LMFDB - Embedded newform 380.2.be.b.51.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(51,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 5]))

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

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

chi := DirichletCharacter("380.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.be (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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			51.7
Character	$\chi$	$=$	380.51
Dual form			380.2.be.b.231.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.803525 - 1.16376i) q^{2} +(1.11886 + 0.407232i) q^{3} +(-0.708694 + 1.87023i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-0.425111 - 1.62931i) q^{6} +(-0.611057 - 0.352794i) q^{7} +(2.74596 - 0.678023i) q^{8} +(-1.21212 - 1.01709i) q^{9} +O(q^{10})$	\(q+(-0.803525 - 1.16376i) q^{2} +(1.11886 + 0.407232i) q^{3} +(-0.708694 + 1.87023i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-0.425111 - 1.62931i) q^{6} +(-0.611057 - 0.352794i) q^{7} +(2.74596 - 0.678023i) q^{8} +(-1.21212 - 1.01709i) q^{9} +(-1.00655 + 0.993404i) q^{10} +(3.43606 - 1.98381i) q^{11} +(-1.55455 + 1.80392i) q^{12} +(-0.265787 - 0.730243i) q^{13} +(0.0804309 + 0.994606i) q^{14} +(0.206757 - 1.17258i) q^{15} +(-2.99551 - 2.65084i) q^{16} +(1.66784 - 1.39948i) q^{17} +(-0.209683 + 2.22788i) q^{18} +(2.09018 - 3.82507i) q^{19} +(1.96488 + 0.373166i) q^{20} +(-0.540019 - 0.643570i) q^{21} +(-5.06966 - 2.40472i) q^{22} +(6.79230 + 1.19767i) q^{23} +(3.34846 + 0.359629i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-0.636264 + 0.896082i) q^{26} +(-2.72800 - 4.72504i) q^{27} +(1.09286 - 0.892794i) q^{28} +(-2.16916 + 2.58511i) q^{29} +(-1.53074 + 0.701579i) q^{30} +(4.68498 - 8.11462i) q^{31} +(-0.677986 + 5.61608i) q^{32} +(4.65235 - 0.820335i) q^{33} +(-2.96882 - 0.816451i) q^{34} +(-0.241325 + 0.663036i) q^{35} +(2.76122 - 1.54614i) q^{36} +8.06619i q^{37} +(-6.13099 + 0.641062i) q^{38} -0.925277i q^{39} +(-1.14455 - 2.58650i) q^{40} +(0.167128 - 0.459180i) q^{41} +(-0.315044 + 1.14558i) q^{42} +(-2.88156 + 0.508097i) q^{43} +(1.27506 + 7.83214i) q^{44} +(-0.791157 + 1.37032i) q^{45} +(-4.06398 - 8.86699i) q^{46} +(-6.27735 + 7.48106i) q^{47} +(-2.27205 - 4.18578i) q^{48} +(-3.25107 - 5.63102i) q^{49} +(1.15310 + 0.818759i) q^{50} +(2.43599 - 0.886629i) q^{51} +(1.55408 + 0.0204371i) q^{52} +(-8.25049 - 1.45478i) q^{53} +(-3.30681 + 6.97144i) q^{54} +(-2.55034 - 3.03938i) q^{55} +(-1.91714 - 0.554447i) q^{56} +(3.89631 - 3.42853i) q^{57} +(4.75143 + 0.447194i) q^{58} +(3.63979 - 3.05415i) q^{59} +(2.04646 + 1.21768i) q^{60} +(-1.09052 + 6.18464i) q^{61} +(-13.2080 + 1.06809i) q^{62} +(0.381852 + 1.04913i) q^{63} +(7.08057 - 3.72365i) q^{64} +(-0.672995 + 0.388554i) q^{65} +(-4.69296 - 4.75508i) q^{66} +(2.50692 + 2.10356i) q^{67} +(1.43536 + 4.11104i) q^{68} +(7.11191 + 4.10606i) q^{69} +(0.965529 - 0.251920i) q^{70} +(2.21433 + 12.5581i) q^{71} +(-4.01805 - 1.97104i) q^{72} +(-8.78856 - 3.19877i) q^{73} +(9.38714 - 6.48139i) q^{74} -1.19067 q^{75} +(5.67245 + 6.61992i) q^{76} -2.79951 q^{77} +(-1.07680 + 0.743483i) q^{78} +(2.19489 + 0.798873i) q^{79} +(-2.09040 + 3.41031i) q^{80} +(-0.303771 - 1.72277i) q^{81} +(-0.668669 + 0.174466i) q^{82} +(8.88433 + 5.12937i) q^{83} +(1.58633 - 0.553865i) q^{84} +(-1.66784 - 1.39948i) q^{85} +(2.90671 + 2.94519i) q^{86} +(-3.47973 + 2.00902i) q^{87} +(8.09022 - 7.77720i) q^{88} +(2.09950 + 5.76832i) q^{89} +(2.23045 - 0.180370i) q^{90} +(-0.0952145 + 0.539988i) q^{91} +(-7.05357 + 11.8544i) q^{92} +(8.54637 - 7.17126i) q^{93} +(13.7502 + 1.29414i) q^{94} +(-4.12991 - 1.39421i) q^{95} +(-3.04562 + 6.00751i) q^{96} +(0.738968 + 0.880668i) q^{97} +(-3.94086 + 8.30815i) q^{98} +(-6.18265 - 1.09017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

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 $

$2$	−0.803525	−	1.16376i	−0.568178	−	0.822906i
$2$	−0.803525	−	1.16376i	−0.568178	−	0.822906i
$3$	1.11886	+	0.407232i	0.645974	+	0.235115i	0.644169	−	0.764883i	$-0.277203\pi$
$3$	1.11886	+	0.407232i	0.645974	+	0.235115i	0.00180508	+	0.999998i	$0.499425\pi$
$4$	−0.708694	+	1.87023i	−0.354347	+	0.935114i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	−0.425111	−	1.62931i	−0.173551	−	0.665163i
$7$	−0.611057	−	0.352794i	−0.230958	−	0.133344i	0.380056	−	0.924964i	$-0.375905\pi$
$7$	−0.611057	−	0.352794i	−0.230958	−	0.133344i	−0.611014	+	0.791620i	$0.709238\pi$
$8$	2.74596	−	0.678023i	0.970843	−	0.239717i
$9$	−1.21212	−	1.01709i	−0.404041	−	0.339030i
$10$	−1.00655	+	0.993404i	−0.318300	+	0.314142i
$11$	3.43606	−	1.98381i	1.03601	−	0.598142i	0.117311	−	0.993095i	$-0.462573\pi$
$11$	3.43606	−	1.98381i	1.03601	−	0.598142i	0.918701	+	0.394953i	$0.129239\pi$
$12$	−1.55455	+	1.80392i	−0.448759	+	0.520747i
$13$	−0.265787	−	0.730243i	−0.0737160	−	0.202533i	0.897362	−	0.441295i	$-0.145481\pi$
$13$	−0.265787	−	0.730243i	−0.0737160	−	0.202533i	−0.971078	+	0.238762i	$0.923258\pi$
$14$	0.0804309	+	0.994606i	0.0214961	+	0.265820i
$15$	0.206757	−	1.17258i	0.0533844	−	0.302758i
$16$	−2.99551	−	2.65084i	−0.748876	−	0.662710i
$17$	1.66784	−	1.39948i	0.404510	−	0.339424i	−0.417724	−	0.908574i	$-0.637172\pi$
$17$	1.66784	−	1.39948i	0.404510	−	0.339424i	0.822234	+	0.569150i	$0.192728\pi$
$18$	−0.209683	+	2.22788i	−0.0494229	+	0.525117i
$19$	2.09018	−	3.82507i	0.479520	−	0.877531i
$19$	2.09018	−	3.82507i	0.479520	−	0.877531i
$20$	1.96488	+	0.373166i	0.439360	+	0.0834424i
$21$	−0.540019	−	0.643570i	−0.117842	−	0.140438i
$22$	−5.06966	−	2.40472i	−1.08085	−	0.512689i
$23$	6.79230	+	1.19767i	1.41629	+	0.249731i	0.828821	−	0.559514i	$-0.189012\pi$
$23$	6.79230	+	1.19767i	1.41629	+	0.249731i	0.587471	+	0.809245i	$0.300123\pi$
$24$	3.34846	+	0.359629i	0.683501	+	0.0734089i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	−0.636264	+	0.896082i	−0.124782	+	0.175736i
$27$	−2.72800	−	4.72504i	−0.525005	−	0.909334i
$28$	1.09286	−	0.892794i	0.206531	−	0.168722i
$29$	−2.16916	+	2.58511i	−0.402803	+	0.480042i	−0.928873	−	0.370400i	$-0.879221\pi$
$29$	−2.16916	+	2.58511i	−0.402803	+	0.480042i	0.526069	+	0.850442i	$0.323665\pi$
$30$	−1.53074	+	0.701579i	−0.279473	+	0.128090i
$31$	4.68498	−	8.11462i	0.841447	−	1.45743i	−0.0472239	−	0.998884i	$-0.515037\pi$
$31$	4.68498	−	8.11462i	0.841447	−	1.45743i	0.888671	−	0.458545i	$-0.151629\pi$
$32$	−0.677986	+	5.61608i	−0.119852	+	0.992792i
$33$	4.65235	−	0.820335i	0.809870	−	0.142802i
$34$	−2.96882	−	0.816451i	−0.509148	−	0.140020i
$35$	−0.241325	+	0.663036i	−0.0407914	+	0.112074i
$36$	2.76122	−	1.54614i	0.460203	−	0.257690i
$37$			8.06619i			1.32607i	0.748587	+	0.663036i	$0.230733\pi$
$37$			8.06619i			1.32607i	−0.748587	+	0.663036i	$0.769267\pi$
$38$	−6.13099	+	0.641062i	−0.994578	+	0.103994i
$39$		−	0.925277i		−	0.148163i
$40$	−1.14455	−	2.58650i	−0.180970	−	0.408962i
$41$	0.167128	−	0.459180i	0.0261010	−	0.0717119i	−0.925958	−	0.377627i	$-0.876740\pi$
$41$	0.167128	−	0.459180i	0.0261010	−	0.0717119i	0.952059	+	0.305915i	$0.0989624\pi$
$42$	−0.315044	+	1.14558i	−0.0486124	+	0.176767i
$43$	−2.88156	+	0.508097i	−0.439434	+	0.0774841i	−0.388988	−	0.921243i	$-0.627175\pi$
$43$	−2.88156	+	0.508097i	−0.439434	+	0.0774841i	−0.0504458	+	0.998727i	$0.516064\pi$
$44$	1.27506	+	7.83214i	0.192223	+	1.18074i
$45$	−0.791157	+	1.37032i	−0.117939	+	0.204276i
$46$	−4.06398	−	8.86699i	−0.599202	−	1.30737i
$47$	−6.27735	+	7.48106i	−0.915646	+	1.09122i	0.0798861	+	0.996804i	$0.474544\pi$
$47$	−6.27735	+	7.48106i	−0.915646	+	1.09122i	−0.995532	+	0.0944207i	$0.969900\pi$
$48$	−2.27205	−	4.18578i	−0.327942	−	0.604166i
$49$	−3.25107	−	5.63102i	−0.464439	−	0.804432i
$50$	1.15310	+	0.818759i	0.163073	+	0.115790i
$51$	2.43599	−	0.886629i	0.341107	−	0.124153i
$52$	1.55408	+	0.0204371i	0.215512	+	0.00283411i
$53$	−8.25049	−	1.45478i	−1.13329	−	0.199830i	−0.424623	−	0.905370i	$-0.639593\pi$
$53$	−8.25049	−	1.45478i	−1.13329	−	0.199830i	−0.708670	+	0.705541i	$0.750704\pi$
$54$	−3.30681	+	6.97144i	−0.450000	+	0.948693i
$55$	−2.55034	−	3.03938i	−0.343888	−	0.409830i
$56$	−1.91714	−	0.554447i	−0.256189	−	0.0740911i
$57$	3.89631	−	3.42853i	0.516079	−	0.454120i
$58$	4.75143	+	0.447194i	0.623893	+	0.0587195i
$59$	3.63979	−	3.05415i	0.473860	−	0.397616i	−0.374340	−	0.927291i	$-0.622131\pi$
$59$	3.63979	−	3.05415i	0.473860	−	0.397616i	0.848200	+	0.529676i	$0.177686\pi$
$60$	2.04646	+	1.21768i	0.264197	+	0.157202i
$61$	−1.09052	+	6.18464i	−0.139627	+	0.791862i	0.831899	+	0.554927i	$0.187254\pi$
$61$	−1.09052	+	6.18464i	−0.139627	+	0.791862i	−0.971526	+	0.236935i	$0.923857\pi$
$62$	−13.2080	+	1.06809i	−1.67742	+	0.135648i
$63$	0.381852	+	1.04913i	0.0481089	+	0.132178i
$64$	7.08057	−	3.72365i	0.885071	−	0.465456i
$65$	−0.672995	+	0.388554i	−0.0834748	+	0.0481942i
$66$	−4.69296	−	4.75508i	−0.577663	−	0.585310i
$67$	2.50692	+	2.10356i	0.306269	+	0.256990i	0.782948	−	0.622087i	$-0.213715\pi$
$67$	2.50692	+	2.10356i	0.306269	+	0.256990i	−0.476679	+	0.879078i	$0.658160\pi$
$68$	1.43536	+	4.11104i	0.174063	+	0.498537i
$69$	7.11191	+	4.10606i	0.856173	+	0.494312i
$70$	0.965529	−	0.251920i	0.115403	−	0.0301103i
$71$	2.21433	+	12.5581i	0.262792	+	1.49037i	0.775248	+	0.631657i	$0.217625\pi$
$71$	2.21433	+	12.5581i	0.262792	+	1.49037i	−0.512456	+	0.858714i	$0.671264\pi$
