LMFDB - Embedded newform 192.2.s.a.107.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8]))

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

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

chi := DirichletCharacter("192.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			107.12
Character	$\chi$	$=$	192.107
Dual form			192.2.s.a.131.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.484976 + 1.32846i) q^{2} +(1.60917 - 0.640769i) q^{3} +(-1.52960 - 1.28854i) q^{4} +(-2.22872 - 3.33552i) q^{5} +(0.0708277 + 2.44847i) q^{6} +(0.140254 - 0.338604i) q^{7} +(2.45359 - 1.40709i) q^{8} +(2.17883 - 2.06221i) q^{9} +O(q^{10})$	\(q+(-0.484976 + 1.32846i) q^{2} +(1.60917 - 0.640769i) q^{3} +(-1.52960 - 1.28854i) q^{4} +(-2.22872 - 3.33552i) q^{5} +(0.0708277 + 2.44847i) q^{6} +(0.140254 - 0.338604i) q^{7} +(2.45359 - 1.40709i) q^{8} +(2.17883 - 2.06221i) q^{9} +(5.51197 - 1.34312i) q^{10} +(4.16199 + 0.827871i) q^{11} +(-3.28703 - 1.09336i) q^{12} +(-1.81231 - 1.21095i) q^{13} +(0.381801 + 0.350537i) q^{14} +(-5.72369 - 3.93931i) q^{15} +(0.679331 + 3.94189i) q^{16} +(2.34477 + 2.34477i) q^{17} +(1.68288 + 3.89460i) q^{18} +(-5.58598 - 3.73243i) q^{19} +(-0.888903 + 7.97380i) q^{20} +(0.00872547 - 0.634741i) q^{21} +(-3.11826 + 5.12753i) q^{22} +(0.561434 + 1.35542i) q^{23} +(3.04661 - 3.83643i) q^{24} +(-4.24507 + 10.2485i) q^{25} +(2.48762 - 1.82030i) q^{26} +(2.18470 - 4.71456i) q^{27} +(-0.650837 + 0.337204i) q^{28} +(0.511665 + 2.57231i) q^{29} +(8.00905 - 5.69320i) q^{30} +7.17816 q^{31} +(-5.56609 - 1.00926i) q^{32} +(7.22781 - 1.33469i) q^{33} +(-4.25209 + 1.97777i) q^{34} +(-1.44201 + 0.286833i) q^{35} +(-5.98997 + 0.346838i) q^{36} +(2.65038 + 3.96658i) q^{37} +(7.66744 - 5.61059i) q^{38} +(-3.69225 - 0.787342i) q^{39} +(-10.1618 - 5.04797i) q^{40} +(-5.19602 + 2.15226i) q^{41} +(0.838994 + 0.319425i) q^{42} +(-0.439507 - 0.0874234i) q^{43} +(-5.29942 - 6.62920i) q^{44} +(-11.7345 - 2.67144i) q^{45} +(-2.07290 + 0.0884939i) q^{46} +(-2.23583 + 2.23583i) q^{47} +(3.61900 + 5.90786i) q^{48} +(4.85477 + 4.85477i) q^{49} +(-11.5560 - 10.6097i) q^{50} +(5.27558 + 2.27067i) q^{51} +(1.21175 + 4.18749i) q^{52} +(1.03488 - 5.20272i) q^{53} +(5.20357 + 5.18873i) q^{54} +(-6.51454 - 15.7275i) q^{55} +(-0.132321 - 1.02815i) q^{56} +(-11.3804 - 2.42678i) q^{57} +(-3.66535 - 0.567786i) q^{58} +(6.44677 - 4.30759i) q^{59} +(3.67897 + 13.4008i) q^{60} +(2.26118 + 11.3677i) q^{61} +(-3.48123 + 9.53587i) q^{62} +(-0.392682 - 1.02699i) q^{63} +(4.04018 - 6.90485i) q^{64} +8.74387i q^{65} +(-1.73223 + 10.2491i) q^{66} +(3.80620 - 0.757101i) q^{67} +(-0.565223 - 6.60788i) q^{68} +(1.77195 + 1.82135i) q^{69} +(0.318294 - 2.05475i) q^{70} +(-3.54274 - 1.46745i) q^{71} +(2.44423 - 8.12562i) q^{72} +(-8.70231 + 3.60462i) q^{73} +(-6.55480 + 1.59722i) q^{74} +(-0.264094 + 19.2117i) q^{75} +(3.73490 + 12.9069i) q^{76} +(0.864058 - 1.29315i) q^{77} +(2.83660 - 4.52315i) q^{78} +(2.50332 - 2.50332i) q^{79} +(11.6342 - 11.0513i) q^{80} +(0.494594 - 8.98640i) q^{81} +(-0.339242 - 7.94648i) q^{82} +(1.65223 - 2.47273i) q^{83} +(-0.831235 + 0.959654i) q^{84} +(2.59519 - 13.0469i) q^{85} +(0.329289 - 0.541468i) q^{86} +(2.47161 + 3.81142i) q^{87} +(11.3767 - 3.82505i) q^{88} +(11.1954 + 4.63728i) q^{89} +(9.23987 - 14.2933i) q^{90} +(-0.664216 + 0.443815i) q^{91} +(0.887747 - 2.79668i) q^{92} +(11.5508 - 4.59954i) q^{93} +(-1.88588 - 4.05453i) q^{94} +26.9507i q^{95} +(-9.60347 + 1.94251i) q^{96} -10.0855i q^{97} +(-8.80379 + 4.09490i) q^{98} +(10.7755 - 6.77910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

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 $

$2$	−0.484976	+	1.32846i	−0.342930	+	0.939361i
$2$	−0.484976	+	1.32846i	−0.342930	+	0.939361i
$3$	1.60917	−	0.640769i	0.929052	−	0.369948i
$3$	1.60917	−	0.640769i	0.929052	−	0.369948i
$4$	−1.52960	−	1.28854i	−0.764798	−	0.644270i
$5$	−2.22872	−	3.33552i	−0.996716	−	1.49169i	−0.865858	−	0.500289i	$-0.833227\pi$
$5$	−2.22872	−	3.33552i	−0.996716	−	1.49169i	−0.130857	−	0.991401i	$-0.541773\pi$
$6$	0.0708277	+	2.44847i	0.0289153	+	0.999582i
$7$	0.140254	−	0.338604i	0.0530112	−	0.127980i	−0.895155	−	0.445755i	$-0.852935\pi$
$7$	0.140254	−	0.338604i	0.0530112	−	0.127980i	0.948166	+	0.317774i	$0.102935\pi$
$8$	2.45359	−	1.40709i	0.867474	−	0.497482i
$9$	2.17883	−	2.06221i	0.726276	−	0.687403i
$10$	5.51197	−	1.34312i	1.74304	−	0.424731i
$11$	4.16199	+	0.827871i	1.25489	+	0.249613i	0.777389	−	0.629020i	$-0.216544\pi$
$11$	4.16199	+	0.827871i	1.25489	+	0.249613i	0.477498	+	0.878633i	$0.341544\pi$
$12$	−3.28703	−	1.09336i	−0.948884	−	0.315625i
$13$	−1.81231	−	1.21095i	−0.502644	−	0.335856i	0.278261	−	0.960505i	$-0.410242\pi$
$13$	−1.81231	−	1.21095i	−0.502644	−	0.335856i	−0.780905	+	0.624649i	$0.785242\pi$
$14$	0.381801	+	0.350537i	0.102041	+	0.0936849i
$15$	−5.72369	−	3.93931i	−1.47785	−	1.01713i
$16$	0.679331	+	3.94189i	0.169833	+	0.985473i
$17$	2.34477	+	2.34477i	0.568690	+	0.568690i	0.931761	−	0.363071i	$-0.118272\pi$
$17$	2.34477	+	2.34477i	0.568690	+	0.568690i	−0.363071	+	0.931761i	$0.618272\pi$
$18$	1.68288	+	3.89460i	0.396657	+	0.917967i
$19$	−5.58598	−	3.73243i	−1.28151	−	0.856278i	−0.286700	−	0.958020i	$-0.592558\pi$
$19$	−5.58598	−	3.73243i	−1.28151	−	0.856278i	−0.994811	+	0.101742i	$0.967558\pi$
$20$	−0.888903	+	7.97380i	−0.198765	+	1.78300i
$21$	0.00872547	−	0.634741i	0.00190405	−	0.138512i
$22$	−3.11826	+	5.12753i	−0.664815	+	1.09319i
$23$	0.561434	+	1.35542i	0.117067	+	0.282625i	0.971542	−	0.236868i	$-0.0761209\pi$
$23$	0.561434	+	1.35542i	0.117067	+	0.282625i	−0.854475	+	0.519493i	$0.826121\pi$
$24$	3.04661	−	3.83643i	0.621886	−	0.783108i
$25$	−4.24507	+	10.2485i	−0.849015	+	2.04970i
$26$	2.48762	−	1.82030i	0.487862	−	0.356989i
$27$	2.18470	−	4.71456i	0.420445	−	0.907318i
$28$	−0.650837	+	0.337204i	−0.122997	+	0.0637256i
$29$	0.511665	+	2.57231i	0.0950138	+	0.477667i	0.998768	+	0.0496157i	$0.0157997\pi$
$29$	0.511665	+	2.57231i	0.0950138	+	0.477667i	−0.903755	+	0.428051i	$0.859200\pi$
$30$	8.00905	−	5.69320i	1.46225	−	1.03943i
$31$	7.17816			1.28924			0.644618	−	0.764505i	$-0.277017\pi$
$31$	7.17816			1.28924			0.644618	+	0.764505i	$0.277017\pi$
$32$	−5.56609	−	1.00926i	−0.983956	−	0.178414i
$33$	7.22781	−	1.33469i	1.25820	−	0.232340i
$34$	−4.25209	+	1.97777i	−0.729227	+	0.339185i
$35$	−1.44201	+	0.286833i	−0.243744	+	0.0484837i
$36$	−5.98997	+	0.346838i	−0.998328	+	0.0578064i
$37$	2.65038	+	3.96658i	0.435720	+	0.652101i	0.982734	−	0.185022i	$-0.0592357\pi$
$37$	2.65038	+	3.96658i	0.435720	+	0.652101i	−0.547014	+	0.837123i	$0.684236\pi$
$38$	7.66744	−	5.61059i	1.24382	−	0.910158i
$39$	−3.69225	−	0.787342i	−0.591233	−	0.126076i
$40$	−10.1618	−	5.04797i	−1.60671	−	0.798155i
$41$	−5.19602	+	2.15226i	−0.811482	+	0.336127i	−0.749545	−	0.661953i	$-0.769728\pi$
$41$	−5.19602	+	2.15226i	−0.811482	+	0.336127i	−0.0619368	+	0.998080i	$0.519728\pi$
$42$	0.838994	+	0.319425i	0.129460	+	0.0492884i
$43$	−0.439507	−	0.0874234i	−0.0670242	−	0.0133319i	0.161464	−	0.986879i	$-0.448378\pi$
$43$	−0.439507	−	0.0874234i	−0.0670242	−	0.0133319i	−0.228489	+	0.973547i	$0.573378\pi$
$44$	−5.29942	−	6.62920i	−0.798918	−	0.999389i
$45$	−11.7345	−	2.67144i	−1.74928	−	0.398235i
$46$	−2.07290	+	0.0884939i	−0.305633	+	0.0130477i
$47$	−2.23583	+	2.23583i	−0.326129	+	0.326129i	−0.851113	−	0.524983i	$-0.824072\pi$
$47$	−2.23583	+	2.23583i	−0.326129	+	0.326129i	0.524983	+	0.851113i	$0.324072\pi$
$48$	3.61900	+	5.90786i	0.522358	+	0.852727i
$49$	4.85477	+	4.85477i	0.693538	+	0.693538i
$50$	−11.5560	−	10.6097i	−1.63426	−	1.50044i
$51$	5.27558	+	2.27067i	0.738729	+	0.317957i
$52$	1.21175	+	4.18749i	0.168040	+	0.580701i
$53$	1.03488	−	5.20272i	0.142152	−	0.714648i	−0.842302	−	0.539006i	$-0.818800\pi$
$53$	1.03488	−	5.20272i	0.142152	−	0.714648i	0.984454	−	0.175642i	$-0.0562001\pi$
$54$	5.20357	+	5.18873i	0.708116	+	0.706096i
$55$	−6.51454	−	15.7275i	−0.878421	−	2.12070i
$56$	−0.132321	−	1.02815i	−0.0176821	−	0.137392i
$57$	−11.3804	−	2.42678i	−1.50737	−	0.321434i
$58$	−3.66535	−	0.567786i	−0.481285	−	0.0745539i
$59$	6.44677	−	4.30759i	0.839298	−	0.560801i	−0.0599697	−	0.998200i	$-0.519100\pi$
$59$	6.44677	−	4.30759i	0.839298	−	0.560801i	0.899267	+	0.437399i	$0.144100\pi$
$60$	3.67897	+	13.4008i	0.474954	+	1.73003i
$61$	2.26118	+	11.3677i	0.289514	+	1.45548i	0.802276	+	0.596954i	$0.203622\pi$
$61$	2.26118	+	11.3677i	0.289514	+	1.45548i	−0.512762	+	0.858531i	$0.671378\pi$
$62$	−3.48123	+	9.53587i	−0.442117	+	1.21106i
$63$	−0.392682	−	1.02699i	−0.0494732	−	0.129389i
$64$	4.04018	−	6.90485i	0.505023	−	0.863106i
$65$			8.74387i			1.08454i
$66$	−1.73223	+	10.2491i	−0.213223	+	1.26158i
$67$	3.80620	−	0.757101i	0.465002	−	0.0924946i	0.0429713	−	0.999076i	$-0.486318\pi$
$67$	3.80620	−	0.757101i	0.465002	−	0.0924946i	0.422030	+	0.906582i	$0.361318\pi$
$68$	−0.565223	−	6.60788i	−0.0685433	−	0.801324i
$69$	1.77195	+	1.82135i	0.213318	+	0.219264i
$70$	0.318294	−	2.05475i	0.0380434	−	0.245590i
$71$	−3.54274	−	1.46745i	−0.420446	−	0.174154i	0.162422	−	0.986721i	$-0.448069\pi$
$71$	−3.54274	−	1.46745i	−0.420446	−	0.174154i	−0.582868	+	0.812567i	$0.698069\pi$
$72$	2.44423	−	8.12562i	0.288055	−	0.957614i
$73$	−8.70231	+	3.60462i	−1.01853	+	0.421888i	−0.828559	−	0.559902i	$-0.810839\pi$
