LMFDB - Embedded newform 114.2.l.a.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(29,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17]))

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

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

chi := DirichletCharacter("114.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.l (of order $18$, degree $6$, 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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.2
Root			$-1.73189 + 0.0237018i$ of defining polynomial
Character	$\chi$	$=$	114.89
Dual form			114.2.l.a.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-0.845418 + 1.51171i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.22841 + 0.392929i) q^{5} +(-0.324081 - 1.70146i) q^{6} +(-1.16829 + 2.02354i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.57054 - 2.55605i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.845418 + 1.51171i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.22841 + 0.392929i) q^{5} +(-0.324081 - 1.70146i) q^{6} +(-1.16829 + 2.02354i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.57054 - 2.55605i) q^{9} +(1.45449 - 1.73339i) q^{10} +(-2.52163 + 1.45586i) q^{11} +(1.34194 + 1.09508i) q^{12} +(-0.451929 - 1.24167i) q^{13} +(-0.405743 - 2.30108i) q^{14} +(1.28994 - 3.70090i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.72112 + 4.43466i) q^{17} +(2.84610 + 0.948529i) q^{18} +(-1.79800 + 3.97079i) q^{19} +2.26279i q^{20} +(-2.07131 - 3.47685i) q^{21} +(0.995869 - 2.73613i) q^{22} +(8.06194 + 1.42154i) q^{23} +(-1.73189 + 0.0237018i) q^{24} +(0.112953 - 0.0411116i) q^{25} +(1.14432 + 0.660676i) q^{26} +(5.19177 - 0.213263i) q^{27} +(1.78993 + 1.50193i) q^{28} +(-1.64718 - 1.38215i) q^{29} +(1.39074 + 3.66421i) q^{30} +(5.27928 + 3.04799i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.0690131 - 5.04278i) q^{33} +(-5.70108 - 1.00525i) q^{34} +(1.80832 - 4.96833i) q^{35} +(-2.78994 + 1.10282i) q^{36} -2.98954i q^{37} +(-1.17503 - 4.19754i) q^{38} +(2.25911 + 0.366540i) q^{39} +(-1.45449 - 1.73339i) q^{40} +(-8.52555 - 3.10304i) q^{41} +(3.82159 + 1.33201i) q^{42} +(-0.0666074 - 0.377749i) q^{43} +(0.995869 + 2.73613i) q^{44} +(4.50415 + 5.07883i) q^{45} +(-7.08955 + 4.09315i) q^{46} +(-6.57494 + 7.83571i) q^{47} +(1.31147 - 1.13139i) q^{48} +(0.770194 + 1.33401i) q^{49} +(-0.0601011 + 0.104098i) q^{50} +(-9.84981 + 1.87612i) q^{51} +(-1.30128 + 0.229450i) q^{52} +(0.494197 - 2.80273i) q^{53} +(-3.84005 + 3.50058i) q^{54} +(5.04717 - 4.23508i) q^{55} -2.33658 q^{56} +(-4.48263 - 6.07503i) q^{57} +2.15025 q^{58} +(2.53779 - 2.12946i) q^{59} +(-3.42068 - 1.91300i) q^{60} +(1.01879 - 5.77787i) q^{61} +(-6.00337 + 1.05856i) q^{62} +(7.00712 - 0.191828i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.49497 + 2.58936i) q^{65} +(3.29431 + 3.81864i) q^{66} +(-10.4361 + 12.4373i) q^{67} +(5.01345 - 2.89452i) q^{68} +(-8.96466 + 10.9855i) q^{69} +(1.80832 + 4.96833i) q^{70} +(-2.29622 - 13.0225i) q^{71} +(1.42834 - 2.63815i) q^{72} +(5.84733 + 2.12826i) q^{73} +(1.92164 + 2.29012i) q^{74} +(-0.0333438 + 0.205509i) q^{75} +(3.59825 + 2.46020i) q^{76} -6.80348i q^{77} +(-1.96618 + 1.17134i) q^{78} +(1.77569 - 4.87866i) q^{79} +(2.22841 + 0.392929i) q^{80} +(-4.06683 + 8.02876i) q^{81} +(8.52555 - 3.10304i) q^{82} +(1.62533 + 0.938386i) q^{83} +(-3.78371 + 1.43609i) q^{84} +(-10.0347 - 8.42009i) q^{85} +(0.293837 + 0.246558i) q^{86} +(3.48197 - 1.32157i) q^{87} +(-2.52163 - 1.45586i) q^{88} +(5.82289 - 2.11936i) q^{89} +(-6.71498 - 0.995397i) q^{90} +(3.04054 + 0.536130i) q^{91} +(2.79988 - 7.69261i) q^{92} +(-9.07088 + 5.40391i) q^{93} -10.2288i q^{94} +(2.44644 - 9.55504i) q^{95} +(-0.277398 + 1.70969i) q^{96} +(6.13336 + 7.30946i) q^{97} +(-1.44749 - 0.526843i) q^{98} +(7.68157 + 4.15893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) $ 18 * q + 3 * q^6 + 9 * q^8	$ 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) $ 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−0.845418	+	1.51171i	−0.488102	+	0.872786i
$3$	−0.845418	+	1.51171i	−0.488102	+	0.872786i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−2.22841	+	0.392929i	−0.996575	+	0.175723i	−0.648067	−	0.761583i	$-0.724423\pi$
$5$	−2.22841	+	0.392929i	−0.996575	+	0.175723i	−0.348508	+	0.937306i	$0.613311\pi$
$6$	−0.324081	−	1.70146i	−0.132306	−	0.694619i
$7$	−1.16829	+	2.02354i	−0.441572	+	0.764826i	−0.997806	−	0.0661999i	$-0.978912\pi$
$7$	−1.16829	+	2.02354i	−0.441572	+	0.764826i	0.556234	+	0.831026i	$0.312246\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.57054	−	2.55605i	−0.523512	−	0.852018i
$10$	1.45449	−	1.73339i	0.459950	−	0.548148i
$11$	−2.52163	+	1.45586i	−0.760299	+	0.438959i	−0.829403	−	0.558650i	$-0.811319\pi$
$11$	−2.52163	+	1.45586i	−0.760299	+	0.438959i	0.0691039	+	0.997609i	$0.477986\pi$
$12$	1.34194	+	1.09508i	0.387384	+	0.316122i
$13$	−0.451929	−	1.24167i	−0.125343	−	0.344376i	0.861111	−	0.508417i	$-0.169769\pi$
$13$	−0.451929	−	1.24167i	−0.125343	−	0.344376i	−0.986453	+	0.164041i	$0.947547\pi$
$14$	−0.405743	−	2.30108i	−0.108439	−	0.614990i
$15$	1.28994	−	3.70090i	0.333062	−	0.955568i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.72112	+	4.43466i	0.902504	+	1.07556i	0.996793	+	0.0800172i	$0.0254975\pi$
$17$	3.72112	+	4.43466i	0.902504	+	1.07556i	−0.0942898	+	0.995545i	$0.530058\pi$
$18$	2.84610	+	0.948529i	0.670832	+	0.223571i
$19$	−1.79800	+	3.97079i	−0.412489	+	0.910962i
$19$	−1.79800	+	3.97079i	−0.412489	+	0.910962i
$20$			2.26279i			0.505974i
$21$	−2.07131	−	3.47685i	−0.451997	−	0.758712i
$22$	0.995869	−	2.73613i	0.212320	−	0.583344i
$23$	8.06194	+	1.42154i	1.68103	+	0.296411i	0.931007	−	0.365001i	$-0.118931\pi$
$23$	8.06194	+	1.42154i	1.68103	+	0.296411i	0.750023	+	0.661412i	$0.230042\pi$
$24$	−1.73189	+	0.0237018i	−0.353520	+	0.00483811i
$25$	0.112953	−	0.0411116i	0.0225906	−	0.00822231i
$26$	1.14432	+	0.660676i	0.224421	+	0.129569i
$27$	5.19177	−	0.213263i	0.999157	−	0.0410425i
$28$	1.78993	+	1.50193i	0.338264	+	0.283837i
$29$	−1.64718	−	1.38215i	−0.305875	−	0.256659i	0.476910	−	0.878952i	$-0.341757\pi$
$29$	−1.64718	−	1.38215i	−0.305875	−	0.256659i	−0.782784	+	0.622293i	$0.786201\pi$
$30$	1.39074	+	3.66421i	0.253913	+	0.668991i
$31$	5.27928	+	3.04799i	0.948186	+	0.547436i	0.892517	−	0.451014i	$-0.148937\pi$
$31$	5.27928	+	3.04799i	0.948186	+	0.547436i	0.0556692	+	0.998449i	$0.482271\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−0.0690131	−	5.04278i	−0.0120136	−	0.877836i
$34$	−5.70108	−	1.00525i	−0.977728	−	0.172400i
$35$	1.80832	−	4.96833i	0.305662	−	0.839801i
$36$	−2.78994	+	1.10282i	−0.464990	+	0.183804i
$37$		−	2.98954i		−	0.491477i	−0.969336	−	0.245738i	$-0.920970\pi$
$37$		−	2.98954i		−	0.491477i	0.969336	−	0.245738i	$-0.0790304\pi$
$38$	−1.17503	−	4.19754i	−0.190615	−	0.680930i
$39$	2.25911	+	0.366540i	0.361747	+	0.0586934i
$40$	−1.45449	−	1.73339i	−0.229975	−	0.274074i
$41$	−8.52555	−	3.10304i	−1.33147	−	0.484614i	−0.424352	−	0.905497i	$-0.639498\pi$
$41$	−8.52555	−	3.10304i	−1.33147	−	0.484614i	−0.907115	+	0.420883i	$0.861720\pi$
$42$	3.82159	+	1.33201i	0.589685	+	0.205534i
$43$	−0.0666074	−	0.377749i	−0.0101575	−	0.0576062i	0.979308	−	0.202377i	$-0.0648666\pi$
$43$	−0.0666074	−	0.377749i	−0.0101575	−	0.0576062i	−0.989465	+	0.144771i	$0.953756\pi$
$44$	0.995869	+	2.73613i	0.150133	+	0.412487i
$45$	4.50415	+	5.07883i	0.671439	+	0.757107i
$46$	−7.08955	+	4.09315i	−1.04530	+	0.603502i
$47$	−6.57494	+	7.83571i	−0.959054	+	1.14296i	0.0306076	+	0.999531i	$0.490256\pi$
$47$	−6.57494	+	7.83571i	−0.959054	+	1.14296i	−0.989661	+	0.143424i	$0.954189\pi$
$48$	1.31147	−	1.13139i	0.189294	−	0.163303i
$49$	0.770194	+	1.33401i	0.110028	+	0.190574i
$50$	−0.0601011	+	0.104098i	−0.00849958	+	0.0147217i
$51$	−9.84981	+	1.87612i	−1.37925	+	0.262709i
$52$	−1.30128	+	0.229450i	−0.180455	+	0.0318191i
$53$	0.494197	−	2.80273i	0.0678832	−	0.384985i	−0.931870	−	0.362791i	$-0.881824\pi$
$53$	0.494197	−	2.80273i	0.0678832	−	0.384985i	0.999754	−	0.0221937i	$-0.00706506\pi$
$54$	−3.84005	+	3.50058i	−0.522564	+	0.476368i
$55$	5.04717	−	4.23508i	0.680560	−	0.571058i
$56$	−2.33658			−0.312239
$57$	−4.48263	−	6.07503i	−0.593739	−	0.804658i
$58$	2.15025			0.282341
$59$	2.53779	−	2.12946i	0.330392	−	0.277232i	−0.462468	−	0.886636i	$-0.653036\pi$
$59$	2.53779	−	2.12946i	0.330392	−	0.277232i	0.792860	+	0.609404i	$0.208591\pi$
$60$	−3.42068	−	1.91300i	−0.441608	−	0.246967i
$61$	1.01879	−	5.77787i	0.130443	−	0.739780i	−0.847482	−	0.530824i	$-0.821882\pi$
$61$	1.01879	−	5.77787i	0.130443	−	0.739780i	0.977925	−	0.208956i	$-0.0670064\pi$
$62$	−6.00337	+	1.05856i	−0.762429	+	0.134437i
$63$	7.00712	−	0.191828i	0.882814	−	0.0241681i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.49497	+	2.58936i	0.185428	+	0.321171i
$66$	3.29431	+	3.81864i	0.405501	+	0.470042i
$67$	−10.4361	+	12.4373i	−1.27497	+	1.51945i	−0.539305	+	0.842111i	$0.681313\pi$
$67$	−10.4361	+	12.4373i	−1.27497	+	1.51945i	−0.735668	+	0.677342i	$0.763132\pi$
$68$	5.01345	−	2.89452i	0.607970	−	0.351012i
$69$	−8.96466	+	10.9855i	−1.07922	+	1.32250i
$70$	1.80832	+	4.96833i	0.216136	+	0.593829i
$71$	−2.29622	−	13.0225i	−0.272511	−	1.54549i	−0.746758	−	0.665095i	$-0.768391\pi$
$71$	−2.29622	−	13.0225i	−0.272511	−	1.54549i	0.474247	−	0.880392i	$-0.342720\pi$
