LMFDB - Embedded newform 108.3.j.a.31.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(7,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("108.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			31.8
Character	$\chi$	$=$	108.31
Dual form			108.3.j.a.7.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59321 + 1.20900i) q^{2} +(2.60238 + 1.49253i) q^{3} +(1.07665 - 3.85238i) q^{4} +(-0.890579 + 5.05073i) q^{5} +(-5.95060 + 0.768354i) q^{6} +(0.0265129 + 0.0315969i) q^{7} +(2.94218 + 7.43932i) q^{8} +(4.54473 + 7.76823i) q^{9} +O(q^{10})$	\(q+(-1.59321 + 1.20900i) q^{2} +(2.60238 + 1.49253i) q^{3} +(1.07665 - 3.85238i) q^{4} +(-0.890579 + 5.05073i) q^{5} +(-5.95060 + 0.768354i) q^{6} +(0.0265129 + 0.0315969i) q^{7} +(2.94218 + 7.43932i) q^{8} +(4.54473 + 7.76823i) q^{9} +(-4.68743 - 9.12359i) q^{10} +(4.18050 - 0.737135i) q^{11} +(8.55163 - 8.41841i) q^{12} +(-1.91152 + 0.695736i) q^{13} +(-0.0804412 - 0.0182865i) q^{14} +(-9.85597 + 11.8147i) q^{15} +(-13.6816 - 8.29533i) q^{16} +(-15.1353 + 26.2152i) q^{17} +(-16.6325 - 6.88189i) q^{18} +(-5.91027 + 3.41230i) q^{19} +(18.4985 + 8.86872i) q^{20} +(0.0218374 + 0.121798i) q^{21} +(-5.76923 + 6.22863i) q^{22} +(25.3540 - 30.2157i) q^{23} +(-3.44673 + 23.7512i) q^{24} +(-1.22440 - 0.445645i) q^{25} +(2.20431 - 3.41948i) q^{26} +(0.232786 + 26.9990i) q^{27} +(0.150268 - 0.0681190i) q^{28} +(-20.7044 - 7.53578i) q^{29} +(1.41874 - 30.7391i) q^{30} +(25.1859 - 30.0153i) q^{31} +(31.8268 - 3.32485i) q^{32} +(11.9794 + 4.32121i) q^{33} +(-7.58027 - 60.0649i) q^{34} +(-0.183199 + 0.105770i) q^{35} +(34.8193 - 9.14433i) q^{36} +(15.9508 - 27.6276i) q^{37} +(5.29086 - 12.5820i) q^{38} +(-6.01290 - 1.04243i) q^{39} +(-40.1943 + 8.23486i) q^{40} +(53.8833 - 19.6119i) q^{41} +(-0.182045 - 0.167649i) q^{42} +(40.8395 - 7.20111i) q^{43} +(1.66121 - 16.8985i) q^{44} +(-43.2827 + 16.0359i) q^{45} +(-3.86358 + 78.7930i) q^{46} +(9.40005 + 11.2025i) q^{47} +(-23.2238 - 42.0078i) q^{48} +(8.50847 - 48.2539i) q^{49} +(2.48951 - 0.770289i) q^{50} +(-78.5146 + 45.6318i) q^{51} +(0.622201 + 8.11296i) q^{52} -43.0946 q^{53} +(-33.0126 - 42.7337i) q^{54} +21.7710i q^{55} +(-0.157053 + 0.290202i) q^{56} +(-20.4737 + 0.0588402i) q^{57} +(42.0972 - 13.0254i) q^{58} +(-40.5818 - 7.15567i) q^{59} +(34.9032 + 50.6892i) q^{60} +(14.2464 - 11.9542i) q^{61} +(-3.83795 + 78.2705i) q^{62} +(-0.124958 + 0.349558i) q^{63} +(-46.6871 + 43.7757i) q^{64} +(-1.81161 - 10.2742i) q^{65} +(-24.3101 + 7.59850i) q^{66} +(16.7275 + 45.9585i) q^{67} +(84.6952 + 86.5316i) q^{68} +(111.078 - 40.7912i) q^{69} +(0.163999 - 0.390001i) q^{70} +(-111.053 - 64.1166i) q^{71} +(-44.4190 + 56.6653i) q^{72} +(63.7153 + 110.358i) q^{73} +(7.98870 + 63.3012i) q^{74} +(-2.52121 - 2.98718i) q^{75} +(6.78216 + 26.4424i) q^{76} +(0.134128 + 0.112547i) q^{77} +(10.8401 - 5.60877i) q^{78} +(1.11267 - 3.05705i) q^{79} +(54.0821 - 61.7146i) q^{80} +(-39.6909 + 70.6090i) q^{81} +(-62.1368 + 96.3907i) q^{82} +(40.0201 - 109.954i) q^{83} +(0.492724 + 0.0470081i) q^{84} +(-118.926 - 99.7911i) q^{85} +(-56.3599 + 60.8477i) q^{86} +(-42.6332 - 50.5128i) q^{87} +(17.7836 + 28.9313i) q^{88} +(-26.9272 - 46.6393i) q^{89} +(49.5711 - 77.8773i) q^{90} +(-0.0726630 - 0.0419520i) q^{91} +(-89.1050 - 130.205i) q^{92} +(110.342 - 40.5206i) q^{93} +(-28.5201 - 6.48339i) q^{94} +(-11.9710 - 32.8901i) q^{95} +(87.7878 + 38.8498i) q^{96} +(-5.60171 - 31.7689i) q^{97} +(44.7831 + 87.1654i) q^{98} +(24.7255 + 29.1250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.59321	+	1.20900i	−0.796606	+	0.604499i
$2$	−1.59321	+	1.20900i	−0.796606	+	0.604499i
$3$	2.60238	+	1.49253i	0.867459	+	0.497509i
$3$	2.60238	+	1.49253i	0.867459	+	0.497509i
$4$	1.07665	−	3.85238i	0.269163	−	0.963095i
$5$	−0.890579	+	5.05073i	−0.178116	+	1.01015i	0.756370	+	0.654144i	$0.226971\pi$
$5$	−0.890579	+	5.05073i	−0.178116	+	1.01015i	−0.934486	+	0.356001i	$0.884140\pi$
$6$	−5.95060	+	0.768354i	−0.991767	+	0.128059i
$7$	0.0265129	+	0.0315969i	0.00378756	+	0.00451384i	0.767935	−	0.640528i	$-0.221284\pi$
$7$	0.0265129	+	0.0315969i	0.00378756	+	0.00451384i	−0.764147	+	0.645042i	$0.776840\pi$
$8$	2.94218	+	7.43932i	0.367773	+	0.929916i
$9$	4.54473	+	7.76823i	0.504970	+	0.863137i
$10$	−4.68743	−	9.12359i	−0.468743	−	0.912359i
$11$	4.18050	−	0.737135i	0.380045	−	0.0670123i	0.0196378	−	0.999807i	$-0.493749\pi$
$11$	4.18050	−	0.737135i	0.380045	−	0.0670123i	0.360408	+	0.932795i	$0.382638\pi$
$12$	8.55163	−	8.41841i	0.712636	−	0.701534i
$13$	−1.91152	+	0.695736i	−0.147040	+	0.0535182i	−0.414492	−	0.910053i	$-0.636041\pi$
$13$	−1.91152	+	0.695736i	−0.147040	+	0.0535182i	0.267452	+	0.963571i	$0.413818\pi$
$14$	−0.0804412	−	0.0182865i	−0.00574580	−	0.00130618i
$15$	−9.85597	+	11.8147i	−0.657065	+	0.787645i
$16$	−13.6816	−	8.29533i	−0.855103	−	0.518458i
$17$	−15.1353	+	26.2152i	−0.890313	+	1.54207i	−0.0508130	+	0.998708i	$0.516181\pi$
$17$	−15.1353	+	26.2152i	−0.890313	+	1.54207i	−0.839500	+	0.543359i	$0.817152\pi$
$18$	−16.6325	−	6.88189i	−0.924027	−	0.382327i
$19$	−5.91027	+	3.41230i	−0.311067	+	0.179595i	−0.647404	−	0.762147i	$-0.724145\pi$
$19$	−5.91027	+	3.41230i	−0.311067	+	0.179595i	0.336337	+	0.941742i	$0.390812\pi$
$20$	18.4985	+	8.86872i	0.924924	+	0.443436i
$21$	0.0218374	+	0.121798i	0.00103988	+	0.00579991i
$22$	−5.76923	+	6.22863i	−0.262238	+	0.283119i
$23$	25.3540	−	30.2157i	1.10235	−	1.31373i	0.157024	−	0.987595i	$-0.449810\pi$
$23$	25.3540	−	30.2157i	1.10235	−	1.31373i	0.945324	−	0.326133i	$-0.105746\pi$
$24$	−3.44673	+	23.7512i	−0.143614	+	0.989634i
$25$	−1.22440	−	0.445645i	−0.0489760	−	0.0178258i
$26$	2.20431	−	3.41948i	0.0847813	−	0.131518i
$27$	0.232786	+	26.9990i	0.00862169	+	0.999963i
$28$	0.150268	−	0.0681190i	0.00536672	−	0.00243282i
$29$	−20.7044	−	7.53578i	−0.713944	−	0.259854i	−0.0405915	−	0.999176i	$-0.512924\pi$
$29$	−20.7044	−	7.53578i	−0.713944	−	0.259854i	−0.673353	+	0.739321i	$0.735146\pi$
$30$	1.41874	−	30.7391i	0.0472912	−	1.02464i
$31$	25.1859	−	30.0153i	0.812447	−	0.968237i	−0.187454	−	0.982273i	$-0.560024\pi$
$31$	25.1859	−	30.0153i	0.812447	−	0.968237i	0.999901	+	0.0140364i	$0.00446809\pi$
$32$	31.8268	−	3.32485i	0.994588	−	0.103902i
$33$	11.9794	+	4.32121i	0.363013	+	0.130946i
$34$	−7.58027	−	60.0649i	−0.222949	−	1.76661i
$35$	−0.183199	+	0.105770i	−0.00523426	+	0.00302200i
$36$	34.8193	−	9.14433i	0.967202	−	0.254009i
$37$	15.9508	−	27.6276i	0.431103	−	0.746693i	−0.565865	−	0.824498i	$-0.691458\pi$
$37$	15.9508	−	27.6276i	0.431103	−	0.746693i	0.996969	+	0.0778047i	$0.0247911\pi$
$38$	5.29086	−	12.5820i	0.139233	−	0.331106i
$39$	−6.01290	−	1.04243i	−0.154177	−	0.0267289i
$40$	−40.1943	+	8.23486i	−1.00486	+	0.205871i
$41$	53.8833	−	19.6119i	1.31423	−	0.478340i	0.412623	−	0.910902i	$-0.364613\pi$
$41$	53.8833	−	19.6119i	1.31423	−	0.478340i	0.901604	+	0.432562i	$0.142390\pi$
$42$	−0.182045	−	0.167649i	−0.00433441	−	0.00399164i
$43$	40.8395	−	7.20111i	0.949756	−	0.167468i	0.322752	−	0.946484i	$-0.395392\pi$
$43$	40.8395	−	7.20111i	0.949756	−	0.167468i	0.627004	+	0.779016i	$0.284281\pi$
$44$	1.66121	−	16.8985i	0.0377549	−	0.384057i
$45$	−43.2827	+	16.0359i	−0.961837	+	0.356354i
$46$	−3.86358	+	78.7930i	−0.0839908	+	1.71289i
$47$	9.40005	+	11.2025i	0.200001	+	0.238352i	0.856718	−	0.515785i	$-0.172500\pi$
$47$	9.40005	+	11.2025i	0.200001	+	0.238352i	−0.656717	+	0.754137i	$0.728055\pi$
$48$	−23.2238	−	42.0078i	−0.483829	−	0.875163i
$49$	8.50847	−	48.2539i	0.173642	−	0.984774i
$50$	2.48951	−	0.770289i	0.0497902	−	0.0154058i
$51$	−78.5146	+	45.6318i	−1.53950	+	0.894741i
$52$	0.622201	+	8.11296i	0.0119654	+	0.156019i
$53$	−43.0946			−0.813105			−0.406553	−	0.913627i	$-0.633269\pi$
$53$	−43.0946			−0.813105			−0.406553	+	0.913627i	$0.633269\pi$
$54$	−33.0126	−	42.7337i	−0.611344	−	0.791365i
$55$			21.7710i			0.395837i
$56$	−0.157053	+	0.290202i	−0.00280453	+	0.00518218i
$57$	−20.4737	+	0.0588402i	−0.359188	+	0.00103228i
$58$	42.0972	−	13.0254i	0.725814	−	0.224577i
$59$	−40.5818	−	7.15567i	−0.687828	−	0.121283i	−0.181199	−	0.983447i	$-0.557998\pi$
$59$	−40.5818	−	7.15567i	−0.687828	−	0.121283i	−0.506629	+	0.862164i	$0.669109\pi$
$60$	34.9032	+	50.6892i	0.581720	+	0.844820i
$61$	14.2464	−	11.9542i	0.233548	−	0.195970i	−0.518501	−	0.855077i	$-0.673510\pi$
$61$	14.2464	−	11.9542i	0.233548	−	0.195970i	0.752050	+	0.659107i	$0.229065\pi$
$62$	−3.83795	+	78.2705i	−0.0619025	+	1.26243i
$63$	−0.124958	+	0.349558i	−0.00198346	+	0.00554853i
$64$	−46.6871	+	43.7757i	−0.729486	+	0.683996i
$65$	−1.81161	−	10.2742i	−0.0278710	−	0.158064i
$66$	−24.3101	+	7.59850i	−0.368335	+	0.115129i
$67$	16.7275	+	45.9585i	0.249664	+	0.685948i	0.999699	+	0.0245484i	$0.00781479\pi$
$67$	16.7275	+	45.9585i	0.249664	+	0.685948i	−0.750034	+	0.661399i	$0.769963\pi$
$68$	84.6952	+	86.5316i	1.24552	+	1.27252i
$69$	111.078	−	40.7912i	1.60983	−	0.591176i
$70$	0.163999	−	0.390001i	0.00234285	−	0.00557144i
$71$	−111.053	−	64.1166i	−1.56413	−	0.903051i	−0.996832	−	0.0795386i	$-0.974655\pi$
$71$	−111.053	−	64.1166i	−1.56413	−	0.903051i	−0.567298	−	0.823512i	$-0.692011\pi$
$72$	−44.4190	+	56.6653i	−0.616931	+	0.787018i
$73$	63.7153	+	110.358i	0.872813	+	1.51176i	0.859075	+	0.511851i	$0.171040\pi$
$73$	63.7153	+	110.358i	0.872813	+	1.51176i	0.0137383	+	0.999906i	$0.495627\pi$
$74$	7.98870	+	63.3012i	0.107955	+	0.855422i
$75$	−2.52121	−	2.98718i	−0.0336161	−	0.0398291i
