LMFDB - Embedded newform 150.2.l.a.113.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.3
Character	$\chi$	$=$	150.113
Dual form			150.2.l.a.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 - 0.987688i) q^{2} +(-0.0929751 + 1.72955i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.59953 + 1.56253i) q^{5} +(1.72280 - 0.178731i) q^{6} +(-3.45255 + 3.45255i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-2.98271 - 0.321611i) q^{9} +O(q^{10})$	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.0929751 + 1.72955i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.59953 + 1.56253i) q^{5} +(1.72280 - 0.178731i) q^{6} +(-3.45255 + 3.45255i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-2.98271 - 0.321611i) q^{9} +(1.29307 - 1.82427i) q^{10} +(1.48978 - 2.05051i) q^{11} +(-0.446037 - 1.67363i) q^{12} +(3.77229 + 0.597472i) q^{13} +(3.95014 + 2.86994i) q^{14} +(-2.85120 + 2.62120i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.27947 - 2.18050i) q^{17} +(0.148947 + 2.99630i) q^{18} +(0.596005 + 0.193654i) q^{19} +(-2.00409 - 0.991774i) q^{20} +(-5.65036 - 6.29237i) q^{21} +(-2.25832 - 1.15067i) q^{22} +(-0.643277 + 0.101885i) q^{23} +(-1.58325 + 0.702359i) q^{24} +(0.116992 + 4.99863i) q^{25} -3.81931i q^{26} +(0.833561 - 5.12886i) q^{27} +(2.21667 - 4.35046i) q^{28} +(-2.50850 - 7.72038i) q^{29} +(3.03495 + 2.40605i) q^{30} +(0.501043 - 1.54205i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.40795 + 2.76731i) q^{33} +(-2.82311 - 3.88568i) q^{34} +(-10.9172 + 0.127739i) q^{35} +(2.93611 - 0.615838i) q^{36} +(-0.576743 + 3.64141i) q^{37} +(0.0980339 - 0.618961i) q^{38} +(-1.38409 + 6.46882i) q^{39} +(-0.666054 + 2.13457i) q^{40} +(3.69305 + 5.08304i) q^{41} +(-5.33098 + 6.56514i) q^{42} +(-0.951098 - 0.951098i) q^{43} +(-0.783225 + 2.41052i) q^{44} +(-4.26841 - 5.17501i) q^{45} +(0.201261 + 0.619419i) q^{46} +(-1.95031 + 3.82769i) q^{47} +(0.941388 + 1.45389i) q^{48} -16.8402i q^{49} +(4.91879 - 0.897510i) q^{50} +(3.37340 + 7.60430i) q^{51} +(-3.77229 + 0.597472i) q^{52} +(-0.456180 - 0.232435i) q^{53} +(-5.19611 - 0.0209688i) q^{54} +(5.58694 - 0.952020i) q^{55} +(-4.64367 - 1.50882i) q^{56} +(-0.390348 + 1.01282i) q^{57} +(-7.23291 + 3.68535i) q^{58} +(8.96720 - 6.51505i) q^{59} +(1.90166 - 3.37397i) q^{60} +(3.22382 + 2.34224i) q^{61} +(-1.60145 - 0.253644i) q^{62} +(11.4083 - 9.18757i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(5.10032 + 6.84999i) q^{65} +(2.20011 - 3.79890i) q^{66} +(1.95065 + 3.82837i) q^{67} +(-3.39620 + 3.39620i) q^{68} +(-0.116407 - 1.12205i) q^{69} +(1.83399 + 10.7628i) q^{70} +(-0.917028 + 0.297960i) q^{71} +(-1.06757 - 2.80362i) q^{72} +(-1.21191 - 7.65167i) q^{73} +3.68680 q^{74} +(-8.65628 - 0.262405i) q^{75} -0.626677 q^{76} +(1.93594 + 12.2230i) q^{77} +(6.60570 + 0.355101i) q^{78} +(0.139017 - 0.0451693i) q^{79} +(2.21248 + 0.323934i) q^{80} +(8.79313 + 1.91855i) q^{81} +(4.44274 - 4.44274i) q^{82} +(3.59418 + 7.05397i) q^{83} +(7.31826 + 4.23834i) q^{84} +(10.2522 + 3.19903i) q^{85} +(-0.790603 + 1.08817i) q^{86} +(13.5860 - 3.62079i) q^{87} +(2.50336 + 0.396494i) q^{88} +(-8.93519 - 6.49179i) q^{89} +(-4.44357 + 5.02541i) q^{90} +(-15.0868 + 10.9612i) q^{91} +(0.580309 - 0.295682i) q^{92} +(2.62047 + 1.00995i) q^{93} +(4.08566 + 1.32751i) q^{94} +(0.650738 + 1.24103i) q^{95} +(1.28872 - 1.15724i) q^{96} +(-13.5240 - 6.89084i) q^{97} +(-16.6328 + 2.63438i) q^{98} +(-5.10306 + 5.63695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

Coefficient data

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

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

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

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$	−0.0929751	+	1.72955i	−0.0536792	+	0.998558i
$3$	−0.0929751	+	1.72955i	−0.0536792	+	0.998558i
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	1.59953	+	1.56253i	0.715332	+	0.698785i
$5$	1.59953	+	1.56253i	0.715332	+	0.698785i
$6$	1.72280	−	0.178731i	0.703332	−	0.0729668i
$7$	−3.45255	+	3.45255i	−1.30494	+	1.30494i	−0.379921	+	0.925019i	$0.624049\pi$
$7$	−3.45255	+	3.45255i	−1.30494	+	1.30494i	−0.925019	+	0.379921i	$0.875951\pi$
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$	−2.98271	−	0.321611i	−0.994237	−	0.107204i
$10$	1.29307	−	1.82427i	0.408905	−	0.576885i
$11$	1.48978	−	2.05051i	0.449186	−	0.618252i	−0.523036	−	0.852310i	$-0.675201\pi$
$11$	1.48978	−	2.05051i	0.449186	−	0.618252i	0.972223	+	0.234059i	$0.0752007\pi$
$12$	−0.446037	−	1.67363i	−0.128760	−	0.483137i
$13$	3.77229	+	0.597472i	1.04624	+	0.165709i	0.655813	−	0.754923i	$-0.272326\pi$
$13$	3.77229	+	0.597472i	1.04624	+	0.165709i	0.390431	+	0.920632i	$0.372326\pi$
$14$	3.95014	+	2.86994i	1.05572	+	0.767025i
$15$	−2.85120	+	2.62120i	−0.736176	+	0.676790i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	4.27947	−	2.18050i	1.03792	−	0.528848i	0.149926	−	0.988697i	$-0.452096\pi$
$17$	4.27947	−	2.18050i	1.03792	−	0.528848i	0.887997	+	0.459849i	$0.152096\pi$
$18$	0.148947	+	2.99630i	0.0351073	+	0.706235i
$19$	0.596005	+	0.193654i	0.136733	+	0.0444272i	0.376584	−	0.926382i	$-0.377099\pi$
$19$	0.596005	+	0.193654i	0.136733	+	0.0444272i	−0.239851	+	0.970810i	$0.577099\pi$
$20$	−2.00409	−	0.991774i	−0.448129	−	0.221767i
$21$	−5.65036	−	6.29237i	−1.23301	−	1.37311i
$22$	−2.25832	−	1.15067i	−0.481475	−	0.245324i
$23$	−0.643277	+	0.101885i	−0.134133	+	0.0212445i	−0.223140	−	0.974786i	$-0.571631\pi$
$23$	−0.643277	+	0.101885i	−0.134133	+	0.0212445i	0.0890072	+	0.996031i	$0.471631\pi$
$24$	−1.58325	+	0.702359i	−0.323180	+	0.143369i
$25$	0.116992	+	4.99863i	0.0233983	+	0.999726i
$26$		−	3.81931i		−	0.749028i
$27$	0.833561	−	5.12886i	0.160419	−	0.987049i
$28$	2.21667	−	4.35046i	0.418912	−	0.822160i
$29$	−2.50850	−	7.72038i	−0.465817	−	1.43364i	−0.857952	−	0.513731i	$-0.828263\pi$
$29$	−2.50850	−	7.72038i	−0.465817	−	1.43364i	0.392134	−	0.919908i	$-0.371737\pi$
$30$	3.03495	+	2.40605i	0.554104	+	0.439283i
$31$	0.501043	−	1.54205i	0.0899899	−	0.276960i	−0.895926	−	0.444204i	$-0.853487\pi$
$31$	0.501043	−	1.54205i	0.0899899	−	0.276960i	0.985916	+	0.167243i	$0.0534866\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	3.40795	+	2.76731i	0.593249	+	0.481726i
$34$	−2.82311	−	3.88568i	−0.484159	−	0.666388i
$35$	−10.9172	+	0.127739i	−1.84534	+	0.0215919i
$36$	2.93611	−	0.615838i	0.489352	−	0.102640i
$37$	−0.576743	+	3.64141i	−0.0948160	+	0.598644i	0.893833	+	0.448400i	$0.148006\pi$
$37$	−0.576743	+	3.64141i	−0.0948160	+	0.598644i	−0.988649	+	0.150244i	$0.951994\pi$
$38$	0.0980339	−	0.618961i	0.0159032	−	0.100409i
$39$	−1.38409	+	6.46882i	−0.221631	+	1.03584i
$40$	−0.666054	+	2.13457i	−0.105312	+	0.337505i
$41$	3.69305	+	5.08304i	0.576757	+	0.793838i	0.993335	−	0.115262i	$-0.0367708\pi$
$41$	3.69305	+	5.08304i	0.576757	+	0.793838i	−0.416578	+	0.909100i	$0.636771\pi$
$42$	−5.33098	+	6.56514i	−0.822589	+	1.01302i
$43$	−0.951098	−	0.951098i	−0.145041	−	0.145041i	0.630858	−	0.775899i	$-0.282703\pi$
$43$	−0.951098	−	0.951098i	−0.145041	−	0.145041i	−0.775899	+	0.630858i	$0.782703\pi$
$44$	−0.783225	+	2.41052i	−0.118076	+	0.363399i
$45$	−4.26841	−	5.17501i	−0.636297	−	0.771444i
$46$	0.201261	+	0.619419i	0.0296744	+	0.0913283i
$47$	−1.95031	+	3.82769i	−0.284481	+	0.558326i	−0.988385	−	0.151969i	$-0.951439\pi$
$47$	−1.95031	+	3.82769i	−0.284481	+	0.558326i	0.703904	+	0.710295i	$0.251439\pi$
$48$	0.941388	+	1.45389i	0.135878	+	0.209851i
$49$		−	16.8402i		−	2.40574i
$50$	4.91879	−	0.897510i	0.695622	−	0.126927i
$51$	3.37340	+	7.60430i	0.472371	+	1.06482i
$52$	−3.77229	+	0.597472i	−0.523122	+	0.0828544i
$53$	−0.456180	−	0.232435i	−0.0626611	−	0.0319274i	0.422379	−	0.906419i	$-0.361195\pi$
$53$	−0.456180	−	0.232435i	−0.0626611	−	0.0319274i	−0.485040	+	0.874492i	$0.661195\pi$
$54$	−5.19611	−	0.0209688i	−0.707101	−	0.00285349i
$55$	5.58694	−	0.952020i	0.753342	−	0.128370i
$56$	−4.64367	−	1.50882i	−0.620536	−	0.201624i
$57$	−0.390348	+	1.01282i	−0.0517029	+	0.134151i
$58$	−7.23291	+	3.68535i	−0.949728	+	0.483911i
$59$	8.96720	−	6.51505i	1.16743	−	0.848188i	0.176731	−	0.984259i	$-0.443448\pi$
$59$	8.96720	−	6.51505i	1.16743	−	0.848188i	0.990699	+	0.136071i	$0.0434476\pi$
$60$	1.90166	−	3.37397i	0.245503	−	0.435578i
$61$	3.22382	+	2.34224i	0.412767	+	0.299893i	0.774721	−	0.632303i	$-0.217890\pi$
$61$	3.22382	+	2.34224i	0.412767	+	0.299893i	−0.361954	+	0.932196i	$0.617890\pi$
$62$	−1.60145	−	0.253644i	−0.203384	−	0.0322128i
$63$	11.4083	−	9.18757i	1.43731	−	1.15753i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	5.10032	+	6.84999i	0.632617	+	0.849637i
$66$	2.20011	−	3.79890i	0.270815	−	0.467612i
$67$	1.95065	+	3.82837i	0.238310	+	0.467710i	0.978925	−	0.204220i	$-0.0654658\pi$
$67$	1.95065	+	3.82837i	0.238310	+	0.467710i	−0.740615	+	0.671929i	$0.765466\pi$
$68$	−3.39620	+	3.39620i	−0.411850	+	0.411850i
$69$	−0.116407	−	1.12205i	−0.0140137	−	0.135080i
$70$	1.83399	+	10.7628i	0.219203	+	1.28640i
$71$	−0.917028	+	0.297960i	−0.108831	+	0.0353614i	−0.362926	−	0.931818i	$-0.618222\pi$
$71$	−0.917028	+	0.297960i	−0.108831	+	0.0353614i	0.254095	+	0.967179i	$0.418222\pi$
$72$	−1.06757	−	2.80362i	−0.125814	−	0.330410i
$73$	−1.21191	−	7.65167i	−0.141843	−	0.895561i	−0.951274	−	0.308346i	$-0.900224\pi$
$73$	−1.21191	−	7.65167i	−0.141843	−	0.895561i	0.809431	−	0.587215i	$-0.199776\pi$
$74$	3.68680			0.428582
