LMFDB - Embedded newform 114.2.l.b.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.b.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-0.324081 + 1.70146i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.22841 - 0.392929i) q^{5} +(0.845418 + 1.51171i) q^{6} +(-1.16829 + 2.02354i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.78994 - 1.10282i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-0.324081 + 1.70146i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.22841 - 0.392929i) q^{5} +(0.845418 + 1.51171i) q^{6} +(-1.16829 + 2.02354i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.78994 - 1.10282i) q^{9} +(1.45449 - 1.73339i) q^{10} +(2.52163 - 1.45586i) q^{11} +(1.61934 + 0.614613i) q^{12} +(-0.451929 - 1.24167i) q^{13} +(0.405743 + 2.30108i) q^{14} +(-0.0536321 + 3.91889i) 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} +(-3.06435 - 2.64359i) q^{21} +(0.995869 - 2.73613i) q^{22} +(-8.06194 - 1.42154i) q^{23} +(1.63555 - 0.570068i) q^{24} +(0.112953 - 0.0411116i) q^{25} +(-1.14432 - 0.660676i) q^{26} +(2.78058 - 4.38958i) q^{27} +(1.78993 + 1.50193i) q^{28} +(1.64718 + 1.38215i) q^{29} +(2.47793 + 3.03652i) q^{30} +(5.27928 + 3.04799i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(1.65988 + 4.76227i) q^{33} +(-5.70108 - 1.00525i) q^{34} +(-1.80832 + 4.96833i) q^{35} +(-1.57054 + 2.55605i) 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} +(-4.04670 - 0.0553812i) q^{42} +(-0.0666074 - 0.377749i) q^{43} +(-0.995869 - 2.73613i) q^{44} +(-6.65047 - 1.36129i) q^{45} +(-7.08955 + 4.09315i) q^{46} +(6.57494 - 7.83571i) q^{47} +(0.886471 - 1.48801i) q^{48} +(0.770194 + 1.33401i) q^{49} +(0.0601011 - 0.104098i) q^{50} +(8.75134 - 4.89415i) q^{51} +(-1.30128 + 0.229450i) q^{52} +(-0.494197 + 2.80273i) q^{53} +(-0.691519 - 5.14993i) q^{54} +(5.04717 - 4.23508i) q^{55} +2.33658 q^{56} +(-6.17345 - 4.34609i) q^{57} +2.15025 q^{58} +(-2.53779 + 2.12946i) q^{59} +(3.85004 + 0.733326i) q^{60} +(1.01879 - 5.77787i) q^{61} +(6.00337 - 1.05856i) q^{62} +(5.49107 - 4.35714i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.49497 - 2.58936i) q^{65} +(4.33267 + 2.58116i) q^{66} +(-10.4361 + 12.4373i) q^{67} +(-5.01345 + 2.89452i) q^{68} +(5.03141 - 13.2564i) q^{69} +(1.80832 + 4.96833i) q^{70} +(2.29622 + 13.0225i) q^{71} +(0.439899 + 2.96757i) 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} +(1.49497 - 1.73291i) q^{78} +(1.77569 - 4.87866i) q^{79} +(-2.22841 - 0.392929i) q^{80} +(6.56756 + 6.15363i) q^{81} +(8.52555 - 3.10304i) q^{82} +(-1.62533 - 0.938386i) q^{83} +(-3.13555 + 2.55874i) q^{84} +(-10.0347 - 8.42009i) q^{85} +(-0.293837 - 0.246558i) q^{86} +(-2.88550 + 2.35469i) q^{87} +(-2.52163 - 1.45586i) q^{88} +(-5.82289 + 2.11936i) q^{89} +(-5.96957 + 3.23203i) q^{90} +(3.04054 + 0.536130i) q^{91} +(-2.79988 + 7.69261i) q^{92} +(-6.89696 + 7.99469i) 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} +(-8.64076 + 1.28086i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35} + 3 q^{38} + 6 q^{39} + 3 q^{41} - 6 q^{43} + 24 q^{44} - 54 q^{45} + 18 q^{46} + 30 q^{47} + 21 q^{49} + 3 q^{50} + 42 q^{51} - 6 q^{52} - 60 q^{53} + 54 q^{54} + 30 q^{55} + 12 q^{57} + 12 q^{58} + 3 q^{59} + 24 q^{60} + 54 q^{61} + 6 q^{62} - 18 q^{63} - 9 q^{64} + 24 q^{65} - 27 q^{66} - 15 q^{67} - 27 q^{68} + 30 q^{69} + 24 q^{70} + 36 q^{71} + 6 q^{72} - 42 q^{73} + 6 q^{74} - 24 q^{78} - 6 q^{79} - 3 q^{81} + 3 q^{82} + 36 q^{83} - 30 q^{84} - 6 q^{86} - 60 q^{89} - 18 q^{91} - 66 q^{93} + 6 q^{95} + 9 q^{97} + 12 q^{98} - 102 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * 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
$3$	−0.324081	+	1.70146i	−0.187108	+	0.982339i
$3$	−0.324081	+	1.70146i	−0.187108	+	0.982339i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	2.22841	−	0.392929i	0.996575	−	0.175723i	0.348508	−	0.937306i	$-0.386689\pi$
$5$	2.22841	−	0.392929i	0.996575	−	0.175723i	0.648067	+	0.761583i	$0.275577\pi$
$6$	0.845418	+	1.51171i	0.345140	+	0.617153i
$7$	−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
$9$	−2.78994	−	1.10282i	−0.929981	−	0.367608i
$10$	1.45449	−	1.73339i	0.459950	−	0.548148i
$11$	2.52163	−	1.45586i	0.760299	−	0.438959i	−0.0691039	−	0.997609i	$-0.522014\pi$
$11$	2.52163	−	1.45586i	0.760299	−	0.438959i	0.829403	+	0.558650i	$0.188681\pi$
$12$	1.61934	+	0.614613i	0.467462	+	0.177424i
$13$	−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
$15$	−0.0536321	+	3.91889i	−0.0138478	+	1.01185i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−3.72112	−	4.43466i	−0.902504	−	1.07556i	−0.996793	−	0.0800172i	$-0.974502\pi$
$17$	−3.72112	−	4.43466i	−0.902504	−	1.07556i	0.0942898	−	0.995545i	$-0.469942\pi$
$18$	−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
$21$	−3.06435	−	2.64359i	−0.668697	−	0.576879i
$22$	0.995869	−	2.73613i	0.212320	−	0.583344i
$23$	−8.06194	−	1.42154i	−1.68103	−	0.296411i	−0.750023	−	0.661412i	$-0.769958\pi$
$23$	−8.06194	−	1.42154i	−1.68103	−	0.296411i	−0.931007	+	0.365001i	$0.881069\pi$
$24$	1.63555	−	0.570068i	0.333855	−	0.116365i
$25$	0.112953	−	0.0411116i	0.0225906	−	0.00822231i
$26$	−1.14432	−	0.660676i	−0.224421	−	0.129569i
$27$	2.78058	−	4.38958i	0.535123	−	0.844774i
$28$	1.78993	+	1.50193i	0.338264	+	0.283837i
$29$	1.64718	+	1.38215i	0.305875	+	0.256659i	0.782784	−	0.622293i	$-0.213799\pi$
$29$	1.64718	+	1.38215i	0.305875	+	0.256659i	−0.476910	+	0.878952i	$0.658243\pi$
$30$	2.47793	+	3.03652i	0.452406	+	0.554390i
$31$	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
$33$	1.65988	+	4.76227i	0.288948	+	0.829005i
$34$	−5.70108	−	1.00525i	−0.977728	−	0.172400i
$35$	−1.80832	+	4.96833i	−0.305662	+	0.839801i
$36$	−1.57054	+	2.55605i	−0.261756	+	0.426009i
$37$		−	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	0.907115	−	0.420883i	$-0.138280\pi$
$41$	8.52555	+	3.10304i	1.33147	+	0.484614i	0.424352	+	0.905497i	$0.360502\pi$
$42$	−4.04670	−	0.0553812i	−0.624419	−	0.00854550i
$43$	−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
$45$	−6.65047	−	1.36129i	−0.991393	−	0.202929i
$46$	−7.08955	+	4.09315i	−1.04530	+	0.603502i
$47$	6.57494	−	7.83571i	0.959054	−	1.14296i	−0.0306076	−	0.999531i	$-0.509744\pi$
$47$	6.57494	−	7.83571i	0.959054	−	1.14296i	0.989661	−	0.143424i	$-0.0458113\pi$
$48$	0.886471	−	1.48801i	0.127951	−	0.214776i
$49$	0.770194	+	1.33401i	0.110028	+	0.190574i
$50$	0.0601011	−	0.104098i	0.00849958	−	0.0147217i
$51$	8.75134	−	4.89415i	1.22543	−	0.685318i
$52$	−1.30128	+	0.229450i	−0.180455	+	0.0318191i
$53$	−0.494197	+	2.80273i	−0.0678832	+	0.384985i	0.931870	+	0.362791i	$0.118176\pi$
$53$	−0.494197	+	2.80273i	−0.0678832	+	0.384985i	−0.999754	+	0.0221937i	$0.992935\pi$
$54$	−0.691519	−	5.14993i	−0.0941038	−	0.700817i
$55$	5.04717	−	4.23508i	0.680560	−	0.571058i
$56$	2.33658			0.312239
$57$	−6.17345	−	4.34609i	−0.817694	−	0.575653i
$58$	2.15025			0.282341
$59$	−2.53779	+	2.12946i	−0.330392	+	0.277232i	−0.792860	−	0.609404i	$-0.791409\pi$
$59$	−2.53779	+	2.12946i	−0.330392	+	0.277232i	0.462468	+	0.886636i	$0.346964\pi$
$60$	3.85004	+	0.733326i	0.497039	+	0.0946720i
