LMFDB - Embedded newform 155.2.x.a.117.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(3,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 2]))

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

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

chi := DirichletCharacter("155.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.x (of order $60$, degree $16$, 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:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			117.2
Character	$\chi$	$=$	155.117
Dual form			155.2.x.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06639 + 2.09291i) q^{2} +(2.55847 + 1.66149i) q^{3} +(-2.06752 - 2.84570i) q^{4} +(1.70092 - 1.45151i) q^{5} +(-6.20568 + 3.58285i) q^{6} +(0.386520 + 1.00692i) q^{7} +(3.52057 - 0.557603i) q^{8} +(2.56500 + 5.76109i) q^{9} +O(q^{10})$	\(q+(-1.06639 + 2.09291i) q^{2} +(2.55847 + 1.66149i) q^{3} +(-2.06752 - 2.84570i) q^{4} +(1.70092 - 1.45151i) q^{5} +(-6.20568 + 3.58285i) q^{6} +(0.386520 + 1.00692i) q^{7} +(3.52057 - 0.557603i) q^{8} +(2.56500 + 5.76109i) q^{9} +(1.22403 + 5.10775i) q^{10} +(-4.03806 + 0.424417i) q^{11} +(-0.561591 - 10.7158i) q^{12} +(0.291801 - 5.56789i) q^{13} +(-2.51958 - 0.264818i) q^{14} +(6.76341 - 0.887572i) q^{15} +(-0.413370 + 1.27222i) q^{16} +(-0.995483 - 1.22932i) q^{17} +(-14.7927 - 0.775255i) q^{18} +(-2.79431 - 2.51601i) q^{19} +(-7.64724 - 1.83929i) q^{20} +(-0.684085 + 3.21837i) q^{21} +(3.41789 - 8.90390i) q^{22} +(0.305372 + 1.92804i) q^{23} +(9.93370 + 4.42277i) q^{24} +(0.786260 - 4.93779i) q^{25} +(11.3419 + 6.54827i) q^{26} +(-1.57784 + 9.96207i) q^{27} +(2.06625 - 3.18175i) q^{28} +(1.18962 + 3.66129i) q^{29} +(-5.35484 + 15.1017i) q^{30} +(-5.54370 + 0.517145i) q^{31} +(2.81906 + 2.81906i) q^{32} +(-11.0364 - 5.62333i) q^{33} +(3.63443 - 0.772523i) q^{34} +(2.11899 + 1.15165i) q^{35} +(11.0911 - 19.2104i) q^{36} +(7.74543 + 2.07538i) q^{37} +(8.24562 - 3.16520i) q^{38} +(9.99754 - 13.7604i) q^{39} +(5.17884 - 6.05856i) q^{40} +(-1.63679 - 0.347910i) q^{41} +(-6.00626 - 4.86377i) q^{42} +(-5.72843 + 0.300214i) q^{43} +(9.55654 + 10.6136i) q^{44} +(12.7251 + 6.07603i) q^{45} +(-4.36087 - 1.41693i) q^{46} +(-5.25125 + 2.67565i) q^{47} +(-3.17137 + 2.56813i) q^{48} +(4.33753 - 3.90553i) q^{49} +(9.49591 + 6.91120i) q^{50} +(-0.504412 - 4.79916i) q^{51} +(-16.4478 + 10.6814i) q^{52} +(10.2506 + 3.93485i) q^{53} +(-19.1672 - 13.9258i) q^{54} +(-6.25238 + 6.58317i) q^{55} +(1.92223 + 3.32940i) q^{56} +(-2.96883 - 11.0798i) q^{57} +(-8.93136 - 1.41459i) q^{58} +(1.14957 + 5.40830i) q^{59} +(-16.5093 - 17.4115i) q^{60} +7.50440i q^{61} +(4.82941 - 12.1540i) q^{62} +(-4.80952 + 4.80952i) q^{63} +(-11.4507 + 3.72056i) q^{64} +(-7.58550 - 9.89409i) q^{65} +(23.5383 - 17.1016i) q^{66} +(3.11210 - 0.833884i) q^{67} +(-1.44009 + 5.37449i) q^{68} +(-2.42213 + 5.44020i) q^{69} +(-4.66998 + 3.20675i) q^{70} +(-6.71312 + 2.98887i) q^{71} +(12.2427 + 18.8520i) q^{72} +(1.83060 - 2.26060i) q^{73} +(-12.6033 + 13.9973i) q^{74} +(10.2157 - 11.3268i) q^{75} +(-1.38251 + 13.1537i) q^{76} +(-1.98815 - 3.90195i) q^{77} +(18.1381 + 35.5980i) q^{78} +(0.241801 - 2.30058i) q^{79} +(1.14353 + 2.76395i) q^{80} +(-7.92951 + 8.80661i) q^{81} +(2.47360 - 3.05465i) q^{82} +(-1.99189 - 3.06725i) q^{83} +(10.5729 - 4.70734i) q^{84} +(-3.47760 - 0.646024i) q^{85} +(5.48043 - 12.3093i) q^{86} +(-3.03957 + 11.3438i) q^{87} +(-13.9796 + 3.74582i) q^{88} +(-0.253245 + 0.183994i) q^{89} +(-26.2866 + 20.1531i) q^{90} +(5.71920 - 1.85828i) q^{91} +(4.85526 - 4.85526i) q^{92} +(-15.0426 - 7.88768i) q^{93} -13.8437i q^{94} +(-8.40490 - 0.223571i) q^{95} +(2.52864 + 11.8963i) q^{96} +(-1.55038 - 0.245557i) q^{97} +(3.54842 + 13.2429i) q^{98} +(-12.8027 - 22.1750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8}+O(q^{10}) $ 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8	$ 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8} - 10 q^{10} - 28 q^{11} - 40 q^{12} - 14 q^{13} - 20 q^{15} + 24 q^{16} - 14 q^{17} - 40 q^{18} - 44 q^{20} - 44 q^{21} + 30 q^{22} - 30 q^{23} - 22 q^{25} - 48 q^{26} + 100 q^{27} - 48 q^{28} - 44 q^{31} + 28 q^{32} + 20 q^{33} - 72 q^{35} + 16 q^{36} + 30 q^{37} + 38 q^{38} - 4 q^{40} - 20 q^{41} - 130 q^{42} + 22 q^{43} - 34 q^{45} - 28 q^{47} - 156 q^{48} + 158 q^{50} - 36 q^{51} - 10 q^{52} + 26 q^{53} + 98 q^{55} - 48 q^{56} - 20 q^{58} + 260 q^{60} + 30 q^{62} + 152 q^{63} + 32 q^{65} - 152 q^{66} + 38 q^{67} - 126 q^{68} + 166 q^{70} - 128 q^{71} - 156 q^{72} - 30 q^{73} + 26 q^{75} + 128 q^{76} + 30 q^{78} + 154 q^{80} - 64 q^{81} + 8 q^{82} - 82 q^{83} + 60 q^{85} - 28 q^{86} - 24 q^{87} + 252 q^{88} + 38 q^{90} + 194 q^{93} - 74 q^{95} + 60 q^{96} - 38 q^{97} + 174 q^{98}+O(q^{100}) $ 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8 - 10 * q^10 - 28 * q^11 - 40 * q^12 - 14 * q^13 - 20 * q^15 + 24 * q^16 - 14 * q^17 - 40 * q^18 - 44 * q^20 - 44 * q^21 + 30 * q^22 - 30 * q^23 - 22 * q^25 - 48 * q^26 + 100 * q^27 - 48 * q^28 - 44 * q^31 + 28 * q^32 + 20 * q^33 - 72 * q^35 + 16 * q^36 + 30 * q^37 + 38 * q^38 - 4 * q^40 - 20 * q^41 - 130 * q^42 + 22 * q^43 - 34 * q^45 - 28 * q^47 - 156 * q^48 + 158 * q^50 - 36 * q^51 - 10 * q^52 + 26 * q^53 + 98 * q^55 - 48 * q^56 - 20 * q^58 + 260 * q^60 + 30 * q^62 + 152 * q^63 + 32 * q^65 - 152 * q^66 + 38 * q^67 - 126 * q^68 + 166 * q^70 - 128 * q^71 - 156 * q^72 - 30 * q^73 + 26 * q^75 + 128 * q^76 + 30 * q^78 + 154 * q^80 - 64 * q^81 + 8 * q^82 - 82 * q^83 + 60 * q^85 - 28 * q^86 - 24 * q^87 + 252 * q^88 + 38 * q^90 + 194 * q^93 - 74 * q^95 + 60 * q^96 - 38 * q^97 + 174 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{30}\right)$

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 $

$2$	−1.06639	+	2.09291i	−0.754053	+	1.47991i	0.119317	+	0.992856i	$0.461930\pi$
$2$	−1.06639	+	2.09291i	−0.754053	+	1.47991i	−0.873370	+	0.487057i	$0.838070\pi$
$3$	2.55847	+	1.66149i	1.47713	+	0.959260i	0.996609	+	0.0822778i	$0.0262195\pi$
$3$	2.55847	+	1.66149i	1.47713	+	0.959260i	0.480522	+	0.876983i	$0.340447\pi$
$4$	−2.06752	−	2.84570i	−1.03376	−	1.42285i
$5$	1.70092	−	1.45151i	0.760675	−	0.649133i
$5$	1.70092	−	1.45151i	0.760675	−	0.649133i
$6$	−6.20568	+	3.58285i	−2.53346	+	1.46269i
$7$	0.386520	+	1.00692i	0.146091	+	0.380580i	0.987027	−	0.160555i	$-0.0513283\pi$
$7$	0.386520	+	1.00692i	0.146091	+	0.380580i	−0.840936	+	0.541134i	$0.817995\pi$
$8$	3.52057	−	0.557603i	1.24471	−	0.197142i
$9$	2.56500	+	5.76109i	0.855000	+	1.92036i
$10$	1.22403	+	5.10775i	0.387071	+	1.61521i
$11$	−4.03806	+	0.424417i	−1.21752	+	0.127967i	−0.691418	−	0.722454i	$-0.743014\pi$
$11$	−4.03806	+	0.424417i	−1.21752	+	0.127967i	−0.526103	+	0.850421i	$0.676347\pi$
$12$	−0.561591	−	10.7158i	−0.162117	−	3.09338i
$13$	0.291801	−	5.56789i	0.0809310	−	1.54425i	−0.592844	−	0.805318i	$-0.701995\pi$
$13$	0.291801	−	5.56789i	0.0809310	−	1.54425i	0.673775	−	0.738937i	$-0.264672\pi$
$14$	−2.51958	−	0.264818i	−0.673385	−	0.0707756i
$15$	6.76341	−	0.887572i	1.74630	−	0.229170i
$16$	−0.413370	+	1.27222i	−0.103342	+	0.318055i
$17$	−0.995483	−	1.22932i	−0.241440	−	0.298154i	0.641993	−	0.766710i	$-0.278108\pi$
$17$	−0.995483	−	1.22932i	−0.241440	−	0.298154i	−0.883434	+	0.468556i	$0.844774\pi$
$18$	−14.7927	−	0.775255i	−3.48668	−	0.182729i
$19$	−2.79431	−	2.51601i	−0.641059	−	0.577212i	0.283161	−	0.959072i	$-0.408617\pi$
$19$	−2.79431	−	2.51601i	−0.641059	−	0.577212i	−0.924220	+	0.381861i	$0.875283\pi$
$20$	−7.64724	−	1.83929i	−1.70997	−	0.411277i
$21$	−0.684085	+	3.21837i	−0.149280	+	0.702305i
$22$	3.41789	−	8.90390i	0.728696	−	1.89832i
$23$	0.305372	+	1.92804i	0.0636744	+	0.402024i	0.998854	+	0.0478516i	$0.0152375\pi$
$23$	0.305372	+	1.92804i	0.0636744	+	0.402024i	−0.935180	+	0.354173i	$0.884763\pi$
$24$	9.93370	+	4.42277i	2.02771	+	0.902794i
$25$	0.786260	−	4.93779i	0.157252	−	0.987559i
$26$	11.3419	+	6.54827i	2.22434	+	1.28422i
$27$	−1.57784	+	9.96207i	−0.303655	+	1.91720i
$28$	2.06625	−	3.18175i	0.390485	−	0.601294i
$29$	1.18962	+	3.66129i	0.220908	+	0.679884i	0.998681	+	0.0513392i	$0.0163490\pi$
$29$	1.18962	+	3.66129i	0.220908	+	0.679884i	−0.777774	+	0.628544i	$0.783651\pi$
$30$	−5.35484	+	15.1017i	−0.977655	+	2.75718i
$31$	−5.54370	+	0.517145i	−0.995677	+	0.0928821i
$31$	−5.54370	+	0.517145i	−0.995677	+	0.0928821i
$32$	2.81906	+	2.81906i	0.498344	+	0.498344i
$33$	−11.0364	−	5.62333i	−1.92119	−	0.978896i
$34$	3.63443	−	0.772523i	0.623300	−	0.132487i
$35$	2.11899	+	1.15165i	0.358175	+	0.194665i
$36$	11.0911	−	19.2104i	1.84852	−	3.20173i
$37$	7.74543	+	2.07538i	1.27334	+	0.341191i	0.831310	−	0.555809i	$-0.187592\pi$
$37$	7.74543	+	2.07538i	1.27334	+	0.341191i	0.442031	+	0.897000i	$0.354258\pi$
$38$	8.24562	−	3.16520i	1.33762	−	0.513462i
$39$	9.99754	−	13.7604i	1.60089	−	2.20343i
$40$	5.17884	−	6.05856i	0.818846	−	0.957942i
$41$	−1.63679	−	0.347910i	−0.255623	−	0.0543344i	0.0783175	−	0.996928i	$-0.475045\pi$
$41$	−1.63679	−	0.347910i	−0.255623	−	0.0543344i	−0.333941	+	0.942594i	$0.608379\pi$
$42$	−6.00626	−	4.86377i	−0.926786	−	0.750496i
$43$	−5.72843	+	0.300214i	−0.873577	+	0.0457822i	−0.483853	−	0.875149i	$-0.660763\pi$
$43$	−5.72843	+	0.300214i	−0.873577	+	0.0457822i	−0.389724	+	0.920932i	$0.627430\pi$
$44$	9.55654	+	10.6136i	1.44070	+	1.60006i
$45$	12.7251	+	6.07603i	1.89695	+	0.905762i
$46$	−4.36087	−	1.41693i	−0.642975	−	0.208915i
$47$	−5.25125	+	2.67565i	−0.765974	+	0.390283i	−0.792898	−	0.609354i	$-0.791429\pi$
$47$	−5.25125	+	2.67565i	−0.765974	+	0.390283i	0.0269242	+	0.999637i	$0.491429\pi$
$48$	−3.17137	+	2.56813i	−0.457748	+	0.370677i
$49$	4.33753	−	3.90553i	0.619646	−	0.557932i
$50$	9.49591	+	6.91120i	1.34292	+	0.977391i
$51$	−0.504412	−	4.79916i	−0.0706318	−	0.672016i
$52$	−16.4478	+	10.6814i	−2.28090	+	1.48124i
$53$	10.2506	+	3.93485i	1.40803	+	0.540493i	0.939376	−	0.342888i	$-0.111405\pi$
