LMFDB - Embedded newform 136.2.s.c.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(3,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 8, 1]))

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

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

chi := DirichletCharacter("136.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.s (of order $16$, degree $8$, 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:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			107.4
Character	$\chi$	$=$	136.107
Dual form			136.2.s.c.75.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.950422 - 1.04723i) q^{2} +(-0.476222 - 0.712717i) q^{3} +(-0.193397 + 1.99063i) q^{4} +(3.02707 + 0.602122i) q^{5} +(-0.293769 + 1.17610i) q^{6} +(0.952929 - 0.189549i) q^{7} +(2.26846 - 1.68940i) q^{8} +(0.866872 - 2.09281i) q^{9} +O(q^{10})$	\(q+(-0.950422 - 1.04723i) q^{2} +(-0.476222 - 0.712717i) q^{3} +(-0.193397 + 1.99063i) q^{4} +(3.02707 + 0.602122i) q^{5} +(-0.293769 + 1.17610i) q^{6} +(0.952929 - 0.189549i) q^{7} +(2.26846 - 1.68940i) q^{8} +(0.866872 - 2.09281i) q^{9} +(-2.24643 - 3.74232i) q^{10} +(-2.60689 - 1.74187i) q^{11} +(1.51085 - 0.810144i) q^{12} +(-1.58016 + 1.58016i) q^{13} +(-1.10419 - 0.817787i) q^{14} +(-1.01242 - 2.44419i) q^{15} +(-3.92520 - 0.769963i) q^{16} +(3.89953 - 1.33927i) q^{17} +(-3.01556 + 1.08124i) q^{18} +(-0.0290025 - 0.0700182i) q^{19} +(-1.78403 + 5.90933i) q^{20} +(-0.588901 - 0.588901i) q^{21} +(0.653502 + 4.38554i) q^{22} +(6.03453 + 4.03215i) q^{23} +(-2.28436 - 0.812239i) q^{24} +(4.18123 + 1.73192i) q^{25} +(3.15662 + 0.152979i) q^{26} +(-4.42653 + 0.880492i) q^{27} +(0.193028 + 1.93358i) q^{28} +(-0.355742 + 1.78844i) q^{29} +(-1.59742 + 3.38325i) q^{30} +(-3.16242 - 4.73290i) q^{31} +(2.92426 + 4.84239i) q^{32} +2.68749i q^{33} +(-5.10873 - 2.81085i) q^{34} +2.99872 q^{35} +(3.99836 + 2.13036i) q^{36} +(-9.56893 + 6.39375i) q^{37} +(-0.0457608 + 0.0969192i) q^{38} +(1.87872 + 0.373700i) q^{39} +(7.88403 - 3.74806i) q^{40} +(0.717320 + 3.60621i) q^{41} +(-0.0570127 + 1.17642i) q^{42} +(-0.518515 + 1.25181i) q^{43} +(3.97158 - 4.85248i) q^{44} +(3.88422 - 5.81314i) q^{45} +(-1.51275 - 10.1518i) q^{46} +(-7.47101 + 7.47101i) q^{47} +(1.32050 + 3.16423i) q^{48} +(-5.59501 + 2.31753i) q^{49} +(-2.16020 - 6.02478i) q^{50} +(-2.81157 - 2.14147i) q^{51} +(-2.83992 - 3.45111i) q^{52} +(5.63693 - 2.33489i) q^{53} +(5.12915 + 3.79877i) q^{54} +(-6.84243 - 6.84243i) q^{55} +(1.84146 - 2.03987i) q^{56} +(-0.0360916 + 0.0540148i) q^{57} +(2.21101 - 1.32722i) q^{58} +(-4.26316 - 1.76586i) q^{59} +(5.06127 - 1.54265i) q^{60} +(-0.161091 - 0.809857i) q^{61} +(-1.95082 + 7.81005i) q^{62} +(0.429376 - 2.15862i) q^{63} +(2.29183 - 7.66469i) q^{64} +(-5.73472 + 3.83182i) q^{65} +(2.81443 - 2.55425i) q^{66} +13.3446i q^{67} +(1.91183 + 8.02153i) q^{68} -6.22112i q^{69} +(-2.85005 - 3.14036i) q^{70} +(4.29199 - 2.86782i) q^{71} +(-1.56914 - 6.21197i) q^{72} +(1.60806 - 8.08428i) q^{73} +(15.7903 + 3.94414i) q^{74} +(-0.756824 - 3.80481i) q^{75} +(0.144989 - 0.0441919i) q^{76} +(-2.81435 - 1.16574i) q^{77} +(-1.39422 - 2.32263i) q^{78} +(2.82218 - 4.22369i) q^{79} +(-11.4182 - 4.69418i) q^{80} +(-2.06976 - 2.06976i) q^{81} +(3.09479 - 4.17862i) q^{82} +(13.9679 - 5.78571i) q^{83} +(1.28617 - 1.05839i) q^{84} +(12.6106 - 1.70608i) q^{85} +(1.80374 - 0.646738i) q^{86} +(1.44406 - 0.598150i) q^{87} +(-8.85635 + 0.452730i) q^{88} +(-2.44821 + 2.44821i) q^{89} +(-9.77936 + 1.45725i) q^{90} +(-1.20626 + 1.80530i) q^{91} +(-9.19356 + 11.2327i) q^{92} +(-1.86720 + 4.50783i) q^{93} +(14.9245 + 0.723284i) q^{94} +(-0.0456332 - 0.229413i) q^{95} +(2.05865 - 4.39022i) q^{96} +(2.89469 + 0.575790i) q^{97} +(7.74462 + 3.65665i) q^{98} +(-5.90525 + 3.94576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26} + 32 q^{27} + 40 q^{28} - 72 q^{30} + 32 q^{32} - 72 q^{34} - 32 q^{35} + 56 q^{36} + 48 q^{38} + 56 q^{40} - 16 q^{41} - 56 q^{42} - 96 q^{43} + 24 q^{44} - 24 q^{46} + 16 q^{48} - 16 q^{49} - 16 q^{51} - 16 q^{52} - 24 q^{54} + 32 q^{56} + 32 q^{57} + 48 q^{58} - 16 q^{59} + 96 q^{60} + 48 q^{62} + 40 q^{64} + 64 q^{65} - 16 q^{66} + 80 q^{68} + 64 q^{70} + 96 q^{72} - 96 q^{73} + 40 q^{74} - 16 q^{75} + 48 q^{76} + 96 q^{78} + 8 q^{80} - 96 q^{81} + 32 q^{82} + 128 q^{83} + 64 q^{86} - 72 q^{88} - 16 q^{89} + 152 q^{90} - 16 q^{91} - 120 q^{92} + 88 q^{94} - 160 q^{96} - 16 q^{97} + 128 q^{98} + 48 q^{99}+O(q^{100}) $ 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 - 56 * q^24 - 16 * q^25 - 40 * q^26 + 32 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 + 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 96 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 - 24 * q^54 + 32 * q^56 + 32 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 - 16 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 - 96 * q^81 + 32 * q^82 + 128 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$	−0.950422	−	1.04723i	−0.672050	−	0.740506i
$2$	−0.950422	−	1.04723i	−0.672050	−	0.740506i
$3$	−0.476222	−	0.712717i	−0.274947	−	0.411487i	0.668139	−	0.744037i	$-0.267091\pi$
$3$	−0.476222	−	0.712717i	−0.274947	−	0.411487i	−0.943086	+	0.332549i	$0.892091\pi$
$4$	−0.193397	+	1.99063i	−0.0966985	+	0.995314i
$5$	3.02707	+	0.602122i	1.35375	+	0.269277i	0.818057	−	0.575137i	$-0.195051\pi$
$5$	3.02707	+	0.602122i	1.35375	+	0.269277i	0.535691	+	0.844414i	$0.320051\pi$
$6$	−0.293769	+	1.17610i	−0.119931	+	0.480140i
$7$	0.952929	−	0.189549i	0.360173	−	0.0716429i	−0.0116868	−	0.999932i	$-0.503720\pi$
$7$	0.952929	−	0.189549i	0.360173	−	0.0716429i	0.371860	+	0.928289i	$0.378720\pi$
$8$	2.26846	−	1.68940i	0.802022	−	0.597294i
$9$	0.866872	−	2.09281i	0.288957	−	0.697605i
$10$	−2.24643	−	3.74232i	−0.710385	−	1.18343i
$11$	−2.60689	−	1.74187i	−0.786007	−	0.525193i	0.0965893	−	0.995324i	$-0.469207\pi$
$11$	−2.60689	−	1.74187i	−0.786007	−	0.525193i	−0.882597	+	0.470131i	$0.844207\pi$
$12$	1.51085	−	0.810144i	0.436146	−	0.233868i
$13$	−1.58016	+	1.58016i	−0.438258	+	0.438258i	−0.891426	−	0.453167i	$-0.850294\pi$
$13$	−1.58016	+	1.58016i	−0.438258	+	0.438258i	0.453167	+	0.891426i	$0.350294\pi$
$14$	−1.10419	−	0.817787i	−0.295106	−	0.218563i
$15$	−1.01242	−	2.44419i	−0.261405	−	0.631088i
$16$	−3.92520	−	0.769963i	−0.981299	−	0.192491i
$17$	3.89953	−	1.33927i	0.945776	−	0.324821i
$17$	3.89953	−	1.33927i	0.945776	−	0.324821i
$18$	−3.01556	+	1.08124i	−0.710774	+	0.254850i
$19$	−0.0290025	−	0.0700182i	−0.00665363	−	0.0160633i	0.920518	−	0.390701i	$-0.127767\pi$
$19$	−0.0290025	−	0.0700182i	−0.00665363	−	0.0160633i	−0.927171	+	0.374637i	$0.877767\pi$
$20$	−1.78403	+	5.90933i	−0.398921	+	1.32137i
$21$	−0.588901	−	0.588901i	−0.128509	−	0.128509i
$22$	0.653502	+	4.38554i	0.139327	+	0.934999i
$23$	6.03453	+	4.03215i	1.25829	+	0.840761i	0.992377	−	0.123237i	$-0.0393275\pi$
$23$	6.03453	+	4.03215i	1.25829	+	0.840761i	0.265910	+	0.963998i	$0.414328\pi$
$24$	−2.28436	−	0.812239i	−0.466293	−	0.165798i
$25$	4.18123	+	1.73192i	0.836245	+	0.346384i
$26$	3.15662	+	0.152979i	0.619064	+	0.0300016i
$27$	−4.42653	+	0.880492i	−0.851886	+	0.169451i
$28$	0.193028	+	1.93358i	0.0364790	+	0.365413i
$29$	−0.355742	+	1.78844i	−0.0660596	+	0.332104i	−0.999656	−	0.0262219i	$-0.991652\pi$
$29$	−0.355742	+	1.78844i	−0.0660596	+	0.332104i	0.933597	+	0.358326i	$0.116652\pi$
$30$	−1.59742	+	3.38325i	−0.291647	+	0.617694i
$31$	−3.16242	−	4.73290i	−0.567988	−	0.850054i	0.430634	−	0.902526i	$-0.358290\pi$
$31$	−3.16242	−	4.73290i	−0.567988	−	0.850054i	−0.998622	+	0.0524723i	$0.983290\pi$
$32$	2.92426	+	4.84239i	0.516941	+	0.856021i
$33$			2.68749i			0.467833i
$34$	−5.10873	−	2.81085i	−0.876140	−	0.482057i
$35$	2.99872			0.506876
$36$	3.99836	+	2.13036i	0.666394	+	0.355061i
$37$	−9.56893	+	6.39375i	−1.57312	+	1.05113i	−0.606446	+	0.795124i	$0.707406\pi$
$37$	−9.56893	+	6.39375i	−1.57312	+	1.05113i	−0.966676	+	0.256002i	$0.917594\pi$
$38$	−0.0457608	+	0.0969192i	−0.00742339	+	0.0157224i
$39$	1.87872	+	0.373700i	0.300836	+	0.0598399i
$40$	7.88403	−	3.74806i	1.24657	−	0.592620i
$41$	0.717320	+	3.60621i	0.112027	+	0.563195i	0.995504	+	0.0947214i	$0.0301960\pi$
$41$	0.717320	+	3.60621i	0.112027	+	0.563195i	−0.883477	+	0.468474i	$0.844804\pi$
$42$	−0.0570127	+	1.17642i	−0.00879725	+	0.181526i
$43$	−0.518515	+	1.25181i	−0.0790729	+	0.190899i	−0.958472	−	0.285186i	$-0.907945\pi$
$43$	−0.518515	+	1.25181i	−0.0790729	+	0.190899i	0.879399	+	0.476085i	$0.157945\pi$
$44$	3.97158	−	4.85248i	0.598738	−	0.731538i
$45$	3.88422	−	5.81314i	0.579025	−	0.866572i
$46$	−1.51275	−	10.1518i	−0.223043	−	1.49680i
$47$	−7.47101	+	7.47101i	−1.08976	+	1.08976i	−0.0942060	+	0.995553i	$0.530031\pi$
$47$	−7.47101	+	7.47101i	−1.08976	+	1.08976i	−0.995553	+	0.0942060i	$0.969969\pi$
$48$	1.32050	+	3.16423i	0.190598	+	0.456717i
$49$	−5.59501	+	2.31753i	−0.799287	+	0.331076i
$50$	−2.16020	−	6.02478i	−0.305499	−	0.852032i
$51$	−2.81157	−	2.14147i	−0.393698	−	0.299866i
$52$	−2.83992	−	3.45111i	−0.393826	−	0.478583i
$53$	5.63693	−	2.33489i	0.774292	−	0.320722i	0.0396827	−	0.999212i	$-0.487365\pi$
$53$	5.63693	−	2.33489i	0.774292	−	0.320722i	0.734610	+	0.678490i	$0.237365\pi$
$54$	5.12915	+	3.79877i	0.697989	+	0.516948i
$55$	−6.84243	−	6.84243i	−0.922634	−	0.922634i
$56$	1.84146	−	2.03987i	0.246075	−	0.272589i
$57$	−0.0360916	+	0.0540148i	−0.00478044	+	0.00715444i
$58$	2.21101	−	1.32722i	0.290320	−	0.174273i
$59$	−4.26316	−	1.76586i	−0.555016	−	0.229895i	0.0875039	−	0.996164i	$-0.472111\pi$
$59$	−4.26316	−	1.76586i	−0.555016	−	0.229895i	−0.642520	+	0.766269i	$0.722111\pi$
$60$	5.06127	−	1.54265i	0.653408	−	0.199155i
