LMFDB - Embedded newform 84.2.o.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(19,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("84.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$0.0777157 - 1.41208i$ of defining polynomial
Character	$\chi$	$=$	84.31
Dual form			84.2.o.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18404 + 0.773342i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.803884 - 1.83133i) q^{4} +(0.380152 - 0.219481i) q^{5} +(0.0777157 + 1.41208i) q^{6} +(2.02350 - 1.70453i) q^{7} +(0.464416 + 2.79004i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.18404 + 0.773342i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.803884 - 1.83133i) q^{4} +(0.380152 - 0.219481i) q^{5} +(0.0777157 + 1.41208i) q^{6} +(2.02350 - 1.70453i) q^{7} +(0.464416 + 2.79004i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.280380 + 0.553861i) q^{10} +(1.83249 + 1.05799i) q^{11} +(-1.18404 - 1.61185i) q^{12} +3.84803i q^{13} +(-1.07772 + 3.58309i) q^{14} -0.438962i q^{15} +(-2.70754 - 2.94435i) q^{16} +(-4.89158 - 2.82415i) q^{17} +(1.26175 + 0.638735i) q^{18} +(-1.48792 - 2.57715i) q^{19} +(-0.0963438 - 0.872621i) q^{20} +(-0.464416 - 2.60467i) q^{21} +(-2.98792 + 0.164445i) q^{22} +(-4.13127 + 2.38519i) q^{23} +(2.64845 + 0.992823i) q^{24} +(-2.40366 + 4.16325i) q^{25} +(-2.97584 - 4.55620i) q^{26} -1.00000 q^{27} +(-1.49490 - 5.07595i) q^{28} +7.02285 q^{29} +(0.339468 + 0.519747i) q^{30} +(-3.71264 + 6.43048i) q^{31} +(5.48282 + 1.39237i) q^{32} +(1.83249 - 1.05799i) q^{33} +(7.97584 - 0.438962i) q^{34} +(0.395127 - 1.09210i) q^{35} +(-1.98792 + 0.219481i) q^{36} +(2.64335 + 4.57842i) q^{37} +(3.75477 + 1.90077i) q^{38} +(3.33249 + 1.92401i) q^{39} +(0.788909 + 0.958709i) q^{40} -6.81813i q^{41} +(2.56419 + 2.72487i) q^{42} +4.38646i q^{43} +(3.41063 - 2.50539i) q^{44} +(-0.380152 - 0.219481i) q^{45} +(3.04701 - 6.01904i) q^{46} +(-0.844569 - 1.46284i) q^{47} +(-3.90366 + 0.872621i) q^{48} +(1.18914 - 6.89826i) q^{49} +(-0.373604 - 6.78829i) q^{50} +(-4.89158 + 2.82415i) q^{51} +(7.04701 + 3.09337i) q^{52} +(-5.35599 + 9.27685i) q^{53} +(1.18404 - 0.773342i) q^{54} +0.928833 q^{55} +(5.69546 + 4.85404i) q^{56} -2.97584 q^{57} +(-8.31531 + 5.43106i) q^{58} +(4.05909 - 7.03055i) q^{59} +(-0.803884 - 0.352875i) q^{60} +(5.35787 - 3.09337i) q^{61} +(-0.577061 - 10.4851i) q^{62} +(-2.48792 - 0.900140i) q^{63} +(-7.56863 + 2.59148i) q^{64} +(0.844569 + 1.46284i) q^{65} +(-1.35155 + 2.66984i) q^{66} +(-6.79878 - 3.92528i) q^{67} +(-9.10422 + 6.68780i) q^{68} +4.77038i q^{69} +(0.376724 + 1.59866i) q^{70} -1.16982i q^{71} +(2.18404 - 1.79722i) q^{72} +(-8.69036 - 5.01738i) q^{73} +(-6.67051 - 3.37680i) q^{74} +(2.40366 + 4.16325i) q^{75} +(-5.91574 + 0.653140i) q^{76} +(5.51142 - 0.982694i) q^{77} +(-5.43371 + 0.299052i) q^{78} +(13.4958 - 7.79180i) q^{79} +(-1.67551 - 0.525049i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.27275 + 8.07291i) q^{82} +5.49645 q^{83} +(-5.14335 - 1.24335i) q^{84} -2.47939 q^{85} +(-3.39223 - 5.19372i) q^{86} +(3.51142 - 6.08197i) q^{87} +(-2.10079 + 5.60406i) q^{88} +(-9.02285 + 5.20934i) q^{89} +(0.619848 - 0.0341142i) q^{90} +(6.55909 + 7.78650i) q^{91} +(1.04701 + 9.48314i) q^{92} +(3.71264 + 6.43048i) q^{93} +(2.13127 + 1.07891i) q^{94} +(-1.13127 - 0.653140i) q^{95} +(3.94724 - 4.05208i) q^{96} -2.22605i q^{97} +(3.92673 + 9.08740i) q^{98} -2.11598i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 + 4 * q^3 - q^4 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 4 * q^9	$ 8 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 4 q^{9} - 13 q^{10} - 6 q^{11} + q^{12} - 10 q^{14} + 7 q^{16} + q^{18} + 6 q^{19} - 22 q^{20} - 4 q^{21} - 6 q^{22} + 11 q^{24} + 2 q^{25} + 12 q^{26} - 8 q^{27} - 7 q^{28} - 16 q^{29} - 5 q^{30} - 6 q^{31} + 21 q^{32} - 6 q^{33} + 28 q^{34} + 12 q^{35} + 2 q^{36} + 6 q^{37} + 8 q^{38} + 6 q^{39} - 13 q^{40} + 7 q^{42} + 19 q^{44} - 12 q^{46} - 4 q^{47} - 10 q^{48} + 4 q^{49} + 2 q^{50} + 20 q^{52} - 4 q^{53} - q^{54} + 8 q^{55} - q^{56} + 12 q^{57} - 23 q^{58} + 14 q^{59} + q^{60} + 12 q^{61} + 48 q^{62} - 2 q^{63} + 2 q^{64} + 4 q^{65} - 21 q^{66} - 42 q^{67} - 10 q^{68} + 35 q^{70} + 7 q^{72} - 18 q^{73} - 28 q^{74} - 2 q^{75} - 44 q^{76} + 8 q^{77} - 6 q^{78} + 6 q^{79} - 33 q^{80} - 4 q^{81} - 14 q^{82} - 4 q^{83} - 26 q^{84} - 32 q^{85} - 42 q^{86} - 8 q^{87} + 11 q^{88} + 8 q^{90} + 34 q^{91} - 28 q^{92} + 6 q^{93} - 16 q^{94} + 24 q^{95} + 9 q^{96} - 19 q^{98}+O(q^{100}) $ 8 * q + q^2 + 4 * q^3 - q^4 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 4 * q^9 - 13 * q^10 - 6 * q^11 + q^12 - 10 * q^14 + 7 * q^16 + q^18 + 6 * q^19 - 22 * q^20 - 4 * q^21 - 6 * q^22 + 11 * q^24 + 2 * q^25 + 12 * q^26 - 8 * q^27 - 7 * q^28 - 16 * q^29 - 5 * q^30 - 6 * q^31 + 21 * q^32 - 6 * q^33 + 28 * q^34 + 12 * q^35 + 2 * q^36 + 6 * q^37 + 8 * q^38 + 6 * q^39 - 13 * q^40 + 7 * q^42 + 19 * q^44 - 12 * q^46 - 4 * q^47 - 10 * q^48 + 4 * q^49 + 2 * q^50 + 20 * q^52 - 4 * q^53 - q^54 + 8 * q^55 - q^56 + 12 * q^57 - 23 * q^58 + 14 * q^59 + q^60 + 12 * q^61 + 48 * q^62 - 2 * q^63 + 2 * q^64 + 4 * q^65 - 21 * q^66 - 42 * q^67 - 10 * q^68 + 35 * q^70 + 7 * q^72 - 18 * q^73 - 28 * q^74 - 2 * q^75 - 44 * q^76 + 8 * q^77 - 6 * q^78 + 6 * q^79 - 33 * q^80 - 4 * q^81 - 14 * q^82 - 4 * q^83 - 26 * q^84 - 32 * q^85 - 42 * q^86 - 8 * q^87 + 11 * q^88 + 8 * q^90 + 34 * q^91 - 28 * q^92 + 6 * q^93 - 16 * q^94 + 24 * q^95 + 9 * q^96 - 19 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.18404	+	0.773342i	−0.837240	+	0.546835i
$2$	−1.18404	+	0.773342i	−0.837240	+	0.546835i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.803884	−	1.83133i	0.401942	−	0.915665i
$5$	0.380152	−	0.219481i	0.170009	−	0.0981549i	−0.412581	−	0.910921i	$-0.635373\pi$
$5$	0.380152	−	0.219481i	0.170009	−	0.0981549i	0.582590	+	0.812766i	$0.302039\pi$
$6$	0.0777157	+	1.41208i	0.0317273	+	0.576478i
$7$	2.02350	−	1.70453i	0.764813	−	0.644253i
$7$	2.02350	−	1.70453i	0.764813	−	0.644253i
$8$	0.464416	+	2.79004i	0.164196	+	0.986428i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.280380	+	0.553861i	−0.0886640	+	0.175146i
$11$	1.83249	+	1.05799i	0.552516	+	0.318995i	0.750136	−	0.661283i	$-0.229988\pi$
$11$	1.83249	+	1.05799i	0.552516	+	0.318995i	−0.197620	+	0.980279i	$0.563321\pi$
$12$	−1.18404	−	1.61185i	−0.341802	−	0.465301i
$13$			3.84803i			1.06725i	0.845721	+	0.533625i	$0.179171\pi$
$13$			3.84803i			1.06725i	−0.845721	+	0.533625i	$0.820829\pi$
$14$	−1.07772	+	3.58309i	−0.288032	+	0.957621i
$15$		−	0.438962i		−	0.113339i
$16$	−2.70754	−	2.94435i	−0.676885	−	0.736089i
$17$	−4.89158	−	2.82415i	−1.18638	−	0.684958i	−0.228899	−	0.973450i	$-0.573513\pi$
$17$	−4.89158	−	2.82415i	−1.18638	−	0.684958i	−0.957482	+	0.288492i	$0.906846\pi$
$18$	1.26175	+	0.638735i	0.297398	+	0.150551i
$19$	−1.48792	−	2.57715i	−0.341352	−	0.591240i	0.643332	−	0.765588i	$-0.277552\pi$
$19$	−1.48792	−	2.57715i	−0.341352	−	0.591240i	−0.984684	+	0.174348i	$0.944218\pi$
$20$	−0.0963438	−	0.872621i	−0.0215431	−	0.195124i
$21$	−0.464416	−	2.60467i	−0.101344	−	0.568386i
$22$	−2.98792	+	0.164445i	−0.637027	+	0.0350597i
$23$	−4.13127	+	2.38519i	−0.861430	+	0.497347i	−0.864491	−	0.502649i	$-0.832359\pi$
$23$	−4.13127	+	2.38519i	−0.861430	+	0.497347i	0.00306100	+	0.999995i	$0.499026\pi$
$24$	2.64845	+	0.992823i	0.540613	+	0.202659i
$25$	−2.40366	+	4.16325i	−0.480731	+	0.832651i
$26$	−2.97584	−	4.55620i	−0.583610	−	0.893545i
$27$	−1.00000			−0.192450
$28$	−1.49490	−	5.07595i	−0.282509	−	0.959265i
$29$	7.02285			1.30411			0.652055	−	0.758172i	$-0.273907\pi$
$29$	7.02285			1.30411			0.652055	+	0.758172i	$0.273907\pi$
$30$	0.339468	+	0.519747i	0.0619780	+	0.0948924i
$31$	−3.71264	+	6.43048i	−0.666810	+	1.15495i	0.311981	+	0.950088i	$0.399007\pi$
$31$	−3.71264	+	6.43048i	−0.666810	+	1.15495i	−0.978791	+	0.204861i	$0.934326\pi$
$32$	5.48282	+	1.39237i	0.969235	+	0.246138i
$33$	1.83249	−	1.05799i	0.318995	−	0.184172i
$34$	7.97584	−	0.438962i	1.36785	−	0.0752813i
$35$	0.395127	−	1.09210i	0.0667887	−	0.184599i
$36$	−1.98792	+	0.219481i	−0.331320	+	0.0365802i
$37$	2.64335	+	4.57842i	0.434564	+	0.752688i	0.997260	−	0.0739766i	$-0.0235690\pi$
$37$	2.64335	+	4.57842i	0.434564	+	0.752688i	−0.562696	+	0.826664i	$0.690236\pi$
$38$	3.75477	+	1.90077i	0.609105	+	0.308346i
$39$	3.33249	+	1.92401i	0.533625	+	0.308089i
$40$	0.788909	+	0.958709i	0.124738	+	0.151585i
$41$		−	6.81813i		−	1.06481i	−0.846489	−	0.532407i	$-0.821288\pi$
$41$		−	6.81813i		−	1.06481i	0.846489	−	0.532407i	$-0.178712\pi$
$42$	2.56419	+	2.72487i	0.395663	+	0.420457i
$43$			4.38646i			0.668928i	0.942408	+	0.334464i	$0.108555\pi$
$43$			4.38646i			0.668928i	−0.942408	+	0.334464i	$0.891445\pi$
$44$	3.41063	−	2.50539i	0.514173	−	0.377702i
$45$	−0.380152	−	0.219481i	−0.0566697	−	0.0327183i
$46$	3.04701	−	6.01904i	0.449257	−	0.887459i
$47$	−0.844569	−	1.46284i	−0.123193	−	0.213377i	0.797832	−	0.602880i	$-0.205980\pi$
$47$	−0.844569	−	1.46284i	−0.123193	−	0.213377i	−0.921025	+	0.389503i	$0.872647\pi$
$48$	−3.90366	+	0.872621i	−0.563444	+	0.125952i
$49$	1.18914	−	6.89826i	0.169877	−	0.985465i
$50$	−0.373604	−	6.78829i	−0.0528355	−	0.960010i
$51$	−4.89158	+	2.82415i	−0.684958	+	0.395461i
$52$	7.04701	+	3.09337i	0.977244	+	0.428973i
$53$	−5.35599	+	9.27685i	−0.735702	+	1.27427i	0.218712	+	0.975789i	$0.429814\pi$
$53$	−5.35599	+	9.27685i	−0.735702	+	1.27427i	−0.954415	+	0.298484i	$0.903519\pi$
$54$	1.18404	−	0.773342i	0.161127	−	0.105239i
$55$	0.928833			0.125244
$56$	5.69546	+	4.85404i	0.761088	+	0.648649i
$57$	−2.97584			−0.394160
