LMFDB - Embedded newform 114.2.l.b.59.2

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			59.2
Root			$0.0786547 + 1.73026i$ of defining polynomial
Character	$\chi$	$=$	114.59
Dual form			114.2.l.b.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 - 0.984808i) q^{2} +(0.517874 - 1.65282i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.258510 - 0.710252i) q^{5} +(-1.53778 - 0.797015i) q^{6} +(0.777943 + 1.34744i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.46361 - 1.71190i) q^{9} +O(q^{10})$	\(q+(0.173648 - 0.984808i) q^{2} +(0.517874 - 1.65282i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.258510 - 0.710252i) q^{5} +(-1.53778 - 0.797015i) q^{6} +(0.777943 + 1.34744i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.46361 - 1.71190i) q^{9} +(-0.744351 + 0.131249i) q^{10} +(0.832399 + 0.480586i) q^{11} +(-1.05194 + 1.37602i) q^{12} +(0.416982 + 0.496940i) q^{13} +(1.46205 - 0.532144i) q^{14} +(-1.30779 + 0.0594499i) q^{15} +(0.766044 + 0.642788i) q^{16} +(6.73013 + 1.18670i) q^{17} +(-2.11370 + 2.12892i) q^{18} +(-4.14364 + 1.35288i) q^{19} +0.755834i q^{20} +(2.62994 - 0.587996i) q^{21} +(0.617829 - 0.736300i) q^{22} +(0.400647 - 1.10077i) q^{23} +(1.17245 + 1.27490i) q^{24} +(3.39259 - 2.84672i) q^{25} +(0.561798 - 0.324354i) q^{26} +(-4.10530 + 3.18535i) q^{27} +(-0.270177 - 1.53225i) q^{28} +(1.39666 + 7.92086i) q^{29} +(-0.168549 + 1.29825i) q^{30} +(-2.63927 + 1.52379i) q^{31} +(0.766044 - 0.642788i) q^{32} +(1.22540 - 1.12692i) q^{33} +(2.33735 - 6.42181i) q^{34} +(0.755913 - 0.900862i) q^{35} +(1.72953 + 2.45127i) q^{36} +4.12648i q^{37} +(0.612788 + 4.31561i) q^{38} +(1.03729 - 0.431843i) q^{39} +(0.744351 + 0.131249i) q^{40} +(-4.09755 - 3.43825i) q^{41} +(-0.122378 - 2.69209i) q^{42} +(-7.34330 + 2.67274i) q^{43} +(-0.617829 - 0.736300i) q^{44} +(-0.579012 + 2.19233i) q^{45} +(-1.01447 - 0.585707i) q^{46} +(-3.11004 + 0.548383i) q^{47} +(1.45913 - 0.933249i) q^{48} +(2.28961 - 3.96572i) q^{49} +(-2.21436 - 3.83538i) q^{50} +(5.44676 - 10.5091i) q^{51} +(-0.221871 - 0.609587i) q^{52} +(-13.6276 - 4.96002i) q^{53} +(2.42408 + 4.59607i) q^{54} +(0.126153 - 0.715449i) q^{55} -1.55589 q^{56} +(0.0901766 + 7.54930i) q^{57} +8.04306 q^{58} +(2.02192 - 11.4669i) q^{59} +(1.24926 + 0.391427i) q^{60} +(10.1813 + 3.70568i) q^{61} +(1.04233 + 2.86378i) q^{62} +(0.390129 - 4.65133i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.245158 - 0.424626i) q^{65} +(-0.897012 - 1.40247i) q^{66} +(-9.19012 + 1.62047i) q^{67} +(-5.91837 - 3.41697i) q^{68} +(-1.61189 - 1.23226i) q^{69} +(-0.755913 - 0.900862i) q^{70} +(0.0322101 - 0.0117235i) q^{71} +(2.71436 - 1.27760i) q^{72} +(-3.04446 - 2.55461i) q^{73} +(4.06379 + 0.716556i) q^{74} +(-2.94818 - 7.08158i) q^{75} +(4.35646 + 0.145920i) q^{76} +1.49547i q^{77} +(-0.245158 - 1.09652i) q^{78} +(-0.893115 + 1.06437i) q^{79} +(0.258510 - 0.710252i) q^{80} +(3.13878 + 8.43493i) q^{81} +(-4.09755 + 3.43825i) q^{82} +(-10.4856 + 6.05389i) q^{83} +(-2.67245 - 0.346959i) q^{84} +(-0.896950 - 5.08686i) q^{85} +(1.35699 + 7.69585i) q^{86} +(13.8150 + 1.79358i) q^{87} +(-0.832399 + 0.480586i) q^{88} +(4.68075 - 3.92762i) q^{89} +(2.05848 + 0.950909i) q^{90} +(-0.345207 + 0.948448i) q^{91} +(-0.752970 + 0.897355i) q^{92} +(1.15173 + 5.15137i) q^{93} +3.15801i q^{94} +(2.03206 + 2.59329i) q^{95} +(-0.665696 - 1.59901i) q^{96} +(9.54804 + 1.68358i) q^{97} +(-3.50789 - 2.94347i) q^{98} +(-1.22799 - 2.60896i) 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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	0.517874	−	1.65282i	0.298995	−	0.954255i
$3$	0.517874	−	1.65282i	0.298995	−	0.954255i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.258510	−	0.710252i	−0.115609	−	0.317634i	0.868370	−	0.495917i	$-0.165168\pi$
$5$	−0.258510	−	0.710252i	−0.115609	−	0.317634i	−0.983979	+	0.178283i	$0.942946\pi$
$6$	−1.53778	−	0.797015i	−0.627796	−	0.325380i
$7$	0.777943	+	1.34744i	0.294035	+	0.509283i	0.974760	−	0.223256i	$-0.0716685\pi$
$7$	0.777943	+	1.34744i	0.294035	+	0.509283i	−0.680725	+	0.732539i	$0.738335\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.46361	−	1.71190i	−0.821204	−	0.570634i
$10$	−0.744351	+	0.131249i	−0.235384	+	0.0415046i
$11$	0.832399	+	0.480586i	0.250978	+	0.144902i	0.620212	−	0.784434i	$-0.287047\pi$
$11$	0.832399	+	0.480586i	0.250978	+	0.144902i	−0.369234	+	0.929336i	$0.620380\pi$
$12$	−1.05194	+	1.37602i	−0.303669	+	0.397222i
$13$	0.416982	+	0.496940i	0.115650	+	0.137826i	0.820763	−	0.571268i	$-0.193548\pi$
$13$	0.416982	+	0.496940i	0.115650	+	0.137826i	−0.705113	+	0.709095i	$0.749104\pi$
$14$	1.46205	−	0.532144i	0.390751	−	0.142222i
$15$	−1.30779	+	0.0594499i	−0.337671	+	0.0153499i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	6.73013	+	1.18670i	1.63230	+	0.287818i	0.913328	−	0.407226i	$-0.133504\pi$
$17$	6.73013	+	1.18670i	1.63230	+	0.287818i	0.718968	+	0.695043i	$0.244615\pi$
$18$	−2.11370	+	2.12892i	−0.498203	+	0.501790i
$19$	−4.14364	+	1.35288i	−0.950615	+	0.310371i
$19$	−4.14364	+	1.35288i	−0.950615	+	0.310371i
$20$			0.755834i			0.169010i
$21$	2.62994	−	0.587996i	0.573901	−	0.128311i
$22$	0.617829	−	0.736300i	0.131722	−	0.156980i
$23$	0.400647	−	1.10077i	0.0835407	−	0.229526i	−0.890888	−	0.454223i	$-0.849917\pi$
$23$	0.400647	−	1.10077i	0.0835407	−	0.229526i	0.974429	+	0.224697i	$0.0721392\pi$
$24$	1.17245	+	1.27490i	0.239324	+	0.260238i
$25$	3.39259	−	2.84672i	0.678519	−	0.569345i
$26$	0.561798	−	0.324354i	0.110178	−	0.0636111i
$27$	−4.10530	+	3.18535i	−0.790066	+	0.613022i
$28$	−0.270177	−	1.53225i	−0.0510586	−	0.289568i
$29$	1.39666	+	7.92086i	0.259354	+	1.47087i	0.784645	+	0.619945i	$0.212845\pi$
$29$	1.39666	+	7.92086i	0.259354	+	1.47087i	−0.525292	+	0.850922i	$0.676044\pi$
$30$	−0.168549	+	1.29825i	−0.0307727	+	0.237026i
$31$	−2.63927	+	1.52379i	−0.474028	+	0.273680i	−0.717924	−	0.696121i	$-0.754908\pi$
$31$	−2.63927	+	1.52379i	−0.474028	+	0.273680i	0.243897	+	0.969801i	$0.421574\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	1.22540	−	1.12692i	0.213314	−	0.196172i
$34$	2.33735	−	6.42181i	0.400852	−	1.10133i
$35$	0.755913	−	0.900862i	0.127773	−	0.152273i
$36$	1.72953	+	2.45127i	0.288256	+	0.408545i
$37$			4.12648i			0.678389i	0.940716	+	0.339195i	$0.110154\pi$
$37$			4.12648i			0.678389i	−0.940716	+	0.339195i	$0.889846\pi$
$38$	0.612788	+	4.31561i	0.0994073	+	0.700084i
$39$	1.03729	−	0.431843i	0.166100	−	0.0691502i
$40$	0.744351	+	0.131249i	0.117692	+	0.0207523i
$41$	−4.09755	−	3.43825i	−0.639929	−	0.536964i	0.264067	−	0.964504i	$-0.414936\pi$
$41$	−4.09755	−	3.43825i	−0.639929	−	0.536964i	−0.903996	+	0.427540i	$0.859380\pi$
$42$	−0.122378	−	2.69209i	−0.0188833	−	0.415399i
$43$	−7.34330	+	2.67274i	−1.11984	+	0.407589i	−0.834595	−	0.550865i	$-0.814298\pi$
$43$	−7.34330	+	2.67274i	−1.11984	+	0.407589i	−0.285248	+	0.958454i	$0.592076\pi$
$44$	−0.617829	−	0.736300i	−0.0931412	−	0.111001i
$45$	−0.579012	+	2.19233i	−0.0863139	+	0.326813i
$46$	−1.01447	−	0.585707i	−0.149576	−	0.0863578i
$47$	−3.11004	+	0.548383i	−0.453646	+	0.0799899i	−0.395802	−	0.918336i	$-0.629533\pi$
$47$	−3.11004	+	0.548383i	−0.453646	+	0.0799899i	−0.0578432	+	0.998326i	$0.518422\pi$
$48$	1.45913	−	0.933249i	0.210607	−	0.134703i
$49$	2.28961	−	3.96572i	0.327087	−	0.566531i
$50$	−2.21436	−	3.83538i	−0.313157	−	0.542405i
$51$	5.44676	−	10.5091i	0.762699	−	1.47157i
$52$	−0.221871	−	0.609587i	−0.0307680	−	0.0845345i
$53$	−13.6276	−	4.96002i	−1.87189	−	0.681312i	−0.966462	−	0.256809i	$-0.917329\pi$
$53$	−13.6276	−	4.96002i	−1.87189	−	0.681312i	−0.905427	−	0.424503i	$-0.860449\pi$
$54$	2.42408	+	4.59607i	0.329876	+	0.625445i
$55$	0.126153	−	0.715449i	0.0170105	−	0.0964711i
$56$	−1.55589			−0.207914
$57$	0.0901766	+	7.54930i	0.0119442	+	0.999929i
$58$	8.04306			1.05610
$59$	2.02192	−	11.4669i	0.263231	−	1.49286i	−0.510793	−	0.859704i	$-0.670648\pi$
$59$	2.02192	−	11.4669i	0.263231	−	1.49286i	0.774024	−	0.633156i	$-0.218241\pi$
$60$	1.24926	+	0.391427i	0.161278	+	0.0505330i
$61$	10.1813	+	3.70568i	1.30358	+	0.474464i	0.898161	−	0.439667i	$-0.144903\pi$
$61$	10.1813	+	3.70568i	1.30358	+	0.474464i	0.405419	+	0.914131i	$0.367126\pi$
$62$	1.04233	+	2.86378i	0.132376	+	0.363700i
$63$	0.390129	−	4.65133i	0.0491517	−	0.586012i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.245158	−	0.424626i	0.0304081	−	0.0526684i
$66$	−0.897012	−	1.40247i	−0.110415	−	0.172632i
$67$	−9.19012	+	1.62047i	−1.12275	+	0.197972i	−0.704049	−	0.710151i	$-0.748626\pi$
$67$	−9.19012	+	1.62047i	−1.12275	+	0.197972i	−0.418703	+	0.908123i	$0.637515\pi$
$68$	−5.91837	−	3.41697i	−0.717708	−	0.414369i
$69$	−1.61189	−	1.23226i	−0.194048	−	0.148346i
$70$	−0.755913	−	0.900862i	−0.0903489	−	0.107674i
$71$	0.0322101	−	0.0117235i	0.00382263	−	0.00139132i	−0.340108	−	0.940386i	$-0.610464\pi$
$71$	0.0322101	−	0.0117235i	0.00382263	−	0.00139132i	0.343931	+	0.938995i	$0.388241\pi$
$72$	2.71436	−	1.27760i	0.319890	−	0.150567i
$73$	−3.04446	−	2.55461i	−0.356327	−	0.298994i	0.446998	−	0.894535i	$-0.352493\pi$
$73$	−3.04446	−	2.55461i	−0.356327	−	0.298994i	−0.803325	+	0.595541i	$0.796938\pi$
$74$	4.06379	+	0.716556i	0.472406	+	0.0832979i
$75$	−2.94818	−	7.08158i	−0.340426	−	0.817711i
$76$	4.35646	+	0.145920i	0.499720	+	0.0167381i
$77$			1.49547i			0.170425i