$61$	−0.161091	−	0.809857i	−0.0206255	−	0.103692i	0.969101	−	0.246663i	$-0.0793342\pi$
$61$	−0.161091	−	0.809857i	−0.0206255	−	0.103692i	−0.989727	+	0.142972i	$0.954334\pi$
$62$	−1.95082	+	7.81005i	−0.247754	+	0.991877i
$63$	0.429376	−	2.15862i	0.0540963	−	0.271960i
$64$	2.29183	−	7.66469i	0.286479	−	0.958087i
$65$	−5.73472	+	3.83182i	−0.711305	+	0.475279i
$66$	2.81443	−	2.55425i	0.346433	−	0.314407i
$67$			13.3446i			1.63030i	0.579251	+	0.815149i	$0.303345\pi$
$67$			13.3446i			1.63030i	−0.579251	+	0.815149i	$0.696655\pi$
$68$	1.91183	+	8.02153i	0.231844	+	0.972753i
$69$		−	6.22112i		−	0.748934i
$70$	−2.85005	−	3.14036i	−0.340646	−	0.375345i
$71$	4.29199	−	2.86782i	0.509366	−	0.340347i	−0.274183	−	0.961677i	$-0.588407\pi$
$71$	4.29199	−	2.86782i	0.509366	−	0.340347i	0.783549	+	0.621330i	$0.213407\pi$
$72$	−1.56914	−	6.21197i	−0.184925	−	0.732087i
$73$	1.60806	−	8.08428i	0.188210	−	0.946193i	−0.765034	−	0.643990i	$-0.777278\pi$
$73$	1.60806	−	8.08428i	0.188210	−	0.946193i	0.953243	−	0.302203i	$-0.0977222\pi$
$74$	15.7903	+	3.94414i	1.83558	+	0.458497i
$75$	−0.756824	−	3.80481i	−0.0873905	−	0.439342i
$76$	0.144989	−	0.0441919i	0.0166314	−	0.00506915i
$77$	−2.81435	−	1.16574i	−0.320725	−	0.132849i
$78$	−1.39422	−	2.32263i	−0.157865	−	0.262986i
$79$	2.82218	−	4.22369i	0.317520	−	0.475202i	−0.638038	−	0.770005i	$-0.720254\pi$
$79$	2.82218	−	4.22369i	0.317520	−	0.475202i	0.955558	+	0.294802i	$0.0952538\pi$
$80$	−11.4182	−	4.69418i	−1.27660	−	0.524826i
$81$	−2.06976	−	2.06976i	−0.229973	−	0.229973i
$82$	3.09479	−	4.17862i	0.341762	−	0.461452i
$83$	13.9679	−	5.78571i	1.53318	−	0.635064i	0.553002	−	0.833180i	$-0.313482\pi$
$83$	13.9679	−	5.78571i	1.53318	−	0.635064i	0.980179	+	0.198116i	$0.0634822\pi$
$84$	1.28617	−	1.05839i	0.140333	−	0.115480i
$85$	12.6106	−	1.70608i	1.36781	−	0.185050i
$86$	1.80374	−	0.646738i	0.194503	−	0.0697395i
$87$	1.44406	−	0.598150i	0.154820	−	0.0641284i
$88$	−8.85635	+	0.452730i	−0.944090	+	0.0482611i
$89$	−2.44821	+	2.44821i	−0.259510	+	0.259510i	−0.824855	−	0.565345i	$-0.808743\pi$
$89$	−2.44821	+	2.44821i	−0.259510	+	0.259510i	0.565345	+	0.824855i	$0.308743\pi$
$90$	−9.77936	+	1.45725i	−1.03084	+	0.153608i
$91$	−1.20626	+	1.80530i	−0.126451	+	0.189247i
$92$	−9.19356	+	11.2327i	−0.958495	+	1.17109i
$93$	−1.86720	+	4.50783i	−0.193620	+	0.467440i
$94$	14.9245	+	0.723284i	1.53934	+	0.0746010i
$95$	−0.0456332	−	0.229413i	−0.00468186	−	0.0235373i
$96$	2.05865	−	4.39022i	0.210111	−	0.448075i
$97$	2.89469	+	0.575790i	0.293911	+	0.0584626i	0.339844	−	0.940482i	$-0.389626\pi$
$97$	2.89469	+	0.575790i	0.293911	+	0.0584626i	−0.0459323	+	0.998945i	$0.514626\pi$
$98$	7.74462	+	3.65665i	0.782324	+	0.369378i
$99$	−5.90525	+	3.94576i	−0.593500	+	0.396564i
$100$	−4.25625	+	7.98832i	−0.425625	+	0.798832i
$101$	−16.3100			−1.62291			−0.811453	−	0.584418i	$-0.801323\pi$
$101$	−16.3100			−1.62291			−0.811453	+	0.584418i	$0.801323\pi$
$102$	0.429551	+	4.97967i	0.0425318	+	0.493061i
$103$			16.6955i			1.64506i	0.568724	+	0.822528i	$0.307437\pi$
$103$			16.6955i			1.64506i	−0.568724	+	0.822528i	$0.692563\pi$
$104$	−0.915005	+	6.25407i	−0.0897236	+	0.613262i
$105$	−1.42806	−	2.13724i	−0.139364	−	0.208573i
$106$	−7.80264	−	3.68405i	−0.757860	−	0.357827i
$107$	1.87066	−	9.40446i	0.180844	−	0.909163i	−0.778655	−	0.627452i	$-0.784098\pi$
$107$	1.87066	−	9.40446i	0.180844	−	0.909163i	0.959499	−	0.281712i	$-0.0909021\pi$
$108$	−0.896653	−	8.98186i	−0.0862805	−	0.864280i
$109$	−1.78498	+	0.355055i	−0.170970	+	0.0340081i	−0.279833	−	0.960049i	$-0.590279\pi$
$109$	−1.78498	+	0.355055i	−0.170970	+	0.0340081i	0.108863	+	0.994057i	$0.465279\pi$
$110$	−0.662430	+	13.6688i	−0.0631602	+	1.30327i
$111$	9.11388	+	3.77509i	0.865051	+	0.358316i
$112$	−3.88638	+	0.0102982i	−0.367228	+	0.000973087i
$113$	−16.0269	−	10.7088i	−1.50768	−	1.00740i	−0.988243	−	0.152893i	$-0.951141\pi$
$113$	−16.0269	−	10.7088i	−1.50768	−	1.00740i	−0.519438	−	0.854508i	$-0.673859\pi$
$114$	0.0908683	−	0.0135406i	0.00851060	−	0.00126819i
$115$	15.8391	+	15.8391i	1.47701	+	1.47701i
$116$	−3.49131	−	1.05403i	−0.324160	−	0.0978640i
$117$	1.93719	+	4.67679i	0.179093	+	0.432369i
$118$	2.20253	+	6.14283i	0.202760	+	0.565494i
$119$	3.46212	−	2.01538i	0.317372	−	0.184750i
$120$	−6.42586	−	3.83417i	−0.586598	−	0.350010i
$121$	−0.447743	−	1.08095i	−0.0407039	−	0.0982679i
$122$	−0.695005	+	0.938405i	−0.0629228	+	0.0849592i
$123$	2.22860	−	2.22860i	0.200946	−	0.200946i
$124$	10.0330	−	5.37988i	0.900994	−	0.483127i
$125$	−1.21709	−	0.813234i	−0.108860	−	0.0727379i
$126$	−2.66867	+	1.60194i	−0.237744	+	0.142712i
$127$	−4.96467	+	11.9858i	−0.440543	+	1.06357i	0.535215	+	0.844716i	$0.320231\pi$
$127$	−4.96467	+	11.9858i	−0.440543	+	1.06357i	−0.975758	+	0.218850i	$0.929769\pi$
$128$	−10.2049	+	4.88461i	−0.901997	+	0.431742i
$129$	1.13911	−	0.226584i	0.100293	−	0.0199496i
$130$	9.46321	+	2.36375i	0.829979	+	0.207315i
$131$	13.8424	+	2.75343i	1.20942	+	0.240568i	0.758306	−	0.651899i	$-0.226027\pi$
$131$	13.8424	+	2.75343i	1.20942	+	0.240568i	0.451112	+	0.892467i	$0.351027\pi$
$132$	−5.34980	−	0.519753i	−0.465640	−	0.0452387i
$133$	−0.0409092	−	0.0612250i	−0.00354728	−	0.00530888i
$134$	13.9749	−	12.6830i	1.20725	−	1.09564i
$135$	−13.9296			−1.19887
$136$	6.58337	−	9.62597i	0.564519	−	0.825420i
$137$	6.18839			0.528710			0.264355	−	0.964425i	$-0.414841\pi$
$137$	6.18839			0.528710			0.264355	+	0.964425i	$0.414841\pi$
$138$	−6.51496	+	5.91268i	−0.554590	+	0.503321i
$139$	−2.95138	−	4.41705i	−0.250332	−	0.374649i	0.684927	−	0.728612i	$-0.259834\pi$
$139$	−2.95138	−	4.41705i	−0.250332	−	0.374649i	−0.935260	+	0.353963i	$0.884834\pi$
$140$	−0.579943	+	5.96933i	−0.0490141	+	0.504500i
$141$	8.88258	+	1.76685i	0.748048	+	0.148796i
$142$	−7.08247	−	1.76908i	−0.594348	−	0.148458i
$143$	6.87175	−	1.36688i	0.574645	−	0.114304i
$144$	−5.01403	+	7.54725i	−0.417836	+	0.628937i
$145$	−2.15371	+	5.19953i	−0.178856	+	0.431797i
$146$	−9.99447	+	5.99946i	−0.827148	+	0.496519i
$147$	4.31621	+	2.88400i	0.355995	+	0.237868i
$148$	−10.8770	−	20.2847i	−0.894082	−	1.66739i
$149$	5.88907	−	5.88907i	0.482451	−	0.482451i	−0.423462	−	0.905914i	$-0.639185\pi$
$149$	5.88907	−	5.88907i	0.482451	−	0.482451i	0.905914	+	0.423462i	$0.139185\pi$
$150$	−3.26523	+	4.40875i	−0.266605	+	0.359973i
$151$	0.452102	+	1.09147i	0.0367915	+	0.0888226i	0.941207	−	0.337830i	$-0.109693\pi$
$151$	0.452102	+	1.09147i	0.0367915	+	0.0888226i	−0.904416	+	0.426652i	$0.859693\pi$
$152$	−0.184080	−	0.109837i	−0.0149309	−	0.00890893i
$153$	0.577551	−	9.32198i	0.0466922	−	0.753637i
$154$	1.45402	+	4.05523i	0.117168	+	0.326780i
$155$	−6.72310	−	16.2310i	−0.540013	−	1.30371i
$156$	−1.10724	+	3.66756i	−0.0886499	+	0.293639i
$157$	0.742246	+	0.742246i	0.0592377	+	0.0592377i	0.736105	−	0.676867i	$-0.236663\pi$
$157$	0.742246	+	0.742246i	0.0592377	+	0.0592377i	−0.676867	+	0.736105i	$0.736663\pi$
$158$	−7.10545	+	1.05881i	−0.565279	+	0.0842340i
$159$	−4.34855	−	2.90561i	−0.344863	−	0.230430i
$160$	5.93624	+	16.4190i	0.469301	+	1.29804i
$161$	6.51477	+	2.69851i	0.513436	+	0.212672i
$162$	−0.200378	+	4.13466i	−0.0157431	+	0.324850i
$163$	12.3438	−	2.45534i	0.966843	−	0.192317i	0.313675	−	0.949530i	$-0.398440\pi$
$163$	12.3438	−	2.45534i	0.966843	−	0.192317i	0.653168	+	0.757213i	$0.273440\pi$
$164$	−7.31735	+	0.730486i	−0.571389	+	0.0570414i
$165$	−1.61820	+	8.13524i	−0.125977	+	0.633328i
$166$	−19.3344	−	9.12883i	−1.50064	−	0.708535i
$167$	−10.1354	−	15.1687i	−0.784299	−	1.17379i	−0.981130	−	0.193349i	$-0.938065\pi$
$167$	−10.1354	−	15.1687i	−0.784299	−	1.17379i	0.196831	−	0.980437i	$-0.436935\pi$
$168$	−2.33079	−	0.341008i	−0.179824	−	0.0263093i
$169$			8.00617i			0.615859i
$170$	−13.7720	−	11.5847i	−1.05627	−	0.888508i
$171$	−0.171677			−0.0131284
$172$	−2.39160	−	1.27427i	−0.182358	−	0.0971619i
$173$	11.6821	−	7.80571i	0.888172	−	0.593457i	−0.0256059	−	0.999672i	$-0.508151\pi$
$173$	11.6821	−	7.80571i	0.888172	−	0.593457i	0.913778	+	0.406215i	$0.133151\pi$
$174$	−1.99887	−	0.943775i	−0.151534	−	0.0715474i
$175$	4.31270	+	0.857849i	0.326009	+	0.0648473i
$176$	8.89138	+	8.84439i	0.670213	+	0.666671i
$177$	0.771654	+	3.87937i	0.0580011	+	0.291591i
$178$	4.89069	+	0.237017i	0.366573	+	0.0177651i
$179$	1.72160	−	4.15632i	0.128679	−	0.310658i	−0.846389	−	0.532565i	$-0.821228\pi$
$179$	1.72160	−	4.15632i	0.128679	−	0.310658i	0.975068	+	0.221907i	$0.0712282\pi$
$180$	10.8206	+	8.85627i	0.806520	+	0.660108i
$181$	7.67619	−	11.4882i	0.570566	−	0.853913i	−0.428194	−	0.903687i	$-0.640850\pi$
$181$	7.67619	−	11.4882i	0.570566	−	0.853913i	0.998761	+	0.0497739i	$0.0158501\pi$
$182$	3.03703	−	0.452558i	0.225120	−	0.0335458i
$183$	−0.500484	+	0.500484i	−0.0369968	+	0.0369968i
$184$	20.5010	−	1.04800i	1.51136	−	0.0772593i
$185$	−32.8157	+	13.5927i	−2.41266	+	0.999355i
$186$	6.49538	−	2.32894i	0.476264	−	0.170766i
$187$	−12.4985	−	3.30114i	−0.913980	−	0.241403i
$188$	−13.4271	−	16.3169i	−0.979274	−	1.19003i
$189$	−4.05127	+	1.67809i	−0.294687	+	0.122063i
$190$	−0.196879	+	0.265828i	−0.0142831	+	0.0192852i
$191$	14.8703	+	14.8703i	1.07598	+	1.07598i	0.996866	+	0.0791129i	$0.0252088\pi$
$191$	14.8703	+	14.8703i	1.07598	+	1.07598i	0.0791129	+	0.996866i	$0.474791\pi$
$192$	−6.55418	+	2.01667i	−0.473007	+	0.145541i
$193$	9.70926	−	14.5309i	0.698888	−	1.04596i	−0.296957	−	0.954891i	$-0.595972\pi$
$193$	9.70926	−	14.5309i	0.698888	−	1.04596i	0.995845	−	0.0910685i	$-0.0290282\pi$
$194$	−2.14819	−	3.57866i	−0.154231	−	0.256933i
$195$	5.46201	+	2.26244i	0.391142	+	0.162016i
$196$	−3.53128	−	11.5858i	−0.252234	−	0.827556i
$197$	−1.04188	−	5.23788i	−0.0742308	−	0.373183i	0.925757	−	0.378119i	$-0.123429\pi$