$73$	−8.70231	+	3.60462i	−1.01853	+	0.421888i	−0.189970	+	0.981790i	$0.560839\pi$
$74$	−6.55480	+	1.59722i	−0.761980	+	0.185673i
$75$	−0.264094	+	19.2117i	−0.0304949	+	2.21837i
$76$	3.73490	+	12.9069i	0.428423	+	1.48052i
$77$	0.864058	−	1.29315i	0.0984685	−	0.147369i
$78$	2.83660	−	4.52315i	0.321182	−	0.512146i
$79$	2.50332	−	2.50332i	0.281645	−	0.281645i	−0.552120	−	0.833765i	$-0.686181\pi$
$79$	2.50332	−	2.50332i	0.281645	−	0.281645i	0.833765	+	0.552120i	$0.186181\pi$
$80$	11.6342	−	11.0513i	1.30075	−	1.23557i
$81$	0.494594	−	8.98640i	0.0549549	−	0.998489i
$82$	−0.339242	−	7.94648i	−0.0374631	−	0.877542i
$83$	1.65223	−	2.47273i	0.181356	−	0.271418i	−0.729642	−	0.683829i	$-0.760313\pi$
$83$	1.65223	−	2.47273i	0.181356	−	0.271418i	0.910998	+	0.412411i	$0.135313\pi$
$84$	−0.831235	+	0.959654i	−0.0906952	+	0.104707i
$85$	2.59519	−	13.0469i	0.281487	−	1.41513i
$86$	0.329289	−	0.541468i	0.0355081	−	0.0583880i
$87$	2.47161	+	3.81142i	0.264985	+	0.408627i
$88$	11.3767	−	3.82505i	1.21276	−	0.407752i
$89$	11.1954	+	4.63728i	1.18671	+	0.491551i	0.886682	−	0.462379i	$-0.153004\pi$
$89$	11.1954	+	4.63728i	1.18671	+	0.491551i	0.300027	+	0.953931i	$0.403004\pi$
$90$	9.23987	−	14.2933i	0.973967	−	1.50664i
$91$	−0.664216	+	0.443815i	−0.0696288	+	0.0465245i
$92$	0.887747	−	2.79668i	0.0925540	−	0.291574i
$93$	11.5508	−	4.59954i	1.19777	−	0.476950i
$94$	−1.88588	−	4.05453i	−0.194514	−	0.418193i
$95$			26.9507i			2.76508i
$96$	−9.60347	+	1.94251i	−0.980150	+	0.198257i
$97$		−	10.0855i		−	1.02403i	−0.858977	−	0.512014i	$-0.828900\pi$
$97$		−	10.0855i		−	1.02403i	0.858977	−	0.512014i	$-0.171100\pi$
$98$	−8.80379	+	4.09490i	−0.889317	+	0.413648i
$99$	10.7755	−	6.77910i	1.08298	−	0.681325i
$100$	19.6989	−	10.2061i	1.96989	−	1.02061i
$101$	−0.0228565	+	0.0152722i	−0.00227431	+	0.00151964i	−0.556707	−	0.830709i	$-0.687935\pi$
$101$	−0.0228565	+	0.0152722i	−0.00227431	+	0.00151964i	0.554433	+	0.832229i	$0.312935\pi$
$102$	−5.57502	+	5.90717i	−0.552009	+	0.584897i
$103$	1.11844	+	0.463273i	0.110203	+	0.0456477i	0.437104	−	0.899411i	$-0.356004\pi$
$103$	1.11844	+	0.463273i	0.110203	+	0.0456477i	−0.326901	+	0.945059i	$0.606004\pi$
$104$	−6.15058	−	0.421076i	−0.603114	−	0.0412899i
$105$	−2.13664	+	1.38556i	−0.208515	+	0.135217i
$106$	6.40969	+	3.89799i	0.622564	+	0.378607i
$107$	−1.80798	+	9.08932i	−0.174784	+	0.878698i	0.789485	+	0.613770i	$0.210348\pi$
$107$	−1.80798	+	9.08932i	−0.174784	+	0.878698i	−0.964268	+	0.264927i	$0.914652\pi$
$108$	−9.41661	+	4.39631i	−0.906113	+	0.423035i
$109$	1.95411	−	2.92454i	0.187170	−	0.280120i	−0.726003	−	0.687691i	$-0.758624\pi$
$109$	1.95411	−	2.92454i	0.187170	−	0.280120i	0.913173	+	0.407572i	$0.133624\pi$
$110$	24.0527	−	1.02683i	2.29334	−	0.0979045i
$111$	6.80656	+	4.68460i	0.646050	+	0.444642i
$112$	1.43002	+	0.322843i	0.135124	+	0.0305058i
$113$	−12.9804	+	12.9804i	−1.22110	+	1.22110i	−0.253852	+	0.967243i	$0.581698\pi$
$113$	−12.9804	+	12.9804i	−1.22110	+	1.22110i	−0.967243	+	0.253852i	$0.918302\pi$
$114$	8.74308	−	13.9414i	0.818865	−	1.30573i
$115$	3.26975	−	4.89353i	0.304906	−	0.456324i
$116$	2.53189	−	4.59390i	0.235080	−	0.426533i
$117$	−6.44594	+	1.09891i	−0.595927	+	0.101595i
$118$	2.59592	+	10.6533i	0.238974	+	0.980719i
$119$	1.12281	−	0.465084i	0.102928	−	0.0426342i
$120$	−19.5865	−	1.61168i	−1.78800	−	0.147126i
$121$	6.47411	+	2.68166i	0.588556	+	0.243788i
$122$	−16.1981	−	2.50919i	−1.46651	−	0.227171i
$123$	−6.98215	+	6.79280i	−0.629560	+	0.612486i
$124$	−10.9797	−	9.24934i	−0.986005	−	0.830615i
$125$	23.9727	−	4.76846i	2.14418	−	0.426504i
$126$	1.55476	−	0.0235932i	0.138509	−	0.00210185i
$127$			14.4290i			1.28037i	0.768222	+	0.640184i	$0.221142\pi$
$127$			14.4290i			1.28037i	−0.768222	+	0.640184i	$0.778858\pi$
$128$	7.21340	+	8.71589i	0.637581	+	0.770384i
$129$	−0.763258	+	0.140944i	−0.0672011	+	0.0124094i
$130$	−11.6159	−	4.24057i	−1.01878	−	0.371922i
$131$	−2.97311	−	14.9468i	−0.259762	−	1.30591i	−0.861720	−	0.507384i	$-0.830613\pi$
$131$	−2.97311	−	14.9468i	−0.259762	−	1.30591i	0.601958	−	0.798528i	$-0.294387\pi$
$132$	−12.7754	−	7.27177i	−1.11196	−	0.632927i
$133$	−2.04727	+	1.36794i	−0.177521	+	0.118616i
$134$	−0.840141	+	5.42355i	−0.0725771	+	0.468523i
$135$	−20.5946	+	3.22035i	−1.77250	+	0.277164i
$136$	9.05241	+	2.45379i	0.776238	+	0.210411i
$137$	−0.0142442	−	0.0343885i	−0.00121696	−	0.00293800i	0.923270	−	0.384152i	$-0.125506\pi$
$137$	−0.0142442	−	0.0343885i	−0.00121696	−	0.00293800i	−0.924487	+	0.381214i	$0.875506\pi$
$138$	−3.27894	+	1.47065i	−0.279122	+	0.125190i
$139$	0.748199	−	3.76145i	0.0634614	−	0.319042i	−0.935995	−	0.352014i	$-0.885497\pi$
$139$	0.748199	−	3.76145i	0.0634614	−	0.319042i	0.999456	+	0.0329715i	$0.0104971\pi$
$140$	2.57529	+	1.41935i	0.217652	+	0.119957i
$141$	−2.16517	+	5.03047i	−0.182340	+	0.423642i
$142$	3.66759	−	3.99470i	0.307777	−	0.335228i
$143$	−6.54031	−	6.54031i	−0.546928	−	0.546928i
$144$	9.60915	+	7.18779i	0.800762	+	0.598982i
$145$	7.43965	−	7.43965i	0.617829	−	0.617829i
$146$	−0.568164	−	13.3088i	−0.0470216	−	1.10144i
$147$	10.9229	+	4.70134i	0.900906	+	0.387760i
$148$	1.05708	−	9.48238i	0.0868912	−	0.779447i
$149$	5.53720	+	1.10142i	0.453625	+	0.0902316i	0.416614	−	0.909083i	$-0.363217\pi$
$149$	5.53720	+	1.10142i	0.453625	+	0.0902316i	0.0370105	+	0.999315i	$0.488217\pi$
$150$	−25.3938	−	9.66804i	−2.07340	−	0.789392i
$151$	−22.1679	+	9.18223i	−1.80400	+	0.747239i	−0.819203	+	0.573504i	$0.805584\pi$
$151$	−22.1679	+	9.18223i	−1.80400	+	0.747239i	−0.984792	+	0.173735i	$0.944416\pi$
$152$	−18.9576	−	1.29786i	−1.53766	−	0.105270i
$153$	9.94426	+	0.273450i	0.803946	+	0.0221071i
$154$	1.29885	+	1.77501i	0.104664	+	0.143035i
$155$	−15.9981	−	23.9429i	−1.28500	−	1.92314i
$156$	4.63313	+	5.96192i	0.370947	+	0.477336i
$157$	−14.2842	+	2.84130i	−1.14000	+	0.226761i	−0.728763	−	0.684766i	$-0.759904\pi$
$157$	−14.2842	+	2.84130i	−1.14000	+	0.226761i	−0.411240	+	0.911527i	$0.634904\pi$
$158$	2.11150	+	4.53960i	0.167982	+	0.361151i
$159$	−1.66844	−	9.03516i	−0.132316	−	0.716535i
$160$	9.03887	+	20.8152i	0.714586	+	1.64559i
$161$	0.537695			0.0423763
$162$	11.6982	+	5.01524i	0.919096	+	0.394034i
$163$	−0.412821	−	2.07539i	−0.0323346	−	0.162557i	0.961244	−	0.275698i	$-0.0889089\pi$
$163$	−0.412821	−	2.07539i	−0.0323346	−	0.162557i	−0.993579	+	0.113141i	$0.963909\pi$
$164$	10.7211	+	3.40319i	0.837176	+	0.265744i
$165$	−20.5607	−	21.1338i	−1.60065	−	1.64527i
$166$	2.48363	+	3.39413i	0.192767	+	0.263436i
$167$	1.47763	−	3.56732i	0.114343	−	0.276047i	−0.856340	−	0.516412i	$-0.827267\pi$
$167$	1.47763	−	3.56732i	0.114343	−	0.276047i	0.970683	+	0.240365i	$0.0772672\pi$
$168$	−0.871730	−	1.56967i	−0.0672554	−	0.121103i
$169$	−3.15681	−	7.62121i	−0.242831	−	0.586247i
$170$	16.0736	+	9.77502i	1.23279	+	0.749710i
$171$	−19.8679	+	3.38712i	−1.51934	+	0.259019i
$172$	0.559620	+	0.700045i	0.0426706	+	0.0533779i
$173$	−16.3732	−	10.9402i	−1.24483	−	0.831771i	−0.254045	−	0.967192i	$-0.581761\pi$
$173$	−16.3732	−	10.9402i	−1.24483	−	0.831771i	−0.990788	+	0.135421i	$0.956761\pi$
$174$	−6.26198	+	1.43499i	−0.474720	+	0.108786i
$175$	2.87480	+	2.87480i	0.217314	+	0.217314i
$176$	−0.436011	+	16.9685i	−0.0328656	+	1.27905i
$177$	7.61374	−	11.0625i	0.572284	−	0.831510i
$178$	−11.5899	+	12.6236i	−0.868702	+	0.946181i
$179$	2.39937	+	1.60321i	0.179337	+	0.119829i	0.641999	−	0.766706i	$-0.278105\pi$
$179$	2.39937	+	1.60321i	0.179337	+	0.119829i	−0.462661	+	0.886535i	$0.653105\pi$
$180$	14.5069	+	19.2067i	1.08128	+	1.43158i
$181$	−0.427803	−	0.0850953i	−0.0317983	−	0.00632508i	0.179166	−	0.983819i	$-0.442660\pi$
$181$	−0.427803	−	0.0850953i	−0.0317983	−	0.00632508i	−0.210964	+	0.977494i	$0.567660\pi$
$182$	−0.267460	−	1.09762i	−0.0198255	−	0.0813612i
$183$	10.9227	+	16.8436i	0.807428	+	1.24512i
$184$	3.28473	+	2.53565i	0.242153	+	0.186931i
$185$	7.32363	−	17.6808i	0.538444	−	1.29992i
$186$	0.508412	+	17.5755i	0.0372786	+	1.28870i
$187$	7.81774	+	11.7001i	0.571690	+	0.855595i
$188$	6.30088	−	0.538962i	0.459539	−	0.0393079i
$189$	−1.28996	−	1.40099i	−0.0938305	−	0.101907i
$190$	−35.8028	−	13.0704i	−2.59741	−	0.948230i
$191$	8.44165			0.610817			0.305408	−	0.952221i	$-0.401207\pi$
$191$	8.44165			0.610817			0.305408	+	0.952221i	$0.401207\pi$
$192$	2.07691	−	13.6999i	0.149888	−	0.988703i
$193$	14.2667			1.02694			0.513468	−	0.858109i	$-0.328360\pi$
$193$	14.2667			1.02694			0.513468	+	0.858109i	$0.328360\pi$
$194$	13.3982	+	4.89123i	0.961932	+	0.351170i
$195$	5.60280	+	14.0703i	0.401225	+	1.00760i
$196$	−1.17027	−	13.6814i	−0.0835910	−	0.977242i
$197$	4.86093	+	7.27490i	0.346327	+	0.518315i	0.963214	−	0.268737i	$-0.0866062\pi$
$197$	4.86093	+	7.27490i	0.346327	+	0.518315i	−0.616886	+	0.787052i	$0.711606\pi$
$198$	3.77988	+	17.6025i	0.268624	+	1.25096i
$199$	7.01661	−	16.9396i	0.497394	−	1.20082i	−0.453488	−	0.891262i	$-0.649821\pi$
$199$	7.01661	−	16.9396i	0.497394	−	1.20082i	0.950882	−	0.309553i	$-0.100179\pi$
$200$	4.00495	+	31.1188i	0.283193	+	2.20043i
$201$	5.63968	−	3.65720i	0.397793	−	0.257959i
$202$	−0.00920365	−	0.0377706i	−0.000647566	−	0.00265753i
$203$	0.942759	+	0.187526i	0.0661687	+	0.0131618i
$204$	−5.14367	−	10.2710i	−0.360129	−	0.719114i
$205$	18.7594	+	12.5346i	1.31021	+	0.875457i
$206$	−1.15786	+	1.26112i	−0.0806716	+	0.0878666i
$207$	4.01843	+	1.79544i	0.279300	+	0.124792i
$208$	3.54226	−	7.96656i	0.245612	−	0.552382i