$58$	−8.31531	+	5.43106i	−1.09185	+	0.713134i
$59$	4.05909	−	7.03055i	0.528448	−	0.915299i	−0.471002	−	0.882132i	$-0.656107\pi$
$59$	4.05909	−	7.03055i	0.528448	−	0.915299i	0.999450	−	0.0331668i	$-0.0105593\pi$
$60$	−0.803884	−	0.352875i	−0.103781	−	0.0455559i
$61$	5.35787	−	3.09337i	0.686005	−	0.396065i	−0.116109	−	0.993237i	$-0.537042\pi$
$61$	5.35787	−	3.09337i	0.686005	−	0.396065i	0.802114	+	0.597171i	$0.203709\pi$
$62$	−0.577061	−	10.4851i	−0.0732868	−	1.33160i
$63$	−2.48792	−	0.900140i	−0.313449	−	0.113407i
$64$	−7.56863	+	2.59148i	−0.946079	+	0.323935i
$65$	0.844569	+	1.46284i	0.104756	+	0.181442i
$66$	−1.35155	+	2.66984i	−0.166364	+	0.328634i
$67$	−6.79878	−	3.92528i	−0.830604	−	0.479549i	0.0234557	−	0.999725i	$-0.492533\pi$
$67$	−6.79878	−	3.92528i	−0.830604	−	0.479549i	−0.854059	+	0.520176i	$0.825866\pi$
$68$	−9.10422	+	6.68780i	−1.10405	+	0.811015i
$69$			4.77038i			0.574287i
$70$	0.376724	+	1.59866i	0.0450271	+	0.191076i
$71$		−	1.16982i		−	0.138833i	−0.997588	−	0.0694163i	$-0.977886\pi$
$71$		−	1.16982i		−	0.138833i	0.997588	−	0.0694163i	$-0.0221137\pi$
$72$	2.18404	−	1.79722i	0.257391	−	0.211804i
$73$	−8.69036	−	5.01738i	−1.01713	−	0.587240i	−0.103858	−	0.994592i	$-0.533119\pi$
$73$	−8.69036	−	5.01738i	−1.01713	−	0.587240i	−0.913271	+	0.407352i	$0.866452\pi$
$74$	−6.67051	−	3.37680i	−0.775431	−	0.392545i
$75$	2.40366	+	4.16325i	0.277550	+	0.480731i
$76$	−5.91574	+	0.653140i	−0.678581	+	0.0749203i
$77$	5.51142	−	0.982694i	0.628085	−	0.111988i
$78$	−5.43371	+	0.299052i	−0.615246	+	0.0338610i
$79$	13.4958	−	7.79180i	1.51840	−	0.876646i	0.518630	−	0.854999i	$-0.326442\pi$
$79$	13.4958	−	7.79180i	1.51840	−	0.876646i	0.999766	−	0.0216472i	$-0.00689107\pi$
$80$	−1.67551	−	0.525049i	−0.187327	−	0.0587023i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.27275	+	8.07291i	0.582277	+	0.891504i
$83$	5.49645			0.603314			0.301657	−	0.953417i	$-0.402460\pi$
$83$	5.49645			0.603314			0.301657	+	0.953417i	$0.402460\pi$
$84$	−5.14335	−	1.24335i	−0.561186	−	0.135661i
$85$	−2.47939			−0.268928
$86$	−3.39223	−	5.19372i	−0.365794	−	0.560054i
$87$	3.51142	−	6.08197i	0.376464	−	0.652055i
$88$	−2.10079	+	5.60406i	−0.223945	+	0.597395i
$89$	−9.02285	+	5.20934i	−0.956420	+	0.552189i	−0.895069	−	0.445927i	$-0.852874\pi$
$89$	−9.02285	+	5.20934i	−0.956420	+	0.552189i	−0.0613507	+	0.998116i	$0.519541\pi$
$90$	0.619848	−	0.0341142i	0.0653377	−	0.00359595i
$91$	6.55909	+	7.78650i	0.687579	+	0.816247i
$92$	1.04701	+	9.48314i	0.109158	+	0.988686i
$93$	3.71264	+	6.43048i	0.384983	+	0.666810i
$94$	2.13127	+	1.07891i	0.219824	+	0.111281i
$95$	−1.13127	−	0.653140i	−0.116066	−	0.0670108i
$96$	3.94724	−	4.05208i	0.402863	−	0.413563i
$97$		−	2.22605i		−	0.226021i	−0.993594	−	0.113011i	$-0.963951\pi$
$97$		−	2.22605i		−	0.226021i	0.993594	−	0.113011i	$-0.0360494\pi$
$98$	3.92673	+	9.08740i	0.396660	+	0.917966i
$99$		−	2.11598i		−	0.212664i
$100$	5.69203	+	7.74866i	0.569203	+	0.774866i
$101$	−0.664978	−	0.383925i	−0.0661678	−	0.0382020i	0.466551	−	0.884494i	$-0.345496\pi$
$101$	−0.664978	−	0.383925i	−0.0661678	−	0.0382020i	−0.532719	+	0.846292i	$0.678830\pi$
$102$	3.60777	−	7.12676i	0.357222	−	0.705655i
$103$	−4.31939	−	7.48141i	−0.425602	−	0.737165i	0.570874	−	0.821038i	$-0.306604\pi$
$103$	−4.31939	−	7.48141i	−0.425602	−	0.737165i	−0.996476	+	0.0838727i	$0.973271\pi$
$104$	−10.7361	+	1.78709i	−1.05277	+	0.175238i
$105$	−0.748225	−	0.888241i	−0.0730193	−	0.0866835i
$106$	−0.832489	−	15.1261i	−0.0808585	−	1.46918i
$107$	2.20346	−	1.27217i	0.213016	−	0.122985i	−0.389696	−	0.920943i	$-0.627420\pi$
$107$	2.20346	−	1.27217i	0.213016	−	0.122985i	0.602712	+	0.797959i	$0.294087\pi$
$108$	−0.803884	+	1.83133i	−0.0773538	+	0.176220i
$109$	3.40366	−	5.89531i	0.326011	−	0.564668i	−0.655705	−	0.755017i	$-0.727629\pi$
$109$	3.40366	−	5.89531i	0.326011	−	0.564668i	0.981716	+	0.190349i	$0.0609620\pi$
$110$	−1.09977	+	0.718306i	−0.104859	+	0.0684878i
$111$	5.28670			0.501792
$112$	−10.4975	−	1.34282i	−0.991917	−	0.126885i
$113$	13.6408			1.28322			0.641610	−	0.767031i	$-0.278267\pi$
$113$	13.6408			1.28322			0.641610	+	0.767031i	$0.278267\pi$
$114$	3.52350	−	2.30134i	0.330006	−	0.215541i
$115$	−1.04701	+	1.81347i	−0.0976340	+	0.169107i
$116$	5.64556	−	12.8612i	0.524177	−	1.19413i
$117$	3.33249	−	1.92401i	0.308089	−	0.177875i
$118$	0.630909	+	11.4635i	0.0580799	+	1.05530i
$119$	−14.7120	+	2.62317i	−1.34865	+	0.240465i
$120$	1.22472	−	0.203861i	0.111801	−	0.0186099i
$121$	−3.26132	−	5.64878i	−0.296484	−	0.513525i
$122$	−3.95168	+	7.80613i	−0.357768	+	0.706734i
$123$	−5.90467	−	3.40907i	−0.532407	−	0.307385i
$124$	8.79180	+	11.9684i	0.789527	+	1.07480i
$125$			4.30504i			0.385054i
$126$	3.64190	−	0.858216i	0.324447	−	0.0764559i
$127$		−	3.51914i		−	0.312273i	−0.987735	−	0.156137i	$-0.950096\pi$
$127$		−	3.51914i		−	0.312273i	0.987735	−	0.156137i	$-0.0499040\pi$
$128$	6.95744	−	8.92155i	0.614956	−	0.788561i
$129$	3.79878	+	2.19323i	0.334464	+	0.193103i
$130$	−2.13127	−	1.07891i	−0.186925	−	0.0946267i
$131$	9.80833	+	16.9885i	0.856958	+	1.48429i	0.874817	+	0.484454i	$0.160982\pi$
$131$	9.80833	+	16.9885i	0.856958	+	1.48429i	−0.0178590	+	0.999841i	$0.505685\pi$
$132$	−0.464416	−	4.20639i	−0.0404223	−	0.366119i
$133$	−7.40366	−	2.67867i	−0.641978	−	0.232270i
$134$	11.0856	−	0.610111i	0.957649	−	0.0527056i
$135$	−0.380152	+	0.219481i	−0.0327183	+	0.0188899i
$136$	5.60777	−	14.9593i	0.480862	−	1.28275i
$137$	1.68914	−	2.92567i	0.144313	−	0.249957i	−0.784804	−	0.619745i	$-0.787236\pi$
$137$	1.68914	−	2.92567i	0.144313	−	0.249957i	0.929116	+	0.369788i	$0.120570\pi$
$138$	−3.68914	−	5.64831i	−0.314040	−	0.480816i
$139$	−16.4481			−1.39511			−0.697556	−	0.716530i	$-0.745729\pi$
$139$	−16.4481			−1.39511			−0.697556	+	0.716530i	$0.745729\pi$
$140$	−1.68236	−	1.60153i	−0.142186	−	0.135354i
$141$	−1.68914			−0.142251
$142$	0.904674	+	1.38511i	0.0759186	+	0.116236i
$143$	−4.07117	+	7.05147i	−0.340448	+	0.589673i
$144$	−1.19612	+	3.81698i	−0.0996763	+	0.318081i
$145$	2.66975	−	1.54138i	0.221711	−	0.128005i
$146$	14.1699	−	0.779858i	1.17271	−	0.0645415i
$147$	−5.37950	−	4.47895i	−0.443693	−	0.369418i
$148$	10.5095	−	1.16033i	0.863879	−	0.0953786i
$149$	−3.23970	−	5.61132i	−0.265406	−	0.459697i	0.702264	−	0.711917i	$-0.252173\pi$
$149$	−3.23970	−	5.61132i	−0.265406	−	0.459697i	−0.967670	+	0.252220i	$0.918839\pi$
$150$	−6.06564	−	3.07060i	−0.495257	−	0.250713i
$151$	6.72827	+	3.88457i	0.547539	+	0.316122i	0.748129	−	0.663554i	$-0.230953\pi$
$151$	6.72827	+	3.88457i	0.547539	+	0.316122i	−0.200590	+	0.979675i	$0.564286\pi$
$152$	6.49935	−	5.34823i	0.527167	−	0.433799i
$153$			5.64831i			0.456639i
$154$	−5.76577	+	5.42576i	−0.464619	+	0.437220i
$155$			3.25942i			0.261803i
$156$	6.20244	−	4.55620i	0.496593	−	0.364788i
$157$	7.32996	+	4.23195i	0.584994	+	0.337747i	0.763116	−	0.646262i	$-0.223669\pi$
$157$	7.32996	+	4.23195i	0.584994	+	0.337747i	−0.178121	+	0.984009i	$0.557002\pi$
$158$	−9.95378	+	19.6626i	−0.791881	+	1.56428i
$159$	5.35599	+	9.27685i	0.424758	+	0.735702i
$160$	2.38990	−	0.674063i	0.188939	−	0.0532893i
$161$	−4.29401	+	11.8683i	−0.338415	+	0.935356i
$162$	−0.0777157	−	1.41208i	−0.00610592	−	0.110943i
$163$	6.02285	−	3.47729i	0.471746	−	0.272363i	−0.245224	−	0.969466i	$-0.578862\pi$
$163$	6.02285	−	3.47729i	0.471746	−	0.272363i	0.716970	+	0.697104i	$0.245528\pi$
$164$	−12.4862	−	5.48099i	−0.975012	−	0.427993i
$165$	0.464416	−	0.804393i	0.0361548	−	0.0626219i
$166$	−6.50800	+	4.25064i	−0.505118	+	0.329913i
$167$	−8.12021			−0.628361			−0.314180	−	0.949363i	$-0.601730\pi$
$167$	−8.12021			−0.628361			−0.314180	+	0.949363i	$0.601730\pi$
$168$	7.05145	−	2.50539i	0.544032	−	0.193295i
$169$	−1.80731			−0.139024
$170$	2.93569	−	1.91742i	0.225157	−	0.147059i
$171$	−1.48792	+	2.57715i	−0.113784	+	0.197080i
$172$	8.03305	+	3.52620i	0.612514	+	0.268870i
$173$	−1.22660	+	0.708177i	−0.0932565	+	0.0538417i	−0.545903	−	0.837848i	$-0.683813\pi$
$173$	−1.22660	+	0.708177i	−0.0932565	+	0.0538417i	0.452646	+	0.891690i	$0.350480\pi$
$174$	0.545785	+	9.91680i	0.0413759	+	0.751791i
$175$	2.23260	+	12.5215i	0.168768	+	0.946534i
$176$	−1.84645	−	8.26004i	−0.139181	−	0.622624i
$177$	−4.05909	−	7.03055i	−0.305100	−	0.528448i
$178$	6.65478	−	13.1458i	0.498797	−	0.985320i
$179$	−9.29401	−	5.36590i	−0.694667	−	0.401066i	0.110691	−	0.993855i	$-0.464694\pi$
$179$	−9.29401	−	5.36590i	−0.694667	−	0.401066i	−0.805358	+	0.592789i	$0.798027\pi$
$180$	−0.707540	+	0.519747i	−0.0527369	+	0.0387396i
$181$		−	1.21426i		−	0.0902549i	−0.998981	−	0.0451275i	$-0.985631\pi$
$181$		−	1.21426i		−	0.0902549i	0.998981	−	0.0451275i	$-0.0143694\pi$
$182$	−13.7878	−	4.14708i	−1.02202	−	0.307402i
$183$		−	6.18674i		−	0.457337i
$184$	−8.57341	−	10.4187i	−0.632040	−	0.768076i
$185$	2.00975	+	1.16033i	0.147760	+	0.0853092i
$186$	−9.36887	−	4.74278i	−0.686959	−	0.347758i
$187$	−5.97584	−	10.3505i	−0.436997	−	0.756901i
$188$	−3.35787	+	0.370733i	−0.244898	+	0.0270385i
$189$	−2.02350	+	1.70453i	−0.147188	+	0.123987i
$190$	1.84457	−	0.101518i	0.133819	−	0.00736493i
$191$	−5.67473	+	3.27631i	−0.410609	+	0.237065i	−0.691051	−	0.722806i	$-0.742852\pi$
$191$	−5.67473	+	3.27631i	−0.410609	+	0.237065i	0.280442	+	0.959871i	$0.409519\pi$
$192$	−1.54003	+	7.85037i	−0.111142	+	0.566552i
$193$	1.61818	−	2.80276i	0.116479	−	0.201747i	−0.801891	−	0.597470i	$-0.796173\pi$
$193$	1.61818	−	2.80276i	0.116479	−	0.201747i	0.918370	+	0.395723i	$0.129506\pi$
$194$	1.72150	+	2.63572i	0.123596	+	0.189234i
$195$	1.68914			0.120962
$196$	−11.6771	−	7.72310i	−0.834076	−	0.551650i
$197$	−19.2554			−1.37189			−0.685947	−	0.727652i	$-0.740612\pi$
