LMFDB - Embedded newform 136.2.s.c.107.12

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			107.12
Character	$\chi$	$=$	136.107
Dual form			136.2.s.c.75.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06794 - 0.927095i) q^{2} +(1.52493 + 2.28221i) q^{3} +(0.280990 - 1.98016i) q^{4} +(0.326417 + 0.0649284i) q^{5} +(3.74436 + 1.02351i) q^{6} +(-3.74882 + 0.745687i) q^{7} +(-1.53572 - 2.37520i) q^{8} +(-1.73505 + 4.18878i) q^{9} +O(q^{10})$	\(q+(1.06794 - 0.927095i) q^{2} +(1.52493 + 2.28221i) q^{3} +(0.280990 - 1.98016i) q^{4} +(0.326417 + 0.0649284i) q^{5} +(3.74436 + 1.02351i) q^{6} +(-3.74882 + 0.745687i) q^{7} +(-1.53572 - 2.37520i) q^{8} +(-1.73505 + 4.18878i) q^{9} +(0.408789 - 0.233280i) q^{10} +(-3.13072 - 2.09188i) q^{11} +(4.94764 - 2.37832i) q^{12} +(2.87411 - 2.87411i) q^{13} +(-3.31219 + 4.27186i) q^{14} +(0.349582 + 0.843965i) q^{15} +(-3.84209 - 1.11281i) q^{16} +(4.11134 + 0.311272i) q^{17} +(2.03047 + 6.08192i) q^{18} +(0.183139 + 0.442137i) q^{19} +(0.220289 - 0.628115i) q^{20} +(-7.41850 - 7.41850i) q^{21} +(-5.28280 + 0.668475i) q^{22} +(1.77614 + 1.18678i) q^{23} +(3.07885 - 7.12684i) q^{24} +(-4.51707 - 1.87103i) q^{25} +(0.404802 - 5.73395i) q^{26} +(-4.12935 + 0.821378i) q^{27} +(0.423202 + 7.63281i) q^{28} +(-0.575123 + 2.89134i) q^{29} +(1.15577 + 0.577208i) q^{30} +(4.13105 + 6.18255i) q^{31} +(-5.13480 + 2.37357i) q^{32} -10.3350i q^{33} +(4.67924 - 3.47918i) q^{34} -1.27210 q^{35} +(7.80693 + 4.61268i) q^{36} +(-3.97723 + 2.65750i) q^{37} +(0.605485 + 0.302388i) q^{38} +(10.9421 + 2.17653i) q^{39} +(-0.347067 - 0.875017i) q^{40} +(1.10836 + 5.57210i) q^{41} +(-14.8002 - 1.04485i) q^{42} +(0.938212 - 2.26505i) q^{43} +(-5.02197 + 5.61155i) q^{44} +(-0.838321 + 1.25464i) q^{45} +(2.99707 - 0.379243i) q^{46} +(-9.23171 + 9.23171i) q^{47} +(-3.31923 - 10.4654i) q^{48} +(7.03047 - 2.91212i) q^{49} +(-6.55857 + 2.18960i) q^{50} +(5.55910 + 9.85762i) q^{51} +(-4.88361 - 6.49880i) q^{52} +(7.71191 - 3.19438i) q^{53} +(-3.64840 + 4.70548i) q^{54} +(-0.886100 - 0.886100i) q^{55} +(7.52830 + 7.75903i) q^{56} +(-0.729778 + 1.09219i) q^{57} +(2.06635 + 3.62097i) q^{58} +(2.37335 + 0.983072i) q^{59} +(1.76942 - 0.455084i) q^{60} +(-2.45803 - 12.3573i) q^{61} +(10.1435 + 2.77272i) q^{62} +(3.38087 - 16.9968i) q^{63} +(-3.28313 + 7.29528i) q^{64} +(1.12477 - 0.751547i) q^{65} +(-9.58148 - 11.0371i) q^{66} -13.0111i q^{67} +(1.77161 - 8.05366i) q^{68} +5.86328i q^{69} +(-1.35852 + 1.17935i) q^{70} +(1.11335 - 0.743917i) q^{71} +(12.6137 - 2.31170i) q^{72} +(0.580003 - 2.91587i) q^{73} +(-1.78368 + 6.52531i) q^{74} +(-2.61810 - 13.1621i) q^{75} +(0.926964 - 0.238410i) q^{76} +(13.2964 + 5.50756i) q^{77} +(13.7034 - 7.82000i) q^{78} +(4.26291 - 6.37989i) q^{79} +(-1.18187 - 0.612701i) q^{80} +(1.44635 + 1.44635i) q^{81} +(6.34953 + 4.92311i) q^{82} +(3.77409 - 1.56328i) q^{83} +(-16.7744 + 12.6053i) q^{84} +(1.32180 + 0.368547i) q^{85} +(-1.09796 - 3.28874i) q^{86} +(-7.47567 + 3.09652i) q^{87} +(-0.160723 + 10.6486i) q^{88} +(-9.04404 + 9.04404i) q^{89} +(0.267891 + 2.11708i) q^{90} +(-8.63134 + 12.9177i) q^{91} +(2.84909 - 3.18357i) q^{92} +(-7.81036 + 18.8559i) q^{93} +(-1.30023 + 18.4176i) q^{94} +(0.0310725 + 0.156212i) q^{95} +(-13.2472 - 8.09919i) q^{96} +(-10.4371 - 2.07606i) q^{97} +(4.80831 - 9.62788i) q^{98} +(14.1944 - 9.48439i) 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 $

$2$	1.06794	−	0.927095i	0.755147	−	0.655555i
$2$	1.06794	−	0.927095i	0.755147	−	0.655555i
$3$	1.52493	+	2.28221i	0.880417	+	1.31764i	0.947456	+	0.319886i	$0.103645\pi$
$3$	1.52493	+	2.28221i	0.880417	+	1.31764i	−0.0670391	+	0.997750i	$0.521355\pi$
$4$	0.280990	−	1.98016i	0.140495	−	0.990081i
$5$	0.326417	+	0.0649284i	0.145978	+	0.0290369i	0.267538	−	0.963547i	$-0.413790\pi$
$5$	0.326417	+	0.0649284i	0.145978	+	0.0290369i	−0.121560	+	0.992584i	$0.538790\pi$
$6$	3.74436	+	1.02351i	1.52863	+	0.417848i
$7$	−3.74882	+	0.745687i	−1.41692	+	0.281843i	−0.843373	−	0.537328i	$-0.819434\pi$
$7$	−3.74882	+	0.745687i	−1.41692	+	0.281843i	−0.573549	+	0.819171i	$0.694434\pi$
$8$	−1.53572	−	2.37520i	−0.542959	−	0.839759i
$9$	−1.73505	+	4.18878i	−0.578350	+	1.39626i
$10$	0.408789	−	0.233280i	0.129270	−	0.0737697i
$11$	−3.13072	−	2.09188i	−0.943949	−	0.630727i	−0.0145860	−	0.999894i	$-0.504643\pi$
$11$	−3.13072	−	2.09188i	−0.943949	−	0.630727i	−0.929363	+	0.369167i	$0.879643\pi$
$12$	4.94764	−	2.37832i	1.42826	−	0.686563i
$13$	2.87411	−	2.87411i	0.797134	−	0.797134i	−0.185508	−	0.982643i	$-0.559393\pi$
$13$	2.87411	−	2.87411i	0.797134	−	0.797134i	0.982643	+	0.185508i	$0.0593932\pi$
$14$	−3.31219	+	4.27186i	−0.885221	+	1.14170i
$15$	0.349582	+	0.843965i	0.0902616	+	0.217911i
$16$	−3.84209	−	1.11281i	−0.960522	−	0.278202i
$17$	4.11134	+	0.311272i	0.997146	+	0.0754945i
$17$	4.11134	+	0.311272i	0.997146	+	0.0754945i
$18$	2.03047	+	6.08192i	0.478586	+	1.43352i
$19$	0.183139	+	0.442137i	0.0420150	+	0.101433i	0.943494	−	0.331390i	$-0.107518\pi$
$19$	0.183139	+	0.442137i	0.0420150	+	0.101433i	−0.901479	+	0.432823i	$0.857518\pi$
$20$	0.220289	−	0.628115i	0.0492580	−	0.140451i
$21$	−7.41850	−	7.41850i	−1.61885	−	1.61885i
$22$	−5.28280	+	0.668475i	−1.12630	+	0.142519i
$23$	1.77614	+	1.18678i	0.370351	+	0.247460i	0.726792	−	0.686857i	$-0.241010\pi$
$23$	1.77614	+	1.18678i	0.370351	+	0.247460i	−0.356442	+	0.934318i	$0.616010\pi$
$24$	3.07885	−	7.12684i	0.628468	−	1.45476i
$25$	−4.51707	−	1.87103i	−0.903413	−	0.374206i
$26$	0.404802	−	5.73395i	0.0793882	−	1.12452i
$27$	−4.12935	+	0.821378i	−0.794693	+	0.158074i
$28$	0.423202	+	7.63281i	0.0799777	+	1.44247i
$29$	−0.575123	+	2.89134i	−0.106798	+	0.536908i	0.889932	+	0.456094i	$0.150752\pi$
$29$	−0.575123	+	2.89134i	−0.106798	+	0.536908i	−0.996729	+	0.0808138i	$0.974248\pi$
$30$	1.15577	+	0.577208i	0.211013	+	0.105383i
$31$	4.13105	+	6.18255i	0.741959	+	1.11042i	0.989917	+	0.141649i	$0.0452404\pi$
$31$	4.13105	+	6.18255i	0.741959	+	1.11042i	−0.247958	+	0.968771i	$0.579760\pi$
$32$	−5.13480	+	2.37357i	−0.907713	+	0.419592i
$33$		−	10.3350i		−	1.79908i
$34$	4.67924	−	3.47918i	0.802483	−	0.596675i
$35$	−1.27210			−0.215024
$36$	7.80693	+	4.61268i	1.30116	+	0.768780i
$37$	−3.97723	+	2.65750i	−0.653852	+	0.436890i	−0.837749	−	0.546056i	$-0.816129\pi$
$37$	−3.97723	+	2.65750i	−0.653852	+	0.436890i	0.183897	+	0.982946i	$0.441129\pi$
$38$	0.605485	+	0.302388i	0.0982226	+	0.0490539i
$39$	10.9421	+	2.17653i	1.75214	+	0.348523i
$40$	−0.347067	−	0.875017i	−0.0548762	−	0.138352i
$41$	1.10836	+	5.57210i	0.173097	+	0.870216i	0.965537	+	0.260266i	$0.0838103\pi$
$41$	1.10836	+	5.57210i	0.173097	+	0.870216i	−0.792440	+	0.609949i	$0.791190\pi$
$42$	−14.8002	−	1.04485i	−2.28371	−	0.161225i
$43$	0.938212	−	2.26505i	0.143076	−	0.345416i	−0.836055	−	0.548645i	$-0.815144\pi$
$43$	0.938212	−	2.26505i	0.143076	−	0.345416i	0.979131	+	0.203229i	$0.0651437\pi$
$44$	−5.02197	+	5.61155i	−0.757091	+	0.845973i
$45$	−0.838321	+	1.25464i	−0.124969	+	0.187030i
$46$	2.99707	−	0.379243i	0.441893	−	0.0559163i
$47$	−9.23171	+	9.23171i	−1.34658	+	1.34658i	−0.457240	+	0.889343i	$0.651162\pi$
$47$	−9.23171	+	9.23171i	−1.34658	+	1.34658i	−0.889343	+	0.457240i	$0.848838\pi$
$48$	−3.31923	−	10.4654i	−0.479090	−	1.51055i
$49$	7.03047	−	2.91212i	1.00435	−	0.416017i
$50$	−6.55857	+	2.18960i	−0.927523	+	0.309657i
$51$	5.55910	+	9.85762i	0.778430	+	1.38034i
$52$	−4.88361	−	6.49880i	−0.677235	−	0.901221i
$53$	7.71191	−	3.19438i	1.05931	−	0.438781i	0.216105	−	0.976370i	$-0.430665\pi$
$53$	7.71191	−	3.19438i	1.05931	−	0.438781i	0.843207	+	0.537589i	$0.180665\pi$
$54$	−3.64840	+	4.70548i	−0.496484	+	0.640335i
$55$	−0.886100	−	0.886100i	−0.119482	−	0.119482i
$56$	7.52830	+	7.75903i	1.00601	+	1.03684i
$57$	−0.729778	+	1.09219i	−0.0966614	+	0.144664i
$58$	2.06635	+	3.62097i	0.271325	+	0.475456i
$59$	2.37335	+	0.983072i	0.308983	+	0.127985i	0.531787	−	0.846878i	$-0.321521\pi$
$59$	2.37335	+	0.983072i	0.308983	+	0.127985i	−0.222803	+	0.974863i	$0.571521\pi$
$60$	1.76942	−	0.455084i	0.228431	−	0.0587510i
$61$	−2.45803	−	12.3573i	−0.314718	−	1.58220i	−0.737104	−	0.675779i	$-0.763807\pi$
$61$	−2.45803	−	12.3573i	−0.314718	−	1.58220i	0.422386	−	0.906416i	$-0.361193\pi$
$62$	10.1435	+	2.77272i	1.28823	+	0.352135i
$63$	3.38087	−	16.9968i	0.425950	−	2.14140i
$64$	−3.28313	+	7.29528i	−0.410391	+	0.911909i
$65$	1.12477	−	0.751547i	0.139511	−	0.0932180i
$66$	−9.58148	−	11.0371i	−1.17940	−	1.35857i
$67$		−	13.0111i		−	1.58956i	−0.606899	−	0.794779i	$-0.707587\pi$
$67$		−	13.0111i		−	1.58956i	0.606899	−	0.794779i	$-0.292413\pi$
$68$	1.77161	−	8.05366i	0.214840	−	0.976649i
$69$			5.86328i			0.705856i
$70$	−1.35852	+	1.17935i	−0.162375	+	0.140960i
$71$	1.11335	−	0.743917i	0.132130	−	0.0882867i	−0.487749	−	0.872984i	$-0.662182\pi$
$71$	1.11335	−	0.743917i	0.132130	−	0.0882867i	0.619879	+	0.784697i	$0.287182\pi$
$72$	12.6137	−	2.31170i	1.48654	−	0.272437i
$73$	0.580003	−	2.91587i	0.0678842	−	0.341277i	−0.931885	−	0.362754i	$-0.881837\pi$
$73$	0.580003	−	2.91587i	0.0678842	−	0.341277i	0.999769	+	0.0214764i	$0.00683668\pi$
$74$	−1.78368	+	6.52531i	−0.207349	+	0.758552i
$75$	−2.61810	−	13.1621i	−0.302312	−	1.51983i
$76$	0.926964	−	0.238410i	0.106330	−	0.0273475i
