LMFDB - Embedded newform 114.2.l.a.59.3

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			59.3
Root			$0.0786547 - 1.73026i$ of defining polynomial
Character	$\chi$	$=$	114.59
Dual form			114.2.l.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(1.53778 - 0.797015i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.258510 + 0.710252i) q^{5} +(0.517874 + 1.65282i) q^{6} +(0.777943 + 1.34744i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.72953 - 2.45127i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(1.53778 - 0.797015i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.258510 + 0.710252i) q^{5} +(0.517874 + 1.65282i) q^{6} +(0.777943 + 1.34744i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.72953 - 2.45127i) q^{9} +(-0.744351 + 0.131249i) q^{10} +(-0.832399 - 0.480586i) q^{11} +(-1.71764 + 0.222997i) q^{12} +(0.416982 + 0.496940i) q^{13} +(-1.46205 + 0.532144i) q^{14} +(0.963613 + 0.886174i) 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} +(2.27023 + 1.45203i) q^{21} +(0.617829 - 0.736300i) q^{22} +(-0.400647 + 1.10077i) q^{23} +(0.0786547 - 1.73026i) q^{24} +(3.39259 - 2.84672i) q^{25} +(-0.561798 + 0.324354i) q^{26} +(0.705946 - 5.14797i) q^{27} +(-0.270177 - 1.53225i) q^{28} +(-1.39666 - 7.92086i) q^{29} +(-1.04004 + 0.795091i) q^{30} +(-2.63927 + 1.52379i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-1.66308 - 0.0756007i) q^{33} +(2.33735 - 6.42181i) q^{34} +(-0.755913 + 0.900862i) q^{35} +(-2.46361 + 1.71190i) 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} +(-1.82419 + 1.98360i) q^{42} +(-7.34330 + 2.67274i) q^{43} +(0.617829 + 0.736300i) q^{44} +(2.18812 + 0.594726i) q^{45} +(-1.01447 - 0.585707i) q^{46} +(3.11004 - 0.548383i) q^{47} +(1.69032 + 0.377917i) q^{48} +(2.28961 - 3.96572i) q^{49} +(2.21436 + 3.83538i) q^{50} +(-11.2953 + 3.53912i) q^{51} +(-0.221871 - 0.609587i) q^{52} +(13.6276 + 4.96002i) q^{53} +(4.94718 + 1.58916i) q^{54} +(0.126153 - 0.715449i) q^{55} +1.55589 q^{56} +(-5.29374 + 5.38297i) q^{57} +8.04306 q^{58} +(-2.02192 + 11.4669i) q^{59} +(-0.602411 - 1.16231i) q^{60} +(10.1813 + 3.70568i) q^{61} +(-1.04233 - 2.86378i) q^{62} +(4.64841 + 0.423492i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.245158 + 0.424626i) q^{65} +(0.363243 - 1.62469i) q^{66} +(-9.19012 + 1.62047i) q^{67} +(5.91837 + 3.41697i) q^{68} +(0.261222 + 2.01206i) q^{69} +(-0.755913 - 0.900862i) q^{70} +(-0.0322101 + 0.0117235i) q^{71} +(-1.25809 - 2.72345i) 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} +(-0.605407 + 0.946547i) q^{78} +(-0.893115 + 1.06437i) q^{79} +(-0.258510 + 0.710252i) q^{80} +(-3.01742 - 8.47910i) q^{81} +(-4.09755 + 3.43825i) q^{82} +(10.4856 - 6.05389i) q^{83} +(-1.63670 - 2.14093i) q^{84} +(-0.896950 - 5.08686i) q^{85} +(-1.35699 - 7.69585i) q^{86} +(-8.46081 - 11.0674i) q^{87} +(-0.832399 + 0.480586i) q^{88} +(-4.68075 + 3.92762i) q^{89} +(-0.965654 + 2.05160i) q^{90} +(-0.345207 + 0.948448i) q^{91} +(0.752970 - 0.897355i) q^{92} +(-2.84414 + 4.44679i) 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} +(-2.61771 + 1.20924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) $ 18 * q + 3 * q^6 + 9 * q^8	$ 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) $ 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.53778	−	0.797015i	0.887838	−	0.460157i
$3$	1.53778	−	0.797015i	0.887838	−	0.460157i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.258510	+	0.710252i	0.115609	+	0.317634i	0.983979	−	0.178283i	$-0.0570542\pi$
$5$	0.258510	+	0.710252i	0.115609	+	0.317634i	−0.868370	+	0.495917i	$0.834832\pi$
$6$	0.517874	+	1.65282i	0.211421	+	0.674760i
$7$	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
$9$	1.72953	−	2.45127i	0.576511	−	0.817089i
$10$	−0.744351	+	0.131249i	−0.235384	+	0.0415046i
$11$	−0.832399	−	0.480586i	−0.250978	−	0.144902i	0.369234	−	0.929336i	$-0.379620\pi$
$11$	−0.832399	−	0.480586i	−0.250978	−	0.144902i	−0.620212	+	0.784434i	$0.712953\pi$
$12$	−1.71764	+	0.222997i	−0.495839	+	0.0643738i
$13$	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
$15$	0.963613	+	0.886174i	0.248804	+	0.228809i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−6.73013	−	1.18670i	−1.63230	−	0.287818i	−0.718968	−	0.695043i	$-0.755385\pi$
$17$	−6.73013	−	1.18670i	−1.63230	−	0.287818i	−0.913328	+	0.407226i	$0.866496\pi$
$18$	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
$21$	2.27023	+	1.45203i	0.495405	+	0.316859i
$22$	0.617829	−	0.736300i	0.131722	−	0.156980i
$23$	−0.400647	+	1.10077i	−0.0835407	+	0.229526i	−0.974429	−	0.224697i	$-0.927861\pi$
$23$	−0.400647	+	1.10077i	−0.0835407	+	0.229526i	0.890888	+	0.454223i	$0.150083\pi$
$24$	0.0786547	−	1.73026i	0.0160553	−	0.353189i
$25$	3.39259	−	2.84672i	0.678519	−	0.569345i
$26$	−0.561798	+	0.324354i	−0.110178	+	0.0636111i
$27$	0.705946	−	5.14797i	0.135859	−	0.990728i
$28$	−0.270177	−	1.53225i	−0.0510586	−	0.289568i
$29$	−1.39666	−	7.92086i	−0.259354	−	1.47087i	−0.784645	−	0.619945i	$-0.787155\pi$
$29$	−1.39666	−	7.92086i	−0.259354	−	1.47087i	0.525292	−	0.850922i	$-0.323956\pi$
$30$	−1.04004	+	0.795091i	−0.189885	+	0.145163i
$31$	−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
$33$	−1.66308	−	0.0756007i	−0.289505	−	0.0131604i
$34$	2.33735	−	6.42181i	0.400852	−	1.10133i
$35$	−0.755913	+	0.900862i	−0.127773	+	0.152273i
$36$	−2.46361	+	1.71190i	−0.410602	+	0.285317i
$37$			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	0.903996	−	0.427540i	$-0.140620\pi$
$41$	4.09755	+	3.43825i	0.639929	+	0.536964i	−0.264067	+	0.964504i	$0.585064\pi$
$42$	−1.82419	+	1.98360i	−0.281479	+	0.306076i
$43$	−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
$45$	2.18812	+	0.594726i	0.326186	+	0.0886566i
$46$	−1.01447	−	0.585707i	−0.149576	−	0.0863578i
$47$	3.11004	−	0.548383i	0.453646	−	0.0799899i	0.0578432	−	0.998326i	$-0.481578\pi$
$47$	3.11004	−	0.548383i	0.453646	−	0.0799899i	0.395802	+	0.918336i	$0.370467\pi$
$48$	1.69032	+	0.377917i	0.243977	+	0.0545476i
$49$	2.28961	−	3.96572i	0.327087	−	0.566531i
$50$	2.21436	+	3.83538i	0.313157	+	0.542405i
$51$	−11.2953	+	3.53912i	−1.58165	+	0.495576i
$52$	−0.221871	−	0.609587i	−0.0307680	−	0.0845345i
$53$	13.6276	+	4.96002i	1.87189	+	0.681312i	0.966462	+	0.256809i	$0.0826711\pi$
$53$	13.6276	+	4.96002i	1.87189	+	0.681312i	0.905427	+	0.424503i	$0.139551\pi$
$54$	4.94718	+	1.58916i	0.673226	+	0.216257i
$55$	0.126153	−	0.715449i	0.0170105	−	0.0964711i
$56$	1.55589			0.207914
$57$	−5.29374	+	5.38297i	−0.701173	+	0.712991i
$58$	8.04306			1.05610
$59$	−2.02192	+	11.4669i	−0.263231	+	1.49286i	0.510793	+	0.859704i	$0.329352\pi$
$59$	−2.02192	+	11.4669i	−0.263231	+	1.49286i	−0.774024	+	0.633156i	$0.781759\pi$
$60$	−0.602411	−	1.16231i	−0.0777709	−	0.150053i
$61$	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
$63$	4.64841	+	0.423492i	0.585644	+	0.0533549i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.245158	+	0.424626i	−0.0304081	+	0.0526684i
$66$	0.363243	−	1.62469i	0.0447121	−	0.199985i
$67$	−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