$76$	6.78216	+	26.4424i	0.0892390	+	0.347927i
$77$	0.134128	+	0.112547i	0.00174193	+	0.00146165i
$78$	10.8401	−	5.60877i	0.138976	−	0.0719073i
$79$	1.11267	−	3.05705i	0.0140845	−	0.0386968i	−0.932451	−	0.361296i	$-0.882334\pi$
$79$	1.11267	−	3.05705i	0.0140845	−	0.0386968i	0.946536	+	0.322599i	$0.104557\pi$
$80$	54.0821	−	61.7146i	0.676026	−	0.771433i
$81$	−39.6909	+	70.6090i	−0.490012	+	0.871716i
$82$	−62.1368	+	96.3907i	−0.757766	+	1.17550i
$83$	40.0201	−	109.954i	0.482169	−	1.32475i	−0.425460	−	0.904977i	$-0.639888\pi$
$83$	40.0201	−	109.954i	0.482169	−	1.32475i	0.907629	−	0.419772i	$-0.137890\pi$
$84$	0.492724	+	0.0470081i	0.00586576	+	0.000559620i
$85$	−118.926	−	99.7911i	−1.39913	−	1.17401i
$86$	−56.3599	+	60.8477i	−0.655347	+	0.707532i
$87$	−42.6332	−	50.5128i	−0.490037	−	0.580607i
$88$	17.7836	+	28.9313i	0.202086	+	0.328765i
$89$	−26.9272	−	46.6393i	−0.302553	−	0.524037i	0.674160	−	0.738585i	$-0.264506\pi$
$89$	−26.9272	−	46.6393i	−0.302553	−	0.524037i	−0.976714	+	0.214548i	$0.931172\pi$
$90$	49.5711	−	77.8773i	0.550790	−	0.865303i
$91$	−0.0726630	−	0.0419520i	−0.000798495	−	0.000461011i
$92$	−89.1050	−	130.205i	−0.968533	−	1.41527i
$93$	110.342	−	40.5206i	1.18647	−	0.435706i
$94$	−28.5201	−	6.48339i	−0.303406	−	0.0689723i
$95$	−11.9710	−	32.8901i	−0.126011	−	0.346211i
$96$	87.7878	+	38.8498i	0.914456	+	0.404686i
$97$	−5.60171	−	31.7689i	−0.0577496	−	0.327514i	0.942222	−	0.334988i	$-0.108732\pi$
$97$	−5.60171	−	31.7689i	−0.0577496	−	0.327514i	−0.999972	+	0.00747351i	$0.997621\pi$
$98$	44.7831	+	87.1654i	0.456970	+	0.889443i
$99$	24.7255	+	29.1250i	0.249752	+	0.294192i
$100$	−3.03504	+	4.23705i	−0.0303504	+	0.0423705i
$101$	−105.877	+	88.8411i	−1.04828	+	0.879615i	−0.992912	−	0.118851i	$-0.962079\pi$
$101$	−105.877	+	88.8411i	−1.04828	+	0.879615i	−0.0553723	+	0.998466i	$0.517635\pi$
$102$	69.9217	−	167.625i	0.685507	−	1.64338i
$103$	−70.1342	−	12.3665i	−0.680914	−	0.120064i	−0.177516	−	0.984118i	$-0.556806\pi$
$103$	−70.1342	−	12.3665i	−0.680914	−	0.120064i	−0.503398	+	0.864054i	$0.667917\pi$
$104$	−10.7999	−	12.1734i	−0.103845	−	0.117052i
$105$	−0.634617	+	0.00182385i	−0.00604397	+	1.73700e-5i
$106$	68.6588	−	52.1012i	0.647725	−	0.491521i
$107$			106.755i			0.997712i	0.866685	+	0.498856i	$0.166246\pi$
$107$			106.755i			0.997712i	−0.866685	+	0.498856i	$0.833754\pi$
$108$	104.261	+	28.1717i	0.965380	+	0.260849i
$109$	53.1106			0.487253			0.243627	−	0.969869i	$-0.421663\pi$
$109$	53.1106			0.487253			0.243627	+	0.969869i	$0.421663\pi$
$110$	−26.3211	−	34.6859i	−0.239283	−	0.315326i
$111$	82.7451	−	48.0905i	0.745451	−	0.433248i
$112$	−0.100634	−	0.652230i	−0.000898517	−	0.00582349i
$113$	22.6559	−	128.488i	0.200494	−	1.13706i	−0.703880	−	0.710319i	$-0.748551\pi$
$113$	22.6559	−	128.488i	0.200494	−	1.13706i	0.904374	−	0.426740i	$-0.140338\pi$
$114$	32.5478	−	24.8464i	0.285507	−	0.217951i
$115$	130.032	+	154.966i	1.13071	+	1.34753i
$116$	−51.3221	+	71.6477i	−0.442432	+	0.617653i
$117$	−14.0920	−	11.6872i	−0.120444	−	0.0998906i
$118$	73.3067	−	37.6628i	0.621243	−	0.319177i
$119$	−1.22960	+	0.216811i	−0.0103328	+	0.00182194i
$120$	−116.891	−	38.5608i	−0.974094	−	0.321340i
$121$	−96.7696	+	35.2213i	−0.799749	+	0.291085i
$122$	−8.24503	+	36.2695i	−0.0675822	+	0.297291i
$123$	169.496	+	29.3847i	1.37802	+	0.238900i
$124$	−88.5141	−	129.342i	−0.713823	−	1.04308i
$125$	−60.7668	+	105.251i	−0.486134	+	0.842009i
$126$	−0.223530	−	0.707993i	−0.00177405	−	0.00561899i
$127$	90.4208	−	52.2045i	0.711975	−	0.411059i	−0.0998168	−	0.995006i	$-0.531826\pi$
$127$	90.4208	−	52.2045i	0.711975	−	0.411059i	0.811792	+	0.583947i	$0.198492\pi$
$128$	21.4577	−	126.189i	0.167639	−	0.985849i
$129$	117.028	+	42.2141i	0.907191	+	0.327241i
$130$	15.3077	+	14.1787i	0.117752	+	0.109067i
$131$	−87.8938	+	104.748i	−0.670945	+	0.799601i	−0.988912	−	0.148501i	$-0.952555\pi$
$131$	−87.8938	+	104.748i	−0.670945	+	0.799601i	0.317968	+	0.948102i	$0.397000\pi$
$132$	29.5446	−	41.4969i	0.223823	−	0.314370i
$133$	−0.264516	−	0.0962761i	−0.00198884	−	0.000723880i
$134$	−82.2142	−	52.9981i	−0.613539	−	0.395508i
$135$	−136.572	−	22.8690i	−1.01164	−	0.169400i
$136$	−239.554	−	35.4668i	−1.76143	−	0.260785i
$137$	100.206	+	36.4722i	0.731434	+	0.266220i	0.680772	−	0.732496i	$-0.261645\pi$
$137$	100.206	+	36.4722i	0.731434	+	0.266220i	0.0506624	+	0.998716i	$0.483867\pi$
$138$	−127.655	+	199.283i	−0.925038	+	1.44408i
$139$	−55.0613	+	65.6195i	−0.396124	+	0.472083i	−0.926834	−	0.375471i	$-0.877481\pi$
$139$	−55.0613	+	65.6195i	−0.396124	+	0.472083i	0.530710	+	0.847554i	$0.321925\pi$
$140$	0.210225	+	0.819629i	0.00150161	+	0.00585449i
$141$	7.74237	+	43.1831i	0.0549104	+	0.306263i
$142$	254.448	−	32.1117i	1.79189	−	0.226139i
$143$	−7.47826	+	4.31757i	−0.0522955	+	0.0301928i
$144$	2.26075	−	143.982i	0.0156996	−	0.999877i
$145$	56.5001	−	97.8610i	0.389656	−	0.674903i
$146$	−234.935	−	98.7924i	−1.60914	−	0.676660i
$147$	94.1625	−	112.876i	0.640561	−	0.767862i
$148$	−89.2587	−	91.1939i	−0.603099	−	0.616175i
$149$	147.356	−	53.6331i	0.988965	−	0.359954i	0.203646	−	0.979045i	$-0.434721\pi$
$149$	147.356	−	53.6331i	0.988965	−	0.359954i	0.785319	+	0.619091i	$0.212499\pi$
$150$	7.62832	+	1.71108i	0.0508555	+	0.0114072i
$151$	24.6643	−	4.34897i	0.163339	−	0.0288011i	−0.0913803	−	0.995816i	$-0.529128\pi$
$151$	24.6643	−	4.34897i	0.163339	−	0.0288011i	0.254720	+	0.967015i	$0.418017\pi$
$152$	−42.7743	−	33.9288i	−0.281410	−	0.223216i
$153$	−272.431	+	1.56592i	−1.78060	+	0.0102347i
$154$	−0.349764	−	0.0171505i	−0.00227120	−	0.000111367i
$155$	129.169	+	153.938i	0.833350	+	0.993148i
$156$	−10.4896	+	22.0416i	−0.0672411	+	0.141293i
$157$	−19.7195	+	111.835i	−0.125602	+	0.712324i	0.855347	+	0.518056i	$0.173344\pi$
$157$	−19.7195	+	111.835i	−0.125602	+	0.712324i	−0.980949	+	0.194268i	$0.937767\pi$
$158$	1.92324	+	6.21574i	0.0121724	+	0.0393402i
$159$	−112.148	−	64.3198i	−0.705335	−	0.404527i
$160$	−11.5514	+	163.710i	−0.0721961	+	1.02318i
$161$	1.62693			0.0101052
$162$	−22.1300	−	160.481i	−0.136605	−	0.990626i
$163$		−	228.549i		−	1.40214i	−0.713091	−	0.701072i	$-0.752705\pi$
$163$		−	228.549i		−	1.40214i	0.713091	−	0.701072i	$-0.247295\pi$
$164$	−17.5391	−	228.694i	−0.106945	−	1.39448i
$165$	−32.4939	+	56.6564i	−0.196933	+	0.343372i
$166$	69.1739	+	223.565i	0.416710	+	1.34677i
$167$	−15.9992	−	2.82109i	−0.0958035	−	0.0168927i	0.125541	−	0.992088i	$-0.459933\pi$
$167$	−15.9992	−	2.82109i	−0.0958035	−	0.0168927i	−0.221344	+	0.975196i	$0.571044\pi$
$168$	−0.841846	+	0.520808i	−0.00501099	+	0.00310005i
$169$	−126.292	+	105.971i	−0.747288	+	0.627049i
$170$	310.122	+	15.2067i	1.82425	+	0.0894511i
$171$	−53.3681	−	30.4044i	−0.312094	−	0.177804i
$172$	16.2285	−	165.082i	0.0943516	−	0.959781i
$173$	16.7323	+	94.8933i	0.0967182	+	0.548516i	0.994207	+	0.107480i	$0.0342781\pi$
$173$	16.7323	+	94.8933i	0.0967182	+	0.548516i	−0.897489	+	0.441037i	$0.854611\pi$
$174$	128.994	+	28.9341i	0.741343	+	0.166288i
$175$	−0.0183814	−	0.0505025i	−0.000105037	−	0.000288586i
$176$	−63.3109	−	24.5934i	−0.359721	−	0.139735i
$177$	−94.9292	−	79.1913i	−0.536323	−	0.447408i
$178$	99.2876	+	41.7514i	0.557795	+	0.234558i
$179$	198.630	+	114.679i	1.10967	+	0.640666i	0.938743	−	0.344619i	$-0.111992\pi$
$179$	198.630	+	114.679i	1.10967	+	0.640666i	0.170923	+	0.985284i	$0.445325\pi$
$180$	15.1762	+	184.006i	0.0843122	+	1.02226i
$181$	154.487	+	267.580i	0.853522	+	1.47834i	0.878010	+	0.478643i	$0.158871\pi$
$181$	154.487	+	267.580i	0.853522	+	1.47834i	−0.0244878	+	0.999700i	$0.507795\pi$
$182$	0.166488	−	0.0210109i	0.000914767	−	0.000115445i
$183$	54.9165	−	9.84609i	0.300090	−	0.0538037i
$184$	299.381	+	99.7165i	1.62707	+	0.541937i
$185$	125.334	+	105.168i	0.677482	+	0.568475i
$186$	−126.809	+	197.961i	−0.681767	+	1.06431i
$187$	−43.9491	+	120.749i	−0.235022	+	0.645718i
$188$	53.2770	−	24.1513i	0.283388	−	0.128465i
$189$	−0.846912	+	0.723177i	−0.00448101	+	0.00382633i
$190$	58.8364	+	37.9280i	0.309665	+	0.199621i
$191$	76.7399	−	210.841i	0.401779	−	1.10388i	−0.559626	−	0.828745i	$-0.689055\pi$
$191$	76.7399	−	210.841i	0.401779	−	1.10388i	0.961406	−	0.275135i	$-0.0887224\pi$
$192$	−186.834	+	44.2391i	−0.973093	+	0.230412i
$193$	−130.384	−	109.405i	−0.675564	−	0.566865i	0.239142	−	0.970984i	$-0.423134\pi$
$193$	−130.384	−	109.405i	−0.675564	−	0.566865i	−0.914706	+	0.404119i	$0.867578\pi$
$194$	47.3332	+	43.8421i	0.243986	+	0.225990i
$195$	10.6200	−	29.4412i	0.0544615	−	0.150980i
$196$	−176.732	−	84.7304i	−0.901692	−	0.432298i
$197$	−100.143	−	173.453i	−0.508341	−	0.880473i	−0.999953	−	0.00965858i	$-0.996926\pi$
$197$	−100.143	−	173.453i	−0.508341	−	0.880473i	0.491612	−	0.870814i	$-0.336408\pi$
$198$	−74.6050	−	16.5093i	−0.376793	−	0.0833805i
$199$	−230.445	−	133.047i	−1.15801	−	0.668579i	−0.207186	−	0.978301i	$-0.566431\pi$
$199$	−230.445	−	133.047i	−1.15801	−	0.668579i	−0.950827	+	0.309722i	$0.899764\pi$
$200$	−0.287110	−	10.4199i	−0.00143555	−	0.0520994i
$201$	−25.0630	+	144.568i	−0.124691	+	0.719242i
$202$	61.2754	−	269.547i	0.303344	−	1.33439i
$203$	−0.310826	−	0.853989i	−0.00153117	−	0.00420684i
$204$	91.2582	+	351.598i	0.447344	+	1.72352i
$205$	51.0671	+	289.616i	0.249108	+	1.41276i
$206$	126.690	−	65.0895i	0.614999	−	0.315968i
$207$	349.950	+	59.6337i	1.69058	+	0.288085i
$208$	31.9241	+	6.33787i	0.153481	+	0.0304705i
$209$	−22.1926	+	18.6218i	−0.106184	+	0.0890994i