$77$	13.2964	+	5.50756i	1.51527	+	0.627645i
$78$	13.7034	−	7.82000i	1.55160	−	0.885441i
$79$	4.26291	−	6.37989i	0.479614	−	0.717794i	−0.510216	−	0.860046i	$-0.670435\pi$
$79$	4.26291	−	6.37989i	0.479614	−	0.717794i	0.989830	+	0.142253i	$0.0454346\pi$
$80$	−1.18187	−	0.612701i	−0.132137	−	0.0685021i
$81$	1.44635	+	1.44635i	0.160705	+	0.160705i
$82$	6.34953	+	4.92311i	0.701188	+	0.543666i
$83$	3.77409	−	1.56328i	0.414260	−	0.171592i	−0.165812	−	0.986157i	$-0.553024\pi$
$83$	3.77409	−	1.56328i	0.414260	−	0.171592i	0.580072	+	0.814565i	$0.303024\pi$
$84$	−16.7744	+	12.6053i	−1.83023	+	1.37535i
$85$	1.32180	+	0.368547i	0.143370	+	0.0399746i
$86$	−1.09796	−	3.28874i	−0.118396	−	0.354634i
$87$	−7.47567	+	3.09652i	−0.801476	+	0.331982i
$88$	−0.160723	+	10.6486i	−0.0171331	+	1.13515i
$89$	−9.04404	+	9.04404i	−0.958667	+	0.958667i	−0.999179	−	0.0405122i	$-0.987101\pi$
$89$	−9.04404	+	9.04404i	−0.958667	+	0.958667i	0.0405122	+	0.999179i	$0.487101\pi$
$90$	0.267891	+	2.11708i	0.0282382	+	0.223160i
$91$	−8.63134	+	12.9177i	−0.904810	+	1.35414i
$92$	2.84909	−	3.18357i	0.297038	−	0.331910i
$93$	−7.81036	+	18.8559i	−0.809897	+	1.95526i
$94$	−1.30023	+	18.4176i	−0.134109	+	1.89963i
$95$	0.0310725	+	0.156212i	0.00318797	+	0.0160270i
$96$	−13.2472	−	8.09919i	−1.35204	−	0.826621i
$97$	−10.4371	−	2.07606i	−1.05972	−	0.210792i	−0.365692	−	0.930736i	$-0.619167\pi$
$97$	−10.4371	−	2.07606i	−1.05972	−	0.210792i	−0.694032	+	0.719944i	$0.744167\pi$
$98$	4.80831	−	9.62788i	0.485713	−	0.972563i
$99$	14.1944	−	9.48439i	1.42659	−	0.953217i
$100$	−4.97419	+	8.41878i	−0.497419	+	0.841878i
$101$	10.0464			0.999650			0.499825	−	0.866126i	$-0.333398\pi$
$101$	10.0464			0.999650			0.499825	+	0.866126i	$0.333398\pi$
$102$	15.0757	+	5.37353i	1.49272	+	0.532059i
$103$		−	11.7462i		−	1.15739i	−0.815545	−	0.578694i	$-0.803563\pi$
$103$		−	11.7462i		−	1.15739i	0.815545	−	0.578694i	$-0.196437\pi$
$104$	−11.2404	−	2.41275i	−1.10221	−	0.236590i
$105$	−1.93985	−	2.90320i	−0.189310	−	0.283323i
$106$	5.27436	−	10.5611i	0.512291	−	1.02578i
$107$	−1.53470	+	7.71544i	−0.148365	+	0.745880i	0.832932	+	0.553376i	$0.186661\pi$
$107$	−1.53470	+	7.71544i	−0.148365	+	0.745880i	−0.981296	+	0.192504i	$0.938339\pi$
$108$	0.466159	+	8.40758i	0.0448562	+	0.809020i
$109$	8.18274	−	1.62765i	0.783765	−	0.155900i	0.213042	−	0.977043i	$-0.431663\pi$
$109$	8.18274	−	1.62765i	0.783765	−	0.155900i	0.570723	+	0.821143i	$0.306663\pi$
$110$	−1.76780	−	0.124802i	−0.168553	−	0.0118994i
$111$	−12.1300	−	5.02439i	−1.15132	−	0.476894i
$112$	15.2331	+	1.30673i	1.43940	+	0.123474i
$113$	2.09537	+	1.40008i	0.197116	+	0.131708i	0.650211	−	0.759754i	$-0.274680\pi$
$113$	2.09537	+	1.40008i	0.197116	+	0.131708i	−0.453096	+	0.891462i	$0.649680\pi$
$114$	0.233205	+	1.84297i	0.0218417	+	0.172610i
$115$	0.502707	+	0.502707i	0.0468777	+	0.0468777i
$116$	5.56371	+	1.95127i	0.516578	+	0.181171i
$117$	7.05229	+	17.0257i	0.651984	+	1.57403i
$118$	3.44599	−	1.15046i	0.317229	−	0.105908i
$119$	−15.6448	+	1.89887i	−1.43416	+	0.174069i
$120$	1.46772	−	2.12642i	0.133984	−	0.194115i
$121$	1.21594	+	2.93555i	0.110540	+	0.266868i
$122$	−14.0815	−	10.9181i	−1.27488	−	0.988475i
$123$	−11.0266	+	11.0266i	−0.994231	+	0.994231i
$124$	13.4032	−	6.44292i	1.20365	−	0.578591i
$125$	−2.73658	−	1.82852i	−0.244767	−	0.163548i
$126$	−12.1471	−	21.2859i	−1.08215	−	1.89630i
$127$	3.51222	−	8.47924i	0.311659	−	0.752411i	−0.687985	−	0.725725i	$-0.741504\pi$
$127$	3.51222	−	8.47924i	0.311659	−	0.752411i	0.999644	−	0.0266862i	$-0.00849550\pi$
$128$	3.25723	+	10.8347i	0.287901	+	0.957660i
$129$	6.60002	−	1.31283i	0.581100	−	0.115588i
$130$	0.504430	−	1.84538i	0.0442415	−	0.161850i
$131$	5.27821	+	1.04990i	0.461160	+	0.0917303i	0.420202	−	0.907431i	$-0.361959\pi$
$131$	5.27821	+	1.04990i	0.461160	+	0.0917303i	0.0409575	+	0.999161i	$0.486959\pi$
$132$	−20.4649	−	2.90401i	−1.78124	−	0.252762i
$133$	−1.01625	−	1.52093i	−0.0881203	−	0.131881i
$134$	−12.0625	−	13.8951i	−1.04204	−	1.20035i
$135$	−1.40122			−0.120598
$136$	−5.57453	−	10.2433i	−0.478012	−	0.878353i
$137$	2.51759			0.215092			0.107546	−	0.994200i	$-0.465701\pi$
$137$	2.51759			0.215092			0.107546	+	0.994200i	$0.465701\pi$
$138$	5.43582	+	6.26163i	0.462728	+	0.533025i
$139$	−5.57321	−	8.34090i	−0.472713	−	0.707466i	0.516116	−	0.856519i	$-0.327377\pi$
$139$	−5.57321	−	8.34090i	−0.472713	−	0.707466i	−0.988829	+	0.149053i	$0.952377\pi$
$140$	−0.357446	+	2.51896i	−0.0302097	+	0.212891i
$141$	−35.1464	−	6.99106i	−2.95986	−	0.588753i
$142$	0.499309	−	1.82664i	0.0419011	−	0.153288i
$143$	−15.0103	+	2.98574i	−1.25523	+	0.249680i
$144$	11.3275	−	14.1629i	0.943961	−	1.18024i
$145$	−0.375460	+	0.906440i	−0.0311802	+	0.0752758i
$146$	−2.08388	−	3.65169i	−0.172463	−	0.302216i
$147$	17.3670	+	11.6043i	1.43241	+	0.957105i
$148$	4.14472	+	8.62228i	0.340694	+	0.708747i
$149$	−5.20232	+	5.20232i	−0.426191	+	0.426191i	−0.887329	−	0.461138i	$-0.847441\pi$
$149$	−5.20232	+	5.20232i	−0.426191	+	0.426191i	0.461138	+	0.887329i	$0.347441\pi$
$150$	−14.9985	−	11.6291i	−1.22462	−	0.949511i
$151$	5.65251	+	13.6464i	0.459995	+	1.11053i	0.968399	+	0.249407i	$0.0802358\pi$
$151$	5.65251	+	13.6464i	0.459995	+	1.11053i	−0.508404	+	0.861119i	$0.669764\pi$
$152$	0.768913	−	1.11399i	0.0623671	−	0.0903566i
$153$	−8.43722	+	16.6814i	−0.682109	+	1.34861i
$154$	19.3058	−	6.44531i	1.55571	−	0.519378i
$155$	0.947023	+	2.28632i	0.0760667	+	0.183641i
$156$	7.38450	−	21.0556i	0.591233	−	1.68580i
$157$	−1.48582	−	1.48582i	−0.118581	−	0.118581i	0.645326	−	0.763907i	$-0.276722\pi$
$157$	−1.48582	−	1.48582i	−0.118581	−	0.118581i	−0.763907	+	0.645326i	$0.776722\pi$
$158$	−1.36224	−	10.7655i	−0.108374	−	0.856454i
$159$	19.0503	+	12.7290i	1.51079	+	1.00948i
$160$	−1.83020	+	0.441379i	−0.144690	+	0.0348941i
$161$	−7.54340	−	3.12458i	−0.594503	−	0.246251i
$162$	2.88551	+	0.203710i	0.226707	+	0.0160050i
$163$	−8.68521	+	1.72760i	−0.680278	+	0.135316i	−0.523122	−	0.852258i	$-0.675233\pi$
$163$	−8.68521	+	1.72760i	−0.680278	+	0.135316i	−0.157156	+	0.987574i	$0.550233\pi$
$164$	11.3451	−	0.629031i	0.885903	−	0.0491190i
$165$	0.671032	−	3.37351i	0.0522398	−	0.262627i
$166$	2.58119	−	5.16843i	0.200339	−	0.401148i
$167$	−10.3052	−	15.4228i	−0.797439	−	1.19345i	−0.977736	−	0.209840i	$-0.932706\pi$
$167$	−10.3052	−	15.4228i	−0.797439	−	1.19345i	0.180297	−	0.983612i	$-0.442294\pi$
$168$	−6.22767	+	29.0131i	−0.480475	+	2.23841i
$169$		−	3.52100i		−	0.270846i
$170$	1.75328	−	0.831850i	0.134471	−	0.0637999i
$171$	−2.16977			−0.165927
$172$	−4.22153	−	2.49427i	−0.321889	−	0.190186i
$173$	−7.97261	+	5.32713i	−0.606147	+	0.405014i	−0.820421	−	0.571759i	$-0.806261\pi$
$173$	−7.97261	+	5.32713i	−0.606147	+	0.405014i	0.214275	+	0.976773i	$0.431261\pi$
$174$	−5.11279	+	10.2376i	−0.387600	+	0.776107i
$175$	18.3289	+	3.64584i	1.38553	+	0.275600i
$176$	9.70066	+	11.5211i	0.731215	+	0.868436i
$177$	1.37560	+	6.91560i	0.103396	+	0.519808i
$178$	−1.27380	+	18.0432i	−0.0954756	+	1.35239i
$179$	−0.385295	+	0.930185i	−0.0287983	+	0.0695253i	−0.937624	−	0.347650i	$-0.886980\pi$
$179$	−0.385295	+	0.930185i	−0.0287983	+	0.0695253i	0.908826	+	0.417175i	$0.136980\pi$
$180$	2.24882	+	2.01255i	0.167617	+	0.150007i
$181$	−3.36791	+	5.04043i	−0.250334	+	0.374652i	−0.935260	−	0.353961i	$-0.884835\pi$
$181$	−3.36791	+	5.04043i	−0.250334	+	0.374652i	0.684926	+	0.728613i	$0.259835\pi$
$182$	2.75820	+	21.7974i	0.204451	+	1.61573i
$183$	24.4538	−	24.4538i	1.80768	−	1.80768i
$184$	0.0911821	−	6.04124i	0.00672203	−	0.445366i
$185$	−1.47078	+	0.609218i	−0.108134	+	0.0447906i
$186$	9.14020	+	27.3779i	0.670192	+	2.00744i
$187$	−12.2203	−	9.57495i	−0.893639	−	0.700190i
$188$	15.6863	+	20.8743i	1.14404	+	1.52241i
$189$	14.8677	−	6.15840i	1.08147	−	0.447958i
$190$	0.178007	+	0.138018i	0.0129140	+	0.0100129i
$191$	3.79672	+	3.79672i	0.274721	+	0.274721i	0.830997	−	0.556276i	$-0.187770\pi$
$191$	3.79672	+	3.79672i	0.274721	+	0.274721i	−0.556276	+	0.830997i	$0.687770\pi$
$192$	−21.6559	+	3.63195i	−1.56288	+	0.262113i
$193$	−5.97383	+	8.94047i	−0.430006	+	0.643549i	−0.981686	−	0.190507i	$-0.938987\pi$
$193$	−5.97383	+	8.94047i	−0.430006	+	0.643549i	0.551680	+	0.834056i	$0.313987\pi$
$194$	−13.0709	+	7.45905i	−0.938433	+	0.535528i
$195$	3.43038	+	1.42091i	0.245655	+	0.101754i
$196$	−3.79098	−	14.7398i	−0.270784	−	1.05284i
$197$	−3.28973	−	16.5386i	−0.234384	−	1.17833i	−0.901301	−	0.433194i	$-0.857387\pi$
$197$	−3.28973	−	16.5386i	−0.234384	−	1.17833i	0.666917	−	0.745132i	$-0.267613\pi$
$198$	6.36582	−	23.2883i	0.452399	−	1.65503i
$199$	1.14461	−	5.75433i	0.0811391	−	0.407914i	−0.918775	−	0.394782i	$-0.870820\pi$
$199$	1.14461	−	5.75433i	0.0811391	−	0.407914i	0.999914	−	0.0131314i	$-0.00417997\pi$
$200$	2.49288	+	13.6023i	0.176273	+	0.961828i
$201$	29.6941	−	19.8410i	2.09446	−	1.39947i
$202$	10.7289	−	9.31393i	0.754883	−	0.655326i
$203$		−	11.2680i		−	0.790857i
$204$	21.0817	−	8.23804i	1.47602	−	0.576778i
$205$			1.89079i			0.132059i
$206$	−10.8898	−	12.5442i	−0.758731	−	0.873998i
$207$	−8.05284	+	5.38074i	−0.559711	+	0.373987i
$208$	−14.2409	+	7.84425i	−0.987430	+	0.543901i
$209$	0.351541	−	1.76732i	0.0243166	−	0.122248i
$210$	−4.76319	−	1.30201i	−0.328691	−	0.0898472i
$211$	4.89952	+	24.6316i	0.337297	+	1.69571i	0.661684	+	0.749783i	$0.269842\pi$