$69$	0.261222	+	2.01206i	0.0314475	+	0.242224i
$70$	−0.755913	−	0.900862i	−0.0903489	−	0.107674i
$71$	−0.0322101	+	0.0117235i	−0.00382263	+	0.00139132i	−0.343931	−	0.938995i	$-0.611759\pi$
$71$	−0.0322101	+	0.0117235i	−0.00382263	+	0.00139132i	0.340108	+	0.940386i	$0.389536\pi$
$72$	−1.25809	−	2.72345i	−0.148268	−	0.320962i
$73$	−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
$78$	−0.605407	+	0.946547i	−0.0685488	+	0.107175i
$79$	−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
$81$	−3.01742	−	8.47910i	−0.335269	−	0.942122i
$82$	−4.09755	+	3.43825i	−0.452498	+	0.379691i
$83$	10.4856	−	6.05389i	1.15095	−	0.664500i	0.201830	−	0.979421i	$-0.435311\pi$
$83$	10.4856	−	6.05389i	1.15095	−	0.664500i	0.949118	+	0.314920i	$0.101978\pi$
$84$	−1.63670	−	2.14093i	−0.178578	−	0.233594i
$85$	−0.896950	−	5.08686i	−0.0972879	−	0.551747i
$86$	−1.35699	−	7.69585i	−0.146328	−	0.829865i
$87$	−8.46081	−	11.0674i	−0.907094	−	1.18655i
$88$	−0.832399	+	0.480586i	−0.0887340	+	0.0512306i
$89$	−4.68075	+	3.92762i	−0.496159	+	0.416327i	−0.856227	−	0.516599i	$-0.827198\pi$
$89$	−4.68075	+	3.92762i	−0.496159	+	0.416327i	0.360069	+	0.932926i	$0.382753\pi$
$90$	−0.965654	+	2.05160i	−0.101789	+	0.216258i
$91$	−0.345207	+	0.948448i	−0.0361875	+	0.0994243i
$92$	0.752970	−	0.897355i	0.0785026	−	0.0935557i
$93$	−2.84414	+	4.44679i	−0.294924	+	0.461110i
$94$			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
$99$	−2.61771	+	1.20924i	−0.263089	+	0.121533i
$100$	−4.16163	+	1.51471i	−0.416163	+	0.151471i
$101$	−12.0945	−	14.4137i	−1.20345	−	1.43422i	−0.871130	−	0.491053i	$-0.836612\pi$
$101$	−12.0945	−	14.4137i	−1.20345	−	1.43422i	−0.332323	−	0.943166i	$-0.607832\pi$
$102$	−1.52395	−	11.7382i	−0.150894	−	1.16226i
$103$	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
$105$	−0.444427	+	1.98780i	−0.0433716	+	0.193990i
$106$	−7.25107	+	12.5592i	−0.704286	+	1.21986i
$107$	1.17826	+	2.04080i	0.113906	+	0.197292i	0.917342	−	0.398100i	$-0.130330\pi$
$107$	1.17826	+	2.04080i	0.113906	+	0.197292i	−0.803436	+	0.595392i	$0.796997\pi$
$108$	−2.42408	+	4.59607i	−0.233258	+	0.442257i
$109$	−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
$111$	3.28887	+	6.34562i	0.312165	+	0.602299i
$112$	−0.270177	+	1.53225i	−0.0255293	+	0.144784i
$113$	10.0387			0.944358			0.472179	−	0.881503i	$-0.343468\pi$
$113$	10.0387			0.944358			0.472179	+	0.881503i	$0.343468\pi$
$114$	−4.38194	−	6.14806i	−0.410406	−	0.575818i
$115$	−0.885394			−0.0825635
$116$	−1.39666	+	7.92086i	−0.129677	+	0.735434i
$117$	1.93932	−	0.162660i	0.179290	−	0.0150379i
$118$	−10.9416	−	3.98240i	−1.00725	−	0.366610i
$119$	−3.63665	−	9.99161i	−0.333371	−	0.915929i
$120$	1.24926	−	0.391427i	0.114041	−	0.0357322i
$121$	−5.03807	−	8.72620i	−0.458007	−	0.793291i
$122$	−5.41735	+	9.38312i	−0.490464	+	0.849508i
$123$	9.04146	+	2.02147i	0.815241	+	0.182269i
$124$	3.00127	−	0.529205i	0.269522	−	0.0475240i
$125$	6.17177	+	3.56327i	0.552020	+	0.318709i
$126$	−1.22425	+	4.50425i	−0.109064	+	0.401270i
$127$	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
$129$	−9.16216	+	9.96280i	−0.806683	+	0.877176i
$130$	−0.375604	−	0.315169i	−0.0329426	−	0.0276422i
$131$	−10.9610	−	1.93273i	−0.957671	−	0.168863i	−0.327096	−	0.944991i	$-0.606070\pi$
$131$	−10.9610	−	1.93273i	−0.957671	−	0.168863i	−0.630575	+	0.776128i	$0.717181\pi$
$132$	1.53693	+	0.639848i	0.133772	+	0.0556916i
$133$	−5.04643	−	4.53083i	−0.437581	−	0.392873i
$134$		−	9.33190i		−	0.806153i
$135$	3.83885	−	0.829406i	0.330396	−	0.0713839i
$136$	−4.39278	+	5.23511i	−0.376678	+	0.448907i
$137$	1.69757	−	4.66403i	0.145033	−	0.398475i	−0.845812	−	0.533482i	$-0.820883\pi$
$137$	1.69757	−	4.66403i	0.145033	−	0.398475i	0.990845	+	0.135007i	$0.0431056\pi$
$138$	−2.02686	−	0.0921372i	−0.172537	−	0.00784324i
$139$	−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
$141$	4.34548	−	3.32204i	0.365956	−	0.279766i
$142$	−0.00595218	−	0.0337565i	−0.000499496	−	0.00283278i
$143$	−0.108273	−	0.614047i	−0.00905425	−	0.0513492i
$144$	2.90054	−	0.766057i	0.241712	−	0.0638380i
$145$	5.26475	−	3.03961i	0.437214	−	0.252426i
$146$	3.04446	−	2.55461i	0.251961	−	0.211421i
$147$	0.360177	−	7.92326i	0.0297069	−	0.653499i
$148$	1.41134	−	3.87762i	0.116011	−	0.318739i
$149$	−12.3170	+	14.6788i	−1.00904	+	1.20253i	−0.0298610	+	0.999554i	$0.509506\pi$
$149$	−12.3170	+	14.6788i	−1.00904	+	1.20253i	−0.979183	+	0.202978i	$0.934938\pi$
$150$	6.46205	+	4.13309i	0.527624	+	0.337466i
$151$		−	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
$156$	−0.827039	−	0.760575i	−0.0662161	−	0.0608948i
$157$	−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
$159$	24.9094	−	3.23394i	1.97544	−	0.256468i
$160$	−0.654571	−	0.377917i	−0.0517484	−	0.0298770i
$161$	−1.79490	+	0.316489i	−0.141458	+	0.0249428i
$162$	8.87425	−	1.49920i	0.697227	−	0.117788i
$163$	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
$165$	−0.376228	−	1.20075i	−0.0292893	−	0.0934782i
$166$	4.14110	+	11.3776i	0.321412	+	0.883072i
$167$	8.87982	+	3.23199i	0.687141	+	0.250099i	0.661911	−	0.749583i	$-0.269746\pi$
$167$	8.87982	+	3.23199i	0.687141	+	0.250099i	0.0252305	+	0.999682i	$0.491968\pi$
$168$	2.39261	−	1.24006i	0.184594	−	0.0956731i
$169$	2.18435	−	12.3881i	0.168027	−	0.952929i
$170$	5.16533			0.396163
$171$	−3.85030	+	12.4970i	−0.294440	+	0.955670i
$172$	7.81457			0.595856
$173$	−2.33529	+	13.2441i	−0.177549	+	1.00693i	0.757612	+	0.652705i	$0.226366\pi$
$173$	−2.33529	+	13.2441i	−0.177549	+	1.00693i	−0.935161	+	0.354224i	$0.884745\pi$
$174$	12.3684	−	6.41044i	0.937650	−	0.485974i
$175$	6.47502	+	2.35672i	0.489466	+	0.178151i
$176$	−0.328740	−	0.903205i	−0.0247797	−	0.0680817i
$177$	6.03000	+	19.2450i	0.453243	+	1.44655i
$178$	−3.05514	−	5.29167i	−0.228993	−	0.396627i
$179$	−8.34644	+	14.4565i	−0.623842	+	1.08053i	0.364921	+	0.931038i	$0.381096\pi$
$179$	−8.34644	+	14.4565i	−0.623842	+	1.08053i	−0.988764	+	0.149488i	$0.952237\pi$
$180$	−1.85275	−	1.30724i	−0.138096	−	0.0974360i
$181$	−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
$183$	18.6101	−	2.41611i	1.37570	−	0.178604i
$184$	0.752970	+	0.897355i	0.0555097	+	0.0661539i
$185$	−2.93084	+	1.06674i	−0.215480	+	0.0784281i
$186$	−3.88535	−	3.57311i	−0.284888	−	0.261993i
$187$	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	$-0.856198\pi$
$191$		−	12.0667i		−	0.873115i	0.899676	−	0.436558i	$-0.143802\pi$
$192$	−1.45913	−	0.933249i	−0.105303	−	0.0673514i
$193$	−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
$195$	−0.0385657	+	0.848376i	−0.00276175	+	0.0607535i
$196$	−3.50789	+	2.94347i	−0.250563	+	0.210248i
$197$	−5.15098	+	2.97392i	−0.366992	+	0.211883i	−0.672144	−	0.740421i	$-0.734626\pi$
$197$	−5.15098	+	2.97392i	−0.366992	+	0.211883i	0.305151	+	0.952304i	$0.401293\pi$
$198$	−0.736311	−	2.78792i	−0.0523274	−	0.198129i
$199$	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
$201$	−12.8409	+	9.81659i	−0.905724	+	0.692409i
$202$	16.2949	−	9.40789i	1.14651	−	0.661937i
$203$	9.58634	−	8.04389i	0.672829	−	0.564571i
$204$	11.8245	+	0.537522i	0.827883	+	0.0376341i
