LMFDB - Embedded newform 760.2.f.b.381.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [760,2,Mod(381,760)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("760.381"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			381.8
Character	$\chi$	$=$	760.381
Dual form			760.2.f.b.381.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25358 + 0.654621i) q^{2} +2.81164i q^{3} +(1.14294 - 1.64124i) q^{4} -1.00000i q^{5} +(-1.84056 - 3.52463i) q^{6} -3.31936 q^{7} +(-0.358379 + 2.80563i) q^{8} -4.90534 q^{9} +(0.654621 + 1.25358i) q^{10} +2.83466i q^{11} +(4.61460 + 3.21355i) q^{12} +5.28252i q^{13} +(4.16109 - 2.17292i) q^{14} +2.81164 q^{15} +(-1.38737 - 3.75169i) q^{16} +2.60669 q^{17} +(6.14926 - 3.21114i) q^{18} -1.00000i q^{19} +(-1.64124 - 1.14294i) q^{20} -9.33286i q^{21} +(-1.85563 - 3.55348i) q^{22} -8.40647 q^{23} +(-7.88844 - 1.00763i) q^{24} -1.00000 q^{25} +(-3.45805 - 6.62208i) q^{26} -5.35715i q^{27} +(-3.79383 + 5.44788i) q^{28} -9.95431i q^{29} +(-3.52463 + 1.84056i) q^{30} +5.25911 q^{31} +(4.19512 + 3.79486i) q^{32} -7.97005 q^{33} +(-3.26770 + 1.70640i) q^{34} +3.31936i q^{35} +(-5.60652 + 8.05087i) q^{36} -10.5281i q^{37} +(0.654621 + 1.25358i) q^{38} -14.8526 q^{39} +(2.80563 + 0.358379i) q^{40} -9.40558 q^{41} +(6.10949 + 11.6995i) q^{42} -2.39830i q^{43} +(4.65237 + 3.23985i) q^{44} +4.90534i q^{45} +(10.5382 - 5.50305i) q^{46} +0.543335 q^{47} +(10.5484 - 3.90079i) q^{48} +4.01815 q^{49} +(1.25358 - 0.654621i) q^{50} +7.32908i q^{51} +(8.66991 + 6.03762i) q^{52} +0.748858i q^{53} +(3.50690 + 6.71563i) q^{54} +2.83466 q^{55} +(1.18959 - 9.31290i) q^{56} +2.81164 q^{57} +(6.51630 + 12.4786i) q^{58} +12.0213i q^{59} +(3.21355 - 4.61460i) q^{60} -8.50410i q^{61} +(-6.59273 + 3.44272i) q^{62} +16.2826 q^{63} +(-7.74313 - 2.01096i) q^{64} +5.28252 q^{65} +(9.99112 - 5.21736i) q^{66} -5.01155i q^{67} +(2.97929 - 4.27822i) q^{68} -23.6360i q^{69} +(-2.17292 - 4.16109i) q^{70} -5.99873 q^{71} +(1.75797 - 13.7626i) q^{72} -8.46514 q^{73} +(6.89190 + 13.1978i) q^{74} -2.81164i q^{75} +(-1.64124 - 1.14294i) q^{76} -9.40925i q^{77} +(18.6189 - 9.72281i) q^{78} -3.62585 q^{79} +(-3.75169 + 1.38737i) q^{80} +0.346365 q^{81} +(11.7907 - 6.15709i) q^{82} +5.76753i q^{83} +(-15.3175 - 10.6669i) q^{84} -2.60669i q^{85} +(1.56998 + 3.00646i) q^{86} +27.9880 q^{87} +(-7.95300 - 1.01588i) q^{88} +0.348473 q^{89} +(-3.21114 - 6.14926i) q^{90} -17.5346i q^{91} +(-9.60810 + 13.7971i) q^{92} +14.7867i q^{93} +(-0.681115 + 0.355679i) q^{94} -1.00000 q^{95} +(-10.6698 + 11.7952i) q^{96} +1.47141 q^{97} +(-5.03709 + 2.63037i) q^{98} -13.9050i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.25358	+	0.654621i	−0.886417	+	0.462887i
$2$	−1.25358	+	0.654621i	−0.886417	+	0.462887i
$3$			2.81164i			1.62330i	0.584142	+	0.811652i	$0.301431\pi$
$3$			2.81164i			1.62330i	−0.584142	+	0.811652i	$0.698569\pi$
$4$	1.14294	−	1.64124i	0.571471	−	0.820622i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.84056	−	3.52463i	−0.751406	−	1.43892i
$7$	−3.31936			−1.25460			−0.627300	−	0.778778i	$-0.715840\pi$
$7$	−3.31936			−1.25460			−0.627300	+	0.778778i	$0.715840\pi$
$8$	−0.358379	+	2.80563i	−0.126706	+	0.991940i
$9$	−4.90534			−1.63511
$10$	0.654621	+	1.25358i	0.207009	+	0.396418i
$11$			2.83466i			0.854681i	0.904091	+	0.427341i	$0.140549\pi$
$11$			2.83466i			0.854681i	−0.904091	+	0.427341i	$0.859451\pi$
$12$	4.61460	+	3.21355i	1.33212	+	0.927671i
$13$			5.28252i			1.46511i	0.680709	+	0.732554i	$0.261672\pi$
$13$			5.28252i			1.46511i	−0.680709	+	0.732554i	$0.738328\pi$
$14$	4.16109	−	2.17292i	1.11210	−	0.580738i
$15$	2.81164			0.725963
$16$	−1.38737	−	3.75169i	−0.346842	−	0.937924i
$17$	2.60669			0.632215			0.316108	−	0.948723i	$-0.397624\pi$
$17$	2.60669			0.632215			0.316108	+	0.948723i	$0.397624\pi$
$18$	6.14926	−	3.21114i	1.44939	−	0.756874i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−1.64124	−	1.14294i	−0.366993	−	0.255570i
$21$		−	9.33286i		−	2.03660i
$22$	−1.85563	−	3.55348i	−0.395621	−	0.757604i
$23$	−8.40647			−1.75287			−0.876435	−	0.481521i	$-0.840085\pi$
$23$	−8.40647			−1.75287			−0.876435	+	0.481521i	$0.840085\pi$
$24$	−7.88844	−	1.00763i	−1.61022	−	0.205682i