$211$	4.89952	+	24.6316i	0.337297	+	1.69571i	−0.324387	+	0.945925i	$0.605158\pi$
$212$	−4.15842	−	16.1684i	−0.285601	−	1.11045i
$213$	3.39556	+	1.40649i	0.232660	+	0.0963708i
$214$	5.51398	+	9.66243i	0.376928	+	0.660510i
$215$	0.453315	−	0.678433i	0.0309158	−	0.0462688i
$216$	8.29245	+	8.54661i	0.564230	+	0.581523i
$217$	−20.0968	−	20.0968i	−1.36426	−	1.36426i
$218$	7.22969	−	9.32441i	0.489656	−	0.631529i
$219$	7.53911	−	3.12280i	0.509446	−	0.211019i
$220$	−2.00361	+	1.50564i	−0.135083	+	0.101510i
$221$	12.7111	−	10.9218i	0.855039	−	0.734680i
$222$	−17.6121	+	5.87987i	−1.18205	+	0.394631i
$223$	−20.9755	+	8.68833i	−1.40462	+	0.581814i	−0.950947	−	0.309353i	$-0.899888\pi$
$223$	−20.9755	+	8.68833i	−1.40462	+	0.581814i	−0.453676	+	0.891167i	$0.649888\pi$
$224$	17.4795	−	12.7270i	1.16790	−	0.850362i
$225$	15.6747	−	15.6747i	1.04498	−	1.04498i
$226$	3.53573	−	0.447404i	0.235193	−	0.0297609i
$227$	13.8262	−	20.6923i	0.917674	−	1.37340i	−0.00997714	−	0.999950i	$-0.503176\pi$
$227$	13.8262	−	20.6923i	0.917674	−	1.37340i	0.927652	−	0.373447i	$-0.121824\pi$
$228$	1.95765	+	1.75197i	0.129649	+	0.116027i
$229$	2.27094	−	5.48252i	0.150068	−	0.362295i	−0.830913	−	0.556403i	$-0.812181\pi$
$229$	2.27094	−	5.48252i	0.150068	−	0.362295i	0.980980	+	0.194108i	$0.0621811\pi$
$230$	1.00292	+	0.0708035i	0.0661304	+	0.00466864i
$231$	7.70664	+	38.7439i	0.507060	+	2.54916i
$232$	7.75072	−	3.07425i	0.508860	−	0.201834i
$233$	−0.170079	−	0.0338307i	−0.0111422	−	0.00221632i	0.189516	−	0.981878i	$-0.439308\pi$
$233$	−0.170079	−	0.0338307i	−0.0111422	−	0.00221632i	−0.200658	+	0.979661i	$0.564308\pi$
$234$	23.3159	+	11.6443i	1.52421	+	0.761212i
$235$	−3.61279	+	2.41399i	−0.235672	+	0.157471i
$236$	2.61353	−	4.42338i	0.170126	−	0.287937i
$237$	21.0609			1.36805
$238$	−14.9473	+	16.5321i	−0.968887	+	1.07162i
$239$		−	11.0361i		−	0.713866i	−0.934130	−	0.356933i	$-0.883822\pi$
$239$		−	11.0361i		−	0.713866i	0.934130	−	0.356933i	$-0.116178\pi$
$240$	−0.403952	−	3.63161i	−0.0260750	−	0.234419i
$241$	7.13749	+	10.6820i	0.459766	+	0.688089i	0.986834	−	0.161734i	$-0.0517087\pi$
$241$	7.13749	+	10.6820i	0.459766	+	0.688089i	−0.527068	+	0.849823i	$0.676709\pi$
$242$	4.02009	+	2.00769i	0.258421	+	0.129059i
$243$	−3.55943	+	17.8945i	−0.228338	+	1.14793i
$244$	−25.1602	+	1.39501i	−1.61072	+	0.0893065i
$245$	2.48395	−	0.494088i	0.158694	−	0.0315661i
$246$	−1.55303	+	21.9984i	−0.0990175	+	1.40256i
$247$	1.79711	+	0.744388i	0.114348	+	0.0473643i
$248$	8.34066	−	19.3067i	0.529632	−	1.22598i
$249$	9.32294	+	6.22939i	0.590818	+	0.394772i
$250$	−4.61772	+	0.584317i	−0.292050	+	0.0369554i
$251$	−14.3875	−	14.3875i	−0.908129	−	0.908129i	0.0879919	−	0.996121i	$-0.471955\pi$
$251$	−14.3875	−	14.3875i	−0.908129	−	0.908129i	−0.996121	+	0.0879919i	$0.971955\pi$
$252$	−32.7064	−	11.4706i	−2.06031	−	0.722580i
$253$	−3.07800	−	7.43095i	−0.193512	−	0.467180i
$254$	−4.11023	−	12.3115i	−0.257899	−	0.772491i
$255$	1.17455	+	3.57864i	0.0735530	+	0.224103i
$256$	13.5233	+	8.55103i	0.845207	+	0.534439i
$257$	5.12481	+	12.3724i	0.319677	+	0.771768i	0.999271	+	0.0381799i	$0.0121560\pi$
$257$	5.12481	+	12.3724i	0.319677	+	0.771768i	−0.679594	+	0.733589i	$0.737844\pi$
$258$	5.83131	−	7.52087i	0.363042	−	0.468229i
$259$	12.9283	−	12.9283i	0.803323	−	0.803323i
$260$	−1.17214	−	2.43840i	−0.0726929	−	0.151223i
$261$	−11.1133	−	7.42567i	−0.687896	−	0.459638i
$262$	6.61017	−	3.77217i	0.408378	−	0.233046i
$263$	−3.72607	+	8.99554i	−0.229760	+	0.554689i	−0.996148	−	0.0876888i	$-0.972052\pi$
$263$	−3.72607	+	8.99554i	−0.229760	+	0.554689i	0.766388	+	0.642378i	$0.222052\pi$
$264$	−24.5476	+	15.8716i	−1.51080	+	0.976829i
$265$	2.72471	−	0.541978i	0.167377	−	0.0332934i
$266$	−2.49534	−	0.682098i	−0.152999	−	0.0418221i
$267$	−34.4319	−	6.84894i	−2.10720	−	0.419148i
$268$	−25.7641	−	3.65598i	−1.57379	−	0.223324i
$269$	3.40992	+	5.10331i	0.207907	+	0.311154i	0.920738	−	0.390181i	$-0.127588\pi$
$269$	3.40992	+	5.10331i	0.207907	+	0.311154i	−0.712831	+	0.701335i	$0.752588\pi$
$270$	−1.49642	+	1.29906i	−0.0910692	+	0.0790586i
$271$	8.96459			0.544560			0.272280	−	0.962218i	$-0.412222\pi$
$271$	8.96459			0.544560			0.272280	+	0.962218i	$0.412222\pi$
$272$	−15.4497	−	5.77107i	−0.936779	−	0.349923i
$273$	−42.6431			−2.58088
$274$	2.68863	−	2.33404i	0.162426	−	0.141005i
$275$	10.2277	+	15.3069i	0.616754	+	0.923038i
$276$	11.6102	+	1.64752i	0.698855	+	0.0991691i
$277$	−17.4252	−	3.46609i	−1.04698	−	0.208257i	−0.358512	−	0.933525i	$-0.616716\pi$
$277$	−17.4252	−	3.46609i	−1.04698	−	0.208257i	−0.688467	+	0.725268i	$0.741716\pi$
$278$	−13.6847	−	3.74068i	−0.820751	−	0.224351i
$279$	−33.0649	+	6.57702i	−1.97955	+	0.393756i
$280$	1.95358	+	3.02148i	0.116749	+	0.180568i
$281$	0.173426	−	0.418688i	0.0103458	−	0.0249769i	−0.918622	−	0.395137i	$-0.870697\pi$
$281$	0.173426	−	0.418688i	0.0103458	−	0.0249769i	0.928968	+	0.370160i	$0.120697\pi$
$282$	−44.0156	+	25.1180i	−2.62109	+	1.49576i
$283$	9.31857	+	6.22647i	0.553931	+	0.370125i	0.800807	−	0.598922i	$-0.204404\pi$
$283$	9.31857	+	6.22647i	0.553931	+	0.370125i	−0.246876	+	0.969047i	$0.579404\pi$
$284$	−1.16024	−	2.41365i	−0.0688474	−	0.143224i
$285$	−0.309126	+	0.309126i	−0.0183111	+	0.0183111i
$286$	−13.2621	+	17.1046i	−0.784203	+	1.01142i
$287$	−8.31009	−	20.0623i	−0.490529	−	1.18424i
$288$	−1.03322	−	25.6268i	−0.0608834	−	1.51007i
$289$	16.8062	+	2.55949i	0.988601	+	0.150558i
$290$	0.439388	+	1.31611i	0.0258017	+	0.0772847i
$291$	−11.1777	−	26.9855i	−0.655251	−	1.58192i
$292$	−5.61093	−	1.96783i	−0.328355	−	0.115159i
$293$	21.0702	+	21.0702i	1.23093	+	1.23093i	0.963606	+	0.267326i	$0.0861400\pi$
$293$	21.0702	+	21.0702i	1.23093	+	1.23093i	0.267326	+	0.963606i	$0.413860\pi$
$294$	29.3052	−	3.70822i	1.70911	−	0.216268i
$295$	0.710872	+	0.474989i	0.0413886	+	0.0276549i
$296$	12.4200	+	5.36553i	0.721897	+	0.311865i
$297$	14.6461	+	6.06660i	0.849851	+	0.352020i
$298$	−0.732718	+	10.3788i	−0.0424452	+	0.601228i
$299$	8.51575	−	1.69389i	0.492478	−	0.0979600i
$300$	−26.7987	+	1.48586i	−1.54723	+	0.0857862i
$301$	−1.82818	+	9.19087i	−0.105374	+	0.529753i
$302$	18.6880	+	9.33309i	1.07538	+	0.537059i
$303$	15.3200	+	22.9279i	0.880109	+	1.31718i
$304$	−0.211623	−	1.90253i	−0.0121374	−	0.109118i
$305$		−	4.19325i		−	0.240105i
$306$	6.45482	+	25.6369i	0.368997	+	1.46556i
$307$	5.89758			0.336592			0.168296	−	0.985736i	$-0.446173\pi$
$307$	5.89758			0.336592			0.168296	+	0.985736i	$0.446173\pi$
$308$	14.6420	−	24.7815i	0.834307	−	1.41206i
$309$	26.8073	−	17.9121i	1.52502	−	1.01898i
$310$	3.13099	+	1.56367i	0.177829	+	0.0888103i
$311$	6.36168	+	1.26542i	0.360738	+	0.0717552i	0.372132	−	0.928180i	$-0.378627\pi$
$311$	6.36168	+	1.26542i	0.360738	+	0.0717552i	−0.0113941	+	0.999935i	$0.503627\pi$
$312$	−11.6344	−	29.3323i	−0.658666	−	1.66061i
$313$	−2.69975	−	13.5726i	−0.152599	−	0.767167i	−0.978964	−	0.204032i	$-0.934595\pi$
$313$	−2.69975	−	13.5726i	−0.152599	−	0.767167i	0.826365	−	0.563134i	$-0.190405\pi$
$314$	−2.96426	−	0.209270i	−0.167283	−	0.0118098i
$315$	2.20715	−	5.32853i	0.124359	−	0.300229i
$316$	−11.4354	−	10.2339i	−0.643291	−	0.575703i
$317$	−11.9360	+	17.8635i	−0.670392	+	1.00331i	0.327890	+	0.944716i	$0.393662\pi$
$317$	−11.9360	+	17.8635i	−0.670392	+	1.00331i	−0.998282	+	0.0585963i	$0.981338\pi$
$318$	32.1456	−	4.06764i	1.80264	−	0.228102i
$319$	7.84889	−	7.84889i	0.439453	−	0.439453i
$320$	−1.54534	+	2.16814i	−0.0863872	+	0.121202i
$321$	−19.9486	+	8.26297i	−1.11342	+	0.461194i
$322$	−10.9527	+	3.65659i	−0.610369	+	0.203774i
$323$	0.615323	+	1.87478i	0.0342375	+	0.104316i
$324$	3.27041	−	2.45759i	0.181689	−	0.136533i
$325$	−18.3601	+	7.60499i	−1.01843	+	0.421849i
$326$	−7.67363	+	9.89698i	−0.425003	+	0.548143i
$327$	16.1927	+	16.1927i	0.895460	+	0.895460i
$328$	11.5327	−	11.1898i	0.636787	−	0.617851i
$329$	27.7241	−	41.4920i	1.52848	−	2.28753i
$330$	−2.41094	−	4.22481i	−0.132718	−	0.232568i
$331$	−16.2857	−	6.74575i	−0.895142	−	0.370780i	−0.112792	−	0.993619i	$-0.535979\pi$
$331$	−16.2857	−	6.74575i	−0.895142	−	0.370780i	−0.782350	+	0.622839i	$0.785979\pi$
$332$	−2.03507	−	7.91257i	−0.111689	−	0.434259i
$333$	−4.23099	−	21.2706i	−0.231857	−	1.16562i
$334$	−25.3037	−	6.91673i	−1.38456	−	0.378467i
$335$	0.844790	−	4.24704i	0.0461558	−	0.232041i
$336$	20.2472	+	36.7579i	1.10457	+	2.00531i
$337$	−28.5162	+	19.0539i	−1.55337	+	1.03793i	−0.578361	+	0.815781i	$0.696308\pi$
$337$	−28.5162	+	19.0539i	−1.55337	+	1.03793i	−0.975012	+	0.222151i	$0.928692\pi$
$338$	−3.26430	−	3.76021i	−0.177555	−	0.204529i
$339$			6.91709i			0.375685i
$340$	1.10120	−	2.51382i	0.0597207	−	0.136331i
$341$		−	27.9976i		−	1.51615i
$342$	−2.31718	+	2.01158i	−0.125299	+	0.108774i
$343$	−1.93777	+	1.29478i	−0.104630	+	0.0699115i
$344$	−6.82076	+	1.25003i	−0.367751	+	0.0673973i
$345$	−0.380694	+	1.91388i	−0.0204959	+	0.103040i
$346$	−3.57551	+	13.0804i	−0.192221	+	0.703208i
$347$	−0.600433	−	3.01858i	−0.0322329	−	0.162046i	0.961316	−	0.275446i	$-0.0888257\pi$
$347$	−0.600433	−	3.01858i	−0.0322329	−	0.162046i	−0.993549	+	0.113401i	$0.963826\pi$
$348$	4.03104	+	15.6731i	0.216086	+	0.840168i
$349$	13.0435	+	5.40281i	0.698204	+	0.289206i	0.703414	−	0.710781i	$-0.251658\pi$