$75$	−8.65628	−	0.262405i	−0.999541	−	0.0302999i
$76$	−0.626677			−0.0718848
$77$	1.93594	+	12.2230i	0.220620	+	1.39294i
$78$	6.60570	+	0.355101i	0.747948	+	0.0402072i
$79$	0.139017	−	0.0451693i	0.0156406	−	0.00508194i	−0.301186	−	0.953565i	$-0.597383\pi$
$79$	0.139017	−	0.0451693i	0.0156406	−	0.00508194i	0.316827	+	0.948483i	$0.397383\pi$
$80$	2.21248	+	0.323934i	0.247363	+	0.0362170i
$81$	8.79313	+	1.91855i	0.977015	+	0.213172i
$82$	4.44274	−	4.44274i	0.490619	−	0.490619i
$83$	3.59418	+	7.05397i	0.394512	+	0.774274i	0.999763	−	0.0217608i	$-0.00692722\pi$
$83$	3.59418	+	7.05397i	0.394512	+	0.774274i	−0.605251	+	0.796035i	$0.706927\pi$
$84$	7.31826	+	4.23834i	0.798488	+	0.462440i
$85$	10.2522	+	3.19903i	1.11201	+	0.346984i
$86$	−0.790603	+	1.08817i	−0.0852530	+	0.117341i
$87$	13.5860	−	3.62079i	1.45658	−	0.388189i
$88$	2.50336	+	0.396494i	0.266860	+	0.0422664i
$89$	−8.93519	−	6.49179i	−0.947128	−	0.688129i	0.00299774	−	0.999996i	$-0.499046\pi$
$89$	−8.93519	−	6.49179i	−0.947128	−	0.688129i	−0.950126	+	0.311867i	$0.899046\pi$
$90$	−4.44357	+	5.02541i	−0.468393	+	0.529724i
$91$	−15.0868	+	10.9612i	−1.58153	+	1.14905i
$92$	0.580309	−	0.295682i	0.0605013	−	0.0308270i
$93$	2.62047	+	1.00995i	0.271731	+	0.104727i
$94$	4.08566	+	1.32751i	0.421404	+	0.136922i
$95$	0.650738	+	1.24103i	0.0667643	+	0.127327i
$96$	1.28872	−	1.15724i	0.131530	−	0.118110i
$97$	−13.5240	−	6.89084i	−1.37316	−	0.699659i	−0.397223	−	0.917722i	$-0.630026\pi$
$97$	−13.5240	−	6.89084i	−1.37316	−	0.699659i	−0.975935	+	0.218063i	$0.930026\pi$
$98$	−16.6328	+	2.63438i	−1.68017	+	0.266113i
$99$	−5.10306	+	5.63695i	−0.512877	+	0.566535i
$100$	−1.65593	−	4.71783i	−0.165593	−	0.471783i
$101$		−	1.94974i		−	0.194007i	−0.995284	−	0.0970033i	$-0.969074\pi$
$101$		−	1.94974i		−	0.194007i	0.995284	−	0.0970033i	$-0.0309258\pi$
$102$	6.98296	−	4.52145i	0.691416	−	0.447690i
$103$	−1.56955	+	3.08042i	−0.154653	+	0.303523i	−0.955313	−	0.295595i	$-0.904482\pi$
$103$	−1.56955	+	3.08042i	−0.154653	+	0.303523i	0.800661	+	0.599118i	$0.204482\pi$
$104$	1.18023	+	3.63238i	0.115731	+	0.356184i
$105$	0.794093	−	18.8937i	0.0774955	−	1.84384i
$106$	−0.158211	+	0.486924i	−0.0153668	+	0.0472943i
$107$	−7.77089	−	7.77089i	−0.751240	−	0.751240i	0.223470	−	0.974711i	$-0.428261\pi$
$107$	−7.77089	−	7.77089i	−0.751240	−	0.751240i	−0.974711	+	0.223470i	$0.928261\pi$
$108$	0.792140	+	5.13542i	0.0762237	+	0.494156i
$109$	10.4733	+	14.4153i	1.00316	+	1.38073i	0.923366	+	0.383920i	$0.125426\pi$
$109$	10.4733	+	14.4153i	1.00316	+	1.38073i	0.0797938	+	0.996811i	$0.474574\pi$
$110$	−1.81429	−	5.36922i	−0.172986	−	0.511935i
$111$	−6.24439	−	1.33607i	−0.592692	−	0.126814i
$112$	−0.763813	+	4.82253i	−0.0721735	+	0.455686i
$113$	2.93571	−	18.5354i	0.276169	−	1.74366i	−0.326071	−	0.945345i	$-0.605725\pi$
$113$	2.93571	−	18.5354i	0.276169	−	1.74366i	0.602240	−	0.798315i	$-0.294275\pi$
$114$	1.06141	+	0.227103i	0.0994104	+	0.0212701i
$115$	−1.18814	−	0.842172i	−0.110795	−	0.0785330i
$116$	4.77146	+	6.56735i	0.443019	+	0.609763i
$117$	−11.0595	−	2.99529i	−1.02245	−	0.276915i
$118$	−7.83762	−	7.83762i	−0.721512	−	0.721512i
$119$	−7.24679	+	22.3033i	−0.664312	+	2.04454i
$120$	−3.62992	−	1.35044i	−0.331365	−	0.123278i
$121$	1.41405	+	4.35199i	0.128550	+	0.395636i
$122$	1.80909	−	3.55053i	0.163787	−	0.321450i
$123$	−9.13475	+	5.91472i	−0.823653	+	0.533313i
$124$			1.62141i			0.145607i
$125$	−7.62339	+	8.17826i	−0.681856	+	0.731486i
$126$	−10.8591	−	9.83062i	−0.967407	−	0.875781i
$127$	2.27911	−	0.360976i	0.202239	−	0.0320315i	−0.0544931	−	0.998514i	$-0.517354\pi$
$127$	2.27911	−	0.360976i	0.202239	−	0.0320315i	0.256732	+	0.966483i	$0.417354\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$	1.73340	−	1.55655i	0.152618	−	0.137046i
$130$	5.96779	−	6.10910i	0.523410	−	0.535803i
$131$	−5.16079	−	1.67684i	−0.450901	−	0.146506i	0.0747587	−	0.997202i	$-0.476181\pi$
$131$	−5.16079	−	1.67684i	−0.450901	−	0.146506i	−0.525659	+	0.850695i	$0.676181\pi$
$132$	−4.09630	−	1.57875i	−0.356537	−	0.137412i
$133$	−2.72633	+	1.38914i	−0.236403	+	0.120453i
$134$	3.47608	−	2.52552i	0.300288	−	0.218172i
$135$	9.34731	−	6.90129i	0.804488	−	0.593969i
$136$	3.88568	+	2.82311i	0.333194	+	0.242080i
$137$	−4.24769	−	0.672768i	−0.362904	−	0.0574784i	−0.0276803	−	0.999617i	$-0.508812\pi$
$137$	−4.24769	−	0.672768i	−0.362904	−	0.0574784i	−0.335224	+	0.942138i	$0.608812\pi$
$138$	−1.09003	+	0.290502i	−0.0927895	+	0.0247292i
$139$	1.72794	−	2.37830i	0.146562	−	0.201725i	−0.729424	−	0.684062i	$-0.760212\pi$
$139$	1.72794	−	2.37830i	0.146562	−	0.201725i	0.875986	+	0.482337i	$0.160212\pi$
$140$	10.3434	−	3.49508i	0.874174	−	0.295388i
$141$	−6.43887	−	3.72904i	−0.542251	−	0.314042i
$142$	0.437747	+	0.859126i	0.0367349	+	0.0720963i
$143$	6.84501	−	6.84501i	0.572408	−	0.572408i
$144$	−2.60210	+	1.49300i	−0.216842	+	0.124417i
$145$	8.05091	−	16.2686i	0.668592	−	1.35103i
$146$	−7.36789	+	2.39397i	−0.609771	+	0.198126i
$147$	29.1260	+	1.56572i	2.40227	+	0.129138i
$148$	−0.576743	−	3.64141i	−0.0474080	−	0.299322i
$149$	−6.09696			−0.499482			−0.249741	−	0.968313i	$-0.580346\pi$
$149$	−6.09696			−0.499482			−0.249741	+	0.968313i	$0.580346\pi$
$150$	1.09497	+	8.59075i	0.0894036	+	0.701432i
$151$	17.4743			1.42203			0.711017	−	0.703175i	$-0.248235\pi$
$151$	17.4743			1.42203			0.711017	+	0.703175i	$0.248235\pi$
$152$	0.0980339	+	0.618961i	0.00795160	+	0.0502044i
$153$	−13.4657	+	5.12747i	−1.08864	+	0.414531i
$154$	11.7697	−	3.82420i	0.948429	−	0.308163i
$155$	3.21094	−	1.68366i	0.257909	−	0.135235i
$156$	−0.682630	−	6.57992i	−0.0546542	−	0.526815i
$157$	−1.62980	+	1.62980i	−0.130072	+	0.130072i	−0.769146	−	0.639074i	$-0.779318\pi$
$157$	−1.62980	+	1.62980i	−0.130072	+	0.130072i	0.639074	+	0.769146i	$0.279318\pi$
$158$	−0.0663602	−	0.130239i	−0.00527934	−	0.0103613i
$159$	0.444422	−	0.767377i	0.0352450	−	0.0608569i
$160$	−0.0261619	−	2.23591i	−0.00206828	−	0.176765i
$161$	1.86918	−	2.57271i	0.147312	−	0.202758i
$162$	0.519376	−	8.98500i	0.0408060	−	0.705928i
$163$	−22.6112	−	3.58126i	−1.77105	−	0.280506i	−0.816235	−	0.577719i	$-0.803943\pi$
$163$	−22.6112	−	3.58126i	−1.77105	−	0.280506i	−0.954811	+	0.297213i	$0.903943\pi$
$164$	−5.08304	−	3.69305i	−0.396919	−	0.288378i
$165$	1.12712	+	9.75142i	0.0877464	+	0.759147i
$166$	6.40487	−	4.65341i	0.497114	−	0.361175i
$167$	7.89344	−	4.02191i	0.610813	−	0.311225i	−0.121082	−	0.992643i	$-0.538636\pi$
$167$	7.89344	−	4.02191i	0.610813	−	0.311225i	0.731895	+	0.681418i	$0.238636\pi$
$168$	3.04133	−	7.89119i	0.234644	−	0.608818i
$169$	1.50944	+	0.490448i	0.116111	+	0.0377268i
$170$	1.55584	−	10.6264i	0.119328	−	0.815011i
$171$	−1.71543	−	0.769295i	−0.131182	−	0.0588295i
$172$	1.19845	+	0.610642i	0.0913812	+	0.0465610i
$173$	−16.2880	+	2.57976i	−1.23835	+	0.196136i	−0.741055	−	0.671445i	$-0.765674\pi$
$173$	−16.2880	+	2.57976i	−1.23835	+	0.196136i	−0.497297	+	0.867580i	$0.665674\pi$
$174$	−5.70154	−	12.8524i	−0.432232	−	0.974335i
$175$	−17.6619	−	16.8541i	−1.33512	−	1.27405i
$176$		−	2.53457i		−	0.191050i
$177$	10.4344	+	16.1150i	0.784298	+	1.21128i
$178$	−5.01410	+	9.84072i	−0.375823	+	0.737593i
$179$	−1.95323	−	6.01143i	−0.145991	−	0.449315i	0.851146	−	0.524929i	$-0.175908\pi$
$179$	−1.95323	−	6.01143i	−0.145991	−	0.449315i	−0.997137	+	0.0756142i	$0.975908\pi$
$180$	5.65866	+	3.60271i	0.421772	+	0.268530i
$181$	−5.79522	+	17.8358i	−0.430755	+	1.32573i	0.466620	+	0.884458i	$0.345472\pi$
$181$	−5.79522	+	17.8358i	−0.430755	+	1.32573i	−0.897375	+	0.441269i	$0.854528\pi$
$182$	13.1863	+	13.1863i	0.977437	+	0.977437i
$183$	−4.35076	+	5.35799i	−0.321618	+	0.396074i
$184$	−0.382822	−	0.526909i	−0.0282220	−	0.0388443i
$185$	−6.61234	+	4.92337i	−0.486149	+	0.361973i
$186$	0.587586	−	2.74620i	0.0430839	−	0.201361i
$187$	1.90434	−	12.0236i	0.139259	−	0.879250i
$188$	0.672030	−	4.24303i	0.0490128	−	0.309455i
$189$	14.8297	+	20.5855i	1.07870	+	1.49738i
$190$	1.12395	−	0.836866i	0.0815402	−	0.0607127i
$191$	−9.23596	−	12.7122i	−0.668290	−	0.919823i	0.331430	−	0.943480i	$-0.392469\pi$
$191$	−9.23596	−	12.7122i	−0.668290	−	0.919823i	−0.999720	+	0.0236572i	$0.992469\pi$
$192$	−1.34459	−	1.09182i	−0.0970373	−	0.0787956i
$193$	1.83504	+	1.83504i	0.132089	+	0.132089i	0.770060	−	0.637971i	$-0.220226\pi$
$193$	1.83504	+	1.83504i	0.132089	+	0.132089i	−0.637971	+	0.770060i	$0.720226\pi$
$194$	−4.69038	+	14.4355i	−0.336749	+	1.03641i
$195$	−12.3216	+	8.18439i	−0.882370	+	0.586097i
$196$	5.20390	+	16.0159i	0.371707	+	1.14400i
$197$	−2.63453	+	5.17056i	−0.187703	+	0.368387i	−0.965611	−	0.259990i	$-0.916281\pi$
$197$	−2.63453	+	5.17056i	−0.187703	+	0.368387i	0.777909	+	0.628377i	$0.216281\pi$
$198$	6.36584	+	4.15842i	0.452401	+	0.295526i
$199$			3.86400i			0.273911i	0.990577	+	0.136956i	$0.0437318\pi$
$199$			3.86400i			0.273911i	−0.990577	+	0.136956i	$0.956268\pi$
$200$	−4.40070	+	2.37357i	−0.311176	+	0.167837i
$201$	−6.80273	+	3.01781i	−0.479827	+	0.212860i
$202$	−1.92574	+	0.305007i	−0.135494	+	0.0214602i
$203$	35.3157	+	17.9942i	2.47868	+	1.26295i
$204$	−5.55816	−	6.18968i	−0.389149	−	0.433364i
$205$	−2.03527	+	13.9010i	−0.142150	+	0.970886i
$206$	3.28803	+	1.06835i	0.229088	+	0.0744352i
$207$	1.95148	−	0.0970088i	0.135637	−	0.00674258i
$208$	3.40303	−	1.73393i	0.235958	−	0.120226i
$209$	1.28501	−	0.933612i	0.0888858	−	0.0645793i
$210$	−18.7853	+	2.17131i	−1.29631	+	0.149835i