$25$	−1.00000			−0.200000
$26$	−3.45805	−	6.62208i	−0.678180	−	1.29870i
$27$		−	5.35715i		−	1.03098i
$28$	−3.79383	+	5.44788i	−0.716967	+	1.02955i
$29$		−	9.95431i		−	1.84847i	−0.381826	−	0.924234i	$-0.624705\pi$
$29$		−	9.95431i		−	1.84847i	0.381826	−	0.924234i	$-0.375295\pi$
$30$	−3.52463	+	1.84056i	−0.643506	+	0.336039i
$31$	5.25911			0.944564			0.472282	−	0.881448i	$-0.343430\pi$
$31$	5.25911			0.944564			0.472282	+	0.881448i	$0.343430\pi$
$32$	4.19512	+	3.79486i	0.741600	+	0.670843i
$33$	−7.97005			−1.38741
$34$	−3.26770	+	1.70640i	−0.560406	+	0.292644i
$35$			3.31936i			0.561074i
$36$	−5.60652	+	8.05087i	−0.934420	+	1.34181i
$37$		−	10.5281i		−	1.73080i	−0.501078	−	0.865402i	$-0.667063\pi$
$37$		−	10.5281i		−	1.73080i	0.501078	−	0.865402i	$-0.332937\pi$
$38$	0.654621	+	1.25358i	0.106194	+	0.203358i
$39$	−14.8526			−2.37832
$40$	2.80563	+	0.358379i	0.443609	+	0.0566646i
$41$	−9.40558			−1.46890			−0.734452	−	0.678660i	$-0.762561\pi$
$41$	−9.40558			−1.46890			−0.734452	+	0.678660i	$0.762561\pi$
$42$	6.10949	+	11.6995i	0.942715	+	1.80527i
$43$		−	2.39830i		−	0.365737i	−0.983137	−	0.182868i	$-0.941462\pi$
$43$		−	2.39830i		−	0.365737i	0.983137	−	0.182868i	$-0.0585382\pi$
$44$	4.65237	+	3.23985i	0.701371	+	0.488425i
$45$			4.90534i			0.731245i
$46$	10.5382	−	5.50305i	1.55377	−	0.811381i
$47$	0.543335			0.0792535			0.0396268	−	0.999215i	$-0.487383\pi$
$47$	0.543335			0.0792535			0.0396268	+	0.999215i	$0.487383\pi$
$48$	10.5484	−	3.90079i	1.52253	−	0.563030i
$49$	4.01815			0.574022
$50$	1.25358	−	0.654621i	0.177283	−	0.0925774i
$51$			7.32908i			1.02628i
$52$	8.66991	+	6.03762i	1.20230	+	0.837267i
$53$			0.748858i			0.102863i	0.998677	+	0.0514317i	$0.0163785\pi$
$53$			0.748858i			0.102863i	−0.998677	+	0.0514317i	$0.983622\pi$
$54$	3.50690	+	6.71563i	0.477229	+	0.913882i
$55$	2.83466			0.382225
$56$	1.18959	−	9.31290i	0.158965	−	1.24449i
$57$	2.81164			0.372411
$58$	6.51630	+	12.4786i	0.855632	+	1.63851i
$59$			12.0213i			1.56505i	0.622622	+	0.782523i	$0.286067\pi$
$59$			12.0213i			1.56505i	−0.622622	+	0.782523i	$0.713933\pi$
$60$	3.21355	−	4.61460i	0.414867	−	0.595742i
$61$		−	8.50410i		−	1.08884i	−0.838813	−	0.544419i	$-0.816750\pi$
$61$		−	8.50410i		−	1.08884i	0.838813	−	0.544419i	$-0.183250\pi$
$62$	−6.59273	+	3.44272i	−0.837277	+	0.437226i
$63$	16.2826			2.05141
$64$	−7.74313	−	2.01096i	−0.967891	−	0.251369i
$65$	5.28252			0.655216
$66$	9.99112	−	5.21736i	1.22982	−	0.642213i
$67$		−	5.01155i		−	0.612258i	−0.951990	−	0.306129i	$-0.900966\pi$
$67$		−	5.01155i		−	0.612258i	0.951990	−	0.306129i	$-0.0990338\pi$
$68$	2.97929	−	4.27822i	0.361293	−	0.518810i
$69$		−	23.6360i		−	2.84544i
$70$	−2.17292	−	4.16109i	−0.259714	−	0.497346i
$71$	−5.99873			−0.711918			−0.355959	−	0.934502i	$-0.615846\pi$
$71$	−5.99873			−0.711918			−0.355959	+	0.934502i	$0.615846\pi$
$72$	1.75797	−	13.7626i	0.207179	−	1.62194i
$73$	−8.46514			−0.990770			−0.495385	−	0.868673i	$-0.664973\pi$
$73$	−8.46514			−0.990770			−0.495385	+	0.868673i	$0.664973\pi$
$74$	6.89190	+	13.1978i	0.801167	+	1.53422i
$75$		−	2.81164i		−	0.324661i
$76$	−1.64124	−	1.14294i	−0.188264	−	0.131104i
$77$		−	9.40925i		−	1.07228i
$78$	18.6189	−	9.72281i	2.10818	−	1.10089i
$79$	−3.62585			−0.407940			−0.203970	−	0.978977i	$-0.565384\pi$
$79$	−3.62585			−0.407940			−0.203970	+	0.978977i	$0.565384\pi$
$80$	−3.75169	+	1.38737i	−0.419452	+	0.155113i
$81$	0.346365			0.0384850
$82$	11.7907	−	6.15709i	1.30206	−	0.679937i
$83$			5.76753i			0.633069i	0.948581	+	0.316534i	$0.102519\pi$
$83$			5.76753i			0.633069i	−0.948581	+	0.316534i	$0.897481\pi$
$84$	−15.3175	−	10.6669i	−1.67128	−	1.16386i
$85$		−	2.60669i		−	0.282735i
$86$	1.56998	+	3.00646i	0.169295	+	0.324195i
$87$	27.9880			3.00062
$88$	−7.95300	−	1.01588i	−0.847793	−	0.108293i
$89$	0.348473			0.0369381			0.0184690	−	0.999829i	$-0.494121\pi$
$89$	0.348473			0.0369381			0.0184690	+	0.999829i	$0.494121\pi$
$90$	−3.21114	−	6.14926i	−0.338484	−	0.648189i
$91$		−	17.5346i		−	1.83813i
$92$	−9.60810	+	13.7971i	−1.00171	+	1.43844i
$93$			14.7867i			1.53331i
$94$	−0.681115	+	0.355679i	−0.0702517	+	0.0366854i
$95$	−1.00000			−0.102598
$96$	−10.6698	+	11.7952i	−1.08898	+	1.20384i
