399i	−0.0145486	−	0.101188i
$85$	−1.87636	−	2.16543i	−0.203519	−	0.234874i
$86$	−7.76672	−	17.0068i	−0.837507	−	1.83389i
$87$	−8.26028	+	2.42544i	−0.885595	+	0.260034i
$88$	3.92579	−	8.59627i	0.418490	−	0.916366i
$89$	1.65356	−	11.5007i	0.175276	−	1.21907i	−0.692240	−	0.721667i	$-0.743376\pi$
$89$	1.65356	−	11.5007i	0.175276	−	1.21907i	0.867517	−	0.497408i	$-0.165715\pi$
$90$	−2.60149	+	1.67188i	−0.274221	+	0.176231i
$91$	−3.91899			−0.410821
$92$	−1.73203	+	0.715255i	−0.180576	+	0.0745705i
$93$	1.30037			0.134842
$94$	−6.07211	+	3.90231i	−0.626290	+	0.402492i
$95$	−0.258432	+	1.79743i	−0.0265146	+	0.184413i
$96$	−0.905836	+	1.98350i	−0.0924515	+	0.202441i
$97$	5.95288	−	1.74792i	0.604423	−	0.177475i	0.0348189	−	0.999394i	$-0.488915\pi$
$97$	5.95288	−	1.74792i	0.604423	−	0.177475i	0.569605	+	0.821919i	$0.307096\pi$
$98$	0.803012	+	1.75835i	0.0811164	+	0.177620i
$99$	4.97428	+	5.74062i	0.499934	+	0.576954i
$100$	−0.0556075	−	0.386758i	−0.00556075	−	0.0386758i
$101$	−12.2111	−	3.58550i	−1.21505	−	0.356771i	−0.389460	−	0.921043i	$-0.627339\pi$
$101$	−12.2111	−	3.58550i	−1.21505	−	0.356771i	−0.825589	+	0.564273i	$0.809157\pi$
$102$	2.90122	−	3.34819i	0.287264	−	0.331520i
$103$	0.426053	+	0.273808i	0.0419803	+	0.0269791i	0.561463	−	0.827502i	$-0.310239\pi$
$103$	0.426053	+	0.273808i	0.0419803	+	0.0269791i	−0.519482	+	0.854481i	$0.673875\pi$
$104$	3.42111	+	2.19861i	0.335467	+	0.215592i
$105$	1.57028	−	1.81219i	0.153243	−	0.176852i
$106$	−7.59071	−	2.22883i	−0.737275	−	0.216483i
$107$	1.35499	+	9.42415i	0.130992	+	0.911067i	0.944265	+	0.329185i	$0.106774\pi$
$107$	1.35499	+	9.42415i	0.130992	+	0.911067i	−0.813274	+	0.581881i	$0.802317\pi$
$108$	−1.27939	−	1.47649i	−0.123109	−	0.142075i
$109$	−3.35462	−	7.34559i	−0.321314	−	0.703580i	0.678196	−	0.734881i	$-0.262762\pi$
$109$	−3.35462	−	7.34559i	−0.321314	−	0.703580i	−0.999510	+	0.0313010i	$0.990035\pi$
$110$	−5.63454	+	1.65445i	−0.537233	+	0.157746i
$111$	−2.84905	+	6.23856i	−0.270420	+	0.592137i
$112$	−1.57959	+	10.9863i	−0.149258	+	1.03811i
$113$	−2.97601	+	1.91257i	−0.279960	+	0.179919i	−0.673084	−	0.739566i	$-0.735031\pi$
$113$	−2.97601	+	1.91257i	−0.279960	+	0.179919i	0.393124	+	0.919485i	$0.371394\pi$
$114$	−2.80777			−0.262972
$115$	−4.28625	−	2.15129i	−0.399695	−	0.200609i
$116$	−3.36385			−0.312325
$117$	−2.74982	+	1.76720i	−0.254221	+	0.163378i
$118$	1.59744	−	11.1104i	0.147056	−	1.02280i
$119$	2.85414	−	6.24970i	0.261639	−	0.572909i
$120$	−2.38745	+	0.701020i	−0.217944	+	0.0639941i
$121$	1.42261	+	3.11508i	0.129328	+	0.283189i
$122$	8.77570	+	10.1277i	0.794514	+	0.916919i
$123$	0.892473	+	6.20729i	0.0804716	+	0.559692i
$124$	0.487518	+	0.143148i	0.0437804	+	0.0128551i
$125$	0.654861	−	0.755750i	0.0585725	−	0.0675963i
$126$	−6.23806	−	4.00896i	−0.555731	−	0.357146i
$127$	0.256571	+	0.164888i	0.0227670	+	0.0146315i	0.551975	−	0.833861i	$-0.313874\pi$
$127$	0.256571	+	0.164888i	0.0227670	+	0.0146315i	−0.529208	+	0.848492i	$0.677511\pi$
$128$	8.81578	−	10.1740i	0.779213	−	0.899259i
$129$	11.6020	+	3.40665i	1.02150	+	0.299938i
$130$	−0.359636	−	2.50132i	−0.0315421	−	0.219380i
$131$	14.5546	+	16.7968i	1.27164	+	1.46755i	0.816743	+	0.577002i	$0.195778\pi$
$131$	14.5546	+	16.7968i	1.27164	+	1.46755i	0.454894	+	0.890545i	$0.349677\pi$
$132$	−0.616476	−	1.34989i	−0.0536574	−	0.117493i
$133$	−4.17796	+	1.22676i	−0.362275	+	0.106374i
$134$	−3.33315	+	7.29859i	−0.287940	+	0.630502i
$135$	0.711574	−	4.94911i	0.0612426	−	0.425951i
$136$	−5.99772	+	3.85450i	−0.514301	+	0.330521i
$137$	13.2706			1.13379			0.566893	−	0.823791i	$-0.308145\pi$
$137$	13.2706			1.13379			0.566893	+	0.823791i	$0.308145\pi$
$138$	2.34929	−	7.03333i	0.199985	−	0.598717i
$139$	−22.1390			−1.87781			−0.938905	−	0.344177i	$-0.888158\pi$
$139$	−22.1390			−1.87781			−0.938905	+	0.344177i	$0.888158\pi$
$140$	0.788201	−	0.506546i	0.0666151	−	0.0428109i
$141$	0.664350	−	4.62066i	0.0559484	−	0.389130i
$142$	1.81872	−	3.98245i	0.152624	−	0.334200i
$143$	−5.95579	+	1.74878i	−0.498049	+	0.146240i
$144$	3.84574	+	8.42100i	0.320479	+	0.701750i
$145$	−5.63770	−	6.50625i	−0.468186	−	0.540315i
$146$	−0.462022	−	3.21343i	−0.0382372	−	0.265946i
$147$	−1.19954	−	0.352218i	−0.0989366	−	0.0290504i
$148$	−1.75489	+	2.02525i	−0.144251	+	0.166475i
$149$	19.0366	+	12.2341i	1.55954	+	1.00225i	0.982659	+	0.185421i	$0.0593650\pi$
$149$	19.0366	+	12.2341i	1.55954	+	1.00225i	0.576877	+	0.816831i	$0.304271\pi$
$150$	1.30075	+	0.835939i	0.106206	+	0.0682541i
$151$	−1.31207	+	1.51421i	−0.106775	+	0.123224i	−0.806621	−	0.591069i	$-0.798706\pi$
$151$	−1.31207	+	1.51421i	−0.106775	+	0.123224i	0.699847	+	0.714293i	$0.253252\pi$
$152$	4.33542	+	1.27299i	0.351649	+	0.103253i
$153$	−0.815542	−	5.67222i	−0.0659327	−	0.458572i
$154$	−9.22131	−	10.6420i	−0.743075	−	0.857554i
$155$	0.540192	+	1.18286i	0.0433893	+	0.0950093i
$156$	0.612733	−	0.179915i	0.0490579	−	0.0144047i
$157$	2.66378	−	5.83287i	0.212593	−	0.465514i	−0.773052	−	0.634342i	$-0.781271\pi$
$157$	2.66378	−	5.83287i	0.212593	−	0.465514i	0.985645	+	0.168828i	$0.0539984\pi$
$158$	−2.72056	+	18.9219i	−0.216436	+	1.50535i
$159$	4.30429	−	2.76620i	0.341352	−	0.219374i
$160$	−2.18056			−0.172388
$161$	0.422774	−	11.4920i	0.0333193	−	0.905700i
$162$	−1.54620			−0.121481
$163$	5.60419	−	3.60160i	0.438954	−	0.282099i	−0.302440	−	0.953168i	$-0.597801\pi$
$163$	5.60419	−	3.60160i	0.438954	−	0.282099i	0.741394	+	0.671070i	$0.234165\pi$
$164$	−0.348721	+	2.42541i	−0.0272305	+	0.189393i
$165$	1.57773	−	3.45475i	0.122826	−	0.268952i
$166$	20.2588	−	5.94853i	1.57239	−	0.461695i
$167$	−1.73519	−	3.79953i	−0.134273	−	0.294016i	0.830538	−	0.556962i	$-0.188033\pi$
$167$	−1.73519	−	3.79953i	−0.134273	−	0.294016i	−0.964811	+	0.262946i	$0.915306\pi$
$168$	−3.90723	−	4.50919i	−0.301449	−	0.347891i
$169$	1.46995	+	10.2237i	0.113073	+	0.786442i
$170$	4.25083	+	1.24816i	0.326024	+	0.0957293i
$171$	−2.37835	+	2.74476i	−0.181877	+	0.209897i
$172$	3.97466	+	2.55436i	0.303065	+	0.194768i
$173$	−20.8088	−	13.3730i	−1.58207	−	1.01673i	−0.975034	−	0.222053i	$-0.928724\pi$
$173$	−20.8088	−	13.3730i	−1.58207	−	1.01673i	−0.607031	−	0.794678i	$-0.707640\pi$
$174$	8.71702	−	10.0600i	0.660835	−	0.762645i
$175$	2.30075	+	0.675560i	0.173920	+	0.0510675i
$176$	2.50190	+	17.4011i	0.188588	+	1.31166i
$177$	4.75399	+	5.48639i	0.357331	+	0.412383i
$178$	7.46305	+	16.3418i	0.559379	+	1.22487i
$179$	4.59863	−	1.35028i	0.343718	−	0.100925i	−0.105318	−	0.994439i	$-0.533586\pi$
$179$	4.59863	−	1.35028i	0.343718	−	0.100925i	0.449035	+	0.893514i	$0.351768\pi$
$180$	0.324635	−	0.710851i	0.0241968	−	0.0529837i
$181$	0.395108	−	2.74804i	0.0293681	−	0.204260i	−0.969854	−	0.243685i	$-0.921644\pi$
$181$	0.395108	−	2.74804i	0.0293681	−	0.204260i	0.999223	+	0.0394253i	$0.0125527\pi$
$182$	5.09761	−	3.27603i	0.377860	−	0.242836i
$183$	−8.66696			−0.640680
$184$	−6.81628	+	9.79488i	−0.502503	+	0.722088i
$185$	−6.85833			−0.504234
$186$	−1.69145	+	1.08703i	−0.124023	+	0.0797048i
$187$	1.54870	−	10.7715i	0.113252	−	0.787687i
$188$	0.757726	−	1.65919i	0.0552628	−	0.121009i
$189$	11.5037	−	3.37780i	0.836773	−	0.245699i
$190$	−1.16639	−	2.55404i	−0.0846188	−	0.185289i
$191$	−0.0274926	−	0.0317282i	−0.00198930	−	0.00229577i	0.754754	−	0.656008i	$-0.227756\pi$
$191$	−0.0274926	−	0.0317282i	−0.00198930	−	0.00229577i	−0.756743	+	0.653712i	$0.773211\pi$
$192$	0.837667	+	5.82611i	0.0604534	+	0.420463i
$193$	15.7302	+	4.61879i	1.13228	+	0.332468i	0.793604	−	0.608434i	$-0.208202\pi$
$193$	15.7302	+	4.61879i	1.13228	+	0.332468i	0.338678	+	0.940902i	$0.390020\pi$
$194$	−6.28203	+	7.24985i	−0.451024	+	0.520509i
$195$	1.37491	+	0.883600i	0.0984592	+	0.0632759i
$196$	−0.410945	−	0.264098i	−0.0293532	−	0.0188642i
$197$	−15.3171	+	17.6768i	−1.09130	+	1.25942i	−0.127770	+	0.991804i	$0.540782\pi$
$197$	−15.3171	+	17.6768i	−1.09130	+	1.25942i	−0.963525	+	0.267618i	$0.913763\pi$
$198$	−11.2691	−	3.30890i	−0.800859	−	0.235153i
$199$	0.0188178	+	0.130881i	0.00133396	+	0.00927789i	0.990478	−	0.137674i	$-0.0439627\pi$
$199$	0.0188178	+	0.130881i	0.00133396	+	0.00927789i	−0.989144	+	0.146952i	$0.953054\pi$