$205$	−1.38276	+	3.79911i	−0.0965764	+	0.265342i
$206$	−7.36940	+	8.78251i	−0.513450	+	0.611906i
$207$	2.00535	+	2.88591i	0.139381	+	0.200585i
$208$			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
$213$	−0.0401882	+	0.0437001i	−0.00275365	+	0.00299428i
$214$	−2.21440	+	0.805976i	−0.151373	+	0.0550954i
$215$	−3.79664	−	4.52466i	−0.258928	−	0.308579i
$216$	−4.10530	−	3.18535i	−0.279331	−	0.216736i
$217$	−4.10641	−	2.37084i	−0.278761	−	0.160943i
$218$	6.38297	−	1.12549i	0.432309	−	0.0762278i
$219$	−6.71777	−	1.50194i	−0.453945	−	0.101492i
$220$	−0.363243	+	0.629155i	−0.0244898	+	0.0424176i
$221$	−2.21662	−	3.83930i	−0.149106	−	0.258259i
$222$	−6.82032	+	2.13700i	−0.457750	+	0.143426i
$223$	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
$225$	−1.11047	−	13.2397i	−0.0740316	−	0.882644i
$226$	−1.74320	+	9.88615i	−0.115956	+	0.657617i
$227$	−16.1886			−1.07448			−0.537238	−	0.843430i	$-0.680532\pi$
$227$	−16.1886			−1.07448			−0.537238	+	0.843430i	$0.680532\pi$
$228$	6.81557	−	3.24777i	0.451372	−	0.215089i
$229$	−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
$231$	−1.19191	−	2.29971i	−0.0784222	−	0.151310i
$232$	−7.55800	−	2.75089i	−0.496207	−	0.180605i
$233$	−3.98107	−	10.9379i	−0.260808	−	0.716565i	−0.999113	−	0.0420981i	$-0.986596\pi$
$233$	−3.98107	−	10.9379i	−0.260808	−	0.716565i	0.738305	−	0.674467i	$-0.235626\pi$
$234$	−0.176570	+	1.93810i	−0.0115427	+	0.126698i
$235$	1.19347	+	2.06715i	0.0778532	+	0.134846i
$236$	5.82188	−	10.0838i	0.378972	−	0.656399i
$237$	−0.525093	+	2.34860i	−0.0341085	+	0.152558i
$238$	10.4713	−	1.84637i	0.678754	−	0.119683i
$239$	13.1831	+	7.61128i	0.852746	+	0.492333i	0.861576	−	0.507628i	$-0.169478\pi$
$239$	13.1831	+	7.61128i	0.852746	+	0.492333i	−0.00883069	+	0.999961i	$0.502811\pi$
$240$	0.168549	+	1.29825i	0.0108798	+	0.0838015i
$241$	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
$243$	−11.3981	−	10.6341i	−0.731189	−	0.682175i
$244$	−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
$249$	11.2996	−	17.6668i	0.716081	−	1.11958i
$250$	−4.58085	+	5.45925i	−0.289719	+	0.345273i
$251$	3.71032	−	10.1940i	0.234193	−	0.643441i	−0.765807	−	0.643071i	$-0.777660\pi$
$251$	3.71032	−	10.1940i	0.234193	−	0.643441i	1.00000		0.000369965i	$-0.000117763\pi$
$252$	−4.22323	−	1.98780i	−0.266039	−	0.125220i
$253$	0.862512	−	0.723733i	0.0542257	−	0.0455007i
$254$	−12.0603	+	6.96300i	−0.756728	+	0.436897i
$255$	−5.43361	−	7.10759i	−0.340266	−	0.445094i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	0.00786014	+	0.0445771i	0.000490302	+	0.00278064i	0.985052	−	0.172258i	$-0.0551062\pi$
$257$	0.00786014	+	0.0445771i	0.000490302	+	0.00278064i	−0.984562	+	0.175038i	$0.943995\pi$
$258$	−8.22045	−	10.7530i	−0.511783	−	0.669452i
$259$	−5.56017	+	3.21017i	−0.345492	+	0.199470i
$260$	0.375604	−	0.315169i	0.0232940	−	0.0195460i
$261$	−21.8317	−	10.2758i	−1.35135	−	0.636057i
$262$	3.80673	−	10.4589i	0.235181	−	0.646153i
$263$	3.52577	−	4.20185i	0.217408	−	0.259097i	−0.646307	−	0.763078i	$-0.723687\pi$
$263$	3.52577	−	4.20185i	0.217408	−	0.259097i	0.863715	+	0.503981i	$0.168132\pi$
$264$	−0.897012	+	1.40247i	−0.0552073	+	0.0863160i
$265$			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	0.595775	−	0.803152i	$-0.296845\pi$
$269$	−1.50432	−	1.26228i	−0.0917202	−	0.0769623i	−0.687495	+	0.726189i	$0.741290\pi$
$270$	0.150196	+	3.92456i	0.00914061	+	0.238841i
$271$	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
$273$	0.225075	+	1.73364i	0.0136222	+	0.104925i
$274$	4.29839	+	2.48168i	0.259675	+	0.149924i
$275$	−4.19208	+	0.739177i	−0.252792	+	0.0445741i
$276$	0.442697	−	1.98006i	0.0266472	−	0.119186i
$277$	−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
$279$	−0.829509	+	9.10501i	−0.0496614	+	0.545102i
$280$	0.402213	+	1.10507i	0.0240368	+	0.0660406i
$281$	11.0064	+	4.00600i	0.656587	+	0.238978i	0.648762	−	0.760991i	$-0.275287\pi$
$281$	11.0064	+	4.00600i	0.656587	+	0.238978i	0.00782495	+	0.999969i	$0.497509\pi$
$282$	2.51698	+	4.85633i	0.149884	+	0.289190i
$283$	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
$285$	−5.19175	−	2.36833i	−0.307533	−	0.140288i
$286$	0.623520			0.0368695
$287$	−1.44517	+	8.19595i	−0.0853055	+	0.483791i
$288$	0.250744	+	2.98950i	0.0147752	+	0.176158i
$289$	27.9116	+	10.1590i	1.64186	+	0.597587i
$290$	2.07921	+	5.71259i	0.122096	+	0.335455i
$291$	16.0246	−	5.02096i	0.939380	−	0.294334i
$292$	1.98713	+	3.44181i	0.116288	+	0.201417i
$293$	1.29095	−	2.23599i	0.0754180	−	0.130628i	−0.825850	−	0.563890i	$-0.809304\pi$
$293$	1.29095	−	2.23599i	0.0754180	−	0.130628i	0.901268	+	0.433262i	$0.142638\pi$
$294$	7.74034	+	1.73056i	0.451426	+	0.100929i
$295$	−8.66705	+	1.52824i	−0.504615	+	0.0889773i
$296$	3.57364	+	2.06324i	0.207713	+	0.119923i
$297$	−3.06167	+	3.94590i	−0.177656	+	0.228964i
$298$	−12.3170	−	14.6788i	−0.713502	−	0.850319i
$299$	−0.714078	+	0.259903i	−0.0412962	+	0.0150306i
$300$	−5.19243	+	5.64617i	−0.299785	+	0.325982i
$301$	−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
$306$	−11.6991	−	16.8362i	−0.668790	−	0.962462i
$307$	−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
$309$	19.8370	+	0.901757i	1.12849	+	0.0512991i
$310$	1.76455	−	1.48063i	0.100220	−	0.0840944i
$311$	−22.4909	+	12.9851i	−1.27534	+	0.736320i	−0.975989	−	0.217822i	$-0.930105\pi$
$311$	−22.4909	+	12.9851i	−1.27534	+	0.736320i	−0.299355	+	0.954142i	$0.596771\pi$
$312$	0.892634	−	0.682402i	0.0505355	−	0.0386334i
$313$	−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
$315$	0.900876	+	3.41102i	0.0507586	+	0.192189i
$316$	1.20329	−	0.694720i	0.0676904	−	0.0390811i
$317$	23.3056	−	19.5557i	1.30897	−	1.09836i	0.320454	−	0.947264i	$-0.396165\pi$
$317$	23.3056	−	19.5557i	1.30897	−	1.09836i	0.988519	−	0.151095i	$-0.0482799\pi$
$318$	−1.14066	+	25.0925i	−0.0639652	+	1.40712i
$319$	−2.64407	+	7.26453i	−0.148040	+	0.406736i
$320$	0.485841	−	0.579002i	0.0271593	−	0.0323672i
$321$	3.43845	+	2.19922i	0.191916	+	0.122748i
$322$		−	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
$327$	−8.26319	−	7.59913i	−0.456956	−	0.420233i
$328$	5.02638	−	1.82945i	0.277536	−	0.101015i
$329$	3.15834	+	3.76397i	0.174125	+	0.207514i
$330$	1.24784	−	0.162004i	0.0686912	−	0.00891805i
$331$	−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
$333$	10.1151	+	7.13689i	0.554304	+	0.391099i
$334$	−4.72485	+	8.18369i	−0.258533	+	0.447791i
$335$	−3.52668	−	6.10839i	−0.192683	−	0.333737i
$336$	0.805753	+	2.57160i	0.0439574	+	0.140292i
$337$	−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
$339$	15.4373	−	8.00096i	0.838436	−	0.434553i
$340$	−0.896950	+	5.08686i	−0.0486440	+	0.275874i
$341$	2.92924			0.158627
$342$	−11.6386	−	5.96189i	−0.629341	−	0.322382i
$343$	18.0159			0.972770
$344$	−1.35699	+	7.69585i	−0.0731638	+	0.414932i
$345$	−1.36154	+	0.705673i	−0.0733029	+	0.0379921i
$346$	−12.6374	−	4.59962i	−0.679389	−	0.247277i
$347$	9.63081	+	26.4604i	0.517009	+	1.42047i	0.873799	+	0.486287i	$0.161649\pi$
$347$	9.63081	+	26.4604i	0.517009	+	1.42047i	−0.356790	+	0.934185i	$0.616129\pi$
$348$	4.16529	+	13.2937i	0.223283	+	0.712617i