$97$	1.47141			0.149399			0.0746996	−	0.997206i	$-0.476200\pi$
$97$	1.47141			0.149399			0.0746996	+	0.997206i	$0.476200\pi$
$98$	−5.03709	+	2.63037i	−0.508823	+	0.265707i
$99$		−	13.9050i		−	1.39750i
$100$	−1.14294	+	1.64124i	−0.114294	+	0.164124i
$101$			19.4328i			1.93364i	0.255461	+	0.966819i	$0.417773\pi$
$101$			19.4328i			1.93364i	−0.255461	+	0.966819i	$0.582227\pi$
$102$	−4.79778	−	9.18762i	−0.475051	−	0.909710i
$103$	0.305852			0.0301365			0.0150683	−	0.999886i	$-0.495203\pi$
$103$	0.305852			0.0301365			0.0150683	+	0.999886i	$0.495203\pi$
$104$	−14.8208	−	1.89314i	−1.45330	−	0.185638i
$105$	−9.33286			−0.910794
$106$	−0.490218	−	0.938755i	−0.0476142	−	0.0911800i
$107$			15.4289i			1.49157i	0.666186	+	0.745786i	$0.267926\pi$
$107$			15.4289i			1.49157i	−0.666186	+	0.745786i	$0.732074\pi$
$108$	−8.79239	−	6.12291i	−0.846048	−	0.589177i
$109$			1.73243i			0.165937i	0.996552	+	0.0829685i	$0.0264401\pi$
$109$			1.73243i			0.165937i	−0.996552	+	0.0829685i	$0.973560\pi$
$110$	−3.55348	+	1.85563i	−0.338811	+	0.176927i
$111$	29.6012			2.80962
$112$	4.60518	+	12.4532i	0.435148	+	1.17672i
$113$	10.1330			0.953228			0.476614	−	0.879113i	$-0.341864\pi$
$113$	10.1330			0.953228			0.476614	+	0.879113i	$0.341864\pi$
$114$	−3.52463	+	1.84056i	−0.330112	+	0.172384i
$115$			8.40647i			0.783907i
$116$	−16.3375	−	11.3772i	−1.51689	−	1.05635i
$117$		−	25.9126i		−	2.39562i
$118$	−7.86943	−	15.0698i	−0.724440	−	1.38728i
$119$	−8.65254			−0.793177
$120$	−1.00763	+	7.88844i	−0.0919839	+	0.720112i
$121$	2.96472			0.269520
$122$	5.56697	+	10.6606i	0.504010	+	0.965166i
$123$		−	26.4451i		−	2.38448i
$124$	6.01085	−	8.63148i	0.539791	−	0.775130i
$125$			1.00000i			0.0894427i
$126$	−20.4116	+	10.6589i	−1.81841	+	0.949574i
$127$	−19.0142			−1.68724			−0.843620	−	0.536941i	$-0.819580\pi$
$127$	−19.0142			−1.68724			−0.843620	+	0.536941i	$0.819580\pi$
$128$	11.0231	−	2.54792i	0.974311	−	0.225206i
$129$	6.74316			0.593702
$130$	−6.62208	+	3.45805i	−0.580795	+	0.303291i
$131$		−	4.68843i		−	0.409630i	−0.978801	−	0.204815i	$-0.934341\pi$
$131$		−	4.68843i		−	0.409630i	0.978801	−	0.204815i	$-0.0656593\pi$
$132$	−9.10930	+	13.0808i	−0.792863	+	1.13854i
$133$			3.31936i			0.287825i
$134$	3.28066	+	6.28239i	0.283406	+	0.542716i
$135$	−5.35715			−0.461070
$136$	−0.934182	+	7.31341i	−0.0801054	+	0.627120i
$137$	−9.29846			−0.794421			−0.397211	−	0.917728i	$-0.630022\pi$
$137$	−9.29846			−0.794421			−0.397211	+	0.917728i	$0.630022\pi$
$138$	15.4726	+	29.6297i	1.31712	+	2.52225i
$139$			6.15072i			0.521697i	0.965380	+	0.260849i	$0.0840023\pi$
$139$			6.15072i			0.521697i	−0.965380	+	0.260849i	$0.915998\pi$
$140$	5.44788	+	3.79383i	0.460430	+	0.320638i
$141$			1.52766i			0.128653i
$142$	7.51990	−	3.92690i	0.631056	−	0.329538i
$143$	−14.9741			−1.25220
$144$	6.80552	+	18.4033i	0.567127	+	1.53361i
$145$	−9.95431			−0.826660
$146$	10.6118	−	5.54146i	0.878236	−	0.458615i
$147$			11.2976i			0.931811i
$148$	−17.2791	−	12.0330i	−1.42034	−	0.989104i
$149$			21.3894i			1.75228i	0.482053	+	0.876142i	$0.339891\pi$
$149$			21.3894i			1.75228i	−0.482053	+	0.876142i	$0.660109\pi$
$150$	1.84056	+	3.52463i	0.150281	+	0.287785i
$151$	8.98581			0.731255			0.365627	−	0.930761i	$-0.380854\pi$
$151$	8.98581			0.731255			0.365627	+	0.930761i	$0.380854\pi$
$152$	2.80563	+	0.358379i	0.227567	+	0.0290683i
$153$	−12.7867			−1.03374
$154$	6.15949	+	11.7953i	0.496346	+	0.950490i
$155$		−	5.25911i		−	0.422422i
$156$	−16.9756	+	24.3767i	−1.35914	+	1.95170i
$157$			12.7403i			1.01678i	0.861125	+	0.508392i	$0.169760\pi$
$157$			12.7403i			1.01678i	−0.861125	+	0.508392i	$0.830240\pi$
$158$	4.54530	−	2.37356i	0.361605	−	0.188830i
$159$	−2.10552			−0.166979
$160$	3.79486	−	4.19512i	0.300010	−	0.331653i
$161$	27.9041			2.19915
$162$	−0.434197	+	0.226738i	−0.0341138	+	0.0178142i
$163$		−	14.6737i		−	1.14933i	−0.818389	−	0.574665i	$-0.805132\pi$
$163$		−	14.6737i		−	1.14933i	0.818389	−	0.574665i	$-0.194868\pi$
$164$	−10.7500	+	15.4369i	−0.839436	+	1.20542i
$165$			7.97005i			0.620467i
$166$	−3.77555	−	7.23008i	−0.293039	−	0.561163i
$167$	−5.47101			−0.423360			−0.211680	−	0.977339i	$-0.567893\pi$
$167$	−5.47101			−0.423360			−0.211680	+	0.977339i	$0.567893\pi$