$209$	−20.1588	−	20.1588i	−1.39441	−	1.39441i
$210$	−0.804436	−	3.51039i	−0.0555114	−	0.242240i
$211$	−2.22777	−	1.48855i	−0.153366	−	0.102476i	0.476520	−	0.879164i	$-0.341898\pi$
$211$	−2.22777	−	1.48855i	−0.153366	−	0.102476i	−0.629885	+	0.776688i	$0.716898\pi$
$212$	−8.28686	+	6.62457i	−0.569144	+	0.454977i
$213$	−6.64115	−	0.0912927i	−0.455044	−	0.00625527i
$214$	−11.1979	−	6.80992i	−0.765476	−	0.465517i
$215$	0.687938	+	1.66083i	0.0469170	+	0.113268i
$216$	−1.27348	−	14.6417i	−0.0866492	−	0.996239i
$217$	1.00677	−	2.43055i	0.0683439	−	0.164997i
$218$	2.93742	+	4.01428i	0.198947	+	0.271882i
$219$	−11.6937	+	11.3766i	−0.790189	+	0.768759i
$220$	−10.3009	+	32.4510i	−0.694486	+	2.18784i
$221$	−1.41006	−	7.08885i	−0.0948508	−	0.476847i
$222$	−9.52430	+	6.77031i	−0.639229	+	0.454394i
$223$	−2.59755			−0.173945			−0.0869723	−	0.996211i	$-0.527719\pi$
$223$	−2.59755			−0.173945			−0.0869723	+	0.996211i	$0.527719\pi$
$224$	−1.12241	+	1.74315i	−0.0749941	+	0.116469i
$225$	11.8853	+	31.0840i	0.792352	+	2.07227i
$226$	−10.9487	−	23.5391i	−0.728299	−	1.56580i
$227$	5.53623	−	1.10122i	0.367452	−	0.0730908i	−0.00791067	−	0.999969i	$-0.502518\pi$
$227$	5.53623	−	1.10122i	0.367452	−	0.0730908i	0.375363	+	0.926878i	$0.377518\pi$
$228$	14.2804	+	18.3761i	0.945743	+	1.21698i
$229$	−2.89283	−	4.32943i	−0.191164	−	0.286097i	0.723490	−	0.690335i	$-0.242537\pi$
$229$	−2.89283	−	4.32943i	−0.191164	−	0.286097i	−0.914654	+	0.404238i	$0.867537\pi$
$230$	4.91510	+	6.71698i	0.324092	+	0.442904i
$231$	0.561799	−	2.63456i	0.0369637	−	0.173341i
$232$	4.87490	+	5.59144i	0.320053	+	0.367096i
$233$	−25.1634	+	10.4230i	−1.64851	+	0.682836i	−0.997115	−	0.0759023i	$-0.975816\pi$
$233$	−25.1634	+	10.4230i	−1.64851	+	0.682836i	−0.651396	+	0.758738i	$0.725816\pi$
$234$	1.66627	−	9.09610i	0.108927	−	0.594631i
$235$	12.4407	+	2.47461i	0.811543	+	0.161426i
$236$	−15.4115	−	1.71804i	−1.00320	−	0.111835i
$237$	2.42420	−	5.63230i	0.157469	−	0.365857i
$238$	0.0733072	+	1.71716i	0.00475180	+	0.111307i
$239$	17.0796	−	17.0796i	1.10479	−	1.10479i	0.110963	−	0.993824i	$-0.464606\pi$
$239$	17.0796	−	17.0796i	1.10479	−	1.10479i	0.993824	−	0.110963i	$-0.0353937\pi$
$240$	11.6401	−	25.2382i	0.751362	−	1.62912i
$241$	−12.8300	−	12.8300i	−0.826450	−	0.826450i	0.160574	−	0.987024i	$-0.448666\pi$
$241$	−12.8300	−	12.8300i	−0.826450	−	0.826450i	−0.987024	+	0.160574i	$0.948666\pi$
$242$	−6.70227	+	7.30004i	−0.430838	+	0.469264i
$243$	−4.96233	−	14.7775i	−0.318333	−	0.947979i
$244$	11.1890	−	20.3016i	0.716305	−	1.29968i
$245$	5.37324	−	27.0131i	0.343284	−	1.72580i
$246$	−5.63776	−	12.5698i	−0.359451	−	0.801423i
$247$	5.60375	+	13.5286i	0.356558	+	0.860807i
$248$	17.6122	−	10.1003i	1.11838	−	0.641372i
$249$	1.07426	−	5.03774i	0.0680783	−	0.319254i
$250$	−5.29147	+	34.1592i	−0.334662	+	2.16042i
$251$	−3.99447	+	2.66902i	−0.252129	+	0.168467i	−0.675212	−	0.737624i	$-0.735948\pi$
$251$	−3.99447	+	2.66902i	−0.252129	+	0.168467i	0.423083	+	0.906091i	$0.360948\pi$
$252$	−0.722678	+	2.07687i	−0.0455245	+	0.130831i
$253$	1.21457	+	6.10604i	0.0763592	+	0.383884i
$254$	−19.1683	−	6.99772i	−1.20273	−	0.439076i
$255$	−4.18396	−	22.6575i	−0.262010	−	1.41887i
$256$	−15.0770	+	5.35570i	−0.942314	+	0.334731i
$257$			9.78815i			0.610568i	0.952261	+	0.305284i	$0.0987514\pi$
$257$			9.78815i			0.610568i	−0.952261	+	0.305284i	$0.901249\pi$
$258$	0.182924	−	1.08231i	0.0113883	−	0.0673817i
$259$	1.71483	−	0.341100i	0.106554	−	0.0211949i
$260$	11.2668	−	13.3746i	0.698739	−	0.829457i
$261$	6.41948	+	4.54947i	0.397356	+	0.281605i
$262$	21.2981	+	3.29921i	1.31580	+	0.203826i
$263$	6.98342	+	2.89263i	0.430616	+	0.178367i	0.587454	−	0.809257i	$-0.300130\pi$
$263$	6.98342	+	2.89263i	0.430616	+	0.178367i	−0.156838	+	0.987624i	$0.550130\pi$
$264$	15.8560	−	13.4450i	0.975870	−	0.827481i
$265$	−19.6602	+	8.14354i	−1.20772	+	0.500254i
$266$	−0.824377	−	3.38313i	−0.0505458	−	0.207433i
$267$	20.9867	+	0.288494i	1.28436	+	0.0176555i
$268$	−6.79751	−	3.74638i	−0.415224	−	0.228847i
$269$	−13.1871	+	19.7359i	−0.804034	+	1.20332i	0.171870	+	0.985120i	$0.445019\pi$
$269$	−13.1871	+	19.7359i	−0.804034	+	1.20332i	−0.975904	+	0.218202i	$0.929981\pi$
$270$	5.70979	−	28.9209i	0.347487	−	1.76007i
$271$	17.2260	−	17.2260i	1.04640	−	1.04640i	0.0475332	−	0.998870i	$-0.484864\pi$
$271$	17.2260	−	17.2260i	1.04640	−	1.04640i	0.998870	−	0.0475332i	$-0.0151360\pi$
$272$	−7.64996	+	10.8357i	−0.463847	+	0.657011i
$273$	−0.784451	+	1.13978i	−0.0474771	+	0.0689827i
$274$	0.0525917	−	0.00224518i	0.00317718	−	0.000135637i
$275$	−26.1524	+	39.1398i	−1.57705	+	2.36022i
$276$	−0.363493	−	5.06916i	−0.0218797	−	0.305127i
$277$	−2.48800	+	12.5080i	−0.149489	+	0.751533i	0.831202	+	0.555970i	$0.187653\pi$
$277$	−2.48800	+	12.5080i	−0.149489	+	0.751533i	−0.980691	+	0.195562i	$0.937347\pi$
$278$	4.63407	+	2.81816i	0.277933	+	0.169022i
$279$	15.6400	−	14.8029i	0.936341	−	0.886224i
$280$	−3.13449	+	2.73281i	−0.187322	+	0.163317i
$281$	−10.4632	−	4.33399i	−0.624181	−	0.258544i	0.0480973	−	0.998843i	$-0.484684\pi$
$281$	−10.4632	−	4.33399i	−0.624181	−	0.258544i	−0.672278	+	0.740298i	$0.734684\pi$
$282$	−5.63271	−	5.31600i	−0.335423	−	0.316563i
$283$	−19.3945	+	12.9590i	−1.15289	+	0.770333i	−0.976824	−	0.214046i	$-0.931336\pi$
$283$	−19.3945	+	12.9590i	−1.15289	+	0.770333i	−0.176062	+	0.984379i	$0.556336\pi$
$284$	3.52809	+	6.80957i	0.209354	+	0.404073i
$285$	17.2692	+	43.3681i	1.02294	+	2.56891i
$286$	11.8604	−	5.51663i	0.701321	−	0.326205i
$287$			2.06126i			0.121672i
$288$	−14.2089	+	9.27943i	−0.837266	+	0.546796i
$289$		−	6.00410i		−	0.353182i
$290$	6.27520	+	13.4913i	0.368493	+	0.792237i
$291$	−6.46248	−	16.2293i	−0.378838	−	0.951376i
$292$	17.9557	+	5.69967i	1.05078	+	0.333548i
$293$	−14.1470	+	9.45270i	−0.826475	+	0.552233i	−0.895335	−	0.445393i	$-0.853064\pi$
$293$	−14.1470	+	9.45270i	−0.826475	+	0.552233i	0.0688600	+	0.997626i	$0.478064\pi$
$294$	−11.5429	+	12.2306i	−0.673194	+	0.713302i
$295$	−28.7361	−	11.9029i	−1.67308	−	0.693013i
$296$	12.0843	+	6.00301i	0.702385	+	0.348918i
$297$	12.9957	−	17.8133i	0.754089	−	1.03363i
$298$	−4.14859	+	6.82177i	−0.240322	+	0.395174i
$299$	0.623851	−	3.13631i	0.0360782	−	0.181378i
$300$	25.1590	−	29.0458i	1.45255	−	1.67696i
$301$	−0.0912447	+	0.136557i	−0.00525926	+	0.00787104i
$302$	−1.44732	−	33.9022i	−0.0832836	−	1.95085i
$303$	−0.0269939	+	0.0392213i	−0.00155076	+	0.00225321i
$304$	10.9181	−	24.5549i	0.626196	−	1.40832i
$305$	32.8777	−	32.8777i	1.88257	−	1.88257i
$306$	−5.18599	+	13.0779i	−0.296464	+	0.747614i
$307$	−0.832524	+	1.24596i	−0.0475146	+	0.0711107i	−0.854466	−	0.519507i	$-0.826116\pi$
$307$	−0.832524	+	1.24596i	−0.0475146	+	0.0711107i	0.806952	+	0.590617i	$0.201116\pi$
$308$	−2.98794	+	0.864631i	−0.170254	+	0.0492669i
$309$	2.09661	+	0.0288210i	0.119272	+	0.00163957i
$310$	39.5658	−	9.64110i	2.24719	−	0.547578i
$311$	22.5180	−	9.32727i	1.27688	−	0.528901i	0.361831	−	0.932244i	$-0.382152\pi$
$311$	22.5180	−	9.32727i	1.27688	−	0.528901i	0.915049	+	0.403343i	$0.132152\pi$
$312$	−10.1671	+	3.26352i	−0.575599	+	0.184760i
$313$	5.19710	+	2.15271i	0.293757	+	0.121678i	0.524695	−	0.851290i	$-0.324179\pi$
$313$	5.19710	+	2.15271i	0.293757	+	0.121678i	−0.230938	+	0.972969i	$0.574179\pi$
$314$	3.15294	−	20.3539i	0.177931	−	1.14864i
$315$	−2.55038	+	3.59868i	−0.143698	+	0.202763i
$316$	−7.05469	+	0.603441i	−0.396857	+	0.0339462i
$317$	−18.2362	+	3.62741i	−1.02425	+	0.203736i	−0.678507	−	0.734594i	$-0.737373\pi$
$317$	−18.2362	+	3.62741i	−1.02425	+	0.203736i	−0.345742	+	0.938330i	$0.612373\pi$
$318$	12.8120	+	2.16538i	0.718460	+	0.121429i
$319$			11.1295i			0.623134i
$320$	−32.0357	+	1.91289i	−1.79085	+	0.106934i
$321$	2.91482	+	15.7847i	0.162689	+	0.881017i
$322$	−0.260769	+	0.714304i	−0.0145321	+	0.0398066i
$323$	−4.34614	−	21.8495i	−0.241826	−	1.21574i
$324$	−12.3359	+	13.1083i	−0.685326	+	0.728237i
$325$	20.1038	−	13.4329i	1.11516	−	0.745125i
$326$	2.95728	+	0.458100i	0.163788	+	0.0253718i
$327$	1.27054	−	5.95820i	0.0702609	−	0.329489i
$328$	−9.72046	+	12.5920i	−0.536722	+	0.695279i
$329$	0.443476	+	1.07065i	0.0244496	+	0.0590267i
$330$	38.0468	−	17.0646i	2.09441	−	0.939374i
$331$	1.75591	−	8.82758i	0.0965138	−	0.485208i	−0.902050	−	0.431632i	$-0.857938\pi$
$331$	1.75591	−	8.82758i	0.0965138	−	0.485208i	0.998564	−	0.0535760i	$-0.0170619\pi$
$332$	−5.71346	+	1.65332i	−0.313567	+	0.0907379i
$333$	13.9546	+	3.17685i	0.764709	+	0.174091i
$334$	4.02241	+	3.69303i	0.220097	+	0.202074i
$335$	−11.0083	−	11.0083i	−0.601448	−	0.601448i
$336$	2.50801	−	0.396804i	0.136823	−	0.0216474i
$337$	−6.70835	+	6.70835i	−0.365427	+	0.365427i	−0.865806	−	0.500379i	$-0.833194\pi$
$337$	−6.70835	+	6.70835i	−0.365427	+	0.365427i	0.500379	+	0.865806i	$0.333194\pi$
$338$	11.6554	−	0.497580i	0.633972	−	0.0270648i
$339$	−12.5702	+	29.2051i	−0.682719	+	1.58620i
$340$	−20.7810	+	16.6125i	−1.12701	+	0.900937i
$341$	29.8754	+	5.94259i	1.61784	+	0.321809i
$342$	5.13583	−	28.0364i	0.277714	−	1.51603i
$343$	4.69497	−	1.94472i	0.253505	−	0.105005i
$344$	−1.20138	+	0.403926i	−0.0647742	+	0.0217782i
$345$	2.12595	−	9.96967i	0.114457	−	0.536749i
$346$	22.4743	−	16.4454i	1.20822	−	0.884109i
$347$	−4.11240	−	6.15464i	−0.220765	−	0.330398i	0.704511	−	0.709693i	$-0.251167\pi$
$347$	−4.11240	−	6.15464i	−0.220765	−	0.330398i	−0.925276	+	0.379295i	$0.876167\pi$