$200$	−1.62945	−	1.88049i	−0.115220	−	0.132971i
$201$	−2.15571	−	4.72034i	−0.152052	−	0.332947i
$202$	18.8808	−	5.54390i	1.32845	−	0.390068i
$203$	8.57556	−	18.7779i	0.601886	−	1.31795i
$204$	−0.159331	+	1.10817i	−0.0111554	+	0.0775874i
$205$	−5.27560	+	3.39042i	−0.368464	+	0.236797i
$206$	−0.783074			−0.0545594
$207$	−4.88549	−	8.25421i	−0.339565	−	0.573707i
$208$	−7.56510			−0.524546
$209$	−5.80195	+	3.72869i	−0.401329	+	0.257919i
$210$	−0.527646	+	3.66986i	−0.0364111	+	0.253244i
$211$	−10.3073	+	22.5698i	−0.709582	+	1.55377i	0.118370	+	0.992970i	$0.462233\pi$
$211$	−10.3073	+	22.5698i	−0.709582	+	1.55377i	−0.827952	+	0.560799i	$0.810494\pi$
$212$	1.91822	−	0.563241i	0.131744	−	0.0386836i
$213$	1.17625	+	2.57564i	0.0805956	+	0.176480i
$214$	−9.64051	−	11.1257i	−0.659012	−	0.760540i
$215$	1.72084	+	11.9687i	0.117360	+	0.816258i
$216$	−11.9373	−	3.50510i	−0.812228	−	0.238492i
$217$	−2.04194	+	2.35652i	−0.138616	+	0.159971i
$218$	10.5040	+	6.75050i	0.711419	+	0.457201i
$219$	1.76634	+	1.13516i	0.119358	+	0.0767067i
$220$	0.971814	−	1.12153i	0.0655197	−	0.0756137i
$221$	4.49319	+	1.31932i	0.302245	+	0.0887471i
$222$	−1.50916	−	10.4964i	−0.101288	−	0.704473i
$223$	13.2408	+	15.2807i	0.886669	+	1.02327i	0.999560	+	0.0296631i	$0.00944345\pi$
$223$	13.2408	+	15.2807i	0.886669	+	1.02327i	−0.112891	+	0.993607i	$0.536011\pi$
$224$	−2.17208	−	4.75620i	−0.145128	−	0.317787i
$225$	1.91899	−	0.563465i	0.127932	−	0.0375643i
$226$	2.27225	−	4.97553i	0.151148	−	0.330968i
$227$	1.79655	−	12.4953i	0.119241	−	0.829339i	−0.839154	−	0.543894i	$-0.816949\pi$
$227$	1.79655	−	12.4953i	0.119241	−	0.829339i	0.958395	−	0.285445i	$-0.0921415\pi$
$228$	0.596906	−	0.383608i	0.0395310	−	0.0254051i
$229$	17.5666			1.16084			0.580418	−	0.814319i	$-0.302889\pi$
$229$	17.5666			1.16084			0.580418	+	0.814319i	$0.302889\pi$
$230$	7.37367	−	0.784758i	0.486206	−	0.0517454i
$231$	9.10706			0.599200
$232$	−18.0208	+	11.5812i	−1.18312	+	0.760346i
$233$	−0.975427	+	6.78424i	−0.0639023	+	0.444451i	0.932602	+	0.360907i	$0.117533\pi$
$233$	−0.975427	+	6.78424i	−0.0639023	+	0.444451i	−0.996504	+	0.0835435i	$0.973376\pi$
$234$	2.09954	−	4.59736i	0.137251	−	0.300539i
$235$	4.47908	−	1.31518i	0.292183	−	0.0857926i
$236$	1.17835	+	2.58023i	0.0767040	+	0.167958i
$237$	−8.09638	−	9.34373i	−0.525917	−	0.606940i
$238$	1.51185	+	10.5152i	0.0979988	+	0.681597i
$239$	−8.41649	−	2.47130i	−0.544418	−	0.159855i	−0.00205178	−	0.999998i	$-0.500653\pi$
$239$	−8.41649	−	2.47130i	−0.544418	−	0.159855i	−0.542366	+	0.840142i	$0.682471\pi$
$240$	3.03122	−	3.49821i	0.195664	−	0.225809i
$241$	−8.54608	−	5.49223i	−0.550501	−	0.353786i	0.235632	−	0.971842i	$-0.424284\pi$
$241$	−8.54608	−	5.49223i	−0.550501	−	0.353786i	−0.786134	+	0.618057i	$0.787920\pi$
$242$	−4.45447	−	2.86272i	−0.286344	−	0.184022i
$243$	10.4778	−	12.0920i	0.672149	−	0.775702i
$244$	−3.24931	−	0.954085i	−0.208016	−	0.0610790i
$245$	−0.177920	−	1.23746i	−0.0113669	−	0.0790584i
$246$	−6.34980	−	7.32806i	−0.404848	−	0.467220i
$247$	−1.23289	−	2.69966i	−0.0784470	−	0.171775i
$248$	3.10457	−	0.911583i	0.197140	−	0.0578856i
$249$	−5.67269	+	12.4215i	−0.359492	+	0.787178i
$250$	−0.220047	+	1.53046i	−0.0139170	+	0.0967949i
$251$	10.5748	−	6.79599i	0.667473	−	0.428959i	−0.162541	−	0.986702i	$-0.551969\pi$
$251$	10.5748	−	6.79599i	0.667473	−	0.428959i	0.830014	+	0.557743i	$0.188332\pi$
$252$	1.87387			0.118043
$253$	−4.48562	−	17.6534i	−0.282009	−	1.10986i
$254$	−0.471570			−0.0295890
$255$	−2.41042	+	1.54908i	−0.150947	+	0.0970075i
$256$	−1.28696	+	8.95099i	−0.0804348	+	0.559437i
$257$	−13.1799	+	28.8599i	−0.822137	+	1.80023i	−0.279826	+	0.960051i	$0.590277\pi$
$257$	−13.1799	+	28.8599i	−0.822137	+	1.80023i	−0.542311	+	0.840178i	$0.682450\pi$
$258$	−17.9390	+	5.26736i	−1.11683	+	0.327931i
$259$	−6.83168	−	14.9593i	−0.424500	−	0.929525i
$260$	0.418195	+	0.482622i	0.0259353	+	0.0299310i
$261$	−2.45038	−	17.0428i	−0.151675	−	1.05492i
$262$	−32.9729	−	9.68172i	−2.03707	−	0.598139i
$263$	−9.95732	+	11.4914i	−0.613994	+	0.708587i	−0.974555	−	0.224148i	$-0.928040\pi$
$263$	−9.95732	+	11.4914i	−0.613994	+	0.708587i	0.360561	+	0.932736i	$0.382585\pi$
$264$	−7.95008	−	5.10920i	−0.489293	−	0.314450i
$265$	4.30429	+	2.76620i	0.264410	+	0.169926i
$266$	4.40897	−	5.08823i	0.270332	−	0.311979i
$267$	−11.1483	−	3.27345i	−0.682267	−	0.200332i
$268$	−0.288563	−	2.00700i	−0.0176268	−	0.122597i
$269$	−14.8927	−	17.1870i	−0.908022	−	1.04791i	−0.998646	−	0.0520276i	$-0.983432\pi$
$269$	−14.8927	−	17.1870i	−0.908022	−	1.04791i	0.0906241	−	0.995885i	$-0.471114\pi$
$270$	3.21157	+	7.03237i	0.195450	+	0.427976i
$271$	21.6374	−	6.35333i	1.31438	−	0.385937i	0.451919	−	0.892059i	$-0.350740\pi$
$271$	21.6374	−	6.35333i	1.31438	−	0.385937i	0.862462	+	0.506122i	$0.168921\pi$
$272$	5.50956	−	12.0642i	0.334066	−	0.731502i
$273$	−0.557730	+	3.87910i	−0.0337553	+	0.234774i
$274$	−17.2617	+	11.0934i	−1.04282	+	0.670179i
$275$	3.79797			0.229026
$276$	0.461482	+	1.81619i	0.0277779	+	0.109322i
$277$	−2.56712			−0.154244			−0.0771218	−	0.997022i	$-0.524573\pi$
$277$	−2.56712			−0.154244			−0.0771218	+	0.997022i	$0.524573\pi$
$278$	28.7973	−	18.5069i	1.72715	−	1.10997i
$279$	−0.370123	+	2.57426i	−0.0221587	+	0.154117i
$280$	2.47858	−	5.42733i	0.148123	−	0.324345i
$281$	25.8504	−	7.59036i	1.54211	−	0.452803i	0.603376	−	0.797457i	$-0.293822\pi$
$281$	25.8504	−	7.59036i	1.54211	−	0.452803i	0.938730	+	0.344654i	$0.112004\pi$
$282$	2.99844	+	6.56566i	0.178554	+	0.390979i
$283$	1.64025	+	1.89295i	0.0975028	+	0.112524i	0.802404	−	0.596781i	$-0.203554\pi$
$283$	1.64025	+	1.89295i	0.0975028	+	0.112524i	−0.704901	+	0.709306i	$0.749009\pi$
$284$	0.157453	+	1.09511i	0.00934314	+	0.0649830i
$285$	1.74236	+	0.511603i	0.103208	+	0.0303047i
$286$	6.28511	−	7.25340i	0.371646	−	0.428902i
$287$	−12.6502	−	8.12982i	−0.746720	−	0.479888i
$288$	−3.66880	−	2.35780i	−0.216186	−	0.138934i
$289$	5.75635	−	6.64319i	0.338609	−	0.390776i
$290$	12.7721	+	3.75021i	0.750001	+	0.220220i
$291$	−0.882949	−	6.14104i	−0.0517594	−	0.359994i
$292$	0.537253	+	0.620023i	0.0314403	+	0.0362841i
$293$	8.16641	+	17.8819i	0.477087	+	1.04467i	0.983254	+	0.182239i	$0.0583345\pi$
$293$	8.16641	+	17.8819i	0.477087	+	1.04467i	−0.506167	+	0.862435i	$0.668938\pi$
$294$	1.85473	−	0.544599i	0.108170	−	0.0317617i
$295$	−3.01572	+	6.60351i	−0.175582	+	0.384471i
$296$	−2.42863	+	16.8915i	−0.141161	+	0.981799i
$297$	15.9753	−	10.2667i	0.926979	−	0.595733i
$298$	−34.9887			−2.02684
$299$	7.79408	−	0.829500i	0.450743	−	0.0479712i
$300$	−0.390736			−0.0225591
$301$	−24.3918	+	15.6757i	−1.40592	+	0.903530i
$302$	0.440883	−	3.06641i	0.0253700	−	0.176452i
$303$	−5.28682	+	11.5765i	−0.303720	+	0.665054i
$304$	−8.06503	+	2.36811i	−0.462561	+	0.135820i
$305$	−3.60039	−	7.88375i	−0.206158	−	0.451422i
$306$	5.80245	+	6.69638i	0.331704	+	0.382807i
$307$	−0.898392	−	6.24845i	−0.0512739	−	0.356618i	−0.999265	−	0.0383224i	$-0.987799\pi$
$307$	−0.898392	−	6.24845i	−0.0512739	−	0.356618i	0.947991	−	0.318296i	$-0.103110\pi$
$308$	3.41431	+	1.00253i	0.194548	+	0.0571245i
$309$	0.331655	−	0.382750i	0.0188672	−	0.0217739i
$310$	−1.69145	−	1.08703i	−0.0960678	−	0.0617390i
$311$	−19.8840	−	12.7787i	−1.12752	−	0.724612i	−0.162478	−	0.986712i	$-0.551949\pi$
$311$	−19.8840	−	12.7787i	−1.12752	−	0.724612i	−0.965041	+	0.262100i	$0.915585\pi$
$312$	2.66311	−	3.07339i	0.150769	−	0.173997i
$313$	30.0708	+	8.82958i	1.69970	+	0.499078i	0.980632	−	0.195860i	$-0.0627498\pi$
$313$	30.0708	+	8.82958i	1.69970	+	0.499078i	0.719070	+	0.694937i	$0.244568\pi$
$314$	1.41102	+	9.81384i	0.0796283	+	0.553827i
$315$	3.14055	+	3.62439i	0.176950	+	0.204211i
$316$	−2.00681	−	4.39431i	−0.112892	−	0.247199i
$317$	−6.67638	+	1.96036i	−0.374983	+	0.110105i	−0.463793	−	0.885944i	$-0.653512\pi$
$317$	−6.67638	+	1.96036i	−0.374983	+	0.110105i	0.0888101	+	0.996049i	$0.471694\pi$
$318$	−3.28642	+	7.19625i	−0.184293	+	0.403546i
$319$	4.65323	−	32.3639i	0.260531	−	1.81203i
$320$	−4.95163	+	3.18222i	−0.276805	+	0.177892i
$321$	9.52106			0.531414
$322$	9.05672	+	15.3016i	0.504712	+	0.852727i
$323$	5.20310			0.289508
$324$	0.328708	−	0.211248i	0.0182615	−	0.0117360i