$78$	−0.245158	−	1.09652i	−0.0277587	−	0.124157i
$79$	−0.893115	+	1.06437i	−0.100483	+	0.119751i	−0.813943	−	0.580945i	$-0.802683\pi$
$79$	−0.893115	+	1.06437i	−0.100483	+	0.119751i	0.713459	+	0.700697i	$0.247127\pi$
$80$	0.258510	−	0.710252i	0.0289023	−	0.0794085i
$81$	3.13878	+	8.43493i	0.348753	+	0.937215i
$82$	−4.09755	+	3.43825i	−0.452498	+	0.379691i
$83$	−10.4856	+	6.05389i	−1.15095	+	0.664500i	−0.949118	−	0.314920i	$-0.898022\pi$
$83$	−10.4856	+	6.05389i	−1.15095	+	0.664500i	−0.201830	+	0.979421i	$0.564689\pi$
$84$	−2.67245	−	0.346959i	−0.291588	−	0.0378563i
$85$	−0.896950	−	5.08686i	−0.0972879	−	0.551747i
$86$	1.35699	+	7.69585i	0.146328	+	0.829865i
$87$	13.8150	+	1.79358i	1.48113	+	0.192292i
$88$	−0.832399	+	0.480586i	−0.0887340	+	0.0512306i
$89$	4.68075	−	3.92762i	0.496159	−	0.416327i	−0.360069	−	0.932926i	$-0.617247\pi$
$89$	4.68075	−	3.92762i	0.496159	−	0.416327i	0.856227	+	0.516599i	$0.172802\pi$
$90$	2.05848	+	0.950909i	0.216983	+	0.100235i
$91$	−0.345207	+	0.948448i	−0.0361875	+	0.0994243i
$92$	−0.752970	+	0.897355i	−0.0785026	+	0.0935557i
$93$	1.15173	+	5.15137i	0.119429	+	0.534172i
$94$			3.15801i			0.325724i
$95$	2.03206	+	2.59329i	0.208485	+	0.266066i
$96$	−0.665696	−	1.59901i	−0.0679424	−	0.163199i
$97$	9.54804	+	1.68358i	0.969457	+	0.170941i	0.635885	−	0.771784i	$-0.280635\pi$
$97$	9.54804	+	1.68358i	0.969457	+	0.170941i	0.333571	+	0.942725i	$0.391746\pi$
$98$	−3.50789	−	2.94347i	−0.354350	−	0.297335i
$99$	−1.22799	−	2.60896i	−0.123418	−	0.262211i
$100$	−4.16163	+	1.51471i	−0.416163	+	0.151471i
$101$	12.0945	+	14.4137i	1.20345	+	1.43422i	0.871130	+	0.491053i	$0.163388\pi$
$101$	12.0945	+	14.4137i	1.20345	+	1.43422i	0.332323	+	0.943166i	$0.392168\pi$
$102$	−9.40363	−	7.18890i	−0.931098	−	0.711807i
$103$	9.92876	+	5.73237i	0.978310	+	0.564828i	0.901759	−	0.432238i	$-0.142276\pi$
$103$	9.92876	+	5.73237i	0.978310	+	0.564828i	0.0765505	+	0.997066i	$0.475609\pi$
$104$	−0.638853	+	0.112647i	−0.0626447	+	0.0110460i
$105$	−1.09749	−	1.71592i	−0.107104	−	0.167457i
$106$	−7.25107	+	12.5592i	−0.704286	+	1.21986i
$107$	−1.17826	−	2.04080i	−0.113906	−	0.197292i	0.803436	−	0.595392i	$-0.203003\pi$
$107$	−1.17826	−	2.04080i	−0.113906	−	0.197292i	−0.917342	+	0.398100i	$0.869670\pi$
$108$	4.94718	−	1.58916i	0.476043	−	0.152917i
$109$	−2.21678	−	6.09056i	−0.212329	−	0.583370i	0.787111	−	0.616811i	$-0.211576\pi$
$109$	−2.21678	−	6.09056i	−0.212329	−	0.583370i	−0.999441	+	0.0334410i	$0.989353\pi$
$110$	−0.682673	−	0.248473i	−0.0650904	−	0.0236910i
$111$	6.82032	+	2.13700i	0.647356	+	0.202835i
$112$	−0.270177	+	1.53225i	−0.0255293	+	0.144784i
$113$	−10.0387			−0.944358			−0.472179	−	0.881503i	$-0.656532\pi$
$113$	−10.0387			−0.944358			−0.472179	+	0.881503i	$0.656532\pi$
$114$	7.45026	+	1.22211i	0.697781	+	0.114462i
$115$	−0.885394			−0.0825635
$116$	1.39666	−	7.92086i	0.129677	−	0.735434i
$117$	−0.176570	−	1.93810i	−0.0163239	−	0.179177i
$118$	−10.9416	−	3.98240i	−1.00725	−	0.366610i
$119$	3.63665	+	9.99161i	0.333371	+	0.915929i
$120$	0.602411	−	1.16231i	0.0549923	−	0.106104i
$121$	−5.03807	−	8.72620i	−0.458007	−	0.793291i
$122$	5.41735	−	9.38312i	0.490464	−	0.849508i
$123$	−7.80481	+	4.99192i	−0.703736	+	0.450106i
$124$	3.00127	−	0.529205i	0.269522	−	0.0475240i
$125$	−6.17177	−	3.56327i	−0.552020	−	0.318709i
$126$	−4.51292	−	1.19190i	−0.402043	−	0.106183i
$127$	8.95146	+	10.6679i	0.794313	+	0.946626i	0.999485	−	0.0321003i	$-0.0102196\pi$
$127$	8.95146	+	10.6679i	0.794313	+	0.946626i	−0.205171	+	0.978726i	$0.565775\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	0.614653	+	13.5213i	0.0541172	+	1.19048i
$130$	−0.375604	−	0.315169i	−0.0329426	−	0.0276422i
$131$	10.9610	+	1.93273i	0.957671	+	0.168863i	0.630575	−	0.776128i	$-0.282819\pi$
$131$	10.9610	+	1.93273i	0.957671	+	0.168863i	0.327096	+	0.944991i	$0.393930\pi$
$132$	−1.53693	+	0.639848i	−0.133772	+	0.0556916i
$133$	−5.04643	−	4.53083i	−0.437581	−	0.392873i
$134$			9.33190i			0.806153i
$135$	3.32367	+	2.09235i	0.286056	+	0.180081i
$136$	−4.39278	+	5.23511i	−0.376678	+	0.448907i
$137$	−1.69757	+	4.66403i	−0.145033	+	0.398475i	−0.990845	−	0.135007i	$-0.956894\pi$
$137$	−1.69757	+	4.66403i	−0.145033	+	0.398475i	0.845812	+	0.533482i	$0.179117\pi$
$138$	−1.49344	+	1.37342i	−0.127130	+	0.116913i
$139$	−2.76202	+	2.31761i	−0.234272	+	0.196577i	−0.752364	−	0.658747i	$-0.771087\pi$
$139$	−2.76202	+	2.31761i	−0.234272	+	0.196577i	0.518093	+	0.855325i	$0.326642\pi$
$140$	−1.01844	+	0.587996i	−0.0860738	+	0.0496947i
$141$	−0.704229	+	5.42432i	−0.0593068	+	0.456810i
$142$	−0.00595218	−	0.0337565i	−0.000499496	−	0.00283278i
$143$	0.108273	+	0.614047i	0.00905425	+	0.0513492i
$144$	−0.786848	−	2.89497i	−0.0655706	−	0.241248i
$145$	5.26475	−	3.03961i	0.437214	−	0.252426i
$146$	−3.04446	+	2.55461i	−0.251961	+	0.211421i
$147$	−5.36888	−	5.83805i	−0.442818	−	0.481514i
$148$	1.41134	−	3.87762i	0.116011	−	0.318739i
$149$	12.3170	−	14.6788i	1.00904	−	1.20253i	0.0298610	−	0.999554i	$-0.490494\pi$
$149$	12.3170	−	14.6788i	1.00904	−	1.20253i	0.979183	−	0.202978i	$-0.0650620\pi$
$150$	−7.48594	+	1.67369i	−0.611225	+	0.136656i
$151$		−	19.2624i		−	1.56755i	−0.621042	−	0.783777i	$-0.713290\pi$
$151$		−	19.2624i		−	1.56755i	0.621042	−	0.783777i	$-0.286710\pi$
$152$	0.900193	−	4.26493i	0.0730153	−	0.345932i
$153$	−14.5489	−	14.4449i	−1.17621	−	1.16780i
$154$	1.47275	+	0.259686i	0.118678	+	0.0209261i
$155$	1.76455	+	1.48063i	0.141732	+	0.118927i
$156$	−1.12244	+	0.0510240i	−0.0898669	+	0.00408519i
$157$	−0.200940	+	0.0731363i	−0.0160368	+	0.00583691i	−0.350026	−	0.936740i	$-0.613827\pi$
$157$	−0.200940	+	0.0731363i	−0.0160368	+	0.00583691i	0.333989	+	0.942577i	$0.391605\pi$
$158$	0.893115	+	1.06437i	0.0710524	+	0.0846770i
$159$	−15.2554	+	19.9552i	−1.20983	+	1.58255i
$160$	−0.654571	−	0.377917i	−0.0517484	−	0.0298770i
$161$	1.79490	−	0.316489i	0.141458	−	0.0249428i
$162$	8.85183	−	1.62639i	0.695465	−	0.127781i
$163$	7.51668	−	13.0193i	0.588752	−	1.01975i	−0.405645	−	0.914031i	$-0.632953\pi$
$163$	7.51668	−	13.0193i	0.588752	−	1.01975i	0.994396	−	0.105717i	$-0.0337138\pi$
$164$	2.67448	+	4.63234i	0.208842	+	0.361725i
$165$	−1.11718	−	0.579020i	−0.0869720	−	0.0450767i
$166$	4.14110	+	11.3776i	0.321412	+	0.883072i
$167$	−8.87982	−	3.23199i	−0.687141	−	0.250099i	−0.0252305	−	0.999682i	$-0.508032\pi$
$167$	−8.87982	−	3.23199i	−0.687141	−	0.250099i	−0.661911	+	0.749583i	$0.730254\pi$
$168$	−0.805753	+	2.57160i	−0.0621652	+	0.198403i
$169$	2.18435	−	12.3881i	0.168027	−	0.952929i
$170$	−5.16533			−0.396163
$171$	12.5243	+	3.76054i	0.957758	+	0.287575i
$172$	7.81457			0.595856
$173$	2.33529	−	13.2441i	0.177549	−	1.00693i	−0.757612	−	0.652705i	$-0.773634\pi$
$173$	2.33529	−	13.2441i	0.177549	−	1.00693i	0.935161	−	0.354224i	$-0.115255\pi$
$174$	4.16529	−	13.2937i	0.315770	−	1.00779i
$175$	6.47502	+	2.35672i	0.489466	+	0.178151i
$176$	0.328740	+	0.903205i	0.0247797	+	0.0680817i
$177$	−17.9056	−	9.28026i	−1.34586	−	0.697547i
$178$	−3.05514	−	5.29167i	−0.228993	−	0.396627i
$179$	8.34644	−	14.4565i	0.623842	−	1.08053i	−0.364921	−	0.931038i	$-0.618904\pi$
$179$	8.34644	−	14.4565i	0.623842	−	1.08053i	0.988764	−	0.149488i	$-0.0477625\pi$
$180$	1.29391	−	1.86208i	0.0964426	−	0.138791i
$181$	−10.0398	+	1.77029i	−0.746251	+	0.131584i	−0.533828	−	0.845593i	$-0.679247\pi$
$181$	−10.0398	+	1.77029i	−0.746251	+	0.131584i	−0.212424	+	0.977178i	$0.568136\pi$
$182$	0.874094	+	0.504658i	0.0647922	+	0.0374078i
$183$	11.3974	−	14.9087i	0.842523	−	1.10209i
$184$	0.752970	+	0.897355i	0.0555097	+	0.0661539i
$185$	2.93084	−	1.06674i	0.215480	−	0.0784281i
$186$	5.27310	−	0.239706i	0.386643	−	0.0175761i
$187$	5.03184	+	4.22221i	0.367964	+	0.308759i
$188$	3.11004	+	0.548383i	0.226823	+	0.0399950i
$189$	−7.48576	−	3.05361i	−0.544509	−	0.222118i
$190$	2.90676	−	1.55086i	0.210878	−	0.112511i
$191$			12.0667i			0.873115i	0.899676	+	0.436558i	$0.143802\pi$
$191$			12.0667i			0.873115i	−0.899676	+	0.436558i	$0.856198\pi$
$192$	−1.69032	+	0.377917i	−0.121988	+	0.0272738i
$193$	−2.14990	+	2.56215i	−0.154753	+	0.184427i	−0.837850	−	0.545900i	$-0.816188\pi$
$193$	−2.14990	+	2.56215i	−0.154753	+	0.184427i	0.683098	+	0.730327i	$0.260632\pi$
$194$	3.31600	−	9.11063i	0.238075	−	0.654105i
$195$	−0.574869	−	0.625104i	−0.0411672	−	0.0447647i
$196$	−3.50789	+	2.94347i	−0.250563	+	0.210248i
$197$	5.15098	−	2.97392i	0.366992	−	0.211883i	−0.305151	−	0.952304i	$-0.598707\pi$
$197$	5.15098	−	2.97392i	0.366992	−	0.211883i	0.672144	+	0.740421i	$0.265374\pi$
$198$	−2.78256	+	0.756295i	−0.197748	+	0.0537476i
$199$	1.94088	+	11.0073i	0.137585	+	0.780286i	0.973024	+	0.230703i	$0.0741024\pi$
$199$	1.94088	+	11.0073i	0.137585	+	0.780286i	−0.835439	+	0.549583i	$0.814786\pi$
$200$	0.769038	+	4.36143i	0.0543792	+	0.308400i
$201$	−2.08099	+	16.0288i	−0.146782	+	1.13058i
$202$	16.2949	−	9.40789i	1.14651	−	0.661937i
$203$	−9.58634	+	8.04389i	−0.672829	+	0.564571i
$204$	−8.71261	+	8.01243i	−0.610005	+	0.560982i
$205$	−1.38276	+	3.79911i	−0.0965764	+	0.265342i
$206$	7.36940	−	8.78251i	0.513450	−	0.611906i
$207$	−2.87145	+	2.02600i	−0.199579	+	0.140817i
$208$			0.648709i			0.0449799i
$209$	−4.09933	−	0.865240i	−0.283557	−	0.0598499i
$210$	−1.88043	+	0.782853i	−0.129762	+	0.0540220i
$211$	−20.9377	−	3.69188i	−1.44141	−	0.254159i	−0.602364	−	0.798222i	$-0.705774\pi$