$211$	−8.84519	−	6.42640i	−0.608928	−	0.442412i	0.240109	−	0.970746i	$-0.422817\pi$
$211$	−8.84519	−	6.42640i	−0.608928	−	0.442412i	−0.849037	+	0.528334i	$0.822817\pi$
$212$	0.505679	+	0.0800917i	0.0347302	+	0.00550072i
$213$	−0.430078	−	1.61375i	−0.0294684	−	0.110572i
$214$	−6.45958	+	8.89085i	−0.441568	+	0.607766i
$215$	−0.0351892	−	3.00743i	−0.00239989	−	0.205105i
$216$	4.94827	−	1.58574i	0.336687	−	0.107896i
$217$	3.59413	+	7.05388i	0.243985	+	0.478848i
$218$	12.5994	−	12.5994i	0.853339	−	0.853339i
$219$	13.3467	−	1.38464i	0.901884	−	0.0935654i
$220$	−5.01930	+	2.63188i	−0.338401	+	0.177442i
$221$	17.4462	−	5.66860i	1.17356	−	0.381311i
$222$	−0.342781	+	6.37652i	−0.0230059	+	0.427964i
$223$	−3.05289	−	19.2752i	−0.204437	−	1.29076i	−0.849889	−	0.526962i	$-0.823331\pi$
$223$	−3.05289	−	19.2752i	−0.204437	−	1.29076i	0.645452	−	0.763800i	$-0.276669\pi$
$224$	4.88264			0.326235
$225$	1.25866	−	14.9471i	0.0839108	−	0.996473i
$226$	−18.7664			−1.24832
$227$	−3.87090	−	24.4399i	−0.256921	−	1.62213i	−0.692108	−	0.721794i	$-0.743318\pi$
$227$	−3.87090	−	24.4399i	−0.256921	−	1.62213i	0.435187	−	0.900340i	$-0.356682\pi$
$228$	0.0582654	−	1.08387i	0.00385872	−	0.0717811i
$229$	2.89806	−	0.941635i	0.191509	−	0.0622250i	−0.211692	−	0.977336i	$-0.567897\pi$
$229$	2.89806	−	0.941635i	0.191509	−	0.0622250i	0.403201	+	0.915111i	$0.367897\pi$
$230$	−0.645938	+	1.30526i	−0.0425919	+	0.0860660i
$231$	−21.3204	+	2.21187i	−1.40278	+	0.145530i
$232$	5.74007	−	5.74007i	0.376854	−	0.376854i
$233$	8.40887	+	16.5033i	0.550883	+	1.08117i	0.983722	+	0.179698i	$0.0575120\pi$
$233$	8.40887	+	16.5033i	0.550883	+	1.08117i	−0.432839	+	0.901471i	$0.642488\pi$
$234$	−1.22833	+	11.3919i	−0.0802985	+	0.744712i
$235$	−9.10046	+	3.07509i	−0.593649	+	0.200597i
$236$	−6.51505	+	8.96720i	−0.424094	+	0.583715i
$237$	0.0651976	+	0.244637i	0.00423504	+	0.0158909i
$238$	23.1624	+	3.66856i	1.50139	+	0.237798i
$239$	10.8076	+	7.85218i	0.699086	+	0.507915i	0.879634	−	0.475651i	$-0.157787\pi$
$239$	10.8076	+	7.85218i	0.699086	+	0.507915i	−0.180549	+	0.983566i	$0.557787\pi$
$240$	−0.765967	+	3.79648i	−0.0494430	+	0.245062i
$241$	4.13071	−	3.00113i	0.266082	−	0.193320i	−0.446742	−	0.894663i	$-0.647416\pi$
$241$	4.13071	−	3.00113i	0.266082	−	0.193320i	0.712824	+	0.701343i	$0.247416\pi$
$242$	4.07721	−	2.07744i	0.262093	−	0.133543i
$243$	−4.13577	+	15.0298i	−0.265310	+	0.964163i
$244$	−3.78982	−	1.23139i	−0.242618	−	0.0788315i
$245$	26.3133	−	26.9363i	1.68109	−	1.72090i
$246$	7.27090	+	8.09702i	0.463575	+	0.516247i
$247$	2.13260	+	1.08661i	0.135694	+	0.0691396i
$248$	1.60145	−	0.253644i	0.101692	−	0.0161064i
$249$	−12.5344	+	5.56048i	−0.794335	+	0.352381i
$250$	9.27014	+	6.25017i	0.586295	+	0.395295i
$251$			10.4406i			0.659004i	0.944155	+	0.329502i	$0.106881\pi$
$251$			10.4406i			0.659004i	−0.944155	+	0.329502i	$0.893119\pi$
$252$	−8.01085	+	12.2633i	−0.504636	+	0.772513i
$253$	−0.749426	+	1.47083i	−0.0471160	+	0.0924704i
$254$	−0.713064	−	2.19459i	−0.0447416	−	0.137701i
$255$	−6.48610	+	17.4344i	−0.406175	+	1.09178i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	15.7777	+	15.7777i	0.984185	+	0.984185i	0.999877	−	0.0156919i	$-0.00499509\pi$
$257$	15.7777	+	15.7777i	0.984185	+	0.984185i	−0.0156919	+	0.999877i	$0.504995\pi$
$258$	−1.80855	−	1.46856i	−0.112595	−	0.0914288i
$259$	−10.5809	−	14.5634i	−0.657466	−	0.904924i
$260$	−6.96745	−	4.93864i	−0.432103	−	0.306282i
$261$	4.99918	+	23.8344i	0.309442	+	1.47531i
$262$	−0.848873	+	5.35957i	−0.0524435	+	0.331115i
$263$	2.08135	−	13.1411i	0.128342	−	0.810318i	−0.836592	−	0.547826i	$-0.815456\pi$
$263$	2.08135	−	13.1411i	0.128342	−	0.810318i	0.964934	−	0.262492i	$-0.0845444\pi$
$264$	−0.918508	+	4.29284i	−0.0565303	+	0.264206i
$265$	−0.366486	−	1.08458i	−0.0225130	−	0.0666254i
$266$	1.79853	+	2.47546i	0.110275	+	0.151780i
$267$	12.0587	−	14.8503i	0.737978	−	0.908824i
$268$	−3.03821	−	3.03821i	−0.185588	−	0.185588i
$269$	2.51822	−	7.75028i	0.153539	−	0.472543i	−0.844471	−	0.535601i	$-0.820085\pi$
$269$	2.51822	−	7.75028i	0.153539	−	0.472543i	0.998010	+	0.0630577i	$0.0200852\pi$
$270$	−8.27857	−	8.15262i	−0.503818	−	0.496153i
$271$	−2.73922	−	8.43044i	−0.166396	−	0.512113i	0.832741	−	0.553663i	$-0.186770\pi$
$271$	−2.73922	−	8.43044i	−0.166396	−	0.512113i	−0.999136	+	0.0415500i	$0.986770\pi$
$272$	2.18050	−	4.27947i	0.132212	−	0.259481i
$273$	−17.5553	−	27.1125i	−1.06249	−	1.64093i
$274$			4.30064i			0.259811i
$275$	10.4240	+	7.20698i	0.628593	+	0.434597i
$276$	0.457444	+	1.03117i	0.0275349	+	0.0620689i
$277$	12.0346	−	1.90609i	0.723088	−	0.114526i	0.215967	−	0.976401i	$-0.430710\pi$
$277$	12.0346	−	1.90609i	0.723088	−	0.114526i	0.507121	+	0.861875i	$0.330710\pi$
$278$	−2.61933	−	1.33461i	−0.157097	−	0.0800448i
$279$	−1.99041	+	4.43835i	−0.119162	+	0.265717i
$280$	−5.07011	−	9.66927i	−0.302997	−	0.577850i
$281$	1.89696	+	0.616361i	0.113163	+	0.0367690i	0.365051	−	0.930987i	$-0.381051\pi$
$281$	1.89696	+	0.616361i	0.113163	+	0.0367690i	−0.251888	+	0.967756i	$0.581051\pi$
$282$	−2.67587	+	6.94295i	−0.159346	+	0.413446i
$283$	1.85853	−	0.946967i	0.110478	−	0.0562913i	−0.397878	−	0.917438i	$-0.630253\pi$
$283$	1.85853	−	0.946967i	0.110478	−	0.0562913i	0.508356	+	0.861147i	$0.330253\pi$
$284$	0.780070	−	0.566754i	0.0462887	−	0.0336307i
$285$	−2.20693	+	1.01010i	−0.130727	+	0.0598332i
$286$	−7.83153	−	5.68994i	−0.463088	−	0.336453i
$287$	−30.2999	−	4.79903i	−1.78854	−	0.283278i
$288$	1.88168	+	2.33651i	0.110879	+	0.137680i
$289$	3.56692	−	4.90945i	0.209819	−	0.288791i
$290$	−17.3277	−	5.40682i	−1.01752	−	0.317499i
$291$	13.1755	−	22.7499i	0.772360	−	1.33362i
$292$	3.51709	+	6.90267i	0.205822	+	0.403948i
$293$	−14.1457	+	14.1457i	−0.826402	+	0.826402i	−0.987017	−	0.160615i	$-0.948652\pi$
$293$	−14.1457	+	14.1457i	−0.826402	+	0.826402i	0.160615	+	0.987017i	$0.448652\pi$
$294$	−3.00986	−	29.0123i	−0.175539	−	1.69203i
$295$	24.5233	+	3.59051i	1.42780	+	0.209048i
$296$	−3.50636	+	1.13928i	−0.203803	+	0.0662196i
$297$	−9.27495	−	9.35011i	−0.538187	−	0.542548i
$298$	0.953774	+	6.02189i	0.0552507	+	0.348839i
$299$	−2.48750			−0.143856
$300$	8.31370	−	2.42537i	0.479992	−	0.140029i
$301$	6.56742			0.378540
$302$	−2.73358	−	17.2591i	−0.157300	−	0.993151i
$303$	3.37218	+	0.181278i	0.193727	+	0.0104141i
$304$	0.596005	−	0.193654i	0.0341832	−	0.0111068i
$305$	1.49677	+	8.78379i	0.0857046	+	0.502959i
$306$	7.17084	+	12.4978i	0.409930	+	0.714451i
$307$	6.59880	−	6.59880i	0.376613	−	0.376613i	−0.493266	−	0.869879i	$-0.664197\pi$
$307$	6.59880	−	6.59880i	0.376613	−	0.376613i	0.869879	+	0.493266i	$0.164197\pi$
$308$	−5.61831	−	11.0265i	−0.320133	−	0.628296i
$309$	−5.18183	−	3.00103i	−0.294784	−	0.170723i
$310$	−2.16523	−	2.90802i	−0.122977	−	0.165164i
$311$	4.60146	−	6.33337i	0.260925	−	0.359133i	−0.658375	−	0.752690i	$-0.728756\pi$
$311$	4.60146	−	6.33337i	0.260925	−	0.359133i	0.919300	+	0.393558i	$0.128756\pi$
$312$	−6.39213	+	1.70355i	−0.361883	+	0.0964447i
$313$	−2.82529	−	0.447482i	−0.159695	−	0.0252932i	0.0760751	−	0.997102i	$-0.475761\pi$
$313$	−2.82529	−	0.447482i	−0.159695	−	0.0252932i	−0.235770	+	0.971809i	$0.575761\pi$
$314$	1.86469	+	1.35478i	0.105231	+	0.0764545i
$315$	32.6038	+	3.13007i	1.83702	+	0.176359i
$316$	−0.118255	+	0.0859171i	−0.00665235	+	0.00483322i
$317$	−22.7876	+	11.6109i	−1.27988	+	0.652131i	−0.955833	−	0.293910i	$-0.905043\pi$
$317$	−22.7876	+	11.6109i	−1.27988	+	0.652131i	−0.324046	+	0.946041i	$0.605043\pi$
$318$	−0.827452	−	0.318907i	−0.0464012	−	0.0178834i
$319$	−19.5678	−	6.35798i	−1.09559	−	0.355978i
$320$	−2.20429	+	0.375614i	−0.123224	+	0.0209975i
$321$	14.1627	−	12.7177i	0.790483	−	0.709831i
$322$	−2.83344	−	1.44371i	−0.157901	−	0.0804547i
$323$	2.97285	−	0.470853i	0.165414	−	0.0261989i
$324$	−8.95563	+	0.892583i	−0.497535	+	0.0495879i
$325$	−2.54521	+	18.9262i	−0.141183	+	1.04984i
$326$			22.8931i			1.26793i
$327$	−25.9057	+	16.7739i	−1.43259	+	0.927597i
$328$	−2.85242	+	5.59818i	−0.157498	+	0.309108i
$329$	−6.48176	−	19.9488i	−0.357351	−	1.09981i
$330$	9.45504	−	2.63870i	0.520483	−	0.145256i
$331$	9.88000	−	30.4075i	0.543054	−	1.67135i	−0.182518	−	0.983203i	$-0.558425\pi$
$331$	9.88000	−	30.4075i	0.543054	−	1.67135i	0.725572	−	0.688146i	$-0.241575\pi$
$332$	−5.59806	−	5.59806i	−0.307234	−	0.307234i
$333$	2.89138	−	10.6758i	0.158446	−	0.585030i
$334$	−5.20720	−	7.16710i	−0.284925	−	0.392166i
$335$	−2.86182	+	9.17154i	−0.156358	+	0.501095i
$336$	−8.26980	−	1.76943i	−0.451155	−	0.0965303i
$337$	−2.91531	+	18.4065i	−0.158807	+	1.00267i	0.771592	+	0.636118i	$0.219461\pi$
$337$	−2.91531	+	18.4065i	−0.158807	+	1.00267i	−0.930399	+	0.366549i	$0.880539\pi$
$338$	0.248281	−	1.56758i	0.0135047	−	0.0852653i
$339$	31.7850	+	6.80080i	1.72632	+	0.369369i
$340$	−10.7390	+	0.125655i	−0.582404	+	0.00681458i
$341$	−2.41555	−	3.32471i	−0.130809	−	0.180043i
$342$	−0.491471	+	1.81465i	−0.0265757	+	0.0981253i
$343$	33.9736	+	33.9736i	1.83440	+	1.83440i
$344$	0.415645	−	1.27922i	0.0224101	−	0.0689711i
$345$	1.56705	−	1.97665i	0.0843671	−	0.106419i
$346$	5.09600	+	15.6839i	0.273963	+	0.843170i
$347$	−10.8108	+	21.2173i	−0.580353	+	1.13901i	0.395067	+	0.918652i	$0.370721\pi$
$347$	−10.8108	+	21.2173i	−0.580353	+	1.13901i	−0.975420	+	0.220354i	$0.929279\pi$
$348$	−11.8022	+	7.64189i	−0.632665	+	0.409648i
$349$			8.63569i			0.462258i	0.972923	+	0.231129i	$0.0742419\pi$
$349$			8.63569i			0.462258i	−0.972923	+	0.231129i	$0.925758\pi$