$210$	1.00887	−	0.770156i	0.00480417	−	0.00366741i
$211$	−393.246	−	69.3398i	−1.86372	−	0.328625i	−0.875691	−	0.482872i	$-0.839594\pi$
$211$	−393.246	−	69.3398i	−1.86372	−	0.328625i	−0.988032	+	0.154247i	$0.950705\pi$
$212$	−46.3978	+	166.017i	−0.218858	+	0.783097i
$213$	−193.307	−	332.606i	−0.907542	−	1.56153i
$214$	−129.067	−	170.084i	−0.603116	−	0.794784i
$215$			212.682i			0.989220i
$216$	−200.169	+	81.1678i	−0.926710	+	0.375777i
$217$	1.61614			0.00744765
$218$	−84.6165	+	64.2106i	−0.388149	+	0.294544i
$219$	1.09868	+	382.290i	0.00501680	+	1.74562i
$220$	83.8703	+	23.4398i	0.381229	+	0.106545i
$221$	10.6926	−	60.6410i	0.0483830	−	0.274394i
$222$	−73.6892	+	176.657i	−0.331933	+	0.795752i
$223$	−178.190	−	212.358i	−0.799056	−	0.952278i	0.200568	−	0.979680i	$-0.435721\pi$
$223$	−178.190	−	212.358i	−0.799056	−	0.952278i	−0.999625	+	0.0274016i	$0.991277\pi$
$224$	0.948876	+	0.917475i	0.00423605	+	0.00409587i
$225$	−2.10268	−	11.5368i	−0.00934526	−	0.0512745i
$226$	119.246	+	232.099i	0.527636	+	1.02699i
$227$	−157.783	+	27.8214i	−0.695079	+	0.122561i	−0.510015	−	0.860165i	$-0.670360\pi$
$227$	−157.783	+	27.8214i	−0.695079	+	0.122561i	−0.185064	+	0.982727i	$0.559249\pi$
$228$	−21.8163	+	78.9358i	−0.0956857	+	0.346209i
$229$	391.957	−	142.661i	1.71160	−	0.622972i	0.714540	−	0.699594i	$-0.246636\pi$
$229$	391.957	−	142.661i	1.71160	−	0.622972i	0.997060	+	0.0766226i	$0.0244136\pi$
$230$	−394.521	−	89.6853i	−1.71531	−	0.389936i
$231$	0.181073	+	0.493080i	0.000783866	+	0.00213455i
$232$	−4.85498	−	176.198i	−0.0209267	−	0.759475i
$233$	113.470	−	196.537i	0.486998	−	0.843505i	−0.512890	−	0.858454i	$-0.671425\pi$
$233$	113.470	−	196.537i	0.486998	−	0.843505i	0.999888	+	0.0149492i	$0.00475865\pi$
$234$	36.5813	+	1.58303i	0.156330	+	0.00676510i
$235$	−64.9525	+	37.5003i	−0.276394	+	0.159576i
$236$	−71.2588	+	148.632i	−0.301944	+	0.629799i
$237$	7.45832	−	6.29489i	0.0314697	−	0.0265607i
$238$	1.69689	−	1.83201i	0.00712977	−	0.00769751i
$239$	100.927	−	120.281i	0.422290	−	0.503266i	−0.512391	−	0.858752i	$-0.671240\pi$
$239$	100.927	−	120.281i	0.422290	−	0.503266i	0.934682	+	0.355486i	$0.115685\pi$
$240$	232.853	−	79.8857i	0.970219	−	0.332857i
$241$	−113.715	−	41.3887i	−0.471845	−	0.171737i	0.0951430	−	0.995464i	$-0.469669\pi$
$241$	−113.715	−	41.3887i	−0.471845	−	0.171737i	−0.566988	+	0.823726i	$0.691891\pi$
$242$	111.592	−	173.109i	0.461124	−	0.715327i
$243$	−208.677	+	124.511i	−0.858751	+	0.512392i
$244$	−30.7136	−	67.7532i	−0.125875	−	0.277677i
$245$	236.140	+	85.9479i	0.963836	+	0.350808i
$246$	−305.569	+	158.104i	−1.24215	+	0.642700i
$247$	8.92354	−	10.6347i	0.0361277	−	0.0430553i
$248$	297.395	+	99.0552i	1.19917	+	0.399416i
$249$	268.257	−	226.411i	1.07734	−	0.909282i
$250$	−30.4340	−	241.154i	−0.121736	−	0.964617i
$251$	3.42052	−	1.97484i	0.0136276	−	0.00786788i	−0.493171	−	0.869933i	$-0.664162\pi$
$251$	3.42052	−	1.97484i	0.0136276	−	0.00786788i	0.506798	+	0.862065i	$0.330829\pi$
$252$	1.21209	+	0.857736i	0.00480989	+	0.00340372i
$253$	83.7194	−	145.006i	0.330907	−	0.573147i
$254$	−80.9445	+	192.491i	−0.318679	+	0.757840i
$255$	−160.550	−	437.195i	−0.629609	−	1.71449i
$256$	118.375	+	226.988i	0.462402	+	0.886670i
$257$	70.1778	−	25.5426i	0.273065	−	0.0993876i	−0.201858	−	0.979415i	$-0.564698\pi$
$257$	70.1778	−	25.5426i	0.273065	−	0.0993876i	0.474923	+	0.880027i	$0.342476\pi$
$258$	−237.486	+	74.2301i	−0.920490	+	0.287713i
$259$	1.29585	−	0.228493i	0.00500328	−	0.000882213i
$260$	−41.5305	−	4.08267i	−0.159733	−	0.0157026i
$261$	−35.5560	−	195.085i	−0.136230	−	0.747450i
$262$	13.3937	−	273.149i	0.0511210	−	1.04255i
$263$	258.741	+	308.356i	0.983807	+	1.17246i	0.985017	+	0.172456i	$0.0551702\pi$
$263$	258.741	+	308.356i	0.983807	+	1.17246i	−0.00121067	+	0.999999i	$0.500385\pi$
$264$	3.09881	+	101.833i	0.0117379	+	0.385730i
$265$	38.3791	−	217.659i	0.144827	−	0.821354i
$266$	0.537828	−	0.166411i	0.00202191	−	0.000625606i
$267$	−0.464321	−	161.563i	−0.00173903	−	0.605104i
$268$	195.059	−	14.9595i	0.727833	−	0.0558191i
$269$	−256.494			−0.953508			−0.476754	−	0.879037i	$-0.658187\pi$
$269$	−256.494			−0.953508			−0.476754	+	0.879037i	$0.658187\pi$
$270$	245.237	−	128.680i	0.908284	−	0.476592i
$271$			98.1325i			0.362112i	0.983473	+	0.181056i	$0.0579516\pi$
$271$			98.1325i			0.362112i	−0.983473	+	0.181056i	$0.942048\pi$
$272$	424.540	−	233.114i	1.56081	−	0.857036i
$273$	−0.126482	−	0.217627i	−0.000463304	−	0.000797167i
$274$	−203.745	+	63.0415i	−0.743595	+	0.230078i
$275$	−5.44710	−	0.960471i	−0.0198076	−	0.00349262i
$276$	−37.5503	−	471.834i	−0.136052	−	1.70954i
$277$	−240.716	+	201.985i	−0.869011	+	0.729187i	−0.963890	−	0.266302i	$-0.914198\pi$
$277$	−240.716	+	201.985i	−0.869011	+	0.729187i	0.0948788	+	0.995489i	$0.469754\pi$
$278$	8.39053	−	171.115i	0.0301818	−	0.615521i
$279$	347.629	+	59.2382i	1.24598	+	0.212323i
$280$	−1.32586	−	1.05168i	−0.00473522	−	0.00375601i
$281$	13.7932	+	78.2252i	0.0490862	+	0.278381i	0.999465	−	0.0327143i	$-0.0104151\pi$
$281$	13.7932	+	78.2252i	0.0490862	+	0.278381i	−0.950379	+	0.311096i	$0.899304\pi$
$282$	−64.5435	−	59.4393i	−0.228877	−	0.210778i
$283$	49.7122	+	136.583i	0.175661	+	0.482626i	0.996010	−	0.0892374i	$-0.0284430\pi$
$283$	49.7122	+	136.583i	0.175661	+	0.482626i	−0.820349	+	0.571863i	$0.806221\pi$
$284$	−366.567	+	358.788i	−1.29073	+	1.26334i
$285$	17.9363	−	103.459i	0.0629343	−	0.363016i
$286$	6.69452	−	15.9200i	0.0234074	−	0.0556644i
$287$	2.04828	+	1.18257i	0.00713686	+	0.00412047i
$288$	170.472	+	232.128i	0.591918	+	0.805998i
$289$	−313.656	−	543.268i	−1.08532	−	1.87982i
$290$	28.2971	+	224.222i	0.0975761	+	0.773178i
$291$	32.8382	−	91.0353i	0.112846	−	0.312836i
$292$	493.741	−	126.638i	1.69089	−	0.433693i
$293$	−91.9061	−	77.1184i	−0.313673	−	0.263203i	0.472335	−	0.881419i	$-0.343411\pi$
$293$	−91.9061	−	77.1184i	−0.313673	−	0.263203i	−0.786008	+	0.618216i	$0.787856\pi$
$294$	−13.5544	+	293.677i	−0.0461034	+	0.998902i
$295$	72.2827	−	198.595i	0.245026	−	0.673204i
$296$	252.461	+	37.3778i	0.852910	+	0.126276i
$297$	20.8751	+	112.698i	0.0702864	+	0.379454i
$298$	−169.927	+	263.602i	−0.570224	+	0.884570i
$299$	−27.4425	+	75.3977i	−0.0917810	+	0.252166i
$300$	−14.2222	+	6.49650i	−0.0474074	+	0.0216550i
$301$	1.31031	+	1.09948i	0.00435318	+	0.00365275i
$302$	−34.0375	+	36.7479i	−0.112707	+	0.121682i
$303$	−408.129	+	73.1742i	−1.34696	+	0.241499i
$304$	109.168	+	2.34182i	0.359106	+	0.00770335i
$305$	47.6897	+	82.6010i	0.156360	+	0.270823i
$306$	432.148	−	331.864i	1.41225	−	1.08452i
$307$	177.597	+	102.536i	0.578491	+	0.333992i	0.760534	−	0.649299i	$-0.224937\pi$
$307$	177.597	+	102.536i	0.578491	+	0.333992i	−0.182042	+	0.983291i	$0.558271\pi$
$308$	0.577983	−	0.395539i	0.00187657	−	0.00128422i
$309$	−164.058	−	136.860i	−0.530932	−	0.442911i
$310$	−391.905	−	89.0905i	−1.26421	−	0.287389i
$311$	−83.6144	−	229.729i	−0.268857	−	0.738677i	−0.998495	−	0.0548442i	$-0.982534\pi$
$311$	−83.6144	−	229.729i	−0.268857	−	0.738677i	0.729638	−	0.683833i	$-0.239688\pi$
$312$	−9.93610	−	47.7989i	−0.0318465	−	0.153202i
$313$	23.7303	+	134.581i	0.0758156	+	0.429971i	0.998963	+	0.0455257i	$0.0144963\pi$
$313$	23.7303	+	134.581i	0.0758156	+	0.429971i	−0.923148	+	0.384446i	$0.874393\pi$
$314$	−103.791	−	202.017i	−0.330544	−	0.643368i
$315$	−1.65424	−	0.942437i	−0.00525154	−	0.00299186i
$316$	−10.5789	−	7.57781i	−0.0334777	−	0.0239804i
$317$	−108.274	+	90.8524i	−0.341557	+	0.286601i	−0.797389	−	0.603465i	$-0.793786\pi$
$317$	−108.274	+	90.8524i	−0.341557	+	0.286601i	0.455832	+	0.890066i	$0.349342\pi$
$318$	256.439	−	33.1119i	0.806410	−	0.104125i
$319$	−92.1095	−	16.2414i	−0.288745	−	0.0509135i
$320$	−179.521	−	274.790i	−0.561002	−	0.858718i
$321$	−159.335	+	277.817i	−0.496371	+	0.865474i
$322$	−2.59205	+	1.96696i	−0.00804983	+	0.00610856i
$323$		−	206.585i		−	0.639581i
$324$	229.279	+	228.926i	0.707652	+	0.706561i
$325$	2.65051			0.00815543
$326$	276.316	+	364.128i	0.847594	+	1.11696i
$327$	138.214	+	79.2690i	0.422672	+	0.242413i
$328$	304.434	+	343.154i	0.928153	+	1.04620i
$329$	−0.104742	+	0.594024i	−0.000318366	+	0.00180554i
$330$	−16.7279	−	129.551i	−0.0506905	−	0.392578i
$331$	97.6833	+	116.414i	0.295116	+	0.351705i	0.893145	−	0.449769i	$-0.148494\pi$
$331$	97.6833	+	116.414i	0.295116	+	0.351705i	−0.598029	+	0.801474i	$0.704049\pi$
$332$	−380.498	−	272.555i	−1.14608	−	0.820948i
$333$	287.110	−	1.65029i	0.862193	−	0.00495582i
$334$	28.9008	−	14.8484i	0.0865293	−	0.0444562i
$335$	−247.021	+	43.5565i	−0.737376	+	0.130019i
$336$	0.711584	−	1.84755i	0.00211781	−	0.00549865i
$337$	119.675	−	43.5582i	0.355119	−	0.129253i	−0.158299	−	0.987391i	$-0.550601\pi$
$337$	119.675	−	43.5582i	0.355119	−	0.129253i	0.513418	+	0.858138i	$0.328379\pi$
$338$	73.0904	−	321.521i	0.216244	−	0.951246i
$339$	250.730	−	300.559i	0.739618	−	0.886604i
$340$	−512.475	+	350.709i	−1.50728	+	1.03150i
$341$	83.1641	−	144.045i	0.243883	−	0.422418i
$342$	121.786	−	16.0812i	0.356098	−	0.0470210i
$343$	3.50057	−	2.02106i	0.0102058	−	0.00589229i
$344$	173.729	+	282.631i	0.505025	+	0.821603i
$345$	107.101	+	597.355i	0.310437	+	1.73146i
$346$	−141.384	−	130.956i	−0.408624	−	0.378485i
$347$	19.4708	−	23.2044i	0.0561119	−	0.0668715i	−0.737258	−	0.675611i	$-0.763880\pi$
$347$	19.4708	−	23.2044i	0.0561119	−	0.0668715i	0.793370	+	0.608739i	$0.208324\pi$
$348$	−240.495	+	109.855i	−0.691079	+	0.315675i