$211$	−20.9377	−	3.69188i	−1.44141	−	0.254159i	−0.839045	+	0.544063i	$0.816885\pi$
$212$	11.1093	+	9.32180i	0.762989	+	0.640224i
$213$	−0.00269607	−	0.0593087i	−0.000184731	−	0.00406376i
$214$	−2.21440	+	0.805976i	−0.151373	+	0.0550954i
$215$	3.79664	+	4.52466i	0.258928	+	0.308579i
$216$	−0.705946	−	5.14797i	−0.0480336	−	0.350275i
$217$	−4.10641	−	2.37084i	−0.278761	−	0.160943i
$218$	−6.38297	+	1.12549i	−0.432309	+	0.0762278i
$219$	−5.79895	+	3.70898i	−0.391856	+	0.250629i
$220$	−0.363243	+	0.629155i	−0.0244898	+	0.0424176i
$221$	2.21662	+	3.83930i	0.149106	+	0.258259i
$222$	3.28887	−	6.34562i	0.220734	−	0.425890i
$223$	4.71184	+	12.9457i	0.315528	+	0.866907i	0.991515	+	0.129993i	$0.0414955\pi$
$223$	4.71184	+	12.9457i	0.315528	+	0.866907i	−0.675987	+	0.736914i	$0.736282\pi$
$224$	1.46205	+	0.532144i	0.0976876	+	0.0355554i
$225$	−13.2313	+	1.20544i	−0.882090	+	0.0803625i
$226$	−1.74320	+	9.88615i	−0.115956	+	0.657617i
$227$	16.1886			1.07448			0.537238	−	0.843430i	$-0.319468\pi$
$227$	16.1886			1.07448			0.537238	+	0.843430i	$0.319468\pi$
$228$	2.49727	−	7.12486i	0.165386	−	0.471855i
$229$	−25.6462			−1.69475			−0.847374	−	0.530997i	$-0.821817\pi$
$229$	−25.6462			−1.69475			−0.847374	+	0.530997i	$0.821817\pi$
$230$	−0.153747	+	0.871943i	−0.0101378	+	0.0574942i
$231$	2.47174	+	0.774466i	0.162629	+	0.0509561i
$232$	−7.55800	−	2.75089i	−0.496207	−	0.180605i
$233$	3.98107	+	10.9379i	0.260808	+	0.716565i	0.999113	+	0.0420981i	$0.0134042\pi$
$233$	3.98107	+	10.9379i	0.260808	+	0.716565i	−0.738305	+	0.674467i	$0.764374\pi$
$234$	−1.93932	−	0.162660i	−0.126777	−	0.0106334i
$235$	1.19347	+	2.06715i	0.0778532	+	0.134846i
$236$	−5.82188	+	10.0838i	−0.378972	+	0.656399i
$237$	1.29669	+	2.02737i	0.0842293	+	0.131692i
$238$	10.4713	−	1.84637i	0.678754	−	0.119683i
$239$	−13.1831	−	7.61128i	−0.852746	−	0.492333i	0.00883069	−	0.999961i	$-0.497189\pi$
$239$	−13.1831	−	7.61128i	−0.852746	−	0.492333i	−0.861576	+	0.507628i	$0.830522\pi$
$240$	−1.04004	−	0.795091i	−0.0671343	−	0.0513229i
$241$	9.76016	+	11.6317i	0.628707	+	0.749264i	0.982541	−	0.186044i	$-0.0595666\pi$
$241$	9.76016	+	11.6317i	0.628707	+	0.749264i	−0.353834	+	0.935308i	$0.615122\pi$
$242$	−9.46848	+	3.44625i	−0.608657	+	0.221533i
$243$	15.5669	−	0.819603i	0.998617	−	0.0525776i
$244$	−8.29986	−	6.96441i	−0.531344	−	0.445851i
$245$	−3.40855	−	0.601019i	−0.217764	−	0.0383977i
$246$	3.56079	+	8.55308i	0.227028	+	0.545324i
$247$	−2.40012	−	1.49501i	−0.152716	−	0.0951254i
$248$		−	3.04757i		−	0.193521i
$249$	4.57573	+	20.4660i	0.289975	+	1.29698i
$250$	−4.58085	+	5.45925i	−0.289719	+	0.345273i
$251$	−3.71032	+	10.1940i	−0.234193	+	0.643441i	0.765807	+	0.643071i	$0.222340\pi$
$251$	−3.71032	+	10.1940i	−0.234193	+	0.643441i	−1.00000		0.000369965i	$0.999882\pi$
$252$	−1.95745	+	4.23738i	−0.123308	+	0.266930i
$253$	0.862512	−	0.723733i	0.0542257	−	0.0455007i
$254$	12.0603	−	6.96300i	0.756728	−	0.436897i
$255$	−8.87216	−	1.15186i	−0.555596	−	0.0721320i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−0.00786014	−	0.0445771i	−0.000490302	−	0.00278064i	0.984562	−	0.175038i	$-0.0560049\pi$
$257$	−0.00786014	−	0.0445771i	−0.000490302	−	0.00278064i	−0.985052	+	0.172258i	$0.944894\pi$
$258$	13.4226	+	1.74263i	0.835654	+	0.108491i
$259$	−5.56017	+	3.21017i	−0.345492	+	0.199470i
$260$	−0.375604	+	0.315169i	−0.0232940	+	0.0195460i
$261$	10.1189	−	21.9049i	0.626345	−	1.35588i
$262$	3.80673	−	10.4589i	0.235181	−	0.646153i
$263$	−3.52577	+	4.20185i	−0.217408	+	0.259097i	−0.863715	−	0.503981i	$-0.831868\pi$
$263$	−3.52577	+	4.20185i	−0.217408	+	0.259097i	0.646307	+	0.763078i	$0.276313\pi$
$264$	0.363243	+	1.62469i	0.0223561	+	0.0999925i
$265$			10.9612i			0.673342i
$266$	−5.33830	+	4.18299i	−0.327312	+	0.256476i
$267$	−4.06760	−	9.77044i	−0.248933	−	0.597941i
$268$	9.19012	+	1.62047i	0.561376	+	0.0989858i
$269$	1.50432	+	1.26228i	0.0917202	+	0.0769623i	0.687495	−	0.726189i	$-0.258710\pi$
$269$	1.50432	+	1.26228i	0.0917202	+	0.0769623i	−0.595775	+	0.803152i	$0.703155\pi$
$270$	2.63771	−	2.90984i	0.160526	−	0.177087i
$271$	19.8494	−	7.22458i	1.20576	−	0.438862i	0.340531	−	0.940233i	$-0.389393\pi$
$271$	19.8494	−	7.22458i	1.20576	−	0.438862i	0.865232	+	0.501371i	$0.167171\pi$
$272$	4.39278	+	5.23511i	0.266351	+	0.317425i
$273$	1.38884	+	1.06174i	0.0840563	+	0.0642594i
$274$	4.29839	+	2.48168i	0.259675	+	0.149924i
$275$	4.19208	−	0.739177i	0.252792	−	0.0445741i
$276$	1.09322	+	1.70924i	0.0658042	+	0.102884i
$277$	−3.91899	+	6.78789i	−0.235469	+	0.407845i	−0.959409	−	0.282018i	$-0.908996\pi$
$277$	−3.91899	+	6.78789i	−0.235469	+	0.407845i	0.723940	+	0.689863i	$0.242329\pi$
$278$	1.80278	+	3.12251i	0.108124	+	0.187276i
$279$	9.11072	+	0.764161i	0.545445	+	0.0457491i
$280$	0.402213	+	1.10507i	0.0240368	+	0.0660406i
$281$	−11.0064	−	4.00600i	−0.656587	−	0.238978i	−0.00782495	−	0.999969i	$-0.502491\pi$
$281$	−11.0064	−	4.00600i	−0.656587	−	0.238978i	−0.648762	+	0.760991i	$0.724713\pi$
$282$	5.21962	+	1.63545i	0.310824	+	0.0973898i
$283$	1.21905	−	6.91356i	0.0724648	−	0.410968i	−0.926899	−	0.375310i	$-0.877536\pi$
$283$	1.21905	−	6.91356i	0.0724648	−	0.410968i	0.999364	−	0.0356581i	$-0.0113527\pi$
$284$	−0.0342772			−0.00203398
$285$	5.33859	−	2.01562i	0.316231	−	0.119395i
$286$	0.623520			0.0368695
$287$	1.44517	−	8.19595i	0.0853055	−	0.483791i
$288$	−2.98763	+	0.272187i	−0.176048	+	0.0160388i
$289$	27.9116	+	10.1590i	1.64186	+	0.597587i
$290$	−2.07921	−	5.71259i	−0.122096	−	0.335455i
$291$	7.72733	−	14.9093i	0.452984	−	0.873998i
$292$	1.98713	+	3.44181i	0.116288	+	0.201417i
$293$	−1.29095	+	2.23599i	−0.0754180	+	0.130628i	−0.901268	−	0.433262i	$-0.857362\pi$
$293$	−1.29095	+	2.23599i	−0.0754180	+	0.130628i	0.825850	+	0.563890i	$0.190696\pi$
$294$	−6.68165	+	4.27355i	−0.389682	+	0.249239i
$295$	−8.66705	+	1.52824i	−0.504615	+	0.0889773i
$296$	−3.57364	−	2.06324i	−0.207713	−	0.119923i
$297$	−4.94808	+	0.678535i	−0.287117	+	0.0393726i
$298$	−12.3170	−	14.6788i	−0.713502	−	0.850319i
$299$	0.714078	−	0.259903i	0.0412962	−	0.0150306i
$300$	0.348339	+	7.66285i	0.0201114	+	0.442415i
$301$	−9.31401	−	7.81539i	−0.536851	−	0.450471i
$302$	−18.9698	−	3.34489i	−1.09159	−	0.192477i
$303$	30.0867	−	12.5256i	1.72844	−	0.719577i
$304$	−4.04382	−	1.62712i	−0.231929	−	0.0933215i
$305$		−	8.18923i		−	0.468914i
$306$	−16.7518	+	11.8195i	−0.957639	+	0.675679i
$307$	−1.26629	+	1.50910i	−0.0722709	+	0.0861290i	−0.800968	−	0.598707i	$-0.795682\pi$
$307$	−1.26629	+	1.50910i	−0.0722709	+	0.0861290i	0.728698	+	0.684836i	$0.240126\pi$
$308$	0.511482	−	1.40528i	0.0291444	−	0.0800735i
$309$	14.6164	−	13.4418i	0.831499	−	0.764677i
$310$	1.76455	−	1.48063i	0.100220	−	0.0840944i
$311$	22.4909	−	12.9851i	1.27534	−	0.736320i	0.299355	−	0.954142i	$-0.403229\pi$
$311$	22.4909	−	12.9851i	1.27534	−	0.736320i	0.975989	+	0.217822i	$0.0698952\pi$
$312$	−0.144660	+	1.11425i	−0.00818978	+	0.0630817i
$313$	−2.32842	−	13.2051i	−0.131610	−	0.746398i	−0.977161	−	0.212502i	$-0.931839\pi$
$313$	−2.32842	−	13.2051i	−0.131610	−	0.746398i	0.845551	−	0.533895i	$-0.179272\pi$
$314$	0.0371323	+	0.210588i	0.00209550	+	0.0118841i
$315$	−3.40446	+	0.925326i	−0.191820	+	0.0521362i
$316$	1.20329	−	0.694720i	0.0676904	−	0.0390811i
$317$	−23.3056	+	19.5557i	−1.30897	+	1.09836i	−0.320454	+	0.947264i	$0.603835\pi$
$317$	−23.3056	+	19.5557i	−1.30897	+	1.09836i	−0.988519	+	0.151095i	$0.951720\pi$
$318$	17.0030	+	18.4888i	0.953479	+	1.03680i
$319$	−2.64407	+	7.26453i	−0.148040	+	0.406736i
$320$	−0.485841	+	0.579002i	−0.0271593	+	0.0323672i
$321$	−3.98326	+	0.890567i	−0.222324	+	0.0497066i
$322$		−	1.82259i		−	0.101569i
$323$	−29.4927	+	4.18776i	−1.64102	+	0.233013i
$324$	−0.0645734	−	8.99977i	−0.00358741	−	0.499987i
$325$	2.82930	+	0.498882i	0.156941	+	0.0276730i
$326$	−11.5162	−	9.66326i	−0.637824	−	0.535198i
$327$	−11.2146	+	0.509796i	−0.620169	+	0.0281918i
$328$	5.02638	−	1.82945i	0.277536	−	0.101015i
$329$	−3.15834	−	3.76397i	−0.174125	−	0.207514i
$330$	−0.764219	+	0.999657i	−0.0420689	+	0.0550293i
$331$	−9.22014	−	5.32325i	−0.506785	−	0.292592i	0.224726	−	0.974422i	$-0.427851\pi$
$331$	−9.22014	−	5.32325i	−0.506785	−	0.292592i	−0.731511	+	0.681830i	$0.761185\pi$
$332$	11.9238	−	2.10249i	0.654405	−	0.115389i
$333$	7.06413	−	10.1660i	0.387112	−	0.557096i
$334$	−4.72485	+	8.18369i	−0.258533	+	0.447791i
$335$	3.52668	+	6.10839i	0.192683	+	0.333737i
$336$	2.39261	+	1.24006i	0.130528	+	0.0676511i
$337$	−2.38138	−	6.54278i	−0.129722	−	0.356408i	0.857780	−	0.514018i	$-0.171843\pi$
$337$	−2.38138	−	6.54278i	−0.129722	−	0.356408i	−0.987501	+	0.157610i	$0.949621\pi$
$338$	−11.8206	−	4.30233i	−0.642954	−	0.234016i
$339$	−5.19876	+	16.5921i	−0.282358	+	0.901158i
$340$	−0.896950	+	5.08686i	−0.0486440	+	0.275874i
$341$	−2.92924			−0.158627
$342$	5.87823	−	11.6810i	0.317858	−	0.631638i
$343$	18.0159			0.972770
$344$	1.35699	−	7.69585i	0.0731638	−	0.414932i
$345$	−0.458523	+	1.46340i	−0.0246860	+	0.0787866i
$346$	−12.6374	−	4.59962i	−0.679389	−	0.247277i
$347$	−9.63081	−	26.4604i	−0.517009	−	1.42047i	−0.873799	−	0.486287i	$-0.838351\pi$
$347$	−9.63081	−	26.4604i	−0.517009	−	1.42047i	0.356790	−	0.934185i	$-0.383871\pi$
$348$	−12.3684	−	6.41044i	−0.663018	−	0.343635i
$349$	9.79155	+	16.9595i	0.524130	+	0.907819i	0.999605	+	0.0280904i	$0.00894261\pi$