$168$	26.1846	+	3.34470i	2.02018	+	0.258049i
$169$	−14.9050			−1.14654
$170$	1.70640	+	3.26770i	0.130875	+	0.250621i
$171$			4.90534i			0.375121i
$172$	−3.93619	−	2.74111i	−0.300132	−	0.209008i
$173$		−	7.26036i		−	0.551995i	−0.961158	−	0.275998i	$-0.910992\pi$
$173$		−	7.26036i		−	0.551995i	0.961158	−	0.275998i	$-0.0890082\pi$
$174$	−35.0852	+	18.3215i	−2.65981	+	1.38895i
$175$	3.31936			0.250920
$176$	10.6348	−	3.93271i	0.801626	−	0.296440i
$177$	−33.7997			−2.54054
$178$	−0.436840	+	0.228118i	−0.0327426	+	0.0170982i
$179$		−	2.86114i		−	0.213852i	−0.994267	−	0.106926i	$-0.965899\pi$
$179$		−	2.86114i		−	0.213852i	0.994267	−	0.106926i	$-0.0341007\pi$
$180$	8.05087	+	5.60652i	0.600076	+	0.417885i
$181$		−	2.83734i		−	0.210898i	−0.994425	−	0.105449i	$-0.966372\pi$
$181$		−	2.83734i		−	0.210898i	0.994425	−	0.105449i	$-0.0336280\pi$
$182$	11.4785	+	21.9811i	0.850845	+	1.62935i
$183$	23.9105			1.76752
$184$	3.01270	−	23.5854i	0.222099	−	1.73874i
$185$	−10.5281			−0.774039
$186$	−9.67972	−	18.5364i	−0.709751	−	1.35916i
$187$			7.38907i			0.540342i
$188$	0.621000	−	0.891745i	0.0452911	−	0.0650372i
$189$			17.7823i			1.29347i
$190$	1.25358	−	0.654621i	0.0909445	−	0.0474912i
$191$	−13.1874			−0.954210			−0.477105	−	0.878846i	$-0.658314\pi$
$191$	−13.1874			−0.954210			−0.477105	+	0.878846i	$0.658314\pi$
$192$	5.65409	−	21.7709i	0.408049	−	1.57118i
$193$	−1.50682			−0.108463			−0.0542315	−	0.998528i	$-0.517271\pi$
$193$	−1.50682			−0.108463			−0.0542315	+	0.998528i	$0.517271\pi$
$194$	−1.84454	+	0.963218i	−0.132430	+	0.0691550i
$195$			14.8526i			1.06362i
$196$	4.59251	−	6.59477i	0.328037	−	0.471055i
$197$			0.841859i			0.0599800i	0.999550	+	0.0299900i	$0.00954754\pi$
$197$			0.841859i			0.0599800i	−0.999550	+	0.0299900i	$0.990452\pi$
$198$	9.10249	+	17.4310i	0.646886	+	1.23877i
$199$	2.38747			0.169243			0.0846215	−	0.996413i	$-0.473032\pi$
$199$	2.38747			0.169243			0.0846215	+	0.996413i	$0.473032\pi$
$200$	0.358379	−	2.80563i	0.0253412	−	0.198388i
$201$	14.0907			0.993880
$202$	−12.7211	−	24.3607i	−0.895057	−	1.71401i
$203$			33.0419i			2.31909i
$204$	12.0288	+	8.37672i	0.842186	+	0.586487i
$205$			9.40558i			0.656914i
$206$	−0.383411	+	0.200217i	−0.0267135	+	0.0139498i
$207$	41.2366			2.86614
$208$	19.8184	−	7.32881i	1.37416	−	0.508161i
$209$	2.83466			0.196077
$210$	11.6995	−	6.10949i	0.807343	−	0.421595i
$211$			12.5085i			0.861121i	0.902562	+	0.430561i	$0.141684\pi$
$211$			12.5085i			0.861121i	−0.902562	+	0.430561i	$0.858316\pi$
$212$	1.22906	+	0.855901i	0.0844121	+	0.0587835i
$213$		−	16.8663i		−	1.15566i
$214$	−10.1001	−	19.3414i	−0.690429	−	1.32215i
$215$	−2.39830			−0.163562
$216$	15.0302	+	1.91989i	1.02267	+	0.130632i
$217$	−17.4569			−1.18505
$218$	−1.13409	−	2.17175i	−0.0768101	−	0.147089i
$219$		−	23.8010i		−	1.60832i
$220$	3.23985	−	4.65237i	0.218430	−	0.313662i
$221$			13.7699i			0.926264i
$222$	−37.1076	+	19.3776i	−2.49050	+	1.30054i
$223$	6.48682			0.434390			0.217195	−	0.976128i	$-0.430309\pi$
$223$	6.48682			0.434390			0.217195	+	0.976128i	$0.430309\pi$
$224$	−13.9251	−	12.5965i	−0.930411	−	0.841639i
$225$	4.90534			0.327023
$226$	−12.7025	+	6.63325i	−0.844958	+	0.441237i
$227$			18.6861i			1.24024i	0.784507	+	0.620120i	$0.212916\pi$
$227$			18.6861i			1.24024i	−0.784507	+	0.620120i	$0.787084\pi$
$228$	3.21355	−	4.61460i	0.212822	−	0.305609i
$229$			16.4298i			1.08571i	0.839826	+	0.542855i	$0.182657\pi$
$229$			16.4298i			1.08571i	−0.839826	+	0.542855i	$0.817343\pi$
$230$	−5.50305	−	10.5382i	−0.362861	−	0.694869i
$231$	26.4555			1.74064
$232$	27.9281	+	3.56741i	1.83357	+	0.234212i
$233$	−7.76941			−0.508991			−0.254495	−	0.967074i	$-0.581909\pi$
$233$	−7.76941			−0.508991			−0.254495	+	0.967074i	$0.581909\pi$
$234$	16.9629	+	32.4836i	1.10890	+	2.12352i
$235$		−	0.543335i		−	0.0354433i
$236$	19.7300	+	13.7397i	1.28431	+	0.894378i
$237$		−	10.1946i		−	0.662210i
$238$	10.8467	−	5.66414i	0.703086	−	0.367152i
$239$	−19.4104			−1.25556			−0.627778	−	0.778392i	$-0.716035\pi$
$239$	−19.4104			−1.25556			−0.627778	+	0.778392i	$0.716035\pi$
$240$	−3.90079	−	10.5484i	−0.251795	−	0.680898i
$241$	14.6787			0.945541			0.472770	−	0.881186i	$-0.343254\pi$