$349$	162.407	+	59.1115i	0.465351	+	0.169374i	0.564045	−	0.825744i	$-0.309244\pi$
$349$	162.407	+	59.1115i	0.465351	+	0.169374i	−0.0986944	+	0.995118i	$0.531467\pi$
$350$	0.0903429	+	0.0582381i	0.000258123	+	0.000166395i
$351$	−19.2292	−	51.4472i	−0.0547839	−	0.146573i
$352$	130.601	−	37.3602i	0.371026	−	0.106137i
$353$	364.507	+	132.670i	1.03260	+	0.375835i	0.802069	−	0.597231i	$-0.203733\pi$
$353$	364.507	+	132.670i	1.03260	+	0.375835i	0.230528	+	0.973066i	$0.425955\pi$
$354$	246.984	+	11.3993i	0.697696	+	0.0322015i
$355$	422.737	−	503.799i	1.19081	−	1.41915i
$356$	−208.664	+	53.5196i	−0.586133	+	0.150336i
$357$	−3.52347	−	1.27098i	−0.00986967	−	0.00356018i
$358$	−455.107	+	57.4351i	−1.27125	+	0.160433i
$359$	−494.326	+	285.399i	−1.37695	+	0.794983i	−0.991791	−	0.127866i	$-0.959187\pi$
$359$	−494.326	+	285.399i	−1.37695	+	0.794983i	−0.385160	+	0.922850i	$0.625854\pi$
$360$	−246.642	−	274.813i	−0.685117	−	0.763370i
$361$	−157.212	+	272.300i	−0.435492	+	0.754294i
$362$	−569.635	−	239.537i	−1.57358	−	0.661704i
$363$	−304.400	−	52.7723i	−0.838566	−	0.145378i
$364$	−0.239848	+	0.234758i	−0.000658923	+	0.000644939i
$365$	−614.133	+	223.526i	−1.68256	+	0.612400i
$366$	−75.5898	+	82.0809i	−0.206530	+	0.224265i
$367$	−77.7710	+	13.7131i	−0.211910	+	0.0373655i	−0.278595	−	0.960409i	$-0.589869\pi$
$367$	−77.7710	+	13.7131i	−0.211910	+	0.0373655i	0.0666852	+	0.997774i	$0.478758\pi$
$368$	−597.534	+	203.081i	−1.62373	+	0.551851i
$369$	397.235	+	329.447i	1.07652	+	0.892811i
$370$	−326.832	−	16.0260i	−0.883329	−	0.0433136i
$371$	−1.14256	−	1.36165i	−0.00307968	−	0.00367022i
$372$	−37.3013	−	468.705i	−0.100272	−	1.25996i
$373$	−102.883	+	583.480i	−0.275827	+	1.56429i	0.460498	+	0.887661i	$0.347671\pi$
$373$	−102.883	+	583.480i	−0.275827	+	1.56429i	−0.736324	+	0.676629i	$0.763440\pi$
$374$	−75.9652	−	245.513i	−0.203116	−	0.656453i
$375$	−315.228	+	183.207i	−0.840609	+	0.488552i
$376$	−55.6827	+	102.890i	−0.148092	+	0.273644i
$377$	44.8198			0.118885
$378$	0.474990	−	2.17609i	0.00125659	−	0.00575685i
$379$			93.1184i			0.245695i	0.992426	+	0.122847i	$0.0392026\pi$
$379$			93.1184i			0.245695i	−0.992426	+	0.122847i	$0.960797\pi$
$380$	−139.594	+	10.7057i	−0.367352	+	0.0281730i
$381$	313.226	−	0.900192i	0.822115	−	0.00236271i
$382$	132.643	+	428.693i	0.347234	+	1.12223i
$383$	185.774	+	32.7570i	0.485051	+	0.0855275i	0.410825	−	0.911714i	$-0.365241\pi$
$383$	185.774	+	32.7570i	0.485051	+	0.0855275i	0.0742251	+	0.997242i	$0.476352\pi$
$384$	244.181	−	296.364i	0.635888	−	0.771781i
$385$	−0.687896	+	0.577214i	−0.00178674	+	0.00149926i
$386$	340.000	+	16.6717i	0.880828	+	0.0431910i
$387$	241.544	+	284.524i	0.624145	+	0.735203i
$388$	−128.417	−	12.6241i	−0.330971	−	0.0325363i
$389$	−27.7003	−	157.096i	−0.0712091	−	0.403847i	−0.999489	−	0.0319646i	$-0.989824\pi$
$389$	−27.7003	−	157.096i	−0.0712091	−	0.403847i	0.928280	−	0.371882i	$-0.121288\pi$
$390$	18.6744	+	59.7455i	0.0478831	+	0.153194i
$391$	408.369	+	1121.98i	1.04442	+	2.86952i
$392$	384.010	−	78.6746i	0.979617	−	0.200701i
$393$	−385.071	+	141.409i	−0.979825	+	0.359820i
$394$	369.254	+	155.275i	0.937192	+	0.394098i
$395$	14.4494	+	8.34236i	0.0365807	+	0.0211199i
$396$	138.821	−	63.8944i	0.350559	−	0.161349i
$397$	58.9618	+	102.125i	0.148518	+	0.257241i	0.930680	−	0.365834i	$-0.119216\pi$
$397$	58.9618	+	102.125i	0.148518	+	0.257241i	−0.782162	+	0.623075i	$0.785883\pi$
$398$	528.001	−	66.6344i	1.32664	−	0.167423i
$399$	−0.544676	−	0.645344i	−0.00136510	−	0.00161740i
$400$	13.0550	+	16.2540i	0.0326376	+	0.0406349i
$401$	−104.236	−	87.4644i	−0.259940	−	0.218116i	0.503498	−	0.863996i	$-0.332046\pi$
$401$	−104.236	−	87.4644i	−0.259940	−	0.218116i	−0.763439	+	0.645881i	$0.776490\pi$
$402$	−134.851	−	260.628i	−0.335451	−	0.648328i
$403$	−27.2605	+	74.8977i	−0.0676440	+	0.185850i
$404$	228.257	+	503.528i	0.564994	+	1.24636i
$405$	−321.279	−	263.351i	−0.793281	−	0.650249i
$406$	1.52768	+	0.984797i	0.00376277	+	0.00242561i
$407$	46.3171	−	127.255i	0.113801	−	0.312667i
$408$	−570.474	−	449.839i	−1.39822	−	1.10255i
$409$	−98.1152	−	82.3284i	−0.239890	−	0.201292i	0.514914	−	0.857242i	$-0.327824\pi$
$409$	−98.1152	−	82.3284i	−0.239890	−	0.201292i	−0.754804	+	0.655950i	$0.772268\pi$
$410$	−431.506	−	399.680i	−1.05245	−	0.974828i
$411$	206.339	+	244.475i	0.502042	+	0.594830i
$412$	−123.151	+	256.869i	−0.298909	+	0.623468i
$413$	−0.849846	−	1.47198i	−0.00205774	−	0.00356411i
$414$	−629.641	+	328.079i	−1.52087	+	0.792462i
$415$	519.708	+	300.053i	1.25231	+	0.723020i
$416$	−58.5243	+	28.4986i	−0.140684	+	0.0685062i
$417$	−241.229	+	88.5861i	−0.578487	+	0.212437i
$418$	12.8438	−	56.4992i	0.0307268	−	0.135165i
$419$	−139.827	−	384.171i	−0.333716	−	0.916876i	−0.987136	−	0.159881i	$-0.948889\pi$
$419$	−139.827	−	384.171i	−0.333716	−	0.916876i	0.653421	−	0.756995i	$-0.273333\pi$
$420$	−0.676235	+	2.44675i	−0.00161008	+	0.00582559i
$421$	−26.5187	−	150.395i	−0.0629897	−	0.357233i	−0.999969	−	0.00784813i	$-0.997502\pi$
$421$	−26.5187	−	150.395i	−0.0629897	−	0.357233i	0.936979	−	0.349384i	$-0.113609\pi$
$422$	710.355	−	364.960i	1.68331	−	0.864834i
$423$	−44.3033	+	123.934i	−0.104736	+	0.292989i
$424$	−126.792	−	320.595i	−0.299038	−	0.756119i
$425$	30.2143	−	25.3528i	0.0710925	−	0.0596537i
$426$	710.098	+	296.204i	1.66690	+	0.695315i
$427$	0.755429	+	0.133203i	0.00176916	+	0.000311950i
$428$	411.262	+	114.938i	0.960892	+	0.268547i
$429$	−25.9053	+	0.0744504i	−0.0603854	+	0.000173544i
$430$	−257.132	−	338.848i	−0.597982	−	0.788019i
$431$		−	640.109i		−	1.48517i	−0.669751	−	0.742585i	$-0.733599\pi$
$431$		−	640.109i		−	1.48517i	0.669751	−	0.742585i	$-0.266401\pi$
$432$	220.781	−	371.322i	0.511067	−	0.859541i
$433$	343.700			0.793765			0.396883	−	0.917869i	$-0.370092\pi$
$433$	343.700			0.793765			0.396883	+	0.917869i	$0.370092\pi$
$434$	−2.57486	+	1.95391i	−0.00593285	+	0.00450210i
$435$	293.095	−	170.343i	0.673781	−	0.391594i
$436$	57.1815	−	204.602i	0.131150	−	0.469271i
$437$	−46.7440	+	265.099i	−0.106966	+	0.606633i
$438$	−463.939	−	607.742i	−1.05922	−	1.38754i
$439$	−58.0596	−	69.1928i	−0.132254	−	0.157615i	0.695853	−	0.718184i	$-0.255027\pi$
$439$	−58.0596	−	69.1928i	−0.132254	−	0.157615i	−0.828107	+	0.560570i	$0.810582\pi$
$440$	−161.962	+	64.0544i	−0.368095	+	0.145578i
$441$	413.516	−	153.205i	0.937679	−	0.347404i
$442$	56.2791	+	109.541i	0.127328	+	0.247831i
$443$	−288.931	+	50.9464i	−0.652215	+	0.115003i	−0.489959	−	0.871746i	$-0.662988\pi$
$443$	−288.931	+	50.9464i	−0.652215	+	0.115003i	−0.162256	+	0.986749i	$0.551877\pi$
$444$	−96.1753	−	370.542i	−0.216611	−	0.834554i
$445$	259.543	−	94.4660i	0.583243	−	0.212283i
$446$	540.634	+	122.901i	1.21218	+	0.275562i
$447$	463.524	+	80.3589i	1.03697	+	0.179774i
$448$	−2.62099	−	0.314544i	−0.00585042	−	0.000702108i
$449$	63.8556	−	110.601i	0.142217	−	0.246328i	−0.786114	−	0.618082i	$-0.787910\pi$
$449$	63.8556	−	110.601i	0.142217	−	0.246328i	0.928331	+	0.371754i	$0.121243\pi$
$450$	17.2979	+	15.8384i	0.0384398	+	0.0351963i
$451$	210.803	−	121.707i	0.467411	−	0.269860i
$452$	−470.591	−	225.615i	−1.04113	−	0.499149i
$453$	70.6766	+	25.4944i	0.156019	+	0.0562790i
$454$	217.746	−	235.085i	0.479616	−	0.517807i
$455$	0.276600	−	0.329640i	0.000607913	−	0.000724483i
$456$	−60.6751	−	152.137i	−0.133059	−	0.333634i
$457$	−394.951	−	143.750i	−0.864225	−	0.314552i	−0.128399	−	0.991723i	$-0.540984\pi$
$457$	−394.951	−	143.750i	−0.864225	−	0.314552i	−0.735826	+	0.677170i	$0.763206\pi$
$458$	−451.994	+	701.163i	−0.986886	+	1.53092i
$459$	−711.306	−	402.536i	−1.54969	−	0.876985i
$460$	736.985	−	334.087i	1.60214	−	0.726277i
$461$	−648.376	−	235.990i	−1.40646	−	0.511908i	−0.476368	−	0.879246i	$-0.658047\pi$
$461$	−648.376	−	235.990i	−1.40646	−	0.511908i	−0.930088	+	0.367338i	$0.880269\pi$
$462$	−0.884620	−	0.566664i	−0.00191476	−	0.00122655i
$463$	354.216	−	422.138i	0.765045	−	0.911745i	−0.233111	−	0.972450i	$-0.574891\pi$
$463$	354.216	−	422.138i	0.765045	−	0.911745i	0.998156	+	0.0607054i	$0.0193350\pi$
$464$	220.758	+	274.852i	0.475772	+	0.592352i
$465$	106.391	+	593.393i	0.228797	+	1.27611i
$466$	56.8297	+	450.310i	0.121952	+	0.966331i
$467$	535.942	−	309.426i	1.14763	−	0.662583i	0.199320	−	0.979934i	$-0.436127\pi$
$467$	535.942	−	309.426i	1.14763	−	0.662583i	0.948308	+	0.317351i	$0.102793\pi$
$468$	−60.1957	+	41.7046i	−0.128623	+	0.0891124i
$469$	−1.00865	+	1.74703i	−0.00215064	+	0.00372501i
$470$	58.1453	−	138.273i	0.123713	−	0.294199i
$471$	−218.234	+	261.604i	−0.463342	+	0.555424i
$472$	−66.1659	−	322.955i	−0.140182	−	0.684226i
$473$	165.421	−	60.2084i	0.349728	−	0.127291i
$474$	−4.27218	+	19.0462i	−0.00901305	+	0.0401818i
$475$	8.75720	−	1.54413i	0.0184362	−	0.00325080i
$476$	−0.488608	+	4.97031i	−0.00102649	+	0.0104418i
$477$	−195.853	−	334.769i	−0.410593	−	0.701821i
$478$	−15.3798	+	313.653i	−0.0321754	+	0.656179i
$479$	−205.959	−	245.453i	−0.429977	−	0.512427i	0.506938	−	0.861982i	$-0.330777\pi$
$479$	−205.959	−	245.453i	−0.429977	−	0.512427i	−0.936916	+	0.349555i	$0.886333\pi$
$480$	−274.402	+	408.793i	−0.571671	+	0.851652i
$481$	−11.2688	+	63.9084i	−0.0234278	+	0.132866i
$482$	231.210	−	71.5396i	0.479690	−	0.148422i
$483$	4.23389	+	2.42824i	0.00876581	+	0.00502741i
$484$	31.4986	+	410.714i	0.0650797	+	0.848583i
$485$	165.445			0.341123
$486$	181.932	−	450.662i	0.374346	−	0.927289i