$197$	−1.04188	−	5.23788i	−0.0742308	−	0.373183i	−0.999988	+	0.00493555i	$0.998429\pi$
$198$	9.74462	+	2.43404i	0.692520	+	0.172980i
$199$	−0.566039	+	2.84567i	−0.0401254	+	0.201724i	−0.995648	−	0.0931939i	$-0.970292\pi$
$199$	−0.566039	+	2.84567i	−0.0401254	+	0.201724i	0.955523	+	0.294918i	$0.0952923\pi$
$200$	12.4109	−	3.13499i	0.877581	−	0.221677i
$201$	9.51090	−	6.35498i	0.670847	−	0.448246i
$202$	15.5014	+	17.0804i	1.09067	+	1.20177i
$203$			1.77168i			0.124348i
$204$	4.80662	−	5.18263i	0.336531	−	0.362856i
$205$			11.3482i			0.792591i
$206$	17.4841	−	15.8678i	1.21817	−	1.10556i
$207$	13.6697	−	9.13381i	0.950110	−	0.634843i
$208$	7.41911	−	4.98578i	0.514423	−	0.345702i
$209$	−0.0463562	+	0.233048i	−0.00320653	+	0.0161203i
$210$	−0.880931	+	3.52679i	−0.0607900	+	0.243371i
$211$	−3.91913	−	19.7028i	−0.269804	−	1.35640i	−0.843413	−	0.537266i	$-0.819457\pi$
$211$	−3.91913	−	19.7028i	−0.269804	−	1.35640i	0.573609	−	0.819129i	$-0.305543\pi$
$212$	3.55774	+	11.6726i	0.244346	+	0.801677i
$213$	−4.08788	−	1.69326i	−0.280097	−	0.116020i
$214$	−11.6266	+	6.97918i	−0.794777	+	0.477087i
$215$	−2.32333	+	3.47710i	−0.158449	+	0.237136i
$216$	−8.55391	+	9.47556i	−0.582020	+	0.644730i
$217$	−3.91068	−	3.91068i	−0.265474	−	0.265474i
$218$	2.06831	+	1.53184i	0.140084	+	0.103749i
$219$	−6.52760	+	2.70382i	−0.441094	+	0.182707i
$220$	14.9440	−	12.2974i	1.00753	−	0.829093i
$221$	−4.04563	+	8.27816i	−0.272139	+	0.556849i
$222$	−4.70862	−	13.1323i	−0.316022	−	0.881382i
$223$	0.210517	−	0.0871989i	0.0140972	−	0.00583927i	−0.375624	−	0.926772i	$-0.622571\pi$
$223$	0.210517	−	0.0871989i	0.0140972	−	0.00583927i	0.389721	+	0.920933i	$0.372571\pi$
$224$	3.70448	+	4.06016i	0.247516	+	0.271281i
$225$	7.24918	−	7.24918i	0.483279	−	0.483279i
$226$	4.01766	+	26.9618i	0.267251	+	1.79347i
$227$	−8.32200	+	12.4548i	−0.552351	+	0.826651i	−0.997635	−	0.0687382i	$-0.978103\pi$
$227$	−8.32200	+	12.4548i	−0.552351	+	0.826651i	0.445284	+	0.895389i	$0.353103\pi$
$228$	−0.100543	−	0.0822911i	−0.00665865	−	0.00544986i
$229$	−3.98356	+	9.61716i	−0.263241	+	0.635520i	−0.999135	−	0.0415764i	$-0.986762\pi$
$229$	−3.98356	+	9.61716i	−0.263241	+	0.635520i	0.735894	+	0.677096i	$0.236762\pi$
$230$	1.53342	−	31.6411i	0.101111	−	2.08635i
$231$	0.509413	+	2.56099i	0.0335169	+	0.168501i
$232$	2.21440	+	4.65799i	0.145383	+	0.305812i
$233$	10.0107	+	1.99126i	0.655826	+	0.130452i	0.511777	−	0.859119i	$-0.328988\pi$
$233$	10.0107	+	1.99126i	0.655826	+	0.130452i	0.144049	+	0.989571i	$0.453988\pi$
$234$	3.05654	−	6.47361i	0.199812	−	0.423193i
$235$	−27.1138	+	18.1168i	−1.76871	+	1.18181i
$236$	4.33965	−	8.14485i	0.282487	−	0.530184i
$237$	−4.35428			−0.282841
$238$	−5.40105	−	1.71018i	−0.350098	−	0.110855i
$239$		−	17.7319i		−	1.14698i	−0.819212	−	0.573491i	$-0.805589\pi$
$239$		−	17.7319i		−	1.14698i	0.819212	−	0.573491i	$-0.194411\pi$
$240$	2.09200	+	10.3735i	0.135038	+	0.669604i
$241$	7.96800	+	11.9250i	0.513264	+	0.768154i	0.994078	−	0.108669i	$-0.0346588\pi$
$241$	7.96800	+	11.9250i	0.513264	+	0.768154i	−0.480814	+	0.876823i	$0.659659\pi$
$242$	−0.706459	+	1.49625i	−0.0454129	+	0.0961824i
$243$	−3.13096	+	15.7404i	−0.200851	+	1.00975i
$244$	1.64328	−	0.164047i	0.105200	−	0.0105021i
$245$	−18.3320	+	3.64645i	−1.17119	+	0.232963i
$246$	−4.45198	−	0.215756i	−0.283848	−	0.0137561i
$247$	0.156469	+	0.0648115i	0.00995588	+	0.00412386i
$248$	−15.1696	−	5.39379i	−0.963272	−	0.342506i
$249$	−10.7754	−	7.19991i	−0.682865	−	0.456275i
$250$	0.305103	+	2.04749i	0.0192964	+	0.129495i
$251$	1.84387	+	1.84387i	0.116384	+	0.116384i	0.762900	−	0.646516i	$-0.223775\pi$
$251$	1.84387	+	1.84387i	0.116384	+	0.116384i	−0.646516	+	0.762900i	$0.723775\pi$
$252$	4.21397	+	1.27220i	0.265455	+	0.0801409i
$253$	−8.70790	−	21.0227i	−0.547461	−	1.32169i
$254$	17.2704	−	6.19237i	1.08364	−	0.388544i
$255$	−7.22139	−	8.17530i	−0.452221	−	0.511957i
$256$	14.8143	+	6.04451i	0.925895	+	0.377782i
$257$	7.95090	+	19.1952i	0.495963	+	1.19736i	0.951640	+	0.307216i	$0.0993974\pi$
$257$	7.95090	+	19.1952i	0.495963	+	1.19736i	−0.455676	+	0.890145i	$0.650603\pi$
$258$	−1.31992	−	0.977568i	−0.0821749	−	0.0608607i
$259$	−7.90658	+	7.90658i	−0.491291	+	0.491291i
$260$	−6.51864	−	12.1568i	−0.404269	−	0.753930i
$261$	3.43448	+	2.29485i	0.212589	+	0.142047i
$262$	−10.2727	−	17.1132i	−0.634647	−	1.05725i
$263$	8.18893	−	19.7698i	0.504951	−	1.21906i	−0.441806	−	0.897111i	$-0.645662\pi$
$263$	8.18893	−	19.7698i	0.504951	−	1.21906i	0.946757	−	0.321949i	$-0.104338\pi$
$264$	4.54026	+	6.09647i	0.279434	+	0.375212i
$265$	18.4693	−	3.67377i	1.13456	−	0.225678i
$266$	−0.0252359	+	0.101031i	−0.00154731	+	0.00619461i
$267$	2.91078	+	0.578990i	0.178137	+	0.0354336i
$268$	−26.5641	−	2.58080i	−1.62266	−	0.157647i
$269$	−6.41702	−	9.60375i	−0.391253	−	0.585551i	0.582592	−	0.812765i	$-0.302038\pi$
$269$	−6.41702	−	9.60375i	−0.391253	−	0.585551i	−0.973845	+	0.227214i	$0.927038\pi$
$270$	13.2390	+	14.5875i	0.805700	+	0.887770i
$271$	−21.5356			−1.30820			−0.654098	−	0.756410i	$-0.726952\pi$
$271$	−21.5356			−1.30820			−0.654098	+	0.756410i	$0.726952\pi$
$272$	−16.3376	+	2.25440i	−0.990613	+	0.136693i
$273$	1.86112			0.112640
$274$	−5.88158	−	6.48069i	−0.355319	−	0.391513i
$275$	−7.88323	−	11.7981i	−0.475376	−	0.711451i
$276$	12.3839	+	1.20315i	0.745425	+	0.0724208i
$277$	−2.70972	−	0.538997i	−0.162811	−	0.0323852i	0.113011	−	0.993594i	$-0.463950\pi$
$277$	−2.70972	−	0.538997i	−0.162811	−	0.0323852i	−0.275823	+	0.961208i	$0.588950\pi$
$278$	−1.82063	+	7.28884i	−0.109194	+	0.437155i
$279$	−12.6465	+	2.51555i	−0.757126	+	0.150602i
$280$	6.80247	−	5.06605i	0.406526	−	0.302754i
$281$	−7.93908	+	19.1666i	−0.473606	+	1.14339i	0.488953	+	0.872310i	$0.337379\pi$
$281$	−7.93908	+	19.1666i	−0.473606	+	1.14339i	−0.962558	+	0.271075i	$0.912621\pi$
$282$	−6.59189	−	10.9814i	−0.392541	−	0.653932i
$283$	4.42553	+	2.95705i	0.263071	+	0.175778i	0.680110	−	0.733110i	$-0.261932\pi$
$283$	4.42553	+	2.95705i	0.263071	+	0.175778i	−0.417039	+	0.908889i	$0.636932\pi$
$284$	4.87870	+	9.09838i	0.289497	+	0.539890i
$285$	−0.141775	+	0.141775i	−0.00839805	+	0.00839805i
$286$	−7.96250	−	5.89722i	−0.470832	−	0.348710i
$287$	1.36711	+	3.30049i	0.0806979	+	0.194822i
$288$	12.6692	−	1.92220i	0.746538	−	0.113267i
$289$	13.4127	−	10.4451i	0.788983	−	0.614415i
$290$	7.49206	−	2.68630i	0.439949	−	0.157745i
$291$	−0.968141	−	2.33730i	−0.0567535	−	0.137015i
$292$	15.7818	+	4.76453i	0.923560	+	0.278823i
$293$	16.3573	+	16.3573i	0.955605	+	0.955605i	0.999056	−	0.0434506i	$-0.0138351\pi$
$293$	16.3573	+	16.3573i	0.955605	+	0.955605i	−0.0434506	+	0.999056i	$0.513835\pi$
$294$	−1.08200	−	7.26110i	−0.0631035	−	0.423476i
$295$	−11.8416	−	7.91233i	−0.689446	−	0.460673i
$296$	−10.9051	+	30.6698i	−0.633847	+	1.78264i
$297$	13.0732	+	5.41509i	0.758583	+	0.314215i
$298$	−11.7643	−	0.570133i	−0.681489	−	0.0330269i
$299$	−15.9070	+	3.16410i	−0.919925	+	0.182985i
$300$	7.72033	−	0.770716i	0.445734	−	0.0444973i
$301$	−0.256829	+	1.29117i	−0.0148034	+	0.0744216i
$302$	0.713338	−	1.51081i	0.0410480	−	0.0869376i
$303$	7.76719	+	11.6244i	0.446213	+	0.667805i
$304$	0.0599290	+	0.297166i	0.00343717	+	0.0170436i
$305$		−	2.54849i		−	0.145926i
$306$	−10.3112	+	8.25498i	−0.589452	+	0.471906i
$307$	7.78071			0.444069			0.222034	−	0.975039i	$-0.428730\pi$
$307$	7.78071			0.444069			0.222034	+	0.975039i	$0.428730\pi$
$308$	2.86485	−	5.37688i	0.163240	−	0.306376i
$309$	11.8992	−	7.95077i	0.676920	−	0.452304i
$310$	−10.6079	+	22.4670i	−0.602487	+	1.27604i
$311$	−4.66647	−	0.928218i	−0.264611	−	0.0526344i	0.0610016	−	0.998138i	$-0.480571\pi$
$311$	−4.66647	−	0.928218i	−0.264611	−	0.0526344i	−0.325613	+	0.945503i	$0.605571\pi$
$312$	4.89313	−	2.32619i	0.277019	−	0.131695i
$313$	3.79165	+	19.0619i	0.214316	+	1.07744i	0.926743	+	0.375695i	$0.122596\pi$
$313$	3.79165	+	19.0619i	0.214316	+	1.07744i	−0.712427	+	0.701746i	$0.752404\pi$
$314$	0.0718584	−	1.48275i	0.00405520	−	0.0836766i
$315$	2.59951	−	6.27576i	0.146466	−	0.353599i
$316$	7.86199	+	6.43476i	0.442272	+	0.361983i
$317$	−5.71646	+	8.55529i	−0.321068	+	0.480513i	−0.956536	−	0.291615i	$-0.905807\pi$
$317$	−5.71646	+	8.55529i	−0.321068	+	0.480513i	0.635467	+	0.772128i	$0.280807\pi$
$318$	1.09011	+	7.31551i	0.0611301	+	0.410233i
$319$	4.04260	−	4.04260i	0.226342	−	0.226342i
$320$	11.5526	−	21.8216i	0.645811	−	1.21987i
$321$	−7.59357	+	3.14536i	−0.423832	+	0.175557i
$322$	−3.36581	−	9.38721i	−0.187569	−	0.523129i
$323$	−0.206870	−	0.234196i	−0.0115105	−	0.0130310i
$324$	4.52040	−	3.71983i	0.251134	−	0.206657i
$325$	−9.34374	+	3.87030i	−0.518297	+	0.214686i
$326$	−14.3032	−	10.5933i	−0.792178	−	0.586706i
$327$	1.10310	+	1.10310i	0.0610016	+	0.0610016i
$328$	7.71956	+	6.96870i	0.426241	+	0.384782i
$329$	−5.70322	+	8.53547i	−0.314428	+	0.470575i
$330$	10.0575	−	6.03728i	0.553646	−	0.332341i
$331$	−22.5103	−	9.32406i	−1.23728	−	0.512497i	−0.334414	−	0.942426i	$-0.608538\pi$
$331$	−22.5103	−	9.32406i	−1.23728	−	0.512497i	−0.902862	+	0.429929i	$0.858538\pi$
$332$	8.81583	+	28.9239i	0.483832	+	1.58741i
$333$	5.08590	+	25.5686i	0.278706	+	1.40115i
$334$	−6.25226	+	25.0307i	−0.342108	+	1.36962i
$335$	−8.03506	+	40.3950i	−0.439002	+	2.20701i
$336$	1.85812	+	2.76498i	0.101369	+	0.150842i
$337$	4.18986	−	2.79958i	0.228236	−	0.152503i	−0.436195	−	0.899852i	$-0.643674\pi$
$337$	4.18986	−	2.79958i	0.228236	−	0.152503i	0.664431	+	0.747350i	$0.268674\pi$
$338$	8.38433	−	7.60924i	0.456048	−	0.413888i
$339$			16.5224i			0.897374i
$340$	0.957312	+	25.4329i	0.0519175	+	1.37929i
$341$			17.8467i			0.966452i
$342$	0.163165	+	0.179786i	0.00882296	+	0.00972169i