$241$	14.6787			0.945541			0.472770	+	0.881186i	$0.343254\pi$
$242$	−3.71652	+	1.94077i	−0.238907	+	0.124757i
$243$		−	15.0976i		−	0.968511i
$244$	−13.9573	−	9.71969i	−0.893526	−	0.622240i
$245$		−	4.01815i		−	0.256710i
$246$	17.3116	+	33.1512i	1.10374	+	2.11364i
$247$	5.28252			0.336119
$248$	−1.88475	+	14.7551i	−0.119682	+	0.936951i
$249$	−16.2162			−1.02766
$250$	−0.654621	−	1.25358i	−0.0414019	−	0.0792836i
$251$		−	12.8960i		−	0.813986i	−0.913431	−	0.406993i	$-0.866577\pi$
$251$		−	12.8960i		−	0.813986i	0.913431	−	0.406993i	$-0.133423\pi$
$252$	18.6101	−	26.7237i	1.17232	−	1.68344i
$253$		−	23.8294i		−	1.49814i
$254$	23.8359	−	12.4471i	1.49560	−	0.781002i
$255$	7.32908			0.458965
$256$	−12.1504	+	10.4100i	−0.759401	+	0.650623i
$257$	−24.5149			−1.52919			−0.764597	−	0.644508i	$-0.777062\pi$
$257$	−24.5149			−1.52919			−0.764597	+	0.644508i	$0.777062\pi$
$258$	−8.45311	+	4.41421i	−0.526268	+	0.274817i
$259$			34.9465i			2.17147i
$260$	6.03762	−	8.66991i	0.374437	−	0.537685i
$261$			48.8293i			3.02246i
$262$	3.06915	+	5.87734i	0.189613	+	0.363103i
$263$	−11.8823			−0.732691			−0.366346	−	0.930479i	$-0.619391\pi$
$263$	−11.8823			−0.732691			−0.366346	+	0.930479i	$0.619391\pi$
$264$	2.85629	−	22.3610i	0.175793	−	1.37623i
$265$	0.748858			0.0460020
$266$	−2.17292	−	4.16109i	−0.133231	−	0.255133i
$267$			0.979783i			0.0599617i
$268$	−8.22517	−	5.72790i	−0.502432	−	0.349887i
$269$		−	7.17068i		−	0.437204i	−0.975814	−	0.218602i	$-0.929850\pi$
$269$		−	7.17068i		−	0.437204i	0.975814	−	0.218602i	$-0.0701497\pi$
$270$	6.71563	−	3.50690i	0.408700	−	0.213423i
$271$	18.9924			1.15370			0.576852	−	0.816849i	$-0.304281\pi$
$271$	18.9924			1.15370			0.576852	+	0.816849i	$0.304281\pi$
$272$	−3.61644	−	9.77950i	−0.219279	−	0.592969i
$273$	49.3010			2.98384
$274$	11.6564	−	6.08697i	0.704188	−	0.367727i
$275$		−	2.83466i		−	0.170936i
$276$	−38.7924	−	27.0146i	−2.33503	−	1.62609i
$277$		−	21.4917i		−	1.29131i	−0.763630	−	0.645655i	$-0.776585\pi$
$277$		−	21.4917i		−	1.29131i	0.763630	−	0.645655i	$-0.223415\pi$
$278$	−4.02639	−	7.71044i	−0.241487	−	0.462441i
$279$	−25.7977			−1.54447
$280$	−9.31290	−	1.18959i	−0.556552	−	0.0710914i
$281$	7.07129			0.421838			0.210919	−	0.977504i	$-0.432354\pi$
$281$	7.07129			0.421838			0.210919	+	0.977504i	$0.432354\pi$
$282$	−1.00004	−	1.91505i	−0.0595516	−	0.114040i
$283$			21.3693i			1.27027i	0.772400	+	0.635136i	$0.219056\pi$
$283$			21.3693i			1.27027i	−0.772400	+	0.635136i	$0.780944\pi$
$284$	−6.85620	+	9.84538i	−0.406840	+	0.584216i
$285$		−	2.81164i		−	0.166547i
$286$	18.7713	−	9.80239i	1.10997	−	0.579628i
$287$	31.2205			1.84289
$288$	−20.5785	−	18.6151i	−1.21260	−	1.09690i
$289$	−10.2052			−0.600304
$290$	12.4786	−	6.51630i	0.732766	−	0.382650i
$291$			4.13709i			0.242520i
$292$	−9.67517	+	13.8934i	−0.566196	+	0.813048i
$293$			32.7336i			1.91232i	0.292852	+	0.956158i	$0.405396\pi$
$293$			32.7336i			1.91232i	−0.292852	+	0.956158i	$0.594604\pi$
$294$	−7.39566	−	14.1625i	−0.431324	−	0.825974i
$295$	12.0213			0.699910
$296$	29.5379	+	3.77304i	1.71686	+	0.219303i
$297$	15.1857			0.881162
$298$	−14.0019	−	26.8133i	−0.811110	−	1.55326i
$299$		−	44.4073i		−	2.56814i
$300$	−4.61460	−	3.21355i	−0.266424	−	0.185534i
$301$			7.96081i			0.458853i
$302$	−11.2645	+	5.88230i	−0.648197	+	0.338488i
$303$	−54.6382			−3.13888
$304$	−3.75169	+	1.38737i	−0.215174	+	0.0795711i
$305$	−8.50410			−0.486944
$306$	16.0292	−	8.37045i	0.916329	−	0.478507i
$307$			6.51210i			0.371665i	0.982581	+	0.185833i	$0.0594982\pi$
$307$			6.51210i			0.371665i	−0.982581	+	0.185833i	$0.940502\pi$
$308$	−15.4429	−	10.7542i	−0.879940	−	0.612779i
$309$			0.859948i			0.0489207i
$310$	3.44272	+	6.59273i	0.195534	+	0.374442i
$311$	−7.47578			−0.423913			−0.211956	−	0.977279i	$-0.567983\pi$
$311$	−7.47578			−0.423913			−0.211956	+	0.977279i	$0.567983\pi$
$312$	5.32284	−	41.6708i	0.301347	−	2.35915i
$313$	−23.9698			−1.35485			−0.677426	−	0.735591i	$-0.736904\pi$
$313$	−23.9698			−1.35485			−0.677426	+	0.735591i	$0.736904\pi$
$314$	−8.34006	−	15.9710i	−0.470657	−	0.901296i
$315$		−	16.2826i		−	0.917421i
$316$	−4.14413	+	5.95091i	−0.233126	+	0.334765i