$72$	1.42834	−	2.63815i	0.168331	−	0.310909i
$73$	5.84733	+	2.12826i	0.684379	+	0.249093i	0.660726	−	0.750627i	$-0.270248\pi$
$73$	5.84733	+	2.12826i	0.684379	+	0.249093i	0.0236522	+	0.999720i	$0.492471\pi$
$74$	1.92164	+	2.29012i	0.223386	+	0.266221i
$75$	−0.0333438	+	0.205509i	−0.00385021	+	0.0237301i
$76$	3.59825	+	2.46020i	0.412747	+	0.282205i
$77$		−	6.80348i		−	0.775329i
$78$	−1.96618	+	1.17134i	−0.222627	+	0.132628i
$79$	1.77569	−	4.87866i	0.199781	−	0.548893i	−0.798832	−	0.601554i	$-0.794548\pi$
$79$	1.77569	−	4.87866i	0.199781	−	0.548893i	0.998612	+	0.0526618i	$0.0167705\pi$
$80$	2.22841	+	0.392929i	0.249144	+	0.0439308i
$81$	−4.06683	+	8.02876i	−0.451870	+	0.892084i
$82$	8.52555	−	3.10304i	0.941489	−	0.342674i
$83$	1.62533	+	0.938386i	0.178403	+	0.103001i	0.586542	−	0.809919i	$-0.300489\pi$
$83$	1.62533	+	0.938386i	0.178403	+	0.103001i	−0.408139	+	0.912920i	$0.633822\pi$
$84$	−3.78371	+	1.43609i	−0.412837	+	0.156691i
$85$	−10.0347	−	8.42009i	−1.08841	−	0.913288i
$86$	0.293837	+	0.246558i	0.0316852	+	0.0265871i
$87$	3.48197	−	1.32157i	0.373307	−	0.141687i
$88$	−2.52163	−	1.45586i	−0.268806	−	0.155195i
$89$	5.82289	−	2.11936i	0.617225	−	0.224651i	−0.0144367	−	0.999896i	$-0.504595\pi$
$89$	5.82289	−	2.11936i	0.617225	−	0.224651i	0.631661	+	0.775244i	$0.282373\pi$
$90$	−6.71498	−	0.995397i	−0.707821	−	0.104924i
$91$	3.04054	+	0.536130i	0.318735	+	0.0562017i
$92$	2.79988	−	7.69261i	0.291908	−	0.802010i
$93$	−9.07088	+	5.40391i	−0.940606	+	0.560360i
$94$		−	10.2288i		−	1.05502i
$95$	2.44644	−	9.55504i	0.251000	−	0.980326i
$96$	−0.277398	+	1.70969i	−0.0283118	+	0.174495i
$97$	6.13336	+	7.30946i	0.622748	+	0.742163i	0.981540	−	0.191255i	$-0.0612557\pi$
$97$	6.13336	+	7.30946i	0.622748	+	0.742163i	−0.358792	+	0.933418i	$0.616811\pi$
$98$	−1.44749	−	0.526843i	−0.146219	−	0.0532192i
$99$	7.68157	+	4.15893i	0.772027	+	0.417988i
$100$	−0.0208729	−	0.118376i	−0.00208729	−	0.0118376i
$101$	4.28105	+	11.7621i	0.425980	+	1.17037i	0.948232	+	0.317580i	$0.102870\pi$
$101$	4.28105	+	11.7621i	0.425980	+	1.17037i	−0.522251	+	0.852792i	$0.674908\pi$
$102$	6.33945	−	7.76853i	0.627699	−	0.769199i
$103$	7.59279	−	4.38370i	0.748140	−	0.431939i	−0.0768818	−	0.997040i	$-0.524496\pi$
$103$	7.59279	−	4.38370i	0.748140	−	0.431939i	0.825021	+	0.565102i	$0.191163\pi$
$104$	0.849349	−	1.01221i	0.0832855	−	0.0992558i
$105$	5.98188	+	6.93398i	0.583772	+	0.676687i
$106$	1.42298	+	2.46468i	0.138212	+	0.239391i
$107$	−4.04583	+	7.00758i	−0.391125	+	0.677449i	−0.992598	−	0.121444i	$-0.961247\pi$
$107$	−4.04583	+	7.00758i	−0.391125	+	0.677449i	0.601473	+	0.798893i	$0.294581\pi$
$108$	0.691519	−	5.14993i	0.0665415	−	0.495552i
$109$	7.26213	−	1.28051i	0.695586	−	0.122651i	0.185334	−	0.982676i	$-0.440663\pi$
$109$	7.26213	−	1.28051i	0.695586	−	0.122651i	0.510252	+	0.860025i	$0.329552\pi$
$110$	−1.14410	+	6.48852i	−0.109086	+	0.618656i
$111$	4.51931	+	2.52741i	0.428954	+	0.239891i
$112$	1.78993	−	1.50193i	0.169132	−	0.141919i
$113$	14.8779			1.39960			0.699799	−	0.714340i	$-0.253273\pi$
$113$	14.8779			1.39960			0.699799	+	0.714340i	$0.253273\pi$
$114$	7.33885	+	1.77237i	0.687346	+	0.165998i
$115$	−18.5239			−1.72736
$116$	−1.64718	+	1.38215i	−0.152937	+	0.128330i
$117$	−2.46399	+	3.10524i	−0.227796	+	0.287079i
$118$	−0.575270	+	3.26252i	−0.0529579	+	0.300339i
$119$	−13.3210	+	2.34886i	−1.22114	+	0.215320i
$120$	3.85004	−	0.733326i	0.351459	−	0.0669432i
$121$	−1.26093	+	2.18399i	−0.114630	+	0.198545i
$122$	2.93350	+	5.08097i	0.265587	+	0.460009i
$123$	11.8986	−	10.2648i	1.07286	−	0.925545i
$124$	3.91842	−	4.66980i	0.351885	−	0.419360i
$125$	9.56260	−	5.52097i	0.855305	−	0.493811i
$126$	−5.24446	+	4.65104i	−0.467214	+	0.414347i
$127$	−2.54056	−	6.98012i	−0.225438	−	0.619386i	0.774475	−	0.632605i	$-0.218014\pi$
$127$	−2.54056	−	6.98012i	−0.225438	−	0.619386i	−0.999913	+	0.0132192i	$0.995792\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	0.627359	+	0.218665i	0.0552358	+	0.0192524i
$130$	−2.80962	−	1.02262i	−0.246420	−	0.0896896i
$131$	11.4406	+	13.6344i	0.999574	+	1.19125i	0.981510	+	0.191409i	$0.0613057\pi$
$131$	11.4406	+	13.6344i	0.999574	+	1.19125i	0.0180637	+	0.999837i	$0.494250\pi$
$132$	−4.97816	−	0.807705i	−0.433293	−	0.0703017i
$133$	−5.93447	−	8.27736i	−0.514584	−	0.717738i
$134$		−	16.2357i		−	1.40255i
$135$	−11.4856	+	2.51523i	−0.988523	+	0.216477i
$136$	−1.97997	+	5.43991i	−0.169781	+	0.466468i
$137$	−16.1747	−	2.85204i	−1.38190	−	0.243666i	−0.567215	−	0.823570i	$-0.691979\pi$
$137$	−16.1747	−	2.85204i	−1.38190	−	0.243666i	−0.814685	+	0.579904i	$0.803090\pi$
$138$	−0.194030	−	14.1778i	−0.0165169	−	1.20689i
$139$	−18.1680	+	6.61260i	−1.54099	+	0.560873i	−0.966282	−	0.257487i	$-0.917106\pi$
$139$	−18.1680	+	6.61260i	−1.54099	+	0.560873i	−0.574705	+	0.818360i	$0.694883\pi$
$140$	−4.57884	−	2.64359i	−0.386982	−	0.223424i
$141$	−6.28675	−	16.5639i	−0.529440	−	1.39493i
$142$	10.1297	+	8.49984i	0.850067	+	0.713290i
$143$	2.94729	+	2.47307i	0.246465	+	0.206809i
$144$	0.601600	+	2.93906i	0.0501333	+	0.244922i
$145$	4.21369	+	2.43277i	0.349928	+	0.202031i
$146$	−5.84733	+	2.12826i	−0.483929	+	0.176136i
$147$	−2.66778	+	0.0365100i	−0.220035	+	0.00301129i
$148$	−2.94412	−	0.519128i	−0.242005	−	0.0426720i
$149$	2.20295	−	6.05256i	0.180473	−	0.495845i	−0.816161	−	0.577824i	$-0.803902\pi$
$149$	2.20295	−	6.05256i	0.180473	−	0.495845i	0.996634	+	0.0819794i	$0.0261242\pi$
$150$	−0.106556	−	0.178862i	−0.00870024	−	0.0146040i
$151$			3.02833i			0.246442i	0.992379	+	0.123221i	$0.0393223\pi$
$151$			3.02833i			0.246442i	−0.992379	+	0.123221i	$0.960678\pi$
$152$	−4.33781	+	0.428283i	−0.351843	+	0.0347384i
$153$	5.49107	−	16.4762i	0.443926	−	1.33202i
$154$	4.37319	+	5.21177i	0.352402	+	0.419976i
$155$	−12.9620	−	4.71780i	−1.04114	−	0.378942i
$156$	0.753261	−	2.16114i	0.0603092	−	0.173029i
$157$	3.32082	+	18.8333i	0.265030	+	1.50306i	0.768949	+	0.639311i	$0.220780\pi$
$157$	3.32082	+	18.8333i	0.265030	+	1.50306i	−0.503918	+	0.863751i	$0.668109\pi$
$158$	1.77569	+	4.87866i	0.141266	+	0.388126i
$159$	3.81912	+	3.11656i	0.302876	+	0.247160i
$160$	−1.95963	+	1.13139i	−0.154922	+	0.0894445i
$161$	−12.2952	+	14.6529i	−0.968999	+	1.15481i
$162$	−2.04541	−	8.76449i	−0.160703	−	0.688603i
$163$	−3.09435	−	5.35958i	−0.242368	−	0.419794i	0.719020	−	0.694989i	$-0.244591\pi$
$163$	−3.09435	−	5.35958i	−0.242368	−	0.419794i	−0.961388	+	0.275195i	$0.911258\pi$
$164$	−4.53635	+	7.85718i	−0.354229	+	0.613543i
$165$	2.13524	+	11.2103i	0.166229	+	0.872718i
$166$	−1.84826	+	0.325898i	−0.143453	+	0.0252946i
$167$	−0.758731	+	4.30298i	−0.0587124	+	0.332975i	−0.999989	−	0.00466148i	$-0.998516\pi$
$167$	−0.758731	+	4.30298i	−0.0587124	+	0.332975i	0.941277	+	0.337636i	$0.109627\pi$
$168$	1.97539	−	3.53223i	0.152404	−	0.272518i
$169$	8.62108	−	7.23395i	0.663160	−	0.556458i
$170$	13.0993			1.00467
$171$	12.9734	−	1.64049i	0.992100	−	0.125452i
$172$	−0.383577			−0.0292474
$173$	−11.4117	+	9.57556i	−0.867616	+	0.728016i	−0.963595	−	0.267367i	$-0.913846\pi$
$173$	−11.4117	+	9.57556i	−0.867616	+	0.728016i	0.0959786	+	0.995383i	$0.469402\pi$
$174$	−1.81786	+	3.25055i	−0.137811	+	0.246424i
$175$	−0.0487712	+	0.276595i	−0.00368676	+	0.0209086i
$176$	2.86749	−	0.505616i	0.216145	−	0.0381122i
$177$	1.07363	+	5.63668i	0.0806991	+	0.423679i
$178$	−3.09829	+	5.36640i	−0.232227	+	0.402229i
$179$	−1.68012	−	2.91005i	−0.125578	−	0.217507i	0.796381	−	0.604796i	$-0.206745\pi$
$179$	−1.68012	−	2.91005i	−0.125578	−	0.217507i	−0.921959	+	0.387288i	$0.873412\pi$
$180$	5.78380	−	3.55379i	0.431099	−	0.264884i
$181$	12.7706	−	15.2194i	0.949231	−	1.13125i	−0.0420013	−	0.999118i	$-0.513373\pi$
$181$	12.7706	−	15.2194i	0.949231	−	1.13125i	0.991232	−	0.132132i	$-0.0421822\pi$
$182$	−2.67381	+	1.54372i	−0.198196	+	0.114428i
$183$	7.87315	+	6.42483i	0.582000	+	0.474937i
$184$	2.79988	+	7.69261i	0.206410	+	0.567107i
$185$	1.17467	+	6.66191i	0.0863638	+	0.489794i
$186$	3.47513	−	9.97028i	0.254809	−	0.731057i
$187$	−15.8395	−	5.76511i	−1.15830	−	0.421587i
$188$	6.57494	+	7.83571i	0.479527	+	0.571478i
$189$	−5.63396	+	10.7549i	−0.409810	+	0.782305i
$190$	4.26778	+	8.89213i	0.309617	+	0.645103i
$191$			10.2346i			0.740548i	0.928923	+	0.370274i	$0.120736\pi$
$191$			10.2346i			0.740548i	−0.928923	+	0.370274i	$0.879264\pi$
$192$	−0.886471	−	1.48801i	−0.0639755	−	0.107388i
$193$	−0.784644	+	2.15579i	−0.0564799	+	0.155177i	−0.964724	−	0.263264i	$-0.915201\pi$
$193$	−0.784644	+	2.15579i	−0.0564799	+	0.155177i	0.908244	+	0.418441i	$0.137423\pi$
$194$	−9.39685	−	1.65692i	−0.674655	−	0.118960i
$195$	−5.17824	+	0.0708669i	−0.370822	+	0.00507489i
$196$	1.44749	−	0.526843i	0.103392	−	0.0376317i
$197$	−5.46822	−	3.15708i	−0.389595	−	0.224933i	0.292390	−	0.956299i	$-0.405550\pi$
$197$	−5.46822	−	3.15708i	−0.389595	−	0.224933i	−0.681984	+	0.731367i	$0.738883\pi$
$198$	−8.55774	+	1.75169i	−0.608172	+	0.124487i
$199$	−7.96251	−	6.68134i	−0.564447	−	0.473628i	0.315351	−	0.948975i	$-0.397878\pi$
$199$	−7.96251	−	6.68134i	−0.564447	−	0.473628i	−0.879798	+	0.475348i	$0.842322\pi$
$200$	0.0920802	+	0.0772645i	0.00651105	+	0.00546342i
$201$	−9.97867	−	26.2910i	−0.703841	−	1.85443i
$202$	−10.8400	−	6.25847i	−0.762699	−	0.440345i
$203$	4.72123	−	1.71839i	0.331365	−	0.120607i
$204$	0.137210	+	10.0260i	0.00960666	+	0.701957i
$205$	20.2177	+	3.56492i	1.41206	+	0.248985i