$349$	9.79155	+	16.9595i	0.524130	+	0.907819i	−0.475476	+	0.879729i	$0.657724\pi$
$350$	3.44529	−	5.96741i	0.184158	−	0.318972i
$351$	−3.29477	−	0.711853i	−0.175862	−	0.0379959i
$352$	0.946569	−	0.166906i	0.0504523	−	0.00889610i
$353$	−3.55050	−	2.04988i	−0.188974	−	0.109104i	0.402528	−	0.915408i	$-0.368132\pi$
$353$	−3.55050	−	2.04988i	−0.188974	−	0.109104i	−0.591502	+	0.806303i	$0.701465\pi$
$354$	−12.2485	+	16.0220i	−0.651002	+	0.851561i
$355$	−0.0166533	−	0.0198466i	−0.000883864	−	0.00105335i
$356$	−5.74179	+	2.08984i	−0.304314	+	0.110761i
$357$	18.3976	−	0.836324i	0.973706	−	0.0442629i
$358$	−12.7875	−	10.7300i	−0.675840	−	0.567097i
$359$	−5.52450	−	0.974118i	−0.291572	−	0.0514120i	0.0259490	−	0.999663i	$-0.491739\pi$
$359$	−5.52450	−	0.974118i	−0.291572	−	0.0514120i	−0.317521	+	0.948251i	$0.602850\pi$
$360$	−1.60911	−	1.59760i	−0.0848074	−	0.0842011i
$361$	15.3395	−	11.2117i	0.807340	−	0.590087i
$362$			10.1947i			0.535820i
$363$	−17.0319	+	3.80795i	−0.893943	+	0.199865i
$364$	0.648776	−	0.773182i	0.0340051	−	0.0405257i
$365$	−1.02739	+	2.82273i	−0.0537760	+	0.147748i
$366$	−12.7031	−	13.8132i	−0.664001	−	0.722026i
$367$	−2.28539	+	1.91767i	−0.119296	+	0.100101i	−0.700484	−	0.713668i	$-0.747033\pi$
$367$	−2.28539	+	1.91767i	−0.119296	+	0.100101i	0.581188	+	0.813769i	$0.302588\pi$
$368$	1.01447	−	0.585707i	0.0528831	−	0.0305321i
$369$	4.20882	+	15.4851i	0.219103	+	0.806123i
$370$	−0.541597	−	3.07155i	−0.0281563	−	0.159682i
$371$	−3.91814	−	22.2209i	−0.203420	−	1.15365i
$372$	0.679600	−	5.23462i	0.0352356	−	0.271402i
$373$	−18.2415	+	10.5317i	−0.944510	+	0.545313i	−0.891371	−	0.453274i	$-0.850256\pi$
$373$	−18.2415	+	10.5317i	−0.944510	+	0.545313i	−0.0531391	+	0.998587i	$0.516923\pi$
$374$	5.03184	−	4.22221i	0.260190	−	0.218325i
$375$	−9.08564	+	8.35548i	−0.469180	+	0.431475i
$376$	1.08010	−	2.96756i	0.0557021	−	0.153040i
$377$	−3.35381	+	3.99691i	−0.172730	+	0.205852i
$378$	−4.30711	+	6.84178i	−0.221534	+	0.351903i
$379$		−	9.54057i		−	0.490066i	−0.969515	−	0.245033i	$-0.921201\pi$
$379$		−	9.54057i		−	0.490066i	0.969515	−	0.245033i	$-0.0787988\pi$
$380$	−1.02255	−	3.13190i	−0.0524557	−	0.160663i
$381$	22.2679	−	9.27048i	1.14082	−	0.474941i
$382$	11.8834	+	2.09536i	0.608006	+	0.107208i
$383$	5.96084	+	5.00173i	0.304584	+	0.255577i	0.782249	−	0.622965i	$-0.214072\pi$
$383$	5.96084	+	5.00173i	0.304584	+	0.255577i	−0.477665	+	0.878542i	$0.658517\pi$
$384$	0.0786547	+	1.73026i	0.00401383	+	0.0882972i
$385$	1.06216	−	0.386595i	0.0541328	−	0.0197027i
$386$	2.14990	+	2.56215i	0.109427	+	0.130410i
$387$	22.6665	+	5.98640i	1.15220	+	0.304306i
$388$	−8.39641	−	4.84767i	−0.426263	−	0.246103i
$389$	9.63724	−	1.69931i	0.488627	−	0.0861582i	0.0760939	−	0.997101i	$-0.475755\pi$
$389$	9.63724	−	1.69931i	0.488627	−	0.0861582i	0.412533	+	0.910942i	$0.364644\pi$
$390$	−0.715433	+	0.457587i	−0.0362273	+	0.0231708i
$391$	4.00269	−	6.93287i	0.202425	−	0.350610i
$392$	2.28961	+	3.96572i	0.115643	+	0.200299i
$393$	8.87089	−	17.1157i	0.447477	−	0.863373i
$394$	−2.03428	−	5.58914i	−0.102486	−	0.281577i
$395$	0.986853	+	0.359185i	0.0496539	+	0.0180726i
$396$	0.261618	+	2.87162i	0.0131468	+	0.144304i
$397$	−2.05329	+	11.6448i	−0.103052	+	0.584435i	0.888929	+	0.458045i	$0.151450\pi$
$397$	−2.05329	+	11.6448i	−0.103052	+	0.584435i	−0.991981	+	0.126390i	$0.959661\pi$
$398$	11.1771			0.560257
$399$	−10.1020	+	5.99443i	−0.505735	+	0.300097i
$400$	4.42872			0.221436
$401$	−3.59086	+	20.3648i	−0.179319	+	1.01697i	0.753720	+	0.657195i	$0.228257\pi$
$401$	−3.59086	+	20.3648i	−0.179319	+	1.01697i	−0.933039	+	0.359774i	$0.882854\pi$
$402$	15.4239	+	4.83275i	0.769275	+	0.241035i
$403$	−1.85776	−	0.676169i	−0.0925416	−	0.0336824i
$404$	−6.43537	−	17.6810i	−0.320172	−	0.879665i
$405$	5.17952	−	4.40984i	0.257372	−	0.219127i
$406$	6.25704	+	10.8375i	0.310532	+	0.537857i
$407$	−1.98313	+	3.43488i	−0.0982999	+	0.170260i
$408$	6.37778	+	9.97159i	0.315747	+	0.493667i
$409$	3.39761	−	0.599090i	0.168001	−	0.0296231i	−0.0890148	−	0.996030i	$-0.528372\pi$
$409$	3.39761	−	0.599090i	0.168001	−	0.0296231i	0.257016	+	0.966407i	$0.417261\pi$
$410$	3.50128	+	2.02147i	0.172916	+	0.0998331i
$411$	6.82966	+	5.22115i	0.336882	+	0.257540i
$412$	−7.36940	−	8.78251i	−0.363064	−	0.432683i
$413$	17.0238	−	6.19617i	0.837688	−	0.304893i
$414$	1.49660	+	3.17964i	0.0735538	+	0.156271i
$415$	7.01043	+	5.88245i	0.344128	+	0.288758i
$416$	0.638853	+	0.112647i	0.0313224	+	0.00552298i
$417$	2.40021	+	5.76535i	0.117539	+	0.282331i
$418$	−1.56394	+	3.88681i	−0.0764946	+	0.190110i
$419$			25.3156i			1.23675i	0.785884	+	0.618374i	$0.212208\pi$
$419$			25.3156i			1.23675i	−0.785884	+	0.618374i	$0.787792\pi$
$420$	0.444427	+	1.98780i	0.0216858	+	0.0969948i
$421$	20.4536	−	24.3756i	0.996845	−	1.18799i	0.0146955	−	0.999892i	$-0.495322\pi$
$421$	20.4536	−	24.3756i	0.996845	−	1.18799i	0.982150	−	0.188102i	$-0.0602334\pi$
$422$	−7.27158	+	19.9785i	−0.353975	+	0.972538i
$423$	8.60071	+	3.97307i	0.418181	+	0.193178i
$424$	11.1093	−	9.32180i	0.539515	−	0.452706i
$425$	26.2108	−	15.1328i	1.27141	−	0.734049i
$426$	−0.0588758	−	0.00764373i	−0.00285254	−	0.000370340i
$427$	2.92728	+	16.6014i	0.141661	+	0.803400i
$428$	0.409205	+	2.32072i	0.0197797	+	0.112176i
$429$	1.07098	+	0.139043i	0.0517074	+	0.00671308i
$430$	5.11520	−	2.95326i	0.246677	−	0.142419i
$431$	−25.2345	+	21.1742i	−1.21550	+	1.01993i	−0.216455	+	0.976293i	$0.569449\pi$
$431$	−25.2345	+	21.1742i	−1.21550	+	1.01993i	−0.999048	+	0.0436350i	$0.986106\pi$
$432$	−5.19235	−	0.198715i	−0.249817	−	0.00956069i
$433$	−5.46188	+	15.0064i	−0.262481	+	0.721161i	0.736517	+	0.676419i	$0.236469\pi$
$433$	−5.46188	+	15.0064i	−0.262481	+	0.721161i	−0.998999	+	0.0447423i	$0.985753\pi$
$434$	−3.04789	+	3.63233i	−0.146303	+	0.174358i
$435$	−2.29744	−	10.2758i	−0.110154	−	0.492688i
$436$			6.48144i			0.310405i
$437$	−0.170932	+	5.10321i	−0.00817679	+	0.244120i
$438$	2.64565	+	6.35490i	0.126414	+	0.303649i
$439$	−30.5401	−	5.38505i	−1.45760	−	0.257014i	−0.612011	−	0.790849i	$-0.709639\pi$
$439$	−30.5401	−	5.38505i	−1.45760	−	0.257014i	−0.845589	+	0.533835i	$0.820750\pi$
$440$	0.556520	+	0.466976i	0.0265311	+	0.0222622i
$441$	−12.4296	+	5.85041i	−0.591887	+	0.278591i
$442$	4.16589	−	1.51626i	0.198151	−	0.0721211i
$443$	12.5287	+	14.9311i	0.595257	+	0.709400i	0.976607	−	0.215031i	$-0.0689852\pi$
$443$	12.5287	+	14.9311i	0.595257	+	0.709400i	−0.381350	+	0.924431i	$0.624541\pi$
$444$	−5.67811	−	4.34081i	−0.269471	−	0.206006i
$445$	−3.99962	−	2.30918i	−0.189600	−	0.109466i
$446$	13.5672	−	2.39226i	0.642426	−	0.113277i
$447$	−17.8827	−	27.9594i	−0.845823	−	1.32244i
$448$	0.777943	−	1.34744i	0.0367544	−	0.0636604i
$449$	6.61607	+	11.4594i	0.312232	+	0.540801i	0.978845	−	0.204602i	$-0.0655901\pi$
$449$	6.61607	+	11.4594i	0.312232	+	0.540801i	−0.666613	+	0.745404i	$0.732257\pi$
$450$	−1.11047	+	13.2397i	−0.0523483	+	0.624123i
$451$	−1.75842	−	4.83122i	−0.0828007	−	0.227493i
$452$	9.43326	+	3.43342i	0.443703	+	0.161495i
$453$	−31.8373	−	9.97551i	−1.49585	−	0.468690i
$454$	2.81112	−	15.9427i	0.131933	−	0.748227i
$455$	0.762876			0.0357642
$456$	−6.58297	−	3.69655i	−0.308276	−	0.173107i
$457$	−15.4038			−0.720559			−0.360279	−	0.932844i	$-0.617319\pi$
$457$	−15.4038			−0.720559			−0.360279	+	0.932844i	$0.617319\pi$
$458$	−4.45341	+	25.2566i	−0.208094	+	1.18016i
$459$	−31.4093	+	16.5661i	−1.46606	+	0.773238i
$460$	0.831999	+	0.302823i	0.0387921	+	0.0141192i
$461$	−5.65076	−	15.5253i	−0.263182	−	0.723087i	−0.998948	−	0.0458511i	$-0.985400\pi$
$461$	−5.65076	−	15.5253i	−0.263182	−	0.723087i	0.735766	−	0.677236i	$-0.236822\pi$
$462$	1.19191	−	2.29971i	0.0554529	−	0.106992i
$463$	−4.69170	−	8.12625i	−0.218042	−	0.377659i	0.736168	−	0.676799i	$-0.236634\pi$
$463$	−4.69170	−	8.12625i	−0.218042	−	0.377659i	−0.954209	+	0.299140i	$0.903300\pi$
$464$	−4.02153	+	6.96549i	−0.186695	+	0.323365i
$465$	3.36103	−	2.14970i	0.155864	−	0.0996899i
$466$	11.4630	−	2.02124i	0.531014	−	0.0936321i
$467$	18.5458	+	10.7074i	0.858196	+	0.495480i	0.863408	−	0.504507i	$-0.168326\pi$
$467$	18.5458	+	10.7074i	0.858196	+	0.495480i	−0.00521153	+	0.999986i	$0.501659\pi$
$468$	−0.496948	+	1.88161i	−0.0229714	+	0.0869774i
$469$	−9.33287	−	11.1225i	−0.430952	−	0.513588i
$470$	2.24298	−	0.816380i	0.103461	−	0.0376568i
$471$	0.0168192	+	0.369993i	0.000774989	+	0.0170484i
$472$	8.91965	+	7.48447i	0.410560	+	0.344501i
$473$	−7.39703	−	1.30430i	−0.340116	−	0.0599716i
$474$	2.22174	−	0.924946i	0.102048	−	0.0424842i
$475$	−10.2064	+	16.3855i	−0.468302	+	0.751820i
$476$		−	10.6328i		−	0.487356i
$477$	25.0820	+	35.5486i	1.14842	+	1.62766i
$478$	−9.78488	+	11.6612i	−0.447550	+	0.533369i
$479$	11.4165	−	31.3665i	0.521632	−	1.43317i	−0.347071	−	0.937839i	$-0.612824\pi$
$479$	11.4165	−	31.3665i	0.521632	−	1.43317i	0.868703	−	0.495333i	$-0.164954\pi$
$480$	−0.963613	+	0.886174i	−0.0439827	+	0.0404481i
$481$	−2.05061	+	1.72067i	−0.0934998	+	0.0784557i
$482$	13.1498	−	7.59206i	0.598959	−	0.345809i
$483$	0.406432	−	3.13054i	0.0184933	−	0.142444i
$484$	1.74971	+	9.92307i	0.0795320	+	0.451049i
$485$	−1.27250	−	7.21673i	−0.0577815	−	0.327695i
$486$	1.89601	−	15.4727i	0.0860048	−	0.701857i
$487$	−28.9750	+	16.7288i	−1.31298	+	0.758052i	−0.982589	−	0.185791i	$-0.940515\pi$