$325$	−0.232593	+	1.61772i	−0.0129019	+	0.0897350i
$326$	−4.27892	+	9.36953i	−0.236987	+	0.518930i
$327$	−7.74824	+	2.27509i	−0.428479	+	0.125813i
$328$	6.48217	+	14.1940i	0.357918	+	0.783731i
$329$	7.33032	+	8.45964i	0.404134	+	0.466395i
$330$	0.835732	+	5.81264i	0.0460055	+	0.319976i
$331$	20.4435	+	6.00275i	1.12368	+	0.329941i	0.790219	−	0.612825i	$-0.209967\pi$
$331$	20.4435	+	6.00275i	1.12368	+	0.329941i	0.333457	+	0.942765i	$0.391785\pi$
$332$	−3.49413	+	4.03244i	−0.191765	+	0.221309i
$333$	−11.5392	−	7.41578i	−0.632344	−	0.406383i
$334$	5.43321	+	3.49171i	0.297292	+	0.191058i
$335$	3.39826	−	3.92180i	0.185667	−	0.214271i
$336$	10.6497	+	3.12703i	0.580988	+	0.170594i
$337$	2.73086	+	18.9936i	0.148760	+	1.03465i	0.918254	+	0.395992i	$0.129599\pi$
$337$	2.73086	+	18.9936i	0.148760	+	1.03465i	−0.769494	+	0.638653i	$0.779492\pi$
$338$	−10.4585	−	12.0697i	−0.568865	−	0.656506i
$339$	1.46957	+	3.21791i	0.0798161	+	0.174773i
$340$	−1.07421	+	0.315418i	−0.0582575	+	0.0171059i
$341$	−2.05163	+	4.49245i	−0.111102	+	0.243280i
$342$	0.799175	−	5.55838i	0.0432144	−	0.300563i
$343$	16.6425	−	10.6955i	0.898608	−	0.577501i
$344$	30.0873			1.62220
$345$	−2.73939	+	3.93646i	−0.147484	+	0.211932i
$346$	38.2460			2.05612
$347$	12.3328	−	7.92583i	0.662061	−	0.425481i	−0.165995	−	0.986127i	$-0.553084\pi$
$347$	12.3328	−	7.92583i	0.662061	−	0.425481i	0.828056	+	0.560646i	$0.189447\pi$
$348$	−0.478725	+	3.32961i	−0.0256624	+	0.178486i
$349$	−4.91073	+	10.7530i	−0.262865	+	0.575595i	−0.994337	−	0.106278i	$-0.966107\pi$
$349$	−4.91073	+	10.7530i	−0.262865	+	0.575595i	0.731471	+	0.681872i	$0.238834\pi$
$350$	−3.55742	+	1.04455i	−0.190152	+	0.0558336i
$351$	3.39468	+	7.43331i	0.181195	+	0.396761i
$352$	−5.42335	−	6.25888i	−0.289065	−	0.333599i
$353$	1.38530	+	9.63498i	0.0737321	+	0.512818i	0.992900	+	0.118952i	$0.0379535\pi$
$353$	1.38530	+	9.63498i	0.0737321	+	0.512818i	−0.919168	+	0.393866i	$0.871137\pi$
$354$	−10.7700	−	3.16236i	−0.572420	−	0.168078i
$355$	−1.85425	+	2.13992i	−0.0984133	+	0.113575i
$356$	−3.81925	−	2.45448i	−0.202420	−	0.130087i
$357$	−5.77990	−	3.71452i	−0.305905	−	0.196593i
$358$	−4.85290	+	5.60054i	−0.256484	+	0.295998i
$359$	20.2194	+	5.93694i	1.06714	+	0.313340i	0.767722	−	0.640783i	$-0.221390\pi$
$359$	20.2194	+	5.93694i	1.06714	+	0.313340i	0.299416	+	0.954123i	$0.403208\pi$
$360$	−0.708228	−	4.92584i	−0.0373269	−	0.259614i
$361$	10.2829	+	11.8671i	0.541206	+	0.624585i
$362$	1.78326	+	3.90479i	0.0937258	+	0.205231i
$363$	3.28583	−	0.964808i	0.172462	−	0.0506393i
$364$	−0.636120	+	1.39291i	−0.0333417	+	0.0730082i
$365$	−0.298811	+	2.07828i	−0.0156405	+	0.108782i
$366$	11.2735	−	7.24505i	0.589277	−	0.378705i
$367$	−2.10006			−0.109622			−0.0548112	−	0.998497i	$-0.517456\pi$
$367$	−2.10006			−0.109622			−0.0548112	+	0.998497i	$0.517456\pi$
$368$	0.816112	−	22.1839i	0.0425428	−	1.15642i
$369$	−12.5422			−0.652923
$370$	8.92095	−	5.73314i	0.463778	−	0.298052i
$371$	−1.74603	+	12.1439i	−0.0906494	+	0.630480i
$372$	0.211072	−	0.462184i	0.0109436	−	0.0239631i
$373$	−20.0752	+	5.89462i	−1.03946	+	0.305212i	−0.756550	−	0.653935i	$-0.773117\pi$
$373$	−20.0752	+	5.89462i	−1.03946	+	0.305212i	−0.282906	+	0.959148i	$0.591299\pi$
$374$	6.98981	+	15.3056i	0.361435	+	0.791431i
$375$	−0.654861	−	0.755750i	−0.0338169	−	0.0390267i
$376$	−1.65307	−	11.4973i	−0.0852504	−	0.592929i
$377$	13.5002	+	3.96403i	0.695298	+	0.204158i
$378$	−12.1398	+	14.0101i	−0.624404	+	0.720601i
$379$	−3.16651	−	2.03499i	−0.162652	−	0.104530i	0.456782	−	0.889578i	$-0.349002\pi$
$379$	−3.16651	−	2.03499i	−0.162652	−	0.104530i	−0.619435	+	0.785048i	$0.712638\pi$
$380$	0.596906	+	0.383608i	0.0306206	+	0.0196787i
$381$	0.199724	−	0.230493i	0.0102322	−	0.0118085i
$382$	0.0622838	+	0.0182882i	0.00318672	+	0.000935704i
$383$	−2.94122	−	20.4566i	−0.150289	−	1.04528i	−0.915735	−	0.401783i	$-0.868390\pi$
$383$	−2.94122	−	20.4566i	−0.150289	−	1.04528i	0.765446	−	0.643501i	$-0.222519\pi$
$384$	−8.81578	−	10.1740i	−0.449879	−	0.519188i
$385$	3.78321	+	8.28407i	0.192810	+	0.422195i
$386$	−24.3220	+	7.14158i	−1.23796	+	0.363497i
$387$	−10.0462	+	21.9981i	−0.510677	+	1.11823i
$388$	0.344999	−	2.39952i	0.0175147	−	0.121817i
$389$	−31.6110	+	20.3152i	−1.60274	+	1.03002i	−0.636882	+	0.770962i	$0.719776\pi$
$389$	−31.6110	+	20.3152i	−1.60274	+	1.03002i	−0.965862	+	0.259059i	$0.916588\pi$
$390$	−2.52704			−0.127962
$391$	−4.35350	+	13.0335i	−0.220166	+	0.659133i
$392$	−3.11076			−0.157117
$393$	18.6972	−	12.0160i	0.943149	−	0.606125i
$394$	5.14686	−	35.7972i	0.259295	−	1.80344i
$395$	5.13599	−	11.2463i	0.258420	−	0.565860i
$396$	2.84778	−	0.836183i	0.143106	−	0.0420198i
$397$	1.32511	+	2.90158i	0.0665052	+	0.145626i	0.939966	−	0.341269i	$-0.110857\pi$
$397$	1.32511	+	2.90158i	0.0665052	+	0.145626i	−0.873460	+	0.486895i	$0.838129\pi$
$398$	−0.133886	−	0.154512i	−0.00671107	−	0.00774499i
$399$	0.619688	+	4.31002i	0.0310232	+	0.215771i
$400$	4.44130	+	1.30408i	0.222065	+	0.0652041i
$401$	−4.53998	+	5.23942i	−0.226716	+	0.261644i	−0.857699	−	0.514153i	$-0.828106\pi$
$401$	−4.53998	+	5.23942i	−0.226716	+	0.261644i	0.630983	+	0.775797i	$0.282652\pi$
$402$	6.74994	+	4.33792i	0.336656	+	0.216356i
$403$	−1.78789	−	1.14900i	−0.0890609	−	0.0572360i
$404$	−3.25645	+	3.75814i	−0.162014	+	0.186975i
$405$	0.959493	+	0.281733i	0.0476776	+	0.0139994i
$406$	4.54251	+	31.5939i	0.225441	+	1.56798i
$407$	−17.0576	−	19.6855i	−0.845515	−	0.975776i
$408$	2.96170	+	6.48523i	0.146626	+	0.321067i
$409$	−10.6400	+	3.12417i	−0.526112	+	0.154480i	−0.533994	−	0.845488i	$-0.679309\pi$
$409$	−10.6400	+	3.12417i	−0.526112	+	0.154480i	0.00788151	+	0.999969i	$0.497491\pi$
$410$	4.02803	−	8.82016i	0.198930	−	0.435597i
$411$	1.88861	−	13.1356i	0.0931582	−	0.647929i
$412$	0.166474	−	0.106986i	0.00820159	−	0.00527084i
$413$	−17.4075			−0.856566
$414$	13.2548	+	6.65266i	0.651438	+	0.326960i
$415$	−13.6555			−0.670321
$416$	2.99806	−	1.92674i	0.146992	−	0.0944662i
$417$	−3.15071	+	21.9137i	−0.154291	+	1.07312i
$418$	4.42991	−	9.70015i	0.216674	−	0.474450i
$419$	−16.8802	+	4.95649i	−0.824654	+	0.242140i	−0.666719	−	0.745309i	$-0.732302\pi$
$419$	−16.8802	+	4.95649i	−0.824654	+	0.242140i	−0.157935	+	0.987450i	$0.550484\pi$
$420$	−0.389217	−	0.852267i	−0.0189919	−	0.0415864i
$421$	−10.4546	−	12.0652i	−0.509526	−	0.588024i	0.441451	−	0.897285i	$-0.354464\pi$
$421$	−10.4546	−	12.0652i	−0.509526	−	0.588024i	−0.950977	+	0.309261i	$0.899918\pi$
$422$	−5.45981	−	37.9738i	−0.265779	−	1.84854i
$423$	8.95816	+	2.63035i	0.435561	+	0.127892i
$424$	8.33713	−	9.62156i	0.404887	−	0.467264i
$425$	−2.41042	−	1.54908i	−0.116923	−	0.0751417i
$426$	−3.68308	−	2.36697i	−0.178446	−	0.114680i
$427$	13.6095	−	15.7062i	0.658611	−	0.760078i
$428$	3.56952	+	1.04811i	0.172539	+	0.0506621i
$429$	0.883381	+	6.14405i	0.0426500	+	0.296638i
$430$	−12.2435	−	14.1297i	−0.590433	−	0.681396i
$431$	1.62218	+	3.55209i	0.0781379	+	0.171098i	0.944669	−	0.328025i	$-0.106383\pi$
$431$	1.62218	+	3.55209i	0.0781379	+	0.171098i	−0.866531	+	0.499123i	$0.833656\pi$
$432$	22.2065	−	6.52041i	1.06841	−	0.313714i
$433$	16.5608	−	36.2631i	0.795861	−	1.74269i	0.136805	−	0.990598i	$-0.456316\pi$
$433$	16.5608	−	36.2631i	0.795861	−	1.74269i	0.659055	−	0.752094i	$-0.270956\pi$
$434$	0.686134	−	4.77217i	0.0329355	−	0.229071i
$435$	−7.24236	+	4.65438i	−0.347245	+	0.223161i
$436$	−3.15533			−0.151113
$437$	8.04948	−	3.32410i	0.385059	−	0.159013i
$438$	−3.24648			−0.155123
$439$	−23.3284	+	14.9922i	−1.11340	+	0.715541i	−0.962032	−	0.272936i	$-0.912005\pi$
$439$	−23.3284	+	14.9922i	−1.11340	+	0.715541i	−0.151371	+	0.988477i	$0.548369\pi$
$440$	1.34491	−	9.35408i	0.0641163	−	0.445938i
$441$	1.03869	−	2.27441i	0.0494614	−	0.108305i
$442$	−6.94737	+	2.03993i	−0.330453	+	0.0970297i
$443$	−12.3128	−	26.9613i	−0.585000	−	1.28097i	−0.938417	−	0.345505i	$-0.887708\pi$
$443$	−12.3128	−	26.9613i	−0.585000	−	1.28097i	0.353417	−	0.935466i	$-0.385020\pi$
$444$	1.75489	+	2.02525i	0.0832834	+	0.0961142i
$445$	−1.65356	−	11.5007i	−0.0783860	−	0.545187i
$446$	−29.9966	−	8.80781i	−1.42038	−	0.417062i
$447$	14.8187	−	17.1017i	0.700901	−	0.808883i