$487$		−	5.24750i		−	0.0107752i	−0.999985	−	0.00538758i	$-0.998285\pi$
$487$		−	5.24750i		−	0.0107752i	0.999985	−	0.00538758i	$-0.00171493\pi$
$488$	130.847	+	70.8125i	0.268129	+	0.145108i
$489$	341.116	−	594.772i	0.697579	−	1.21630i
$490$	−480.132	+	148.559i	−0.979861	+	0.303182i
$491$	−593.831	−	104.708i	−1.20943	−	0.213255i	−0.467660	−	0.883908i	$-0.654903\pi$
$491$	−593.831	−	104.708i	−1.20943	−	0.213255i	−0.741771	+	0.670653i	$0.766014\pi$
$492$	295.689	−	621.326i	0.600994	−	1.26286i
$493$	510.919	−	428.712i	1.03635	−	0.869598i
$494$	−1.35982	+	27.7318i	−0.00275266	+	0.0561373i
$495$	−169.123	+	98.9434i	−0.341662	+	0.199886i
$496$	−593.571	+	201.734i	−1.19672	+	0.406722i
$497$	−0.918461	−	5.20885i	−0.00184801	−	0.0104806i
$498$	−153.660	+	685.043i	−0.308553	+	1.37559i
$499$	−1.99347	−	5.47702i	−0.00399494	−	0.0109760i	0.937679	−	0.347502i	$-0.112970\pi$
$499$	−1.99347	−	5.47702i	−0.00399494	−	0.0109760i	−0.941674	+	0.336526i	$0.890748\pi$
$500$	340.043	+	347.415i	0.680085	+	0.694831i
$501$	−37.4254	−	31.2208i	−0.0747013	−	0.0623169i
$502$	−3.06204	+	7.28174i	−0.00609968	+	0.0145055i
$503$	103.706	+	59.8746i	0.206175	+	0.119035i	0.599532	−	0.800350i	$-0.295353\pi$
$503$	103.706	+	59.8746i	0.206175	+	0.119035i	−0.393358	+	0.919386i	$0.628687\pi$
$504$	−2.96812	+	0.0988601i	−0.00588913	+	0.000196151i
$505$	−354.421	−	613.875i	−0.701823	−	1.21559i
$506$	41.9294	+	332.242i	0.0828644	+	0.656605i
$507$	−486.823	+	87.2834i	−0.960204	+	0.172157i
$508$	−103.760	−	404.541i	−0.204252	−	0.796341i
$509$	−280.047	−	234.987i	−0.550190	−	0.461664i	0.324816	−	0.945777i	$-0.394698\pi$
$509$	−280.047	−	234.987i	−0.550190	−	0.461664i	−0.875005	+	0.484113i	$0.839142\pi$
$510$	784.358	+	502.439i	1.53796	+	0.985175i
$511$	−1.79769	+	4.93912i	−0.00351799	+	0.00966560i
$512$	−463.024	−	218.524i	−0.904343	−	0.426805i
$513$	−93.5044	−	158.777i	−0.182270	−	0.309507i
$514$	−80.9271	+	125.540i	−0.157446	+	0.244240i
$515$	124.920	−	343.215i	0.242563	−	0.666437i
$516$	288.622	−	405.385i	0.559346	−	0.785629i
$517$	47.5547	+	39.9031i	0.0919820	+	0.0771821i
$518$	−1.78832	+	1.93072i	−0.00345235	+	0.00372725i
$519$	−98.0873	+	271.922i	−0.188993	+	0.523934i
$520$	71.1028	−	43.7057i	0.136736	−	0.0840494i
$521$	109.267	+	189.256i	0.209726	+	0.363255i	0.951628	−	0.307253i	$-0.0994096\pi$
$521$	109.267	+	189.256i	0.209726	+	0.363255i	−0.741903	+	0.670508i	$0.766076\pi$
$522$	292.505	+	267.824i	0.560354	+	0.513073i
$523$	−696.524	−	402.138i	−1.33179	−	0.768907i	−0.346212	−	0.938156i	$-0.612532\pi$
$523$	−696.524	−	402.138i	−1.33179	−	0.768907i	−0.985573	+	0.169250i	$0.945866\pi$
$524$	308.897	+	451.377i	0.589498	+	0.861406i
$525$	0.0275410	−	0.158861i	5.24591e−5	−	0.000302593i
$526$	−785.031	−	178.459i	−1.49245	−	0.339275i
$527$	405.661	+	1114.54i	0.769754	+	2.11488i
$528$	−128.052	−	158.495i	−0.242524	−	0.300179i
$529$	−178.305	−	1011.22i	−0.337060	−	1.91156i
$530$	202.003	+	393.177i	0.381138	+	0.741844i
$531$	−128.846	−	347.770i	−0.242649	−	0.654934i
$532$	−0.655683	+	0.915361i	−0.00123249	+	0.00172060i
$533$	−89.3543	+	74.9772i	−0.167644	+	0.140670i
$534$	196.069	+	256.842i	0.367170	+	0.480978i
$535$	−539.192	−	95.0740i	−1.00783	−	0.177708i
$536$	−292.685	+	259.660i	−0.546053	+	0.484440i
$537$	345.749	+	594.899i	0.643852	+	1.10782i
$538$	408.649	−	310.100i	0.759571	−	0.576395i
$539$		−	207.997i		−	0.385895i
$540$	−235.140	+	501.505i	−0.435445	+	0.928712i
$541$	−172.884			−0.319563			−0.159782	−	0.987152i	$-0.551079\pi$
$541$	−172.884			−0.319563			−0.159782	+	0.987152i	$0.551079\pi$
$542$	−118.642	−	156.346i	−0.218897	−	0.288461i
$543$	2.66391	+	926.921i	0.00490592	+	1.70704i
$544$	−394.547	+	884.667i	−0.725271	+	1.62623i
$545$	−47.2992	+	268.247i	−0.0867875	+	0.492197i
$546$	0.464623	+	0.193809i	0.000850957	+	0.000354961i
$547$	164.443	+	195.975i	0.300627	+	0.358273i	0.895118	−	0.445829i	$-0.147091\pi$
$547$	164.443	+	195.975i	0.300627	+	0.358273i	−0.594491	+	0.804102i	$0.702647\pi$
$548$	248.392	−	346.766i	0.453270	−	0.632784i
$549$	157.609	+	56.3412i	0.287084	+	0.102625i
$550$	9.83959	−	5.05530i	0.0178902	−	0.00919145i
$551$	148.083	−	26.1110i	0.268753	−	0.0473884i
$552$	630.272	+	706.334i	1.14180	+	1.27959i
$553$	0.126093	−	0.0458942i	0.000228017	−	8.29913e-5i
$554$	139.313	−	612.829i	0.251467	−	1.10619i
$555$	169.201	+	460.751i	0.304866	+	0.830182i
$556$	193.509	+	282.766i	0.348038	+	0.508572i
$557$	−177.380	+	307.231i	−0.318456	+	0.551582i	−0.980166	−	0.198178i	$-0.936498\pi$
$557$	−177.380	+	307.231i	−0.318456	+	0.551582i	0.661710	+	0.749760i	$0.269831\pi$
$558$	−625.466	+	325.904i	−1.12091	+	0.584057i
$559$	−73.0554	+	42.1786i	−0.130690	+	0.0754536i
$560$	3.38386	+	0.0725887i	0.00604261	+	0.000129623i
$561$	−294.594	+	248.640i	−0.525122	+	0.443208i
$562$	−116.550	−	107.953i	−0.207384	−	0.192088i
$563$	−7.92579	+	9.44559i	−0.0140778	+	0.0167773i	−0.773037	−	0.634360i	$-0.781264\pi$
$563$	−7.92579	+	9.44559i	−0.0140778	+	0.0167773i	0.758960	+	0.651138i	$0.225708\pi$
$564$	174.693	+	16.6665i	0.309740	+	0.0295506i
$565$	628.780	+	228.857i	1.11288	+	0.405057i
$566$	−244.331	−	157.504i	−0.431680	−	0.278276i
$567$	−3.28334	+	0.617941i	−0.00579073	+	0.00108984i
$568$	150.245	−	1014.80i	0.264516	−	1.78663i
$569$	−168.484	−	61.3233i	−0.296106	−	0.107774i	0.189695	−	0.981843i	$-0.439250\pi$
$569$	−168.484	−	61.3233i	−0.296106	−	0.107774i	−0.485801	+	0.874069i	$0.661472\pi$
$570$	96.5059	+	186.518i	0.169309	+	0.327224i
$571$	254.026	−	302.737i	0.444880	−	0.530187i	−0.496274	−	0.868166i	$-0.665299\pi$
$571$	254.026	−	302.737i	0.444880	−	0.530187i	0.941154	+	0.337979i	$0.109743\pi$
$572$	8.58146	+	33.4576i	0.0150026	+	0.0584923i
$573$	514.392	−	434.151i	0.897717	−	0.757681i
$574$	−4.69307	+	0.592272i	−0.00817608	+	0.00103183i
$575$	−44.5089	+	25.6972i	−0.0774068	+	0.0446908i
$576$	−552.240	−	163.728i	−0.958750	−	0.284250i
$577$	−344.513	+	596.713i	−0.597075	+	1.03417i	0.396175	+	0.918175i	$0.370337\pi$
$577$	−344.513	+	596.713i	−0.597075	+	1.03417i	−0.993250	+	0.115990i	$0.962996\pi$
$578$	1156.53	+	486.332i	2.00092	+	0.841405i
$579$	−176.018	−	479.314i	−0.304003	−	0.827832i
$580$	−316.167	−	323.022i	−0.545115	−	0.556934i
$581$	4.53526	−	1.65070i	0.00780595	−	0.00284113i
$582$	57.7433	+	184.740i	0.0992153	+	0.317422i
$583$	−180.157	+	31.7665i	−0.309017	+	0.0544880i
$584$	−633.528	+	798.693i	−1.08481	+	1.36763i
$585$	71.5789	−	60.7664i	0.122357	−	0.103874i
$586$	239.662	+	11.7517i	0.408979	+	0.0200541i
$587$	−207.235	−	246.973i	−0.353040	−	0.420737i	0.560073	−	0.828443i	$-0.310773\pi$
$587$	−207.235	−	246.973i	−0.353040	−	0.420737i	−0.913113	+	0.407706i	$0.866329\pi$
$588$	−333.460	−	484.277i	−0.567109	−	0.823601i
$589$	−46.4340	+	263.340i	−0.0788353	+	0.447097i
$590$	124.939	+	403.794i	0.211762	+	0.684396i
$591$	−1.72683	−	600.857i	−0.00292187	−	1.01668i
$592$	−447.414	+	245.674i	−0.755767	+	0.414990i
$593$	469.564			0.791846			0.395923	−	0.918284i	$-0.370425\pi$
$593$	469.564			0.791846			0.395923	+	0.918284i	$0.370425\pi$
$594$	−169.510	−	154.313i	−0.285370	−	0.259787i
$595$		−	6.40345i		−	0.0107621i
$596$	−47.9644	−	625.414i	−0.0804772	−	1.04935i
$597$	−401.127	−	690.184i	−0.671905	−	1.15609i
$598$	−47.4339	−	153.302i	−0.0793208	−	0.256359i
$599$	527.632	+	93.0357i	0.880854	+	0.155318i	0.595742	−	0.803176i	$-0.296858\pi$
$599$	527.632	+	93.0357i	0.880854	+	0.155318i	0.285112	+	0.958494i	$0.407969\pi$
$600$	14.8048	−	27.5449i	0.0246746	−	0.0459082i
$601$	647.757	−	543.533i	1.07780	−	0.904381i	0.0820627	−	0.996627i	$-0.473849\pi$
$601$	647.757	−	543.533i	1.07780	−	0.904381i	0.995736	+	0.0922465i	$0.0294048\pi$
$602$	−3.41686	−	0.167544i	−0.00567585	−	0.000278313i
$603$	−280.994	+	338.812i	−0.465994	+	0.561877i
$604$	9.80089	−	99.6984i	0.0162266	−	0.165064i
$605$	−91.7119	−	520.124i	−0.151590	−	0.859709i
$606$	561.769	−	610.009i	0.927011	−	1.00662i
$607$	−138.471	−	380.445i	−0.228123	−	0.626763i	0.771836	−	0.635822i	$-0.219339\pi$
$607$	−138.471	−	380.445i	−0.228123	−	0.626763i	−0.999959	+	0.00905875i	$0.997116\pi$
$608$	−176.760	+	128.253i	−0.290723	+	0.210943i
$609$	0.465714	−	2.68632i	0.000764719	−	0.00441103i
$610$	−175.844	−	73.9442i	−0.288269	−	0.121220i
$611$	−25.7624	−	14.8739i	−0.0421643	−	0.0243436i
$612$	−287.281	+	1051.19i	−0.469413	+	1.71764i
$613$	62.6459	+	108.506i	0.102196	+	0.177008i	0.912589	−	0.408878i	$-0.134080\pi$
$613$	62.6459	+	108.506i	0.102196	+	0.177008i	−0.810393	+	0.585886i	$0.800747\pi$
$614$	−406.915	+	51.3532i	−0.662727	+	0.0836371i
$615$	−299.364	+	829.909i	−0.486770	+	1.34944i
$616$	−0.442644	+	1.32896i	−0.000718578	+	0.00215740i
$617$	221.013	+	185.452i	0.358205	+	0.300570i	0.804075	−	0.594528i	$-0.202661\pi$
$617$	221.013	+	185.452i	0.358205	+	0.300570i	−0.445870	+	0.895098i	$0.647105\pi$
$618$	426.842	+	19.7005i	0.690683	+	0.0318778i
$619$	122.807	−	337.411i	0.198397	−	0.545090i	−0.800102	−	0.599864i	$-0.795221\pi$
$619$	122.807	−	337.411i	0.198397	−	0.545090i	0.998499	+	0.0547735i	$0.0174437\pi$
$620$	732.098	−	331.872i	1.18080	−	0.535277i
$621$	821.696	+	677.499i	1.32318	+	1.09098i
$622$	410.957	+	264.917i	0.660702	+	0.425911i
$623$	0.759737	−	2.08736i	0.00121948	−	0.00335050i
$624$	73.6191	+	64.1411i	0.117979	+	0.102790i
$625$	−502.431	−	421.589i	−0.803889	−	0.674543i
$626$	−200.516	−	185.726i	−0.320312	−	0.296687i
$627$	−85.5469	+	15.3379i	−0.136438	+	0.0244623i
$628$	409.599	+	196.374i	0.652228	+	0.312698i