$348$	1.13059	−	9.01471i	0.0606063	−	0.483239i
$349$	−27.2302	+	5.41641i	−1.45760	+	0.289934i	−0.859354	−	0.511381i	$-0.829134\pi$
$349$	−27.2302	+	5.41641i	−1.45760	+	0.289934i	−0.598243	+	0.801315i	$0.704134\pi$
$350$	−5.21326	+	2.42484i	−0.278660	+	0.129613i
$351$	−9.66844	+	5.89870i	−0.516063	+	0.314849i
$352$	−22.3305	−	8.80854i	−1.19022	−	0.469497i
$353$	−16.2512			−0.864962			−0.432481	−	0.901643i	$-0.642362\pi$
$353$	−16.2512			−0.864962			−0.432481	+	0.901643i	$0.642362\pi$
$354$	11.0036	+	15.4796i	0.584835	+	0.822731i
$355$	3.00107	+	15.0874i	0.159281	+	0.800757i
$356$	−11.1491	−	21.5189i	−0.590902	−	1.14050i
$357$	1.50878	−	1.46786i	0.0798532	−	0.0776875i
$358$	−3.29343	+	2.40994i	−0.174063	+	0.127370i
$359$	−12.2259	+	29.5159i	−0.645258	+	1.55779i	0.174237	+	0.984704i	$0.444254\pi$
$359$	−12.2259	+	29.5159i	−0.645258	+	1.55779i	−0.819495	+	0.573086i	$0.805746\pi$
$360$	−32.5507	+	9.95699i	−1.71557	+	0.524779i
$361$	10.0011	+	24.1448i	0.526374	+	1.27078i
$362$	0.320520	−	0.527049i	0.0168461	−	0.0277011i
$363$	12.1362	+	0.166831i	0.636988	+	0.00875636i
$364$	1.58786	+	0.177011i	0.0832263	+	0.00927790i
$365$	31.4183	+	20.9931i	1.64451	+	1.09883i
$366$	−27.6733	+	6.34156i	−1.44650	+	0.331479i
$367$	16.2016	+	16.2016i	0.845719	+	0.845719i	0.989596	−	0.143877i	$-0.0459568\pi$
$367$	16.2016	+	16.2016i	0.845719	+	0.845719i	−0.143877	+	0.989596i	$0.545957\pi$
$368$	−4.96152	+	3.13389i	−0.258637	+	0.163365i
$369$	−6.88283	+	15.4047i	−0.358306	+	0.801936i
$370$	19.9364	+	18.3039i	1.03644	+	0.951574i
$371$	−1.61651	−	1.08012i	−0.0839252	−	0.0560770i
$372$	−23.5948	−	7.84828i	−1.22333	−	0.406914i
$373$	−4.50225	−	0.895553i	−0.233118	−	0.0463700i	0.0771490	−	0.997020i	$-0.475418\pi$
$373$	−4.50225	−	0.895553i	−0.233118	−	0.0463700i	−0.310267	+	0.950650i	$0.600418\pi$
$374$	−19.3345	+	4.71128i	−0.999762	+	0.243614i
$375$	35.5205	−	23.0342i	1.83427	−	1.18948i
$376$	−2.33979	+	8.63183i	−0.120665	+	0.445153i
$377$	2.18764	−	5.28143i	0.112669	−	0.272008i
$378$	2.48675	−	1.03421i	0.127904	−	0.0531939i
$379$	−15.3580	−	22.9849i	−0.788888	−	1.18065i	−0.979983	−	0.199082i	$-0.936204\pi$
$379$	−15.3580	−	22.9849i	−0.788888	−	1.18065i	0.191095	−	0.981572i	$-0.438796\pi$
$380$	34.7270	−	41.2237i	1.78146	−	2.11473i
$381$	9.24566	+	23.2187i	0.473670	+	1.18953i
$382$	−4.09400	+	11.2144i	−0.209467	+	0.573777i
$383$	−1.94291			−0.0992783			−0.0496391	−	0.998767i	$-0.515807\pi$
$383$	−1.94291			−0.0992783			−0.0496391	+	0.998767i	$0.515807\pi$
$384$	17.1924	+	9.40319i	0.877348	+	0.479855i
$385$	−6.23909			−0.317973
$386$	−6.91899	+	18.9526i	−0.352167	+	0.964664i
$387$	−1.13790	+	0.715875i	−0.0578425	+	0.0363900i
$388$	−12.9956	+	15.4268i	−0.659750	+	0.783175i
$389$	12.6774	+	18.9731i	0.642771	+	0.961974i	0.999613	+	0.0278098i	$0.00885328\pi$
$389$	12.6774	+	18.9731i	0.642771	+	0.961974i	−0.356843	+	0.934165i	$0.616147\pi$
$390$	−21.4091	+	0.619308i	−1.08409	+	0.0313599i
$391$	−1.86172	+	4.49459i	−0.0941511	+	0.227301i
$392$	18.7427	+	5.08049i	0.946649	+	0.256603i
$393$	−14.3617	−	22.1469i	−0.724452	−	1.11716i
$394$	−12.0218	+	2.92939i	−0.605651	+	0.147580i
$395$	−13.9291	−	2.77066i	−0.700847	−	0.139407i
$396$	−25.2173	−	3.51538i	−1.26722	−	0.176655i
$397$	−23.7866	−	15.8937i	−1.19382	−	0.797682i	−0.210147	−	0.977670i	$-0.567394\pi$
$397$	−23.7866	−	15.8937i	−1.19382	−	0.797682i	−0.983669	+	0.179988i	$0.942394\pi$
$398$	19.1006	+	17.5366i	0.957428	+	0.879028i
$399$	−2.41787	+	3.51308i	−0.121045	+	0.175874i
$400$	−43.2824	−	9.77149i	−2.16412	−	0.488575i
$401$	22.2618	+	22.2618i	1.11170	+	1.11170i	0.992920	+	0.118783i	$0.0378992\pi$
$401$	22.2618	+	22.2618i	1.11170	+	1.11170i	0.118783	+	0.992920i	$0.462101\pi$
$402$	2.12332	+	9.26573i	0.105902	+	0.462133i
$403$	−13.0090	−	8.69237i	−0.648027	−	0.432998i
$404$	0.0546401	+	0.00609117i	0.00271845	+	0.000303047i
$405$	−31.0766	+	18.3785i	−1.54421	+	0.913234i
$406$	−0.706337	+	1.16147i	−0.0350549	+	0.0576428i
$407$	7.74705	+	18.7030i	0.384007	+	0.927074i
$408$	16.1391	−	1.85195i	0.799007	−	0.0916852i
$409$	0.669404	−	1.61609i	0.0330999	−	0.0799103i	−0.906465	−	0.422281i	$-0.861230\pi$
$409$	0.669404	−	1.61609i	0.0330999	−	0.0799103i	0.939565	+	0.342370i	$0.111230\pi$
$410$	−25.7496	+	18.8421i	−1.27168	+	0.930544i
$411$	−0.0449563	−	0.0462095i	−0.00221753	−	0.00227935i
$412$	−1.11382	−	2.14978i	−0.0548738	−	0.105912i
$413$	−0.554381	−	2.78706i	−0.0272793	−	0.137142i
$414$	−4.33400	+	4.46757i	−0.213005	+	0.219569i
$415$	−11.9302			−0.585631
$416$	8.86533	+	8.56934i	0.434658	+	0.420146i
$417$	−1.20625	−	6.53222i	−0.0590701	−	0.319884i
$418$	36.5566	−	17.0036i	1.78804	−	0.831672i
$419$	18.8136	−	3.74226i	0.919106	−	0.182821i	0.287203	−	0.957870i	$-0.407274\pi$
$419$	18.8136	−	3.74226i	0.919106	−	0.182821i	0.631902	+	0.775048i	$0.282274\pi$
$420$	5.05354	+	0.633798i	0.246588	+	0.0309262i
$421$	9.60096	+	14.3688i	0.467922	+	0.700295i	0.988109	−	0.153758i	$-0.0491376\pi$
$421$	9.60096	+	14.3688i	0.467922	+	0.700295i	−0.520187	+	0.854053i	$0.674138\pi$
$422$	3.05789	−	2.23758i	0.148856	−	0.108924i
$423$	−0.260745	+	9.48224i	−0.0126778	+	0.461042i
$424$	−4.78152	−	14.2215i	−0.232211	−	0.690657i
$425$	−33.9842	+	14.0767i	−1.64847	+	0.682820i
$426$	3.34208	−	8.77821i	0.161924	−	0.425306i
$427$	4.16629	+	0.828726i	0.201621	+	0.0401049i
$428$	14.4774	−	11.5733i	0.699793	−	0.559419i
$429$	−14.7153	−	6.33361i	−0.710460	−	0.305790i
$430$	−2.53997	+	0.108434i	−0.122488	+	0.00522913i
$431$	18.2671	−	18.2671i	0.879896	−	0.879896i	−0.113628	−	0.993523i	$-0.536247\pi$
$431$	18.2671	−	18.2671i	0.879896	−	0.879896i	0.993523	+	0.113628i	$0.0362471\pi$
$432$	20.0684	+	5.40910i	0.965543	+	0.260245i
$433$	17.2171	+	17.2171i	0.827401	+	0.827401i	0.987157	−	0.159755i	$-0.0510706\pi$
$433$	17.2171	+	17.2171i	0.827401	+	0.827401i	−0.159755	+	0.987157i	$0.551071\pi$
$434$	2.74063	+	2.51621i	0.131554	+	0.120782i
$435$	7.20453	−	16.7387i	0.345431	−	0.802561i
$436$	−6.75738	+	1.95541i	−0.323620	+	0.0936471i
$437$	1.92286	−	9.66686i	0.0919828	−	0.462429i
$438$	−9.44214	−	21.0520i	−0.451163	−	1.00590i
$439$	1.63353	+	3.94370i	0.0779643	+	0.188222i	0.958056	−	0.286582i	$-0.0925189\pi$
$439$	1.63353	+	3.94370i	0.0779643	+	0.188222i	−0.880092	+	0.474804i	$0.842519\pi$
$440$	−38.1141	−	29.4222i	−1.81702	−	1.40265i
$441$	20.5892	+	0.566168i	0.980440	+	0.0269604i
$442$	10.1011	+	1.56472i	0.480459	+	0.0744260i
$443$	−19.6650	+	13.1397i	−0.934310	+	0.624286i	−0.926747	−	0.375685i	$-0.877407\pi$
$443$	−19.6650	+	13.1397i	−0.934310	+	0.624286i	−0.00756283	+	0.999971i	$0.502407\pi$
$444$	−4.37501	−	15.9361i	−0.207629	−	0.756292i
$445$	−9.48369	−	47.6777i	−0.449570	−	2.26014i
$446$	1.25975	−	3.45073i	0.0596508	−	0.163397i
$447$	9.61602	−	1.77570i	0.454822	−	0.0839879i
$448$	−1.77136	−	2.33646i	−0.0836887	−	0.110387i
$449$		−	14.1363i		−	0.667131i	−0.942727	−	0.333565i	$-0.891748\pi$
$449$		−	14.1363i		−	0.667131i	0.942727	−	0.333565i	$-0.108252\pi$
$450$	−47.0578	+	0.714095i	−2.21833	+	0.0336628i
$451$	−23.4076	+	4.65606i	−1.10222	+	0.219245i
$452$	36.5806	−	3.12902i	1.72061	−	0.147177i
$453$	−29.7881	+	28.9802i	−1.39957	+	1.36161i
$454$	−1.22201	+	7.88871i	−0.0573517	+	0.370235i
$455$	2.96071	+	1.22637i	0.138800	+	0.0574929i
$456$	−31.3375	+	10.0589i	−1.46751	+	0.471053i
$457$	14.2104	−	5.88613i	0.664733	−	0.275342i	−0.0246955	−	0.999695i	$-0.507862\pi$
$457$	14.2104	−	5.88613i	0.664733	−	0.275342i	0.689429	+	0.724353i	$0.257862\pi$
$458$	7.15441	−	1.74333i	0.334304	−	0.0814606i
$459$	16.1772	−	5.93195i	0.755086	−	0.276880i
$460$	−11.3069	+	3.27192i	−0.527188	+	0.152554i
$461$	12.6297	−	18.9017i	0.588225	−	0.880341i	−0.411289	−	0.911505i	$-0.634921\pi$
$461$	12.6297	−	18.9017i	0.588225	−	0.880341i	0.999514	+	0.0311642i	$0.00992147\pi$
$462$	3.22744	+	2.02402i	0.150154	+	0.0941661i
$463$	−14.7383	+	14.7383i	−0.684947	+	0.684947i	−0.961111	−	0.276164i	$-0.910937\pi$
$463$	−14.7383	+	14.7383i	−0.684947	+	0.684947i	0.276164	+	0.961111i	$0.410937\pi$
$464$	−9.79219	+	3.76438i	−0.454591	+	0.174757i
$465$	−41.0855	−	28.2770i	−1.90530	−	1.31131i
$466$	−1.64289	−	38.4835i	−0.0761055	−	1.78271i
$467$	13.2315	−	19.8024i	0.612282	−	0.916344i	−0.387704	−	0.921784i	$-0.626732\pi$
$467$	13.2315	−	19.8024i	0.612282	−	0.916344i	0.999985	+	0.00543998i	$0.00173161\pi$
$468$	11.2757	+	6.62495i	0.521219	+	0.306239i
$469$	0.277479	−	1.39498i	0.0128128	−	0.0644143i
$470$	−9.32086	+	15.3268i	−0.429939	+	0.706974i
$471$	−21.1650	+	13.7250i	−0.975233	+	0.632415i
$472$	9.75653	−	19.6403i	0.449081	−	0.904016i
$473$	−1.75685	−	0.727711i	−0.0807800	−	0.0334602i
$474$	6.30659	+	5.95198i	0.289671	+	0.273383i
$475$	61.9647	−	41.4035i	2.84314	−	1.89972i
$476$	−2.31673	−	0.735398i	−0.106187	−	0.0337069i
$477$	−8.47425	−	13.4700i	−0.388009	−	0.616748i
$478$	14.4063	+	30.9727i	0.658930	+	1.41666i
$479$			1.01380i			0.0463216i	0.999732	+	0.0231608i	$0.00737297\pi$
$479$			1.01380i			0.0463216i	−0.999732	+	0.0231608i	$0.992627\pi$
$480$	27.8828	+	27.7033i	1.27267	+	1.26447i
$481$		−	10.3981i		−	0.474114i
$482$	23.2663	−	10.8218i	1.05975	−	0.492921i
$483$	0.865240	−	0.344538i	0.0393698	−	0.0156770i
$484$	−6.44735	−	12.4440i	−0.293061	−	0.565637i
$485$	−33.6404	+	22.4778i	−1.52753	+	1.02066i
$486$	22.0379	+	0.574510i	0.999660	+	0.0260603i