$206$	−2.99863	+	8.23866i	−0.208924	+	0.574014i
$207$	−9.02805	−	22.8393i	−0.627493	−	1.58744i
$208$			1.32135i			0.0916193i
$209$	−1.24704	−	12.6305i	−0.0862598	−	0.873670i
$210$	−9.03946	−	1.46665i	−0.623782	−	0.101209i
$211$	−3.58388	−	4.27111i	−0.246725	−	0.294035i	0.628442	−	0.777856i	$-0.283693\pi$
$211$	−3.58388	−	4.27111i	−0.246725	−	0.294035i	−0.875167	+	0.483821i	$0.839248\pi$
$212$	−2.67434	−	0.973379i	−0.183674	−	0.0668519i
$213$	21.6275	+	7.53824i	1.48189	+	0.516512i
$214$	−1.40510	−	7.96873i	−0.0960508	−	0.544731i
$215$	0.296857	+	0.815608i	0.0202455	+	0.0556240i
$216$	2.78058	+	4.38958i	0.189194	+	0.298673i
$217$	−12.3355	+	7.12188i	−0.837386	+	0.483465i
$218$	−4.74002	+	5.64893i	−0.321034	+	0.382594i
$219$	−8.16075	+	7.04021i	−0.551452	+	0.475733i
$220$	−3.29431	−	5.70590i	−0.222102	−	0.384692i
$221$	3.82468	−	6.62453i	0.257276	−	0.445614i
$222$	−5.08658	+	0.968852i	−0.341389	+	0.0650251i
$223$	5.10735	−	0.900564i	0.342014	−	0.0603062i	−3.40741e−6	−	1.00000i	$-0.500001\pi$
$223$	5.10735	−	0.900564i	0.342014	−	0.0603062i	0.342017	+	0.939694i	$0.388890\pi$
$224$	−0.405743	+	2.30108i	−0.0271099	+	0.153748i
$225$	−0.282480	−	0.224147i	−0.0188320	−	0.0149431i
$226$	−11.3972	+	9.56335i	−0.758128	+	0.636145i
$227$	17.0369			1.13078			0.565391	−	0.824823i	$-0.308725\pi$
$227$	17.0369			1.13078			0.565391	+	0.824823i	$0.308725\pi$
$228$	−6.76114	+	3.35961i	−0.447768	+	0.222495i
$229$	24.5203			1.62035			0.810173	−	0.586191i	$-0.199373\pi$
$229$	24.5203			1.62035			0.810173	+	0.586191i	$0.199373\pi$
$230$	14.1901	−	11.9069i	0.935668	−	0.785118i
$231$	10.2849	+	5.75179i	0.676696	+	0.378440i
$232$	0.373386	−	2.11758i	0.0245140	−	0.139026i
$233$	22.4936	−	3.96623i	1.47360	−	0.259836i	0.621585	−	0.783346i	$-0.286489\pi$
$233$	22.4936	−	3.96623i	1.47360	−	0.259836i	0.852019	+	0.523510i	$0.175378\pi$
$234$	−0.108480	−	3.96257i	−0.00709157	−	0.259042i
$235$	11.5728	−	20.0447i	0.754925	−	1.30757i
$236$	−1.65642	−	2.86901i	−0.107824	−	0.186757i
$237$	5.87393	+	6.80884i	0.381553	+	0.442282i
$238$	8.69469	−	10.3619i	0.563593	−	0.671664i
$239$	−2.62883	+	1.51775i	−0.170045	+	0.0981753i	−0.582607	−	0.812754i	$-0.697967\pi$
$239$	−2.62883	+	1.51775i	−0.170045	+	0.0981753i	0.412562	+	0.910929i	$0.364634\pi$
$240$	−2.47793	+	3.03652i	−0.159950	+	0.196007i
$241$	−1.35157	−	3.71341i	−0.0870624	−	0.239202i	0.888519	−	0.458840i	$-0.151735\pi$
$241$	−1.35157	−	3.71341i	−0.0870624	−	0.239202i	−0.975582	+	0.219638i	$0.929512\pi$
$242$	−0.437916	−	2.48355i	−0.0281503	−	0.159648i
$243$	−8.69898	−	12.9355i	−0.558040	−	0.829814i
$244$	−5.51318	−	2.00663i	−0.352945	−	0.128461i
$245$	−2.24048	−	2.67010i	−0.143139	−	0.170586i
$246$	−2.51674	+	15.5115i	−0.160462	+	0.988979i
$247$	5.74296	+	0.437996i	0.365416	+	0.0278690i
$248$			6.09598i			0.387095i
$249$	−2.79265	+	1.66370i	−0.176977	+	0.105433i
$250$	−3.77657	+	10.3760i	−0.238851	+	0.656238i
$251$	−7.14276	−	1.25946i	−0.450847	−	0.0794965i	−0.0563857	−	0.998409i	$-0.517958\pi$
$251$	−7.14276	−	1.25946i	−0.450847	−	0.0794965i	−0.394461	+	0.918913i	$0.629069\pi$
$252$	1.02786	−	6.93398i	0.0647491	−	0.436799i
$253$	−22.3988	+	8.15248i	−1.40820	+	0.512542i
$254$	6.43292	+	3.71405i	0.403637	+	0.233040i
$255$	21.2122	−	8.05103i	1.32836	−	0.504175i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−7.10091	−	5.95837i	−0.442942	−	0.371673i	0.393867	−	0.919168i	$-0.371137\pi$
$257$	−7.10091	−	5.95837i	−0.442942	−	0.371673i	−0.836809	+	0.547495i	$0.815582\pi$
$258$	−0.621140	+	0.235751i	−0.0386705	+	0.0146772i
$259$	6.04944	+	3.49265i	0.375894	+	0.217023i
$260$	2.80962	−	1.02262i	0.174245	−	0.0634202i
$261$	−0.945891	+	6.38102i	−0.0585492	+	0.394975i
$262$	−17.5281	−	3.09067i	−1.08289	−	0.190943i
$263$	−1.21399	+	3.33541i	−0.0748578	+	0.205670i	−0.971478	−	0.237131i	$-0.923793\pi$
$263$	−1.21399	+	3.33541i	−0.0748578	+	0.205670i	0.896620	+	0.442801i	$0.146015\pi$
$264$	4.33267	−	2.58116i	0.266658	−	0.158859i
$265$			6.43982i			0.395595i
$266$	9.86665	+	2.52623i	0.604963	+	0.154893i
$267$	−1.71892	+	10.5943i	−0.105196	+	0.648358i
$268$	10.4361	+	12.4373i	0.637486	+	0.759727i
$269$	4.70855	+	1.71377i	0.287086	+	0.104491i	0.481549	−	0.876419i	$-0.340074\pi$
$269$	4.70855	+	1.71377i	0.287086	+	0.104491i	−0.194463	+	0.980910i	$0.562297\pi$
$270$	7.18172	−	9.30958i	0.437066	−	0.566563i
$271$	−1.60600	−	9.10806i	−0.0975574	−	0.553275i	−0.993934	−	0.109981i	$-0.964921\pi$
$271$	−1.60600	−	9.10806i	−0.0975574	−	0.553275i	0.896376	−	0.443294i	$-0.146190\pi$
$272$	−1.97997	−	5.43991i	−0.120053	−	0.329843i
$273$	−3.38100	+	4.14317i	−0.204628	+	0.250756i
$274$	14.2238	−	8.21212i	0.859292	−	0.496112i
$275$	−0.224973	+	0.268112i	−0.0135664	+	0.0161678i
$276$	9.26193	+	10.7361i	0.557503	+	0.646236i
$277$	3.80040	+	6.58248i	0.228344	+	0.395503i	0.957317	−	0.289039i	$-0.0933356\pi$
$277$	3.80040	+	6.58248i	0.228344	+	0.395503i	−0.728974	+	0.684542i	$0.760002\pi$
$278$	9.66698	−	16.7437i	0.579787	−	1.00422i
$279$	−0.500467	−	18.2811i	−0.0299622	−	1.09446i
$280$	5.20686	−	0.918110i	0.311169	−	0.0548676i
$281$	−2.50185	+	14.1887i	−0.149248	+	0.846425i	0.814610	+	0.580009i	$0.196951\pi$
$281$	−2.50185	+	14.1887i	−0.149248	+	0.846425i	−0.963858	+	0.266417i	$0.914160\pi$
$282$	15.4630	+	8.64760i	0.920807	+	0.514957i
$283$	7.59307	−	6.37134i	0.451361	−	0.378737i	−0.388579	−	0.921415i	$-0.627034\pi$
$283$	7.59307	−	6.37134i	0.451361	−	0.378737i	0.839941	+	0.542678i	$0.182590\pi$
$284$	−13.2234			−0.784664
$285$	12.3762	+	11.7763i	0.733102	+	0.697568i
$286$	−3.84742			−0.227502
$287$	16.2394	−	13.6265i	0.958584	−	0.804348i
$288$	−2.35004	−	1.86475i	−0.138478	−	0.109881i
$289$	−2.86743	+	16.2620i	−0.168673	+	0.956589i
$290$	−4.79163	+	0.844894i	−0.281374	+	0.0496139i
$291$	−16.2350	+	3.09232i	−0.951715	+	0.181275i
$292$	3.11130	−	5.38893i	0.182075	−	0.315363i
$293$	4.11218	+	7.12251i	0.240236	+	0.416102i	0.960782	−	0.277306i	$-0.0894417\pi$
$293$	4.11218	+	7.12251i	0.240236	+	0.416102i	−0.720545	+	0.693408i	$0.756108\pi$
$294$	2.02017	−	1.74278i	0.117819	−	0.101641i
$295$	−4.81851	+	5.74247i	−0.280544	+	0.334340i
$296$	2.58901	−	1.49477i	0.150483	−	0.0868816i
$297$	−12.7812	+	8.09628i	−0.741643	+	0.469794i
$298$	2.20295	+	6.05256i	0.127614	+	0.350615i
$299$	−1.87835	−	10.6527i	−0.108628	−	0.616059i
$300$	0.196597	+	0.0685235i	0.0113505	+	0.00395620i
$301$	0.842207	+	0.306538i	0.0485440	+	0.0176686i
$302$	−1.94657	−	2.31983i	−0.112013	−	0.133491i
$303$	−21.4001	−	3.47217i	−1.22941	−	0.199471i
$304$	3.04766	−	3.11637i	0.174795	−	0.178736i
$305$			13.2758i			0.760168i
$306$	6.38428	+	16.1511i	0.364965	+	0.923295i
$307$	−3.47152	+	9.53794i	−0.198130	+	0.544359i	−0.998476	−	0.0551795i	$-0.982427\pi$
$307$	−3.47152	+	9.53794i	−0.198130	+	0.544359i	0.800346	+	0.599538i	$0.204649\pi$
$308$	−6.70012	−	1.18141i	−0.381775	−	0.0673172i
$309$	0.207803	+	15.1842i	0.0118215	+	0.863796i
$310$	12.9620	−	4.71780i	0.736194	−	0.267953i
$311$	−9.98316	−	5.76378i	−0.566093	−	0.326834i	0.189494	−	0.981882i	$-0.439315\pi$
$311$	−9.98316	−	5.76378i	−0.566093	−	0.326834i	−0.755587	+	0.655048i	$0.772648\pi$
$312$	0.812121	+	2.13971i	0.0459773	+	0.121137i
$313$	2.29638	+	1.92690i	0.129799	+	0.108915i	0.705376	−	0.708833i	$-0.250778\pi$
$313$	2.29638	+	1.92690i	0.129799	+	0.108915i	−0.575577	+	0.817748i	$0.695222\pi$
$314$	−14.6497	−	12.2926i	−0.826731	−	0.693710i
$315$	−15.5394	+	3.18077i	−0.875544	+	0.179216i
$316$	−4.49620	−	2.59588i	−0.252931	−	0.146030i
$317$	15.4509	−	5.62366i	0.867808	−	0.315856i	0.130529	−	0.991445i	$-0.458333\pi$
$317$	15.4509	−	5.62366i	0.867808	−	0.315856i	0.737279	+	0.675588i	$0.236110\pi$
$318$	−4.92890	+	0.0674546i	−0.276399	+	0.00378267i
$319$	6.16581	+	1.08720i	0.345219	+	0.0608714i
$320$	0.773919	−	2.12632i	0.0432634	−	0.118865i
$321$	−7.17302	−	12.0405i	−0.400359	−	0.672033i
$322$		−	19.1280i		−	1.06596i
$323$	−24.2997	+	6.80228i	−1.35207	+	0.378489i
$324$	7.20058	+	5.39922i	0.400032	+	0.299957i
$325$	−0.102094	−	0.121670i	−0.00566313	−	0.00674906i
$326$	5.81548	+	2.11666i	0.322090	+	0.117231i
$327$	−4.20377	+	12.0608i	−0.232469	+	0.666964i
$328$	−1.57546	−	8.93486i	−0.0869901	−	0.493345i
$329$	−8.17442	−	22.4590i	−0.450670	−	1.23821i
$330$	−8.84151	−	7.21506i	−0.486709	−	0.397176i
$331$	1.51206	−	0.872986i	0.0831101	−	0.0479837i	−0.457869	−	0.889020i	$-0.651387\pi$
$331$	1.51206	−	0.872986i	0.0831101	−	0.0479837i	0.540979	+	0.841036i	$0.318054\pi$
$332$	1.20637	−	1.43769i	0.0662079	−	0.0789036i
$333$	−7.64142	+	4.69518i	−0.418747	+	0.257294i
$334$	−2.18468	−	3.78398i	−0.119540	−	0.207050i
$335$	18.3689	−	31.8160i	1.00360	−	1.73829i
$336$	0.757242	+	3.97560i	0.0413109	+	0.216887i
$337$	−14.3139	+	2.52392i	−0.779727	+	0.137487i	−0.549325	−	0.835609i	$-0.685115\pi$
$337$	−14.3139	+	2.52392i	−0.779727	+	0.137487i	−0.230402	+	0.973096i	$0.574004\pi$
$338$	−1.95424	+	11.0831i	−0.106297	+	0.602839i
$339$	−12.5781	+	22.4911i	−0.683147	+	1.22155i
$340$	−10.0347	+	8.42009i	−0.544207	+	0.456644i
$341$	−17.7498			−0.961207
$342$	−8.88370	+	9.59582i	−0.480376	+	0.518883i
$343$	−19.9553			−1.07749
$344$	0.293837	−	0.246558i	0.0158426	−	0.0132935i
$345$	15.6604	−	28.0027i	0.843128	−	1.50762i
$346$	2.58682	−	14.6706i	0.139069	−	0.788697i
$347$	5.30901	−	0.936123i	0.285003	−	0.0502537i	−0.0293192	−	0.999570i	$-0.509334\pi$