$343$	−10.5473	+	7.04751i	−0.569503	+	0.380530i
$344$	0.938575	+	3.71566i	0.0506046	+	0.200335i
$345$	3.74587	−	18.8318i	0.201671	−	1.01387i
$346$	−19.2773	−	4.81514i	−1.03635	−	0.258864i
$347$	−5.60134	−	28.1598i	−0.300696	−	1.51170i	−0.775353	−	0.631528i	$-0.782428\pi$
$347$	−5.60134	−	28.1598i	−0.300696	−	1.51170i	0.474657	−	0.880171i	$-0.342572\pi$
$348$	0.911416	+	2.99027i	0.0488570	+	0.160295i
$349$	4.02874	+	1.66876i	0.215653	+	0.0893265i	0.487895	−	0.872902i	$-0.337765\pi$
$349$	4.02874	+	1.66876i	0.215653	+	0.0893265i	−0.272241	+	0.962229i	$0.587765\pi$
$350$	−3.20051	−	5.33172i	−0.171075	−	0.284992i
$351$	5.60332	−	8.38596i	0.299083	−	0.447609i
$352$	0.811576	−	17.7173i	0.0432572	−	0.944333i
$353$	−9.82158	−	9.82158i	−0.522750	−	0.522750i	0.395651	−	0.918401i	$-0.370519\pi$
$353$	−9.82158	−	9.82158i	−0.522750	−	0.522750i	−0.918401	+	0.395651i	$0.870519\pi$
$354$	3.32921	−	4.49514i	0.176945	−	0.238914i
$355$	14.7189	−	6.09679i	0.781201	−	0.323584i
$356$	−4.40001	−	5.34696i	−0.233200	−	0.283388i
$357$	−3.08514	−	1.50774i	−0.163283	−	0.0797981i
$358$	−5.98889	+	2.14733i	−0.316523	+	0.113490i
$359$	22.7016	−	9.40329i	1.19814	−	0.496287i	0.307744	−	0.951469i	$-0.400426\pi$
$359$	22.7016	−	9.40329i	1.19814	−	0.496287i	0.890398	+	0.455182i	$0.150426\pi$
$360$	−1.00955	−	19.7489i	−0.0532078	−	1.04086i
$361$	13.4310	−	13.4310i	0.706893	−	0.706893i
$362$	−19.3265	+	2.87990i	−1.01578	+	0.151364i
$363$	−0.557184	+	0.833885i	−0.0292446	+	0.0437676i
$364$	−3.36039	−	2.75036i	−0.176133	−	0.144158i
$365$	9.73545	−	23.5035i	0.509577	−	1.23023i
$366$	0.999795	+	0.0484529i	0.0522601	+	0.00253267i
$367$	−3.71805	−	18.6919i	−0.194081	−	0.975710i	−0.947886	−	0.318611i	$-0.896784\pi$
$367$	−3.71805	−	18.6919i	−0.194081	−	0.975710i	0.753805	−	0.657098i	$-0.228216\pi$
$368$	−20.5821	−	20.4733i	−1.07292	−	1.06725i
$369$	8.16896	+	1.62491i	0.425259	+	0.0845892i
$370$	45.4235	+	21.4469i	2.36145	+	1.11497i
$371$	4.92902	−	3.29347i	0.255902	−	0.170988i
$372$	−8.61229	−	4.58871i	−0.446527	−	0.237913i
$373$	24.0238			1.24390			0.621952	−	0.783055i	$-0.286340\pi$
$373$	24.0238			1.24390			0.621952	+	0.783055i	$0.286340\pi$
$374$	8.42177	+	16.2263i	0.435479	+	0.839043i
$375$			1.25472i			0.0647936i
$376$	−4.32614	+	29.5692i	−0.223104	+	1.52492i
$377$	−2.26389	−	3.38815i	−0.116596	−	0.174499i
$378$	5.60777	+	2.64773i	0.288433	+	0.136185i
$379$	−0.205859	+	1.03492i	−0.0105743	+	0.0531603i	−0.985712	−	0.168438i	$-0.946128\pi$
$379$	−0.205859	+	1.03492i	−0.0105743	+	0.0531603i	0.975138	+	0.221599i	$0.0711275\pi$
$380$	0.465502	−	0.0464707i	0.0238797	−	0.00238390i
$381$	10.9068	−	2.16949i	0.558770	−	0.111146i
$382$	1.43963	−	29.7058i	0.0736577	−	1.51988i
$383$	−26.2680	−	10.8805i	−1.34223	−	0.555970i	−0.408111	−	0.912932i	$-0.633813\pi$
$383$	−26.2680	−	10.8805i	−1.34223	−	0.555970i	−0.934119	+	0.356962i	$0.883813\pi$
$384$	8.34116	+	4.94707i	0.425658	+	0.252454i
$385$	−7.81733	−	5.22337i	−0.398408	−	0.266208i
$386$	−24.4452	+	3.64265i	−1.24423	+	0.185406i
$387$	2.17031	+	2.17031i	0.110323	+	0.110323i
$388$	−1.70601	+	5.65090i	−0.0866094	+	0.286881i
$389$	−13.8739	−	33.4946i	−0.703435	−	1.69824i	−0.715788	−	0.698318i	$-0.753932\pi$
$389$	−13.8739	−	33.4946i	−0.703435	−	1.69824i	0.0123532	−	0.999924i	$-0.496068\pi$
$390$	−2.82191	−	7.87027i	−0.142893	−	0.398526i
$391$	28.9320	+	7.64161i	1.46315	+	0.386453i
$392$	−8.77682	+	14.7095i	−0.443297	+	0.742940i
$393$	−4.62965	−	11.1770i	−0.233535	−	0.563804i
$394$	−4.49506	+	6.06928i	−0.226458	+	0.305766i
$395$	11.0861	−	11.0861i	0.557803	−	0.557803i
$396$	−6.71249	−	12.5183i	−0.337315	−	0.629066i
$397$	6.07754	+	4.06089i	0.305023	+	0.203810i	0.698656	−	0.715458i	$-0.253782\pi$
$397$	6.07754	+	4.06089i	0.305023	+	0.203810i	−0.393633	+	0.919268i	$0.628782\pi$
$398$	3.51806	−	2.11181i	0.176344	−	0.105855i
$399$	−0.0241542	+	0.0583134i	−0.00120922	+	0.00291932i
$400$	−15.0786	−	10.0175i	−0.753931	−	0.500876i
$401$	12.7756	−	2.54122i	0.637981	−	0.126902i	0.134507	−	0.990913i	$-0.457055\pi$
$401$	12.7756	−	2.54122i	0.637981	−	0.126902i	0.503474	+	0.864010i	$0.332055\pi$
$402$	−15.6945	−	3.92022i	−0.782771	−	0.195523i
$403$	12.4759	+	2.48161i	0.621469	+	0.123618i
$404$	3.15431	−	32.4671i	0.156933	−	1.61530i
$405$	−5.01906	−	7.51156i	−0.249399	−	0.373252i
$406$	1.85537	−	1.68385i	0.0920802	−	0.0835678i
$407$	36.0822			1.78853
$408$	−9.99574	−	0.107978i	−0.494863	−	0.00534572i
$409$	−25.8779			−1.27958			−0.639789	−	0.768550i	$-0.720978\pi$
$409$	−25.8779			−1.27958			−0.639789	+	0.768550i	$0.720978\pi$
$410$	11.8842	−	10.7856i	0.586919	−	0.532661i
$411$	−2.94705	−	4.41057i	−0.145367	−	0.217557i
$412$	−33.2345	−	3.22886i	−1.63735	−	0.159075i
$413$	−4.39720	−	0.874658i	−0.216372	−	0.0430391i
$414$	−22.5572	−	5.63441i	−1.10863	−	0.276916i
$415$	45.7657	−	9.10336i	2.24655	−	0.446866i
$416$	−12.2726	−	3.03095i	−0.601712	−	0.148605i
$417$	−1.74259	+	4.20699i	−0.0853352	+	0.206017i
$418$	0.288114	−	0.172949i	0.0140921	−	0.00845919i
$419$	11.6963	+	7.81525i	0.571404	+	0.381800i	0.807445	−	0.589943i	$-0.200850\pi$
$419$	11.6963	+	7.81525i	0.571404	+	0.381800i	−0.236041	+	0.971743i	$0.575850\pi$
$420$	4.53063	−	2.42939i	0.221072	−	0.118542i
$421$	−5.15477	+	5.15477i	−0.251228	+	0.251228i	−0.821474	−	0.570246i	$-0.806848\pi$
$421$	−5.15477	+	5.15477i	−0.251228	+	0.251228i	0.570246	+	0.821474i	$0.306848\pi$
$422$	−16.9086	+	22.8302i	−0.823098	+	1.11136i
$423$	9.15903	+	22.1119i	0.445327	+	1.07511i
$424$	8.84259	−	14.8197i	0.429434	−	0.719707i
$425$	18.6243	+	1.15389i	0.903413	+	0.0559717i
$426$	2.11198	+	5.89028i	0.102326	+	0.285385i
$427$	−0.307016	−	0.741201i	−0.0148575	−	0.0358692i
$428$	18.3590	+	5.54259i	0.887416	+	0.267911i
$429$	−4.24668	−	4.24668i	−0.205032	−	0.205032i
$430$	5.84948	−	0.871649i	0.282087	−	0.0420346i
$431$	−15.5897	−	10.4167i	−0.750931	−	0.501756i	0.120235	−	0.992746i	$-0.461635\pi$
$431$	−15.5897	−	10.4167i	−0.750931	−	0.501756i	−0.871165	+	0.490989i	$0.836635\pi$
$432$	18.0529	−	0.0478370i	0.868573	−	0.00230156i
$433$	−33.0166	−	13.6759i	−1.58668	−	0.657223i	−0.597223	−	0.802076i	$-0.703729\pi$
$433$	−33.0166	−	13.6759i	−1.58668	−	0.657223i	−0.989453	+	0.144853i	$0.953729\pi$
$434$	−0.378601	+	7.81220i	−0.0181734	+	0.374997i
$435$	4.73144	−	0.941142i	0.226855	−	0.0451243i
$436$	−0.361572	−	3.62190i	−0.0173161	−	0.173457i
$437$	0.107307	−	0.539470i	0.00513320	−	0.0258063i
$438$	9.03551	+	4.26615i	0.431733	+	0.203845i
$439$	−0.996315	−	1.49109i	−0.0475515	−	0.0711659i	0.806932	−	0.590644i	$-0.201126\pi$
$439$	−0.996315	−	1.49109i	−0.0475515	−	0.0711659i	−0.854484	+	0.519478i	$0.826126\pi$
$440$	−27.0814	−	3.96216i	−1.29106	−	0.188889i
$441$			13.7183i			0.653254i
$442$	12.5142	−	3.63102i	0.595241	−	0.172710i
$443$	36.5324			1.73571			0.867854	−	0.496820i	$-0.165499\pi$
$443$	36.5324			1.73571			0.867854	+	0.496820i	$0.165499\pi$
$444$	−9.27740	+	17.4122i	−0.440286	+	0.826349i
$445$	−8.88505	+	5.93680i	−0.421192	+	0.281431i
$446$	−0.291397	−	0.137585i	−0.0137981	−	0.00651482i
$447$	−7.00175	−	1.39273i	−0.331171	−	0.0658740i
$448$	0.731114	−	7.73832i	0.0345419	−	0.365601i
$449$	1.56405	+	7.86301i	0.0738120	+	0.371078i	0.999982	−	0.00602861i	$-0.00191898\pi$
$449$	1.56405	+	7.86301i	0.0738120	+	0.371078i	−0.926170	+	0.377107i	$0.876919\pi$
$450$	−14.4814	−	0.701808i	−0.682658	−	0.0330835i
$451$	4.41157	−	10.6505i	0.207733	−	0.501511i
$452$	24.4168	−	29.8325i	1.14847	−	1.40320i
$453$	0.562609	−	0.842004i	0.0264337	−	0.0395608i
$454$	20.9525	−	3.12219i	0.983347	−	0.146532i
$455$	−4.73846	+	4.73846i	−0.222143	+	0.222143i
$456$	0.00938056	+	0.183504i	0.000439285	+	0.00859335i
$457$	−1.58706	+	0.657380i	−0.0742394	+	0.0307509i	−0.419494	−	0.907758i	$-0.637793\pi$
$457$	−1.58706	+	0.657380i	−0.0742394	+	0.0307509i	0.345255	+	0.938509i	$0.387793\pi$
$458$	13.8575	−	4.96864i	0.647517	−	0.232169i
$459$	−16.0822	+	9.36183i	−0.750652	+	0.436973i
$460$	−34.5931	+	28.4666i	−1.61291	+	1.32726i
$461$	−11.6473	+	4.82446i	−0.542468	+	0.224697i	−0.637054	−	0.770819i	$-0.719847\pi$
$461$	−11.6473	+	4.82446i	−0.542468	+	0.224697i	0.0945863	+	0.995517i	$0.469847\pi$
$462$	2.19780	−	2.96749i	0.102251	−	0.138060i
$463$	−0.143250	−	0.143250i	−0.00665738	−	0.00665738i	0.703770	−	0.710428i	$-0.251498\pi$
$463$	−0.143250	−	0.143250i	−0.00665738	−	0.00665738i	−0.710428	+	0.703770i	$0.751498\pi$
$464$	2.77339	−	6.74605i	0.128751	−	0.313177i
$465$	−8.36643	+	12.5212i	−0.387984	+	0.580659i
$466$	−7.42912	−	12.3761i	−0.344147	−	0.573313i
$467$	−12.8100	−	5.30609i	−0.592778	−	0.245537i	0.0660672	−	0.997815i	$-0.478955\pi$
$467$	−12.8100	−	5.30609i	−0.592778	−	0.245537i	−0.658845	+	0.752278i	$0.728955\pi$
$468$	−9.68439	+	2.95174i	−0.447661	+	0.136444i
$469$	2.52945	+	12.7164i	0.116799	+	0.587190i
$470$	44.7421	+	11.1758i	2.06380	+	0.515502i
$471$	0.175537	−	0.882486i	0.00808834	−	0.0406628i
$472$	−12.6541	+	3.19642i	−0.582450	+	0.147127i
$473$	3.53220	−	2.36014i	0.162411	−	0.108519i
$474$	4.13840	+	4.55995i	0.190083	+	0.209445i
$475$		−	0.342992i		−	0.0157376i
$476$	3.34231	+	7.28156i	0.153195	+	0.333750i
$477$		−	13.8211i		−	0.632825i
$478$	−18.5695	+	16.8528i	−0.849347	+	0.770829i
$479$	−26.0129	+	17.3813i	−1.18856	+	0.794170i	−0.982844	−	0.184441i	$-0.940952\pi$
$479$	−26.0129	+	17.3813i	−1.18856	+	0.794170i	−0.205716	+	0.978612i	$0.565952\pi$
$480$	8.87515	−	12.0500i	0.405093	−	0.550003i
$481$	5.01729	−	25.2236i	0.228769	−	1.15010i
$482$	4.91525	−	19.6781i	0.223884	−	0.896312i
$483$	−1.17921	−	5.92828i	−0.0536558	−	0.269746i
$484$	2.23835	−	0.682237i	0.101743	−	0.0310108i
$485$	8.41575	+	3.48592i	0.382139	+	0.158287i