$350$	−13.8837	+	20.0810i	−0.742112	+	1.07338i
$351$	6.20878	−	18.8495i	0.331400	−	1.00611i
$352$	−2.50336	+	0.396494i	−0.133430	+	0.0211332i
$353$	−25.4664	−	12.9758i	−1.35544	−	0.690631i	−0.382992	−	0.923751i	$-0.625106\pi$
$353$	−25.4664	−	12.9758i	−1.35544	−	0.690631i	−0.972448	+	0.233120i	$0.925106\pi$
$354$	14.2843	−	12.8269i	0.759202	−	0.681741i
$355$	−1.93239	−	0.956288i	−0.102560	−	0.0507545i
$356$	10.5039	+	3.41294i	0.556708	+	0.180885i
$357$	−37.9010	−	14.6074i	−2.00594	−	0.773104i
$358$	−5.63186	+	2.86958i	−0.297653	+	0.151662i
$359$	6.72833	−	4.88842i	0.355108	−	0.258001i	−0.395901	−	0.918293i	$-0.629568\pi$
$359$	6.72833	−	4.88842i	0.355108	−	0.258001i	0.751009	+	0.660292i	$0.229568\pi$
$360$	2.67315	−	6.15258i	0.140887	−	0.324270i
$361$	−15.0536	−	10.9371i	−0.792295	−	0.575636i
$362$	18.5228	+	2.93373i	0.973538	+	0.154193i
$363$	−7.65848	+	2.04105i	−0.401966	+	0.107127i
$364$	10.9612	−	15.0868i	0.574523	−	0.790763i
$365$	10.0175	−	14.1327i	0.524340	−	0.739741i
$366$	5.97263	+	3.45902i	0.312195	+	0.180806i
$367$	−7.05620	−	13.8486i	−0.368331	−	0.722889i	0.630237	−	0.776403i	$-0.282958\pi$
$367$	−7.05620	−	13.8486i	−0.368331	−	0.722889i	−0.998567	+	0.0535138i	$0.982958\pi$
$368$	−0.460535	+	0.460535i	−0.0240071	+	0.0240071i
$369$	−9.38053	−	16.3490i	−0.488331	−	0.851093i
$370$	5.89715	+	5.76074i	0.306578	+	0.299487i
$371$	2.37748	−	0.772489i	0.123432	−	0.0401056i
$372$	−2.80431	−	0.150751i	−0.145397	−	0.00781606i
$373$	2.33980	+	14.7729i	0.121150	+	0.764912i	0.971210	+	0.238225i	$0.0765657\pi$
$373$	2.33980	+	14.7729i	0.121150	+	0.764912i	−0.850060	+	0.526686i	$0.823434\pi$
$374$	−12.1734			−0.629473
$375$	−13.4360	−	13.9454i	−0.693830	−	0.720139i
$376$	−4.29592			−0.221545
$377$	−4.85009	−	30.6223i	−0.249792	−	1.57713i
$378$	18.0122	−	17.8674i	0.926448	−	0.919001i
$379$	5.98428	−	1.94441i	0.307392	−	0.0998776i	−0.151259	−	0.988494i	$-0.548333\pi$
$379$	5.98428	−	1.94441i	0.307392	−	0.0998776i	0.458651	+	0.888617i	$0.348333\pi$
$380$	−1.00239	−	0.979202i	−0.0514214	−	0.0502320i
$381$	0.412427	+	3.97541i	0.0211293	+	0.203667i
$382$	−11.1109	+	11.1109i	−0.568482	+	0.568482i
$383$	−5.34769	−	10.4954i	−0.273254	−	0.536292i	0.713073	−	0.701090i	$-0.247303\pi$
$383$	−5.34769	−	10.4954i	−0.273254	−	0.536292i	−0.986327	+	0.164798i	$0.947303\pi$
$384$	−0.868042	+	1.49883i	−0.0442971	+	0.0764870i
$385$	−16.0023	+	22.5761i	−0.815551	+	1.15058i
$386$	1.52538	−	2.09951i	0.0776400	−	0.106862i
$387$	2.53097	+	3.14273i	0.128656	+	0.159754i
$388$	14.9915	+	2.37442i	0.761078	+	0.120543i
$389$	−19.3894	−	14.0872i	−0.983082	−	0.714251i	−0.0246869	−	0.999695i	$-0.507859\pi$
$389$	−19.3894	−	14.0872i	−0.983082	−	0.714251i	−0.958395	+	0.285444i	$0.907859\pi$
$390$	10.0112	+	10.8896i	0.506935	+	0.551417i
$391$	−2.53072	+	1.83868i	−0.127984	+	0.0929859i
$392$	15.0047	−	7.64527i	0.757851	−	0.386145i
$393$	3.38002	−	8.76996i	0.170499	−	0.442386i
$394$	5.51903	+	1.79324i	0.278045	+	0.0903423i
$395$	0.292940	+	0.144969i	0.0147394	+	0.00729416i
$396$	3.11138	−	6.93799i	0.156353	−	0.348647i
$397$	−7.12795	−	3.63187i	−0.357741	−	0.182278i	0.265878	−	0.964007i	$-0.414338\pi$
$397$	−7.12795	−	3.63187i	−0.357741	−	0.182278i	−0.623619	+	0.781728i	$0.714338\pi$
$398$	3.81642	−	0.604462i	0.191300	−	0.0302989i
$399$	−2.14911	−	4.84450i	−0.107590	−	0.242528i
$400$	3.03277	+	3.97521i	0.151638	+	0.198761i
$401$			5.93714i			0.296487i	0.988951	+	0.148243i	$0.0473619\pi$
$401$			5.93714i			0.296487i	−0.988951	+	0.148243i	$0.952638\pi$
$402$	4.04484	+	6.24689i	0.201738	+	0.311566i
$403$	2.81141	−	5.51770i	0.140046	−	0.274856i
$404$	0.602504	+	1.85432i	0.0299757	+	0.0922557i
$405$	11.0671	+	16.8083i	0.549928	+	0.835212i
$406$	12.2481	−	37.6958i	0.607864	−	1.87081i
$407$	6.60753	+	6.60753i	0.327523	+	0.327523i
$408$	−5.24399	+	6.45800i	−0.259616	+	0.319719i
$409$	12.3971	+	17.0631i	0.612995	+	0.843715i	0.996820	−	0.0796911i	$-0.0253934\pi$
$409$	12.3971	+	17.0631i	0.612995	+	0.843715i	−0.383825	+	0.923406i	$0.625393\pi$
$410$	14.0482	−	0.164375i	0.693792	−	0.00811790i
$411$	1.55852	−	7.28405i	0.0768760	−	0.359296i
$412$	0.540832	−	3.41468i	0.0266449	−	0.168229i
$413$	−8.46616	+	53.4532i	−0.416592	+	2.63026i
$414$	−0.401093	−	1.91228i	−0.0197126	−	0.0939832i
$415$	−5.27306	+	16.8991i	−0.258844	+	0.829542i
$416$	−2.24493	−	3.08989i	−0.110067	−	0.151494i
$417$	3.95274	+	3.20968i	0.193567	+	0.157179i
$418$	−1.12314	−	1.12314i	−0.0549344	−	0.0549344i
$419$	−11.8698	+	36.5316i	−0.579880	+	1.78469i	0.0390457	+	0.999237i	$0.487568\pi$
$419$	−11.8698	+	36.5316i	−0.579880	+	1.78469i	−0.618926	+	0.785450i	$0.712432\pi$
$420$	5.08325	+	18.2144i	0.248037	+	0.888770i
$421$	−5.24894	−	16.1546i	−0.255818	−	0.787326i	−0.993667	−	0.112361i	$-0.964159\pi$
$421$	−5.24894	−	16.1546i	−0.255818	−	0.787326i	0.737850	−	0.674965i	$-0.235841\pi$
$422$	−4.96359	+	9.74160i	−0.241624	+	0.474214i
$423$	7.04823	−	10.7897i	0.342697	−	0.524611i
$424$		−	0.511982i		−	0.0248641i
$425$	11.4002	+	21.1364i	0.552989	+	1.02526i
$426$	−1.52660	+	0.677229i	−0.0739642	+	0.0328119i
$427$	−19.2171	+	3.04368i	−0.929979	+	0.147294i
$428$	9.79189	+	4.98922i	0.473309	+	0.241163i
$429$	11.2024	+	12.4752i	0.540857	+	0.602310i
$430$	−2.96490	+	0.505221i	−0.142980	+	0.0243639i
$431$	24.9008	+	8.09077i	1.19943	+	0.389719i	0.839551	−	0.543280i	$-0.182818\pi$
$431$	24.9008	+	8.09077i	1.19943	+	0.389719i	0.359879	+	0.932999i	$0.382818\pi$
$432$	−2.34030	−	4.63929i	−0.112598	−	0.223208i
$433$	25.3199	−	12.9012i	1.21680	−	0.619990i	0.276721	−	0.960950i	$-0.410752\pi$
$433$	25.3199	−	12.9012i	1.21680	−	0.619990i	0.940078	+	0.340960i	$0.110752\pi$
$434$	6.40478	−	4.65335i	0.307440	−	0.223368i
$435$	27.3889	+	15.4371i	1.31320	+	0.740150i
$436$	−14.4153	−	10.4733i	−0.690366	−	0.501580i
$437$	−0.403127	−	0.0638490i	−0.0192842	−	0.00305431i
$438$	−3.45547	−	12.9657i	−0.165109	−	0.619527i
$439$	−23.8366	+	32.8083i	−1.13766	+	1.56585i	−0.365032	+	0.930995i	$0.618942\pi$
$439$	−23.8366	+	32.8083i	−1.13766	+	1.56585i	−0.772628	+	0.634859i	$0.781058\pi$
$440$	3.38467	+	4.54579i	0.161358	+	0.216712i
$441$	−5.41598	+	50.2293i	−0.257904	+	2.39187i
$442$	−8.32799	−	16.3446i	−0.396122	−	0.777434i
$443$	4.87049	−	4.87049i	0.231404	−	0.231404i	−0.581875	−	0.813279i	$-0.697681\pi$
$443$	4.87049	−	4.87049i	0.231404	−	0.231404i	0.813279	+	0.581875i	$0.197681\pi$
$444$	6.35164	−	0.658947i	0.301435	−	0.0312722i
$445$	−4.14847	−	24.3453i	−0.196656	−	1.15408i
$446$	−18.5603	+	6.03061i	−0.878856	+	0.285558i
$447$	0.566865	−	10.5450i	0.0268118	−	0.498762i
$448$	−0.763813	−	4.82253i	−0.0360868	−	0.227843i
$449$	38.2829			1.80668			0.903340	−	0.428924i	$-0.141107\pi$
$449$	38.2829			1.80668			0.903340	+	0.428924i	$0.141107\pi$
$450$	−14.9600	+	1.09508i	−0.705220	+	0.0516224i
$451$	15.9247			0.749863
$452$	2.93571	+	18.5354i	0.138084	+	0.871830i
$453$	−1.62467	+	30.2227i	−0.0763337	+	1.41998i
$454$	−23.5335	+	7.64649i	−1.10448	+	0.358868i
$455$	−41.2590	−	6.04083i	−1.93425	−	0.283198i
$456$	−1.07964	+	0.112007i	−0.0505589	+	0.00524520i
$457$	25.3039	−	25.3039i	1.18366	−	1.18366i	0.204877	−	0.978788i	$-0.434321\pi$
$457$	25.3039	−	25.3039i	1.18366	−	1.18366i	0.978788	−	0.204877i	$-0.0656794\pi$
$458$	−1.38340	−	2.71507i	−0.0646419	−	0.126867i
$459$	−7.61626	−	23.7664i	−0.355497	−	1.10932i
$460$	1.39023	+	0.433798i	0.0648200	+	0.0202259i
$461$	4.06138	−	5.59002i	0.189158	−	0.260353i	−0.703896	−	0.710303i	$-0.748558\pi$
$461$	4.06138	−	5.59002i	0.189158	−	0.260353i	0.893054	+	0.449950i	$0.148558\pi$
$462$	5.51988	+	20.7119i	0.256808	+	0.963603i
$463$	21.7821	+	3.44995i	1.01230	+	0.160333i	0.640483	−	0.767973i	$-0.278734\pi$
$463$	21.7821	+	3.44995i	1.01230	+	0.160333i	0.371819	+	0.928305i	$0.378734\pi$
$464$	−6.56735	−	4.77146i	−0.304881	−	0.221509i
$465$	2.61345	+	5.71002i	0.121196	+	0.264796i
$466$	14.9847	−	10.8870i	0.694153	−	0.504332i
$467$	−4.03552	+	2.05620i	−0.186742	+	0.0951496i	−0.544862	−	0.838526i	$-0.683418\pi$
$467$	−4.03552	+	2.05620i	−0.186742	+	0.0951496i	0.358120	+	0.933676i	$0.383418\pi$
$468$	11.4438	−	0.568876i	0.528990	−	0.0262963i
$469$	−19.9523	−	6.48290i	−0.921313	−	0.299353i
$470$	4.46086	+	8.50737i	0.205764	+	0.392416i
$471$	−2.66729	−	2.97036i	−0.122902	−	0.136867i
$472$	9.87598	+	5.03206i	0.454579	+	0.231620i
$473$	−3.36716	+	0.533306i	−0.154822	+	0.0245214i
$474$	0.231426	−	0.102665i	0.0106297	−	0.00471554i
$475$	−0.898276	+	3.00187i	−0.0412157	+	0.137735i
$476$		−	23.4511i		−	1.07488i
$477$	1.28590	+	0.839999i	0.0588773	+	0.0384609i
$478$	6.06483	−	11.9029i	0.277399	−	0.544426i
$479$	11.4075	+	35.1086i	0.521220	+	1.60415i	0.771671	+	0.636022i	$0.219421\pi$
$479$	11.4075	+	35.1086i	0.521220	+	1.60415i	−0.250450	+	0.968129i	$0.580579\pi$
$480$	3.86957	+	0.162636i	0.176621	+	0.00742328i
$481$	−4.35128	+	13.3919i	−0.198401	+	0.610616i
$482$	−3.61037	−	3.61037i	−0.164448	−	0.164448i
$483$	4.27585	+	3.47205i	0.194558	+	0.157984i
$484$	−2.68968	−	3.70203i	−0.122258	−	0.168274i
$485$	−10.8649	−	32.1538i	−0.493352	−	1.46003i
$486$	15.4918	+	1.73367i	0.702720	+	0.0786408i
$487$	−5.38000	+	33.9680i	−0.243791	+	1.53923i	0.497150	+	0.867665i	$0.334380\pi$
$487$	−5.38000	+	33.9680i	−0.243791	+	1.53923i	−0.740941	+	0.671570i	$0.765620\pi$
$488$	−0.623369	+	3.93579i	−0.0282186	+	0.178165i
$489$	8.29627	−	38.7743i	0.375170	−	1.75344i
$490$	−30.7210	−	21.7755i	−1.38783	−	0.983719i