$72$	−4.01805	−	1.97104i	−0.473532	−	0.232290i
$73$	−8.78856	−	3.19877i	−1.02862	−	0.374388i	−0.228066	−	0.973646i	$-0.573240\pi$
$73$	−8.78856	−	3.19877i	−1.02862	−	0.374388i	−0.800556	+	0.599258i	$0.795463\pi$
$74$	9.38714	−	6.48139i	1.09123	−	0.753446i
$75$	−1.19067			−0.137486
$76$	5.67245	+	6.61992i	0.650675	+	0.759357i
$77$	−2.79951			−0.319034
$78$	−1.07680	+	0.743483i	−0.121924	+	0.0841829i
$79$	2.19489	+	0.798873i	0.246944	+	0.0898803i	0.462527	−	0.886605i	$-0.346943\pi$
$79$	2.19489	+	0.798873i	0.246944	+	0.0898803i	−0.215583	+	0.976486i	$0.569165\pi$
$80$	−2.09040	+	3.41031i	−0.233714	+	0.381284i
$81$	−0.303771	−	1.72277i	−0.0337523	−	0.191419i
$82$	−0.668669	+	0.174466i	−0.0738422	+	0.0192665i
$83$	8.88433	+	5.12937i	0.975182	+	0.563021i	0.900812	−	0.434209i	$-0.142972\pi$
$83$	8.88433	+	5.12937i	0.975182	+	0.563021i	0.0743698	+	0.997231i	$0.476305\pi$
$84$	1.58633	−	0.553865i	0.173083	−	0.0604316i
$85$	−1.66784	−	1.39948i	−0.180902	−	0.151795i
$86$	2.90671	+	2.94519i	0.313439	+	0.317588i
$87$	−3.47973	+	2.00902i	−0.373066	+	0.215390i
$88$	8.09022	−	7.77720i	0.862420	−	0.829052i
$89$	2.09950	+	5.76832i	0.222546	+	0.611441i	0.999843	−	0.0176927i	$-0.00563206\pi$
$89$	2.09950	+	5.76832i	0.222546	+	0.611441i	−0.777297	+	0.629134i	$0.783410\pi$
$90$	2.23045	−	0.180370i	0.235110	−	0.0190127i
$91$	−0.0952145	+	0.539988i	−0.00998119	+	0.0566062i
$92$	−7.05357	+	11.8544i	−0.735385	+	1.23590i
$93$	8.54637	−	7.17126i	0.886218	−	0.743625i
$94$	13.7502	+	1.29414i	1.41823	+	0.133480i
$95$	−4.12991	−	1.39421i	−0.423720	−	0.143043i
$96$	−3.04562	+	6.00751i	−0.310842	+	0.613139i
$97$	0.738968	+	0.880668i	0.0750309	+	0.0894183i	0.802254	−	0.596983i	$-0.203634\pi$
$97$	0.738968	+	0.880668i	0.0750309	+	0.0894183i	−0.727223	+	0.686401i	$0.759189\pi$
$98$	−3.94086	+	8.30815i	−0.398087	+	0.839250i
$99$	−6.18265	−	1.09017i	−0.621380	−	0.109566i
$100$	0.0262989	−	1.99983i	0.00262989	−	0.199983i
$101$	16.0545	−	5.84335i	1.59748	−	0.581435i	0.618570	−	0.785729i	$-0.287712\pi$
$101$	16.0545	−	5.84335i	1.59748	−	0.581435i	0.978910	+	0.204294i	$0.0654899\pi$
$102$	−2.98921	−	2.12249i	−0.295976	−	0.210158i
$103$	7.43756	+	12.8822i	0.732845	+	1.26932i	0.955662	+	0.294464i	$0.0951413\pi$
$103$	7.43756	+	12.8822i	0.732845	+	1.26932i	−0.222818	+	0.974860i	$0.571525\pi$
$104$	−1.22496	−	1.82501i	−0.120117	−	0.178957i
$105$	−0.540019	+	0.643570i	−0.0527005	+	0.0628060i
$106$	4.93645	+	10.7706i	0.479471	+	1.04613i
$107$	−3.51534	+	6.08875i	−0.339841	+	0.588621i	−0.984403	−	0.175931i	$-0.943706\pi$
$107$	−3.51534	+	6.08875i	−0.339841	+	0.588621i	0.644562	+	0.764552i	$0.277040\pi$
$108$	10.7702	−	1.75338i	1.03637	−	0.168719i
$109$	6.59747	−	1.16331i	0.631923	−	0.111425i	0.151493	−	0.988458i	$-0.451592\pi$
$109$	6.59747	−	1.16331i	0.631923	−	0.111425i	0.480430	+	0.877033i	$0.340481\pi$
$110$	−1.48786	+	5.41021i	−0.141861	+	0.515843i
$111$	−3.28481	+	9.02494i	−0.311780	+	0.856609i
$112$	0.895226	+	2.67661i	0.0845909	+	0.252916i
$113$			1.09887i			0.103373i	0.998663	+	0.0516864i	$0.0164596\pi$
$113$			1.09887i			0.103373i	−0.998663	+	0.0516864i	$0.983540\pi$
$114$	−7.12078	−	1.77948i	−0.666922	−	0.166663i
$115$		−	6.89708i		−	0.643156i
$116$	−3.29747	−	5.88887i	−0.306162	−	0.546768i
$117$	−0.420558	+	1.15547i	−0.0388806	+	0.106824i
$118$	−6.47897	−	1.78177i	−0.596437	−	0.164025i
$119$	−1.51287	+	0.266761i	−0.138685	+	0.0244539i
$120$	−0.227288	−	3.36003i	−0.0207485	−	0.306728i
$121$	2.37103	−	4.10674i	0.215548	−	0.373340i
$122$	8.07372	−	3.70041i	0.730960	−	0.335019i
$123$	0.373986	−	0.445699i	0.0337212	−	0.0401873i
$124$	11.8560	+	14.5128i	1.06470	+	1.30328i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	0.914113	−	1.28739i	0.0814356	−	0.114690i
$127$	−9.30771	+	3.38773i	−0.825926	+	0.300612i	−0.720186	−	0.693781i	$-0.755943\pi$
$127$	−9.30771	+	3.38773i	−0.825926	+	0.300612i	−0.105740	+	0.994394i	$0.533721\pi$
$128$	−10.0229	−	5.24807i	−0.885904	−	0.463868i
$129$	−3.43098	−	0.604974i	−0.302081	−	0.0532650i
$130$	0.992954	+	0.470995i	0.0870878	+	0.0413090i
$131$	4.52347	+	5.39086i	0.395217	+	0.471002i	0.926555	−	0.376158i	$-0.122755\pi$
$131$	4.52347	+	5.39086i	0.395217	+	0.471002i	−0.531338	+	0.847160i	$0.678311\pi$
$132$	−1.76288	+	9.28232i	−0.153439	+	0.807922i
$133$	−2.62668	+	1.59993i	−0.227762	+	0.138732i
$134$	0.433669	−	4.60773i	0.0374633	−	0.398047i
$135$	−4.17954	+	3.50705i	−0.359718	+	0.301839i
$136$	3.63093	−	4.97375i	0.311350	−	0.426496i
$137$	−2.79596	+	15.8567i	−0.238875	+	1.35473i	0.595423	+	0.803412i	$0.296985\pi$
$137$	−2.79596	+	15.8567i	−0.238875	+	1.35473i	−0.834298	+	0.551314i	$0.814127\pi$
$138$	−0.936111	−	11.5759i	−0.0796870	−	0.985407i
$139$	−4.51553	−	12.4063i	−0.383002	−	1.05229i	−0.970086	−	0.242763i	$-0.921946\pi$
$139$	−4.51553	−	12.4063i	−0.383002	−	1.05229i	0.587084	−	0.809526i	$-0.300276\pi$
$140$	−1.06900	−	0.921223i	−0.0903472	−	0.0778576i
$141$	−10.0700	+	5.81392i	−0.848048	+	0.489621i
$142$	12.8354	−	12.6677i	1.07712	−	1.06305i
$143$	−2.36193	−	1.98189i	−0.197514	−	0.165734i
$144$	0.934774	+	6.25984i	0.0778978	+	0.521654i
$145$	2.92250	+	1.68731i	0.242701	+	0.140123i
$146$	3.33921	+	12.7981i	0.276355	+	1.05918i
$147$	−1.34436	−	7.62427i	−0.110881	−	0.628839i
$148$	−15.0856	−	5.71646i	−1.24003	−	0.469890i
$149$	−8.21228	−	2.98903i	−0.672776	−	0.244871i	−0.0170335	−	0.999855i	$-0.505422\pi$
$149$	−8.21228	−	2.98903i	−0.672776	−	0.244871i	−0.655743	+	0.754984i	$0.727644\pi$
$150$	0.956731	+	1.38565i	0.0781167	+	0.113138i
$151$	−13.1097			−1.06685			−0.533425	−	0.845847i	$-0.679095\pi$
$151$	−13.1097			−1.06685			−0.533425	+	0.845847i	$0.679095\pi$
$152$	3.14606	−	11.9207i	0.255179	−	0.966894i
$153$	−3.44503			−0.278514
$154$	2.24948	+	3.25797i	0.181268	+	0.262535i
$155$	−8.80488	−	3.20472i	−0.707225	−	0.257409i
$156$	1.73048	+	0.655738i	0.138549	+	0.0525011i
$157$	−3.82470	−	21.6909i	−0.305244	−	1.73112i	−0.622354	−	0.782736i	$-0.713823\pi$
$157$	−3.82470	−	21.6909i	−0.305244	−	1.73112i	0.317110	−	0.948389i	$-0.397288\pi$
$158$	−0.833947	−	3.19625i	−0.0663452	−	0.254280i
$159$	−8.63871	−	4.98756i	−0.685095	−	0.395540i
$160$	5.64849	−	0.307536i	0.446552	−	0.0243128i
$161$	−3.72795	−	3.12813i	−0.293804	−	0.246531i
$162$	−1.76081	+	1.73781i	−0.138342	+	0.136535i
$163$	5.26552	−	3.04005i	0.412427	−	0.238115i	−0.279405	−	0.960173i	$-0.590137\pi$
$163$	5.26552	−	3.04005i	0.412427	−	0.238115i	0.691832	+	0.722058i	$0.256804\pi$
$164$	0.740329	+	0.637986i	0.0578100	+	0.0498183i
$165$	−1.61574	−	4.43922i	−0.125785	−	0.345593i
$166$	−1.16941	−	14.4608i	−0.0907636	−	1.12238i
$167$	0.546280	−	3.09811i	0.0422724	−	0.239739i	−0.956349	−	0.292227i	$-0.905604\pi$
$167$	0.546280	−	3.09811i	0.0422724	−	0.239739i	0.998622	+	0.0524876i	$0.0167150\pi$
$168$	−1.91922	−	1.40107i	−0.148071	−	0.108095i
$169$	9.49597	−	7.96806i	0.730459	−	0.612928i
$170$	−0.288517	+	3.06549i	−0.0221283	+	0.235112i
$171$	−6.42400	+	2.51055i	−0.491255	+	0.191986i
$172$	1.09189	−	5.74926i	0.0832557	−	0.438377i
$173$	11.1510	+	13.2892i	0.847793	+	1.01036i	0.999759	+	0.0219747i	$0.00699533\pi$
$173$	11.1510	+	13.2892i	0.847793	+	1.01036i	−0.151965	+	0.988386i	$0.548560\pi$
$174$	5.13408	+	2.43528i	0.389213	+	0.184618i
$175$	0.694869	+	0.122524i	0.0525271	+	0.00926195i
$176$	−15.5515	−	3.16593i	−1.17224	−	0.238641i
$177$	5.31616	−	1.93492i	0.399587	−	0.145438i
$178$	5.02597	−	7.07831i	0.376712	−	0.530542i
$179$	−7.92382	−	13.7245i	−0.592254	−	1.02581i	−0.993928	−	0.110031i	$-0.964905\pi$
$179$	−7.92382	−	13.7245i	−0.592254	−	1.02581i	0.401674	−	0.915783i	$-0.368428\pi$
$180$	−2.00213	−	2.45078i	−0.149230	−	0.182671i
$181$	−9.03035	+	10.7620i	−0.671221	+	0.799930i	−0.988950	−	0.148252i	$-0.952635\pi$
$181$	−9.03035	+	10.7620i	−0.671221	+	0.799930i	0.317729	+	0.948182i	$0.397080\pi$
$182$	0.704926	−	0.323087i	0.0522526	−	0.0239488i
$183$	−3.73872	+	6.47565i	−0.276374	+	0.478694i
$184$	19.4634	−	1.31660i	1.43486	−	0.0970607i
$185$	7.94364	−	1.40068i	0.584028	−	0.102980i
$186$	−15.2129	−	4.18367i	−1.11546	−	0.306762i
$187$	2.95449	−	8.11739i	0.216054	−	0.593602i
$188$	−9.54256	−	17.0419i	−0.695963	−	1.24291i
$189$			3.84969i			0.280024i
$190$	1.69596	+	5.92653i	0.123038	+	0.429955i
$191$			9.43462i			0.682665i	0.939943	+	0.341333i	$0.110878\pi$
$191$			9.43462i			0.682665i	−0.939943	+	0.341333i	$0.889122\pi$
$192$	9.43856	−	1.28281i	0.681169	−	0.0925785i
$193$	−4.09527	+	11.2517i	−0.294784	+	0.809913i	0.700566	+	0.713588i	$0.252931\pi$
$193$	−4.09527	+	11.2517i	−0.294784	+	0.809913i	−0.995350	+	0.0963248i	$0.969291\pi$
$194$	0.431110	−	1.56762i	0.0309519	−	0.112549i
$195$	−0.911220	+	0.160673i	−0.0652538	+	0.0115060i
$196$	12.8353	−	2.08957i	0.916808	−	0.149255i
$197$	4.28554	−	7.42277i	0.305332	−	0.528851i	−0.672003	−	0.740548i	$-0.734566\pi$
$197$	4.28554	−	7.42277i	0.305332	−	0.528851i	0.977335	+	0.211698i	$0.0678992\pi$
$198$	3.69922	+	8.07112i	0.262892	+	0.573590i
$199$	0.594570	−	0.708581i	0.0421480	−	0.0502300i	−0.744559	−	0.667557i	$-0.767340\pi$
$199$	0.594570	−	0.708581i	0.0421480	−	0.0502300i	0.786707	+	0.617327i	$0.211784\pi$
$200$	−2.34846	+	1.57631i	−0.166061	+	0.111462i
$201$	1.94826	+	3.37448i	0.137420	+	0.238018i
$202$	−19.7005	−	13.9883i	−1.38612	−	0.984216i
$203$	2.23749	−	0.814381i	0.157041	−	0.0571583i
$204$	−0.0681753	+	5.18421i	−0.00477323	+	0.362967i
