LMFDB - Embedded newform 150.2.l.a.77.7

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			77.7
Character	$\chi$	$=$	150.77
Dual form			150.2.l.a.113.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 - 0.987688i) q^{2} +(-1.34459 - 1.09182i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.59953 + 1.56253i) q^{5} +(-1.28872 + 1.15724i) q^{6} +(-3.45255 - 3.45255i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.615838 + 2.93611i) q^{9} +O(q^{10})$	\(q+(0.156434 - 0.987688i) q^{2} +(-1.34459 - 1.09182i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.59953 + 1.56253i) q^{5} +(-1.28872 + 1.15724i) q^{6} +(-3.45255 - 3.45255i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.615838 + 2.93611i) q^{9} +(1.29307 + 1.82427i) q^{10} +(-1.48978 - 2.05051i) q^{11} +(0.941388 + 1.45389i) q^{12} +(3.77229 - 0.597472i) q^{13} +(-3.95014 + 2.86994i) q^{14} +(3.85672 - 0.354556i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-4.27947 - 2.18050i) q^{17} +(2.99630 - 0.148947i) q^{18} +(0.596005 - 0.193654i) q^{19} +(2.00409 - 0.991774i) q^{20} +(0.872681 + 8.41183i) 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} +(2.37767 - 4.62025i) q^{27} +(2.21667 + 4.35046i) q^{28} +(2.50850 - 7.72038i) q^{29} +(0.253133 - 3.86470i) q^{30} +(0.501043 + 1.54205i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.235652 + 4.38367i) q^{33} +(-2.82311 + 3.88568i) q^{34} +(10.9172 + 0.127739i) q^{35} +(0.321611 - 2.98271i) q^{36} +(-0.576743 - 3.64141i) q^{37} +(-0.0980339 - 0.618961i) q^{38} +(-5.72451 - 3.31532i) q^{39} +(-0.666054 - 2.13457i) q^{40} +(-3.69305 + 5.08304i) q^{41} +(8.44478 + 0.453964i) q^{42} +(-0.951098 + 0.951098i) q^{43} +(0.783225 + 2.41052i) q^{44} +(-5.57282 - 3.73413i) q^{45} +(0.201261 - 0.619419i) q^{46} +(1.95031 + 3.82769i) q^{47} +(-0.446037 - 1.67363i) 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} +(-4.19142 - 3.07116i) q^{54} +(5.58694 + 0.952020i) q^{55} +(4.64367 - 1.50882i) q^{56} +(-1.01282 - 0.390348i) q^{57} +(-7.23291 - 3.68535i) q^{58} +(-8.96720 - 6.51505i) q^{59} +(-3.77752 - 0.854589i) q^{60} +(3.22382 - 2.34224i) q^{61} +(1.60145 - 0.253644i) q^{62} +(8.01085 - 12.2633i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-5.10032 + 6.84999i) q^{65} +(4.29284 + 0.918508i) q^{66} +(1.95065 - 3.82837i) q^{67} +(3.39620 + 3.39620i) q^{68} +(-0.753702 - 0.839339i) q^{69} +(1.83399 - 10.7628i) q^{70} +(0.917028 + 0.297960i) q^{71} +(-2.89568 - 0.784250i) q^{72} +(-1.21191 + 7.65167i) q^{73} -3.68680 q^{74} +(-5.61493 + 6.59337i) q^{75} -0.626677 q^{76} +(-1.93594 + 12.2230i) q^{77} +(-4.17002 + 5.13540i) q^{78} +(0.139017 + 0.0451693i) q^{79} +(-2.21248 + 0.323934i) q^{80} +(-8.24149 + 3.61634i) q^{81} +(4.44274 + 4.44274i) q^{82} +(-3.59418 + 7.05397i) q^{83} +(1.76943 - 8.26980i) q^{84} +(10.2522 - 3.19903i) q^{85} +(0.790603 + 1.08817i) q^{86} +(-11.8022 + 7.64189i) q^{87} +(2.50336 - 0.396494i) q^{88} +(8.93519 - 6.49179i) q^{89} +(-4.55994 + 4.92006i) q^{90} +(-15.0868 - 10.9612i) q^{91} +(-0.580309 - 0.295682i) q^{92} +(1.00995 - 2.62047i) q^{93} +(4.08566 - 1.32751i) q^{94} +(-0.650738 + 1.24103i) q^{95} +(-1.72280 + 0.178731i) 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

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

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
$3$	−1.34459	−	1.09182i	−0.776299	−	0.630365i
$3$	−1.34459	−	1.09182i	−0.776299	−	0.630365i
$4$	−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
$6$	−1.28872	+	1.15724i	−0.526119	+	0.472440i
$7$	−3.45255	−	3.45255i	−1.30494	−	1.30494i	−0.925019	−	0.379921i	$-0.875951\pi$
$7$	−3.45255	−	3.45255i	−1.30494	−	1.30494i	−0.379921	−	0.925019i	$-0.624049\pi$
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	0.615838	+	2.93611i	0.205279	+	0.978703i
$10$	1.29307	+	1.82427i	0.408905	+	0.576885i
$11$	−1.48978	−	2.05051i	−0.449186	−	0.618252i	0.523036	−	0.852310i	$-0.324799\pi$
$11$	−1.48978	−	2.05051i	−0.449186	−	0.618252i	−0.972223	+	0.234059i	$0.924799\pi$
$12$	0.941388	+	1.45389i	0.271755	+	0.419701i
$13$	3.77229	−	0.597472i	1.04624	−	0.165709i	0.390431	−	0.920632i	$-0.372326\pi$
$13$	3.77229	−	0.597472i	1.04624	−	0.165709i	0.655813	+	0.754923i	$0.272326\pi$
$14$	−3.95014	+	2.86994i	−1.05572	+	0.767025i
$15$	3.85672	−	0.354556i	0.995801	−	0.0915460i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−4.27947	−	2.18050i	−1.03792	−	0.528848i	−0.149926	−	0.988697i	$-0.547904\pi$
$17$	−4.27947	−	2.18050i	−1.03792	−	0.528848i	−0.887997	+	0.459849i	$0.847904\pi$
$18$	2.99630	−	0.148947i	0.706235	−	0.0351073i
$19$	0.596005	−	0.193654i	0.136733	−	0.0444272i	−0.239851	−	0.970810i	$-0.577099\pi$
$19$	0.596005	−	0.193654i	0.136733	−	0.0444272i	0.376584	+	0.926382i	$0.377099\pi$
$20$	2.00409	−	0.991774i	0.448129	−	0.221767i
$21$	0.872681	+	8.41183i	0.190435	+	1.83561i
$22$	−2.25832	+	1.15067i	−0.481475	+	0.245324i
$23$	0.643277	+	0.101885i	0.134133	+	0.0212445i	0.223140	−	0.974786i	$-0.428369\pi$
$23$	0.643277	+	0.101885i	0.134133	+	0.0212445i	−0.0890072	+	0.996031i	$0.528369\pi$
$24$	1.58325	−	0.702359i	0.323180	−	0.143369i
$25$	0.116992	−	4.99863i	0.0233983	−	0.999726i
$26$		−	3.81931i		−	0.749028i
$27$	2.37767	−	4.62025i	0.457582	−	0.889167i
$28$	2.21667	+	4.35046i	0.418912	+	0.822160i
$29$	2.50850	−	7.72038i	0.465817	−	1.43364i	−0.392134	−	0.919908i	$-0.628263\pi$
$29$	2.50850	−	7.72038i	0.465817	−	1.43364i	0.857952	−	0.513731i	$-0.171737\pi$
$30$	0.253133	−	3.86470i	0.0462155	−	0.705595i
$31$	0.501043	+	1.54205i	0.0899899	+	0.276960i	0.985916	−	0.167243i	$-0.0534866\pi$
$31$	0.501043	+	1.54205i	0.0899899	+	0.276960i	−0.895926	+	0.444204i	$0.853487\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.235652	+	4.38367i	−0.0410217	+	0.763100i
$34$	−2.82311	+	3.88568i	−0.484159	+	0.666388i
$35$	10.9172	+	0.127739i	1.84534	+	0.0215919i
$36$	0.321611	−	2.98271i	0.0536018	−	0.497119i
$37$	−0.576743	−	3.64141i	−0.0948160	−	0.598644i	−0.988649	−	0.150244i	$-0.951994\pi$
$37$	−0.576743	−	3.64141i	−0.0948160	−	0.598644i	0.893833	−	0.448400i	$-0.148006\pi$
$38$	−0.0980339	−	0.618961i	−0.0159032	−	0.100409i
$39$	−5.72451	−	3.31532i	−0.916655	−	0.530876i
$40$	−0.666054	−	2.13457i	−0.105312	−	0.337505i
$41$	−3.69305	+	5.08304i	−0.576757	+	0.793838i	−0.993335	−	0.115262i	$-0.963229\pi$
$41$	−3.69305	+	5.08304i	−0.576757	+	0.793838i	0.416578	+	0.909100i	$0.363229\pi$
$42$	8.44478	+	0.453964i	1.30306	+	0.0700482i
$43$	−0.951098	+	0.951098i	−0.145041	+	0.145041i	−0.775899	−	0.630858i	$-0.782703\pi$
$43$	−0.951098	+	0.951098i	−0.145041	+	0.145041i	0.630858	+	0.775899i	$0.282703\pi$
$44$	0.783225	+	2.41052i	0.118076	+	0.363399i
$45$	−5.57282	−	3.73413i	−0.830746	−	0.556651i
$46$	0.201261	−	0.619419i	0.0296744	−	0.0913283i
$47$	1.95031	+	3.82769i	0.284481	+	0.558326i	0.988385	−	0.151969i	$-0.0485614\pi$
$47$	1.95031	+	3.82769i	0.284481	+	0.558326i	−0.703904	+	0.710295i	$0.748561\pi$
$48$	−0.446037	−	1.67363i	−0.0643799	−	0.241568i
$49$			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	$-0.638805\pi$
$53$	0.456180	−	0.232435i	0.0626611	−	0.0319274i	0.485040	+	0.874492i	$0.338805\pi$
$54$	−4.19142	−	3.07116i	−0.570380	−	0.417932i
$55$	5.58694	+	0.952020i	0.753342	+	0.128370i
$56$	4.64367	−	1.50882i	0.620536	−	0.201624i
$57$	−1.01282	−	0.390348i	−0.134151	−	0.0517029i
$58$	−7.23291	−	3.68535i	−0.949728	−	0.483911i
$59$	−8.96720	−	6.51505i	−1.16743	−	0.848188i	−0.176731	−	0.984259i	$-0.556552\pi$
$59$	−8.96720	−	6.51505i	−1.16743	−	0.848188i	−0.990699	+	0.136071i	$0.956552\pi$
$60$	−3.77752	−	0.854589i	−0.487676	−	0.110327i
$61$	3.22382	−	2.34224i	0.412767	−	0.299893i	−0.361954	−	0.932196i	$-0.617890\pi$
$61$	3.22382	−	2.34224i	0.412767	−	0.299893i	0.774721	+	0.632303i	$0.217890\pi$
$62$	1.60145	−	0.253644i	0.203384	−	0.0322128i
$63$	8.01085	−	12.2633i	1.00927	−	1.54503i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−5.10032	+	6.84999i	−0.632617	+	0.849637i
$66$	4.29284	+	0.918508i	0.528412	+	0.113061i
$67$	1.95065	−	3.82837i	0.238310	−	0.467710i	−0.740615	−	0.671929i	$-0.765466\pi$
$67$	1.95065	−	3.82837i	0.238310	−	0.467710i	0.978925	+	0.204220i	$0.0654658\pi$
$68$	3.39620	+	3.39620i	0.411850	+	0.411850i
$69$	−0.753702	−	0.839339i	−0.0907351	−	0.101045i
$70$	1.83399	−	10.7628i	0.219203	−	1.28640i
$71$	0.917028	+	0.297960i	0.108831	+	0.0353614i	0.362926	−	0.931818i	$-0.381778\pi$
$71$	0.917028	+	0.297960i	0.108831	+	0.0353614i	−0.254095	+	0.967179i	$0.581778\pi$
$72$	−2.89568	−	0.784250i	−0.341259	−	0.0924248i
$73$	−1.21191	+	7.65167i	−0.141843	+	0.895561i	0.809431	+	0.587215i	$0.199776\pi$
$73$	−1.21191	+	7.65167i	−0.141843	+	0.895561i	−0.951274	+	0.308346i	$0.900224\pi$
$74$	−3.68680			−0.428582
$75$	−5.61493	+	6.59337i	−0.648357	+	0.761337i
$76$	−0.626677			−0.0718848