$491$	−9.76139	−	13.4354i	−0.440525	−	0.606331i	0.529803	−	0.848120i	$-0.322266\pi$
$491$	−9.76139	−	13.4354i	−0.440525	−	0.606331i	−0.970329	+	0.241789i	$0.922266\pi$
$492$	6.85992	−	8.44803i	0.309269	−	0.380867i
$493$	−27.5693	−	27.5693i	−1.24166	−	1.24166i
$494$	0.739624	−	2.27633i	0.0332772	−	0.102417i
$495$	−16.9704	+	1.04278i	−0.762763	+	0.0468695i
$496$	−0.501043	−	1.54205i	−0.0224975	−	0.0692401i
$497$	2.13736	−	4.19480i	0.0958736	−	0.188163i
$498$	7.45283	+	11.5102i	0.333969	+	0.515785i
$499$			23.6495i			1.05870i	0.848404	+	0.529349i	$0.177564\pi$
$499$			23.6495i			1.05870i	−0.848404	+	0.529349i	$0.822436\pi$
$500$	4.72305	−	10.1337i	0.211221	−	0.453195i
$501$	6.22221	+	14.0261i	0.277988	+	0.626639i
$502$	10.3121	−	1.63327i	0.460249	−	0.0728964i
$503$	−13.2000	−	6.72572i	−0.588557	−	0.299885i	0.134236	−	0.990949i	$-0.457142\pi$
$503$	−13.2000	−	6.72572i	−0.588557	−	0.299885i	−0.722793	+	0.691065i	$0.757142\pi$
$504$	13.3655	+	5.99382i	0.595345	+	0.266986i
$505$	3.04653	−	3.11867i	0.135569	−	0.138779i
$506$	1.56996	+	0.510111i	0.0697932	+	0.0226772i
$507$	−0.988597	+	2.56507i	−0.0439051	+	0.113919i
$508$	−2.05602	+	1.04759i	−0.0912211	+	0.0464795i
$509$	26.7370	−	19.4255i	1.18510	−	0.861022i	0.192358	−	0.981325i	$-0.438386\pi$
$509$	26.7370	−	19.4255i	1.18510	−	0.861022i	0.992737	+	0.120303i	$0.0383865\pi$
$510$	18.2344	+	3.67891i	0.807431	+	0.162905i
$511$	30.6019	+	22.2336i	1.35375	+	0.983557i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$	1.49003	−	2.89540i	0.0657864	−	0.127835i
$514$	13.1153	−	18.0516i	0.578489	−	0.796222i
$515$	−7.32381	+	2.47475i	−0.322726	+	0.109051i
$516$	−1.16756	+	2.01601i	−0.0513992	+	0.0887501i
$517$	4.94319	+	9.70155i	0.217401	+	0.426674i
$518$	−12.7289	+	12.7289i	−0.559274	+	0.559274i
$519$	−2.94746	−	28.4108i	−0.129379	−	1.24709i
$520$	−3.78789	+	7.65425i	−0.166110	+	0.335661i
$521$	−10.1727	+	3.30530i	−0.445672	+	0.144808i	−0.523251	−	0.852179i	$-0.675281\pi$
$521$	−10.1727	+	3.30530i	−0.445672	+	0.144808i	0.0775789	+	0.996986i	$0.475281\pi$
$522$	22.7589	−	8.66616i	0.996132	−	0.379308i
$523$	6.12109	+	38.6470i	0.267656	+	1.68992i	0.645271	+	0.763953i	$0.276744\pi$
$523$	6.12109	+	38.6470i	0.267656	+	1.68992i	−0.377615	+	0.925963i	$0.623256\pi$
$524$	5.42638			0.237052
$525$	30.7922	−	28.9802i	1.34388	−	1.26480i
$526$	−13.3050			−0.580124
$527$	−1.21824	−	7.69168i	−0.0530675	−	0.335055i
$528$	4.38367	+	0.235652i	0.190775	+	0.0102554i
$529$	−21.4709	+	6.97631i	−0.933516	+	0.303318i
$530$	−1.01390	+	0.531640i	−0.0440409	+	0.0230930i
$531$	−28.8419	+	16.5486i	−1.25163	+	0.718147i
$532$	2.16363	−	2.16363i	0.0938053	−	0.0938053i
$533$	10.8943	+	21.3812i	0.471883	+	0.926122i
$534$	−16.5539	−	9.58709i	−0.716356	−	0.414874i
$535$	−0.287512	−	24.5720i	−0.0124302	−	1.06234i
$536$	−2.52552	+	3.47608i	−0.109086	+	0.150144i
$537$	10.5787	−	2.81930i	0.456504	−	0.121662i
$538$	−8.04880	−	1.27480i	−0.347008	−	0.0549607i
$539$	−34.5309	−	25.0882i	−1.48735	−	1.08062i
$540$	−6.75720	+	9.45200i	−0.290784	+	0.406749i
$541$	13.6337	−	9.90543i	0.586157	−	0.425868i	−0.254782	−	0.966999i	$-0.582004\pi$
$541$	13.6337	−	9.90543i	0.586157	−	0.425868i	0.840938	+	0.541131i	$0.182004\pi$
$542$	−7.89814	+	4.02431i	−0.339254	+	0.172859i
$543$	−30.3092	−	11.6814i	−1.30069	−	0.501298i
$544$	−4.56788	−	1.48420i	−0.195846	−	0.0636344i
$545$	−5.77194	+	39.4225i	−0.247243	+	1.68867i
$546$	−24.0325	+	21.5805i	−1.02850	+	0.923560i
$547$	13.9944	+	7.13049i	0.598356	+	0.304878i	0.726811	−	0.686838i	$-0.241002\pi$
$547$	13.9944	+	7.13049i	0.598356	+	0.304878i	−0.128455	+	0.991715i	$0.541002\pi$
$548$	4.24769	−	0.672768i	0.181452	−	0.0287392i
$549$	−8.86242	−	8.02304i	−0.378239	−	0.342415i
$550$	5.48757	−	11.4231i	0.233991	−	0.487083i
$551$		−	5.08717i		−	0.216721i
$552$	0.946910	−	0.613122i	0.0403032	−	0.0260962i
$553$	−0.324013	+	0.635911i	−0.0137784	+	0.0270417i
$554$	−3.76524	−	11.5882i	−0.159970	−	0.492337i
$555$	−7.90045	−	11.8941i	−0.335355	−	0.504878i
$556$	−0.908430	+	2.79586i	−0.0385260	+	0.118571i
$557$	16.7489	+	16.7489i	0.709672	+	0.709672i	0.966466	−	0.256794i	$-0.0826662\pi$
$557$	16.7489	+	16.7489i	0.709672	+	0.709672i	−0.256794	+	0.966466i	$0.582666\pi$
$558$	4.69508	+	1.27159i	0.198758	+	0.0538307i
$559$	−3.01956	−	4.15607i	−0.127714	−	0.175783i
$560$	−8.75709	+	6.52029i	−0.370055	+	0.275533i
$561$	20.6183	+	4.41156i	0.870507	+	0.186256i
$562$	0.312022	−	1.97003i	0.0131619	−	0.0831007i
$563$	7.14192	−	45.0923i	0.300996	−	1.90041i	−0.119011	−	0.992893i	$-0.537973\pi$
$563$	7.14192	−	45.0923i	0.300996	−	1.90041i	0.420007	−	0.907521i	$-0.362027\pi$
$564$	7.27606	+	1.55681i	0.306378	+	0.0655534i
$565$	33.6579	−	25.0607i	1.41600	−	1.05431i
$566$	−1.22605	−	1.68751i	−0.0515345	−	0.0709312i
$567$	−36.9826	+	23.7348i	−1.55312	+	0.996769i
$568$	−0.681806	−	0.681806i	−0.0286080	−	0.0286080i
$569$	−0.701234	+	2.15818i	−0.0293972	+	0.0904754i	−0.964679	−	0.263430i	$-0.915146\pi$
$569$	−0.701234	+	2.15818i	−0.0293972	+	0.0904754i	0.935281	+	0.353905i	$0.115146\pi$
$570$	1.34291	+	2.02175i	0.0562481	+	0.0846817i
$571$	−9.62474	−	29.6219i	−0.402783	−	1.23964i	−0.922733	−	0.385441i	$-0.874049\pi$
$571$	−9.62474	−	29.6219i	−0.402783	−	1.23964i	0.519950	−	0.854197i	$-0.325951\pi$
$572$	−4.39477	+	8.62521i	−0.183754	+	0.360638i
$573$	22.8451	−	14.7922i	0.954370	−	0.617951i
$574$			30.6775i			1.28046i
$575$	−0.584544	−	3.20358i	−0.0243772	−	0.133599i
$576$	2.01338	−	2.22403i	0.0838909	−	0.0926677i
$577$	−13.3526	+	2.11485i	−0.555877	+	0.0880422i	−0.428051	−	0.903755i	$-0.640800\pi$
$577$	−13.3526	+	2.11485i	−0.555877	+	0.0880422i	−0.127825	+	0.991797i	$0.540800\pi$
$578$	−5.40699	−	2.75500i	−0.224901	−	0.114593i
$579$	−3.34441	+	3.00319i	−0.138989	+	0.124808i
$580$	−2.62960	+	17.9602i	−0.109188	+	0.745758i
$581$	−36.7632	−	11.9451i	−1.52520	−	0.495566i
$582$	−24.5309	−	9.45440i	−1.01684	−	0.391897i
$583$	−1.15622	+	0.589123i	−0.0478857	+	0.0243990i
$584$	6.26750	−	4.55360i	0.259351	−	0.188429i
$585$	−13.0097	−	22.0719i	−0.537887	−	0.912559i
$586$	16.1844	+	11.7587i	0.668573	+	0.485747i
$587$	20.8055	+	3.29526i	0.858733	+	0.136010i	0.570246	−	0.821474i	$-0.306848\pi$
$587$	20.8055	+	3.29526i	0.858733	+	0.136010i	0.288487	+	0.957484i	$0.406848\pi$
$588$	−28.1843	+	7.51133i	−1.16230	+	0.309762i
$589$	0.597248	−	0.822041i	0.0246092	−	0.0338716i
$590$	−0.289981	−	24.7830i	−0.0119383	−	1.02030i
$591$	−8.69782	−	5.03730i	−0.357780	−	0.207207i
$592$	1.67377	+	3.28496i	0.0687917	+	0.135011i
$593$	13.4478	−	13.4478i	0.552235	−	0.552235i	−0.374851	−	0.927085i	$-0.622306\pi$
$593$	13.4478	−	13.4478i	0.552235	−	0.552235i	0.927085	+	0.374851i	$0.122306\pi$
$594$	−7.78407	+	10.6234i	−0.319384	+	0.435885i
$595$	−46.4411	+	24.3515i	−1.90390	+	0.998314i
$596$	5.79855	−	1.88406i	0.237518	−	0.0771743i
$597$	−6.68299	−	0.359255i	−0.273516	−	0.0147033i
$598$	0.389131	+	2.45687i	0.0159127	+	0.100469i
$599$	−0.0872460			−0.00356477			−0.00178239	−	0.999998i	$-0.500567\pi$
$599$	−0.0872460			−0.00356477			−0.00178239	+	0.999998i	$0.500567\pi$
$600$	−3.69606	−	7.83193i	−0.150891	−	0.319737i
$601$	5.69768			0.232413			0.116207	−	0.993225i	$-0.462927\pi$
$601$	5.69768			0.232413			0.116207	+	0.993225i	$0.462927\pi$
$602$	−1.02737	−	6.48656i	−0.0418725	−	0.264373i
$603$	−4.58698	−	12.0463i	−0.186796	−	0.490562i
$604$	−16.6190	+	5.39984i	−0.676218	+	0.219716i
$605$	−4.53831	+	9.17064i	−0.184509	+	0.372840i
$606$	−0.348480	−	3.35903i	−0.0141560	−	0.136451i
$607$	29.7432	−	29.7432i	1.20724	−	1.20724i	0.235320	−	0.971918i	$-0.424386\pi$
$607$	29.7432	−	29.7432i	1.20724	−	1.20724i	0.971918	−	0.235320i	$-0.0756138\pi$
$608$	−0.284505	−	0.558373i	−0.0115382	−	0.0226450i
$609$	−34.4055	+	59.4074i	−1.39418	+	2.40731i
$610$	8.44150	−	2.85243i	0.341787	−	0.115491i
$611$	−9.64405	+	13.2739i	−0.390157	+	0.537005i
$612$	11.2222	−	9.03764i	0.453629	−	0.365325i
$613$	−12.4325	−	1.96912i	−0.502145	−	0.0795319i	−0.0997765	−	0.995010i	$-0.531813\pi$
$613$	−12.4325	−	1.96912i	−0.502145	−	0.0795319i	−0.402368	+	0.915478i	$0.631813\pi$
$614$	−7.54983	−	5.48528i	−0.304687	−	0.221368i
$615$	−23.8533	−	4.81256i	−0.961856	−	0.194061i
$616$	−10.0119	+	7.27407i	−0.403391	+	0.293081i
$617$	30.8055	−	15.6962i	1.24018	−	0.631904i	0.294082	−	0.955780i	$-0.404986\pi$
$617$	30.8055	−	15.6962i	1.24018	−	0.631904i	0.946099	+	0.323876i	$0.104986\pi$
$618$	−2.15347	+	5.58750i	−0.0866251	+	0.224762i
$619$	8.55247	+	2.77887i	0.343753	+	0.111692i	0.475805	−	0.879551i	$-0.342157\pi$
$619$	8.55247	+	2.77887i	0.343753	+	0.111692i	−0.132052	+	0.991243i	$0.542157\pi$
$620$	−2.53350	+	2.59349i	−0.101748	+	0.104157i
$621$	−0.0136569	+	3.38420i	−0.000548031	+	0.135803i
$622$	−6.97523	−	3.55406i	−0.279681	−	0.142505i
$623$	53.2624	−	8.43593i	2.13391	−	0.337979i
$624$	2.68253	+	6.04693i	0.107387	+	0.242071i
$625$	−24.9726	+	1.16960i	−0.998905	+	0.0467839i
$626$			2.86051i			0.114329i
$627$	1.49526	+	2.30929i	0.0597149	+	0.0922242i
$628$	1.04640	−	2.05367i	0.0417557	−	0.0819502i
$629$	5.47194	+	16.8409i	0.218180	+	0.671490i
$630$	−2.00883	−	32.6921i	−0.0800337	−	1.30248i
$631$	−5.89667	+	18.1481i	−0.234743	+	0.722463i	0.762413	+	0.647091i	$0.224015\pi$
$631$	−5.89667	+	18.1481i	−0.234743	+	0.722463i	−0.997155	+	0.0753725i	$0.975985\pi$
$632$	0.103358	+	0.103358i	0.00411138	+	0.00411138i
$633$	11.9372	−	14.7007i	0.474461	−	0.584302i
$634$	15.0327	+	20.6907i	0.597024	+	0.821733i