$629$	482.842	+	836.307i	0.767634	+	1.32958i
$630$	3.77495	−	0.498464i	0.00599199	−	0.000791212i
$631$	874.059	+	504.638i	1.38520	+	0.799743i	0.992769	−	0.120040i	$-0.0383023\pi$
$631$	874.059	+	504.638i	1.38520	+	0.799743i	0.392427	+	0.919783i	$0.371636\pi$
$632$	26.0161	−	0.716849i	0.0411646	−	0.00113425i
$633$	−919.881	−	767.378i	−1.45321	−	1.21229i
$634$	62.6626	−	275.650i	0.0988369	−	0.434779i
$635$	183.144	+	503.183i	0.288415	+	0.792415i
$636$	−368.529	+	362.788i	−0.579448	+	0.570421i
$637$	17.3079	+	98.1580i	0.0271710	+	0.154094i
$638$	166.386	−	85.4842i	0.260793	−	0.133988i
$639$	−6.63357	−	1154.08i	−0.0103812	−	1.80607i
$640$	618.234	+	220.758i	0.965991	+	0.344935i
$641$	610.695	−	512.434i	0.952722	−	0.799429i	−0.0270317	−	0.999635i	$-0.508606\pi$
$641$	610.695	−	512.434i	0.952722	−	0.799429i	0.979754	+	0.200206i	$0.0641611\pi$
$642$	−82.0258	−	635.258i	−0.127766	−	0.989498i
$643$	−696.625	−	122.834i	−1.08340	−	0.191032i	−0.396680	−	0.917957i	$-0.629838\pi$
$643$	−696.625	−	122.834i	−1.08340	−	0.191032i	−0.686717	+	0.726925i	$0.740949\pi$
$644$	1.75164	−	6.26755i	0.00271993	−	0.00973223i
$645$	−317.434	+	553.479i	−0.492146	+	0.858108i
$646$	249.761	+	329.133i	0.386626	+	0.509495i
$647$			595.093i			0.919774i	0.887978	+	0.459887i	$0.152110\pi$
$647$			595.093i			0.919774i	−0.887978	+	0.459887i	$0.847890\pi$
$648$	−642.061	−	87.5292i	−0.990835	−	0.135076i
$649$	−174.927			−0.269533
$650$	−4.22283	+	3.20447i	−0.00649667	+	0.00492995i
$651$	4.20581	+	2.41213i	0.00646053	+	0.00370528i
$652$	−880.459	−	246.068i	−1.35040	−	0.377405i
$653$	−128.322	+	727.750i	−0.196511	+	1.11447i	0.713738	+	0.700412i	$0.247001\pi$
$653$	−128.322	+	727.750i	−0.196511	+	1.11447i	−0.910250	+	0.414060i	$0.864111\pi$
$654$	−316.040	+	40.8077i	−0.483241	+	0.0623971i
$655$	−450.776	−	537.214i	−0.688207	−	0.820173i
$656$	−899.900	−	178.657i	−1.37180	−	0.272342i
$657$	−567.720	+	996.503i	−0.864109	+	1.51675i
$658$	−0.551297	−	1.07304i	−0.000837837	−	0.00163076i
$659$	225.185	−	39.7062i	0.341707	−	0.0602522i	−0.000161354	−	1.00000i	$-0.500051\pi$
$659$	225.185	−	39.7062i	0.341707	−	0.0602522i	0.341869	+	0.939748i	$0.388940\pi$
$660$	183.278	+	186.178i	0.277693	+	0.282088i
$661$	247.564	−	90.1059i	0.374529	−	0.136318i	−0.147895	−	0.989003i	$-0.547250\pi$
$661$	247.564	−	90.1059i	0.374529	−	0.136318i	0.522425	+	0.852686i	$0.325028\pi$
$662$	−296.375	−	67.3741i	−0.447697	−	0.101774i
$663$	118.335	−	141.852i	0.178484	−	0.213954i
$664$	935.731	−	25.7832i	1.40923	−	0.0388302i
$665$	0.721837	−	1.25026i	0.00108547	−	0.00188009i
$666$	−455.432	+	349.745i	−0.683832	+	0.525142i
$667$	−752.638	+	434.536i	−1.12839	+	0.651478i
$668$	−28.0934	+	58.5976i	−0.0420560	+	0.0877210i
$669$	−146.766	−	818.588i	−0.219381	−	1.22360i
$670$	340.897	−	368.042i	0.508802	−	0.549317i
$671$	50.7454	−	60.4760i	0.0756265	−	0.0901282i
$672$	1.09998	+	3.80384i	0.00163687	+	0.00566048i
$673$	262.025	+	95.3693i	0.389339	+	0.141708i	0.529270	−	0.848453i	$-0.322466\pi$
$673$	262.025	+	95.3693i	0.389339	+	0.141708i	−0.139931	+	0.990161i	$0.544688\pi$
$674$	−138.006	+	214.084i	−0.204757	+	0.317632i
$675$	11.7469	−	33.1613i	0.0174029	−	0.0491278i
$676$	272.270	+	600.617i	0.402766	+	0.888487i
$677$	−213.983	−	77.8835i	−0.316076	−	0.115042i	0.179111	−	0.983829i	$-0.442678\pi$
$677$	−213.983	−	77.8835i	−0.316076	−	0.115042i	−0.495186	+	0.868787i	$0.664900\pi$
$678$	−36.0919	+	781.987i	−0.0532328	+	1.15337i
$679$	0.855279	−	1.01928i	0.00125962	−	0.00150115i
$680$	392.475	−	1178.34i	0.577169	−	1.73285i
$681$	−452.135	−	163.094i	−0.663928	−	0.239491i
$682$	41.6513	+	330.039i	0.0610723	+	0.483928i
$683$	662.983	−	382.773i	0.970692	−	0.560429i	0.0712449	−	0.997459i	$-0.477303\pi$
$683$	662.983	−	382.773i	0.970692	−	0.560429i	0.899447	+	0.437030i	$0.143969\pi$
$684$	−174.588	+	172.859i	−0.255246	+	0.252718i
$685$	−273.453	+	473.634i	−0.399201	+	0.691437i
$686$	−3.13370	+	7.45216i	−0.00456808	+	0.0108632i
$687$	1232.94	+	213.749i	1.79468	+	0.311135i
$688$	−618.487	−	240.254i	−0.898964	−	0.349207i
$689$	82.3761	−	29.9825i	0.119559	−	0.0435159i
$690$	−892.835	−	822.228i	−1.29396	−	1.19164i
$691$	460.568	−	81.2105i	0.666523	−	0.117526i	0.169858	−	0.985468i	$-0.445669\pi$
$691$	460.568	−	81.2105i	0.666523	−	0.117526i	0.496665	+	0.867942i	$0.334558\pi$
$692$	383.580	+	37.7080i	0.554306	+	0.0544913i
$693$	−0.264715	+	1.55344i	−0.000381985	+	0.00224161i
$694$	−2.96706	+	60.5097i	−0.00427531	+	0.0871898i
$695$	−282.390	−	336.539i	−0.406316	−	0.484229i
$696$	250.346	−	465.780i	0.359693	−	0.669225i
$697$	−301.412	+	1709.39i	−0.432442	+	2.45250i
$698$	−330.215	+	102.173i	−0.473088	+	0.146380i
$699$	588.629	−	342.105i	0.842102	−	0.489420i
$700$	−0.214345	+	0.0164386i	−0.000306207	+	2.34837e-5i
$701$	−88.4726			−0.126209			−0.0631046	−	0.998007i	$-0.520100\pi$
$701$	−88.4726			−0.126209			−0.0631046	+	0.998007i	$0.520100\pi$
$702$	92.8356	+	58.7183i	0.132244	+	0.0836442i
$703$			217.716i			0.309695i
$704$	−162.907	+	217.419i	−0.231402	+	0.308834i
$705$	−225.001	+	0.646640i	−0.319150	+	0.000917219i
$706$	−741.134	+	229.317i	−1.04976	+	0.324811i
$707$	−5.61420	−	0.989935i	−0.00794088	−	0.00140019i
$708$	−407.280	+	280.442i	−0.575255	+	0.396104i
$709$	−0.313958	+	0.263442i	−0.000442819	+	0.000371569i	−0.643009	−	0.765859i	$-0.722314\pi$
$709$	−0.313958	+	0.263442i	−0.000442819	+	0.000371569i	0.642566	+	0.766230i	$0.277870\pi$
$710$	−64.4189	+	1313.75i	−0.0907309	+	1.85035i
$711$	28.8047	−	5.24993i	0.0405129	−	0.00738386i
$712$	267.740	−	337.542i	0.376040	−	0.474075i
$713$	−268.373	−	1522.02i	−0.376400	−	2.13467i
$714$	7.15026	−	2.23492i	0.0100144	−	0.00313014i
$715$	−15.1469	−	41.6158i	−0.0211845	−	0.0582039i
$716$	655.643	−	641.729i	0.915702	−	0.896270i
$717$	442.173	−	162.378i	0.616699	−	0.226469i
$718$	442.519	−	1052.34i	0.616322	−	1.46565i
$719$	−437.936	−	252.842i	−0.609090	−	0.351658i	0.163519	−	0.986540i	$-0.447715\pi$
$719$	−437.936	−	252.842i	−0.609090	−	0.351658i	−0.772609	+	0.634882i	$0.781049\pi$
$720$	725.202	+	139.646i	1.00722	+	0.193953i
$721$	−1.46872	−	2.54389i	−0.00203706	−	0.00352828i
$722$	−78.7372	−	623.901i	−0.109054	−	0.864129i
$723$	−234.154	−	277.431i	−0.323865	−	0.383722i
$724$	1197.15	−	307.054i	1.65352	−	0.424108i
$725$	21.9921	+	18.4536i	0.0303340	+	0.0254532i
$726$	548.775	−	283.941i	0.755888	−	0.391103i
$727$	−317.879	+	873.365i	−0.437247	+	1.20133i	0.504028	+	0.863687i	$0.331851\pi$
$727$	−317.879	+	873.365i	−0.437247	+	1.20133i	−0.941275	+	0.337640i	$0.890371\pi$
$728$	0.0983068	−	0.663995i	0.000135037	−	0.000912080i
$729$	−728.892	+	12.5700i	−0.999851	+	0.0172427i
$730$	708.201	−	1098.61i	0.970139	−	1.50494i
$731$	−429.341	+	1179.60i	−0.587334	+	1.61369i
$732$	21.1951	−	222.160i	0.0289550	−	0.303497i
$733$	465.367	+	390.489i	0.634880	+	0.532728i	0.902441	−	0.430813i	$-0.141773\pi$
$733$	465.367	+	390.489i	0.634880	+	0.532728i	−0.267561	+	0.963541i	$0.586218\pi$
$734$	107.327	−	115.873i	0.146222	−	0.157865i
$735$	486.245	+	576.114i	0.661558	+	0.783828i
$736$	706.474	−	1045.97i	0.959883	−	1.42115i
$737$	103.807	+	179.799i	0.140851	+	0.243961i
$738$	−1031.18	−	44.6237i	−1.39726	−	0.0604657i
$739$	−1027.02	−	592.950i	−1.38974	−	0.802368i	−0.396457	−	0.918053i	$-0.629760\pi$
$739$	−1027.02	−	592.950i	−1.38974	−	0.802368i	−0.993286	+	0.115685i	$0.963094\pi$
$740$	540.088	−	369.606i	0.729848	−	0.499467i
$741$	39.0949	−	14.3568i	0.0527597	−	0.0193749i
$742$	3.46658	+	0.788047i	0.00467194	+	0.00106206i
$743$	66.6908	+	183.232i	0.0897589	+	0.246610i	0.976447	−	0.215758i	$-0.0692221\pi$
$743$	66.6908	+	183.232i	0.0897589	+	0.246610i	−0.886688	+	0.462368i	$0.847000\pi$
$744$	626.092	+	701.649i	0.841522	+	0.943077i
$745$	139.654	+	792.018i	0.187455	+	1.06311i
$746$	−541.511	−	1053.99i	−0.725886	−	1.41286i
$747$	1036.03	−	188.827i	1.38692	−	0.252780i
$748$	417.854	+	299.313i	0.558628	+	0.400152i
$749$	−3.37313	+	2.83039i	−0.00450351	+	0.00377889i
$750$	280.729	−	672.998i	0.374305	−	0.897330i
$751$	352.727	+	62.1954i	0.469677	+	0.0828167i	0.403477	−	0.914990i	$-0.367801\pi$
$751$	352.727	+	62.1954i	0.469677	+	0.0828167i	0.0661997	+	0.997806i	$0.478913\pi$
$752$	−35.6794	−	231.246i	−0.0474460	−	0.307508i
$753$	11.8490	−	0.0340533i	0.0157357	−	4.52235e-5i
$754$	−71.4074	+	54.1870i	−0.0947047	+	0.0718660i
$755$			128.446i			0.170127i
$756$	1.87413	+	4.04123i	0.00247900	+	0.00534555i
$757$	−692.369			−0.914622			−0.457311	−	0.889307i	$-0.651187\pi$
$757$	−692.369			−0.914622			−0.457311	+	0.889307i	$0.651187\pi$
$758$	−112.580	−	148.357i	−0.148522	−	0.195722i
$759$	434.295	−	252.407i	0.572194	−	0.332552i
$760$	209.459	−	185.825i	0.275604	−	0.244506i
$761$	202.751	−	1149.86i	0.266427	−	1.51098i	−0.498514	−	0.866882i	$-0.666121\pi$
$761$	202.751	−	1149.86i	0.266427	−	1.51098i	0.764941	−	0.644100i	$-0.222768\pi$
$762$	−497.947	+	380.123i	−0.653473	+	0.498849i
$763$	1.40812	+	1.67813i	0.00184550	+	0.00219938i
$764$	−729.617	−	522.633i	−0.954997	−	0.684075i
$765$	234.713	−	1377.37i	0.306814	−	1.80048i
$766$	−335.581	+	172.412i	−0.438095	+	0.225081i
$767$	82.5515	−	14.5561i	0.107629	−	0.0189779i
$768$	−30.7290	+	767.385i	−0.0400117	+	0.999199i
$769$	332.286	−	120.942i	0.432102	−	0.157272i	−0.116807	−	0.993155i	$-0.537266\pi$
$769$	332.286	−	120.942i	0.432102	−	0.157272i	0.548908	+	0.835882i	$0.315044\pi$
$770$	0.398115	−	1.75129i	0.000517033	−	0.00227440i