$349$	13.0435	+	5.40281i	0.698204	+	0.289206i	−0.00520939	+	0.999986i	$0.501658\pi$
$350$	22.9542	−	13.0991i	1.22695	−	0.700175i
$351$	−9.50746	+	14.2289i	−0.507471	+	0.759484i
$352$	21.0409	+	3.31041i	1.12148	+	0.176446i
$353$	17.6192	+	17.6192i	0.937774	+	0.937774i	0.998174	−	0.0603998i	$-0.0192376\pi$
$353$	17.6192	+	17.6192i	0.937774	+	0.937774i	−0.0603998	+	0.998174i	$0.519238\pi$
$354$	7.88047	+	6.11013i	0.418842	+	0.324750i
$355$	0.411718	−	0.170539i	0.0218517	−	0.00905129i
$356$	15.3674	+	20.4500i	0.814471	+	1.08385i
$357$	−28.1908	−	32.8091i	−1.49202	−	1.73644i
$358$	0.450898	+	1.35059i	0.0238307	+	0.0713808i
$359$	0.287046	−	0.118898i	0.0151497	−	0.00627521i	−0.375096	−	0.926986i	$-0.622390\pi$
$359$	0.287046	−	0.118898i	0.0151497	−	0.00627521i	0.390245	+	0.920711i	$0.372390\pi$
$360$	4.26743	+	0.0644095i	0.224913	+	0.00339468i
$361$	13.2731	−	13.2731i	0.698583	−	0.698583i
$362$	1.07624	+	8.50524i	0.0565657	+	0.447025i
$363$	−4.84532	+	7.25154i	−0.254313	+	0.380607i
$364$	23.1539	+	20.7212i	1.21359	+	1.08609i
$365$	0.378646	−	0.914133i	0.0198192	−	0.0478479i
$366$	3.44418	−	48.7861i	0.180030	−	2.55009i
$367$	−0.405754	−	2.03987i	−0.0211802	−	0.106480i	0.968749	−	0.248043i	$-0.0797873\pi$
$367$	−0.405754	−	2.03987i	−0.0211802	−	0.106480i	−0.989929	+	0.141563i	$0.954787\pi$
$368$	−5.50343	−	6.53621i	−0.286886	−	0.340724i
$369$	−25.2633	−	5.02519i	−1.31516	−	0.261601i
$370$	−1.00590	+	2.01416i	−0.0522944	+	0.104711i
$371$	−26.5286	+	17.7258i	−1.37729	+	0.920279i
$372$	35.1431	+	20.7641i	1.82208	+	1.07657i
$373$	−32.2087			−1.66770			−0.833851	−	0.551990i	$-0.813869\pi$
$373$	−32.2087			−1.66770			−0.833851	+	0.551990i	$0.813869\pi$
$374$	−21.9275	+	1.10394i	−1.13384	+	0.0570833i
$375$		−	9.03383i		−	0.466505i
$376$	36.1045	+	7.74982i	1.86195	+	0.399667i
$377$	6.65705	+	9.96298i	0.342856	+	0.513120i
$378$	10.1684	−	20.3606i	0.523005	−	1.04723i
$379$	−3.56239	+	17.9093i	−0.182987	+	0.919940i	0.774744	+	0.632275i	$0.217879\pi$
$379$	−3.56239	+	17.9093i	−0.182987	+	0.919940i	−0.957731	+	0.287665i	$0.907121\pi$
$380$	0.318057	−	0.0176347i	0.0163160	−	0.000904641i
$381$	24.7073	−	4.91459i	1.26579	−	0.251782i
$382$	7.57458	+	0.534746i	0.387549	+	0.0273600i
$383$	4.05345	+	1.67899i	0.207122	+	0.0857926i	0.483832	−	0.875161i	$-0.339244\pi$
$383$	4.05345	+	1.67899i	0.207122	+	0.0857926i	−0.276711	+	0.960953i	$0.589244\pi$
$384$	−19.7600	+	23.9558i	−1.00838	+	1.22249i
$385$	3.98259	+	2.66108i	0.202971	+	0.135621i
$386$	1.90898	+	15.0862i	0.0971643	+	0.767867i
$387$	7.85993	+	7.85993i	0.399543	+	0.399543i
$388$	−7.04365	+	20.0837i	−0.357587	+	1.01960i
$389$	9.42638	+	22.7573i	0.477937	+	1.15384i	0.960575	+	0.278021i	$0.0896786\pi$
$389$	9.42638	+	22.7573i	0.477937	+	1.15384i	−0.482638	+	0.875820i	$0.660321\pi$
$390$	4.98076	−	1.66284i	0.252211	−	0.0842014i
$391$	6.93290	+	5.43211i	0.350612	+	0.274714i
$392$	−17.7137	−	12.2266i	−0.894676	−	0.617535i
$393$	5.65279	+	13.6470i	0.285145	+	0.688402i
$394$	−18.8461	−	14.6123i	−0.949452	−	0.736158i
$395$	1.80572	−	1.80572i	0.0908557	−	0.0908557i
$396$	−14.7922	−	30.7722i	−0.743334	−	1.54636i
$397$	2.33711	+	1.56161i	0.117296	+	0.0783749i	0.612835	−	0.790211i	$-0.290029\pi$
$397$	2.33711	+	1.56161i	0.117296	+	0.0783749i	−0.495538	+	0.868586i	$0.665029\pi$
$398$	−4.11244	−	7.20644i	−0.206138	−	0.361226i
$399$	1.92138	−	4.63861i	0.0961891	−	0.232221i
$400$	15.2729	+	12.2153i	0.763643	+	0.610765i
$401$	−20.5799	+	4.09361i	−1.02771	+	0.204425i	−0.680028	−	0.733186i	$-0.738032\pi$
$401$	−20.5799	+	4.09361i	−1.02771	+	0.204425i	−0.347686	+	0.937611i	$0.613032\pi$
$402$	13.3170	−	48.7182i	0.664193	−	2.42984i
$403$	29.6424	+	5.89624i	1.47659	+	0.293713i
$404$	2.82292	−	19.8934i	0.140446	−	0.989735i
$405$	0.378203	+	0.566021i	0.0187931	+	0.0281258i
$406$	−10.4465	−	12.0335i	−0.518450	−	0.597213i
$407$	18.0108			0.892761
$408$	14.8766	−	28.3425i	0.736501	−	1.40316i
$409$	6.22253			0.307684			0.153842	−	0.988095i	$-0.450835\pi$
$409$	6.22253			0.307684			0.153842	+	0.988095i	$0.450835\pi$
$410$	1.75294	+	2.01925i	0.0865718	+	0.0997238i
$411$	3.83913	+	5.74567i	0.189370	+	0.283413i
$412$	−23.2594	−	3.30056i	−1.14591	−	0.162607i
$413$	−9.63032	−	1.91559i	−0.473877	−	0.0942600i
$414$	−3.61149	+	13.2120i	−0.177495	+	0.649337i
$415$	1.33343	−	0.265235i	0.0654554	−	0.0130199i
$416$	−7.93608	+	21.5799i	−0.389098	+	1.05804i
$417$	10.5370	−	25.4385i	0.515998	−	1.24573i
$418$	−1.26305	−	2.21330i	−0.0617776	−	0.108256i
$419$	1.53088	+	1.02290i	0.0747885	+	0.0499721i	0.592402	−	0.805642i	$-0.298180\pi$
$419$	1.53088	+	1.02290i	0.0747885	+	0.0499721i	−0.517614	+	0.855614i	$0.673180\pi$
$420$	−6.29388	+	3.02546i	−0.307110	+	0.147627i
$421$	−9.96212	+	9.96212i	−0.485524	+	0.485524i	−0.906891	−	0.421366i	$-0.861551\pi$
$421$	−9.96212	+	9.96212i	−0.485524	+	0.485524i	0.421366	+	0.906891i	$0.361551\pi$
$422$	28.0682	+	21.7627i	1.36634	+	1.05939i
$423$	−22.6521	−	54.6871i	−1.10138	−	2.65898i
$424$	−19.4306	−	13.4116i	−0.943633	−	0.651327i
$425$	−17.9888	−	9.09847i	−0.872584	−	0.441341i
$426$	4.93019	−	1.64596i	0.238869	−	0.0797471i
$427$	18.4294	+	44.4926i	0.891862	+	2.15315i
$428$	14.8466	+	5.20691i	0.717637	+	0.251685i
$429$	−29.7038	−	29.7038i	−1.43411	−	1.43411i
$430$	−0.144860	−	1.14479i	−0.00698575	−	0.0552067i
$431$	−7.63305	−	5.10024i	−0.367671	−	0.245670i	0.357985	−	0.933727i	$-0.383464\pi$
$431$	−7.63305	−	5.10024i	−0.367671	−	0.245670i	−0.725656	+	0.688057i	$0.758464\pi$
$432$	16.7794	+	1.43937i	0.807297	+	0.0692517i
$433$	24.2678	+	10.0520i	1.16623	+	0.483070i	0.879946	−	0.475073i	$-0.157579\pi$
$433$	24.2678	+	10.0520i	1.16623	+	0.483070i	0.286288	+	0.958144i	$0.407579\pi$
$434$	−40.0939	−	2.83053i	−1.92457	−	0.135870i
$435$	−2.64124	+	0.525375i	−0.126638	+	0.0251898i
$436$	−0.923745	−	16.6605i	−0.0442393	−	0.797894i
$437$	−0.199438	+	1.00264i	−0.00954042	+	0.0479629i
$438$	5.15618	−	10.3244i	0.246372	−	0.493321i
$439$	18.3421	+	27.4510i	0.875423	+	1.31016i	0.949776	+	0.312931i	$0.101311\pi$
$439$	18.3421	+	27.4510i	0.875423	+	1.31016i	−0.0743533	+	0.997232i	$0.523689\pi$
$440$	−0.743862	+	3.46546i	−0.0354622	+	0.165209i
$441$			34.5018i			1.64294i
$442$	3.44909	−	23.4482i	0.164057	−	1.11532i
$443$	2.14916			0.102110			0.0510548	−	0.998696i	$-0.483742\pi$
$443$	2.14916			0.102110			0.0510548	+	0.998696i	$0.483742\pi$
$444$	−13.3575	+	22.6075i	−0.633919	+	1.07290i
$445$	−3.53935	+	2.36492i	−0.167781	+	0.112108i
$446$	−14.3456	+	28.7249i	−0.679286	+	1.36016i
$447$	−19.8060	−	3.93965i	−0.936790	−	0.186339i
$448$	6.86789	−	29.7969i	0.324477	−	1.40777i
$449$	4.26124	+	21.4227i	0.201100	+	1.01100i	0.941032	+	0.338317i	$0.109858\pi$
$449$	4.26124	+	21.4227i	0.201100	+	1.01100i	−0.739932	+	0.672682i	$0.765142\pi$
$450$	2.20769	−	31.2715i	0.104071	−	1.47415i
$451$	8.18621	−	19.7633i	0.385474	−	0.930616i
$452$	3.36116	−	3.75576i	0.158096	−	0.176656i
$453$	−22.5243	+	33.7100i	−1.05828	+	1.58383i
$454$	−4.41824	−	34.9163i	−0.207358	−	1.63870i
$455$	−3.65614	+	3.65614i	−0.171403	+	0.171403i
$456$	3.71490	+	0.0560700i	0.173966	+	0.00262572i
$457$	15.6974	−	6.50208i	0.734294	−	0.304155i	0.0159790	−	0.999872i	$-0.494914\pi$
$457$	15.6974	−	6.50208i	0.734294	−	0.304155i	0.718315	+	0.695718i	$0.244914\pi$
$458$	−2.65760	−	7.96038i	−0.124181	−	0.371964i
$459$	−17.2328	+	2.09161i	−0.804359	+	0.0976282i
$460$	1.13670	−	0.854186i	0.0529988	−	0.0398266i
$461$	14.7222	−	6.09814i	0.685681	−	0.284019i	−0.0125182	−	0.999922i	$-0.503985\pi$
$461$	14.7222	−	6.09814i	0.685681	−	0.284019i	0.698200	+	0.715903i	$0.253985\pi$
$462$	44.1495	+	34.2314i	2.05402	+	1.59259i
$463$	−13.3355	−	13.3355i	−0.619753	−	0.619753i	0.325715	−	0.945468i	$-0.394395\pi$
$463$	−13.3355	−	13.3355i	−0.619753	−	0.619753i	−0.945468	+	0.325715i	$0.894395\pi$
$464$	5.42718	−	10.4688i	0.251951	−	0.486001i
$465$	−3.77372	+	5.64777i	−0.175002	+	0.261909i
$466$	−0.212998	+	0.121550i	−0.00986694	+	0.00563069i
$467$	−17.5386	−	7.26472i	−0.811589	−	0.336171i	−0.0620009	−	0.998076i	$-0.519748\pi$
$467$	−17.5386	−	7.26472i	−0.811589	−	0.336171i	−0.749588	+	0.661905i	$0.769748\pi$
$468$	35.6953	−	9.18062i	1.65002	−	0.424374i
$469$	9.70220	+	48.7763i	0.448006	+	2.25228i
$470$	−1.62024	+	5.92739i	−0.0747363	+	0.273410i
$471$	1.12519	−	5.65673i	0.0518462	−	0.260648i
$472$	−1.30980	−	7.14689i	−0.0602885	−	0.328962i
$473$	−7.67550	+	5.12860i	−0.352920	+	0.235813i
$474$	22.4918	−	19.5254i	1.03308	−	0.896833i
$475$		−	2.33982i		−	0.107358i
$476$	−0.635951	+	31.5128i	−0.0291488	+	1.44439i
$477$			37.8459i			1.73284i
$478$	−10.2315	−	11.7859i	−0.467978	−	0.539074i
$479$	−4.41352	+	2.94902i	−0.201659	+	0.134744i	−0.652300	−	0.757961i	$-0.726196\pi$
$479$	−4.41352	+	2.94902i	−0.201659	+	0.134744i	0.450641	+	0.892705i	$0.351196\pi$
$480$	−3.79824	−	3.50384i	−0.173365	−	0.159927i
$481$	−3.79304	+	19.0689i	−0.172948	+	0.869468i
$482$	17.5257	+	4.79061i	0.798272	+	0.218206i
$483$	−4.37217	−	21.9804i	−0.198941	−	1.00014i
$484$	6.15453	−	1.58291i	0.279751	−	0.0719504i
$485$	−3.27204	−	1.35532i	−0.148576	−	0.0615421i
$486$	12.7886	+	22.4102i	0.580104	+	1.01655i
$487$	6.46086	−	9.66936i	0.292769	−	0.438160i	−0.655704	−	0.755018i	$-0.727628\pi$
$487$	6.46086	−	9.66936i	0.292769	−	0.438160i	0.948473	+	0.316858i	$0.102628\pi$