$61$	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
$63$	5.49107	−	4.35714i	0.691810	−	0.548948i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.49497	−	2.58936i	−0.185428	−	0.321171i
$66$	4.33267	+	2.58116i	0.533315	+	0.317719i
$67$	−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
$69$	5.03141	−	13.2564i	0.605711	−	1.59588i
$70$	1.80832	+	4.96833i	0.216136	+	0.593829i
$71$	2.29622	+	13.0225i	0.272511	+	1.54549i	0.746758	+	0.665095i	$0.231609\pi$
$71$	2.29622	+	13.0225i	0.272511	+	1.54549i	−0.474247	+	0.880392i	$0.657280\pi$
$72$	0.439899	+	2.96757i	0.0518426	+	0.349732i
$73$	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
$78$	1.49497	−	1.73291i	0.169272	−	0.196214i
$79$	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
$81$	6.56756	+	6.15363i	0.729729	+	0.683736i
$82$	8.52555	−	3.10304i	0.941489	−	0.342674i
$83$	−1.62533	−	0.938386i	−0.178403	−	0.103001i	0.408139	−	0.912920i	$-0.366178\pi$
$83$	−1.62533	−	0.938386i	−0.178403	−	0.103001i	−0.586542	+	0.809919i	$0.699511\pi$
$84$	−3.13555	+	2.55874i	−0.342116	+	0.279182i
$85$	−10.0347	−	8.42009i	−1.08841	−	0.913288i
$86$	−0.293837	−	0.246558i	−0.0316852	−	0.0265871i
$87$	−2.88550	+	2.35469i	−0.309358	+	0.252450i
$88$	−2.52163	−	1.45586i	−0.268806	−	0.155195i
$89$	−5.82289	+	2.11936i	−0.617225	+	0.224651i	−0.631661	−	0.775244i	$-0.717627\pi$
$89$	−5.82289	+	2.11936i	−0.617225	+	0.224651i	0.0144367	+	0.999896i	$0.495405\pi$
$90$	−5.96957	+	3.23203i	−0.629248	+	0.340686i
$91$	3.04054	+	0.536130i	0.318735	+	0.0562017i
$92$	−2.79988	+	7.69261i	−0.291908	+	0.802010i
$93$	−6.89696	+	7.99469i	−0.715181	+	0.829011i
$94$		−	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
$99$	−8.64076	+	1.28086i	−0.868429	+	0.128732i
$100$	−0.0208729	−	0.118376i	−0.00208729	−	0.0118376i
$101$	−4.28105	−	11.7621i	−0.425980	−	1.17037i	−0.948232	−	0.317580i	$-0.897130\pi$
$101$	−4.28105	−	11.7621i	−0.425980	−	1.17037i	0.522251	−	0.852792i	$-0.325092\pi$
$102$	3.55802	−	9.37439i	0.352296	−	0.928203i
$103$	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
$105$	−7.86738	−	4.68693i	−0.767777	−	0.457398i
$106$	1.42298	+	2.46468i	0.138212	+	0.239391i
$107$	4.04583	−	7.00758i	0.391125	−	0.677449i	−0.601473	−	0.798893i	$-0.705419\pi$
$107$	4.04583	−	7.00758i	0.391125	−	0.677449i	0.992598	+	0.121444i	$0.0387526\pi$
$108$	−3.84005	−	3.50058i	−0.369509	−	0.336843i
$109$	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
$111$	5.08658	+	0.968852i	0.482797	+	0.0919594i
$112$	1.78993	−	1.50193i	0.169132	−	0.141919i
$113$	−14.8779			−1.39960			−0.699799	−	0.714340i	$-0.746727\pi$
$113$	−14.8779			−1.39960			−0.699799	+	0.714340i	$0.746727\pi$
$114$	−7.52275	+	0.638925i	−0.704570	+	0.0598408i
$115$	−18.5239			−1.72736
$116$	1.64718	−	1.38215i	0.152937	−	0.128330i
$117$	−0.108480	+	3.96257i	−0.0100290	+	0.366340i
$118$	−0.575270	+	3.26252i	−0.0529579	+	0.300339i
$119$	13.3210	−	2.34886i	1.22114	−	0.215320i
$120$	3.42068	−	1.91300i	0.312264	−	0.174632i
$121$	−1.26093	+	2.18399i	−0.114630	+	0.198545i
$122$	−2.93350	−	5.08097i	−0.265587	−	0.460009i
$123$	−8.04268	+	13.5002i	−0.725184	+	1.21728i
$124$	3.91842	−	4.66980i	0.351885	−	0.419360i
$125$	−9.56260	+	5.52097i	−0.855305	+	0.493811i
$126$	1.40569	−	6.86735i	0.125229	−	0.611793i
$127$	−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
$129$	0.664312	+	0.00909146i	0.0584894	+	0.000800458i
$130$	−2.80962	−	1.02262i	−0.246420	−	0.0896896i
$131$	−11.4406	−	13.6344i	−0.999574	−	1.19125i	−0.981510	−	0.191409i	$-0.938694\pi$
$131$	−11.4406	−	13.6344i	−0.999574	−	1.19125i	−0.0180637	−	0.999837i	$-0.505750\pi$
$132$	4.97816	−	0.807705i	0.433293	−	0.0703017i
$133$	−5.93447	−	8.27736i	−0.514584	−	0.717738i
$134$			16.2357i			1.40255i
$135$	4.47148	−	10.8743i	0.384843	−	0.935915i
$136$	−1.97997	+	5.43991i	−0.169781	+	0.466468i
$137$	16.1747	+	2.85204i	1.38190	+	0.243666i	0.814685	−	0.579904i	$-0.196910\pi$
$137$	16.1747	+	2.85204i	1.38190	+	0.243666i	0.567215	+	0.823570i	$0.308021\pi$
$138$	−4.66675	−	13.3891i	−0.397261	−	1.13976i
$139$	−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
$141$	11.2013	+	13.7264i	0.943323	+	1.15597i
$142$	10.1297	+	8.49984i	0.850067	+	0.713290i
$143$	−2.94729	−	2.47307i	−0.246465	−	0.206809i
$144$	2.24450	+	1.99053i	0.187042	+	0.165878i
$145$	4.21369	+	2.43277i	0.349928	+	0.202031i
$146$	5.84733	−	2.12826i	0.483929	−	0.176136i
$147$	−2.51938	+	0.878126i	−0.207795	+	0.0724266i
$148$	−2.94412	−	0.519128i	−0.242005	−	0.0426720i
$149$	−2.20295	+	6.05256i	−0.180473	+	0.495845i	−0.996634	−	0.0819794i	$-0.973876\pi$
$149$	−2.20295	+	6.05256i	−0.180473	+	0.495845i	0.816161	+	0.577824i	$0.196098\pi$
$150$	0.157641	+	0.135996i	0.0128714	+	0.0111040i
$151$			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
$156$	0.0313184	−	2.28844i	0.00250748	−	0.183221i
$157$	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
$159$	−4.60858	−	1.74917i	−0.365484	−	0.138718i
$160$	−1.95963	+	1.13139i	−0.154922	+	0.0894445i
$161$	12.2952	−	14.6529i	0.968999	−	1.15481i
$162$	8.98652	+	0.492402i	0.706048	+	0.0386868i
$163$	−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
$165$	5.57013	+	9.96007i	0.433634	+	0.775391i
$166$	−1.84826	+	0.325898i	−0.143453	+	0.0252946i
$167$	0.758731	−	4.30298i	0.0587124	−	0.332975i	−0.941277	−	0.337636i	$-0.890373\pi$
$167$	0.758731	−	4.30298i	0.0587124	−	0.332975i	0.999989	+	0.00466148i	$0.00148380\pi$
$168$	−0.757242	+	3.97560i	−0.0584225	+	0.306724i
$169$	8.62108	−	7.23395i	0.663160	−	0.556458i
$170$	−13.0993			−1.00467
$171$	9.39540	−	9.09541i	0.718484	−	0.695543i
$172$	−0.383577			−0.0292474
$173$	11.4117	−	9.57556i	0.867616	−	0.728016i	−0.0959786	−	0.995383i	$-0.530598\pi$
$173$	11.4117	−	9.57556i	0.867616	−	0.728016i	0.963595	+	0.267367i	$0.0861536\pi$
$174$	−0.696854	+	3.65856i	−0.0528284	+	0.277355i
$175$	−0.0487712	+	0.276595i	−0.00368676	+	0.0209086i
$176$	−2.86749	+	0.505616i	−0.216145	+	0.0381122i
$177$	−2.80074	−	5.00807i	−0.210517	−	0.376429i
$178$	−3.09829	+	5.36640i	−0.232227	+	0.402229i
$179$	1.68012	+	2.91005i	0.125578	+	0.217507i	0.921959	−	0.387288i	$-0.126588\pi$
$179$	1.68012	+	2.91005i	0.125578	+	0.217507i	−0.796381	+	0.604796i	$0.793255\pi$
$180$	−2.49545	+	6.31304i	−0.186000	+	0.470547i
$181$	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
$183$	9.50065	+	3.60593i	0.702308	+	0.266558i
$184$	2.79988	+	7.69261i	0.206410	+	0.567107i
$185$	−1.17467	−	6.66191i	−0.0863638	−	0.489794i
$186$	−0.144486	+	10.5576i	−0.0105942	+	0.774118i
$187$	−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	$-0.879264\pi$
$191$		−	10.2346i		−	0.740548i	0.928923	−	0.370274i	$-0.120736\pi$
$192$	−1.31147	−	1.13139i	−0.0946471	−	0.0816513i
$193$	−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
$195$	4.89019	−	1.70447i	0.350194	−	0.122060i
$196$	1.44749	−	0.526843i	0.103392	−	0.0376317i
$197$	5.46822	+	3.15708i	0.389595	+	0.224933i	0.681984	−	0.731367i	$-0.261117\pi$
$197$	5.46822	+	3.15708i	0.389595	+	0.224933i	−0.292390	+	0.956299i	$0.594450\pi$
$198$	−5.79588	+	6.53537i	−0.411895	+	0.464449i
$199$	−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
$201$	−17.7794	−	21.7873i	−1.25406	−	1.53676i