$771$	220.752	+	38.2707i	0.286319	+	0.0496378i
$772$	−561.847	+	384.497i	−0.727782	+	0.498053i
$773$	−530.607	+	919.038i	−0.686425	+	1.18892i	0.286561	+	0.958062i	$0.407488\pi$
$773$	−530.607	+	919.038i	−0.686425	+	1.18892i	−0.972987	+	0.230862i	$0.925845\pi$
$774$	−728.820	−	161.280i	−0.941627	−	0.208373i
$775$	−44.2137	+	25.5268i	−0.0570500	+	0.0329378i
$776$	219.858	−	135.143i	0.283322	−	0.174153i
$777$	3.71332	+	1.33947i	0.00477905	+	0.00172389i
$778$	234.062	+	216.798i	0.300851	+	0.278661i
$779$	−251.543	+	299.778i	−0.322905	+	0.384824i
$780$	−101.984	−	72.6100i	−0.130749	−	0.0930898i
$781$	−511.521	−	186.178i	−0.654956	−	0.238384i
$782$	−2007.09	−	1293.84i	−2.56662	−	1.65453i
$783$	198.639	−	560.752i	0.253689	−	0.716158i
$784$	−516.692	+	589.612i	−0.659046	+	0.752057i
$785$	−547.286	−	199.196i	−0.697179	−	0.253752i
$786$	442.537	−	690.845i	0.563024	−	0.878938i
$787$	936.718	−	1116.34i	1.19024	−	1.41847i	0.305621	−	0.952153i	$-0.401136\pi$
$787$	936.718	−	1116.34i	1.19024	−	1.41847i	0.884617	−	0.466318i	$-0.154420\pi$
$788$	−776.027	+	199.041i	−0.984805	+	0.252590i
$789$	213.113	+	1188.64i	0.270105	+	1.50651i
$790$	−33.1068	+	4.17812i	−0.0419074	+	0.00528877i
$791$	4.66048	−	2.69073i	0.00589188	−	0.00340168i
$792$	−143.924	+	269.632i	−0.181722	+	0.340444i
$793$	−18.9154	+	32.7624i	−0.0238530	+	0.0413145i
$794$	−217.407	−	91.4218i	−0.273813	−	0.115141i
$795$	424.739	−	509.149i	0.534263	−	0.640438i
$796$	−760.657	+	744.515i	−0.955599	+	0.935320i
$797$	508.103	−	184.934i	0.637519	−	0.232038i	−0.00298155	−	0.999996i	$-0.500949\pi$
$797$	508.103	−	184.934i	0.637519	−	0.232038i	0.640501	+	0.767958i	$0.278727\pi$
$798$	1.64800	+	0.369658i	0.00206517	+	0.000463231i
$799$	−435.949	+	76.8696i	−0.545618	+	0.0962073i
$800$	−40.4504	−	10.1125i	−0.0505630	−	0.0126406i
$801$	239.928	−	421.140i	0.299536	−	0.525768i
$802$	271.814	+	13.3283i	0.338920	+	0.0166188i
$803$	347.711	+	414.386i	0.433015	+	0.516047i
$804$	529.945	+	252.201i	0.659135	+	0.313683i
$805$	−1.44891	+	8.21718i	−0.00179989	+	0.0102077i
$806$	−47.1193	−	152.286i	−0.0584606	−	0.188940i
$807$	−667.493	−	382.824i	−0.827129	−	0.474379i
$808$	−972.427	−	526.265i	−1.20350	−	0.651317i
$809$	1070.62			1.32338			0.661692	−	0.749776i	$-0.269839\pi$
$809$	1070.62			1.32338			0.661692	+	0.749776i	$0.269839\pi$
$810$	830.256	+	31.1488i	1.02501	+	0.0384553i
$811$			1307.05i			1.61165i	0.592153	+	0.805826i	$0.298278\pi$
$811$			1307.05i			1.61165i	−0.592153	+	0.805826i	$0.701722\pi$
$812$	−3.62454	+	0.277974i	−0.00446372	+	0.000342333i
$813$	−146.465	+	255.378i	−0.180154	+	0.314118i
$814$	80.0583	+	258.742i	0.0983517	+	0.317865i
$815$	1154.34	+	203.541i	1.41637	+	0.249744i
$816$	1452.74	+	26.9866i	1.78032	+	0.0330718i
$817$	−216.800	+	181.917i	−0.265361	+	0.222665i
$818$	255.853	+	12.5456i	0.312779	+	0.0153370i
$819$	−0.00434040	−	0.755124i	−5.29963e−6	−	0.000922007i
$820$	1170.69	+	115.085i	1.42767	+	0.140348i
$821$	113.123	+	641.554i	0.137787	+	0.781430i	0.972878	+	0.231318i	$0.0743038\pi$
$821$	113.123	+	641.554i	0.137787	+	0.781430i	−0.835091	+	0.550112i	$0.814585\pi$
$822$	−624.312	−	140.037i	−0.759504	−	0.170362i
$823$	175.770	+	482.923i	0.213572	+	0.586784i	0.999503	−	0.0315306i	$-0.0100382\pi$
$823$	175.770	+	482.923i	0.213572	+	0.586784i	−0.785931	+	0.618314i	$0.787816\pi$
$824$	−114.349	−	558.135i	−0.138773	−	0.677349i
$825$	−12.7419	−	10.6295i	−0.0154447	−	0.0128842i
$826$	3.13360	+	1.31771i	0.00379371	+	0.00159529i
$827$	−144.231	−	83.2717i	−0.174402	−	0.100691i	0.410258	−	0.911970i	$-0.365439\pi$
$827$	−144.231	−	83.2717i	−0.174402	−	0.100691i	−0.584660	+	0.811278i	$0.698772\pi$
$828$	606.505	−	1283.94i	0.732494	−	1.55065i
$829$	569.032	+	985.592i	0.686407	+	1.18889i	0.972992	+	0.230838i	$0.0741466\pi$
$829$	569.032	+	985.592i	0.686407	+	1.18889i	−0.286585	+	0.958055i	$0.592520\pi$
$830$	−1190.77	+	150.277i	−1.43466	+	0.181056i
$831$	−927.901	+	166.365i	−1.11661	+	0.200199i
$832$	58.7870	−	116.160i	0.0706574	−	0.139615i
$833$	1136.20	+	953.389i	1.36399	+	1.14452i
$834$	277.229	−	432.782i	0.332409	−	0.518923i
$835$	28.4971	−	78.2951i	0.0341283	−	0.0937666i
$836$	47.8445	+	105.543i	0.0572302	+	0.126248i
$837$	816.247	+	673.006i	0.975206	+	0.804069i
$838$	687.236	+	443.016i	0.820091	+	0.528659i
$839$	−254.878	+	700.272i	−0.303788	+	0.834650i	0.690045	+	0.723766i	$0.257591\pi$
$839$	−254.878	+	700.272i	−0.303788	+	0.834650i	−0.993833	+	0.110884i	$0.964632\pi$
$840$	−1.88073	−	4.71576i	−0.00223896	−	0.00561400i
$841$	−272.360	−	228.537i	−0.323853	−	0.271745i
$842$	224.077	+	207.550i	0.266125	+	0.246496i
$843$	−80.8581	+	224.158i	−0.0959171	+	0.265905i
$844$	−690.511	+	1440.28i	−0.818141	+	1.70649i
$845$	−422.759	−	732.241i	−0.500307	−	0.866557i
$846$	−79.2516	−	251.016i	−0.0936780	−	0.296710i
$847$	−3.67852	−	2.12380i	−0.00434300	−	0.00250743i
$848$	589.605	+	357.484i	0.695289	+	0.421561i
$849$	−74.4842	+	429.638i	−0.0877317	+	0.506051i
$850$	−17.4863	+	76.9215i	−0.0205721	+	0.0904958i
$851$	−430.372	−	1182.44i	−0.505725	−	1.38947i
$852$	−1489.45	+	386.590i	−1.74818	+	0.453744i
$853$	−202.360	−	1147.64i	−0.237233	−	1.34542i	−0.837859	−	0.545886i	$-0.816193\pi$
$853$	−202.360	−	1147.64i	−0.237233	−	1.34542i	0.600626	−	0.799530i	$-0.294918\pi$
$854$	−1.36460	+	0.701092i	−0.00159789	+	0.000820951i
$855$	201.093	−	242.470i	0.235196	−	0.283591i
$856$	−794.187	+	314.093i	−0.927788	+	0.366932i
$857$	350.934	−	294.468i	0.409491	−	0.343604i	−0.414658	−	0.909978i	$-0.636099\pi$
$857$	350.934	−	294.468i	0.409491	−	0.343604i	0.824148	+	0.566374i	$0.191654\pi$
$858$	41.1827	−	31.4381i	0.0479985	−	0.0366411i
$859$	1043.94	+	184.076i	1.21530	+	0.214291i	0.744302	−	0.667843i	$-0.232782\pi$
$859$	1043.94	+	184.076i	1.21530	+	0.214291i	0.471000	+	0.882133i	$0.343893\pi$
$860$	819.333	+	228.985i	0.952713	+	0.266261i
$861$	3.56537	+	6.13461i	0.00414096	+	0.00712499i
$862$	773.890	+	1019.83i	0.897784	+	1.18310i
$863$			842.741i			0.976525i	0.872697	+	0.488262i	$0.162369\pi$
$863$			842.741i			0.976525i	−0.872697	+	0.488262i	$0.837631\pi$
$864$	97.1765	+	858.518i	0.112473	+	0.993655i
$865$	−494.182			−0.571308
$866$	−547.588	+	415.533i	−0.632318	+	0.479830i
$867$	−5.40855	−	1881.93i	−0.00623824	−	2.17062i
$868$	1.74002	−	6.22599i	0.00200463	−	0.00717280i
$869$	2.39808	−	13.6002i	0.00275958	−	0.0156504i
$870$	−261.017	+	625.743i	−0.300020	+	0.719245i
$871$	−63.9500	−	76.2126i	−0.0734213	−	0.0875001i
$872$	156.261	+	395.107i	0.179199	+	0.453104i
$873$	221.330	−	187.896i	0.253528	−	0.215231i
$874$	−246.030	−	478.872i	−0.281499	−	0.547908i
$875$	−4.93671	+	0.870475i	−0.00564195	+	0.000994829i
$876$	1473.91	+	407.361i	1.68255	+	0.465024i
$877$	−919.491	+	334.667i	−1.04845	+	0.381605i	−0.808078	−	0.589076i	$-0.799492\pi$
$877$	−919.491	+	334.667i	−1.04845	+	0.381605i	−0.240373	+	0.970681i	$0.577270\pi$
$878$	176.155	+	40.0448i	0.200632	+	0.0456091i
$879$	−124.073	−	337.863i	−0.141152	−	0.384372i
$880$	180.598	−	297.864i	0.205225	−	0.338481i
$881$	22.0835	−	38.2497i	0.0250664	−	0.0434163i	−0.853220	−	0.521551i	$-0.825354\pi$
$881$	22.0835	−	38.2497i	0.0250664	−	0.0434163i	0.878286	+	0.478135i	$0.158687\pi$
$882$	−473.595	+	744.028i	−0.536956	+	0.843569i
$883$	−445.575	+	257.253i	−0.504615	+	0.291339i	−0.730617	−	0.682787i	$-0.760768\pi$
$883$	−445.575	+	257.253i	−0.504615	+	0.291339i	0.226002	+	0.974127i	$0.427434\pi$
$884$	−222.100	−	106.481i	−0.251244	−	0.120454i
$885$	484.516	−	408.935i	0.547475	−	0.462074i
$886$	398.735	−	430.486i	0.450039	−	0.485875i
$887$	−918.503	+	1094.63i	−1.03552	+	1.23408i	−0.0637919	+	0.997963i	$0.520319\pi$
$887$	−918.503	+	1094.63i	−1.03552	+	1.23408i	−0.971725	+	0.236117i	$0.924125\pi$
$888$	601.212	+	474.076i	0.677040	+	0.533870i
$889$	4.04682	+	1.47292i	0.00455210	+	0.00165683i
$890$	−299.298	+	464.292i	−0.336290	+	0.521676i
$891$	−113.880	+	324.438i	−0.127811	+	0.364128i
$892$	−1009.93	+	457.818i	−1.13221	+	0.513249i
$893$	−93.7832	−	34.1343i	−0.105020	−	0.0382243i
$894$	−835.646	+	432.371i	−0.934727	+	0.483636i
$895$	−756.109	+	901.096i	−0.844814	+	1.00681i
$896$	4.55607	−	2.66763i	0.00508490	−	0.00297727i
$897$	−183.949	+	155.254i	−0.205071	+	0.173082i
$898$	31.9810	+	253.413i	0.0356136	+	0.282197i
$899$	−747.647	+	431.654i	−0.831643	+	0.480149i
$900$	−46.7078	−	4.32071i	−0.0518976	−	0.00480079i
$901$	652.250	−	1129.73i	0.723918	−	1.25386i
$902$	−188.710	+	448.765i	−0.209213	+	0.497522i
$903$	1.76891	+	4.81692i	0.00195893	+	0.00533435i
$904$	1022.52	−	209.490i	1.13111	−	0.231737i
$905$	−1489.06	+	541.973i	−1.64537	+	0.598865i
$906$	−143.426	+	44.8299i	−0.158306	+	0.0494811i
$907$	−1252.53	+	220.855i	−1.38096	+	0.243501i	−0.814297	−	0.580449i	$-0.802877\pi$
$907$	−1252.53	+	220.855i	−1.38096	+	0.243501i	−0.566663	+	0.823949i	$0.691766\pi$
$908$	−62.6985	+	637.794i	−0.0690513	+	0.702416i
$909$	−1171.32	−	418.717i	−1.28858	−	0.460634i
$910$	−0.0421498	+	0.859595i	−4.63185e−5	+	0.000944610i
$911$	−985.284	−	1174.22i	−1.08154	−	1.28893i	−0.954882	−	0.296985i	$-0.904019\pi$
$911$	−985.284	−	1174.22i	−1.08154	−	1.28893i	−0.126659	−	0.991946i	$-0.540425\pi$
$912$	280.602	+	169.031i	0.307678	+	0.185341i
$913$	86.2528	−	489.164i	0.0944718	−	0.535776i
$914$	803.034	−	248.470i	0.878593	−	0.271849i
$915$	0.822341	+	286.137i	0.000898734	+	0.312718i
$916$	−127.582	−	1663.56i	−0.139282	−	1.81611i
$917$	−5.64002			−0.00615051