$635$	4.20955	+	2.98379i	0.167051	+	0.118408i
$636$	−0.185538	+	0.867153i	−0.00735708	+	0.0343848i
$637$	10.0615	−	63.5259i	0.398652	−	2.51699i
$638$	−3.21861	+	20.3215i	−0.127426	+	0.804537i
$639$	2.83106	−	0.593804i	0.111995	−	0.0234905i
$640$	0.715817	+	2.11840i	0.0282952	+	0.0837370i
$641$	−5.82328	−	8.01506i	−0.230006	−	0.316576i	0.678378	−	0.734713i	$-0.262683\pi$
$641$	−5.82328	−	8.01506i	−0.230006	−	0.316576i	−0.908384	+	0.418137i	$0.862683\pi$
$642$	−14.7766	−	11.9988i	−0.583187	−	0.473556i
$643$	14.9895	+	14.9895i	0.591130	+	0.591130i	0.937937	−	0.346807i	$-0.112734\pi$
$643$	14.9895	+	14.9895i	0.591130	+	0.591130i	−0.346807	+	0.937937i	$0.612734\pi$
$644$	−0.982687	+	3.02440i	−0.0387233	+	0.119178i
$645$	5.20478	+	0.218754i	0.204938	+	0.00861345i
$646$	−0.930111	−	2.86259i	−0.0365947	−	0.112627i
$647$	9.58156	−	18.8049i	0.376690	−	0.739296i	−0.622366	−	0.782726i	$-0.713829\pi$
$647$	9.58156	−	18.8049i	0.376690	−	0.739296i	0.999056	+	0.0434301i	$0.0138286\pi$
$648$	2.28256	+	8.70574i	0.0896675	+	0.341994i
$649$		−	28.0934i		−	1.10276i
$650$	19.0913	−	0.446827i	0.748823	−	0.0175260i
$651$	−12.5342	+	5.56040i	−0.491255	+	0.217929i
$652$	22.6112	−	3.58126i	0.885523	−	0.140253i
$653$	−28.9032	−	14.7269i	−1.13107	−	0.576309i	−0.214715	−	0.976677i	$-0.568882\pi$
$653$	−28.9032	−	14.7269i	−1.13107	−	0.576309i	−0.916355	+	0.400368i	$0.868882\pi$
$654$	20.6199	+	22.9628i	0.806302	+	0.897915i
$655$	−5.63472	−	10.7461i	−0.220167	−	0.419883i
$656$	5.97547	+	1.94155i	0.233303	+	0.0758048i
$657$	1.15390	+	23.2125i	0.0450181	+	0.905606i
$658$	−18.6892	+	9.52264i	−0.728582	+	0.371231i
$659$	−21.9545	+	15.9509i	−0.855225	+	0.621357i	−0.926582	−	0.376094i	$-0.877267\pi$
$659$	−21.9545	+	15.9509i	−0.855225	+	0.621357i	0.0713570	+	0.997451i	$0.477267\pi$
$660$	−4.08531	−	8.92585i	−0.159021	−	0.347438i
$661$	−20.1069	−	14.6085i	−0.782069	−	0.568206i	0.123531	−	0.992341i	$-0.460578\pi$
$661$	−20.1069	−	14.6085i	−0.782069	−	0.568206i	−0.905599	+	0.424135i	$0.860578\pi$
$662$	−31.5787	−	5.00158i	−1.22734	−	0.194392i
$663$	8.18209	+	30.7011i	0.317766	+	1.19233i
$664$	−4.65341	+	6.40487i	−0.180587	+	0.248557i
$665$	−6.53142	−	2.03802i	−0.253278	−	0.0790309i
$666$	−10.9967	−	1.18572i	−0.426112	−	0.0459456i
$667$	2.40025	+	4.71076i	0.0929382	+	0.182402i
$668$	−6.26427	+	6.26427i	−0.242372	+	0.242372i
$669$	33.6213	−	3.48802i	1.29988	−	0.134855i
$670$	9.50631	+	1.39184i	0.367261	+	0.0537715i
$671$	9.60557	−	3.12104i	0.370819	−	0.120486i
$672$	−0.453964	+	8.44478i	−0.0175120	+	0.325765i
$673$	3.13319	+	19.7822i	0.120775	+	0.762546i	0.971518	+	0.236964i	$0.0761524\pi$
$673$	3.13319	+	19.7822i	0.120775	+	0.762546i	−0.850743	+	0.525582i	$0.823848\pi$
$674$	18.6360			0.717830
$675$	25.7348	+	3.56663i	0.990532	+	0.137280i
$676$	−1.58712			−0.0610432
$677$	3.76633	+	23.7796i	0.144752	+	0.913926i	0.947997	+	0.318278i	$0.103105\pi$
$677$	3.76633	+	23.7796i	0.144752	+	0.913926i	−0.803246	+	0.595648i	$0.796895\pi$
$678$	1.74481	−	32.4575i	0.0670090	−	1.24652i
$679$	70.4833	−	22.9014i	2.70490	−	0.878876i
$680$	1.80406	+	10.5871i	0.0691825	+	0.405998i
$681$	42.6300	−	4.42263i	1.63359	−	0.169476i
$682$	−2.90591	+	2.90591i	−0.111273	+	0.111273i
$683$	−5.04753	−	9.90634i	−0.193138	−	0.379056i	0.774047	−	0.633129i	$-0.218230\pi$
$683$	−5.04753	−	9.90634i	−0.193138	−	0.379056i	−0.967185	+	0.254073i	$0.918230\pi$
$684$	1.86920	+	0.201546i	0.0714705	+	0.00770631i
$685$	−5.74308	−	7.71326i	−0.219432	−	0.294708i
$686$	28.2407	−	38.8700i	1.07823	−	1.48406i
$687$	1.35916	+	5.09989i	0.0518552	+	0.194573i
$688$	−1.32850	−	0.210413i	−0.0506484	−	0.00802192i
$689$	−1.58197	−	1.14937i	−0.0602682	−	0.0437874i
$690$	−2.19745	−	1.23854i	−0.0836557	−	0.0471504i
$691$	−26.5202	+	19.2681i	−1.00888	+	0.732992i	−0.963973	−	0.265999i	$-0.914298\pi$
$691$	−26.5202	+	19.2681i	−1.00888	+	0.732992i	−0.0449036	+	0.998991i	$0.514298\pi$
$692$	14.6936	−	7.48676i	0.558567	−	0.284604i
$693$	−1.84328	−	37.0804i	−0.0700205	−	1.40857i
$694$	22.6473	+	7.35855i	0.859680	+	0.279327i
$695$	6.48005	−	1.10421i	0.245802	−	0.0418850i
$696$	9.39408	+	10.4614i	0.356082	+	0.396540i
$697$	26.8878	+	13.7000i	1.01845	+	0.518926i
$698$	8.52937	−	1.35092i	0.322841	−	0.0511330i
$699$	−29.3252	+	13.0092i	−1.10918	+	0.492053i
$700$	22.0057	+	10.5714i	0.831737	+	0.399560i
$701$		−	25.1992i		−	0.951759i	−0.879510	−	0.475880i	$-0.842130\pi$
$701$		−	25.1992i		−	0.951759i	0.879510	−	0.475880i	$-0.157870\pi$
$702$	−19.5887	−	3.18363i	−0.739328	−	0.120158i
$703$	−1.04891	+	2.05861i	−0.0395606	+	0.0776420i
$704$	0.783225	+	2.41052i	0.0295189	+	0.0908498i
$705$	−4.47242	−	16.0256i	−0.168441	−	0.603561i
$706$	−8.83221	+	27.1827i	−0.332405	+	1.02304i
$707$	6.73158	+	6.73158i	0.253167	+	0.253167i
$708$	−14.9035	−	12.1019i	−0.560109	−	0.454816i
$709$	15.3258	+	21.0942i	0.575574	+	0.792209i	0.993201	−	0.116409i	$-0.0371383\pi$
$709$	15.3258	+	21.0942i	0.575574	+	0.792209i	−0.417628	+	0.908618i	$0.637138\pi$
$710$	−0.642223	+	2.05819i	−0.0241022	+	0.0772425i
$711$	−0.429174	+	0.0900177i	−0.0160953	+	0.00337593i
$712$	1.72774	−	10.9085i	0.0647498	−	0.408814i
$713$	−0.165197	+	1.04301i	−0.00618669	+	0.0390612i
$714$	−8.49850	+	39.7195i	−0.318048	+	1.48647i
$715$	21.6443	−	0.253255i	0.809452	−	0.00947122i
$716$	3.71527	+	5.11362i	0.138846	+	0.191105i
$717$	−14.5856	+	17.9623i	−0.544709	+	0.670813i
$718$	−5.88078	−	5.88078i	−0.219469	−	0.219469i
$719$	10.3692	−	31.9130i	0.386705	−	1.19016i	−0.548531	−	0.836130i	$-0.684813\pi$
$719$	10.3692	−	31.9130i	0.386705	−	1.19016i	0.935236	−	0.354025i	$-0.115187\pi$
$720$	−6.49501	−	1.67776i	−0.242055	−	0.0625264i
$721$	−5.21635	−	16.0543i	−0.194267	−	0.597892i
$722$	−8.44753	+	16.5792i	−0.314384	+	0.617014i
$723$	4.80657	+	7.42331i	0.178758	+	0.276076i
$724$		−	18.7537i		−	0.696976i
$725$	38.2979	−	13.4423i	1.42235	−	0.499235i
$726$	3.21397	+	7.24490i	0.119282	+	0.268883i
$727$	39.1616	−	6.20259i	1.45242	−	0.230042i	0.620184	−	0.784456i	$-0.287058\pi$
$727$	39.1616	−	6.20259i	1.45242	−	0.230042i	0.832241	+	0.554415i	$0.187058\pi$
$728$	−16.6158	−	8.46615i	−0.615821	−	0.313777i
$729$	−25.6104	−	8.55043i	−0.948532	−	0.316683i
$730$	−15.5258	−	7.68332i	−0.574636	−	0.284373i
$731$	−6.14406	−	1.99632i	−0.227246	−	0.0738367i
$732$	2.48211	−	6.44021i	0.0917414	−	0.238037i
$733$	−20.5512	+	10.4714i	−0.759077	+	0.386769i	−0.790281	−	0.612744i	$-0.790066\pi$
$733$	−20.5512	+	10.4714i	−0.759077	+	0.386769i	0.0312046	+	0.999513i	$0.490066\pi$
$734$	−12.5742	+	9.13572i	−0.464124	+	0.337206i
$735$	44.1414	+	48.0146i	1.62818	+	1.77105i
$736$	0.526909	+	0.382822i	0.0194221	+	0.0141110i
$737$	10.7561	+	1.70361i	0.396208	+	0.0627532i
$738$	−14.6802	+	11.8226i	−0.540387	+	0.435195i
$739$	−1.10089	+	1.51525i	−0.0404970	+	0.0557393i	−0.828785	−	0.559567i	$-0.810968\pi$
$739$	−1.10089	+	1.51525i	−0.0404970	+	0.0557393i	0.788288	+	0.615306i	$0.210968\pi$
$740$	4.76730	−	6.72573i	0.175250	−	0.247243i
$741$	−2.07764	+	3.58742i	−0.0763239	+	0.131787i
$742$	−1.13490	−	2.22736i	−0.0416634	−	0.0817690i
$743$	−32.5148	+	32.5148i	−1.19285	+	1.19285i	−0.216587	+	0.976263i	$0.569493\pi$
$743$	−32.5148	+	32.5148i	−1.19285	+	1.19285i	−0.976263	+	0.216587i	$0.930507\pi$
$744$	0.289796	+	2.79337i	0.0106245	+	0.102410i
$745$	−9.75227	−	9.52669i	−0.357295	−	0.349031i
$746$	14.2250	−	4.62198i	0.520814	−	0.169223i
$747$	−8.45176	−	22.1959i	−0.309234	−	0.812105i
$748$	1.90434	+	12.0236i	0.0696297	+	0.439625i
$749$	53.6587			1.96065
$750$	−11.6719	+	15.4521i	−0.426197	+	0.564230i
$751$	−30.1750			−1.10110			−0.550550	−	0.834802i	$-0.685582\pi$
$751$	−30.1750			−1.10110			−0.550550	+	0.834802i	$0.685582\pi$
$752$	0.672030	+	4.24303i	0.0245064	+	0.154727i
$753$	−18.0576	−	0.970716i	−0.658054	−	0.0353748i
$754$	−29.4865	+	9.58075i	−1.07384	+	0.348910i
$755$	27.9506	+	27.3041i	1.01723	+	0.993697i
$756$	−20.4652	−	14.9954i	−0.744311	−	0.545376i
$757$	−32.7271	+	32.7271i	−1.18949	+	1.18949i	−0.212277	+	0.977210i	$0.568088\pi$
$757$	−32.7271	+	32.7271i	−1.18949	+	1.18949i	−0.977210	+	0.212277i	$0.931912\pi$
$758$	−2.85662	−	5.60643i	−0.103757	−	0.203635i
$759$	−2.47421	−	1.43292i	−0.0898080	−	0.0520118i
$760$	−0.810339	+	1.14323i	−0.0293941	+	0.0414692i
$761$	−16.4848	+	22.6894i	−0.597574	+	0.822490i	−0.995483	−	0.0949348i	$-0.969736\pi$
$761$	−16.4848	+	22.6894i	−0.597574	+	0.822490i	0.397910	+	0.917425i	$0.369736\pi$
$762$	3.86195	−	1.02924i	0.139904	−	0.0372855i
$763$	−85.9289	−	13.6098i	−3.11084	−	0.492708i
$764$	12.7122	+	9.23596i	0.459911	+	0.334145i
$765$	−29.5506	−	12.8390i	−1.06840	−	0.464196i
$766$	−9.52966	+	6.92370i	−0.344321	+	0.250164i
$767$	37.7194	−	19.2190i	1.36197	−	0.693958i
$768$	1.61617	+	0.622886i	0.0583186	+	0.0224765i
$769$	18.8694	+	6.13105i	0.680449	+	0.221091i	0.628792	−	0.777574i	$-0.283550\pi$
$769$	18.8694	+	6.13105i	0.680449	+	0.221091i	0.0516570	+	0.998665i	$0.483550\pi$
$770$	24.8014	+	12.2736i	0.893781	+	0.442309i
$771$	−28.7553	+	25.8214i	−1.03560	+	0.929936i
$772$	−2.31229	−	1.17817i	−0.0832210	−	0.0424032i
$773$	17.2870	−	2.73800i	0.621771	−	0.0984789i	0.162403	−	0.986725i	$-0.448076\pi$
$773$	17.2870	−	2.73800i	0.621771	−	0.0984789i	0.459369	+	0.888246i	$0.348076\pi$
$774$	2.70811	−	2.99144i	0.0973410	−	0.107525i
$775$	7.76676	+	2.32412i	0.278990	+	0.0834849i
$776$		−	15.1784i		−	0.544872i
$777$	26.1719	−	16.9462i	0.938912	−	0.607942i
$778$	−10.8806	+	21.3544i	−0.390089	+	0.765593i