$77$	−1.93594	+	12.2230i	−0.220620	+	1.39294i
$78$	−4.17002	+	5.13540i	−0.472161	+	0.581470i
$79$	0.139017	+	0.0451693i	0.0156406	+	0.00508194i	0.316827	−	0.948483i	$-0.397383\pi$
$79$	0.139017	+	0.0451693i	0.0156406	+	0.00508194i	−0.301186	+	0.953565i	$0.597383\pi$
$80$	−2.21248	+	0.323934i	−0.247363	+	0.0362170i
$81$	−8.24149	+	3.61634i	−0.915721	+	0.401815i
$82$	4.44274	+	4.44274i	0.490619	+	0.490619i
$83$	−3.59418	+	7.05397i	−0.394512	+	0.774274i	−0.999763	−	0.0217608i	$-0.993073\pi$
$83$	−3.59418	+	7.05397i	−0.394512	+	0.774274i	0.605251	+	0.796035i	$0.293073\pi$
$84$	1.76943	−	8.26980i	0.193061	−	0.902309i
$85$	10.2522	−	3.19903i	1.11201	−	0.346984i
$86$	0.790603	+	1.08817i	0.0852530	+	0.117341i
$87$	−11.8022	+	7.64189i	−1.26533	+	0.819297i
$88$	2.50336	−	0.396494i	0.266860	−	0.0422664i
$89$	8.93519	−	6.49179i	0.947128	−	0.688129i	−0.00299774	−	0.999996i	$-0.500954\pi$
$89$	8.93519	−	6.49179i	0.947128	−	0.688129i	0.950126	+	0.311867i	$0.100954\pi$
$90$	−4.55994	+	4.92006i	−0.480660	+	0.518620i
$91$	−15.0868	−	10.9612i	−1.58153	−	1.14905i
$92$	−0.580309	−	0.295682i	−0.0605013	−	0.0308270i
$93$	1.00995	−	2.62047i	0.104727	−	0.271731i
$94$	4.08566	−	1.32751i	0.421404	−	0.136922i
$95$	−0.650738	+	1.24103i	−0.0667643	+	0.127327i
$96$	−1.72280	+	0.178731i	−0.175833	+	0.0182417i
$97$	−13.5240	+	6.89084i	−1.37316	+	0.699659i	−0.975935	−	0.218063i	$-0.930026\pi$
$97$	−13.5240	+	6.89084i	−1.37316	+	0.699659i	−0.397223	+	0.917722i	$0.630026\pi$
$98$	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	$-0.0309258\pi$
$102$	8.03840	−	2.14230i	0.795920	−	0.212119i
$103$	−1.56955	−	3.08042i	−0.154653	−	0.303523i	0.800661	−	0.599118i	$-0.204482\pi$
$103$	−1.56955	−	3.08042i	−0.154653	−	0.303523i	−0.955313	+	0.295595i	$0.904482\pi$
$104$	−1.18023	+	3.63238i	−0.115731	+	0.356184i
$105$	−14.5396	−	12.0914i	−1.41892	−	1.18000i
$106$	−0.158211	−	0.486924i	−0.0153668	−	0.0472943i
$107$	7.77089	−	7.77089i	0.751240	−	0.751240i	−0.223470	−	0.974711i	$-0.571739\pi$
$107$	7.77089	−	7.77089i	0.751240	−	0.751240i	0.974711	+	0.223470i	$0.0717386\pi$
$108$	−3.68903	+	3.65938i	−0.354977	+	0.352124i
$109$	10.4733	−	14.4153i	1.00316	−	1.38073i	0.0797938	−	0.996811i	$-0.474574\pi$
$109$	10.4733	−	14.4153i	1.00316	−	1.38073i	0.923366	−	0.383920i	$-0.125426\pi$
$110$	1.81429	−	5.36922i	0.172986	−	0.511935i
$111$	−3.20030	+	5.52590i	−0.303759	+	0.524496i
$112$	−0.763813	−	4.82253i	−0.0721735	−	0.455686i
$113$	−2.93571	−	18.5354i	−0.276169	−	1.74366i	−0.602240	−	0.798315i	$-0.705725\pi$
$113$	−2.93571	−	18.5354i	−0.276169	−	1.74366i	0.326071	−	0.945345i	$-0.394275\pi$
$114$	−0.543982	+	0.939284i	−0.0509486	+	0.0879720i
$115$	−1.18814	+	0.842172i	−0.110795	+	0.0785330i
$116$	−4.77146	+	6.56735i	−0.443019	+	0.609763i
$117$	4.07736	+	10.7079i	0.376952	+	0.989946i
$118$	−7.83762	+	7.83762i	−0.721512	+	0.721512i
$119$	7.24679	+	22.3033i	0.664312	+	2.04454i
$120$	−1.43500	+	3.59733i	−0.130997	+	0.328390i
$121$	1.41405	−	4.35199i	0.128550	−	0.395636i
$122$	−1.80909	−	3.55053i	−0.163787	−	0.321450i
$123$	10.5154	−	2.80244i	0.948143	−	0.252688i
$124$		−	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	0.256732	−	0.966483i	$-0.417354\pi$
$127$	2.27911	+	0.360976i	0.202239	+	0.0320315i	−0.0544931	+	0.998514i	$0.517354\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$	2.31727	−	0.240403i	0.204024	−	0.0211663i
$130$	5.96779	+	6.10910i	0.523410	+	0.535803i
$131$	5.16079	−	1.67684i	0.450901	−	0.146506i	−0.0747587	−	0.997202i	$-0.523819\pi$
$131$	5.16079	−	1.67684i	0.450901	−	0.146506i	0.525659	+	0.850695i	$0.323819\pi$
$132$	1.57875	−	4.09630i	0.137412	−	0.356537i
$133$	−2.72633	−	1.38914i	−0.236403	−	0.120453i
$134$	−3.47608	−	2.52552i	−0.300288	−	0.218172i
$135$	3.41613	+	11.1054i	0.294014	+	0.955801i
$136$	3.88568	−	2.82311i	0.333194	−	0.242080i
$137$	4.24769	−	0.672768i	0.362904	−	0.0574784i	0.0276803	−	0.999617i	$-0.491188\pi$
$137$	4.24769	−	0.672768i	0.362904	−	0.0574784i	0.335224	+	0.942138i	$0.391188\pi$
$138$	−0.946910	+	0.613122i	−0.0806064	+	0.0521924i
$139$	1.72794	+	2.37830i	0.146562	+	0.201725i	0.875986	−	0.482337i	$-0.160212\pi$
$139$	1.72794	+	2.37830i	0.146562	+	0.201725i	−0.729424	+	0.684062i	$0.760212\pi$
$140$	−10.3434	−	3.49508i	−0.874174	−	0.295388i
$141$	1.55681	−	7.27606i	0.131107	−	0.612755i
$142$	0.437747	−	0.859126i	0.0367349	−	0.0720963i
$143$	−6.84501	−	6.84501i	−0.572408	−	0.572408i
$144$	−1.22758	+	2.73734i	−0.102298	+	0.228112i
$145$	8.05091	+	16.2686i	0.668592	+	1.35103i
$146$	7.36789	+	2.39397i	0.609771	+	0.198126i
$147$	18.3865	−	22.6431i	1.51649	−	1.86757i
$148$	−0.576743	+	3.64141i	−0.0474080	+	0.299322i
$149$	6.09696			0.499482			0.249741	−	0.968313i	$-0.419654\pi$
$149$	6.09696			0.499482			0.249741	+	0.968313i	$0.419654\pi$
$150$	5.63382	+	6.57723i	0.460000	+	0.537029i
$151$	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
$153$	3.76672	−	13.9078i	0.304521	−	1.12438i
$154$	11.7697	+	3.82420i	0.948429	+	0.308163i
$155$	−3.21094	−	1.68366i	−0.257909	−	0.135235i
$156$	4.41984	+	4.92203i	0.353871	+	0.394078i
$157$	−1.62980	−	1.62980i	−0.130072	−	0.130072i	0.639074	−	0.769146i	$-0.279318\pi$
$157$	−1.62980	−	1.62980i	−0.130072	−	0.130072i	−0.769146	+	0.639074i	$0.779318\pi$
$158$	0.0663602	−	0.130239i	0.00527934	−	0.0103613i
$159$	−0.867153	−	0.185538i	−0.0687697	−	0.0147142i
$160$	−0.0261619	+	2.23591i	−0.00206828	+	0.176765i
$161$	−1.86918	−	2.57271i	−0.147312	−	0.202758i
$162$	2.28256	+	8.70574i	0.179335	+	0.683988i
$163$	−22.6112	+	3.58126i	−1.77105	+	0.280506i	−0.954811	−	0.297213i	$-0.903943\pi$
$163$	−22.6112	+	3.58126i	−1.77105	+	0.280506i	−0.816235	+	0.577719i	$0.803943\pi$
$164$	5.08304	−	3.69305i	0.396919	−	0.288378i
$165$	−6.47270	−	7.38003i	−0.503899	−	0.574535i
$166$	6.40487	+	4.65341i	0.497114	+	0.361175i
$167$	−7.89344	−	4.02191i	−0.610813	−	0.311225i	0.121082	−	0.992643i	$-0.461364\pi$
$167$	−7.89344	−	4.02191i	−0.610813	−	0.311225i	−0.731895	+	0.681418i	$0.761364\pi$
$168$	−7.89119	−	3.04133i	−0.608818	−	0.234644i
$169$	1.50944	−	0.490448i	0.116111	−	0.0377268i
$170$	−1.55584	−	10.6264i	−0.119328	−	0.815011i
$171$	0.935632	+	1.63068i	0.0715495	+	0.124701i
$172$	1.19845	−	0.610642i	0.0913812	−	0.0465610i
$173$	16.2880	+	2.57976i	1.23835	+	0.196136i	0.741055	−	0.671445i	$-0.234326\pi$
$173$	16.2880	+	2.57976i	1.23835	+	0.196136i	0.497297	+	0.867580i	$0.334326\pi$
$174$	5.70154	+	12.8524i	0.432232	+	0.974335i
$175$	−17.6619	+	16.8541i	−1.33512	+	1.27405i
$176$		−	2.53457i		−	0.191050i
$177$	4.94391	+	18.5507i	0.371607	+	1.39435i
$178$	−5.01410	−	9.84072i	−0.375823	−	0.737593i
$179$	1.95323	−	6.01143i	0.145991	−	0.449315i	−0.851146	−	0.524929i	$-0.824092\pi$
$179$	1.95323	−	6.01143i	0.145991	−	0.449315i	0.997137	+	0.0756142i	$0.0240918\pi$
$180$	4.14615	+	5.27346i	0.309036	+	0.393061i
$181$	−5.79522	−	17.8358i	−0.430755	−	1.32573i	−0.897375	−	0.441269i	$-0.854528\pi$
$181$	−5.79522	−	17.8358i	−0.430755	−	1.32573i	0.466620	−	0.884458i	$-0.345472\pi$
$182$	−13.1863	+	13.1863i	−0.977437	+	0.977437i
$183$	−6.89202	−	0.370492i	−0.509473	−	0.0273876i
$184$	−0.382822	+	0.526909i	−0.0282220	+	0.0388443i
$185$	6.61234	+	4.92337i	0.486149	+	0.361973i
$186$	−2.43022	−	1.40745i	−0.178192	−	0.103199i
$187$	1.90434	+	12.0236i	0.139259	+	0.879250i
$188$	−0.672030	−	4.24303i	−0.0490128	−	0.309455i
$189$	−24.1606	+	7.74261i	−1.75743	+	0.563192i
$190$	1.12395	+	0.836866i	0.0815402	+	0.0607127i
$191$	9.23596	−	12.7122i	0.668290	−	0.919823i	−0.331430	−	0.943480i	$-0.607531\pi$
$191$	9.23596	−	12.7122i	0.668290	−	0.919823i	0.999720	+	0.0236572i	$0.00753102\pi$
$192$	−0.0929751	+	1.72955i	−0.00670990	+	0.124820i
$193$	1.83504	−	1.83504i	0.132089	−	0.132089i	−0.637971	−	0.770060i	$-0.720226\pi$
$193$	1.83504	−	1.83504i	0.132089	−	0.132089i	0.770060	+	0.637971i	$0.220226\pi$
$194$	4.69038	+	14.4355i	0.336749	+	1.03641i
$195$	14.3368	−	3.64177i	1.02668	−	0.260792i
$196$	5.20390	−	16.0159i	0.371707	−	1.14400i
$197$	2.63453	+	5.17056i	0.187703	+	0.368387i	0.965611	−	0.259990i	$-0.0837194\pi$
$197$	2.63453	+	5.17056i	0.187703	+	0.368387i	−0.777909	+	0.628377i	$0.783719\pi$
$198$	−4.76925	−	5.92204i	−0.338936	−	0.420861i
$199$		−	3.86400i		−	0.273911i	−0.990577	−	0.136956i	$-0.956268\pi$
$199$		−	3.86400i		−	0.273911i	0.990577	−	0.136956i	$-0.0437318\pi$
$200$	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
$204$	−0.858439	−	8.27456i	−0.0601028	−	0.579335i
$205$	−2.03527	−	13.9010i	−0.142150	−	0.970886i
$206$	−3.28803	+	1.06835i	−0.229088	+	0.0744352i
$207$	0.0970088	+	1.95148i	0.00674258	+	0.135637i
$208$	3.40303	+	1.73393i	0.235958	+	0.120226i
$209$	−1.28501	−	0.933612i	−0.0888858	−	0.0645793i
$210$	−14.2170	+	12.4691i	−0.981068	+	0.860450i
$211$	−8.84519	+	6.42640i	−0.608928	+	0.442412i	−0.849037	−	0.528334i	$-0.822817\pi$