$53$	10.2506	+	3.93485i	1.40803	+	0.540493i	0.468656	+	0.883381i	$0.344739\pi$
$54$	−19.1672	−	13.9258i	−2.60832	−	1.89506i
$55$	−6.25238	+	6.58317i	−0.843070	+	0.887674i
$56$	1.92223	+	3.32940i	0.256869	+	0.444910i
$57$	−2.96883	−	11.0798i	−0.393231	−	1.46756i
$58$	−8.93136	−	1.41459i	−1.17274	−	0.185744i
$59$	1.14957	+	5.40830i	0.149661	+	0.704101i	0.987428	+	0.158072i	$0.0505278\pi$
$59$	1.14957	+	5.40830i	0.149661	+	0.704101i	−0.837766	+	0.546029i	$0.816139\pi$
$60$	−16.5093	−	17.4115i	−2.13134	−	2.24782i
$61$			7.50440i			0.960840i	0.877038	+	0.480420i	$0.159516\pi$
$61$			7.50440i			0.960840i	−0.877038	+	0.480420i	$0.840484\pi$
$62$	4.82941	−	12.1540i	0.613336	−	1.54355i
$63$	−4.80952	+	4.80952i	−0.605943	+	0.605943i
$64$	−11.4507	+	3.72056i	−1.43134	+	0.465070i
$65$	−7.58550	−	9.89409i	−0.940865	−	1.22721i
$66$	23.5383	−	17.1016i	2.89736	−	2.10506i
$67$	3.11210	−	0.833884i	0.380203	−	0.101875i	−0.0636556	−	0.997972i	$-0.520276\pi$
$67$	3.11210	−	0.833884i	0.380203	−	0.101875i	0.443859	+	0.896097i	$0.353609\pi$
$68$	−1.44009	+	5.37449i	−0.174637	+	0.651753i
$69$	−2.42213	+	5.44020i	−0.291590	+	0.654923i
$70$	−4.66998	+	3.20675i	−0.558170	+	0.383279i
$71$	−6.71312	+	2.98887i	−0.796700	+	0.354714i	−0.764382	−	0.644764i	$-0.776956\pi$
$71$	−6.71312	+	2.98887i	−0.796700	+	0.354714i	−0.0323185	+	0.999478i	$0.510289\pi$
$72$	12.2427	+	18.8520i	1.44281	+	2.22173i
$73$	1.83060	−	2.26060i	0.214255	−	0.264583i	−0.658676	−	0.752427i	$-0.728883\pi$
$73$	1.83060	−	2.26060i	0.214255	−	0.264583i	0.872931	+	0.487844i	$0.162216\pi$
$74$	−12.6033	+	13.9973i	−1.46510	+	1.62716i
$75$	10.2157	−	11.3268i	1.17961	−	1.30791i
$76$	−1.38251	+	13.1537i	−0.158584	+	1.50883i
$77$	−1.98815	−	3.90195i	−0.226570	−	0.444669i
$78$	18.1381	+	35.5980i	2.05373	+	4.03068i
$79$	0.241801	−	2.30058i	0.0272047	−	0.258835i	−0.972463	−	0.233057i	$-0.925127\pi$
$79$	0.241801	−	2.30058i	0.0272047	−	0.258835i	0.999668	−	0.0257780i	$-0.00820630\pi$
$80$	1.14353	+	2.76395i	0.127850	+	0.309019i
$81$	−7.92951	+	8.80661i	−0.881056	+	0.978512i
$82$	2.47360	−	3.05465i	0.273164	−	0.337329i
$83$	−1.99189	−	3.06725i	−0.218639	−	0.336674i	0.712283	−	0.701892i	$-0.247661\pi$
$83$	−1.99189	−	3.06725i	−0.218639	−	0.336674i	−0.930922	+	0.365218i	$0.880995\pi$
$84$	10.5729	−	4.70734i	1.15359	−	0.513613i
$85$	−3.47760	−	0.646024i	−0.377199	−	0.0700712i
$86$	5.48043	−	12.3093i	0.590970	−	1.32734i
$87$	−3.03957	+	11.3438i	−0.325876	+	1.21619i
$88$	−13.9796	+	3.74582i	−1.49023	+	0.399306i
$89$	−0.253245	+	0.183994i	−0.0268440	+	0.0195033i	−0.601126	−	0.799154i	$-0.705281\pi$
$89$	−0.253245	+	0.183994i	−0.0268440	+	0.0195033i	0.574282	+	0.818657i	$0.305281\pi$
$90$	−26.2866	+	20.1531i	−2.77085	+	2.12433i
$91$	5.71920	−	1.85828i	0.599535	−	0.194801i
$92$	4.85526	−	4.85526i	0.506196	−	0.506196i
$93$	−15.0426	−	7.88768i	−1.55984	−	0.817915i
$94$		−	13.8437i		−	1.42787i
$95$	−8.40490	−	0.223571i	−0.862324	−	0.0229379i
$96$	2.52864	+	11.8963i	0.258078	+	1.21416i
$97$	−1.55038	−	0.245557i	−0.157418	−	0.0249325i	0.0772281	−	0.997013i	$-0.475393\pi$
$97$	−1.55038	−	0.245557i	−0.157418	−	0.0249325i	−0.234646	+	0.972081i	$0.575393\pi$
$98$	3.54842	+	13.2429i	0.358445	+	1.33773i
$99$	−12.8027	−	22.1750i	−1.28672	−	2.22867i
$100$	−15.6771	+	7.97153i	−1.56771	+	0.797153i
$101$	−4.73616	−	3.44102i	−0.471265	−	0.342394i	0.326669	−	0.945139i	$-0.394074\pi$
$101$	−4.73616	−	3.44102i	−0.471265	−	0.342394i	−0.797934	+	0.602745i	$0.794074\pi$
$102$	10.5821	+	4.06209i	1.04779	+	0.402207i
$103$	13.5466	−	8.79728i	1.33479	−	0.866822i	0.337566	−	0.941302i	$-0.390397\pi$
$103$	13.5466	−	8.79728i	1.33479	−	0.866822i	0.997222	+	0.0744804i	$0.0237298\pi$
$104$	−2.07737	−	19.7648i	−0.203703	−	1.93810i
$105$	3.50791	+	6.46714i	0.342337	+	0.631128i
$106$	−19.1665	+	17.2576i	−1.86161	+	1.67620i
$107$	1.81775	−	1.47199i	0.175729	−	0.142302i	−0.537421	−	0.843314i	$-0.680601\pi$
$107$	1.81775	−	1.47199i	0.175729	−	0.142302i	0.713150	+	0.701012i	$0.247268\pi$
$108$	31.6113	−	16.1068i	3.04180	−	1.54987i
$109$	−8.22695	−	2.67310i	−0.787998	−	0.256036i	−0.112747	−	0.993624i	$-0.535965\pi$
$109$	−8.22695	−	2.67310i	−0.787998	−	0.256036i	−0.675252	+	0.737588i	$0.735965\pi$
$110$	−7.11052	−	20.1059i	−0.677961	−	1.91702i
$111$	16.3682	+	18.1787i	1.55360	+	1.72545i
$112$	−1.44080	+	0.0755091i	−0.136143	+	0.00713494i
$113$	2.57147	+	2.08234i	0.241904	+	0.195890i	0.742604	−	0.669731i	$-0.233591\pi$
$113$	2.57147	+	2.08234i	0.241904	+	0.195890i	−0.500700	+	0.865621i	$0.666924\pi$
$114$	26.3551	+	5.60194i	2.46838	+	0.524670i
$115$	3.31798	+	2.83619i	0.309403	+	0.264477i
$116$	7.95934	−	10.9551i	0.739006	−	1.01716i
$117$	32.8256	−	12.6006i	3.03472	−	1.16492i
$118$	−12.5450	−	3.36142i	−1.15486	−	0.309444i
$119$	0.853051	−	1.47753i	0.0781991	−	0.135445i
$120$	23.3161	−	6.89605i	2.12846	−	0.629520i
$121$	5.36618	−	1.14062i	0.487835	−	0.103692i
$122$	−15.7061	−	8.00264i	−1.42196	−	0.724525i
$123$	−3.60962	−	3.60962i	−0.325468	−	0.325468i
$124$	12.9333	+	14.7065i	1.16145	+	1.32068i
$125$	−5.82987	−	9.54005i	−0.521439	−	0.853288i
$126$	−4.93707	−	15.1948i	−0.439830	−	1.35366i
$127$	4.20272	−	6.47162i	0.372931	−	0.574264i	−0.601521	−	0.798857i	$-0.705439\pi$
$127$	4.20272	−	6.47162i	0.372931	−	0.574264i	0.974453	+	0.224593i	$0.0721052\pi$
$128$	3.17681	−	20.0576i	0.280793	−	1.77286i
$129$	−15.1548	−	8.74963i	−1.33431	−	0.770362i
$130$	28.7966	−	5.32480i	2.52563	−	0.467016i
$131$	−0.536977	−	0.239077i	−0.0469159	−	0.0208883i	0.383145	−	0.923688i	$-0.374841\pi$
$131$	−0.536977	−	0.239077i	−0.0469159	−	0.0208883i	−0.430060	+	0.902800i	$0.641508\pi$
$132$	6.81570	+	43.0327i	0.593231	+	3.74551i
$133$	1.45336	−	3.78613i	0.126022	−	0.328299i
$134$	−1.57347	+	7.40259i	−0.135927	+	0.639487i
$135$	11.7762	+	19.2349i	1.01354	+	1.65548i
$136$	−4.19014	−	3.77282i	−0.359301	−	0.323516i
$137$	−17.6780	−	0.926463i	−1.51033	−	0.0791531i	−0.720920	−	0.693018i	$-0.756280\pi$
$137$	−17.6780	−	0.926463i	−1.51033	−	0.0791531i	−0.789411	+	0.613865i	$0.789614\pi$
$138$	−8.80292	−	10.8707i	−0.749354	−	0.925375i
$139$	−6.80888	+	20.9556i	−0.577522	+	1.77743i	0.0499056	+	0.998754i	$0.484108\pi$
$139$	−6.80888	+	20.9556i	−0.577522	+	1.77743i	−0.627427	+	0.778675i	$0.715892\pi$
$140$	−1.10380	−	8.41107i	−0.0932879	−	0.710865i
$141$	−17.8807	−	1.87934i	−1.50583	−	0.158269i
$142$	0.903368	−	17.2373i	0.0758089	−	1.44652i
$143$	1.18480	+	22.6073i	0.0990779	+	1.89052i
$144$	−8.38967	+	0.881789i	−0.699139	+	0.0734824i
$145$	7.33783	+	4.50081i	0.609374	+	0.373772i
$146$	2.77910	+	6.24197i	0.230000	+	0.516589i
$147$	17.5864	−	2.78541i	1.45050	−	0.229737i
$148$	−10.1079	−	26.3320i	−0.830866	−	2.16448i
$149$	2.48560	−	1.43506i	0.203628	−	0.117565i	−0.394718	−	0.918802i	$-0.629158\pi$
$149$	2.48560	−	1.43506i	0.203628	−	0.117565i	0.598347	+	0.801237i	$0.295825\pi$
$150$	12.8121	+	33.4594i	1.04610	+	2.73195i
$151$	−4.79792	−	6.60376i	−0.390449	−	0.537407i	0.567866	−	0.823121i	$-0.307769\pi$
$151$	−4.79792	−	6.60376i	−0.390449	−	0.537407i	−0.958315	+	0.285714i	$0.907769\pi$
$152$	−11.2405	−	7.29965i	−0.911723	−	0.592080i
$153$	4.52880	−	8.88827i	0.366132	−	0.718574i
$154$	10.2866			0.828917
$155$	−8.67874	+	8.92633i	−0.697094	+	0.716980i
$156$	−59.8282			−4.79009
$157$	−10.9134	+	21.4188i	−0.870985	+	1.70940i	−0.183743	+	0.982974i	$0.558822\pi$
$157$	−10.9134	+	21.4188i	−0.870985	+	1.70940i	−0.687241	+	0.726429i	$0.741178\pi$
$158$	4.55706	+	2.95939i	0.362540	+	0.235436i
$159$	19.6882	+	27.0985i	1.56137	+	2.14905i
$160$	8.88688	+	0.703114i	0.702570	+	0.0555860i
$161$	−1.82335	+	1.05271i	−0.143700	+	0.0829652i
$162$	−9.97550	−	25.9871i	−0.783749	−	2.04174i
$163$	22.2050	−	3.51693i	1.73923	−	0.275467i	0.795445	−	0.606026i	$-0.207237\pi$
$163$	22.2050	−	3.51693i	1.73923	−	0.275467i	0.943785	+	0.330559i	$0.107237\pi$
$164$	2.39405	+	5.37712i	0.186944	+	0.419882i
$165$	−26.9344	+	6.45458i	−2.09684	+	0.502488i
$166$	8.54363	−	0.897971i	0.663114	−	0.0696961i
$167$	0.696324	+	13.2866i	0.0538831	+	1.02815i	0.883088	+	0.469207i	$0.155460\pi$
$167$	0.696324	+	13.2866i	0.0538831	+	1.02815i	−0.829205	+	0.558945i	$0.811206\pi$
$168$	−0.613796	+	11.7119i	−0.0473554	+	0.903594i
$169$	−17.9875	−	1.89056i	−1.38365	−	0.145428i
$170$	5.06056	−	6.58940i	0.388127	−	0.505384i
$171$	7.32753	−	22.5518i	0.560350	−	1.72458i
$172$	12.6980	+	15.6807i	0.968211	+	1.19564i
$173$	−9.94283	−	0.521082i	−0.755940	−	0.0396171i	−0.329527	−	0.944146i	$-0.606889\pi$
$173$	−9.94283	−	0.521082i	−0.755940	−	0.0396171i	−0.426412	+	0.904529i	$0.640223\pi$
$174$	−20.5003	−	18.4585i	−1.55412	−	1.39934i
$175$	5.27586	−	1.11686i	0.398818	−	0.0844263i
$176$	1.12926	−	5.31274i	0.0851211	−	0.400463i
$177$	−6.04469	+	15.7470i	−0.454347	+	1.18361i
$178$	−0.115024	−	0.726230i	−0.00862138	−	0.0544332i
$179$	−7.32303	−	3.26042i	−0.547349	−	0.243696i	0.114382	−	0.993437i	$-0.463511\pi$
$179$	−7.32303	−	3.26042i	−0.547349	−	0.243696i	−0.661731	+	0.749741i	$0.730178\pi$
$180$	−9.01888	−	48.7742i	−0.672228	−	3.63541i
$181$	−4.27332	−	2.46720i	−0.317633	−	0.183386i	0.332704	−	0.943031i	$-0.392039\pi$
$181$	−4.27332	−	2.46720i	−0.317633	−	0.183386i	−0.650337	+	0.759646i	$0.725372\pi$
$182$	−2.20969	+	13.9514i	−0.163793	+	1.03415i
$183$	−12.4685	+	19.1998i	−0.921696	+	1.41929i
$184$	2.15016	+	6.61752i	0.158512	+	0.487850i
$185$	16.1868	−	7.71248i	1.19008	−	0.567033i
$186$	32.5495	−	23.0715i	2.38665	−	1.69168i
$187$	4.54157	+	4.54157i	0.332112	+	0.332112i
$188$	18.4712	+	9.41153i	1.34715	+	0.686406i
$189$	−10.6409	+	2.26179i	−0.774009	+	0.164521i
$190$	9.43083	−	17.3523i	0.684185	−	1.25887i
$191$	11.2504	−	19.4863i	0.814053	−	1.40998i	−0.0959532	−	0.995386i	$-0.530590\pi$
$191$	11.2504	−	19.4863i	0.814053	−	1.40998i	0.910006	−	0.414595i	$-0.136077\pi$
$192$	−35.4779	−	9.50628i	−2.56040	−	0.686057i