$487$	−28.9750	+	16.7288i	−1.31298	+	0.758052i	−0.330395	+	0.943843i	$0.607182\pi$
$488$	−8.29986	+	6.96441i	−0.375717	+	0.315264i
$489$	−17.6258	−	19.1660i	−0.797066	−	0.866718i
$490$	−1.18378	+	3.25240i	−0.0534775	+	0.146928i
$491$	0.635055	−	0.756829i	0.0286596	−	0.0341552i	−0.751524	−	0.659705i	$-0.770681\pi$
$491$	0.635055	−	0.756829i	0.0286596	−	0.0341552i	0.780184	+	0.625550i	$0.215125\pi$
$492$	9.04146	−	2.02147i	0.407621	−	0.0911347i
$493$			54.9658i			2.47554i
$494$	−1.88908	+	2.10405i	−0.0849936	+	0.0946657i
$495$	−1.53557	+	1.54663i	−0.0690188	+	0.0695158i
$496$	−3.00127	−	0.529205i	−0.134761	−	0.0237620i
$497$	0.0408543	+	0.0342808i	0.00183256	+	0.00153770i
$498$	20.9496	−	0.952333i	0.938776	−	0.0426751i
$499$	−4.11402	+	1.49738i	−0.184169	+	0.0670319i	−0.432458	−	0.901654i	$-0.642354\pi$
$499$	−4.11402	+	1.49738i	−0.184169	+	0.0670319i	0.248290	+	0.968686i	$0.420132\pi$
$500$	4.58085	+	5.45925i	0.204862	+	0.244145i
$501$	−9.94052	+	13.0030i	−0.444110	+	0.580930i
$502$	9.39486	+	5.42413i	0.419313	+	0.242091i
$503$	31.7905	−	5.60552i	1.41747	−	0.249938i	0.588167	−	0.808740i	$-0.299850\pi$
$503$	31.7905	−	5.60552i	1.41747	−	0.249938i	0.829301	+	0.558802i	$0.188739\pi$
$504$	3.83310	+	2.66352i	0.170740	+	0.118643i
$505$	7.11080	−	12.3163i	0.316426	−	0.548067i
$506$	−0.562965	−	0.975083i	−0.0250268	−	0.0433477i
$507$	−19.3440	−	10.0258i	−0.859097	−	0.445261i
$508$	−4.76297	−	13.0862i	−0.211323	−	0.580604i
$509$	21.2608	+	7.73831i	0.942370	+	0.342994i	0.767101	−	0.641526i	$-0.221698\pi$
$509$	21.2608	+	7.73831i	0.942370	+	0.342994i	0.175268	+	0.984521i	$0.443921\pi$
$510$	−2.67499	+	8.53735i	−0.118451	+	0.378040i
$511$	1.07375	−	6.08956i	0.0475000	−	0.269386i
$512$	1.00000			0.0441942
$513$	12.7015	−	18.7529i	0.560785	−	0.827962i
$514$	−0.0452647			−0.00199654
$515$	1.50474	−	8.53380i	0.0663067	−	0.376044i
$516$	4.04696	−	12.9161i	0.178158	−	0.568598i
$517$	−2.85234	−	1.03817i	−0.125446	−	0.0456585i
$518$	2.19588	+	6.03314i	0.0964815	+	0.265081i
$519$	−20.6807	−	10.7186i	−0.907781	−	0.470493i
$520$	0.245158	+	0.424626i	0.0107509	+	0.0186211i
$521$	4.86213	−	8.42145i	0.213014	−	0.368950i	−0.739643	−	0.673000i	$-0.765005\pi$
$521$	4.86213	−	8.42145i	0.213014	−	0.368950i	0.952656	+	0.304049i	$0.0983388\pi$
$522$	−19.8150	−	13.7689i	−0.867278	−	0.602649i
$523$	33.5671	−	5.91879i	1.46779	−	0.258810i	0.618101	−	0.786099i	$-0.287902\pi$
$523$	33.5671	−	5.91879i	1.46779	−	0.258810i	0.849686	+	0.527288i	$0.176791\pi$
$524$	−9.63898	−	5.56507i	−0.421081	−	0.243111i
$525$	7.24847	−	9.48155i	0.316349	−	0.413809i
$526$	3.52577	+	4.20185i	0.153731	+	0.183209i
$527$	−19.5709	+	7.12324i	−0.852523	+	0.310293i
$528$	1.66308	−	0.0756007i	0.0723763	−	0.00329010i
$529$	16.5678	+	13.9021i	0.720341	+	0.604438i
$530$	10.7947	+	1.90339i	0.468891	+	0.0826782i
$531$	−24.6114	+	24.7886i	−1.06804	+	1.07573i
$532$	3.19246	+	5.98357i	0.138411	+	0.259420i
$533$		−	3.46992i		−	0.150299i
$534$	−10.3283	+	2.30918i	−0.446951	+	0.0999281i
$535$	−1.14489	+	1.36443i	−0.0494980	+	0.0589894i
$536$	3.19170	−	8.76911i	0.137860	−	0.378768i
$537$	−19.5715	−	21.2818i	−0.844572	−	0.918376i
$538$	1.50432	−	1.26228i	0.0648559	−	0.0544206i
$539$	3.81174	−	2.20071i	0.164183	−	0.0947911i
$540$	−2.40760	−	3.10293i	−0.103607	−	0.133529i
$541$	0.180608	+	1.02428i	0.00776495	+	0.0440372i	0.988444	−	0.151586i	$-0.0484381\pi$
$541$	0.180608	+	1.02428i	0.00776495	+	0.0440372i	−0.980679	+	0.195623i	$0.937327\pi$
$542$	−3.66802	−	20.8024i	−0.157555	−	0.893537i
$543$	−2.27338	+	17.5107i	−0.0975603	+	0.751457i
$544$	5.91837	−	3.41697i	0.253748	−	0.146502i
$545$	−3.75277	+	3.14895i	−0.160751	+	0.134886i
$546$	1.28678	−	1.18337i	0.0550691	−	0.0506435i
$547$	8.86889	−	24.3671i	0.379207	−	1.04186i	−0.592480	−	0.805586i	$-0.701851\pi$
$547$	8.86889	−	24.3671i	0.379207	−	1.04186i	0.971686	−	0.236276i	$-0.0759269\pi$
$548$	3.19038	−	3.80215i	0.136286	−	0.162420i
$549$	−18.7390	−	26.5587i	−0.799760	−	1.13350i
$550$		−	4.25675i		−	0.181509i
$551$	−16.5032	−	30.9317i	−0.703060	−	1.31773i
$552$	1.87311	−	0.779806i	0.0797248	−	0.0331907i
$553$	−2.12897	−	0.375395i	−0.0905330	−	0.0159634i
$554$	6.00424	+	5.03816i	0.255096	+	0.214051i
$555$	−0.245319	−	5.39658i	−0.0104132	−	0.229072i
$556$	3.38812	−	1.23318i	0.143688	−	0.0522983i
$557$	−2.42914	−	2.89494i	−0.102926	−	0.122662i	0.712122	−	0.702055i	$-0.247734\pi$
$557$	−2.42914	−	2.89494i	−0.102926	−	0.122662i	−0.815048	+	0.579393i	$0.803290\pi$
$558$	2.33461	−	8.83962i	0.0988320	−	0.374211i
$559$	−4.39021	−	2.53469i	−0.185686	−	0.107206i
$560$	1.15813	−	0.204209i	0.0489397	−	0.00862940i
$561$	9.58440	−	6.13013i	0.404654	−	0.258814i
$562$	−5.85639	+	10.1436i	−0.247037	+	0.427880i
$563$	5.99208	+	10.3786i	0.252536	+	0.437406i	0.964223	−	0.265091i	$-0.0854020\pi$
$563$	5.99208	+	10.3786i	0.252536	+	0.437406i	−0.711687	+	0.702496i	$0.752069\pi$
$564$	2.51698	−	4.85633i	0.105984	−	0.204488i
$565$	2.59510	+	7.12998i	0.109177	+	0.299960i
$566$	−6.59684	−	2.40105i	−0.277286	−	0.100924i
$567$	−8.92374	+	10.7912i	−0.374762	+	0.453188i
$568$	−0.00595218	+	0.0337565i	−0.000249748	+	0.00141639i
$569$	11.2148			0.470147			0.235074	−	0.971978i	$-0.424467\pi$
$569$	11.2148			0.470147			0.235074	+	0.971978i	$0.424467\pi$
$570$	−1.05796	−	5.60749i	−0.0443132	−	0.234872i
$571$	16.2525			0.680144			0.340072	−	0.940399i	$-0.389548\pi$
$571$	16.2525			0.680144			0.340072	+	0.940399i	$0.389548\pi$
$572$	0.108273	−	0.614047i	0.00452713	−	0.0256746i
$573$	19.9440	+	6.24902i	0.833174	+	0.261057i
$574$	−7.82048	−	2.84642i	−0.326421	−	0.118807i
$575$	−1.77435	−	4.87499i	−0.0739956	−	0.203301i
$576$	−0.250744	+	2.98950i	−0.0104477	+	0.124563i
$577$	−4.02000	−	6.96284i	−0.167355	−	0.289867i	0.770134	−	0.637882i	$-0.220189\pi$
$577$	−4.02000	−	6.96284i	−0.167355	−	0.289867i	−0.937489	+	0.348015i	$0.886856\pi$
$578$	14.8514	−	25.7234i	0.617738	−	1.06995i
$579$	3.12138	+	4.88025i	0.129720	+	0.202816i
$580$	−5.98686	+	1.05564i	−0.248591	+	0.0438333i
$581$	−16.3145	−	9.41916i	−0.676838	−	0.390772i
$582$	−13.3409	−	10.1989i	−0.553000	−	0.422758i
$583$	−8.95984	−	10.6779i	−0.371079	−	0.442234i
$584$	3.73458	−	1.35928i	0.154538	−	0.0562473i
$585$	−1.33089	+	0.626428i	−0.0550257	+	0.0258996i
$586$	1.97785	+	1.65961i	0.0817041	+	0.0685579i
$587$	−19.5628	−	3.44945i	−0.807444	−	0.142374i	−0.245336	−	0.969438i	$-0.578898\pi$
$587$	−19.5628	−	3.44945i	−0.807444	−	0.142374i	−0.562108	+	0.827064i	$0.690009\pi$
$588$	3.04837	+	7.32224i	0.125713	+	0.301964i
$589$	8.87470	−	9.88463i	0.365676	−	0.407289i
$590$			8.80076i			0.362321i
$591$	−2.24779	−	10.0537i	−0.0924617	−	0.413556i
$592$	−2.65245	+	3.16107i	−0.109015	+	0.129919i
$593$	−7.64203	+	20.9963i	−0.313821	+	0.862215i	0.678056	+	0.735010i	$0.262823\pi$
$593$	−7.64203	+	20.9963i	−0.313821	+	0.862215i	−0.991876	+	0.127205i	$0.959399\pi$
$594$	−0.190999	+	4.99074i	−0.00783679	+	0.204772i
$595$	6.15644	−	5.16587i	0.252390	−	0.211780i
$596$	−16.5946	+	9.58089i	−0.679741	+	0.392449i
$597$	19.1982	+	2.49246i	0.785729	+	0.102010i
$598$	−0.131956	−	0.748362i	−0.00539610	−	0.0306028i
$599$	2.89198	+	16.4012i	0.118163	+	0.670136i	0.985135	+	0.171780i	$0.0549517\pi$
$599$	2.89198	+	16.4012i	0.118163	+	0.670136i	−0.866972	+	0.498356i	$0.833937\pi$
$600$	7.60692	+	0.987592i	0.310551	+	0.0403183i
$601$	17.9204	−	10.3464i	0.730990	−	0.422037i	−0.0877940	−	0.996139i	$-0.527982\pi$
$601$	17.9204	−	10.3464i	0.730990	−	0.422037i	0.818784	+	0.574101i	$0.194648\pi$
$602$	−9.31401	+	7.81539i	−0.379611	+	0.318531i
$603$	25.4150	+	11.7404i	1.03498	+	0.478106i
$604$	−6.58814	+	18.1008i	−0.268068	+	0.736510i
$605$	−4.89540	+	5.83411i	−0.199026	+	0.237191i
$606$	−7.11080	−	31.8047i	−0.288857	−	1.29198i
$607$		−	39.3916i		−	1.59886i	−0.600761	−	0.799428i	$-0.705136\pi$
$607$		−	39.3916i		−	1.59886i	0.600761	−	0.799428i	$-0.294864\pi$
$608$	−2.30460	+	3.69984i	−0.0934638	+	0.150048i
$609$	8.33058	+	20.0102i	0.337572	+	0.810854i
$610$	−8.06482	−	1.42205i	−0.326535	−	0.0575769i
$611$	−1.56934	−	1.31683i	−0.0634888	−	0.0532734i
$612$	8.73106	+	18.5498i	0.352932	+	0.749831i
$613$	−26.4005	+	9.60900i	−1.06631	+	0.388104i	−0.814794	−	0.579750i	$-0.803150\pi$
$613$	−26.4005	+	9.60900i	−1.06631	+	0.388104i	−0.251512	+	0.967854i	$0.580928\pi$
$614$	1.26629	+	1.50910i	0.0511032	+	0.0609024i
$615$	5.56314	+	4.25292i	0.224328	+	0.171494i
$616$	−1.29512	−	0.747736i	−0.0521818	−	0.0301272i
$617$	20.3648	−	3.59086i	0.819854	−	0.144562i	0.252038	−	0.967717i	$-0.418899\pi$
$617$	20.3648	−	3.59086i	0.819854	−	0.144562i	0.567817	+	0.823155i	$0.307788\pi$
$618$	−10.6995	−	16.7285i	−0.430396	−	0.672919i
$619$	16.8830	−	29.2423i	0.678586	−	1.17535i	−0.296821	−	0.954933i	$-0.595926\pi$
$619$	16.8830	−	29.2423i	0.678586	−	1.17535i	0.975407	−	0.220412i	$-0.0707402\pi$
$620$	−1.15173	−	1.99485i	−0.0462545	−	0.0801152i
$621$	1.86156	+	5.79519i	0.0747019	+	0.232553i
$622$	−8.88236	−	24.4041i	−0.356150	−	0.978515i
$623$	8.93358	+	3.25156i	0.357916	+	0.130271i
$624$	1.07220	+	0.335949i	0.0429222	+	0.0134487i
$625$	2.90984	−	16.5025i	0.116394	−	0.660101i
$626$	−13.4088			−0.535925
$627$	−3.55302	+	6.32736i	−0.141894	+	0.252690i
$628$	0.213836			0.00853299
$629$	−4.89690	+	27.7717i	−0.195252	+	1.10733i
$630$	0.320089	+	3.51342i	0.0127527	+	0.139978i