$211$	−8.84519	+	6.42640i	−0.608928	+	0.442412i	0.240109	+	0.970746i	$0.422817\pi$
$212$	−0.505679	+	0.0800917i	−0.0347302	+	0.00550072i
$213$	−0.907705	−	1.40187i	−0.0621949	−	0.0960544i
$214$	−6.45958	−	8.89085i	−0.441568	−	0.607766i
$215$	0.0351892	−	3.00743i	0.00239989	−	0.205105i
$216$	3.03723	+	4.21607i	0.206658	+	0.286867i
$217$	3.59413	−	7.05388i	0.243985	−	0.478848i
$218$	−12.5994	−	12.5994i	−0.853339	−	0.853339i
$219$	9.98380	−	8.96517i	0.674643	−	0.605810i
$220$	−5.01930	−	2.63188i	−0.338401	−	0.177442i
$221$	−17.4462	−	5.66860i	−1.17356	−	0.381311i
$222$	4.95723	+	4.02534i	0.332708	+	0.270163i
$223$	−3.05289	+	19.2752i	−0.204437	+	1.29076i	0.645452	+	0.763800i	$0.276669\pi$
$223$	−3.05289	+	19.2752i	−0.204437	+	1.29076i	−0.849889	+	0.526962i	$0.823331\pi$
$224$	−4.88264			−0.326235
$225$	14.7486	−	2.73485i	0.983239	−	0.182323i
$226$	−18.7664			−1.24832
$227$	3.87090	−	24.4399i	0.256921	−	1.62213i	−0.435187	−	0.900340i	$-0.643318\pi$
$227$	3.87090	−	24.4399i	0.256921	−	1.62213i	0.692108	−	0.721794i	$-0.256682\pi$
$228$	0.842623	+	0.684221i	0.0558041	+	0.0453137i
$229$	2.89806	+	0.941635i	0.191509	+	0.0622250i	0.403201	−	0.915111i	$-0.367897\pi$
$229$	2.89806	+	0.941635i	0.191509	+	0.0622250i	−0.211692	+	0.977336i	$0.567897\pi$
$230$	0.645938	+	1.30526i	0.0425919	+	0.0860660i
$231$	15.9484	−	14.3212i	1.04933	−	0.942268i
$232$	5.74007	+	5.74007i	0.376854	+	0.376854i
$233$	−8.40887	+	16.5033i	−0.550883	+	1.08117i	0.432839	+	0.901471i	$0.357512\pi$
$233$	−8.40887	+	16.5033i	−0.550883	+	1.08117i	−0.983722	+	0.179698i	$0.942488\pi$
$234$	11.2139	−	2.35208i	0.733076	−	0.153760i
$235$	−9.10046	−	3.07509i	−0.593649	−	0.200597i
$236$	6.51505	+	8.96720i	0.424094	+	0.583715i
$237$	−0.137604	−	0.212516i	−0.00893831	−	0.0138044i
$238$	23.1624	−	3.66856i	1.50139	−	0.237798i
$239$	−10.8076	+	7.85218i	−0.699086	+	0.507915i	−0.879634	−	0.475651i	$-0.842213\pi$
$239$	−10.8076	+	7.85218i	−0.699086	+	0.507915i	0.180549	+	0.983566i	$0.442213\pi$
$240$	3.32856	+	1.98008i	0.214857	+	0.127814i
$241$	4.13071	+	3.00113i	0.266082	+	0.193320i	0.712824	−	0.701343i	$-0.247416\pi$
$241$	4.13071	+	3.00113i	0.266082	+	0.193320i	−0.446742	+	0.894663i	$0.647416\pi$
$242$	−4.07721	−	2.07744i	−0.262093	−	0.133543i
$243$	15.0298	+	4.13577i	0.964163	+	0.265310i
$244$	−3.78982	+	1.23139i	−0.242618	+	0.0788315i
$245$	−26.3133	−	26.9363i	−1.68109	−	1.72090i
$246$	−1.12297	−	10.8244i	−0.0715977	−	0.690136i
$247$	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	$0.893119\pi$
$252$	−11.4083	+	9.18757i	−0.718657	+	0.578763i
$253$	−0.749426	−	1.47083i	−0.0471160	−	0.0924704i
$254$	0.713064	−	2.19459i	0.0447416	−	0.137701i
$255$	−17.2778	−	6.89226i	−1.08198	−	0.431610i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−15.7777	+	15.7777i	−0.984185	+	0.984185i	−0.999877	−	0.0156919i	$-0.995005\pi$
$257$	−15.7777	+	15.7777i	−0.984185	+	0.984185i	0.0156919	+	0.999877i	$0.495005\pi$
$258$	0.125057	−	2.32634i	0.00778569	−	0.144832i
$259$	−10.5809	+	14.5634i	−0.657466	+	0.904924i
$260$	6.96745	−	4.93864i	0.432103	−	0.306282i
$261$	24.2127	+	2.61074i	1.49873	+	0.161601i
$262$	−0.848873	−	5.35957i	−0.0524435	−	0.331115i
$263$	−2.08135	−	13.1411i	−0.128342	−	0.810318i	−0.964934	−	0.262492i	$-0.915456\pi$
$263$	−2.08135	−	13.1411i	−0.128342	−	0.810318i	0.836592	−	0.547826i	$-0.184544\pi$
$264$	−3.79890	−	2.20011i	−0.233806	−	0.135408i
$265$	−0.366486	+	1.08458i	−0.0225130	+	0.0666254i
$266$	−1.79853	+	2.47546i	−0.110275	+	0.151780i
$267$	−19.1021	−	1.02686i	−1.16903	−	0.0628430i
$268$	−3.03821	+	3.03821i	−0.185588	+	0.185588i
$269$	−2.51822	−	7.75028i	−0.153539	−	0.472543i	0.844471	−	0.535601i	$-0.179915\pi$
$269$	−2.51822	−	7.75028i	−0.153539	−	0.472543i	−0.998010	+	0.0630577i	$0.979915\pi$
$270$	11.5031	−	1.63681i	0.700055	−	0.0996128i
$271$	−2.73922	+	8.43044i	−0.166396	+	0.512113i	−0.999136	−	0.0415500i	$-0.986770\pi$
$271$	−2.73922	+	8.43044i	−0.166396	+	0.512113i	0.832741	+	0.553663i	$0.186770\pi$
$272$	−2.18050	−	4.27947i	−0.132212	−	0.259481i
$273$	8.31783	+	31.2104i	0.503418	+	1.88894i
$274$		−	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	0.507121	−	0.861875i	$-0.330710\pi$
$277$	12.0346	+	1.90609i	0.723088	+	0.114526i	0.215967	+	0.976401i	$0.430710\pi$
$278$	2.61933	−	1.33461i	0.157097	−	0.0800448i
$279$	−4.21907	+	2.42077i	−0.252589	+	0.144928i
$280$	−5.07011	+	9.66927i	−0.302997	+	0.577850i
$281$	−1.89696	+	0.616361i	−0.113163	+	0.0367690i	−0.365051	−	0.930987i	$-0.618949\pi$
$281$	−1.89696	+	0.616361i	−0.113163	+	0.0367690i	0.251888	+	0.967756i	$0.418949\pi$
$282$	−6.94295	−	2.67587i	−0.413446	−	0.159346i
$283$	1.85853	+	0.946967i	0.110478	+	0.0562913i	0.508356	−	0.861147i	$-0.330253\pi$
$283$	1.85853	+	0.946967i	0.110478	+	0.0562913i	−0.397878	+	0.917438i	$0.630253\pi$
$284$	−0.780070	−	0.566754i	−0.0462887	−	0.0336307i
$285$	2.22996	−	0.958186i	0.132092	−	0.0567580i
$286$	−7.83153	+	5.68994i	−0.463088	+	0.336453i
$287$	30.2999	−	4.79903i	1.78854	−	0.283278i
$288$	2.51161	+	1.64068i	0.147998	+	0.0966780i
$289$	3.56692	+	4.90945i	0.209819	+	0.288791i
$290$	17.3277	−	5.40682i	1.01752	−	0.317499i
$291$	25.7079	+	5.50053i	1.50702	+	0.322447i
$292$	3.51709	−	6.90267i	0.205822	−	0.403948i
$293$	14.1457	+	14.1457i	0.826402	+	0.826402i	0.987017	−	0.160615i	$-0.0513479\pi$
$293$	14.1457	+	14.1457i	0.826402	+	0.826402i	−0.160615	+	0.987017i	$0.551348\pi$
$294$	−19.4880	−	21.7023i	−1.13657	−	1.26570i
$295$	24.5233	−	3.59051i	1.42780	−	0.209048i
$296$	3.50636	+	1.13928i	0.203803	+	0.0662196i
$297$	−13.0161	+	2.00773i	−0.755269	+	0.116501i
$298$	0.953774	−	6.02189i	0.0552507	−	0.348839i
$299$	2.48750			0.143856
$300$	7.37758	−	4.53556i	0.425945	−	0.261860i
$301$	6.56742			0.378540
$302$	2.73358	−	17.2591i	0.157300	−	0.993151i
$303$	−2.12878	+	2.62160i	−0.122295	+	0.150607i
$304$	0.596005	+	0.193654i	0.0341832	+	0.0111068i
$305$	−1.49677	+	8.78379i	−0.0857046	+	0.502959i
$306$	−13.1473	−	5.89601i	−0.751584	−	0.337052i
$307$	6.59880	+	6.59880i	0.376613	+	0.376613i	0.869879	−	0.493266i	$-0.164197\pi$
$307$	6.59880	+	6.59880i	0.376613	+	0.376613i	−0.493266	+	0.869879i	$0.664197\pi$
$308$	5.61831	−	11.0265i	0.320133	−	0.628296i
$309$	−1.25288	+	5.85558i	−0.0712737	+	0.333112i
$310$	−2.16523	+	2.90802i	−0.122977	+	0.165164i
$311$	−4.60146	−	6.33337i	−0.260925	−	0.359133i	0.658375	−	0.752690i	$-0.271244\pi$
$311$	−4.60146	−	6.33337i	−0.260925	−	0.359133i	−0.919300	+	0.393558i	$0.871244\pi$
$312$	5.55285	−	3.59545i	0.314368	−	0.203552i
$313$	−2.82529	+	0.447482i	−0.159695	+	0.0252932i	−0.235770	−	0.971809i	$-0.575761\pi$
$313$	−2.82529	+	0.447482i	−0.159695	+	0.0252932i	0.0760751	+	0.997102i	$0.475761\pi$
$314$	−1.86469	+	1.35478i	−0.105231	+	0.0764545i
$315$	6.34815	+	32.1327i	0.357678	+	1.81047i
$316$	−0.118255	−	0.0859171i	−0.00665235	−	0.00483322i
$317$	22.7876	+	11.6109i	1.27988	+	0.652131i	0.955833	−	0.293910i	$-0.0949566\pi$
$317$	22.7876	+	11.6109i	1.27988	+	0.652131i	0.324046	+	0.946041i	$0.394957\pi$
$318$	−0.318907	+	0.827452i	−0.0178834	+	0.0464012i
$319$	−19.5678	+	6.35798i	−1.09559	+	0.355978i
$320$	2.20429	+	0.375614i	0.123224	+	0.0209975i
$321$	−18.9331	+	1.96420i	−1.05674	+	0.109631i
$322$	−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
$327$	−29.8212	+	7.94759i	−1.64912	+	0.439503i
$328$	−2.85242	−	5.59818i	−0.157498	−	0.309108i
$329$	6.48176	−	19.9488i	0.357351	−	1.09981i
$330$	−8.30172	+	5.23851i	−0.456995	+	0.288371i
$331$	9.88000	+	30.4075i	0.543054	+	1.67135i	0.725572	+	0.688146i	$0.241575\pi$
$331$	9.88000	+	30.4075i	0.543054	+	1.67135i	−0.182518	+	0.983203i	$0.558425\pi$
$332$	5.59806	−	5.59806i	0.307234	−	0.307234i
$333$	10.3364	−	3.93590i	0.566432	−	0.215686i
$334$	−5.20720	+	7.16710i	−0.284925	+	0.392166i
$335$	2.86182	+	9.17154i	0.156358	+	0.501095i
$336$	−4.23834	+	7.31826i	−0.231220	+	0.399244i
$337$	−2.91531	−	18.4065i	−0.158807	−	1.00267i	−0.930399	−	0.366549i	$-0.880539\pi$
$337$	−2.91531	−	18.4065i	−0.158807	−	1.00267i	0.771592	−	0.636118i	$-0.219461\pi$
$338$	−0.248281	−	1.56758i	−0.0135047	−	0.0852653i
$339$	−16.2900	+	28.1277i	−0.884754	+	1.52769i
$340$	−10.7390	−	0.125655i	−0.582404	−	0.00681458i
$341$	2.41555	−	3.32471i	0.130809	−	0.180043i
$342$	1.75697	−	0.669018i	0.0950058	−	0.0361764i
$343$	33.9736	−	33.9736i	1.83440	−	1.83440i
$344$	−0.415645	−	1.27922i	−0.0224101	−	0.0689711i
$345$	2.51706	+	0.164864i	0.135514	+	0.00887600i
$346$	5.09600	−	15.6839i	0.273963	−	0.843170i
$347$	10.8108	+	21.2173i	0.580353	+	1.13901i	0.975420	+	0.220354i	$0.0707214\pi$
$347$	10.8108	+	21.2173i	0.580353	+	1.13901i	−0.395067	+	0.918652i	$0.629279\pi$
$348$	13.5860	−	3.62079i	0.728288	−	0.194095i
$349$		−	8.63569i		−	0.462258i	−0.972923	−	0.231129i	$-0.925758\pi$