$205$	−0.481226	−	0.0848531i	−0.0336103	−	0.00592640i
$206$	9.01562	−	19.0068i	0.628148	−	1.32426i
$207$	−7.01496	−	8.36011i	−0.487574	−	0.581067i
$208$	−1.13959	+	2.89200i	−0.0790164	+	0.200524i
$209$	−0.406224	−	17.2897i	−0.0280991	−	1.19595i
$210$	1.18288	+	0.111330i	0.0816266	+	0.00768252i
$211$	10.0223	−	8.40970i	0.689963	−	0.578948i	−0.228935	−	0.973442i	$-0.573524\pi$
$211$	10.0223	−	8.40970i	0.689963	−	0.578948i	0.918899	+	0.394494i	$0.129080\pi$
$212$	8.56785	−	14.3993i	0.588442	−	0.988948i
$213$	−2.63653	+	14.9525i	−0.180652	+	1.02453i
$214$	9.91053	−	0.801436i	0.677470	−	0.0547850i
$215$	1.00076	+	2.74955i	0.0682510	+	0.187518i
$216$	−10.6947	−	11.1251i	−0.727680	−	0.756968i
$217$	−5.72558	+	3.30567i	−0.388678	+	0.224403i
$218$	−6.65506	−	6.74315i	−0.450737	−	0.456704i
$219$	−8.53053	−	7.15796i	−0.576440	−	0.483690i
$220$	7.49174	−	2.61573i	0.505093	−	0.176352i
$221$	−1.46525	−	0.845963i	−0.0985635	−	0.0569056i
$222$	13.1423	−	3.42902i	0.882055	−	0.230141i
$223$	2.14760	+	12.1796i	0.143814	+	0.815608i	0.968312	+	0.249744i	$0.0803464\pi$
$223$	2.14760	+	12.1796i	0.143814	+	0.815608i	−0.824498	+	0.565865i	$0.808543\pi$
$224$	2.39561	−	3.19256i	0.160063	−	0.213312i
$225$	1.48689	+	0.541183i	0.0991259	+	0.0360789i
$226$	1.27882	−	0.882969i	0.0850661	−	0.0587342i
$227$	18.5968			1.23431			0.617156	−	0.786841i	$-0.288285\pi$
$227$	18.5968			1.23431			0.617156	+	0.786841i	$0.288285\pi$
$228$	3.65084	+	9.71677i	0.241783	+	0.643509i
$229$	−23.4443			−1.54924			−0.774622	−	0.632424i	$-0.782060\pi$
$229$	−23.4443			−1.54924			−0.774622	+	0.632424i	$0.782060\pi$
$230$	−8.02658	+	5.54198i	−0.529257	+	0.365427i
$231$	−3.13226	−	1.14005i	−0.206088	−	0.0750098i
$232$	−4.20366	+	8.56933i	−0.275984	+	0.562604i
$233$	−4.07670	−	23.1201i	−0.267073	−	1.51465i	−0.763066	−	0.646321i	$-0.776307\pi$
$233$	−4.07670	−	23.1201i	−0.267073	−	1.51465i	0.495993	−	0.868327i	$-0.334804\pi$
$234$	1.68263	−	0.439022i	0.109997	−	0.0286998i
$235$	8.45746	+	4.88291i	0.551704	+	0.318526i
$236$	3.13245	+	8.97169i	0.203905	+	0.584007i
$237$	2.13044	+	1.78766i	0.138387	+	0.116121i
$238$	1.52608	+	1.54628i	0.0989210	+	0.100230i
$239$	6.60852	−	3.81543i	0.427469	−	0.246800i	−0.270799	−	0.962636i	$-0.587288\pi$
$239$	6.60852	−	3.81543i	0.427469	−	0.246800i	0.698268	+	0.715836i	$0.253954\pi$
$240$	−3.72766	+	2.96438i	−0.240619	+	0.191350i
$241$	−1.37588	−	3.78020i	−0.0886282	−	0.243504i	0.887458	−	0.460889i	$-0.152469\pi$
$241$	−1.37588	−	3.78020i	−0.0886282	−	0.243504i	−0.976086	+	0.217385i	$0.930247\pi$
$242$	−6.68446	+	0.540553i	−0.429693	+	0.0347481i
$243$	−2.48059	+	14.0681i	−0.159130	+	0.902470i
$244$	−10.7938	−	6.42253i	−0.691005	−	0.411161i
$245$	−4.98093	+	4.17950i	−0.318220	+	0.267018i
$246$	−0.819196	−	0.0771009i	−0.0522300	−	0.00491577i
$247$	−3.34877	−	0.509687i	−0.213077	−	0.0324306i
$248$	7.36286	−	25.4589i	0.467542	−	1.61664i
$249$	7.85148	+	9.35703i	0.497567	+	0.592978i
$250$	0.606087	−	1.27776i	0.0383323	−	0.0808124i
$251$	11.9276	+	2.10315i	0.752861	+	0.132750i	0.536893	−	0.843651i	$-0.319598\pi$
$251$	11.9276	+	2.10315i	0.752861	+	0.132750i	0.215968	+	0.976400i	$0.430709\pi$
$252$	−2.23273	−	0.0293617i	−0.140649	−	0.00184961i
$253$	25.7147	−	9.35939i	1.61667	−	0.588420i
$254$	11.4215	+	8.10985i	0.716649	+	0.508857i
$255$	−1.29616	−	2.24502i	−0.0811690	−	0.140589i
$256$	1.94611	+	15.8812i	0.121632	+	0.992575i
$257$	−11.8091	+	14.0736i	−0.736633	+	0.877885i	−0.996133	−	0.0878579i	$-0.971998\pi$
$257$	−11.8091	+	14.0736i	−0.736633	+	0.877885i	0.259500	+	0.965743i	$0.416442\pi$
$258$	2.05283	+	4.47896i	0.127804	+	0.278848i
$259$	2.84570	−	4.92890i	0.176823	−	0.306267i
$260$	−0.249737	−	1.53402i	−0.0154880	−	0.0951359i
$261$	5.25858	−	0.927229i	0.325498	−	0.0573940i
$262$	2.63897	−	9.59595i	0.163036	−	0.592840i
$263$	−1.73354	+	4.76285i	−0.106894	+	0.293690i	−0.981595	−	0.190973i	$-0.938836\pi$
$263$	−1.73354	+	4.76285i	−0.106894	+	0.293690i	0.874701	+	0.484663i	$0.161058\pi$
$264$	12.2189	−	5.40700i	0.752024	−	0.332778i
$265$			8.37777i			0.514642i
$266$	3.97255	+	1.77125i	0.243573	+	0.108602i
$267$			7.30893i			0.447299i
$268$	−5.71077	+	3.19774i	−0.348841	+	0.195333i
$269$	−3.67263	+	10.0905i	−0.223924	+	0.615227i	−0.999879	−	0.0155620i	$-0.995046\pi$
$269$	−3.67263	+	10.0905i	−0.223924	+	0.615227i	0.775955	+	0.630789i	$0.217268\pi$
$270$	7.43975	+	2.04600i	0.452769	+	0.124515i
$271$	−22.5169	+	3.97034i	−1.36781	+	0.241181i	−0.808849	−	0.588016i	$-0.799909\pi$
$271$	−22.5169	+	3.97034i	−1.36781	+	0.241181i	−0.558956	+	0.829197i	$0.688798\pi$
$272$	−8.70582	−	0.229013i	−0.527868	−	0.0138859i
$273$	−0.326432	+	0.565397i	−0.0197566	+	0.0342194i
$274$	20.7000	−	9.48740i	1.25054	−	0.573155i
$275$	−2.55034	+	3.03938i	−0.153791	+	0.183281i
$276$	−12.7194	+	10.3909i	−0.765620	+	0.625461i
$277$	−1.19385	−	2.06780i	−0.0717313	−	0.124242i	0.827929	−	0.560833i	$-0.189519\pi$
$277$	−1.19385	−	2.06780i	−0.0717313	−	0.124242i	−0.899660	+	0.436591i	$0.856186\pi$
$278$	−10.8097	+	15.2238i	−0.648321	+	0.913062i
$279$	−13.9321	+	5.07086i	−0.834092	+	0.303585i
$280$	−0.213116	+	1.98429i	−0.0127361	+	0.118584i
$281$	−0.817767	−	0.144194i	−0.0487839	−	0.00860192i	0.149203	−	0.988807i	$-0.452329\pi$
$281$	−0.817767	−	0.144194i	−0.0487839	−	0.00860192i	−0.197987	+	0.980205i	$0.563440\pi$
$282$	14.8575	+	7.04748i	0.884754	+	0.419671i
$283$	−3.69824	−	4.40738i	−0.219837	−	0.261992i	0.644842	−	0.764316i	$-0.276923\pi$
$283$	−3.69824	−	4.40738i	−0.219837	−	0.261992i	−0.864680	+	0.502324i	$0.832479\pi$
$284$	−25.0558	−	4.75854i	−1.48679	−	0.282367i
$285$	−4.05303	−	3.24176i	−0.240081	−	0.192025i
$286$	−0.408586	+	4.34122i	−0.0241602	+	0.256702i
$287$	−0.264121	+	0.221624i	−0.0155906	+	0.0130820i
$288$	6.53387	−	6.11780i	0.385012	−	0.360495i
$289$	−2.12889	+	12.0735i	−0.125229	+	0.710207i
$290$	−0.384677	−	4.75690i	−0.0225890	−	0.279335i
$291$	0.468166	+	1.28628i	0.0274444	+	0.0754029i
$292$	12.2108	−	14.1697i	0.714585	−	0.829216i
$293$	−0.683709	+	0.394740i	−0.0399427	+	0.0230609i	−0.519838	−	0.854265i	$-0.674008\pi$
$293$	−0.683709	+	0.394740i	−0.0399427	+	0.0230609i	0.479896	+	0.877326i	$0.340675\pi$
$294$	−7.79262	+	7.69082i	−0.454475	+	0.448538i
$295$	−3.63979	−	3.05415i	−0.211917	−	0.177819i
$296$	5.46906	+	22.1494i	0.317883	+	1.28741i
$297$	−18.7472	−	10.8237i	−1.08782	−	0.628055i
$298$	3.12026	+	11.9589i	0.180752	+	0.692761i
$299$	−0.930716	−	5.27835i	−0.0538247	−	0.305255i
$300$	0.843818	−	2.22682i	0.0487179	−	0.128565i
$301$	1.94005	+	0.706122i	0.111823	+	0.0407002i
$302$	10.5340	+	15.2566i	0.606161	+	0.877917i
$303$	20.3423			1.16864
$304$	−16.4008	+	5.91728i	−0.940650	+	0.339379i
$305$	6.28005			0.359594
$306$	2.76817	+	4.00920i	0.158245	+	0.229191i
$307$	20.4801	+	7.45415i	1.16886	+	0.425431i	0.852255	−	0.523126i	$-0.175234\pi$
$307$	20.4801	+	7.45415i	1.16886	+	0.425431i	0.316607	+	0.948557i	$0.397456\pi$
$308$	1.98400	−	5.23572i	0.113049	−	0.298333i
$309$	3.07554	+	17.4422i	0.174961	+	0.992254i
$310$	3.34541	+	12.8219i	0.190007	+	0.728234i
$311$	22.8108	+	13.1698i	1.29348	+	0.746793i	0.979270	−	0.202559i	$-0.0649259\pi$
$311$	22.8108	+	13.1698i	1.29348	+	0.746793i	0.314213	+	0.949352i	$0.398259\pi$
$312$	−0.627359	−	2.54077i	−0.0355172	−	0.143843i
$313$	10.2417	+	8.59379i	0.578894	+	0.485750i	0.884584	−	0.466382i	$-0.154443\pi$
$313$	10.2417	+	8.59379i	0.578894	+	0.485750i	−0.305690	+	0.952131i	$0.598887\pi$
$314$	−22.1699	+	21.8803i	−1.25112	+	1.23477i
$315$	0.966884	−	0.558231i	0.0544778	−	0.0314527i
$316$	−3.04958	+	3.53878i	−0.171552	+	0.199072i
$317$	2.81156	+	7.72471i	0.157913	+	0.433863i	0.993267	−	0.115850i	$-0.0369593\pi$
$317$	2.81156	+	7.72471i	0.157913	+	0.433863i	−0.835354	+	0.549713i	$0.814737\pi$
$318$	1.13708	+	14.0611i	0.0637642	+	0.788505i
$319$	−2.32501	+	13.1858i	−0.130176	+	0.738263i
$320$	−4.89660	−	6.32640i	−0.273728	−	0.353656i
$321$	−6.41270	+	5.38090i	−0.357922	+	0.300332i
$322$	−0.644894	+	6.85199i	−0.0359385	+	0.381846i
$323$	−1.86703	−	9.30477i	−0.103884	−	0.517731i
$324$	3.43725	+	0.652795i	0.190958	+	0.0362664i
$325$	0.499516	+	0.595299i	0.0277081	+	0.0330213i
$326$	−7.76888	−	3.68507i	−0.430278	−	0.204097i
$327$	7.85539	+	1.38512i	0.434404	+	0.0765972i
$328$	0.147592	−	1.37421i	0.00814938	−	0.0758779i
$329$	6.47510	−	2.35674i	0.356984	−	0.129931i
$330$	−3.86791	+	5.44737i	−0.212922	+	0.299868i
$331$	−10.4654	−	18.1266i	−0.575232	−	0.996330i	−0.996016	−	0.0891700i	$-0.971579\pi$
$331$	−10.4654	−	18.1266i	−0.575232	−	0.996330i	0.420785	−	0.907161i	$-0.361755\pi$
$332$	−15.8894	+	12.9806i	−0.872042	+	0.712401i
$333$	8.20405	−	9.77721i	0.449579	−	0.535788i
$334$	−4.04442	+	1.85367i	−0.221301	+	0.101428i
$335$	1.63628	−	2.83411i	0.0893993	−	0.154844i
$336$	−0.0883692	+	3.35932i	−0.00482093	+	0.183266i
$337$	29.0323	−	5.11919i	1.58149	−	0.278860i	0.687243	−	0.726428i	$-0.258821\pi$
$337$	29.0323	−	5.11919i	1.58149	−	0.278860i	0.894250	+	0.447568i	$0.147710\pi$
$338$	−16.9032	−	4.64853i	−0.919413	−	0.252846i
$339$	−0.447495	+	1.22948i	−0.0243046	+	0.0667762i
$340$	3.79934	−	2.12743i	0.206048	−	0.115376i
$341$		−	37.1765i		−	2.01322i
$342$	8.08353	+	5.45873i	0.437107	+	0.295174i
$343$			9.52696i			0.514407i
$344$	−7.56814	+	3.34898i	−0.408047	+	0.180565i
$345$	2.80871	−	7.71687i	0.151216	−	0.415462i