$197$	−19.2554			−1.37189			−0.685947	+	0.727652i	$0.740612\pi$
$198$	1.63637	+	2.50539i	0.116292	+	0.178051i
$199$	−4.31086	+	7.46663i	−0.305589	+	0.529296i	−0.977392	−	0.211434i	$-0.932187\pi$
$199$	−4.31086	+	7.46663i	−0.305589	+	0.529296i	0.671803	+	0.740730i	$0.265520\pi$
$200$	−12.7319	−	4.77281i	−0.900284	−	0.337489i
$201$	−6.79878	+	3.92528i	−0.479549	+	0.276868i
$202$	1.08426	−	0.0596741i	0.0762886	−	0.00419865i
$203$	14.2108	−	11.9707i	0.997400	−	0.840177i
$204$	1.23970	+	11.2284i	0.0867961	+	0.786144i
$205$	−1.49645	−	2.59193i	−0.104517	−	0.181028i
$206$	10.9000	+	5.51789i	0.759439	+	0.384450i
$207$	4.13127	+	2.38519i	0.287143	+	0.165782i
$208$	11.3300	−	10.4187i	0.785591	−	0.722406i
$209$		−	6.29681i		−	0.435559i
$210$	1.57284	+	0.473076i	0.108536	+	0.0326454i
$211$			6.09787i			0.419795i	0.977723	+	0.209897i	$0.0673130\pi$
$211$			6.09787i			0.419795i	−0.977723	+	0.209897i	$0.932687\pi$
$212$	12.6834	+	17.2661i	0.871098	+	1.18584i
$213$	−1.01310	−	0.584912i	−0.0694163	−	0.0400775i
$214$	−1.62515	+	3.21032i	−0.111093	+	0.219453i
$215$	0.962744	+	1.66752i	0.0656586	+	0.113724i
$216$	−0.464416	−	2.79004i	−0.0315995	−	0.189838i
$217$	3.44842	+	19.3404i	0.234094	+	1.31291i
$218$	0.529035	+	9.61245i	0.0358308	+	0.651037i
$219$	−8.69036	+	5.01738i	−0.587240	+	0.339043i
$220$	0.746674	−	1.70100i	0.0503408	−	0.114681i
$221$	10.8674	−	18.8229i	0.731022	−	1.26617i
$222$	−6.25965	+	4.08843i	−0.420120	+	0.274397i
$223$	−2.44944			−0.164027			−0.0820134	−	0.996631i	$-0.526135\pi$
$223$	−2.44944			−0.164027			−0.0820134	+	0.996631i	$0.526135\pi$
$224$	13.4678	−	6.52818i	0.899858	−	0.436182i
$225$	4.80731			0.320487
$226$	−16.1512	+	10.5490i	−1.07436	+	0.701710i
$227$	11.6398	−	20.1607i	0.772561	−	1.33811i	−0.163595	−	0.986528i	$-0.552309\pi$
$227$	11.6398	−	20.1607i	0.772561	−	1.33811i	0.936155	−	0.351587i	$-0.114358\pi$
$228$	−2.39223	+	5.44975i	−0.158429	+	0.360918i
$229$	−10.1385	+	5.85346i	−0.669970	+	0.386808i	−0.796065	−	0.605211i	$-0.793089\pi$
$229$	−10.1385	+	5.85346i	−0.669970	+	0.386808i	0.126095	+	0.992018i	$0.459756\pi$
$230$	−0.162738	−	2.95691i	−0.0107306	−	0.194973i
$231$	1.90467	−	5.26438i	0.125318	−	0.346371i
$232$	3.26153	+	19.5940i	0.214130	+	1.28641i
$233$	4.08426	+	7.07415i	0.267569	+	0.463443i	0.968234	−	0.250048i	$-0.0804463\pi$
$233$	4.08426	+	7.07415i	0.267569	+	0.463443i	−0.700664	+	0.713491i	$0.747113\pi$
$234$	−2.45787	+	4.85526i	−0.160676	+	0.317398i
$235$	−0.642129	−	0.370733i	−0.0418879	−	0.0241840i
$236$	−9.61221	−	13.0853i	−0.625702	−	0.851779i
$237$		−	15.5836i		−	1.01226i
$238$	15.3909	−	14.4833i	0.997645	−	0.938814i
$239$		−	18.1984i		−	1.17716i	−0.808439	−	0.588579i	$-0.799687\pi$
$239$		−	18.1984i		−	1.17716i	0.808439	−	0.588579i	$-0.200313\pi$
$240$	−1.29246	+	1.18851i	−0.0834279	+	0.0767178i
$241$	25.0409	+	14.4574i	1.61303	+	0.931282i	0.988663	+	0.150149i	$0.0479753\pi$
$241$	25.0409	+	14.4574i	1.61303	+	0.931282i	0.624364	+	0.781133i	$0.285358\pi$
$242$	8.22996	+	4.16624i	0.529042	+	0.267816i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.35787	−	12.2987i	−0.0869288	−	0.787346i
$245$	−1.06198	−	2.88338i	−0.0678476	−	0.184212i
$246$	9.62772	−	0.529876i	0.613841	−	0.0337836i
$247$	9.91696	−	5.72556i	0.631001	−	0.364309i
$248$	−19.6655	−	7.37199i	−1.24876	−	0.468122i
$249$	2.74822	−	4.76007i	0.174162	−	0.301657i
$250$	−3.32927	−	5.09732i	−0.210561	−	0.322383i
$251$	20.3586			1.28502			0.642512	−	0.766276i	$-0.277892\pi$
$251$	20.3586			1.28502			0.642512	+	0.766276i	$0.277892\pi$
$252$	−3.64845	+	3.83260i	−0.229831	+	0.241431i
$253$	−10.0940			−0.634605
$254$	2.72150	+	4.16679i	0.170762	+	0.261447i
$255$	−1.23970	+	2.14722i	−0.0776328	+	0.134464i
$256$	−1.33845	+	15.9439i	−0.0836531	+	0.996495i
$257$	18.4350	−	10.6435i	1.14995	−	0.663922i	0.201072	−	0.979577i	$-0.435558\pi$
$257$	18.4350	−	10.6435i	1.14995	−	0.663922i	0.948874	+	0.315655i	$0.102224\pi$
$258$	−6.19401	+	0.340896i	−0.385622	+	0.0212233i
$259$	13.1529	+	4.75877i	0.817281	+	0.295696i
$260$	3.35787	−	0.370733i	0.208246	−	0.0229919i
$261$	−3.51142	−	6.08197i	−0.217352	−	0.376464i
$262$	−24.7514	−	12.5298i	−1.52914	−	0.774096i
$263$	17.4760	+	10.0898i	1.07762	+	0.622164i	0.930253	−	0.366918i	$-0.119587\pi$
$263$	17.4760	+	10.0898i	1.07762	+	0.622164i	0.147366	+	0.989082i	$0.452920\pi$
$264$	3.80287	+	4.62137i	0.234050	+	0.284426i
$265$			4.70215i			0.288851i
$266$	10.8377	−	2.55391i	0.664504	−	0.156590i
$267$			10.4187i			0.637613i
$268$	−12.6539	+	9.29535i	−0.772961	+	0.567804i
$269$	14.1764	+	8.18475i	0.864351	+	0.499033i	0.865467	−	0.500966i	$-0.167022\pi$
$269$	14.1764	+	8.18475i	0.864351	+	0.499033i	−0.00111621	+	0.999999i	$0.500355\pi$
$270$	0.280380	−	0.553861i	0.0170634	−	0.0337069i
$271$	−6.72696	−	11.6514i	−0.408634	−	0.707775i	0.586103	−	0.810236i	$-0.300661\pi$
$271$	−6.72696	−	11.6514i	−0.408634	−	0.707775i	−0.994737	+	0.102462i	$0.967328\pi$
$272$	4.92883	+	22.0490i	0.298854	+	1.33692i
$273$	10.0228	−	1.78709i	0.606610	−	0.108159i
$274$	0.262545	+	4.77038i	0.0158609	+	0.288189i
$275$	−8.80935	+	5.08608i	−0.531224	+	0.306702i
$276$	8.73615	+	3.83484i	0.525854	+	0.230830i
$277$	−1.40366	+	2.43120i	−0.0843375	+	0.146077i	−0.905109	−	0.425180i	$-0.860211\pi$
$277$	−1.40366	+	2.43120i	−0.0843375	+	0.146077i	0.820771	+	0.571257i	$0.193544\pi$
$278$	19.4752	−	12.7200i	1.16804	−	0.762897i
$279$	7.42528			0.444540
$280$	3.23051	+	0.595229i	0.193060	+	0.0355718i
$281$	−25.4502			−1.51823			−0.759115	−	0.650957i	$-0.774368\pi$
$281$	−25.4502			−1.51823			−0.759115	+	0.650957i	$0.774368\pi$
$282$	2.00000	−	1.30628i	0.119098	−	0.0777879i
$283$	2.36975	−	4.10452i	0.140867	−	0.243988i	−0.786957	−	0.617008i	$-0.788344\pi$
$283$	2.36975	−	4.10452i	0.140867	−	0.243988i	0.927823	+	0.373020i	$0.121678\pi$
$284$	−2.14233	−	0.940403i	−0.127124	−	0.0558027i
$285$	−1.13127	+	0.653140i	−0.0670108	+	0.0386887i
$286$	−0.632787	−	11.4976i	−0.0374175	−	0.679867i
$287$	−11.6217	−	13.7965i	−0.686009	−	0.814382i
$288$	−1.53558	−	5.44445i	−0.0904851	−	0.320817i
$289$	7.45168	+	12.9067i	0.438334	+	0.759217i
$290$	−1.96907	+	3.88968i	−0.115628	+	0.228410i
$291$	−1.92782	−	1.11302i	−0.113011	−	0.0652467i
$292$	−16.1745	+	11.8815i	−0.946543	+	0.695314i
$293$		−	3.22818i		−	0.188592i	−0.995544	−	0.0942960i	$-0.969940\pi$
$293$		−	3.22818i		−	0.188592i	0.995544	−	0.0942960i	$-0.0300600\pi$
$294$	9.83328	+	1.14305i	0.573489	+	0.0666640i
$295$		−	3.56357i		−	0.207479i
$296$	−11.5464	+	9.50135i	−0.671118	+	0.552255i
$297$	−1.83249	−	1.05799i	−0.106332	−	0.0613907i
$298$	8.17539	+	4.13861i	0.473587	+	0.239743i
$299$	−9.17828	−	15.8972i	−0.530794	−	0.919362i
$300$	9.55656	−	1.05511i	0.551748	−	0.0609170i
$301$	7.47686	+	8.87601i	0.430959	+	0.511605i
$302$	−10.9706	+	0.603784i	−0.631288	+	0.0347439i
$303$	−0.664978	+	0.383925i	−0.0382020	+	0.0220559i
$304$	−3.55945	+	11.3587i	−0.204148	+	0.651467i
$305$	1.35787	−	2.35190i	0.0777515	−	0.134669i
$306$	−4.36807	−	6.68780i	−0.249706	−	0.382316i
$307$	−5.45523			−0.311347			−0.155673	−	0.987809i	$-0.549755\pi$
$307$	−5.45523			−0.311347			−0.155673	+	0.987809i	$0.549755\pi$
$308$	2.63091	−	10.8832i	0.149910	−	0.620128i
$309$	−8.63878			−0.491443
$310$	−2.52064	−	3.85927i	−0.143163	−	0.219192i
$311$	−15.2625	+	26.4355i	−0.865460	+	1.49902i	0.00113066	+	0.999999i	$0.499640\pi$
$311$	−15.2625	+	26.4355i	−0.865460	+	1.49902i	−0.866590	+	0.499020i	$0.833693\pi$
$312$	−3.82041	+	10.1913i	−0.216288	+	0.576970i
$313$	−16.3093	+	9.41621i	−0.921859	+	0.532235i	−0.884228	−	0.467056i	$-0.845315\pi$
$313$	−16.3093	+	9.41621i	−0.921859	+	0.532235i	−0.0376312	+	0.999292i	$0.511981\pi$
$314$	−11.9517	+	0.657778i	−0.674472	+	0.0371206i
$315$	−1.14335	+	0.203861i	−0.0644206	+	0.0114863i
$316$	−3.42030	−	30.9790i	−0.192407	−	1.74270i
$317$	−8.58259	−	14.8655i	−0.482046	−	0.834929i	0.517741	−	0.855537i	$-0.326773\pi$
$317$	−8.58259	−	14.8655i	−0.482046	−	0.834929i	−0.999788	+	0.0206085i	$0.993440\pi$
$318$	−13.5159	−	6.84212i	−0.757932	−	0.383687i
$319$	12.8693	+	7.43009i	0.720542	+	0.416005i
$320$	−2.30845	+	2.64633i	−0.129046	+	0.147934i
$321$		−	2.54433i		−	0.142011i
$322$	−4.09402	−	17.3733i	−0.228151	−	0.968175i
$323$			16.8085i			0.935248i
$324$	1.18404	+	1.61185i	0.0657798	+	0.0895472i
$325$	−16.0203	−	9.24933i	−0.888647	−	0.513061i
$326$	−4.44214	+	8.77496i	−0.246027	+	0.486000i
$327$	−3.40366	−	5.89531i	−0.188223	−	0.326011i
$328$	19.0228	−	3.16645i	1.05036	−	0.174838i
$329$	−4.20244	−	1.52046i	−0.231688	−	0.0838256i
$330$	0.0721849	+	1.31158i	0.00397365	+	0.0722003i
$331$	−18.6081	+	10.7434i	−1.02280	+	0.590511i	−0.914912	−	0.403652i	$-0.867741\pi$
$331$	−18.6081	+	10.7434i	−1.02280	+	0.590511i	−0.107883	+	0.994164i	$0.534407\pi$
$332$	4.41851	−	10.0658i	0.242497	−	0.552433i
$333$	2.64335	−	4.57842i	0.144855	−	0.250896i
$334$	9.61462	−	6.27970i	0.526089	−	0.343610i
$335$	−3.44610			−0.188280
$336$	−6.41165	+	8.41966i	−0.349784	+	0.459330i
$337$	5.91046			0.321964			0.160982	−	0.986957i	$-0.448534\pi$
$337$	5.91046			0.321964			0.160982	+	0.986957i	$0.448534\pi$
$338$	2.13992	−	1.39767i	0.116397	−	0.0760233i
$339$	6.82041	−	11.8133i	0.370434	−	0.641610i
$340$	−1.99314	+	4.54058i	−0.108093	+	0.246248i
$341$	−13.6068	+	7.85586i	−0.736847	+	0.425419i
$342$	−0.231269	−	4.20212i	−0.0125056	−	0.227224i
$343$	−9.35208	−	15.9856i	−0.504965	−	0.863140i
$344$	−12.2384	+	2.03714i	−0.659850	+	0.109835i
$345$	1.04701	+	1.81347i	0.0563690	+	0.0976340i
$346$	0.904674	−	1.78709i	0.0486356	−	0.0960744i
$347$	2.43838	+	1.40780i	0.130899	+	0.0755746i	0.564020	−	0.825761i	$-0.309254\pi$