$347$	5.30901	−	0.936123i	0.285003	−	0.0502537i	0.314322	+	0.949316i	$0.398223\pi$
$348$	−0.696854	−	3.65856i	−0.0373553	−	0.196120i
$349$	−1.57657	+	2.73070i	−0.0843920	+	0.146171i	−0.905132	−	0.425131i	$-0.860228\pi$
$349$	−1.57657	+	2.73070i	−0.0843920	+	0.146171i	0.820740	+	0.571302i	$0.193561\pi$
$350$	−0.140431	−	0.243234i	−0.00750636	−	0.0130014i
$351$	−2.61112	−	6.35007i	−0.139371	−	0.338941i
$352$	−1.87162	+	2.23051i	−0.0997577	+	0.118887i
$353$	−19.6094	+	11.3215i	−1.04370	+	0.602582i	−0.920880	−	0.389847i	$-0.872528\pi$
$353$	−19.6094	+	11.3215i	−1.04370	+	0.602582i	−0.122822	+	0.992429i	$0.539195\pi$
$354$	−4.44564	−	3.62783i	−0.236283	−	0.192817i
$355$	10.2338	+	28.1172i	0.543155	+	1.49231i
$356$	−1.07603	−	6.10245i	−0.0570293	−	0.323429i
$357$	7.71106	−	22.1233i	0.408112	−	1.17089i
$358$	3.15759	+	1.14927i	0.166884	+	0.0607407i
$359$	10.4708	+	12.4786i	0.552628	+	0.658596i	0.967969	−	0.251069i	$-0.0807822\pi$
$359$	10.4708	+	12.4786i	0.552628	+	0.658596i	−0.415341	+	0.909666i	$0.636338\pi$
$360$	−2.14632	+	6.44012i	−0.113121	+	0.339424i
$361$	−12.5344	−	14.2790i	−0.659705	−	0.751525i
$362$			19.8675i			1.04421i
$363$	−2.23555	−	3.75255i	−0.117336	−	0.196958i
$364$	1.05597	−	2.90125i	0.0553478	−	0.152067i
$365$	−13.8665	−	2.44504i	−0.725806	−	0.127979i
$366$	−10.1610	+	0.139058i	−0.531123	+	0.00726870i
$367$	13.5022	−	4.91441i	0.704811	−	0.256530i	0.0353474	−	0.999375i	$-0.488746\pi$
$367$	13.5022	−	4.91441i	0.704811	−	0.256530i	0.669464	+	0.742845i	$0.266524\pi$
$368$	−7.08955	−	4.09315i	−0.369568	−	0.213370i
$369$	5.45813	+	26.6652i	0.284139	+	1.38813i
$370$	−5.18205	−	4.34825i	−0.269402	−	0.226055i
$371$	5.09407	+	4.27443i	0.264471	+	0.221918i
$372$	3.74667	+	9.87145i	0.194256	+	0.511811i
$373$	−31.7907	−	18.3543i	−1.64606	−	0.950352i	−0.978617	−	0.205689i	$-0.934056\pi$
$373$	−31.7907	−	18.3543i	−1.64606	−	0.950352i	−0.667441	−	0.744663i	$-0.732610\pi$
$374$	15.8395	−	5.76511i	0.819042	−	0.298107i
$375$	0.261714	+	19.1234i	0.0135148	+	0.987529i
$376$	−10.0734	−	1.77621i	−0.519496	−	0.0916011i
$377$	−0.971760	+	2.66989i	−0.0500482	+	0.137506i
$378$	−2.59726	−	11.8602i	−0.133589	−	0.610022i
$379$			26.0481i			1.33800i	0.743263	+	0.669000i	$0.233277\pi$
$379$			26.0481i			1.33800i	−0.743263	+	0.669000i	$0.766723\pi$
$380$	−8.98506	−	4.06849i	−0.460924	−	0.208709i
$381$	12.6998	+	2.06053i	0.650628	+	0.105564i
$382$	−6.57866	−	7.84014i	−0.336593	−	0.401136i
$383$	−2.22943	−	0.811445i	−0.113918	−	0.0414629i	0.284432	−	0.958696i	$-0.408195\pi$
$383$	−2.22943	−	0.811445i	−0.113918	−	0.0414629i	−0.398350	+	0.917233i	$0.630417\pi$
$384$	1.63555	+	0.570068i	0.0834638	+	0.0290912i
$385$	2.67328	+	15.1609i	0.136243	+	0.772673i
$386$	−0.784644	−	2.15579i	−0.0399374	−	0.109727i
$387$	−0.860938	+	0.763521i	−0.0437639	+	0.0388120i
$388$	8.26346	−	4.77091i	0.419513	−	0.242206i
$389$	15.0557	−	17.9426i	0.763353	−	0.909728i	−0.234702	−	0.972067i	$-0.575412\pi$
$389$	15.0557	−	17.9426i	0.763353	−	0.909728i	0.998055	+	0.0623389i	$0.0198560\pi$
$390$	3.92121	−	3.38280i	0.198558	−	0.171295i
$391$	23.6954	+	41.0416i	1.19833	+	2.07556i
$392$	−0.770194	+	1.33401i	−0.0389007	+	0.0673779i
$393$	−30.2834	+	5.76815i	−1.52760	+	0.290965i
$394$	6.21823	−	1.09644i	0.313270	−	0.0552380i
$395$	−2.03999	+	11.5694i	−0.102643	+	0.582119i
$396$	5.42964	−	6.84268i	0.272850	−	0.343858i
$397$	5.26511	−	4.41795i	0.264248	−	0.221731i	−0.501031	−	0.865430i	$-0.667046\pi$
$397$	5.26511	−	4.41795i	0.264248	−	0.221731i	0.765279	+	0.643699i	$0.222601\pi$
$398$	10.3943			0.521020
$399$	17.5301	−	1.97337i	0.877602	−	0.0987919i
$400$	−0.120202			−0.00601011
$401$	23.7988	−	19.9695i	1.18845	−	0.997231i	0.188569	−	0.982060i	$-0.439615\pi$
$401$	23.7988	−	19.9695i	1.18845	−	0.997231i	0.999885	−	0.0151712i	$-0.00482933\pi$
$402$	24.5437	+	13.7259i	1.22413	+	0.684588i
$403$	1.39873	−	7.93257i	0.0696755	−	0.395150i
$404$	12.3268	−	2.17355i	0.613281	−	0.108138i
$405$	5.90783	−	19.4893i	0.293562	−	0.968433i
$406$	−2.51211	+	4.35111i	−0.124674	+	0.215942i
$407$	4.35235	+	7.53850i	0.215738	+	0.373670i
$408$	−6.54967	−	7.59213i	−0.324257	−	0.375867i
$409$	−5.64702	+	6.72985i	−0.279227	+	0.332770i	−0.887370	−	0.461057i	$-0.847470\pi$
$409$	−5.64702	+	6.72985i	−0.279227	+	0.332770i	0.608143	+	0.793827i	$0.291915\pi$
$410$	−17.7791	+	10.2648i	−0.878049	+	0.506942i
$411$	17.9859	−	22.0403i	0.887177	−	1.08717i
$412$	−2.99863	−	8.23866i	−0.147732	−	0.405889i
$413$	1.34417	+	7.62314i	0.0661420	+	0.375110i
$414$	21.5967	+	11.6928i	1.06142	+	0.574671i
$415$	−3.99063	−	1.45247i	−0.195892	−	0.0712989i
$416$	−0.849349	−	1.01221i	−0.0416428	−	0.0496279i
$417$	5.36319	−	33.0551i	0.262637	−	1.61872i
$418$	9.07402	+	8.87394i	0.443825	+	0.434039i
$419$			0.268652i			0.0131245i	0.999978	+	0.00656225i	$0.00208885\pi$
$419$			0.268652i			0.0131245i	−0.999978	+	0.00656225i	$0.997911\pi$
$420$	7.86738	−	4.68693i	0.383889	−	0.228699i
$421$	6.44528	−	17.7083i	0.314124	−	0.863048i	−0.677689	−	0.735348i	$-0.737019\pi$
$421$	6.44528	−	17.7083i	0.314124	−	0.863048i	0.991813	−	0.127699i	$-0.0407592\pi$
$422$	5.49083	+	0.968181i	0.267289	+	0.0471303i
$423$	30.3547	+	4.49963i	1.47590	+	0.218780i
$424$	2.67434	−	0.973379i	0.129877	−	0.0472714i
$425$	0.602627	+	0.347927i	0.0292317	+	0.0168769i
$426$	−21.4131	+	8.12728i	−1.03747	+	0.393768i
$427$	10.5015	+	8.81180i	0.508203	+	0.426433i
$428$	6.19857	+	5.20122i	0.299619	+	0.251410i
$429$	−6.23026	+	2.36467i	−0.300800	+	0.114167i
$430$	−0.751668	−	0.433976i	−0.0362487	−	0.0209282i
$431$	−8.09752	+	2.94726i	−0.390044	+	0.141964i	−0.529595	−	0.848250i	$-0.677656\pi$
$431$	−8.09752	+	2.94726i	−0.390044	+	0.141964i	0.139551	+	0.990215i	$0.455434\pi$
$432$	−4.95161	−	1.57529i	−0.238235	−	0.0757912i
$433$	8.52374	+	1.50296i	0.409625	+	0.0722279i	0.374664	−	0.927161i	$-0.377758\pi$
$433$	8.52374	+	1.50296i	0.409625	+	0.0722279i	0.0349610	+	0.999389i	$0.488869\pi$
$434$	4.87165	−	13.3848i	0.233847	−	0.642489i
$435$	−7.23998	+	4.31317i	−0.347130	+	0.206801i
$436$		−	7.37416i		−	0.353158i
$437$	−20.1400	+	29.4564i	−0.963426	+	1.40909i
$438$	1.72613	−	10.6387i	0.0824779	−	0.508339i
$439$	−16.0959	−	19.1824i	−0.768216	−	0.915524i	0.230122	−	0.973162i	$-0.426088\pi$
$439$	−16.0959	−	19.1824i	−0.768216	−	0.915524i	−0.998338	+	0.0576380i	$0.981643\pi$
$440$	6.19127	+	2.25344i	0.295157	+	0.107428i
$441$	2.20020	−	4.06378i	0.104771	−	0.193513i
$442$	1.32830	+	7.53314i	0.0631806	+	0.358315i
$443$	2.20842	+	6.06757i	0.104925	+	0.288279i	0.981035	−	0.193833i	$-0.0620920\pi$
$443$	2.20842	+	6.06757i	0.104925	+	0.288279i	−0.876110	+	0.482112i	$0.839870\pi$
$444$	3.27378	−	4.01178i	0.155367	−	0.190390i
$445$	−12.1430	+	7.01078i	−0.575634	+	0.332343i
$446$	−3.33359	+	3.97281i	−0.157850	+	0.188118i
$447$	7.28730	+	8.44716i	0.344677	+	0.399537i
$448$	−1.16829	−	2.02354i	−0.0551965	−	0.0956032i
$449$	11.3528	−	19.6637i	0.535774	−	0.927988i	−0.463351	−	0.886175i	$-0.653353\pi$
$449$	11.3528	−	19.6637i	0.535774	−	0.927988i	0.999125	−	0.0418133i	$-0.0133135\pi$
$450$	0.360471	−	0.00986833i	0.0169928	−	0.000465197i
$451$	26.0159	−	4.58730i	1.22504	−	0.216007i
$452$	2.58353	−	14.6519i	0.121519	−	0.689168i
$453$	−4.57795	−	2.56020i	−0.215091	−	0.120289i
$454$	−13.0510	+	10.9511i	−0.612516	+	0.513962i
$455$	−6.98624			−0.327520
$456$	3.01982	−	6.91959i	0.141416	−	0.324039i
$457$	9.08970			0.425198			0.212599	−	0.977140i	$-0.431807\pi$
$457$	9.08970			0.425198			0.212599	+	0.977140i	$0.431807\pi$
$458$	−18.7836	+	15.7613i	−0.877701	+	0.736479i
$459$	20.2650	+	22.2302i	0.945887	+	1.03761i
$460$	−3.21663	+	18.2424i	−0.149976	+	0.850558i
$461$	19.6634	−	3.46719i	0.915818	−	0.161483i	0.304174	−	0.952617i	$-0.401620\pi$
$461$	19.6634	−	3.46719i	0.915818	−	0.161483i	0.611644	+	0.791133i	$0.290509\pi$
$462$	−11.5759	+	2.20488i	−0.538558	+	0.102580i
$463$	0.304139	−	0.526785i	0.0141346	−	0.0244818i	−0.858872	−	0.512191i	$-0.828834\pi$
$463$	0.304139	−	0.526785i	0.0141346	−	0.0244818i	0.873006	+	0.487709i	$0.162167\pi$
$464$	1.07512	+	1.86217i	0.0499114	+	0.0864490i
$465$	18.0903	−	15.6063i	0.838917	−	0.723727i
$466$	−14.6817	+	17.4969i	−0.680115	+	0.810529i
$467$	13.6575	−	7.88518i	0.631995	−	0.364883i	−0.149529	−	0.988757i	$-0.547776\pi$
$467$	13.6575	−	7.88518i	0.631995	−	0.364883i	0.781524	+	0.623875i	$0.214442\pi$
$468$	2.63019	+	2.96578i	0.121581	+	0.137093i
$469$	−12.9749	−	35.6482i	−0.599124	−	1.64608i
$470$	4.01919	+	22.7939i	0.185391	+	1.05141i
$471$	−31.2780	−	10.9019i	−1.44121	−	0.502333i
$472$	3.11306	+	1.13306i	0.143290	+	0.0521533i
$473$	0.717910	+	0.855572i	0.0330095	+	0.0393392i
$474$	−8.87633	−	1.44018i	−0.407703	−	0.0661498i
$475$	−0.0398441	+	0.522432i	−0.00182817	+	0.0239708i
$476$			13.5265i			0.619988i
$477$	−7.94009	+	3.13860i	−0.363552	+	0.143707i
$478$	1.03820	−	2.85244i	0.0474864	−	0.130468i
$479$	−9.47350	−	1.67043i	−0.432855	−	0.0763241i	−0.0470248	−	0.998894i	$-0.514974\pi$
$479$	−9.47350	−	1.67043i	−0.432855	−	0.0763241i	−0.385831	+	0.922570i	$0.626085\pi$
$480$	−0.0536321	−	3.91889i	−0.00244796	−	0.178872i
$481$	−3.71200	+	1.35106i	−0.169253	+	0.0616030i
$482$	3.42230	+	1.97587i	0.155881	+	0.0899982i
$483$	−11.7563	−	30.9746i	−0.534930	−	1.40939i
$484$	1.93186	+	1.62102i	0.0878116	+	0.0736827i
$485$	−16.5397	−	13.8785i	−0.751031	−	0.630190i
$486$	14.9786	+	4.31758i	0.679443	+	0.195850i