$346$	6.50542	−	23.6553i	0.349734	−	1.27172i
$347$	29.5169	−	5.20462i	1.58455	−	0.279399i	0.689134	−	0.724634i	$-0.257991\pi$
$347$	29.5169	−	5.20462i	1.58455	−	0.279399i	0.895414	+	0.445235i	$0.146880\pi$
$348$	−1.29127	−	7.93166i	−0.0692191	−	0.425182i
$349$	9.34056	−	16.1783i	0.499988	−	0.866005i	−0.500012	−	0.866019i	$-0.666671\pi$
$349$	9.34056	−	16.1783i	0.499988	−	0.866005i	1.00000		1.32845e-5i	$4.22860e-6\pi$
$350$	−0.415756	−	0.907115i	−0.0222231	−	0.0484873i
$351$	−2.72536	+	3.24796i	−0.145469	+	0.173363i
$352$	8.81164	+	20.6422i	0.469662	+	1.10023i
$353$	−6.00070	−	10.3935i	−0.319385	−	0.553191i	0.660975	−	0.750408i	$-0.270143\pi$
$353$	−6.00070	−	10.3935i	−0.319385	−	0.553191i	−0.980360	+	0.197217i	$0.936810\pi$
$354$	−6.52347	−	4.63200i	−0.346718	−	0.246188i
$355$	11.9828	−	4.36138i	0.635980	−	0.231478i
$356$	−12.2760	−	0.161436i	−0.650626	−	0.00855609i
$357$	−1.80133	−	0.317623i	−0.0953364	−	0.0168104i
$358$	−9.60504	+	20.2494i	−0.507642	+	1.07021i
$359$	−9.78149	−	11.6571i	−0.516247	−	0.615239i	0.443442	−	0.896303i	$-0.353757\pi$
$359$	−9.78149	−	11.6571i	−0.516247	−	0.615239i	−0.959689	+	0.281064i	$0.909313\pi$
$360$	−1.24337	+	4.29927i	−0.0655315	+	0.226592i
$361$	−10.2623	−	15.9902i	−0.540121	−	0.841588i
$362$	19.7805	+	1.86170i	1.03964	+	0.0978486i
$363$	4.32524	−	3.62931i	0.227016	−	0.190489i
$364$	−0.942423	−	0.560759i	−0.0493964	−	0.0293918i
$365$	−1.62406	+	9.21050i	−0.0850072	+	0.482100i
$366$	10.5403	−	0.852363i	0.550950	−	0.0445537i
$367$	−5.44394	−	14.9571i	−0.284171	−	0.780754i	−0.996853	−	0.0792671i	$-0.974742\pi$
$367$	−5.44394	−	14.9571i	−0.284171	−	0.780754i	0.712682	−	0.701487i	$-0.247480\pi$
$368$	−17.1716	−	21.5929i	−0.895129	−	1.12561i
$369$	−0.669608	+	0.386598i	−0.0348584	+	0.0201255i
$370$	−8.01298	−	8.11905i	−0.416575	−	0.422089i
$371$	4.52828	+	3.79968i	0.235097	+	0.197270i
$372$	7.35513	+	21.0659i	0.381345	+	1.09222i
$373$	10.6041	+	6.12226i	0.549058	+	0.316999i	0.748742	−	0.662862i	$-0.230658\pi$
$373$	10.6041	+	6.12226i	0.549058	+	0.316999i	−0.199684	+	0.979860i	$0.563992\pi$
$374$	−11.8207	+	3.08420i	−0.611236	+	0.159480i
$375$	0.206757	+	1.17258i	0.0106769	+	0.0605516i
$376$	−12.1650	+	24.7989i	−0.627363	+	1.27890i
$377$	2.46429	+	0.896928i	0.126917	+	0.0461941i
$378$	4.48014	−	3.09333i	0.230433	−	0.159104i
$379$	−10.7396			−0.551657			−0.275828	−	0.961207i	$-0.588952\pi$
$379$	−10.7396			−0.551657			−0.275828	+	0.961207i	$0.588952\pi$
$380$	5.53433	−	6.73581i	0.283905	−	0.345540i
$381$	−11.7936			−0.604206
$382$	10.9797	−	7.58096i	0.561769	−	0.387875i
$383$	−5.38067	−	1.95840i	−0.274939	−	0.100070i	0.200871	−	0.979618i	$-0.435623\pi$
$383$	−5.38067	−	1.95840i	−0.274939	−	0.100070i	−0.475810	+	0.879548i	$0.657845\pi$
$384$	−9.07700	−	9.95349i	−0.463209	−	0.507937i
$385$	0.486130	+	2.75698i	0.0247755	+	0.140509i
$386$	16.3849	−	4.27507i	0.833971	−	0.217595i
$387$	4.00959	+	2.31494i	0.203819	+	0.117675i
$388$	−2.17075	+	0.757915i	−0.110203	+	0.0384773i
$389$	−29.0880	−	24.4077i	−1.47482	−	1.23752i	−0.911512	−	0.411274i	$-0.865084\pi$
$389$	−29.0880	−	24.4077i	−1.47482	−	1.23752i	−0.563308	−	0.826247i	$-0.690472\pi$
$390$	0.919173	+	0.931340i	0.0465441	+	0.0471602i
$391$	13.0046	−	7.50819i	0.657669	−	0.379705i
$392$	−12.7453	−	13.2582i	−0.643733	−	0.669643i
$393$	2.86580	+	7.87372i	0.144561	+	0.397177i
$394$	−12.0819	+	0.977028i	−0.608677	+	0.0492220i
$395$	0.405599	−	2.30026i	0.0204079	−	0.115739i
$396$	6.42047	−	10.7904i	0.322641	−	0.542236i
$397$	−4.01038	+	3.36511i	−0.201275	+	0.168890i	−0.737854	−	0.674960i	$-0.764161\pi$
$397$	−4.01038	+	3.36511i	−0.201275	+	0.168890i	0.536579	+	0.843850i	$0.319716\pi$
$398$	−1.30237	−	0.122577i	−0.0652821	−	0.00614421i
$399$	−3.59043	+	0.720433i	−0.179747	+	0.0360668i
$400$	3.72149	+	1.46645i	0.186075	+	0.0733225i
$401$	22.9498	+	27.3504i	1.14606	+	1.36582i	0.920102	+	0.391678i	$0.128105\pi$
$401$	22.9498	+	27.3504i	1.14606	+	1.36582i	0.225954	+	0.974138i	$0.427450\pi$
$402$	2.36163	−	4.97880i	0.117787	−	0.248320i
$403$	−7.17085	−	1.26441i	−0.357206	−	0.0629850i
$404$	−0.449311	+	34.1667i	−0.0223541	+	1.69986i
$405$	−1.64385	+	0.598311i	−0.0816834	+	0.0297303i
$406$	−2.74563	−	1.94954i	−0.136263	−	0.0967539i
$407$	16.0018	+	27.7159i	0.793180	+	1.37383i
$408$	6.08798	−	4.08630i	0.301400	−	0.202302i
$409$	−17.6619	+	21.0486i	−0.873325	+	1.04079i	0.125489	+	0.992095i	$0.459950\pi$
$409$	−17.6619	+	21.0486i	−0.873325	+	1.04079i	−0.998814	+	0.0486934i	$0.984494\pi$
$410$	0.287928	+	0.628215i	0.0142198	+	0.0310253i
$411$	−9.58563	+	16.6028i	−0.472824	+	0.818956i
$412$	−29.3637	+	4.78038i	−1.44664	+	0.235512i
$413$	−3.30160	+	0.582162i	−0.162461	+	0.0286463i
$414$	−4.09249	+	14.8813i	−0.201135	+	0.731377i
$415$	3.50870	−	9.64006i	0.172235	−	0.473212i
$416$	4.28130	−	0.997584i	0.209908	−	0.0489106i
$417$		−	15.7198i		−	0.769802i
$418$	−19.7947	+	14.3655i	−0.968192	+	0.702638i
$419$			13.1773i			0.643753i	0.946782	+	0.321877i	$0.104314\pi$
$419$			13.1773i			0.643753i	−0.946782	+	0.321877i	$0.895686\pi$
$420$	−0.820914	−	1.46605i	−0.0400565	−	0.0715360i
$421$	5.03739	−	13.8401i	0.245508	−	0.674527i	−0.754330	−	0.656496i	$-0.772038\pi$
$421$	5.03739	−	13.8401i	0.245508	−	0.674527i	0.999837	−	0.0180310i	$-0.00573974\pi$
$422$	−17.8401	−	4.90618i	−0.868441	−	0.238829i
$423$	15.2178	−	2.68332i	0.739917	−	0.130467i
$424$	−23.6419	+	1.59925i	−1.14815	+	0.0776663i
$425$	−1.08860	+	1.88552i	−0.0528051	+	0.0914610i
$426$	19.5197	−	8.94641i	0.945732	−	0.433455i
$427$	2.84827	−	3.39444i	0.137838	−	0.164268i
$428$	−8.89604	−	10.8895i	−0.430006	−	0.526366i
$429$	−1.83558	−	3.17931i	−0.0886224	−	0.153499i
$430$	2.39570	−	3.37398i	0.115531	−	0.162708i
$431$	6.92973	−	2.52221i	0.333793	−	0.121491i	−0.169686	−	0.985498i	$-0.554275\pi$
$431$	6.92973	−	2.52221i	0.333793	−	0.121491i	0.503479	+	0.864007i	$0.332053\pi$
$432$	−4.35357	+	21.3854i	−0.209461	+	1.02890i
$433$	−0.238265	−	0.0420125i	−0.0114503	−	0.00201899i	0.167920	−	0.985801i	$-0.446295\pi$
$433$	−0.238265	−	0.0420125i	−0.0114503	−	0.00201899i	−0.179370	+	0.983782i	$0.557406\pi$
$434$	8.44767	+	4.00704i	0.405501	+	0.192344i
$435$	2.58275	+	3.07800i	0.123833	+	0.147579i
$436$	−2.49993	+	13.1632i	−0.119725	+	0.630403i
$437$	18.7783	−	23.4777i	0.898287	−	1.12309i
$438$	−1.47568	+	15.6791i	−0.0705109	+	0.749177i
$439$	−2.80982	+	2.35772i	−0.134105	+	0.112528i	−0.707373	−	0.706840i	$-0.750120\pi$
$439$	−2.80982	+	2.35772i	−0.134105	+	0.112528i	0.573268	+	0.819368i	$0.305675\pi$
$440$	−9.06390	−	6.61681i	−0.432104	−	0.315444i
$441$	−1.78657	+	10.1321i	−0.0850746	+	0.482482i
$442$	0.192865	+	2.38496i	0.00917365	+	0.113441i
$443$	−2.81335	−	7.72961i	−0.133666	−	0.367245i	0.854744	−	0.519049i	$-0.173714\pi$
$443$	−2.81335	−	7.72961i	−0.133666	−	0.367245i	−0.988411	+	0.151804i	$0.951492\pi$
$444$	−14.5508	−	12.5393i	−0.690549	−	0.595087i
$445$	5.31611	−	3.06926i	0.252008	−	0.145497i
$446$	12.4486	−	12.2859i	0.589457	−	0.581756i
$447$	−7.97117	−	6.68861i	−0.377023	−	0.316360i
$448$	−5.64031	−	0.222623i	−0.266480	−	0.0105179i
$449$	26.7270	+	15.4308i	1.26132	+	0.728226i	0.973331	−	0.229407i	$-0.0736785\pi$
$449$	26.7270	+	15.4308i	1.26132	+	0.728226i	0.287993	+	0.957632i	$0.407012\pi$
$450$	−0.564943	−	2.16524i	−0.0266317	−	0.102070i
$451$	−0.336665	−	1.90932i	−0.0158530	−	0.0899066i
$452$	−2.05514	−	0.778762i	−0.0966654	−	0.0366299i
$453$	−14.6679	−	5.33868i	−0.689158	−	0.250833i
$454$	−14.9430	−	21.6423i	−0.701310	−	1.01572i
$455$	0.548318			0.0257056
$456$	8.37448	−	12.0564i	0.392171	−	0.564592i
$457$	−18.1257			−0.847883			−0.423941	−	0.905690i	$-0.639354\pi$
$457$	−18.1257			−0.847883			−0.423941	+	0.905690i	$0.639354\pi$
$458$	18.8381	+	27.2837i	0.880247	+	1.27488i
$459$	−11.1625	−	4.06281i	−0.521020	−	0.189636i
$460$	12.8991	+	4.88792i	0.601424	+	0.227900i
$461$	2.82518	+	16.0224i	0.131582	+	0.746238i	0.977179	+	0.212417i	$0.0681335\pi$
$461$	2.82518	+	16.0224i	0.131582	+	0.746238i	−0.845597	+	0.533822i	$0.820755\pi$
$462$	1.19010	+	4.56127i	0.0553686	+	0.212210i
$463$	−32.6515	−	18.8513i	−1.51744	−	0.876096i	−0.999790	−	0.0205049i	$-0.993473\pi$
$463$	−32.6515	−	18.8513i	−1.51744	−	0.876096i	−0.517653	−	0.855591i	$-0.673194\pi$
$464$	13.3504	−	1.99360i	0.619778	−	0.0925507i
$465$	−8.54637	−	7.17126i	−0.396329	−	0.332559i
$466$	−23.6306	+	23.3219i	−1.09467	+	1.08037i
$467$	6.29391	−	3.63379i	0.291247	−	0.168152i	−0.347257	−	0.937770i	$-0.612887\pi$
$467$	6.29391	−	3.63379i	0.291247	−	0.168152i	0.638504	+	0.769618i	$0.279553\pi$
$468$	−1.86295	−	1.60542i	−0.0861149	−	0.0742104i
$469$	−0.789750	−	2.16982i	−0.0364673	−	0.100193i
$470$	−1.11322	−	13.7660i	−0.0513490	−	0.634980i
$471$	4.55394	−	25.8267i	0.209834	−	1.19003i
$472$	7.92393	−	10.8544i	0.364728	−	0.499615i
$473$	−8.89326	+	7.46233i	−0.408913	+	0.343118i
$474$	0.368543	−	3.91576i	0.0169277	−	0.179857i
$475$	−0.655877	+	4.30927i	−0.0300937	+	0.197723i
$476$	0.573262	−	3.01847i	0.0262754	−	0.138351i
$477$	8.52096	+	10.1549i	0.390148	+	0.464960i
$478$	−9.75037	−	4.62496i	−0.445972	−	0.211541i
$479$	17.6834	+	3.11805i	0.807973	+	0.142467i	0.562351	−	0.826898i	$-0.309897\pi$
$479$	17.6834	+	3.11805i	0.807973	+	0.142467i	0.245622	+	0.969366i	$0.421008\pi$
$480$	6.44511	+	1.95616i	0.294178	+	0.0892859i
$481$	5.89028	−	2.14388i	0.268573	−	0.0977527i