$317$		−	4.96527i		−	0.278877i	−0.990231	−	0.139439i	$-0.955470\pi$
$317$		−	4.96527i		−	0.278877i	0.990231	−	0.139439i	$-0.0445298\pi$
$318$	2.63945	−	1.37832i	0.148013	−	0.0772923i
$319$	28.2170			1.57985
$320$	−2.01096	+	7.74313i	−0.112416	+	0.432854i
$321$	−43.3807			−2.42127
$322$	−34.9801	+	18.2666i	−1.94936	+	1.01796i
$323$		−	2.60669i		−	0.145040i
$324$	0.395875	−	0.568470i	0.0219931	−	0.0315817i
$325$		−	5.28252i		−	0.293022i
$326$	9.60569	+	18.3947i	0.532010	+	1.01879i
$327$	−4.87099			−0.269366
$328$	3.37076	−	26.3886i	0.186119	−	1.45707i
$329$	−1.80352			−0.0994315
$330$	−5.21736	−	9.99112i	−0.287206	−	0.549993i
$331$		−	18.5190i		−	1.01790i	−0.860797	−	0.508948i	$-0.830035\pi$
$331$		−	18.5190i		−	1.01790i	0.860797	−	0.508948i	$-0.169965\pi$
$332$	9.46593	+	6.59195i	0.519510	+	0.361780i
$333$			51.6438i			2.83006i
$334$	6.85837	−	3.58144i	0.375273	−	0.195968i
$335$	−5.01155			−0.273810
$336$	−35.0140	+	12.9481i	−1.91017	+	0.706378i
$337$	−4.76915			−0.259792			−0.129896	−	0.991528i	$-0.541464\pi$
$337$	−4.76915			−0.259792			−0.129896	+	0.991528i	$0.541464\pi$
$338$	18.6847	−	9.75716i	1.01631	−	0.530720i
$339$			28.4903i			1.54738i
$340$	−4.27822	−	2.97929i	−0.232019	−	0.161575i
$341$			14.9078i			0.807301i
$342$	−3.21114	−	6.14926i	−0.173639	−	0.332514i
$343$	9.89783			0.534433
$344$	6.72874	+	0.859498i	0.362789	+	0.0463410i
$345$	−23.6360			−1.27252
$346$	4.75279	+	9.10147i	0.255512	+	0.489298i
$347$		−	25.4364i		−	1.36550i	−0.730654	−	0.682748i	$-0.760785\pi$
$347$		−	25.4364i		−	1.36550i	0.730654	−	0.682748i	$-0.239215\pi$
$348$	31.9886	−	45.9351i	1.71477	−	2.46238i
$349$			0.195250i			0.0104515i	0.999986	+	0.00522576i	$0.00166342\pi$
$349$			0.195250i			0.0104515i	−0.999986	+	0.00522576i	$0.998337\pi$
$350$	−4.16109	+	2.17292i	−0.222420	+	0.116148i
$351$	28.2993			1.51050
$352$	−10.7571	+	11.8917i	−0.573357	+	0.633831i
$353$	21.4626			1.14234			0.571170	−	0.820832i	$-0.306490\pi$
$353$	21.4626			1.14234			0.571170	+	0.820832i	$0.306490\pi$
$354$	42.3708	−	22.1260i	2.25198	−	1.17599i
$355$			5.99873i			0.318379i
$356$	0.398285	−	0.571930i	0.0211090	−	0.0303122i
$357$		−	24.3279i		−	1.28757i
$358$	1.87296	+	3.58668i	0.0989892	+	0.189562i
$359$	−1.39745			−0.0737544			−0.0368772	−	0.999320i	$-0.511741\pi$
$359$	−1.39745			−0.0737544			−0.0368772	+	0.999320i	$0.511741\pi$
$360$	−13.7626	−	1.75797i	−0.725352	−	0.0926531i
$361$	−1.00000			−0.0526316
$362$	1.85738	+	3.55684i	0.0976220	+	0.186944i
$363$			8.33573i			0.437513i
$364$	−28.7786	−	20.0410i	−1.50841	−	1.05043i
$365$			8.46514i			0.443086i
$366$	−29.9738	+	15.6523i	−1.56676	+	0.818161i
$367$	−4.22726			−0.220661			−0.110331	−	0.993895i	$-0.535191\pi$
$367$	−4.22726			−0.220661			−0.110331	+	0.993895i	$0.535191\pi$
$368$	11.6629	+	31.5385i	0.607969	+	1.64406i
$369$	46.1376			2.40183
$370$	13.1978	−	6.89190i	0.686122	−	0.358293i
$371$		−	2.48573i		−	0.129053i
$372$	24.2687	+	16.9004i	1.25827	+	0.876244i
$373$		−	16.0901i		−	0.833113i	−0.909110	−	0.416556i	$-0.863237\pi$
$373$		−	16.0901i		−	0.833113i	0.909110	−	0.416556i	$-0.136763\pi$
$374$	−4.83704	−	9.26282i	−0.250118	−	0.478969i
$375$	−2.81164			−0.145193
$376$	−0.194720	+	1.52440i	−0.0100419	+	0.0786148i
$377$	52.5838			2.70821
$378$	−11.6407	−	22.2916i	−0.598732	−	1.14656i
$379$		−	8.13831i		−	0.418037i	−0.977912	−	0.209019i	$-0.932973\pi$
$379$		−	8.13831i		−	0.418037i	0.977912	−	0.209019i	$-0.0670269\pi$
$380$	−1.14294	+	1.64124i	−0.0586317	+	0.0841941i
$381$		−	53.4613i		−	2.73890i
$382$	16.5316	−	8.63279i	0.845828	−	0.441692i
$383$	−19.6666			−1.00492			−0.502459	−	0.864601i	$-0.667571\pi$
$383$	−19.6666			−1.00492			−0.502459	+	0.864601i	$0.667571\pi$
$384$	7.16384	+	30.9930i	0.365578	+	1.58160i
$385$	−9.40925			−0.479540
$386$	1.88892	−	0.986394i	0.0961434	−	0.0502061i
$387$			11.7645i			0.598022i
$388$	1.68174	−	2.41495i	0.0853773	−	0.122600i
$389$		−	2.16269i		−	0.109653i	−0.998496	−	0.0548264i	$-0.982539\pi$
$389$		−	2.16269i		−	0.109653i	0.998496	−	0.0548264i	$-0.0174605\pi$
$390$	−9.72281	−	18.6189i	−0.492334	−	0.942807i
$391$	−21.9130			−1.10819
$392$	−1.44002	+	11.2734i	−0.0727319	+	0.569395i
$393$	13.1822			0.664954
$394$	−0.551099	−	1.05534i	−0.0277640	−	0.0531673i