$193$	3.66708	−	1.40766i	0.263962	−	0.101326i	−0.222788	−	0.974867i	$-0.571516\pi$
$193$	3.66708	−	1.40766i	0.263962	−	0.101326i	0.486750	+	0.873541i	$0.338182\pi$
$194$	2.16725	−	2.98296i	0.155599	−	0.214164i
$195$	−2.96833	−	37.9169i	−0.212567	−	2.71529i
$196$	−20.0819	−	4.26853i	−1.43442	−	0.304895i
$197$	2.43961	+	1.97556i	0.173815	+	0.140753i	0.712280	−	0.701895i	$-0.247662\pi$
$197$	2.43961	+	1.97556i	0.173815	+	0.140753i	−0.538465	+	0.842648i	$0.680996\pi$
$198$	60.0631	−	3.14777i	4.26850	−	0.223702i
$199$	2.25209	+	2.50120i	0.159647	+	0.177305i	0.817661	−	0.575700i	$-0.195270\pi$
$199$	2.25209	+	2.50120i	0.159647	+	0.177305i	−0.658015	+	0.753005i	$0.728604\pi$
$200$	0.0147532	−	17.8222i	0.00104321	−	1.26022i
$201$	9.34768	+	3.03725i	0.659335	+	0.214231i
$202$	12.2524	−	6.24288i	0.862072	−	0.439248i
$203$	−3.22680	+	2.61301i	−0.226477	+	0.183398i
$204$	−12.6141	+	11.3578i	−0.883162	+	0.795202i
$205$	−3.28904	+	1.78404i	−0.229716	+	0.124603i
$206$	3.96592	+	37.7332i	0.276319	+	2.62900i
$207$	−10.3243	+	6.70470i	−0.717590	+	0.466009i
$208$	6.96296	+	2.67283i	0.482794	+	0.185327i
$209$	12.3514	+	8.97384i	0.854366	+	0.620733i
$210$	−17.2760	+	0.445232i	−1.19215	+	0.0307239i
$211$	0.510399	+	0.884036i	0.0351373	+	0.0608596i	0.883059	−	0.469261i	$-0.155480\pi$
$211$	0.510399	+	0.884036i	0.0351373	+	0.0608596i	−0.847922	+	0.530121i	$0.822146\pi$
$212$	−9.99600	−	37.3056i	−0.686528	−	2.56216i
$213$	−22.1413	−	3.50683i	−1.51709	−	0.240284i
$214$	1.14230	+	5.37411i	0.0780862	+	0.367367i
$215$	−9.30784	+	8.82549i	−0.634789	+	0.601893i
$216$			35.9519i			2.44622i
$217$	−2.66347	−	5.38217i	−0.180808	−	0.365365i
$218$	14.3677	−	14.3677i	0.973104	−	0.973104i
$219$	8.43949	−	2.74216i	0.570288	−	0.185298i
$220$	31.6606	+	4.18153i	2.13456	+	0.281919i
$221$	−7.13520	+	5.18402i	−0.479965	+	0.348715i
$222$	−55.5014	+	14.8716i	−3.72501	+	0.998114i
$223$	−5.15917	+	19.2543i	−0.345484	+	1.28936i	0.546562	+	0.837419i	$0.315936\pi$
$223$	−5.15917	+	19.2543i	−0.345484	+	1.28936i	−0.892046	+	0.451945i	$0.850730\pi$
$224$	−1.74894	+	3.92819i	−0.116856	+	0.262463i
$225$	30.4638	−	8.13573i	2.03092	−	0.542382i
$226$	−7.10035	+	3.16128i	−0.472308	+	0.210285i
$227$	−8.69108	−	13.3831i	−0.576847	−	0.888267i	0.422993	−	0.906133i	$-0.360979\pi$
$227$	−8.69108	−	13.3831i	−0.576847	−	0.888267i	−0.999840	+	0.0178659i	$0.994313\pi$
$228$	−25.3917	+	31.3562i	−1.68161	+	2.07661i
$229$	6.82507	−	7.58001i	0.451013	−	0.500901i	−0.474164	−	0.880437i	$-0.657250\pi$
$229$	6.82507	−	7.58001i	0.451013	−	0.500901i	0.925177	+	0.379536i	$0.123916\pi$
$230$	−9.47417	+	3.91974i	−0.624708	+	0.258460i
$231$	1.39645	−	13.2863i	0.0918794	−	0.874174i
$232$	6.22969	+	12.2265i	0.408999	+	0.802706i
$233$	−0.959827	−	1.88377i	−0.0628803	−	0.123410i	0.857427	−	0.514605i	$-0.172062\pi$
$233$	−0.959827	−	1.88377i	−0.0628803	−	0.123410i	−0.920308	+	0.391196i	$0.872062\pi$
$234$	−8.63307	+	82.1382i	−0.564361	+	5.36954i
$235$	−5.04824	+	12.1733i	−0.329311	+	0.794098i
$236$	13.0136	−	14.4531i	0.847116	−	0.940817i
$237$	4.44102	−	5.48420i	0.288475	−	0.356237i
$238$	2.18265	+	3.36099i	0.141480	+	0.217860i
$239$	9.09417	−	4.04898i	0.588253	−	0.261907i	−0.0909527	−	0.995855i	$-0.528991\pi$
$239$	9.09417	−	4.04898i	0.588253	−	0.261907i	0.679205	+	0.733948i	$0.262325\pi$
$240$	−1.66660	+	8.97144i	−0.107579	+	0.579104i
$241$	−2.83596	+	6.36967i	−0.182680	+	0.410307i	−0.981552	−	0.191195i	$-0.938764\pi$
$241$	−2.83596	+	6.36967i	−0.182680	+	0.410307i	0.798872	+	0.601501i	$0.205431\pi$
$242$	−3.33524	+	12.4473i	−0.214397	+	0.800142i
$243$	−5.69174	+	1.52510i	−0.365125	+	0.0978350i
$244$	21.3553	−	15.5155i	1.36713	−	0.993279i
$245$	1.70889	−	12.9389i	0.109177	−	0.826638i
$246$	11.4039	−	3.70535i	0.727085	−	0.236244i
$247$	−14.8242	+	14.8242i	−0.943243	+	0.943243i
$248$	−19.2286	+	4.91182i	−1.22102	+	0.311901i
$249$		−	11.1570i		−	0.707044i
$250$	26.1834	−	2.02797i	1.65599	−	0.128260i
$251$	−1.38931	−	6.53619i	−0.0876924	−	0.412560i	−0.999995	−	0.00304443i	$-0.999031\pi$
$251$	−1.38931	−	6.53619i	−0.0876924	−	0.412560i	0.912303	−	0.409516i	$-0.134302\pi$
$252$	23.6302	+	3.74266i	1.48857	+	0.235766i
$253$	−2.05140	−	7.65594i	−0.128971	−	0.481325i
$254$	9.06279	+	15.6972i	0.568650	+	0.984931i
$255$	−7.82397	−	7.43083i	−0.489956	−	0.465336i
$256$	19.1099	+	13.8842i	1.19437	+	0.867761i
$257$	11.1856	+	4.29376i	0.697740	+	0.267837i	0.681275	−	0.732027i	$-0.261426\pi$
$257$	11.1856	+	4.29376i	0.697740	+	0.267837i	0.0164644	+	0.999864i	$0.494759\pi$
$258$	34.4732	−	22.3871i	2.14621	−	1.39376i
$259$	0.904022	+	8.60120i	0.0561732	+	0.534452i
$260$	−12.4724	+	42.0423i	−0.773507	+	2.60735i
$261$	−18.0416	+	16.2447i	−1.11675	+	1.00552i
$262$	1.07300	−	0.868895i	0.0662899	−	0.0536805i
$263$	10.0809	−	5.13649i	0.621617	−	0.316730i	−0.114665	−	0.993404i	$-0.536580\pi$
$263$	10.0809	−	5.13649i	0.621617	−	0.316730i	0.736282	+	0.676675i	$0.236580\pi$
$264$	−41.9900	−	13.6434i	−2.58430	−	0.839691i
$265$	23.1470	−	8.18599i	1.42191	−	0.502861i
$266$	6.37419	+	7.07926i	0.390827	+	0.434057i
$267$	−0.953623	+	0.0499773i	−0.0583608	+	0.00305856i
$268$	−8.80731	−	7.13202i	−0.537992	−	0.435657i
$269$	1.92280	+	0.408703i	0.117235	+	0.0249191i	0.266156	−	0.963930i	$-0.414247\pi$
$269$	1.92280	+	0.408703i	0.117235	+	0.0249191i	−0.148921	+	0.988849i	$0.547580\pi$
$270$	−52.8151	+	4.13465i	−3.21423	+	0.251627i
$271$	−10.7933	+	14.8557i	−0.655646	+	0.902419i	−0.999328	−	0.0366674i	$-0.988326\pi$
$271$	−10.7933	+	14.8557i	−0.655646	+	0.902419i	0.343682	+	0.939086i	$0.388326\pi$
$272$	1.97547	−	0.758311i	0.119780	−	0.0459794i
$273$	17.7199	+	4.74803i	1.07246	+	0.287364i
$274$	20.7907	−	36.0105i	1.25601	−	2.17547i
$275$	−1.07928	+	20.2728i	−0.0650831	+	1.22250i
$276$	20.4890	−	4.35507i	1.23329	−	0.262144i
$277$	27.8857	+	14.2085i	1.67549	+	0.853705i	0.992355	+	0.123413i	$0.0393840\pi$
$277$	27.8857	+	14.2085i	1.67549	+	0.853705i	0.683135	+	0.730292i	$0.260616\pi$
$278$	−36.5973	−	36.5973i	−2.19496	−	2.19496i
$279$	−17.1989	−	30.6112i	−1.02967	−	1.83265i
$280$	8.10220	+	2.87292i	0.484199	+	0.171690i
$281$	−8.44127	−	25.9795i	−0.503564	−	1.54981i	−0.803172	−	0.595747i	$-0.796856\pi$
$281$	−8.44127	−	25.9795i	−0.503564	−	1.54981i	0.299608	−	0.954062i	$-0.403144\pi$
$282$	23.0011	−	35.4187i	1.36970	−	2.10915i
$283$	−1.72967	+	10.9207i	−0.102818	+	0.649168i	0.881422	+	0.472330i	$0.156587\pi$
$283$	−1.72967	+	10.9207i	−0.102818	+	0.649168i	−0.984240	+	0.176838i	$0.943413\pi$
$284$	22.3849	+	12.9240i	1.32830	+	0.766896i
$285$	−21.1322	−	14.5366i	−1.25176	−	0.861076i
$286$	−48.5786	−	21.6286i	−2.87251	−	1.27893i
$287$	−0.282334	−	1.78259i	−0.0166657	−	0.105223i
$288$	−9.00996	+	23.4717i	−0.530917	+	1.38309i
$289$	3.01426	−	14.1810i	0.177309	−	0.834175i
$290$	−17.2448	+	10.5578i	−1.01265	+	0.619976i
$291$	−3.55862	−	3.20419i	−0.208610	−	0.187833i
$292$	−10.2178	−	0.535492i	−0.597951	−	0.0313373i
$293$	−10.2546	−	12.6634i	−0.599080	−	0.739802i	0.383929	−	0.923363i	$-0.374571\pi$
$293$	−10.2546	−	12.6634i	−0.599080	−	0.739802i	−0.983008	+	0.183561i	$0.941238\pi$
$294$	−12.9244	+	39.7771i	−0.753765	+	2.31985i
$295$	9.80551	+	7.53048i	0.570899	+	0.438442i
$296$	28.4255	+	2.98764i	1.65220	+	0.173653i
$297$	2.14333	−	40.8971i	0.124368	−	2.37309i
$298$	0.352834	+	6.73248i	0.0204392	+	0.390002i
$299$	10.8242	−	1.13767i	0.625981	−	0.0657933i
$300$	−53.3539	−	5.65238i	−3.08039	−	0.326340i
$301$	−2.51644	−	5.65203i	−0.145045	−	0.325777i
$302$	18.9376	−	2.99942i	1.08973	−	0.172597i
$303$	−6.40009	−	16.6728i	−0.367675	−	0.957827i
$304$	4.35600	−	2.51494i	0.249834	−	0.144242i
$305$	10.8927	+	12.7644i	0.623713	+	0.730887i
$306$	13.7729	+	18.9568i	0.787344	+	1.08369i
$307$	−5.76907	−	3.74648i	−0.329259	−	0.213823i	0.369413	−	0.929265i	$-0.379559\pi$
$307$	−5.76907	−	3.74648i	−0.329259	−	0.213823i	−0.698672	+	0.715442i	$0.746225\pi$
$308$	−6.99326	+	13.7250i	−0.398478	+	0.782057i
$309$	49.2751			2.80317
$310$	−9.42709	−	27.6828i	−0.535423	−	1.57228i
$311$	9.07396			0.514537			0.257269	−	0.966340i	$-0.417177\pi$
$311$	9.07396			0.514537			0.257269	+	0.966340i	$0.417177\pi$
$312$	27.5241	−	54.0192i	1.55825	−	3.05823i
$313$	8.84032	+	5.74097i	0.499684	+	0.324499i	0.769753	−	0.638342i	$-0.220380\pi$
$313$	8.84032	+	5.74097i	0.499684	+	0.324499i	−0.270068	+	0.962841i	$0.587046\pi$
$314$	−33.1896	−	45.6816i	−1.87300	−	2.57796i
$315$	−1.19956	+	15.1617i	−0.0675878	+	0.854263i
$316$	−7.04668	+	4.06840i	−0.396407	+	0.228866i
$317$	8.33221	+	21.7062i	0.467984	+	1.21914i	0.941097	+	0.338137i	$0.109797\pi$
$317$	8.33221	+	21.7062i	0.467984	+	1.21914i	−0.473113	+	0.881002i	$0.656870\pi$
$318$	−77.7101	+	12.3081i	−4.35776	+	0.690202i
$319$	−6.35768	−	14.2796i	−0.355962	−	0.799504i
$320$	−14.0763	+	22.9492i	−0.786891	+	1.28290i
$321$	7.09635	−	0.745856i	0.396080	−	0.0416296i
$322$	−0.258827	−	4.93871i	−0.0144239	−	0.275224i
$323$	−0.311289	+	5.93974i	−0.0173206	+	0.330496i
$324$	41.4554	+	4.35714i	2.30308	+	0.242063i
$325$	−27.2636	−	5.81866i	−1.51232	−	0.322761i
$326$	−16.3186	+	50.2236i	−0.903805	+	2.78163i
$327$	−16.6070	−	20.5080i	−0.918372	−	1.13409i
$328$	−5.95641	−	0.312162i	−0.328888	−	0.0172363i
$329$	−4.72387	−	4.25340i	−0.260436	−	0.234497i
$330$	15.2137	−	63.2544i	0.837488	−	3.48204i
$331$	5.58767	−	26.2879i	0.307126	−	1.44491i	−0.505852	−	0.862620i	$-0.668822\pi$
$331$	5.58767	−	26.2879i	0.307126	−	1.44491i	0.812978	−	0.582294i	$-0.197845\pi$
$332$	−4.61018	+	12.0099i	−0.253017	+	0.659131i
$333$	7.91058	+	49.9454i	0.433497	+	2.73699i
$334$	−28.5503	−	12.7114i	−1.56221	−	0.695539i
$335$	4.08304	−	5.93560i	0.223080	−	0.324296i
$336$	−3.81169	−	2.20068i	−0.207945	−	0.120057i
$337$	−0.925738	+	5.84488i	−0.0504282	+	0.318391i	0.949560	+	0.313585i	$0.101530\pi$
$337$	−0.925738	+	5.84488i	−0.0504282	+	0.318391i	−0.999988	+	0.00480633i	$0.998470\pi$