$488$	−25.5763	+	24.8157i	−1.15778	+	1.12335i
$489$	−17.1870	−	17.1870i	−0.777225	−	0.777225i
$490$	2.19464	−	2.83051i	0.0991436	−	0.127869i
$491$	34.5393	−	14.3066i	1.55873	−	0.645649i	0.573866	−	0.818949i	$-0.305443\pi$
$491$	34.5393	−	14.3066i	1.55873	−	0.645649i	0.984869	+	0.173300i	$0.0554431\pi$
$492$	18.7360	+	24.9327i	0.844685	+	1.12405i
$493$	−3.26452	+	11.7082i	−0.147026	+	0.527313i
$494$	2.60933	−	0.871132i	0.117399	−	0.0391941i
$495$	5.24910	−	2.17425i	0.235930	−	0.0977253i
$496$	−8.99186	−	28.3510i	−0.403746	−	1.27300i
$497$	−3.61903	+	3.61903i	−0.162335	+	0.162335i
$498$	15.7316	−	1.99064i	0.704949	−	0.0892028i
$499$	11.5213	−	17.2429i	0.515764	−	0.771896i	−0.478586	−	0.878041i	$-0.658851\pi$
$499$	11.5213	−	17.2429i	0.515764	−	0.771896i	0.994351	+	0.106144i	$0.0338506\pi$
$500$	−4.38973	+	4.90508i	−0.196315	+	0.219362i
$501$	19.4835	−	47.0373i	0.870457	−	2.10147i
$502$	−28.7035	−	2.02640i	−1.28110	−	0.0904425i
$503$	−6.38686	−	32.1089i	−0.284776	−	1.43167i	−0.812852	−	0.582470i	$-0.802087\pi$
$503$	−6.38686	−	32.1089i	−0.284776	−	1.43167i	0.528076	−	0.849197i	$-0.322913\pi$
$504$	−45.5628	+	18.0721i	−2.02953	+	0.804994i
$505$	3.27931	+	0.652294i	0.145927	+	0.0290267i
$506$	−10.1763	−	5.08221i	−0.452393	−	0.225932i
$507$	8.03567	−	5.36927i	0.356877	−	0.238457i
$508$	−15.8034	−	9.33734i	−0.701162	−	0.414278i
$509$	−9.65912			−0.428133			−0.214066	−	0.976819i	$-0.568671\pi$
$509$	−9.65912			−0.428133			−0.214066	+	0.976819i	$0.568671\pi$
$510$	4.57209	+	2.73286i	0.202455	+	0.121013i
$511$			11.3636i			0.502696i
$512$	22.3697	−	3.40541i	0.988610	−	0.150499i
$513$	−1.11941	−	1.67531i	−0.0494230	−	0.0739668i
$514$	16.9434	+	8.46178i	0.747340	+	0.373233i
$515$	0.762662	−	3.83416i	0.0336069	−	0.168953i
$516$	−0.745072	−	13.4380i	−0.0328000	−	0.591575i
$517$	48.2136	−	9.59028i	2.12043	−	0.421780i
$518$	1.82087	−	25.7923i	0.0800046	−	1.13325i
$519$	−24.3153	−	10.0717i	−1.06732	−	0.442100i
$520$	−3.51240	−	1.51739i	−0.154029	−	0.0665418i
$521$	−28.4757	−	19.0268i	−1.24754	−	0.833580i	−0.256423	−	0.966565i	$-0.582544\pi$
$521$	−28.4757	−	19.0268i	−1.24754	−	0.833580i	−0.991118	+	0.132984i	$0.957544\pi$
$522$	−18.7526	+	2.37292i	−0.820781	+	0.103860i
$523$	7.62209	+	7.62209i	0.333291	+	0.333291i	0.853835	−	0.520544i	$-0.174271\pi$
$523$	7.62209	+	7.62209i	0.333291	+	0.333291i	−0.520544	+	0.853835i	$0.674271\pi$
$524$	3.56210	−	10.1567i	0.155611	−	0.443698i
$525$	19.6296	+	47.3901i	0.856706	+	2.06827i
$526$	4.36050	+	13.0611i	0.190127	+	0.569492i
$527$	15.0597	+	26.7045i	0.656011	+	1.16326i
$528$	−11.5008	+	39.7078i	−0.500510	+	1.72806i
$529$	−7.05549	−	17.0335i	−0.306760	−	0.740585i
$530$	2.40736	−	3.10486i	0.104569	−	0.134867i
$531$	−8.23574	+	8.23574i	−0.357401	+	0.357401i
$532$	−3.29725	+	1.58498i	−0.142954	+	0.0687176i
$533$	19.2004	+	12.8293i	0.831660	+	0.555697i
$534$	−43.1209	+	24.6074i	−1.86602	+	1.06487i
$535$	−1.00190	+	2.41881i	−0.0433160	+	0.104574i
$536$	−30.9039	+	19.9814i	−1.33485	+	0.863064i
$537$	−2.71043	+	0.539138i	−0.116964	+	0.0232655i
$538$	8.37285	+	2.28870i	0.360979	+	0.0986731i
$539$	−28.1023	−	5.58989i	−1.21045	−	0.240774i
$540$	−0.393728	+	2.77465i	−0.0169434	+	0.119402i
$541$	−14.2821	−	21.3746i	−0.614034	−	0.918966i	0.385960	−	0.922515i	$-0.373870\pi$
$541$	−14.2821	−	21.3746i	−0.614034	−	0.918966i	−0.999994	+	0.00354934i	$0.998870\pi$
$542$	9.57363	−	8.31102i	0.411223	−	0.356989i
$543$	−16.6391			−0.714054
$544$	−21.8497	+	8.16023i	−0.936799	+	0.349867i
$545$	2.77667			0.118939
$546$	−45.5403	+	39.5342i	−1.94894	+	1.69191i
$547$	−10.6145	−	15.8858i	−0.453844	−	0.679226i	0.532028	−	0.846727i	$-0.321430\pi$
$547$	−10.6145	−	15.8858i	−0.453844	−	0.679226i	−0.985872	+	0.167501i	$0.946430\pi$
$548$	0.707415	−	4.98523i	0.0302193	−	0.212958i
$549$	56.0270	+	11.1445i	2.39117	+	0.475634i
$550$	25.1135	+	6.86473i	1.07084	+	0.292713i
$551$	−1.38369	+	0.275234i	−0.0589474	+	0.0117254i
$552$	13.9265	−	9.00435i	0.592749	−	0.383251i
$553$	−11.2235	+	27.0959i	−0.477271	+	1.15223i
$554$	−21.8225	+	12.4533i	−0.927148	+	0.529088i
$555$	−3.63320	−	2.42763i	−0.154221	−	0.103047i
$556$	−18.0823	+	8.69216i	−0.766862	+	0.368630i
$557$	6.00560	−	6.00560i	0.254466	−	0.254466i	−0.568333	−	0.822799i	$-0.692411\pi$
$557$	6.00560	−	6.00560i	0.254466	−	0.254466i	0.822799	+	0.568333i	$0.192411\pi$
$558$	−29.2138	+	37.6782i	−1.23672	+	1.59505i
$559$	−3.81346	−	9.20651i	−0.161292	−	0.389394i
$560$	4.88751	+	1.41560i	0.206535	+	0.0598201i
$561$	3.21698	−	42.4905i	0.135821	−	1.79395i
$562$	−0.202955	−	0.607917i	−0.00856114	−	0.0256434i
$563$	−13.7667	−	33.2357i	−0.580197	−	1.40072i	−0.892635	−	0.450781i	$-0.851146\pi$
$563$	−13.7667	−	33.2357i	−0.580197	−	1.40072i	0.312438	−	0.949938i	$-0.398854\pi$
$564$	−23.7192	+	67.6312i	−0.998759	+	2.84779i
$565$	0.593059	+	0.593059i	0.0249502	+	0.0249502i
$566$	15.7242	−	1.98971i	0.660937	−	0.0836336i
$567$	−6.50062	−	4.34357i	−0.273000	−	0.182413i
$568$	−3.47674	−	1.50198i	−0.145881	−	0.0630217i
$569$	−12.3563	−	5.11813i	−0.518001	−	0.214563i	0.108337	−	0.994114i	$-0.465447\pi$
$569$	−12.3563	−	5.11813i	−0.518001	−	0.214563i	−0.626339	+	0.779551i	$0.715447\pi$
$570$	−0.0435387	+	0.616718i	−0.00182364	+	0.0258315i
$571$	6.76206	−	1.34506i	0.282984	−	0.0562889i	−0.0515577	−	0.998670i	$-0.516419\pi$
$571$	6.76206	−	1.34506i	0.282984	−	0.0562889i	0.334541	+	0.942381i	$0.391419\pi$
$572$	1.69451	+	30.5619i	0.0708509	+	1.27786i
$573$	−2.87521	+	14.4546i	−0.120113	+	0.603851i
$574$	−27.4743	−	13.7211i	−1.14676	−	0.572708i
$575$	−5.80244	−	8.68396i	−0.241978	−	0.362146i
$576$	−24.8619	−	26.4100i	−1.03591	−	1.10042i
$577$		−	47.0898i		−	1.96038i	−0.198070	−	0.980188i	$-0.563467\pi$
$577$		−	47.0898i		−	1.96038i	0.198070	−	0.980188i	$-0.436533\pi$
$578$	20.3209	−	12.8476i	0.845239	−	0.534389i
$579$	−29.5137			−1.22655
$580$	1.68940	+	0.998172i	0.0701485	+	0.0414468i
$581$	−12.9827	+	8.67475i	−0.538612	+	0.359889i
$582$	−36.9552	−	18.4560i	−1.53184	−	0.765026i
$583$	−30.8261	−	6.13170i	−1.27669	−	0.253949i
$584$	−7.81650	+	3.10034i	−0.323449	+	0.128293i
$585$	1.19653	+	6.01538i	0.0494706	+	0.248706i
$586$	42.0357	+	2.96762i	1.73648	+	0.122591i
$587$	3.30499	−	7.97895i	0.136412	−	0.329327i	−0.840881	−	0.541219i	$-0.817963\pi$
$587$	3.30499	−	7.97895i	0.136412	−	0.329327i	0.977293	+	0.211893i	$0.0679628\pi$
$588$	27.8583	−	31.1289i	1.14886	−	1.28373i
$589$	−1.97698	+	2.95876i	−0.0814600	+	0.121914i
$590$	1.19953	−	0.151786i	0.0493838	−	0.00624892i
$591$	32.7280	−	32.7280i	1.34625	−	1.34625i
$592$	18.2381	−	5.78445i	0.749583	−	0.237739i
$593$	−2.34044	+	0.969441i	−0.0961103	+	0.0398102i	−0.430221	−	0.902724i	$-0.641564\pi$
$593$	−2.34044	+	0.969441i	−0.0961103	+	0.0398102i	0.334110	+	0.942534i	$0.391564\pi$
$594$	21.2654	−	7.09954i	0.872532	−	0.291298i
$595$	−5.23002	−	0.395968i	−0.214410	−	0.0162331i
$596$	8.83964	+	11.7632i	0.362086	+	0.481841i
$597$	14.8781	−	6.16269i	0.608918	−	0.252222i
$598$	7.52391	−	9.70388i	0.307675	−	0.396821i
$599$	0.372520	+	0.372520i	0.0152207	+	0.0152207i	0.714676	−	0.699455i	$-0.246574\pi$
$599$	0.372520	+	0.372520i	0.0152207	+	0.0152207i	−0.699455	+	0.714676i	$0.746574\pi$
$600$	−27.2419	+	26.4318i	−1.11215	+	1.07907i
$601$	−0.453280	+	0.678382i	−0.0184897	+	0.0276718i	−0.840599	−	0.541657i	$-0.817797\pi$
$601$	−0.453280	+	0.678382i	−0.0184897	+	0.0276718i	0.822110	+	0.569329i	$0.192797\pi$
$602$	6.56843	+	11.5102i	0.267709	+	0.469120i
$603$	54.5006	+	22.5749i	2.21943	+	0.919320i
$604$	28.6103	−	7.35841i	1.16414	−	0.299409i
$605$	0.206304	+	1.03716i	0.00838747	+	0.0421667i
$606$	37.6172	+	10.2826i	1.52809	+	0.417702i
$607$	0.958124	−	4.81682i	0.0388891	−	0.195509i	−0.956457	−	0.291873i	$-0.905721\pi$
$607$	0.958124	−	4.81682i	0.0388891	−	0.195509i	0.995346	+	0.0963646i	$0.0307215\pi$
$608$	−1.98983	−	1.83559i	−0.0806981	−	0.0744431i
$609$	25.7159	−	17.1828i	1.04206	−	0.696283i
$610$	−3.88754	−	4.47813i	−0.157402	−	0.181314i
$611$			53.0659i			2.14682i
$612$	30.6612	+	21.3944i	1.23940	+	0.864817i
$613$			12.2129i			0.493276i	0.969108	+	0.246638i	$0.0793258\pi$
$613$			12.2129i			0.493276i	−0.969108	+	0.246638i	$0.920674\pi$
$614$	6.29826	−	5.46761i	0.254177	−	0.220655i
$615$	−4.31519	+	2.88332i	−0.174005	+	0.116267i
$616$	−7.33803	−	40.0397i	−0.295658	−	1.61325i
$617$	1.33065	−	6.68962i	0.0535699	−	0.269314i	−0.944713	−	0.327900i	$-0.893659\pi$
$617$	1.33065	−	6.68962i	0.0535699	−	0.269314i	0.998282	+	0.0585859i	$0.0186592\pi$
$618$	12.0224	−	43.9820i	0.483612	−	1.76921i
$619$	−0.848271	−	4.26454i	−0.0340949	−	0.171406i	0.959986	−	0.280047i	$-0.0903502\pi$
$619$	−0.848271	−	4.26454i	−0.0340949	−	0.171406i	−0.994081	+	0.108641i	$0.965350\pi$
$620$	4.79338	−	1.23283i	0.192507	−	0.0495116i
$621$	−8.30909	−	3.44174i	−0.333432	−	0.138112i
$622$	7.96705	−	4.54649i	0.319450	−	0.182298i
$623$	27.1605	−	40.6486i	1.08816	−	1.62855i
$624$	−39.6186	−	20.5389i	−1.58601	−	0.822215i
$625$	16.5115	+	16.5115i	0.660461	+	0.660461i
$626$	−15.4662	−	11.9917i	−0.618155	−	0.479287i
$627$	4.56947	−	1.89274i	0.182487	−	0.0755886i
$628$	−3.35967	+	2.52467i	−0.134065	+	0.100745i
$629$	−17.1789	+	9.68787i	−0.684969	+	0.386281i
$630$	−2.58295	−	7.73679i	−0.102907	−	0.308241i