$448$	−11.8734	−	7.63057i	−0.560966	−	0.360511i
$449$	13.0579	+	8.39181i	0.616241	+	0.396034i	0.811193	−	0.584779i	$-0.198819\pi$
$449$	13.0579	+	8.39181i	0.616241	+	0.396034i	−0.194952	+	0.980813i	$0.562455\pi$
$450$	−2.02509	+	2.33708i	−0.0954637	+	0.110171i
$451$	−22.8527	−	6.71017i	−1.07609	−	0.315969i
$452$	0.196717	+	1.36819i	0.00925277	+	0.0643545i
$453$	1.31207	+	1.51421i	0.0616463	+	0.0711436i
$454$	8.10842	+	17.7550i	0.380547	+	0.833281i
$455$	−3.76024	+	1.10411i	−0.176283	+	0.0517613i
$456$	1.87703	−	4.11012i	0.0879000	−	0.192474i
$457$	−0.0952955	+	0.662795i	−0.00445774	+	0.0310042i	−0.991929	−	0.126795i	$-0.959531\pi$
$457$	−0.0952955	+	0.662795i	−0.00445774	+	0.0310042i	0.987471	+	0.157800i	$0.0504400\pi$
$458$	−22.8497	+	14.6846i	−1.06770	+	0.686168i
$459$	−14.3264			−0.668698
$460$	−1.46036	+	1.17425i	−0.0680895	+	0.0547497i
$461$	18.1826			0.846846			0.423423	−	0.905932i	$-0.360828\pi$
$461$	18.1826			0.846846			0.423423	+	0.905932i	$0.360828\pi$
$462$	−11.8460	+	7.61295i	−0.551125	+	0.354186i
$463$	2.00963	−	13.9773i	0.0933955	−	0.649580i	−0.888320	−	0.459225i	$-0.848127\pi$
$463$	2.00963	−	13.9773i	0.0933955	−	0.649580i	0.981715	−	0.190355i	$-0.0609638\pi$
$464$	16.5540	−	36.2482i	0.768501	−	1.68278i
$465$	1.24769	−	0.366356i	0.0578604	−	0.0169893i
$466$	−4.40243	−	9.63998i	−0.203939	−	0.446563i
$467$	−5.38591	−	6.21568i	−0.249230	−	0.287627i	0.617325	−	0.786708i	$-0.288216\pi$
$467$	−5.38591	−	6.21568i	−0.249230	−	0.287627i	−0.866555	+	0.499081i	$0.833671\pi$
$468$	0.181765	+	1.26420i	0.00840208	+	0.0584378i
$469$	11.9392	+	3.50567i	0.551302	+	0.161877i
$470$	−4.72674	+	5.45495i	−0.218028	+	0.251618i
$471$	−5.39440	−	3.46677i	−0.248561	−	0.159740i
$472$	15.1960	+	9.76587i	0.699452	+	0.449511i
$473$	−30.0739	+	34.7072i	−1.38280	+	1.59584i
$474$	18.3421	+	5.38573i	0.842482	+	0.247375i
$475$	0.258432	+	1.79743i	0.0118577	+	0.0824719i
$476$	−1.75803	−	2.02887i	−0.0805790	−	0.0929931i
$477$	4.25096	+	9.30830i	0.194638	+	0.426198i
$478$	13.0136	−	3.82113i	0.595227	−	0.174775i
$479$	−0.394315	+	0.863430i	−0.0180167	+	0.0394511i	−0.918426	−	0.395592i	$-0.870540\pi$
$479$	−0.394315	+	0.863430i	−0.0180167	+	0.0394511i	0.900410	+	0.435043i	$0.143267\pi$
$480$	−0.310326	+	2.15836i	−0.0141644	+	0.0985153i
$481$	9.42957	−	6.06002i	0.429951	−	0.276313i
$482$	15.7075			0.715455
$483$	−11.3149	−	2.05396i	−0.514846	−	0.0934584i
$484$	1.33809			0.0608225
$485$	5.21930	−	3.35424i	0.236996	−	0.152308i
$486$	−3.52076	+	24.4874i	−0.159705	+	1.11077i
$487$	−5.19851	+	11.3832i	−0.235567	+	0.515820i	−0.990087	−	0.140458i	$-0.955143\pi$
$487$	−5.19851	+	11.3832i	−0.235567	+	0.515820i	0.754520	+	0.656277i	$0.227870\pi$
$488$	−20.6920	+	6.07571i	−0.936682	+	0.275035i
$489$	−2.76738	−	6.05971i	−0.125145	−	0.274030i
$490$	1.26587	+	1.46089i	0.0571861	+	0.0659963i
$491$	−4.19660	−	29.1880i	−0.189390	−	1.31724i	−0.833592	−	0.552381i	$-0.813720\pi$
$491$	−4.19660	−	29.1880i	−0.189390	−	1.31724i	0.644202	−	0.764855i	$-0.277190\pi$
$492$	2.35109	+	0.690343i	0.105995	+	0.0311231i
$493$	−16.1536	+	18.6422i	−0.727520	+	0.839603i
$494$	3.86043	+	2.48095i	0.173689	+	0.111623i
$495$	6.39011	+	4.10667i	0.287214	+	0.184581i
$496$	−3.94170	+	4.54896i	−0.176987	+	0.204254i
$497$	−6.51460	−	1.91286i	−0.292220	−	0.0858034i
$498$	−3.00485	−	20.8992i	−0.134650	−	0.936515i
$499$	8.18657	+	9.44781i	0.366481	+	0.422942i	0.908801	−	0.417230i	$-0.136999\pi$
$499$	8.18657	+	9.44781i	0.366481	+	0.422942i	−0.542319	+	0.840172i	$0.682454\pi$
$500$	−0.162317	−	0.355426i	−0.00725905	−	0.0158951i
$501$	−4.00780	+	1.17680i	−0.179055	+	0.0525754i
$502$	−8.07405	+	17.6797i	−0.360363	+	0.789084i
$503$	0.273285	−	1.90074i	0.0121852	−	0.0847497i	−0.982821	−	0.184559i	$-0.940914\pi$
$503$	0.273285	−	1.90074i	0.0121852	−	0.0847497i	0.995007	+	0.0998095i	$0.0318233\pi$
$504$	10.0387	−	6.45147i	0.447159	−	0.287372i
$505$	−12.7266			−0.566327
$506$	20.5919	+	19.2129i	0.915420	+	0.854119i
$507$	10.3289			0.458722
$508$	0.100251	−	0.0644277i	0.00444794	−	0.00285852i
$509$	−5.15255	+	35.8368i	−0.228383	+	1.58844i	0.476540	+	0.879153i	$0.341891\pi$
$509$	−5.15255	+	35.8368i	−0.228383	+	1.58844i	−0.704923	+	0.709284i	$0.749018\pi$
$510$	1.84041	−	4.02993i	0.0814947	−	0.178448i
$511$	−4.83076	+	1.41844i	−0.213700	+	0.0627481i
$512$	5.37622	+	11.7723i	0.237598	+	0.520266i
$513$	5.94586	+	6.86189i	0.262516	+	0.302960i
$514$	−6.98143	−	48.5569i	−0.307938	−	2.14175i
$515$	0.485936	+	0.142684i	0.0214129	+	0.00628739i
$516$	3.09401	−	3.57068i	0.136206	−	0.157190i
$517$	14.9151	+	9.58533i	0.655963	+	0.421562i
$518$	21.3913	+	13.7474i	0.939881	+	0.604025i
$519$	−16.1983	+	18.6938i	−0.711027	+	0.820568i
$520$	3.90195	+	1.14572i	0.171112	+	0.0502430i
$521$	1.23847	+	8.61372i	0.0542582	+	0.377374i	0.998800	+	0.0489818i	$0.0155976\pi$
$521$	1.23847	+	8.61372i	0.0542582	+	0.377374i	−0.944542	+	0.328392i	$0.893493\pi$
$522$	17.4340	+	20.1199i	0.763067	+	0.880626i
$523$	4.68026	+	10.2483i	0.204654	+	0.448129i	0.983931	−	0.178551i	$-0.0571408\pi$
$523$	4.68026	+	10.2483i	0.204654	+	0.448129i	−0.779277	+	0.626680i	$0.784414\pi$
$524$	8.33249	−	2.44664i	0.364006	−	0.106882i
$525$	0.996114	−	2.18119i	0.0434740	−	0.0951948i
$526$	3.34587	−	23.2711i	0.145887	−	1.01467i
$527$	3.13444	−	2.01438i	0.136538	−	0.0877478i
$528$	17.5800			0.765072
$529$	1.59161	+	22.9449i	0.0692006	+	0.997603i
$530$	−7.91116			−0.343639
$531$	−12.2142	+	7.84960i	−0.530052	+	0.340644i
$532$	−0.242134	+	1.68408i	−0.0104978	+	0.0730141i
$533$	4.25769	−	9.32304i	0.184421	−	0.403826i
$534$	17.2376	−	5.06141i	0.745943	−	0.219029i
$535$	3.95519	+	8.66066i	0.170998	+	0.374433i
$536$	−8.45570	−	9.75839i	−0.365230	−	0.421498i
$537$	−0.682082	−	4.74399i	−0.0294340	−	0.204718i
$538$	33.7389	+	9.90663i	1.45459	+	0.427105i
$539$	3.10938	−	3.58842i	0.133931	−	0.154564i
$540$	−1.64354	−	1.05624i	−0.0707266	−	0.0454532i
$541$	−15.6463	−	10.0553i	−0.672688	−	0.432311i	0.159205	−	0.987245i	$-0.449107\pi$
$541$	−15.6463	−	10.0553i	−0.672688	−	0.432311i	−0.831894	+	0.554935i	$0.812743\pi$
$542$	−22.8338	+	26.3517i	−0.980797	+	1.13190i
$543$	−2.66384	−	0.782173i	−0.114316	−	0.0335662i
$544$	0.889168	+	6.18430i	0.0381228	+	0.265150i
$545$	−5.28823	−	6.10294i	−0.226523	−	0.261421i
$546$	−2.51722	−	5.51195i	−0.107727	−	0.235890i
$547$	9.61453	−	2.82308i	0.411088	−	0.120706i	−0.0696483	−	0.997572i	$-0.522188\pi$
$547$	9.61453	−	2.82308i	0.411088	−	0.120706i	0.480736	+	0.876865i	$0.340370\pi$
$548$	2.15406	−	4.71672i	0.0920167	−	0.201488i
$549$	2.46688	−	17.1575i	0.105284	−	0.732264i
$550$	−4.94019	+	3.17487i	−0.210650	+	0.135377i
$551$	15.6332			0.665999
$552$	8.72513	+	8.14086i	0.371366	+	0.346498i
$553$	29.6462			1.26068
$554$	3.33918	−	2.14596i	0.141868	−	0.0911731i
$555$	−0.976042	+	6.78852i	−0.0414307	+	0.288157i
$556$	−3.59355	+	7.86878i	−0.152401	+	0.333711i
$557$	15.7921	−	4.63697i	0.669131	−	0.196475i	0.0705153	−	0.997511i	$-0.477536\pi$
$557$	15.7921	−	4.63697i	0.669131	−	0.196475i	0.598616	+	0.801036i	$0.295717\pi$
$558$	−1.67049	−	3.65786i	−0.0707175	−	0.154850i
$559$	−12.9415	−	14.9353i	−0.547368	−	0.631697i
$560$	1.57959	+	10.9863i	0.0667500	+	0.464256i
$561$	−10.4414	−	3.06588i	−0.440837	−	0.129441i
$562$	−27.2797	+	31.4825i	−1.15073	+	1.32801i
$563$	5.62436	+	3.61456i	0.237039	+	0.152335i	0.653768	−	0.756695i	$-0.273187\pi$
$563$	5.62436	+	3.61456i	0.237039	+	0.152335i	−0.416729	+	0.909031i	$0.636824\pi$
$564$	−1.53446	−	0.986140i	−0.0646126	−	0.0415240i
$565$	−2.31663	+	2.67354i	−0.0974614	+	0.112476i
$566$	−3.71594	−	1.09110i	−0.156193	−	0.0458623i
$567$	0.341254	+	2.37347i	0.0143313	+	0.0996764i
$568$	4.61382	+	5.32464i	0.193592	+	0.223417i
$569$	−9.29438	−	20.3518i	−0.389641	−	0.853194i	−0.998216	−	0.0596982i	$-0.980986\pi$
$569$	−9.29438	−	20.3518i	−0.389641	−	0.853194i	0.608576	−	0.793496i	$-0.291741\pi$
$570$	−2.69404	+	0.791041i	−0.112841	+	0.0331330i
$571$	−16.5325	+	36.2012i	−0.691864	+	1.51497i	0.157701	+	0.987487i	$0.449592\pi$
$571$	−16.5325	+	36.2012i	−0.691864	+	1.51497i	−0.849565	+	0.527484i	$0.823135\pi$
$572$	−0.345168	+	2.40070i	−0.0144322	+	0.100378i