$338$	23.1385	−	35.6301i	1.25857	−	1.93802i
$339$	3.11925	+	9.60006i	0.169414	+	0.521403i
$340$	5.35163	+	11.2319i	0.290233	+	0.609134i
$341$	22.1663	−	4.44110i	1.20037	−	0.240499i
$342$	39.3850	+	39.3850i	2.12970	+	2.12970i
$343$	12.3361	+	6.28555i	0.666086	+	0.339388i
$344$	−19.9999	+	4.25111i	−1.07832	+	0.229205i
$345$	3.77663	+	12.7691i	0.203327	+	0.687464i
$346$	11.6935	−	20.2538i	0.628649	−	1.08885i
$347$	8.54190	+	2.28880i	0.458553	+	0.122869i	0.480699	−	0.876886i	$-0.340383\pi$
$347$	8.54190	+	2.28880i	0.458553	+	0.122869i	−0.0221454	+	0.999755i	$0.507050\pi$
$348$	38.5655	−	14.8039i	2.06733	−	0.793572i
$349$	−16.5079	+	22.7212i	−0.883648	+	1.21624i	0.0917495	+	0.995782i	$0.470754\pi$
$349$	−16.5079	+	22.7212i	−0.883648	+	1.21624i	−0.975397	+	0.220455i	$0.929246\pi$
$350$	−3.28866	+	12.2329i	−0.175786	+	0.653877i
$351$	55.0073	+	11.6922i	2.93607	+	0.624082i
$352$	−12.5800	−	10.1871i	−0.670516	−	0.542973i
$353$	−28.2945	+	1.48285i	−1.50596	+	0.0789242i	−0.787359	−	0.616495i	$-0.788552\pi$
$353$	−28.2945	+	1.48285i	−1.50596	+	0.0789242i	−0.718604	+	0.695419i	$0.755219\pi$
$354$	−26.5110	−	29.4434i	−1.40904	−	1.56490i
$355$	−7.08011	+	14.8280i	−0.375773	+	0.786987i
$356$	1.04718	+	0.340250i	0.0555004	+	0.0180332i
$357$	4.63740	−	2.36287i	0.245437	−	0.125056i
$358$	14.6330	−	11.8496i	0.773379	−	0.626270i
$359$	6.52673	−	5.87670i	0.344468	−	0.310160i	−0.478678	−	0.877991i	$-0.658884\pi$
$359$	6.52673	−	5.87670i	0.344468	−	0.310160i	0.823145	+	0.567831i	$0.192217\pi$
$360$	48.1876	+	14.2955i	2.53971	+	0.753440i
$361$	−0.508169	−	4.83491i	−0.0267458	−	0.254469i
$362$	9.72067	−	6.31268i	0.510907	−	0.331787i
$363$	15.6243	+	5.99761i	0.820064	+	0.314793i
$364$	−17.1127	−	12.4331i	−0.896948	−	0.651671i
$365$	−0.167574	−	6.50223i	−0.00877121	−	0.340342i
$366$	−26.8872	−	46.5699i	−1.40541	−	2.43425i
$367$	4.61895	+	17.2381i	0.241107	+	0.899824i	0.975300	+	0.220883i	$0.0708940\pi$
$367$	4.61895	+	17.2381i	0.241107	+	0.899824i	−0.734193	+	0.678941i	$0.762439\pi$
$368$	−2.57912	−	0.408493i	−0.134446	−	0.0212942i
$369$	−2.19402	−	10.3221i	−0.114216	−	0.537345i
$370$	−1.11992	+	42.1021i	−0.0582218	+	2.18878i
$371$			11.8424i			0.614829i
$372$	8.65491	+	59.1146i	0.448736	+	3.06495i
$373$	11.1969	−	11.1969i	0.579755	−	0.579755i	−0.355081	−	0.934836i	$-0.615547\pi$
$373$	11.1969	−	11.1969i	0.579755	−	0.579755i	0.934836	+	0.355081i	$0.115547\pi$
$374$	−14.3482	+	4.66201i	−0.741927	+	0.241067i
$375$	0.935152	−	34.0942i	0.0482910	−	1.76062i
$376$	−16.9954	+	12.3479i	−0.876472	+	0.636794i
$377$	20.7328	−	5.55533i	1.06779	−	0.286114i
$378$	6.61362	−	24.6824i	0.340168	−	1.26952i
$379$	0.543552	−	1.22084i	0.0279204	−	0.0627103i	−0.899047	−	0.437852i	$-0.855739\pi$
$379$	0.543552	−	1.22084i	0.0279204	−	0.0627103i	0.926967	+	0.375142i	$0.122406\pi$
$380$	16.7411	+	24.3800i	0.858800	+	1.25067i
$381$	21.5050	−	9.57466i	1.10174	−	0.490525i
$382$	28.7858	+	44.3262i	1.47281	+	2.26793i
$383$	9.12129	−	11.2639i	0.466076	−	0.575556i	−0.488862	−	0.872361i	$-0.662588\pi$
$383$	9.12129	−	11.2639i	0.466076	−	0.575556i	0.954938	+	0.296805i	$0.0959212\pi$
$384$	41.4532	−	46.0384i	2.11540	−	2.34939i
$385$	−9.04539	−	3.75111i	−0.460996	−	0.191174i
$386$	−0.964436	+	9.17600i	−0.0490885	+	0.467046i
$387$	−16.4230	−	32.2319i	−0.834827	−	1.63844i
$388$	2.50667	+	4.91962i	0.127257	+	0.249756i
$389$	−0.776002	+	7.38316i	−0.0393449	+	0.374341i	0.957078	+	0.289831i	$0.0935992\pi$
$389$	−0.776002	+	7.38316i	−0.0393449	+	0.374341i	−0.996423	+	0.0845101i	$0.973067\pi$
$390$	82.5222	+	34.2218i	4.17867	+	1.73289i
$391$	2.06619	−	2.29473i	0.104491	−	0.116050i
$392$	13.0928	−	16.1683i	0.661287	−	0.816621i
$393$	−0.976613	−	1.50385i	−0.0492636	−	0.0758593i
$394$	−6.73625	+	2.99917i	−0.339367	+	0.151096i
$395$	−2.92802	−	4.26408i	−0.147325	−	0.214549i
$396$	−36.6334	+	82.2800i	−1.84090	+	4.13472i
$397$	3.13790	−	11.7108i	0.157487	−	0.587749i	−0.841393	−	0.540424i	$-0.818264\pi$
$397$	3.13790	−	11.7108i	0.157487	−	0.587749i	0.998880	−	0.0473249i	$-0.0150696\pi$
$398$	−7.63641	+	2.04617i	−0.382779	+	0.102565i
$399$	10.0090	−	7.27195i	0.501076	−	0.364053i
$400$	5.95694	+	3.04143i	0.297847	+	0.152071i
$401$	−20.1591	+	6.55010i	−1.00670	+	0.327096i	−0.765539	−	0.643389i	$-0.777528\pi$
$401$	−20.1591	+	6.55010i	−1.00670	+	0.327096i	−0.241160	+	0.970485i	$0.577528\pi$
$402$	−16.3250	+	16.3250i	−0.814216	+	0.814216i
$403$	1.26175	+	31.0176i	0.0628525	+	1.54510i
$404$			20.5920i			1.02449i
$405$	−0.704612	+	26.4891i	−0.0350125	+	1.31625i
$406$	−2.02777	−	9.53992i	−0.100637	−	0.473458i
$407$	−32.1573	−	5.09322i	−1.59398	−	0.252462i
$408$	−4.45184	−	16.6145i	−0.220399	−	0.822539i
$409$	−11.1160	−	19.2535i	−0.549652	−	0.952025i	−0.998298	−	0.0583154i	$-0.981427\pi$
$409$	−11.1160	−	19.2535i	−0.549652	−	0.952025i	0.448646	−	0.893709i	$-0.351906\pi$
$410$	−0.226435	−	8.78616i	−0.0111828	−	0.433917i
$411$	−43.6892	−	31.7421i	−2.15503	−	1.56572i
$412$	−53.0423	−	20.3610i	−2.61321	−	1.00312i
$413$	−5.00139	+	3.24794i	−0.246102	+	0.159821i
$414$	−3.02256	−	28.7578i	−0.148551	−	1.41337i
$415$	−7.84019	−	2.32590i	−0.384860	−	0.114174i
$416$	16.5188	−	14.8736i	0.809902	−	0.729239i
$417$	−52.2377	+	42.3013i	−2.55809	+	2.07150i
$418$	−31.9529	+	16.2808i	−1.56287	+	0.796321i
$419$	−21.3149	−	6.92564i	−1.04130	−	0.338340i	−0.262053	−	0.965054i	$-0.584399\pi$
$419$	−21.3149	−	6.92564i	−1.04130	−	0.338340i	−0.779249	+	0.626714i	$0.784399\pi$
$420$	11.1509	−	23.3534i	0.544106	−	1.13953i
$421$	4.57836	+	5.08478i	0.223136	+	0.247817i	0.844310	−	0.535855i	$-0.180011\pi$
$421$	4.57836	+	5.08478i	0.223136	+	0.247817i	−0.621174	+	0.783672i	$0.713344\pi$
$422$	−2.39450	+	0.125490i	−0.116562	+	0.00610877i
$423$	−28.8841	−	23.3899i	−1.40439	−	1.13725i
$424$	38.2821	+	8.13711i	1.85914	+	0.395173i
$425$	−6.85283	+	3.94893i	−0.332411	+	0.191551i
$426$	30.9508	−	42.6001i	1.49957	−	2.06398i
$427$	−7.55633	+	2.90060i	−0.365676	+	0.140370i
$428$	−7.94708	−	2.12941i	−0.384136	−	0.102929i
$429$	−34.5305	+	59.8086i	−1.66715	+	2.88759i
$430$	−8.54517	−	28.8919i	−0.412085	−	1.39329i
$431$	12.3716	−	2.62966i	0.595917	−	0.126666i	0.0999279	−	0.994995i	$-0.468139\pi$
$431$	12.3716	−	2.62966i	0.595917	−	0.126666i	0.495989	+	0.868329i	$0.334805\pi$
$432$	−12.0217	−	6.12538i	−0.578396	−	0.294707i
$433$	8.70745	+	8.70745i	0.418453	+	0.418453i	0.884670	−	0.466217i	$-0.154383\pi$
$433$	8.70745	+	8.70745i	0.418453	+	0.418453i	−0.466217	+	0.884670i	$0.654383\pi$
$434$	14.1047	+	0.165084i	0.677048	+	0.00792427i
$435$	11.2956	+	23.7069i	0.541581	+	1.13666i
$436$	9.40256	+	28.9381i	0.450301	+	1.38588i
$437$	3.99766	−	6.15586i	0.191234	−	0.294475i
$438$	−3.26071	+	20.5873i	−0.155803	+	0.983700i
$439$	20.5515	+	11.8654i	0.980872	+	0.566307i	0.902533	−	0.430620i	$-0.141705\pi$
$439$	20.5515	+	11.8654i	0.980872	+	0.566307i	0.0783386	+	0.996927i	$0.475038\pi$
$440$	−18.3411	+	26.6628i	−0.874378	+	1.27110i
$441$	33.6258	+	14.9712i	1.60123	+	0.712913i
$442$	−3.24079	−	20.4616i	−0.154149	−	0.973257i
$443$	−2.57274	+	6.70223i	−0.122235	+	0.318432i	−0.981021	−	0.193902i	$-0.937886\pi$
$443$	−2.57274	+	6.70223i	−0.122235	+	0.318432i	0.858786	+	0.512334i	$0.171219\pi$
$444$	17.8896	−	84.1639i	0.849002	−	3.99424i
$445$	−0.163682	+	0.680546i	−0.00775929	+	0.0322610i
$446$	−34.7959	−	31.3303i	−1.64763	−	1.48353i
$447$	8.74366	+	0.458236i	0.413561	+	0.0216738i
$448$	−8.17224	−	10.0919i	−0.386102	−	0.476796i
$449$	−5.40389	+	16.6314i	−0.255025	+	0.784887i	0.738800	+	0.673925i	$0.235393\pi$
$449$	−5.40389	+	16.6314i	−0.255025	+	0.784887i	−0.993825	+	0.110961i	$0.964607\pi$
$450$	−15.4590	+	72.4340i	−0.728744	+	3.41457i
$451$	6.75711	+	0.710201i	0.318180	+	0.0334420i
$452$	0.609131	−	11.6229i	0.0286511	−	0.546696i
$453$	−1.30323	−	24.8672i	−0.0612313	−	1.16836i
$454$	37.2778	−	3.91805i	1.74953	−	0.183883i
$455$	7.03060	−	11.4622i	0.329600	−	0.537358i
$456$	−16.6301	−	37.3518i	−0.778776	−	1.74916i
$457$	37.4813	−	5.93646i	1.75330	−	0.277696i	0.804589	−	0.593833i	$-0.202386\pi$
$457$	37.4813	−	5.93646i	1.75330	−	0.277696i	0.948714	+	0.316137i	$0.102386\pi$
$458$	8.58609	+	22.3675i	0.401202	+	1.04517i
$459$	13.8173	−	7.97741i	0.644936	−	0.372354i
$460$	1.21097	−	15.3059i	0.0564618	−	0.713639i
$461$	24.5864	+	33.8403i	1.14510	+	1.57610i	0.755543	+	0.655099i	$0.227373\pi$
$461$	24.5864	+	33.8403i	1.14510	+	1.57610i	0.389561	+	0.921001i	$0.372627\pi$
$462$	26.3179	+	17.0911i	1.22442	+	0.795148i
$463$	3.35309	−	6.58080i	0.155831	−	0.305836i	−0.799871	−	0.600172i	$-0.795099\pi$
$463$	3.35309	−	6.58080i	0.155831	−	0.305836i	0.955702	+	0.294337i	$0.0950986\pi$
$464$	−5.14972			−0.239070
$465$	−37.0353	+	8.41809i	−1.71747	+	0.390380i
$466$	4.96611			0.230051
$467$	9.72546	−	19.0873i	0.450041	−	0.883254i	−0.548839	−	0.835928i	$-0.684930\pi$
$467$	9.72546	−	19.0873i	0.450041	−	0.883254i	0.998879	−	0.0473261i	$-0.0150700\pi$
$468$	−103.725	−	67.3597i	−4.79469	−	3.11371i
$469$	2.04254	+	2.81132i	0.0943158	+	0.129815i
$470$	−20.0942	−	23.5470i	−0.926877	−	1.08614i
$471$	−63.5086	+	36.6667i	−2.92632	+	1.68951i
$472$	7.06282	+	18.3993i	0.325093	+	0.846895i
$473$	23.0043	−	3.64353i	1.05774	−	0.167530i
$474$	6.74209	+	15.1430i	0.309675	+	0.695540i
$475$	−14.6206	+	11.8195i	−0.670838	+	0.542315i
$476$	−5.96830	+	0.627294i	−0.273557	+	0.0287520i
$477$	3.62387	+	69.1476i	0.165926	+	3.16605i
$478$	−1.22378	+	23.3511i	−0.0559744	+	1.06805i
$479$	32.0962	+	3.37345i	1.46651	+	0.154137i	0.803873	−	0.594801i	$-0.202769\pi$
$479$	32.0962	+	3.37345i	1.46651	+	0.154137i	0.662640	+	0.748938i	$0.269436\pi$
$480$	21.5686	+	16.5643i	0.984466	+	0.756055i
$481$	13.8156	−	42.5201i	0.629938	−	1.93875i
$482$	−10.3069	−	12.7280i	−0.469467	−	0.579744i
$483$	−6.41404	−	0.336146i	−0.291849	−	0.0152952i
$484$	−14.3405	−	12.9123i	−0.651843	−	0.586922i