$202$	−10.8400	−	6.25847i	−0.762699	−	0.440345i
$203$	−4.72123	+	1.71839i	−0.331365	+	0.120607i
$204$	−3.30014	−	9.46825i	−0.231056	−	0.662910i
$205$	20.2177	+	3.56492i	1.41206	+	0.248985i
$206$	2.99863	−	8.23866i	0.208924	−	0.574014i
$207$	20.9246	+	12.8569i	1.45436	+	0.893616i
$208$			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
$213$	−22.9015	−	0.313418i	−1.56918	−	0.0214751i
$214$	−1.40510	−	7.96873i	−0.0960508	−	0.544731i
$215$	−0.296857	−	0.815608i	−0.0202455	−	0.0556240i
$216$	−5.19177	−	0.213263i	−0.353255	−	0.0145107i
$217$	−12.3355	+	7.12188i	−0.837386	+	0.483465i
$218$	4.74002	−	5.64893i	0.321034	−	0.382594i
$219$	−5.51615	+	9.25929i	−0.372747	+	0.625685i
$220$	−3.29431	−	5.70590i	−0.222102	−	0.384692i
$221$	−3.82468	+	6.62453i	−0.257276	+	0.445614i
$222$	4.51931	−	2.52741i	0.303316	−	0.169629i
$223$	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
$225$	−0.360471	−	0.00986833i	−0.0240314	−	0.000657889i
$226$	−11.3972	+	9.56335i	−0.758128	+	0.636145i
$227$	−17.0369			−1.13078			−0.565391	−	0.824823i	$-0.691275\pi$
$227$	−17.0369			−1.13078			−0.565391	+	0.824823i	$0.691275\pi$
$228$	−5.35207	+	5.32498i	−0.354449	+	0.352655i
$229$	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
$231$	−11.5759	−	2.20488i	−0.761636	−	0.145070i
$232$	0.373386	−	2.11758i	0.0245140	−	0.139026i
$233$	−22.4936	+	3.96623i	−1.47360	+	0.259836i	−0.852019	−	0.523510i	$-0.824622\pi$
$233$	−22.4936	+	3.96623i	−1.47360	+	0.259836i	−0.621585	+	0.783346i	$0.713511\pi$
$234$	2.46399	+	3.10524i	0.161076	+	0.202996i
$235$	11.5728	−	20.0447i	0.754925	−	1.30757i
$236$	1.65642	+	2.86901i	0.107824	+	0.186757i
$237$	7.72539	+	4.60235i	0.501818	+	0.298955i
$238$	8.69469	−	10.3619i	0.563593	−	0.671664i
$239$	2.62883	−	1.51775i	0.170045	−	0.0981753i	−0.412562	−	0.910929i	$-0.635366\pi$
$239$	2.62883	−	1.51775i	0.170045	−	0.0981753i	0.582607	+	0.812754i	$0.302033\pi$
$240$	1.39074	−	3.66421i	0.0897718	−	0.236524i
$241$	−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
$243$	−12.5986	+	9.18018i	−0.808199	+	0.588909i
$244$	−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
$249$	2.12337	−	2.46133i	0.134563	−	0.155980i
$250$	−3.77657	+	10.3760i	−0.238851	+	0.656238i
$251$	7.14276	+	1.25946i	0.450847	+	0.0794965i	0.394461	−	0.918913i	$-0.370931\pi$
$251$	7.14276	+	1.25946i	0.450847	+	0.0794965i	0.0563857	+	0.998409i	$0.482042\pi$
$252$	−3.33743	−	6.16426i	−0.210238	−	0.388312i
$253$	−22.3988	+	8.15248i	−1.40820	+	0.512542i
$254$	−6.43292	−	3.71405i	−0.403637	−	0.233040i
$255$	17.5785	−	14.3448i	1.10081	−	0.898308i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	7.10091	+	5.95837i	0.442942	+	0.371673i	0.836809	−	0.547495i	$-0.184418\pi$
$257$	7.10091	+	5.95837i	0.442942	+	0.371673i	−0.393867	+	0.919168i	$0.628863\pi$
$258$	0.514736	−	0.420047i	0.0320461	−	0.0261510i
$259$	6.04944	+	3.49265i	0.375894	+	0.217023i
$260$	−2.80962	+	1.02262i	−0.174245	+	0.0634202i
$261$	−3.07128	−	5.67268i	−0.190108	−	0.351130i
$262$	−17.5281	−	3.09067i	−1.08289	−	0.190943i
$263$	1.21399	−	3.33541i	0.0748578	−	0.205670i	−0.896620	−	0.442801i	$-0.853985\pi$
$263$	1.21399	−	3.33541i	0.0748578	−	0.205670i	0.971478	+	0.237131i	$0.0762070\pi$
$264$	3.29431	−	3.81864i	0.202751	−	0.235021i
$265$			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	0.194463	−	0.980910i	$-0.437703\pi$
$269$	−4.70855	−	1.71377i	−0.287086	−	0.104491i	−0.481549	+	0.876419i	$0.659926\pi$
$270$	−3.56454	−	11.2044i	−0.216931	−	0.681881i
$271$	−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
$273$	−1.89759	+	4.99962i	−0.114847	+	0.302591i
$274$	14.2238	−	8.21212i	0.859292	−	0.496112i
$275$	0.224973	−	0.268112i	0.0135664	−	0.0161678i
$276$	−12.1813	−	7.25692i	−0.733228	−	0.436815i
$277$	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
$279$	−11.3675	−	14.3258i	−0.680554	−	0.857665i
$280$	5.20686	−	0.918110i	0.311169	−	0.0548676i
$281$	2.50185	−	14.1887i	0.149248	−	0.846425i	−0.814610	−	0.580009i	$-0.803049\pi$
$281$	2.50185	−	14.1887i	0.149248	−	0.846425i	0.963858	−	0.266417i	$-0.0858397\pi$
$282$	17.4039	+	3.31496i	1.03639	+	0.197403i
$283$	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
$285$	−15.4647	−	7.25913i	−0.916049	−	0.429994i
$286$	−3.84742			−0.227502
$287$	−16.2394	+	13.6265i	−0.958584	+	0.804348i
$288$	2.99888	+	0.0820978i	0.176710	+	0.00483766i
$289$	−2.86743	+	16.2620i	−0.168673	+	0.956589i
$290$	4.79163	−	0.844894i	0.281374	−	0.0496139i
$291$	−14.4245	+	8.06682i	−0.845577	+	0.472886i
$292$	3.11130	−	5.38893i	0.182075	−	0.315363i
$293$	−4.11218	−	7.12251i	−0.240236	−	0.416102i	0.720545	−	0.693408i	$-0.243892\pi$
$293$	−4.11218	−	7.12251i	−0.240236	−	0.416102i	−0.960782	+	0.277306i	$0.910558\pi$
$294$	−1.36551	+	2.29211i	−0.0796381	+	0.133679i
$295$	−4.81851	+	5.74247i	−0.280544	+	0.334340i
$296$	−2.58901	+	1.49477i	−0.150483	+	0.0868816i
$297$	0.620963	−	15.1170i	0.0360319	−	0.877178i
$298$	2.20295	+	6.05256i	0.127614	+	0.350615i
$299$	1.87835	+	10.6527i	0.108628	+	0.616059i
$300$	0.208177	+	0.00284901i	0.0120191	+	0.000164488i
$301$	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
$306$	14.7971	+	9.09189i	0.845893	+	0.519749i
$307$	−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
$309$	4.99801	+	14.3395i	0.284327	+	0.815746i
$310$	12.9620	−	4.71780i	0.736194	−	0.267953i
$311$	9.98316	+	5.76378i	0.566093	+	0.326834i	0.755587	−	0.655048i	$-0.227352\pi$
$311$	9.98316	+	5.76378i	0.566093	+	0.326834i	−0.189494	+	0.981882i	$0.560685\pi$
$312$	−1.44699	−	1.77317i	−0.0819195	−	0.100386i
$313$	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
$315$	10.5243	−	11.8671i	0.592977	−	0.668635i
$316$	−4.49620	−	2.59588i	−0.252931	−	0.146030i
$317$	−15.4509	+	5.62366i	−0.867808	+	0.315856i	−0.737279	−	0.675588i	$-0.763890\pi$
$317$	−15.4509	+	5.62366i	−0.867808	+	0.315856i	−0.130529	+	0.991445i	$0.541667\pi$
$318$	−4.65472	+	1.62240i	−0.261024	+	0.0909795i
$319$	6.16581	+	1.08720i	0.345219	+	0.0608714i
$320$	−0.773919	+	2.12632i	−0.0432634	+	0.118865i
$321$	10.6120	+	9.15485i	0.592302	+	0.510974i
$322$		−	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
$327$	−0.174781	+	12.7712i	−0.00966540	+	0.706250i
$328$	−1.57546	−	8.93486i	−0.0869901	−	0.493345i
$329$	8.17442	+	22.4590i	0.450670	+	1.23821i
$330$	10.6692	+	4.04945i	0.587319	+	0.222915i
$331$	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
$333$	−3.29693	+	8.34064i	−0.180671	+	0.457064i
$334$	−2.18468	−	3.78398i	−0.119540	−	0.207050i
$335$	−18.3689	+	31.8160i	−1.00360	+	1.73829i
$336$	1.97539	+	3.53223i	0.107766	+	0.192699i
$337$	−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
$339$	4.82166	−	25.3142i	0.261876	−	1.37488i
$340$	−10.0347	+	8.42009i	−0.544207	+	0.456644i
$341$	17.7498			0.961207
$342$	1.35087	−	13.0067i	0.0730469	−	0.703324i
$343$	−19.9553			−1.07749
$344$	−0.293837	+	0.246558i	−0.0158426	+	0.0132935i
$345$	6.00323	−	31.5176i	0.323203	−	1.69685i
$346$	2.58682	−	14.6706i	0.139069	−	0.788697i
$347$	−5.30901	+	0.936123i	−0.285003	+	0.0502537i	−0.314322	−	0.949316i	$-0.601777\pi$
$347$	−5.30901	+	0.936123i	−0.285003	+	0.0502537i	0.0293192	+	0.999570i	$0.490666\pi$