$487$	25.3253	+	10.4901i	1.14760	+	0.475352i	0.873728	−	0.486415i	$-0.161696\pi$
$487$	25.3253	+	10.4901i	1.14760	+	0.475352i	0.273872	+	0.961766i	$0.411696\pi$
$488$	21.5434	+	24.7100i	0.975224	+	1.11857i
$489$	−1.99414	−	3.07512i	−0.0901783	−	0.139062i
$490$	33.2799	+	20.2388i	1.50343	+	0.914297i
$491$	−2.91875	+	14.6735i	−0.131721	+	0.662207i	0.857346	+	0.514741i	$0.172112\pi$
$491$	−2.91875	+	14.6735i	−0.131721	+	0.662207i	−0.989067	+	0.147466i	$0.952888\pi$
$492$	19.4327	−	1.39345i	0.876092	−	0.0628218i
$493$	−4.83175	+	7.23123i	−0.217611	+	0.325678i
$494$	−20.6899	+	0.883270i	−0.930883	+	0.0397402i
$495$	−46.6275	−	20.8332i	−2.09575	−	0.936382i
$496$	4.87634	+	28.2955i	0.218954	+	1.27051i
$497$	−0.993769	+	0.993769i	−0.0445766	+	0.0445766i
$498$	6.17143	+	3.87029i	0.276548	+	0.173432i
$499$	−19.0969	+	28.5805i	−0.854894	+	1.27944i	0.103685	+	0.994610i	$0.466937\pi$
$499$	−19.0969	+	28.5805i	−0.854894	+	1.27944i	−0.958579	+	0.284828i	$0.908063\pi$
$500$	−42.8129	−	23.5959i	−1.91465	−	1.05524i
$501$	0.0919261	−	6.68723i	0.00410695	−	0.298763i
$502$	−1.60846	−	6.60089i	−0.0717889	−	0.294612i
$503$	−18.0858	+	7.49138i	−0.806406	+	0.334024i	−0.747519	−	0.664240i	$-0.768755\pi$
$503$	−18.0858	+	7.49138i	−0.806406	+	0.334024i	−0.0588869	+	0.998265i	$0.518755\pi$
$504$	−2.40855	−	1.96728i	−0.107286	−	0.0876296i
$505$	0.101882	+	0.0422008i	0.00453368	+	0.00187791i
$506$	−8.70065	−	1.34778i	−0.386791	−	0.0599163i
$507$	−9.96327	−	10.2410i	−0.442484	−	0.454819i
$508$	18.5923	−	22.0706i	0.824902	−	0.979222i
$509$	28.6563	−	5.70009i	1.27017	−	0.252652i	0.486417	−	0.873727i	$-0.338304\pi$
$509$	28.6563	−	5.70009i	1.27017	−	0.252652i	0.783751	+	0.621075i	$0.213304\pi$
$510$	32.1286	+	5.43014i	1.42268	+	0.240451i
$511$			3.45220i			0.152716i
$512$	0.197181	−	22.6266i	0.00871427	−	0.999962i
$513$	−29.8004	+	18.1812i	−1.31572	+	0.802720i
$514$	−13.0031	−	4.74702i	−0.573544	−	0.209382i
$515$	−0.947437	−	4.76309i	−0.0417491	−	0.209887i
$516$	1.34909	+	0.767901i	0.0593903	+	0.0338050i
$517$	−11.1565	+	7.45453i	−0.490662	+	0.327850i
$518$	−0.378513	+	2.44350i	−0.0166309	+	0.107361i
$519$	−33.3574	−	7.11320i	−1.46423	−	0.312235i
$520$	12.3034	+	21.4538i	0.539541	+	0.940813i
$521$	13.5271	+	32.6574i	0.592634	+	1.43074i	0.880950	+	0.473209i	$0.156905\pi$
$521$	13.5271	+	32.6574i	0.592634	+	1.43074i	−0.288316	+	0.957535i	$0.593095\pi$
$522$	−9.15707	+	6.32162i	−0.400794	+	0.276690i
$523$	1.35913	−	6.83280i	0.0594305	−	0.298778i	−0.939626	−	0.342203i	$-0.888827\pi$
$523$	1.35913	−	6.83280i	0.0594305	−	0.298778i	0.999057	+	0.0434252i	$0.0138270\pi$
$524$	−14.7119	+	26.6936i	−0.642694	+	1.16612i
$525$	6.46811	+	2.78394i	0.282291	+	0.121501i
$526$	−7.22952	+	7.87432i	−0.315222	+	0.343336i
$527$	16.8311	+	16.8311i	0.733176	+	0.733176i
$528$	10.1713	+	27.5845i	0.442648	+	1.20046i
$529$	14.7415	−	14.7415i	0.640935	−	0.640935i
$530$	−1.28360	−	30.0672i	−0.0557558	−	1.30604i
$531$	5.16325	−	22.6801i	0.224066	−	0.984232i
$532$	4.89415	+	0.545590i	0.212188	+	0.0236543i
$533$	12.0231	+	2.39154i	0.520777	+	0.103589i
$534$	−10.5613	+	27.7400i	−0.457032	+	1.20043i
$535$	34.3471	−	14.2270i	1.48496	−	0.615089i
$536$	8.27354	−	7.21329i	0.357362	−	0.311567i
$537$	4.88828	+	1.04239i	0.210945	+	0.0449822i
$538$	−19.8229	−	27.0900i	−0.854626	−	1.16793i
$539$	16.1864	+	24.2246i	0.697196	+	1.04343i
$540$	35.6510	+	21.6111i	1.53417	+	0.929995i
$541$	27.1068	−	5.39188i	1.16541	−	0.231815i	0.425781	−	0.904826i	$-0.359999\pi$
$541$	27.1068	−	5.39188i	1.16541	−	0.231815i	0.739632	+	0.673011i	$0.234999\pi$
$542$	14.5298	+	31.2381i	0.624107	+	1.34179i
$543$	−0.742932	+	0.137191i	−0.0318823	+	0.00588741i
$544$	−10.6847	−	15.4177i	−0.458104	−	0.661028i
$545$	−14.1100			−0.604407
$546$	−1.13371	−	1.59488i	−0.0485183	−	0.0682544i
$547$	3.30956	+	16.6383i	0.141507	+	0.711402i	0.984765	+	0.173893i	$0.0556346\pi$
$547$	3.30956	+	16.6383i	0.141507	+	0.711402i	−0.843258	+	0.537509i	$0.819365\pi$
$548$	−0.0225231	+	0.0709547i	−0.000962138	+	0.00303103i
$549$	28.3693	+	20.1053i	1.21077	+	0.858072i
$550$	−39.3123	−	53.7242i	−1.67628	−	2.29081i
$551$	6.74283	−	16.2786i	0.287254	−	0.693493i
$552$	6.91044	+	1.97554i	0.294128	+	0.0840844i
$553$	−0.496532	−	1.19873i	−0.0211147	−	0.0509754i
$554$	−15.4097	−	9.37128i	−0.654696	−	0.398147i
$555$	0.455616	−	33.1441i	0.0193398	−	1.40689i
$556$	−5.99122	+	4.78942i	−0.254084	+	0.203117i
$557$	−20.6452	−	13.7947i	−0.874765	−	0.584499i	0.0351095	−	0.999383i	$-0.488822\pi$
$557$	−20.6452	−	13.7947i	−0.874765	−	0.584499i	−0.909874	+	0.414884i	$0.863822\pi$
$558$	12.0799	+	27.9561i	0.511385	+	1.18347i
$559$	0.690658	+	0.690658i	0.0292117	+	0.0292117i
$560$	−2.11027	−	5.48939i	−0.0891751	−	0.231969i
$561$	20.0771	+	13.8180i	0.847656	+	0.583396i
$562$	10.8319	−	11.7980i	0.456917	−	0.497669i
$563$	−9.92024	−	6.62849i	−0.418088	−	0.279358i	0.328681	−	0.944441i	$-0.393396\pi$
$563$	−9.92024	−	6.62849i	−0.418088	−	0.279358i	−0.746769	+	0.665083i	$0.768396\pi$
$564$	9.79380	−	4.90469i	0.412394	−	0.206525i
$565$	72.2262	+	14.3667i	3.03858	+	0.604411i
$566$	−7.80961	−	32.0496i	−0.328262	−	1.34715i
$567$	−2.97346	−	1.42785i	−0.124874	−	0.0599642i
$568$	−10.7573	+	1.38444i	−0.451364	+	0.0580899i
$569$	4.82694	−	11.6533i	0.202356	−	0.488530i	−0.789826	−	0.613331i	$-0.789829\pi$
$569$	4.82694	−	11.6533i	0.202356	−	0.488530i	0.992182	+	0.124801i	$0.0398292\pi$
$570$	−65.9879	+	1.90886i	−2.76393	+	0.0799532i
$571$	8.09501	+	12.1150i	0.338765	+	0.506998i	0.961266	−	0.275621i	$-0.0888833\pi$
$571$	8.09501	+	12.1150i	0.338765	+	0.506998i	−0.622501	+	0.782619i	$0.713883\pi$
$572$	1.57659	+	18.4315i	0.0659203	+	0.770659i
$573$	13.5840	−	5.40915i	0.567481	−	0.225971i
$574$	−2.73829	−	0.999660i	−0.114294	−	0.0417250i
$575$	−16.2744			−0.678689
$576$	−5.43637	−	23.3762i	−0.226515	−	0.974008i
$577$	−20.9086			−0.870436			−0.435218	−	0.900325i	$-0.643329\pi$
$577$	−20.9086			−0.870436			−0.435218	+	0.900325i	$0.643329\pi$
$578$	7.97619	+	2.91184i	0.331766	+	0.121117i
$579$	22.9574	−	9.14164i	0.954078	−	0.379913i
$580$	−20.9659	+	1.79338i	−0.870563	+	0.0744659i
$581$	−0.605545	−	0.906263i	−0.0251223	−	0.0375981i
$582$	24.6940	−	0.714333i	1.02360	−	0.0296101i
$583$	8.61436	−	20.7969i	0.356770	−	0.861320i
$584$	−16.2799	+	21.0892i	−0.673665	+	0.872677i
$585$	18.0317	+	19.0514i	0.745518	+	0.787678i
$586$	−5.69657	−	23.3780i	−0.235323	−	0.965735i
$587$	−23.8495	−	4.74395i	−0.984372	−	0.195804i	−0.323439	−	0.946249i	$-0.604839\pi$
$587$	−23.8495	−	4.74395i	−0.984372	−	0.195804i	−0.660933	+	0.750445i	$0.729839\pi$
$588$	−10.6498	−	21.2658i	−0.439190	−	0.876985i
$589$	−40.0970	−	26.7920i	−1.65217	−	1.10394i
$590$	29.7488	−	32.4021i	1.22474	−	1.33397i
$591$	12.4836	+	8.59178i	0.513506	+	0.353419i
$592$	−13.8353	+	13.1421i	−0.568628	+	0.540138i
$593$	−11.8849	−	11.8849i	−0.488055	−	0.488055i	0.419637	−	0.907692i	$-0.362157\pi$
$593$	−11.8849	−	11.8849i	−0.488055	−	0.488055i	−0.907692	+	0.419637i	$0.862157\pi$
$594$	17.3616	+	25.9033i	0.712355	+	1.06283i
$595$	−4.05374	−	2.70862i	−0.166187	−	0.111043i
$596$	−7.05046	−	8.81962i	−0.288798	−	0.361266i
$597$	0.436515	−	31.7546i	0.0178654	−	1.29963i
$598$	3.86390	+	2.34979i	0.158007	+	0.0960902i
$599$	−15.2586	−	36.8376i	−0.623451	−	1.50514i	−0.847626	−	0.530595i	$-0.821969\pi$
$599$	−15.2586	−	36.8376i	−0.623451	−	1.50514i	0.224174	−	0.974549i	$-0.428031\pi$
$600$	26.3846	+	47.5091i	1.07715	+	1.93955i
$601$	−12.5646	+	30.3336i	−0.512520	+	1.23733i	0.429893	+	0.902880i	$0.358551\pi$
$601$	−12.5646	+	30.3336i	−0.512520	+	1.23733i	−0.942413	+	0.334452i	$0.891449\pi$
$602$	−0.137159	−	0.187442i	−0.00559019	−	0.00763956i
$603$	6.73176	−	9.49877i	0.274139	−	0.386820i
$604$	45.7396	+	14.5191i	1.86112	+	0.590772i
$605$	−5.48426	−	27.5712i	−0.222967	−	1.12093i
$606$	−0.0390124	−	0.0548817i	−0.00158477	−	0.00222942i
$607$	31.1174			1.26302			0.631509	−	0.775369i	$-0.282436\pi$
$607$	31.1174			1.26302			0.631509	+	0.775369i	$0.282436\pi$
$608$	27.3251	+	26.4128i	1.10818	+	1.07118i
$609$	1.63722	−	0.302330i	0.0663434	−	0.0122510i
$610$	27.7317	+	59.6214i	1.12282	+	2.41400i
$611$	6.75949	−	1.34455i	0.273460	−	0.0543945i
$612$	−14.8584	−	13.2318i	−0.600613	−	0.534866i
$613$	0.293500	+	0.439254i	0.0118544	+	0.0177413i	0.837349	−	0.546668i	$-0.184104\pi$
$613$	0.293500	+	0.439254i	0.0118544	+	0.0177413i	−0.825495	+	0.564409i	$0.809104\pi$
$614$	−1.25145	−	1.71023i	−0.0505044	−	0.0690194i
$615$	38.2188	+	8.14985i	1.54113	+	0.328634i
$616$	0.300454	−	4.38868i	0.0121057	−	0.176825i
$617$	31.0290	−	12.8526i	1.24918	−	0.517427i	0.342608	−	0.939478i	$-0.388690\pi$
$617$	31.0290	−	12.8526i	1.24918	−	0.517427i	0.906572	+	0.422051i	$0.138690\pi$
$618$	−1.05509	+	2.77128i	−0.0424420	+	0.111477i
$619$	−5.40007	−	1.07414i	−0.217047	−	0.0431734i	0.0853687	−	0.996349i	$-0.472793\pi$
$619$	−5.40007	−	1.07414i	−0.217047	−	0.0431734i	−0.302416	+	0.953176i	$0.597793\pi$
$620$	−6.38069	+	57.2372i	−0.256255	+	2.29870i
$621$	7.61678	+	0.314271i	0.305651	+	0.0126113i
$622$	1.47018	+	34.4377i	0.0589487	+	1.38083i
$623$	3.14041	−	3.14041i	0.125818	−	0.125818i
$624$	0.595360	−	15.0893i	0.0238335	−	0.604055i
$625$	−30.1144	−	30.1144i	−1.20458	−	1.20458i
$626$	−5.38025	+	5.86011i	−0.215038	+	0.234217i
$627$	−45.3560	−	19.5217i	−1.81134	−	0.779622i
$628$	25.5102	+	14.0597i	1.01797	+	0.561044i