$779$	1.21672	+	3.74469i	0.0435937	+	0.134167i
$780$	9.18945	−	11.5914i	0.329035	−	0.415039i
$781$	−0.755201	+	2.32427i	−0.0270232	+	0.0831689i
$782$	2.21193	+	2.21193i	0.0790986	+	0.0790986i
$783$	−41.6877	+	6.43035i	−1.48980	+	0.229802i
$784$	−9.89840	−	13.6240i	−0.353514	−	0.486571i
$785$	−5.15352	+	0.0603002i	−0.183937	+	0.00215221i
$786$	−9.19074	−	1.96648i	−0.327823	−	0.0701419i
$787$	−5.84029	+	36.8741i	−0.208184	+	1.31442i	0.633202	+	0.773986i	$0.281740\pi$
$787$	−5.84029	+	36.8741i	−0.208184	+	1.31442i	−0.841386	+	0.540435i	$0.818260\pi$
$788$	0.907798	−	5.73161i	0.0323390	−	0.204180i
$789$	22.5348	+	4.82161i	0.802260	+	0.171654i
$790$	0.0973578	−	0.312012i	0.00346383	−	0.0111009i
$791$	53.8585	+	74.1299i	1.91499	+	2.63576i
$792$	−7.33930	−	1.98774i	−0.260791	−	0.0706311i
$793$	10.7617	+	10.7617i	0.382160	+	0.382160i
$794$	−2.47210	+	7.60834i	−0.0877315	+	0.270010i
$795$	1.90992	−	0.533018i	0.0677378	−	0.0189042i
$796$	−1.19404	−	3.67488i	−0.0423216	−	0.130253i
$797$	−9.33967	+	18.3301i	−0.330828	+	0.649286i	−0.995173	−	0.0981399i	$-0.968711\pi$
$797$	−9.33967	+	18.3301i	−0.330828	+	0.649286i	0.664345	+	0.747426i	$0.268711\pi$
$798$	−4.44866	+	2.88049i	−0.157481	+	0.101968i
$799$			20.6331i			0.729947i
$800$	3.45184	−	3.61729i	0.122041	−	0.127891i
$801$	24.5633	+	22.2368i	0.867900	+	0.785699i
$802$	5.86405	−	0.928774i	0.207067	−	0.0327961i
$803$	−17.4953	−	8.91431i	−0.617396	−	0.314579i
$804$	5.53722	−	4.97227i	0.195283	−	0.175358i
$805$	7.00975	−	1.19447i	0.247061	−	0.0420995i
$806$	−5.88957	−	1.91364i	−0.207451	−	0.0674050i
$807$	13.1704	+	5.07598i	0.463620	+	0.178683i
$808$	1.73723	−	0.885165i	0.0611157	−	0.0311400i
$809$	−35.2216	+	25.5900i	−1.23833	+	0.899696i	−0.997486	−	0.0708691i	$-0.977423\pi$
$809$	−35.2216	+	25.5900i	−1.23833	+	0.899696i	−0.240840	+	0.970565i	$0.577423\pi$
$810$	14.8701	−	13.5602i	0.522482	−	0.476458i
$811$	9.88364	+	7.18088i	0.347062	+	0.252155i	0.747635	−	0.664110i	$-0.231189\pi$
$811$	9.88364	+	7.18088i	0.347062	+	0.252155i	−0.400574	+	0.916265i	$0.631189\pi$
$812$	−39.1478	−	6.20040i	−1.37382	−	0.217591i
$813$	14.8356	−	3.95380i	0.520307	−	0.138666i
$814$	5.49253	−	7.55982i	0.192513	−	0.264972i
$815$	−30.5715	−	41.0591i	−1.07087	−	1.43824i
$816$	7.19884	+	4.16917i	0.252010	+	0.145950i
$817$	−0.382675	−	0.751043i	−0.0133881	−	0.0262757i
$818$	14.9137	−	14.9137i	0.521444	−	0.521444i
$819$	48.5248	−	27.8420i	1.69559	−	0.972879i
$820$	−2.35998	−	13.8496i	−0.0824140	−	0.483647i
$821$	−9.18310	+	2.98377i	−0.320492	+	0.104134i	−0.464845	−	0.885392i	$-0.653890\pi$
$821$	−9.18310	+	2.98377i	−0.320492	+	0.104134i	0.144353	+	0.989526i	$0.453890\pi$
$822$	−7.43818	−	0.399852i	−0.259436	−	0.0139464i
$823$	−4.59608	−	29.0185i	−0.160209	−	1.01152i	−0.928476	−	0.371392i	$-0.878881\pi$
$823$	−4.59608	−	29.0185i	−0.160209	−	1.01152i	0.768267	−	0.640129i	$-0.221119\pi$
$824$	−3.45724			−0.120439
$825$	−13.4340	+	17.3589i	−0.467713	+	0.604358i
$826$	54.1195			1.88306
$827$	2.81343	+	17.7633i	0.0978325	+	0.617690i	0.987076	+	0.160255i	$0.0512317\pi$
$827$	2.81343	+	17.7633i	0.0978325	+	0.617690i	−0.889243	+	0.457435i	$0.848768\pi$
$828$	−1.82599	+	0.695300i	−0.0634574	+	0.0241634i
$829$	−16.6482	+	5.40933i	−0.578216	+	0.187874i	−0.583501	−	0.812112i	$-0.698318\pi$
$829$	−16.6482	+	5.40933i	−0.578216	+	0.187874i	0.00528527	+	0.999986i	$0.498318\pi$
$830$	17.5159	+	2.56454i	0.607985	+	0.0890165i
$831$	2.17777	+	20.9917i	0.0755459	+	0.728193i
$832$	−2.70066	+	2.70066i	−0.0936285	+	0.0936285i
$833$	−36.7199	−	72.0669i	−1.27227	−	2.49697i
$834$	2.55182	−	4.40618i	0.0883623	−	0.152574i
$835$	18.9102	+	5.90059i	0.654413	+	0.204198i
$836$	−0.933612	+	1.28501i	−0.0322897	+	0.0444429i
$837$	−7.49131	−	3.85517i	−0.258937	−	0.133254i
$838$	37.9387	+	6.00890i	1.31057	+	0.207574i
$839$	−24.8896	−	18.0833i	−0.859284	−	0.624306i	0.0684060	−	0.997658i	$-0.478209\pi$
$839$	−24.8896	−	18.0833i	−0.859284	−	0.624306i	−0.927690	+	0.373351i	$0.878209\pi$
$840$	17.1949	−	7.87002i	0.593281	−	0.271541i
$841$	−29.8502	+	21.6874i	−1.02932	+	0.747843i
$842$	−15.1346	+	7.71145i	−0.521572	+	0.265754i
$843$	−1.24240	+	3.22359i	−0.0427905	+	0.111027i
$844$	10.3981	+	3.37856i	0.357919	+	0.116295i
$845$	1.64806	+	3.14304i	0.0566950	+	0.108124i
$846$	−11.7594	−	5.27358i	−0.404297	−	0.181309i
$847$	−19.9075	−	10.1434i	−0.684031	−	0.348531i
$848$	−0.505679	+	0.0800917i	−0.0173651	+	0.00275036i
$849$	1.46503	+	3.30247i	0.0502798	+	0.113340i
$850$	19.0928	−	14.5663i	0.654877	−	0.499619i
$851$		−	2.40120i		−	0.0823120i
$852$	0.907705	+	1.40187i	0.0310975	+	0.0480272i
$853$	18.7621	−	36.8228i	0.642403	−	1.26079i	−0.308478	−	0.951231i	$-0.599820\pi$
$853$	18.7621	−	36.8228i	0.642403	−	1.26079i	0.950881	−	0.309556i	$-0.100180\pi$
$854$	6.01242	+	18.5043i	0.205741	+	0.633205i
$855$	−1.54183	−	3.91092i	−0.0527296	−	0.133751i
$856$	3.39600	−	10.4518i	0.116073	−	0.357236i
$857$	−9.23819	−	9.23819i	−0.315570	−	0.315570i	0.531493	−	0.847063i	$-0.321631\pi$
$857$	−9.23819	−	9.23819i	−0.315570	−	0.315570i	−0.847063	+	0.531493i	$0.821631\pi$
$858$	10.5692	−	13.0160i	0.360826	−	0.444360i
$859$	−31.7094	−	43.6442i	−1.08191	−	1.48912i	−0.857401	−	0.514649i	$-0.827922\pi$
$859$	−31.7094	−	43.6442i	−1.08191	−	1.48912i	−0.224508	−	0.974472i	$-0.572078\pi$
$860$	0.962813	+	2.84936i	0.0328317	+	0.0971624i
$861$	11.1173	−	51.9590i	0.378877	−	1.77076i
$862$	4.09581	−	25.8599i	0.139504	−	0.880793i
$863$	−5.91581	+	37.3509i	−0.201376	+	1.27144i	0.655214	+	0.755443i	$0.272578\pi$
$863$	−5.91581	+	37.3509i	−0.201376	+	1.27144i	−0.856590	+	0.515997i	$0.827422\pi$
$864$	−4.21607	+	3.03723i	−0.143433	+	0.103329i
$865$	−30.0841	−	21.3241i	−1.02289	−	0.725040i
$866$	−16.7032	−	22.9900i	−0.567599	−	0.781233i
$867$	8.15952	+	6.62564i	0.277112	+	0.225019i
$868$	−5.59799	−	5.59799i	−0.190008	−	0.190008i
$869$	0.114485	−	0.352348i	0.00388363	−	0.0119526i
$870$	10.9624	−	29.4666i	0.371661	−	0.999010i
$871$	5.07107	+	15.6072i	0.171827	+	0.528828i
$872$	−8.08931	+	15.8762i	−0.273939	+	0.537635i
$873$	38.1221	+	24.9029i	1.29024	+	0.842834i
$874$			0.408152i			0.0138059i
$875$	−1.91574	−	54.5559i	−0.0647638	−	1.84433i
$876$	−12.2655	+	5.44122i	−0.414414	+	0.183842i
$877$	−23.3056	+	3.69125i	−0.786976	+	0.124645i	−0.536972	−	0.843600i	$-0.680432\pi$
$877$	−23.3056	+	3.69125i	−0.786976	+	0.124645i	−0.250004	+	0.968245i	$0.580432\pi$
$878$	36.1332	+	18.4108i	1.21944	+	0.621334i
$879$	−23.1506	−	25.7810i	−0.780850	−	0.869571i
$880$	3.96034	−	4.05412i	0.133503	−	0.136664i
$881$	−1.56237	−	0.507643i	−0.0526374	−	0.0171029i	0.282580	−	0.959244i	$-0.408810\pi$
$881$	−1.56237	−	0.507643i	−0.0526374	−	0.0171029i	−0.335217	+	0.942141i	$0.608810\pi$
$882$	50.4582	−	2.50830i	1.69901	−	0.0844588i
$883$	41.1010	−	20.9420i	1.38316	−	0.704755i	0.405332	−	0.914170i	$-0.367156\pi$
$883$	41.1010	−	20.9420i	1.38316	−	0.704755i	0.977827	+	0.209415i	$0.0671559\pi$
$884$	−14.8406	+	10.7823i	−0.499143	+	0.362649i
$885$	−8.49004	+	42.0805i	−0.285390	+	1.41452i
$886$	−5.57244	−	4.04861i	−0.187210	−	0.136016i
$887$	−41.9970	−	6.65167i	−1.41012	−	0.223341i	−0.595510	−	0.803348i	$-0.703050\pi$
$887$	−41.9970	−	6.65167i	−1.41012	−	0.223341i	−0.814612	+	0.580007i	$0.803050\pi$
$888$	−1.64445	−	6.17036i	−0.0551841	−	0.207064i
$889$	−6.62246	+	9.11504i	−0.222110	+	0.305708i
$890$	−23.3966	+	7.90584i	−0.784257	+	0.265004i
$891$	17.0339	−	15.1722i	0.570655	−	0.508287i
$892$	8.85983	+	17.3884i	0.296649	+	0.582207i
$893$	−1.90364	+	1.90364i	−0.0637029	+	0.0637029i
$894$	−10.5039	+	1.08972i	−0.351302	+	0.0364456i
$895$	6.26879	−	12.6674i	0.209543	−	0.423426i
$896$	−4.64367	+	1.50882i	−0.155134	+	0.0504061i
$897$	0.231276	−	4.30226i	0.00772207	−	0.143648i
$898$	−5.98876	−	37.8116i	−0.199848	−	1.26179i
$899$	−13.1621			−0.438980
$900$	3.42185	+	14.6045i	0.114062	+	0.486816i
$901$	−2.45903			−0.0819222
$902$	−2.49117	−	15.7286i	−0.0829468	−	0.523705i
$903$	−0.610606	+	11.3587i	−0.0203197	+	0.377994i
$904$	17.8479	−	5.79914i	0.593613	−	0.192877i
$905$	−37.1387	+	19.4738i	−1.23453	+	0.647329i
$906$	30.1047	−	3.12320i	1.00016	−	0.103761i
$907$	−11.6182	+	11.6182i	−0.385775	+	0.385775i	−0.873177	−	0.487403i	$-0.837944\pi$
$907$	−11.6182	+	11.6182i	−0.385775	+	0.385775i	0.487403	+	0.873177i	$0.337944\pi$
$908$	11.2338	+	22.0476i	0.372807	+	0.731674i
$909$	−0.627059	+	5.81552i	−0.0207982	+	0.192889i
$910$	0.487876	+	41.6960i	0.0161729	+	1.38221i
$911$	−31.9965	+	44.0394i	−1.06009	+	1.45909i	−0.180371	+	0.983599i	$0.557730\pi$
$911$	−31.9965	+	44.0394i	−1.06009	+	1.45909i	−0.879720	+	0.475492i	$0.842270\pi$
$912$	0.279521	+	1.04883i	0.00925586	+	0.0347302i
$913$	19.8188	+	3.13899i	0.655906	+	0.103885i
$914$	−28.9507	−	21.0339i	−0.957605	−	0.695741i
$915$	−15.3312	+	1.77206i	−0.506834	+	0.0585827i
$916$	−2.46523	+	1.79110i	−0.0814536	+	0.0591795i
$917$	23.6073	−	12.0285i	0.779580	−	0.397216i
$918$	−22.2823	+	11.2404i	−0.735426	+	0.370987i
$919$	47.1407	+	15.3170i	1.55503	+	0.505260i	0.955474	−	0.295074i	$-0.0953443\pi$
$919$	47.1407	+	15.3170i	1.55503	+	0.505260i	0.599555	+	0.800334i	$0.295344\pi$
$920$	0.210977	−	1.44098i	0.00695570	−	0.0475076i
$921$	10.7994	+	12.0265i	0.355854	+	0.396287i
$922$	−6.15653	−	3.13691i	−0.202755	−	0.103309i
$923$	−3.63731	+	0.576094i	−0.119724	+	0.0189624i
$924$	19.5934	−	8.69197i	0.644575	−	0.285945i
$925$	−18.2695	−	2.45691i	−0.600699	−	0.0807827i