$348$	1.81786	+	3.25055i	0.0974474	+	0.174248i
$349$	−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
$351$	−6.70701	−	1.46877i	−0.357994	−	0.0783971i
$352$	−1.87162	+	2.23051i	−0.0997577	+	0.118887i
$353$	19.6094	−	11.3215i	1.04370	−	0.602582i	0.122822	−	0.992429i	$-0.460805\pi$
$353$	19.6094	−	11.3215i	1.04370	−	0.602582i	0.920880	+	0.389847i	$0.127472\pi$
$354$	−5.36462	−	2.03612i	−0.285126	−	0.108219i
$355$	10.2338	+	28.1172i	0.543155	+	1.49231i
$356$	1.07603	+	6.10245i	0.0570293	+	0.323429i
$357$	−0.320603	+	23.4265i	−0.0169681	+	1.23986i
$358$	3.15759	+	1.14927i	0.166884	+	0.0607407i
$359$	−10.4708	−	12.4786i	−0.552628	−	0.658596i	0.415341	−	0.909666i	$-0.363662\pi$
$359$	−10.4708	−	12.4786i	−0.552628	−	0.658596i	−0.967969	+	0.251069i	$0.919218\pi$
$360$	2.14632	+	6.44012i	0.113121	+	0.339424i
$361$	−12.5344	−	14.2790i	−0.659705	−	0.751525i
$362$		−	19.8675i		−	1.04421i
$363$	−3.30734	−	2.85321i	−0.173590	−	0.149755i
$364$	1.05597	−	2.90125i	0.0553478	−	0.152067i
$365$	13.8665	+	2.44504i	0.725806	+	0.127979i
$366$	9.59577	−	3.34459i	0.501579	−	0.174825i
$367$	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
$369$	−20.3637	−	18.0595i	−1.06009	−	0.940139i
$370$	−5.18205	−	4.34825i	−0.269402	−	0.226055i
$371$	−5.09407	−	4.27443i	−0.264471	−	0.221918i
$372$	6.67559	+	8.18044i	0.346113	+	0.424136i
$373$	−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
$375$	−6.29466	−	18.0596i	−0.325055	−	0.932596i
$376$	−10.0734	−	1.77621i	−0.519496	−	0.0916011i
$377$	0.971760	−	2.66989i	0.0500482	−	0.137506i
$378$	11.2290	+	4.61730i	0.577557	+	0.237488i
$379$			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	0.398350	−	0.917233i	$-0.369583\pi$
$383$	2.22943	+	0.811445i	0.113918	+	0.0414629i	−0.284432	+	0.958696i	$0.591805\pi$
$384$	−1.73189	−	0.0237018i	−0.0883801	−	0.00120953i
$385$	2.67328	+	15.1609i	0.136243	+	0.772673i
$386$	0.784644	+	2.15579i	0.0399374	+	0.109727i
$387$	−0.230760	+	1.12735i	−0.0117302	+	0.0573067i
$388$	8.26346	−	4.77091i	0.419513	−	0.242206i
$389$	−15.0557	+	17.9426i	−0.763353	+	0.909728i	−0.998055	−	0.0623389i	$-0.980144\pi$
$389$	−15.0557	+	17.9426i	−0.763353	+	0.909728i	0.234702	+	0.972067i	$0.424588\pi$
$390$	2.65049	−	4.44905i	0.134213	−	0.225287i
$391$	23.6954	+	41.0416i	1.19833	+	2.07556i
$392$	0.770194	−	1.33401i	0.0389007	−	0.0673779i
$393$	26.9062	−	15.0472i	1.35724	−	0.759029i
$394$	6.21823	−	1.09644i	0.313270	−	0.0552380i
$395$	2.03999	−	11.5694i	0.102643	−	0.582119i
$396$	−0.239046	+	8.73190i	−0.0120125	+	0.438795i
$397$	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
$399$	16.0069	−	7.41473i	0.801345	−	0.371201i
$400$	−0.120202			−0.00601011
$401$	−23.7988	+	19.9695i	−1.18845	+	0.997231i	−0.188569	+	0.982060i	$0.560385\pi$
$401$	−23.7988	+	19.9695i	−1.18845	+	0.997231i	−0.999885	+	0.0151712i	$0.995171\pi$
$402$	−27.6244	−	5.26168i	−1.37778	−	0.262429i
$403$	1.39873	−	7.93257i	0.0696755	−	0.395150i
$404$	−12.3268	+	2.17355i	−0.613281	+	0.108138i
$405$	17.0532	+	11.1322i	0.847378	+	0.553164i
$406$	−2.51211	+	4.35111i	−0.124674	+	0.215942i
$407$	−4.35235	−	7.53850i	−0.215738	−	0.373670i
$408$	−8.61413	−	5.13181i	−0.426463	−	0.254062i
$409$	−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
$411$	−10.0946	+	26.5964i	−0.497928	+	1.31190i
$412$	−2.99863	−	8.23866i	−0.147732	−	0.405889i
$413$	−1.34417	−	7.62314i	−0.0661420	−	0.375110i
$414$	24.2935	−	3.60115i	1.19396	−	0.176987i
$415$	−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	$-0.997911\pi$
$419$		−	0.268652i		−	0.0131245i	0.999978	−	0.00656225i	$-0.00208885\pi$
$420$	−5.98188	+	6.93398i	−0.291886	+	0.338343i
$421$	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
$423$	−26.9851	+	14.6102i	−1.31206	+	0.710372i
$424$	2.67434	−	0.973379i	0.129877	−	0.0472714i
$425$	−0.602627	−	0.347927i	−0.0292317	−	0.0168769i
$426$	−17.7450	+	14.4807i	−0.859748	+	0.701591i
$427$	10.5015	+	8.81180i	0.508203	+	0.426433i
$428$	−6.19857	−	5.20122i	−0.299619	−	0.251410i
$429$	5.16300	−	4.21323i	0.249272	−	0.203417i
$430$	−0.751668	−	0.433976i	−0.0362487	−	0.0209282i
$431$	8.09752	−	2.94726i	0.390044	−	0.141964i	−0.139551	−	0.990215i	$-0.544566\pi$
$431$	8.09752	−	2.94726i	0.390044	−	0.141964i	0.529595	+	0.848250i	$0.322344\pi$
$432$	−4.11421	+	3.17384i	−0.197945	+	0.152701i
$433$	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
$435$	−5.50485	+	6.38102i	−0.263937	+	0.305946i
$436$		−	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
$441$	−0.677615	−	4.57121i	−0.0322674	−	0.217677i
$442$	1.32830	+	7.53314i	0.0631806	+	0.358315i
$443$	−2.20842	−	6.06757i	−0.104925	−	0.288279i	0.876110	−	0.482112i	$-0.160130\pi$
$443$	−2.20842	−	6.06757i	−0.104925	−	0.288279i	−0.981035	+	0.193833i	$0.937908\pi$
$444$	1.83741	−	4.84107i	0.0871996	−	0.229747i
$445$	−12.1430	+	7.01078i	−0.575634	+	0.332343i
$446$	3.33359	−	3.97281i	0.157850	−	0.188118i
$447$	−9.58426	−	5.70975i	−0.453320	−	0.270062i
$448$	−1.16829	−	2.02354i	−0.0551965	−	0.0956032i
$449$	−11.3528	+	19.6637i	−0.535774	+	0.927988i	0.463351	+	0.886175i	$0.346647\pi$
$449$	−11.3528	+	19.6637i	−0.535774	+	0.927988i	−0.999125	+	0.0418133i	$0.986687\pi$
$450$	−0.282480	+	0.224147i	−0.0133163	+	0.0105664i
$451$	26.0159	−	4.58730i	1.22504	−	0.216007i
$452$	−2.58353	+	14.6519i	−0.121519	+	0.689168i
$453$	−5.15258	−	0.981423i	−0.242089	−	0.0461113i
$454$	−13.0510	+	10.9511i	−0.612516	+	0.513962i
$455$	6.98624			0.327520
$456$	−0.677094	+	7.51941i	−0.0317078	+	0.352129i
$457$	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
$459$	−29.8131	+	4.00323i	−1.39156	+	0.186855i
$460$	−3.21663	+	18.2424i	−0.149976	+	0.850558i
$461$	−19.6634	+	3.46719i	−0.915818	+	0.161483i	−0.611644	−	0.791133i	$-0.709491\pi$
$461$	−19.6634	+	3.46719i	−0.915818	+	0.161483i	−0.304174	+	0.952617i	$0.598380\pi$
$462$	−10.2849	+	5.75179i	−0.478497	+	0.267597i
$463$	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
$465$	−12.2279	+	20.5255i	−0.567055	+	0.951845i
$466$	−14.6817	+	17.4969i	−0.680115	+	0.810529i
$467$	−13.6575	+	7.88518i	−0.631995	+	0.364883i	−0.781524	−	0.623875i	$-0.785558\pi$
$467$	−13.6575	+	7.88518i	−0.631995	+	0.364883i	0.149529	+	0.988757i	$0.452224\pi$
$468$	3.88354	+	0.794926i	0.179516	+	0.0367455i
$469$	−12.9749	−	35.6482i	−0.599124	−	1.64608i
$470$	−4.01919	−	22.7939i	−0.185391	−	1.05141i
$471$	−33.1204	−	0.453270i	−1.52611	−	0.0208856i
$472$	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
$477$	4.46970	−	7.27445i	0.204653	−	0.333074i
$478$	1.03820	−	2.85244i	0.0474864	−	0.130468i
$479$	9.47350	+	1.67043i	0.432855	+	0.0763241i	0.385831	−	0.922570i	$-0.373915\pi$
$479$	9.47350	+	1.67043i	0.432855	+	0.0763241i	0.0470248	+	0.998894i	$0.485026\pi$
$480$	−1.28994	−	3.70090i	−0.0588776	−	0.168922i
$481$	−3.71200	+	1.35106i	−0.169253	+	0.0616030i
$482$	−3.42230	−	1.97587i	−0.155881	−	0.0899982i
$483$	20.9467	+	25.6686i	0.953106	+	1.16796i
$484$	1.93186	+	1.62102i	0.0878116	+	0.0736827i
$485$	16.5397	+	13.8785i	0.751031	+	0.630190i
$486$	−3.75016	+	15.1306i	−0.170111	+	0.686340i
$487$	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