$573$	−0.0353179	+	0.0226974i	−0.00147542	+	0.000948198i
$574$	23.2508			0.970469
$575$	−4.71872	−	0.856574i	−0.196784	−	0.0357216i
$576$	−11.7720			−0.490501
$577$	31.3403	−	20.1412i	1.30472	−	0.838490i	0.310999	−	0.950410i	$-0.399337\pi$
$577$	31.3403	−	20.1412i	1.30472	−	0.838490i	0.993717	+	0.111920i	$0.0357002\pi$
$578$	−1.93426	+	13.4531i	−0.0804545	+	0.559574i
$579$	6.81042	−	14.9127i	0.283031	−	0.619752i
$580$	−3.22759	+	0.947705i	−0.134018	+	0.0393513i
$581$	−13.6024	−	29.7851i	−0.564323	−	1.23570i
$582$	6.28203	+	7.24985i	0.260399	+	0.300516i
$583$	2.76551	+	19.2346i	0.114536	+	0.796615i
$584$	5.01282	+	1.47190i	0.207432	+	0.0609075i
$585$	−2.14055	+	2.47033i	−0.0885009	+	0.102135i
$586$	−25.5706	−	16.4333i	−1.05631	−	0.678852i
$587$	−18.4513	−	11.8579i	−0.761566	−	0.489429i	0.101304	−	0.994856i	$-0.467699\pi$
$587$	−18.4513	−	11.8579i	−0.761566	−	0.489429i	−0.862869	+	0.505427i	$0.831335\pi$
$588$	−0.319894	+	0.369177i	−0.0131922	+	0.0152246i
$589$	−2.26571	−	0.665272i	−0.0933569	−	0.0274120i
$590$	−1.59744	−	11.1104i	−0.0657656	−	0.457410i
$591$	15.3171	+	17.6768i	0.630060	+	0.727128i
$592$	−13.1877	−	28.8770i	−0.542011	−	1.18684i
$593$	1.99058	−	0.584486i	0.0817431	−	0.0240020i	−0.240605	−	0.970623i	$-0.577346\pi$
$593$	1.99058	−	0.584486i	0.0817431	−	0.0240020i	0.322348	+	0.946621i	$0.395528\pi$
$594$	−12.1975	+	26.7087i	−0.500468	+	1.09587i
$595$	0.977785	−	6.80065i	0.0400853	−	0.278799i
$596$	7.43826	−	4.78028i	0.304683	−	0.195808i
$597$	0.132227			0.00541168
$598$	−9.44471	+	7.59435i	−0.386223	+	0.310556i
$599$	9.26542			0.378575			0.189287	−	0.981922i	$-0.439382\pi$
$599$	9.26542			0.378575			0.189287	+	0.981922i	$0.439382\pi$
$600$	−2.09325	+	1.34525i	−0.0854564	+	0.0549195i
$601$	4.28647	−	29.8130i	0.174849	−	1.21610i	−0.693615	−	0.720346i	$-0.743983\pi$
$601$	4.28647	−	29.8130i	0.174849	−	1.21610i	0.868463	−	0.495753i	$-0.165108\pi$
$602$	18.6237	−	40.7801i	0.759043	−	1.66207i
$603$	9.95816	−	2.92398i	0.405528	−	0.119074i
$604$	0.325216	+	0.712124i	0.0132329	+	0.0289759i
$605$	2.24260	+	2.58810i	0.0911748	+	0.105221i
$606$	−2.80046	−	19.4776i	−0.113761	−	0.791223i
$607$	27.8553	+	8.17906i	1.13061	+	0.331978i	0.792949	−	0.609289i	$-0.208545\pi$
$607$	27.8553	+	8.17906i	1.13061	+	0.331978i	0.337664	+	0.941267i	$0.390363\pi$
$608$	2.59306	−	2.99255i	0.105162	−	0.121364i
$609$	−17.3663	−	11.1606i	−0.703718	−	0.452252i
$610$	11.2735	+	7.24505i	0.456452	+	0.293344i
$611$	−4.99623	+	5.76596i	−0.202126	+	0.233266i
$612$	−2.14843	−	0.630836i	−0.0868451	−	0.0255000i
$613$	−4.07218	−	28.3226i	−0.164474	−	1.14394i	−0.890071	−	0.455821i	$-0.849346\pi$
$613$	−4.07218	−	28.3226i	−0.164474	−	1.14394i	0.725597	−	0.688119i	$-0.241563\pi$
$614$	6.39191	+	7.37665i	0.257956	+	0.297697i
$615$	2.60512	+	5.70441i	0.105048	+	0.230024i
$616$	21.7427	−	6.38423i	0.876038	−	0.257228i
$617$	3.36621	−	7.37096i	0.135518	−	0.296744i	−0.829691	−	0.558223i	$-0.811483\pi$
$617$	3.36621	−	7.37096i	0.135518	−	0.296744i	0.965209	+	0.261480i	$0.0842105\pi$
$618$	−0.111443	+	0.775104i	−0.00448290	+	0.0311792i
$619$	25.1807	−	16.1826i	1.01210	−	0.650435i	0.0741618	−	0.997246i	$-0.476372\pi$
$619$	25.1807	−	16.1826i	1.01210	−	0.650435i	0.937935	+	0.346811i	$0.112736\pi$
$620$	0.508100			0.0204058
$621$	−22.1637	+	9.15267i	−0.889398	+	0.367284i
$622$	36.5462			1.46537
$623$	23.4381	−	15.0628i	0.939028	−	0.603476i
$624$	−1.07663	+	7.48810i	−0.0430996	+	0.299764i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−46.4955	+	13.6523i	−1.85833	+	0.545656i
$627$	2.86503	+	6.27354i	0.114418	+	0.250541i
$628$	−1.64077	−	1.89355i	−0.0654740	−	0.0755610i
$629$	2.79663	+	19.4510i	0.111509	+	0.775562i
$630$	−7.11483	−	2.08910i	−0.283462	−	0.0832318i
$631$	−5.37867	+	6.20731i	−0.214121	+	0.247109i	−0.852642	−	0.522495i	$-0.825001\pi$
$631$	−5.37867	+	6.20731i	−0.214121	+	0.247109i	0.638521	+	0.769605i	$0.279547\pi$
$632$	−25.8799	−	16.6320i	−1.02945	−	0.661585i
$633$	20.8732	+	13.4144i	0.829634	+	0.533174i
$634$	7.04553	−	8.13098i	0.279814	−	0.322922i
$635$	0.292632	+	0.0859247i	0.0116128	+	0.00340982i
$636$	−0.284517	−	1.97886i	−0.0112818	−	0.0784668i
$637$	1.33804	+	1.54418i	0.0530151	+	0.0611827i
$638$	21.0016	+	45.9871i	0.831461	+	1.82065i
$639$	−5.43364	+	1.59546i	−0.214951	+	0.0631154i
$640$	5.59235	−	12.2455i	0.221057	−	0.484047i
$641$	−1.44375	+	10.0415i	−0.0570248	+	0.396616i	0.941240	+	0.337737i	$0.109662\pi$
$641$	−1.44375	+	10.0415i	−0.0570248	+	0.396616i	−0.998265	+	0.0588787i	$0.981247\pi$
$642$	−12.3845	+	7.95902i	−0.488777	+	0.314118i
$643$	−39.0668			−1.54065			−0.770323	−	0.637654i	$-0.779905\pi$
$643$	−39.0668			−1.54065			−0.770323	+	0.637654i	$0.779905\pi$
$644$	−4.01594	−	2.01562i	−0.158250	−	0.0794267i
$645$	12.0918			0.476113
$646$	−6.76792	+	4.34948i	−0.266280	+	0.171128i
$647$	−0.578678	+	4.02479i	−0.0227502	+	0.158231i	−0.998030	−	0.0627440i	$-0.980015\pi$
$647$	−0.578678	+	4.02479i	−0.0227502	+	0.158231i	0.975279	+	0.220975i	$0.0709239\pi$
$648$	1.03365	−	2.26339i	0.0406058	−	0.0889143i
$649$	−26.4546	+	7.76778i	−1.03844	+	0.304912i
$650$	−1.04977	−	2.29868i	−0.0411754	−	0.0901616i
$651$	2.04194	+	2.35652i	0.0800298	+	0.0923593i
$652$	−0.370441	−	2.57647i	−0.0145076	−	0.100903i
$653$	28.5978	+	8.39708i	1.11912	+	0.328603i	0.788423	−	0.615134i	$-0.210898\pi$
$653$	28.5978	+	8.39708i	1.11912	+	0.328603i	0.330697	+	0.943737i	$0.392716\pi$
$654$	8.17666	−	9.43637i	0.319733	−	0.368991i
$655$	18.6972	+	12.0160i	0.730560	+	0.469503i
$656$	−24.4197	−	15.6936i	−0.953429	−	0.612731i
$657$	−2.74996	+	3.17362i	−0.107286	+	0.123815i
$658$	−16.6066	−	4.87615i	−0.647394	−	0.190092i
$659$	1.11615	+	7.76299i	0.0434790	+	0.302403i	0.999944	+	0.0105569i	$0.00336043\pi$
$659$	1.11615	+	7.76299i	0.0434790	+	0.302403i	−0.956465	+	0.291846i	$0.905730\pi$
$660$	−0.971814	−	1.12153i	−0.0378278	−	0.0436556i
$661$	−17.9335	−	39.2688i	−0.697531	−	1.52738i	−0.842939	−	0.538009i	$-0.819177\pi$
$661$	−17.9335	−	39.2688i	−0.697531	−	1.52738i	0.145408	−	0.989372i	$-0.453551\pi$
$662$	−31.6097	+	9.28145i	−1.22855	+	0.360734i
$663$	1.94534	−	4.25970i	0.0755507	−	0.165433i
$664$	−4.83560	+	33.6323i	−0.187658	+	1.30519i
$665$	−3.66311	+	2.35414i	−0.142049	+	0.0912895i
$666$	21.2087			0.821820
$667$	−13.0805	+	39.1605i	−0.506480	+	1.51630i
$668$	−1.63210			−0.0631479
$669$	17.0095	−	10.9314i	0.657626	−	0.422630i
$670$	−1.14189	+	7.94200i	−0.0441149	+	0.306826i
$671$	13.6742	−	29.9422i	0.527885	−	1.15591i
$672$	−5.01691	+	1.47310i	−0.193531	+	0.0568260i
$673$	2.12649	+	4.65636i	0.0819701	+	0.179489i	0.946179	−	0.323644i	$-0.104908\pi$
$673$	2.12649	+	4.65636i	0.0819701	+	0.179489i	−0.864209	+	0.503133i	$0.832181\pi$
$674$	−19.4296	−	22.4230i	−0.748401	−	0.863701i
$675$	−0.711574	−	4.94911i	−0.0273885	−	0.190491i
$676$	3.87238	+	1.13703i	0.148938	+	0.0437320i
$677$	18.3071	−	21.1275i	0.703598	−	0.811995i	−0.285636	−	0.958338i	$-0.592205\pi$
$677$	18.3071	−	21.1275i	0.703598	−	0.811995i	0.989234	+	0.146343i	$0.0467503\pi$
$678$	−4.60151	−	2.95721i	−0.176720	−	0.113571i
$679$	12.5152	+	8.04306i	0.480291	+	0.308664i
$680$	−4.66884	+	5.38812i	−0.179042	+	0.206625i
$681$	−12.1124	−	3.55652i	−0.464148	−	0.136286i
$682$	−1.08676	−	7.55858i	−0.0416142	−	0.289433i
$683$	−9.95826	−	11.4924i	−0.381042	−	0.439746i	0.532537	−	0.846407i	$-0.321239\pi$
$683$	−9.95826	−	11.4924i	−0.381042	−	0.439746i	−0.913579	+	0.406660i	$0.866693\pi$
$684$	0.589510	+	1.29085i	0.0225405	+	0.0493567i
$685$	12.7331	−	3.73877i	0.486506	−	0.142851i
$686$	−12.7069	+	27.8242i	−0.485151	+	1.06233i
$687$	2.49999	−	17.3878i	0.0953807	−	0.663387i
$688$	−47.0853	+	30.2599i	−1.79511	+	1.15365i
$689$	−8.36221			−0.318575
$690$	0.272613	−	7.41030i	0.0103782	−	0.282105i
$691$	11.0471			0.420251			0.210126	−	0.977674i	$-0.432613\pi$
$691$	11.0471			0.420251			0.210126	+	0.977674i	$0.432613\pi$
$692$	−8.13075	+	5.22531i	−0.309085	+	0.198637i
$693$	−2.59214	+	18.0287i	−0.0984672	+	0.684855i
$694$	−9.41637	+	20.6190i	−0.357441	+	0.782686i
$695$	−21.2423	+	6.23729i	−0.805765	+	0.236594i
$696$	8.89874	+	19.4855i	0.337306	+	0.738597i
$697$	11.7669	+	13.5797i	0.445701	+	0.514367i