$347$	2.43838	+	1.40780i	0.130899	+	0.0755746i	−0.433121	+	0.901336i	$0.642588\pi$
$348$	−8.31531	−	11.3198i	−0.445747	−	0.606804i
$349$		−	9.54077i		−	0.510705i	−0.966848	−	0.255353i	$-0.917808\pi$
$349$		−	9.54077i		−	0.510705i	0.966848	−	0.255353i	$-0.0821916\pi$
$350$	−12.3269	−	13.0993i	−0.658898	−	0.700188i
$351$		−	3.84803i		−	0.205392i
$352$	8.57410	+	8.35226i	0.457001	+	0.445177i
$353$	8.63351	+	4.98456i	0.459516	+	0.265301i	0.711841	−	0.702341i	$-0.247862\pi$
$353$	8.63351	+	4.98456i	0.459516	+	0.265301i	−0.252325	+	0.967643i	$0.581195\pi$
$354$	10.2431	+	5.18536i	0.544416	+	0.275599i
$355$	−0.256754	−	0.444711i	−0.0136271	−	0.0236028i
$356$	2.28670	+	20.7115i	0.121195	+	1.09771i
$357$	−5.08426	+	14.0525i	−0.269088	+	0.743739i
$358$	15.1541	−	0.834029i	0.800920	−	0.0440798i
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	−0.649906	−	0.760014i	$-0.725192\pi$
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	0.333238	+	0.942843i	$0.391859\pi$
$360$	0.435811	−	1.16257i	0.0229693	−	0.0612728i
$361$	5.07218	−	8.78528i	0.266957	−	0.462383i
$362$	0.939035	+	1.43772i	0.0493546	+	0.0755650i
$363$	−6.52264			−0.342350
$364$	19.5324	−	5.75241i	1.02378	−	0.301508i
$365$	−4.40488			−0.230562
$366$	4.78446	+	7.32532i	0.250088	+	0.382901i
$367$	−8.95234	+	15.5059i	−0.467308	+	0.809402i	−0.999302	−	0.0373465i	$-0.988109\pi$
$367$	−8.95234	+	15.5059i	−0.467308	+	0.809402i	0.531994	+	0.846748i	$0.321443\pi$
$368$	18.2084	+	5.70593i	0.949180	+	0.297442i
$369$	−5.90467	+	3.40907i	−0.307385	+	0.177469i
$370$	−3.27695	+	0.180352i	−0.170361	+	0.00937604i
$371$	4.97482	+	27.9012i	0.258280	+	1.44856i
$372$	14.7609	−	1.62971i	0.765316	−	0.0844964i
$373$	−7.23716	−	12.5351i	−0.374726	−	0.649045i	0.615560	−	0.788090i	$-0.288930\pi$
$373$	−7.23716	−	12.5351i	−0.374726	−	0.649045i	−0.990286	+	0.139045i	$0.955597\pi$
$374$	15.0801	+	7.63395i	0.779771	+	0.394742i
$375$	3.72827	+	2.15252i	0.192527	+	0.111156i
$376$	3.68914	−	3.03574i	0.190253	−	0.156557i
$377$			27.0241i			1.39181i
$378$	1.07772	−	3.58309i	0.0554317	−	0.184294i
$379$			21.5969i			1.10936i	0.832064	+	0.554679i	$0.187159\pi$
$379$			21.5969i			1.10936i	−0.832064	+	0.554679i	$0.812841\pi$
$380$	−2.10553	+	1.54668i	−0.108011	+	0.0793432i
$381$	−3.04766	−	1.75957i	−0.156137	−	0.0901455i
$382$	4.18538	−	8.26777i	0.214143	−	0.423016i
$383$	0.318169	+	0.551085i	0.0162577	+	0.0281591i	0.874040	−	0.485854i	$-0.161491\pi$
$383$	0.318169	+	0.551085i	0.0162577	+	0.0281591i	−0.857782	+	0.514013i	$0.828158\pi$
$384$	−4.24757	−	10.4861i	−0.216758	−	0.535116i
$385$	1.87950	−	1.58323i	0.0957881	−	0.0806887i
$386$	0.251515	+	4.56997i	0.0128018	+	0.232606i
$387$	3.79878	−	2.19323i	0.193103	−	0.111488i
$388$	−4.07663	−	1.78949i	−0.206960	−	0.0908474i
$389$	0.509547	−	0.882561i	0.0258351	−	0.0447476i	−0.852819	−	0.522207i	$-0.825109\pi$
$389$	0.509547	−	0.882561i	0.0258351	−	0.0447476i	0.878654	+	0.477459i	$0.158442\pi$
$390$	−2.00000	+	1.30628i	−0.101274	+	0.0661461i
$391$	26.9446			1.36265
$392$	19.7987	+	0.114075i	0.999983	+	0.00576166i
$393$	19.6167			0.989530
$394$	22.7991	−	14.8910i	1.14860	−	0.750200i
$395$	3.42030	−	5.92414i	0.172094	−	0.298076i
$396$	−3.87505	−	1.70100i	−0.194729	−	0.0854785i
$397$	25.8035	−	14.8976i	1.29504	−	0.747691i	0.315496	−	0.948927i	$-0.397829\pi$
$397$	25.8035	−	14.8976i	1.29504	−	0.747691i	0.979543	+	0.201236i	$0.0644957\pi$
$398$	−0.670043	−	12.1745i	−0.0335862	−	0.610254i
$399$	−6.02163	+	5.07242i	−0.301458	+	0.253939i
$400$	18.7661	−	4.19496i	0.938305	−	0.209748i
$401$	3.39513	+	5.88053i	0.169545	+	0.293660i	0.938260	−	0.345931i	$-0.112437\pi$
$401$	3.39513	+	5.88053i	0.169545	+	0.293660i	−0.768715	+	0.639591i	$0.779104\pi$
$402$	5.01442	−	9.90546i	0.250097	−	0.494039i
$403$	−24.7447	−	14.2863i	−1.23262	−	0.711654i
$404$	−1.23766	+	0.909163i	−0.0615759	+	0.0452326i
$405$			0.438962i			0.0218122i
$406$	−7.56863	+	25.1635i	−0.375625	+	1.24884i
$407$			11.1865i			0.554496i
$408$	−10.1512	−	12.3361i	−0.502561	−	0.610728i
$409$	3.21574	+	1.85661i	0.159008	+	0.0918034i	0.577393	−	0.816467i	$-0.304070\pi$
$409$	3.21574	+	1.85661i	0.159008	+	0.0918034i	−0.418384	+	0.908270i	$0.637404\pi$
$410$	3.77630	+	1.91167i	0.186498	+	0.0944106i
$411$	−1.68914	−	2.92567i	−0.0833190	−	0.144313i
$412$	−17.1732	+	1.89605i	−0.846064	+	0.0934116i
$413$	−3.77021	−	21.1452i	−0.185520	−	1.04049i
$414$	−6.73615	+	0.370733i	−0.331063	+	0.0182206i
$415$	2.08949	−	1.20637i	0.102569	−	0.0592182i
$416$	−5.35787	+	21.0980i	−0.262691	+	1.03442i
$417$	−8.22407	+	14.2445i	−0.402734	+	0.697556i
$418$	4.86959	+	7.45565i	0.238179	+	0.364668i
$419$	−20.7082			−1.01166			−0.505832	−	0.862632i	$-0.668814\pi$
$419$	−20.7082			−1.01166			−0.505832	+	0.862632i	$0.668814\pi$
$420$	−2.22815	+	0.656204i	−0.108723	+	0.0320195i
$421$	15.6579			0.763118			0.381559	−	0.924344i	$-0.375387\pi$
$421$	15.6579			0.763118			0.381559	+	0.924344i	$0.375387\pi$
$422$	−4.71574	−	7.22010i	−0.229559	−	0.351469i
$423$	−0.844569	+	1.46284i	−0.0410643	+	0.0711255i
$424$	−28.3702	−	10.6351i	−1.37778	−	0.516486i
$425$	23.5153	−	13.5766i	1.14066	−	0.658561i
$426$	1.65188	−	0.0909137i	0.0800339	−	0.00440478i
$427$	5.56893	−	15.3921i	0.269499	−	0.744876i
$428$	−0.558433	−	5.05793i	−0.0269929	−	0.244484i
$429$	4.07117	+	7.05147i	0.196558	+	0.340448i
$430$	−2.42949	−	1.22988i	−0.117160	−	0.0593099i
$431$	−10.2723	−	5.93071i	−0.494799	−	0.285672i	0.231764	−	0.972772i	$-0.425550\pi$
$431$	−10.2723	−	5.93071i	−0.494799	−	0.285672i	−0.726563	+	0.687100i	$0.758884\pi$
$432$	2.70754	+	2.94435i	0.130267	+	0.141660i
$433$		−	16.9269i		−	0.813454i	−0.913550	−	0.406727i	$-0.866670\pi$
$433$		−	16.9269i		−	0.813454i	0.913550	−	0.406727i	$-0.133330\pi$
$434$	−19.0398	−	20.2330i	−0.913941	−	0.971213i
$435$		−	3.08276i		−	0.147807i
$436$	−8.06011	−	10.9724i	−0.386009	−	0.525481i
$437$	12.2940	+	7.09795i	0.588102	+	0.339541i
$438$	6.40955	−	12.6614i	0.306260	−	0.604984i
$439$	1.17640	+	2.03759i	0.0561467	+	0.0972489i	0.892733	−	0.450587i	$-0.148785\pi$
$439$	1.17640	+	2.03759i	0.0561467	+	0.0972489i	−0.836586	+	0.547836i	$0.815452\pi$
$440$	0.431365	+	2.59148i	0.0205645	+	0.123544i
$441$	−6.56863	+	2.41931i	−0.312792	+	0.115205i
$442$	1.68914	+	30.6913i	0.0803441	+	1.45983i
$443$	1.38904	−	0.801965i	0.0659955	−	0.0381025i	−0.466639	−	0.884448i	$-0.654535\pi$
$443$	1.38904	−	0.801965i	0.0659955	−	0.0381025i	0.532635	+	0.846345i	$0.321202\pi$
$444$	4.24990	−	9.68170i	0.201691	−	0.459473i
$445$	−2.28670	+	3.96069i	−0.108400	+	0.187755i
$446$	2.90023	−	1.89426i	0.137330	−	0.0896956i
$447$	−6.47939			−0.306465
$448$	−10.8979	+	18.1449i	−0.514877	+	0.857264i
$449$	1.35208			0.0638086			0.0319043	−	0.999491i	$-0.489843\pi$
$449$	1.35208			0.0638086			0.0319043	+	0.999491i	$0.489843\pi$
$450$	−5.69203	+	3.71770i	−0.268325	+	0.175254i
$451$	7.21350	−	12.4942i	0.339670	−	0.588327i
$452$	10.9656	−	24.9808i	0.515780	−	1.17500i
$453$	6.72827	−	3.88457i	0.316122	−	0.182513i
$454$	1.80919	+	32.8726i	0.0849095	+	1.54279i
$455$	4.20244	+	1.52046i	0.197013	+	0.0712802i
$456$	−1.38203	−	8.30271i	−0.0647195	−	0.388810i
$457$	−11.0734	−	19.1797i	−0.517992	−	0.897189i	−0.999782	−	0.0209017i	$-0.993346\pi$
$457$	−11.0734	−	19.1797i	−0.517992	−	0.897189i	0.481789	−	0.876287i	$-0.339987\pi$
$458$	7.47762	−	14.7712i	0.349406	−	0.690214i
$459$	4.89158	+	2.82415i	0.228319	+	0.131820i
$460$	2.47939	+	3.37524i	0.115602	+	0.157371i
$461$			30.7842i			1.43376i	0.697195	+	0.716882i	$0.254431\pi$
$461$			30.7842i			1.43376i	−0.697195	+	0.716882i	$0.745569\pi$
$462$	1.81596	+	7.70618i	0.0844863	+	0.358524i
$463$		−	13.8120i		−	0.641897i	−0.947097	−	0.320948i	$-0.895998\pi$
$463$		−	13.8120i		−	0.641897i	0.947097	−	0.320948i	$-0.104002\pi$
$464$	−19.0146	−	20.6778i	−0.882733	−	0.959941i
$465$	2.82274	+	1.62971i	0.130901	+	0.0755759i
$466$	−10.3067	−	5.21752i	−0.477447	−	0.241697i
$467$	8.51330	+	14.7455i	0.393949	+	0.682339i	0.992966	−	0.118397i	$-0.0377754\pi$
$467$	8.51330	+	14.7455i	0.393949	+	0.682339i	−0.599018	+	0.800736i	$0.704442\pi$
$468$	−0.844569	−	7.64957i	−0.0390402	−	0.353602i
$469$	−20.4481	+	3.64593i	−0.944207	+	0.168353i
$470$	1.04701	−	0.0576236i	0.0482949	−	0.00265798i
$471$	7.32996	−	4.23195i	0.337747	−	0.194998i
$472$	21.5006	+	8.05991i	0.989646	+	0.370987i
$473$	−4.64082	+	8.03814i	−0.213385	+	0.369594i
$474$	12.0515	+	18.4516i	0.553542	+	0.847508i
$475$	14.3058			0.656395
$476$	−7.02285	+	29.0512i	−0.321892	+	1.33156i
$477$	10.7120			0.490468
$478$	14.0736	+	21.5476i	0.643712	+	0.985565i
$479$	15.8903	−	27.5227i	0.726045	−	1.25755i	−0.232498	−	0.972597i	$-0.574690\pi$
$479$	15.8903	−	27.5227i	0.726045	−	1.25755i	0.958543	−	0.284950i	$-0.0919769\pi$
$480$	0.611197	−	2.40675i	0.0278972	−	0.109853i
$481$	−17.6179	+	10.1717i	−0.803306	+	0.463789i
$482$	−40.8299	+	2.24713i	−1.85975	+	0.102354i
$483$	8.13127	+	9.65289i	0.369986	+	0.439222i
$484$	−12.9665	+	1.43160i	−0.589386	+	0.0650726i
$485$	−0.488575	−	0.846237i	−0.0221851	−	0.0384257i
$486$	−1.26175	−	0.638735i	−0.0572342	−	0.0289736i
$487$	4.99690	+	2.88496i	0.226431	+	0.130730i	0.608925	−	0.793228i	$-0.291601\pi$
$487$	4.99690	+	2.88496i	0.226431	+	0.130730i	−0.382493	+	0.923958i	$0.624935\pi$
$488$	11.1189	+	13.5121i	0.503329	+	0.611662i
$489$		−	6.95459i		−	0.314497i
$490$	3.48727	+	2.59275i	0.157539	+	0.117129i
$491$		−	22.6443i		−	1.02192i	−0.859603	−	0.510962i	$-0.829289\pi$
$491$		−	22.6443i		−	1.02192i	0.859603	−	0.510962i	$-0.170711\pi$
$492$	−10.9898	+	8.07291i	−0.495458	+	0.363955i
$493$	−34.3528	−	19.8336i	−1.54717	−	0.893261i