$489$	10.1219	−	3.52798i	0.457730	−	0.159541i
$490$	3.43261	+	0.605262i	0.155070	+	0.0273430i
$491$	−3.75074	+	10.3051i	−0.169268	+	0.465061i	−0.995102	−	0.0988527i	$-0.968483\pi$
$491$	−3.75074	+	10.3051i	−0.169268	+	0.465061i	0.825834	+	0.563914i	$0.190705\pi$
$492$	11.8986	+	10.2648i	0.536428	+	0.462772i
$493$		−	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
$498$	0.0444829	−	3.25036i	0.00199333	−	0.145652i
$499$	−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
$501$	7.07546	+	2.68547i	0.316108	+	0.119978i
$502$	6.28124	−	3.62647i	0.280345	−	0.161857i
$503$	10.7776	−	12.8442i	0.480550	−	0.572697i	−0.470238	−	0.882540i	$-0.655832\pi$
$503$	10.7776	−	12.8442i	0.480550	−	0.572697i	0.950788	+	0.309843i	$0.100276\pi$
$504$	−6.51893	−	2.57684i	−0.290376	−	0.114781i
$505$	−14.1616	−	24.5286i	−0.630182	−	1.09151i
$506$	−11.9181	+	20.6428i	−0.529826	+	0.917685i
$507$	9.51436	+	17.0128i	0.422547	+	0.755566i
$508$	−7.31524	+	1.28987i	−0.324561	+	0.0572289i
$509$	7.27364	−	41.2508i	0.322398	−	1.82841i	−0.204962	−	0.978770i	$-0.565707\pi$
$509$	7.27364	−	41.2508i	0.322398	−	1.82841i	0.527360	−	0.849642i	$-0.323182\pi$
$510$	4.24525	−	22.2880i	0.187983	−	0.986930i
$511$	−11.1380	+	9.34588i	−0.492716	+	0.413438i
$512$	1.00000			0.0441942
$513$	12.4306	+	18.9336i	0.548825	+	0.835937i
$514$	9.26957			0.408863
$515$	15.1974	−	12.7521i	0.669676	−	0.561925i
$516$	0.124310	−	0.652641i	0.00547244	−	0.0287309i
$517$	5.17184	−	29.3310i	0.227457	−	1.28997i
$518$	6.87917	−	1.21298i	0.302254	−	0.0532955i
$519$	12.5941	+	22.5198i	0.552821	+	0.988511i
$520$	−1.49497	+	2.58936i	−0.0655587	+	0.113551i
$521$	5.82256	+	10.0850i	0.255091	+	0.441831i	0.964920	−	0.262543i	$-0.0845612\pi$
$521$	5.82256	+	10.0850i	0.255091	+	0.441831i	−0.709829	+	0.704374i	$0.751228\pi$
$522$	−5.99907	−	2.37134i	−0.262572	−	0.103791i
$523$	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
$525$	−0.454810	−	0.172622i	−0.0198495	−	0.00753382i
$526$	−1.21399	−	3.33541i	−0.0529325	−	0.145431i
$527$	−6.12802	−	34.7537i	−0.266941	−	1.51390i
$528$	0.0690131	−	5.04278i	0.00300341	−	0.219459i
$529$	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
$534$	−8.12663	−	7.01078i	−0.351674	−	0.303386i
$535$	6.26229	−	17.2055i	0.270742	−	0.743858i
$536$	15.9890	+	2.81930i	0.690621	+	0.121775i
$537$	−5.49583	+	1.91557i	−0.237163	+	0.0826627i
$538$	−4.70855	+	1.71377i	−0.203000	+	0.0738860i
$539$	3.88428	+	2.24259i	0.167308	+	0.0965953i
$540$	−9.93267	−	6.29185i	−0.427434	−	0.270758i
$541$	−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
$543$	21.7565	+	26.6610i	0.933662	+	1.14413i
$544$	5.01345	+	2.89452i	0.214950	+	0.124101i
$545$	15.6798	−	5.70700i	0.671651	−	0.244461i
$546$	1.76006	+	5.04967i	0.0753235	+	0.216106i
$547$	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
$549$	−9.21434	+	14.9964i	−0.393258	+	0.640029i
$550$		−	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
$555$	11.7157	+	0.160335i	0.497303	+	0.00680585i
$556$	3.35731	+	19.0402i	0.142381	+	0.807485i
$557$	−6.96784	−	19.1440i	−0.295237	−	0.811156i	−0.995279	−	0.0970547i	$-0.969058\pi$
$557$	−6.96784	−	19.1440i	−0.295237	−	0.811156i	0.700042	−	0.714101i	$-0.253164\pi$
$558$	−17.9165	−	3.66734i	−0.758465	−	0.155251i
$559$	−0.438936	+	0.253420i	−0.0185650	+	0.0107185i
$560$	3.39854	−	4.05022i	0.143614	−	0.171153i
$561$	14.9424	−	25.0820i	0.630869	−	1.05896i
$562$	−7.20378	−	12.4773i	−0.303873	−	0.526324i
$563$	0.391026	−	0.677277i	0.0164798	−	0.0285438i	−0.857668	−	0.514204i	$-0.828087\pi$
$563$	0.391026	−	0.677277i	0.0164798	−	0.0285438i	0.874148	+	0.485660i	$0.161421\pi$
$564$	15.4630	−	8.64760i	0.651109	−	0.364130i
$565$	−33.1541	+	5.84597i	−1.39481	+	0.245942i
$566$	1.72121	−	9.76147i	0.0723478	−	0.410305i
$567$	−20.1249	+	6.10050i	−0.845167	+	0.256197i
$568$	10.1297	−	8.49984i	0.425033	−	0.356645i
$569$	12.5732			0.527098			0.263549	−	0.964646i	$-0.415107\pi$
$569$	12.5732			0.527098			0.263549	+	0.964646i	$0.415107\pi$
$570$	−16.5127	+	4.37969i	−0.691642	+	0.183445i
$571$	−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
$573$	17.4137	+	3.31683i	0.727469	+	0.138563i
$574$	−3.68118	+	20.8770i	−0.153650	+	0.871390i
$575$	−0.969062	+	0.170872i	−0.0404127	+	0.00712585i
$576$	2.35004	−	1.86475i	0.0979185	−	0.0776979i
$577$	−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
$579$	−3.41371	−	2.03369i	−0.141869	−	0.0845174i
$580$	3.12752	−	3.72723i	0.129863	−	0.154765i
$581$	3.79772	−	2.19262i	0.157556	−	0.0909650i
$582$	−5.86453	+	15.4514i	−0.243092	+	0.640482i
$583$	2.83421	+	7.78693i	0.117381	+	0.322502i
$584$	−1.08054	−	6.12807i	−0.0447132	−	0.253581i
$585$	1.31527	+	8.87286i	0.0543798	+	0.366848i
$586$	−7.72838	−	2.81290i	−0.319256	−	0.116200i
$587$	28.9490	+	34.5001i	1.19485	+	1.42397i	0.880095	+	0.474797i	$0.157479\pi$
$587$	28.9490	+	34.5001i	1.19485	+	1.42397i	0.314757	+	0.949172i	$0.398077\pi$
$588$	0.427300	+	2.63359i	0.0176215	+	0.108607i
$589$	−21.5951	+	15.4826i	−0.889810	+	0.637951i
$590$			7.49627i			0.308616i
$591$	−7.14380	+	8.28082i	−0.293856	+	0.340627i
$592$	−1.02248	+	2.80925i	−0.0420237	+	0.115459i
$593$	29.2417	+	5.15610i	1.20081	+	0.211736i	0.738050	−	0.674746i	$-0.235747\pi$
$593$	29.2417	+	5.15610i	1.20081	+	0.211736i	0.462763	+	0.886482i	$0.346858\pi$
$594$	−9.24135	−	11.9795i	−0.379177	−	0.491523i
$595$	28.7618	−	10.4684i	1.17912	−	0.429164i
$596$	5.57807	+	3.22050i	0.228487	+	0.131917i
$597$	13.9485	−	11.3826i	0.570876	−	0.465859i
$598$	8.28630	+	6.95303i	0.338852	+	0.284331i
$599$	23.2268	+	19.4896i	0.949023	+	0.796325i	0.979133	−	0.203222i	$-0.0651413\pi$
$599$	23.2268	+	19.4896i	0.949023	+	0.796325i	−0.0301101	+	0.999547i	$0.509586\pi$
$600$	0.161304	−	0.131631i	0.00658521	−	0.00537381i
$601$	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
$603$	42.8322	−	23.1901i	1.74426	−	0.944373i
$604$	2.98232	+	0.525863i	0.121349	+	0.0213971i
$605$	−1.95171	+	5.36229i	−0.0793484	+	0.218008i
$606$	14.1616	−	16.4156i	0.575275	−	0.666837i
$607$			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
$612$	17.1794	−	2.54659i	0.694435	−	0.102940i
$613$	−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
$615$	−12.6177	+	33.2443i	−0.508797	+	1.34054i
$616$	5.89199	−	3.40174i	0.237395	−	0.137060i
$617$	−3.45217	+	4.11414i	−0.138979	+	0.165629i	−0.831045	−	0.556206i	$-0.812257\pi$
$617$	−3.45217	+	4.11414i	−0.138979	+	0.165629i	0.692065	+	0.721835i	$0.256701\pi$
$618$	13.0460	+	7.77204i	0.524785	+	0.312637i
$619$	−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
$621$	−28.6568	+	31.4358i	−1.14996	+	1.26148i
$622$	11.3524	−	2.00174i	0.455191	−	0.0802625i
$623$	2.51422	−	14.2589i	0.100730	−	0.571269i
$624$	−2.24823	−	0.428225i	−0.0900013	−	0.0171427i
$625$	−19.6004	+	16.4467i	−0.784018	+	0.657869i
$626$	2.99772			0.119813
$627$	−21.8945	−	1.97151i	−0.874380	−	0.0787345i
$628$	19.1238			0.763124
$629$	−13.2576	+	11.1244i	−0.528614	+	0.443560i
$630$	0.434066	−	15.8556i	0.0172936	−	0.631703i
$631$	−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
$633$	8.42859	−	4.71366i	0.335006	−	0.187351i
$634$	−8.22124	+	14.2396i	−0.326507	+	0.565527i