$918$	1619.93	−	218.642i	1.76463	−	0.238172i
$919$		−	958.663i		−	1.04316i	−0.853203	−	0.521580i	$-0.825343\pi$
$919$		−	958.663i		−	1.04316i	0.853203	−	0.521580i	$-0.174657\pi$
$920$	−770.263	+	1423.29i	−0.837243	+	1.54705i
$921$	309.137	+	531.904i	0.335653	+	0.577529i
$922$	1318.31	−	407.904i	1.42984	−	0.442412i
$923$	256.889	+	45.2964i	0.278319	+	0.0490752i
$924$	2.09448	−	0.166687i	0.00226676	−	0.000180397i
$925$	−31.8423	+	26.7189i	−0.0344241	+	0.0288853i
$926$	−53.9772	+	1100.80i	−0.0582908	+	1.18877i
$927$	−222.674	−	601.021i	−0.240210	−	0.648351i
$928$	−684.010	−	171.001i	−0.737079	−	0.184268i
$929$	249.626	+	1415.70i	0.268704	+	1.52389i	0.758277	+	0.651933i	$0.226042\pi$
$929$	249.626	+	1415.70i	0.268704	+	1.52389i	−0.489573	+	0.871962i	$0.662847\pi$
$930$	−886.914	−	816.776i	−0.953671	−	0.878253i
$931$	114.369	+	314.227i	0.122846	+	0.337516i
$932$	−634.966	−	648.733i	−0.681294	−	0.696065i
$933$	125.280	−	722.637i	0.134277	−	0.774531i
$934$	−479.774	+	1140.93i	−0.513677	+	1.22156i
$935$	−570.731	−	329.512i	−0.610408	−	0.352419i
$936$	45.4837	−	139.221i	0.0485937	−	0.148740i
$937$	151.138	+	261.779i	0.161300	+	0.279380i	0.935335	−	0.353763i	$-0.115098\pi$
$937$	151.138	+	261.779i	0.161300	+	0.279380i	−0.774035	+	0.633143i	$0.781765\pi$
$938$	−0.505164	−	4.00284i	−0.000538555	−	0.00426742i
$939$	−139.111	+	385.649i	−0.148148	+	0.410701i
$940$	74.5344	+	290.596i	0.0792919	+	0.309145i
$941$	−629.923	−	528.568i	−0.669419	−	0.561709i	0.243475	−	0.969907i	$-0.421713\pi$
$941$	−629.923	−	528.568i	−0.669419	−	0.561709i	−0.912893	+	0.408198i	$0.866157\pi$
$942$	31.4141	−	680.636i	0.0333483	−	0.722543i
$943$	773.569	−	2125.36i	0.820328	−	2.25383i
$944$	495.868	+	434.541i	0.525284	+	0.460319i
$945$	−2.89833	−	4.92157i	−0.00306702	−	0.00520801i
$946$	−190.759	+	295.919i	−0.201648	+	0.312811i
$947$	−456.809	+	1255.07i	−0.482375	+	1.32531i	0.425076	+	0.905158i	$0.360247\pi$
$947$	−456.809	+	1255.07i	−0.482375	+	1.32531i	−0.907451	+	0.420157i	$0.861975\pi$
$948$	−16.2203	−	35.5097i	−0.0171100	−	0.0374575i
$949$	−198.573	−	166.623i	−0.209245	−	0.175577i
$950$	−12.0852	+	13.0476i	−0.0127213	+	0.0137343i
$951$	−417.369	+	74.8307i	−0.438873	+	0.0786864i
$952$	−5.23063	−	8.50948i	−0.00549436	−	0.00893853i
$953$	−156.667	−	271.356i	−0.164394	−	0.284739i	0.772046	−	0.635567i	$-0.219233\pi$
$953$	−156.667	−	271.356i	−0.164394	−	0.284739i	−0.936440	+	0.350828i	$0.885900\pi$
$954$	716.770	+	296.572i	0.751331	+	0.310872i
$955$	996.558	+	575.363i	1.04352	+	0.602474i
$956$	−354.703	−	518.311i	−0.371028	−	0.542166i
$957$	−215.463	−	179.742i	−0.225144	−	0.187818i
$958$	624.888	+	142.054i	0.652284	+	0.148282i
$959$	1.50436	+	4.13319i	0.00156868	+	0.00430990i
$960$	−57.0493	−	983.045i	−0.0594263	−	1.02401i
$961$	−99.7172	−	565.524i	−0.103764	−	0.588475i
$962$	−59.3115	−	115.444i	−0.0616544	−	0.120004i
$963$	−829.300	+	485.173i	−0.861163	+	0.503814i
$964$	−281.876	+	393.511i	−0.292402	+	0.408206i
$965$	668.692	−	561.099i	0.692945	−	0.581450i
$966$	−9.68121	+	1.25006i	−0.0100220	+	0.00129406i
$967$	−1793.17	−	316.184i	−1.85437	−	0.326975i	−0.868654	−	0.495419i	$-0.835014\pi$
$967$	−1793.17	−	316.184i	−1.85437	−	0.326975i	−0.985711	+	0.168444i	$0.946126\pi$
$968$	−546.736	−	616.273i	−0.564810	−	0.636646i
$969$	308.333	−	537.611i	0.318198	−	0.554811i
$970$	−263.589	+	200.022i	−0.271741	+	0.206209i
$971$		−	1200.07i		−	1.23592i	−0.786211	−	0.617958i	$-0.787960\pi$
$971$		−	1200.07i		−	1.23592i	0.786211	−	0.617958i	$-0.212040\pi$
$972$	254.993	+	937.957i	0.262339	+	0.964976i
$973$	−3.53321			−0.00363125
$974$	6.34422	+	8.36038i	0.00651357	+	0.00858356i
$975$	6.89764	+	3.95597i	0.00707450	+	0.00405740i
$976$	−294.079	+	45.3740i	−0.301310	+	0.0464897i
$977$	35.8447	−	203.285i	0.0366885	−	0.208071i	−0.960953	−	0.276712i	$-0.910755\pi$
$977$	35.8447	−	203.285i	0.0366885	−	0.208071i	0.997641	+	0.0686410i	$0.0218663\pi$
$978$	175.607	+	1360.01i	0.179557	+	1.39060i
$979$	−146.949	−	175.127i	−0.150101	−	0.178883i
$980$	585.344	−	817.164i	0.597290	−	0.833841i
$981$	241.373	+	412.576i	0.246048	+	0.420566i
$982$	1072.69	−	551.117i	1.09235	−	0.561219i
$983$	1420.62	−	250.494i	1.44519	−	0.254826i	0.604612	−	0.796520i	$-0.293328\pi$
$983$	1420.62	−	250.494i	1.44519	−	0.254826i	0.840575	+	0.541695i	$0.182217\pi$
$984$	280.086	+	1347.39i	0.284640	+	1.36930i
$985$	965.250	−	351.322i	0.979949	−	0.356672i
$986$	−295.691	+	1300.73i	−0.299889	+	1.31920i
$987$	−1.15918	+	1.38954i	−0.00117444	+	0.00140785i
$988$	−31.3612	−	45.8267i	−0.0317421	−	0.0463833i
$989$	817.858	−	1416.57i	0.826955	−	1.43233i
$990$	149.826	−	362.107i	0.151339	−	0.365764i
$991$	814.600	−	470.309i	0.821998	−	0.474581i	−0.0291073	−	0.999576i	$-0.509266\pi$
$991$	814.600	−	470.309i	0.821998	−	0.474581i	0.851105	+	0.524996i	$0.175933\pi$
$992$	701.789	−	1039.03i	0.707448	−	1.04741i
$993$	80.4571	+	448.749i	0.0810242	+	0.451913i
$994$	7.76079	+	7.18839i	0.00780764	+	0.00723178i
$995$	877.215	−	1045.42i	0.881623	−	1.05068i
$996$	−583.403	−	1277.19i	−0.585746	−	1.28232i
$997$	173.772	+	63.2477i	0.174294	+	0.0634380i	0.427693	−	0.903924i	$-0.359326\pi$
$997$	173.772	+	63.2477i	0.174294	+	0.0634380i	−0.253399	+	0.967362i	$0.581549\pi$
$998$	9.79773	+	6.31596i	0.00981737	+	0.00632861i
$999$	749.632	+	424.225i	0.750382	+	0.424650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.31.8	yes	204
3.2	odd	2		324.3.j.a.307.27		204
4.3	odd	2	inner	108.3.j.a.31.16	yes	204
12.11	even	2		324.3.j.a.307.19		204
27.7	even	9	inner	108.3.j.a.7.16	yes	204
27.20	odd	18		324.3.j.a.19.19		204
108.7	odd	18	inner	108.3.j.a.7.8	✓	204
108.47	even	18		324.3.j.a.19.27		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.8	✓	204	108.7	odd	18	inner
108.3.j.a.7.16	yes	204	27.7	even	9	inner
108.3.j.a.31.8	yes	204	1.1	even	1	trivial
108.3.j.a.31.16	yes	204	4.3	odd	2	inner
324.3.j.a.19.19		204	27.20	odd	18
324.3.j.a.19.27		204	108.47	even	18
324.3.j.a.307.19		204	12.11	even	2
324.3.j.a.307.27		204	3.2	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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59321 + 1.20900i) q^{2} +(2.60238 + 1.49253i) q^{3} +(1.07665 - 3.85238i) q^{4} +(-0.890579 + 5.05073i) q^{5} +(-5.95060 + 0.768354i) q^{6} +(0.0265129 + 0.0315969i) q^{7} +(2.94218 + 7.43932i) q^{8} +(4.54473 + 7.76823i) q^{9} +O(q^{10})\)	\(q+(-1.59321 + 1.20900i) q^{2} +(2.60238 + 1.49253i) q^{3} +(1.07665 - 3.85238i) q^{4} +(-0.890579 + 5.05073i) q^{5} +(-5.95060 + 0.768354i) q^{6} +(0.0265129 + 0.0315969i) q^{7} +(2.94218 + 7.43932i) q^{8} +(4.54473 + 7.76823i) q^{9} +(-4.68743 - 9.12359i) q^{10} +(4.18050 - 0.737135i) q^{11} +(8.55163 - 8.41841i) q^{12} +(-1.91152 + 0.695736i) q^{13} +(-0.0804412 - 0.0182865i) q^{14} +(-9.85597 + 11.8147i) q^{15} +(-13.6816 - 8.29533i) q^{16} +(-15.1353 + 26.2152i) q^{17} +(-16.6325 - 6.88189i) q^{18} +(-5.91027 + 3.41230i) q^{19} +(18.4985 + 8.86872i) q^{20} +(0.0218374 + 0.121798i) q^{21} +(-5.76923 + 6.22863i) q^{22} +(25.3540 - 30.2157i) q^{23} +(-3.44673 + 23.7512i) q^{24} +(-1.22440 - 0.445645i) q^{25} +(2.20431 - 3.41948i) q^{26} +(0.232786 + 26.9990i) q^{27} +(0.150268 - 0.0681190i) q^{28} +(-20.7044 - 7.53578i) q^{29} +(1.41874 - 30.7391i) q^{30} +(25.1859 - 30.0153i) q^{31} +(31.8268 - 3.32485i) q^{32} +(11.9794 + 4.32121i) q^{33} +(-7.58027 - 60.0649i) q^{34} +(-0.183199 + 0.105770i) q^{35} +(34.8193 - 9.14433i) q^{36} +(15.9508 - 27.6276i) q^{37} +(5.29086 - 12.5820i) q^{38} +(-6.01290 - 1.04243i) q^{39} +(-40.1943 + 8.23486i) q^{40} +(53.8833 - 19.6119i) q^{41} +(-0.182045 - 0.167649i) q^{42} +(40.8395 - 7.20111i) q^{43} +(1.66121 - 16.8985i) q^{44} +(-43.2827 + 16.0359i) q^{45} +(-3.86358 + 78.7930i) q^{46} +(9.40005 + 11.2025i) q^{47} +(-23.2238 - 42.0078i) q^{48} +(8.50847 - 48.2539i) q^{49} +(2.48951 - 0.770289i) q^{50} +(-78.5146 + 45.6318i) q^{51} +(0.622201 + 8.11296i) q^{52} -43.0946 q^{53} +(-33.0126 - 42.7337i) q^{54} +21.7710i q^{55} +(-0.157053 + 0.290202i) q^{56} +(-20.4737 + 0.0588402i) q^{57} +(42.0972 - 13.0254i) q^{58} +(-40.5818 - 7.15567i) q^{59} +(34.9032 + 50.6892i) q^{60} +(14.2464 - 11.9542i) q^{61} +(-3.83795 + 78.2705i) q^{62} +(-0.124958 + 0.349558i) q^{63} +(-46.6871 + 43.7757i) q^{64} +(-1.81161 - 10.2742i) q^{65} +(-24.3101 + 7.59850i) q^{66} +(16.7275 + 45.9585i) q^{67} +(84.6952 + 86.5316i) q^{68} +(111.078 - 40.7912i) q^{69} +(0.163999 - 0.390001i) q^{70} +(-111.053 - 64.1166i) q^{71} +(-44.4190 + 56.6653i) q^{72} +(63.7153 + 110.358i) q^{73} +(7.98870 + 63.3012i) q^{74} +(-2.52121 - 2.98718i) q^{75} +(6.78216 + 26.4424i) q^{76} +(0.134128 + 0.112547i) q^{77} +(10.8401 - 5.60877i) q^{78} +(1.11267 - 3.05705i) q^{79} +(54.0821 - 61.7146i) q^{80} +(-39.6909 + 70.6090i) q^{81} +(-62.1368 + 96.3907i) q^{82} +(40.0201 - 109.954i) q^{83} +(0.492724 + 0.0470081i) q^{84} +(-118.926 - 99.7911i) q^{85} +(-56.3599 + 60.8477i) q^{86} +(-42.6332 - 50.5128i) q^{87} +(17.7836 + 28.9313i) q^{88} +(-26.9272 - 46.6393i) q^{89} +(49.5711 - 77.8773i) q^{90} +(-0.0726630 - 0.0419520i) q^{91} +(-89.1050 - 130.205i) q^{92} +(110.342 - 40.5206i) q^{93} +(-28.5201 - 6.48339i) q^{94} +(-11.9710 - 32.8901i) q^{95} +(87.7878 + 38.8498i) q^{96} +(-5.60171 - 31.7689i) q^{97} +(44.7831 + 87.1654i) q^{98} +(24.7255 + 29.1250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

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