$349$	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
$351$	2.85260	−	1.79580i	0.152261	−	0.0958527i
$352$	0.946569	−	0.166906i	0.0504523	−	0.00889610i
$353$	3.55050	+	2.04988i	0.188974	+	0.109104i	0.591502	−	0.806303i	$-0.298535\pi$
$353$	3.55050	+	2.04988i	0.188974	+	0.109104i	−0.402528	+	0.915408i	$0.631868\pi$
$354$	−19.9998	+	2.59653i	−1.06297	+	0.138004i
$355$	−0.0166533	−	0.0198466i	−0.000883864	−	0.00105335i
$356$	5.74179	−	2.08984i	0.304314	−	0.110761i
$357$	−13.5558	−	12.4664i	−0.717450	−	0.659793i
$358$	−12.7875	−	10.7300i	−0.675840	−	0.567097i
$359$	5.52450	+	0.974118i	0.291572	+	0.0514120i	0.317521	−	0.948251i	$-0.397150\pi$
$359$	5.52450	+	0.974118i	0.291572	+	0.0514120i	−0.0259490	+	0.999663i	$0.508261\pi$
$360$	1.60911	−	1.59760i	0.0848074	−	0.0842011i
$361$	15.3395	−	11.2117i	0.807340	−	0.590087i
$362$		−	10.1947i		−	0.535820i
$363$	−14.7024	−	9.40356i	−0.771674	−	0.493559i
$364$	0.648776	−	0.773182i	0.0340051	−	0.0405257i
$365$	1.02739	−	2.82273i	0.0537760	−	0.147748i
$366$	−0.852200	+	18.7469i	−0.0445452	+	0.979915i
$367$	−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
$369$	15.5149	−	4.09761i	0.807674	−	0.213313i
$370$	−0.541597	−	3.07155i	−0.0281563	−	0.159682i
$371$	3.91814	+	22.2209i	0.203420	+	1.15365i
$372$	4.19351	−	3.20586i	0.217423	−	0.166216i
$373$	−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
$375$	12.3308	+	0.560536i	0.636760	+	0.0289460i
$376$	1.08010	−	2.96756i	0.0557021	−	0.153040i
$377$	3.35381	−	3.99691i	0.172730	−	0.205852i
$378$	1.70733	+	7.90228i	0.0878158	+	0.406450i
$379$		−	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	0.477665	−	0.878542i	$-0.341483\pi$
$383$	−5.96084	−	5.00173i	−0.304584	−	0.255577i	−0.782249	+	0.622965i	$0.785928\pi$
$384$	1.17245	−	1.27490i	0.0598311	−	0.0650595i
$385$	1.06216	−	0.386595i	0.0541328	−	0.0197027i
$386$	−2.14990	−	2.56215i	−0.109427	−	0.130410i
$387$	−6.14888	+	22.6230i	−0.312565	+	1.14999i
$388$	−8.39641	−	4.84767i	−0.426263	−	0.246103i
$389$	−9.63724	+	1.69931i	−0.488627	+	0.0861582i	−0.412533	−	0.910942i	$-0.635356\pi$
$389$	−9.63724	+	1.69931i	−0.488627	+	0.0861582i	−0.0760939	+	0.997101i	$0.524245\pi$
$390$	−0.828791	−	0.185299i	−0.0419674	−	0.00938297i
$391$	4.00269	−	6.93287i	0.202425	−	0.350610i
$392$	−2.28961	−	3.96572i	−0.115643	−	0.200299i
$393$	−18.3961	+	5.76401i	−0.927960	+	0.290756i
$394$	−2.03428	−	5.58914i	−0.102486	−	0.281577i
$395$	−0.986853	−	0.359185i	−0.0496539	−	0.0180726i
$396$	2.87342	−	0.241008i	0.144395	−	0.0121111i
$397$	−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
$399$	−11.3714	−	2.94534i	−0.569284	−	0.147451i
$400$	4.42872			0.221436
$401$	3.59086	−	20.3648i	0.179319	−	1.01697i	−0.753720	−	0.657195i	$-0.771743\pi$
$401$	3.59086	−	20.3648i	0.179319	−	1.01697i	0.933039	−	0.359774i	$-0.117146\pi$
$402$	−7.43766	−	14.3504i	−0.370957	−	0.715733i
$403$	−1.85776	−	0.676169i	−0.0925416	−	0.0336824i
$404$	6.43537	+	17.6810i	0.320172	+	0.879665i
$405$	5.24226	−	4.33507i	0.260490	−	0.215411i
$406$	6.25704	+	10.8375i	0.310532	+	0.537857i
$407$	1.98313	−	3.43488i	0.0982999	−	0.170260i
$408$	−2.58267	+	11.5516i	−0.127861	+	0.571887i
$409$	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
$411$	−1.10682	−	8.52524i	−0.0545952	−	0.420519i
$412$	−7.36940	−	8.78251i	−0.363064	−	0.432683i
$413$	−17.0238	+	6.19617i	−0.837688	+	0.304893i
$414$	−3.19029	+	1.47375i	−0.156794	+	0.0724307i
$415$	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	$-0.787792\pi$
$419$		−	25.3156i		−	1.23675i	0.785884	−	0.618374i	$-0.212208\pi$
$420$	1.09749	−	1.71592i	0.0535522	−	0.0837283i
$421$	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
$423$	4.03468	−	8.57198i	0.196173	−	0.416784i
$424$	11.1093	−	9.32180i	0.539515	−	0.452706i
$425$	−26.2108	+	15.1328i	−1.27141	+	0.734049i
$426$	−0.0360576	−	0.0471661i	−0.00174699	−	0.00228520i
$427$	2.92728	+	16.6014i	0.141661	+	0.803400i
$428$	−0.409205	−	2.32072i	−0.0197797	−	0.112176i
$429$	−0.655905	−	0.857975i	−0.0316674	−	0.0414234i
$430$	5.11520	−	2.95326i	0.246677	−	0.142419i
$431$	25.2345	−	21.1742i	1.21550	−	1.01993i	0.216455	−	0.976293i	$-0.430551\pi$
$431$	25.2345	−	21.1742i	1.21550	−	1.01993i	0.999048	−	0.0436350i	$-0.0138938\pi$
$432$	3.84984	−	3.48980i	0.185226	−	0.167903i
$433$	−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
$435$	5.67342	−	8.87034i	0.272020	−	0.425300i
$436$			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
$441$	−5.76108	−	12.4713i	−0.274337	−	0.593871i
$442$	4.16589	−	1.51626i	0.198151	−	0.0721211i
$443$	−12.5287	−	14.9311i	−0.595257	−	0.709400i	0.381350	−	0.924431i	$-0.375459\pi$
$443$	−12.5287	−	14.9311i	−0.595257	−	0.709400i	−0.976607	+	0.215031i	$0.931015\pi$
$444$	−0.920194	−	7.08779i	−0.0436705	−	0.336372i
$445$	−3.99962	−	2.30918i	−0.189600	−	0.109466i
$446$	−13.5672	+	2.39226i	−0.642426	+	0.113277i
$447$	−7.24156	+	32.3895i	−0.342514	+	1.53197i
$448$	0.777943	−	1.34744i	0.0367544	−	0.0636604i
$449$	−6.61607	−	11.4594i	−0.312232	−	0.540801i	0.666613	−	0.745404i	$-0.267743\pi$
$449$	−6.61607	−	11.4594i	−0.312232	−	0.540801i	−0.978845	+	0.204602i	$0.934410\pi$
$450$	13.2313	+	1.20544i	0.623732	+	0.0568249i
$451$	−1.75842	−	4.83122i	−0.0828007	−	0.227493i
$452$	−9.43326	−	3.43342i	−0.443703	−	0.161495i
$453$	−15.3524	−	29.6214i	−0.721321	−	1.39173i
$454$	2.81112	−	15.9427i	0.131933	−	0.748227i
$455$	−0.762876			−0.0357642
$456$	2.01492	+	7.27600i	0.0943571	+	0.340730i
$457$	−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
$459$	−10.8602	+	33.8088i	−0.506912	+	1.57806i
$460$	0.831999	+	0.302823i	0.0387921	+	0.0141192i
$461$	5.65076	+	15.5253i	0.263182	+	0.723087i	0.998948	+	0.0458511i	$0.0146000\pi$
$461$	5.65076	+	15.5253i	0.263182	+	0.723087i	−0.735766	+	0.677236i	$0.763178\pi$
$462$	2.47174	−	0.774466i	0.114996	−	0.0360314i
$463$	−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
$465$	−3.89358	−	0.870516i	−0.180560	−	0.0403692i
$466$	11.4630	−	2.02124i	0.531014	−	0.0936321i
$467$	−18.5458	−	10.7074i	−0.858196	−	0.495480i	0.00521153	−	0.999986i	$-0.498341\pi$
$467$	−18.5458	−	10.7074i	−0.858196	−	0.495480i	−0.863408	+	0.504507i	$0.831674\pi$
$468$	−1.87799	−	0.510435i	−0.0868103	−	0.0235949i
$469$	−9.33287	−	11.1225i	−0.430952	−	0.513588i
$470$	−2.24298	+	0.816380i	−0.103461	+	0.0376568i
$471$	−0.250711	+	0.272620i	−0.0115522	+	0.0125617i
$472$	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
$477$	35.7277	−	24.8262i	1.63586	−	1.13672i
$478$	−9.78488	+	11.6612i	−0.447550	+	0.533369i
$479$	−11.4165	+	31.3665i	−0.521632	+	1.43317i	0.347071	+	0.937839i	$0.387176\pi$
$479$	−11.4165	+	31.3665i	−0.521632	+	1.43317i	−0.868703	+	0.495333i	$0.835046\pi$
$480$	−1.30779	−	0.0594499i	−0.0596923	−	0.00271350i
$481$	−2.05061	+	1.72067i	−0.0934998	+	0.0784557i
$482$	−13.1498	+	7.59206i	−0.598959	+	0.345809i
$483$	−2.50791	+	1.91725i	−0.114114	+	0.0872379i
$484$	1.74971	+	9.92307i	0.0795320	+	0.451049i
$485$	1.27250	+	7.21673i	0.0577815	+	0.327695i
$486$	12.4518	−	9.37836i	0.564824	−	0.425411i
$487$	−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