$395$			3.62585i			0.182436i
$396$	−22.8215	−	15.8926i	−1.14682	−	0.798632i
$397$			12.8974i			0.647302i	0.946177	+	0.323651i	$0.104910\pi$
$397$			12.8974i			0.647302i	−0.946177	+	0.323651i	$0.895090\pi$
$398$	−2.99289	+	1.56289i	−0.150020	+	0.0783405i
$399$	−9.33286			−0.467227
$400$	1.38737	+	3.75169i	0.0693684	+	0.187585i
$401$	−21.1857			−1.05796			−0.528981	−	0.848634i	$-0.677426\pi$
$401$	−21.1857			−1.05796			−0.528981	+	0.848634i	$0.677426\pi$
$402$	−17.6638	+	9.22406i	−0.880992	+	0.460054i
$403$			27.7814i			1.38389i
$404$	31.8940	+	22.2106i	1.58679	+	1.10502i
$405$		−	0.346365i		−	0.0172110i
$406$	−21.6300	−	41.4208i	−1.07348	−	2.05568i
$407$	29.8435			1.47929
$408$	−20.5627	−	2.62659i	−1.01801	−	0.130035i
$409$	25.3162			1.25181			0.625903	−	0.779901i	$-0.284730\pi$
$409$	25.3162			1.25181			0.625903	+	0.779901i	$0.284730\pi$
$410$	−6.15709	−	11.7907i	−0.304077	−	0.582300i
$411$		−	26.1440i		−	1.28959i
$412$	0.349571	−	0.501978i	0.0172221	−	0.0247307i
$413$		−	39.9032i		−	1.96351i
$414$	−51.6935	+	26.9944i	−2.54060	+	1.32670i
$415$	5.76753			0.283117
$416$	−20.0464	+	22.1608i	−0.982857	+	1.08652i
$417$	−17.2936			−0.846873
$418$	−3.55348	+	1.85563i	−0.173806	+	0.0907617i
$419$			16.2067i			0.791748i	0.918305	+	0.395874i	$0.129558\pi$
$419$			16.2067i			0.791748i	−0.918305	+	0.395874i	$0.870442\pi$
$420$	−10.6669	+	15.3175i	−0.520492	+	0.747418i
$421$		−	11.2341i		−	0.547516i	−0.961799	−	0.273758i	$-0.911733\pi$
$421$		−	11.2341i		−	0.547516i	0.961799	−	0.273758i	$-0.0882667\pi$
$422$	−8.18834	−	15.6805i	−0.398602	−	0.763312i
$423$	−2.66524			−0.129589
$424$	−2.10102	−	0.268374i	−0.102034	−	0.0130334i
$425$	−2.60669			−0.126443
$426$	11.0410	+	21.1433i	0.534940	+	1.02440i
$427$			28.2282i			1.36606i
$428$	25.3227	+	17.6344i	1.22402	+	0.852389i
$429$		−	42.1020i		−	2.03270i
$430$	3.00646	−	1.56998i	0.144985	−	0.0757110i
$431$	6.21447			0.299340			0.149670	−	0.988736i	$-0.452179\pi$
$431$	6.21447			0.299340			0.149670	+	0.988736i	$0.452179\pi$
$432$	−20.0984	+	7.43234i	−0.966984	+	0.357589i
$433$	−7.21735			−0.346844			−0.173422	−	0.984848i	$-0.555482\pi$
$433$	−7.21735			−0.346844			−0.173422	+	0.984848i	$0.555482\pi$
$434$	21.8836	−	11.4276i	1.05045	−	0.548544i
$435$		−	27.9880i		−	1.34192i
$436$	2.84335	+	1.98007i	0.136172	+	0.0948282i
$437$			8.40647i			0.402136i
$438$	15.5806	+	29.8365i	0.744471	+	1.42564i
$439$	11.7060			0.558696			0.279348	−	0.960190i	$-0.409882\pi$
$439$	11.7060			0.558696			0.279348	+	0.960190i	$0.409882\pi$
$440$	−1.01588	+	7.95300i	−0.0484302	+	0.379144i
$441$	−19.7104			−0.938591
$442$	−9.01407	−	17.2617i	−0.428756	−	0.821056i
$443$		−	5.52447i		−	0.262475i	−0.991351	−	0.131238i	$-0.958105\pi$
$443$		−	5.52447i		−	0.262475i	0.991351	−	0.131238i	$-0.0418951\pi$
$444$	33.8324	−	48.5828i	1.60562	−	2.30564i
$445$		−	0.348473i		−	0.0165192i
$446$	−8.13177	+	4.24641i	−0.385050	+	0.201073i
$447$	−60.1393			−2.84449
$448$	25.7022	+	6.67509i	1.21432	+	0.315368i
$449$	28.2910			1.33513			0.667567	−	0.744550i	$-0.267336\pi$
$449$	28.2910			1.33513			0.667567	+	0.744550i	$0.267336\pi$
$450$	−6.14926	+	3.21114i	−0.289879	+	0.151375i
$451$		−	26.6616i		−	1.25545i
$452$	11.5814	−	16.6307i	0.544742	−	0.782240i
$453$			25.2649i			1.18705i
$454$	−12.2323	−	23.4246i	−0.574091	−	1.09937i
$455$	−17.5346			−0.822035
$456$	−1.00763	+	7.88844i	−0.0471867	+	0.369410i
$457$	24.1741			1.13082			0.565408	−	0.824811i	$-0.308719\pi$
$457$	24.1741			1.13082			0.565408	+	0.824811i	$0.308719\pi$
$458$	−10.7553	−	20.5961i	−0.502561	−	0.962392i
$459$		−	13.9644i		−	0.651804i
$460$	13.7971	+	9.60810i	0.643292	+	0.447980i
$461$		−	16.4899i		−	0.768011i	−0.923331	−	0.384005i	$-0.874544\pi$
$461$		−	16.4899i		−	0.768011i	0.923331	−	0.384005i	$-0.125456\pi$
$462$	−33.1641	+	17.3183i	−1.54293	+	0.805721i
$463$	−17.6034			−0.818100			−0.409050	−	0.912512i	$-0.634140\pi$
$463$	−17.6034			−0.818100			−0.409050	+	0.912512i	$0.634140\pi$
$464$	−37.3455	+	13.8103i	−1.73372	+	0.641127i
$465$	14.7867			0.685719
$466$	9.73960	−	5.08602i	0.451178	−	0.235605i
$467$			5.05294i			0.233822i	0.993142	+	0.116911i	$0.0372992\pi$