$494$	−7.31422	+	14.4485i	−0.329083	+	0.650067i
$495$	−0.464416	−	0.804393i	−0.0208740	−	0.0361548i
$496$	28.9858	−	6.47946i	1.30150	−	0.290936i
$497$	−1.99400	−	2.36714i	−0.0894433	−	0.106181i
$498$	0.427160	+	7.76141i	0.0191415	+	0.347797i
$499$	16.8383	−	9.72159i	0.753785	−	0.435198i	−0.0732749	−	0.997312i	$-0.523345\pi$
$499$	16.8383	−	9.72159i	0.753785	−	0.435198i	0.827060	+	0.562114i	$0.190012\pi$
$500$	7.88394	+	3.46075i	0.352581	+	0.154769i
$501$	−4.06011	+	7.03231i	−0.181392	+	0.314180i
$502$	−24.1053	+	15.7442i	−1.07587	+	0.702696i
$503$	11.7570			0.524217			0.262108	−	0.965038i	$-0.415582\pi$
$503$	11.7570			0.524217			0.262108	+	0.965038i	$0.415582\pi$
$504$	1.35599	−	7.35943i	0.0604007	−	0.327815i
$505$	−0.337057			−0.0149989
$506$	11.9517	−	7.80613i	0.531317	−	0.347025i
$507$	−0.903656	+	1.56518i	−0.0401328	+	0.0695120i
$508$	−6.44470	−	2.82898i	−0.285937	−	0.125516i
$509$	−17.4476	+	10.0734i	−0.773350	+	0.446494i	−0.834068	−	0.551661i	$-0.813994\pi$
$509$	−17.4476	+	10.0734i	−0.773350	+	0.446494i	0.0607186	+	0.998155i	$0.480661\pi$
$510$	−0.192688	−	3.50109i	−0.00853235	−	0.155031i
$511$	−26.1373	+	4.66031i	−1.15624	+	0.206160i
$512$	−10.7453	−	19.9133i	−0.474881	−	0.880050i
$513$	1.48792	+	2.57715i	0.0656933	+	0.113784i
$514$	−13.5967	+	26.8588i	−0.599725	+	1.18469i
$515$	−3.28405	−	1.89605i	−0.144713	−	0.0835499i
$516$	7.07031	−	5.19372i	0.311253	−	0.228641i
$517$		−	3.57417i		−	0.157192i
$518$	−19.2537	+	4.53713i	−0.845958	+	0.199350i
$519$			1.41635i			0.0621710i
$520$	−3.68914	+	3.03574i	−0.161779	+	0.133126i
$521$	−31.0965	−	17.9536i	−1.36236	−	0.786559i	−0.372423	−	0.928063i	$-0.621473\pi$
$521$	−31.0965	−	17.9536i	−1.36236	−	0.786559i	−0.989938	+	0.141504i	$0.954806\pi$
$522$	8.86109	+	4.48574i	0.387840	+	0.196335i
$523$	22.6480	+	39.2276i	0.990330	+	1.71530i	0.615312	+	0.788283i	$0.289030\pi$
$523$	22.6480	+	39.2276i	0.990330	+	1.71530i	0.375017	+	0.927018i	$0.377637\pi$
$524$	38.9964	−	4.30548i	1.70356	−	0.188086i
$525$	11.9602	+	4.32725i	0.521986	+	0.188857i
$526$	−28.4951	+	1.56827i	−1.24245	+	0.0683799i
$527$	36.3213	−	20.9701i	1.58218	−	0.913473i
$528$	−8.07663	−	2.53095i	−0.351490	−	0.110146i
$529$	−0.121725	+	0.210835i	−0.00529241	+	0.00916672i
$530$	−3.63637	−	5.56752i	−0.157954	−	0.241838i
$531$	−8.11818			−0.352299
$532$	−10.8572	+	11.4052i	−0.470720	+	0.494478i
$533$	26.2364			1.13642
$534$	−8.05721	−	12.3361i	−0.348670	−	0.533836i
$535$	0.558433	−	0.967234i	0.0241432	−	0.0418172i
$536$	7.79422	−	20.7918i	0.336659	−	0.898070i
$537$	−9.29401	+	5.36590i	−0.401066	+	0.231556i
$538$	−23.1150	+	1.27217i	−0.996558	+	0.0548470i
$539$	9.47736	−	11.3829i	0.408219	−	0.490296i
$540$	0.0963438	+	0.872621i	0.00414598	+	0.0375516i
$541$	16.9491	+	29.3568i	0.728701	+	1.26215i	0.957432	+	0.288657i	$0.0932089\pi$
$541$	16.9491	+	29.3568i	0.728701	+	1.26215i	−0.228732	+	0.973490i	$0.573458\pi$
$542$	16.9755	+	8.59349i	0.729161	+	0.369122i
$543$	−1.05158	−	0.607128i	−0.0451275	−	0.0260543i
$544$	−22.8874	−	22.2952i	−0.981288	−	0.955899i
$545$		−	2.98815i		−	0.127998i
$546$	−10.4854	+	9.86707i	−0.448733	+	0.422271i
$547$		−	7.83251i		−	0.334894i	−0.985881	−	0.167447i	$-0.946448\pi$
$547$		−	7.83251i		−	0.334894i	0.985881	−	0.167447i	$-0.0535523\pi$
$548$	−4.00000	−	5.44527i	−0.170872	−	0.232610i
$549$	−5.35787	−	3.09337i	−0.228668	−	0.132022i
$550$	6.49731	−	12.8347i	0.277046	−	0.547275i
$551$	−10.4494	−	18.0990i	−0.445161	−	0.771042i
$552$	−13.3096	+	2.21544i	−0.566492	+	0.0942956i
$553$	14.0274	−	38.7708i	0.596506	−	1.64870i
$554$	−0.218172	−	3.96414i	−0.00926925	−	0.168420i
$555$	2.00975	−	1.16033i	0.0853092	−	0.0492533i
$556$	−13.2224	+	30.1220i	−0.560754	+	1.27746i
$557$	−7.69701	+	13.3316i	−0.326133	+	0.564879i	−0.981741	−	0.190223i	$-0.939079\pi$
$557$	−7.69701	+	13.3316i	−0.326133	+	0.564879i	0.655608	+	0.755101i	$0.272412\pi$
$558$	−8.79180	+	5.74228i	−0.372187	+	0.243090i
$559$	−16.8792			−0.713914
$560$	−4.28536	+	1.79352i	−0.181089	+	0.0757899i
$561$	−11.9517			−0.504600
$562$	30.1339	−	19.6817i	1.27112	−	0.830222i
$563$	−8.22052	+	14.2384i	−0.346453	+	0.600075i	−0.985617	−	0.168996i	$-0.945947\pi$
$563$	−8.22052	+	14.2384i	−0.346453	+	0.600075i	0.639163	+	0.769071i	$0.279281\pi$
$564$	−1.35787	+	3.09337i	−0.0571767	+	0.130254i
$565$	5.18559	−	2.99390i	0.218159	−	0.125954i
$566$	0.368333	+	6.69252i	0.0154822	+	0.281308i
$567$	0.464416	+	2.60467i	0.0195037	+	0.109386i
$568$	3.26385	−	0.543286i	0.136948	−	0.0227958i
$569$	18.6146	+	32.2415i	0.780366	+	1.35163i	0.931729	+	0.363155i	$0.118300\pi$
$569$	18.6146	+	32.2415i	0.780366	+	1.35163i	−0.151363	+	0.988478i	$0.548366\pi$
$570$	0.834367	−	1.64820i	0.0349478	−	0.0690356i
$571$	−17.9660	−	10.3727i	−0.751854	−	0.434083i	0.0745095	−	0.997220i	$-0.476261\pi$
$571$	−17.9660	−	10.3727i	−0.751854	−	0.434083i	−0.826363	+	0.563137i	$0.809594\pi$
$572$	9.64082	+	13.1242i	0.403103	+	0.548751i
$573$			6.55261i			0.273739i
$574$	24.4300	+	7.34801i	1.01969	+	0.306700i
$575$		−	22.9327i		−	0.956361i
$576$	6.02861	+	5.25889i	0.251192	+	0.219120i
$577$	−13.3550	−	7.71054i	−0.555978	−	0.320994i	0.195552	−	0.980693i	$-0.437350\pi$
$577$	−13.3550	−	7.71054i	−0.555978	−	0.320994i	−0.751530	+	0.659699i	$0.770684\pi$
$578$	−18.8044	−	9.51929i	−0.782158	−	0.395950i
$579$	−1.61818	−	2.80276i	−0.0672491	−	0.116479i
$580$	−0.676608	−	6.12829i	−0.0280946	−	0.254463i
$581$	11.1221	−	9.36888i	0.461422	−	0.388687i
$582$	3.14335	−	0.172999i	0.130296	−	0.00717104i
$583$	−19.6296	+	11.3332i	−0.812975	+	0.469371i
$584$	9.96274	−	26.5766i	0.412261	−	1.09975i
$585$	0.844569	−	1.46284i	0.0349186	−	0.0604808i
$586$	2.49648	+	3.82228i	0.103129	+	0.157897i
$587$	−34.0410			−1.40502			−0.702512	−	0.711672i	$-0.747938\pi$
$587$	−34.0410			−1.40502			−0.702512	+	0.711672i	$0.747938\pi$
$588$	−12.5269	+	6.25108i	−0.516602	+	0.257790i
$589$	22.0965			0.910469
$590$	2.75586	+	4.21940i	0.113457	+	0.173710i
$591$	−9.62772	+	16.6757i	−0.396032	+	0.685947i
$592$	6.32351	−	20.1792i	0.259895	−	0.829361i
$593$	27.5697	−	15.9173i	1.13215	−	0.653647i	0.187675	−	0.982231i	$-0.439905\pi$
$593$	27.5697	−	15.9173i	1.13215	−	0.653647i	0.944475	+	0.328584i	$0.106571\pi$
$594$	2.98792	−	0.164445i	0.122596	−	0.00674724i
$595$	−5.01706	+	4.22620i	−0.205679	+	0.173257i
$596$	−12.8805	+	1.42210i	−0.527606	+	0.0582516i
$597$	4.31086	+	7.46663i	0.176432	+	0.305589i
$598$	23.1614	+	11.7250i	0.947141	+	0.479470i
$599$	18.0000	+	10.3923i	0.735460	+	0.424618i	0.820416	−	0.571767i	$-0.193742\pi$
$599$	18.0000	+	10.3923i	0.735460	+	0.424618i	−0.0849563	+	0.996385i	$0.527075\pi$
$600$	−10.4993	+	8.63978i	−0.428634	+	0.352717i
$601$			15.8614i			0.646999i	0.946228	+	0.323499i	$0.104859\pi$
$601$			15.8614i			0.646999i	−0.946228	+	0.323499i	$0.895141\pi$
$602$	−15.7171	−	4.72735i	−0.640580	−	0.192673i
$603$			7.85056i			0.319699i
$604$	12.5227	−	9.19894i	0.509541	−	0.374300i
$605$	−2.47960	−	1.43160i	−0.100810	−	0.0582027i
$606$	0.490453	−	0.968837i	0.0199233	−	0.0393563i
$607$	21.7151	+	37.6116i	0.881388	+	1.52661i	0.849798	+	0.527108i	$0.176724\pi$
$607$	21.7151	+	37.6116i	0.881388	+	1.52661i	0.0315900	+	0.999501i	$0.489943\pi$
$608$	−4.56965	−	16.2018i	−0.185324	−	0.657070i
$609$	−3.26153	−	18.2922i	−0.132164	−	0.741238i
$610$	0.211056	+	3.83484i	0.00854539	+	0.155268i
$611$	5.62903	−	3.24992i	0.227726	−	0.131478i
$612$	10.3439	+	4.54058i	0.418128	+	0.183542i
$613$	−7.76030	+	13.4412i	−0.313436	+	0.542887i	−0.979104	−	0.203361i	$-0.934813\pi$
$613$	−7.76030	+	13.4412i	−0.313436	+	0.542887i	0.665668	+	0.746248i	$0.268147\pi$
$614$	6.45919	−	4.21876i	0.260672	−	0.170255i
$615$	−2.99290			−0.120685
$616$	5.30135	+	14.9207i	0.213598	+	0.601173i
$617$	−19.8053			−0.797330			−0.398665	−	0.917097i	$-0.630526\pi$
$617$	−19.8053			−0.797330			−0.398665	+	0.917097i	$0.630526\pi$
$618$	10.2286	−	6.68073i	0.411456	−	0.268739i
$619$	8.15665	−	14.1277i	0.327844	−	0.567842i	−0.654240	−	0.756287i	$-0.727011\pi$
$619$	8.15665	−	14.1277i	0.327844	−	0.567842i	0.982084	+	0.188445i	$0.0603448\pi$
$620$	5.96907	+	2.62019i	0.239724	+	0.105229i
$621$	4.13127	−	2.38519i	0.165782	−	0.0957144i
$622$	−2.37228	−	43.1038i	−0.0951197	−	1.72830i
$623$	−9.37827	+	25.9209i	−0.375733	+	1.03850i
$624$	−3.35787	−	15.0214i	−0.134422	−	0.601336i
$625$	−11.0734	−	19.1797i	−0.442936	−	0.767188i
$626$	12.0289	−	23.7618i	0.480772	−	0.949714i
$627$	−5.45320	−	3.14840i	−0.217780	−	0.125735i
$628$	13.6425	−	10.0216i	0.544397	−	0.399904i
$629$		−	29.8609i		−	1.19063i
$630$	1.19612	−	1.12558i	0.0476544	−	0.0448442i
$631$		−	27.3095i		−	1.08717i	−0.839353	−	0.543587i	$-0.817066\pi$
$631$		−	27.3095i		−	1.08717i	0.839353	−	0.543587i	$-0.182934\pi$
$632$	28.0071	+	34.0352i	1.11406	+	1.35385i
$633$	5.28091	+	3.04894i	0.209897	+	0.121184i
$634$	21.6582	+	10.9640i	0.860157	+	0.435436i
$635$	−0.772384	−	1.33781i	−0.0306511	−	0.0530893i
$636$	21.2946	−	2.35108i	0.844385	−	0.0932263i
$637$	26.5447	+	4.57583i	1.05174	+	0.181301i
$638$	−20.9837	+	1.15487i	−0.830753	+	0.0457217i
$639$	−1.01310	+	0.584912i	−0.0400775	+	0.0231388i
$640$	0.686775	−	4.91857i	0.0271472	−	0.194424i
$641$	−4.89533	+	8.47896i	−0.193354	+	0.334899i	−0.946360	−	0.323115i	$-0.895270\pi$
$641$	−4.89533	+	8.47896i	−0.193354	+	0.334899i	0.753006	+	0.658014i	$0.228603\pi$
$642$	1.96764	+	3.01258i	0.0776566	+	0.118897i
$643$	7.26458			0.286487			0.143244	−	0.989687i	$-0.454247\pi$
$643$	7.26458			0.286487			0.143244	+	0.989687i	$0.454247\pi$
$644$	18.2829	+	17.4045i	0.720449	+	0.685834i
$645$	1.92549			0.0758160
$646$	−12.9987	−	19.9018i	−0.511427	−	0.783027i