$486$	19.4596	−	11.6812i	0.882706	−	0.529869i
$487$	−12.9774	+	19.4220i	−0.588062	+	0.880097i	−0.999509	−	0.0313368i	$-0.990024\pi$
$487$	−12.9774	+	19.4220i	−0.588062	+	0.880097i	0.411447	+	0.911434i	$0.365024\pi$
$488$	−1.73360	−	1.56498i	−0.0784765	−	0.0708434i
$489$	−7.62837	−	7.62837i	−0.344967	−	0.344967i
$490$	21.2418	+	15.7322i	0.959606	+	0.710707i
$491$	20.9742	−	8.68778i	0.946550	−	0.392074i	0.144617	−	0.989488i	$-0.453805\pi$
$491$	20.9742	−	8.68778i	0.946550	−	0.392074i	0.801933	+	0.597414i	$0.203805\pi$
$492$	4.00532	+	4.86733i	0.180574	+	0.219436i
$493$	1.00797	+	7.45050i	0.0453968	+	0.335553i
$494$	−0.0808386	−	0.225458i	−0.00363710	−	0.0101438i
$495$	−20.2515	+	8.38843i	−0.910236	+	0.377032i
$496$	8.76897	+	21.0125i	0.393738	+	0.943490i
$497$	3.54637	−	3.54637i	0.159076	−	0.159076i
$498$	2.70121	+	18.1273i	0.121044	+	0.812305i
$499$	3.18371	−	4.76475i	0.142522	−	0.213300i	−0.753340	−	0.657631i	$-0.771559\pi$
$499$	3.18371	−	4.76475i	0.142522	−	0.213300i	0.895863	+	0.444331i	$0.146559\pi$
$500$	1.85423	−	2.26550i	0.0829236	−	0.101316i
$501$	−5.98428	+	14.4473i	−0.267358	+	0.645459i
$502$	0.178509	−	3.68342i	0.00796723	−	0.164399i
$503$	6.84911	+	34.4328i	0.305387	+	1.53528i	0.763158	+	0.646212i	$0.223648\pi$
$503$	6.84911	+	34.4328i	0.305387	+	1.53528i	−0.457771	+	0.889070i	$0.651352\pi$
$504$	−2.67276	−	5.62213i	−0.119054	−	0.250430i
$505$	−49.3716	−	9.82062i	−2.19701	−	0.437012i
$506$	−13.7395	+	29.0997i	−0.610797	+	1.29364i
$507$	5.70614	−	3.81272i	0.253418	−	0.169329i
$508$	−22.8991	−	12.2008i	−1.01598	−	0.541324i
$509$	6.62188			0.293510			0.146755	−	0.989173i	$-0.453117\pi$
$509$	6.62188			0.293510			0.146755	+	0.989173i	$0.453117\pi$
$510$	−1.69809	+	15.3325i	−0.0751927	+	0.678933i
$511$		−	8.00855i		−	0.354277i
$512$	−7.74983	−	21.2589i	−0.342497	−	0.939519i
$513$	0.190031	+	0.284401i	0.00839007	+	0.0125566i
$514$	12.5451	−	26.5700i	0.553341	−	1.17195i
$515$	−10.0527	+	50.5385i	−0.442977	+	2.22699i
$516$	0.230743	+	2.31137i	0.0101579	+	0.101752i
$517$	32.4896	−	6.46259i	1.42889	−	0.284224i
$518$	15.7946	+	0.765452i	0.693976	+	0.0336320i
$519$	−11.1265	−	4.60876i	−0.488401	−	0.202302i
$520$	−6.53550	+	18.3806i	−0.286601	+	0.806042i
$521$	15.1565	+	10.1273i	0.664020	+	0.443684i	0.841367	−	0.540465i	$-0.181752\pi$
$521$	15.1565	+	10.1273i	0.664020	+	0.443684i	−0.177347	+	0.984148i	$0.556752\pi$
$522$	−0.860964	−	5.77778i	−0.0376834	−	0.252886i
$523$	22.5030	+	22.5030i	0.983989	+	0.983989i	0.999874	−	0.0158844i	$-0.00505639\pi$
$523$	22.5030	+	22.5030i	0.983989	+	0.983989i	−0.0158844	+	0.999874i	$0.505056\pi$
$524$	−8.15813	+	27.0226i	−0.356390	+	1.18049i
$525$	−1.44240	−	3.48226i	−0.0629515	−	0.151978i
$526$	−28.4866	+	10.2140i	−1.24207	+	0.445349i
$527$	−18.6706	−	14.2208i	−0.813305	−	0.619466i
$528$	2.06927	−	10.5489i	0.0900534	−	0.459084i
$529$	11.3557	+	27.4150i	0.493725	+	1.19196i
$530$	−21.4009	−	15.8500i	−0.929597	−	0.688482i
$531$	−7.39123	+	7.39123i	−0.320752	+	0.320752i
$532$	0.129788	−	0.0695943i	0.00562702	−	0.00301730i
$533$	−6.83188	−	4.56492i	−0.295922	−	0.197729i
$534$	−2.16013	−	3.59855i	−0.0934780	−	0.155725i
$535$	11.3253	−	27.3416i	0.489634	−	1.18208i
$536$	22.5444	+	30.2716i	0.973768	+	1.30753i
$537$	−3.78215	+	0.752316i	−0.163212	+	0.0324648i
$538$	−3.95850	+	15.8477i	−0.170663	+	0.683244i
$539$	18.6224	+	3.70423i	0.802125	+	0.159553i
$540$	2.69394	−	27.7286i	0.115929	−	1.19325i
$541$	13.3456	+	19.9731i	0.573772	+	0.858710i	0.998922	−	0.0464127i	$-0.0147789\pi$
$541$	13.3456	+	19.9731i	0.573772	+	0.858710i	−0.425151	+	0.905123i	$0.639779\pi$
$542$	20.4679	+	22.5528i	0.879172	+	0.968727i
$543$	−11.8434			−0.508250
$544$	17.8885	+	14.9667i	0.766964	+	0.641691i
$545$	−5.61705			−0.240608
$546$	−1.76885	−	1.94903i	−0.0756997	−	0.0834107i
$547$	−12.4669	−	18.6580i	−0.533045	−	0.797758i	0.463024	−	0.886346i	$-0.346765\pi$
$547$	−12.4669	−	18.6580i	−0.533045	−	0.797758i	−0.996068	+	0.0885881i	$0.971765\pi$
$548$	−1.19682	+	12.3188i	−0.0511254	+	0.526232i
$549$	−1.83453	−	0.364910i	−0.0782956	−	0.0155740i
$550$	−4.86296	+	19.4687i	−0.207357	+	0.830150i
$551$	0.135540	−	0.0269607i	0.00577422	−	0.00114856i
$552$	−10.5100	−	14.1124i	−0.447334	−	0.600662i
$553$	1.88874	−	4.55982i	0.0803173	−	0.193903i
$554$	2.01092	+	3.34999i	0.0854359	+	0.142327i
$555$	25.3153	+	16.9152i	1.07458	+	0.718008i
$556$	9.36348	−	5.02085i	0.397100	−	0.212931i
$557$	1.43952	−	1.43952i	0.0609945	−	0.0609945i	−0.675952	−	0.736946i	$-0.736267\pi$
$557$	1.43952	−	1.43952i	0.0609945	−	0.0609945i	0.736946	+	0.675952i	$0.236267\pi$
$558$	14.6539	+	10.8530i	0.620348	+	0.459445i
$559$	−1.15872	−	2.79740i	−0.0490086	−	0.118317i
$560$	−11.7706	−	2.30890i	−0.497397	−	0.0975689i
$561$	3.59928	+	10.4800i	0.151962	+	0.442465i
$562$	27.6174	−	9.90231i	1.16497	−	0.417704i
$563$	0.236562	+	0.571111i	0.00996989	+	0.0240694i	0.928786	−	0.370616i	$-0.120853\pi$
$563$	0.236562	+	0.571111i	0.00996989	+	0.0240694i	−0.918816	+	0.394686i	$0.870853\pi$
$564$	−5.23501	+	17.3402i	−0.220434	+	0.730154i
$565$	−42.0665	−	42.0665i	−1.76975	−	1.76975i
$566$	−1.10940	−	7.44501i	−0.0466317	−	0.312937i
$567$	−2.36465	−	1.58001i	−0.0993061	−	0.0663542i
$568$	4.89131	−	13.7564i	0.205235	−	0.577207i
$569$	−13.8104	−	5.72048i	−0.578964	−	0.239815i	0.0739307	−	0.997263i	$-0.476446\pi$
$569$	−13.8104	−	5.72048i	−0.578964	−	0.239815i	−0.652895	+	0.757449i	$0.726446\pi$
$570$	0.283218	+	0.0137256i	0.0118627	+	0.000574900i
$571$	−38.2110	+	7.60064i	−1.59908	+	0.318077i	−0.912532	−	0.409006i	$-0.865875\pi$
$571$	−38.2110	+	7.60064i	−1.59908	+	0.318077i	−0.686549	+	0.727083i	$0.740875\pi$
$572$	1.39196	+	13.9434i	0.0582010	+	0.583005i
$573$	3.51675	−	17.6799i	0.146914	−	0.738589i
$574$	2.15706	−	4.56854i	0.0900339	−	0.190687i
$575$	18.2484	+	27.3107i	0.761011	+	1.13893i
$576$	−14.0541	−	11.4407i	−0.585586	−	0.476695i
$577$		−	4.65481i		−	0.193782i	−0.995295	−	0.0968911i	$-0.969110\pi$
$577$		−	4.65481i		−	0.193782i	0.995295	−	0.0968911i	$-0.0308899\pi$
$578$	−23.6861	−	4.11903i	−0.985214	−	0.171329i
$579$	−14.9802			−0.622556
$580$	−9.93380	−	5.29282i	−0.412478	−	0.219772i
$581$	12.2138	−	8.16098i	0.506713	−	0.338575i
$582$	−1.52756	+	3.23529i	−0.0633193	+	0.134107i
$583$	−18.7620	−	3.73198i	−0.777041	−	0.154563i
$584$	−10.0098	−	21.0555i	−0.414208	−	0.871285i
$585$	3.04802	+	15.3234i	0.126020	+	0.633545i
$586$	1.58359	−	32.6763i	0.0654173	−	1.34985i
$587$	0.408975	−	0.987353i	0.0168802	−	0.0407524i	−0.915215	−	0.402967i	$-0.867979\pi$
$587$	0.408975	−	0.987353i	0.0168802	−	0.0407524i	0.932095	+	0.362214i	$0.117979\pi$
$588$	−6.57572	+	8.03422i	−0.271178	+	0.331325i
$589$	−0.239671	+	0.358693i	−0.00987548	+	0.0147797i
$590$	2.96849	+	19.9210i	0.122211	+	0.820135i
$591$	−3.23696	+	3.23696i	−0.133151	+	0.133151i
$592$	42.4829	−	17.7290i	1.74604	−	0.728658i
$593$	−25.9928	+	10.7666i	−1.06740	+	0.442130i	−0.846071	−	0.533070i	$-0.821038\pi$
$593$	−25.9928	+	10.7666i	−1.06740	+	0.442130i	−0.221326	+	0.975200i	$0.571038\pi$
$594$	−6.75417	−	18.8373i	−0.277127	−	0.772904i
$595$	11.6936	−	4.01610i	0.479391	−	0.164644i
$596$	10.5840	+	12.8619i	0.433538	+	0.526843i
$597$	2.29772	−	0.951746i	0.0940393	−	0.0389524i
$598$	18.4319	+	13.6511i	0.753737	+	0.558236i
$599$	−22.4162	−	22.4162i	−0.915901	−	0.915901i	0.0808269	−	0.996728i	$-0.474244\pi$
$599$	−22.4162	−	22.4162i	−0.915901	−	0.915901i	−0.996728	+	0.0808269i	$0.974244\pi$
$600$	−8.14469	−	7.35249i	−0.332506	−	0.300164i
$601$	1.77474	−	2.65608i	0.0723930	−	0.108344i	−0.793507	−	0.608562i	$-0.791747\pi$
$601$	1.77474	−	2.65608i	0.0723930	−	0.108344i	0.865900	+	0.500218i	$0.166747\pi$
$602$	1.59625	−	0.958193i	0.0650583	−	0.0390530i
$603$	27.9277	+	11.5680i	1.13730	+	0.471087i
$604$	−2.26015	+	0.688880i	−0.0919641	+	0.0280301i
$605$	−0.704488	−	3.54170i	−0.0286415	−	0.143991i
$606$	4.79138	−	19.1822i	0.194636	−	0.779222i
$607$	5.09604	−	25.6195i	0.206842	−	1.03986i	−0.728210	−	0.685354i	$-0.759648\pi$
$607$	5.09604	−	25.6195i	0.206842	−	1.03986i	0.935052	−	0.354510i	$-0.115352\pi$
$608$	0.254244	−	0.345193i	0.0103110	−	0.0139994i
$609$	1.26271	−	0.843715i	0.0511675	−	0.0341890i
$610$	−2.66887	+	2.42214i	−0.108059	+	0.0980697i
$611$		−	23.6108i		−	0.955192i
$612$	18.4449	+	2.95253i	0.745590	+	0.119349i
$613$		−	9.86702i		−	0.398525i	−0.979946	−	0.199263i	$-0.936145\pi$
$613$		−	9.86702i		−	0.398525i	0.979946	−	0.199263i	$-0.0638547\pi$
$614$	−7.39496	−	8.14822i	−0.298436	−	0.328836i
$615$	8.08804	−	5.40426i	0.326141	−	0.217921i
$616$	−8.35366	+	2.11013i	−0.336578	+	0.0850198i
$617$	0.829657	−	4.17097i	0.0334007	−	0.167917i	−0.960485	−	0.278333i	$-0.910218\pi$
$617$	0.829657	−	4.17097i	0.0334007	−	0.167917i	0.993885	+	0.110416i	$0.0352182\pi$
$618$	−19.6356	−	4.90463i	−0.789858	−	0.197293i
$619$	−3.29293	−	16.5547i	−0.132354	−	0.665388i	−0.988811	−	0.149171i	$-0.952340\pi$
$619$	−3.29293	−	16.5547i	−0.132354	−	0.665388i	0.856457	−	0.516218i	$-0.172660\pi$
$620$	33.6101	−	10.2442i	1.34981	−	0.411416i
$621$	−30.2623	−	12.5351i	−1.21439	−	0.503015i
$622$	3.46305	+	5.76908i	0.138856	+	0.231319i
$623$	−1.86892	+	2.79703i	−0.0748766	+	0.112061i
$624$	−7.08660	−	2.91339i	−0.283691	−	0.116629i
$625$	−19.1954	−	19.1954i	−0.767817	−	0.767817i
$626$	16.3586	−	22.0876i	0.653821	−	0.882797i
$627$	0.188174	−	0.0779440i	0.00751493	−	0.00311278i
$628$	−1.62108	+	1.33399i	−0.0646883	+	0.0532319i
$629$	−28.7514	+	37.7480i	−1.14639	+	1.50511i
$630$	−9.04282	+	3.24233i	−0.360274	+	0.129178i
$631$	10.3970	−	4.30660i	0.413900	−	0.171443i	−0.166009	−	0.986124i	$-0.553088\pi$
$631$	10.3970	−	4.30660i	0.413900	−	0.171443i	0.579909	+	0.814681i	$0.303088\pi$