$489$	1.18244	−	26.0117i	0.0534720	−	1.17629i
$490$	−1.18378	+	3.25240i	−0.0534775	+	0.146928i
$491$	−0.635055	+	0.756829i	−0.0286596	+	0.0341552i	−0.780184	−	0.625550i	$-0.784875\pi$
$491$	−0.635055	+	0.756829i	−0.0286596	+	0.0341552i	0.751524	+	0.659705i	$0.229319\pi$
$492$	−7.80481	−	4.99192i	−0.351868	−	0.225053i
$493$			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
$498$	15.4362	+	14.1957i	0.691713	+	0.636124i
$499$	−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
$501$	16.2312	−	2.10726i	0.725155	−	0.0941454i
$502$	9.39486	+	5.42413i	0.419313	+	0.242091i
$503$	−31.7905	+	5.60552i	−1.41747	+	0.249938i	−0.829301	−	0.558802i	$-0.811261\pi$
$503$	−31.7905	+	5.60552i	−1.41747	+	0.249938i	−0.588167	+	0.808740i	$0.700150\pi$
$504$	2.69096	−	3.81389i	0.119865	−	0.169884i
$505$	7.11080	−	12.3163i	0.316426	−	0.548067i
$506$	0.562965	+	0.975083i	0.0250268	+	0.0433477i
$507$	−6.51443	−	20.7911i	−0.289316	−	0.923365i
$508$	−4.76297	−	13.0862i	−0.211323	−	0.580604i
$509$	−21.2608	−	7.73831i	−0.942370	−	0.342994i	−0.175268	−	0.984521i	$-0.556079\pi$
$509$	−21.2608	−	7.73831i	−0.942370	−	0.342994i	−0.767101	+	0.641526i	$0.778302\pi$
$510$	7.94314	−	4.11685i	0.351728	−	0.182297i
$511$	1.07375	−	6.08956i	0.0475000	−	0.269386i
$512$	−1.00000			−0.0441942
$513$	4.03939	+	22.2864i	0.178343	+	0.983968i
$514$	−0.0452647			−0.00199654
$515$	−1.50474	+	8.53380i	−0.0663067	+	0.376044i
$516$	12.0171	−	6.22833i	0.529023	−	0.274187i
$517$	−2.85234	−	1.03817i	−0.125446	−	0.0456585i
$518$	−2.19588	−	6.03314i	−0.0964815	−	0.265081i
$519$	6.96458	+	22.2278i	0.305711	+	0.975690i
$520$	0.245158	+	0.424626i	0.0107509	+	0.0186211i
$521$	−4.86213	+	8.42145i	−0.213014	+	0.368950i	−0.952656	−	0.304049i	$-0.901661\pi$
$521$	−4.86213	+	8.42145i	−0.213014	+	0.368950i	0.739643	+	0.673000i	$0.234995\pi$
$522$	13.9107	−	19.7157i	0.608857	−	0.862932i
$523$	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
$525$	11.8355	−	1.53658i	0.516544	−	0.0670619i
$526$	3.52577	+	4.20185i	0.153731	+	0.183209i
$527$	19.5709	−	7.12324i	0.852523	−	0.310293i
$528$	−1.22540	−	1.12692i	−0.0533286	−	0.0490429i
$529$	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
$534$	−8.91568	−	5.70242i	−0.385819	−	0.246768i
$535$	−1.14489	+	1.36443i	−0.0494980	+	0.0589894i
$536$	−3.19170	+	8.76911i	−0.137860	+	0.378768i
$537$	−1.31297	+	28.8831i	−0.0566590	+	1.24640i
$538$	1.50432	−	1.26228i	0.0648559	−	0.0544206i
$539$	−3.81174	+	2.20071i	−0.164183	+	0.0947911i
$540$	−3.89101	−	0.533578i	−0.167443	−	0.0229615i
$541$	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
$543$	−14.0280	+	10.7242i	−0.602001	+	0.460218i
$544$	5.91837	−	3.41697i	0.253748	−	0.146502i
$545$	3.75277	−	3.14895i	0.160751	−	0.134886i
$546$	−1.74638	−	0.0793875i	−0.0747384	−	0.00339747i
$547$	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
$549$	26.6925	−	18.5479i	1.13921	−	0.791607i
$550$		−	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
$555$	−3.65678	+	3.97633i	−0.155222	+	0.168786i
$556$	3.38812	−	1.23318i	0.143688	−	0.0522983i
$557$	2.42914	+	2.89494i	0.102926	+	0.122662i	0.815048	−	0.579393i	$-0.196710\pi$
$557$	2.42914	+	2.89494i	0.102926	+	0.122662i	−0.712122	+	0.702055i	$0.752266\pi$
$558$	−8.82264	−	2.39797i	−0.373492	−	0.101514i
$559$	−4.39021	−	2.53469i	−0.185686	−	0.107206i
$560$	−1.15813	+	0.204209i	−0.0489397	+	0.00862940i
$561$	11.1030	+	2.48238i	0.468770	+	0.104806i
$562$	−5.85639	+	10.1436i	−0.247037	+	0.427880i
$563$	−5.99208	−	10.3786i	−0.252536	−	0.437406i	0.711687	−	0.702496i	$-0.247931\pi$
$563$	−5.99208	−	10.3786i	−0.252536	−	0.437406i	−0.964223	+	0.265091i	$0.914598\pi$
$564$	−5.21962	+	1.63545i	−0.219786	+	0.0688650i
$565$	2.59510	+	7.12998i	0.109177	+	0.299960i
$566$	6.59684	+	2.40105i	0.277286	+	0.100924i
$567$	9.07767	−	10.6620i	0.381226	−	0.447764i
$568$	−0.00595218	+	0.0337565i	−0.000249748	+	0.00141639i
$569$	−11.2148			−0.470147			−0.235074	−	0.971978i	$-0.575533\pi$
$569$	−11.2148			−0.470147			−0.235074	+	0.971978i	$0.575533\pi$
$570$	3.23389	−	4.70162i	0.135453	−	0.196929i
$571$	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
$573$	−9.61733	−	18.5559i	−0.401770	−	0.775185i
$574$	−7.82048	−	2.84642i	−0.326421	−	0.118807i
$575$	1.77435	+	4.87499i	0.0739956	+	0.203301i
$576$	−2.98763	−	0.272187i	−0.124484	−	0.0113411i
$577$	−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
$579$	−1.26400	+	5.65351i	−0.0525299	+	0.234952i
$580$	−5.98686	+	1.05564i	−0.248591	+	0.0438333i
$581$	16.3145	+	9.41916i	0.676838	+	0.390772i
$582$	2.16203	+	16.6531i	0.0896192	+	0.690291i
$583$	−8.95984	−	10.6779i	−0.371079	−	0.442234i
$584$	−3.73458	+	1.35928i	−0.154538	+	0.0562473i
$585$	0.616863	+	1.33535i	0.0255041	+	0.0552101i
$586$	1.97785	+	1.65961i	0.0817041	+	0.0685579i
$587$	19.5628	+	3.44945i	0.807444	+	0.142374i	0.562108	−	0.827064i	$-0.309991\pi$
$587$	19.5628	+	3.44945i	0.807444	+	0.142374i	0.245336	+	0.969438i	$0.421102\pi$
$588$	−3.04837	+	7.32224i	−0.125713	+	0.301964i
$589$	8.87470	−	9.88463i	0.365676	−	0.407289i
$590$		−	8.80076i		−	0.362321i
$591$	−5.55081	+	8.67864i	−0.228330	+	0.356992i
$592$	−2.65245	+	3.16107i	−0.109015	+	0.129919i
$593$	7.64203	−	20.9963i	0.313821	−	0.862215i	−0.678056	−	0.735010i	$-0.737177\pi$
$593$	7.64203	−	20.9963i	0.313821	−	0.862215i	0.991876	−	0.127205i	$-0.0406006\pi$
$594$	−3.35430	−	3.70036i	−0.137629	−	0.151827i
$595$	6.15644	−	5.16587i	0.252390	−	0.211780i
$596$	16.5946	−	9.58089i	0.679741	−	0.392449i
$597$	11.7576	+	15.3799i	0.481208	+	0.629456i
$598$	−0.131956	−	0.748362i	−0.00539610	−	0.0306028i
$599$	−2.89198	−	16.4012i	−0.118163	−	0.670136i	−0.985135	−	0.171780i	$-0.945048\pi$
$599$	−2.89198	−	16.4012i	−0.118163	−	0.670136i	0.866972	−	0.498356i	$-0.166063\pi$
$600$	−4.65874	−	6.09399i	−0.190192	−	0.248786i
$601$	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
$603$	−11.9224	+	25.3301i	−0.485519	+	1.03152i
$604$	−6.58814	+	18.1008i	−0.268068	+	0.736510i
$605$	4.89540	−	5.83411i	0.199026	−	0.237191i
$606$	17.5598	−	27.4546i	0.713318	−	1.11527i
$607$		−	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
$612$	18.6119	−	8.59774i	0.752343	−	0.347543i
$613$	−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
$615$	0.901563	+	6.94428i	0.0363545	+	0.280020i
$616$	−1.29512	−	0.747736i	−0.0521818	−	0.0301272i
$617$	−20.3648	+	3.59086i	−0.819854	+	0.144562i	−0.567817	−	0.823155i	$-0.692212\pi$
$617$	−20.3648	+	3.59086i	−0.819854	+	0.144562i	−0.252038	+	0.967717i	$0.581101\pi$
$618$	−4.33272	+	19.3791i	−0.174288	+	0.779541i
$619$	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
$621$	5.38390	+	2.83960i	0.216048	+	0.113949i
$622$	−8.88236	−	24.4041i	−0.356150	−	0.978515i
$623$	−8.93358	−	3.25156i	−0.357916	−	0.130271i
$624$	0.517031	+	0.997571i	0.0206978	+	0.0399348i
$625$	2.90984	−	16.5025i	0.116394	−	0.660101i
$626$	13.4088			0.535925
$627$	6.99348	−	1.93668i	0.279293	−	0.0773435i
$628$	0.213836			0.00853299
$629$	4.89690	−	27.7717i	0.195252	−	1.10733i
$630$	−3.51563	+	0.294873i	−0.140066	+	0.0117480i