$485$	−2.99351	+	1.83272i	−0.135928	+	0.0832195i
$486$	2.87773	−	13.5387i	0.130537	−	0.614126i
$487$	13.6340	−	35.5178i	0.617816	−	1.60947i	−0.164355	−	0.986401i	$-0.552554\pi$
$487$	13.6340	−	35.5178i	0.617816	−	1.60947i	0.782171	−	0.623064i	$-0.214112\pi$
$488$	4.18448	+	26.4197i	0.189422	+	1.19597i
$489$	62.6541	+	27.8954i	2.83332	+	1.26147i
$490$	25.2577	+	17.3745i	1.14103	+	0.784902i
$491$	−0.729020	−	0.420900i	−0.0329002	−	0.0189949i	0.483460	−	0.875367i	$-0.339380\pi$
$491$	−0.729020	−	0.420900i	−0.0329002	−	0.0189949i	−0.516360	+	0.856372i	$0.672713\pi$
$492$	−2.80892	+	17.7349i	−0.126636	+	0.799549i
$493$	3.31664	−	5.10718i	0.149374	−	0.230016i
$494$	−15.2174	−	46.8343i	−0.684662	−	2.10717i
$495$	−53.9636	−	19.1346i	−2.42548	−	0.860038i
$496$	1.63367	−	7.26658i	0.0733540	−	0.326279i
$497$	−5.60431	−	5.60431i	−0.251388	−	0.251388i
$498$	23.3506	+	11.8977i	1.04636	+	0.533149i
$499$	−23.1601	+	4.92282i	−1.03679	+	0.220376i	−0.694705	−	0.719294i	$-0.744465\pi$
$499$	−23.1601	+	4.92282i	−1.03679	+	0.220376i	−0.342082	+	0.939670i	$0.611132\pi$
$500$	−15.0947	+	36.3143i	−0.675057	+	1.62403i
$501$	−20.2941	+	35.1504i	−0.906673	+	1.57040i
$502$	15.1612	+	4.06244i	0.676678	+	0.181315i
$503$	−18.3845	+	7.05716i	−0.819726	+	0.314663i	−0.731848	−	0.681468i	$-0.761342\pi$
$503$	−18.3845	+	7.05716i	−0.819726	+	0.314663i	−0.0878779	+	0.996131i	$0.528009\pi$
$504$	−14.2504	+	19.6140i	−0.634765	+	0.873679i
$505$	−13.0505	+	1.02166i	−0.580739	+	0.0454633i
$506$	18.2108	+	3.87083i	0.809569	+	0.172079i
$507$	−42.8792	−	34.7229i	−1.90433	−	1.54210i
$508$	−27.1055	+	1.42054i	−1.20261	+	0.0630262i
$509$	12.3465	+	13.7121i	0.547247	+	0.607780i	0.951794	−	0.306738i	$-0.0992374\pi$
$509$	12.3465	+	13.7121i	0.547247	+	0.607780i	−0.404547	+	0.914517i	$0.632571\pi$
$510$	23.8955	−	8.45071i	1.05811	−	0.374204i
$511$	2.98381	+	0.969497i	0.131996	+	0.0428880i
$512$	−13.2487	+	6.75053i	−0.585514	+	0.298334i
$513$	29.4736	−	23.8673i	1.30129	−	1.05377i
$514$	−20.9147	+	18.8317i	−0.922509	+	0.830630i
$515$	10.2724	−	34.6265i	0.452657	−	1.52582i
$516$	6.43406	+	61.2160i	0.283244	+	2.69489i
$517$	20.0693	−	13.0331i	0.882646	−	0.573197i
$518$	−18.9656	−	7.28021i	−0.833300	−	0.319874i
$519$	−24.5726	−	17.8531i	−1.07862	−	0.783663i
$520$	−32.2222	−	30.6031i	−1.41304	−	1.34203i
$521$	1.40583	+	2.43497i	0.0615906	+	0.106678i	0.895177	−	0.445712i	$-0.147049\pi$
$521$	1.40583	+	2.43497i	0.0615906	+	0.106678i	−0.833586	+	0.552390i	$0.813716\pi$
$522$	−14.7594	−	55.0827i	−0.646000	−	2.41091i
$523$	12.0976	+	1.91608i	0.528993	+	0.0837842i	0.415217	−	0.909722i	$-0.363706\pi$
$523$	12.0976	+	1.91608i	0.528993	+	0.0837842i	0.113775	+	0.993506i	$0.463706\pi$
$524$	0.429868	+	2.02237i	0.0187789	+	0.0883477i
$525$	15.3538	+	5.90834i	0.670093	+	0.257861i
$526$			26.5760i			1.15877i
$527$	6.15439	+	6.30016i	0.268090	+	0.274439i
$528$	11.7162	−	11.7162i	0.509884	−	0.509884i
$529$	18.2502	−	5.92985i	0.793487	−	0.257820i
$530$	−7.55118	+	57.1740i	−0.328002	+	2.48348i
$531$	−28.2090	+	20.4951i	−1.22417	+	0.889410i
$532$	−13.7790	+	3.69208i	−0.597397	+	0.160072i
$533$	−2.41474	+	9.01193i	−0.104594	+	0.390350i
$534$	0.912338	−	2.04914i	0.0394807	−	0.0886752i
$535$	0.955254	−	5.14221i	0.0412992	−	0.222317i
$536$	10.4914	−	4.67106i	0.453158	−	0.201759i
$537$	−13.3186	−	20.5088i	−0.574739	−	0.885021i
$538$	−2.90584	+	3.58841i	−0.125280	+	0.154707i
$539$	−15.8576	+	17.6117i	−0.683036	+	0.758588i
$540$	30.3892	−	73.2803i	1.30774	−	3.15348i
$541$	−0.460998	+	4.38611i	−0.0198199	+	0.188573i	−0.999952	−	0.00977090i	$-0.996890\pi$
$541$	−0.460998	+	4.38611i	−0.0198199	+	0.188573i	0.980132	+	0.198344i	$0.0635564\pi$
$542$	−19.5818	−	38.4314i	−0.841109	−	1.65077i
$543$	−6.83392	−	13.4123i	−0.293272	−	0.575578i
$544$	0.659198	−	6.27185i	0.0282629	−	0.268903i
$545$	−17.8734	+	7.39474i	−0.765612	+	0.316756i
$546$	−28.8336	+	32.0229i	−1.23396	+	1.37046i
$547$	−0.484470	+	0.598271i	−0.0207144	+	0.0255802i	−0.787398	−	0.616445i	$-0.788572\pi$
$547$	−0.484470	+	0.598271i	−0.0207144	+	0.0255802i	0.766683	+	0.642025i	$0.221906\pi$
$548$	33.9131	+	52.2217i	1.44870	+	2.23080i
$549$	−43.2335	+	19.2488i	−1.84516	+	0.821519i
$550$	−41.2783	−	23.8776i	−1.76011	−	1.01814i
$551$	5.88764	−	13.2239i	0.250822	−	0.563356i
$552$	−5.49381	+	20.5032i	−0.233832	+	0.872673i
$553$	2.40996	−	0.645746i	0.102482	−	0.0274599i
$554$	−59.4742	+	43.2106i	−2.52682	+	1.83584i
$555$	54.2275	+	7.16203i	2.30183	+	0.304011i
$556$	73.7108	−	23.9501i	3.12603	−	1.01571i
$557$	3.86000	−	3.86000i	0.163554	−	0.163554i	−0.620585	−	0.784139i	$-0.713105\pi$
$557$	3.86000	−	3.86000i	0.163554	−	0.163554i	0.784139	+	0.620585i	$0.213105\pi$
$558$	82.4074	−	3.35222i	3.48858	−	0.141911i
$559$			31.9829i			1.35273i
$560$	−2.34108	+	2.21976i	−0.0989288	+	0.0938021i
$561$	4.07369	+	19.1652i	0.171991	+	0.809156i
$562$	63.3746	+	10.0376i	2.67330	+	0.423409i
$563$	0.298315	+	1.11333i	0.0125725	+	0.0469211i	0.971927	−	0.235282i	$-0.0756014\pi$
$563$	0.298315	+	1.11333i	0.0125725	+	0.0469211i	−0.959355	+	0.282203i	$0.908935\pi$
$564$	31.6207	+	54.7687i	1.33147	+	2.30618i
$565$	7.39639	−	0.190618i	0.311169	−	0.00801936i
$566$	−21.0115	−	15.2658i	−0.883181	−	0.641669i
$567$	−11.9325	−	4.58044i	−0.501116	−	0.192360i
$568$	−21.9674	+	14.2658i	−0.921730	+	0.598579i
$569$	2.77102	+	26.3645i	0.116167	+	1.10526i	0.884931	+	0.465723i	$0.154206\pi$
$569$	2.77102	+	26.3645i	0.116167	+	1.10526i	−0.768763	+	0.639533i	$0.779128\pi$
$570$	52.9591	−	28.7261i	2.21821	−	1.20320i
$571$	24.5411	−	22.0969i	1.02701	−	0.924726i	0.0298160	−	0.999555i	$-0.490508\pi$
$571$	24.5411	−	22.0969i	1.02701	−	0.924726i	0.997196	+	0.0748293i	$0.0238412\pi$
$572$	61.8840	−	50.1127i	2.58750	−	2.09532i
$573$	61.1601	−	31.1627i	2.55500	−	1.30184i
$574$	4.03188	+	1.31004i	0.168287	+	0.0546799i
$575$	9.76037	+	0.00807959i	0.407035	+	0.000336942i
$576$	−50.8056	−	56.4253i	−2.11690	−	2.35105i
$577$	−19.6425	+	1.02942i	−0.817729	+	0.0428553i	−0.456613	−	0.889666i	$-0.650937\pi$
$577$	−19.6425	+	1.02942i	−0.817729	+	0.0428553i	−0.361116	+	0.932521i	$0.617604\pi$
$578$	26.4652	+	21.4311i	1.10081	+	0.891415i
$579$	11.7209	+	2.49136i	0.487105	+	0.103537i
$580$	−2.36318	−	30.1868i	−0.0981257	−	1.25344i
$581$	2.31856	−	3.19123i	0.0961903	−	0.132395i
$582$	10.5010	−	4.03095i	0.435280	−	0.167088i
$583$	−43.0627	−	11.5386i	−1.78347	−	0.477880i
$584$	5.18422	−	8.97934i	0.214525	−	0.371568i
$585$	37.5439	−	69.0790i	1.55225	−	2.85607i
$586$	37.4387	−	7.95785i	1.54658	−	0.328736i
$587$	−31.8305	−	16.2185i	−1.31379	−	0.669408i	−0.350168	−	0.936687i	$-0.613876\pi$
$587$	−31.8305	−	16.2185i	−1.31379	−	0.669408i	−0.963619	+	0.267279i	$0.913876\pi$
$588$	−44.2867	−	44.2867i	−1.82635	−	1.82635i
$589$	16.7919	+	12.5029i	0.691900	+	0.515174i
$590$	−26.2172	+	12.4916i	−1.07934	+	0.514272i
$591$	2.95930	+	9.10778i	0.121729	+	0.374644i
$592$	−5.84207	+	8.99599i	−0.240107	+	0.369733i
$593$	7.31690	−	46.1971i	0.300469	−	1.89709i	−0.125072	−	0.992148i	$-0.539916\pi$
$593$	7.31690	−	46.1971i	0.300469	−	1.89709i	0.425541	−	0.904939i	$-0.360084\pi$
$594$	83.3085	+	48.0982i	3.41819	+	1.97349i
$595$	−0.693669	−	3.75137i	−0.0284376	−	0.153791i
$596$	−9.22278	−	4.10625i	−0.377780	−	0.168198i
$597$	1.60619	+	10.1411i	0.0657368	+	0.415046i
$598$	−9.16182	+	23.8674i	−0.374655	+	0.976009i
$599$	6.00275	−	28.2407i	0.245266	−	1.15388i	−0.667248	−	0.744836i	$-0.732528\pi$
$599$	6.00275	−	28.2407i	0.245266	−	1.15388i	0.912513	−	0.409048i	$-0.134139\pi$
$600$	29.6492	−	45.5731i	1.21042	−	1.86051i
$601$	19.9617	+	17.9736i	0.814255	+	0.733158i	0.966909	−	0.255121i	$-0.0821155\pi$
$601$	19.9617	+	17.9736i	0.814255	+	0.733158i	−0.152654	+	0.988280i	$0.548782\pi$
$602$	14.5127	+	0.760579i	0.591494	+	0.0309989i
$603$	12.7866	+	15.7901i	0.520711	+	0.643024i
$604$	−8.87253	+	27.3068i	−0.361018	+	1.11110i
$605$	7.47183	−	9.72914i	0.303773	−	0.395546i
$606$	41.7197	+	4.38492i	1.69475	+	0.178125i
$607$	−1.14797	+	21.9046i	−0.0465948	+	0.889081i	0.870931	+	0.491405i	$0.163516\pi$
$607$	−1.14797	+	21.9046i	−0.0465948	+	0.889081i	−0.917526	+	0.397676i	$0.869817\pi$
$608$	−0.784550	−	14.9701i	−0.0318177	−	0.607118i
$609$	−12.5972	+	1.32402i	−0.510463	+	0.0536518i
$610$	−38.3306	+	9.18560i	−1.55196	+	0.371914i
$611$	13.3654	+	30.0191i	0.540706	+	1.21444i
$612$	−34.6567	+	5.48909i	−1.40092	+	0.221883i
$613$	10.0378	+	26.1494i	0.405423	+	1.05616i	0.972583	+	0.232556i	$0.0747087\pi$
$613$	10.0378	+	26.1494i	0.405423	+	1.05616i	−0.567160	+	0.823608i	$0.691958\pi$
$614$	13.9932	−	8.07895i	0.564718	−	0.326040i
$615$	−11.3791	−	0.900290i	−0.458848	−	0.0363032i
$616$	−9.17514	−	12.6285i	−0.369677	−	0.508816i
$617$	−35.0453	−	22.7587i	−1.41087	−	0.916230i	−0.999990	−	0.00454118i	$-0.998554\pi$
$617$	−35.0453	−	22.7587i	−1.41087	−	0.916230i	−0.410881	−	0.911689i	$-0.634779\pi$
$618$	−52.5466	+	103.129i	−2.11374	+	4.14844i
$619$	−33.9092			−1.36292			−0.681462	−	0.731854i	$-0.738656\pi$
$619$	−33.9092			−1.36292			−0.681462	+	0.731854i	$0.738656\pi$
$620$	43.3451	+	6.24172i	1.74078	+	0.250673i
$621$	−19.6891			−0.790097
$622$	−9.67640	+	18.9910i	−0.387988	+	0.761470i
$623$	−0.283151	−	0.183880i	−0.0113442	−	0.00736701i
$624$	13.3736	+	18.4072i	0.535374	+	0.736879i
$625$	−23.7636	−	7.76478i	−0.950544	−	0.310591i
$626$	−21.4426	+	12.3799i	−0.857019	+	0.494800i
$627$	16.6908	+	43.4810i	0.666566	+	1.73646i
$628$	83.5151	−	13.2275i	3.33261	−	0.527834i
$629$	−5.15914	−	11.5876i	−0.205708	−	0.462028i
$630$	−30.4528	−	18.6789i	−1.21327	−	0.744184i
$631$	31.0746	−	3.26608i	1.23706	−	0.130020i	0.536678	−	0.843787i	$-0.319679\pi$
$631$	31.0746	−	3.26608i	1.23706	−	0.130020i	0.700384	+	0.713767i	$0.253012\pi$
$632$	−0.431534	−	8.23416i	−0.0171655	−	0.327537i
$633$	−0.162978	+	3.10980i	−0.00647778	+	0.123603i
$634$	−54.3145	−	5.70868i	−2.15710	−	0.226721i