$635$	−8.40409	−	14.5563i	−0.333506	−	0.577650i
$636$	−2.52287	+	4.23483i	−0.100038	+	0.167922i
$637$	1.30833	−	1.55920i	0.0518378	−	0.0617779i
$638$	5.42212	−	3.13046i	0.214664	−	0.123936i
$639$	7.95520	−	38.8644i	0.314703	−	1.53745i
$640$	0.773919	+	2.12632i	0.0305918	+	0.0840503i
$641$	1.24354	+	7.05244i	0.0491167	+	0.278555i	0.999468	−	0.0326255i	$-0.0103869\pi$
$641$	1.24354	+	7.05244i	0.0491167	+	0.278555i	−0.950351	+	0.311180i	$0.899276\pi$
$642$	14.0139	+	0.191787i	0.553083	+	0.00756923i
$643$	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	$0.165342\pi$
$647$			25.2527i			0.992786i	−0.868098	+	0.496393i	$0.834658\pi$
$648$	2.04541	−	8.76449i	0.0803515	−	0.344302i
$649$	−3.29916	+	9.06437i	−0.129503	+	0.355808i
$650$	−0.156416	−	0.0275804i	−0.00613516	−	0.00108179i
$651$	−8.11992	−	23.2964i	−0.318245	−	0.913057i
$652$	−5.81548	+	2.11666i	−0.227752	+	0.0828949i
$653$	4.44155	+	2.56433i	0.173811	+	0.100350i	0.584382	−	0.811479i	$-0.301337\pi$
$653$	4.44155	+	2.56433i	0.173811	+	0.100350i	−0.410570	+	0.911829i	$0.634670\pi$
$654$	8.07529	+	9.89567i	0.315769	+	0.386951i
$655$	−30.8518	−	25.8877i	−1.20548	−	1.01152i
$656$	−6.95009	−	5.83182i	−0.271355	−	0.227694i
$657$	−13.9666	−	12.3863i	−0.544890	−	0.483235i
$658$	20.6984	+	11.9502i	0.806906	+	0.465867i
$659$	−39.0596	+	14.2165i	−1.52154	+	0.553797i	−0.961533	−	0.274688i	$-0.911425\pi$
$659$	−39.0596	+	14.2165i	−1.52154	+	0.553797i	−0.560011	+	0.828485i	$0.689203\pi$
$660$	10.7760	−	3.75596i	0.419455	−	0.146201i
$661$	−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
$663$	−10.0319	−	8.65443i	−0.389606	−	0.336110i
$664$			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
$669$	−0.122921	+	8.98182i	−0.00475240	+	0.347257i
$670$	6.37947	+	36.1798i	0.246460	+	1.39775i
$671$	−5.84276	−	16.0529i	−0.225557	−	0.619713i
$672$	3.78371	+	1.43609i	0.145960	+	0.0553985i
$673$	−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
$675$	0.133613	−	0.610130i	0.00514275	−	0.0234839i
$676$	−5.62701	−	9.74627i	−0.216424	−	0.374857i
$677$	−16.0186	+	27.7451i	−0.615646	+	1.06633i	0.374625	+	0.927176i	$0.377771\pi$
$677$	−16.0186	+	27.7451i	−0.615646	+	1.06633i	−0.990271	+	0.139153i	$0.955562\pi$
$678$	−12.5781	−	22.4911i	−0.483058	−	0.863767i
$679$	−21.9565	+	3.87153i	−0.842614	+	0.148576i
$680$	−2.27468	+	12.9003i	−0.0872299	+	0.494705i
$681$	5.52135	−	28.9877i	0.211578	−	1.11081i
$682$	13.5972	−	11.4094i	0.520662	−	0.436887i
$683$	−8.09665			−0.309810			−0.154905	−	0.987929i	$-0.549507\pi$
$683$	−8.09665			−0.309810			−0.154905	+	0.987929i	$0.549507\pi$
$684$	−7.32574	−	10.8321i	−0.280107	−	0.414174i
$685$	37.1646			1.41998
$686$	−15.2867	+	12.8270i	−0.583647	+	0.489738i
$687$	−7.94656	+	41.7203i	−0.303180	+	1.59173i
$688$	−0.0666074	+	0.377749i	−0.00253938	+	0.0144016i
$689$	3.70340	−	0.653009i	0.141088	−	0.0248777i
$690$	−15.6604	−	28.0027i	−0.596181	−	1.06605i
$691$	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
$693$	7.50304	−	18.9813i	0.285017	−	0.721041i
$694$	−3.46521	+	4.12968i	−0.131538	+	0.156761i
$695$	−37.8874	+	21.8743i	−1.43715	+	0.829740i
$696$	3.48197	+	1.32157i	0.131984	+	0.0500940i
$697$	−17.9636	−	49.3547i	−0.680421	−	1.86944i
$698$	0.547538	+	3.10524i	0.0207246	+	0.117535i
$699$	0.541363	−	39.5574i	0.0204762	−	1.49620i
$700$	0.263924	+	0.0960605i	0.00997539	+	0.00363075i
$701$	−6.18601	−	7.37220i	−0.233642	−	0.278444i	0.636466	−	0.771305i	$-0.280396\pi$
$701$	−6.18601	−	7.37220i	−0.233642	−	0.278444i	−0.870108	+	0.492861i	$0.835951\pi$
$702$	−6.08197	+	3.18604i	−0.229549	+	0.120249i
$703$	11.8708	+	5.37519i	0.447717	+	0.202729i
$704$			2.91172i			0.109740i
$705$	30.3547	+	26.1867i	1.14322	+	0.986250i
$706$	7.74435	−	21.2774i	0.291462	−	0.800787i
$707$	28.8025	+	5.07867i	1.08323	+	0.191003i
$708$	−5.41833	+	1.88855i	−0.203633	+	0.0709760i
$709$	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
$711$	−10.3344	+	11.6529i	−0.387569	+	0.437019i
$712$	4.74686	+	3.98309i	0.177896	+	0.149273i
$713$	−38.2284	−	32.0774i	−1.43166	−	1.20131i
$714$	14.8126	+	18.1518i	0.554349	+	0.679314i
$715$	−7.53951	−	4.35294i	−0.281962	−	0.162791i
$716$	3.15759	−	1.14927i	0.118005	−	0.0429502i
$717$	1.73045	+	4.96472i	0.0646247	+	0.185411i
$718$	−16.0422	−	2.82867i	−0.598690	−	0.105565i
$719$	3.02583	−	8.31341i	0.112845	−	0.310038i	−0.870396	−	0.492353i	$-0.836137\pi$
$719$	3.02583	−	8.31341i	0.112845	−	0.310038i	0.983240	+	0.182315i	$0.0583591\pi$
$720$	5.78380	+	3.55379i	0.215550	+	0.132442i
$721$			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
$726$	−4.36758	−	0.0597726i	−0.162096	−	0.00221837i
$727$	−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
$729$	−11.5368	−	24.4111i	−0.427288	−	0.904116i
$730$	12.1940	−	7.04021i	0.451320	−	0.260570i
$731$	−1.42733	+	1.70103i	−0.0527918	+	0.0629149i
$732$	5.20092	−	8.73014i	0.192232	−	0.322675i
$733$	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
$735$	−5.26917	+	2.94676i	−0.194356	+	0.108693i
$736$	8.06194	−	1.42154i	0.297167	−	0.0523986i
$737$	−8.20902	+	46.5557i	−0.302383	+	1.71490i
$738$	−27.2079	−	0.744848i	−1.00154	−	0.0274182i
$739$	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
$741$	−2.60642	+	9.62949i	−0.0957492	+	0.353748i
$742$	−6.64984			−0.244123
$743$	24.2865	−	20.3788i	0.890984	−	0.747624i	−0.0774234	−	0.996998i	$-0.524669\pi$
$743$	24.2865	−	20.3788i	0.890984	−	0.747624i	0.968407	+	0.249374i	$0.0802249\pi$
$744$	10.3721	+	1.97559i	0.380259	+	0.0724288i
$745$	−2.53085	+	14.3532i	−0.0927233	+	0.525860i
$746$	−36.1510	+	6.37440i	−1.32358	+	0.233383i
$747$	3.49971	+	4.41050i	0.128048	+	0.161372i
$748$	−8.42803	+	14.5978i	−0.308159	+	0.533748i
$749$	9.45341	+	16.3738i	0.345420	+	0.598285i
$750$	−16.4305	−	9.78836i	−0.599957	−	0.357420i
$751$	−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
$753$	−4.45776	+	11.7450i	−0.162450	+	0.428010i
$754$	−0.971760	−	2.66989i	−0.0353894	−	0.0972316i
$755$	1.18992	+	6.74835i	0.0433055	+	0.245598i
$756$	11.5698	−	3.68079i	0.420791	−	0.133869i
$757$	−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	$0.157453\pi$
$761$			26.1918i			0.949453i	−0.880133	+	0.474727i	$0.842547\pi$
$762$	8.40409	−	9.74171i	0.304448	−	0.352905i
$763$	−5.89312	+	16.1912i	−0.213345	+	0.586161i
$764$	−10.0791	−	1.77722i	−0.364649	−	0.0642974i
$765$	18.7103	+	34.5581i	0.676473	+	1.24945i
$766$	2.22943	−	0.811445i	0.0805525	−	0.0293187i
$767$	3.79097	+	2.18872i	0.136884	+	0.0790301i
$768$	−1.34194	+	1.09508i	−0.0484230	+	0.0395153i
$769$	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
$771$	−12.4392	+	10.1509i	−0.447987	+	0.365577i
$772$	1.98679	+	1.14707i	0.0715061	+	0.0412841i
$773$	6.91607	−	2.51724i	0.248754	−	0.0905390i	−0.214634	−	0.976695i	$-0.568856\pi$
$773$	6.91607	−	2.51724i	0.248754	−	0.0905390i	0.463388	+	0.886156i	$0.346634\pi$
$774$	0.547878	+	1.01193i	0.0196931	+	0.0363732i
$775$	0.721618	+	0.127241i	0.0259213	+	0.00457062i
$776$	3.26349	−	8.96637i	0.117153	−	0.321874i
$777$	−7.90312	+	9.16100i	−0.283523	+	0.328649i
$778$			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
$783$	10.6472	−	3.38726i	0.380500	−	0.121051i