$629$	−3.08618	+	15.5153i	−0.123054	+	0.618634i
$630$	−3.54382	−	5.13335i	−0.141189	−	0.204518i
$631$	−10.9902	−	26.5328i	−0.437514	−	1.05625i	−0.976805	−	0.214133i	$-0.931307\pi$
$631$	−10.9902	−	26.5328i	−0.437514	−	1.05625i	0.539290	−	0.842120i	$-0.318693\pi$
$632$	2.61971	−	9.66450i	0.104206	−	0.384433i
$633$	−4.53866	−	0.967834i	−0.180396	−	0.0384679i
$634$	4.02527	−	25.9853i	0.159864	−	1.03201i
$635$	48.1283	−	32.1583i	1.90991	−	1.27616i
$636$	−9.09012	+	15.9700i	−0.360447	+	0.633252i
$637$	−2.91948	−	14.6772i	−0.115674	−	0.581532i
$638$	−14.7851	−	5.39756i	−0.585348	−	0.213691i
$639$	−10.7452	+	4.10854i	−0.425074	+	0.162531i
$640$	12.9954	−	43.4858i	0.513687	−	1.71893i
$641$		−	8.16041i		−	0.322317i	−0.986929	−	0.161158i	$-0.948477\pi$
$641$		−	8.16041i		−	0.322317i	0.986929	−	0.161158i	$-0.0515230\pi$
$642$	−22.3829	−	3.78300i	−0.883384	−	0.149303i
$643$	−7.56760	+	1.50529i	−0.298437	+	0.0593628i	−0.342038	−	0.939686i	$-0.611117\pi$
$643$	−7.56760	+	1.50529i	−0.298437	+	0.0593628i	0.0436007	+	0.999049i	$0.486117\pi$
$644$	−0.822456	−	0.692841i	−0.0324093	−	0.0273018i
$645$	2.17121	+	2.23174i	0.0854915	+	0.0878746i
$646$	31.1339	+	4.82283i	1.22495	+	0.189752i
$647$	9.49957	+	3.93485i	0.373466	+	0.154695i	0.561518	−	0.827464i	$-0.310217\pi$
$647$	9.49957	+	3.93485i	0.373466	+	0.154695i	−0.188052	+	0.982159i	$0.560217\pi$
$648$	−11.4312	−	22.7449i	−0.449059	−	0.893502i
$649$	30.3975	−	12.5911i	1.19321	−	0.494242i
$650$	8.09521	+	33.2217i	0.317520	+	1.30306i
$651$	0.0626328	−	4.55627i	0.00245477	−	0.178574i
$652$	−2.04277	+	3.70645i	−0.0800012	+	0.145156i
$653$	−3.56357	+	5.33326i	−0.139453	+	0.208707i	−0.894622	−	0.446824i	$-0.852555\pi$
$653$	−3.56357	+	5.33326i	−0.139453	+	0.208707i	0.755169	+	0.655531i	$0.227555\pi$
$654$	7.29903	+	4.57744i	0.285415	+	0.178992i
$655$	−43.2293	+	43.2293i	−1.68911	+	1.68911i
$656$	−12.0138	−	19.0200i	−0.469060	−	0.742608i
$657$	−11.5274	+	25.7998i	−0.449726	+	1.00655i
$658$	−1.63738	+	0.0699013i	−0.0638318	+	0.00272504i
$659$	−3.09503	+	4.63204i	−0.120565	+	0.180439i	−0.886843	−	0.462071i	$-0.847107\pi$
$659$	−3.09503	+	4.63204i	−0.120565	+	0.180439i	0.766278	+	0.642509i	$0.222107\pi$
$660$	4.21776	+	58.8195i	0.164176	+	2.28955i
$661$	0.0949033	−	0.477111i	0.00369131	−	0.0185575i	−0.978896	−	0.204360i	$-0.934489\pi$
$661$	0.0949033	−	0.477111i	0.00369131	−	0.0185575i	0.982587	+	0.185803i	$0.0594886\pi$
$662$	10.8755	+	6.61382i	0.422688	+	0.257053i
$663$	−6.81133	−	10.5036i	−0.264530	−	0.407926i
$664$	0.574521	−	8.39191i	0.0222957	−	0.325669i
$665$	9.12561	+	3.77995i	0.353876	+	0.146580i
$666$	−10.9880	+	16.9974i	−0.425775	+	0.658637i
$667$	−3.19930	+	2.13771i	−0.123877	+	0.0827723i
$668$	−6.85681	+	3.55257i	−0.265298	+	0.137453i
$669$	−4.17989	+	1.66443i	−0.161604	+	0.0643506i
$670$	19.9628	−	9.28529i	0.771231	−	0.358722i
$671$			49.1842i			1.89874i
$672$	−0.689186	+	3.52422i	−0.0265859	+	0.135950i
$673$		−	29.3484i		−	1.13130i	−0.824646	−	0.565649i	$-0.808626\pi$
$673$		−	29.3484i		−	1.13130i	0.824646	−	0.565649i	$-0.191374\pi$
$674$	−5.65837	−	12.1651i	−0.217952	−	0.468584i
$675$	39.0431	+	42.4036i	1.50277	+	1.63211i
$676$	−4.99159	+	15.7250i	−0.191984	+	0.604810i
$677$	−2.15349	+	1.43892i	−0.0827654	+	0.0553021i	−0.596264	−	0.802788i	$-0.703349\pi$
$677$	−2.15349	+	1.43892i	−0.0827654	+	0.0553021i	0.513499	+	0.858090i	$0.328349\pi$
$678$	−32.7015	−	30.8627i	−1.25589	−	1.18528i
$679$	−3.41499	−	1.41454i	−0.131055	−	0.0542849i
$680$	−11.9907	−	35.6633i	−0.459820	−	1.36763i
$681$	8.20308	−	5.31950i	0.314343	−	0.203844i
$682$	−22.3833	+	36.8062i	−0.857102	+	1.40938i
$683$	−6.25649	+	31.4535i	−0.239398	+	1.20353i	0.654779	+	0.755821i	$0.272762\pi$
$683$	−6.25649	+	31.4535i	−0.239398	+	1.20353i	−0.894177	+	0.447714i	$0.852238\pi$
$684$	34.7544	+	20.4197i	1.32887	+	0.780767i
$685$	−0.0829571	+	0.124154i	−0.00316963	+	0.00474369i
$686$	0.306530	+	7.18021i	0.0117034	+	0.274142i
$687$	−7.42921	−	5.11313i	−0.283442	−	0.195078i
$688$	0.0460429	−	1.79188i	0.00175537	−	0.0683148i
$689$	−8.17575	+	8.17575i	−0.311471	+	0.311471i
$690$	12.2132	+	7.65928i	0.464950	+	0.291584i
$691$	−24.0652	+	36.0161i	−0.915482	+	1.37012i	0.0134670	+	0.999909i	$0.495713\pi$
$691$	−24.0652	+	36.0161i	−0.915482	+	1.37012i	−0.928949	+	0.370207i	$0.879287\pi$
$692$	10.9475	+	37.8317i	0.416161	+	1.43815i
$693$	−0.784118	−	4.59943i	−0.0297862	−	0.174718i
$694$	10.1706	−	2.47829i	0.386070	−	0.0940747i
$695$	−14.2139	+	5.88760i	−0.539165	+	0.223330i
$696$	11.4273	+	5.87386i	0.433152	+	0.222648i
$697$	−17.2300	−	7.13691i	−0.652634	−	0.270330i
$698$	6.01050	−	38.8009i	0.227501	−	1.46864i
$699$	−33.8134	+	32.8963i	−1.27894	+	1.24425i
$700$	−0.692990	−	8.10157i	−0.0261925	−	0.306211i
$701$	−44.5050	+	8.85259i	−1.68093	+	0.334358i	−0.941021	−	0.338349i	$-0.890132\pi$
$701$	−44.5050	+	8.85259i	−1.68093	+	0.334358i	−0.739909	+	0.672707i	$0.765132\pi$
$702$	−3.14721	−	15.7048i	−0.118784	−	0.592741i
$703$		−	32.0496i		−	1.20877i
$704$	22.5315	−	25.3932i	0.849189	−	0.957041i
$705$	21.6048	−	3.98957i	0.813685	−	0.150256i
$706$	7.88142	−	21.5890i	0.296621	−	0.812512i
$707$	0.00196551	+	0.00988131i	7.39208e−5	+	0.000371625i
$708$	−25.9005	+	7.11058i	−0.973399	+	0.267232i
$709$	−3.89531	+	2.60276i	−0.146291	+	0.0977487i	−0.626562	−	0.779372i	$-0.715538\pi$
$709$	−3.89531	+	2.60276i	−0.146291	+	0.0977487i	0.480271	+	0.877120i	$0.340538\pi$
$710$	−21.4984	−	3.33024i	−0.806822	−	0.124982i
$711$	0.291939	−	10.6167i	0.0109486	−	0.398156i
$712$	33.9940	−	4.37497i	1.27398	−	0.163959i
$713$	4.03006	+	9.72942i	0.150927	+	0.364370i
$714$	1.21827	+	2.71623i	0.0455926	+	0.101652i
$715$	−7.23880	+	36.3919i	−0.270716	+	1.36098i
$716$	−1.60427	−	5.54395i	−0.0599545	−	0.207187i
$717$	16.5398	−	38.4280i	0.617691	−	1.43512i
$718$	−33.2813	−	30.5561i	−1.24205	−	1.14034i
$719$	−25.9326	−	25.9326i	−0.967123	−	0.967123i	0.0323536	−	0.999476i	$-0.489700\pi$
$719$	−25.9326	−	25.9326i	−0.967123	−	0.967123i	−0.999476	+	0.0323536i	$0.989700\pi$
$720$	2.55888	−	48.0711i	0.0953639	−	1.79150i
$721$	0.313732	−	0.313732i	0.0116840	−	0.0116840i
$722$	−36.9256	+	1.57639i	−1.37423	+	0.0586671i
$723$	−28.8666	−	12.4245i	−1.07356	−	0.462072i
$724$	0.544717	+	0.681403i	0.0202443	+	0.0253241i
$725$	−28.5345	−	5.67586i	−1.05974	−	0.210796i
$726$	−6.10742	+	16.0416i	−0.226668	+	0.595359i
$727$	−0.0273404	+	0.0113248i	−0.00101400	+	0.000420013i	−0.383190	−	0.923669i	$-0.625175\pi$
$727$	−0.0273404	+	0.0113248i	−0.00101400	+	0.000420013i	0.382176	+	0.924089i	$0.375175\pi$
$728$	−1.00522	+	2.02355i	−0.0372561	+	0.0749978i
$729$	−17.4542	−	20.5998i	−0.646452	−	0.762955i
$730$	−43.1255	+	31.5568i	−1.59615	+	1.16797i
$731$	−0.825556	−	1.23553i	−0.0305343	−	0.0456978i
$732$	4.99638	−	39.8382i	0.184672	−	1.47246i
$733$	43.1730	−	8.58763i	1.59463	−	0.317192i	0.683703	−	0.729760i	$-0.260368\pi$
$733$	43.1730	−	8.58763i	1.59463	−	0.317192i	0.910926	+	0.412569i	$0.135368\pi$
$734$	−29.3806	+	13.6658i	−1.08446	+	0.504413i
$735$	−8.66274	−	46.9116i	−0.319530	−	1.73036i
$736$	−1.75702	−	8.11103i	−0.0647646	−	0.298977i
$737$	16.4682			0.606612
$738$	−17.1265	−	16.6144i	−0.630434	−	0.611586i
$739$	4.79179	+	24.0900i	0.176269	+	0.886164i	0.963131	+	0.269034i	$0.0867045\pi$
$739$	4.79179	+	24.0900i	0.176269	+	0.886164i	−0.786862	+	0.617129i	$0.788295\pi$
$740$	−33.9846	+	17.6077i	−1.24930	+	0.647272i
$741$	17.6861	+	18.1791i	0.649715	+	0.667827i
$742$	2.21886	−	1.62364i	0.0814570	−	0.0596056i
$743$	−4.64304	+	11.2093i	−0.170336	+	0.411229i	−0.985877	−	0.167471i	$-0.946440\pi$
$743$	−4.64304	+	11.2093i	−0.170336	+	0.411229i	0.815540	+	0.578700i	$0.196440\pi$
$744$	21.8690	−	27.5385i	0.801757	−	1.00961i
$745$	−8.66709	−	20.9242i	−0.317537	−	0.766603i
$746$	3.37319	−	5.54672i	0.123501	−	0.203080i
$747$	−1.49937	−	8.79490i	−0.0548591	−	0.321789i
$748$	3.11803	−	27.9699i	0.114006	−	1.02268i
$749$	2.82410	+	1.88701i	0.103191	+	0.0689497i
$750$	13.3733	+	58.3585i	0.488325	+	2.13095i
$751$	−5.26705	−	5.26705i	−0.192197	−	0.192197i	0.604448	−	0.796645i	$-0.293394\pi$
$751$	−5.26705	−	5.26705i	−0.192197	−	0.192197i	−0.796645	+	0.604448i	$0.793394\pi$
$752$	−10.3323	−	7.29454i	−0.376779	−	0.266004i
$753$	−4.71754	+	6.85443i	−0.171917	+	0.249789i
$754$	5.95520	+	5.46755i	0.216876	+	0.199117i
$755$	80.0336	+	53.4767i	2.91272	+	1.94622i
$756$	0.167887	+	3.80510i	0.00610600	+	0.138390i
$757$	−38.9154	−	7.74076i	−1.41441	−	0.281343i	−0.572030	−	0.820233i	$-0.693844\pi$
$757$	−38.9154	−	7.74076i	−1.41441	−	0.281343i	−0.842376	+	0.538890i	$0.818844\pi$
$758$	37.9827	−	9.25533i	1.37959	−	0.336169i
$759$	5.86701	+	9.04738i	0.212959	+	0.328399i
$760$	37.9221	+	66.1259i	1.37558	+	2.39864i
$761$	5.85971	−	14.1466i	0.212414	−	0.512813i	−0.781379	−	0.624057i	$-0.785483\pi$
$761$	5.85971	−	14.1466i	0.212414	−	0.512813i	0.993793	+	0.111244i	$0.0354834\pi$
$762$	−35.3289	+	1.02197i	−1.27983	+	0.0370222i
$763$	−0.716187	−	1.07185i	−0.0259277	−	0.0388035i
$764$	−12.9123	−	10.8774i	−0.467152	−	0.393531i
$765$	−21.2509	−	33.7787i	−0.768329	−	1.22127i
$766$	0.942267	−	2.58108i	0.0340455	−	0.0932582i
$767$	−16.8998			−0.610217
$768$	−20.8297	+	18.2791i	−0.751626	+	0.659590i
$769$	−31.9264			−1.15129			−0.575647	−	0.817698i	$-0.695250\pi$
$769$	−31.9264			−1.15129			−0.575647	+	0.817698i	$0.695250\pi$
$770$	3.02581	−	8.28836i	0.109043	−	0.298692i