$647$	−23.0419	+	39.9098i	−0.905872	+	1.56902i	−0.0861302	+	0.996284i	$0.527450\pi$
$647$	−23.0419	+	39.9098i	−0.905872	+	1.56902i	−0.819742	+	0.572733i	$0.805883\pi$
$648$	−2.64845	−	0.992823i	−0.104041	−	0.0390018i
$649$	14.8765	−	8.58893i	0.583952	−	0.337145i
$650$	26.1215	−	1.43764i	1.02457	−	0.0563887i
$651$	18.4735	+	6.68379i	0.724034	+	0.261958i
$652$	−1.52640	−	13.8252i	−0.0597784	−	0.541435i
$653$	3.38990	+	5.87149i	0.132657	+	0.229769i	0.924700	−	0.380696i	$-0.124316\pi$
$653$	3.38990	+	5.87149i	0.132657	+	0.229769i	−0.792043	+	0.610465i	$0.790982\pi$
$654$	8.58914	+	4.34807i	0.335862	+	0.170023i
$655$	7.45732	+	4.30548i	0.291381	+	0.168229i
$656$	−20.0750	+	18.4604i	−0.783797	+	0.720756i
$657$			10.0348i			0.391493i
$658$	6.15168	−	1.44964i	0.239817	−	0.0565130i
$659$			29.3184i			1.14208i	0.820921	+	0.571041i	$0.193460\pi$
$659$			29.3184i			1.14208i	−0.820921	+	0.571041i	$0.806540\pi$
$660$	−1.09977	−	1.49714i	−0.0428086	−	0.0582760i
$661$	26.4813	+	15.2890i	1.03000	+	0.594674i	0.916986	−	0.398919i	$-0.130615\pi$
$661$	26.4813	+	15.2890i	1.03000	+	0.594674i	0.113019	+	0.993593i	$0.463948\pi$
$662$	13.7244	−	27.1110i	0.533413	−	1.05370i
$663$	−10.8674	−	18.8229i	−0.422056	−	0.731022i
$664$	2.55264	+	15.3353i	0.0990617	+	0.595125i
$665$	−3.40243	+	0.606658i	−0.131941	+	0.0235252i
$666$	0.410860	+	7.46523i	0.0159205	+	0.289272i
$667$	−29.0133	+	16.7508i	−1.12340	+	0.648595i
$668$	−6.52771	+	14.8708i	−0.252565	+	0.575368i
$669$	−1.22472	+	2.12128i	−0.0473504	+	0.0820134i
$670$	4.08030	−	2.66501i	0.157636	−	0.102958i
$671$	13.0910			0.505372
$672$	1.08035	−	14.9276i	0.0416754	−	0.575844i
$673$	−6.37827			−0.245864			−0.122932	−	0.992415i	$-0.539230\pi$
$673$	−6.37827			−0.245864			−0.122932	+	0.992415i	$0.539230\pi$
$674$	−6.99821	+	4.57081i	−0.269561	+	0.176061i
$675$	2.40366	−	4.16325i	0.0925168	−	0.160244i
$676$	−1.45287	+	3.30979i	−0.0558796	+	0.127299i
$677$	−10.8219	+	6.24801i	−0.415919	+	0.240131i	−0.693330	−	0.720621i	$-0.743857\pi$
$677$	−10.8219	+	6.24801i	−0.415919	+	0.240131i	0.277411	+	0.960751i	$0.410524\pi$
$678$	1.06011	+	19.2619i	0.0407131	+	0.739748i
$679$	−3.79437	−	4.50442i	−0.145615	−	0.172864i
$680$	−1.15147	−	6.91760i	−0.0441569	−	0.265278i
$681$	−11.6398	−	20.1607i	−0.446038	−	0.772561i
$682$	10.0356	−	19.8243i	0.384284	−	0.759112i
$683$	−39.1917	−	22.6273i	−1.49963	−	0.865811i	−0.499629	−	0.866240i	$-0.666530\pi$
$683$	−39.1917	−	22.6273i	−1.49963	−	0.865811i	−1.00000		0.000428478i	$0.999864\pi$
$684$	3.52350	+	4.79661i	0.134725	+	0.183403i
$685$		−	1.48293i		−	0.0566600i
$686$	23.4355	+	11.6951i	0.894772	+	0.446523i
$687$			11.7069i			0.446647i
$688$	12.9153	−	11.8765i	0.492391	−	0.452788i
$689$	−35.6976	−	20.6100i	−1.35997	−	0.785179i
$690$	−2.64213	−	1.33752i	−0.100584	−	0.0509185i
$691$	5.29654	+	9.17388i	0.201490	+	0.348991i	0.949009	−	0.315250i	$-0.102088\pi$
$691$	5.29654	+	9.17388i	0.201490	+	0.348991i	−0.747519	+	0.664241i	$0.768755\pi$
$692$	0.310863	+	2.81560i	0.0118172	+	0.107033i
$693$	−3.60675	−	4.28169i	−0.137009	−	0.162648i
$694$	−3.97584	+	0.218816i	−0.150921	+	0.00830615i
$695$	−6.25279	+	3.61005i	−0.237182	+	0.136937i
$696$	18.5997	+	6.97245i	0.705019	+	0.264290i
$697$	−19.2554	+	33.3514i	−0.729352	+	1.26327i
$698$	7.37827	+	11.2966i	0.279272	+	0.427583i
$699$	8.16853			0.308962
$700$	24.7257	+	5.97720i	0.934544	+	0.225917i
$701$	29.6566			1.12011			0.560057	−	0.828454i	$-0.310779\pi$
$701$	29.6566			1.12011			0.560057	+	0.828454i	$0.310779\pi$
$702$	2.97584	+	4.55620i	0.112316	+	0.171963i
$703$	7.86620	−	13.6246i	0.296679	−	0.513863i
$704$	−16.6112	−	3.25867i	−0.626058	−	0.122816i
$705$	−0.642129	+	0.370733i	−0.0241840	+	0.0139626i
$706$	−14.0772	+	0.774757i	−0.529801	+	0.0291584i
$707$	−2.00000	+	0.356603i	−0.0752177	+	0.0134114i
$708$	−16.1383	+	1.78178i	−0.606514	+	0.0669636i
$709$	17.8506	+	30.9181i	0.670392	+	1.16115i	0.977793	+	0.209573i	$0.0672074\pi$
$709$	17.8506	+	30.9181i	0.670392	+	1.16115i	−0.307401	+	0.951580i	$0.599459\pi$
$710$	0.647920	+	0.327995i	0.0243160	+	0.0123094i
$711$	−13.4958	−	7.79180i	−0.506132	−	0.292215i
$712$	−18.7246	−	22.7548i	−0.701735	−	0.852772i
$713$		−	35.4214i		−	1.32654i
$714$	−4.84746	−	20.5706i	−0.181412	−	0.769835i
$715$			3.57417i			0.133667i
$716$	−17.2980	+	12.7068i	−0.646458	+	0.474877i
$717$	−15.7603	−	9.09922i	−0.588579	−	0.339816i
$718$	4.42528	−	8.74167i	0.165150	−	0.326236i
$719$	6.40447	+	11.0929i	0.238846	+	0.413694i	0.960384	−	0.278682i	$-0.0898974\pi$
$719$	6.40447	+	11.0929i	0.238846	+	0.413694i	−0.721537	+	0.692376i	$0.756564\pi$
$720$	0.383048	+	1.71356i	0.0142753	+	0.0638605i
$721$	−21.4926	−	7.77611i	−0.800427	−	0.289598i
$722$	0.788376	+	14.3246i	0.0293403	+	0.533107i
$723$	25.0409	−	14.4574i	0.931282	−	0.537676i
$724$	−2.22370	−	0.976121i	−0.0826433	−	0.0362772i
$725$	−16.8805	+	29.2379i	−0.626927	+	1.08587i
$726$	7.72305	−	5.04424i	0.286629	−	0.187209i
$727$	−19.3286			−0.716860			−0.358430	−	0.933557i	$-0.616688\pi$
$727$	−19.3286			−0.716860			−0.358430	+	0.933557i	$0.616688\pi$
$728$	−18.6785	+	21.9163i	−0.692271	+	0.812272i
$729$	1.00000			0.0370370
$730$	5.21554	−	3.40648i	0.193036	−	0.126079i
$731$	12.3880	−	21.4567i	0.458188	−	0.793604i
$732$	−11.3300	−	4.97342i	−0.418767	−	0.183823i
$733$	−32.6407	+	18.8451i	−1.20561	+	0.696061i	−0.961798	−	0.273761i	$-0.911732\pi$
$733$	−32.6407	+	18.8451i	−1.20561	+	0.696061i	−0.243815	+	0.969822i	$0.578399\pi$
$734$	−1.39147	−	25.2828i	−0.0513602	−	0.933204i
$735$	−3.02807	−	0.521986i	−0.111692	−	0.0192537i
$736$	−25.9721	+	7.32532i	−0.957344	+	0.270015i
$737$	−8.30580	−	14.3861i	−0.305948	−	0.529917i
$738$	4.35498	−	8.60279i	0.160309	−	0.316673i
$739$	12.0072	+	6.93237i	0.441693	+	0.255011i	0.704315	−	0.709887i	$-0.251254\pi$
$739$	12.0072	+	6.93237i	0.441693	+	0.255011i	−0.262623	+	0.964899i	$0.584587\pi$
$740$	3.74056	−	2.74775i	0.137506	−	0.101009i
$741$		−	11.4511i		−	0.420667i
$742$	−27.4676	−	29.1888i	−1.00837	−	1.07155i
$743$			18.9927i			0.696773i	0.937351	+	0.348387i	$0.113270\pi$
$743$			18.9927i			0.696773i	−0.937351	+	0.348387i	$0.886730\pi$
$744$	−16.2171	+	13.3448i	−0.594547	+	0.489245i
$745$	−2.46315	−	1.42210i	−0.0902430	−	0.0521018i
$746$	18.2630	+	9.24525i	0.668656	+	0.338493i
$747$	−2.74822	−	4.76007i	−0.100552	−	0.174162i
$748$	−23.7590	+	2.62317i	−0.868715	+	0.0959125i
$749$	2.29026	−	6.33010i	0.0836841	−	0.231297i
$750$	−6.07904	+	0.334569i	−0.221975	+	0.0122167i
$751$	−25.2868	+	14.5993i	−0.922728	+	0.532737i	−0.884504	−	0.466532i	$-0.845503\pi$
$751$	−25.2868	+	14.5993i	−0.922728	+	0.532737i	−0.0382233	+	0.999269i	$0.512170\pi$
$752$	−2.02040	+	6.44740i	−0.0736765	+	0.235112i
$753$	10.1793	−	17.6311i	0.370954	−	0.642512i
$754$	−20.8989	−	31.9975i	−0.761092	−	1.16528i
$755$	3.41036			0.124116
$756$	1.49490	+	5.07595i	0.0543690	+	0.184611i
$757$	−10.8022			−0.392614			−0.196307	−	0.980542i	$-0.562895\pi$
$757$	−10.8022			−0.392614			−0.196307	+	0.980542i	$0.562895\pi$
$758$	−16.7018	−	25.5715i	−0.606636	−	0.928799i
$759$	−5.04701	+	8.74167i	−0.183195	+	0.317303i
$760$	1.29691	−	3.45962i	0.0470437	−	0.125494i
$761$	−0.203165	+	0.117298i	−0.00736474	+	0.00425204i	−0.503678	−	0.863892i	$-0.668020\pi$
$761$	−0.203165	+	0.117298i	−0.00736474	+	0.00425204i	0.496313	+	0.868144i	$0.334687\pi$
$762$	4.96929	−	0.273492i	0.180018	−	0.00990758i
$763$	−3.16143	−	17.7308i	−0.114451	−	0.641899i
$764$	1.43817	+	13.0261i	0.0520313	+	0.471267i
$765$	1.23970	+	2.14722i	0.0448213	+	0.0776328i
$766$	−0.802901	−	0.406451i	−0.0290100	−	0.0146857i
$767$	27.0537	+	15.6195i	0.976854	+	0.563987i
$768$	13.1386	+	9.13109i	0.474099	+	0.329490i
$769$			34.8540i			1.25687i	0.777863	+	0.628434i	$0.216304\pi$
$769$			34.8540i			1.25687i	−0.777863	+	0.628434i	$0.783696\pi$
$770$	−1.00102	+	3.32809i	−0.0360742	+	0.119936i
$771$		−	21.2869i		−	0.766631i
$772$	−3.83196	−	5.21651i	−0.137915	−	0.187746i
$773$	17.0362	+	9.83583i	0.612748	+	0.353770i	0.774040	−	0.633137i	$-0.218233\pi$
$773$	17.0362	+	9.83583i	0.612748	+	0.353770i	−0.161292	+	0.986907i	$0.551566\pi$
$774$	−2.80178	+	5.53462i	−0.100708	+	0.198938i
$775$	−17.8478	−	30.9133i	−0.641113	−	1.11044i
$776$	6.21076	−	1.03381i	0.222953	−	0.0371118i
$777$	10.6977	−	9.01136i	0.383777	−	0.323281i
$778$	0.0791996	+	1.43904i	0.00283944	+	0.0515920i
$779$	−17.5714	+	10.1448i	−0.629560	+	0.363476i
$780$	1.35787	−	3.09337i	0.0486196	−	0.110760i
$781$	1.23766	−	2.14369i	0.0442870	−	0.0767073i
$782$	−31.9034	+	20.8374i	−1.14086	+	0.745143i
$783$	−7.02285			−0.250976
$784$	−23.5306	+	15.1761i	−0.840377	+	0.542002i
$785$	3.71533			0.132606
$786$	−23.2268	+	15.1704i	−0.828474	+	0.541110i
$787$	19.4781	−	33.7370i	0.694319	−	1.20260i	−0.276091	−	0.961131i	$-0.589039\pi$
$787$	19.4781	−	33.7370i	0.694319	−	1.20260i	0.970410	−	0.241464i	$-0.0776275\pi$
$788$	−15.4791	+	35.2631i	−0.551422	+	1.25620i
$789$	17.4760	−	10.0898i	0.622164	−	0.359206i
$790$	0.531622	+	9.65946i	0.0189143	+	0.343668i
$791$	27.6023	−	23.2512i	0.981423	−	0.826718i
$792$	5.90366	−	0.982694i	0.209777	−	0.0349185i
$793$	11.9034	+	20.6172i	0.422701	+	0.732139i
$794$	−19.0313	+	37.5943i	−0.675395	+	1.33417i
$795$	4.07218	+	2.35108i	0.144426	+	0.0833841i
$796$	10.2084	+	13.8969i	0.361828	+	0.492563i
$797$			20.4557i			0.724579i	0.932066	+	0.362289i	$0.118005\pi$
$797$			20.4557i			0.724579i	−0.932066	+	0.362289i	$0.881995\pi$
$798$	3.20711	−	10.6627i	0.113530	−	0.377456i
$799$			9.54077i			0.337528i
$800$	−18.9756	+	19.4796i	−0.670889	+	0.688708i
$801$	9.02285	+	5.20934i	0.318807	+	0.184063i
$802$	−8.56762	−	4.33717i	−0.302533	−	0.153151i