$631$	−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
$633$	−35.1400	+	11.0103i	−1.39669	+	0.437622i
$634$	15.2117	+	26.3474i	0.604132	+	1.04639i
$635$	−5.26287	+	9.11556i	−0.208851	+	0.361740i
$636$	−24.5132	−	5.48061i	−0.972014	−	0.217320i
$637$	2.92545	−	0.515836i	0.115911	−	0.0204382i
$638$	−6.69503	−	3.86538i	−0.265059	−	0.153032i
$639$	−0.0269710	+	0.0992317i	−0.00106695	+	0.00392554i
$640$	0.485841	+	0.579002i	0.0192045	+	0.0228871i
$641$	7.37099	−	2.68282i	0.291137	−	0.105965i	−0.192323	−	0.981332i	$-0.561602\pi$
$641$	7.37099	−	2.68282i	0.291137	−	0.105965i	0.483460	+	0.875367i	$0.339380\pi$
$642$	−2.76289	+	3.00432i	−0.109042	+	0.118571i
$643$	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	$0.0389747\pi$
$647$			6.21339i			0.244274i	−0.992513	+	0.122137i	$0.961025\pi$
$648$	−8.85183	−	1.62639i	−0.347733	−	0.0638905i
$649$	7.19386	−	8.57331i	0.282384	−	0.336532i
$650$	−0.982605	+	2.69969i	−0.0385410	+	0.105890i
$651$	−8.20435	−	0.372955i	−0.321554	−	0.0146173i
$652$	−11.5162	+	9.66326i	−0.451010	+	0.378442i
$653$	23.3831	−	13.5002i	0.915050	−	0.528304i	0.0329976	−	0.999455i	$-0.489495\pi$
$653$	23.3831	−	13.5002i	0.915050	−	0.528304i	0.882053	+	0.471151i	$0.156161\pi$
$654$	8.91857	−	6.81808i	0.348744	−	0.266608i
$655$	−1.46082	−	8.28473i	−0.0570790	−	0.323711i
$656$	0.928838	+	5.26770i	0.0362650	+	0.205669i
$657$	−11.5275	+	3.04451i	−0.449731	+	0.118778i
$658$	−4.25522	+	2.45676i	−0.165886	+	0.0957743i
$659$	−23.3482	+	19.5915i	−0.909517	+	0.763176i	−0.972027	−	0.234869i	$-0.924534\pi$
$659$	−23.3482	+	19.5915i	−0.909517	+	0.763176i	0.0625097	+	0.998044i	$0.480090\pi$
$660$	−0.0571415	+	1.25701i	−0.00222423	+	0.0489291i
$661$	−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
$663$	−6.46866	−	4.13732i	−0.251222	−	0.160680i
$664$		−	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
$669$	17.5637	+	16.1522i	0.679051	+	0.624480i
$670$	6.62799	−	2.41239i	0.256062	−	0.0931989i
$671$	−6.69399	−	7.97759i	−0.258419	−	0.307971i
$672$	−2.67245	+	0.346959i	−0.103092	+	0.0133842i
$673$	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
$675$	−12.2599	−	19.4746i	−0.471883	−	0.749578i
$676$	−6.28959	+	10.8939i	−0.241907	+	0.418996i
$677$	19.6720	+	34.0729i	0.756057	+	1.30953i	0.944847	+	0.327511i	$0.106210\pi$
$677$	19.6720	+	34.0729i	0.756057	+	1.30953i	−0.188791	+	0.982017i	$0.560457\pi$
$678$	5.19876	+	16.5921i	0.199657	+	0.637215i
$679$	5.15932	+	14.1751i	0.197996	+	0.543991i
$680$	−4.85382	−	1.76665i	−0.186136	−	0.0677478i
$681$	−24.8945	+	12.9026i	−0.953961	+	0.494428i
$682$	−0.508657	+	2.88474i	−0.0194775	+	0.110462i
$683$	−12.0176			−0.459840			−0.229920	−	0.973210i	$-0.573846\pi$
$683$	−12.0176			−0.459840			−0.229920	+	0.973210i	$0.573846\pi$
$684$	7.89233	−	10.4265i	0.301771	−	0.398666i
$685$	3.75147			0.143336
$686$	−3.12844	+	17.7422i	−0.119444	+	0.677402i
$687$	−39.4382	+	20.4404i	−1.50466	+	0.779849i
$688$	−7.34330	−	2.67274i	−0.279961	−	0.101897i
$689$	3.21761	+	8.84031i	0.122581	+	0.336789i
$690$	−0.458523	−	1.46340i	−0.0174557	−	0.0557105i
$691$	−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
$693$	−3.66580	−	2.58647i	−0.139252	−	0.0982519i
$694$	−27.7308	+	4.88969i	−1.05265	+	0.185610i
$695$	−2.36010	−	1.36260i	−0.0895237	−	0.0516865i
$696$	−13.8150	+	1.79358i	−0.523658	+	0.0679855i
$697$	−23.4968	−	28.0024i	−0.890006	−	1.06067i
$698$	−18.4021	+	6.69781i	−0.696530	+	0.253516i
$699$	−14.8397	−	13.6471i	−0.561288	−	0.516181i
$700$	−5.27849	−	4.42918i	−0.199508	−	0.167407i
$701$	2.95841	+	0.521647i	0.111738	+	0.0197023i	0.229237	−	0.973371i	$-0.426377\pi$
$701$	2.95841	+	0.521647i	0.111738	+	0.0197023i	−0.117500	+	0.993073i	$0.537488\pi$
$702$	1.27317	+	3.12110i	0.0480527	+	0.117798i
$703$	−5.58262	−	17.0986i	−0.210552	−	0.644887i
$704$			0.961171i			0.0362255i
$705$	3.48284	+	2.22760i	0.131171	+	0.0838964i
$706$	−2.63528	+	3.14061i	−0.0991801	+	0.118198i
$707$	10.0127	−	27.5097i	0.376567	−	1.03461i
$708$	0.915838	−	20.1468i	0.0344193	−	0.757163i
$709$	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
$711$	1.06439	+	4.03013i	0.0399178	+	0.151142i
$712$	1.06104	+	6.01746i	0.0397642	+	0.225514i
$713$	−0.619918	−	3.51573i	−0.0232161	−	0.131665i
$714$	14.6310	−	11.1851i	0.547551	−	0.418592i
$715$	0.408138	−	0.235639i	0.0152635	−	0.00881239i
$716$	12.7875	−	10.7300i	0.477891	−	0.400998i
$717$	26.3391	+	1.19733i	0.983650	+	0.0447150i
$718$	−1.91864	+	5.27142i	−0.0716030	+	0.196728i
$719$	−7.13781	+	8.50651i	−0.266195	+	0.317239i	−0.882540	−	0.470237i	$-0.844168\pi$
$719$	−7.13781	+	8.50651i	−0.266195	+	0.317239i	0.616345	+	0.787476i	$0.288613\pi$
$720$	1.29391	+	1.86208i	0.0482213	+	0.0693957i
$721$			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
$726$	11.8137	−	12.8461i	0.438449	−	0.476763i
$727$	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
$729$	−26.0033	−	7.26839i	−0.963084	−	0.269199i
$730$	2.60144	+	1.50194i	0.0962835	+	0.0555893i
$731$	52.5931	−	9.27357i	1.94522	−	0.342996i
$732$	−18.3141	−	4.09462i	−0.676908	−	0.151341i
$733$	−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
$735$	5.72062	−	1.79243i	0.211008	−	0.0661147i
$736$	−0.400647	−	1.10077i	−0.0147681	−	0.0405749i
$737$	8.42862	+	3.06777i	0.310472	+	0.113003i
$738$	1.34122	+	15.9908i	0.0493711	+	0.588628i
$739$	−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
$741$	−4.88240	−	0.386069i	−0.179360	−	0.0141826i
$742$	−22.5637			−0.828339
$743$	4.59818	−	26.0776i	0.168691	−	0.956693i	−0.776486	−	0.630134i	$-0.783000\pi$
$743$	4.59818	−	26.0776i	0.168691	−	0.956693i	0.945177	−	0.326559i	$-0.105889\pi$
$744$	2.42896	+	4.68649i	0.0890500	+	0.171815i
$745$	−13.6097	−	4.95352i	−0.498620	−	0.181483i
$746$	−7.20414	−	19.7932i	−0.263762	−	0.724681i
$747$	3.29558	−	36.1735i	0.120579	−	1.32352i
$748$	−3.28430	−	5.68857i	−0.120086	−	0.207995i
$749$	−1.83324	+	3.17526i	−0.0669850	+	0.116021i
$750$	−2.69324	+	12.0461i	−0.0983433	+	0.439863i
$751$	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
$753$	−2.41913	−	18.6333i	−0.0881581	−	0.679037i
$754$	3.35381	+	3.99691i	0.122139	+	0.145559i
$755$	13.6812	−	4.97954i	0.497909	−	0.181224i
$756$	−8.07871	+	0.309178i	−0.293820	+	0.0112447i
$757$	−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	$-0.886877\pi$
$761$		−	19.1974i		−	0.695906i	0.937512	−	0.347953i	$-0.113123\pi$
$762$	−12.9964	+	20.3198i	−0.470811	+	0.736108i
$763$	6.48211	−	7.72508i	0.234668	−	0.279667i
$764$	−4.12705	+	11.3390i	−0.149311	+	0.410230i
$765$	−14.0206	−	6.59923i	−0.506914	−	0.238596i
$766$	5.96084	−	5.00173i	0.215374	−	0.180720i
$767$	−6.54145	+	3.77671i	−0.236198	+	0.136369i
$768$	1.05194	+	1.37602i	0.0379586	+	0.0496528i
$769$	−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
$771$	0.0476157	+	0.0622851i	0.00171484	+	0.00224314i
$772$	2.89655	−	1.67232i	0.104249	−	0.0601882i
$773$	−21.9958	+	18.4567i	−0.791134	+	0.663840i	−0.946026	−	0.324091i	$-0.894942\pi$
$773$	−21.9958	+	18.4567i	−0.791134	+	0.663840i	0.154892	+	0.987931i	$0.450497\pi$
$774$	−21.2115	−	9.98390i	−0.762433	−	0.358864i
$775$	−4.61619	+	12.6829i	−0.165818	+	0.455582i