$632$	−0.733513	−	14.3491i	−0.0291776	−	0.570776i
$633$	−12.1761	+	12.1761i	−0.483958	+	0.483958i
$634$	14.3924	−	2.14466i	0.571597	−	0.0851754i
$635$	−22.2453	+	33.2925i	−0.882779	+	1.32117i
$636$	6.62499	−	8.09441i	0.262698	−	0.320964i
$637$	5.17896	−	12.5031i	0.205198	−	0.495391i
$638$	−8.07572	−	0.391372i	−0.319721	−	0.0154946i
$639$	−2.28120	−	11.4684i	−0.0902429	−	0.453682i
$640$	−33.8322	+	8.64145i	−1.33734	+	0.341583i
$641$	17.2299	+	3.42724i	0.680540	+	0.135368i	0.523243	−	0.852183i	$-0.324722\pi$
$641$	17.2299	+	3.42724i	0.680540	+	0.135368i	0.157297	+	0.987551i	$0.449722\pi$
$642$	10.5110	+	4.96283i	0.414837	+	0.195867i
$643$	13.4862	−	9.01118i	0.531843	−	0.355366i	−0.260469	−	0.965482i	$-0.583877\pi$
$643$	13.4862	−	9.01118i	0.531843	−	0.355366i	0.792312	+	0.610116i	$0.208877\pi$
$644$	−6.63166	+	12.4466i	−0.261324	+	0.490465i
$645$	3.58461			0.141144
$646$	−0.0486448	+	0.439226i	−0.00191390	+	0.0172811i
$647$			32.2230i			1.26682i	0.773818	+	0.633408i	$0.218345\pi$
$647$			32.2230i			1.26682i	−0.773818	+	0.633408i	$0.781655\pi$
$648$	−8.19183	−	1.19851i	−0.321805	−	0.0470819i
$649$	8.03770	+	12.0293i	0.315507	+	0.472190i
$650$	12.9336	+	6.10666i	0.507298	+	0.239523i
$651$	−0.924856	+	4.64957i	−0.0362480	+	0.182231i
$652$	2.50041	+	25.0468i	0.0979235	+	0.980909i
$653$	−10.8454	+	2.15728i	−0.424413	+	0.0844210i	−0.402676	−	0.915343i	$-0.631920\pi$
$653$	−10.8454	+	2.15728i	−0.424413	+	0.0844210i	−0.0217372	+	0.999764i	$0.506920\pi$
$654$	0.106793	−	2.20362i	0.00417595	−	0.0861682i
$655$	40.2441	+	16.6697i	1.57247	+	0.651338i
$656$	−0.0389719	−	14.7074i	−0.00152160	−	0.574227i
$657$	−15.5249	−	10.3734i	−0.605685	−	0.404706i
$658$	14.3591	−	2.13969i	0.559776	−	0.0834139i
$659$	−10.4801	−	10.4801i	−0.408245	−	0.408245i	0.472881	−	0.881126i	$-0.343214\pi$
$659$	−10.4801	−	10.4801i	−0.408245	−	0.408245i	−0.881126	+	0.472881i	$0.843214\pi$
$660$	−15.8813	−	4.79457i	−0.618178	−	0.186628i
$661$	1.21912	+	2.94322i	0.0474184	+	0.114478i	0.945814	−	0.324709i	$-0.105266\pi$
$661$	1.21912	+	2.94322i	0.0474184	+	0.114478i	−0.898396	+	0.439187i	$0.855266\pi$
$662$	11.6298	+	32.4353i	0.452004	+	1.26063i
$663$	7.82661	−	1.05886i	0.303960	−	0.0411226i
$664$	21.9113	−	36.7221i	0.850324	−	1.42510i
$665$	−0.0869703	−	0.209965i	−0.00337256	−	0.00814209i
$666$	21.9425	−	29.6271i	0.850255	−	1.14803i
$667$	−9.35797	+	9.35797i	−0.362342	+	0.362342i
$668$	32.1553	−	17.2422i	1.24413	−	0.667120i
$669$	−0.162401	−	0.108513i	−0.00627878	−	0.00419535i
$670$	49.9397	−	29.9777i	1.92934	−	1.15814i
$671$	−0.990719	+	2.39181i	−0.0382463	+	0.0923347i
$672$	1.12959	−	4.57379i	0.0435748	−	0.176438i
$673$	−3.32275	+	0.660935i	−0.128082	+	0.0254772i	−0.258715	−	0.965954i	$-0.583299\pi$
$673$	−3.32275	+	0.660935i	−0.128082	+	0.0254772i	0.130633	+	0.991431i	$0.458299\pi$
$674$	−6.91394	−	1.72699i	−0.266315	−	0.0665210i
$675$	−20.0333	−	3.98487i	−0.771081	−	0.153378i
$676$	−15.9373	−	1.54837i	−0.612973	−	0.0595527i
$677$	10.2747	+	15.3771i	0.394888	+	0.590992i	0.974634	−	0.223806i	$-0.0718481\pi$
$677$	10.2747	+	15.3771i	0.394888	+	0.590992i	−0.579746	+	0.814797i	$0.696848\pi$
$678$	17.3028	−	15.7033i	0.664511	−	0.603080i
$679$	2.86758			0.110047
$680$	25.7244	−	25.1745i	0.986484	−	0.965399i
$681$	12.8398			0.492024
$682$	18.6897	−	16.9619i	0.715664	−	0.649504i
$683$	11.2632	+	16.8566i	0.430974	+	0.644998i	0.981866	−	0.189579i	$-0.0607122\pi$
$683$	11.2632	+	16.8566i	0.430974	+	0.644998i	−0.550891	+	0.834577i	$0.685712\pi$
$684$	0.0332018	−	0.341744i	0.00126950	−	0.0130669i
$685$	18.7327	+	3.72617i	0.715740	+	0.142370i
$686$	17.4048	+	4.34743i	0.664519	+	0.165986i
$687$	8.75138	−	1.74076i	0.333886	−	0.0664140i
$688$	2.99912	−	4.51435i	0.114340	−	0.172108i
$689$	−5.21776	+	12.5968i	−0.198781	+	0.479899i
$690$	−23.2814	+	13.9753i	−0.886309	+	0.532031i
$691$	−21.6668	−	14.4773i	−0.824245	−	0.550743i	0.0704007	−	0.997519i	$-0.477572\pi$
$691$	−21.6668	−	14.4773i	−0.824245	−	0.550743i	−0.894646	+	0.446776i	$0.852572\pi$
$692$	13.2790	+	24.7643i	0.504791	+	0.941396i
$693$	−4.87937	+	4.87937i	−0.185352	+	0.185352i
$694$	−24.1663	+	32.6296i	−0.917340	+	1.23860i
$695$	−6.27443	−	15.1478i	−0.238003	−	0.574589i
$696$	2.26528	−	3.79648i	0.0858652	−	0.143905i
$697$	7.62690	+	13.1018i	0.288890	+	0.496268i
$698$	−2.08142	−	5.80505i	−0.0787829	−	0.219724i
$699$	−3.34814	−	8.08312i	−0.126638	−	0.305731i
$700$	−2.54172	+	8.41907i	−0.0960680	+	0.318211i
$701$	27.5821	+	27.5821i	1.04176	+	1.04176i	0.999089	+	0.0426726i	$0.0135873\pi$
$701$	27.5821	+	27.5821i	1.04176	+	1.04176i	0.0426726	+	0.999089i	$0.486413\pi$
$702$	−14.1076	+	2.10221i	−0.532456	+	0.0793429i
$703$	0.725202	+	0.484565i	0.0273515	+	0.0182757i
$704$	−19.3254	+	15.9890i	−0.728355	+	0.602606i
$705$	25.8244	+	10.6968i	0.972602	+	0.402865i
$706$	−0.950847	+	19.6201i	−0.0357856	+	0.738414i
$707$	−15.5423	+	3.09155i	−0.584527	+	0.116270i
$708$	−7.87161	+	0.785818i	−0.295833	+	0.0295328i
$709$	3.90934	−	19.6536i	0.146818	−	0.738105i	−0.835293	−	0.549805i	$-0.814702\pi$
$709$	3.90934	−	19.6536i	0.146818	−	0.738105i	0.982112	−	0.188300i	$-0.0602978\pi$
$710$	−20.3740	−	9.61966i	−0.764621	−	0.361019i
$711$	−6.39293	−	9.56770i	−0.239754	−	0.358817i
$712$	−1.41766	+	9.68970i	−0.0531289	+	0.363137i
$713$		−	41.3122i		−	1.54715i
$714$	1.35322	+	4.66385i	0.0506431	+	0.174540i
$715$	21.6243			0.808704
$716$	7.94073	+	4.23089i	0.296759	+	0.158116i
$717$	−12.6378	+	8.44433i	−0.471969	+	0.315359i
$718$	−31.4235	−	14.8367i	−1.17271	−	0.553702i
$719$	6.96310	+	1.38505i	0.259680	+	0.0516535i	0.323213	−	0.946326i	$-0.395237\pi$
$719$	6.96310	+	1.38505i	0.259680	+	0.0516535i	−0.0635333	+	0.997980i	$0.520237\pi$
$720$	−19.7222	+	19.8270i	−0.735004	+	0.738909i
$721$	3.16462	+	15.9096i	0.117857	+	0.592505i
$722$	−26.8304	−	1.30028i	−0.998526	−	0.0483914i
$723$	4.70458	−	11.3579i	0.174965	−	0.422403i
$724$	21.3842	+	17.5022i	0.794738	+	0.650465i
$725$	−4.58487	+	6.86174i	−0.170278	+	0.254839i
$726$	1.40283	−	0.209040i	0.0520640	−	0.00775821i
$727$	5.44083	−	5.44083i	0.201789	−	0.201789i	−0.598977	−	0.800766i	$-0.704426\pi$
$727$	5.44083	−	5.44083i	0.201789	−	0.201789i	0.800766	+	0.598977i	$0.204426\pi$
$728$	0.313520	+	6.13312i	0.0116198	+	0.227309i
$729$	4.59668	−	1.90401i	0.170248	−	0.0705189i
$730$	−33.8664	+	12.1429i	−1.25345	+	0.449429i
$731$	−0.345459	+	5.57589i	−0.0127773	+	0.206232i
$732$	−0.899485	−	1.09307i	−0.0332459	−	0.0404010i
$733$	−0.145043	+	0.0600787i	−0.00535728	+	0.00221906i	−0.385360	−	0.922766i	$-0.625923\pi$
$733$	−0.145043	+	0.0600787i	−0.00535728	+	0.00221906i	0.380003	+	0.924985i	$0.375923\pi$
$734$	−16.0411	+	21.6589i	−0.592087	+	0.799443i
$735$	11.3290	+	11.3290i	0.417876	+	0.417876i
$736$	−1.87867	+	41.0126i	−0.0692486	+	1.51174i
$737$	23.2445	−	34.7878i	0.856222	−	1.28143i
$738$	−6.06230	−	10.0992i	−0.223156	−	0.371755i
$739$	−0.0154455	−	0.00639775i	−0.000568173	−	0.000235345i	0.382399	−	0.923997i	$-0.375098\pi$
$739$	−0.0154455	−	0.00639775i	−0.000568173	−	0.000235345i	−0.382968	+	0.923762i	$0.625098\pi$
$740$	−20.7115	−	67.9526i	−0.761372	−	2.49799i
$741$	−0.0283217	−	0.142383i	−0.00104042	−	0.00523056i
$742$	−8.13367	−	2.03165i	−0.298597	−	0.0745844i
$743$	2.81029	−	14.1283i	0.103100	−	0.518317i	−0.894377	−	0.447315i	$-0.852380\pi$
$743$	2.81029	−	14.1283i	0.103100	−	0.518317i	0.997476	−	0.0710019i	$-0.0226197\pi$
$744$	3.37986	+	13.3803i	0.123912	+	0.490545i
$745$	21.3726	−	14.2807i	0.783031	−	0.523204i
$746$	−22.8327	−	25.1585i	−0.835966	−	0.921119i
$747$		−	34.2478i		−	1.25306i
$748$	8.98852	−	24.2414i	0.328653	−	0.886354i
$749$		−	9.31636i		−	0.340413i
$750$	1.31399	−	1.19251i	0.0479800	−	0.0435445i
$751$	6.03523	−	4.03261i	0.220229	−	0.147152i	−0.440562	−	0.897722i	$-0.645221\pi$
$751$	6.03523	−	4.03261i	0.220229	−	0.147152i	0.660791	+	0.750570i	$0.270221\pi$
$752$	35.0776	−	23.5728i	1.27915	−	0.859610i
$753$	0.436065	−	2.19225i	0.0158911	−	0.0798900i
$754$	−1.39653	+	5.59099i	−0.0508588	+	0.203612i
$755$	0.711347	+	3.57618i	0.0258886	+	0.130151i
$756$	−2.55695	−	8.38911i	−0.0929954	−	0.305109i
$757$	0.339538	+	0.140641i	0.0123407	+	0.00511169i	0.388845	−	0.921303i	$-0.372874\pi$
$757$	0.339538	+	0.140641i	0.0123407	+	0.00511169i	−0.376505	+	0.926415i	$0.622874\pi$
$758$	1.27946	−	0.768030i	0.0464720	−	0.0278961i
$759$	−10.8364	+	16.2178i	−0.393335	+	0.588668i
$760$	−0.491089	−	0.443323i	−0.0178137	−	0.0160810i
$761$	5.51288	+	5.51288i	0.199842	+	0.199842i	0.799932	−	0.600090i	$-0.204869\pi$
$761$	5.51288	+	5.51288i	0.199842	+	0.199842i	−0.600090	+	0.799932i	$0.704869\pi$
$762$	−12.6380	−	9.36000i	−0.457826	−	0.339077i
$763$	−1.63366	+	0.676684i	−0.0591424	+	0.0244976i
$764$	−32.4771	+	26.7254i	−1.17498	+	0.966891i
$765$	7.36126	−	27.8706i	0.266147	−	1.00766i
$766$	13.5712	+	37.8498i	0.490346	+	1.36757i
$767$	9.52683	−	3.94614i	0.343994	−	0.142487i
$768$	−2.74688	−	13.4369i	−0.0991196	−	0.484864i
$769$	−20.4838	+	20.4838i	−0.738665	+	0.738665i	−0.972320	−	0.233654i	$-0.924932\pi$
$769$	−20.4838	+	20.4838i	−0.738665	+	0.738665i	0.233654	+	0.972320i	$0.424932\pi$
$770$	1.95967	+	13.1510i	0.0706216	+	0.473929i
$771$	9.89433	−	14.8079i	0.356336	−	0.533294i
$772$	27.0479	+	22.1378i	0.973476	+	0.796755i
$773$	10.3795	−	25.0583i	0.373324	−	0.901284i	−0.619859	−	0.784714i	$-0.712810\pi$
$773$	10.3795	−	25.0583i	0.373324	−	0.901284i	0.993182	−	0.116570i	$-0.0371900\pi$
$774$	0.210112	−	4.33554i	0.00755234	−	0.155838i
$775$	−5.02580	−	25.2664i	−0.180532	−	0.907596i
$776$	7.53924	−	3.58415i	0.270643	−	0.128663i
$777$	9.40044	+	1.86986i	0.337239	+	0.0670810i
$778$	−21.8906	+	46.3632i	−0.784815	+	1.66220i