$803$	−10.6167	−	18.3886i	−0.374654	−	0.648919i
$804$	1.72305	+	15.6063i	0.0607672	+	0.550391i
$805$	0.972496	+	5.45423i	0.0342760	+	0.192236i
$806$	40.3468	−	2.22055i	1.42116	−	0.0782154i
$807$	14.1764	−	8.18475i	0.499033	−	0.288117i
$808$	0.762340	−	2.03362i	0.0268190	−	0.0715424i
$809$	24.4650	−	42.3746i	0.860143	−	1.48981i	−0.0116472	−	0.999932i	$-0.503708\pi$
$809$	24.4650	−	42.3746i	0.860143	−	1.48981i	0.871790	−	0.489879i	$-0.162959\pi$
$810$	−0.339468	−	0.519747i	−0.0119277	−	0.0182620i
$811$	51.9424			1.82394			0.911972	−	0.410253i	$-0.134560\pi$
$811$	51.9424			1.82394			0.911972	+	0.410253i	$0.134560\pi$
$812$	−10.4985	−	35.6476i	−0.368423	−	1.25099i
$813$	−13.4539			−0.471850
$814$	−8.65102	−	13.2453i	−0.303218	−	0.464246i
$815$	1.52640	−	2.64380i	0.0534674	−	0.0926083i
$816$	21.5595	+	6.75603i	0.754732	+	0.236508i
$817$	11.3046	−	6.52670i	0.395497	−	0.228340i
$818$	−5.24335	+	0.288575i	−0.183329	+	0.0100898i
$819$	3.46376	−	9.57359i	0.121034	−	0.334528i
$820$	−5.94965	+	0.656884i	−0.207771	+	0.0229394i
$821$	−15.7322	−	27.2490i	−0.549059	−	0.950998i	−0.998339	−	0.0576069i	$-0.981653\pi$
$821$	−15.7322	−	27.2490i	−0.549059	−	0.950998i	0.449281	−	0.893391i	$-0.351680\pi$
$822$	4.26254	+	2.15782i	0.148673	+	0.0752626i
$823$	35.9504	+	20.7560i	1.25315	+	0.723507i	0.971734	−	0.236078i	$-0.0758622\pi$
$823$	35.9504	+	20.7560i	1.25315	+	0.723507i	0.281417	+	0.959586i	$0.409196\pi$
$824$	18.8674	−	15.5258i	0.657278	−	0.540865i
$825$			10.1722i			0.354149i
$826$	20.8165	+	22.1210i	0.724300	+	0.769688i
$827$			38.6850i			1.34521i	0.740003	+	0.672604i	$0.234824\pi$
$827$			38.6850i			1.34521i	−0.740003	+	0.672604i	$0.765176\pi$
$828$	7.68914	−	5.64831i	0.267216	−	0.196292i
$829$	8.94508	+	5.16444i	0.310675	+	0.179369i	0.647229	−	0.762296i	$-0.275928\pi$
$829$	8.94508	+	5.16444i	0.310675	+	0.179369i	−0.336553	+	0.941664i	$0.609261\pi$
$830$	−1.54110	+	3.04427i	−0.0534922	+	0.105668i
$831$	1.40366	+	2.43120i	0.0486923	+	0.0843375i
$832$	−9.97209	−	29.1243i	−0.345720	−	1.00970i
$833$	−25.2985	+	30.3850i	−0.876541	+	1.05278i
$834$	−1.27828	−	23.2260i	−0.0442631	−	0.804251i
$835$	−3.08692	+	1.78223i	−0.106827	+	0.0616767i
$836$	−11.5315	−	5.06191i	−0.398827	−	0.175070i
$837$	3.71264	−	6.43048i	0.128328	−	0.222270i
$838$	24.5193	−	16.0145i	0.847005	−	0.553213i
$839$	10.4794			0.361789			0.180894	−	0.983503i	$-0.442101\pi$
$839$	10.4794			0.361789			0.180894	+	0.983503i	$0.442101\pi$
$840$	2.13074	−	2.50009i	0.0735175	−	0.0862613i
$841$	20.3204			0.700704
$842$	−18.5395	+	12.1089i	−0.638913	+	0.417300i
$843$	−12.7251	+	22.0405i	−0.438275	+	0.759115i
$844$	11.1672	+	4.90198i	0.384392	+	0.168733i
$845$	−0.687054	+	0.396671i	−0.0236354	+	0.0136459i
$846$	−0.131272	−	2.38519i	−0.00451324	−	0.0820046i
$847$	−16.2278	−	5.87129i	−0.557595	−	0.201740i
$848$	41.8159	−	9.34751i	1.43596	−	0.320995i
$849$	−2.36975	−	4.10452i	−0.0813295	−	0.140867i
$850$	−17.3437	+	34.2606i	−0.594883	+	1.17513i
$851$	−21.8408	−	12.6098i	−0.748693	−	0.432258i
$852$	−1.88558	+	1.38511i	−0.0645989	+	0.0474532i
$853$			25.5157i			0.873642i	0.899548	+	0.436821i	$0.143896\pi$
$853$			25.5157i			0.873642i	−0.899548	+	0.436821i	$0.856104\pi$
$854$	5.30955	+	22.5315i	0.181689	+	0.771012i
$855$			1.30628i			0.0446739i
$856$	4.57272	+	5.55692i	0.156292	+	0.189931i
$857$	−9.99828	−	5.77251i	−0.341535	−	0.197185i	0.319416	−	0.947615i	$-0.396513\pi$
$857$	−9.99828	−	5.77251i	−0.341535	−	0.197185i	−0.660951	+	0.750429i	$0.729847\pi$
$858$	−10.2736	−	5.20079i	−0.350735	−	0.177552i
$859$	−16.4552	−	28.5013i	−0.561445	−	0.972452i	−0.997371	−	0.0724689i	$-0.976912\pi$
$859$	−16.4552	−	28.5013i	−0.561445	−	0.972452i	0.435925	−	0.899983i	$-0.356421\pi$
$860$	3.82772	−	0.422608i	0.130524	−	0.0144108i
$861$	−17.7590	+	3.16645i	−0.605225	+	0.107912i
$862$	16.7492	−	0.921819i	0.570481	−	0.0313973i
$863$	49.6075	−	28.6409i	1.68866	−	0.974948i	0.733114	−	0.680106i	$-0.238066\pi$
$863$	49.6075	−	28.6409i	1.68866	−	0.974948i	0.955546	−	0.294842i	$-0.0952671\pi$
$864$	−5.48282	−	1.39237i	−0.186529	−	0.0473693i
$865$	−0.310863	+	0.538430i	−0.0105696	+	0.0183072i
$866$	13.0903	+	20.0420i	0.444825	+	0.681056i
$867$	14.9034			0.506145
$868$	38.1908	+	9.23226i	1.29628	+	0.313363i
$869$	32.9745			1.11858
$870$	2.38403	+	3.65010i	0.0808262	+	0.123750i
$871$	15.1046	−	26.1619i	0.511799	−	0.886462i
$872$	18.0288	+	6.75846i	0.610534	+	0.228870i
$873$	−1.92782	+	1.11302i	−0.0652467	+	0.0376702i
$874$	−20.0457	+	1.10324i	−0.678056	+	0.0373178i
$875$	7.33808	+	8.71126i	0.248072	+	0.294494i
$876$	2.20244	+	19.9483i	0.0744135	+	0.673991i
$877$	−17.0215	−	29.4822i	−0.574777	−	0.995542i	−0.996066	−	0.0886159i	$-0.971756\pi$
$877$	−17.0215	−	29.4822i	−0.574777	−	0.995542i	0.421289	−	0.906926i	$-0.361578\pi$
$878$	−2.96866	−	1.50282i	−0.100187	−	0.0507177i
$879$	−2.79568	−	1.61409i	−0.0942960	−	0.0544418i
$880$	−2.51485	−	2.73481i	−0.0847757	−	0.0921906i
$881$		−	23.4638i		−	0.790514i	−0.918571	−	0.395257i	$-0.870656\pi$
$881$		−	23.4638i		−	0.790514i	0.918571	−	0.395257i	$-0.129344\pi$
$882$	5.90655	−	7.94435i	0.198884	−	0.267500i
$883$		−	8.14468i		−	0.274090i	−0.990565	−	0.137045i	$-0.956239\pi$
$883$		−	8.14468i		−	0.274090i	0.990565	−	0.137045i	$-0.0437606\pi$
$884$	−25.7348	−	35.0333i	−0.865556	−	1.17830i
$885$	−3.08614	−	1.78178i	−0.103740	−	0.0598940i
$886$	−1.02449	+	2.02376i	−0.0344183	+	0.0679896i
$887$	−14.6109	−	25.3068i	−0.490585	−	0.849718i	0.509356	−	0.860556i	$-0.329884\pi$
$887$	−14.6109	−	25.3068i	−0.490585	−	0.849718i	−0.999941	+	0.0108376i	$0.996550\pi$
$888$	2.45523	+	14.7501i	0.0823922	+	0.494981i
$889$	−5.99849	−	7.12099i	−0.201183	−	0.238830i
$890$	−0.355425	−	6.45800i	−0.0119139	−	0.216473i
$891$	−1.83249	+	1.05799i	−0.0613907	+	0.0354439i
$892$	−1.96907	+	4.48574i	−0.0659293	+	0.150194i
$893$	−2.51330	+	4.35317i	−0.0841044	+	0.145673i
$894$	7.67183	−	5.01079i	0.256585	−	0.167586i
$895$	−4.71085			−0.157466
$896$	−1.12867	−	29.9120i	−0.0377062	−	0.999289i
$897$	−18.3566			−0.612908
$898$	−1.60091	+	1.04562i	−0.0534231	+	0.0348928i
$899$	−26.0733	+	45.1603i	−0.869594	+	1.50618i
$900$	3.86452	−	8.80378i	0.128817	−	0.293459i
$901$	52.3985	−	30.2523i	1.74565	−	1.00785i
$902$	1.12120	+	20.3720i	0.0373320	+	0.678314i
$903$	11.4253	−	2.03714i	0.380210	−	0.0677919i
$904$	6.33502	+	38.0584i	0.210700	+	1.26580i
$905$	−0.266506	−	0.461602i	−0.00885896	−	0.0153442i
$906$	−4.96242	+	9.80273i	−0.164865	+	0.325674i
$907$	48.5997	+	28.0591i	1.61373	+	0.931686i	0.988496	+	0.151246i	$0.0483286\pi$
$907$	48.5997	+	28.0591i	1.61373	+	0.931686i	0.625231	+	0.780440i	$0.285005\pi$
$908$	−27.5639	−	37.5232i	−0.914740	−	1.24525i
$909$			0.767851i			0.0254680i
$910$	−6.15168	+	1.44964i	−0.203926	+	0.0480552i
$911$		−	43.1536i		−	1.42974i	−0.699256	−	0.714871i	$-0.746485\pi$
$911$		−	43.1536i		−	1.42974i	0.699256	−	0.714871i	$-0.253515\pi$
$912$	8.05721	+	8.76193i	0.266801	+	0.290137i
$913$	10.0722	+	5.81518i	0.333341	+	0.192454i
$914$	27.9438	+	14.1459i	0.924298	+	0.467906i
$915$	−1.35787	−	2.35190i	−0.0448898	−	0.0777515i
$916$	2.56945	+	23.2724i	0.0848969	+	0.768943i
$917$	48.8047	+	17.6577i	1.61167	+	0.583110i
$918$	−7.97584	+	0.438962i	−0.263242	+	0.0144879i
$919$	−33.3617	+	19.2614i	−1.10050	+	0.635375i	−0.936353	−	0.351060i	$-0.885821\pi$
$919$	−33.3617	+	19.2614i	−1.10050	+	0.635375i	−0.164149	+	0.986435i	$0.552488\pi$
$920$	−5.54590	−	2.07899i	−0.182843	−	0.0685422i
$921$	−2.72762	+	4.72437i	−0.0898780	+	0.155673i
$922$	−23.8067	−	36.4496i	−0.784033	−	1.20040i
$923$	4.50151			0.148169
$924$	−8.10968	−	7.72004i	−0.266789	−	0.253971i
$925$	−25.4148			−0.835635
$926$	10.6814	+	16.3539i	0.351012	+	0.537422i
$927$	−4.31939	+	7.48141i	−0.141867	+	0.245722i
$928$	38.5050	+	9.77839i	1.26399	+	0.320991i
$929$	−41.3034	+	23.8465i	−1.35512	+	0.782379i	−0.988961	−	0.148173i	$-0.952661\pi$
$929$	−41.3034	+	23.8465i	−1.35512	+	0.782379i	−0.366159	+	0.930552i	$0.619327\pi$
$930$	−4.60255	+	0.253308i	−0.150923	+	0.00830629i
$931$	−19.5472	+	7.19947i	−0.640634	+	0.235953i
$932$	16.2384	−	1.79284i	0.531906	−	0.0587263i
$933$	15.2625	+	26.4355i	0.499673	+	0.865460i
$934$	−21.4834	−	10.8755i	−0.702957	−	0.355857i
$935$	−4.54346	−	2.62317i	−0.148587	−	0.0857867i
$936$	6.91574	+	8.40423i	0.226048	+	0.274701i
$937$		−	6.18932i		−	0.202196i	−0.994876	−	0.101098i	$-0.967764\pi$
$937$		−	6.18932i		−	0.202196i	0.994876	−	0.101098i	$-0.0322356\pi$
$938$	21.3918	−	20.1303i	0.698466	−	0.657278i
$939$			18.8324i			0.614573i
$940$	−1.19513	+	0.877924i	−0.0389809	+	0.0286347i
$941$	−6.33052	−	3.65493i	−0.206369	−	0.119147i	0.393254	−	0.919430i	$-0.371349\pi$
$941$	−6.33052	−	3.65493i	−0.206369	−	0.119147i	−0.599623	+	0.800283i	$0.704683\pi$
$942$	−5.40619	+	10.6793i	−0.176143	+	0.347952i
$943$	16.2625	+	28.1676i	0.529581	+	0.917262i
$944$	−31.6906	+	7.08409i	−1.03144	+	0.230568i
$945$	−0.395127	+	1.09210i	−0.0128535	+	0.0355261i
$946$	−0.721329	−	13.1064i	−0.0234524	−	0.426125i
$947$	−13.1805	+	7.60978i	−0.428309	+	0.247285i	−0.698626	−	0.715487i	$-0.746205\pi$
$947$	−13.1805	+	7.60978i	−0.428309	+	0.247285i	0.270317	+	0.962771i	$0.412872\pi$
$948$	−28.5387	−	12.5274i	−0.926895	−	0.406871i
$949$	19.3070	−	33.4407i	0.626732	−	1.08553i
$950$	−16.9386	+	11.0633i	−0.549560	+	0.358940i
$951$	−17.1652			−0.556619
$952$	−14.1512	−	39.8288i	−0.458644	−	1.29086i
$953$	17.5899			0.569792			0.284896	−	0.958558i	$-0.408041\pi$
$953$	17.5899			0.569792			0.284896	+	0.958558i	$0.408041\pi$
$954$	−12.6834	+	8.28403i	−0.410640	+	0.268205i
$955$	−1.43817	+	2.49099i	−0.0465382	+	0.0806066i
$956$	−33.3273	−	14.6294i	−1.07788	−	0.473150i