$631$	−5.62807	+	2.33122i	−0.224050	+	0.0928045i	−0.491885	−	0.870660i	$-0.663692\pi$
$631$	−5.62807	+	2.33122i	−0.224050	+	0.0928045i	0.267835	+	0.963465i	$0.413692\pi$
$632$	−21.7001	−	0.327526i	−0.863185	−	0.0130283i
$633$	−48.7431	+	48.7431i	−1.93736	+	1.93736i
$634$	3.81422	+	30.1429i	0.151482	+	1.19713i
$635$	1.69699	−	2.53973i	0.0673431	−	0.100786i
$636$	30.5585	−	34.1461i	1.21172	−	1.35398i
$637$	11.8366	−	28.5761i	0.468983	−	1.13223i
$638$	1.10547	−	15.6588i	0.0437661	−	0.619938i
$639$	1.18439	+	5.95431i	0.0468536	+	0.235549i
$640$	0.359736	+	3.74812i	0.0142198	+	0.148157i
$641$	6.70646	+	1.33400i	0.264889	+	0.0526898i	0.325748	−	0.945457i	$-0.394384\pi$
$641$	6.70646	+	1.33400i	0.264889	+	0.0526898i	−0.0608587	+	0.998146i	$0.519384\pi$
$642$	−13.6433	+	27.3186i	−0.538459	+	1.07818i
$643$	1.66361	−	1.11159i	0.0656064	−	0.0438368i	−0.522335	−	0.852741i	$-0.674939\pi$
$643$	1.66361	−	1.11159i	0.0656064	−	0.0438368i	0.587941	+	0.808904i	$0.299939\pi$
$644$	−8.30679	+	14.0592i	−0.327333	+	0.554009i
$645$	2.23960			0.0881842
$646$	2.39523	+	1.43169i	0.0942390	+	0.0563291i
$647$			30.8754i			1.21384i	0.794764	+	0.606919i	$0.207595\pi$
$647$			30.8754i			1.21384i	−0.794764	+	0.606919i	$0.792405\pi$
$648$	1.21418	−	5.65654i	0.0476974	−	0.222210i
$649$	−5.37382	−	8.04249i	−0.210941	−	0.315695i
$650$	−12.5569	+	25.1432i	−0.492522	+	0.986198i
$651$	15.2191	−	76.5115i	0.596483	−	2.99872i
$652$	0.980468	+	17.6836i	0.0383981	+	0.692542i
$653$	−16.8928	+	3.36019i	−0.661066	+	0.131494i	−0.514211	−	0.857664i	$-0.671915\pi$
$653$	−16.8928	+	3.36019i	−0.661066	+	0.131494i	−0.146855	+	0.989158i	$0.546915\pi$
$654$	32.3050	+	2.28065i	1.26323	+	0.0891807i
$655$	1.65473	+	0.685412i	0.0646557	+	0.0267813i
$656$	1.94227	−	22.6419i	0.0758329	−	0.884017i
$657$	11.2076	+	7.48869i	0.437251	+	0.292162i
$658$	−8.85941	−	70.0138i	−0.345376	−	2.72942i
$659$	25.4940	+	25.4940i	0.993106	+	0.993106i	0.999976	−	0.00687086i	$-0.00218708\pi$
$659$	25.4940	+	25.4940i	0.993106	+	0.993106i	−0.00687086	+	0.999976i	$0.502187\pi$
$660$	−6.49154	−	2.27667i	−0.252683	−	0.0886194i
$661$	4.66823	+	11.2701i	0.181573	+	0.438356i	0.988291	−	0.152580i	$-0.0487583\pi$
$661$	4.66823	+	11.2701i	0.181573	+	0.438356i	−0.806718	+	0.590937i	$0.798758\pi$
$662$	−23.6461	+	7.89432i	−0.919030	+	0.306821i
$663$	44.3093	+	12.3544i	1.72083	+	0.479806i
$664$	−9.50904	−	6.56345i	−0.369022	−	0.254711i
$665$	−0.232971	−	0.562441i	−0.00903422	−	0.0218105i
$666$	−24.2383	−	18.7932i	−0.939215	−	0.728221i
$667$	−4.45287	+	4.45287i	−0.172416	+	0.172416i
$668$	−33.4353	+	16.0723i	−1.29365	+	0.621856i
$669$	−51.8147	−	34.6215i	−2.00327	−	1.33854i
$670$	−3.03523	−	5.31879i	−0.117261	−	0.205483i
$671$	−18.1547	+	43.8293i	−0.700855	+	1.69201i
$672$	55.7008	+	20.4842i	2.14871	+	0.790195i
$673$	40.5716	−	8.07020i	1.56392	−	0.311083i	0.664203	−	0.747553i	$-0.268771\pi$
$673$	40.5716	−	8.07020i	1.56392	−	0.311083i	0.899719	+	0.436469i	$0.143771\pi$
$674$	−12.7888	+	46.7856i	−0.492605	+	1.80211i
$675$	20.1894	+	4.01591i	0.777088	+	0.154573i
$676$	−6.97215	−	0.989364i	−0.268160	−	0.0380525i
$677$	−23.5485	−	35.2429i	−0.905044	−	1.35449i	−0.934889	−	0.354940i	$-0.884501\pi$
$677$	−23.5485	−	35.2429i	−0.905044	−	1.35449i	0.0298450	−	0.999555i	$-0.490499\pi$
$678$	6.41280	+	7.38704i	0.246282	+	0.283697i
$679$	40.6748			1.56096
$680$	−1.15454	−	3.70553i	−0.0442747	−	0.142100i
$681$	68.3082			2.61757
$682$	−25.9564	−	29.8997i	−0.993922	−	1.14492i
$683$	12.7070	+	19.0173i	0.486218	+	0.727677i	0.990748	−	0.135718i	$-0.0433340\pi$
$683$	12.7070	+	19.0173i	0.486218	+	0.727677i	−0.504529	+	0.863395i	$0.668334\pi$
$684$	−0.609683	+	4.29650i	−0.0233118	+	0.164281i
$685$	0.821783	+	0.163463i	0.0313987	+	0.00624560i
$686$	−0.869042	+	3.17925i	−0.0331802	+	0.121384i
$687$	15.9753	−	3.17768i	0.609496	−	0.121236i
$688$	−6.12526	+	7.65845i	−0.233523	+	0.291976i
$689$	12.9839	−	31.3458i	0.494646	−	1.19418i
$690$	1.36779	+	2.39684i	0.0520708	+	0.0912462i
$691$	−20.8945	−	13.9613i	−0.794865	−	0.531112i	0.0905617	−	0.995891i	$-0.471134\pi$
$691$	−20.8945	−	13.9613i	−0.794865	−	0.531112i	−0.885427	+	0.464779i	$0.846134\pi$
$692$	8.30836	+	17.2839i	0.315837	+	0.657037i
$693$	−46.1399	+	46.1399i	−1.75271	+	1.75271i
$694$	−3.43974	−	2.66700i	−0.130571	−	0.101238i
$695$	−1.27763	−	3.08447i	−0.0484633	−	0.117001i
$696$	18.8354	+	13.0008i	0.713953	+	0.492794i
$697$	2.82240	+	23.2538i	0.106906	+	0.880800i
$698$	18.9386	−	6.32272i	0.716837	−	0.239319i
$699$	−0.182148	−	0.439745i	−0.00688948	−	0.0166327i
$700$	12.3696	−	35.2697i	0.467526	−	1.33307i
$701$	17.7469	+	17.7469i	0.670292	+	0.670292i	0.957783	−	0.287491i	$-0.0928213\pi$
$701$	17.7469	+	17.7469i	0.670292	+	0.670292i	−0.287491	+	0.957783i	$0.592821\pi$
$702$	3.03817	+	24.0099i	0.114668	+	0.906197i
$703$	−1.90336	−	1.27179i	−0.0717868	−	0.0479664i
$704$	25.5394	−	15.9716i	0.962554	−	0.601951i
$705$	−11.0185	−	4.56400i	−0.414980	−	0.171890i
$706$	35.1509	+	2.48156i	1.32292	+	0.0933949i
$707$	−37.6620	+	7.49144i	−1.41643	+	0.281745i
$708$	14.0805	−	0.780697i	0.529179	−	0.0293404i
$709$	9.13862	−	45.9429i	0.343208	−	1.72542i	−0.294946	−	0.955514i	$-0.595302\pi$
$709$	9.13862	−	45.9429i	0.343208	−	1.72542i	0.638154	−	0.769909i	$-0.279698\pi$
$710$	0.281584	−	0.563828i	0.0105677	−	0.0211601i
$711$	19.3276	+	28.9258i	0.724841	+	1.08480i
$712$	35.3705	+	7.59228i	1.32557	+	0.284533i
$713$			15.8837i			0.594850i
$714$	−60.5232	−	8.90262i	−2.26503	−	0.333172i
$715$	−5.09349			−0.190486
$716$	1.73365	+	1.02432i	0.0647897	+	0.0382806i
$717$	25.1867	−	16.8292i	0.940616	−	0.628499i
$718$	0.196318	−	0.393095i	0.00732651	−	0.0146702i
$719$	25.2894	+	5.03037i	0.943134	+	0.187601i	0.642628	−	0.766179i	$-0.277844\pi$
$719$	25.2894	+	5.03037i	0.943134	+	0.187601i	0.300507	+	0.953780i	$0.402844\pi$
$720$	4.61707	−	3.88753i	0.172068	−	0.144880i
$721$	8.75899	+	44.0344i	0.326202	+	1.63993i
$722$	1.86944	−	26.4803i	0.0695733	−	0.985493i
$723$	−13.4945	+	32.5786i	−0.501865	+	1.21161i
$724$	9.03452	+	8.08531i	0.335765	+	0.300488i
$725$	8.00764	−	11.9843i	0.297396	−	0.445085i
$726$	1.54835	+	12.2363i	0.0574648	+	0.454131i
$727$	−22.6936	+	22.6936i	−0.841659	+	0.841659i	−0.989075	−	0.147415i	$-0.952905\pi$
$727$	−22.6936	+	22.6936i	−0.841659	+	0.841659i	0.147415	+	0.989075i	$0.452905\pi$
$728$	43.9374	+	0.663160i	1.62843	+	0.0245783i
$729$	−40.5977	+	16.8161i	−1.50362	+	0.622819i
$730$	−0.443117	−	1.32728i	−0.0164005	−	0.0491248i
$731$	4.56235	−	9.02033i	0.168745	−	0.333629i
$732$	−41.5512	−	55.2937i	−1.53578	−	2.04372i
$733$	−1.17238	+	0.485614i	−0.0433027	+	0.0179366i	−0.404230	−	0.914658i	$-0.632460\pi$
$733$	−1.17238	+	0.485614i	−0.0433027	+	0.0179366i	0.360927	+	0.932594i	$0.382460\pi$
$734$	−2.32447	−	1.80228i	−0.0857978	−	0.0665234i
$735$	4.91545	+	4.91545i	0.181309	+	0.181309i
$736$	−11.9370	−	1.87808i	−0.440004	−	0.0692270i
$737$	−27.2177	+	40.7341i	−1.00258	+	1.50046i
$738$	−31.6386	+	18.0549i	−1.16463	+	0.664611i
$739$	1.56708	+	0.649105i	0.0576459	+	0.0238777i	0.411320	−	0.911491i	$-0.365068\pi$
$739$	1.56708	+	0.649105i	0.0576459	+	0.0238777i	−0.353674	+	0.935369i	$0.615068\pi$
$740$	0.793076	+	3.08357i	0.0291541	+	0.113354i
$741$	1.04161	+	5.23653i	0.0382645	+	0.192369i
$742$	−11.8974	+	43.5246i	−0.436767	+	1.59784i
$743$	−5.34546	+	26.8734i	−0.196106	+	0.985891i	0.749853	+	0.661604i	$0.230124\pi$
$743$	−5.34546	+	26.8734i	−0.196106	+	0.985891i	−0.945959	+	0.324286i	$0.894876\pi$
$744$	56.7810	−	10.4062i	2.08169	−	0.381509i
$745$	−2.03591	+	1.36035i	−0.0745898	+	0.0498393i
$746$	−34.3969	+	29.8605i	−1.25936	+	1.09327i
$747$			18.5212i			0.677655i
$748$	−22.3937	+	21.5078i	−0.818796	+	0.786402i
$749$		−	30.0682i		−	1.09867i
$750$	−8.37522	−	9.64758i	−0.305820	−	0.352280i
$751$	−44.8088	+	29.9403i	−1.63510	+	1.09254i	−0.716309	+	0.697783i	$0.754170\pi$
$751$	−44.8088	+	29.9403i	−1.63510	+	1.09254i	−0.918787	+	0.394754i	$0.870830\pi$
$752$	45.7422	−	25.1959i	1.66805	−	0.918801i
$753$	10.8955	−	54.7751i	0.397052	−	1.99612i
$754$	16.3460	+	4.46814i	0.595285	+	0.162720i
$755$	0.959040	+	4.82142i	0.0349030	+	0.175469i
$756$	−8.01697	−	31.1709i	−0.291574	−	1.13368i
$757$	−21.0351	−	8.71301i	−0.764533	−	0.316680i	−0.0338771	−	0.999426i	$-0.510785\pi$
$757$	−21.0351	−	8.71301i	−0.764533	−	0.316680i	−0.730656	+	0.682746i	$0.760785\pi$
$758$	12.7992	+	22.4287i	0.464889	+	0.814649i
$759$	12.2653	−	18.3563i	0.445202	−	0.666292i
$760$	0.323316	−	0.313701i	0.0117279	−	0.0113791i
$761$	−24.5023	−	24.5023i	−0.888207	−	0.888207i	0.106144	−	0.994351i	$-0.466150\pi$
$761$	−24.5023	−	24.5023i	−0.888207	−	0.888207i	−0.994351	+	0.106144i	$0.966150\pi$
$762$	21.8296	−	28.1545i	0.790804	−	1.01993i
$763$	−29.4619	+	12.2035i	−1.06659	+	0.441798i
$764$	8.58495	−	6.45128i	0.310593	−	0.233399i
$765$	−3.83715	+	4.89729i	−0.138733	+	0.177062i
$766$	5.88543	−	1.96487i	0.212649	−	0.0709936i
$767$	9.64671	−	3.99580i	0.348323	−	0.144280i
$768$	1.10677	+	43.9028i	0.0399371	+	1.58420i
$769$	15.4640	−	15.4640i	0.557647	−	0.557647i	−0.370990	−	0.928637i	$-0.620982\pi$
$769$	15.4640	−	15.4640i	0.557647	−	0.557647i	0.928637	+	0.370990i	$0.120982\pi$
$770$	6.72023	−	0.850364i	0.242180	−	0.0306450i
$771$	−20.4215	+	30.5629i	−0.735462	+	1.10070i
$772$	16.0250	+	14.3413i	0.576752	+	0.516156i