$784$	−0.267485	−	1.51699i	−0.00955305	−	0.0541780i
$785$	14.8003	+	40.6635i	0.528245	+	1.45134i
$786$	10.9392	−	28.8217i	0.390188	−	1.02804i
$787$	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
$789$	5.28164	+	3.14650i	0.188031	+	0.112018i
$790$	−5.87393	−	10.1739i	−0.208985	−	0.361973i
$791$	17.3818	−	30.1061i	0.618024	−	1.07045i
$792$	5.42964	+	6.84268i	0.192934	+	0.243144i
$793$	−7.63460	+	1.34619i	−0.271113	+	0.0478045i
$794$	1.19350	−	6.76869i	0.0423558	−	0.240212i
$795$	−10.9571	−	2.08702i	−0.388609	−	0.0740191i
$796$	−7.96251	+	6.68134i	−0.282224	+	0.236814i
$797$	4.12081			0.145966			0.0729832	−	0.997333i	$-0.476748\pi$
$797$	4.12081			0.145966			0.0729832	+	0.997333i	$0.476748\pi$
$798$	7.49587	−	15.9690i	0.265351	−	0.565297i
$799$	−59.2148			−2.09487
$800$	−0.0920802	+	0.0772645i	−0.00325553	+	0.00273171i
$801$	18.5828	+	0.508726i	0.656591	+	0.0179749i
$802$	−5.39474	+	30.5951i	−0.190495	+	1.08035i
$803$	17.8432	−	3.14625i	0.629674	−	0.111029i
$804$	−24.5437	+	13.7259i	−0.865588	+	0.484077i
$805$	21.6413	−	37.4838i	0.762754	−	1.32113i
$806$	−4.02747	−	6.97579i	−0.141862	−	0.245712i
$807$	4.44187	−	7.45602i	0.156361	−	0.262464i
$808$	−8.04574	+	9.58854i	−0.283048	+	0.337324i
$809$	31.6692	−	18.2842i	1.11343	−	0.642839i	0.173714	−	0.984796i	$-0.444423\pi$
$809$	31.6692	−	18.2842i	1.11343	−	0.642839i	0.939716	+	0.341957i	$0.111090\pi$
$810$	20.2191	−	2.43379i	0.710428	−	0.0855146i
$811$	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
$813$	16.0175	+	0.219208i	0.561758	+	0.00768795i
$814$	−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
$819$	−7.89168	−	4.84895i	−0.275758	−	0.169436i
$820$	7.02153	−	19.2915i	0.245202	−	0.673688i
$821$	−40.6182	−	7.16208i	−1.41758	−	0.249958i	−0.588235	−	0.808690i	$-0.700177\pi$
$821$	−40.6182	−	7.16208i	−1.41758	−	0.249958i	−0.829349	+	0.558732i	$0.811288\pi$
$822$	9.36294	+	26.8627i	0.326570	+	0.936943i
$823$	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
$825$	0.383273	+	0.469673i	0.0133439	+	0.0163519i
$826$	−5.92975	−	4.97565i	−0.206322	−	0.173125i
$827$	−17.4100	−	14.6087i	−0.605405	−	0.507995i	0.287773	−	0.957699i	$-0.407085\pi$
$827$	−17.4100	−	14.6087i	−0.605405	−	0.507995i	−0.893178	+	0.449704i	$0.851530\pi$
$828$	16.2951	−	18.3742i	0.566294	−	0.638547i
$829$	−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
$831$	−12.4315	+	4.33298i	−0.431243	+	0.150309i
$832$	1.30128	+	0.229450i	0.0451137	+	0.00795476i
$833$	3.04991	−	8.37957i	0.105673	−	0.290335i
$834$	−25.3559	−	21.8743i	−0.878002	−	0.757445i
$835$		−	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	0.313630	−	0.949545i	$-0.398455\pi$
$839$	−1.63571	−	0.595349i	−0.0564710	−	0.0205537i	−0.370101	+	0.928991i	$0.620677\pi$
$840$	−0.125316	+	9.15681i	−0.00432381	+	0.315940i
$841$	−4.23292	−	24.0061i	−0.145963	−	0.827797i
$842$	−6.44528	−	17.7083i	−0.222119	−	0.610267i
$843$	23.3307	+	8.85508i	0.803551	+	0.304985i
$844$	−4.82855	+	2.78777i	−0.166206	+	0.0959589i
$845$	16.3689	−	19.5077i	0.563107	−	0.671084i
$846$	−11.2805	+	28.5377i	−0.387833	+	0.981148i
$847$	−2.94626	−	5.10308i	−0.101235	−	0.175344i
$848$	1.42298	−	2.46468i	0.0488655	−	0.0846375i
$849$	8.37983	+	14.9842i	0.287595	+	0.514255i
$850$	−0.685283	+	0.120834i	−0.0235050	+	0.00414457i
$851$	−4.24974	+	24.1015i	−0.145679	+	0.826187i
$852$	−4.28545	+	22.4991i	−0.146817	+	0.770807i
$853$	−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
$855$	17.3629	−	23.9600i	0.593800	−	0.819415i
$856$	−8.09166			−0.276567
$857$	9.31787	−	7.81862i	0.318292	−	0.267079i	−0.469617	−	0.882870i	$-0.655608\pi$
$857$	9.31787	−	7.81862i	0.318292	−	0.267079i	0.787909	+	0.615791i	$0.211164\pi$
$858$	1.24687	−	6.54623i	0.0425676	−	0.223485i
$859$	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
$861$	−17.9221	−	32.0469i	−0.610783	−	1.09216i
$862$	4.30860	−	7.46272i	0.146752	−	0.254181i
$863$	22.3079	+	38.6385i	0.759371	+	1.31527i	0.943172	+	0.332306i	$0.107827\pi$
$863$	22.3079	+	38.6385i	0.759371	+	1.31527i	−0.183800	+	0.982964i	$0.558840\pi$
$864$	−1.11157	+	5.07587i	−0.0378162	+	0.172684i
$865$	21.6674	−	25.8223i	0.736715	−	0.877983i
$866$	7.49565	−	4.32761i	0.254712	−	0.147058i
$867$	−26.7399	−	10.1490i	−0.908135	−	0.344679i
$868$	4.87165	+	13.3848i	0.165355	+	0.454308i
$869$	−2.62504	−	14.8873i	−0.0890483	−	0.505018i
$870$	−0.115322	+	8.42659i	−0.00390979	+	0.285688i
$871$	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
$876$	8.16075	+	7.04021i	0.275726	+	0.237867i
$877$	−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
$879$	13.4514	−	4.68845i	0.453703	−	0.158138i
$880$	−6.19127	+	2.25344i	−0.208708	+	0.0759634i
$881$	−9.81390	−	5.66606i	−0.330639	−	0.190894i	0.325486	−	0.945547i	$-0.394472\pi$
$881$	−9.81390	−	5.66606i	−0.330639	−	0.190894i	−0.656125	+	0.754653i	$0.727805\pi$
$882$	−3.45740	−	3.06619i	−0.116417	−	0.103244i
$883$	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
$885$	−8.20901	−	10.0595i	−0.275943	−	0.338147i
$886$	−5.59191	−	3.22849i	−0.187864	−	0.108463i
$887$	38.4635	−	13.9996i	1.29148	−	0.470059i	0.397266	−	0.917704i	$-0.369959\pi$
$887$	38.4635	−	13.9996i	1.29148	−	0.470059i	0.894212	+	0.447644i	$0.147737\pi$
$888$	−1.70424	−	4.88954i	−0.0571906	−	0.164082i
$889$	17.0927	+	3.01390i	0.573269	+	0.101083i
$890$	−4.79565	+	13.1760i	−0.160751	+	0.441659i
$891$	25.5198	+	5.95568i	0.854945	+	0.199523i
$892$		−	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
$897$	−18.7338	−	0.256382i	−0.625505	−	0.00856036i
$898$	3.94280	+	22.3607i	0.131573	+	0.746188i
$899$	4.48316	+	12.3174i	0.149522	+	0.410807i
$900$	−0.0723136	+	0.353281i	−0.00241045	+	0.0117760i
$901$	14.2681	−	8.23770i	0.475340	−	0.274438i
$902$	16.9806	−	20.2367i	0.565394	−	0.673810i
$903$	−0.794506	+	1.33364i	−0.0264395	+	0.0443808i
$904$	7.43897	+	12.8847i	0.247416	+	0.428538i
$905$	22.4780	−	38.9330i	0.747193	−	1.29418i
$906$	−4.57795	+	2.56020i	−0.152092	+	0.0850570i
$907$	−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
$909$	−1.02761	+	37.5368i	−0.0340838	+	1.24502i
$910$	5.35177	−	4.49067i	0.177409	−	0.148864i
$911$	−41.3461			−1.36986			−0.684928	−	0.728610i	$-0.740167\pi$
$911$	−41.3461			−1.36986			−0.684928	+	0.728610i	$0.740167\pi$
$912$	4.31470	+	6.19543i	0.142874	+	0.205151i
$913$	−5.46465			−0.180853
$914$	6.96311	−	5.84275i	0.230319	−	0.193261i
$915$	22.5882	+	4.30242i	0.746743	+	0.142234i
$916$	4.25790	−	24.1478i	0.140685	−	0.797865i
$917$	40.9558	−	7.22161i	1.35248	−	0.238479i
$918$	−20.2650	+	22.2302i	−0.668843	+	0.733704i
$919$	−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
$921$	−15.1034	−	8.99773i	−0.497673	−	0.296485i
$922$	−12.8344	+	15.2954i	−0.422678	+	0.503728i
$923$	15.1319	−	8.73639i	0.498071	−	0.287562i
$924$	−4.18151	+	11.0171i	−0.137562	+	0.362437i
$925$	−0.122905	−	0.337677i	−0.00404108	−	0.0111028i
$926$	−0.105627	−	0.599038i	−0.00347110	−	0.0196856i
$927$	−26.0179	+	3.85677i	−0.854539	+	0.126673i
$928$	−2.02057	−	0.735428i	−0.0663285	−	0.0241416i
$929$	−3.69874	−	4.40799i	−0.121352	−	0.144621i	0.701948	−	0.712228i	$-0.252314\pi$
$929$	−3.69874	−	4.40799i	−0.121352	−	0.144621i	−0.823300	+	0.567607i	$0.807869\pi$