$776$	6.23204	−	7.42706i	0.223717	−	0.266616i
$777$	−5.99177	+	9.36807i	−0.214953	+	0.336078i
$778$		−	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
$783$	−41.7624	+	1.59828i	−1.49247	+	0.0571177i
$784$	4.30306	−	1.56619i	0.153681	−	0.0559352i
$785$	−0.103890	−	0.123812i	−0.00370800	−	0.00441903i
$786$	−2.48199	−	19.1175i	−0.0885297	−	0.681899i
$787$	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
$789$	2.07292	−	9.27161i	0.0737980	−	0.330078i
$790$	0.525093	−	0.909488i	0.0186820	−	0.0323581i
$791$	7.80951	+	13.5265i	0.277674	+	0.480946i
$792$	−0.261618	+	2.87162i	−0.00929620	+	0.102039i
$793$	2.40391	+	6.60469i	0.0853653	+	0.234539i
$794$	−11.1113	−	4.04419i	−0.394326	−	0.143523i
$795$	8.73625	+	16.8559i	0.309843	+	0.597818i
$796$	1.94088	−	11.0073i	0.0687927	−	0.390143i
$797$	32.4074			1.14793			0.573965	−	0.818880i	$-0.305405\pi$
$797$	32.4074			1.14793			0.573965	+	0.818880i	$0.305405\pi$
$798$	4.87522	−	10.6872i	0.172581	−	0.378324i
$799$	−21.5817			−0.763506
$800$	−0.769038	+	4.36143i	−0.0271896	+	0.154200i
$801$	1.53212	+	18.2667i	0.0541348	+	0.645423i
$802$	19.4319	+	7.07262i	0.686163	+	0.249743i
$803$	1.30650	+	3.58957i	0.0461053	+	0.126673i
$804$	15.4239	−	4.83275i	0.543960	−	0.170438i
$805$	−0.688786	−	1.19301i	−0.0242765	−	0.0420482i
$806$	0.988493	−	1.71212i	0.0348182	−	0.0603069i
$807$	−3.31937	−	0.742136i	−0.116847	−	0.0261244i
$808$	−18.5299	+	3.26732i	−0.651880	+	0.114944i
$809$	30.3938	+	17.5479i	1.06859	+	0.616950i	0.927796	−	0.373089i	$-0.121701\pi$
$809$	30.3938	+	17.5479i	1.06859	+	0.616950i	0.140793	+	0.990039i	$0.455035\pi$
$810$	3.35890	+	5.91539i	0.118020	+	0.207846i
$811$	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
$813$	24.7659	−	26.9301i	0.868577	−	0.944479i
$814$	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
$819$	1.72785	+	2.48657i	0.0603760	+	0.0868877i
$820$	2.59875	−	3.09706i	0.0907521	−	0.108154i
$821$	−4.83332	+	13.2794i	−0.168684	+	0.463455i	−0.995015	−	0.0997301i	$-0.968202\pi$
$821$	−4.83332	+	13.2794i	−0.168684	+	0.463455i	0.826331	+	0.563185i	$0.190424\pi$
$822$	8.58792	+	0.390391i	0.299538	+	0.0136165i
$823$	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
$825$	−5.85737	+	4.47785i	−0.203927	+	0.155899i
$826$	−3.14588	−	17.8411i	−0.109459	−	0.620773i
$827$	−3.63051	−	20.5896i	−0.126245	−	0.715972i	−0.980561	−	0.196217i	$-0.937134\pi$
$827$	−3.63051	−	20.5896i	−0.126245	−	0.715972i	0.854315	−	0.519755i	$-0.173977\pi$
$828$	−0.897369	−	3.39774i	−0.0311857	−	0.118080i
$829$	−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
$831$	−0.616494	+	13.5618i	−0.0213859	+	0.470453i
$832$	0.221871	−	0.609587i	0.00769201	−	0.0211336i
$833$	−20.1155	+	23.9727i	−0.696960	+	0.830605i
$834$	−5.26097	−	3.36489i	−0.182173	−	0.116517i
$835$			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	$0.138884\pi$
$839$	42.8654	+	35.9683i	1.47988	+	1.24176i	0.573563	+	0.819162i	$0.305561\pi$
$840$	1.49927	+	1.37879i	0.0517298	+	0.0475726i
$841$	−33.5383	+	12.2070i	−1.15649	+	0.420929i
$842$	20.4536	+	24.3756i	0.704876	+	0.840038i
$843$	20.1183	−	2.61192i	0.692910	−	0.0899592i
$844$	18.4123	+	10.6303i	0.633777	+	0.365911i
$845$	9.36332	−	1.65101i	0.322108	−	0.0567964i
$846$	7.74114	+	5.46189i	0.266146	+	0.187784i
$847$	7.83867	−	13.5770i	0.269340	−	0.466510i
$848$	7.25107	+	12.5592i	0.249003	+	0.431286i
$849$	−3.63558	−	11.6031i	−0.124773	−	0.398218i
$850$	−10.3515	−	28.4404i	−0.355052	−	0.975497i
$851$	−4.54230	−	1.65326i	−0.155708	−	0.0566731i
$852$	0.0527108	−	0.0273195i	0.00180584	−	0.000935950i
$853$	−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
$855$	−9.87136	+	0.495925i	−0.337593	+	0.0169603i
$856$	2.35652			0.0805441
$857$	−8.77792	+	49.7820i	−0.299848	+	1.70052i	0.346969	+	0.937877i	$0.387211\pi$
$857$	−8.77792	+	49.7820i	−0.299848	+	1.70052i	−0.646817	+	0.762645i	$0.723900\pi$
$858$	0.958837	−	0.496955i	0.0327341	−	0.0169658i
$859$	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
$861$	4.30994	+	13.7554i	0.146883	+	0.468782i
$862$	16.4706	+	28.5280i	0.560992	+	0.971667i
$863$	16.9638	−	29.3822i	0.577455	−	1.00018i	−0.418315	−	0.908302i	$-0.637379\pi$
$863$	16.9638	−	29.3822i	0.577455	−	1.00018i	0.995770	−	0.0918798i	$-0.0292876\pi$
$864$	2.76827	+	4.39735i	0.0941784	+	0.149601i
$865$	−10.0103	+	1.76509i	−0.340362	+	0.0600149i
$866$	−13.8300	−	7.98473i	−0.469961	−	0.271332i
$867$	51.0187	−	6.62366i	1.73269	−	0.224951i
$868$	3.04789	+	3.63233i	0.103452	+	0.123289i
$869$	1.25495	−	0.456765i	0.0425713	−	0.0154947i
$870$	7.75040	+	7.12755i	0.262763	+	0.241646i
$871$	−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
$876$	5.79895	+	3.70898i	0.195928	+	0.125315i
$877$	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
$879$	0.203078	−	4.46736i	0.00684966	−	0.150680i
$880$	0.556520	−	0.466976i	0.0187603	−	0.0157418i
$881$	9.59448	−	5.53938i	0.323246	−	0.186626i	−0.329592	−	0.944123i	$-0.606911\pi$
$881$	9.59448	−	5.53938i	0.323246	−	0.186626i	0.652839	+	0.757497i	$0.273578\pi$
$882$	13.2822	−	3.50794i	0.447236	−	0.118119i
$883$	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
$885$	−12.1100	+	9.25786i	−0.407073	+	0.311200i
$886$	16.8799	−	9.74561i	0.567091	−	0.327410i
$887$	−19.9548	+	16.7441i	−0.670017	+	0.562211i	−0.913070	−	0.407802i	$-0.866295\pi$
$887$	−19.9548	+	16.7441i	−0.670017	+	0.562211i	0.243054	+	0.970013i	$0.421851\pi$
$888$	7.13990	+	0.324567i	0.239599	+	0.0108918i
$889$	−7.41064	+	20.3606i	−0.248545	+	0.682871i
$890$	2.96863	−	3.53787i	0.0995086	−	0.118590i
$891$	−1.56324	+	8.50812i	−0.0523703	+	0.285033i
$892$		−	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
$897$	−0.890949	+	0.968805i	−0.0297479	+	0.0323475i
$898$	12.4342	−	4.52566i	0.414933	−	0.151023i
$899$	15.7559	+	18.7771i	0.525488	+	0.626252i
$900$	−3.48472	+	12.8210i	−0.116157	+	0.427367i
$901$	−85.8291	−	49.5535i	−2.85938	−	1.65086i
$902$	5.06317	−	0.892773i	0.168585	−	0.0297261i
$903$	−20.5519	−	4.59493i	−0.683924	−	0.152910i
$904$	5.01933	−	8.69374i	0.166940	−	0.289149i
$905$	−3.85274	−	6.67314i	−0.128069	−	0.221823i
$906$	31.8373	−	9.97551i	1.05772	−	0.331414i
$907$	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
$909$	−56.2498	+	4.71795i	−1.86569	+	0.156484i
$910$	0.132472	−	0.751286i	0.00439140	−	0.0249049i
$911$	−35.0957			−1.16277			−0.581386	−	0.813628i	$-0.697489\pi$
$911$	−35.0957			−1.16277			−0.581386	+	0.813628i	$0.697489\pi$
$912$	−7.51534	+	0.720842i	−0.248858	+	0.0238695i
$913$	−11.6376			−0.385150
$914$	2.67484	−	15.1698i	0.0884758	−	0.501771i
$915$	6.52694	+	12.5932i	0.215774	+	0.416320i
$916$	24.0995	+	8.77151i	0.796271	+	0.289819i
$917$	−5.92284	−	16.2729i	−0.195589	−	0.537377i
$918$	−31.4093	−	16.5661i	−1.03666	−	0.546762i
$919$	−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
$921$	−0.744494	+	3.32992i	−0.0245319	+	0.109725i
$922$	−16.2707	+	2.86896i	−0.535847	+	0.0944843i
$923$	−0.0192569	−	0.0111180i	−0.000633848	−	0.000365952i
$924$	0.333487	+	2.56868i	0.0109709	+	0.0845033i
$925$	11.7469	+	13.9995i	0.386237	+	0.460300i