$482$	−3.29371	+	4.63869i	−0.150024	+	0.211286i
$483$	−2.89719	−	5.01808i	−0.131827	−	0.228330i
$484$	6.00021	+	7.34478i	0.272737	+	0.333854i
$485$	0.738968	−	0.880668i	0.0335548	−	0.0399891i
$486$	18.3652	−	8.41727i	0.833061	−	0.381815i
$487$	−18.7578	+	32.4895i	−0.849998	+	1.47224i	0.0312108	+	0.999513i	$0.490064\pi$
$487$	−18.7578	+	32.4895i	−0.849998	+	1.47224i	−0.881209	+	0.472727i	$0.843270\pi$
$488$	1.19881	+	17.7221i	0.0542675	+	0.802244i
$489$	7.12939	−	1.25710i	0.322402	−	0.0568482i
$490$	8.86626	+	2.43830i	0.400537	+	0.110151i
$491$	12.2432	−	33.6379i	0.552527	−	1.51806i	−0.277721	−	0.960662i	$-0.589579\pi$
$491$	12.2432	−	33.6379i	0.552527	−	1.51806i	0.830248	−	0.557394i	$-0.188199\pi$
$492$	0.568517	+	1.01530i	0.0256307	+	0.0457734i
$493$			7.34724i			0.330903i
$494$	2.09767	+	4.30673i	0.0943785	+	0.193769i
$495$			6.27803i			0.282176i
$496$	−35.5444	+	11.8883i	−1.59599	+	0.533799i
$497$	3.07734	−	8.45491i	0.138037	−	0.379255i
$498$	4.58051	−	16.6559i	0.205258	−	0.746368i
$499$	30.0236	−	5.29396i	1.34404	−	0.236990i	0.545084	−	0.838381i	$-0.316498\pi$
$499$	30.0236	−	5.29396i	1.34404	−	0.236990i	0.798955	+	0.601391i	$0.205387\pi$
$500$	−1.97401	+	0.321367i	−0.0882805	+	0.0143720i
$501$	1.87286	−	3.24389i	0.0836733	−	0.144926i
$502$	−7.13653	−	15.5708i	−0.318519	−	0.694959i
$503$	7.10501	−	8.46742i	0.316797	−	0.377543i	−0.584023	−	0.811737i	$-0.698522\pi$
$503$	7.10501	−	8.46742i	0.316797	−	0.377543i	0.900820	+	0.434194i	$0.142967\pi$
$504$	1.75989	+	2.62196i	0.0783915	+	0.116792i
$505$	−8.54241	−	14.7959i	−0.380132	−	0.658408i
$506$	−31.5546	−	22.4054i	−1.40277	−	0.996040i
$507$	13.8695	−	5.04809i	0.615967	−	0.224193i
$508$	0.260492	−	19.8084i	0.0115575	−	0.878856i
$509$	7.30012	+	1.28721i	0.323572	+	0.0570545i	0.333075	−	0.942900i	$-0.391914\pi$
$509$	7.30012	+	1.28721i	0.323572	+	0.0570545i	−0.00950285	+	0.999955i	$0.503025\pi$
$510$	−1.57118	+	3.31236i	−0.0695728	+	0.146674i
$511$	4.24180	+	5.05519i	0.187646	+	0.223628i
$512$	16.9182	−	15.0258i	0.747687	−	0.664051i
$513$	−23.7756	+	0.558611i	−1.04972	+	0.0246633i
$514$	25.8673	+	2.43457i	1.14096	+	0.107384i
$515$	11.3950	−	9.56155i	0.502124	−	0.421332i
$516$	3.56295	−	5.98797i	0.156850	−	0.263606i
$517$	−6.72837	+	38.1585i	−0.295914	+	1.67821i
$518$	−8.02268	+	0.648771i	−0.352496	+	0.0285054i
$519$	7.06460	+	19.4098i	0.310101	+	0.851996i
$520$	−1.58457	+	1.52326i	−0.0694879	+	0.0667994i
$521$	−35.2484	+	20.3507i	−1.54426	+	0.891580i	−0.545700	+	0.837981i	$0.683736\pi$
$521$	−35.2484	+	20.3507i	−1.54426	+	0.891580i	−0.998563	+	0.0535997i	$0.982931\pi$
$522$	−5.30448	−	5.37469i	−0.232171	−	0.235244i
$523$	−0.556013	−	0.466550i	−0.0243127	−	0.0204008i	0.630550	−	0.776148i	$-0.282829\pi$
$523$	−0.556013	−	0.466550i	−0.0243127	−	0.0204008i	−0.654863	+	0.755748i	$0.727274\pi$
$524$	−13.2879	+	4.63945i	−0.580484	+	0.202675i
$525$	0.727566	+	0.420060i	0.0317536	+	0.0183329i
$526$	6.93577	−	1.80964i	0.302414	−	0.0789042i
$527$	−3.54248	−	20.0904i	−0.154313	−	0.875153i
$528$	−16.1107	−	9.87531i	−0.701129	−	0.429768i
$529$	23.0880	+	8.40334i	1.00383	+	0.365363i
$530$	9.74975	−	6.73175i	0.423502	−	0.292409i
$531$	−7.51821			−0.326263
$532$	−1.13073	−	6.04636i	−0.0490232	−	0.262143i
$533$	−0.379734			−0.0164481
$534$	8.50587	−	5.87291i	0.368085	−	0.254146i
$535$	6.60668	+	2.40463i	0.285631	+	0.103961i
$536$	8.31016	+	4.07653i	0.358944	+	0.176079i
$537$	−3.27661	−	18.5826i	−0.141396	−	0.801898i
$538$	14.6940	−	3.83387i	0.633502	−	0.165290i
$539$	−22.3418	−	12.8990i	−0.962329	−	0.555601i
$540$	−3.59697	−	10.3021i	−0.154789	−	0.443333i
$541$	33.6394	+	28.2268i	1.44627	+	1.21357i	0.935246	+	0.353999i	$0.115179\pi$
$541$	33.6394	+	28.2268i	1.44627	+	1.21357i	0.511025	+	0.859566i	$0.329266\pi$
$542$	22.7135	+	23.0141i	0.975626	+	0.988541i
$543$	−14.4863	+	8.36368i	−0.621667	+	0.358920i
$544$	6.72883	+	10.3155i	0.288496	+	0.442275i
$545$	−2.29128	−	6.29524i	−0.0981476	−	0.269658i
$546$	0.920286	−	0.0744209i	0.0393846	−	0.00318492i
$547$	−3.14979	+	17.8633i	−0.134675	+	0.763781i	0.840410	+	0.541951i	$0.182314\pi$
$547$	−3.14979	+	17.8633i	−0.134675	+	0.763781i	−0.975085	+	0.221830i	$0.928797\pi$
$548$	−27.6741	−	16.4666i	−1.18218	−	0.703418i
$549$	7.61218	−	6.38738i	0.324880	−	0.272607i
$550$	5.58638	+	0.525778i	0.238204	+	0.0224192i
$551$	5.35427	+	13.7005i	0.228099	+	0.583662i
$552$	22.3130	+	6.45304i	0.949704	+	0.274659i
$553$	−1.05936	−	1.26250i	−0.0450487	−	0.0536870i
$554$	−1.44715	+	3.05089i	−0.0614835	+	0.129620i
$555$	9.45823	+	1.66774i	0.401480	+	0.0707917i
$556$	26.4028	+	0.347211i	1.11973	+	0.0147250i
$557$	−4.33267	+	1.57696i	−0.183581	+	0.0668180i	−0.432175	−	0.901790i	$-0.642254\pi$
$557$	−4.33267	+	1.57696i	−0.183581	+	0.0668180i	0.248594	+	0.968608i	$0.420032\pi$
$558$	17.0961	+	12.1391i	0.723734	+	0.513889i
$559$	1.13691	+	1.96919i	0.0480864	+	0.0832880i
$560$	2.48049	−	1.34641i	0.104820	−	0.0568964i
$561$	6.61132	−	7.87907i	0.279130	−	0.332654i
$562$	0.489289	+	1.06755i	0.0206394	+	0.0450320i
$563$	22.4975	−	38.9669i	0.948159	−	1.64226i	0.198859	−	0.980028i	$-0.436277\pi$
$563$	22.4975	−	38.9669i	0.948159	−	1.64226i	0.749300	−	0.662231i	$-0.230390\pi$
$564$	−3.73681	−	22.9535i	−0.157348	−	0.966517i
$565$	1.08217	−	0.190817i	0.0455274	−	0.00802771i
$566$	−2.15753	+	7.84532i	−0.0906878	+	0.329763i
$567$	−0.422161	+	1.15988i	−0.0177291	+	0.0487103i
$568$	14.5951	+	32.9826i	0.612398	+	1.38392i
$569$		−	6.16529i		−	0.258462i	−0.991615	−	0.129231i	$-0.958749\pi$
$569$		−	6.16529i		−	0.258462i	0.991615	−	0.129231i	$-0.0412509\pi$
$570$	−0.515930	+	7.32161i	−0.0216099	+	0.306668i
$571$		−	17.3126i		−	0.724511i	−0.932079	−	0.362256i	$-0.882007\pi$
$571$		−	17.3126i		−	0.724511i	0.932079	−	0.362256i	$-0.117993\pi$
$572$	5.38047	−	3.01278i	0.224969	−	0.125971i
$573$	−3.84208	+	10.5560i	−0.160505	+	0.440984i
$574$	0.470146	+	0.129294i	0.0196235	+	0.00539663i
$575$	−6.79230	+	1.19767i	−0.283258	+	0.0499461i
$576$	−12.3698	−	2.68807i	−0.515408	−	0.112003i
$577$	−6.96676	+	12.0668i	−0.290030	+	0.502346i	−0.973816	−	0.227336i	$-0.926999\pi$
$577$	−6.96676	+	12.0668i	−0.290030	+	0.502346i	0.683787	+	0.729682i	$0.260332\pi$
$578$	15.7613	−	7.22385i	0.655585	−	0.300473i
$579$	−9.16407	+	10.9213i	−0.380846	+	0.453874i
$580$	−5.22681	+	4.26996i	−0.217032	+	0.177301i
$581$	−3.61922	−	6.26868i	−0.150151	−	0.260069i
$582$	1.12074	−	1.57839i	0.0464561	−	0.0654264i
$583$	−31.2352	+	11.3687i	−1.29363	+	0.470843i
$584$	−26.3018	−	2.82485i	−1.08838	−	0.116893i
$585$	1.21095	+	0.213523i	0.0500665	+	0.00882808i
$586$	1.00876	+	0.478493i	0.0416716	+	0.0197664i
$587$	9.09877	+	10.8435i	0.375547	+	0.447559i	0.920403	−	0.390970i	$-0.127860\pi$
$587$	9.09877	+	10.8435i	0.375547	+	0.447559i	−0.544857	+	0.838529i	$0.683416\pi$
$588$	15.2119	+	2.88901i	0.627327	+	0.119141i
$589$	−21.2465	−	34.8814i	−0.875448	−	1.43726i
$590$	−0.629642	+	6.68994i	−0.0259220	+	0.275420i
$591$	7.81771	−	6.55984i	0.321578	−	0.269836i
$592$	21.3822	−	24.1623i	0.878801	−	0.993065i
$593$	−5.65641	+	32.0791i	−0.232281	+	1.31733i	0.615984	+	0.787759i	$0.288759\pi$
$593$	−5.65641	+	32.0791i	−0.232281	+	1.31733i	−0.848265	+	0.529572i	$0.822352\pi$
$594$	2.46761	+	30.5144i	0.101247	+	1.25202i
$595$	0.525416	+	1.44357i	0.0215399	+	0.0591805i
$596$	11.4102	−	13.2405i	0.467378	−	0.542353i
$597$	0.953798	−	0.550676i	0.0390364	−	0.0225377i
$598$	−5.39490	+	5.32442i	−0.220614	+	0.217732i
$599$	36.5294	+	30.6518i	1.49255	+	1.25240i	0.891360	+	0.453297i	$0.149752\pi$
$599$	36.5294	+	30.6518i	1.49255	+	1.25240i	0.601193	+	0.799104i	$0.294692\pi$
$600$	−3.26952	+	0.807299i	−0.133478	+	0.0329579i
$601$	−25.0013	−	14.4345i	−1.01982	−	0.588795i	−0.105771	−	0.994391i	$-0.533731\pi$
$601$	−25.0013	−	14.4345i	−1.01982	−	0.588795i	−0.914053	+	0.405595i	$0.867064\pi$
$602$	−0.737123	−	2.82515i	−0.0300429	−	0.115145i
$603$	−0.899186	−	5.09954i	−0.0366177	−	0.207669i
$604$	9.29075	−	24.5181i	0.378035	−	0.997627i
$605$	−4.45607	−	1.62188i	−0.181165	−	0.0659387i
$606$	−16.3456	−	23.6737i	−0.663993	−	0.961677i
$607$	−0.199379			−0.00809255			−0.00404627	−	0.999992i	$-0.501288\pi$
$607$	−0.199379			−0.00809255			−0.00404627	+	0.999992i	$0.501288\pi$
$608$	20.0648	+	14.3320i	0.813734	+	0.581238i
$609$	2.83508			0.114883
$610$	−5.04618	−	7.30849i	−0.204314	−	0.295912i
$611$	7.13143	+	2.59563i	0.288507	+	0.105008i
$612$	2.44147	−	6.44298i	0.0986905	−	0.260442i
$613$	−5.18728	−	29.4185i	−0.209512	−	1.18820i	−0.890179	−	0.455610i	$-0.849421\pi$
$613$	−5.18728	−	29.4185i	−0.209512	−	1.18820i	0.680667	−	0.732593i	$-0.261690\pi$
$614$	−7.78142	−	29.8236i	−0.314032	−	1.20358i
$615$	−0.503870	−	0.290909i	−0.0203180	−	0.0117306i
$616$	−7.68734	+	1.89813i	−0.309732	+	0.0764779i
$617$	−7.44779	−	6.24944i	−0.299837	−	0.251593i	0.480440	−	0.877028i	$-0.340477\pi$
$617$	−7.44779	−	6.24944i	−0.299837	−	0.251593i	−0.780276	+	0.625435i	$0.784922\pi$
$618$	17.8274	−	17.5945i	0.717122	−	0.707754i
$619$	−29.3738	+	16.9590i	−1.18063	+	0.681638i	−0.956161	−	0.292843i	$-0.905399\pi$
$619$	−29.3738	+	16.9590i	−1.18063	+	0.681638i	−0.224471	+	0.974481i	$0.572065\pi$
$620$	12.2335	−	14.1960i	0.491310	−	0.570124i
$621$	−12.8704	−	35.3611i	−0.516471	−	1.41899i
$622$	−3.00249	−	37.1287i	−0.120389	−	1.48873i
$623$	0.752117	−	4.26547i	0.0301329	−	0.170892i