$930$	3.82640	+	23.5834i	0.125473	+	0.773329i
$931$	−6.68190	+	0.659722i	−0.218991	+	0.0216215i
$932$			22.8406i			0.748169i
$933$	−13.0422	+	15.1180i	−0.426983	+	0.494942i
$934$	−5.39378	+	14.8193i	−0.176490	+	0.484902i
$935$	−37.5622	−	6.62323i	−1.22842	−	0.216603i
$936$	3.48593	−	1.88734i	0.113941	−	0.0616896i
$937$	−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
$939$	−4.02275	+	3.28274i	−0.131278	+	0.107128i
$940$	−17.7305	−	14.8777i	−0.578306	−	0.485257i
$941$	13.7670	+	11.5519i	0.448792	+	0.376581i	0.838987	−	0.544151i	$-0.183148\pi$
$941$	13.7670	+	11.5519i	0.448792	+	0.376581i	−0.390196	+	0.920732i	$0.627593\pi$
$942$	−25.6630	+	20.9421i	−0.836147	+	0.682332i
$943$	−64.3213	−	37.1359i	−2.09459	−	1.20931i
$944$	3.11306	−	1.13306i	0.101321	−	0.0368780i
$945$	16.7807	+	21.7526i	0.545875	+	0.707612i
$946$	−1.09990	−	0.193942i	−0.0357609	−	0.00630561i
$947$	3.35631	−	9.22139i	0.109065	−	0.299655i	−0.873139	−	0.487472i	$-0.837919\pi$
$947$	3.35631	−	9.22139i	0.109065	−	0.299655i	0.982204	+	0.187817i	$0.0601413\pi$
$948$	5.87393	−	6.80884i	0.190776	−	0.221141i
$949$		−	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	0.182366	−	0.983231i	$-0.441624\pi$
$953$	−9.56813	−	3.48251i	−0.309942	−	0.112810i	−0.492308	+	0.870421i	$0.663847\pi$
$954$	−1.25194	−	8.44562i	−0.0405330	−	0.273437i
$955$	−4.02146	−	22.8068i	−0.130131	−	0.738012i
$956$	−1.03820	−	2.85244i	−0.0335779	−	0.0922546i
$957$	−3.84805	+	10.1385i	−0.124390	+	0.327733i
$958$	8.33086	−	4.80982i	0.269158	−	0.155398i
$959$	−24.6680	+	29.3982i	−0.796571	+	0.949316i
$960$	−3.36705	−	2.00589i	−0.108671	−	0.0647399i
$961$	3.08051	+	5.33561i	0.0993714	+	0.172116i
$962$	−1.97512	+	3.42100i	−0.0636803	+	0.110298i
$963$	−19.0158	+	15.0889i	−0.612774	+	0.486234i
$964$	−3.89169	+	0.686211i	−0.125343	+	0.0221014i
$965$	−0.901436	+	5.11230i	−0.0290183	+	0.164571i
$966$	32.5455	+	6.19901i	1.04713	+	0.199450i
$967$	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
$969$	3.69876	+	43.5494i	0.118821	+	1.39901i
$970$	21.5911			0.693248
$971$	11.6835	−	9.80361i	0.374941	−	0.314613i	−0.435772	−	0.900057i	$-0.643524\pi$
$971$	11.6835	−	9.80361i	0.374941	−	0.314613i	0.810712	+	0.585444i	$0.199080\pi$
$972$	6.85300	+	14.0013i	0.219810	+	0.449092i
$973$	7.84462	−	44.4890i	0.251487	−	1.42625i
$974$	32.6948	−	5.76497i	1.04761	−	0.184722i
$975$	0.240104	−	0.134277i	0.00768949	−	0.00430031i
$976$	−2.93350	+	5.08097i	−0.0938990	+	0.162638i
$977$	−29.3626	−	50.8576i	−0.939394	−	1.62708i	−0.766605	−	0.642119i	$-0.778055\pi$
$977$	−29.3626	−	50.8576i	−0.939394	−	1.62708i	−0.172789	−	0.984959i	$-0.555278\pi$
$978$	5.48611	−	9.20885i	0.175426	−	0.294466i
$979$	−11.5977	+	13.8216i	−0.370663	+	0.441739i
$980$	3.01859	−	1.74278i	0.0964253	−	0.0556712i
$981$	−21.6731	−	4.43629i	−0.691969	−	0.141640i
$982$	3.75074	+	10.3051i	0.119691	+	0.328848i
$983$	6.80396	+	38.5872i	0.217013	+	1.23074i	0.877380	+	0.479797i	$0.159290\pi$
$983$	6.80396	+	38.5872i	0.217013	+	1.23074i	−0.660367	+	0.750943i	$0.729599\pi$
$984$	15.7129	+	0.215039i	0.500909	+	0.00685520i
$985$	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
$990$	−10.3477	+	16.8408i	−0.328870	+	0.535237i
$991$	−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
$993$	0.995324	+	2.85562i	0.0315856	+	0.0906205i
$994$	−29.0342	+	10.5676i	−0.920909	+	0.335183i
$995$	−20.3690	−	11.7601i	−0.645742	−	0.372819i
$996$	−2.05522	−	2.51851i	−0.0651220	−	0.0798022i
$997$	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
$999$	−13.1228	−	8.31264i	−0.415187	−	0.263000i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.324081 + 1.70146i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.22841 - 0.392929i) q^{5} +(0.845418 + 1.51171i) q^{6} +(-1.16829 + 2.02354i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.78994 - 1.10282i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.324081 + 1.70146i) q^{3} +(0.173648 - 0.984808i) q^{4} +(2.22841 - 0.392929i) q^{5} +(0.845418 + 1.51171i) q^{6} +(-1.16829 + 2.02354i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.78994 - 1.10282i) q^{9} +(1.45449 - 1.73339i) q^{10} +(2.52163 - 1.45586i) q^{11} +(1.61934 + 0.614613i) q^{12} +(-0.451929 - 1.24167i) q^{13} +(0.405743 + 2.30108i) q^{14} +(-0.0536321 + 3.91889i) 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} +(-3.06435 - 2.64359i) q^{21} +(0.995869 - 2.73613i) q^{22} +(-8.06194 - 1.42154i) q^{23} +(1.63555 - 0.570068i) q^{24} +(0.112953 - 0.0411116i) q^{25} +(-1.14432 - 0.660676i) q^{26} +(2.78058 - 4.38958i) q^{27} +(1.78993 + 1.50193i) q^{28} +(1.64718 + 1.38215i) q^{29} +(2.47793 + 3.03652i) q^{30} +(5.27928 + 3.04799i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(1.65988 + 4.76227i) q^{33} +(-5.70108 - 1.00525i) q^{34} +(-1.80832 + 4.96833i) q^{35} +(-1.57054 + 2.55605i) 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} +(-4.04670 - 0.0553812i) q^{42} +(-0.0666074 - 0.377749i) q^{43} +(-0.995869 - 2.73613i) q^{44} +(-6.65047 - 1.36129i) q^{45} +(-7.08955 + 4.09315i) q^{46} +(6.57494 - 7.83571i) q^{47} +(0.886471 - 1.48801i) q^{48} +(0.770194 + 1.33401i) q^{49} +(0.0601011 - 0.104098i) q^{50} +(8.75134 - 4.89415i) q^{51} +(-1.30128 + 0.229450i) q^{52} +(-0.494197 + 2.80273i) q^{53} +(-0.691519 - 5.14993i) q^{54} +(5.04717 - 4.23508i) q^{55} +2.33658 q^{56} +(-6.17345 - 4.34609i) q^{57} +2.15025 q^{58} +(-2.53779 + 2.12946i) q^{59} +(3.85004 + 0.733326i) q^{60} +(1.01879 - 5.77787i) q^{61} +(6.00337 - 1.05856i) q^{62} +(5.49107 - 4.35714i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.49497 - 2.58936i) q^{65} +(4.33267 + 2.58116i) q^{66} +(-10.4361 + 12.4373i) q^{67} +(-5.01345 + 2.89452i) q^{68} +(5.03141 - 13.2564i) q^{69} +(1.80832 + 4.96833i) q^{70} +(2.29622 + 13.0225i) q^{71} +(0.439899 + 2.96757i) 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} +(1.49497 - 1.73291i) q^{78} +(1.77569 - 4.87866i) q^{79} +(-2.22841 - 0.392929i) q^{80} +(6.56756 + 6.15363i) q^{81} +(8.52555 - 3.10304i) q^{82} +(-1.62533 - 0.938386i) q^{83} +(-3.13555 + 2.55874i) q^{84} +(-10.0347 - 8.42009i) q^{85} +(-0.293837 - 0.246558i) q^{86} +(-2.88550 + 2.35469i) q^{87} +(-2.52163 - 1.45586i) q^{88} +(-5.82289 + 2.11936i) q^{89} +(-5.96957 + 3.23203i) q^{90} +(3.04054 + 0.536130i) q^{91} +(-2.79988 + 7.69261i) q^{92} +(-6.89696 + 7.99469i) 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} +(-8.64076 + 1.28086i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35} + 3 q^{38} + 6 q^{39} + 3 q^{41} - 6 q^{43} + 24 q^{44} - 54 q^{45} + 18 q^{46} + 30 q^{47} + 21 q^{49} + 3 q^{50} + 42 q^{51} - 6 q^{52} - 60 q^{53} + 54 q^{54} + 30 q^{55} + 12 q^{57} + 12 q^{58} + 3 q^{59} + 24 q^{60} + 54 q^{61} + 6 q^{62} - 18 q^{63} - 9 q^{64} + 24 q^{65} - 27 q^{66} - 15 q^{67} - 27 q^{68} + 30 q^{69} + 24 q^{70} + 36 q^{71} + 6 q^{72} - 42 q^{73} + 6 q^{74} - 24 q^{78} - 6 q^{79} - 3 q^{81} + 3 q^{82} + 36 q^{83} - 30 q^{84} - 6 q^{86} - 60 q^{89} - 18 q^{91} - 66 q^{93} + 6 q^{95} + 9 q^{97} + 12 q^{98} - 102 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

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