$349$		−	8.63569i		−	0.462258i	0.972923	−	0.231129i	$-0.0742419\pi$
$350$	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	$-0.374894\pi$
$353$	25.4664	−	12.9758i	1.35544	−	0.690631i	0.972448	+	0.233120i	$0.0748935\pi$
$354$	19.0957	−	1.98107i	1.01492	−	0.105293i
$355$	−1.93239	+	0.956288i	−0.102560	+	0.0507545i
$356$	−10.5039	+	3.41294i	−0.556708	+	0.180885i
$357$	14.6074	−	37.9010i	0.773104	−	2.00594i
$358$	−5.63186	−	2.86958i	−0.297653	−	0.151662i
$359$	−6.72833	−	4.88842i	−0.355108	−	0.258001i	0.395901	−	0.918293i	$-0.370432\pi$
$359$	−6.72833	−	4.88842i	−0.355108	−	0.258001i	−0.751009	+	0.660292i	$0.770432\pi$
$360$	5.85714	−	3.27016i	0.308698	−	0.172352i
$361$	−15.0536	+	10.9371i	−0.792295	+	0.575636i
$362$	−18.5228	+	2.93373i	−0.973538	+	0.154193i
$363$	−6.65293	+	4.30775i	−0.349188	+	0.226098i
$364$	10.9612	+	15.0868i	0.574523	+	0.790763i
$365$	−10.0175	−	14.1327i	−0.524340	−	0.739741i
$366$	−1.44408	+	6.74921i	−0.0754833	+	0.352787i
$367$	−7.05620	+	13.8486i	−0.368331	+	0.722889i	−0.998567	−	0.0535138i	$-0.982958\pi$
$367$	−7.05620	+	13.8486i	−0.368331	+	0.722889i	0.630237	+	0.776403i	$0.282958\pi$
$368$	0.460535	+	0.460535i	0.0240071	+	0.0240071i
$369$	−17.1987	−	7.71286i	−0.895328	−	0.401515i
$370$	5.89715	−	5.76074i	0.306578	−	0.299487i
$371$	−2.37748	−	0.772489i	−0.123432	−	0.0401056i
$372$	−1.77029	+	2.18013i	−0.0917854	+	0.113034i
$373$	2.33980	−	14.7729i	0.121150	−	0.764912i	−0.850060	−	0.526686i	$-0.823434\pi$
$373$	2.33980	−	14.7729i	0.121150	−	0.764912i	0.971210	−	0.238225i	$-0.0765657\pi$
$374$	12.1734			0.629473
$375$	−1.32109	−	19.3198i	−0.0682209	−	0.997670i
$376$	−4.29592			−0.221545
$377$	4.85009	−	30.6223i	0.249792	−	1.57713i
$378$	3.86773	+	25.0744i	0.198935	+	1.28969i
$379$	5.98428	+	1.94441i	0.307392	+	0.0998776i	0.458651	−	0.888617i	$-0.348333\pi$
$379$	5.98428	+	1.94441i	0.307392	+	0.0998776i	−0.151259	+	0.988494i	$0.548333\pi$
$380$	1.00239	−	0.979202i	0.0514214	−	0.0502320i
$381$	−2.67035	−	2.97376i	−0.136806	−	0.152350i
$382$	−11.1109	−	11.1109i	−0.568482	−	0.568482i
$383$	5.34769	−	10.4954i	0.273254	−	0.536292i	−0.713073	−	0.701090i	$-0.752697\pi$
$383$	5.34769	−	10.4954i	0.273254	−	0.536292i	0.986327	+	0.164798i	$0.0526972\pi$
$384$	1.69372	+	0.362392i	0.0864321	+	0.0184933i
$385$	−16.0023	−	22.5761i	−0.815551	−	1.15058i
$386$	−1.52538	−	2.09951i	−0.0776400	−	0.106862i
$387$	−3.37825	−	2.20680i	−0.171726	−	0.112178i
$388$	14.9915	−	2.37442i	0.761078	−	0.120543i
$389$	19.3894	−	14.0872i	0.983082	−	0.714251i	0.0246869	−	0.999695i	$-0.492141\pi$
$389$	19.3894	−	14.0872i	0.983082	−	0.714251i	0.958395	+	0.285444i	$0.0921411\pi$
$390$	−1.35416	−	14.7300i	−0.0685705	−	0.745883i
$391$	−2.53072	−	1.83868i	−0.127984	−	0.0929859i
$392$	−15.0047	−	7.64527i	−0.757851	−	0.386145i
$393$	−8.76996	−	3.38002i	−0.442386	−	0.170499i
$394$	5.51903	−	1.79324i	0.278045	−	0.0903423i
$395$	−0.292940	+	0.144969i	−0.0147394	+	0.00729416i
$396$	−6.59521	+	3.78412i	−0.331422	+	0.190159i
$397$	−7.12795	+	3.63187i	−0.357741	+	0.182278i	−0.623619	−	0.781728i	$-0.714338\pi$
$397$	−7.12795	+	3.63187i	−0.357741	+	0.182278i	0.265878	+	0.964007i	$0.414338\pi$
$398$	−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	$0.952638\pi$
$402$	1.91648	+	7.19107i	0.0955852	+	0.358658i
$403$	2.81141	+	5.51770i	0.140046	+	0.274856i
$404$	−0.602504	+	1.85432i	−0.0299757	+	0.0922557i
$405$	7.53186	−	18.6620i	0.374261	−	0.927323i
$406$	12.2481	+	37.6958i	0.607864	+	1.87081i
$407$	−6.60753	+	6.60753i	−0.327523	+	0.327523i
$408$	−8.30697	−	0.446556i	−0.411256	−	0.0221078i
$409$	12.3971	−	17.0631i	0.612995	−	0.843715i	−0.383825	−	0.923406i	$-0.625393\pi$
$409$	12.3971	−	17.0631i	0.612995	−	0.843715i	0.996820	+	0.0796911i	$0.0253934\pi$
$410$	−14.0482	−	0.164375i	−0.693792	−	0.00811790i
$411$	−6.44594	−	3.73313i	−0.317955	−	0.184142i
$412$	0.540832	+	3.41468i	0.0266449	+	0.168229i
$413$	8.46616	+	53.4532i	0.416592	+	2.63026i
$414$	1.94263	+	0.209464i	0.0954749	+	0.0102946i
$415$	−5.27306	−	16.8991i	−0.258844	−	0.829542i
$416$	2.24493	−	3.08989i	0.110067	−	0.151494i
$417$	0.273323	−	5.08444i	0.0133847	−	0.248986i
$418$	−1.12314	+	1.12314i	−0.0549344	+	0.0549344i
$419$	11.8698	+	36.5316i	0.579880	+	1.78469i	0.618926	+	0.785450i	$0.287568\pi$
$419$	11.8698	+	36.5316i	0.579880	+	1.78469i	−0.0390457	+	0.999237i	$0.512432\pi$
$420$	10.0916	+	15.9926i	0.492418	+	0.780358i
$421$	−5.24894	+	16.1546i	−0.255818	+	0.787326i	0.737850	+	0.674965i	$0.235841\pi$
$421$	−5.24894	+	16.1546i	−0.255818	+	0.787326i	−0.993667	+	0.112361i	$0.964159\pi$
$422$	4.96359	+	9.74160i	0.241624	+	0.474214i
$423$	−10.0375	+	8.08355i	−0.488038	+	0.393036i
$424$			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
$429$	1.73017	+	16.6773i	0.0835336	+	0.805186i
$430$	−2.96490	−	0.505221i	−0.142980	−	0.0243639i
$431$	−24.9008	+	8.09077i	−1.19943	+	0.389719i	−0.839551	−	0.543280i	$-0.817182\pi$
$431$	−24.9008	+	8.09077i	−1.19943	+	0.389719i	−0.359879	+	0.932999i	$0.617182\pi$
$432$	4.63929	−	2.34030i	0.223208	−	0.112598i
$433$	25.3199	+	12.9012i	1.21680	+	0.619990i	0.940078	−	0.340960i	$-0.110752\pi$
$433$	25.3199	+	12.9012i	1.21680	+	0.619990i	0.276721	+	0.960950i	$0.410752\pi$
$434$	−6.40478	−	4.65335i	−0.307440	−	0.223368i
$435$	6.93729	−	30.6648i	0.332617	−	1.47026i
$436$	−14.4153	+	10.4733i	−0.690366	+	0.501580i
$437$	0.403127	−	0.0638490i	0.0192842	−	0.00305431i
$438$	−7.29298	−	11.2633i	−0.348472	−	0.538183i
$439$	−23.8366	−	32.8083i	−1.13766	−	1.56585i	−0.772628	−	0.634859i	$-0.781058\pi$
$439$	−23.8366	−	32.8083i	−1.13766	−	1.56585i	−0.365032	−	0.930995i	$-0.618942\pi$
$440$	−3.38467	+	4.54579i	−0.161358	+	0.216712i
$441$	−49.4446	+	10.3708i	−2.35450	+	0.493848i
$442$	−8.32799	+	16.3446i	−0.396122	+	0.777434i
$443$	−4.87049	−	4.87049i	−0.231404	−	0.231404i	0.581875	−	0.813279i	$-0.302319\pi$
$443$	−4.87049	−	4.87049i	−0.231404	−	0.231404i	−0.813279	+	0.581875i	$0.802319\pi$
$444$	4.75126	−	4.26650i	0.225485	−	0.202479i
$445$	−4.14847	+	24.3453i	−0.196656	+	1.15408i
$446$	18.5603	+	6.03061i	0.878856	+	0.285558i
$447$	−8.19790	−	6.65681i	−0.387747	−	0.314856i
$448$	−0.763813	+	4.82253i	−0.0360868	+	0.227843i
$449$	−38.2829			−1.80668			−0.903340	−	0.428924i	$-0.858893\pi$
$449$	−38.2829			−1.80668			−0.903340	+	0.428924i	$0.858893\pi$
$450$	−0.393991	−	14.9948i	−0.0185729	−	0.706863i
$451$	15.9247			0.749863
$452$	−2.93571	+	18.5354i	−0.138084	+	0.871830i
$453$	−23.4957	−	19.0788i	−1.10392	−	0.896401i
$454$	−23.5335	−	7.64649i	−1.10448	−	0.358868i
$455$	41.2590	−	6.04083i	1.93425	−	0.283198i
$456$	0.807613	−	0.725213i	0.0378199	−	0.0339612i
$457$	25.3039	+	25.3039i	1.18366	+	1.18366i	0.978788	+	0.204877i	$0.0656794\pi$
$457$	25.3039	+	25.3039i	1.18366	+	1.18366i	0.204877	+	0.978788i	$0.434321\pi$
$458$	1.38340	−	2.71507i	0.0646419	−	0.126867i
$459$	−20.2496	+	14.5877i	−0.945170	+	0.680896i
$460$	1.39023	−	0.433798i	0.0648200	−	0.0202259i
$461$	−4.06138	−	5.59002i	−0.189158	−	0.260353i	0.703896	−	0.710303i	$-0.251442\pi$
$461$	−4.06138	−	5.59002i	−0.189158	−	0.260353i	−0.893054	+	0.449950i	$0.851442\pi$
$462$	−11.6500	−	17.9924i	−0.542009	−	0.837083i
$463$	21.7821	−	3.44995i	1.01230	−	0.160333i	0.371819	−	0.928305i	$-0.378734\pi$
$463$	21.7821	−	3.44995i	1.01230	−	0.160333i	0.640483	+	0.767973i	$0.278734\pi$
$464$	6.56735	−	4.77146i	0.304881	−	0.221509i
$465$	2.47912	+	5.76961i	0.114967	+	0.267559i
$466$	14.9847	+	10.8870i	0.694153	+	0.504332i
$467$	4.03552	+	2.05620i	0.186742	+	0.0951496i	0.544862	−	0.838526i	$-0.316582\pi$
$467$	4.03552	+	2.05620i	0.186742	+	0.0951496i	−0.358120	+	0.933676i	$0.616582\pi$
$468$	−0.568876	−	11.4438i	−0.0262963	−	0.528990i
$469$	−19.9523	+	6.48290i	−0.921313	+	0.299353i
$470$	−4.46086	+	8.50737i	−0.205764	+	0.392416i
$471$	0.411955	+	3.97086i	0.0189819	+	0.182968i
$472$	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
$477$	0.963388	+	1.19625i	0.0441105	+	0.0547726i
$478$	6.06483	+	11.9029i	0.277399	+	0.544426i
$479$	−11.4075	+	35.1086i	−0.521220	+	1.60415i	0.250450	+	0.968129i	$0.419421\pi$
$479$	−11.4075	+	35.1086i	−0.521220	+	1.60415i	−0.771671	+	0.636022i	$0.780579\pi$
$480$	2.47640	−	2.97782i	0.113032	−	0.135918i
$481$	−4.35128	−	13.3919i	−0.198401	−	0.610616i
$482$	3.61037	−	3.61037i	0.164448	−	0.164448i
$483$	−0.295665	+	5.50005i	−0.0134532	+	0.250261i
$484$	−2.68968	+	3.70203i	−0.122258	+	0.168274i
$485$	10.8649	−	32.1538i	0.493352	−	1.46003i
$486$	6.43603	−	14.1978i	0.291944	−	0.644025i
$487$	−5.38000	−	33.9680i	−0.243791	−	1.53923i	−0.740941	−	0.671570i	$-0.765620\pi$
$487$	−5.38000	−	33.9680i	−0.243791	−	1.53923i	0.497150	−	0.867665i	$-0.334380\pi$
$488$	0.623369	+	3.93579i	0.0282186	+	0.178165i
$489$	34.3129	+	19.8721i	1.55168	+	0.898650i
$490$	−30.7210	+	21.7755i	−1.38783	+	0.983719i