$624$	−2.45276	+	2.77167i	−0.0981890	+	0.110956i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	1.77169	−	18.8242i	0.0708112	−	0.752367i
$627$	6.58641	−	19.5102i	0.263036	−	0.779162i
$628$	43.2775	+	8.21918i	1.72696	+	0.327981i
$629$	11.2885	+	13.4531i	0.450101	+	0.536410i
$630$	−1.42657	−	0.676673i	−0.0568357	−	0.0269593i
$631$	−20.2149	−	3.56444i	−0.804743	−	0.141898i	−0.243879	−	0.969806i	$-0.578420\pi$
$631$	−20.2149	−	3.56444i	−0.804743	−	0.141898i	−0.560864	+	0.827908i	$0.689531\pi$
$632$	6.56872	+	0.705489i	0.261290	+	0.0280628i
$633$	14.6382	−	5.32789i	0.581818	−	0.211765i
$634$	6.73057	−	9.47899i	0.267305	−	0.376459i
$635$	4.95253	+	8.57803i	0.196535	+	0.340409i
$636$	15.4501	−	12.6217i	0.612636	−	0.500483i
$637$	−3.24792	+	3.87072i	−0.128687	+	0.153364i
$638$	17.2134	−	7.88936i	0.681484	−	0.312343i
$639$	10.0887	−	17.4741i	0.399102	−	0.691265i
$640$	−3.42789	+	10.7819i	−0.135499	+	0.426192i
$641$	3.11917	−	0.549993i	0.123200	−	0.0217234i	−0.111708	−	0.993741i	$-0.535632\pi$
$641$	3.11917	−	0.549993i	0.123200	−	0.0217234i	0.234908	+	0.972018i	$0.424521\pi$
$642$	11.4149	+	3.13919i	0.450509	+	0.123894i
$643$	−8.34807	+	22.9361i	−0.329216	+	0.904513i	0.659095	+	0.752060i	$0.270940\pi$
$643$	−8.34807	+	22.9361i	−0.329216	+	0.904513i	−0.988311	+	0.152453i	$0.951283\pi$
$644$	8.49229	−	4.75524i	0.334643	−	0.187383i
$645$			3.48391i			0.137179i
$646$	−9.32834	+	9.64940i	−0.367019	+	0.379651i
$647$		−	39.4490i		−	1.55090i	−0.631408	−	0.775451i	$-0.717523\pi$
$647$		−	39.4490i		−	1.55090i	0.631408	−	0.775451i	$-0.282477\pi$
$648$	−2.00222	−	4.52469i	−0.0786545	−	0.177746i
$649$	6.44770	−	17.7149i	0.253094	−	0.695371i
$650$	0.291415	−	1.05966i	0.0114302	−	0.0415631i
$651$	−7.75230	+	1.36694i	−0.303837	+	0.0535746i
$652$	1.95394	+	12.0022i	0.0765223	+	0.470042i
$653$	0.914147	−	1.58335i	0.0357733	−	0.0619612i	−0.847584	−	0.530661i	$-0.821944\pi$
$653$	0.914147	−	1.58335i	0.0357733	−	0.0619612i	0.883358	+	0.468699i	$0.155277\pi$
$654$	−4.70006	−	10.2548i	−0.183787	−	0.400994i
$655$	4.52347	−	5.39086i	0.176747	−	0.210638i
$656$	−1.71785	+	0.932448i	−0.0670706	+	0.0364060i
$657$	7.39936	+	12.8161i	0.288677	+	0.500002i
$658$	−7.94560	−	5.64178i	−0.309752	−	0.219940i
$659$	−30.4043	+	11.0663i	−1.18438	+	0.431081i	−0.857749	−	0.514069i	$-0.828137\pi$
$659$	−30.4043	+	11.0663i	−1.18438	+	0.431081i	−0.326636	+	0.945150i	$0.605915\pi$
$660$	9.44742	+	0.124239i	0.367740	+	0.00483599i
$661$	19.0414	+	3.35751i	0.740624	+	0.130592i	0.531216	−	0.847236i	$-0.321735\pi$
$661$	19.0414	+	3.35751i	0.740624	+	0.130592i	0.209408	+	0.977828i	$0.432846\pi$
$662$	−12.6859	+	26.7445i	−0.493052	+	1.03945i
$663$	−1.29491	−	1.54321i	−0.0502901	−	0.0599334i
$664$	27.8738	+	8.06125i	1.08171	+	0.312837i
$665$	2.03174	+	2.30895i	0.0787877	+	0.0895373i
$666$	−17.9705	−	1.69135i	−0.696344	−	0.0655383i
$667$	−17.8297	+	14.9609i	−0.690368	+	0.579288i
$668$	5.40703	+	3.21728i	0.209204	+	0.124480i
$669$	−2.55707	+	14.5019i	−0.0988621	+	0.560675i
$670$	−4.61303	+	0.373043i	−0.178217	+	0.0144119i
$671$	8.52207	+	23.4142i	0.328991	+	0.903895i
$672$	3.98046	−	2.59646i	0.153550	−	0.100161i
$673$	−42.7364	+	24.6739i	−1.64737	+	0.951107i	−0.669253	+	0.743034i	$0.733386\pi$
$673$	−42.7364	+	24.6739i	−1.64737	+	0.951107i	−0.978113	+	0.208073i	$0.933281\pi$
$674$	−29.2857	−	29.6734i	−1.12804	−	1.14298i
$675$	4.17954	+	3.50705i	0.160871	+	0.134987i
$676$	8.17236	+	23.4065i	0.314321	+	0.900251i
$677$	16.6240	+	9.59786i	0.638912	+	0.368876i	0.784195	−	0.620514i	$-0.213076\pi$
$677$	16.6240	+	9.59786i	0.638912	+	0.368876i	−0.145283	+	0.989390i	$0.546409\pi$
$678$	1.79040	−	0.467141i	0.0687599	−	0.0179404i
$679$	−0.140857	−	0.798843i	−0.00540561	−	0.0306568i
$680$	−5.52869	−	2.71209i	−0.212016	−	0.104004i
$681$	20.8072	+	7.57321i	0.797334	+	0.290206i
$682$	−43.2647	+	29.8723i	−1.65669	+	1.14387i
$683$	−50.9093			−1.94799			−0.973996	−	0.226566i	$-0.927250\pi$
$683$	−50.9093			−1.94799			−0.973996	+	0.226566i	$0.927250\pi$
$684$	−0.142644	−	13.7935i	−0.00545414	−	0.527410i
$685$	16.1013			0.615198
$686$	11.0871	−	7.65515i	0.423309	−	0.292275i
$687$	−26.2309	−	9.54728i	−1.00077	−	0.364251i
$688$	9.97862	+	6.11655i	0.380431	+	0.233191i
$689$	1.13052	+	6.41152i	0.0430696	+	0.244260i
$690$	−11.2375	+	2.93202i	−0.427804	+	0.111620i
$691$	−34.7296	−	20.0511i	−1.32118	−	0.762782i	−0.337260	−	0.941412i	$-0.609500\pi$
$691$	−34.7296	−	20.0511i	−1.32118	−	0.762782i	−0.983916	+	0.178630i	$0.942834\pi$
$692$	−32.7565	+	11.4369i	−1.24522	+	0.434765i
$693$	3.39335	+	2.84736i	0.128903	+	0.108162i
$694$	−29.7745	−	30.1686i	−1.13022	−	1.14518i
$695$	−11.4337	+	6.60126i	−0.433706	+	0.250400i
$696$	−8.19302	+	7.87602i	−0.310556	+	0.298540i
$697$	−0.363872	−	0.999731i	−0.0137827	−	0.0378675i
$698$	−26.3331	+	2.12948i	−0.996723	+	0.0806022i
$699$	4.85399	−	27.5283i	0.183595	−	1.04122i
$700$	−0.721597	+	1.21273i	−0.0272738	+	0.0458369i
$701$	−23.0430	+	19.3354i	−0.870323	+	0.730287i	−0.964166	−	0.265300i	$-0.914529\pi$
$701$	−23.0430	+	19.3354i	−0.870323	+	0.730287i	0.0938435	+	0.995587i	$0.470085\pi$
$702$	5.96975	+	0.561860i	0.225314	+	0.0212060i
$703$	30.8537	+	16.8598i	1.16367	+	0.635879i
$704$	16.9423	−	26.8412i	0.638536	−	1.01162i
$705$	7.47424	+	8.90745i	0.281496	+	0.335474i
$706$	−7.27389	+	15.3349i	−0.273756	+	0.577135i
$707$	−11.8717	−	2.09330i	−0.446481	−	0.0787267i
$708$	−0.148782	+	11.3137i	−0.00559156	+	0.425195i
$709$	−8.67981	+	3.15919i	−0.325977	+	0.118646i	−0.499825	−	0.866127i	$-0.666602\pi$
$709$	−8.67981	+	3.15919i	−0.325977	+	0.118646i	0.173848	+	0.984773i	$0.444380\pi$
$710$	−14.7041	−	10.4407i	−0.551834	−	0.391831i
$711$	−1.84794	−	3.20073i	−0.0693033	−	0.120037i
$712$	9.67619	+	14.4161i	0.362630	+	0.540265i
$713$	41.5404	−	49.5059i	1.55570	−	1.85401i
$714$	1.07778	+	2.35154i	0.0403347	+	0.0880042i
$715$	−1.54164	+	2.67019i	−0.0576540	+	0.0998596i
$716$	31.2834	−	5.09291i	1.16912	−	0.190331i
$717$	8.94777	−	1.57773i	0.334161	−	0.0589216i
$718$	−5.70647	+	20.7501i	−0.212963	+	0.774388i
$719$	−8.32363	+	22.8690i	−0.310419	+	0.852869i	0.682153	+	0.731210i	$0.261044\pi$
$719$	−8.32363	+	22.8690i	−0.310419	+	0.852869i	−0.992572	+	0.121660i	$0.961178\pi$
$720$	6.00242	−	2.00758i	0.223697	−	0.0748182i
$721$		−	10.4957i		−	0.390881i
$722$	−10.3628	+	24.7914i	−0.385662	+	0.922640i
$723$		−	4.78982i		−	0.178135i
$724$	−13.7276	−	24.5158i	−0.510180	−	0.911121i
$725$	1.15419	−	3.17110i	0.0428654	−	0.117772i
$726$	−7.69910	−	2.11732i	−0.285741	−	0.0785811i
$727$	−39.7241	+	7.00442i	−1.47328	+	0.259780i	−0.851891	−	0.523719i	$-0.824544\pi$
$727$	−39.7241	+	7.00442i	−1.47328	+	0.259780i	−0.621393	+	0.783499i	$0.713433\pi$
$728$	0.104669	+	1.54734i	0.00387931	+	0.0573483i
$729$	−11.1284	+	19.2750i	−0.412164	+	0.713889i
$730$	12.0238	−	5.51085i	0.445022	−	0.203966i
$731$	−4.09491	+	4.88012i	−0.151456	+	0.180498i
$732$	−9.46134	−	11.5815i	−0.349701	−	0.428065i
$733$	−23.6933	−	41.0380i	−0.875133	−	1.51577i	−0.856621	−	0.515946i	$-0.827440\pi$
$733$	−23.6933	−	41.0380i	−0.875133	−	1.51577i	−0.0185118	−	0.999829i	$-0.505893\pi$
$734$	−13.0322	+	18.3539i	−0.481027	+	0.677454i
$735$	−7.27499	+	2.64788i	−0.268342	+	0.0976686i
$736$	−11.3313	+	37.3341i	−0.417676	+	1.37615i
$737$	12.7870	+	2.25469i	0.471015	+	0.0830527i
$738$	0.987956	+	0.468624i	0.0363672	+	0.0172503i
$739$	28.6365	+	34.1276i	1.05341	+	1.25541i	0.965810	+	0.259250i	$0.0834754\pi$
$739$	28.6365	+	34.1276i	1.05341	+	1.25541i	0.0876003	+	0.996156i	$0.472080\pi$
$740$	−3.01002	+	15.8491i	−0.110651	+	0.582624i
$741$	−3.53925	−	1.93400i	−0.130017	−	0.0710471i
$742$	0.783342	−	8.32300i	0.0287574	−	0.305547i
$743$	−6.41201	+	5.38032i	−0.235234	+	0.197385i	−0.752783	−	0.658269i	$-0.771289\pi$
$743$	−6.41201	+	5.38032i	−0.235234	+	0.197385i	0.517549	+	0.855654i	$0.326845\pi$
$744$	18.6057	−	25.4866i	0.682118	−	0.934384i
$745$	−1.51757	+	8.60656i	−0.0555994	+	0.315320i
$746$	−1.39577	−	17.2600i	−0.0511027	−	0.631934i
$747$	−5.55186	−	15.2536i	−0.203132	−	0.558100i
$748$	13.0875	+	11.2783i	0.478528	+	0.412376i
$749$	4.29615	−	2.48038i	0.156978	−	0.0906312i
$750$	1.19847	−	1.18281i	0.0437619	−	0.0431902i
$751$	−24.4665	−	20.5298i	−0.892795	−	0.749144i	0.0759741	−	0.997110i	$-0.475793\pi$
$751$	−24.4665	−	20.5298i	−0.892795	−	0.749144i	−0.968769	+	0.247966i	$0.920238\pi$
$752$	38.6349	−	5.76930i	1.40887	−	0.210385i
$753$	12.4888	+	7.21042i	0.455117	+	0.262762i
$754$	−0.936306	−	3.58856i	−0.0340983	−	0.130687i
$755$	2.27647	+	12.9105i	0.0828493	+	0.469862i
$756$	−7.19981	−	2.72826i	−0.261854	−	0.0992257i
$757$	15.9896	+	5.81976i	0.581154	+	0.211523i	0.615834	−	0.787876i	$-0.288819\pi$
$757$	15.9896	+	5.81976i	0.581154	+	0.211523i	−0.0346805	+	0.999398i	$0.511041\pi$
$758$	8.62955	+	12.4984i	0.313439	+	0.453961i
$759$	32.5826			1.18267
$760$	−12.2859	−	1.02827i	−0.445655	−	0.0372991i
$761$	5.62197			0.203796			0.101898	−	0.994795i	$-0.467508\pi$
$761$	5.62197			0.203796			0.101898	+	0.994795i	$0.467508\pi$
$762$	9.47647	+	13.7250i	0.343296	+	0.497204i
$763$	−4.44184	−	1.61670i	−0.160806	−	0.0585284i
$764$	−17.6449	−	6.68626i	−0.638370	−	0.241900i
$765$	0.598222	+	3.39269i	0.0216288	+	0.122663i
$766$	2.04439	+	7.83546i	0.0738666	+	0.283107i
$767$	−3.19767	−	1.84618i	−0.115461	−	0.0666616i
$768$	−4.28991	+	18.5614i	−0.154799	+	0.669776i
$769$	15.0651	+	12.6411i	0.543261	+	0.455850i	0.872651	−	0.488343i	$-0.162399\pi$