$957$	12.8693	−	7.43009i	0.416005	−	0.240181i
$958$	2.46985	+	44.8765i	0.0797971	+	1.44990i
$959$	−1.56893	−	8.79930i	−0.0506633	−	0.284144i
$960$	1.13756	+	3.32234i	0.0367146	+	0.107228i
$961$	−12.0674	−	20.9014i	−0.389271	−	0.674238i
$962$	12.9940	−	25.6683i	0.418944	−	0.827579i
$963$	−2.20346	−	1.27217i	−0.0710054	−	0.0409950i
$964$	46.6062	−	34.2361i	1.50109	−	1.10267i
$965$		−	1.42063i		−	0.0457318i
$966$	−17.0927	−	5.14112i	−0.549949	−	0.165413i
$967$			15.0905i			0.485279i	0.970117	+	0.242640i	$0.0780132\pi$
$967$			15.0905i			0.485279i	−0.970117	+	0.242640i	$0.921987\pi$
$968$	14.2457	−	11.7226i	0.457874	−	0.376779i
$969$	14.5566	+	8.40423i	0.467624	+	0.269983i
$970$	1.23292	+	0.624140i	0.0395867	+	0.0200399i
$971$	−22.4660	−	38.9123i	−0.720968	−	1.24875i	−0.960612	−	0.277893i	$-0.910364\pi$
$971$	−22.4660	−	38.9123i	−0.720968	−	1.24875i	0.239644	−	0.970861i	$-0.422969\pi$
$972$	1.98792	−	0.219481i	0.0637626	−	0.00703985i
$973$	−33.2829	+	28.0364i	−1.06700	+	0.898805i
$974$	−8.14757	+	0.448413i	−0.261065	+	0.0143681i
$975$	−16.0203	+	9.24933i	−0.513061	+	0.296216i
$976$	−23.6146	−	7.40005i	−0.755886	−	0.236870i
$977$	−6.04122	+	10.4637i	−0.193276	+	0.334763i	−0.946334	−	0.323191i	$-0.895245\pi$
$977$	−6.04122	+	10.4637i	−0.193276	+	0.334763i	0.753058	+	0.657954i	$0.228578\pi$
$978$	5.37827	+	8.23448i	0.171978	+	0.263310i
$979$	−22.0457			−0.704584
$980$	−6.13413	−	0.373063i	−0.195948	−	0.0119170i
$981$	−6.80731			−0.217341
$982$	17.5118	+	26.8117i	0.558825	+	0.855597i
$983$	8.67473	−	15.0251i	0.276681	−	0.479225i	−0.693877	−	0.720094i	$-0.744099\pi$
$983$	8.67473	−	15.0251i	0.276681	−	0.479225i	0.970558	+	0.240868i	$0.0774322\pi$
$984$	6.76920	−	18.0575i	0.215794	−	0.575652i
$985$	−7.32000	+	4.22620i	−0.233235	+	0.134658i
$986$	56.0131	−	3.08276i	1.78382	−	0.0981752i
$987$	−3.41798	+	2.87919i	−0.108795	+	0.0916456i
$988$	−2.51330	−	22.7639i	−0.0799588	−	0.724216i
$989$	−10.4625	−	18.1216i	−0.332689	−	0.576235i
$990$	1.17196	+	0.593278i	0.0372472	+	0.0188556i
$991$	−42.5136	−	24.5452i	−1.35049	−	0.779705i	−0.362171	−	0.932112i	$-0.617964\pi$
$991$	−42.5136	−	24.5452i	−1.35049	−	0.779705i	−0.988318	+	0.152407i	$0.951298\pi$
$992$	−29.3093	+	30.0878i	−0.930573	+	0.955289i
$993$			21.4868i			0.681864i
$994$	4.19158	+	1.26074i	0.132949	+	0.0399882i
$995$			3.78461i			0.119980i
$996$	−6.50800	−	8.85945i	−0.206214	−	0.280722i
$997$	7.88043	+	4.54977i	0.249576	+	0.144093i	0.619570	−	0.784941i	$-0.287307\pi$
$997$	7.88043	+	4.54977i	0.249576	+	0.144093i	−0.369994	+	0.929034i	$0.620640\pi$
$998$	−12.4190	+	24.5325i	−0.393117	+	0.776562i
$999$	−2.64335	−	4.57842i	−0.0836320	−	0.144855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.o.b.31.1	yes	8
3.2	odd	2		252.2.bf.f.199.4		8
4.3	odd	2		84.2.o.a.31.4	yes	8
7.2	even	3		588.2.o.d.19.4		8
7.3	odd	6		588.2.b.b.391.5		8
7.4	even	3		588.2.b.a.391.5		8
7.5	odd	6		84.2.o.a.19.4	✓	8
7.6	odd	2		588.2.o.b.31.1		8
8.3	odd	2		1344.2.bl.j.703.3		8
8.5	even	2		1344.2.bl.i.703.3		8
12.11	even	2		252.2.bf.g.199.1		8
21.5	even	6		252.2.bf.g.19.1		8
21.11	odd	6		1764.2.b.j.1567.4		8
21.17	even	6		1764.2.b.i.1567.4		8
28.3	even	6		588.2.b.a.391.6		8
28.11	odd	6		588.2.b.b.391.6		8
28.19	even	6	inner	84.2.o.b.19.1	yes	8
28.23	odd	6		588.2.o.b.19.1		8
28.27	even	2		588.2.o.d.31.4		8
56.5	odd	6		1344.2.bl.j.1279.3		8
56.19	even	6		1344.2.bl.i.1279.3		8
84.11	even	6		1764.2.b.i.1567.3		8
84.47	odd	6		252.2.bf.f.19.4		8
84.59	odd	6		1764.2.b.j.1567.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.4	✓	8	7.5	odd	6
84.2.o.a.31.4	yes	8	4.3	odd	2
84.2.o.b.19.1	yes	8	28.19	even	6	inner
84.2.o.b.31.1	yes	8	1.1	even	1	trivial
252.2.bf.f.19.4		8	84.47	odd	6
252.2.bf.f.199.4		8	3.2	odd	2
252.2.bf.g.19.1		8	21.5	even	6
252.2.bf.g.199.1		8	12.11	even	2
588.2.b.a.391.5		8	7.4	even	3
588.2.b.a.391.6		8	28.3	even	6
588.2.b.b.391.5		8	7.3	odd	6
588.2.b.b.391.6		8	28.11	odd	6
588.2.o.b.19.1		8	28.23	odd	6
588.2.o.b.31.1		8	7.6	odd	2
588.2.o.d.19.4		8	7.2	even	3
588.2.o.d.31.4		8	28.27	even	2
1344.2.bl.i.703.3		8	8.5	even	2
1344.2.bl.i.1279.3		8	56.19	even	6
1344.2.bl.j.703.3		8	8.3	odd	2
1344.2.bl.j.1279.3		8	56.5	odd	6
1764.2.b.i.1567.3		8	84.11	even	6
1764.2.b.i.1567.4		8	21.17	even	6
1764.2.b.j.1567.3		8	84.59	odd	6
1764.2.b.j.1567.4		8	21.11	odd	6

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18404 + 0.773342i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.803884 - 1.83133i) q^{4} +(0.380152 - 0.219481i) q^{5} +(0.0777157 + 1.41208i) q^{6} +(2.02350 - 1.70453i) q^{7} +(0.464416 + 2.79004i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.18404 + 0.773342i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.803884 - 1.83133i) q^{4} +(0.380152 - 0.219481i) q^{5} +(0.0777157 + 1.41208i) q^{6} +(2.02350 - 1.70453i) q^{7} +(0.464416 + 2.79004i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.280380 + 0.553861i) q^{10} +(1.83249 + 1.05799i) q^{11} +(-1.18404 - 1.61185i) q^{12} +3.84803i q^{13} +(-1.07772 + 3.58309i) q^{14} -0.438962i q^{15} +(-2.70754 - 2.94435i) q^{16} +(-4.89158 - 2.82415i) q^{17} +(1.26175 + 0.638735i) q^{18} +(-1.48792 - 2.57715i) q^{19} +(-0.0963438 - 0.872621i) q^{20} +(-0.464416 - 2.60467i) q^{21} +(-2.98792 + 0.164445i) q^{22} +(-4.13127 + 2.38519i) q^{23} +(2.64845 + 0.992823i) q^{24} +(-2.40366 + 4.16325i) q^{25} +(-2.97584 - 4.55620i) q^{26} -1.00000 q^{27} +(-1.49490 - 5.07595i) q^{28} +7.02285 q^{29} +(0.339468 + 0.519747i) q^{30} +(-3.71264 + 6.43048i) q^{31} +(5.48282 + 1.39237i) q^{32} +(1.83249 - 1.05799i) q^{33} +(7.97584 - 0.438962i) q^{34} +(0.395127 - 1.09210i) q^{35} +(-1.98792 + 0.219481i) q^{36} +(2.64335 + 4.57842i) q^{37} +(3.75477 + 1.90077i) q^{38} +(3.33249 + 1.92401i) q^{39} +(0.788909 + 0.958709i) q^{40} -6.81813i q^{41} +(2.56419 + 2.72487i) q^{42} +4.38646i q^{43} +(3.41063 - 2.50539i) q^{44} +(-0.380152 - 0.219481i) q^{45} +(3.04701 - 6.01904i) q^{46} +(-0.844569 - 1.46284i) q^{47} +(-3.90366 + 0.872621i) q^{48} +(1.18914 - 6.89826i) q^{49} +(-0.373604 - 6.78829i) q^{50} +(-4.89158 + 2.82415i) q^{51} +(7.04701 + 3.09337i) q^{52} +(-5.35599 + 9.27685i) q^{53} +(1.18404 - 0.773342i) q^{54} +0.928833 q^{55} +(5.69546 + 4.85404i) q^{56} -2.97584 q^{57} +(-8.31531 + 5.43106i) q^{58} +(4.05909 - 7.03055i) q^{59} +(-0.803884 - 0.352875i) q^{60} +(5.35787 - 3.09337i) q^{61} +(-0.577061 - 10.4851i) q^{62} +(-2.48792 - 0.900140i) q^{63} +(-7.56863 + 2.59148i) q^{64} +(0.844569 + 1.46284i) q^{65} +(-1.35155 + 2.66984i) q^{66} +(-6.79878 - 3.92528i) q^{67} +(-9.10422 + 6.68780i) q^{68} +4.77038i q^{69} +(0.376724 + 1.59866i) q^{70} -1.16982i q^{71} +(2.18404 - 1.79722i) q^{72} +(-8.69036 - 5.01738i) q^{73} +(-6.67051 - 3.37680i) q^{74} +(2.40366 + 4.16325i) q^{75} +(-5.91574 + 0.653140i) q^{76} +(5.51142 - 0.982694i) q^{77} +(-5.43371 + 0.299052i) q^{78} +(13.4958 - 7.79180i) q^{79} +(-1.67551 - 0.525049i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.27275 + 8.07291i) q^{82} +5.49645 q^{83} +(-5.14335 - 1.24335i) q^{84} -2.47939 q^{85} +(-3.39223 - 5.19372i) q^{86} +(3.51142 - 6.08197i) q^{87} +(-2.10079 + 5.60406i) q^{88} +(-9.02285 + 5.20934i) q^{89} +(0.619848 - 0.0341142i) q^{90} +(6.55909 + 7.78650i) q^{91} +(1.04701 + 9.48314i) q^{92} +(3.71264 + 6.43048i) q^{93} +(2.13127 + 1.07891i) q^{94} +(-1.13127 - 0.653140i) q^{95} +(3.94724 - 4.05208i) q^{96} -2.22605i q^{97} +(3.92673 + 9.08740i) q^{98} -2.11598i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 + 4 * q^3 - q^4 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 4 * q^9	\( 8 q + q^{2} + 4 q^{3} - q^{4} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 4 q^{9} - 13 q^{10} - 6 q^{11} + q^{12} - 10 q^{14} + 7 q^{16} + q^{18} + 6 q^{19} - 22 q^{20} - 4 q^{21} - 6 q^{22} + 11 q^{24} + 2 q^{25} + 12 q^{26} - 8 q^{27} - 7 q^{28} - 16 q^{29} - 5 q^{30} - 6 q^{31} + 21 q^{32} - 6 q^{33} + 28 q^{34} + 12 q^{35} + 2 q^{36} + 6 q^{37} + 8 q^{38} + 6 q^{39} - 13 q^{40} + 7 q^{42} + 19 q^{44} - 12 q^{46} - 4 q^{47} - 10 q^{48} + 4 q^{49} + 2 q^{50} + 20 q^{52} - 4 q^{53} - q^{54} + 8 q^{55} - q^{56} + 12 q^{57} - 23 q^{58} + 14 q^{59} + q^{60} + 12 q^{61} + 48 q^{62} - 2 q^{63} + 2 q^{64} + 4 q^{65} - 21 q^{66} - 42 q^{67} - 10 q^{68} + 35 q^{70} + 7 q^{72} - 18 q^{73} - 28 q^{74} - 2 q^{75} - 44 q^{76} + 8 q^{77} - 6 q^{78} + 6 q^{79} - 33 q^{80} - 4 q^{81} - 14 q^{82} - 4 q^{83} - 26 q^{84} - 32 q^{85} - 42 q^{86} - 8 q^{87} + 11 q^{88} + 8 q^{90} + 34 q^{91} - 28 q^{92} + 6 q^{93} - 16 q^{94} + 24 q^{95} + 9 q^{96} - 19 q^{98}+O(q^{100}) \) 8 * q + q^2 + 4 * q^3 - q^4 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 4 * q^9 - 13 * q^10 - 6 * q^11 + q^12 - 10 * q^14 + 7 * q^16 + q^18 + 6 * q^19 - 22 * q^20 - 4 * q^21 - 6 * q^22 + 11 * q^24 + 2 * q^25 + 12 * q^26 - 8 * q^27 - 7 * q^28 - 16 * q^29 - 5 * q^30 - 6 * q^31 + 21 * q^32 - 6 * q^33 + 28 * q^34 + 12 * q^35 + 2 * q^36 + 6 * q^37 + 8 * q^38 + 6 * q^39 - 13 * q^40 + 7 * q^42 + 19 * q^44 - 12 * q^46 - 4 * q^47 - 10 * q^48 + 4 * q^49 + 2 * q^50 + 20 * q^52 - 4 * q^53 - q^54 + 8 * q^55 - q^56 + 12 * q^57 - 23 * q^58 + 14 * q^59 + q^60 + 12 * q^61 + 48 * q^62 - 2 * q^63 + 2 * q^64 + 4 * q^65 - 21 * q^66 - 42 * q^67 - 10 * q^68 + 35 * q^70 + 7 * q^72 - 18 * q^73 - 28 * q^74 - 2 * q^75 - 44 * q^76 + 8 * q^77 - 6 * q^78 + 6 * q^79 - 33 * q^80 - 4 * q^81 - 14 * q^82 - 4 * q^83 - 26 * q^84 - 32 * q^85 - 42 * q^86 - 8 * q^87 + 11 * q^88 + 8 * q^90 + 34 * q^91 - 28 * q^92 + 6 * q^93 - 16 * q^94 + 24 * q^95 + 9 * q^96 - 19 * q^98

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