$771$	6.27195	+	15.7508i	0.225879	+	0.567250i
$772$	−21.8222	−	18.3832i	−0.785399	−	0.661624i
$773$	−16.1121	−	24.1135i	−0.579512	−	0.867301i	0.419673	−	0.907675i	$-0.362145\pi$
$773$	−16.1121	−	24.1135i	−0.579512	−	0.867301i	−0.999185	+	0.0403748i	$0.987145\pi$
$774$	−0.399156	−	1.85883i	−0.0143474	−	0.0668142i
$775$	−30.4718	+	73.5655i	−1.09458	+	2.64255i
$776$	−14.1912	−	24.7457i	−0.509436	−	0.888318i
$777$	2.54087	−	1.64769i	0.0911533	−	0.0591107i
$778$	−31.3532	+	7.63991i	−1.12407	+	0.273904i
$779$	37.0580	+	7.37130i	1.32774	+	0.264104i
$780$	9.56016	−	28.7414i	0.342308	−	1.02911i
$781$	−13.5300	−	9.04044i	−0.484141	−	0.323493i
$782$	−5.06798	−	4.65298i	−0.181230	−	0.166390i
$783$	13.2452	+	3.20745i	0.473344	+	0.114625i
$784$	−15.8390	+	22.4350i	−0.565678	+	0.801248i
$785$	41.3128	+	41.3128i	1.47452	+	1.47452i
$786$	36.3863	−	8.33821i	1.29785	−	0.297414i
$787$	31.4237	+	20.9967i	1.12013	+	0.748450i	0.970694	−	0.240321i	$-0.0772526\pi$
$787$	31.4237	+	20.9967i	1.12013	+	0.748450i	0.149441	+	0.988771i	$0.452253\pi$
$788$	1.93873	−	17.3912i	0.0690645	−	0.619535i
$789$	13.0910	+	0.179955i	0.466051	+	0.00640658i
$790$	10.4360	−	17.1605i	0.371295	−	0.610542i
$791$	2.57466	+	6.21578i	0.0915444	+	0.221008i
$792$	16.8998	−	31.7952i	0.600509	−	1.12979i
$793$	9.66773	−	23.3400i	0.343311	−	0.828826i
$794$	32.6500	−	23.8914i	1.15871	−	0.847875i
$795$	−26.4185	+	25.7020i	−0.936966	+	0.911556i
$796$	−32.5599	+	16.8696i	−1.15406	+	0.597926i
$797$	1.15789	+	5.82109i	0.0410144	+	0.206194i	0.995859	−	0.0909127i	$-0.0289784\pi$
$797$	1.15789	+	5.82109i	0.0410144	+	0.206194i	−0.954844	+	0.297106i	$0.903978\pi$
$798$	−3.49437	−	4.91579i	−0.123699	−	0.174017i
$799$	−10.4850			−0.370933
$800$	33.9719	−	52.7598i	1.20109	−	1.86534i
$801$	33.9559	−	12.9834i	1.19977	−	0.458745i
$802$	−40.3704	+	18.7774i	−1.42553	+	0.663054i
$803$	−39.2031	+	7.79798i	−1.38345	+	0.275185i
$804$	−13.3389	−	1.67292i	−0.470426	−	0.0589993i
$805$	−1.19837	−	1.79349i	−0.0422371	−	0.0632123i
$806$	17.8565	−	13.0664i	0.628969	−	0.460243i
$807$	−8.57410	+	40.2083i	−0.301823	+	1.41540i
$808$	−0.0345910	+	0.0696330i	−0.00121691	+	0.00244968i
$809$	5.17491	−	2.14352i	0.181940	−	0.0753621i	−0.289854	−	0.957071i	$-0.593607\pi$
$809$	5.17491	−	2.14352i	0.181940	−	0.0753621i	0.471794	+	0.881709i	$0.343607\pi$
$810$	−9.34359	−	50.1971i	−0.328300	−	1.76375i
$811$	1.22166	+	0.243003i	0.0428983	+	0.00853300i	0.216493	−	0.976284i	$-0.430538\pi$
$811$	1.22166	+	0.243003i	0.0428983	+	0.00853300i	−0.173595	+	0.984817i	$0.555538\pi$
$812$	−1.20041	−	1.50162i	−0.0421260	−	0.0526966i
$813$	16.6816	−	38.7573i	0.585048	−	1.35928i
$814$	−28.6033	+	1.22110i	−1.00254	+	0.0427995i
$815$	−6.00245	+	6.00245i	−0.210257	+	0.210257i
$816$	−5.36686	+	22.3383i	−0.187878	+	0.781997i
$817$	2.12877	+	2.12877i	0.0744764	+	0.0744764i
$818$	1.82225	+	1.67304i	0.0637137	+	0.0584964i
$819$	−0.531974	+	2.33675i	−0.0185887	+	0.0816526i
$820$	−12.5429	−	43.3452i	−0.438019	−	1.51368i
$821$	0.494489	−	2.48597i	0.0172578	−	0.0867608i	−0.971197	−	0.238280i	$-0.923416\pi$
$821$	0.494489	−	2.48597i	0.0172578	−	0.0867608i	0.988454	+	0.151519i	$0.0484165\pi$
$822$	0.0831901	−	0.0373120i	0.00290159	−	0.00130141i
$823$	10.4360	+	25.1947i	0.363776	+	0.878233i	0.994741	+	0.102422i	$0.0326592\pi$
$823$	10.4360	+	25.1947i	0.363776	+	0.878233i	−0.630965	+	0.775811i	$0.717341\pi$
$824$	3.39606	−	0.437068i	0.118307	−	0.0152260i
$825$	−17.0039	+	79.7402i	−0.592001	+	2.77620i
$826$	3.97135	+	0.615186i	0.138181	+	0.0214051i
$827$	29.4603	−	19.6847i	1.02444	−	0.684506i	0.0745862	−	0.997215i	$-0.476236\pi$
$827$	29.4603	−	19.6847i	1.02444	−	0.684506i	0.949849	+	0.312709i	$0.101236\pi$
$828$	−3.83308	−	7.92420i	−0.133209	−	0.275385i
$829$	8.97071	+	45.0988i	0.311566	+	1.56635i	0.746189	+	0.665734i	$0.231882\pi$
$829$	8.97071	+	45.0988i	0.311566	+	1.56635i	−0.434623	+	0.900613i	$0.643118\pi$
$830$	5.78587	−	15.8488i	0.200830	−	0.550119i
$831$	4.01114	+	21.7217i	0.139145	+	0.753517i
$832$	−15.6835	+	7.62128i	−0.543727	+	0.264220i
$833$			22.7666i			0.788817i
$834$	9.26278	+	1.56553i	0.320744	+	0.0542097i
$835$	−15.1921	+	3.02190i	−0.525744	+	0.104577i
$836$	4.85941	+	56.8102i	0.168066	+	1.96482i
$837$	15.6821	−	33.8419i	0.542053	−	1.16975i
$838$	−4.15272	+	26.8080i	−0.143453	+	0.926067i
$839$	6.79083	+	2.81286i	0.234446	+	0.0971106i	0.496813	−	0.867857i	$-0.334503\pi$
$839$	6.79083	+	2.81286i	0.234446	+	0.0971106i	−0.262368	+	0.964968i	$0.584503\pi$
$840$	−3.29282	+	6.40603i	−0.113613	+	0.221029i
$841$	20.4375	−	8.46549i	0.704742	−	0.291914i
$842$	−23.7446	+	5.78591i	−0.818294	+	0.199396i
$843$	−19.6141	−	0.269625i	−0.675545	−	0.00928639i
$844$	1.48953	+	5.14744i	0.0512719	+	0.177182i
$845$	−18.3851	+	27.5152i	−0.632465	+	0.946551i
$846$	−12.4703	−	4.94505i	−0.428738	−	0.170014i
$847$	1.81605	−	1.81605i	0.0624000	−	0.0624000i
$848$	21.2116	+	0.545038i	0.728408	+	0.0187167i
$849$	−22.9053	+	33.2806i	−0.786107	+	1.14219i
$850$	−2.21879	−	51.9733i	−0.0761038	−	1.78267i
$851$	−3.88837	+	5.81935i	−0.133292	+	0.199485i
$852$	10.0406	+	8.69703i	0.343987	+	0.297955i
$853$	1.37332	−	6.90412i	0.0470214	−	0.236393i	−0.950126	−	0.311865i	$-0.899046\pi$
$853$	1.37332	−	6.90412i	0.0470214	−	0.236393i	0.997148	+	0.0754721i	$0.0240464\pi$
$854$	−3.12148	+	5.13282i	−0.106815	+	0.175642i
$855$	55.5779	+	58.7210i	1.90073	+	2.00821i
$856$	8.35348	+	24.8454i	0.285516	+	0.849200i
$857$	35.7564	+	14.8108i	1.22141	+	0.505927i	0.897859	−	0.440283i	$-0.145122\pi$
$857$	35.7564	+	14.8108i	1.22141	+	0.505927i	0.323556	+	0.946209i	$0.395122\pi$
$858$	15.5505	−	16.4770i	0.530885	−	0.562514i
$859$	11.6542	−	7.78710i	0.397637	−	0.265692i	−0.340635	−	0.940196i	$-0.610642\pi$
$859$	11.6542	−	7.78710i	0.397637	−	0.265692i	0.738272	+	0.674503i	$0.235642\pi$
$860$	1.08778	−	3.42683i	0.0370929	−	0.116854i
$861$	1.32079	+	3.31690i	0.0450124	+	0.113040i
$862$	15.4080	+	33.1262i	0.524797	+	1.12828i
$863$		−	44.1433i		−	1.50266i	−0.659929	−	0.751328i	$-0.729413\pi$
$863$		−	44.1433i		−	1.50266i	0.659929	−	0.751328i	$-0.270587\pi$
$864$	−16.9185	+	24.0368i	−0.575578	+	0.817747i
$865$			78.9960i			2.68595i
$866$	−31.2221	+	14.5223i	−1.06097	+	0.493488i
$867$	−3.84724	−	9.66159i	−0.130659	−	0.328125i
$868$	−4.67181	+	2.42050i	−0.158572	+	0.0821573i
$869$	12.4912	−	8.34635i	0.423735	−	0.283131i
$870$	18.7427	+	17.6888i	0.635436	+	0.599706i
$871$	−7.81483	−	3.23701i	−0.264795	−	0.109682i
$872$	0.679493	−	9.92522i	0.0230106	−	0.336110i
$873$	−20.7984	−	21.9746i	−0.703920	−	0.743727i
$874$	11.9095	+	7.24263i	0.402844	+	0.244986i
$875$	1.74765	−	8.78604i	0.0590814	−	0.297022i
$876$	32.5459	−	2.33376i	1.09962	−	0.0788505i
$877$	−0.977656	+	1.46317i	−0.0330131	+	0.0494076i	−0.847609	−	0.530621i	$-0.821959\pi$
$877$	−0.977656	+	1.46317i	−0.0330131	+	0.0494076i	0.814596	+	0.580029i	$0.196959\pi$
$878$	−6.03126	+	0.257480i	−0.203545	+	0.00868952i
$879$	−16.7078	+	24.2759i	−0.563541	+	0.818806i
$880$	57.5706	−	36.3638i	1.94070	−	1.22582i
$881$	−7.29678	+	7.29678i	−0.245835	+	0.245835i	−0.819259	−	0.573424i	$-0.805615\pi$
$881$	−7.29678	+	7.29678i	−0.245835	+	0.245835i	0.573424	+	0.819259i	$0.305615\pi$
$882$	−10.7374	+	27.0774i	−0.361548	+	0.911742i
$883$	25.5601	−	38.2534i	0.860167	−	1.28733i	−0.0962591	−	0.995356i	$-0.530688\pi$
$883$	25.5601	−	38.2534i	0.860167	−	1.28733i	0.956426	−	0.291975i	$-0.0943123\pi$
$884$	−6.97744	+	12.6600i	−0.234677	+	0.425802i
$885$	−53.8682	−	0.740500i	−1.81076	−	0.0248916i
$886$	−7.91850	−	32.4965i	−0.266027	−	1.09174i
$887$	−47.1042	+	19.5112i	−1.58160	+	0.655122i	−0.988667	−	0.150127i	$-0.952032\pi$
$887$	−47.1042	+	19.5112i	−1.58160	+	0.655122i	−0.592937	+	0.805249i	$0.702032\pi$
$888$	23.2922	+	1.91660i	0.781634	+	0.0643169i
$889$	4.88572	+	2.02373i	0.163862	+	0.0678738i
$890$	67.9371	+	10.5239i	2.27726	+	0.352761i
$891$	9.49808	−	36.9918i	0.318198	−	1.23927i
$892$	3.97320	+	3.34704i	0.133033	+	0.112067i
$893$	20.8344	−	4.14422i	0.697196	−	0.138681i
$894$	−2.30459	+	13.6356i	−0.0770772	+	0.456044i
$895$		−	11.5763i		−	0.386952i
$896$	3.96295	−	1.22004i	0.132393	−	0.0407588i
$897$	−1.00577	−	5.44659i	−0.0335817	−	0.181856i
$898$	18.7794	+	6.85574i	0.626677	+	0.228779i
$899$	3.67281	+	18.4645i	0.122495	+	0.615825i
$900$	21.8733	−	62.8606i	0.729109	−	2.09535i
$901$	14.6257	−	9.77261i	0.487254	−	0.325573i
$902$	5.16674	−	33.3540i	0.172034	−	1.11057i
$903$	−0.0593261	+	0.278210i	−0.00197425	+	0.00925826i
$904$	−13.5839	+	50.1132i	−0.451795	+	1.66674i
$905$	0.669618	+	1.61660i	0.0222588	+	0.0537376i
$906$	−24.0525	−	53.6269i	−0.799090	−	1.78163i
$907$	8.70820	−	43.7791i	0.289151	−	1.45366i	−0.513952	−	0.857819i	$-0.671819\pi$
$907$	8.70820	−	43.7791i	0.289151	−	1.45366i	0.803103	−	0.595841i	$-0.203181\pi$
$908$	−9.88716	−	5.44922i	−0.328117	−	0.180839i
$909$	−0.0183059	+	0.0804105i	−0.000607169	+	0.00266705i
$910$	−3.06505	+	3.33842i	−0.101605	+	0.110667i
$911$	−23.1218	−	23.1218i	−0.766060	−	0.766060i	0.211351	−	0.977410i	$-0.432214\pi$
$911$	−23.1218	−	23.1218i	−0.766060	−	0.766060i	−0.977410	+	0.211351i	$0.932214\pi$
$912$	1.83504	−	46.5088i	0.0607643	−	1.54006i
$913$	8.92366	−	8.92366i	0.295330	−	0.295330i
$914$	0.927780	+	21.7325i	0.0306882	+	0.718847i
$915$	31.8386	−	73.9726i	1.05255	−	2.44546i
$916$	−1.15378	+	10.3498i	−0.0381218	+	0.341967i