$779$	0.231696	−	0.154815i	0.00830138	−	0.00554681i
$780$	−5.56000	+	10.4353i	−0.199080	+	0.373643i
$781$	−16.1841			−0.579113
$782$	−19.4950	−	37.5613i	−0.697141	−	1.34319i
$783$		−	8.22979i		−	0.294109i
$784$	23.7459	−	4.78881i	0.848069	−	0.171029i
$785$	1.79991	+	2.69376i	0.0642416	+	0.0961443i
$786$	−7.30478	+	15.4712i	−0.260553	+	0.551838i
$787$	3.03255	−	15.2456i	0.108099	−	0.543449i	−0.888344	−	0.459178i	$-0.848144\pi$
$787$	3.03255	−	15.2456i	0.108099	−	0.543449i	0.996443	−	0.0842706i	$-0.0268560\pi$
$788$	10.6282	−	1.06100i	0.378613	−	0.0377966i
$789$	−17.9901	+	3.57844i	−0.640463	+	0.127396i
$790$	−22.1463	−	1.07327i	−0.787928	−	0.0381852i
$791$	−17.3023	−	7.16685i	−0.615200	−	0.254824i
$792$	−6.72985	+	18.9272i	−0.239135	+	0.672547i
$793$	1.53425	+	1.02516i	0.0544830	+	0.0364044i
$794$	−1.52353	−	10.2242i	−0.0540682	−	0.362842i
$795$	−11.4139	−	11.4139i	−0.404808	−	0.404808i
$796$	−5.55520	−	1.67712i	−0.196899	−	0.0594438i
$797$	19.6996	+	47.5590i	0.697796	+	1.68463i	0.728451	+	0.685098i	$0.240241\pi$
$797$	19.6996	+	47.5590i	0.697796	+	1.68463i	−0.0306555	+	0.999530i	$0.509759\pi$
$798$	0.0840245	−	0.0301272i	0.00297443	−	0.00106649i
$799$	−19.1277	+	39.1391i	−0.676691	+	1.38464i
$800$	3.84036	+	25.3117i	0.135777	+	0.894904i
$801$	3.00137	+	7.24595i	0.106048	+	0.256023i
$802$	−14.8034	−	10.9638i	−0.522727	−	0.387144i
$803$	−18.2738	+	18.2738i	−0.644869	+	0.644869i
$804$	10.8110	+	20.1617i	0.381275	+	0.711048i
$805$	18.0959	+	12.0913i	0.637795	+	0.426161i
$806$	−9.25854	−	15.4238i	−0.326118	−	0.543279i
$807$	−3.78883	+	9.14704i	−0.133373	+	0.321991i
$808$	−36.9986	+	27.5542i	−1.30161	+	0.969352i
$809$	51.1382	−	10.1720i	1.79792	−	0.357629i	0.820952	−	0.570997i	$-0.193443\pi$
$809$	51.1382	−	10.1720i	1.79792	−	0.357629i	0.976972	+	0.213367i	$0.0684431\pi$
$810$	−3.09613	+	12.3953i	−0.108787	+	0.435526i
$811$	−8.18658	−	1.62841i	−0.287470	−	0.0571813i	0.0492492	−	0.998787i	$-0.484317\pi$
$811$	−8.18658	−	1.62841i	−0.287470	−	0.0571813i	−0.336719	+	0.941605i	$0.609317\pi$
$812$	−3.52676	−	0.342638i	−0.123765	−	0.0120242i
$813$	10.2557	+	15.3488i	0.359685	+	0.538306i
$814$	−34.2934	−	37.7865i	−1.20198	−	1.32442i
$815$	38.8441			1.36065
$816$	9.38709	+	10.5705i	0.328614	+	0.370042i
$817$	0.102688			0.00359258
$818$	24.5949	+	27.1002i	0.859940	+	0.947536i
$819$	2.73249	+	4.08945i	0.0954808	+	0.142897i
$820$	−22.5900	−	2.19470i	−0.788877	−	0.0766424i
$821$	17.1224	+	3.40585i	0.597575	+	0.118865i	0.484605	−	0.874733i	$-0.338963\pi$
$821$	17.1224	+	3.40585i	0.597575	+	0.118865i	0.112971	+	0.993598i	$0.463963\pi$
$822$	−1.81796	+	7.27815i	−0.0634086	+	0.253855i
$823$	−50.1337	+	9.97221i	−1.74755	+	0.347609i	−0.962387	−	0.271681i	$-0.912421\pi$
$823$	−50.1337	+	9.97221i	−1.74755	+	0.347609i	−0.785162	+	0.619290i	$0.787421\pi$
$824$	28.2054	+	37.8731i	0.982583	+	1.31937i
$825$	−4.65453	+	11.2370i	−0.162050	+	0.391223i
$826$	3.26323	+	5.43619i	0.113542	+	0.189149i
$827$	33.2018	+	22.1847i	1.15454	+	0.771439i	0.977118	−	0.212696i	$-0.0682245\pi$
$827$	33.2018	+	22.1847i	1.15454	+	0.771439i	0.177421	+	0.984135i	$0.443224\pi$
$828$	15.5383	+	28.9777i	0.539994	+	1.00705i
$829$	17.0215	−	17.0215i	0.591180	−	0.591180i	−0.346770	−	0.937950i	$-0.612722\pi$
$829$	17.0215	−	17.0215i	0.591180	−	0.591180i	0.937950	+	0.346770i	$0.112722\pi$
$830$	−53.0301	−	39.2753i	−1.84070	−	1.36327i
$831$	0.906277	+	2.18795i	0.0314384	+	0.0758990i
$832$	8.49000	+	15.7329i	0.294338	+	0.545441i
$833$	−18.7141	+	16.5305i	−0.648406	+	0.572749i
$834$	6.06190	−	2.17351i	0.209907	−	0.0752627i
$835$	−21.5471	−	52.0194i	−0.745670	−	1.80021i
$836$	−0.454948	−	0.137349i	−0.0157347	−	0.00475031i
$837$	18.1658	+	18.1658i	0.627903	+	0.627903i
$838$	−2.93207	−	19.6766i	−0.101287	−	0.679716i
$839$	15.0880	+	10.0815i	0.520896	+	0.348052i	0.788059	−	0.615600i	$-0.211086\pi$
$839$	15.0880	+	10.0815i	0.520896	+	0.348052i	−0.267163	+	0.963651i	$0.586086\pi$
$840$	−6.85015	−	2.43568i	−0.236353	−	0.0840388i
$841$	23.7206	+	9.82538i	0.817950	+	0.338806i
$842$	10.2975	+	0.499044i	0.354874	+	0.0171982i
$843$	17.4412	−	3.46926i	0.600705	−	0.119488i
$844$	39.9788	−	3.99106i	1.37613	−	0.137378i
$845$	−4.82070	+	24.2353i	−0.165837	+	0.833719i
$846$	14.4513	−	30.6072i	0.496847	−	1.05230i
$847$	−0.631560	−	0.945196i	−0.0217006	−	0.0324773i
$848$	−23.9238	+	4.82469i	−0.821548	+	0.165680i
$849$		−	4.56237i		−	0.156580i
$850$	−16.4926	−	20.6007i	−0.565691	−	0.706599i
$851$	−83.5246			−2.86319
$852$	4.16123	−	7.80998i	0.142561	−	0.267566i
$853$	−30.1754	+	20.1626i	−1.03319	+	0.690353i	−0.951922	−	0.306340i	$-0.900896\pi$
$853$	−30.1754	+	20.1626i	−1.03319	+	0.690353i	−0.0812638	+	0.996693i	$0.525896\pi$
$854$	−0.484417	+	1.02597i	−0.0165764	+	0.0351080i
$855$	−0.519678	−	0.103370i	−0.0177726	−	0.00353519i
$856$	−11.6444	−	24.4940i	−0.397997	−	0.837186i
$857$	−1.66437	−	8.36734i	−0.0568537	−	0.285823i	0.941891	−	0.335920i	$-0.109047\pi$
$857$	−1.66437	−	8.36734i	−0.0568537	−	0.285823i	−0.998744	+	0.0500968i	$0.984047\pi$
$858$	−0.411129	+	8.48340i	−0.0140357	+	0.289618i
$859$	1.06977	−	2.58267i	0.0365003	−	0.0881194i	−0.904578	−	0.426308i	$-0.859814\pi$
$859$	1.06977	−	2.58267i	0.0365003	−	0.0881194i	0.941078	+	0.338188i	$0.109814\pi$
$860$	−6.47229	−	5.29734i	−0.220703	−	0.180638i
$861$	1.70127	−	2.54613i	0.0579792	−	0.0867719i
$862$	3.90807	+	26.2264i	0.133109	+	0.893274i
$863$	−12.1960	+	12.1960i	−0.415156	+	0.415156i	−0.883530	−	0.468374i	$-0.844840\pi$
$863$	−12.1960	+	12.1960i	−0.415156	+	0.415156i	0.468374	+	0.883530i	$0.344840\pi$
$864$	−17.2080	−	18.8602i	−0.585428	−	0.641637i
$865$	40.0625	−	16.5944i	1.36217	−	0.564228i
$866$	17.0578	+	47.5740i	0.579648	+	1.61663i
$867$	−13.8318	−	4.58530i	−0.469753	−	0.155725i
$868$	8.54103	−	7.02840i	0.289901	−	0.238559i
$869$	−14.7142	+	6.09483i	−0.499146	+	0.206753i
$870$	−5.48246	−	4.06044i	−0.185873	−	0.137662i
$871$	−21.0866	−	21.0866i	−0.714492	−	0.714492i
$872$	−3.44933	+	3.82098i	−0.116809	+	0.129395i
$873$	3.71435	−	5.55892i	0.125712	−	0.188141i
$874$	−0.666938	+	0.400348i	−0.0225595	+	0.0135420i
$875$	−1.31395	−	0.544255i	−0.0444196	−	0.0183992i
$876$	−4.11988	−	13.5169i	−0.139198	−	0.456695i
$877$	−7.25239	−	36.4602i	−0.244896	−	1.23117i	−0.885987	−	0.463710i	$-0.846518\pi$
$877$	−7.25239	−	36.4602i	−0.244896	−	1.23117i	0.641091	−	0.767465i	$-0.278482\pi$
$878$	−0.614601	+	2.46054i	−0.0207418	+	0.0830392i
$879$	3.86842	−	19.4479i	0.130479	−	0.655960i
$880$	21.5895	+	32.1263i	0.727781	+	1.08298i
$881$	26.8880	−	17.9660i	0.905880	−	0.605289i	−0.0129620	−	0.999916i	$-0.504126\pi$
$881$	26.8880	−	17.9660i	0.905880	−	0.605289i	0.918842	+	0.394627i	$0.129126\pi$
$882$	14.3663	−	13.0382i	0.483738	−	0.439019i
$883$			10.7462i			0.361639i	0.983516	+	0.180820i	$0.0578750\pi$
$883$			10.7462i			0.361639i	−0.983516	+	0.180820i	$0.942125\pi$
$884$	−15.6963	−	9.65432i	−0.527925	−	0.324710i
$885$			12.2078i			0.410359i
$886$	−34.7212	−	38.2580i	−1.16648	−	1.28530i
$887$	31.5608	−	21.0882i	1.05971	−	0.708073i	0.101699	−	0.994815i	$-0.467572\pi$
$887$	31.5608	−	21.0882i	1.05971	−	0.708073i	0.958008	+	0.286742i	$0.0925723\pi$
$888$	27.0521	−	6.83337i	0.907810	−	0.229313i
$889$	−2.45908	+	12.3626i	−0.0824750	+	0.414630i
$890$	14.6618	+	3.66226i	0.491463	+	0.122759i
$891$	1.79039	+	9.00089i	0.0599802	+	0.301541i
$892$	0.132867	+	0.435924i	0.00444872	+	0.0145958i
$893$	0.739785	+	0.306429i	0.0247560	+	0.0102543i
$894$	5.19609	+	8.65615i	0.173783	+	0.289505i
$895$	7.71404	−	11.5449i	0.257852	−	0.385902i
$896$	−8.79870	+	6.58902i	−0.293944	+	0.220124i
$897$	9.83037	+	9.83037i	0.328227	+	0.328227i
$898$	6.74790	−	9.11110i	0.225180	−	0.304041i
$899$	9.58949	−	3.97210i	0.319828	−	0.132477i
$900$	13.0284	+	15.8324i	0.434282	+	0.527746i
$901$	18.8544	−	16.6544i	0.628129	−	0.554838i
$902$	−15.3464	+	5.50250i	−0.510979	+	0.183213i
$903$	1.04254	−	0.431836i	0.0346937	−	0.0143706i
$904$	−54.4478	+	2.78333i	−1.81091	+	0.0925722i
$905$	30.1537	−	30.1537i	1.00234	−	1.00234i
$906$	−1.41649	+	0.211076i	−0.0470597	+	0.00701252i
$907$	−9.18613	+	13.7480i	−0.305021	+	0.456496i	−0.952038	−	0.305980i	$-0.901016\pi$
$907$	−9.18613	+	13.7480i	−0.305021	+	0.456496i	0.647018	+	0.762475i	$0.276016\pi$
$908$	−23.1833	−	18.9747i	−0.769366	−	0.629698i
$909$	−14.1387	+	34.1338i	−0.468951	+	1.13215i
$910$	9.46582	+	0.458740i	0.313789	+	0.0152071i
$911$	−3.99943	−	20.1065i	−0.132507	−	0.666159i	−0.988749	−	0.149584i	$-0.952207\pi$
$911$	−3.99943	−	20.1065i	−0.132507	−	0.666159i	0.856242	−	0.516575i	$-0.172793\pi$
$912$	0.183256	−	0.184230i	0.00606821	−	0.00610045i
$913$	−46.4909	−	9.24761i	−1.53862	−	0.306051i
$914$	2.19680	+	1.03723i	0.0726638	+	0.0343085i
$915$	−1.81635	+	1.21365i	−0.0600468	+	0.0401220i
$916$	−18.3738	−	9.78971i	−0.607087	−	0.323461i
$917$	13.7128			0.452835
$918$	25.0889	+	7.94412i	0.828056	+	0.262195i
$919$			29.6364i			0.977615i	0.872392	+	0.488808i	$0.162568\pi$
$919$			29.6364i			0.977615i	−0.872392	+	0.488808i	$0.837432\pi$
$920$	62.6892	+	9.17177i	2.06680	+	0.302384i
$921$	−3.70535	−	5.54545i	−0.122095	−	0.182729i
$922$	16.1222	+	7.61215i	0.530955	+	0.250693i
$923$	−2.25043	+	11.3137i	−0.0740737	+	0.372394i
$924$	−5.19650	+	0.518763i	−0.170952	+	0.0170660i
$925$	−51.0834	+	10.1611i	−1.67961	+	0.334095i
$926$	−0.0138683	+	0.286164i	−0.000455741	+	0.00940392i
$927$	34.9406	+	14.4729i	1.14760	+	0.475351i
$928$	−9.70058	+	3.50721i	−0.318437	+	0.115130i
$929$	5.05759	+	3.37937i	0.165934	+	0.110874i	0.635765	−	0.771883i	$-0.280685\pi$
$929$	5.05759	+	3.37937i	0.165934	+	0.110874i	−0.469830	+	0.882757i	$0.655685\pi$
$930$	21.0643	−	3.13886i	0.690726	−	0.102927i