$698$	−2.60124	−	18.0920i	−0.0984583	−	0.684792i
$699$	6.57637	+	1.93100i	0.248741	+	0.0730370i
$700$	0.613563	−	0.708089i	0.0231905	−	0.0267632i
$701$	31.4181	+	20.1912i	1.18664	+	0.762610i	0.976596	−	0.215082i	$-0.0690018\pi$
$701$	31.4181	+	20.1912i	1.18664	+	0.762610i	0.210048	+	0.977691i	$0.432638\pi$
$702$	−10.6294	−	6.83111i	−0.401181	−	0.257824i
$703$	8.15574	−	9.41222i	0.307599	−	0.354989i
$704$	−21.4494	−	6.29810i	−0.808403	−	0.237369i
$705$	−0.664350	−	4.62066i	−0.0250209	−	0.174024i
$706$	−9.85618	−	11.3746i	−0.370942	−	0.428090i
$707$	−12.6772	−	27.7591i	−0.476774	−	1.04399i
$708$	2.72166	−	0.799151i	0.102286	−	0.0300339i
$709$	8.09489	−	17.7253i	0.304010	−	0.665689i	−0.694544	−	0.719450i	$-0.744394\pi$
$709$	8.09489	−	17.7253i	0.304010	−	0.665689i	0.998554	+	0.0537614i	$0.0171210\pi$
$710$	0.623067	−	4.33353i	0.0233833	−	0.162634i
$711$	20.8017	−	13.3684i	0.780125	−	0.501356i
$712$	−28.9109			−1.08348
$713$	3.56222	−	5.11885i	0.133406	−	0.191702i
$714$	10.6233			0.397567
$715$	−5.22185	+	3.35588i	−0.195286	+	0.125503i
$716$	0.266514	−	1.85364i	0.00996009	−	0.0692739i
$717$	−3.64394	+	7.97912i	−0.136086	+	0.297986i
$718$	−31.2632	+	9.17971i	−1.16673	+	0.342584i
$719$	0.529568	+	1.15959i	0.0197496	+	0.0432455i	0.919250	−	0.393675i	$-0.128796\pi$
$719$	0.529568	+	1.15959i	0.0197496	+	0.0432455i	−0.899500	+	0.436920i	$0.856069\pi$
$720$	6.06243	+	6.99642i	0.225934	+	0.260741i
$721$	0.172828	+	1.20205i	0.00643645	+	0.0447665i
$722$	−23.2957	−	6.84022i	−0.866974	−	0.254567i
$723$	−6.65256	+	7.67747i	−0.247412	+	0.285528i
$724$	−0.912589	−	0.586486i	−0.0339161	−	0.0217966i
$725$	−7.24236	−	4.65438i	−0.268974	−	0.172859i
$726$	−3.46752	+	4.00173i	−0.128692	+	0.148518i
$727$	27.5119	+	8.07821i	1.02036	+	0.299604i	0.748785	−	0.662813i	$-0.230638\pi$
$727$	27.5119	+	8.07821i	1.02036	+	0.299604i	0.271574	+	0.962418i	$0.412456\pi$
$728$	1.38777	+	9.65214i	0.0514341	+	0.357732i
$729$	−8.51319	−	9.82474i	−0.315303	−	0.363879i
$730$	−1.34864	−	2.95310i	−0.0499152	−	0.109299i
$731$	33.2428	−	9.76098i	1.22953	−	0.361023i
$732$	−1.40680	+	3.08046i	−0.0519968	+	0.113857i
$733$	1.11204	−	7.73438i	0.0410740	−	0.285676i	−0.958924	−	0.283663i	$-0.908450\pi$
$733$	1.11204	−	7.73438i	0.0410740	−	0.285676i	0.999998	−	0.00201276i	$-0.000640680\pi$
$734$	2.73165	−	1.75552i	0.100827	−	0.0647976i
$735$	−1.25018			−0.0461137
$736$	5.32655	+	8.99938i	0.196339	+	0.331722i
$737$	19.7087			0.725980
$738$	16.3143	−	10.4845i	0.600537	−	0.385942i
$739$	−1.47513	+	10.2597i	−0.0542634	+	0.377410i	0.944535	+	0.328410i	$0.106513\pi$
$739$	−1.47513	+	10.2597i	−0.0542634	+	0.377410i	−0.998799	+	0.0490005i	$0.984396\pi$
$740$	−1.11323	+	2.43763i	−0.0409230	+	0.0896089i
$741$	−2.84764	+	0.836141i	−0.104611	+	0.0307164i
$742$	−7.88042	−	17.2557i	−0.289299	−	0.633477i
$743$	6.39542	+	7.38071i	0.234625	+	0.270772i	0.860837	−	0.508881i	$-0.169941\pi$
$743$	6.39542	+	7.38071i	0.234625	+	0.270772i	−0.626211	+	0.779653i	$0.715395\pi$
$744$	−0.460479	−	3.20270i	−0.0168820	−	0.117417i
$745$	21.7122	+	6.37527i	0.795473	+	0.233572i
$746$	21.1853	−	24.4491i	0.775647	−	0.895145i
$747$	−22.9754	−	14.7654i	−0.840627	−	0.540238i
$748$	−3.57707	−	2.29884i	−0.130791	−	0.0840540i
$749$	−14.9507	+	17.2540i	−0.546286	+	0.630448i
$750$	1.48357	+	0.435615i	0.0541723	+	0.0159064i
$751$	1.23883	+	8.61624i	0.0452055	+	0.314411i	0.999861	+	0.0166971i	$0.00531510\pi$
$751$	1.23883	+	8.61624i	0.0452055	+	0.314411i	−0.954655	+	0.297714i	$0.903776\pi$
$752$	14.1502	+	16.3303i	0.516006	+	0.595503i
$753$	−5.22187	−	11.4343i	−0.190295	−	0.416689i
$754$	−20.8741	+	6.12918i	−0.760189	+	0.223212i
$755$	−0.832318	+	1.82252i	−0.0302912	+	0.0663284i
$756$	0.666699	−	4.63700i	0.0242476	−	0.168646i
$757$	−4.16337	+	2.67564i	−0.151320	+	0.0972476i	−0.614110	−	0.789220i	$-0.710485\pi$
$757$	−4.16337	+	2.67564i	−0.151320	+	0.0972476i	0.462790	+	0.886468i	$0.346849\pi$
$758$	5.81995			0.211390
$759$	−18.1121	+	1.92762i	−0.657428	+	0.0699681i
$760$	4.51845			0.163901
$761$	24.5583	−	15.7826i	0.890236	−	0.572120i	−0.0136435	−	0.999907i	$-0.504343\pi$
$761$	24.5583	−	15.7826i	0.890236	−	0.572120i	0.903880	+	0.427787i	$0.140707\pi$
$762$	−0.0671115	+	0.466770i	−0.00243119	+	0.0169093i
$763$	8.04397	−	17.6138i	0.291211	−	0.637664i
$764$	−0.0157395	+	0.00462155i	−0.000569437	+	0.000167202i
$765$	−2.38056	−	5.21269i	−0.0860692	−	0.188465i
$766$	20.9263	+	24.1502i	0.756096	+	0.872582i
$767$	−1.68852	−	11.7439i	−0.0609689	−	0.424048i
$768$	8.67672	+	2.54772i	0.313094	+	0.0919328i
$769$	−14.2646	+	16.4622i	−0.514395	+	0.593644i	−0.952219	−	0.305417i	$-0.901204\pi$
$769$	−14.2646	+	16.4622i	−0.514395	+	0.593644i	0.437823	+	0.899061i	$0.355750\pi$
$770$	−11.8460	−	7.61295i	−0.426899	−	0.274352i
$771$	26.6904	+	17.1529i	0.961232	+	0.617746i
$772$	4.19492	−	4.84119i	0.150978	−	0.174238i
$773$	−10.8333	−	3.18094i	−0.389647	−	0.114411i	0.0810404	−	0.996711i	$-0.474176\pi$
$773$	−10.8333	−	3.18094i	−0.389647	−	0.114411i	−0.470687	+	0.882300i	$0.655994\pi$
$774$	−5.32152	−	37.0120i	−0.191278	−	1.33037i
$775$	0.851560	+	0.982752i	0.0305889	+	0.0353015i
$776$	−6.41299	−	14.0425i	−0.230213	−	0.504096i
$777$	−15.7793	+	4.63321i	−0.566078	+	0.166216i
$778$	24.1357	−	52.8498i	0.865307	−	1.89476i
$779$	1.62066	−	11.2719i	0.0580661	−	0.403858i
$780$	0.537225	−	0.345254i	0.0192358	−	0.0123621i
$781$	−10.7540			−0.384808
$782$	−5.23243	−	20.5926i	−0.187111	−	0.736388i
$783$	−43.0450			−1.53830
$784$	4.86821	−	3.12861i	0.173865	−	0.111736i
$785$	0.912571	−	6.34707i	0.0325711	−	0.226537i
$786$	−14.2757	+	31.2595i	−0.509198	+	1.11499i
$787$	−15.4652	+	4.54099i	−0.551275	+	0.161869i	−0.545494	−	0.838114i	$-0.683658\pi$
$787$	−15.4652	+	4.54099i	−0.551275	+	0.161869i	−0.00578022	+	0.999983i	$0.501840\pi$
$788$	3.79657	+	8.31333i	0.135247	+	0.296150i
$789$	9.95732	+	11.4914i	0.354490	+	0.409103i
$790$	2.72056	+	18.9219i	0.0967931	+	0.673211i
$791$	−8.13911	−	2.38986i	−0.289393	−	0.0849736i
$792$	12.3772	−	14.2841i	0.439806	−	0.507563i
$793$	11.9163	+	7.65813i	0.423159	+	0.271948i
$794$	−4.14917	−	2.66651i	−0.147249	−	0.0946309i
$795$	3.35061	−	3.86681i	0.118834	−	0.137142i
$796$	0.0495728	+	0.0145559i	0.00175706	+	0.000515920i
$797$	2.76646	+	19.2411i	0.0979929	+	0.681556i	0.978306	+	0.207163i	$0.0664232\pi$
$797$	2.76646	+	19.2411i	0.0979929	+	0.681556i	−0.880313	+	0.474393i	$0.842668\pi$
$798$	−4.40897	−	5.08823i	−0.156076	−	0.180121i
$799$	−5.55643	−	12.1669i	−0.196572	−	0.430433i
$800$	−2.09223	+	0.614334i	−0.0739715	+	0.0217200i
$801$	9.65341	−	21.1380i	0.341086	−	0.746875i
$802$	1.52553	−	10.6103i	0.0538684	−	0.374663i
$803$	−6.70849	+	4.31128i	−0.236737	+	0.152142i
$804$	−2.02764			−0.0715092
$805$	−2.83203	−	11.1456i	−0.0998161	−	0.392832i
$806$	3.28608			0.115747
$807$	−19.1316	+	12.2951i	−0.673463	+	0.432808i
$808$	−4.50667	+	31.3446i	−0.158544	+	1.10270i
$809$	−5.60048	+	12.2633i	−0.196902	+	0.431156i	−0.982169	−	0.188002i	$-0.939799\pi$
$809$	−5.60048	+	12.2633i	−0.196902	+	0.431156i	0.785266	+	0.619158i	$0.212526\pi$
$810$	−1.48357	+	0.435615i	−0.0521273	+	0.0153060i
$811$	20.5360	+	44.9675i	0.721115	+	1.57902i	0.812335	+	0.583191i	$0.198196\pi$
$811$	20.5360	+	44.9675i	0.721115	+	1.57902i	−0.0912201	+	0.995831i	$0.529077\pi$
$812$	−5.28217	−	6.09594i	−0.185368	−	0.213926i
$813$	−3.20933	−	22.3214i	−0.112556	−	0.782845i
$814$	38.6436	+	11.3468i	1.35446	+	0.397704i
$815$	4.36250	−	5.03459i	0.152812	−	0.176354i
$816$	−11.1574	−	7.17040i	−0.390586	−	0.251014i
$817$	−18.4719	−	11.8712i	−0.646252	−	0.415321i
$818$	11.2283	−	12.9581i	0.392587	−	0.453070i
$819$	−7.52048	−	2.20821i	−0.262787	−	0.0771612i
$820$	0.348721	+	2.42541i	0.0121779	+	0.0846989i
$821$	12.1749	+	14.0506i	0.424907	+	0.490369i	0.927325	−	0.374256i	$-0.122102\pi$
$821$	12.1749	+	14.0506i	0.424907	+	0.490369i	−0.502419	+	0.864624i	$0.667556\pi$
$822$	8.52393	+	18.6648i	0.297306	+	0.651010i
$823$	−25.8876	+	7.60129i	−0.902386	+	0.264964i	−0.699833	−	0.714307i	$-0.746742\pi$
$823$	−25.8876	+	7.60129i	−0.902386	+	0.264964i	−0.202553	+	0.979271i	$0.564924\pi$
$824$	0.523495	−	1.14629i	0.0182368	−	0.0399330i