$487$	28.7513	+	16.5996i	1.30285	+	0.752198i	0.980891	−	0.194557i	$-0.0623269\pi$
$487$	28.7513	+	16.5996i	1.30285	+	0.752198i	0.321954	+	0.946755i	$0.395660\pi$
$488$	5.51318	−	2.00663i	0.249570	−	0.0908360i
$489$	10.7181	−	0.146683i	0.484691	−	0.00663326i
$490$	3.43261	+	0.605262i	0.155070	+	0.0273430i
$491$	3.75074	−	10.3051i	0.169268	−	0.465061i	−0.825834	−	0.563914i	$-0.809295\pi$
$491$	3.75074	−	10.3051i	0.169268	−	0.465061i	0.995102	+	0.0988527i	$0.0315173\pi$
$492$	−8.04268	−	13.5002i	−0.362592	−	0.608638i
$493$		−	12.4478i		−	0.560623i
$494$	−4.68090	+	3.35598i	−0.210604	+	0.150993i
$495$	−18.7519	−	6.24949i	−0.842833	−	0.280894i
$496$	−3.91842	−	4.66980i	−0.175942	−	0.209680i
$497$	29.0342	+	10.5676i	1.30236	+	0.474021i
$498$	1.06989	−	3.06955i	0.0479429	−	0.137550i
$499$	−5.30316	−	30.0757i	−0.237402	−	1.34637i	−0.837496	−	0.546444i	$-0.815981\pi$
$499$	−5.30316	−	30.0757i	−0.237402	−	1.34637i	0.600094	−	0.799930i	$-0.295130\pi$
$500$	−3.77657	−	10.3760i	−0.168893	−	0.464030i
$501$	−5.86341	−	4.78480i	−0.261958	−	0.213769i
$502$	6.28124	−	3.62647i	0.280345	−	0.161857i
$503$	−10.7776	+	12.8442i	−0.480550	+	0.572697i	−0.950788	−	0.309843i	$-0.899724\pi$
$503$	−10.7776	+	12.8442i	−0.480550	+	0.572697i	0.470238	+	0.882540i	$0.344168\pi$
$504$	3.66969	+	5.97243i	0.163461	+	0.266033i
$505$	−14.1616	−	24.5286i	−0.630182	−	1.09151i
$506$	11.9181	−	20.6428i	0.529826	−	0.917685i
$507$	3.64722	+	19.1483i	0.161979	+	0.850406i
$508$	−7.31524	+	1.28987i	−0.324561	+	0.0572289i
$509$	−7.27364	+	41.2508i	−0.322398	+	1.82841i	0.204962	+	0.978770i	$0.434293\pi$
$509$	−7.27364	+	41.2508i	−0.322398	+	1.82841i	−0.527360	+	0.849642i	$0.676818\pi$
$510$	−11.0744	+	19.8024i	−0.490384	+	0.876866i
$511$	−11.1380	+	9.34588i	−0.492716	+	0.413438i
$512$	−1.00000			−0.0441942
$513$	−8.48798	+	20.9989i	−0.374754	+	0.927124i
$514$	9.26957			0.408863
$515$	−15.1974	+	12.7521i	−0.669676	+	0.561925i
$516$	0.324283	−	0.579857i	0.0142757	−	0.0255268i
$517$	5.17184	−	29.3310i	0.227457	−	1.28997i
$518$	−6.87917	+	1.21298i	−0.302254	+	0.0532955i
$519$	−4.82781	−	25.3466i	−0.211917	−	1.11259i
$520$	−1.49497	+	2.58936i	−0.0655587	+	0.113551i
$521$	−5.82256	−	10.0850i	−0.255091	−	0.441831i	0.709829	−	0.704374i	$-0.248772\pi$
$521$	−5.82256	−	10.0850i	−0.255091	−	0.441831i	−0.964920	+	0.262543i	$0.915439\pi$
$522$	−3.37704	−	5.49615i	−0.147809	−	0.240560i
$523$	1.24233	−	1.48055i	0.0543231	−	0.0647398i	−0.738199	−	0.674583i	$-0.764323\pi$
$523$	1.24233	−	1.48055i	0.0543231	−	0.0647398i	0.792522	+	0.609844i	$0.208768\pi$
$524$	15.4139	−	8.89924i	0.673361	−	0.388765i
$525$	−0.376900	−	0.307566i	−0.0164493	−	0.0134233i
$526$	−1.21399	−	3.33541i	−0.0529325	−	0.145431i
$527$	6.12802	+	34.7537i	0.266941	+	1.51390i
$528$	−1.65988	+	4.76227i	−0.0722371	+	0.207251i
$529$	41.3611	+	15.0542i	1.79831	+	0.654531i
$530$	−4.13944	−	4.93319i	−0.179806	−	0.214284i
$531$	−9.42870	−	3.14233i	−0.409171	−	0.136366i
$532$	−9.18212	+	4.40696i	−0.398095	+	0.191066i
$533$			11.9882i			0.519268i
$534$	−5.49309	−	9.22058i	−0.237709	−	0.399013i
$535$	6.26229	−	17.2055i	0.270742	−	0.743858i
$536$	−15.9890	−	2.81930i	−0.690621	−	0.121775i
$537$	5.81956	−	0.0796437i	0.251132	−	0.00343688i
$538$	−4.70855	+	1.71377i	−0.203000	+	0.0738860i
$539$	−3.88428	−	2.24259i	−0.167308	−	0.0965953i
$540$	0.482569	+	11.7479i	0.0207664	+	0.505548i
$541$	−7.95720	−	6.67688i	−0.342107	−	0.287062i	0.455505	−	0.890233i	$-0.349459\pi$
$541$	−7.95720	−	6.67688i	−0.342107	−	0.287062i	−0.797611	+	0.603172i	$0.793903\pi$
$542$	7.08482	+	5.94487i	0.304319	+	0.255354i
$543$	12.2108	+	32.1722i	0.524017	+	1.38064i
$544$	5.01345	+	2.89452i	0.214950	+	0.124101i
$545$	−15.6798	+	5.70700i	−0.671651	+	0.244461i
$546$	−0.0731781	−	5.34712i	−0.00313173	−	0.228835i
$547$	24.0156	+	4.23461i	1.02683	+	0.181059i	0.661600	−	0.749857i	$-0.269878\pi$
$547$	24.0156	+	4.23461i	1.02683	+	0.181059i	0.365235	+	0.930915i	$0.380989\pi$
$548$	−5.61742	+	15.4337i	−0.239964	+	0.659297i
$549$	−16.3686	+	6.47026i	−0.698594	+	0.276144i
$550$		−	0.349996i		−	0.0149239i
$551$	8.44988	−	4.05552i	0.359977	−	0.172771i
$552$	−13.9961	−	2.27086i	−0.595712	−	0.0966543i
$553$	7.79765	+	9.29287i	0.331590	+	0.395173i
$554$	−7.14241	−	2.59963i	−0.303452	−	0.110448i
$555$	−11.0640	−	3.85633i	−0.469640	−	0.163692i
$556$	3.35731	+	19.0402i	0.142381	+	0.807485i
$557$	6.96784	+	19.1440i	0.295237	+	0.811156i	0.995279	+	0.0970547i	$0.0309422\pi$
$557$	6.96784	+	19.1440i	0.295237	+	0.811156i	−0.700042	+	0.714101i	$0.746836\pi$
$558$	12.1342	+	13.6824i	0.513684	+	0.579224i
$559$	−0.438936	+	0.253420i	−0.0185650	+	0.0107185i
$560$	−3.39854	+	4.05022i	−0.143614	+	0.171153i
$561$	22.1062	−	19.0708i	0.933325	−	0.805172i
$562$	−7.20378	−	12.4773i	−0.303873	−	0.526324i
$563$	−0.391026	+	0.677277i	−0.0164798	+	0.0285438i	−0.874148	−	0.485660i	$-0.838579\pi$
$563$	−0.391026	+	0.677277i	−0.0164798	+	0.0285438i	0.857668	+	0.514204i	$0.171913\pi$
$564$	−17.4039	+	3.31496i	−0.732836	+	0.139585i
$565$	−33.1541	+	5.84597i	−1.39481	+	0.245942i
$566$	−1.72121	+	9.76147i	−0.0723478	+	0.410305i
$567$	−11.4953	−	17.6093i	−0.482756	−	0.739521i
$568$	10.1297	−	8.49984i	0.425033	−	0.356645i
$569$	−12.5732			−0.527098			−0.263549	−	0.964646i	$-0.584893\pi$
$569$	−12.5732			−0.527098			−0.263549	+	0.964646i	$0.584893\pi$
$570$	−17.0504	−	1.06592i	−0.714162	−	0.0446464i
$571$	−2.14694			−0.0898468			−0.0449234	−	0.998990i	$-0.514304\pi$
$571$	−2.14694			−0.0898468			−0.0449234	+	0.998990i	$0.514304\pi$
$572$	2.94729	−	2.47307i	0.123232	−	0.103404i
$573$	−15.4717	−	8.65249i	−0.646340	−	0.361463i
$574$	−3.68118	+	20.8770i	−0.153650	+	0.871390i
$575$	0.969062	−	0.170872i	0.0404127	−	0.00712585i
$576$	2.99888	−	0.0820978i	0.124953	−	0.00342074i
$577$	−19.9348	+	34.5282i	−0.829898	+	1.43743i	0.0682191	+	0.997670i	$0.478268\pi$
$577$	−19.9348	+	34.5282i	−0.829898	+	1.43743i	−0.898117	+	0.439756i	$0.855065\pi$
$578$	−8.25644	−	14.3006i	−0.343423	−	0.594826i
$579$	−2.59558	−	3.00870i	−0.107869	−	0.125037i
$580$	3.12752	−	3.72723i	0.129863	−	0.154765i
$581$	−3.79772	+	2.19262i	−0.157556	+	0.0909650i
$582$	10.4491	−	12.8045i	0.433127	−	0.530765i
$583$	2.83421	+	7.78693i	0.117381	+	0.322502i
$584$	1.08054	+	6.12807i	0.0447132	+	0.253581i
$585$	4.27065	−	7.88791i	0.176570	−	0.326125i
$586$	−7.72838	−	2.81290i	−0.319256	−	0.116200i
$587$	−28.9490	−	34.5001i	−1.19485	−	1.42397i	−0.880095	−	0.474797i	$-0.842521\pi$
$587$	−28.9490	−	34.5001i	−1.19485	−	1.42397i	−0.314757	−	0.949172i	$-0.601923\pi$
$588$	−0.427300	+	2.63359i	−0.0176215	+	0.108607i
$589$	−21.5951	+	15.4826i	−0.889810	+	0.637951i
$590$		−	7.49627i		−	0.308616i
$591$	9.39552	−	5.59732i	0.386480	−	0.230243i
$592$	−1.02248	+	2.80925i	−0.0420237	+	0.115459i
$593$	−29.2417	−	5.15610i	−1.20081	−	0.211736i	−0.462763	−	0.886482i	$-0.653142\pi$
$593$	−29.2417	−	5.15610i	−1.20081	−	0.211736i	−0.738050	+	0.674746i	$0.764253\pi$
$594$	4.58681	−	14.4177i	0.188199	−	0.591567i
$595$	28.7618	−	10.4684i	1.17912	−	0.429164i
$596$	−5.57807	−	3.22050i	−0.228487	−	0.131917i
$597$	16.8319	−	6.38849i	0.688884	−	0.261463i
$598$	8.28630	+	6.95303i	0.338852	+	0.284331i
$599$	−23.2268	−	19.4896i	−0.949023	−	0.796325i	0.0301101	−	0.999547i	$-0.490414\pi$
$599$	−23.2268	−	19.4896i	−0.949023	−	0.796325i	−0.979133	+	0.203222i	$0.934859\pi$
$600$	−0.194648	+	0.0738778i	−0.00794646	+	0.00301605i
$601$	19.5471	+	11.2855i	0.797343	+	0.460346i	0.842541	−	0.538632i	$-0.181059\pi$
$601$	19.5471	+	11.2855i	0.797343	+	0.460346i	−0.0451983	+	0.998978i	$0.514392\pi$
$602$	−0.842207	+	0.306538i	−0.0343258	+	0.0124936i
$603$	48.1806	+	7.14206i	1.96207	+	0.290847i
$604$	2.98232	+	0.525863i	0.121349	+	0.0213971i
$605$	1.95171	−	5.36229i	0.0793484	−	0.218008i
$606$	18.6253	−	11.0959i	0.756602	−	0.450740i
$607$			22.1708i			0.899886i	0.893057	+	0.449943i	$0.148556\pi$
$607$			22.1708i			0.899886i	−0.893057	+	0.449943i	$0.851444\pi$
$608$	−0.331476	+	4.34628i	−0.0134431	+	0.176265i
$609$	−1.39371	+	8.58989i	−0.0564759	+	0.348080i
$610$	−8.53350	−	10.1698i	−0.345511	−	0.411764i
$611$	12.7007	+	4.62269i	0.513817	+	0.187014i
$612$	−15.2723	−	8.26870i	−0.617348	−	0.334242i
$613$	−4.39349	−	24.9167i	−0.177451	−	1.00638i	−0.935276	−	0.353919i	$-0.884849\pi$
$613$	−4.39349	−	24.9167i	−0.177451	−	1.00638i	0.757825	−	0.652458i	$-0.226262\pi$
$614$	−3.47152	−	9.53794i	−0.140099	−	0.384920i
$615$	−22.4815	+	27.5494i	−0.906542	+	1.11090i
$616$	5.89199	−	3.40174i	0.237395	−	0.137060i
$617$	3.45217	−	4.11414i	0.138979	−	0.165629i	−0.692065	−	0.721835i	$-0.743299\pi$
$617$	3.45217	−	4.11414i	0.138979	−	0.165629i	0.831045	+	0.556206i	$0.187743\pi$
$618$	−9.91937	−	11.4982i	−0.399016	−	0.462524i
$619$	−10.8898	−	18.8617i	−0.437699	−	0.758117i	0.559813	−	0.828619i	$-0.310873\pi$
$619$	−10.8898	−	18.8617i	−0.437699	−	0.758117i	−0.997512	+	0.0705023i	$0.977540\pi$
$620$	−6.89696	+	11.9459i	−0.276988	+	0.479758i
$621$	42.1589	+	5.66099i	1.69178	+	0.227168i
$622$	11.3524	−	2.00174i	0.455191	−	0.0802625i
$623$	−2.51422	+	14.2589i	−0.100730	+	0.571269i
$624$	−1.99750	−	1.11710i	−0.0799641	−	0.0447196i
$625$	−19.6004	+	16.4467i	−0.784018	+	0.657869i
$626$	−2.99772			−0.119813
$627$	20.1479	+	8.79289i	0.804631	+	0.351154i
$628$	19.1238			0.763124
$629$	13.2576	−	11.1244i	0.528614	−	0.443560i