$769$	15.0651	+	12.6411i	0.543261	+	0.455850i	−0.329390	+	0.944194i	$0.606843\pi$
$770$	2.81786	−	2.78104i	0.101548	−	0.100222i
$771$	−18.9440	+	10.9373i	−0.682251	+	0.393898i
$772$	−18.1409	−	15.6331i	−0.652905	−	0.562647i
$773$	−4.34191	−	11.9293i	−0.156168	−	0.429067i	0.836792	−	0.547521i	$-0.184428\pi$
$773$	−4.34191	−	11.9293i	−0.156168	−	0.429067i	−0.992960	+	0.118454i	$0.962206\pi$
$774$	−0.527765	−	6.52632i	−0.0189701	−	0.234584i
$775$	−1.62708	+	9.22761i	−0.0584463	+	0.331466i
$776$	2.62629	+	1.91724i	0.0942783	+	0.0688249i
$777$	5.19115	−	4.35589i	0.186232	−	0.156267i
$778$	−5.03190	+	53.4638i	−0.180402	+	1.91677i
$779$	−1.40707	−	1.59905i	−0.0504135	−	0.0572918i
$780$	0.345281	−	1.81806i	0.0123631	−	0.0650969i
$781$	32.5215	+	38.7576i	1.16371	+	1.38685i
$782$	−19.1873	−	9.10123i	−0.686135	−	0.325459i
$783$	18.1322	+	3.19720i	0.647992	+	0.114259i
$784$	−5.18833	+	25.4858i	−0.185297	+	0.910208i
$785$	−20.6972	+	7.53318i	−0.738716	+	0.268871i
$786$	6.86041	−	9.66185i	0.244703	−	0.344627i
$787$	25.2056	+	43.6573i	0.898482	+	1.55622i	0.829436	+	0.558602i	$0.188662\pi$
$787$	25.2056	+	43.6573i	0.898482	+	1.55622i	0.0690462	+	0.997613i	$0.478004\pi$
$788$	10.8451	+	13.2754i	0.386342	+	0.472917i
$789$	−3.87917	+	4.62301i	−0.138102	+	0.164584i
$790$	−3.00287	+	1.37630i	−0.106837	+	0.0489665i
$791$	0.387675	−	0.671472i	0.0137841	−	0.0238748i
$792$	−17.7165	+	1.19842i	−0.629527	+	0.0425841i
$793$	4.80613	−	0.847451i	0.170671	−	0.0300939i
$794$	7.13864	+	1.96319i	0.253341	+	0.0696709i
$795$	−3.41169	+	9.37355i	−0.121000	+	0.332446i
$796$	0.903840	+	1.61415i	0.0320358	+	0.0572120i
$797$		−	19.8076i		−	0.701620i	−0.936447	−	0.350810i	$-0.885906\pi$
$797$		−	19.8076i		−	0.701620i	0.936447	−	0.350810i	$-0.114094\pi$
$798$	3.72342	+	3.59953i	0.131808	+	0.127422i
$799$			21.2622i			0.752204i
$800$	−1.28371	−	5.50927i	−0.0453861	−	0.194782i
$801$	3.32206	−	9.12729i	0.117379	−	0.322497i
$802$	13.3888	−	48.6849i	0.472774	−	1.71912i
$803$	−36.5438	+	6.44366i	−1.28960	+	0.227392i
$804$	−7.69178	+	1.25221i	−0.271268	+	0.0441621i
$805$	−2.43325	+	4.21451i	−0.0857608	+	0.148542i
$806$	4.29048	+	9.36117i	0.151126	+	0.329733i
$807$	−8.21832	+	9.79421i	−0.289299	+	0.344773i
$808$	40.1230	−	26.9309i	1.41152	−	0.947426i
$809$	−17.0987	−	29.6158i	−0.601159	−	1.04124i	−0.992646	−	0.121054i	$-0.961373\pi$
$809$	−17.0987	−	29.6158i	−0.601159	−	1.04124i	0.391487	−	0.920183i	$-0.371961\pi$
$810$	2.01717	+	1.43229i	0.0708760	+	0.0503256i
$811$	25.2496	−	9.19010i	0.886633	−	0.322708i	0.141749	−	0.989903i	$-0.454727\pi$
$811$	25.2496	−	9.19010i	0.886633	−	0.322708i	0.744883	+	0.667195i	$0.232505\pi$
$812$	−0.0626199	+	4.76177i	−0.00219753	+	0.167105i
$813$	−26.8101	−	4.72735i	−0.940273	−	0.165795i
$814$	19.3970	−	40.8928i	0.679863	−	1.43329i
$815$	−3.90821	−	4.65762i	−0.136899	−	0.163149i
$816$	−9.64734	−	3.80152i	−0.337724	−	0.133080i
$817$	−4.07948	+	12.0842i	−0.142723	+	0.422772i
$818$	38.6874	+	3.64118i	1.35267	+	0.127311i
$819$	0.664629	−	0.557690i	0.0232240	−	0.0194873i
$820$	0.499737	−	0.839867i	0.0174516	−	0.0293294i
$821$	−1.28778	+	7.30336i	−0.0449438	+	0.254889i	−0.998999	−	0.0447435i	$-0.985753\pi$
$821$	−1.28778	+	7.30336i	−0.0449438	+	0.254889i	0.954055	+	0.299633i	$0.0968641\pi$
$822$	27.0240	−	2.18536i	0.942571	−	0.0762231i
$823$	−2.87205	−	7.89089i	−0.100113	−	0.275059i	0.879517	−	0.475867i	$-0.157866\pi$
$823$	−2.87205	−	7.89089i	−0.100113	−	0.275059i	−0.979631	+	0.200808i	$0.935643\pi$
$824$	29.1577	+	30.3312i	1.01576	+	1.05664i
$825$	−4.09121	+	2.36206i	−0.142438	+	0.0822364i
$826$	3.33042	+	3.37451i	0.115880	+	0.117414i
$827$	−14.5792	−	12.2334i	−0.506969	−	0.425397i	0.353092	−	0.935589i	$-0.385130\pi$
$827$	−14.5792	−	12.2334i	−0.506969	−	0.425397i	−0.860061	+	0.510191i	$0.829575\pi$
$828$	20.6068	−	7.19482i	0.716135	−	0.250037i
$829$	24.1353	+	13.9345i	0.838254	+	0.483966i	0.856670	−	0.515864i	$-0.172529\pi$
$829$	24.1353	+	13.9345i	0.838254	+	0.483966i	−0.0184161	+	0.999830i	$0.505862\pi$
$830$	−14.0381	+	3.66274i	−0.487269	+	0.127136i
$831$	−0.493672	−	2.79976i	−0.0171253	−	0.0971224i
$832$	−4.60109	−	4.18084i	−0.159514	−	0.144945i
$833$	−13.3028	−	4.84182i	−0.460914	−	0.167759i
$834$	−18.2941	+	12.6313i	−0.633474	+	0.437385i
$835$	−3.14590			−0.108868
$836$	32.6236	+	11.4934i	1.12831	+	0.397507i
$837$	−51.1226			−1.76705
$838$	15.3353	−	10.5883i	0.529748	−	0.365767i
$839$	46.1633	+	16.8021i	1.59373	+	0.580072i	0.978132	−	0.207985i	$-0.0666904\pi$
$839$	46.1633	+	16.8021i	1.59373	+	0.580072i	0.615603	+	0.788057i	$0.288913\pi$
$840$	−1.04651	+	2.13336i	−0.0361082	+	0.0736079i
$841$	3.05829	+	17.3444i	0.105458	+	0.598083i
$842$	−20.1543	+	5.25855i	−0.694564	+	0.181222i
$843$	−0.856247	−	0.494355i	−0.0294907	−	0.0170265i
$844$	8.62532	+	24.7039i	0.296896	+	0.850343i
$845$	−9.49597	−	7.96806i	−0.326671	−	0.274110i
$846$	−15.3507	−	15.5539i	−0.527767	−	0.534753i
$847$	−2.89767	+	1.67297i	−0.0995650	+	0.0574839i
$848$	20.8580	+	26.2285i	0.716266	+	0.900692i
$849$	−2.34298	−	6.43729i	−0.0804109	−	0.220927i
$850$	3.06902	−	0.248183i	0.105266	−	0.00851260i
$851$	−9.66059	+	54.7879i	−0.331161	+	1.87811i
$852$	−26.0961	−	15.5276i	−0.894037	−	0.531968i
$853$	2.39029	−	2.00569i	0.0818419	−	0.0686735i	−0.600949	−	0.799287i	$-0.705210\pi$
$853$	2.39029	−	2.00569i	0.0818419	−	0.0686735i	0.682791	+	0.730614i	$0.260766\pi$
$854$	−6.23899	−	0.587200i	−0.213494	−	0.0200936i
$855$	3.58792	+	5.89045i	0.122704	+	0.201449i
$856$	−5.52466	+	19.1029i	−0.188829	+	0.652924i
$857$	−10.4753	−	12.4840i	−0.357829	−	0.426444i	0.556858	−	0.830608i	$-0.312007\pi$
$857$	−10.4753	−	12.4840i	−0.357829	−	0.426444i	−0.914687	+	0.404164i	$0.867562\pi$
$858$	−2.22504	+	4.69083i	−0.0759615	+	0.160142i
$859$	8.20238	+	1.44630i	0.279862	+	0.0493472i	0.311817	−	0.950142i	$-0.399062\pi$
$859$	8.20238	+	1.44630i	0.279862	+	0.0493472i	−0.0319555	+	0.999489i	$0.510173\pi$
$860$	−5.85152	−	0.0769508i	−0.199535	−	0.00262400i
$861$	−0.385767	+	0.140408i	−0.0131469	+	0.00478508i
$862$	−8.50347	−	6.03790i	−0.289629	−	0.205652i
$863$	−24.7608	−	42.8870i	−0.842869	−	1.45989i	−0.887459	−	0.460886i	$-0.847532\pi$
$863$	−24.7608	−	42.8870i	−0.842869	−	1.45989i	0.0445909	−	0.999005i	$-0.485802\pi$
$864$	28.3857	−	12.1172i	0.965703	−	0.412234i
$865$	11.1510	−	13.2892i	0.379145	−	0.451847i
$866$	0.142559	+	0.311042i	0.00484436	+	0.0105696i
$867$	−7.29865	+	12.6416i	−0.247875	+	0.429332i
$868$	−2.12466	−	13.0509i	−0.0721158	−	0.442975i
$869$	9.12659	−	1.60926i	0.309598	−	0.0545905i
$870$	1.50676	−	5.47896i	0.0510840	−	0.185754i
$871$	0.869801	−	2.38976i	0.0294721	−	0.0809739i
$872$	17.3276	−	7.66765i	0.586788	−	0.259659i
$873$		−	1.81908i		−	0.0615664i
$874$	−42.4113	−	2.98859i	−1.43458	−	0.101091i
$875$		−	0.705588i		−	0.0238532i
$876$	19.4326	−	10.8812i	0.656565	−	0.367643i
$877$	−0.344688	+	0.947024i	−0.0116393	+	0.0319787i	−0.945376	−	0.325981i	$-0.894305\pi$
$877$	−0.344688	+	0.947024i	−0.0116393	+	0.0319787i	0.933737	+	0.357960i	$0.116528\pi$
$878$	5.00159	+	1.37548i	0.168795	+	0.0464202i
$879$	−0.925726	+	0.163230i	−0.0312240	+	0.00550563i
$880$	−0.417340	+	15.8650i	−0.0140685	+	0.534810i
$881$	10.4503	−	18.1005i	0.352080	−	0.609821i	−0.634534	−	0.772895i	$-0.718808\pi$
$881$	10.4503	−	18.1005i	0.352080	−	0.609821i	0.986614	+	0.163074i	$0.0521411\pi$
$882$	13.2270	−	6.06228i	0.445375	−	0.204128i
$883$	7.57743	−	9.03043i	0.255001	−	0.303898i	−0.623323	−	0.781965i	$-0.714218\pi$
$883$	7.57743	−	9.03043i	0.255001	−	0.303898i	0.878324	+	0.478066i	$0.158662\pi$
$884$	2.62056	−	2.14082i	0.0881389	−	0.0720037i
$885$	−2.82867	−	4.89940i	−0.0950847	−	0.164692i
$886$	−6.73485	+	9.48502i	−0.226262	+	0.318655i
$887$	27.6340	−	10.0580i	0.927860	−	0.337714i	0.166499	−	0.986042i	$-0.446754\pi$
$887$	27.6340	−	10.0580i	0.927860	−	0.337714i	0.761361	+	0.648328i	$0.224531\pi$
$888$	−2.90083	+	27.0093i	−0.0973455	+	0.906372i
$889$	6.88272	+	1.21361i	0.230839	+	0.0407031i
$890$	−7.84353	−	3.72047i	−0.262916	−	0.124711i
$891$	−4.46142	−	5.31692i	−0.149463	−	0.178123i
$892$	−24.3007	−	4.61513i	−0.813647	−	0.154526i
$893$	15.4948	+	39.6481i	0.518512	+	1.32677i
$894$	−1.37892	+	14.6510i	−0.0461181	+	0.490004i
$895$	−12.1400	+	10.1867i	−0.405795	+	0.340503i
$896$	4.27306	+	6.74288i	0.142753	+	0.225264i
$897$	1.10817	−	6.28476i	0.0370008	−	0.209842i
$898$	−3.51796	−	43.5030i	−0.117396	−	1.45171i
$899$	10.8147	+	29.7131i	0.360690	+	0.990987i
$900$	−2.06588	+	2.39729i	−0.0688628	+	0.0799096i
$901$	−15.7964	+	9.12007i	−0.526255	+	0.303834i
$902$	−1.95148	+	1.92599i	−0.0649773	+	0.0641284i
$903$	1.88309	+	1.58010i	0.0626654	+	0.0525825i
$904$	0.745058	+	3.01745i	0.0247803	+	0.100359i
$905$	12.1666	+	7.02437i	0.404430	+	0.233498i
$906$	5.57307	+	21.3597i	0.185153	+	0.709630i
$907$	0.582237	+	3.30203i	0.0193329	+	0.109642i	0.992947	−	0.118558i	$-0.0378271\pi$
$907$	0.582237	+	3.30203i	0.0193329	+	0.109642i	−0.973614	+	0.228200i	$0.926716\pi$
$908$	−13.1794	+	34.7802i	−0.437375	+	1.15422i
$909$	−25.4032	−	9.24601i	−0.842571	−	0.306671i
$910$	−0.440588	−	0.638113i	−0.0146053	−	0.0211533i
$911$	−23.1895			−0.768301			−0.384151	−	0.923270i	$-0.625506\pi$
$911$	−23.1895			−0.768301			−0.384151	+	0.923270i	$0.625506\pi$
$912$	−20.7599	−	0.0583107i	−0.687429	−	0.00193086i