$931$	0.324539	+	0.324539i	0.0106363	+	0.0106363i
$932$	−5.89991	+	19.5426i	−0.193258	+	0.640138i
$933$	1.56072	+	3.76791i	0.0510956	+	0.123356i
$934$	6.61822	+	18.4581i	0.216555	+	0.603969i
$935$	−35.8462	−	17.5184i	−1.17230	−	0.572914i
$936$	12.2954	+	7.33642i	0.401888	+	0.239798i
$937$	9.28236	+	22.4096i	0.303242	+	0.732090i	0.999892	+	0.0146795i	$0.00467278\pi$
$937$	9.28236	+	22.4096i	0.303242	+	0.732090i	−0.696651	+	0.717411i	$0.745327\pi$
$938$	10.9130	−	14.7349i	0.356323	−	0.481111i
$939$	11.7801	−	11.7801i	0.384428	−	0.384428i
$940$	−30.8201	−	57.4771i	−1.00524	−	1.87470i
$941$	−30.2110	−	20.1863i	−0.984849	−	0.658055i	−0.0447648	−	0.998998i	$-0.514254\pi$
$941$	−30.2110	−	20.1863i	−0.984849	−	0.658055i	−0.940084	+	0.340943i	$0.889254\pi$
$942$	−1.09100	+	0.654905i	−0.0355468	+	0.0213380i
$943$	−10.2121	+	24.6541i	−0.332551	+	0.802849i
$944$	15.3741	+	10.2138i	0.500384	+	0.332431i
$945$	−13.2739	+	2.64035i	−0.431801	+	0.0858905i
$946$	−5.82869	−	1.45591i	−0.189507	−	0.0473357i
$947$	−21.8377	−	4.34378i	−0.709628	−	0.141154i	−0.172938	−	0.984933i	$-0.555326\pi$
$947$	−21.8377	−	4.34378i	−0.709628	−	0.141154i	−0.536691	+	0.843779i	$0.680326\pi$
$948$	0.842105	−	8.66775i	0.0273503	−	0.281515i
$949$	10.2335	+	15.3155i	0.332193	+	0.497162i
$950$	−0.359193	+	0.325987i	−0.0116538	+	0.0105764i
$951$	8.81981			0.286002
$952$	4.44889	−	10.4207i	0.144189	−	0.337738i
$953$	−18.5492			−0.600867			−0.300433	−	0.953803i	$-0.597131\pi$
$953$	−18.5492			−0.600867			−0.300433	+	0.953803i	$0.597131\pi$
$954$	−14.4739	+	13.1359i	−0.468611	+	0.425290i
$955$	36.0598	+	53.9673i	1.16687	+	1.74634i
$956$	35.2976	+	3.42930i	1.14161	+	0.110911i
$957$	−4.80641	−	0.956054i	−0.155369	−	0.0309048i
$958$	42.9255	+	10.7221i	1.38686	+	0.346414i
$959$	5.89709	−	1.17300i	0.190427	−	0.0378783i
$960$	−21.0543	+	2.15819i	−0.679524	+	0.0696554i
$961$	−0.536246	+	1.29461i	−0.0172983	+	0.0417617i
$962$	−31.1836	+	18.7188i	−1.00540	+	0.603519i
$963$	−18.0602	−	12.0674i	−0.581981	−	0.388867i
$964$	−25.2791	+	13.5551i	−0.814186	+	0.436579i
$965$	38.1400	−	38.1400i	1.22777	−	1.22777i
$966$	−5.08755	+	6.86927i	−0.163689	+	0.221015i
$967$	13.1930	+	31.8507i	0.424259	+	1.02425i	0.981077	+	0.193617i	$0.0620219\pi$
$967$	13.1930	+	31.8507i	0.424259	+	1.02425i	−0.556819	+	0.830634i	$0.687978\pi$
$968$	−2.84184	−	1.69567i	−0.0913403	−	0.0545008i
$969$	−0.0683997	+	0.258969i	−0.00219732	+	0.00831928i
$970$	−4.34794	−	12.1263i	−0.139604	−	0.389354i
$971$	18.0336	+	43.5370i	0.578726	+	1.39717i	0.893957	+	0.448153i	$0.147918\pi$
$971$	18.0336	+	43.5370i	0.578726	+	1.39717i	−0.315231	+	0.949015i	$0.602082\pi$
$972$	−30.7278	−	9.27673i	−0.985594	−	0.297551i
$973$	−3.64970	−	3.64970i	−0.117004	−	0.117004i
$974$	32.6734	−	4.86877i	1.04692	−	0.156005i
$975$	7.20813	+	4.81632i	0.230845	+	0.154246i
$976$	0.00875203	+	3.30288i	0.000280146	+	0.105723i
$977$	−27.5025	−	11.3919i	−0.879883	−	0.364459i	−0.103431	−	0.994637i	$-0.532982\pi$
$977$	−27.5025	−	11.3919i	−0.879883	−	0.364459i	−0.776451	+	0.630177i	$0.782982\pi$
$978$	−0.738518	+	15.2389i	−0.0236152	+	0.487285i
$979$	10.6467	−	2.11776i	0.340270	−	0.0676839i
$980$	−3.71338	−	37.1973i	−0.118620	−	1.18822i
$981$	−0.804286	+	4.04342i	−0.0256789	+	0.129096i
$982$	−29.0324	−	13.7078i	−0.926462	−	0.437433i
$983$	−13.0531	−	19.5353i	−0.416328	−	0.623079i	0.562734	−	0.826638i	$-0.309749\pi$
$983$	−13.0531	−	19.5353i	−0.416328	−	0.623079i	−0.979063	+	0.203558i	$0.934749\pi$
$984$	1.29049	−	8.82051i	0.0411393	−	0.281188i
$985$		−	16.4828i		−	0.525185i
$986$	6.84441	−	8.13670i	0.217971	−	0.259125i
$987$	8.79937			0.280087
$988$	−0.159276	+	0.298937i	−0.00506725	+	0.00951045i
$989$	−8.17647	+	5.46334i	−0.259997	+	0.173724i
$990$	28.0321	+	13.2355i	0.890918	+	0.420651i
$991$	−1.52345	−	0.303033i	−0.0483939	−	0.00962614i	0.170834	−	0.985300i	$-0.445354\pi$
$991$	−1.52345	−	0.303033i	−0.0483939	−	0.00962614i	−0.219228	+	0.975674i	$0.570354\pi$
$992$	13.6708	−	29.1539i	0.434048	−	0.925638i
$993$	4.07448	+	20.4838i	0.129300	+	0.650033i
$994$	−7.08442	−	0.343331i	−0.224704	−	0.0108898i
$995$	−3.42688	+	8.27322i	−0.108639	+	0.262279i
$996$	16.4163	−	20.0574i	0.520169	−	0.635543i
$997$	−17.2639	+	25.8372i	−0.546752	+	0.818273i	−0.997220	−	0.0745201i	$-0.976257\pi$
$997$	−17.2639	+	25.8372i	−0.546752	+	0.818273i	0.450467	+	0.892793i	$0.351257\pi$
$998$	−8.01567	+	1.19444i	−0.253732	+	0.0378093i
$999$	36.7275	−	36.7275i	1.16201	−	1.16201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.s.c.107.4	yes	112
4.3	odd	2		544.2.cc.c.175.10		112
8.3	odd	2	inner	136.2.s.c.107.7	yes	112
8.5	even	2		544.2.cc.c.175.9		112
17.7	odd	16	inner	136.2.s.c.75.7	yes	112
68.7	even	16		544.2.cc.c.143.9		112
136.75	even	16	inner	136.2.s.c.75.4	✓	112
136.109	odd	16		544.2.cc.c.143.10		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.s.c.75.4	✓	112	136.75	even	16	inner
136.2.s.c.75.7	yes	112	17.7	odd	16	inner
136.2.s.c.107.4	yes	112	1.1	even	1	trivial
136.2.s.c.107.7	yes	112	8.3	odd	2	inner
544.2.cc.c.143.9		112	68.7	even	16
544.2.cc.c.143.10		112	136.109	odd	16
544.2.cc.c.175.9		112	8.5	even	2
544.2.cc.c.175.10		112	4.3	odd	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.950422 - 1.04723i) q^{2} +(-0.476222 - 0.712717i) q^{3} +(-0.193397 + 1.99063i) q^{4} +(3.02707 + 0.602122i) q^{5} +(-0.293769 + 1.17610i) q^{6} +(0.952929 - 0.189549i) q^{7} +(2.26846 - 1.68940i) q^{8} +(0.866872 - 2.09281i) q^{9} +O(q^{10})\)	\(q+(-0.950422 - 1.04723i) q^{2} +(-0.476222 - 0.712717i) q^{3} +(-0.193397 + 1.99063i) q^{4} +(3.02707 + 0.602122i) q^{5} +(-0.293769 + 1.17610i) q^{6} +(0.952929 - 0.189549i) q^{7} +(2.26846 - 1.68940i) q^{8} +(0.866872 - 2.09281i) q^{9} +(-2.24643 - 3.74232i) q^{10} +(-2.60689 - 1.74187i) q^{11} +(1.51085 - 0.810144i) q^{12} +(-1.58016 + 1.58016i) q^{13} +(-1.10419 - 0.817787i) q^{14} +(-1.01242 - 2.44419i) q^{15} +(-3.92520 - 0.769963i) q^{16} +(3.89953 - 1.33927i) q^{17} +(-3.01556 + 1.08124i) q^{18} +(-0.0290025 - 0.0700182i) q^{19} +(-1.78403 + 5.90933i) q^{20} +(-0.588901 - 0.588901i) q^{21} +(0.653502 + 4.38554i) q^{22} +(6.03453 + 4.03215i) q^{23} +(-2.28436 - 0.812239i) q^{24} +(4.18123 + 1.73192i) q^{25} +(3.15662 + 0.152979i) q^{26} +(-4.42653 + 0.880492i) q^{27} +(0.193028 + 1.93358i) q^{28} +(-0.355742 + 1.78844i) q^{29} +(-1.59742 + 3.38325i) q^{30} +(-3.16242 - 4.73290i) q^{31} +(2.92426 + 4.84239i) q^{32} +2.68749i q^{33} +(-5.10873 - 2.81085i) q^{34} +2.99872 q^{35} +(3.99836 + 2.13036i) q^{36} +(-9.56893 + 6.39375i) q^{37} +(-0.0457608 + 0.0969192i) q^{38} +(1.87872 + 0.373700i) q^{39} +(7.88403 - 3.74806i) q^{40} +(0.717320 + 3.60621i) q^{41} +(-0.0570127 + 1.17642i) q^{42} +(-0.518515 + 1.25181i) q^{43} +(3.97158 - 4.85248i) q^{44} +(3.88422 - 5.81314i) q^{45} +(-1.51275 - 10.1518i) q^{46} +(-7.47101 + 7.47101i) q^{47} +(1.32050 + 3.16423i) q^{48} +(-5.59501 + 2.31753i) q^{49} +(-2.16020 - 6.02478i) q^{50} +(-2.81157 - 2.14147i) q^{51} +(-2.83992 - 3.45111i) q^{52} +(5.63693 - 2.33489i) q^{53} +(5.12915 + 3.79877i) q^{54} +(-6.84243 - 6.84243i) q^{55} +(1.84146 - 2.03987i) q^{56} +(-0.0360916 + 0.0540148i) q^{57} +(2.21101 - 1.32722i) q^{58} +(-4.26316 - 1.76586i) q^{59} +(5.06127 - 1.54265i) q^{60} +(-0.161091 - 0.809857i) q^{61} +(-1.95082 + 7.81005i) q^{62} +(0.429376 - 2.15862i) q^{63} +(2.29183 - 7.66469i) q^{64} +(-5.73472 + 3.83182i) q^{65} +(2.81443 - 2.55425i) q^{66} +13.3446i q^{67} +(1.91183 + 8.02153i) q^{68} -6.22112i q^{69} +(-2.85005 - 3.14036i) q^{70} +(4.29199 - 2.86782i) q^{71} +(-1.56914 - 6.21197i) q^{72} +(1.60806 - 8.08428i) q^{73} +(15.7903 + 3.94414i) q^{74} +(-0.756824 - 3.80481i) q^{75} +(0.144989 - 0.0441919i) q^{76} +(-2.81435 - 1.16574i) q^{77} +(-1.39422 - 2.32263i) q^{78} +(2.82218 - 4.22369i) q^{79} +(-11.4182 - 4.69418i) q^{80} +(-2.06976 - 2.06976i) q^{81} +(3.09479 - 4.17862i) q^{82} +(13.9679 - 5.78571i) q^{83} +(1.28617 - 1.05839i) q^{84} +(12.6106 - 1.70608i) q^{85} +(1.80374 - 0.646738i) q^{86} +(1.44406 - 0.598150i) q^{87} +(-8.85635 + 0.452730i) q^{88} +(-2.44821 + 2.44821i) q^{89} +(-9.77936 + 1.45725i) q^{90} +(-1.20626 + 1.80530i) q^{91} +(-9.19356 + 11.2327i) q^{92} +(-1.86720 + 4.50783i) q^{93} +(14.9245 + 0.723284i) q^{94} +(-0.0456332 - 0.229413i) q^{95} +(2.05865 - 4.39022i) q^{96} +(2.89469 + 0.575790i) q^{97} +(7.74462 + 3.65665i) q^{98} +(-5.90525 + 3.94576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26} + 32 q^{27} + 40 q^{28} - 72 q^{30} + 32 q^{32} - 72 q^{34} - 32 q^{35} + 56 q^{36} + 48 q^{38} + 56 q^{40} - 16 q^{41} - 56 q^{42} - 96 q^{43} + 24 q^{44} - 24 q^{46} + 16 q^{48} - 16 q^{49} - 16 q^{51} - 16 q^{52} - 24 q^{54} + 32 q^{56} + 32 q^{57} + 48 q^{58} - 16 q^{59} + 96 q^{60} + 48 q^{62} + 40 q^{64} + 64 q^{65} - 16 q^{66} + 80 q^{68} + 64 q^{70} + 96 q^{72} - 96 q^{73} + 40 q^{74} - 16 q^{75} + 48 q^{76} + 96 q^{78} + 8 q^{80} - 96 q^{81} + 32 q^{82} + 128 q^{83} + 64 q^{86} - 72 q^{88} - 16 q^{89} + 152 q^{90} - 16 q^{91} - 120 q^{92} + 88 q^{94} - 160 q^{96} - 16 q^{97} + 128 q^{98} + 48 q^{99}+O(q^{100}) \) 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 - 56 * q^24 - 16 * q^25 - 40 * q^26 + 32 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 + 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 96 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 - 24 * q^54 + 32 * q^56 + 32 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 - 16 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 - 96 * q^81 + 32 * q^82 + 128 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 48 * q^99

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