$630$	9.85928	−	12.4251i	0.392803	−	0.495028i
$631$	−2.49759	+	14.1646i	−0.0994276	+	0.563882i	0.893873	+	0.448321i	$0.147978\pi$
$631$	−2.49759	+	14.1646i	−0.0994276	+	0.563882i	−0.993300	+	0.115561i	$0.963133\pi$
$632$	5.11289	−	0.901541i	0.203380	−	0.0358614i
$633$	9.48656	−	1.80692i	0.377057	−	0.0718188i
$634$	−8.22124	+	14.2396i	−0.326507	+	0.565527i
$635$	8.40409	+	14.5563i	0.333506	+	0.577650i
$636$	3.73240	−	3.21991i	0.147999	−	0.127678i
$637$	1.30833	−	1.55920i	0.0518378	−	0.0617779i
$638$	−5.42212	+	3.13046i	−0.214664	+	0.123936i
$639$	−29.6799	+	26.3216i	−1.17412	+	1.04127i
$640$	0.773919	+	2.12632i	0.0305918	+	0.0840503i
$641$	−1.24354	−	7.05244i	−0.0491167	−	0.278555i	0.950351	−	0.311180i	$-0.100724\pi$
$641$	−1.24354	−	7.05244i	−0.0491167	−	0.278555i	−0.999468	+	0.0326255i	$0.989613\pi$
$642$	13.2343	+	4.61280i	0.522317	+	0.182053i
$643$	9.97359	+	3.63009i	0.393320	+	0.143157i	0.531106	−	0.847305i	$-0.321776\pi$
$643$	9.97359	+	3.63009i	0.393320	+	0.143157i	−0.137786	+	0.990462i	$0.543999\pi$
$644$	12.2952	+	14.6529i	0.484500	+	0.577404i
$645$	−1.48393	−	0.240768i	−0.0584297	−	0.00948022i
$646$	14.2422	−	20.8304i	0.560352	−	0.819560i
$647$		−	25.2527i		−	0.992786i	−0.868098	−	0.496393i	$-0.834658\pi$
$647$		−	25.2527i		−	0.992786i	0.868098	−	0.496393i	$-0.165342\pi$
$648$	−8.98652	+	0.492402i	−0.353024	+	0.0193434i
$649$	−3.29916	+	9.06437i	−0.129503	+	0.355808i
$650$	0.156416	+	0.0275804i	0.00613516	+	0.00108179i
$651$	−0.337603	−	24.6686i	−0.0132317	−	0.966839i
$652$	−5.81548	+	2.11666i	−0.227752	+	0.0828949i
$653$	−4.44155	−	2.56433i	−0.173811	−	0.100350i	0.410570	−	0.911829i	$-0.365330\pi$
$653$	−4.44155	−	2.56433i	−0.173811	−	0.100350i	−0.584382	+	0.811479i	$0.698663\pi$
$654$	−4.53225	−	11.9412i	−0.177225	−	0.466940i
$655$	−30.8518	−	25.8877i	−1.20548	−	1.01152i
$656$	6.95009	+	5.83182i	0.271355	+	0.227694i
$657$	−3.74352	−	18.2886i	−0.146049	−	0.713506i
$658$	20.6984	+	11.9502i	0.806906	+	0.465867i
$659$	39.0596	−	14.2165i	1.52154	−	0.553797i	0.560011	−	0.828485i	$-0.310797\pi$
$659$	39.0596	−	14.2165i	1.52154	−	0.553797i	0.961533	+	0.274688i	$0.0885747\pi$
$660$	11.4107	−	0.156162i	0.444163	−	0.00607860i
$661$	−46.7645	−	8.24585i	−1.81893	−	0.320726i	−0.842851	−	0.538147i	$-0.819125\pi$
$661$	−46.7645	−	8.24585i	−1.81893	−	0.320726i	−0.976078	+	0.217421i	$0.930236\pi$
$662$	−0.597158	+	1.64068i	−0.0232092	+	0.0637667i
$663$	6.78093	+	11.3823i	0.263349	+	0.442052i
$664$			1.87677i			0.0728329i
$665$	16.4768	+	16.1135i	0.638944	+	0.624856i
$666$	2.83566	−	8.50852i	0.109880	−	0.329699i
$667$	−11.3147	−	13.4844i	−0.438108	−	0.522116i
$668$	4.10586	+	1.49441i	0.158860	+	0.0578204i
$669$	−2.95645	+	8.48219i	−0.114303	+	0.327940i
$670$	6.37947	+	36.1798i	0.246460	+	1.39775i
$671$	5.84276	+	16.0529i	0.225557	+	0.619713i
$672$	−3.13555	−	2.55874i	−0.120956	−	0.0987057i
$673$	−37.0622	+	21.3979i	−1.42864	+	0.824827i	−0.997014	−	0.0772240i	$-0.975394\pi$
$673$	−37.0622	+	21.3979i	−1.42864	+	0.824827i	−0.431629	+	0.902051i	$0.642061\pi$
$674$	9.34273	−	11.1342i	0.359868	−	0.428874i
$675$	0.577659	−	0.237531i	0.0222341	−	0.00914256i
$676$	−5.62701	−	9.74627i	−0.216424	−	0.374857i
$677$	16.0186	−	27.7451i	0.615646	−	1.06633i	−0.374625	−	0.927176i	$-0.622229\pi$
$677$	16.0186	−	27.7451i	0.615646	−	1.06633i	0.990271	−	0.139153i	$-0.0444381\pi$
$678$	−4.82166	−	25.3142i	−0.185175	−	0.972187i
$679$	−21.9565	+	3.87153i	−0.842614	+	0.148576i
$680$	2.27468	−	12.9003i	0.0872299	−	0.494705i
$681$	−14.4033	+	25.7549i	−0.551937	+	0.986930i
$682$	13.5972	−	11.4094i	0.520662	−	0.436887i
$683$	8.09665			0.309810			0.154905	−	0.987929i	$-0.450493\pi$
$683$	8.09665			0.309810			0.154905	+	0.987929i	$0.450493\pi$
$684$	0.637235	−	13.0612i	0.0243653	−	0.499406i
$685$	37.1646			1.41998
$686$	15.2867	−	12.8270i	0.583647	−	0.489738i
$687$	−20.7299	+	37.0676i	−0.790894	+	1.41422i
$688$	−0.0666074	+	0.377749i	−0.00253938	+	0.0144016i
$689$	−3.70340	+	0.653009i	−0.141088	+	0.0248777i
$690$	6.00323	+	31.5176i	0.228539	+	1.19986i
$691$	14.6326	−	25.3445i	0.556652	−	0.964149i	−0.441121	−	0.897447i	$-0.645419\pi$
$691$	14.6326	−	25.3445i	0.556652	−	0.964149i	0.997773	−	0.0667014i	$-0.0212475\pi$
$692$	7.44846	+	12.9011i	0.283148	+	0.490427i
$693$	−17.3901	+	10.6851i	−0.660594	+	0.405894i
$694$	−3.46521	+	4.12968i	−0.131538	+	0.156761i
$695$	37.8874	−	21.8743i	1.43715	−	0.829740i
$696$	2.88550	+	2.35469i	0.109375	+	0.0892544i
$697$	−17.9636	−	49.3547i	−0.680421	−	1.86944i
$698$	−0.547538	−	3.10524i	−0.0207246	−	0.117535i
$699$	−13.0207	+	37.3569i	−0.492488	+	1.41297i
$700$	0.263924	+	0.0960605i	0.00997539	+	0.00363075i
$701$	6.18601	+	7.37220i	0.233642	+	0.278444i	0.870108	−	0.492861i	$-0.164049\pi$
$701$	6.18601	+	7.37220i	0.233642	+	0.278444i	−0.636466	+	0.771305i	$0.719604\pi$
$702$	6.08197	+	3.18604i	0.229549	+	0.120249i
$703$	11.8708	+	5.37519i	0.447717	+	0.202729i
$704$		−	2.91172i		−	0.109740i
$705$	20.5179	+	34.4408i	0.772748	+	1.29712i
$706$	7.74435	−	21.2774i	0.291462	−	0.800787i
$707$	−28.8025	−	5.07867i	−1.08323	−	0.191003i
$708$	5.73748	−	0.0785205i	0.215628	−	0.00295098i
$709$	2.54680	−	0.926959i	0.0956471	−	0.0348127i	−0.293753	−	0.955881i	$-0.594904\pi$
$709$	2.54680	−	0.926959i	0.0956471	−	0.0348127i	0.389400	+	0.921069i	$0.372682\pi$
$710$	−25.9130	−	14.9609i	−0.972497	−	0.561471i
$711$	−15.2589	+	3.12337i	−0.572254	+	0.117135i
$712$	4.74686	+	3.98309i	0.177896	+	0.149273i
$713$	38.2284	+	32.0774i	1.43166	+	1.20131i
$714$	8.31359	+	21.9040i	0.311128	+	0.819738i
$715$	−7.53951	−	4.35294i	−0.281962	−	0.162791i
$716$	−3.15759	+	1.14927i	−0.118005	+	0.0429502i
$717$	−0.0719470	−	5.25716i	−0.00268691	−	0.196332i
$718$	−16.0422	−	2.82867i	−0.598690	−	0.105565i
$719$	−3.02583	+	8.31341i	−0.112845	+	0.310038i	−0.983240	−	0.182315i	$-0.941641\pi$
$719$	−3.02583	+	8.31341i	−0.112845	+	0.310038i	0.870396	+	0.492353i	$0.163863\pi$
$720$	−2.49545	−	6.31304i	−0.0930000	−	0.235273i
$721$			20.4857i			0.762929i
$722$	18.7802	+	2.88137i	0.698928	+	0.107234i
$723$	6.75625	+	1.09620i	0.251268	+	0.0407681i
$724$	−12.7706	−	15.2194i	−0.474615	−	0.565625i
$725$	−0.242877	−	0.0884000i	−0.00902023	−	0.00328309i
$726$	4.12462	+	1.43763i	0.153079	+	0.0533555i
$727$	−6.48485	−	36.7774i	−0.240510	−	1.36400i	−0.830693	−	0.556730i	$-0.812056\pi$
$727$	−6.48485	−	36.7774i	−0.240510	−	1.36400i	0.590183	−	0.807269i	$-0.299055\pi$
$728$	1.05597	+	2.90125i	0.0391368	+	0.107528i
$729$	26.9090	−	2.21443i	0.996631	−	0.0820158i
$730$	12.1940	−	7.04021i	0.451320	−	0.260570i
$731$	1.42733	−	1.70103i	0.0527918	−	0.0629149i
$732$	7.69438	−	6.63788i	0.284393	−	0.245343i
$733$	17.5306	+	30.3638i	0.647506	+	1.12151i	0.983717	+	0.179726i	$0.0575211\pi$
$733$	17.5306	+	30.3638i	0.647506	+	1.12151i	−0.336211	+	0.941787i	$0.609146\pi$
$734$	−7.18439	+	12.4437i	−0.265181	+	0.459306i
$735$	5.93056	−	1.12961i	0.218752	−	0.0416662i
$736$	8.06194	−	1.42154i	0.297167	−	0.0523986i
$737$	8.20902	−	46.5557i	0.302383	−	1.71490i
$738$	−21.3212	−	16.9183i	−0.784845	−	0.622772i
$739$	20.2995	−	17.0333i	0.746731	−	0.626581i	−0.187905	−	0.982187i	$-0.560170\pi$
$739$	20.2995	−	17.0333i	0.746731	−	0.626581i	0.934636	+	0.355606i	$0.115725\pi$
$740$	6.76468			0.248675
$741$	−5.51733	+	8.31141i	−0.202684	+	0.305327i
$742$	−6.64984			−0.244123
$743$	−24.2865	+	20.3788i	−0.890984	+	0.747624i	−0.968407	−	0.249374i	$-0.919775\pi$
$743$	−24.2865	+	20.3788i	−0.890984	+	0.747624i	0.0774234	+	0.996998i	$0.475331\pi$
$744$	−9.21536	−	5.15365i	−0.337852	−	0.188942i
$745$	−2.53085	+	14.3532i	−0.0927233	+	0.525860i
$746$	36.1510	−	6.37440i	1.32358	−	0.233383i
$747$	−0.154079	−	5.62821i	−0.00563745	−	0.205925i
$748$	−8.42803	+	14.5978i	−0.308159	+	0.533748i
$749$	−9.45341	−	16.3738i	−0.345420	−	0.598285i
$750$	−12.4928	−	14.4812i	−0.456172	−	0.528777i
$751$	−1.60959	+	1.91823i	−0.0587347	+	0.0699973i	−0.794612	−	0.607118i	$-0.792326\pi$
$751$	−1.60959	+	1.91823i	−0.0587347	+	0.0699973i	0.735877	+	0.677115i	$0.236770\pi$
$752$	8.85839	−	5.11440i	0.323032	−	0.186503i
$753$	7.94256	−	9.73301i	0.289443	−	0.354691i
$754$	−0.971760	−	2.66989i	−0.0353894	−	0.0972316i
$755$	−1.18992	−	6.74835i	−0.0433055	−	0.245598i
$756$	9.61319	+	7.41593i	0.349628	+	0.269715i
$757$	−7.22987	−	2.63146i	−0.262774	−	0.0956419i	0.207273	−	0.978283i	$-0.433541\pi$
$757$	−7.22987	−	2.63146i	−0.262774	−	0.0956419i	−0.470048	+	0.882641i	$0.655763\pi$
$758$	−16.7434	−	19.9540i	−0.608147	−	0.724761i
$759$	6.61212	−	40.7527i	0.240005	−	1.47923i
$760$	9.49813	−	2.65884i	0.344533	−	0.0964462i
$761$		−	26.1918i		−	0.949453i	−0.880133	−	0.474727i	$-0.842547\pi$
$761$		−	26.1918i		−	0.949453i	0.880133	−	0.474727i	$-0.157453\pi$
$762$	−11.0531	+	6.58478i	−0.400410	+	0.238542i
$763$	−5.89312	+	16.1912i	−0.213345	+	0.586161i
$764$	10.0791	+	1.77722i	0.364649	+	0.0642974i
$765$	−5.76239	+	38.8733i	−0.208340	+	1.40547i
$766$	2.22943	−	0.811445i	0.0805525	−	0.0293187i
$767$	−3.79097	−	2.18872i	−0.136884	−	0.0790301i
$768$	−1.61934	+	0.614613i	−0.0584328	+	0.0221779i
$769$	35.3779	+	29.6856i	1.27576	+	1.07049i	0.993814	+	0.111061i	$0.0354249\pi$
$769$	35.3779	+	29.6856i	1.27576	+	1.07049i	0.281948	+	0.959430i	$0.409020\pi$
$770$	−11.7931	−	9.89560i	−0.424995	−	0.356613i
$771$	15.0106	−	5.69720i	0.540592	−	0.205180i
$772$	1.98679	+	1.14707i	0.0715061	+	0.0412841i