$491$	9.76139	−	13.4354i	0.440525	−	0.606331i	−0.529803	−	0.848120i	$-0.677734\pi$
$491$	9.76139	−	13.4354i	0.440525	−	0.606331i	0.970329	+	0.241789i	$0.0777343\pi$
$492$	−10.8668	−	0.584161i	−0.489911	−	0.0263360i
$493$	−27.5693	+	27.5693i	−1.24166	+	1.24166i
$494$	−0.739624	−	2.27633i	−0.0332772	−	0.102417i
$495$	0.645415	+	16.9902i	0.0290093	+	0.763651i
$496$	−0.501043	+	1.54205i	−0.0224975	+	0.0692401i
$497$	−2.13736	−	4.19480i	−0.0958736	−	0.188163i
$498$	−3.53121	−	13.2499i	−0.158237	−	0.593743i
$499$		−	23.6495i		−	1.05870i	−0.848404	−	0.529349i	$-0.822436\pi$
$499$		−	23.6495i		−	1.05870i	0.848404	−	0.529349i	$-0.177564\pi$
$500$	−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	$-0.542858\pi$
$503$	13.2000	−	6.72572i	0.588557	−	0.299885i	0.722793	+	0.691065i	$0.242858\pi$
$504$	7.28980	+	12.7051i	0.324714	+	0.565931i
$505$	3.04653	+	3.11867i	0.135569	+	0.138779i
$506$	−1.56996	+	0.510111i	−0.0697932	+	0.0226772i
$507$	−2.56507	−	0.988597i	−0.113919	−	0.0439051i
$508$	−2.05602	−	1.04759i	−0.0912211	−	0.0464795i
$509$	−26.7370	−	19.4255i	−1.18510	−	0.861022i	−0.192358	−	0.981325i	$-0.561614\pi$
$509$	−26.7370	−	19.4255i	−1.18510	−	0.861022i	−0.992737	+	0.120303i	$0.961614\pi$
$510$	−9.51025	+	15.9869i	−0.421121	+	0.707912i
$511$	30.6019	−	22.2336i	1.35375	−	0.983557i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	0.522374	−	3.21414i	0.0230634	−	0.141908i
$514$	13.1153	+	18.0516i	0.578489	+	0.796222i
$515$	7.32381	+	2.47475i	0.322726	+	0.109051i
$516$	−2.27814	−	0.487437i	−0.100290	−	0.0214582i
$517$	4.94319	−	9.70155i	0.217401	−	0.426674i
$518$	12.7289	+	12.7289i	0.559274	+	0.559274i
$519$	−19.0840	−	21.2523i	−0.837694	−	0.932874i
$520$	−3.78789	−	7.65425i	−0.166110	−	0.335661i
$521$	10.1727	+	3.30530i	0.445672	+	0.144808i	0.523251	−	0.852179i	$-0.324719\pi$
$521$	10.1727	+	3.30530i	0.445672	+	0.144808i	−0.0775789	+	0.996986i	$0.524719\pi$
$522$	6.36630	−	23.5062i	0.278645	−	1.02884i
$523$	6.12109	−	38.6470i	0.267656	−	1.68992i	−0.377615	−	0.925963i	$-0.623256\pi$
$523$	6.12109	−	38.6470i	0.267656	−	1.68992i	0.645271	−	0.763953i	$-0.276744\pi$
$524$	−5.42638			−0.237052
$525$	42.1497	−	3.37809i	1.83957	−	0.147432i
$526$	−13.3050			−0.580124
$527$	1.21824	−	7.69168i	0.0530675	−	0.335055i
$528$	−2.76731	+	3.40795i	−0.120431	+	0.148312i
$529$	−21.4709	−	6.97631i	−0.933516	−	0.303318i
$530$	1.01390	+	0.531640i	0.0440409	+	0.0230930i
$531$	13.6066	−	30.3409i	0.590475	−	1.31668i
$532$	2.16363	+	2.16363i	0.0938053	+	0.0938053i
$533$	−10.8943	+	21.3812i	−0.471883	+	0.926122i
$534$	−4.00244	+	18.7062i	−0.173203	+	0.809498i
$535$	−0.287512	+	24.5720i	−0.0124302	+	1.06234i
$536$	2.52552	+	3.47608i	0.109086	+	0.150144i
$537$	−9.18971	+	5.95031i	−0.396565	+	0.256775i
$538$	−8.04880	+	1.27480i	−0.347008	+	0.0549607i
$539$	34.5309	−	25.0882i	1.48735	−	1.08062i
$540$	0.182825	−	11.6175i	0.00786752	−	0.499938i
$541$	13.6337	+	9.90543i	0.586157	+	0.425868i	0.840938	−	0.541131i	$-0.182004\pi$
$541$	13.6337	+	9.90543i	0.586157	+	0.425868i	−0.254782	+	0.966999i	$0.582004\pi$
$542$	7.89814	+	4.02431i	0.339254	+	0.172859i
$543$	−11.6814	+	30.3092i	−0.501298	+	1.30069i
$544$	−4.56788	+	1.48420i	−0.195846	+	0.0636344i
$545$	5.77194	+	39.4225i	0.247243	+	1.68867i
$546$	32.1274	−	3.33304i	1.37493	−	0.142641i
$547$	13.9944	−	7.13049i	0.598356	−	0.304878i	−0.128455	−	0.991715i	$-0.541002\pi$
$547$	13.9944	−	7.13049i	0.598356	−	0.304878i	0.726811	+	0.686838i	$0.241002\pi$
$548$	−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
$552$	1.09003	−	0.290502i	0.0463948	−	0.0123646i
$553$	−0.324013	−	0.635911i	−0.0137784	−	0.0270417i
$554$	3.76524	−	11.5882i	0.159970	−	0.492337i
$555$	−3.51542	−	13.8394i	−0.149221	−	0.587451i
$556$	−0.908430	−	2.79586i	−0.0385260	−	0.118571i
$557$	−16.7489	+	16.7489i	−0.709672	+	0.709672i	−0.966466	−	0.256794i	$-0.917334\pi$
$557$	−16.7489	+	16.7489i	−0.709672	+	0.709672i	0.256794	+	0.966466i	$0.417334\pi$
$558$	1.73096	+	4.54582i	0.0732773	+	0.192440i
$559$	−3.01956	+	4.15607i	−0.127714	+	0.175783i
$560$	8.75709	+	6.52029i	0.370055	+	0.275533i
$561$	10.5671	−	18.2459i	0.446141	−	0.770345i
$562$	0.312022	+	1.97003i	0.0131619	+	0.0831007i
$563$	−7.14192	−	45.0923i	−0.300996	−	1.90041i	−0.420007	−	0.907521i	$-0.637973\pi$
$563$	−7.14192	−	45.0923i	−0.300996	−	1.90041i	0.119011	−	0.992893i	$-0.462027\pi$
$564$	−3.72904	+	6.43887i	−0.157021	+	0.271125i
$565$	33.6579	+	25.0607i	1.41600	+	1.05431i
$566$	1.22605	−	1.68751i	0.0515345	−	0.0709312i
$567$	40.9397	+	15.9685i	1.71931	+	0.670616i
$568$	−0.681806	+	0.681806i	−0.0286080	+	0.0286080i
$569$	0.701234	+	2.15818i	0.0293972	+	0.0904754i	0.964679	−	0.263430i	$-0.0848536\pi$
$569$	0.701234	+	2.15818i	0.0293972	+	0.0904754i	−0.935281	+	0.353905i	$0.884854\pi$
$570$	−0.597546	−	2.35240i	−0.0250284	−	0.0985313i
$571$	−9.62474	+	29.6219i	−0.402783	+	1.23964i	0.519950	+	0.854197i	$0.325951\pi$
$571$	−9.62474	+	29.6219i	−0.402783	+	1.23964i	−0.922733	+	0.385441i	$0.874049\pi$
$572$	4.39477	+	8.62521i	0.183754	+	0.360638i
$573$	−26.2981	+	7.00864i	−1.09862	+	0.292790i
$574$		−	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	−0.127825	−	0.991797i	$-0.540800\pi$
$577$	−13.3526	−	2.11485i	−0.555877	−	0.0880422i	−0.428051	+	0.903755i	$0.640800\pi$
$578$	5.40699	−	2.75500i	0.224901	−	0.114593i
$579$	−4.47092	+	0.463833i	−0.185805	+	0.0192762i
$580$	−2.62960	−	17.9602i	−0.109188	−	0.745758i
$581$	36.7632	−	11.9451i	1.52520	−	0.495566i
$582$	9.45440	−	24.5309i	0.391897	−	1.01684i
$583$	−1.15622	−	0.589123i	−0.0478857	−	0.0243990i
$584$	−6.26750	−	4.55360i	−0.259351	−	0.188429i
$585$	−23.2533	−	10.7566i	−0.961406	−	0.444731i
$586$	16.1844	−	11.7587i	0.668573	−	0.485747i
$587$	−20.8055	+	3.29526i	−0.858733	+	0.136010i	−0.570246	−	0.821474i	$-0.693152\pi$
$587$	−20.8055	+	3.29526i	−0.858733	+	0.136010i	−0.288487	+	0.957484i	$0.593152\pi$
$588$	−24.4837	+	15.8531i	−1.00969	+	0.653772i
$589$	0.597248	+	0.822041i	0.0246092	+	0.0338716i
$590$	0.289981	−	24.7830i	0.0119383	−	1.02030i
$591$	2.10298	−	9.82872i	0.0865051	−	0.404300i
$592$	1.67377	−	3.28496i	0.0687917	−	0.135011i
$593$	−13.4478	−	13.4478i	−0.552235	−	0.552235i	0.374851	−	0.927085i	$-0.377694\pi$
$593$	−13.4478	−	13.4478i	−0.552235	−	0.552235i	−0.927085	+	0.374851i	$0.877694\pi$
$594$	−0.0531468	+	13.1699i	−0.00218064	+	0.540368i
$595$	−46.4411	−	24.3515i	−1.90390	−	0.998314i
$596$	−5.79855	−	1.88406i	−0.237518	−	0.0771743i
$597$	−4.21880	+	5.19548i	−0.172664	+	0.212637i
$598$	0.389131	−	2.45687i	0.0159127	−	0.100469i
$599$	0.0872460			0.00356477			0.00178239	−	0.999998i	$-0.499433\pi$
$599$	0.0872460			0.00356477			0.00178239	+	0.999998i	$0.499433\pi$
$600$	−3.32561	−	7.99627i	−0.135767	−	0.326446i
$601$	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
$603$	12.4418	+	3.36967i	0.506669	+	0.137224i
$604$	−16.6190	−	5.39984i	−0.676218	−	0.219716i
$605$	4.53831	+	9.17064i	0.184509	+	0.372840i
$606$	2.25631	+	2.51268i	0.0916564	+	0.102071i
$607$	29.7432	+	29.7432i	1.20724	+	1.20724i	0.971918	+	0.235320i	$0.0756138\pi$
$607$	29.7432	+	29.7432i	1.20724	+	1.20724i	0.235320	+	0.971918i	$0.424386\pi$
$608$	0.284505	−	0.558373i	0.0115382	−	0.0226450i
$609$	67.1317	+	14.3637i	2.72031	+	0.582046i
$610$	8.44150	+	2.85243i	0.341787	+	0.115491i
$611$	9.64405	+	13.2739i	0.390157	+	0.537005i
$612$	−7.88012	+	12.0631i	−0.318535	+	0.487624i
$613$	−12.4325	+	1.96912i	−0.502145	+	0.0795319i	−0.402368	−	0.915478i	$-0.631813\pi$
$613$	−12.4325	+	1.96912i	−0.502145	+	0.0795319i	−0.0997765	+	0.995010i	$0.531813\pi$
$614$	7.54983	−	5.48528i	0.304687	−	0.221368i
$615$	−12.4408	+	20.9133i	−0.501662	+	0.843304i
$616$	−10.0119	−	7.27407i	−0.403391	−	0.293081i
$617$	−30.8055	−	15.6962i	−1.24018	−	0.631904i	−0.294082	−	0.955780i	$-0.595014\pi$
$617$	−30.8055	−	15.6962i	−1.24018	−	0.631904i	−0.946099	+	0.323876i	$0.895014\pi$
$618$	5.58750	+	2.15347i	0.224762	+	0.0866251i
$619$	8.55247	−	2.77887i	0.343753	−	0.111692i	−0.132052	−	0.991243i	$-0.542157\pi$
$619$	8.55247	−	2.77887i	0.343753	−	0.111692i	0.475805	+	0.879551i	$0.342157\pi$
$620$	2.53350	+	2.59349i	0.101748	+	0.104157i
$621$	2.00023	−	2.72985i	0.0802666	−	0.109545i
$622$	−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
$627$	0.708465	+	2.65833i	0.0282934	+	0.106163i
$628$	1.04640	+	2.05367i	0.0417557	+	0.0819502i
$629$	−5.47194	+	16.8409i	−0.218180	+	0.671490i
$630$	32.7301	−	1.24334i	1.30400	−	0.0495358i
$631$	−5.89667	−	18.1481i	−0.234743	−	0.722463i	−0.997155	−	0.0753725i	$-0.975985\pi$
$631$	−5.89667	−	18.1481i	−0.234743	−	0.722463i	0.762413	−	0.647091i	$-0.224015\pi$
$632$	−0.103358	+	0.103358i	−0.00411138	+	0.00411138i
$633$	18.9096	+	1.01652i	0.751591	+	0.0404031i
$634$	15.0327	−	20.6907i	0.597024	−	0.821733i
$635$	−4.20955	+	2.98379i	−0.167051	+	0.118408i