$635$	−2.24511	−	17.1080i	−0.0890943	−	0.678910i
$636$	36.4083	−	112.053i	1.44368	−	4.44320i
$637$	−20.4798	−	25.2905i	−0.811441	−	1.00205i
$638$	36.6657	+	1.92157i	1.45161	+	0.0760757i
$639$	−34.4383	−	31.0084i	−1.36236	−	1.22667i
$640$	−23.7102	−	38.7275i	−0.937228	−	1.53084i
$641$	−5.25587	+	24.7269i	−0.207594	+	0.976655i	0.743734	+	0.668476i	$0.233053\pi$
$641$	−5.25587	+	24.7269i	−0.207594	+	0.976655i	−0.951328	+	0.308179i	$0.900280\pi$
$642$	−6.00648	+	15.6474i	−0.237057	+	0.617554i
$643$	4.77154	+	30.1263i	0.188171	+	1.18807i	0.883169	+	0.469054i	$0.155405\pi$
$643$	4.77154	+	30.1263i	0.188171	+	1.18807i	−0.694998	+	0.719011i	$0.744595\pi$
$644$	6.76551	+	3.01220i	0.266598	+	0.118697i
$645$	−38.4772	+	7.11486i	−1.51504	+	0.280148i
$646$	−12.0994	−	6.98560i	−0.476045	−	0.274845i
$647$	−1.43105	+	9.03531i	−0.0562605	+	0.355215i	0.943458	+	0.331492i	$0.107552\pi$
$647$	−1.43105	+	9.03531i	−0.0562605	+	0.355215i	−0.999719	+	0.0237230i	$0.992448\pi$
$648$	−23.0058	+	35.4258i	−0.903751	+	1.39166i
$649$	−6.93741	−	21.3512i	−0.272317	−	0.838106i
$650$	41.2517	−	50.8555i	1.61802	−	1.99472i
$651$	2.12800	−	18.1954i	0.0834027	−	0.713135i
$652$	−55.9174	−	55.9174i	−2.18990	−	2.18990i
$653$	−5.96422	−	3.03892i	−0.233398	−	0.118922i	0.333381	−	0.942792i	$-0.391811\pi$
$653$	−5.96422	−	3.03892i	−0.233398	−	0.118922i	−0.566779	+	0.823870i	$0.691811\pi$
$654$	60.6311	−	12.8875i	2.37086	−	0.503942i
$655$	−1.26038	+	0.372773i	−0.0492470	+	0.0145655i
$656$	1.11922	−	1.93854i	0.0436981	−	0.0756873i
$657$	17.7190	+	4.74779i	0.691284	+	0.185229i
$658$	13.9395	−	5.35087i	0.543418	−	0.208599i
$659$	22.3864	−	30.8122i	0.872051	−	1.20027i	−0.106509	−	0.994312i	$-0.533967\pi$
$659$	22.3864	−	30.8122i	0.872051	−	1.20027i	0.978560	−	0.205963i	$-0.0660327\pi$
$660$	74.0551	+	63.3021i	2.88259	+	2.46403i
$661$	−39.2886	−	8.35106i	−1.52815	−	0.324818i	−0.634266	−	0.773115i	$-0.718698\pi$
$661$	−39.2886	−	8.35106i	−1.52815	−	0.324818i	−0.893885	+	0.448297i	$0.852031\pi$
$662$	49.0597	+	39.7277i	1.90676	+	1.54406i
$663$	−26.8684	+	1.40811i	−1.04348	+	0.0546865i
$664$	−8.72290	−	9.68776i	−0.338514	−	0.375958i
$665$	−3.02354	−	8.54947i	−0.117248	−	0.331534i
$666$	−112.967	−	36.7053i	−4.37739	−	1.42230i
$667$	−6.69583	+	3.41170i	−0.259264	+	0.132101i
$668$	36.3701	−	29.4520i	1.40720	−	1.13953i
$669$	−45.1904	+	40.6896i	−1.74716	+	1.57315i
$670$	8.06856	+	14.8751i	0.311716	+	0.574676i
$671$	−3.18500	−	30.3032i	−0.122956	−	1.16984i
$672$	−11.0012	+	7.14429i	−0.424382	+	0.275597i
$673$	−26.5880	−	10.2062i	−1.02489	−	0.393419i	−0.212892	−	0.977076i	$-0.568288\pi$
$673$	−26.5880	−	10.2062i	−1.02489	−	0.393419i	−0.812001	+	0.583657i	$0.801621\pi$
$674$	−11.2456	−	8.17042i	−0.433165	−	0.314713i
$675$	47.9501	+	15.6238i	1.84560	+	0.601361i
$676$	31.8095	+	55.0957i	1.22344	+	2.11906i
$677$	0.0400353	+	0.149414i	0.00153868	+	0.00574244i	0.966691	−	0.255947i	$-0.0823872\pi$
$677$	0.0400353	+	0.149414i	0.00153868	+	0.00574244i	−0.965152	+	0.261689i	$0.915720\pi$
$678$	−23.4184	−	3.70911i	−0.899379	−	0.142448i
$679$	−0.351999	−	1.65602i	−0.0135085	−	0.0635524i
$680$	−12.6034	−	0.335251i	−0.483316	−	0.0128563i
$681$		−	48.6803i		−	1.86543i
$682$	−14.3431	+	51.1281i	−0.549226	+	1.95780i
$683$	−0.670792	+	0.670792i	−0.0256671	+	0.0256671i	−0.719824	−	0.694157i	$-0.755777\pi$
$683$	−0.670792	+	0.670792i	−0.0256671	+	0.0256671i	0.694157	+	0.719824i	$0.255777\pi$
$684$	−79.3255	+	25.7744i	−3.03309	+	0.985510i
$685$	−31.4136	+	24.0838i	−1.20025	+	0.920196i
$686$	−26.3102	+	19.1155i	−1.00453	+	0.729833i
$687$	30.0558	−	8.05343i	1.14670	−	0.307257i
$688$	1.98602	−	7.41192i	0.0757163	−	0.282577i
$689$	24.8999	−	55.9262i	0.948612	−	2.13062i
$690$	−30.7519	−	5.71270i	−1.17071	−	0.217479i
$691$	−38.7472	+	17.2514i	−1.47401	+	0.656274i	−0.977342	−	0.211665i	$-0.932112\pi$
$691$	−38.7472	+	17.2514i	−1.47401	+	0.656274i	−0.496672	+	0.867938i	$0.665445\pi$
$692$	19.0742	+	29.3717i	0.725091	+	1.11654i
$693$	17.3799	−	21.4624i	0.660208	−	0.815289i
$694$	−13.8993	+	15.4367i	−0.527609	+	0.585969i
$695$	18.8358	+	45.5269i	0.714482	+	1.72693i
$696$	−4.37565	+	41.6315i	−0.165859	+	1.57804i
$697$	1.20170	+	2.35847i	0.0455177	+	0.0893336i
$698$	−29.9495	−	58.7793i	−1.13361	−	2.22483i
$699$	0.674169	−	6.41429i	0.0254994	−	0.242611i
$700$	−14.0862	−	12.7044i	−0.532408	−	0.480181i
$701$	21.7842	−	24.1938i	0.822777	−	0.913786i	−0.174711	−	0.984620i	$-0.555899\pi$
$701$	21.7842	−	24.1938i	0.822777	−	0.913786i	0.997488	+	0.0708335i	$0.0225659\pi$
$702$	−83.1301	+	102.657i	−3.13754	+	3.87454i
$703$	−16.4214	−	25.2868i	−0.619347	−	0.953710i
$704$	44.6596	−	19.8837i	1.68317	−	0.749397i
$705$	−33.1415	+	22.7574i	−1.24818	+	0.857092i
$706$	27.0695	−	60.7992i	1.01878	−	2.28821i
$707$	1.63421	−	6.09895i	0.0614607	−	0.229375i
$708$	57.3086	−	15.3558i	2.15379	−	0.577106i
$709$	31.1483	−	22.6306i	1.16980	−	0.849910i	0.178815	−	0.983883i	$-0.442774\pi$
$709$	31.1483	−	22.6306i	1.16980	−	0.849910i	0.990985	+	0.133973i	$0.0427735\pi$
$710$	−23.4835	−	30.6305i	−0.881319	−	1.14954i
$711$	13.8740	−	4.50795i	0.520317	−	0.169061i
$712$	−0.788972	+	0.788972i	−0.0295680	+	0.0295680i
$713$	−2.68996	−	10.5305i	−0.100740	−	0.394372i
$714$			12.2254i			0.457525i
$715$	34.8299	+	36.7335i	1.30256	+	1.37376i
$716$	5.86234	+	27.5801i	0.219086	+	1.03072i
$717$	29.9945	+	4.75066i	1.12016	+	0.177416i
$718$	5.33935	+	19.9267i	0.199263	+	0.743659i
$719$	−13.0446	−	22.5939i	−0.486480	−	0.842609i	0.513399	−	0.858150i	$-0.328386\pi$
$719$	−13.0446	−	22.5939i	−0.486480	−	0.842609i	−0.999879	+	0.0155414i	$0.995053\pi$
$720$	−12.9902	+	13.6775i	−0.484117	+	0.509730i
$721$	14.0942	+	10.2400i	0.524895	+	0.381359i
$722$	10.6610	+	4.09236i	0.396760	+	0.152302i
$723$	−17.8388	+	11.5847i	−0.663434	+	0.430839i
$724$	1.81426	+	17.2616i	0.0674266	+	0.641521i
$725$	19.0140	−	2.99539i	0.706163	−	0.111246i
$726$	−29.2141	+	26.3045i	−1.08424	+	0.976252i
$727$	13.7573	−	11.1404i	0.510230	−	0.413176i	−0.339331	−	0.940667i	$-0.610201\pi$
$727$	13.7573	−	11.1404i	0.510230	−	0.413176i	0.849560	+	0.527491i	$0.176867\pi$
$728$	19.0986	−	9.73124i	0.707843	−	0.360664i
$729$	16.7153	+	5.43114i	0.619086	+	0.201153i
$730$	13.7873	+	6.58321i	0.510291	+	0.243655i
$731$	6.07162	+	6.74321i	0.224567	+	0.249407i
$732$	80.4156	−	4.21440i	2.97225	−	0.155769i
$733$	−5.27611	−	4.27251i	−0.194878	−	0.157809i	0.526915	−	0.849918i	$-0.323348\pi$
$733$	−5.27611	−	4.27251i	−0.194878	−	0.157809i	−0.721793	+	0.692109i	$0.756682\pi$
$734$	−41.0035	−	8.71557i	−1.51347	−	0.321698i
$735$	25.8700	−	30.2645i	0.954230	−	1.11632i
$736$	−4.57440	+	6.29612i	−0.168615	+	0.232078i
$737$	−12.2129	+	4.68810i	−0.449869	+	0.172688i
$738$	23.9429	+	6.41547i	0.881349	+	0.236157i
$739$	−26.1407	+	45.2770i	−0.961600	+	1.66554i	−0.243115	+	0.969997i	$0.578169\pi$
$739$	−26.1407	+	45.2770i	−0.961600	+	1.66554i	−0.718485	+	0.695543i	$0.755164\pi$
$740$	−55.4139	−	30.1170i	−2.03706	−	1.10712i
$741$	−62.5576	+	13.2970i	−2.29811	+	0.488478i
$742$	−24.7852	−	12.6287i	−0.909894	−	0.463614i
$743$	20.5030	+	20.5030i	0.752181	+	0.752181i	0.974886	−	0.222705i	$-0.0714886\pi$
$743$	20.5030	+	20.5030i	0.752181	+	0.752181i	−0.222705	+	0.974886i	$0.571489\pi$
$744$	−57.3566	−	19.3813i	−2.10280	−	0.710553i
$745$	2.14481	−	6.04879i	0.0785796	−	0.221610i
$746$	11.4939	+	35.3745i	0.420821	+	1.29515i
$747$	12.5615	−	19.3430i	0.459600	−	0.707722i
$748$	3.53415	−	22.3137i	0.129221	−	0.815870i
$749$	2.18477	+	1.26138i	0.0798298	+	0.0460897i
$750$	70.3589	+	38.3150i	2.56914	+	1.39906i
$751$	−46.8246	−	20.8477i	−1.70865	−	0.760742i	−0.998385	−	0.0568115i	$-0.981907\pi$
$751$	−46.8246	−	20.8477i	−1.70865	−	0.760742i	−0.710269	−	0.703930i	$-0.751427\pi$
$752$	−1.23331	−	7.78678i	−0.0449740	−	0.283955i
$753$	7.30529	−	19.0309i	0.266220	−	0.693526i
$754$	−10.4824	+	49.3160i	−0.381748	+	1.79598i
$755$	−17.7463	−	4.26827i	−0.645853	−	0.155338i
$756$	28.4366	+	25.6044i	1.03423	+	0.931224i
$757$	−38.0178	−	1.99243i	−1.38178	−	0.0724160i	−0.653101	−	0.757271i	$-0.726532\pi$
$757$	−38.0178	−	1.99243i	−1.38178	−	0.0724160i	−0.728679	+	0.684855i	$0.759866\pi$
$758$	1.97547	+	2.43950i	0.0717523	+	0.0886067i
$759$	7.47180	−	22.9958i	0.271209	−	0.834696i
$760$	−29.7147	+	3.89950i	−1.07786	+	0.141450i
$761$	−21.4665	−	2.25622i	−0.778160	−	0.0817879i	−0.292883	−	0.956148i	$-0.594615\pi$
$761$	−21.4665	−	2.25622i	−0.778160	−	0.0817879i	−0.485277	+	0.874361i	$0.661281\pi$
$762$	−2.89388	+	55.2185i	−0.104834	+	2.00036i
$763$	−0.488287	−	9.31707i	−0.0176772	−	0.337301i
$764$	−78.7127	+	8.27304i	−2.84773	+	0.299308i
$765$	−5.19825	−	21.6918i	−0.187943	−	0.784269i
$766$	13.8474	+	31.1018i	0.500327	+	1.12375i
$767$	30.4483	−	4.82253i	1.09942	−	0.174132i
$768$	25.8237	+	67.2731i	0.931834	+	2.42751i
$769$	8.33914	−	4.81460i	0.300717	−	0.173619i	−0.342048	−	0.939682i	$-0.611121\pi$
$769$	8.33914	−	4.81460i	0.300717	−	0.173619i	0.642765	+	0.766063i	$0.277787\pi$
$770$	17.4967	−	14.9311i	0.630536	−	0.538078i
$771$	21.4840	+	29.5702i	0.773728	+	1.06494i
$772$	−11.5875	−	7.52504i	−0.417045	−	0.270832i
$773$	1.33723	−	2.62446i	0.0480969	−	0.0943954i	−0.865707	−	0.500551i	$-0.833131\pi$
$773$	1.33723	−	2.62446i	0.0480969	−	0.0943954i	0.913804	+	0.406155i	$0.133131\pi$
$774$	84.9720			3.05425
$775$	−1.80523	+	27.7802i	−0.0648458	+	0.997895i
$776$	−5.59515			−0.200854
$777$	−11.9779	+	23.5079i	−0.429704	+	0.843341i
$778$	−14.6248	−	9.49745i	−0.524324	−	0.340500i
$779$	3.69835	+	5.09034i	0.132507	+	0.182380i
$780$	−101.763	+	86.8410i	−3.64370	+	3.10941i
$781$	25.8394	−	14.9184i	0.924608	−	0.533823i
$782$	2.59931	+	6.77143i	0.0929511	+	0.242146i
$783$	−38.3510	+	6.07421i	−1.37055	+	0.217074i
$784$	3.17569	+	7.13271i	0.113417	+	0.254740i
$785$	12.5266	+	52.2725i	0.447095	+	1.86569i
$786$	4.18888	−	0.440269i	0.149413	−	0.0157039i