$773$	−6.91607	+	2.51724i	−0.248754	+	0.0905390i	−0.463388	−	0.886156i	$-0.653366\pi$
$773$	−6.91607	+	2.51724i	−0.248754	+	0.0905390i	0.214634	+	0.976695i	$0.431144\pi$
$774$	0.168735	−	1.13829i	0.00606505	−	0.0409150i
$775$	0.721618	+	0.127241i	0.0259213	+	0.00457062i
$776$	−3.26349	+	8.96637i	−0.117153	+	0.321874i
$777$	−10.3942	+	6.19226i	−0.372889	+	0.222146i
$778$			23.4225i			0.839736i
$779$	27.6505	−	28.2739i	0.990681	−	1.01302i
$780$	−0.829402	+	5.11188i	−0.0296973	+	0.183035i
$781$	24.7492	+	29.4949i	0.885596	+	1.05541i
$782$	−44.5328	−	16.2086i	−1.59249	−	0.579618i
$783$	−8.84657	−	6.82454i	−0.316151	−	0.243889i
$784$	−0.267485	−	1.51699i	−0.00955305	−	0.0541780i
$785$	−14.8003	−	40.6635i	−0.528245	−	1.45134i
$786$	19.4908	−	23.8845i	0.695213	−	0.851931i
$787$	15.0496	−	8.68891i	0.536462	−	0.309726i	−0.207182	−	0.978302i	$-0.566429\pi$
$787$	15.0496	−	8.68891i	0.536462	−	0.309726i	0.743644	+	0.668576i	$0.233096\pi$
$788$	−4.05866	+	4.83693i	−0.144584	+	0.172308i
$789$	−4.01585	−	4.65502i	−0.142968	−	0.165723i
$790$	−5.87393	−	10.1739i	−0.208985	−	0.361973i
$791$	−17.3818	+	30.1061i	−0.618024	+	1.07045i
$792$	0.239046	+	8.73190i	0.00849413	+	0.310275i
$793$	−7.63460	+	1.34619i	−0.271113	+	0.0478045i
$794$	−1.19350	+	6.76869i	−0.0423558	+	0.240212i
$795$	−9.73514	−	5.44434i	−0.345270	−	0.193091i
$796$	−7.96251	+	6.68134i	−0.282224	+	0.236814i
$797$	−4.12081			−0.145966			−0.0729832	−	0.997333i	$-0.523252\pi$
$797$	−4.12081			−0.145966			−0.0729832	+	0.997333i	$0.523252\pi$
$798$	−12.1604	+	12.7798i	−0.430472	+	0.452400i
$799$	−59.2148			−2.09487
$800$	0.0920802	−	0.0772645i	0.00325553	−	0.00273171i
$801$	−14.5623	−	11.5551i	−0.514532	−	0.408279i
$802$	−5.39474	+	30.5951i	−0.190495	+	1.08035i
$803$	−17.8432	+	3.14625i	−0.629674	+	0.111029i
$804$	−27.6244	+	5.26168i	−0.974238	+	0.185565i
$805$	21.6413	−	37.4838i	0.762754	−	1.32113i
$806$	4.02747	+	6.97579i	0.141862	+	0.245712i
$807$	−6.57143	+	5.66912i	−0.231325	+	0.199562i
$808$	−8.04574	+	9.58854i	−0.283048	+	0.337324i
$809$	−31.6692	+	18.2842i	−1.11343	+	0.642839i	−0.939716	−	0.341957i	$-0.888910\pi$
$809$	−31.6692	+	18.2842i	−1.11343	+	0.642839i	−0.173714	+	0.984796i	$0.555577\pi$
$810$	8.00184	+	18.7272i	0.281156	+	0.658006i
$811$	12.5283	+	34.4211i	0.439927	+	1.20869i	0.939540	+	0.342440i	$0.111253\pi$
$811$	12.5283	+	34.4211i	0.439927	+	1.20869i	−0.499613	+	0.866249i	$0.666524\pi$
$812$	−0.872448	−	4.94790i	−0.0306169	−	0.173637i
$813$	15.1265	+	5.27232i	0.530509	+	0.184908i
$814$	−8.17975	−	2.97719i	−0.286700	−	0.104350i
$815$	9.00142	+	10.7275i	0.315306	+	0.375767i
$816$	9.89747	+	1.60586i	0.346481	+	0.0562165i
$817$	1.61972	+	0.414709i	0.0566670	+	0.0145088i
$818$		−	8.78520i		−	0.307167i
$819$	−3.40491	−	8.61380i	−0.118977	−	0.300991i
$820$	7.02153	−	19.2915i	0.245202	−	0.673688i
$821$	40.6182	+	7.16208i	1.41758	+	0.249958i	0.829349	−	0.558732i	$-0.188712\pi$
$821$	40.6182	+	7.16208i	1.41758	+	0.249958i	0.588235	+	0.808690i	$0.299823\pi$
$822$	0.389284	+	28.4450i	0.0135778	+	0.992132i
$823$	40.6757	−	14.8047i	1.41787	−	0.516061i	0.484438	−	0.874826i	$-0.339024\pi$
$823$	40.6757	−	14.8047i	1.41787	−	0.516061i	0.933428	+	0.358765i	$0.116802\pi$
$824$	7.59279	+	4.38370i	0.264507	+	0.152713i
$825$	−0.215112	−	0.566761i	−0.00748924	−	0.0197321i
$826$	−5.92975	−	4.97565i	−0.206322	−	0.173125i
$827$	17.4100	+	14.6087i	0.605405	+	0.507995i	0.893178	−	0.449704i	$-0.148470\pi$
$827$	17.4100	+	14.6087i	0.605405	+	0.507995i	−0.287773	+	0.957699i	$0.592915\pi$
$828$	−24.0600	+	4.92488i	−0.836145	+	0.171151i
$829$	−6.17465	−	3.56494i	−0.214455	−	0.123815i	0.388925	−	0.921269i	$-0.372846\pi$
$829$	−6.17465	−	3.56494i	−0.214455	−	0.123815i	−0.603380	+	0.797454i	$0.706180\pi$
$830$	3.99063	−	1.45247i	0.138517	−	0.0504159i
$831$	−13.1637	+	0.180153i	−0.456645	+	0.00624943i
$832$	1.30128	+	0.229450i	0.0451137	+	0.00795476i
$833$	−3.04991	+	8.37957i	−0.105673	+	0.290335i
$834$	17.1390	+	28.7691i	0.593474	+	0.996192i
$835$		−	9.88693i		−	0.342151i
$836$	−12.6552	−	0.965166i	−0.437688	−	0.0333810i
$837$	28.0588	+	14.6986i	0.969855	+	0.508058i
$838$	−0.172686	−	0.205799i	−0.00596534	−	0.00710922i
$839$	1.63571	+	0.595349i	0.0564710	+	0.0205537i	0.370101	−	0.928991i	$-0.379323\pi$
$839$	1.63571	+	0.595349i	0.0564710	+	0.0205537i	−0.313630	+	0.949545i	$0.601545\pi$
$840$	−3.01406	+	8.64745i	−0.103995	+	0.298365i
$841$	−4.23292	−	24.0061i	−0.145963	−	0.827797i
$842$	6.44528	+	17.7083i	0.222119	+	0.610267i
$843$	−19.3341	−	15.7774i	−0.665901	−	0.543403i
$844$	−4.82855	+	2.78777i	−0.166206	+	0.0959589i
$845$	−16.3689	+	19.5077i	−0.563107	+	0.671084i
$846$	−26.1453	+	16.0647i	−0.898896	+	0.552316i
$847$	−2.94626	−	5.10308i	−0.101235	−	0.175344i
$848$	−1.42298	+	2.46468i	−0.0488655	+	0.0846375i
$849$	3.21231	+	16.8650i	0.110246	+	0.578804i
$850$	−0.685283	+	0.120834i	−0.0235050	+	0.00414457i
$851$	4.24974	−	24.1015i	0.145679	−	0.826187i
$852$	11.1793	−	19.9900i	0.382996	−	0.684844i
$853$	−22.0984	+	18.5427i	−0.756634	+	0.634891i	−0.937248	−	0.348663i	$-0.886636\pi$
$853$	−22.0984	+	18.5427i	−0.756634	+	0.634891i	0.180614	+	0.983554i	$0.442191\pi$
$854$	−13.7087			−0.469103
$855$	−28.2654	+	8.75331i	−0.966657	+	0.299357i
$856$	−8.09166			−0.276567
$857$	−9.31787	+	7.81862i	−0.318292	+	0.267079i	−0.787909	−	0.615791i	$-0.788836\pi$
$857$	−9.31787	+	7.81862i	−0.318292	+	0.267079i	0.469617	+	0.882870i	$0.344392\pi$
$858$	3.25267	−	5.81618i	0.111044	−	0.198561i
$859$	3.16859	−	17.9700i	0.108111	−	0.613127i	−0.881821	−	0.471584i	$-0.843682\pi$
$859$	3.16859	−	17.9700i	0.108111	−	0.613127i	0.989932	−	0.141543i	$-0.0452064\pi$
$860$	0.854766	−	0.150718i	0.0291473	−	0.00513945i
$861$	6.87022	+	36.0694i	0.234137	+	1.22924i
$862$	4.30860	−	7.46272i	0.146752	−	0.254181i
$863$	−22.3079	−	38.6385i	−0.759371	−	1.31527i	−0.943172	−	0.332306i	$-0.892173\pi$
$863$	−22.3079	−	38.6385i	−0.759371	−	1.31527i	0.183800	−	0.982964i	$-0.441160\pi$
$864$	4.80573	−	1.97609i	0.163494	−	0.0672280i
$865$	21.6674	−	25.8223i	0.736715	−	0.877983i
$866$	−7.49565	+	4.32761i	−0.254712	+	0.147058i
$867$	−22.1593	−	18.0829i	−0.752569	−	0.614129i
$868$	4.87165	+	13.3848i	0.165355	+	0.454308i
$869$	2.62504	+	14.8873i	0.0890483	+	0.505018i
$870$	2.77370	−	7.95785i	0.0940371	−	0.269796i
$871$	20.1593	+	7.33738i	0.683072	+	0.248618i
$872$	4.74002	+	5.64893i	0.160517	+	0.191297i
$873$	9.05069	−	27.1570i	0.306320	−	0.919124i
$874$	−3.50606	−	35.5106i	−0.118594	−	1.20116i
$875$			25.8004i			0.872212i
$876$	5.51615	+	9.25929i	0.186374	+	0.312842i
$877$	−1.46003	+	4.01139i	−0.0493016	+	0.135455i	−0.961900	−	0.273403i	$-0.911851\pi$
$877$	−1.46003	+	4.01139i	−0.0493016	+	0.135455i	0.912598	+	0.408858i	$0.134073\pi$
$878$	24.6604	+	4.34829i	0.832247	+	0.146748i
$879$	−14.2437	+	0.194932i	−0.480428	+	0.00657490i
$880$	−6.19127	+	2.25344i	−0.208708	+	0.0759634i
$881$	9.81390	+	5.66606i	0.330639	+	0.190894i	0.656125	−	0.754653i	$-0.272195\pi$
$881$	9.81390	+	5.66606i	0.330639	+	0.190894i	−0.325486	+	0.945547i	$0.605528\pi$
$882$	0.926697	+	4.52729i	0.0312035	+	0.152442i
$883$	30.0308	+	25.1988i	1.01062	+	0.848008i	0.988420	−	0.151746i	$-0.0484895\pi$
$883$	30.0308	+	25.1988i	1.01062	+	0.848008i	0.0221970	+	0.999754i	$0.492934\pi$
$884$	−5.85974	−	4.91691i	−0.197085	−	0.165374i
$885$	−4.60730	−	12.1390i	−0.154873	−	0.408047i
$886$	−5.59191	−	3.22849i	−0.187864	−	0.108463i
$887$	−38.4635	+	13.9996i	−1.29148	+	0.470059i	−0.894212	−	0.447644i	$-0.852263\pi$
$887$	−38.4635	+	13.9996i	−1.29148	+	0.470059i	−0.397266	+	0.917704i	$0.630041\pi$
$888$	0.0708574	+	5.17754i	0.00237782	+	0.173747i
$889$	17.0927	+	3.01390i	0.573269	+	0.101083i
$890$	4.79565	−	13.1760i	0.160751	−	0.441659i
$891$	−1.43374	−	26.1663i	−0.0480321	−	0.876603i
$892$		−	5.18614i		−	0.173645i
$893$	−19.2922	−	40.1963i	−0.645590	−	1.34512i
$894$	−11.0121	−	1.78672i	−0.368301	−	0.0597568i
$895$	4.88744	+	5.82462i	0.163369	+	0.194696i
$896$	2.19567	+	0.799158i	0.0733521	+	0.0266980i
$897$	17.6917	+	6.16643i	0.590710	+	0.205891i
$898$	3.94280	+	22.3607i	0.131573	+	0.746188i
$899$	−4.48316	−	12.3174i	−0.149522	−	0.410807i
$900$	−0.269794	+	0.239266i	−0.00899313	+	0.00797554i
$901$	14.2681	−	8.23770i	0.475340	−	0.274438i
$902$	−16.9806	+	20.2367i	−0.565394	+	0.673810i
$903$	−1.17541	+	1.01402i	−0.0391153	+	0.0337445i
$904$	7.43897	+	12.8847i	0.247416	+	0.428538i
$905$	−22.4780	+	38.9330i	−0.747193	+	1.29418i
$906$	5.15258	−	0.981423i	0.171183	−	0.0326056i
$907$	−21.5815	+	3.80540i	−0.716602	+	0.126356i	−0.520049	−	0.854137i	$-0.674086\pi$
$907$	−21.5815	+	3.80540i	−0.716602	+	0.126356i	−0.196554	+	0.980493i	$0.562975\pi$
$908$	2.95843	−	16.7781i	0.0981790	−	0.556801i
$909$	23.3410	−	29.4154i	0.774171	−	0.975647i
$910$	5.35177	−	4.49067i	0.177409	−	0.148864i
$911$	41.3461			1.36986			0.684928	−	0.728610i	$-0.259833\pi$
$911$	41.3461			1.36986			0.684928	+	0.728610i	$0.259833\pi$
$912$	2.13451	+	7.24181i	0.0706806	+	0.239800i
$913$	−5.46465			−0.180853
$914$	−6.96311	+	5.84275i	−0.230319	+	0.193261i
$915$	−20.0691	−	11.2236i	−0.663464	−	0.371040i
$916$	4.25790	−	24.1478i	0.140685	−	0.797865i
$917$	−40.9558	+	7.22161i	−1.35248	+	0.238479i
$918$	−29.8131	−	4.00323i	−0.983980	−	0.132126i
$919$	−15.0651	+	26.0936i	−0.496953	+	0.860748i	−0.999994	−	0.00351494i	$-0.998881\pi$