$631$	−35.0060	−	12.7411i	−1.39357	−	0.507217i	−0.467304	−	0.884096i	$-0.654775\pi$
$631$	−35.0060	−	12.7411i	−1.39357	−	0.507217i	−0.926262	+	0.376880i	$0.876997\pi$
$632$	−0.475217	−	1.30565i	−0.0189031	−	0.0519359i
$633$	−16.9451	+	32.6942i	−0.673506	+	1.29948i
$634$	15.2117	+	26.3474i	0.604132	+	1.04639i
$635$	5.26287	−	9.11556i	0.208851	−	0.361740i
$636$	21.1604	−	13.5341i	0.839066	−	0.536662i
$637$	2.92545	−	0.515836i	0.115911	−	0.0204382i
$638$	6.69503	+	3.86538i	0.265059	+	0.153032i
$639$	−0.0994226	−	0.0262583i	−0.00393310	−	0.00103876i
$640$	0.485841	+	0.579002i	0.0192045	+	0.0228871i
$641$	−7.37099	+	2.68282i	−0.291137	+	0.105965i	−0.483460	−	0.875367i	$-0.660620\pi$
$641$	−7.37099	+	2.68282i	−0.291137	+	0.105965i	0.192323	+	0.981332i	$0.438398\pi$
$642$	0.185351	+	4.07739i	0.00731523	+	0.160922i
$643$	29.9819	+	25.1578i	1.18237	+	0.992126i	0.999960	+	0.00890393i	$0.00283425\pi$
$643$	29.9819	+	25.1578i	1.18237	+	0.992126i	0.182410	+	0.983223i	$0.441610\pi$
$644$	−1.79490	−	0.316489i	−0.0707289	−	0.0124714i
$645$	9.44461	−	3.93195i	0.371881	−	0.154820i
$646$	−0.997207	+	29.7718i	−0.0392346	+	1.17136i
$647$		−	6.21339i		−	0.244274i	−0.992513	−	0.122137i	$-0.961025\pi$
$647$		−	6.21339i		−	0.244274i	0.992513	−	0.122137i	$-0.0389747\pi$
$648$	−8.87425	−	1.49920i	−0.348614	−	0.0588942i
$649$	7.19386	−	8.57331i	0.282384	−	0.336532i
$650$	0.982605	−	2.69969i	0.0385410	−	0.105890i
$651$	−6.04516	+	5.55935i	−0.236929	+	0.217888i
$652$	−11.5162	+	9.66326i	−0.451010	+	0.378442i
$653$	−23.3831	+	13.5002i	−0.915050	+	0.528304i	−0.882053	−	0.471151i	$-0.843839\pi$
$653$	−23.3831	+	13.5002i	−0.915050	+	0.528304i	−0.0329976	+	0.999455i	$0.510505\pi$
$654$	−1.44534	+	11.1327i	−0.0565174	+	0.435325i
$655$	−1.46082	−	8.28473i	−0.0570790	−	0.323711i
$656$	−0.928838	−	5.26770i	−0.0362650	−	0.205669i
$657$	3.12714	+	11.5054i	0.122001	+	0.448868i
$658$	−4.25522	+	2.45676i	−0.165886	+	0.0957743i
$659$	23.3482	−	19.5915i	0.909517	−	0.763176i	−0.0625097	−	0.998044i	$-0.519910\pi$
$659$	23.3482	−	19.5915i	0.909517	−	0.763176i	0.972027	+	0.234869i	$0.0754660\pi$
$660$	0.851765	+	0.926197i	0.0331549	+	0.0360522i
$661$	−11.2133	+	30.8082i	−0.436146	+	1.19830i	0.505834	+	0.862631i	$0.331185\pi$
$661$	−11.2133	+	30.8082i	−0.436146	+	1.19830i	−0.941980	+	0.335670i	$0.891037\pi$
$662$	−6.84344	+	8.15570i	−0.265978	+	0.316980i
$663$	7.49360	−	1.67540i	0.291027	−	0.0650671i
$664$		−	12.1078i		−	0.469873i
$665$	−1.91347	+	4.75550i	−0.0742013	+	0.184410i
$666$	−8.78493	−	8.72213i	−0.340409	−	0.337975i
$667$	9.27861	+	1.63607i	0.359269	+	0.0633489i
$668$	7.23890	+	6.07416i	0.280081	+	0.235016i
$669$	23.8370	−	1.08359i	0.921591	−	0.0418939i
$670$	6.62799	−	2.41239i	0.256062	−	0.0931989i
$671$	6.69399	+	7.97759i	0.258419	+	0.307971i
$672$	1.63670	−	2.14093i	0.0631370	−	0.0825880i
$673$	26.7750	+	15.4586i	1.03210	+	0.595884i	0.917586	−	0.397537i	$-0.130135\pi$
$673$	26.7750	+	15.4586i	1.03210	+	0.595884i	0.114516	+	0.993421i	$0.463468\pi$
$674$	−6.85690	+	1.20906i	−0.264118	+	0.0465711i
$675$	−4.85980	+	22.4933i	−0.187054	+	0.865766i
$676$	−6.28959	+	10.8939i	−0.241907	+	0.418996i
$677$	−19.6720	−	34.0729i	−0.756057	−	1.30953i	−0.944847	−	0.327511i	$-0.893790\pi$
$677$	−19.6720	−	34.0729i	−0.756057	−	1.30953i	0.188791	−	0.982017i	$-0.439543\pi$
$678$	15.4373	+	8.00096i	0.592864	+	0.307275i
$679$	5.15932	+	14.1751i	0.197996	+	0.543991i
$680$	4.85382	+	1.76665i	0.186136	+	0.0677478i
$681$	8.38366	−	26.7568i	0.321263	−	1.02532i
$682$	−0.508657	+	2.88474i	−0.0194775	+	0.110462i
$683$	12.0176			0.459840			0.229920	−	0.973210i	$-0.426154\pi$
$683$	12.0176			0.459840			0.229920	+	0.973210i	$0.426154\pi$
$684$	−10.4828	−	7.81732i	−0.400821	−	0.298903i
$685$	3.75147			0.143336
$686$	3.12844	−	17.7422i	0.119444	−	0.677402i
$687$	−13.2815	+	42.3885i	−0.506720	+	1.61722i
$688$	−7.34330	−	2.67274i	−0.279961	−	0.101897i
$689$	−3.21761	−	8.84031i	−0.122581	−	0.336789i
$690$	1.36154	+	0.705673i	0.0518330	+	0.0268645i
$691$	−17.5214	−	30.3479i	−0.666544	−	1.15449i	−0.978864	−	0.204512i	$-0.934439\pi$
$691$	−17.5214	−	30.3479i	−0.666544	−	1.15449i	0.312320	−	0.949977i	$-0.398894\pi$
$692$	−6.72420	+	11.6467i	−0.255616	+	0.442739i
$693$	2.56010	−	3.68427i	0.0972503	−	0.139954i
$694$	−27.7308	+	4.88969i	−1.05265	+	0.185610i
$695$	2.36010	+	1.36260i	0.0895237	+	0.0516865i
$696$	−8.46081	+	11.0674i	−0.320706	+	0.419508i
$697$	−23.4968	−	28.0024i	−0.890006	−	1.06067i
$698$	18.4021	−	6.69781i	0.696530	−	0.253516i
$699$	20.1400	−	0.915530i	0.761766	−	0.0346285i
$700$	−5.27849	−	4.42918i	−0.199508	−	0.167407i
$701$	−2.95841	−	0.521647i	−0.111738	−	0.0197023i	0.117500	−	0.993073i	$-0.462512\pi$
$701$	−2.95841	−	0.521647i	−0.111738	−	0.0197023i	−0.229237	+	0.973371i	$0.573623\pi$
$702$	−1.27317	+	3.12110i	−0.0480527	+	0.117798i
$703$	−5.58262	−	17.0986i	−0.210552	−	0.644887i
$704$		−	0.961171i		−	0.0362255i
$705$	4.03468	−	0.902063i	0.151955	−	0.0339737i
$706$	−2.63528	+	3.14061i	−0.0991801	+	0.118198i
$707$	−10.0127	+	27.5097i	−0.376567	+	1.03461i
$708$	13.6517	+	14.8447i	0.513062	+	0.557896i
$709$	2.36012	−	1.98037i	0.0886360	−	0.0743744i	−0.597393	−	0.801949i	$-0.703797\pi$
$709$	2.36012	−	1.98037i	0.0886360	−	0.0743744i	0.686029	+	0.727574i	$0.259352\pi$
$710$	−0.0224369	+	0.0129539i	−0.000842042	+	0.000486153i
$711$	4.02239	−	1.09328i	0.150852	−	0.0410011i
$712$	1.06104	+	6.01746i	0.0397642	+	0.225514i
$713$	0.619918	+	3.51573i	0.0232161	+	0.131665i
$714$	2.37110	−	18.2634i	0.0887361	−	0.683489i
$715$	0.408138	−	0.235639i	0.0152635	−	0.00881239i
$716$	−12.7875	+	10.7300i	−0.477891	+	0.400998i
$717$	−19.4073	+	17.8476i	−0.724777	+	0.666532i
$718$	−1.91864	+	5.27142i	−0.0716030	+	0.196728i
$719$	7.13781	−	8.50651i	0.266195	−	0.317239i	−0.616345	−	0.787476i	$-0.711387\pi$
$719$	7.13781	−	8.50651i	0.266195	−	0.317239i	0.882540	+	0.470237i	$0.155832\pi$
$720$	−1.85275	+	1.30724i	−0.0690480	+	0.0487180i
$721$			17.8378i			0.664316i
$722$	−8.37766	−	17.0533i	−0.311784	−	0.634658i
$723$	24.2796	−	10.1080i	0.902969	−	0.375921i
$724$	10.0398	+	1.77029i	0.373126	+	0.0657921i
$725$	27.2868	+	22.8964i	1.01341	+	0.850349i
$726$	0.792537	+	17.4344i	0.0294138	+	0.647051i
$727$	13.8709	−	5.04860i	0.514444	−	0.187242i	−0.0717355	−	0.997424i	$-0.522854\pi$
$727$	13.8709	−	5.04860i	0.514444	−	0.187242i	0.586179	+	0.810182i	$0.300632\pi$
$728$	−0.648776	−	0.773182i	−0.0240453	−	0.0286560i
$729$	6.70703	−	26.1537i	0.248409	−	0.968655i
$730$	2.60144	+	1.50194i	0.0962835	+	0.0555893i
$731$	−52.5931	+	9.27357i	−1.94522	+	0.342996i
$732$	−15.8092	+	10.1115i	−0.584324	+	0.373731i
$733$	−18.1447	+	31.4276i	−0.670191	+	1.16080i	0.307659	+	0.951497i	$0.400454\pi$
$733$	−18.1447	+	31.4276i	−0.670191	+	1.16080i	−0.977850	+	0.209308i	$0.932879\pi$
$734$	1.49168	+	2.58367i	0.0550589	+	0.0953649i
$735$	−2.75857	+	5.32245i	−0.101751	+	0.196322i
$736$	−0.400647	−	1.10077i	−0.0147681	−	0.0405749i
$737$	−8.42862	−	3.06777i	−0.310472	−	0.113003i
$738$	15.9807	−	1.45592i	0.588258	−	0.0535931i
$739$	−2.94942	+	16.7270i	−0.108496	+	0.615312i	0.881270	+	0.472613i	$0.156689\pi$
$739$	−2.94942	+	16.7270i	−0.108496	+	0.615312i	−0.989766	+	0.142699i	$0.954422\pi$
$740$	−3.11893			−0.114654
$741$	−3.71394	+	3.19273i	−0.136435	+	0.117288i
$742$	−22.5637			−0.828339
$743$	−4.59818	+	26.0776i	−0.168691	+	0.956693i	0.776486	+	0.630134i	$0.217000\pi$
$743$	−4.59818	+	26.0776i	−0.168691	+	0.956693i	−0.945177	+	0.326559i	$0.894111\pi$
$744$	−5.03708	−	1.57826i	−0.184668	−	0.0578617i
$745$	−13.6097	−	4.95352i	−0.498620	−	0.181483i
$746$	7.20414	+	19.7932i	0.263762	+	0.724681i
$747$	36.1962	+	3.03595i	1.32435	+	0.111080i
$748$	−3.28430	−	5.68857i	−0.120086	−	0.207995i
$749$	1.83324	−	3.17526i	0.0669850	−	0.116021i
$750$	6.65084	+	10.3985i	0.242854	+	0.379700i
$751$	46.8929	−	8.26849i	1.71115	−	0.301722i	0.769581	−	0.638549i	$-0.220465\pi$
$751$	46.8929	−	8.26849i	1.71115	−	0.301722i	0.941566	+	0.336827i	$0.109354\pi$
$752$	−2.73492	−	1.57901i	−0.0997323	−	0.0575805i
$753$	14.9274	+	11.4117i	0.543984	+	0.415866i
$754$	3.35381	+	3.99691i	0.122139	+	0.145559i
$755$	−13.6812	+	4.97954i	−0.497909	+	0.181224i
$756$	5.98991	+	5.42974i	0.217851	+	0.197478i
$757$	−12.6519	−	10.6162i	−0.459843	−	0.385854i	0.383230	−	0.923653i	$-0.374812\pi$
$757$	−12.6519	−	10.6162i	−0.459843	−	0.385854i	−0.843073	+	0.537799i	$0.819256\pi$
$758$	−9.39563	−	1.65670i	−0.341264	−	0.0601741i
$759$	−0.749527	−	1.80038i	−0.0272061	−	0.0653496i
$760$	−3.26188	+	0.463166i	−0.118321	+	0.0168008i
$761$			19.1974i			0.695906i	0.937512	+	0.347953i	$0.113123\pi$
$761$			19.1974i			0.695906i	−0.937512	+	0.347953i	$0.886877\pi$
$762$	−5.26287	−	23.5394i	−0.190654	−	0.852742i
$763$	6.48211	−	7.72508i	0.234668	−	0.279667i
$764$	4.12705	−	11.3390i	0.149311	−	0.410230i
$765$	−6.49847	+	14.0675i	−0.234953	+	0.508613i
$766$	5.96084	−	5.00173i	0.215374	−	0.180720i
$767$	6.54145	−	3.77671i	0.236198	−	0.136369i
$768$	1.71764	+	0.222997i	0.0619798	+	0.00804673i
$769$	−5.25863	−	29.8231i	−0.189631	−	1.07545i	−0.919860	−	0.392248i	$-0.871698\pi$
$769$	−5.25863	−	29.8231i	−0.189631	−	1.07545i	0.730229	−	0.683203i	$-0.239413\pi$
$770$	−0.196280	−	1.11316i	−0.00707343	−	0.0401154i
$771$	−0.0777483	−	0.0100939i	−0.00280004	−	0.000363524i
$772$	2.89655	−	1.67232i	0.104249	−	0.0601882i