$636$	0.767377	+	0.444422i	0.0304285	+	0.0176225i
$637$	10.0615	+	63.5259i	0.398652	+	2.51699i
$638$	3.21861	+	20.3215i	0.127426	+	0.804537i
$639$	−0.310104	+	2.87599i	−0.0122675	+	0.113772i
$640$	0.715817	−	2.11840i	0.0282952	−	0.0837370i
$641$	5.82328	−	8.01506i	0.230006	−	0.316576i	−0.678378	−	0.734713i	$-0.737317\pi$
$641$	5.82328	−	8.01506i	0.230006	−	0.316576i	0.908384	+	0.418137i	$0.137317\pi$
$642$	−1.02177	+	19.0073i	−0.0403260	+	0.750157i
$643$	14.9895	−	14.9895i	0.591130	−	0.591130i	−0.346807	−	0.937937i	$-0.612734\pi$
$643$	14.9895	−	14.9895i	0.591130	−	0.591130i	0.937937	+	0.346807i	$0.112734\pi$
$644$	0.982687	+	3.02440i	0.0387233	+	0.119178i
$645$	−3.33090	+	4.00533i	−0.131154	+	0.157710i
$646$	−0.930111	+	2.86259i	−0.0365947	+	0.112627i
$647$	−9.58156	−	18.8049i	−0.376690	−	0.739296i	0.622366	−	0.782726i	$-0.286171\pi$
$647$	−9.58156	−	18.8049i	−0.376690	−	0.739296i	−0.999056	+	0.0434301i	$0.986171\pi$
$648$	0.519376	−	8.98500i	0.0204030	−	0.352964i
$649$			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	$-0.431118\pi$
$653$	28.9032	−	14.7269i	1.13107	−	0.576309i	0.916355	+	0.400368i	$0.131118\pi$
$654$	3.18468	+	30.6973i	0.124531	+	1.20036i
$655$	−5.63472	+	10.7461i	−0.220167	+	0.419883i
$656$	−5.97547	+	1.94155i	−0.233303	+	0.0758048i
$657$	−23.2125	+	1.15390i	−0.905606	+	0.0450181i
$658$	−18.6892	−	9.52264i	−0.728582	−	0.371231i
$659$	21.9545	+	15.9509i	0.855225	+	0.621357i	0.926582	−	0.376094i	$-0.122733\pi$
$659$	21.9545	+	15.9509i	0.855225	+	0.621357i	−0.0713570	+	0.997451i	$0.522733\pi$
$660$	3.87534	+	9.01900i	0.150848	+	0.351064i
$661$	−20.1069	+	14.6085i	−0.782069	+	0.568206i	−0.905599	−	0.424135i	$-0.860578\pi$
$661$	−20.1069	+	14.6085i	−0.782069	+	0.568206i	0.123531	+	0.992341i	$0.460578\pi$
$662$	31.5787	−	5.00158i	1.22734	−	0.194392i
$663$	17.2688	+	26.6701i	0.670665	+	1.03578i
$664$	−4.65341	−	6.40487i	−0.180587	−	0.248557i
$665$	6.53142	−	2.03802i	0.253278	−	0.0790309i
$666$	−2.27047	−	10.8249i	−0.0879791	−	0.419455i
$667$	2.40025	−	4.71076i	0.0929382	−	0.182402i
$668$	6.26427	+	6.26427i	0.242372	+	0.242372i
$669$	25.1500	−	22.5840i	0.972355	−	0.873147i
$670$	9.50631	−	1.39184i	0.367261	−	0.0537715i
$671$	−9.60557	−	3.12104i	−0.370819	−	0.120486i
$672$	6.56514	+	5.33098i	0.253256	+	0.205647i
$673$	3.13319	−	19.7822i	0.120775	−	0.762546i	−0.850743	−	0.525582i	$-0.823848\pi$
$673$	3.13319	−	19.7822i	0.120775	−	0.762546i	0.971518	−	0.236964i	$-0.0761524\pi$
$674$	−18.6360			−0.717830
$675$	−22.8167	−	12.4256i	−0.878217	−	0.478262i
$676$	−1.58712			−0.0610432
$677$	−3.76633	+	23.7796i	−0.144752	+	0.913926i	0.803246	+	0.595648i	$0.203105\pi$
$677$	−3.76633	+	23.7796i	−0.144752	+	0.913926i	−0.947997	+	0.318278i	$0.896895\pi$
$678$	25.2331	+	20.4896i	0.969072	+	0.786900i
$679$	70.4833	+	22.9014i	2.70490	+	0.878876i
$680$	−1.80406	+	10.5871i	−0.0691825	+	0.405998i
$681$	−31.8889	+	28.6353i	−1.22198	+	1.09731i
$682$	−2.90591	−	2.90591i	−0.111273	−	0.111273i
$683$	5.04753	−	9.90634i	0.193138	−	0.379056i	−0.774047	−	0.633129i	$-0.781770\pi$
$683$	5.04753	−	9.90634i	0.193138	−	0.379056i	0.967185	+	0.254073i	$0.0817704\pi$
$684$	−0.385932	−	1.83999i	−0.0147565	−	0.0703539i
$685$	−5.74308	+	7.71326i	−0.219432	+	0.294708i
$686$	−28.2407	−	38.8700i	−1.07823	−	1.48406i
$687$	−2.86859	−	4.43028i	−0.109444	−	0.169026i
$688$	−1.32850	+	0.210413i	−0.0506484	+	0.00802192i
$689$	1.58197	−	1.14937i	0.0602682	−	0.0437874i
$690$	0.556590	−	2.46028i	0.0211890	−	0.0936614i
$691$	−26.5202	−	19.2681i	−1.00888	−	0.732992i	−0.0449036	−	0.998991i	$-0.514298\pi$
$691$	−26.5202	−	19.2681i	−1.00888	−	0.732992i	−0.963973	+	0.265999i	$0.914298\pi$
$692$	−14.6936	−	7.48676i	−0.558567	−	0.284604i
$693$	−37.0804	+	1.84328i	−1.40857	+	0.0700205i
$694$	22.6473	−	7.35855i	0.859680	−	0.279327i
$695$	−6.48005	−	1.10421i	−0.245802	−	0.0418850i
$696$	−1.45089	−	13.9852i	−0.0549957	−	0.530107i
$697$	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	$-0.157870\pi$
$702$	−17.6462	−	9.08105i	−0.666011	−	0.342742i
$703$	−1.04891	−	2.05861i	−0.0395606	−	0.0776420i
$704$	−0.783225	+	2.41052i	−0.0295189	+	0.0908498i
$705$	8.87892	+	14.0708i	0.334399	+	0.529939i
$706$	−8.83221	−	27.1827i	−0.332405	−	1.02304i
$707$	−6.73158	+	6.73158i	−0.253167	+	0.253167i
$708$	1.03054	−	19.1705i	0.0387302	−	0.720471i
$709$	15.3258	−	21.0942i	0.575574	−	0.792209i	−0.417628	−	0.908618i	$-0.637138\pi$
$709$	15.3258	−	21.0942i	0.575574	−	0.792209i	0.993201	+	0.116409i	$0.0371383\pi$
$710$	0.642223	+	2.05819i	0.0241022	+	0.0772425i
$711$	−0.0470102	+	0.435986i	−0.00176302	+	0.0163507i
$712$	1.72774	+	10.9085i	0.0647498	+	0.408814i
$713$	0.165197	+	1.04301i	0.00618669	+	0.0390612i
$714$	−35.1493	−	20.3566i	−1.31543	−	0.761825i
$715$	21.6443	+	0.253255i	0.809452	+	0.00947122i
$716$	−3.71527	+	5.11362i	−0.138846	+	0.191105i
$717$	23.1050	+	1.24205i	0.862871	+	0.0463851i
$718$	−5.88078	+	5.88078i	−0.219469	+	0.219469i
$719$	−10.3692	−	31.9130i	−0.386705	−	1.19016i	−0.935236	−	0.354025i	$-0.884813\pi$
$719$	−10.3692	−	31.9130i	−0.386705	−	1.19016i	0.548531	−	0.836130i	$-0.315187\pi$
$720$	−2.31364	−	6.29659i	−0.0862241	−	0.234660i
$721$	−5.21635	+	16.0543i	−0.194267	+	0.597892i
$722$	8.44753	+	16.5792i	0.314384	+	0.617014i
$723$	−2.27739	−	8.54530i	−0.0846971	−	0.317803i
$724$			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	0.832241	−	0.554415i	$-0.187058\pi$
$727$	39.1616	+	6.20259i	1.45242	+	0.230042i	0.620184	+	0.784456i	$0.287058\pi$
$728$	16.6158	−	8.46615i	0.615821	−	0.313777i
$729$	−15.6934	−	21.9708i	−0.581237	−	0.813735i
$730$	−15.5258	+	7.68332i	−0.574636	+	0.284373i
$731$	6.14406	−	1.99632i	0.227246	−	0.0738367i
$732$	6.44021	+	2.48211i	0.238037	+	0.0917414i
$733$	−20.5512	−	10.4714i	−0.759077	−	0.386769i	0.0312046	−	0.999513i	$-0.490066\pi$
$733$	−20.5512	−	10.4714i	−0.759077	−	0.386769i	−0.790281	+	0.612744i	$0.790066\pi$
$734$	12.5742	+	9.13572i	0.464124	+	0.337206i
$735$	5.97078	+	64.9478i	0.220236	+	2.39563i
$736$	0.526909	−	0.382822i	0.0194221	−	0.0141110i
$737$	−10.7561	+	1.70361i	−0.396208	+	0.0627532i
$738$	−10.3084	+	15.7804i	−0.379456	+	0.580884i
$739$	−1.10089	−	1.51525i	−0.0404970	−	0.0557393i	0.788288	−	0.615306i	$-0.210968\pi$
$739$	−1.10089	−	1.51525i	−0.0404970	−	0.0557393i	−0.828785	+	0.559567i	$0.810968\pi$
$740$	−4.76730	−	6.72573i	−0.175250	−	0.247243i
$741$	−4.05386	−	0.867376i	−0.148922	−	0.0318639i
$742$	−1.13490	+	2.22736i	−0.0416634	+	0.0817690i
$743$	32.5148	+	32.5148i	1.19285	+	1.19285i	0.976263	+	0.216587i	$0.0694927\pi$
$743$	32.5148	+	32.5148i	1.19285	+	1.19285i	0.216587	+	0.976263i	$0.430507\pi$
$744$	1.87635	+	2.08954i	0.0687904	+	0.0766064i
$745$	−9.75227	+	9.52669i	−0.357295	+	0.349031i
$746$	−14.2250	−	4.62198i	−0.520814	−	0.169223i
$747$	−22.9247	−	6.20880i	−0.838770	−	0.227168i
$748$	1.90434	−	12.0236i	0.0696297	−	0.439625i
$749$	−53.6587			−1.96065
$750$	−19.2886	−	1.71746i	−0.704320	−	0.0627126i
$751$	−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
$753$	11.3993	−	14.0383i	0.415413	−	0.511584i
$754$	−29.4865	−	9.58075i	−1.07384	−	0.348910i
$755$	−27.9506	+	27.3041i	−1.01723	+	0.993697i
$756$	25.3707	+	0.102383i	0.922724	+	0.00372363i
$757$	−32.7271	−	32.7271i	−1.18949	−	1.18949i	−0.977210	−	0.212277i	$-0.931912\pi$
$757$	−32.7271	−	32.7271i	−1.18949	−	1.18949i	−0.212277	−	0.977210i	$-0.568088\pi$
$758$	2.85662	−	5.60643i	0.103757	−	0.203635i
$759$	−0.598220	+	2.79591i	−0.0217140	+	0.101485i
$760$	−0.810339	−	1.14323i	−0.0293941	−	0.0414692i
$761$	16.4848	+	22.6894i	0.597574	+	0.822490i	0.995483	−	0.0949348i	$-0.0302643\pi$
$761$	16.4848	+	22.6894i	0.597574	+	0.822490i	−0.397910	+	0.917425i	$0.630264\pi$
$762$	−3.35488	+	2.17227i	−0.121534	+	0.0786932i
$763$	−85.9289	+	13.6098i	−3.11084	+	0.492708i
$764$	−12.7122	+	9.23596i	−0.459911	+	0.334145i
$765$	15.7064	+	28.1316i	0.567867	+	1.01710i
$766$	−9.52966	−	6.92370i	−0.344321	−	0.250164i
$767$	−37.7194	−	19.2190i	−1.36197	−	0.693958i
$768$	0.622886	−	1.61617i	0.0224765	−	0.0583186i
$769$	18.8694	−	6.13105i	0.680449	−	0.221091i	0.0516570	−	0.998665i	$-0.483550\pi$
$769$	18.8694	−	6.13105i	0.680449	−	0.221091i	0.628792	+	0.777574i	$0.283550\pi$
$770$	−24.8014	+	12.2736i	−0.893781	+	0.442309i
$771$	38.4410	−	3.98804i	1.38442	−	0.143626i
$772$	−2.31229	+	1.17817i	−0.0832210	+	0.0424032i
$773$	−17.2870	−	2.73800i	−0.621771	−	0.0984789i	−0.162403	−	0.986725i	$-0.551924\pi$
$773$	−17.2870	−	2.73800i	−0.621771	−	0.0984789i	−0.459369	+	0.888246i	$0.651924\pi$
$774$	−2.70811	+	2.99144i	−0.0973410	+	0.107525i
$775$	7.76676	−	2.32412i	0.278990	−	0.0834849i
$776$		−	15.1784i		−	0.544872i
$777$	30.1276	−	8.02925i	1.08082	−	0.288048i
$778$	−10.8806	−	21.3544i	−0.390089	−	0.765593i
$779$	−1.21672	+	3.74469i	−0.0435937	+	0.134167i
$780$	−14.7605	−	0.966793i	−0.528510	−	0.0346167i