$773$	11.0918	−	26.7780i	0.398944	−	0.963137i	−0.588973	−	0.808153i	$-0.700468\pi$
$773$	11.0918	−	26.7780i	0.398944	−	0.963137i	0.987917	−	0.154984i	$-0.0495325\pi$
$774$	15.6808	+	1.10703i	0.563636	+	0.0397913i
$775$	−7.09248	−	35.6563i	−0.254770	−	1.28081i
$776$	11.0973	+	27.9784i	0.398372	+	1.00436i
$777$	49.2197	+	9.79040i	1.76575	+	0.351229i
$778$	31.1650	+	15.5643i	1.11732	+	0.558006i
$779$	−2.26065	+	1.51052i	−0.0809961	+	0.0541199i
$780$	3.77754	−	6.39346i	0.135258	−	0.228922i
$781$	−5.04178			−0.180409
$782$	12.4400	−	0.626292i	0.444854	−	0.0223962i
$783$		−	12.4117i		−	0.443559i
$784$	−30.2523	+	3.36503i	−1.08044	+	0.120180i
$785$	−0.388525	−	0.581469i	−0.0138671	−	0.0207535i
$786$	18.6889	+	9.33354i	0.666612	+	0.332916i
$787$	2.45957	−	12.3651i	0.0876741	−	0.440767i	−0.911867	−	0.410485i	$-0.865359\pi$
$787$	2.45957	−	12.3651i	0.0876741	−	0.440767i	0.999541	−	0.0302823i	$-0.00964063\pi$
$788$	−33.6735	+	1.86703i	−1.19957	+	0.0665102i
$789$	−26.2117	+	5.21384i	−0.933163	+	0.185618i
$790$	0.254326	−	3.60248i	0.00904851	−	0.128170i
$791$	−8.89918	−	3.68616i	−0.316418	−	0.131065i
$792$	−44.3259	−	19.1491i	−1.57505	−	0.680435i
$793$	−42.5810	−	28.4517i	−1.51209	−	1.01035i
$794$	3.94365	−	0.499022i	0.139955	−	0.0177096i
$795$	5.39188	+	5.39188i	0.191230	+	0.191230i
$796$	−11.0729	−	3.88342i	−0.392468	−	0.137644i
$797$	−6.02581	−	14.5476i	−0.213445	−	0.515302i	0.780503	−	0.625152i	$-0.214963\pi$
$797$	−6.02581	−	14.5476i	−0.213445	−	0.515302i	−0.993948	+	0.109850i	$0.964963\pi$
$798$	−2.24852	−	6.73506i	−0.0795968	−	0.238418i
$799$	−40.8283	+	35.0811i	−1.44440	+	1.24108i
$800$	27.6352	−	1.11420i	0.977053	−	0.0393930i
$801$	−22.1916	−	53.5754i	−0.784103	−	1.89299i
$802$	−18.1830	+	23.4513i	−0.642063	+	0.828094i
$803$	−7.91550	+	7.91550i	−0.279332	+	0.279332i
$804$	−30.9446	−	64.3742i	−1.09133	−	2.27030i
$805$	−2.25942	−	1.50970i	−0.0796341	−	0.0532098i
$806$	37.1227	−	21.1845i	1.30759	−	0.746193i
$807$	−6.44696	+	15.5643i	−0.226944	+	0.547891i
$808$	−15.4284	−	23.8621i	−0.542769	−	0.839466i
$809$	−25.6921	+	5.11048i	−0.903287	+	0.179675i	−0.624818	−	0.780770i	$-0.714827\pi$
$809$	−25.6921	+	5.11048i	−0.903287	+	0.179675i	−0.278469	+	0.960445i	$0.589827\pi$
$810$	0.928654	+	0.253846i	0.0326296	+	0.00891924i
$811$	36.3628	+	7.23302i	1.27687	+	0.253986i	0.786534	−	0.617547i	$-0.211873\pi$
$811$	36.3628	+	7.23302i	1.27687	+	0.253986i	0.490338	+	0.871533i	$0.336873\pi$
$812$	−22.3124	−	3.16618i	−0.783012	−	0.111111i
$813$	13.6703	+	20.4591i	0.479440	+	0.717532i
$814$	19.2344	−	16.6977i	0.674166	−	0.585254i
$815$	−2.94717			−0.103235
$816$	−10.3889	−	44.0601i	−0.363684	−	1.54241i
$817$	1.17328			0.0410480
$818$	6.64528	−	5.76887i	0.232347	−	0.201704i
$819$	−39.1336	−	58.5676i	−1.36744	−	2.04652i
$820$	3.74408	+	0.531293i	0.130749	+	0.0185536i
$821$	6.04443	+	1.20231i	0.210952	+	0.0419610i	0.299435	−	0.954117i	$-0.403202\pi$
$821$	6.04443	+	1.20231i	0.210952	+	0.0419610i	−0.0884829	+	0.996078i	$0.528202\pi$
$822$	9.42674	+	2.57679i	0.328795	+	0.0898757i
$823$	12.7961	−	2.54530i	0.446043	−	0.0887235i	0.0330420	−	0.999454i	$-0.489480\pi$
$823$	12.7961	−	2.54530i	0.446043	−	0.0887235i	0.413001	+	0.910730i	$0.364480\pi$
$824$	−27.8995	+	18.0389i	−0.971927	+	0.628414i
$825$	−19.3370	+	46.6837i	−0.673228	+	1.62532i
$826$	−12.0605	+	6.88249i	−0.419640	+	0.239472i
$827$	−7.61038	−	5.08509i	−0.264639	−	0.176826i	0.416171	−	0.909286i	$-0.363372\pi$
$827$	−7.61038	−	5.08509i	−0.264639	−	0.176826i	−0.680809	+	0.732461i	$0.738372\pi$
$828$	8.39197	+	17.4579i	0.291641	+	0.606703i
$829$	−28.6034	+	28.6034i	−0.993438	+	0.993438i	−0.999979	−	0.00654071i	$-0.997918\pi$
$829$	−28.6034	+	28.6034i	−0.993438	+	0.993438i	0.00654071	+	0.999979i	$0.497918\pi$
$830$	1.17812	−	1.51947i	0.0408932	−	0.0527416i
$831$	−18.6618	−	45.0536i	−0.647371	−	1.56289i
$832$	11.5313	+	30.4035i	0.399777	+	1.05405i
$833$	29.8111	−	9.78431i	1.03289	−	0.339006i
$834$	−12.3311	−	36.9356i	−0.426990	−	1.27897i
$835$	−2.36241	−	5.70337i	−0.0817546	−	0.197373i
$836$	−3.40079	−	1.19271i	−0.117619	−	0.0412506i
$837$	−22.1368	−	22.1368i	−0.765158	−	0.765158i
$838$	2.58322	−	0.326875i	0.0892357	−	0.0112917i
$839$	35.2493	+	23.5529i	1.21694	+	0.813135i	0.987102	−	0.160093i	$-0.0511796\pi$
$839$	35.2493	+	23.5529i	1.21694	+	0.813135i	0.229840	+	0.973228i	$0.426180\pi$
$840$	−3.91660	+	9.06604i	−0.135135	+	0.312808i
$841$	18.7634	+	7.77207i	0.647015	+	0.268003i
$842$	−1.40311	+	19.8748i	−0.0483543	+	0.684930i
$843$	1.22000	−	0.242673i	0.0420190	−	0.00835810i
$844$	50.1512	−	2.78064i	1.72628	−	0.0957137i
$845$	0.228613	−	1.14931i	0.00786452	−	0.0395376i
$846$	−74.8912	−	37.4018i	−2.57481	−	1.28590i
$847$	−6.74736	−	10.0981i	−0.231842	−	0.346976i
$848$	−33.1846	+	3.69119i	−1.13956	+	0.126756i
$849$			30.7619i			1.05574i
$850$	−27.6461	+	6.96070i	−0.948253	+	0.238750i
$851$	−10.2180			−0.350267
$852$	3.73919	−	6.32855i	0.128102	−	0.216812i
$853$	31.6526	−	21.1496i	1.08376	−	0.724148i	0.120503	−	0.992713i	$-0.461549\pi$
$853$	31.6526	−	21.1496i	1.08376	−	0.724148i	0.963262	+	0.268564i	$0.0865492\pi$
$854$	60.9304	+	30.4295i	2.08499	+	1.04128i
$855$	−0.708251	−	0.140880i	−0.0242217	−	0.00481799i
$856$	20.6826	−	8.20354i	0.706915	−	0.280391i
$857$	−2.09184	−	10.5164i	−0.0714559	−	0.359233i	0.928470	−	0.371407i	$-0.121125\pi$
$857$	−2.09184	−	10.5164i	−0.0714559	−	0.359233i	−0.999926	+	0.0121743i	$0.996125\pi$
$858$	−59.2601	−	4.18361i	−2.02310	−	0.142826i
$859$	−4.97874	+	12.0197i	−0.169872	+	0.410108i	−0.985773	−	0.168085i	$-0.946242\pi$
$859$	−4.97874	+	12.0197i	−0.169872	+	0.410108i	0.815900	+	0.578193i	$0.196242\pi$
$860$	−1.21603	−	1.08827i	−0.0414663	−	0.0371097i
$861$	33.1142	−	49.5590i	1.12853	−	1.68896i
$862$	−12.8800	+	1.62981i	−0.438696	+	0.0555117i
$863$	16.9343	−	16.9343i	0.576451	−	0.576451i	−0.357472	−	0.933924i	$-0.616361\pi$
$863$	16.9343	−	16.9343i	0.576451	−	0.576451i	0.933924	+	0.357472i	$0.116361\pi$
$864$	19.2538	−	14.0189i	0.655027	−	0.476933i
$865$	−2.94828	+	1.22122i	−0.100245	+	0.0415227i
$866$	35.2357	−	11.7636i	1.19736	−	0.399742i
$867$	19.7870	+	42.2584i	0.672000	+	1.43517i
$868$	−45.4420	+	34.1480i	−1.54240	+	1.15906i
$869$	−26.6920	+	11.0562i	−0.905463	+	0.375055i
$870$	−2.33361	+	3.00975i	−0.0791168	+	0.102040i
$871$	−37.3953	−	37.3953i	−1.26709	−	1.26709i
$872$	−16.4324	−	16.9360i	−0.556471	−	0.573526i
$873$	26.8050	−	40.1165i	0.907211	−	1.35774i
$874$	0.716558	+	1.25566i	0.0242379	+	0.0424733i
$875$	11.6225	+	4.81418i	0.392911	+	0.162749i
$876$	−4.06524	−	15.8061i	−0.137352	−	0.534040i
$877$	−0.723374	−	3.63665i	−0.0244266	−	0.122801i	0.966648	−	0.256108i	$-0.0824403\pi$
$877$	−0.723374	−	3.63665i	−0.0244266	−	0.122801i	−0.991075	+	0.133307i	$0.957440\pi$
$878$	45.0379	+	12.3110i	1.51996	+	0.415478i
$879$	−15.9562	+	80.2171i	−0.538188	+	2.70565i
$880$	2.41841	+	4.39054i	0.0815247	+	0.148005i
$881$	−32.7641	+	21.8922i	−1.10385	+	0.737568i	−0.967444	−	0.253085i	$-0.918555\pi$
$881$	−32.7641	+	21.8922i	−1.10385	+	0.737568i	−0.136405	+	0.990653i	$0.543555\pi$
$882$	31.9864	+	36.8458i	1.07704	+	1.24066i
$883$		−	28.6802i		−	0.965167i	−0.875850	−	0.482584i	$-0.839698\pi$
$883$		−	28.6802i		−	0.965167i	0.875850	−	0.482584i	$-0.160302\pi$
$884$	−18.0553	−	28.2389i	−0.607265	−	0.949777i
$885$			2.34669i			0.0788830i
$886$	2.29517	−	1.99247i	0.0771077	−	0.0669384i
$887$	4.34142	−	2.90084i	0.145771	−	0.0974008i	−0.480546	−	0.876969i	$-0.659562\pi$
$887$	4.34142	−	2.90084i	0.145771	−	0.0974008i	0.626317	+	0.779569i	$0.284562\pi$
$888$	6.69428	+	36.5271i	0.224645	+	1.22577i
$889$	−6.84382	+	34.4062i	−0.229534	+	1.15395i
$890$	−1.58731	+	5.80690i	−0.0532066	+	0.194648i
$891$	−1.50252	−	7.55370i	−0.0503365	−	0.253058i
$892$	11.3104	+	43.9762i	0.378701	+	1.47243i
$893$	−5.77237	−	2.39099i	−0.193165	−	0.0800116i
$894$	−24.8040	+	14.1547i	−0.829570	+	0.473404i
$895$	−0.186163	+	0.278612i	−0.00622273	+	0.00931297i
$896$	−20.2901	−	38.1885i	−0.677843	−	1.27579i
$897$	16.8517	+	16.8517i	0.562662	+	0.562662i
$898$	24.4116	+	18.9276i	0.814626	+	0.631621i
$899$	−20.2517	+	8.38853i	−0.675432	+	0.279773i
$900$	−26.6340	−	35.4428i	−0.887799	−	1.18143i
$901$	32.7006	−	10.7327i	1.08941	−	0.357557i
$902$	−9.58005	−	28.6954i	−0.318981	−	0.955451i
$903$	−23.7634	+	9.84311i	−0.790795	+	0.327558i
$904$	0.107570	−	7.12704i	0.00357774	−	0.237042i
$905$	−1.42661	+	1.42661i	−0.0474221	+	0.0474221i
$906$	7.19778	+	56.8823i	0.239130	+	1.88979i
$907$	−19.1105	+	28.6009i	−0.634555	+	0.949678i	0.365269	+	0.930902i	$0.380977\pi$
$907$	−19.1105	+	28.6009i	−0.634555	+	0.949678i	−0.999824	+	0.0187763i	$0.994023\pi$
$908$	−37.0891	−	33.1924i	−1.23085	−	1.10153i
$909$	−17.4309	+	42.0820i	−0.578147	+	1.39577i
$910$	−0.514948	+	7.29414i	−0.0170703	+	0.241798i
$911$	3.21339	+	16.1548i	0.106464	+	0.535233i	0.996801	+	0.0799289i	$0.0254693\pi$
$911$	3.21339	+	16.1548i	0.106464	+	0.535233i	−0.890336	+	0.455304i	$0.849531\pi$
$912$	4.01927	−	3.38419i	0.133091	−	0.112062i
$913$	−15.0858	−	3.00076i	−0.499268	−	0.0993106i
$914$	10.7358	−	21.4968i	0.355110	−	0.711052i
$915$	9.56988	−	6.39439i	0.316371	−	0.211392i
$916$	−10.2182	−	6.03735i	−0.337618	−	0.199480i
$917$	−20.5700			−0.679281