$825$	0.540507	−	3.75931i	0.0188180	−	0.130882i
$826$	22.6427	−	14.5516i	0.787841	−	0.506315i
$827$	18.8339			0.654919			0.327460	−	0.944865i	$-0.393807\pi$
$827$	18.8339			0.654919			0.327460	+	0.944865i	$0.393807\pi$
$828$	−3.72676	+	0.396627i	−0.129514	+	0.0137838i
$829$	37.2107			1.29238			0.646191	−	0.763176i	$-0.276361\pi$
$829$	37.2107			1.29238			0.646191	+	0.763176i	$0.276361\pi$
$830$	17.7623	−	11.4151i	0.616539	−	0.396225i
$831$	−0.365340	+	2.54099i	−0.0126735	+	0.0881461i
$832$	3.99623	−	8.75052i	0.138544	−	0.303370i
$833$	−3.43702	+	1.00920i	−0.119086	+	0.0349667i
$834$	−14.2202	−	31.1380i	−0.492407	−	1.07822i
$835$	−2.73535	−	3.15676i	−0.0946607	−	0.109244i
$836$	0.383513	+	2.66739i	0.0132641	+	0.0922537i
$837$	6.23847	+	1.83178i	0.215633	+	0.0633156i
$838$	17.8136	−	20.5580i	0.615361	−	0.710164i
$839$	−15.7729	−	10.1366i	−0.544541	−	0.349955i	0.239272	−	0.970953i	$-0.423091\pi$
$839$	−15.7729	−	10.1366i	−0.544541	−	0.349955i	−0.783812	+	0.620998i	$0.786728\pi$
$840$	−5.01935	−	3.22574i	−0.173184	−	0.111299i
$841$	−29.5441	+	34.0957i	−1.01876	+	1.17571i
$842$	23.6846	+	6.95442i	0.816225	+	0.239665i
$843$	−3.83421	−	26.6675i	−0.132057	−	0.918477i
$844$	6.34883	+	7.32694i	0.218536	+	0.252204i
$845$	4.29077	+	9.39548i	0.147607	+	0.323214i
$846$	−13.8511	+	4.06705i	−0.476211	+	0.139828i
$847$	−3.41124	+	7.46958i	−0.117212	+	0.256658i
$848$	−3.37049	+	23.4423i	−0.115743	+	0.805011i
$849$	2.10711	−	1.35416i	0.0723160	−	0.0464747i
$850$	4.43029			0.151958
$851$	16.7532	+	28.3050i	0.574291	+	0.970284i
$852$	1.10637			0.0379037
$853$	−16.9808	+	10.9129i	−0.581411	+	0.373650i	−0.798041	−	0.602604i	$-0.794130\pi$
$853$	−16.9808	+	10.9129i	−0.581411	+	0.373650i	0.216630	+	0.976254i	$0.430494\pi$
$854$	−4.57309	+	31.8066i	−0.156488	+	1.08840i
$855$	−1.50872	+	3.30363i	−0.0515971	+	0.112982i
$856$	22.7311	−	6.67445i	0.776933	−	0.228128i
$857$	−1.99977	−	4.37889i	−0.0683110	−	0.149580i	0.872397	−	0.488799i	$-0.162565\pi$
$857$	−1.99977	−	4.37889i	−0.0683110	−	0.149580i	−0.940708	+	0.339218i	$0.889837\pi$
$858$	−6.28511	−	7.25340i	−0.214570	−	0.247627i
$859$	1.88417	+	13.1047i	0.0642871	+	0.447126i	0.996387	+	0.0849258i	$0.0270653\pi$
$859$	1.88417	+	13.1047i	0.0642871	+	0.447126i	−0.932100	+	0.362200i	$0.882026\pi$
$860$	4.53330	+	1.33110i	0.154584	+	0.0453900i
$861$	−9.84739	+	11.3645i	−0.335598	+	0.387301i
$862$	−5.07938	−	3.26432i	−0.173004	−	0.111183i
$863$	5.77633	+	3.71222i	0.196629	+	0.126366i	0.635250	−	0.772306i	$-0.280897\pi$
$863$	5.77633	+	3.71222i	0.196629	+	0.126366i	−0.438622	+	0.898672i	$0.644533\pi$
$864$	−7.13980	+	8.23977i	−0.242901	+	0.280323i
$865$	−23.7335	−	6.96879i	−0.806964	−	0.236946i
$866$	8.77233	+	61.0129i	0.298096	+	2.07330i
$867$	−5.75635	−	6.64319i	−0.195496	−	0.225614i
$868$	0.506125	+	1.10826i	0.0171790	+	0.0376168i
$869$	45.0542	−	13.2291i	1.52836	−	0.448767i
$870$	5.52969	−	12.1083i	0.187474	−	0.410511i
$871$	−1.20699	+	8.39481i	−0.0408973	+	0.284447i
$872$	−16.9037	+	10.8633i	−0.572431	+	0.367879i
$873$	12.4084			0.419960
$874$	−7.69159	+	11.0527i	−0.260172	+	0.373863i
$875$	2.39788			0.0810631
$876$	0.690171	−	0.443546i	0.0233187	−	0.0149860i
$877$	0.342014	−	2.37876i	0.0115490	−	0.0803251i	−0.983232	−	0.182360i	$-0.941626\pi$
$877$	0.342014	−	2.37876i	0.0115490	−	0.0803251i	0.994781	+	0.102035i	$0.0325354\pi$
$878$	17.8117	−	39.0022i	0.601116	−	1.31626i
$879$	18.8621	−	5.53842i	0.636204	−	0.186806i
$880$	7.30300	+	15.9913i	0.246184	+	0.539068i
$881$	2.23506	+	2.57940i	0.0753012	+	0.0869022i	0.792150	−	0.610326i	$-0.208962\pi$
$881$	2.23506	+	2.57940i	0.0753012	+	0.0869022i	−0.716849	+	0.697229i	$0.754416\pi$
$882$	0.550199	+	3.82672i	0.0185262	+	0.128852i
$883$	2.78129	+	0.816661i	0.0935979	+	0.0274828i	0.328196	−	0.944610i	$-0.393559\pi$
$883$	2.78129	+	0.816661i	0.0935979	+	0.0274828i	−0.234598	+	0.972092i	$0.575377\pi$
$884$	1.19824	−	1.38285i	0.0403013	−	0.0465102i
$885$	6.10711	+	3.92480i	0.205288	+	0.131931i
$886$	38.5539	+	24.7771i	1.29524	+	0.832402i
$887$	2.67598	−	3.08825i	0.0898506	−	0.103693i	−0.709044	−	0.705164i	$-0.750873\pi$
$887$	2.67598	−	3.08825i	0.0898506	−	0.103693i	0.798894	+	0.601471i	$0.205419\pi$
$888$	16.3739	+	4.80782i	0.549474	+	0.161340i
$889$	0.104078	+	0.723877i	0.00349066	+	0.0242780i
$890$	11.7648	+	13.5773i	0.394356	+	0.455111i
$891$	1.57773	+	3.45475i	0.0528560	+	0.115739i
$892$	7.58036	−	2.22579i	0.253809	−	0.0745251i
$893$	−3.52148	+	7.71096i	−0.117842	+	0.258037i
$894$	−4.97941	+	34.6325i	−0.166536	+	1.15828i
$895$	4.03193	−	2.59117i	0.134773	−	0.0866131i
$896$	32.2804			1.07841
$897$	0.288156	−	7.83280i	0.00962126	−	0.261530i
$898$	−24.0001			−0.800893
$899$	9.41773	−	6.05241i	0.314099	−	0.201859i
$900$	0.111215	−	0.773517i	0.00370716	−	0.0257839i
$901$	6.09008	−	13.3354i	0.202890	−	0.444267i
$902$	35.3349	−	10.3753i	1.17652	−	0.345458i
$903$	12.0448	+	26.3744i	0.400825	+	0.877685i
$904$	5.76435	+	6.65241i	0.191719	+	0.221256i
$905$	−0.395108	−	2.74804i	−0.0131338	−	0.0913478i
$906$	−2.97245	−	0.872790i	−0.0987531	−	0.0289965i
$907$	0.749866	−	0.865391i	0.0248989	−	0.0287348i	−0.743164	−	0.669110i	$-0.766676\pi$
$907$	0.749866	−	0.865391i	0.0248989	−	0.0287348i	0.768062	+	0.640375i	$0.221221\pi$
$908$	−4.14952	−	2.66674i	−0.137707	−	0.0884987i
$909$	−21.4126	−	13.7610i	−0.710211	−	0.456425i
$910$	3.96815	−	4.57949i	0.131543	−	0.151809i
$911$	11.6713	+	3.42700i	0.386687	+	0.113542i	0.469297	−	0.883040i	$-0.344507\pi$
$911$	11.6713	+	3.42700i	0.386687	+	0.113542i	−0.0826098	+	0.996582i	$0.526326\pi$
$912$	1.19623	+	8.31995i	0.0396111	+	0.275501i
$913$	−33.9631	−	39.1955i	−1.12401	−	1.29718i
$914$	−0.430101	−	0.941790i	−0.0142265	−	0.0311516i
$915$	−8.31589	+	2.44177i	−0.274915	+	0.0807223i
$916$	2.85137	−	6.24363i	0.0942119	−	0.206295i
$917$	−7.58450	+	52.7514i	−0.250462	+	1.74200i
$918$	18.6350	−	11.9760i	0.615046	−	0.395266i
$919$	−44.9964			−1.48429			−0.742147	−	0.670237i	$-0.766192\pi$
$919$	−44.9964			−1.48429			−0.742147	+	0.670237i	$0.766192\pi$
$920$	−3.78064	+	11.3185i	−0.124644	+	0.373160i
$921$	−6.31271			−0.208011
$922$	−23.6509	+	15.1995i	−0.778901	+	0.500569i
$923$	0.658591	−	4.58060i	0.0216778	−	0.150772i
$924$	1.47823	−	3.23688i	0.0486303	−	0.106486i
$925$	−6.58052	+	1.93221i	−0.216366	+	0.0635308i
$926$	9.07015	+	19.8608i	0.298063	+	0.652668i
$927$	0.663309	+	0.765500i	0.0217859	+	0.0251423i
$928$	2.67160	+	18.5814i	0.0876994	+	0.609963i
$929$	−48.6600	−	14.2879i	−1.59648	−	0.468770i	−0.641918	−	0.766773i	$-0.721861\pi$
$929$	−48.6600	−	14.2879i	−1.59648	−	0.468770i	−0.954565	+	0.298003i	$0.903679\pi$
$930$	−1.31668	+	1.51953i	−0.0431757	+	0.0498274i
$931$	1.90984	+	1.22738i	0.0625924	+	0.0402257i
$932$	2.25296	+	1.44789i	0.0737983	+	0.0474273i
$933$	−15.4784	+	17.8630i	−0.506740	+	0.584809i
$934$	12.2016	+	3.58272i	0.399250	+	0.117230i
$935$	−1.54870	−	10.7715i	−0.0506480	−	0.352264i
$936$	5.32622	+	6.14678i	0.174093	+	0.200914i
$937$	−12.8876	−	28.2200i	−0.421020	−	0.921906i	−0.994699	−	0.102826i	$-0.967212\pi$
$937$	−12.8876	−	28.2200i	−0.421020	−	0.921906i	0.573679	−	0.819080i	$-0.305516\pi$
$938$	−18.4604	+	5.42047i	−0.602754	+	0.176985i
$939$	13.0192	−	28.5081i	0.424867	−	0.930328i
$940$	0.259585	−	1.80545i	0.00846674	−	0.0588874i
$941$	−3.61091	+	2.32059i	−0.117712	+	0.0756491i	−0.598172	−	0.801368i	$-0.704106\pi$
$941$	−3.61091	+	2.32059i	−0.117712	+	0.0756491i	0.480460	+	0.877017i	$0.340470\pi$
$942$	9.91476			0.323040
$943$	26.8796	+	13.4910i	0.875320	+	0.439328i
$944$	−33.6029			−1.09368
$945$	10.0861	−	6.48195i	0.328101	−	0.210858i
$946$	10.1055	−	70.2852i	0.328558	−	2.28517i
$947$	−17.0788	+	37.3974i	−0.554988	+	1.21525i	0.399426	+	0.916765i	$0.369209\pi$
$947$	−17.0788	+	37.3974i	−0.554988	+	1.21525i	−0.954413	+	0.298488i	$0.903518\pi$
$948$	−4.63518	+	1.36101i	−0.150544	+	0.0442036i
$949$	−1.42553	−	3.12147i	−0.0462746	−	0.101327i
$950$	−1.83870	−	2.12197i	−0.0596553	−	0.0688459i
$951$	0.990260	+	6.88741i	0.0321114	+	0.223340i
$952$	−16.4032	−	4.81641i	−0.531631	−	0.156101i
$953$	5.56361	−	6.42075i	0.180223	−	0.207989i	−0.658449	−	0.752626i	$-0.728787\pi$