$773$	21.9958	−	18.4567i	0.791134	−	0.663840i	−0.154892	−	0.987931i	$-0.549503\pi$
$773$	21.9958	−	18.4567i	0.791134	−	0.663840i	0.946026	+	0.324091i	$0.105058\pi$
$774$	9.83146	−	21.2826i	0.353384	−	0.764988i
$775$	−4.61619	+	12.6829i	−0.165818	+	0.455582i
$776$	−6.23204	+	7.42706i	−0.223717	+	0.266616i
$777$	2.42635	+	10.8524i	0.0870449	+	0.389328i
$778$		−	9.78591i		−	0.350842i
$779$	21.6303	+	8.70339i	0.774985	+	0.311831i
$780$	0.326402	+	0.784023i	0.0116871	+	0.0280725i
$781$	0.0324458	+	0.00572106i	0.00116100	+	0.000204716i
$782$	−6.13248	−	5.14576i	−0.219297	−	0.184012i
$783$	−30.9645	−	28.0687i	−1.10658	−	1.00309i
$784$	4.30306	−	1.56619i	0.153681	−	0.0559352i
$785$	0.103890	+	0.123812i	0.00370800	+	0.00441903i
$786$	−15.3153	−	11.7082i	−0.546277	−	0.417619i
$787$	22.1812	+	12.8063i	0.790673	+	0.456495i	0.840200	−	0.542277i	$-0.182438\pi$
$787$	22.1812	+	12.8063i	0.790673	+	0.456495i	−0.0495262	+	0.998773i	$0.515771\pi$
$788$	−5.85748	+	1.03283i	−0.208664	+	0.0367931i
$789$	5.11899	+	8.00348i	0.182241	+	0.284932i
$790$	0.525093	−	0.909488i	0.0186820	−	0.0323581i
$791$	−7.80951	−	13.5265i	−0.277674	−	0.480946i
$792$	2.87342	+	0.241008i	0.102103	+	0.00856385i
$793$	2.40391	+	6.60469i	0.0853653	+	0.234539i
$794$	11.1113	+	4.04419i	0.394326	+	0.143523i
$795$	18.1169	+	5.67652i	0.642540	+	0.201326i
$796$	1.94088	−	11.0073i	0.0687927	−	0.390143i
$797$	−32.4074			−1.14793			−0.573965	−	0.818880i	$-0.694595\pi$
$797$	−32.4074			−1.14793			−0.573965	+	0.818880i	$0.694595\pi$
$798$	4.14916	+	10.9895i	0.146879	+	0.389024i
$799$	−21.5817			−0.763506
$800$	0.769038	−	4.36143i	0.0271896	−	0.154200i
$801$	−18.2553	+	1.66314i	−0.645018	+	0.0587642i
$802$	19.4319	+	7.07262i	0.686163	+	0.249743i
$803$	−1.30650	−	3.58957i	−0.0461053	−	0.126673i
$804$	7.43766	−	14.3504i	0.262306	−	0.506100i
$805$	−0.688786	−	1.19301i	−0.0242765	−	0.0420482i
$806$	−0.988493	+	1.71212i	−0.0348182	+	0.0603069i
$807$	2.86536	−	1.83267i	0.100866	−	0.0645131i
$808$	−18.5299	+	3.26732i	−0.651880	+	0.114944i
$809$	−30.3938	−	17.5479i	−1.06859	−	0.616950i	−0.140793	−	0.990039i	$-0.544965\pi$
$809$	−30.3938	−	17.5479i	−1.06859	−	0.616950i	−0.927796	+	0.373089i	$0.878299\pi$
$810$	−3.44343	−	5.86659i	−0.120990	−	0.206131i
$811$	14.0733	+	16.7719i	0.494181	+	0.588942i	0.954276	−	0.298928i	$-0.0966290\pi$
$811$	14.0733	+	16.7719i	0.494181	+	0.588942i	−0.460095	+	0.887870i	$0.652185\pi$
$812$	11.7594	−	4.28007i	0.412674	−	0.150201i
$813$	−1.66144	−	36.5488i	−0.0582694	−	1.28182i
$814$	3.03833	+	2.54946i	0.106493	+	0.0893585i
$815$	−11.1901	−	1.97312i	−0.391972	−	0.0691152i
$816$	10.9276	−	4.54934i	0.382542	−	0.159259i
$817$	26.8121	−	21.0094i	0.938035	−	0.735027i
$818$		−	3.45002i		−	0.120627i
$819$	2.47411	−	1.74565i	0.0864522	−	0.0609979i
$820$	2.59875	−	3.09706i	0.0907521	−	0.108154i
$821$	4.83332	−	13.2794i	0.168684	−	0.463455i	−0.826331	−	0.563185i	$-0.809576\pi$
$821$	4.83332	−	13.2794i	0.168684	−	0.463455i	0.995015	+	0.0997301i	$0.0317979\pi$
$822$	6.32779	−	5.81926i	0.220707	−	0.202970i
$823$	11.4669	−	9.62189i	0.399712	−	0.335398i	−0.420670	−	0.907214i	$-0.638205\pi$
$823$	11.4669	−	9.62189i	0.399712	−	0.335398i	0.820382	+	0.571815i	$0.193761\pi$
$824$	−9.92876	+	5.73237i	−0.345885	+	0.199697i
$825$	0.949245	−	7.31155i	0.0330485	−	0.254556i
$826$	−3.14588	−	17.8411i	−0.109459	−	0.620773i
$827$	3.63051	+	20.5896i	0.126245	+	0.715972i	0.980561	+	0.196217i	$0.0628657\pi$
$827$	3.63051	+	20.5896i	0.126245	+	0.715972i	−0.854315	+	0.519755i	$0.826023\pi$
$828$	3.39121	−	0.921724i	0.117853	−	0.0320321i
$829$	−12.1611	+	7.02120i	−0.422371	+	0.243856i	−0.696091	−	0.717953i	$-0.745079\pi$
$829$	−12.1611	+	7.02120i	−0.422371	+	0.243856i	0.273720	+	0.961809i	$0.411746\pi$
$830$	7.01043	−	5.88245i	0.243336	−	0.204183i
$831$	9.18960	+	9.99265i	0.318784	+	0.346641i
$832$	0.221871	−	0.609587i	0.00769201	−	0.0211336i
$833$	20.1155	−	23.9727i	0.696960	−	0.830605i
$834$	6.09456	−	1.36260i	0.211037	−	0.0471831i
$835$			7.14241i			0.247173i
$836$	3.55618	+	2.21511i	0.122993	+	0.0766113i
$837$	5.98122	−	14.6626i	0.206741	−	0.506815i
$838$	24.9310	+	4.39601i	0.861227	+	0.151857i
$839$	−42.8654	−	35.9683i	−1.47988	−	1.24176i	−0.906315	−	0.422603i	$-0.861116\pi$
$839$	−42.8654	−	35.9683i	−1.47988	−	1.24176i	−0.573563	−	0.819162i	$-0.694439\pi$
$840$	2.03478	−	0.0924973i	0.0702064	−	0.00319146i
$841$	−33.5383	+	12.2070i	−1.15649	+	0.420929i
$842$	−20.4536	−	24.3756i	−0.704876	−	0.840038i
$843$	−12.3211	+	16.1170i	−0.424362	+	0.555098i
$844$	18.4123	+	10.6303i	0.633777	+	0.365911i
$845$	−9.36332	+	1.65101i	−0.322108	+	0.0567964i
$846$	5.40621	−	7.78013i	0.185869	−	0.267486i
$847$	7.83867	−	13.5770i	0.269340	−	0.466510i
$848$	−7.25107	−	12.5592i	−0.249003	−	0.431286i
$849$	−10.7955	−	5.59521i	−0.370502	−	0.192027i
$850$	−10.3515	−	28.4404i	−0.355052	−	0.975497i
$851$	4.54230	+	1.65326i	0.155708	+	0.0566731i
$852$	−0.0177513	+	0.0566540i	−0.000608149	+	0.00194093i
$853$	−7.55129	+	42.8255i	−0.258551	+	1.46632i	0.528239	+	0.849096i	$0.322853\pi$
$853$	−7.55129	+	42.8255i	−0.258551	+	1.46632i	−0.786790	+	0.617221i	$0.788259\pi$
$854$	16.8576			0.576854
$855$	−0.566737	−	9.86755i	−0.0193820	−	0.337463i
$856$	2.35652			0.0805441
$857$	8.77792	−	49.7820i	0.299848	−	1.70052i	−0.346969	−	0.937877i	$-0.612789\pi$
$857$	8.77792	−	49.7820i	0.299848	−	1.70052i	0.646817	−	0.762645i	$-0.276100\pi$
$858$	0.322905	−	1.03057i	0.0110238	−	0.0351829i
$859$	23.3783	+	8.50899i	0.797656	+	0.290323i	0.708515	−	0.705696i	$-0.249366\pi$
$859$	23.3783	+	8.50899i	0.797656	+	0.290323i	0.0891412	+	0.996019i	$0.471588\pi$
$860$	−2.02015	−	5.55031i	−0.0688865	−	0.189264i
$861$	−12.7980	−	6.63306i	−0.436154	−	0.226054i
$862$	16.4706	+	28.5280i	0.560992	+	0.971667i
$863$	−16.9638	+	29.3822i	−0.577455	+	1.00018i	0.418315	+	0.908302i	$0.362621\pi$
$863$	−16.9638	+	29.3822i	−0.577455	+	1.00018i	−0.995770	+	0.0918798i	$0.970712\pi$
$864$	−1.09734	+	5.07896i	−0.0373322	+	0.172790i
$865$	−10.0103	+	1.76509i	−0.340362	+	0.0600149i
$866$	13.8300	+	7.98473i	0.469961	+	0.271332i
$867$	31.2456	−	40.8717i	1.06116	−	1.38807i
$868$	3.04789	+	3.63233i	0.103452	+	0.123289i
$869$	−1.25495	+	0.456765i	−0.0425713	+	0.0154947i
$870$	−10.5186	+	0.478159i	−0.356615	+	0.0162111i
$871$	−4.63739	−	3.89123i	−0.157132	−	0.131849i
$872$	6.38297	+	1.12549i	0.216155	+	0.0381139i
$873$	−20.6406	−	20.4930i	−0.698577	−	0.693583i
$874$	4.99600	+	1.05450i	0.168992	+	0.0356690i
$875$		−	11.0881i		−	0.374846i
$876$	6.71777	−	1.50194i	0.226972	−	0.0507459i
$877$	19.1891	−	22.8687i	0.647971	−	0.772222i	−0.337636	−	0.941277i	$-0.609627\pi$
$877$	19.1891	−	22.8687i	0.647971	−	0.772222i	0.985607	+	0.169055i	$0.0540717\pi$
$878$	−10.6065	+	29.1410i	−0.357951	+	0.983463i
$879$	3.02713	+	3.29166i	0.102103	+	0.111025i
$880$	0.556520	−	0.466976i	0.0187603	−	0.0157418i
$881$	−9.59448	+	5.53938i	−0.323246	+	0.186626i	−0.652839	−	0.757497i	$-0.726422\pi$
$881$	−9.59448	+	5.53938i	−0.323246	+	0.186626i	0.329592	+	0.944123i	$0.393089\pi$
$882$	3.60315	+	13.2567i	0.121324	+	0.446377i
$883$	9.62988	+	54.6138i	0.324071	+	1.83790i	0.516122	+	0.856515i	$0.327375\pi$
$883$	9.62988	+	54.6138i	0.324071	+	1.83790i	−0.192051	+	0.981385i	$0.561514\pi$
$884$	−0.769825	−	4.36589i	−0.0258920	−	0.146841i
$885$	−1.96255	+	15.1165i	−0.0659703	+	0.508135i
$886$	16.8799	−	9.74561i	0.567091	−	0.327410i
$887$	19.9548	−	16.7441i	0.670017	−	0.562211i	−0.243054	−	0.970013i	$-0.578149\pi$
$887$	19.9548	−	16.7441i	0.670017	−	0.562211i	0.913070	+	0.407802i	$0.133705\pi$
$888$	−5.26085	+	4.83807i	−0.176543	+	0.162355i
$889$	−7.41064	+	20.3606i	−0.248545	+	0.682871i
$890$	−2.96863	+	3.53787i	−0.0995086	+	0.118590i
$891$	−1.44099	+	8.52968i	−0.0482749	+	0.285755i
$892$		−	13.7765i		−	0.461271i
$893$	12.1450	−	6.47980i	0.406416	−	0.216838i
$894$	−30.6400	+	12.7559i	−1.02475	+	0.426622i
$895$	−12.4254	−	2.19093i	−0.415334	−	0.0732346i
$896$	−1.19188	−	1.00010i	−0.0398178	−	0.0334111i
$897$	−0.0597702	−	1.31484i	−0.00199567	−	0.0439012i
$898$	12.4342	−	4.52566i	0.414933	−	0.151023i
$899$	−15.7559	−	18.7771i	−0.525488	−	0.626252i
$900$	12.8457	+	3.39265i	0.428189	+	0.113088i
$901$	−85.8291	−	49.5535i	−2.85938	−	1.65086i
$902$	−5.06317	+	0.892773i	−0.168585	+	0.0297261i
$903$	−17.7409	+	11.3470i	−0.590380	+	0.377604i
$904$	5.01933	−	8.69374i	0.166940	−	0.289149i
$905$	3.85274	+	6.67314i	0.128069	+	0.221823i
$906$	−15.3524	+	29.6214i	−0.510051	+	0.984105i
$907$	5.92780	+	16.2865i	0.196830	+	0.540785i	0.998365	−	0.0571627i	$-0.0182054\pi$
$907$	5.92780	+	16.2865i	0.196830	+	0.540785i	−0.801535	+	0.597947i	$0.795983\pi$
$908$	−15.2123	−	5.53684i	−0.504839	−	0.183746i
$909$	−5.12141	−	56.2145i	−0.169866	−	1.86452i
$910$	0.132472	−	0.751286i	0.00439140	−	0.0249049i
$911$	35.0957			1.16277			0.581386	−	0.813628i	$-0.302511\pi$
$911$	35.0957			1.16277			0.581386	+	0.813628i	$0.302511\pi$
$912$	−4.78351	+	5.84106i	−0.158398	+	0.193417i
$913$	−11.6376			−0.385150
$914$	−2.67484	+	15.1698i	−0.0884758	+	0.501771i
$915$	−13.5353	−	4.24099i	−0.447463	−	0.140203i
$916$	24.0995	+	8.77151i	0.796271	+	0.289819i
$917$	5.92284	+	16.2729i	0.195589	+	0.537377i
$918$	10.8602	+	33.8088i	0.358441	+	1.11586i
$919$	−15.0221	−	26.0190i	−0.495533	−	0.858288i	0.504454	−	0.863439i	$-0.331694\pi$