$926$	8.81750	−	3.20931i	0.289761	−	0.105464i
$927$	31.2237	−	14.4237i	1.02552	−	0.473737i
$928$	6.16134	+	5.16998i	0.202256	+	0.169713i
$929$	−32.1458	−	5.66817i	−1.05467	−	0.185967i	−0.380680	−	0.924707i	$-0.624310\pi$
$929$	−32.1458	−	5.66817i	−1.05467	−	0.185967i	−0.673990	+	0.738740i	$0.735421\pi$
$930$	1.53340	−	3.68326i	0.0502823	−	0.120779i
$931$	−4.12218	+	19.5301i	−0.135099	+	0.640072i
$932$			11.6399i			0.381276i
$933$	−24.2367	+	37.8939i	−0.793475	+	1.24059i
$934$	13.7652	−	16.4047i	0.450411	−	0.536778i
$935$	−1.69805	+	4.66536i	−0.0555322	+	0.152573i
$936$	0.828791	−	1.76083i	0.0270899	−	0.0575544i
$937$	−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
$939$	−14.1053	−	18.4508i	−0.460308	−	0.602119i
$940$	−0.414487	−	2.35067i	−0.0135191	−	0.0766705i
$941$	−2.50659	−	14.2156i	−0.0817126	−	0.463415i	−0.998018	−	0.0629344i	$-0.979954\pi$
$941$	−2.50659	−	14.2156i	−0.0817126	−	0.463415i	0.916305	−	0.400481i	$-0.131157\pi$
$942$	−0.224943	−	0.294242i	−0.00732903	−	0.00958693i
$943$	−5.42639	+	3.13293i	−0.176708	+	0.102022i
$944$	−8.91965	+	7.48447i	−0.290310	+	0.243599i
$945$	4.10398	+	4.52738i	0.133502	+	0.147276i
$946$	−2.56896	+	7.05816i	−0.0835241	+	0.229481i
$947$	28.2988	−	33.7252i	0.919588	−	1.09592i	−0.0755210	−	0.997144i	$-0.524062\pi$
$947$	28.2988	−	33.7252i	0.919588	−	1.09592i	0.995109	−	0.0987786i	$-0.0314936\pi$
$948$	1.29669	−	2.02737i	0.0421147	−	0.0658459i
$949$		−	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	0.349877	−	0.936796i	$-0.386223\pi$
$953$	−15.8037	−	13.2609i	−0.511932	−	0.429562i	−0.861808	+	0.507234i	$0.830668\pi$
$954$	18.2450	+	39.4959i	0.590705	+	1.27873i
$955$	8.57039	−	3.11937i	0.277331	−	0.100940i
$956$	−9.78488	−	11.6612i	−0.316465	−	0.377149i
$957$	1.72394	+	13.2786i	0.0557270	+	0.429237i
$958$	−28.9075	−	16.6898i	−0.933960	−	0.539222i
$959$	7.60509	−	1.34098i	0.245581	−	0.0433026i
$960$	0.285642	−	1.27760i	0.00921907	−	0.0412344i
$961$	−10.8562	+	18.8034i	−0.350199	+	0.606562i
$962$	−1.33844	−	2.31825i	−0.0431531	−	0.0747433i
$963$	7.04039	+	0.641413i	0.226873	+	0.0206692i
$964$	−5.19328	−	14.2684i	−0.167264	−	0.459554i
$965$	−2.37554	−	0.864625i	−0.0764713	−	0.0278333i
$966$	−1.45263	−	2.80274i	−0.0467376	−	0.0901766i
$967$	−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
$969$	42.0155	−	29.9459i	1.34973	−	0.962003i
$970$	−7.32806			−0.235290
$971$	−0.764165	+	4.33380i	−0.0245232	+	0.139078i	−0.994611	−	0.103676i	$-0.966940\pi$
$971$	−0.764165	+	4.33380i	−0.0245232	+	0.139078i	0.970088	+	0.242754i	$0.0780507\pi$
$972$	7.07365	+	13.8911i	0.226887	+	0.445558i
$973$	−5.27154	−	1.91868i	−0.168998	−	0.0615101i
$974$	−11.4431	−	31.4398i	−0.366662	−	1.00740i
$975$	4.74846	−	1.48782i	0.152072	−	0.0476485i
$976$	5.41735	+	9.38312i	0.173405	+	0.300346i
$977$	−0.538610	+	0.932899i	−0.0172317	+	0.0298461i	−0.874513	−	0.485003i	$-0.838819\pi$
$977$	−0.538610	+	0.932899i	−0.0172317	+	0.0298461i	0.857281	+	0.514849i	$0.172152\pi$
$978$	25.4112	+	5.68136i	0.812560	+	0.181670i
$979$	5.78381	−	1.01984i	0.184851	−	0.0325943i
$980$	−2.99743	−	1.73056i	−0.0957492	−	0.0552809i
$981$	−18.7636	−	5.09990i	−0.599075	−	0.162827i
$982$	−0.635055	−	0.756829i	−0.0202654	−	0.0241514i
$983$	−4.78675	+	1.74223i	−0.152674	+	0.0555687i	−0.417227	−	0.908803i	$-0.636998\pi$
$983$	−4.78675	+	1.74223i	−0.152674	+	0.0555687i	0.264553	+	0.964371i	$0.414776\pi$
$984$	6.27137	−	6.81940i	0.199924	−	0.217395i
$985$	−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
$990$	1.78978	−	1.24367i	0.0568829	−	0.0395265i
$991$	−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
$993$	−18.4213	−	0.837398i	−0.584581	−	0.0265740i
$994$	0.0408543	−	0.0342808i	0.00129582	−	0.00108732i
$995$	−7.31621	+	4.22401i	−0.231939	+	0.133910i
$996$	−16.6605	+	12.7366i	−0.527908	+	0.403576i
$997$	−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
$999$	21.2430	+	2.91307i	0.672099	+	0.0921655i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(1.53778 - 0.797015i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.258510 + 0.710252i) q^{5} +(0.517874 + 1.65282i) q^{6} +(0.777943 + 1.34744i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.72953 - 2.45127i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(1.53778 - 0.797015i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.258510 + 0.710252i) q^{5} +(0.517874 + 1.65282i) q^{6} +(0.777943 + 1.34744i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.72953 - 2.45127i) q^{9} +(-0.744351 + 0.131249i) q^{10} +(-0.832399 - 0.480586i) q^{11} +(-1.71764 + 0.222997i) q^{12} +(0.416982 + 0.496940i) q^{13} +(-1.46205 + 0.532144i) q^{14} +(0.963613 + 0.886174i) 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} +(2.27023 + 1.45203i) q^{21} +(0.617829 - 0.736300i) q^{22} +(-0.400647 + 1.10077i) q^{23} +(0.0786547 - 1.73026i) q^{24} +(3.39259 - 2.84672i) q^{25} +(-0.561798 + 0.324354i) q^{26} +(0.705946 - 5.14797i) q^{27} +(-0.270177 - 1.53225i) q^{28} +(-1.39666 - 7.92086i) q^{29} +(-1.04004 + 0.795091i) q^{30} +(-2.63927 + 1.52379i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-1.66308 - 0.0756007i) q^{33} +(2.33735 - 6.42181i) q^{34} +(-0.755913 + 0.900862i) q^{35} +(-2.46361 + 1.71190i) 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} +(-1.82419 + 1.98360i) q^{42} +(-7.34330 + 2.67274i) q^{43} +(0.617829 + 0.736300i) q^{44} +(2.18812 + 0.594726i) q^{45} +(-1.01447 - 0.585707i) q^{46} +(3.11004 - 0.548383i) q^{47} +(1.69032 + 0.377917i) q^{48} +(2.28961 - 3.96572i) q^{49} +(2.21436 + 3.83538i) q^{50} +(-11.2953 + 3.53912i) q^{51} +(-0.221871 - 0.609587i) q^{52} +(13.6276 + 4.96002i) q^{53} +(4.94718 + 1.58916i) q^{54} +(0.126153 - 0.715449i) q^{55} +1.55589 q^{56} +(-5.29374 + 5.38297i) q^{57} +8.04306 q^{58} +(-2.02192 + 11.4669i) q^{59} +(-0.602411 - 1.16231i) q^{60} +(10.1813 + 3.70568i) q^{61} +(-1.04233 - 2.86378i) q^{62} +(4.64841 + 0.423492i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.245158 + 0.424626i) q^{65} +(0.363243 - 1.62469i) q^{66} +(-9.19012 + 1.62047i) q^{67} +(5.91837 + 3.41697i) q^{68} +(0.261222 + 2.01206i) q^{69} +(-0.755913 - 0.900862i) q^{70} +(-0.0322101 + 0.0117235i) q^{71} +(-1.25809 - 2.72345i) 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} +(-0.605407 + 0.946547i) q^{78} +(-0.893115 + 1.06437i) q^{79} +(-0.258510 + 0.710252i) q^{80} +(-3.01742 - 8.47910i) q^{81} +(-4.09755 + 3.43825i) q^{82} +(10.4856 - 6.05389i) q^{83} +(-1.63670 - 2.14093i) q^{84} +(-0.896950 - 5.08686i) q^{85} +(-1.35699 - 7.69585i) q^{86} +(-8.46081 - 11.0674i) q^{87} +(-0.832399 + 0.480586i) q^{88} +(-4.68075 + 3.92762i) q^{89} +(-0.965654 + 2.05160i) q^{90} +(-0.345207 + 0.948448i) q^{91} +(0.752970 - 0.897355i) q^{92} +(-2.84414 + 4.44679i) 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} +(-2.61771 + 1.20924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) \) 18 * q + 3 * q^6 + 9 * q^8	\( 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) \) 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

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