$953$	5.56361	−	6.42075i	0.180223	−	0.207989i	0.838672	+	0.544637i	$0.183333\pi$
$954$	−13.3106	−	8.55420i	−0.430946	−	0.276952i
$955$	−0.0353179	−	0.0226974i	−0.00114286	−	0.000734471i
$956$	−2.24451	+	2.59030i	−0.0725926	+	0.0837763i
$957$	−31.3723	−	9.21173i	−1.01412	−	0.297773i
$958$	−0.208871	−	1.45273i	−0.00674830	−	0.0469355i
$959$	20.8386	+	24.0490i	0.672912	+	0.776582i
$960$	2.44514	+	5.35411i	0.0789165	+	0.172803i
$961$	28.1218	−	8.25731i	0.907156	−	0.266365i
$962$	−7.19968	+	15.7651i	−0.232127	+	0.508287i
$963$	−2.70998	+	18.8483i	−0.0873277	+	0.607378i
$964$	−3.33926	+	2.14601i	−0.107550	+	0.0691183i
$965$	16.3942			0.527749
$966$	16.4348	−	6.78689i	0.528781	−	0.218365i
$967$	−56.7552			−1.82513			−0.912563	−	0.408937i	$-0.865900\pi$
$967$	−56.7552			−1.82513			−0.912563	+	0.408937i	$0.865900\pi$
$968$	7.16843	−	4.60687i	0.230402	−	0.148070i
$969$	0.740479	−	5.15014i	0.0237876	−	0.165446i
$970$	−3.98505	+	8.72603i	−0.127952	+	0.280176i
$971$	1.07211	−	0.314801i	0.0344057	−	0.0101024i	−0.264484	−	0.964390i	$-0.585202\pi$
$971$	1.07211	−	0.314801i	0.0344057	−	0.0101024i	0.298890	+	0.954288i	$0.403384\pi$
$972$	−2.59708	−	5.68681i	−0.0833013	−	0.182404i
$973$	−34.7644	−	40.1203i	−1.11450	−	1.28620i
$974$	−2.75368	−	19.1522i	−0.0882335	−	0.613677i
$975$	1.56815	+	0.460451i	0.0502211	+	0.0147462i
$976$	26.2715	−	30.3189i	0.840929	−	0.970483i
$977$	1.88221	+	1.20962i	0.0602172	+	0.0386992i	0.570403	−	0.821365i	$-0.306787\pi$
$977$	1.88221	+	1.20962i	0.0602172	+	0.0386992i	−0.510186	+	0.860064i	$0.670423\pi$
$978$	8.66520	+	5.56879i	0.277083	+	0.178070i
$979$	28.8981	−	33.3501i	0.923586	−	1.06587i
$980$	−0.468704	−	0.137624i	−0.0149722	−	0.00439623i
$981$	−2.29848	−	15.9863i	−0.0733849	−	0.510403i
$982$	29.8581	+	34.4581i	0.952810	+	1.09960i
$983$	7.45879	+	16.3325i	0.237898	+	0.520925i	0.990494	−	0.137559i	$-0.0439255\pi$
$983$	7.45879	+	16.3325i	0.237898	+	0.520925i	−0.752595	+	0.658483i	$0.771198\pi$
$984$	14.9720	−	4.39618i	0.477290	−	0.140145i
$985$	−9.71647	+	21.2761i	−0.309593	+	0.677913i
$986$	5.42795	−	37.7522i	0.172861	−	1.20227i
$987$	9.41674	−	6.05177i	0.299738	−	0.192630i
$988$	−1.15965			−0.0368933
$989$	45.1925	−	36.3386i	1.43704	−	1.15550i
$990$	−11.7448			−0.373275
$991$	−46.3210	+	29.7687i	−1.47144	+	0.945635i	−0.473542	+	0.880771i	$0.657025\pi$
$991$	−46.3210	+	29.7687i	−1.47144	+	0.945635i	−0.997894	+	0.0648634i	$0.979339\pi$
$992$	0.403537	−	2.80666i	0.0128123	−	0.0891117i
$993$	8.85106	−	19.3811i	0.280880	−	0.615041i
$994$	10.0729	−	2.95766i	0.319492	−	0.0938114i
$995$	0.0549289	+	0.120278i	0.00174136	+	0.00381306i
$996$	3.49413	+	4.03244i	0.110716	+	0.127773i
$997$	−7.94653	−	55.2693i	−0.251669	−	1.75040i	−0.588192	−	0.808721i	$-0.700160\pi$
$997$	−7.94653	−	55.2693i	−0.251669	−	1.75040i	0.336523	−	0.941675i	$-0.390749\pi$
$998$	−18.5465	−	5.44573i	−0.587078	−	0.172382i
$999$	−22.4563	+	25.9159i	−0.710484	+	0.819943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.a.81.1	yes	10
5.2	odd	4		575.2.p.a.449.1		20
5.3	odd	4		575.2.p.a.449.2		20
5.4	even	2		575.2.k.a.426.1		10
23.2	even	11	inner	115.2.g.a.71.1	✓	10
23.5	odd	22		2645.2.a.o.1.2		5
23.18	even	11		2645.2.a.n.1.2		5
115.2	odd	44		575.2.p.a.324.2		20
115.48	odd	44		575.2.p.a.324.1		20
115.94	even	22		575.2.k.a.301.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.71.1	✓	10	23.2	even	11	inner
115.2.g.a.81.1	yes	10	1.1	even	1	trivial
575.2.k.a.301.1		10	115.94	even	22
575.2.k.a.426.1		10	5.4	even	2
575.2.p.a.324.1		20	115.48	odd	44
575.2.p.a.324.2		20	115.2	odd	44
575.2.p.a.449.1		20	5.2	odd	4
575.2.p.a.449.2		20	5.3	odd	4
2645.2.a.n.1.2		5	23.18	even	11
2645.2.a.o.1.2		5	23.5	odd	22

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30075 + 0.835939i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.162317 - 0.355426i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.642315 + 1.40647i) q^{6} +(1.57028 + 1.81219i) q^{7} +(-0.354114 - 2.46292i) q^{8} +(1.91899 + 0.563465i) q^{9} +O(q^{10})\)	\(q+(-1.30075 + 0.835939i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.162317 - 0.355426i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.642315 + 1.40647i) q^{6} +(1.57028 + 1.81219i) q^{7} +(-0.354114 - 2.46292i) q^{8} +(1.91899 + 0.563465i) q^{9} +(-1.01255 + 1.16854i) q^{10} +(3.19505 + 2.05334i) q^{11} +(-0.328708 - 0.211248i) q^{12} +(-1.07028 + 1.23516i) q^{13} +(-3.55742 - 1.04455i) q^{14} +(-0.142315 - 0.989821i) q^{15} +(3.03122 + 3.49821i) q^{16} +(-1.19028 - 2.60635i) q^{17} +(-2.96714 + 0.871230i) q^{18} +(-0.754359 + 1.65182i) q^{19} +(0.0556075 - 0.386758i) q^{20} +(2.01722 - 1.29639i) q^{21} -5.87242 q^{22} +(-3.50654 - 3.27173i) q^{23} -2.48825 q^{24} +(0.841254 - 0.540641i) q^{25} +(0.359636 - 2.50132i) q^{26} +(2.07708 - 4.54816i) q^{27} +(0.898983 - 0.263965i) q^{28} +(-3.57631 - 7.83103i) q^{29} +(1.01255 + 1.16854i) q^{30} +(0.185062 + 1.28713i) q^{31} +(-2.09223 - 0.614334i) q^{32} +(2.48714 - 2.87031i) q^{33} +(3.72700 + 2.39520i) q^{34} +(2.01722 + 1.29639i) q^{35} +(0.511755 - 0.590596i) q^{36} +(-6.58052 - 1.93221i) q^{37} +(-0.399587 - 2.77919i) q^{38} +(1.07028 + 1.23516i) q^{39} +(-1.03365 - 2.26339i) q^{40} +(-6.01710 + 1.76678i) q^{41} +(-1.54019 + 3.37255i) q^{42} +(-1.72084 + 11.9687i) q^{43} +(1.24842 - 0.802311i) q^{44} +2.00000 q^{45} +(7.29608 + 1.32443i) q^{46} +4.66817 q^{47} +(3.89399 - 2.50252i) q^{48} +(0.177920 - 1.23746i) q^{49} +(-0.642315 + 1.40647i) q^{50} +(-2.74921 + 0.807241i) q^{51} +(0.265284 + 0.580892i) q^{52} +(3.35061 + 3.86681i) q^{53} +(1.10024 + 7.65231i) q^{54} +(3.64412 + 1.07001i) q^{55} +(3.90723 - 4.50919i) q^{56} +(1.52765 + 0.981759i) q^{57} +(11.1981 + 7.19661i) q^{58} +(-4.75399 + 5.48639i) q^{59} +(-0.374908 - 0.110083i) q^{60} +(-1.23344 - 8.57875i) q^{61} +(-1.31668 - 1.51953i) q^{62} +(1.99223 + 4.36237i) q^{63} +(-5.64759 + 1.65828i) q^{64} +(-0.678936 + 1.48666i) q^{65} +(-0.835732 + 5.81264i) q^{66} +(4.36550 - 2.80554i) q^{67} -1.11956 q^{68} +(-3.73746 + 3.00523i) q^{69} -3.70760 q^{70} +(-2.38202 + 1.53083i) q^{71} +(0.708228 - 4.92584i) q^{72} +(-0.872226 + 1.90991i) q^{73} +(10.1748 - 2.98759i) q^{74} +(-0.415415 - 0.909632i) q^{75} +(0.464652 + 0.536237i) q^{76} +(1.29607 + 9.01436i) q^{77} +(-2.42468 - 0.711950i) q^{78} +(8.09638 - 9.34373i) q^{79} +(3.89399 + 2.50252i) q^{80} +(0.841254 + 0.540641i) q^{81} +(6.34980 - 7.32806i) q^{82} +(-13.1023 - 3.84719i) q^{83} +(-0.133340 - 0.927399i) q^{84} +(-1.87636 - 2.16543i) q^{85} +(-7.76672 - 17.0068i) q^{86} +(-8.26028 + 2.42544i) q^{87} +(3.92579 - 8.59627i) q^{88} +(1.65356 - 11.5007i) q^{89} +(-2.60149 + 1.67188i) q^{90} -3.91899 q^{91} +(-1.73203 + 0.715255i) q^{92} +1.30037 q^{93} +(-6.07211 + 3.90231i) q^{94} +(-0.258432 + 1.79743i) q^{95} +(-0.905836 + 1.98350i) q^{96} +(5.95288 - 1.74792i) q^{97} +(0.803012 + 1.75835i) q^{98} +(4.97428 + 5.74062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9	\( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 + q^3 - q^4 + q^5 + 6 * q^6 + 5 * q^7 - 16 * q^8 + 2 * q^9 - 5 * q^10 + 8 * q^11 + q^12 - 3 * q^14 - q^15 + 5 * q^16 - 23 * q^17 - 10 * q^18 - 13 * q^19 + q^20 + 6 * q^21 + 4 * q^22 - 21 * q^23 - 6 * q^24 - q^25 + 11 * q^26 - 5 * q^27 - 6 * q^28 + 2 * q^29 + 5 * q^30 - 20 * q^31 - 15 * q^32 + 3 * q^33 + 16 * q^34 + 6 * q^35 + 24 * q^36 + 13 * q^37 + 21 * q^38 - 6 * q^40 - 5 * q^41 + 3 * q^42 + 15 * q^43 + 19 * q^44 + 20 * q^45 - 16 * q^46 - 52 * q^47 + 6 * q^48 + 4 * q^49 - 6 * q^50 - 10 * q^51 + 22 * q^52 + 6 * q^53 - 30 * q^54 + 3 * q^55 + 3 * q^56 + 2 * q^57 + 45 * q^58 + 5 * q^59 + 10 * q^60 - 3 * q^61 - 54 * q^62 - 10 * q^63 - 34 * q^64 - 4 * q^66 + 20 * q^67 + 32 * q^68 - q^69 - 8 * q^70 - 22 * q^71 + 32 * q^72 + 43 * q^73 + q^74 + q^75 - 2 * q^76 + 4 * q^77 + 11 * q^78 + 51 * q^79 + 6 * q^80 - q^81 + 58 * q^82 - 17 * q^83 + 6 * q^84 + q^85 - 9 * q^86 - 2 * q^87 + 7 * q^88 + 57 * q^89 + 10 * q^90 - 22 * q^91 - 43 * q^92 + 20 * q^93 - 81 * q^94 - 9 * q^95 - 7 * q^96 + 52 * q^97 + 24 * q^98 + 6 * q^99

Introduction

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