$918$	−16.4645	+	18.2102i	−0.543409	+	0.601025i
$919$			14.6931i			0.484679i	0.970192	+	0.242340i	$0.0779148\pi$
$919$			14.6931i			0.484679i	−0.970192	+	0.242340i	$0.922085\pi$
$920$	0.422012	−	1.96605i	0.0139133	−	0.0648186i
$921$	8.99337	+	13.4595i	0.296342	+	0.443507i
$922$	10.0689	−	20.1613i	0.331601	−	0.663978i
$923$	1.06179	−	5.33799i	0.0349493	−	0.175702i
$924$	78.8847	−	4.37378i	2.59512	−	0.143887i
$925$	22.9376	−	4.56258i	0.754185	−	0.150017i
$926$	−26.6048	−	1.87823i	−0.874286	−	0.0617224i
$927$	49.2022	+	20.3802i	1.61601	+	0.669374i
$928$	−3.90965	−	16.2115i	−0.128340	−	0.532169i
$929$	2.68842	+	1.79635i	0.0882043	+	0.0589362i	0.598890	−	0.800831i	$-0.295609\pi$
$929$	2.68842	+	1.79635i	0.0882043	+	0.0589362i	−0.510686	+	0.859767i	$0.670609\pi$
$930$	1.20592	+	9.53007i	0.0395435	+	0.312503i
$931$	2.57511	+	2.57511i	0.0843958	+	0.0843958i
$932$	−0.114781	+	0.327277i	−0.00375976	+	0.0107203i
$933$	6.81314	+	16.4484i	0.223052	+	0.538496i
$934$	−25.4652	+	8.50165i	−0.833248	+	0.278183i
$935$	−3.36724	−	3.91887i	−0.110120	−	0.128161i
$936$	29.6091	−	42.8973i	0.967805	−	1.40214i
$937$	8.87297	+	21.4212i	0.289867	+	0.699801i	0.999991	−	0.00427555i	$-0.00136095\pi$
$937$	8.87297	+	21.4212i	0.289867	+	0.699801i	−0.710124	+	0.704077i	$0.751361\pi$
$938$	55.5816	+	43.0952i	1.81480	+	1.40711i
$939$	26.8586	−	26.8586i	0.876496	−	0.876496i
$940$	3.76494	+	7.83222i	0.122799	+	0.255459i
$941$	29.8240	+	19.9278i	0.972236	+	0.649627i	0.936844	−	0.349746i	$-0.113732\pi$
$941$	29.8240	+	19.9278i	0.972236	+	0.649627i	0.0353914	+	0.999374i	$0.488732\pi$
$942$	−4.04269	−	7.08420i	−0.131718	−	0.230816i
$943$	−4.64425	+	11.2122i	−0.151237	+	0.365119i
$944$	−8.02464	−	6.41813i	−0.261180	−	0.208892i
$945$	5.25293	−	1.04487i	0.170878	−	0.0339897i
$946$	−3.44226	+	12.5929i	−0.111918	+	0.409432i
$947$	−35.8411	−	7.12925i	−1.16468	−	0.231669i	−0.425361	−	0.905024i	$-0.639853\pi$
$947$	−35.8411	−	7.12925i	−1.16468	−	0.231669i	−0.739320	+	0.673354i	$0.764853\pi$
$948$	5.91789	−	41.7040i	0.192204	−	1.35448i
$949$	−6.71354	−	10.0475i	−0.217931	−	0.326157i
$950$	−2.16924	−	2.49879i	−0.0703793	−	0.0810714i
$951$	−58.9698			−1.91223
$952$	28.5362	+	34.2434i	0.924864	+	1.10983i
$953$	1.94768			0.0630915			0.0315458	−	0.999502i	$-0.489957\pi$
$953$	1.94768			0.0630915			0.0315458	+	0.999502i	$0.489957\pi$
$954$	35.0867	+	40.4171i	1.13597	+	1.30855i
$955$	0.992799	+	1.48583i	0.0321262	+	0.0480803i
$956$	−21.8533	−	3.10103i	−0.706785	−	0.100294i
$957$	29.8818	+	5.94386i	0.965942	+	0.192138i
$958$	−1.97935	+	7.24113i	−0.0639500	+	0.233950i
$959$	−9.43799	+	1.87733i	−0.304768	+	0.0606222i
$960$	−7.30468	−	0.220553i	−0.235758	−	0.00711833i
$961$	−9.29521	+	22.4406i	−0.299846	+	0.723891i
$962$	13.6280	+	23.8810i	0.439383	+	0.769953i
$963$	−29.6555	−	19.8152i	−0.955635	−	0.638535i
$964$	23.1577	−	11.1319i	0.745859	−	0.358533i
$965$	−2.53045	+	2.53045i	−0.0814581	+	0.0814581i
$966$	−25.0471	−	19.4203i	−0.805878	−	0.624838i
$967$	6.67770	+	16.1214i	0.214740	+	0.518429i	0.994140	−	0.108098i	$-0.0344760\pi$
$967$	6.67770	+	16.1214i	0.214740	+	0.518429i	−0.779400	+	0.626527i	$0.784476\pi$
$968$	5.10516	−	7.39628i	0.164086	−	0.237726i
$969$	−3.34033	+	4.26320i	−0.107307	+	0.136954i
$970$	−4.75086	+	1.58609i	−0.152541	+	0.0509263i
$971$	6.62819	+	16.0019i	0.212709	+	0.513524i	0.993838	−	0.110846i	$-0.0353559\pi$
$971$	6.62819	+	16.0019i	0.212709	+	0.513524i	−0.781129	+	0.624370i	$0.785356\pi$
$972$	34.4338	+	12.0764i	1.10447	+	0.387351i
$973$	27.1127	+	27.1127i	0.869193	+	0.869193i
$974$	−2.06461	−	16.3161i	−0.0661543	−	0.522802i
$975$	−45.3540	−	30.3046i	−1.45249	−	0.970523i
$976$	−4.30741	+	50.2133i	−0.137877	+	1.60729i
$977$	55.9943	+	23.1936i	1.79142	+	0.742029i	0.989489	+	0.144606i	$0.0461915\pi$
$977$	55.9943	+	23.1936i	1.79142	+	0.742029i	0.801927	+	0.597423i	$0.203808\pi$
$978$	−34.2888	−	2.42070i	−1.09643	−	0.0774054i
$979$	47.2335	−	9.39533i	1.50959	−	0.300276i
$980$	−0.280411	−	5.05745i	−0.00895741	−	0.161554i
$981$	−7.37960	+	37.0997i	−0.235612	+	1.18450i
$982$	23.6222	−	47.2998i	0.753816	−	1.50940i
$983$	−15.2862	−	22.8774i	−0.487554	−	0.729675i	0.503375	−	0.864068i	$-0.332092\pi$
$983$	−15.2862	−	22.8774i	−0.487554	−	0.729675i	−0.990928	+	0.134393i	$0.957092\pi$
$984$	43.1239	+	9.25656i	1.37474	+	0.295088i
$985$		−	5.61208i		−	0.178816i
$986$	7.36835	+	15.5302i	0.234656	+	0.494583i
$987$	136.971			4.35983
$988$	1.97898	−	3.34941i	0.0629597	−	0.106559i
$989$	4.35450	−	2.90959i	0.138465	−	0.0925194i
$990$	3.58999	−	7.18838i	0.114097	−	0.228462i
$991$	25.1440	+	5.00144i	0.798724	+	0.158876i	0.577547	−	0.816358i	$-0.304010\pi$
$991$	25.1440	+	5.00144i	0.798724	+	0.158876i	0.221177	+	0.975234i	$0.429010\pi$
$992$	−35.8868	−	21.9408i	−1.13941	−	0.696623i
$993$	−9.43922	−	47.4542i	−0.299545	−	1.50591i
$994$	−0.509720	+	7.22008i	−0.0161673	+	0.229007i
$995$	0.747239	−	1.80400i	0.0236891	−	0.0571905i
$996$	14.9549	−	16.7106i	0.473863	−	0.529494i
$997$	3.80530	−	5.69504i	0.120515	−	0.180364i	−0.766307	−	0.642475i	$-0.777908\pi$
$997$	3.80530	−	5.69504i	0.120515	−	0.180364i	0.886822	+	0.462111i	$0.152908\pi$
$998$	−3.68171	−	29.0957i	−0.116542	−	0.921007i
$999$	14.2405	−	14.2405i	0.450551	−	0.450551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.s.c.107.12	yes	112
4.3	odd	2		544.2.cc.c.175.2		112
8.3	odd	2	inner	136.2.s.c.107.2	yes	112
8.5	even	2		544.2.cc.c.175.1		112
17.7	odd	16	inner	136.2.s.c.75.2	✓	112
68.7	even	16		544.2.cc.c.143.1		112
136.75	even	16	inner	136.2.s.c.75.12	yes	112
136.109	odd	16		544.2.cc.c.143.2		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.s.c.75.2	✓	112	17.7	odd	16	inner
136.2.s.c.75.12	yes	112	136.75	even	16	inner
136.2.s.c.107.2	yes	112	8.3	odd	2	inner
136.2.s.c.107.12	yes	112	1.1	even	1	trivial
544.2.cc.c.143.1		112	68.7	even	16
544.2.cc.c.143.2		112	136.109	odd	16
544.2.cc.c.175.1		112	8.5	even	2
544.2.cc.c.175.2		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)

\(f(q)\)	\(=\)	\(q+(1.06794 - 0.927095i) q^{2} +(1.52493 + 2.28221i) q^{3} +(0.280990 - 1.98016i) q^{4} +(0.326417 + 0.0649284i) q^{5} +(3.74436 + 1.02351i) q^{6} +(-3.74882 + 0.745687i) q^{7} +(-1.53572 - 2.37520i) q^{8} +(-1.73505 + 4.18878i) q^{9} +O(q^{10})\)	\(q+(1.06794 - 0.927095i) q^{2} +(1.52493 + 2.28221i) q^{3} +(0.280990 - 1.98016i) q^{4} +(0.326417 + 0.0649284i) q^{5} +(3.74436 + 1.02351i) q^{6} +(-3.74882 + 0.745687i) q^{7} +(-1.53572 - 2.37520i) q^{8} +(-1.73505 + 4.18878i) q^{9} +(0.408789 - 0.233280i) q^{10} +(-3.13072 - 2.09188i) q^{11} +(4.94764 - 2.37832i) q^{12} +(2.87411 - 2.87411i) q^{13} +(-3.31219 + 4.27186i) q^{14} +(0.349582 + 0.843965i) q^{15} +(-3.84209 - 1.11281i) q^{16} +(4.11134 + 0.311272i) q^{17} +(2.03047 + 6.08192i) q^{18} +(0.183139 + 0.442137i) q^{19} +(0.220289 - 0.628115i) q^{20} +(-7.41850 - 7.41850i) q^{21} +(-5.28280 + 0.668475i) q^{22} +(1.77614 + 1.18678i) q^{23} +(3.07885 - 7.12684i) q^{24} +(-4.51707 - 1.87103i) q^{25} +(0.404802 - 5.73395i) q^{26} +(-4.12935 + 0.821378i) q^{27} +(0.423202 + 7.63281i) q^{28} +(-0.575123 + 2.89134i) q^{29} +(1.15577 + 0.577208i) q^{30} +(4.13105 + 6.18255i) q^{31} +(-5.13480 + 2.37357i) q^{32} -10.3350i q^{33} +(4.67924 - 3.47918i) q^{34} -1.27210 q^{35} +(7.80693 + 4.61268i) q^{36} +(-3.97723 + 2.65750i) q^{37} +(0.605485 + 0.302388i) q^{38} +(10.9421 + 2.17653i) q^{39} +(-0.347067 - 0.875017i) q^{40} +(1.10836 + 5.57210i) q^{41} +(-14.8002 - 1.04485i) q^{42} +(0.938212 - 2.26505i) q^{43} +(-5.02197 + 5.61155i) q^{44} +(-0.838321 + 1.25464i) q^{45} +(2.99707 - 0.379243i) q^{46} +(-9.23171 + 9.23171i) q^{47} +(-3.31923 - 10.4654i) q^{48} +(7.03047 - 2.91212i) q^{49} +(-6.55857 + 2.18960i) q^{50} +(5.55910 + 9.85762i) q^{51} +(-4.88361 - 6.49880i) q^{52} +(7.71191 - 3.19438i) q^{53} +(-3.64840 + 4.70548i) q^{54} +(-0.886100 - 0.886100i) q^{55} +(7.52830 + 7.75903i) q^{56} +(-0.729778 + 1.09219i) q^{57} +(2.06635 + 3.62097i) q^{58} +(2.37335 + 0.983072i) q^{59} +(1.76942 - 0.455084i) q^{60} +(-2.45803 - 12.3573i) q^{61} +(10.1435 + 2.77272i) q^{62} +(3.38087 - 16.9968i) q^{63} +(-3.28313 + 7.29528i) q^{64} +(1.12477 - 0.751547i) q^{65} +(-9.58148 - 11.0371i) q^{66} -13.0111i q^{67} +(1.77161 - 8.05366i) q^{68} +5.86328i q^{69} +(-1.35852 + 1.17935i) q^{70} +(1.11335 - 0.743917i) q^{71} +(12.6137 - 2.31170i) q^{72} +(0.580003 - 2.91587i) q^{73} +(-1.78368 + 6.52531i) q^{74} +(-2.61810 - 13.1621i) q^{75} +(0.926964 - 0.238410i) q^{76} +(13.2964 + 5.50756i) q^{77} +(13.7034 - 7.82000i) q^{78} +(4.26291 - 6.37989i) q^{79} +(-1.18187 - 0.612701i) q^{80} +(1.44635 + 1.44635i) q^{81} +(6.34953 + 4.92311i) q^{82} +(3.77409 - 1.56328i) q^{83} +(-16.7744 + 12.6053i) q^{84} +(1.32180 + 0.368547i) q^{85} +(-1.09796 - 3.28874i) q^{86} +(-7.47567 + 3.09652i) q^{87} +(-0.160723 + 10.6486i) q^{88} +(-9.04404 + 9.04404i) q^{89} +(0.267891 + 2.11708i) q^{90} +(-8.63134 + 12.9177i) q^{91} +(2.84909 - 3.18357i) q^{92} +(-7.81036 + 18.8559i) q^{93} +(-1.30023 + 18.4176i) q^{94} +(0.0310725 + 0.156212i) q^{95} +(-13.2472 - 8.09919i) q^{96} +(-10.4371 - 2.07606i) q^{97} +(4.80831 - 9.62788i) q^{98} +(14.1944 - 9.48439i) 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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