$917$	−5.47805	−	1.08965i	−0.180901	−	0.0359835i
$918$	0.0347974	+	24.3675i	0.00114849	+	0.804249i
$919$	7.24727	−	3.00192i	0.239065	−	0.0990242i	−0.259934	−	0.965626i	$-0.583701\pi$
$919$	7.24727	−	3.00192i	0.239065	−	0.0990242i	0.499000	+	0.866602i	$0.333701\pi$
$920$	1.13698	−	16.6076i	0.0374850	−	0.547535i
$921$	−0.541296	+	2.53841i	−0.0178363	+	0.0836435i
$922$	18.9850	+	25.9449i	0.625238	+	0.854451i
$923$	4.64354	+	6.94954i	0.152844	+	0.228747i
$924$	−4.25406	+	3.30591i	−0.139948	+	0.108757i
$925$	−51.9026	+	10.3241i	−1.70655	+	0.339453i
$926$	−12.4315	−	26.7269i	−0.408524	−	0.878301i
$927$	3.39226	−	1.29706i	0.111416	−	0.0426012i
$928$	−0.251838	−	14.8341i	−0.00826699	−	0.486955i
$929$	−3.50530			−0.115005			−0.0575026	−	0.998345i	$-0.518314\pi$
$929$	−3.50530			−0.115005			−0.0575026	+	0.998345i	$0.518314\pi$
$930$	57.4902	−	40.8667i	1.88518	−	1.34007i
$931$	−8.99853	−	45.2387i	−0.294915	−	1.48264i
$932$	51.9204	+	16.4810i	1.70071	+	0.539855i
$933$	30.2586	−	29.4380i	0.990622	−	0.963756i
$934$	19.8896	+	27.1812i	0.650808	+	0.889395i
$935$	21.6023	−	52.1525i	0.706470	−	1.70557i
$936$	−14.2694	+	11.7663i	−0.466410	+	0.384594i
$937$	18.5415	+	44.7631i	0.605724	+	1.46235i	0.867608	+	0.497249i	$0.165656\pi$
$937$	18.5415	+	44.7631i	0.605724	+	1.46235i	−0.261884	+	0.965099i	$0.584344\pi$
$938$	1.71860	+	1.04515i	0.0561144	+	0.0341254i
$939$	9.74238	+	0.133924i	0.317931	+	0.00437044i
$940$	−15.8406	−	19.8155i	−0.516665	−	0.646311i
$941$	36.5079	+	24.3938i	1.19012	+	0.795215i	0.983091	−	0.183120i	$-0.0586196\pi$
$941$	36.5079	+	24.3938i	1.19012	+	0.795215i	0.207032	+	0.978334i	$0.433620\pi$
$942$	−7.96855	−	34.7731i	−0.259629	−	1.13297i
$943$	−5.83444	−	5.83444i	−0.189996	−	0.189996i
$944$	21.3595	+	22.4862i	0.695194	+	0.731863i
$945$	−1.79806	+	7.42509i	−0.0584909	+	0.241538i
$946$	1.81876	−	1.98098i	0.0591331	−	0.0644071i
$947$	−25.2311	−	16.8589i	−0.819900	−	0.547840i	0.0733990	−	0.997303i	$-0.476615\pi$
$947$	−25.2311	−	16.8589i	−0.819900	−	0.547840i	−0.893299	+	0.449463i	$0.851615\pi$
$948$	−10.9655	+	5.49146i	−0.356143	+	0.178354i
$949$	20.1363	+	4.00536i	0.653652	+	0.130019i
$950$	24.9514	+	102.397i	0.809530	+	3.32220i
$951$	−27.0208	+	17.5223i	−0.876209	+	0.568200i
$952$	2.10050	−	2.72103i	0.0680777	−	0.0881890i
$953$	7.37516	−	17.8052i	0.238905	−	0.576768i	−0.758265	−	0.651946i	$-0.773953\pi$
$953$	7.37516	−	17.8052i	0.238905	−	0.576768i	0.997170	+	0.0751787i	$0.0239527\pi$
$954$	22.0041	−	4.72506i	0.712409	−	0.152979i
$955$	−18.8141	−	28.1573i	−0.608811	−	0.911149i
$956$	−48.1327	+	4.11715i	−1.55672	+	0.133158i
$957$	7.13147	+	17.9093i	0.230528	+	0.578925i
$958$	−1.34679	−	0.491668i	−0.0435127	−	0.0158851i
$959$	−0.0136419			−0.000440519
$960$	−50.3251	+	23.6057i	−1.62423	+	0.761869i
$961$	20.5259			0.662127
$962$	13.8135	+	5.04285i	0.445365	+	0.162588i
$963$	14.8048	+	23.5325i	0.477078	+	0.758324i
$964$	3.09275	+	36.1566i	0.0996107	+	1.16452i
$965$	−31.7964	−	47.5867i	−1.02356	−	1.53187i
$966$	0.0380837	+	1.31653i	0.00122532	+	0.0423586i
$967$	4.18748	−	10.1095i	0.134660	−	0.325098i	−0.842137	−	0.539263i	$-0.818703\pi$
$967$	4.18748	−	10.1095i	0.134660	−	0.325098i	0.976798	+	0.214165i	$0.0687029\pi$
$968$	19.6581	−	2.52997i	0.631837	−	0.0813164i
$969$	−20.9942	−	32.3746i	−0.674430	−	1.04002i
$970$	−13.5460	−	55.5911i	−0.434936	−	1.78492i
$971$	34.2086	+	6.80451i	1.09781	+	0.218367i	0.710579	−	0.703618i	$-0.248433\pi$
$971$	34.2086	+	6.80451i	1.09781	+	0.218367i	0.387226	+	0.921985i	$0.373433\pi$
$972$	−11.4511	+	28.9978i	−0.367293	+	0.930105i
$973$	−1.16870	−	0.780903i	−0.0374669	−	0.0250346i
$974$	−26.2178	+	28.5562i	−0.840073	+	0.914999i
$975$	23.7429	−	34.4977i	0.760383	−	1.10481i
$976$	−43.2742	+	16.6357i	−1.38517	+	0.532497i
$977$	17.0570	+	17.0570i	0.545702	+	0.545702i	0.925195	−	0.379493i	$-0.123901\pi$
$977$	17.0570	+	17.0570i	0.545702	+	0.545702i	−0.379493	+	0.925195i	$0.623901\pi$
$978$	5.05228	−	1.15777i	0.161554	−	0.0370215i
$979$	42.7560	+	28.5687i	1.36649	+	0.913059i
$980$	−43.0264	+	34.3955i	−1.37443	+	1.09872i
$981$	−1.77332	−	10.4018i	−0.0566179	−	0.332105i
$982$	−18.0776	−	10.9937i	−0.576881	−	0.350824i
$983$	−13.6403	−	32.9306i	−0.435059	−	1.05032i	−0.977633	−	0.210317i	$-0.932550\pi$
$983$	−13.6403	−	32.9306i	−0.435059	−	1.05032i	0.542575	−	0.840008i	$-0.317450\pi$
$984$	−7.57323	+	26.4913i	−0.241426	+	0.844510i
$985$	13.4319	−	32.4275i	0.427976	−	1.03323i
$986$	−7.26309	−	9.92574i	−0.231304	−	0.316100i
$987$	1.39966	+	1.43868i	0.0445518	+	0.0457937i
$988$	8.86072	−	27.9140i	0.281897	−	0.888063i
$989$	−0.128259	−	0.644800i	−0.00407839	−	0.0205034i
$990$	50.2892	−	51.8390i	1.59830	−	1.64755i
$991$	−48.4738			−1.53982			−0.769911	−	0.638151i	$-0.779699\pi$
$991$	−48.4738			−1.53982			−0.769911	+	0.638151i	$0.779699\pi$
$992$	−39.9543	−	7.24464i	−1.26855	−	0.230017i
$993$	−2.83088	−	15.3302i	−0.0898354	−	0.486488i
$994$	−0.838226	−	1.80213i	−0.0265869	−	0.0571602i
$995$	−72.1404	+	14.3496i	−2.28701	+	0.454914i
$996$	−8.13450	+	6.32148i	−0.257752	+	0.200304i
$997$	−0.890075	−	1.33209i	−0.0281889	−	0.0421877i	0.817108	−	0.576485i	$-0.195576\pi$
$997$	−0.890075	−	1.33209i	−0.0281889	−	0.0421877i	−0.845296	+	0.534298i	$0.820576\pi$
$998$	−28.7064	−	39.2302i	−0.908686	−	1.24181i
$999$	24.4910	−	3.82962i	0.774859	−	0.121164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.107.12	✓	240
3.2	odd	2	inner	192.2.s.a.107.19	yes	240
4.3	odd	2		768.2.s.a.335.4		240
12.11	even	2		768.2.s.a.335.1		240
64.3	odd	16	inner	192.2.s.a.131.19	yes	240
64.61	even	16		768.2.s.a.431.1		240
192.125	odd	16		768.2.s.a.431.4		240
192.131	even	16	inner	192.2.s.a.131.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.12	✓	240	1.1	even	1	trivial
192.2.s.a.107.19	yes	240	3.2	odd	2	inner
192.2.s.a.131.12	yes	240	192.131	even	16	inner
192.2.s.a.131.19	yes	240	64.3	odd	16	inner
768.2.s.a.335.1		240	12.11	even	2
768.2.s.a.335.4		240	4.3	odd	2
768.2.s.a.431.1		240	64.61	even	16
768.2.s.a.431.4		240	192.125	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.484976 + 1.32846i) q^{2} +(1.60917 - 0.640769i) q^{3} +(-1.52960 - 1.28854i) q^{4} +(-2.22872 - 3.33552i) q^{5} +(0.0708277 + 2.44847i) q^{6} +(0.140254 - 0.338604i) q^{7} +(2.45359 - 1.40709i) q^{8} +(2.17883 - 2.06221i) q^{9} +O(q^{10})\)	\(q+(-0.484976 + 1.32846i) q^{2} +(1.60917 - 0.640769i) q^{3} +(-1.52960 - 1.28854i) q^{4} +(-2.22872 - 3.33552i) q^{5} +(0.0708277 + 2.44847i) q^{6} +(0.140254 - 0.338604i) q^{7} +(2.45359 - 1.40709i) q^{8} +(2.17883 - 2.06221i) q^{9} +(5.51197 - 1.34312i) q^{10} +(4.16199 + 0.827871i) q^{11} +(-3.28703 - 1.09336i) q^{12} +(-1.81231 - 1.21095i) q^{13} +(0.381801 + 0.350537i) q^{14} +(-5.72369 - 3.93931i) q^{15} +(0.679331 + 3.94189i) q^{16} +(2.34477 + 2.34477i) q^{17} +(1.68288 + 3.89460i) q^{18} +(-5.58598 - 3.73243i) q^{19} +(-0.888903 + 7.97380i) q^{20} +(0.00872547 - 0.634741i) q^{21} +(-3.11826 + 5.12753i) q^{22} +(0.561434 + 1.35542i) q^{23} +(3.04661 - 3.83643i) q^{24} +(-4.24507 + 10.2485i) q^{25} +(2.48762 - 1.82030i) q^{26} +(2.18470 - 4.71456i) q^{27} +(-0.650837 + 0.337204i) q^{28} +(0.511665 + 2.57231i) q^{29} +(8.00905 - 5.69320i) q^{30} +7.17816 q^{31} +(-5.56609 - 1.00926i) q^{32} +(7.22781 - 1.33469i) q^{33} +(-4.25209 + 1.97777i) q^{34} +(-1.44201 + 0.286833i) q^{35} +(-5.98997 + 0.346838i) q^{36} +(2.65038 + 3.96658i) q^{37} +(7.66744 - 5.61059i) q^{38} +(-3.69225 - 0.787342i) q^{39} +(-10.1618 - 5.04797i) q^{40} +(-5.19602 + 2.15226i) q^{41} +(0.838994 + 0.319425i) q^{42} +(-0.439507 - 0.0874234i) q^{43} +(-5.29942 - 6.62920i) q^{44} +(-11.7345 - 2.67144i) q^{45} +(-2.07290 + 0.0884939i) q^{46} +(-2.23583 + 2.23583i) q^{47} +(3.61900 + 5.90786i) q^{48} +(4.85477 + 4.85477i) q^{49} +(-11.5560 - 10.6097i) q^{50} +(5.27558 + 2.27067i) q^{51} +(1.21175 + 4.18749i) q^{52} +(1.03488 - 5.20272i) q^{53} +(5.20357 + 5.18873i) q^{54} +(-6.51454 - 15.7275i) q^{55} +(-0.132321 - 1.02815i) q^{56} +(-11.3804 - 2.42678i) q^{57} +(-3.66535 - 0.567786i) q^{58} +(6.44677 - 4.30759i) q^{59} +(3.67897 + 13.4008i) q^{60} +(2.26118 + 11.3677i) q^{61} +(-3.48123 + 9.53587i) q^{62} +(-0.392682 - 1.02699i) q^{63} +(4.04018 - 6.90485i) q^{64} +8.74387i q^{65} +(-1.73223 + 10.2491i) q^{66} +(3.80620 - 0.757101i) q^{67} +(-0.565223 - 6.60788i) q^{68} +(1.77195 + 1.82135i) q^{69} +(0.318294 - 2.05475i) q^{70} +(-3.54274 - 1.46745i) q^{71} +(2.44423 - 8.12562i) q^{72} +(-8.70231 + 3.60462i) q^{73} +(-6.55480 + 1.59722i) q^{74} +(-0.264094 + 19.2117i) q^{75} +(3.73490 + 12.9069i) q^{76} +(0.864058 - 1.29315i) q^{77} +(2.83660 - 4.52315i) q^{78} +(2.50332 - 2.50332i) q^{79} +(11.6342 - 11.0513i) q^{80} +(0.494594 - 8.98640i) q^{81} +(-0.339242 - 7.94648i) q^{82} +(1.65223 - 2.47273i) q^{83} +(-0.831235 + 0.959654i) q^{84} +(2.59519 - 13.0469i) q^{85} +(0.329289 - 0.541468i) q^{86} +(2.47161 + 3.81142i) q^{87} +(11.3767 - 3.82505i) q^{88} +(11.1954 + 4.63728i) q^{89} +(9.23987 - 14.2933i) q^{90} +(-0.664216 + 0.443815i) q^{91} +(0.887747 - 2.79668i) q^{92} +(11.5508 - 4.59954i) q^{93} +(-1.88588 - 4.05453i) q^{94} +26.9507i q^{95} +(-9.60347 + 1.94251i) q^{96} -10.0855i q^{97} +(-8.80379 + 4.09490i) q^{98} +(10.7755 - 6.77910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

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