$787$	−1.92743	−	36.7775i	−0.0687054	−	1.31098i	−0.787742	−	0.616005i	$-0.788750\pi$
$787$	−1.92743	−	36.7775i	−0.0687054	−	1.31098i	0.719037	−	0.694972i	$-0.244583\pi$
$788$	0.577895	−	11.0269i	0.0205867	−	0.392817i
$789$	34.3259	+	3.60780i	1.22204	+	0.128441i
$790$	12.0468	−	1.58091i	0.428604	−	0.0562464i
$791$	−1.10282	+	3.39413i	−0.0392117	+	0.120681i
$792$	−57.4377	−	70.9296i	−2.04096	−	2.52038i
$793$	41.7837	+	2.18979i	1.48378	+	0.0777617i
$794$	21.1635	+	19.0557i	0.751064	+	0.676261i
$795$	72.8216	+	17.5148i	2.58272	+	0.621186i
$796$	2.46142	−	11.5801i	0.0872426	−	0.410444i
$797$	−10.8459	+	28.2545i	−0.384181	+	1.00082i	0.596047	+	0.802950i	$0.296737\pi$
$797$	−10.8459	+	28.2545i	−0.384181	+	1.00082i	−0.980227	+	0.197875i	$0.936596\pi$
$798$	4.54606	+	28.7027i	0.160929	+	1.01606i
$799$	8.51676	+	3.79191i	0.301301	+	0.134148i
$800$	16.1364	−	11.7034i	0.570510	−	0.413778i
$801$	−1.70958	−	0.987025i	−0.0604049	−	0.0348748i
$802$	7.78876	−	49.1763i	0.275031	−	1.73648i
$803$	−6.43263	+	9.90538i	−0.227003	+	0.349553i
$804$	−10.6834	−	32.8803i	−0.376776	−	1.15960i
$805$	−1.57335	+	4.43718i	−0.0554535	+	0.156390i
$806$	−66.2626	−	30.4362i	−2.33400	−	1.07207i
$807$	4.24036	+	4.24036i	0.149268	+	0.149268i
$808$	−18.5927	−	9.47344i	−0.654088	−	0.333274i
$809$	−15.1978	+	3.23039i	−0.534325	+	0.113574i	−0.467169	−	0.884168i	$-0.654726\pi$
$809$	−15.1978	+	3.23039i	−0.534325	+	0.113574i	−0.0671564	+	0.997742i	$0.521393\pi$
$810$	−54.6879	−	29.7224i	−1.92154	−	1.04434i
$811$	−16.7416	+	28.9972i	−0.587876	+	1.01823i	0.406634	+	0.913591i	$0.366702\pi$
$811$	−16.7416	+	28.9972i	−0.587876	+	1.01823i	−0.994510	+	0.104640i	$0.966631\pi$
$812$	14.1073	+	3.78005i	0.495071	+	0.132654i
$813$	−52.2968	+	20.0749i	−1.83413	+	0.704056i
$814$	44.9520	−	61.8711i	1.57557	−	2.16858i
$815$	32.6641	−	38.2127i	1.14417	−	1.33853i
$816$	6.31409	+	1.34210i	0.221037	+	0.0469830i
$817$	16.7623	+	13.5739i	0.586440	+	0.474890i
$818$	52.1500	−	2.73306i	1.82338	−	0.0955593i
$819$	25.3755	+	28.1823i	0.886691	+	0.984770i
$820$	11.8770	+	5.67107i	0.414763	+	0.198042i
$821$	8.10045	+	2.63199i	0.282708	+	0.0918572i	0.446939	−	0.894565i	$-0.352514\pi$
$821$	8.10045	+	2.63199i	0.282708	+	0.0918572i	−0.164231	+	0.986422i	$0.552514\pi$
$822$	113.023	−	57.5882i	3.94214	−	2.00862i
$823$	−26.5253	+	21.4798i	−0.924614	+	0.748738i	−0.968165	−	0.250314i	$-0.919466\pi$
$823$	−26.5253	+	21.4798i	−0.924614	+	0.748738i	0.0435509	+	0.999051i	$0.486133\pi$
$824$	42.7864	−	38.5250i	1.49053	−	1.34208i
$825$	−36.4443	+	50.0741i	−1.26883	+	1.74336i
$826$	−1.46421	−	13.9311i	−0.0509465	−	0.484723i
$827$	−11.0522	+	7.17736i	−0.384321	+	0.249581i	−0.722311	−	0.691569i	$-0.756920\pi$
$827$	−11.0522	+	7.17736i	−0.384321	+	0.249581i	0.337989	+	0.941150i	$0.390253\pi$
$828$	40.4253	+	15.5178i	1.40488	+	0.539282i
$829$	−16.8472	−	12.2402i	−0.585129	−	0.425121i	0.255441	−	0.966825i	$-0.417779\pi$
$829$	−16.8472	−	12.2402i	−0.585129	−	0.425121i	−0.840569	+	0.541704i	$0.817779\pi$
$830$	13.2286	−	13.9285i	0.459172	−	0.483465i
$831$	47.7375	+	82.6837i	1.65599	+	2.86827i
$832$	17.3744	+	64.8420i	0.602347	+	2.24799i
$833$	−9.11907	−	1.44432i	−0.315957	−	0.0500427i
$834$	−32.8270	−	154.439i	−1.13671	−	5.34778i
$835$	20.4700	+	21.5888i	0.708395	+	0.747112i
$836$		−	53.7020i		−	1.85732i
$837$	3.59521	−	56.0427i	0.124269	−	1.93712i
$838$	37.2248	−	37.2248i	1.28591	−	1.28591i
$839$	7.09514	−	2.30535i	0.244951	−	0.0795896i	−0.183968	−	0.982932i	$-0.558894\pi$
$839$	7.09514	−	2.30535i	0.244951	−	0.0795896i	0.428920	+	0.903343i	$0.358894\pi$
$840$	15.9559	+	20.8120i	0.550531	+	0.718081i
$841$	11.4717	−	8.33467i	0.395575	−	0.287402i
$842$	−15.5243	+	4.15973i	−0.535004	+	0.143354i
$843$	21.5680	−	80.4929i	0.742841	−	2.77232i
$844$	1.46044	−	3.28021i	0.0502705	−	0.112909i
$845$	−33.3394	+	22.8932i	−1.14691	+	0.787551i
$846$	79.7548	−	35.5091i	2.74203	−	1.22083i
$847$	3.22264	+	4.96244i	0.110731	+	0.170511i
$848$	−9.24329	+	11.4145i	−0.317416	+	0.391976i
$849$	−22.5699	+	25.0664i	−0.774597	+	0.860277i
$850$	−0.956947	−	18.5535i	−0.0328230	−	0.636379i
$851$	−1.63619	+	15.5673i	−0.0560877	+	0.533639i
$852$	35.7981	+	70.2578i	1.22642	+	2.40699i
$853$	12.3854	+	24.3077i	0.424067	+	0.832278i	0.999892	+	0.0147051i	$0.00468095\pi$
$853$	12.3854	+	24.3077i	0.424067	+	0.832278i	−0.575825	+	0.817573i	$0.695319\pi$
$854$	1.98730	−	18.9079i	0.0680041	−	0.647016i
$855$	−20.2706	−	48.9948i	−0.693238	−	1.67559i
$856$	5.57873	−	6.19581i	0.190677	−	0.211768i
$857$	−26.1893	+	32.3411i	−0.894609	+	1.10475i	0.0993557	+	0.995052i	$0.468322\pi$
$857$	−26.1893	+	32.3411i	−0.894609	+	1.10475i	−0.993965	+	0.109698i	$0.965011\pi$
$858$	−88.3511	−	136.049i	−3.01626	−	4.64463i
$859$	−17.1911	+	7.65399i	−0.586554	+	0.261151i	−0.678485	−	0.734615i	$-0.737363\pi$
$859$	−17.1911	+	7.65399i	−0.586554	+	0.261151i	0.0919303	+	0.995765i	$0.470696\pi$
$860$	44.3588	+	8.24042i	1.51262	+	0.280996i
$861$	2.23940	−	5.02978i	0.0763187	−	0.171415i
$862$	−7.68930	+	28.6969i	−0.261899	+	0.977419i
$863$	−3.17934	+	0.851902i	−0.108226	+	0.0289991i	−0.312526	−	0.949909i	$-0.601175\pi$
$863$	−3.17934	+	0.851902i	−0.108226	+	0.0289991i	0.204300	+	0.978908i	$0.434508\pi$
$864$	−32.5317	+	23.6357i	−1.10675	+	0.804102i
$865$	−17.6683	+	13.5458i	−0.600741	+	0.460570i
$866$	−27.5095	+	8.93837i	−0.934810	+	0.303738i
$867$	31.2734	−	31.2734i	1.06210	−	1.06210i
$868$	−9.80924	+	18.7072i	−0.332947	+	0.634963i
$869$			9.39250i			0.318619i
$870$	−61.6620	−	1.64021i	−2.09054	−	0.0556085i
$871$	−3.73486	−	17.5711i	−0.126551	−	0.595375i
$872$	−30.4540	−	4.82344i	−1.03130	−	0.163342i
$873$	−2.56206	−	9.56175i	−0.0867127	−	0.323616i
$874$	8.62060	+	14.9313i	0.291596	+	0.505059i
$875$	7.35270	−	9.55763i	0.248567	−	0.323107i
$876$	−25.2522	−	18.3468i	−0.853192	−	0.619880i
$877$	−37.3375	−	14.3325i	−1.26080	−	0.483975i	−0.366070	−	0.930587i	$-0.619297\pi$
$877$	−37.3375	−	14.3325i	−1.26080	−	0.483975i	−0.894728	+	0.446612i	$0.852630\pi$
$878$	−46.7494	+	30.3594i	−1.57771	+	1.02458i
$879$	−5.19600	−	49.4367i	−0.175257	−	1.66746i
$880$	−5.79070	−	10.6757i	−0.195205	−	0.359877i
$881$	−7.82755	+	7.04796i	−0.263717	+	0.237452i	−0.790372	−	0.612627i	$-0.790113\pi$
$881$	−7.82755	+	7.04796i	−0.263717	+	0.237452i	0.526655	+	0.850079i	$0.323446\pi$
$882$	−67.1917	+	54.4108i	−2.26246	+	1.83211i
$883$	−20.8721	+	10.6348i	−0.702400	+	0.357891i	−0.768436	−	0.639926i	$-0.778965\pi$
$883$	−20.8721	+	10.6348i	−0.702400	+	0.357891i	0.0660358	+	0.997817i	$0.478965\pi$
$884$	29.5043	+	9.58654i	0.992338	+	0.322430i
$885$	12.5753	+	35.5582i	0.422713	+	1.19528i
$886$	−11.2836	−	12.5317i	−0.379081	−	0.421012i
$887$	−27.0336	+	1.41677i	−0.907699	+	0.0475705i	−0.500468	−	0.865755i	$-0.666839\pi$
$887$	−27.0336	+	1.41677i	−0.907699	+	0.0475705i	−0.407231	+	0.913325i	$0.633506\pi$
$888$	67.7618	+	54.8724i	2.27394	+	1.84140i
$889$	8.14084	+	1.73039i	0.273035	+	0.0580354i
$890$	−1.24977	−	1.06830i	−0.0418925	−	0.0358096i
$891$	28.2822	−	38.9270i	0.947488	−	1.30411i
$892$	65.4586	−	25.1272i	2.19172	−	0.841321i
$893$	21.4056	+	5.73561i	0.716310	+	0.191935i
$894$	−10.2832	+	17.8111i	−0.343922	+	0.595691i
$895$	−17.1884	+	5.08371i	−0.574546	+	0.169930i
$896$	21.4243	−	4.55387i	0.715734	−	0.152134i
$897$	29.5836	+	15.0736i	0.987769	+	0.503293i
$898$	−29.0455	−	29.0455i	−0.969261	−	0.969261i
$899$	−8.48833	−	19.6818i	−0.283102	−	0.656426i
$900$	−86.1364	−	69.8700i	−2.87121	−	2.32900i
$901$	−5.36714	−	16.5184i	−0.178805	−	0.550307i
$902$	−8.69212	+	13.3847i	−0.289416	+	0.445661i
$903$	2.95253	−	18.6416i	0.0982542	−	0.620352i
$904$	10.2141	+	5.89714i	0.339718	+	0.196136i
$905$	−10.8497	+	2.00623i	−0.360657	+	0.0666895i
$906$	53.4346	+	23.7906i	1.77525	+	0.790391i
$907$	2.07676	+	13.1121i	0.0689576	+	0.435381i	0.997879	+	0.0651031i	$0.0207376\pi$
$907$	2.07676	+	13.1121i	0.0689576	+	0.435381i	−0.928921	+	0.370278i	$0.879262\pi$
$908$	−20.1153	+	52.4020i	−0.667548	+	1.73902i
$909$	7.67576	−	36.1116i	0.254589	−	1.19775i
$910$	16.4921	+	26.9377i	0.546708	+	0.892975i
$911$	1.65746	+	1.49238i	0.0549140	+	0.0494448i	0.696131	−	0.717915i	$-0.254903\pi$
$911$	1.65746	+	1.49238i	0.0549140	+	0.0494448i	−0.641217	+	0.767360i	$0.721570\pi$
$912$	15.3232	+	0.803056i	0.507402	+	0.0265918i
$913$	9.34519	+	11.5403i	0.309280	+	0.381930i
$914$	−27.5453	+	84.7757i	−0.911118	+	2.80413i
$915$	6.66070	+	50.7553i	0.220196	+	1.67792i
$916$	−35.6814	−	3.75027i	−1.17895	−	0.123912i
$917$	0.0331794	−	0.633100i	0.00109568	−	0.0209068i
$918$	1.96138	+	37.4254i	0.0647353	+	1.23522i
$919$	−2.11723	+	0.222530i	−0.0698410	+	0.00734059i	−0.139385	−	0.990238i	$-0.544512\pi$
$919$	−2.11723	+	0.222530i	−0.0698410	+	0.00734059i	0.0695435	+	0.997579i	$0.477846\pi$
$920$	13.2626	+	8.13490i	0.437256	+	0.268200i
$921$	−8.53525	−	19.1705i	−0.281246	−	0.631689i
$922$	−97.0436	+	15.3702i	−3.19596	+	0.506190i
$923$	14.6828	+	38.2500i	0.483291	+	1.25902i
$924$	−40.6960	+	23.4958i	−1.33880	+	0.772956i
$925$	16.3377	−	36.6135i	0.537181	−	1.20385i
$926$	10.1973	+	14.0354i	0.335105	+	0.461233i
$927$	85.4290	+	55.4782i	2.80586	+	1.82214i
$928$	−6.96776	+	13.6750i	−0.228728	+	0.448904i
$929$	−28.4603			−0.933753			−0.466876	−	0.884323i	$-0.654621\pi$
$929$	−28.4603			−0.933753			−0.466876	+	0.884323i	$0.654621\pi$
$930$	21.8758	−	86.4886i	0.717336	−	2.83607i
$931$	−21.9467			−0.719275
$932$	−3.37617	+	6.62610i	−0.110590	+	0.217045i
$933$	23.2154	+	15.0763i	0.760039	+	0.493575i
$934$	29.5769	+	40.7091i	0.967785	+	1.33204i
$935$	14.3170	+	1.13273i	0.468214	+	0.0370443i
$936$	108.538	−	62.6647i	3.54769	−	2.04826i
$937$	1.22352	+	3.18738i	0.0399707	+	0.104127i	0.952113	−	0.305747i	$-0.0989061\pi$
$937$	1.22352	+	3.18738i	0.0399707	+	0.104127i	−0.912142	+	0.409874i	$0.865573\pi$
$938$	−8.06199	+	1.27689i	−0.263233	+	0.0416921i
$939$	13.0791	+	29.3762i	0.426821	+	0.958655i