$913$	40.7028			1.34707
$914$	14.5644	+	21.0940i	0.481748	+	0.697727i
$915$	7.02649	+	2.55743i	0.232289	+	0.0845462i
$916$	16.6148	−	43.8462i	0.548970	−	1.44872i
$917$	−0.862235	−	4.88998i	−0.0284735	−	0.161481i
$918$	4.24118	+	16.2551i	0.139980	+	0.536497i
$919$	38.0623	+	21.9753i	1.25556	+	0.724898i	0.972208	−	0.234119i	$-0.0752204\pi$
$919$	38.0623	+	21.9753i	1.25556	+	0.724898i	0.283351	+	0.959016i	$0.408554\pi$
$920$	−4.67638	−	18.9391i	−0.154176	−	0.624403i
$921$	19.8788	+	16.6803i	0.655030	+	0.549635i
$922$	16.3762	−	16.1623i	0.539322	−	0.532276i
$923$	8.58191	−	4.95477i	0.282477	−	0.163088i
$924$	4.35197	−	5.05010i	0.143169	−	0.166136i
$925$	−2.75880	−	7.57974i	−0.0907087	−	0.249220i
$926$	4.29778	+	53.1461i	0.141234	+	1.74649i
$927$	4.08718	−	23.1795i	0.134240	−	0.761316i
$928$	−13.0475	−	13.9348i	−0.428305	−	0.457434i
$929$	2.83793	−	2.38131i	0.0931095	−	0.0781282i	−0.595045	−	0.803693i	$-0.702866\pi$
$929$	2.83793	−	2.38131i	0.0931095	−	0.0781282i	0.688154	+	0.725564i	$0.258421\pi$
$930$	−1.47843	+	15.7083i	−0.0484795	+	0.515094i
$931$	−28.3344	+	0.665720i	−0.928622	+	0.0218181i
$932$	46.1290	+	8.76072i	1.51100	+	0.286967i
$933$	20.1590	+	24.0245i	0.659975	+	0.786527i
$934$	−9.28619	−	4.40478i	−0.303854	−	0.144129i
$935$	−8.50711	−	1.50003i	−0.278212	−	0.0490563i
$936$	−0.371397	+	3.45803i	−0.0121395	+	0.113029i
$937$	45.6944	−	16.6314i	1.49277	−	0.543324i	0.538593	−	0.842566i	$-0.318956\pi$
$937$	45.6944	−	16.6314i	1.49277	−	0.543324i	0.954177	+	0.299243i	$0.0967340\pi$
$938$	−1.89058	+	2.66259i	−0.0617295	+	0.0869366i
$939$	7.95934	+	13.7860i	0.259743	+	0.449889i
$940$	−15.1259	+	12.3569i	−0.493353	+	0.403037i
$941$	19.9394	−	23.7628i	0.650006	−	0.774647i	−0.335909	−	0.941894i	$-0.609044\pi$
$941$	19.9394	−	23.7628i	0.650006	−	0.774647i	0.985915	+	0.167248i	$0.0534880\pi$
$942$	−33.7154	+	15.4527i	−1.09851	+	0.503475i
$943$	1.68513	−	2.91873i	0.0548753	−	0.0950468i
$944$	−18.9991	−	0.499783i	−0.618367	−	0.0162666i
$945$	3.79121	−	0.668492i	0.123328	−	0.0217461i
$946$	15.8304	+	4.35349i	0.514689	+	0.141544i
$947$	3.93078	−	10.7997i	0.127733	−	0.350944i	−0.859297	−	0.511476i	$-0.829099\pi$
$947$	3.93078	−	10.7997i	0.127733	−	0.350944i	0.987031	+	0.160532i	$0.0513210\pi$
$948$	−4.85316	+	2.71752i	−0.157623	+	0.0882609i
$949$			7.26797i			0.235928i
$950$	5.54199	−	2.69932i	0.179806	−	0.0875776i
$951$			9.78783i			0.317392i
$952$	−3.97342	+	1.75828i	−0.128779	+	0.0569861i
$953$	−12.2195	+	33.5728i	−0.395828	+	1.08753i	0.568469	+	0.822705i	$0.307536\pi$
$953$	−12.2195	+	33.5728i	−0.395828	+	1.08753i	−0.964297	+	0.264824i	$0.914686\pi$
$954$	4.97108	−	18.0761i	0.160945	−	0.585235i
$955$	9.29129	−	1.63830i	0.300659	−	0.0530143i
$956$	2.45231	+	15.0634i	0.0793132	+	0.487185i
$957$	−7.97104	+	13.8063i	−0.257667	+	0.446293i
$958$	−10.5803	−	23.0847i	−0.341835	−	0.745832i
$959$	7.30263	−	8.70294i	0.235814	−	0.281032i
$960$	−2.90231	−	9.07241i	−0.0936715	−	0.292811i
$961$	−28.3981	−	49.1869i	−0.916067	−	1.58667i
$962$	−7.22796	−	5.13223i	−0.233039	−	0.165470i
$963$	10.4538	−	3.80488i	0.336870	−	0.122611i
$964$	8.04491	+	0.105795i	0.259109	+	0.00340743i
$965$	11.7919	+	2.07922i	0.379593	+	0.0669326i
$966$	−3.51190	+	7.40380i	−0.112993	+	0.238213i
$967$	−26.2925	−	31.3342i	−0.845510	−	1.00764i	−0.999808	−	0.0196148i	$-0.993756\pi$
$967$	−26.2925	−	31.3342i	−0.845510	−	1.00764i	0.154298	−	0.988024i	$-0.450688\pi$
$968$	3.72628	−	12.8845i	0.119767	−	0.414125i
$969$	1.70025	−	11.1710i	0.0546198	−	0.358866i
$970$	−1.61867	−	0.152346i	−0.0519724	−	0.00489152i
$971$	−32.9133	+	27.6176i	−1.05624	+	0.886290i	−0.993736	−	0.111755i	$-0.964353\pi$
$971$	−32.9133	+	27.6176i	−1.05624	+	0.886290i	−0.0625031	+	0.998045i	$0.519908\pi$
$972$	−24.5526	−	14.6093i	−0.787525	−	0.468592i
$973$	−1.61763	+	9.17402i	−0.0518587	+	0.294106i
$974$	52.8825	−	4.27646i	1.69446	−	0.137027i
$975$	0.316463	+	0.869476i	0.0101349	+	0.0278455i
$976$	19.6611	−	15.6353i	0.629337	−	0.500475i
$977$	−32.4563	+	18.7386i	−1.03837	+	0.599502i	−0.919371	−	0.393393i	$-0.871301\pi$
$977$	−32.4563	+	18.7386i	−1.03837	+	0.599502i	−0.118997	+	0.992895i	$0.537968\pi$
$978$	−7.19161	−	7.28681i	−0.229962	−	0.233006i
$979$	18.6573	+	15.6553i	0.596289	+	0.500346i
$980$	−4.28666	−	12.2775i	−0.136932	−	0.392189i
$981$	−9.18014	−	5.30016i	−0.293099	−	0.169221i
$982$	−48.9842	+	12.7807i	−1.56315	+	0.407849i
$983$	−1.32124	−	7.49312i	−0.0421410	−	0.238993i	0.956461	−	0.291862i	$-0.0942747\pi$
$983$	−1.32124	−	7.49312i	−0.0421410	−	0.238993i	−0.998601	+	0.0528684i	$0.983164\pi$
$984$	0.724755	−	1.47744i	0.0231044	−	0.0470991i
$985$	−8.05418	−	2.93148i	−0.256628	−	0.0934048i
$986$	8.55046	−	5.90369i	0.272302	−	0.188012i
$987$	8.20447			0.261151
$988$	3.32649	−	5.90175i	0.105830	−	0.187760i
$989$	−20.1810			−0.641717
$990$	7.30614	−	5.04455i	0.232204	−	0.160326i
$991$	−24.7598	−	9.01183i	−0.786521	−	0.286270i	−0.0826319	−	0.996580i	$-0.526333\pi$
$991$	−24.7598	−	9.01183i	−0.786521	−	0.286270i	−0.703889	+	0.710310i	$0.748555\pi$
$992$	42.3960	+	31.8128i	1.34607	+	1.01006i
$993$	−4.32760	−	24.5430i	−0.137332	−	0.778850i
$994$	−12.3122	+	3.21244i	−0.390521	+	0.101892i
$995$	−0.801062	−	0.462494i	−0.0253954	−	0.0146620i
$996$	−23.0641	+	8.05279i	−0.730813	+	0.255162i
$997$	14.1071	+	11.8373i	0.446776	+	0.374889i	0.838238	−	0.545305i	$-0.183586\pi$
$997$	14.1071	+	11.8373i	0.446776	+	0.374889i	−0.391462	+	0.920194i	$0.628031\pi$
$998$	−30.2856	−	30.6865i	−0.958674	−	0.971364i
$999$	38.1131	−	22.0046i	1.20584	−	0.696194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.be.b.51.7	yes	120
4.3	odd	2	inner	380.2.be.b.51.5	✓	120
19.3	odd	18	inner	380.2.be.b.231.5	yes	120
76.3	even	18	inner	380.2.be.b.231.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.be.b.51.5	✓	120	4.3	odd	2	inner
380.2.be.b.51.7	yes	120	1.1	even	1	trivial
380.2.be.b.231.5	yes	120	19.3	odd	18	inner
380.2.be.b.231.7	yes	120	76.3	even	18	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.803525 - 1.16376i) q^{2} +(1.11886 + 0.407232i) q^{3} +(-0.708694 + 1.87023i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-0.425111 - 1.62931i) q^{6} +(-0.611057 - 0.352794i) q^{7} +(2.74596 - 0.678023i) q^{8} +(-1.21212 - 1.01709i) q^{9} +O(q^{10})\)	\(q+(-0.803525 - 1.16376i) q^{2} +(1.11886 + 0.407232i) q^{3} +(-0.708694 + 1.87023i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(-0.425111 - 1.62931i) q^{6} +(-0.611057 - 0.352794i) q^{7} +(2.74596 - 0.678023i) q^{8} +(-1.21212 - 1.01709i) q^{9} +(-1.00655 + 0.993404i) q^{10} +(3.43606 - 1.98381i) q^{11} +(-1.55455 + 1.80392i) q^{12} +(-0.265787 - 0.730243i) q^{13} +(0.0804309 + 0.994606i) q^{14} +(0.206757 - 1.17258i) q^{15} +(-2.99551 - 2.65084i) q^{16} +(1.66784 - 1.39948i) q^{17} +(-0.209683 + 2.22788i) q^{18} +(2.09018 - 3.82507i) q^{19} +(1.96488 + 0.373166i) q^{20} +(-0.540019 - 0.643570i) q^{21} +(-5.06966 - 2.40472i) q^{22} +(6.79230 + 1.19767i) q^{23} +(3.34846 + 0.359629i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-0.636264 + 0.896082i) q^{26} +(-2.72800 - 4.72504i) q^{27} +(1.09286 - 0.892794i) q^{28} +(-2.16916 + 2.58511i) q^{29} +(-1.53074 + 0.701579i) q^{30} +(4.68498 - 8.11462i) q^{31} +(-0.677986 + 5.61608i) q^{32} +(4.65235 - 0.820335i) q^{33} +(-2.96882 - 0.816451i) q^{34} +(-0.241325 + 0.663036i) q^{35} +(2.76122 - 1.54614i) q^{36} +8.06619i q^{37} +(-6.13099 + 0.641062i) q^{38} -0.925277i q^{39} +(-1.14455 - 2.58650i) q^{40} +(0.167128 - 0.459180i) q^{41} +(-0.315044 + 1.14558i) q^{42} +(-2.88156 + 0.508097i) q^{43} +(1.27506 + 7.83214i) q^{44} +(-0.791157 + 1.37032i) q^{45} +(-4.06398 - 8.86699i) q^{46} +(-6.27735 + 7.48106i) q^{47} +(-2.27205 - 4.18578i) q^{48} +(-3.25107 - 5.63102i) q^{49} +(1.15310 + 0.818759i) q^{50} +(2.43599 - 0.886629i) q^{51} +(1.55408 + 0.0204371i) q^{52} +(-8.25049 - 1.45478i) q^{53} +(-3.30681 + 6.97144i) q^{54} +(-2.55034 - 3.03938i) q^{55} +(-1.91714 - 0.554447i) q^{56} +(3.89631 - 3.42853i) q^{57} +(4.75143 + 0.447194i) q^{58} +(3.63979 - 3.05415i) q^{59} +(2.04646 + 1.21768i) q^{60} +(-1.09052 + 6.18464i) q^{61} +(-13.2080 + 1.06809i) q^{62} +(0.381852 + 1.04913i) q^{63} +(7.08057 - 3.72365i) q^{64} +(-0.672995 + 0.388554i) q^{65} +(-4.69296 - 4.75508i) q^{66} +(2.50692 + 2.10356i) q^{67} +(1.43536 + 4.11104i) q^{68} +(7.11191 + 4.10606i) q^{69} +(0.965529 - 0.251920i) q^{70} +(2.21433 + 12.5581i) q^{71} +(-4.01805 - 1.97104i) q^{72} +(-8.78856 - 3.19877i) q^{73} +(9.38714 - 6.48139i) q^{74} -1.19067 q^{75} +(5.67245 + 6.61992i) q^{76} -2.79951 q^{77} +(-1.07680 + 0.743483i) q^{78} +(2.19489 + 0.798873i) q^{79} +(-2.09040 + 3.41031i) q^{80} +(-0.303771 - 1.72277i) q^{81} +(-0.668669 + 0.174466i) q^{82} +(8.88433 + 5.12937i) q^{83} +(1.58633 - 0.553865i) q^{84} +(-1.66784 - 1.39948i) q^{85} +(2.90671 + 2.94519i) q^{86} +(-3.47973 + 2.00902i) q^{87} +(8.09022 - 7.77720i) q^{88} +(2.09950 + 5.76832i) q^{89} +(2.23045 - 0.180370i) q^{90} +(-0.0952145 + 0.539988i) q^{91} +(-7.05357 + 11.8544i) q^{92} +(8.54637 - 7.17126i) q^{93} +(13.7502 + 1.29414i) q^{94} +(-4.12991 - 1.39421i) q^{95} +(-3.04562 + 6.00751i) q^{96} +(0.738968 + 0.880668i) q^{97} +(-3.94086 + 8.30815i) q^{98} +(-6.18265 - 1.09017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Introduction

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