$919$	−15.0221	−	26.0190i	−0.495533	−	0.858288i	−0.999987	+	0.00515052i	$0.998361\pi$
$920$	0.442697	−	0.766774i	0.0145953	−	0.0252798i
$921$	1.83849	+	2.87447i	0.0605805	+	0.0947169i
$922$	−16.2707	+	2.86896i	−0.535847	+	0.0944843i
$923$	0.0192569	+	0.0111180i	0.000633848	+	0.000365952i
$924$	−2.05780	−	1.57315i	−0.0676965	−	0.0517527i
$925$	11.7469	+	13.9995i	0.386237	+	0.460300i
$926$	−8.81750	+	3.20931i	−0.289761	+	0.105464i
$927$	−14.6474	−	31.1194i	−0.481083	−	1.02210i
$928$	6.16134	+	5.16998i	0.202256	+	0.169713i
$929$	32.1458	+	5.66817i	1.05467	+	0.185967i	0.673990	−	0.738740i	$-0.264579\pi$
$929$	32.1458	+	5.66817i	1.05467	+	0.185967i	0.380680	+	0.924707i	$0.375690\pi$
$930$	−1.53340	−	3.68326i	−0.0502823	−	0.120779i
$931$	−4.12218	+	19.5301i	−0.135099	+	0.640072i
$932$		−	11.6399i		−	0.381276i
$933$	−9.81461	−	43.8981i	−0.321316	−	1.43716i
$934$	13.7652	−	16.4047i	0.450411	−	0.536778i
$935$	1.69805	−	4.66536i	0.0555322	−	0.152573i
$936$	1.76673	+	0.816136i	0.0577473	+	0.0266762i
$937$	−24.8914	+	20.8863i	−0.813165	+	0.682327i	−0.951361	−	0.308078i	$-0.900314\pi$
$937$	−24.8914	+	20.8863i	−0.813165	+	0.682327i	0.138196	+	0.990405i	$0.455870\pi$
$938$	−12.5741	+	7.25968i	−0.410560	+	0.237037i
$939$	−23.0315	−	2.99013i	−0.751604	−	0.0975794i
$940$	−0.414487	−	2.35067i	−0.0135191	−	0.0766705i
$941$	2.50659	+	14.2156i	0.0817126	+	0.463415i	0.998018	+	0.0629344i	$0.0200459\pi$
$941$	2.50659	+	14.2156i	0.0817126	+	0.463415i	−0.916305	+	0.400481i	$0.868843\pi$
$942$	0.367293	+	0.0476849i	0.0119670	+	0.00155366i
$943$	−5.42639	+	3.13293i	−0.176708	+	0.102022i
$944$	8.91965	−	7.48447i	0.290310	−	0.243599i
$945$	−0.233687	+	6.10616i	−0.00760185	+	0.198633i
$946$	−2.56896	+	7.05816i	−0.0835241	+	0.229481i
$947$	−28.2988	+	33.7252i	−0.919588	+	1.09592i	0.0755210	+	0.997144i	$0.475938\pi$
$947$	−28.2988	+	33.7252i	−0.919588	+	1.09592i	−0.995109	+	0.0987786i	$0.968506\pi$
$948$	−0.525093	−	2.34860i	−0.0170542	−	0.0762789i
$949$		−	2.57814i		−	0.0836899i
$950$	14.3643	+	12.8967i	0.466039	+	0.418423i
$951$	20.2527	+	48.6473i	0.656738	+	1.57750i
$952$	−10.4713	−	1.84637i	−0.339377	−	0.0598413i
$953$	15.8037	+	13.2609i	0.511932	+	0.429562i	0.861808	−	0.507234i	$-0.169332\pi$
$953$	15.8037	+	13.2609i	0.511932	+	0.429562i	−0.349877	+	0.936796i	$0.613777\pi$
$954$	39.3640	−	18.5279i	1.27446	−	0.599864i
$955$	8.57039	−	3.11937i	0.277331	−	0.100940i
$956$	9.78488	+	11.6612i	0.316465	+	0.377149i
$957$	10.6377	+	8.13228i	0.343866	+	0.262879i
$958$	−28.9075	−	16.6898i	−0.933960	−	0.539222i
$959$	−7.60509	+	1.34098i	−0.245581	+	0.0433026i
$960$	0.705381	+	1.10286i	0.0227661	+	0.0355945i
$961$	−10.8562	+	18.8034i	−0.350199	+	0.606562i
$962$	1.33844	+	2.31825i	0.0431531	+	0.0747433i
$963$	−0.590883	+	7.04481i	−0.0190409	+	0.227016i
$964$	−5.19328	−	14.2684i	−0.167264	−	0.459554i
$965$	2.37554	+	0.864625i	0.0764713	+	0.0278333i
$966$	−3.01240	−	0.943870i	−0.0969225	−	0.0303685i
$967$	−7.05922	+	40.0348i	−0.227009	+	1.28743i	0.631798	+	0.775133i	$0.282317\pi$
$967$	−7.05922	+	40.0348i	−0.227009	+	1.28743i	−0.858807	+	0.512300i	$0.828794\pi$
$968$	10.0761			0.323860
$969$	−8.35187	+	50.9147i	−0.268301	+	1.63562i
$970$	−7.32806			−0.235290
$971$	0.764165	−	4.33380i	0.0245232	−	0.139078i	−0.970088	−	0.242754i	$-0.921949\pi$
$971$	0.764165	−	4.33380i	0.0245232	−	0.139078i	0.994611	+	0.103676i	$0.0330604\pi$
$972$	−14.9084	−	4.55402i	−0.478188	−	0.146070i
$973$	−5.27154	−	1.91868i	−0.168998	−	0.0615101i
$974$	11.4431	+	31.4398i	0.366662	+	1.00740i
$975$	2.28978	−	4.41796i	0.0733317	−	0.141488i
$976$	5.41735	+	9.38312i	0.173405	+	0.300346i
$977$	0.538610	−	0.932899i	0.0172317	−	0.0298461i	−0.857281	−	0.514849i	$-0.827848\pi$
$977$	0.538610	−	0.932899i	0.0172317	−	0.0298461i	0.874513	+	0.485003i	$0.161181\pi$
$978$	−21.9356	+	14.0299i	−0.701422	+	0.448626i
$979$	5.78381	−	1.01984i	0.184851	−	0.0325943i
$980$	2.99743	+	1.73056i	0.0957492	+	0.0552809i
$981$	−4.96515	+	18.7997i	−0.158525	+	0.600228i
$982$	−0.635055	−	0.756829i	−0.0202654	−	0.0241514i
$983$	4.78675	−	1.74223i	0.152674	−	0.0555687i	−0.264553	−	0.964371i	$-0.585224\pi$
$983$	4.78675	−	1.74223i	0.152674	−	0.0555687i	0.417227	+	0.908803i	$0.363002\pi$
$984$	−0.420722	−	9.25512i	−0.0134121	−	0.295043i
$985$	−3.44381	−	2.88970i	−0.109729	−	0.0920736i
$986$	54.1308	+	9.54472i	1.72388	+	0.303966i
$987$	−7.85678	+	3.27091i	−0.250084	+	0.104114i
$988$	1.74405	+	2.22574i	0.0554856	+	0.0708103i
$989$			9.15410i			0.291083i
$990$	1.25648	+	1.78081i	0.0399336	+	0.0565979i
$991$	−7.72397	+	9.20507i	−0.245360	+	0.292409i	−0.874643	−	0.484768i	$-0.838904\pi$
$991$	−7.72397	+	9.20507i	−0.245360	+	0.292409i	0.629283	+	0.777176i	$0.283349\pi$
$992$	−1.04233	+	2.86378i	−0.0330940	+	0.0909251i
$993$	−13.5732	+	12.4824i	−0.430734	+	0.396118i
$994$	0.0408543	−	0.0342808i	0.00129582	−	0.00108732i
$995$	7.31621	−	4.22401i	0.231939	−	0.133910i
$996$	2.70000	−	20.7967i	0.0855528	−	0.658970i
$997$	−6.23994	−	35.3885i	−0.197621	−	1.12076i	−0.908637	−	0.417588i	$-0.862876\pi$
$997$	−6.23994	−	35.3885i	−0.197621	−	1.12076i	0.711016	−	0.703176i	$-0.248235\pi$
$998$	0.760240	+	4.31153i	0.0240650	+	0.136479i
$999$	−13.1443	−	16.9404i	−0.415867	−	0.535972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.b.59.2	yes	18
3.2	odd	2		114.2.l.a.59.3	yes	18
4.3	odd	2		912.2.cc.c.401.2		18
12.11	even	2		912.2.cc.d.401.1		18
19.10	odd	18		114.2.l.a.29.3	✓	18
57.29	even	18	inner	114.2.l.b.29.2	yes	18
76.67	even	18		912.2.cc.d.257.1		18
228.143	odd	18		912.2.cc.c.257.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.29.3	✓	18	19.10	odd	18
114.2.l.a.59.3	yes	18	3.2	odd	2
114.2.l.b.29.2	yes	18	57.29	even	18	inner
114.2.l.b.59.2	yes	18	1.1	even	1	trivial
912.2.cc.c.257.2		18	228.143	odd	18
912.2.cc.c.401.2		18	4.3	odd	2
912.2.cc.d.257.1		18	76.67	even	18
912.2.cc.d.401.1		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)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(0.517874 - 1.65282i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.258510 - 0.710252i) q^{5} +(-1.53778 - 0.797015i) q^{6} +(0.777943 + 1.34744i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.46361 - 1.71190i) q^{9} +O(q^{10})\)	\(q+(0.173648 - 0.984808i) q^{2} +(0.517874 - 1.65282i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.258510 - 0.710252i) q^{5} +(-1.53778 - 0.797015i) q^{6} +(0.777943 + 1.34744i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.46361 - 1.71190i) q^{9} +(-0.744351 + 0.131249i) q^{10} +(0.832399 + 0.480586i) q^{11} +(-1.05194 + 1.37602i) q^{12} +(0.416982 + 0.496940i) q^{13} +(1.46205 - 0.532144i) q^{14} +(-1.30779 + 0.0594499i) q^{15} +(0.766044 + 0.642788i) q^{16} +(6.73013 + 1.18670i) q^{17} +(-2.11370 + 2.12892i) q^{18} +(-4.14364 + 1.35288i) q^{19} +0.755834i q^{20} +(2.62994 - 0.587996i) q^{21} +(0.617829 - 0.736300i) q^{22} +(0.400647 - 1.10077i) q^{23} +(1.17245 + 1.27490i) q^{24} +(3.39259 - 2.84672i) q^{25} +(0.561798 - 0.324354i) q^{26} +(-4.10530 + 3.18535i) q^{27} +(-0.270177 - 1.53225i) q^{28} +(1.39666 + 7.92086i) q^{29} +(-0.168549 + 1.29825i) q^{30} +(-2.63927 + 1.52379i) q^{31} +(0.766044 - 0.642788i) q^{32} +(1.22540 - 1.12692i) q^{33} +(2.33735 - 6.42181i) q^{34} +(0.755913 - 0.900862i) q^{35} +(1.72953 + 2.45127i) q^{36} +4.12648i q^{37} +(0.612788 + 4.31561i) q^{38} +(1.03729 - 0.431843i) q^{39} +(0.744351 + 0.131249i) q^{40} +(-4.09755 - 3.43825i) q^{41} +(-0.122378 - 2.69209i) q^{42} +(-7.34330 + 2.67274i) q^{43} +(-0.617829 - 0.736300i) q^{44} +(-0.579012 + 2.19233i) q^{45} +(-1.01447 - 0.585707i) q^{46} +(-3.11004 + 0.548383i) q^{47} +(1.45913 - 0.933249i) q^{48} +(2.28961 - 3.96572i) q^{49} +(-2.21436 - 3.83538i) q^{50} +(5.44676 - 10.5091i) q^{51} +(-0.221871 - 0.609587i) q^{52} +(-13.6276 - 4.96002i) q^{53} +(2.42408 + 4.59607i) q^{54} +(0.126153 - 0.715449i) q^{55} -1.55589 q^{56} +(0.0901766 + 7.54930i) q^{57} +8.04306 q^{58} +(2.02192 - 11.4669i) q^{59} +(1.24926 + 0.391427i) q^{60} +(10.1813 + 3.70568i) q^{61} +(1.04233 + 2.86378i) q^{62} +(0.390129 - 4.65133i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.245158 - 0.424626i) q^{65} +(-0.897012 - 1.40247i) q^{66} +(-9.19012 + 1.62047i) q^{67} +(-5.91837 - 3.41697i) q^{68} +(-1.61189 - 1.23226i) q^{69} +(-0.755913 - 0.900862i) q^{70} +(0.0322101 - 0.0117235i) q^{71} +(2.71436 - 1.27760i) q^{72} +(-3.04446 - 2.55461i) q^{73} +(4.06379 + 0.716556i) q^{74} +(-2.94818 - 7.08158i) q^{75} +(4.35646 + 0.145920i) q^{76} +1.49547i q^{77} +(-0.245158 - 1.09652i) q^{78} +(-0.893115 + 1.06437i) q^{79} +(0.258510 - 0.710252i) q^{80} +(3.13878 + 8.43493i) q^{81} +(-4.09755 + 3.43825i) q^{82} +(-10.4856 + 6.05389i) q^{83} +(-2.67245 - 0.346959i) q^{84} +(-0.896950 - 5.08686i) q^{85} +(1.35699 + 7.69585i) q^{86} +(13.8150 + 1.79358i) q^{87} +(-0.832399 + 0.480586i) q^{88} +(4.68075 - 3.92762i) q^{89} +(2.05848 + 0.950909i) q^{90} +(-0.345207 + 0.948448i) q^{91} +(-0.752970 + 0.897355i) q^{92} +(1.15173 + 5.15137i) q^{93} +3.15801i q^{94} +(2.03206 + 2.59329i) q^{95} +(-0.665696 - 1.59901i) q^{96} +(9.54804 + 1.68358i) q^{97} +(-3.50789 - 2.94347i) q^{98} +(-1.22799 - 2.60896i) 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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