$781$	−0.755201	−	2.32427i	−0.0270232	−	0.0831689i
$782$	−2.21193	+	2.21193i	−0.0790986	+	0.0790986i
$783$	−29.7057	−	29.9464i	−1.06159	−	1.07020i
$784$	−9.89840	+	13.6240i	−0.353514	+	0.486571i
$785$	5.15352	+	0.0603002i	0.183937	+	0.00215221i
$786$	−4.71033	+	8.13324i	−0.168012	+	0.290103i
$787$	−5.84029	−	36.8741i	−0.208184	−	1.31442i	−0.841386	−	0.540435i	$-0.818260\pi$
$787$	−5.84029	−	36.8741i	−0.208184	−	1.31442i	0.633202	−	0.773986i	$-0.281740\pi$
$788$	−0.907798	−	5.73161i	−0.0323390	−	0.204180i
$789$	−11.5493	+	19.9419i	−0.411165	+	0.709951i
$790$	0.0973578	+	0.312012i	0.00346383	+	0.0111009i
$791$	−53.8585	+	74.1299i	−1.91499	+	2.63576i
$792$	2.70582	+	7.10598i	0.0961471	+	0.252500i
$793$	10.7617	−	10.7617i	0.382160	−	0.382160i
$794$	2.47210	+	7.60834i	0.0877315	+	0.270010i
$795$	1.67695	−	1.05818i	0.0594752	−	0.0375297i
$796$	−1.19404	+	3.67488i	−0.0423216	+	0.130253i
$797$	9.33967	+	18.3301i	0.330828	+	0.649286i	0.995173	−	0.0981399i	$-0.0312893\pi$
$797$	9.33967	+	18.3301i	0.330828	+	0.649286i	−0.664345	+	0.747426i	$0.731289\pi$
$798$	5.12105	−	1.36480i	0.181283	−	0.0483134i
$799$		−	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
$804$	7.40233	−	0.767951i	0.261060	−	0.0270835i
$805$	7.00975	+	1.19447i	0.247061	+	0.0420995i
$806$	5.88957	−	1.91364i	0.207451	−	0.0674050i
$807$	−5.07598	+	13.1704i	−0.178683	+	0.463620i
$808$	1.73723	+	0.885165i	0.0611157	+	0.0311400i
$809$	35.2216	+	25.5900i	1.23833	+	0.899696i	0.997486	−	0.0708691i	$-0.0225773\pi$
$809$	35.2216	+	25.5900i	1.23833	+	0.899696i	0.240840	+	0.970565i	$0.422577\pi$
$810$	−17.2540	−	10.3585i	−0.606244	−	0.363961i
$811$	9.88364	−	7.18088i	0.347062	−	0.252155i	−0.400574	−	0.916265i	$-0.631189\pi$
$811$	9.88364	−	7.18088i	0.347062	−	0.252155i	0.747635	+	0.664110i	$0.231189\pi$
$812$	39.1478	−	6.20040i	1.37382	−	0.217591i
$813$	12.8877	−	8.34474i	0.451991	−	0.292663i
$814$	5.49253	+	7.55982i	0.192513	+	0.264972i
$815$	30.5715	−	41.0591i	1.07087	−	1.43824i
$816$	−1.74055	+	8.13484i	−0.0609316	+	0.284777i
$817$	−0.382675	+	0.751043i	−0.0133881	+	0.0262757i
$818$	−14.9137	−	14.9137i	−0.521444	−	0.521444i
$819$	22.8923	−	51.0468i	0.799920	−	1.78372i
$820$	−2.35998	+	13.8496i	−0.0824140	+	0.483647i
$821$	9.18310	+	2.98377i	0.320492	+	0.104134i	0.464845	−	0.885392i	$-0.346110\pi$
$821$	9.18310	+	2.98377i	0.320492	+	0.104134i	−0.144353	+	0.989526i	$0.546110\pi$
$822$	−4.69554	+	5.78259i	−0.163776	+	0.201691i
$823$	−4.59608	+	29.0185i	−0.160209	+	1.01152i	0.768267	+	0.640129i	$0.221119\pi$
$823$	−4.59608	+	29.0185i	−0.160209	+	1.01152i	−0.928476	+	0.371392i	$0.878881\pi$
$824$	3.45724			0.120439
$825$	21.8848	+	1.69079i	0.761931	+	0.0588658i
$826$	54.1195			1.88306
$827$	−2.81343	+	17.7633i	−0.0978325	+	0.617690i	0.889243	+	0.457435i	$0.151232\pi$
$827$	−2.81343	+	17.7633i	−0.0978325	+	0.617690i	−0.987076	+	0.160255i	$0.948768\pi$
$828$	0.510779	−	1.88594i	0.0177508	−	0.0655410i
$829$	−16.6482	−	5.40933i	−0.578216	−	0.187874i	0.00528527	−	0.999986i	$-0.498318\pi$
$829$	−16.6482	−	5.40933i	−0.578216	−	0.187874i	−0.583501	+	0.812112i	$0.698318\pi$
$830$	−17.5159	+	2.56454i	−0.607985	+	0.0890165i
$831$	−14.1004	−	15.7026i	−0.489139	−	0.544715i
$832$	−2.70066	−	2.70066i	−0.0936285	−	0.0936285i
$833$	36.7199	−	72.0669i	1.27227	−	2.49697i
$834$	−4.97908	−	1.06534i	−0.172412	−	0.0368897i
$835$	18.9102	−	5.90059i	0.654413	−	0.204198i
$836$	0.933612	+	1.28501i	0.0322897	+	0.0444429i
$837$	8.31597	+	1.35154i	0.287442	+	0.0467162i
$838$	37.9387	−	6.00890i	1.31057	−	0.207574i
$839$	24.8896	−	18.0833i	0.859284	−	0.624306i	−0.0684060	−	0.997658i	$-0.521791\pi$
$839$	24.8896	−	18.0833i	0.859284	−	0.624306i	0.927690	+	0.373351i	$0.121791\pi$
$840$	17.3744	−	7.46553i	0.599472	−	0.257585i
$841$	−29.8502	−	21.6874i	−1.02932	−	0.747843i
$842$	15.1346	+	7.71145i	0.521572	+	0.265754i
$843$	3.22359	+	1.24240i	0.111027	+	0.0427905i
$844$	10.3981	−	3.37856i	0.357919	−	0.116295i
$845$	−1.64806	+	3.14304i	−0.0566950	+	0.108124i
$846$	6.41383	+	11.1784i	0.220512	+	0.384322i
$847$	−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
$852$	0.430078	+	1.61375i	0.0147342	+	0.0552862i
$853$	18.7621	+	36.8228i	0.642403	+	1.26079i	0.950881	+	0.309556i	$0.100180\pi$
$853$	18.7621	+	36.8228i	0.642403	+	1.26079i	−0.308478	+	0.951231i	$0.599820\pi$
$854$	−6.01242	+	18.5043i	−0.205741	+	0.633205i
$855$	−4.04456	−	1.14636i	−0.138321	−	0.0392048i
$856$	3.39600	+	10.4518i	0.116073	+	0.357236i
$857$	9.23819	−	9.23819i	0.315570	−	0.315570i	−0.531493	−	0.847063i	$-0.678369\pi$
$857$	9.23819	−	9.23819i	0.315570	−	0.315570i	0.847063	+	0.531493i	$0.178369\pi$
$858$	16.7426	+	0.900028i	0.571583	+	0.0307264i
$859$	−31.7094	+	43.6442i	−1.08191	+	1.48912i	−0.224508	+	0.974472i	$0.572078\pi$
$859$	−31.7094	+	43.6442i	−1.08191	+	1.48912i	−0.857401	+	0.514649i	$0.827922\pi$
$860$	−0.962813	+	2.84936i	−0.0328317	+	0.0971624i
$861$	−45.9805	−	26.6294i	−1.56701	−	0.907528i
$862$	4.09581	+	25.8599i	0.139504	+	0.880793i
$863$	5.91581	+	37.3509i	0.201376	+	1.27144i	0.856590	+	0.515997i	$0.172578\pi$
$863$	5.91581	+	37.3509i	0.201376	+	1.27144i	−0.655214	+	0.755443i	$0.727422\pi$
$864$	−1.58574	−	4.94827i	−0.0539481	−	0.168344i
$865$	−30.0841	+	21.3241i	−1.02289	+	0.725040i
$866$	16.7032	−	22.9900i	0.567599	−	0.781233i
$867$	0.564211	−	10.4956i	0.0191616	−	0.356451i
$868$	−5.59799	+	5.59799i	−0.190008	+	0.190008i
$869$	−0.114485	−	0.352348i	−0.00388363	−	0.0119526i
$870$	−29.2020	−	11.6489i	−0.990040	−	0.394935i
$871$	5.07107	−	15.6072i	0.171827	−	0.528828i
$872$	8.08931	+	15.8762i	0.273939	+	0.537635i
$873$	−28.5609	−	35.4644i	−0.966639	−	1.20029i
$874$		−	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	−0.250004	−	0.968245i	$-0.580432\pi$
$877$	−23.3056	−	3.69125i	−0.786976	−	0.124645i	−0.536972	+	0.843600i	$0.680432\pi$
$878$	−36.1332	+	18.4108i	−1.21944	+	0.621334i
$879$	−3.57553	−	34.4648i	−0.120600	−	1.16247i
$880$	3.96034	+	4.05412i	0.133503	+	0.136664i
$881$	1.56237	−	0.507643i	0.0526374	−	0.0171029i	−0.282580	−	0.959244i	$-0.591190\pi$
$881$	1.56237	−	0.507643i	0.0526374	−	0.0171029i	0.335217	+	0.942141i	$0.391190\pi$
$882$	2.50830	+	50.4582i	0.0844588	+	1.69901i
$883$	41.1010	+	20.9420i	1.38316	+	0.704755i	0.977827	−	0.209415i	$-0.0671559\pi$
$883$	41.1010	+	20.9420i	1.38316	+	0.704755i	0.405332	+	0.914170i	$0.367156\pi$
$884$	14.8406	+	10.7823i	0.499143	+	0.362649i
$885$	−36.8939	−	21.9474i	−1.24018	−	0.737753i
$886$	−5.57244	+	4.04861i	−0.187210	+	0.136016i
$887$	41.9970	−	6.65167i	1.41012	−	0.223341i	0.595510	−	0.803348i	$-0.296950\pi$
$887$	41.9970	−	6.65167i	1.41012	−	0.223341i	0.814612	+	0.580007i	$0.196950\pi$
$888$	−3.47071	−	5.36020i	−0.116469	−	0.179876i
$889$	−6.62246	−	9.11504i	−0.222110	−	0.305708i
$890$	23.3966	+	7.90584i	0.784257	+	0.265004i
$891$	19.6934	+	11.5117i	0.659752	+	0.385656i
$892$	8.85983	−	17.3884i	0.296649	−	0.582207i
$893$	1.90364	+	1.90364i	0.0637029	+	0.0637029i
$894$	−7.85729	+	7.05562i	−0.262787	+	0.235975i
$895$	6.26879	+	12.6674i	0.209543	+	0.423426i
$896$	4.64367	+	1.50882i	0.155134	+	0.0504061i
$897$	−3.34466	−	2.71591i	−0.111675	−	0.0906817i
$898$	−5.98876	+	37.8116i	−0.199848	+	1.26179i
$899$	13.1621			0.438980
$900$	−14.8718	−	1.95657i	−0.495728	−	0.0652189i
$901$	−2.45903			−0.0819222
$902$	2.49117	−	15.7286i	0.0829468	−	0.523705i
$903$	−8.83048	−	7.17047i	−0.293860	−	0.238618i
$904$	17.8479	+	5.79914i	0.593613	+	0.192877i
$905$	37.1387	+	19.4738i	1.23453	+	0.647329i
$906$	−22.5195	+	20.2218i	−0.748159	+	0.671825i
$907$	−11.6182	−	11.6182i	−0.385775	−	0.385775i	0.487403	−	0.873177i	$-0.337944\pi$
$907$	−11.6182	−	11.6182i	−0.385775	−	0.385775i	−0.873177	+	0.487403i	$0.837944\pi$
$908$	−11.2338	+	22.0476i	−0.372807	+	0.731674i
$909$	5.72466	−	1.20073i	0.189875	−	0.0398256i
$910$	0.487876	−	41.6960i	0.0161729	−	1.38221i
$911$	31.9965	+	44.0394i	1.06009	+	1.45909i	0.879720	+	0.475492i	$0.157730\pi$
$911$	31.9965	+	44.0394i	1.06009	+	1.45909i	0.180371	+	0.983599i	$0.442270\pi$
$912$	−0.589946	−	0.911118i	−0.0195351	−	0.0301701i
$913$	19.8188	−	3.13899i	0.655906	−	0.103885i
$914$	28.9507	−	21.0339i	0.957605	−	0.695741i
$915$	11.6029	−	10.1764i	0.383580	−	0.336421i
$916$	−2.46523	−	1.79110i	−0.0814536	−	0.0591795i
$917$	−23.6073	−	12.0285i	−0.779580	−	0.397216i
$918$	11.2404	+	22.2823i	0.370987	+	0.735426i
$919$	47.1407	−	15.3170i	1.55503	−	0.505260i	0.599555	−	0.800334i	$-0.295344\pi$
$919$	47.1407	−	15.3170i	1.55503	−	0.505260i	0.955474	+	0.295074i	$0.0953443\pi$
$920$	−0.210977	−	1.44098i	−0.00695570	−	0.0475076i
$921$	−1.66794	−	16.0774i	−0.0549605	−	0.529768i
$922$	−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
$927$	8.07787	−	6.50543i	0.265312	−	0.213666i
$928$	−3.68535	−	7.23291i	−0.120978	−	0.237432i