$919$	−15.0651	+	26.0936i	−0.496953	+	0.860748i	0.503041	+	0.864263i	$0.332214\pi$
$920$	−9.26193	−	16.0421i	−0.305357	−	0.528894i
$921$	−11.4837	−	13.3115i	−0.378401	−	0.438628i
$922$	−12.8344	+	15.2954i	−0.422678	+	0.503728i
$923$	−15.1319	+	8.73639i	−0.498071	+	0.287562i
$924$	7.45036	−	9.12986i	0.245099	−	0.300350i
$925$	−0.122905	−	0.337677i	−0.00404108	−	0.0111028i
$926$	0.105627	+	0.599038i	0.00347110	+	0.0196856i
$927$	−23.1297	−	12.5228i	−0.759680	−	0.411303i
$928$	−2.02057	−	0.735428i	−0.0663285	−	0.0241416i
$929$	3.69874	+	4.40799i	0.121352	+	0.144621i	0.823300	−	0.567607i	$-0.192131\pi$
$929$	3.69874	+	4.40799i	0.121352	+	0.144621i	−0.701948	+	0.712228i	$0.747686\pi$
$930$	−3.82640	+	23.5834i	−0.125473	+	0.773329i
$931$	−6.68190	+	0.659722i	−0.218991	+	0.0216215i
$932$		−	22.8406i		−	0.748169i
$933$	17.1531	−	10.2188i	0.561568	−	0.334550i
$934$	−5.39378	+	14.8193i	−0.176490	+	0.484902i
$935$	37.5622	+	6.62323i	1.22842	+	0.216603i
$936$	−3.92121	−	0.581262i	−0.128169	−	0.0189991i
$937$	−19.6146	+	7.13914i	−0.640782	+	0.233226i	−0.641917	−	0.766774i	$-0.721861\pi$
$937$	−19.6146	+	7.13914i	−0.640782	+	0.233226i	0.00113542	+	0.999999i	$0.499639\pi$
$938$	32.8535	+	18.9680i	1.07271	+	0.619327i
$939$	−4.85431	+	1.84244i	−0.158415	+	0.0601257i
$940$	−17.7305	−	14.8777i	−0.578306	−	0.485257i
$941$	−13.7670	−	11.5519i	−0.448792	−	0.376581i	0.390196	−	0.920732i	$-0.372407\pi$
$941$	−13.7670	−	11.5519i	−0.448792	−	0.376581i	−0.838987	+	0.544151i	$0.816852\pi$
$942$	30.9679	−	11.7538i	1.00899	−	0.382958i
$943$	−64.3213	−	37.1359i	−2.09459	−	1.20931i
$944$	−3.11306	+	1.13306i	−0.101321	+	0.0368780i
$945$	8.32885	−	26.1801i	0.270937	−	0.851638i
$946$	−1.09990	−	0.193942i	−0.0357609	−	0.00630561i
$947$	−3.35631	+	9.22139i	−0.109065	+	0.299655i	−0.982204	−	0.187817i	$-0.939859\pi$
$947$	−3.35631	+	9.22139i	−0.109065	+	0.299655i	0.873139	+	0.487472i	$0.162081\pi$
$948$	7.72539	−	4.60235i	0.250909	−	0.149477i
$949$		−	8.22225i		−	0.266906i
$950$	−0.305290	−	0.425817i	−0.00990493	−	0.0138153i
$951$	−4.56110	+	28.1116i	−0.147904	+	0.911581i
$952$	−8.69469	−	10.3619i	−0.281797	−	0.335832i
$953$	9.56813	+	3.48251i	0.309942	+	0.112810i	0.492308	−	0.870421i	$-0.336153\pi$
$953$	9.56813	+	3.48251i	0.309942	+	0.112810i	−0.182366	+	0.983231i	$0.558376\pi$
$954$	4.06501	−	7.50810i	0.131610	−	0.243084i
$955$	−4.02146	−	22.8068i	−0.130131	−	0.738012i
$956$	1.03820	+	2.85244i	0.0335779	+	0.0922546i
$957$	−6.85622	+	8.40178i	−0.221630	+	0.271591i
$958$	8.33086	−	4.80982i	0.269158	−	0.155398i
$959$	24.6680	−	29.3982i	0.796571	−	0.949316i
$960$	2.56010	+	2.96757i	0.0826269	+	0.0957780i
$961$	3.08051	+	5.33561i	0.0993714	+	0.172116i
$962$	1.97512	−	3.42100i	0.0636803	−	0.110298i
$963$	24.2659	−	0.664307i	0.781957	−	0.0214070i
$964$	−3.89169	+	0.686211i	−0.125343	+	0.0221014i
$965$	0.901436	−	5.11230i	0.0290183	−	0.164571i
$966$	28.9160	+	16.1711i	0.930356	+	0.520298i
$967$	34.6570	−	29.0807i	1.11449	−	0.935171i	0.116180	−	0.993228i	$-0.462935\pi$
$967$	34.6570	−	29.0807i	1.11449	−	0.935171i	0.998313	+	0.0580574i	$0.0184906\pi$
$968$	−2.52186			−0.0810556
$969$	10.2603	−	42.4848i	0.329608	−	1.36481i
$970$	21.5911			0.693248
$971$	−11.6835	+	9.80361i	−0.374941	+	0.314613i	−0.810712	−	0.585444i	$-0.800920\pi$
$971$	−11.6835	+	9.80361i	−0.374941	+	0.314613i	0.435772	+	0.900057i	$0.356476\pi$
$972$	−14.2496	+	6.32060i	−0.457055	+	0.202733i
$973$	7.84462	−	44.4890i	0.251487	−	1.42625i
$974$	−32.6948	+	5.76497i	−1.04761	+	0.184722i
$975$	0.270242	−	0.0514736i	0.00865468	−	0.00164847i
$976$	−2.93350	+	5.08097i	−0.0938990	+	0.162638i
$977$	29.3626	+	50.8576i	0.939394	+	1.62708i	0.766605	+	0.642119i	$0.221945\pi$
$977$	29.3626	+	50.8576i	0.939394	+	1.62708i	0.172789	+	0.984959i	$0.444722\pi$
$978$	−8.11629	+	7.00186i	−0.259530	+	0.223895i
$979$	−11.5977	+	13.8216i	−0.370663	+	0.441739i
$980$	−3.01859	+	1.74278i	−0.0964253	+	0.0556712i
$981$	−14.6785	−	16.5513i	−0.468648	−	0.528443i
$982$	3.75074	+	10.3051i	0.119691	+	0.328848i
$983$	−6.80396	−	38.5872i	−0.217013	−	1.23074i	−0.877380	−	0.479797i	$-0.840710\pi$
$983$	−6.80396	−	38.5872i	−0.217013	−	1.23074i	0.660367	−	0.750943i	$-0.270401\pi$
$984$	14.8388	+	5.17206i	0.473045	+	0.164879i
$985$	13.4259	+	4.88664i	0.427786	+	0.155701i
$986$	8.00132	+	9.53561i	0.254814	+	0.303676i
$987$	40.8624	+	6.62991i	1.30066	+	0.211033i
$988$	1.42860	−	5.57966i	0.0454497	−	0.177513i
$989$		−	3.14008i		−	0.0998486i
$990$	18.3819	−	7.26607i	0.584214	−	0.230931i
$991$	−13.8647	+	38.0930i	−0.440428	+	1.21007i	0.498784	+	0.866726i	$0.333780\pi$
$991$	−13.8647	+	38.0930i	−0.440428	+	1.21007i	−0.939212	+	0.343339i	$0.888442\pi$
$992$	6.00337	+	1.05856i	0.190607	+	0.0336092i
$993$	0.0413827	+	3.02383i	0.00131324	+	0.0959583i
$994$	−29.0342	+	10.5676i	−0.920909	+	0.335183i
$995$	20.3690	+	11.7601i	0.645742	+	0.372819i
$996$	1.15349	+	3.03913i	0.0365497	+	0.0962984i
$997$	46.7056	+	39.1907i	1.47918	+	1.24118i	0.907052	+	0.421019i	$0.138327\pi$
$997$	46.7056	+	39.1907i	1.47918	+	1.24118i	0.572131	+	0.820162i	$0.306117\pi$
$998$	23.3947	+	19.6305i	0.740548	+	0.621393i
$999$	−0.637557	−	15.5210i	−0.0201714	−	0.491063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.a.89.2	yes	18
3.2	odd	2		114.2.l.b.89.2	yes	18
4.3	odd	2		912.2.cc.d.545.2		18
12.11	even	2		912.2.cc.c.545.2		18
19.3	odd	18		114.2.l.b.41.2	yes	18
57.41	even	18	inner	114.2.l.a.41.2	✓	18
76.3	even	18		912.2.cc.c.497.2		18
228.155	odd	18		912.2.cc.d.497.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.41.2	✓	18	57.41	even	18	inner
114.2.l.a.89.2	yes	18	1.1	even	1	trivial
114.2.l.b.41.2	yes	18	19.3	odd	18
114.2.l.b.89.2	yes	18	3.2	odd	2
912.2.cc.c.497.2		18	76.3	even	18
912.2.cc.c.545.2		18	12.11	even	2
912.2.cc.d.497.2		18	228.155	odd	18
912.2.cc.d.545.2		18	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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.845418 + 1.51171i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.22841 + 0.392929i) q^{5} +(-0.324081 - 1.70146i) q^{6} +(-1.16829 + 2.02354i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.57054 - 2.55605i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.845418 + 1.51171i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-2.22841 + 0.392929i) q^{5} +(-0.324081 - 1.70146i) q^{6} +(-1.16829 + 2.02354i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.57054 - 2.55605i) q^{9} +(1.45449 - 1.73339i) q^{10} +(-2.52163 + 1.45586i) q^{11} +(1.34194 + 1.09508i) q^{12} +(-0.451929 - 1.24167i) q^{13} +(-0.405743 - 2.30108i) q^{14} +(1.28994 - 3.70090i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.72112 + 4.43466i) q^{17} +(2.84610 + 0.948529i) q^{18} +(-1.79800 + 3.97079i) q^{19} +2.26279i q^{20} +(-2.07131 - 3.47685i) q^{21} +(0.995869 - 2.73613i) q^{22} +(8.06194 + 1.42154i) q^{23} +(-1.73189 + 0.0237018i) q^{24} +(0.112953 - 0.0411116i) q^{25} +(1.14432 + 0.660676i) q^{26} +(5.19177 - 0.213263i) q^{27} +(1.78993 + 1.50193i) q^{28} +(-1.64718 - 1.38215i) q^{29} +(1.39074 + 3.66421i) q^{30} +(5.27928 + 3.04799i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.0690131 - 5.04278i) q^{33} +(-5.70108 - 1.00525i) q^{34} +(1.80832 - 4.96833i) q^{35} +(-2.78994 + 1.10282i) q^{36} -2.98954i q^{37} +(-1.17503 - 4.19754i) q^{38} +(2.25911 + 0.366540i) q^{39} +(-1.45449 - 1.73339i) q^{40} +(-8.52555 - 3.10304i) q^{41} +(3.82159 + 1.33201i) q^{42} +(-0.0666074 - 0.377749i) q^{43} +(0.995869 + 2.73613i) q^{44} +(4.50415 + 5.07883i) q^{45} +(-7.08955 + 4.09315i) q^{46} +(-6.57494 + 7.83571i) q^{47} +(1.31147 - 1.13139i) q^{48} +(0.770194 + 1.33401i) q^{49} +(-0.0601011 + 0.104098i) q^{50} +(-9.84981 + 1.87612i) q^{51} +(-1.30128 + 0.229450i) q^{52} +(0.494197 - 2.80273i) q^{53} +(-3.84005 + 3.50058i) q^{54} +(5.04717 - 4.23508i) q^{55} -2.33658 q^{56} +(-4.48263 - 6.07503i) q^{57} +2.15025 q^{58} +(2.53779 - 2.12946i) q^{59} +(-3.42068 - 1.91300i) q^{60} +(1.01879 - 5.77787i) q^{61} +(-6.00337 + 1.05856i) q^{62} +(7.00712 - 0.191828i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.49497 + 2.58936i) q^{65} +(3.29431 + 3.81864i) q^{66} +(-10.4361 + 12.4373i) q^{67} +(5.01345 - 2.89452i) q^{68} +(-8.96466 + 10.9855i) q^{69} +(1.80832 + 4.96833i) q^{70} +(-2.29622 - 13.0225i) q^{71} +(1.42834 - 2.63815i) q^{72} +(5.84733 + 2.12826i) q^{73} +(1.92164 + 2.29012i) q^{74} +(-0.0333438 + 0.205509i) q^{75} +(3.59825 + 2.46020i) q^{76} -6.80348i q^{77} +(-1.96618 + 1.17134i) q^{78} +(1.77569 - 4.87866i) q^{79} +(2.22841 + 0.392929i) q^{80} +(-4.06683 + 8.02876i) q^{81} +(8.52555 - 3.10304i) q^{82} +(1.62533 + 0.938386i) q^{83} +(-3.78371 + 1.43609i) q^{84} +(-10.0347 - 8.42009i) q^{85} +(0.293837 + 0.246558i) q^{86} +(3.48197 - 1.32157i) q^{87} +(-2.52163 - 1.45586i) q^{88} +(5.82289 - 2.11936i) q^{89} +(-6.71498 - 0.995397i) q^{90} +(3.04054 + 0.536130i) q^{91} +(2.79988 - 7.69261i) q^{92} +(-9.07088 + 5.40391i) q^{93} -10.2288i q^{94} +(2.44644 - 9.55504i) q^{95} +(-0.277398 + 1.70969i) q^{96} +(6.13336 + 7.30946i) q^{97} +(-1.44749 - 0.526843i) q^{98} +(7.68157 + 4.15893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) \) 18 * q + 3 * q^6 + 9 * q^8	\( 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) \) 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

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