$940$	45.0789	−	10.8027i	1.47031	−	0.352347i
$941$	41.0697	−	4.31660i	1.33884	−	0.140717i	0.592114	−	0.805854i	$-0.298294\pi$
$941$	41.0697	−	4.31660i	1.33884	−	0.140717i	0.746721	+	0.665137i	$0.231627\pi$
$942$	−9.01514	−	172.019i	−0.293729	−	5.60468i
$943$	0.170956	−	3.26203i	0.00556709	−	0.106226i
$944$	−7.35575	−	0.773121i	−0.239409	−	0.0251629i
$945$	−14.8163	+	19.2924i	−0.481973	+	0.627582i
$946$	−16.9061	+	52.0315i	−0.549663	+	1.69169i
$947$	30.7169	+	37.9323i	0.998166	+	1.23263i	0.972486	+	0.232963i	$0.0748420\pi$
$947$	30.7169	+	37.9323i	0.998166	+	1.23263i	0.0256806	+	0.999670i	$0.491825\pi$
$948$	−24.7883	−	1.29910i	−0.805087	−	0.0421928i
$949$	−12.0526	−	10.8522i	−0.391244	−	0.352278i
$950$	−9.14588	−	43.2038i	−0.296731	−	1.40172i
$951$	−14.7468	+	69.3783i	−0.478198	+	2.24975i
$952$	2.17935	−	5.67740i	0.0706331	−	0.184005i
$953$	−4.50446	−	28.4401i	−0.145914	−	0.921264i	−0.946654	−	0.322252i	$-0.895560\pi$
$953$	−4.50446	−	28.4401i	−0.145914	−	0.921264i	0.800740	−	0.599012i	$-0.204440\pi$
$954$	−148.584	−	66.1541i	−4.81060	−	2.14182i
$955$	−9.14842	−	49.4748i	−0.296036	−	1.60097i
$956$	−30.3246	−	17.5079i	−0.980767	−	0.566246i
$957$	7.45945	−	47.0971i	0.241130	−	1.52243i
$958$	−41.2875	+	63.5772i	−1.33394	+	2.05408i
$959$	−5.90002	−	18.1584i	−0.190521	−	0.586365i
$960$	−74.1436	+	35.3270i	−2.39297	+	1.14017i
$961$	30.4651	−	5.73379i	0.982746	−	0.184961i
$962$	74.2580	+	74.2580i	2.39417	+	2.39417i
$963$	13.1428	+	6.69658i	0.423520	+	0.215794i
$964$	23.9896	−	5.09914i	0.772652	−	0.164232i
$965$	4.19418	−	7.71711i	0.135016	−	0.248422i
$966$	7.54341	−	13.0656i	0.242705	−	0.420378i
$967$	42.5232	+	11.3941i	1.36746	+	0.366408i	0.866549	−	0.499093i	$-0.166333\pi$
$967$	42.5232	+	11.3941i	1.36746	+	0.366408i	0.500907	+	0.865501i	$0.333000\pi$
$968$	18.2560	−	7.00781i	0.586769	−	0.225240i
$969$	−10.6652	+	14.6794i	−0.342617	+	0.471571i
$970$	−0.643469	−	8.21955i	−0.0206606	−	0.263914i
$971$	15.0079	+	3.19003i	0.481627	+	0.102373i	0.442326	−	0.896854i	$-0.354154\pi$
$971$	15.0079	+	3.19003i	0.481627	+	0.102373i	0.0393011	+	0.999227i	$0.487487\pi$
$972$	16.1078	+	13.0438i	0.516657	+	0.418380i
$973$	−23.7323	+	1.24376i	−0.760824	+	0.0398731i
$974$	59.7965	+	66.4107i	1.91600	+	2.12794i
$975$	−60.0855	−	60.1851i	−1.92428	−	1.92746i
$976$	−9.54726	−	3.10209i	−0.305600	−	0.0992955i
$977$	34.2410	−	17.4466i	1.09547	−	0.558167i	0.189655	−	0.981851i	$-0.439263\pi$
$977$	34.2410	−	17.4466i	1.09547	−	0.558167i	0.905810	+	0.423683i	$0.139263\pi$
$978$	−125.197	+	101.382i	−4.00334	+	3.24184i
$979$	0.944530	−	0.850459i	0.0301873	−	0.0271808i
$980$	−40.3535	+	21.8885i	−1.28904	+	0.699203i
$981$	−5.70218	−	54.2526i	−0.182057	−	1.73215i
$982$	1.65833	−	1.07693i	0.0529194	−	0.0343662i
$983$	−9.69316	−	3.72086i	−0.309164	−	0.118677i	0.198839	−	0.980032i	$-0.436283\pi$
$983$	−9.69316	−	3.72086i	−0.309164	−	0.118677i	−0.508003	+	0.861355i	$0.669616\pi$
$984$	−14.7206	−	10.6952i	−0.469277	−	0.340949i
$985$	7.01711	−	0.180843i	0.223584	−	0.00576215i
$986$	7.15204	+	12.3877i	0.227767	+	0.394504i
$987$	−5.01891	−	18.7308i	−0.159754	−	0.596209i
$988$	72.8347	+	11.5359i	2.31718	+	0.367005i
$989$	−2.32813	−	10.9530i	−0.0740301	−	0.348284i
$990$	97.5935	−	92.5360i	3.10172	−	2.94099i
$991$		−	31.0645i		−	0.986797i	−0.869803	−	0.493398i	$-0.835754\pi$
$991$		−	31.0645i		−	0.986797i	0.869803	−	0.493398i	$-0.164246\pi$
$992$	−17.0859	−	14.1701i	−0.542477	−	0.449903i
$993$	57.9729	−	57.9729i	1.83972	−	1.83972i
$994$	17.7057	−	5.75294i	0.561591	−	0.182472i
$995$	7.46114	+	0.985419i	0.236534	+	0.0312399i
$996$	−31.7494	+	23.0673i	−1.00602	+	0.730914i
$997$	36.2321	−	9.70835i	1.14748	−	0.307467i	0.365526	−	0.930801i	$-0.380889\pi$
$997$	36.2321	−	9.70835i	1.14748	−	0.307467i	0.781955	+	0.623335i	$0.214223\pi$
$998$	14.3947	−	53.7217i	0.455655	−	1.70053i
$999$	−32.8961	+	73.8859i	−1.04079	+	2.33765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.x.a.117.2	yes	224
5.2	odd	4		775.2.df.b.768.2		224
5.3	odd	4	inner	155.2.x.a.148.13	yes	224
5.4	even	2		775.2.df.b.582.13		224
31.22	odd	30	inner	155.2.x.a.22.13	✓	224
155.22	even	60		775.2.df.b.518.13		224
155.53	even	60	inner	155.2.x.a.53.2	yes	224
155.84	odd	30		775.2.df.b.332.2		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.x.a.22.13	✓	224	31.22	odd	30	inner
155.2.x.a.53.2	yes	224	155.53	even	60	inner
155.2.x.a.117.2	yes	224	1.1	even	1	trivial
155.2.x.a.148.13	yes	224	5.3	odd	4	inner
775.2.df.b.332.2		224	155.84	odd	30
775.2.df.b.518.13		224	155.22	even	60
775.2.df.b.582.13		224	5.4	even	2
775.2.df.b.768.2		224	5.2	odd	4

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:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06639 + 2.09291i) q^{2} +(2.55847 + 1.66149i) q^{3} +(-2.06752 - 2.84570i) q^{4} +(1.70092 - 1.45151i) q^{5} +(-6.20568 + 3.58285i) q^{6} +(0.386520 + 1.00692i) q^{7} +(3.52057 - 0.557603i) q^{8} +(2.56500 + 5.76109i) q^{9} +O(q^{10})\)	\(q+(-1.06639 + 2.09291i) q^{2} +(2.55847 + 1.66149i) q^{3} +(-2.06752 - 2.84570i) q^{4} +(1.70092 - 1.45151i) q^{5} +(-6.20568 + 3.58285i) q^{6} +(0.386520 + 1.00692i) q^{7} +(3.52057 - 0.557603i) q^{8} +(2.56500 + 5.76109i) q^{9} +(1.22403 + 5.10775i) q^{10} +(-4.03806 + 0.424417i) q^{11} +(-0.561591 - 10.7158i) q^{12} +(0.291801 - 5.56789i) q^{13} +(-2.51958 - 0.264818i) q^{14} +(6.76341 - 0.887572i) q^{15} +(-0.413370 + 1.27222i) q^{16} +(-0.995483 - 1.22932i) q^{17} +(-14.7927 - 0.775255i) q^{18} +(-2.79431 - 2.51601i) q^{19} +(-7.64724 - 1.83929i) q^{20} +(-0.684085 + 3.21837i) q^{21} +(3.41789 - 8.90390i) q^{22} +(0.305372 + 1.92804i) q^{23} +(9.93370 + 4.42277i) q^{24} +(0.786260 - 4.93779i) q^{25} +(11.3419 + 6.54827i) q^{26} +(-1.57784 + 9.96207i) q^{27} +(2.06625 - 3.18175i) q^{28} +(1.18962 + 3.66129i) q^{29} +(-5.35484 + 15.1017i) q^{30} +(-5.54370 + 0.517145i) q^{31} +(2.81906 + 2.81906i) q^{32} +(-11.0364 - 5.62333i) q^{33} +(3.63443 - 0.772523i) q^{34} +(2.11899 + 1.15165i) q^{35} +(11.0911 - 19.2104i) q^{36} +(7.74543 + 2.07538i) q^{37} +(8.24562 - 3.16520i) q^{38} +(9.99754 - 13.7604i) q^{39} +(5.17884 - 6.05856i) q^{40} +(-1.63679 - 0.347910i) q^{41} +(-6.00626 - 4.86377i) q^{42} +(-5.72843 + 0.300214i) q^{43} +(9.55654 + 10.6136i) q^{44} +(12.7251 + 6.07603i) q^{45} +(-4.36087 - 1.41693i) q^{46} +(-5.25125 + 2.67565i) q^{47} +(-3.17137 + 2.56813i) q^{48} +(4.33753 - 3.90553i) q^{49} +(9.49591 + 6.91120i) q^{50} +(-0.504412 - 4.79916i) q^{51} +(-16.4478 + 10.6814i) q^{52} +(10.2506 + 3.93485i) q^{53} +(-19.1672 - 13.9258i) q^{54} +(-6.25238 + 6.58317i) q^{55} +(1.92223 + 3.32940i) q^{56} +(-2.96883 - 11.0798i) q^{57} +(-8.93136 - 1.41459i) q^{58} +(1.14957 + 5.40830i) q^{59} +(-16.5093 - 17.4115i) q^{60} +7.50440i q^{61} +(4.82941 - 12.1540i) q^{62} +(-4.80952 + 4.80952i) q^{63} +(-11.4507 + 3.72056i) q^{64} +(-7.58550 - 9.89409i) q^{65} +(23.5383 - 17.1016i) q^{66} +(3.11210 - 0.833884i) q^{67} +(-1.44009 + 5.37449i) q^{68} +(-2.42213 + 5.44020i) q^{69} +(-4.66998 + 3.20675i) q^{70} +(-6.71312 + 2.98887i) q^{71} +(12.2427 + 18.8520i) q^{72} +(1.83060 - 2.26060i) q^{73} +(-12.6033 + 13.9973i) q^{74} +(10.2157 - 11.3268i) q^{75} +(-1.38251 + 13.1537i) q^{76} +(-1.98815 - 3.90195i) q^{77} +(18.1381 + 35.5980i) q^{78} +(0.241801 - 2.30058i) q^{79} +(1.14353 + 2.76395i) q^{80} +(-7.92951 + 8.80661i) q^{81} +(2.47360 - 3.05465i) q^{82} +(-1.99189 - 3.06725i) q^{83} +(10.5729 - 4.70734i) q^{84} +(-3.47760 - 0.646024i) q^{85} +(5.48043 - 12.3093i) q^{86} +(-3.03957 + 11.3438i) q^{87} +(-13.9796 + 3.74582i) q^{88} +(-0.253245 + 0.183994i) q^{89} +(-26.2866 + 20.1531i) q^{90} +(5.71920 - 1.85828i) q^{91} +(4.85526 - 4.85526i) q^{92} +(-15.0426 - 7.88768i) q^{93} -13.8437i q^{94} +(-8.40490 - 0.223571i) q^{95} +(2.52864 + 11.8963i) q^{96} +(-1.55038 - 0.245557i) q^{97} +(3.54842 + 13.2429i) q^{98} +(-12.8027 - 22.1750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8}+O(q^{10}) \) 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8	\( 224 q - 12 q^{2} - 14 q^{3} - 8 q^{5} - 36 q^{6} + 6 q^{7} - 40 q^{8} - 10 q^{10} - 28 q^{11} - 40 q^{12} - 14 q^{13} - 20 q^{15} + 24 q^{16} - 14 q^{17} - 40 q^{18} - 44 q^{20} - 44 q^{21} + 30 q^{22} - 30 q^{23} - 22 q^{25} - 48 q^{26} + 100 q^{27} - 48 q^{28} - 44 q^{31} + 28 q^{32} + 20 q^{33} - 72 q^{35} + 16 q^{36} + 30 q^{37} + 38 q^{38} - 4 q^{40} - 20 q^{41} - 130 q^{42} + 22 q^{43} - 34 q^{45} - 28 q^{47} - 156 q^{48} + 158 q^{50} - 36 q^{51} - 10 q^{52} + 26 q^{53} + 98 q^{55} - 48 q^{56} - 20 q^{58} + 260 q^{60} + 30 q^{62} + 152 q^{63} + 32 q^{65} - 152 q^{66} + 38 q^{67} - 126 q^{68} + 166 q^{70} - 128 q^{71} - 156 q^{72} - 30 q^{73} + 26 q^{75} + 128 q^{76} + 30 q^{78} + 154 q^{80} - 64 q^{81} + 8 q^{82} - 82 q^{83} + 60 q^{85} - 28 q^{86} - 24 q^{87} + 252 q^{88} + 38 q^{90} + 194 q^{93} - 74 q^{95} + 60 q^{96} - 38 q^{97} + 174 q^{98}+O(q^{100}) \) 224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8 - 10 * q^10 - 28 * q^11 - 40 * q^12 - 14 * q^13 - 20 * q^15 + 24 * q^16 - 14 * q^17 - 40 * q^18 - 44 * q^20 - 44 * q^21 + 30 * q^22 - 30 * q^23 - 22 * q^25 - 48 * q^26 + 100 * q^27 - 48 * q^28 - 44 * q^31 + 28 * q^32 + 20 * q^33 - 72 * q^35 + 16 * q^36 + 30 * q^37 + 38 * q^38 - 4 * q^40 - 20 * q^41 - 130 * q^42 + 22 * q^43 - 34 * q^45 - 28 * q^47 - 156 * q^48 + 158 * q^50 - 36 * q^51 - 10 * q^52 + 26 * q^53 + 98 * q^55 - 48 * q^56 - 20 * q^58 + 260 * q^60 + 30 * q^62 + 152 * q^63 + 32 * q^65 - 152 * q^66 + 38 * q^67 - 126 * q^68 + 166 * q^70 - 128 * q^71 - 156 * q^72 - 30 * q^73 + 26 * q^75 + 128 * q^76 + 30 * q^78 + 154 * q^80 - 64 * q^81 + 8 * q^82 - 82 * q^83 + 60 * q^85 - 28 * q^86 - 24 * q^87 + 252 * q^88 + 38 * q^90 + 194 * q^93 - 74 * q^95 + 60 * q^96 - 38 * q^97 + 174 * q^98

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