$926$		−	22.0536i		−	0.724728i
$927$	5.67222	−	8.68323i	0.186300	−	0.285195i
$928$	−3.68535	+	7.23291i	−0.120978	+	0.237432i
$929$	−11.6949	−	35.9932i	−0.383697	−	1.18090i	−0.937421	−	0.348198i	$-0.886794\pi$
$929$	−11.6949	−	35.9932i	−0.383697	−	1.18090i	0.553723	−	0.832701i	$-0.313206\pi$
$930$	5.23089	−	3.47451i	0.171528	−	0.113934i
$931$	3.26116	−	10.0368i	0.106880	−	0.328944i
$932$	−13.0971	−	13.0971i	−0.429010	−	0.429010i
$933$	10.5261	+	8.54733i	0.344609	+	0.279827i
$934$	2.66218	+	3.66418i	0.0871092	+	0.119896i
$935$	21.8332	−	16.2564i	0.714023	−	0.531642i
$936$	−2.35208	−	11.2139i	−0.0768800	−	0.366538i
$937$	4.74297	−	29.9460i	0.154946	−	0.978292i	−0.780586	−	0.625049i	$-0.785079\pi$
$937$	4.74297	−	29.9460i	0.154946	−	0.978292i	0.935532	−	0.353243i	$-0.114921\pi$
$938$	−3.28186	+	20.7208i	−0.107156	+	0.676559i
$939$	1.03662	−	4.84488i	0.0338290	−	0.158107i
$940$	7.70480	−	5.73678i	0.251303	−	0.187113i
$941$	−18.8958	−	26.0078i	−0.615984	−	0.847829i	0.381069	−	0.924547i	$-0.375556\pi$
$941$	−18.8958	−	26.0078i	−0.615984	−	0.847829i	−0.997053	+	0.0767174i	$0.975556\pi$
$942$	−2.51653	+	3.09912i	−0.0819929	+	0.100975i
$943$	−2.89354	−	2.89354i	−0.0942265	−	0.0942265i
$944$	3.42517	−	10.5416i	0.111480	−	0.343099i
$945$	−8.44497	+	56.0991i	−0.274715	+	1.82490i
$946$	1.05348	+	3.24228i	0.0342516	+	0.105416i
$947$	−7.77062	+	15.2507i	−0.252511	+	0.495581i	−0.982113	−	0.188291i	$-0.939705\pi$
$947$	−7.77062	+	15.2507i	−0.252511	+	0.495581i	0.729602	+	0.683872i	$0.239705\pi$
$948$	−0.137604	−	0.212516i	−0.00446916	−	0.00690220i
$949$		−	29.5884i		−	0.960480i
$950$	3.10543	+	0.417622i	0.100753	+	0.0135494i
$951$	−17.9629	−	40.4919i	−0.582488	−	1.31304i
$952$	−23.1624	+	3.66856i	−0.750697	+	0.118899i
$953$	20.7106	+	10.5526i	0.670882	+	0.341831i	0.756030	−	0.654537i	$-0.227136\pi$
$953$	20.7106	+	10.5526i	0.670882	+	0.341831i	−0.0851482	+	0.996368i	$0.527136\pi$
$954$	0.628499	−	1.40147i	0.0203484	−	0.0453743i
$955$	5.09003	−	34.7650i	0.164709	−	1.12497i
$956$	−12.7051	−	4.12814i	−0.410912	−	0.133513i
$957$	12.8158	−	33.2525i	0.414275	−	1.07490i
$958$	32.8918	−	16.7592i	1.06269	−	0.541466i
$959$	16.9881	−	12.3426i	0.548575	−	0.398563i
$960$	−0.444700	−	3.84737i	−0.0143526	−	0.124173i
$961$	22.9527	+	16.6761i	0.740408	+	0.537938i
$962$	13.9077	+	2.20276i	0.448402	+	0.0710198i
$963$	20.6791	+	25.6775i	0.666375	+	0.827447i
$964$	−3.00113	+	4.13071i	−0.0966600	+	0.133041i
$965$	0.0678938	+	5.80251i	0.00218558	+	0.186789i
$966$	2.76041	−	4.76635i	0.0888147	−	0.153355i
$967$	−11.0422	−	21.6716i	−0.355094	−	0.696912i	0.642496	−	0.766289i	$-0.277899\pi$
$967$	−11.0422	−	21.6716i	−0.355094	−	0.696912i	−0.997591	+	0.0693770i	$0.977899\pi$
$968$	−3.23569	+	3.23569i	−0.103999	+	0.103999i
$969$	0.537964	+	5.18547i	0.0172819	+	0.166581i
$970$	−30.0583	+	15.7611i	−0.965114	+	0.506060i
$971$	5.98620	−	1.94504i	0.192106	−	0.0624192i	−0.211384	−	0.977403i	$-0.567797\pi$
$971$	5.98620	−	1.94504i	0.192106	−	0.0624192i	0.403490	+	0.914984i	$0.367797\pi$
$972$	−0.711119	−	15.5722i	−0.0228091	−	0.499479i
$973$	2.24541	+	14.1770i	0.0719846	+	0.454493i
$974$	34.3914			1.10197
$975$	−32.4972	−	6.16175i	−1.04074	−	0.197334i
$976$	3.98485			0.127552
$977$	2.22604	+	14.0547i	0.0712173	+	0.449649i	0.997369	+	0.0724964i	$0.0230966\pi$
$977$	2.22604	+	14.0547i	0.0712173	+	0.449649i	−0.926151	+	0.377152i	$0.876903\pi$
$978$	−39.5948	−	2.12849i	−1.26610	−	0.0680615i
$979$	−26.6230	+	8.65033i	−0.850874	+	0.276466i
$980$	−16.7016	+	33.7492i	−0.533514	+	1.07808i
$981$	−26.6027	−	46.3649i	−0.849360	−	1.48032i
$982$	−11.7430	+	11.7430i	−0.374733	+	0.374733i
$983$	−7.65935	−	15.0323i	−0.244295	−	0.479457i	0.736003	−	0.676978i	$-0.236711\pi$
$983$	−7.65935	−	15.0323i	−0.244295	−	0.479457i	−0.980299	+	0.197521i	$0.936711\pi$
$984$	−9.41715	−	5.45390i	−0.300208	−	0.173864i
$985$	−12.2932	+	4.15393i	−0.391693	+	0.132355i
$986$	−22.9171	+	31.5427i	−0.729830	+	1.00452i
$987$	35.1052	−	9.35581i	1.11741	−	0.297799i
$988$	−2.36401	−	0.374422i	−0.0752090	−	0.0119119i
$989$	0.708722	+	0.514916i	0.0225360	+	0.0163734i
$990$	3.68470	+	16.5983i	0.117107	+	0.527530i
$991$	24.1908	−	17.5757i	0.768447	−	0.558310i	−0.133042	−	0.991110i	$-0.542475\pi$
$991$	24.1908	−	17.5757i	0.768447	−	0.558310i	0.901490	+	0.432801i	$0.142475\pi$
$992$	−1.44469	+	0.736104i	−0.0458688	+	0.0233713i
$993$	51.6729	+	19.9151i	1.63979	+	0.631988i
$994$	−4.47751	−	1.45483i	−0.142018	−	0.0461445i
$995$	−6.03761	+	6.18058i	−0.191405	+	0.195937i
$996$	10.2026	−	9.16167i	0.323283	−	0.290299i
$997$	−12.5490	−	6.39403i	−0.397431	−	0.202501i	0.243841	−	0.969815i	$-0.421593\pi$
$997$	−12.5490	−	6.39403i	−0.397431	−	0.202501i	−0.641271	+	0.767314i	$0.721593\pi$
$998$	23.3584	−	3.69960i	0.739396	−	0.117109i
$999$	18.1955	+	5.99337i	0.575681	+	0.189622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.113.3	yes	80
3.2	odd	2	inner	150.2.l.a.113.7	yes	80
5.2	odd	4		750.2.l.c.707.10		80
5.3	odd	4		750.2.l.a.707.1		80
5.4	even	2		750.2.l.b.293.8		80
15.2	even	4		750.2.l.c.707.3		80
15.8	even	4		750.2.l.a.707.8		80
15.14	odd	2		750.2.l.b.293.4		80
25.2	odd	20	inner	150.2.l.a.77.7	yes	80
25.11	even	5		750.2.l.c.593.3		80
25.14	even	10		750.2.l.a.593.8		80
25.23	odd	20		750.2.l.b.407.4		80
75.2	even	20	inner	150.2.l.a.77.3	✓	80
75.11	odd	10		750.2.l.c.593.10		80
75.14	odd	10		750.2.l.a.593.1		80
75.23	even	20		750.2.l.b.407.8		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.77.3	✓	80	75.2	even	20	inner
150.2.l.a.77.7	yes	80	25.2	odd	20	inner
150.2.l.a.113.3	yes	80	1.1	even	1	trivial
150.2.l.a.113.7	yes	80	3.2	odd	2	inner
750.2.l.a.593.1		80	75.14	odd	10
750.2.l.a.593.8		80	25.14	even	10
750.2.l.a.707.1		80	5.3	odd	4
750.2.l.a.707.8		80	15.8	even	4
750.2.l.b.293.4		80	15.14	odd	2
750.2.l.b.293.8		80	5.4	even	2
750.2.l.b.407.4		80	25.23	odd	20
750.2.l.b.407.8		80	75.23	even	20
750.2.l.c.593.3		80	25.11	even	5
750.2.l.c.593.10		80	75.11	odd	10
750.2.l.c.707.3		80	15.2	even	4
750.2.l.c.707.10		80	5.2	odd	4

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.0929751 + 1.72955i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.59953 + 1.56253i) q^{5} +(1.72280 - 0.178731i) q^{6} +(-3.45255 + 3.45255i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-2.98271 - 0.321611i) q^{9} +O(q^{10})\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.0929751 + 1.72955i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.59953 + 1.56253i) q^{5} +(1.72280 - 0.178731i) q^{6} +(-3.45255 + 3.45255i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-2.98271 - 0.321611i) q^{9} +(1.29307 - 1.82427i) q^{10} +(1.48978 - 2.05051i) q^{11} +(-0.446037 - 1.67363i) q^{12} +(3.77229 + 0.597472i) q^{13} +(3.95014 + 2.86994i) q^{14} +(-2.85120 + 2.62120i) q^{15} +(0.809017 - 0.587785i) q^{16} +(4.27947 - 2.18050i) q^{17} +(0.148947 + 2.99630i) q^{18} +(0.596005 + 0.193654i) q^{19} +(-2.00409 - 0.991774i) q^{20} +(-5.65036 - 6.29237i) q^{21} +(-2.25832 - 1.15067i) q^{22} +(-0.643277 + 0.101885i) q^{23} +(-1.58325 + 0.702359i) q^{24} +(0.116992 + 4.99863i) q^{25} -3.81931i q^{26} +(0.833561 - 5.12886i) q^{27} +(2.21667 - 4.35046i) q^{28} +(-2.50850 - 7.72038i) q^{29} +(3.03495 + 2.40605i) q^{30} +(0.501043 - 1.54205i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(3.40795 + 2.76731i) q^{33} +(-2.82311 - 3.88568i) q^{34} +(-10.9172 + 0.127739i) q^{35} +(2.93611 - 0.615838i) q^{36} +(-0.576743 + 3.64141i) q^{37} +(0.0980339 - 0.618961i) q^{38} +(-1.38409 + 6.46882i) q^{39} +(-0.666054 + 2.13457i) q^{40} +(3.69305 + 5.08304i) q^{41} +(-5.33098 + 6.56514i) q^{42} +(-0.951098 - 0.951098i) q^{43} +(-0.783225 + 2.41052i) q^{44} +(-4.26841 - 5.17501i) q^{45} +(0.201261 + 0.619419i) q^{46} +(-1.95031 + 3.82769i) q^{47} +(0.941388 + 1.45389i) q^{48} -16.8402i q^{49} +(4.91879 - 0.897510i) q^{50} +(3.37340 + 7.60430i) q^{51} +(-3.77229 + 0.597472i) q^{52} +(-0.456180 - 0.232435i) q^{53} +(-5.19611 - 0.0209688i) q^{54} +(5.58694 - 0.952020i) q^{55} +(-4.64367 - 1.50882i) q^{56} +(-0.390348 + 1.01282i) q^{57} +(-7.23291 + 3.68535i) q^{58} +(8.96720 - 6.51505i) q^{59} +(1.90166 - 3.37397i) q^{60} +(3.22382 + 2.34224i) q^{61} +(-1.60145 - 0.253644i) q^{62} +(11.4083 - 9.18757i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(5.10032 + 6.84999i) q^{65} +(2.20011 - 3.79890i) q^{66} +(1.95065 + 3.82837i) q^{67} +(-3.39620 + 3.39620i) q^{68} +(-0.116407 - 1.12205i) q^{69} +(1.83399 + 10.7628i) q^{70} +(-0.917028 + 0.297960i) q^{71} +(-1.06757 - 2.80362i) q^{72} +(-1.21191 - 7.65167i) q^{73} +3.68680 q^{74} +(-8.65628 - 0.262405i) q^{75} -0.626677 q^{76} +(1.93594 + 12.2230i) q^{77} +(6.60570 + 0.355101i) q^{78} +(0.139017 - 0.0451693i) q^{79} +(2.21248 + 0.323934i) q^{80} +(8.79313 + 1.91855i) q^{81} +(4.44274 - 4.44274i) q^{82} +(3.59418 + 7.05397i) q^{83} +(7.31826 + 4.23834i) q^{84} +(10.2522 + 3.19903i) q^{85} +(-0.790603 + 1.08817i) q^{86} +(13.5860 - 3.62079i) q^{87} +(2.50336 + 0.396494i) q^{88} +(-8.93519 - 6.49179i) q^{89} +(-4.44357 + 5.02541i) q^{90} +(-15.0868 + 10.9612i) q^{91} +(0.580309 - 0.295682i) q^{92} +(2.62047 + 1.00995i) q^{93} +(4.08566 + 1.32751i) q^{94} +(0.650738 + 1.24103i) q^{95} +(1.28872 - 1.15724i) q^{96} +(-13.5240 - 6.89084i) q^{97} +(-16.6328 + 2.63438i) q^{98} +(-5.10306 + 5.63695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

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