$929$	11.6949	−	35.9932i	0.383697	−	1.18090i	−0.553723	−	0.832701i	$-0.686794\pi$
$929$	11.6949	−	35.9932i	0.383697	−	1.18090i	0.937421	−	0.348198i	$-0.113206\pi$
$930$	6.08640	−	1.54604i	0.199581	−	0.0506965i
$931$	3.26116	+	10.0368i	0.106880	+	0.328944i
$932$	13.0971	−	13.0971i	0.429010	−	0.429010i
$933$	−0.727854	+	13.5398i	−0.0238289	+	0.443272i
$934$	2.66218	−	3.66418i	0.0871092	−	0.119896i
$935$	−21.8332	−	16.2564i	−0.714023	−	0.531642i
$936$	−11.3919	−	1.22833i	−0.372356	−	0.0401493i
$937$	4.74297	+	29.9460i	0.154946	+	0.978292i	0.935532	+	0.353243i	$0.114921\pi$
$937$	4.74297	+	29.9460i	0.154946	+	0.978292i	−0.780586	+	0.625049i	$0.785079\pi$
$938$	3.28186	+	20.7208i	0.107156	+	0.676559i
$939$	4.28742	+	2.48304i	0.139915	+	0.0810309i
$940$	7.70480	+	5.73678i	0.251303	+	0.187113i
$941$	18.8958	−	26.0078i	0.615984	−	0.847829i	−0.381069	−	0.924547i	$-0.624444\pi$
$941$	18.8958	−	26.0078i	0.615984	−	0.847829i	0.997053	+	0.0767174i	$0.0244439\pi$
$942$	3.98642	+	0.214297i	0.129885	+	0.00698217i
$943$	−2.89354	+	2.89354i	−0.0942265	+	0.0942265i
$944$	−3.42517	−	10.5416i	−0.111480	−	0.343099i
$945$	26.5476	−	50.1363i	0.863593	−	1.63093i
$946$	1.05348	−	3.24228i	0.0342516	−	0.105416i
$947$	7.77062	+	15.2507i	0.252511	+	0.495581i	0.982113	−	0.188291i	$-0.0602948\pi$
$947$	7.77062	+	15.2507i	0.252511	+	0.495581i	−0.729602	+	0.683872i	$0.760295\pi$
$948$	0.0651976	+	0.244637i	0.00211752	+	0.00794543i
$949$			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	$-0.772864\pi$
$953$	−20.7106	+	10.5526i	−0.670882	+	0.341831i	0.0851482	+	0.996368i	$0.472864\pi$
$954$	1.33223	−	0.764392i	0.0431326	−	0.0247481i
$955$	5.09003	+	34.7650i	0.164709	+	1.12497i
$956$	12.7051	−	4.12814i	0.410912	−	0.133513i
$957$	33.2525	+	12.8158i	1.07490	+	0.414275i
$958$	32.8918	+	16.7592i	1.06269	+	0.541466i
$959$	−16.9881	−	12.3426i	−0.548575	−	0.398563i
$960$	−2.55377	−	2.91175i	−0.0824224	−	0.0939763i
$961$	22.9527	−	16.6761i	0.740408	−	0.537938i
$962$	−13.9077	+	2.20276i	−0.448402	+	0.0710198i
$963$	27.6018	+	18.0306i	0.889456	+	0.581027i
$964$	−3.00113	−	4.13071i	−0.0966600	−	0.133041i
$965$	−0.0678938	+	5.80251i	−0.00218558	+	0.186789i
$966$	5.38608	+	1.15242i	0.173294	+	0.0370786i
$967$	−11.0422	+	21.6716i	−0.355094	+	0.696912i	−0.997591	−	0.0693770i	$-0.977899\pi$
$967$	−11.0422	+	21.6716i	−0.355094	+	0.696912i	0.642496	+	0.766289i	$0.277899\pi$
$968$	3.23569	+	3.23569i	0.103999	+	0.103999i
$969$	3.48317	+	3.87893i	0.111895	+	0.124609i
$970$	−30.0583	−	15.7611i	−0.965114	−	0.506060i
$971$	−5.98620	−	1.94504i	−0.192106	−	0.0624192i	0.211384	−	0.977403i	$-0.432203\pi$
$971$	−5.98620	−	1.94504i	−0.192106	−	0.0624192i	−0.403490	+	0.914984i	$0.632203\pi$
$972$	−13.0162	−	8.57782i	−0.417494	−	0.275134i
$973$	2.24541	−	14.1770i	0.0719846	−	0.454493i
$974$	−34.3914			−1.10197
$975$	−17.2418	+	28.2268i	−0.552179	+	0.903983i
$976$	3.98485			0.127552
$977$	−2.22604	+	14.0547i	−0.0712173	+	0.449649i	0.926151	+	0.377152i	$0.123097\pi$
$977$	−2.22604	+	14.0547i	−0.0712173	+	0.449649i	−0.997369	+	0.0724964i	$0.976903\pi$
$978$	24.9952	−	30.7818i	0.799259	−	0.984292i
$979$	−26.6230	−	8.65033i	−0.850874	−	0.276466i
$980$	16.7016	+	33.7492i	0.533514	+	1.07808i
$981$	48.7747	+	21.8733i	1.55725	+	0.698360i
$982$	−11.7430	−	11.7430i	−0.374733	−	0.374733i
$983$	7.65935	−	15.0323i	0.244295	−	0.479457i	−0.736003	−	0.676978i	$-0.763289\pi$
$983$	7.65935	−	15.0323i	0.244295	−	0.479457i	0.980299	+	0.197521i	$0.0632892\pi$
$984$	−2.27691	+	10.6416i	−0.0725851	+	0.339241i
$985$	−12.2932	−	4.15393i	−0.391693	−	0.132355i
$986$	22.9171	+	31.5427i	0.729830	+	1.00452i
$987$	−30.4959	+	19.7460i	−0.970695	+	0.628522i
$988$	−2.36401	+	0.374422i	−0.0752090	+	0.0119119i
$989$	−0.708722	+	0.514916i	−0.0225360	+	0.0163734i
$990$	16.8819	+	2.02038i	0.536543	+	0.0642118i
$991$	24.1908	+	17.5757i	0.768447	+	0.558310i	0.901490	−	0.432801i	$-0.142475\pi$
$991$	24.1908	+	17.5757i	0.768447	+	0.558310i	−0.133042	+	0.991110i	$0.542475\pi$
$992$	1.44469	+	0.736104i	0.0458688	+	0.0233713i
$993$	19.9151	−	51.6729i	0.631988	−	1.63979i
$994$	−4.47751	+	1.45483i	−0.142018	+	0.0461445i
$995$	6.03761	+	6.18058i	0.191405	+	0.195937i
$996$	−13.6392	+	1.41499i	−0.432174	+	0.0448357i
$997$	−12.5490	+	6.39403i	−0.397431	+	0.202501i	−0.641271	−	0.767314i	$-0.721593\pi$
$997$	−12.5490	+	6.39403i	−0.397431	+	0.202501i	0.243841	+	0.969815i	$0.421593\pi$
$998$	−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.77.7	yes	80
3.2	odd	2	inner	150.2.l.a.77.3	✓	80
5.2	odd	4		750.2.l.a.593.8		80
5.3	odd	4		750.2.l.c.593.3		80
5.4	even	2		750.2.l.b.407.4		80
15.2	even	4		750.2.l.a.593.1		80
15.8	even	4		750.2.l.c.593.10		80
15.14	odd	2		750.2.l.b.407.8		80
25.9	even	10		750.2.l.a.707.1		80
25.12	odd	20		750.2.l.b.293.8		80
25.13	odd	20	inner	150.2.l.a.113.3	yes	80
25.16	even	5		750.2.l.c.707.10		80
75.38	even	20	inner	150.2.l.a.113.7	yes	80
75.41	odd	10		750.2.l.c.707.3		80
75.59	odd	10		750.2.l.a.707.8		80
75.62	even	20		750.2.l.b.293.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.77.3	✓	80	3.2	odd	2	inner
150.2.l.a.77.7	yes	80	1.1	even	1	trivial
150.2.l.a.113.3	yes	80	25.13	odd	20	inner
150.2.l.a.113.7	yes	80	75.38	even	20	inner
750.2.l.a.593.1		80	15.2	even	4
750.2.l.a.593.8		80	5.2	odd	4
750.2.l.a.707.1		80	25.9	even	10
750.2.l.a.707.8		80	75.59	odd	10
750.2.l.b.293.4		80	75.62	even	20
750.2.l.b.293.8		80	25.12	odd	20
750.2.l.b.407.4		80	5.4	even	2
750.2.l.b.407.8		80	15.14	odd	2
750.2.l.c.593.3		80	5.3	odd	4
750.2.l.c.593.10		80	15.8	even	4
750.2.l.c.707.3		80	75.41	odd	10
750.2.l.c.707.10		80	25.16	even	5

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)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(-1.34459 - 1.09182i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.59953 + 1.56253i) q^{5} +(-1.28872 + 1.15724i) q^{6} +(-3.45255 - 3.45255i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.615838 + 2.93611i) q^{9} +O(q^{10})\)	\(q+(0.156434 - 0.987688i) q^{2} +(-1.34459 - 1.09182i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-1.59953 + 1.56253i) q^{5} +(-1.28872 + 1.15724i) q^{6} +(-3.45255 - 3.45255i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.615838 + 2.93611i) q^{9} +(1.29307 + 1.82427i) q^{10} +(-1.48978 - 2.05051i) q^{11} +(0.941388 + 1.45389i) q^{12} +(3.77229 - 0.597472i) q^{13} +(-3.95014 + 2.86994i) q^{14} +(3.85672 - 0.354556i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-4.27947 - 2.18050i) q^{17} +(2.99630 - 0.148947i) q^{18} +(0.596005 - 0.193654i) q^{19} +(2.00409 - 0.991774i) q^{20} +(0.872681 + 8.41183i) 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} +(2.37767 - 4.62025i) q^{27} +(2.21667 + 4.35046i) q^{28} +(2.50850 - 7.72038i) q^{29} +(0.253133 - 3.86470i) q^{30} +(0.501043 + 1.54205i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.235652 + 4.38367i) q^{33} +(-2.82311 + 3.88568i) q^{34} +(10.9172 + 0.127739i) q^{35} +(0.321611 - 2.98271i) q^{36} +(-0.576743 - 3.64141i) q^{37} +(-0.0980339 - 0.618961i) q^{38} +(-5.72451 - 3.31532i) q^{39} +(-0.666054 - 2.13457i) q^{40} +(-3.69305 + 5.08304i) q^{41} +(8.44478 + 0.453964i) q^{42} +(-0.951098 + 0.951098i) q^{43} +(0.783225 + 2.41052i) q^{44} +(-5.57282 - 3.73413i) q^{45} +(0.201261 - 0.619419i) q^{46} +(1.95031 + 3.82769i) q^{47} +(-0.446037 - 1.67363i) 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} +(-4.19142 - 3.07116i) q^{54} +(5.58694 + 0.952020i) q^{55} +(4.64367 - 1.50882i) q^{56} +(-1.01282 - 0.390348i) q^{57} +(-7.23291 - 3.68535i) q^{58} +(-8.96720 - 6.51505i) q^{59} +(-3.77752 - 0.854589i) q^{60} +(3.22382 - 2.34224i) q^{61} +(1.60145 - 0.253644i) q^{62} +(8.01085 - 12.2633i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-5.10032 + 6.84999i) q^{65} +(4.29284 + 0.918508i) q^{66} +(1.95065 - 3.82837i) q^{67} +(3.39620 + 3.39620i) q^{68} +(-0.753702 - 0.839339i) q^{69} +(1.83399 - 10.7628i) q^{70} +(0.917028 + 0.297960i) q^{71} +(-2.89568 - 0.784250i) q^{72} +(-1.21191 + 7.65167i) q^{73} -3.68680 q^{74} +(-5.61493 + 6.59337i) q^{75} -0.626677 q^{76} +(-1.93594 + 12.2230i) q^{77} +(-4.17002 + 5.13540i) q^{78} +(0.139017 + 0.0451693i) q^{79} +(-2.21248 + 0.323934i) q^{80} +(-8.24149 + 3.61634i) q^{81} +(4.44274 + 4.44274i) q^{82} +(-3.59418 + 7.05397i) q^{83} +(1.76943 - 8.26980i) q^{84} +(10.2522 - 3.19903i) q^{85} +(0.790603 + 1.08817i) q^{86} +(-11.8022 + 7.64189i) q^{87} +(2.50336 - 0.396494i) q^{88} +(8.93519 - 6.49179i) q^{89} +(-4.55994 + 4.92006i) q^{90} +(-15.0868 - 10.9612i) q^{91} +(-0.580309 - 0.295682i) q^{92} +(1.00995 - 2.62047i) q^{93} +(4.08566 - 1.32751i) q^{94} +(-0.650738 + 1.24103i) q^{95} +(-1.72280 + 0.178731i) 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

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