$467$			5.05294i			0.233822i	−0.993142	+	0.116911i	$0.962701\pi$
$468$	−42.5289	−	29.6166i	−1.96590	−	1.36903i
$469$			16.6351i			0.768139i
$470$	0.355679	+	0.681115i	0.0164062	+	0.0314175i
$471$	−35.8211			−1.65055
$472$	−33.7275	−	4.30819i	−1.55243	−	0.198301i
$473$	6.79835			0.312588
$474$	6.67360	+	12.7798i	0.306529	+	0.586995i
$475$			1.00000i			0.0458831i
$476$	−9.88935	+	14.2009i	−0.453278	+	0.650899i
$477$		−	3.67340i		−	0.168194i
$478$	24.3326	−	12.7065i	1.11295	−	0.581181i
$479$	−27.8345			−1.27179			−0.635896	−	0.771775i	$-0.719369\pi$
$479$	−27.8345			−1.27179			−0.635896	+	0.771775i	$0.719369\pi$
$480$	11.7952	+	10.6698i	0.538374	+	0.487007i
$481$	55.6148			2.53582
$482$	−18.4010	+	9.60902i	−0.838144	+	0.437679i
$483$			78.4564i			3.56989i
$484$	3.38850	−	4.86583i	0.154023	−	0.221174i
$485$		−	1.47141i		−	0.0668134i
$486$	9.88321	+	18.9261i	0.448311	+	0.858505i
$487$	−10.5772			−0.479298			−0.239649	−	0.970860i	$-0.577032\pi$
$487$	−10.5772			−0.479298			−0.239649	+	0.970860i	$0.577032\pi$
$488$	23.8594	+	3.04769i	1.08006	+	0.137962i
$489$	41.2571			1.86571
$490$	2.63037	+	5.03709i	0.118828	+	0.227552i
$491$		−	17.8052i		−	0.803535i	−0.915742	−	0.401768i	$-0.868396\pi$
$491$		−	17.8052i		−	0.803535i	0.915742	−	0.401768i	$-0.131604\pi$
$492$	−43.4029	−	30.2253i	−1.95676	−	1.36266i
$493$		−	25.9478i		−	1.16863i
$494$	−6.62208	+	3.45805i	−0.297942	+	0.155585i
$495$	−13.9050			−0.624982
$496$	−7.29632	−	19.7306i	−0.327615	−	0.885928i
$497$	19.9119			0.893172
$498$	20.3284	−	10.6155i	0.910938	−	0.475692i
$499$			6.46483i			0.289406i	0.989475	+	0.144703i	$0.0462226\pi$
$499$			6.46483i			0.289406i	−0.989475	+	0.144703i	$0.953777\pi$
$500$	1.64124	+	1.14294i	0.0733987	+	0.0511139i
$501$		−	15.3825i		−	0.687241i
$502$	8.44198	+	16.1662i	0.376784	+	0.721532i
$503$	3.89673			0.173747			0.0868734	−	0.996219i	$-0.472312\pi$
$503$	3.89673			0.173747			0.0868734	+	0.996219i	$0.472312\pi$
$504$	−5.83533	+	45.6830i	−0.259926	+	2.03488i
$505$	19.4328			0.864750
$506$	15.5993	+	29.8722i	0.693472	+	1.32798i
$507$		−	41.9077i		−	1.86119i
$508$	−21.7322	+	31.2070i	−0.964209	+	1.38459i
$509$			36.7308i			1.62806i	0.580820	+	0.814032i	$0.302732\pi$
$509$			36.7308i			1.62806i	−0.580820	+	0.814032i	$0.697268\pi$
$510$	−9.18762	+	4.79778i	−0.406835	+	0.212449i
$511$	28.0989			1.24302
$512$	8.41697	−	21.0037i	0.371981	−	0.928240i
$513$	−5.35715			−0.236524
$514$	30.7314	−	16.0479i	1.35550	−	0.707845i
$515$		−	0.305852i		−	0.0134775i
$516$	7.70703	−	11.0672i	0.339283	−	0.487205i
$517$			1.54017i			0.0677365i
$518$	−22.8767	−	43.8083i	−1.00514	−	1.92483i
$519$	20.4136			0.896056
$520$	−1.89314	+	14.8208i	−0.0830198	+	0.649936i
$521$	−25.3304			−1.10974			−0.554872	−	0.831936i	$-0.687233\pi$
$521$	−25.3304			−1.10974			−0.554872	+	0.831936i	$0.687233\pi$
$522$	−31.9647	−	61.2116i	−1.39906	−	2.67916i
$523$		−	16.7701i		−	0.733303i	−0.930358	−	0.366652i	$-0.880504\pi$
$523$		−	16.7701i		−	0.733303i	0.930358	−	0.366652i	$-0.119496\pi$
$524$	−7.69486	−	5.35860i	−0.336152	−	0.234092i
$525$			9.33286i			0.407319i
$526$	14.8954	−	7.77838i	0.649470	−	0.339153i
$527$	13.7089			0.597167
$528$	11.0574	+	29.9012i	0.481211	+	1.30128i
$529$	47.6687			2.07255
$530$	−0.938755	+	0.490218i	−0.0407769	+	0.0212937i
$531$		−	58.9688i		−	2.55903i
$532$	5.44788	+	3.79383i	0.236196	+	0.164484i
$533$		−	49.6852i		−	2.15210i
$534$	−0.641387	−	1.22824i	−0.0277555	−	0.0531511i
$535$	15.4289			0.667051
$536$	14.0605	+	1.79603i	0.607323	+	0.0775767i
$537$	8.04451			0.347146
$538$	4.69408	+	8.98905i	0.202376	+	0.387545i
$539$			11.3901i			0.490606i
$540$	−6.12291	+	8.79239i	−0.263488	+	0.378364i
$541$			39.1226i			1.68201i	0.541025	+	0.841006i	$0.318036\pi$
$541$			39.1226i			1.68201i	−0.541025	+	0.841006i	$0.681964\pi$
$542$	−23.8085	+	12.4328i	−1.02266	+	0.534035i
$543$	7.97760			0.342351
$544$	10.9354	+	9.89202i	0.468851	+	0.424117i
$545$	1.73243			0.0742093
$546$	−61.8030	+	32.2735i	−2.64492	+	1.38118i
$547$			40.8808i			1.74794i	0.485981	+	0.873969i	$0.338462\pi$
$547$			40.8808i			1.74794i	−0.485981	+	0.873969i	$0.661538\pi$
$548$	−10.6276	+	15.2610i	−0.453988	+	0.651920i
$549$			41.7156i			1.78038i
$550$	1.85563	+	3.55348i	0.0791242	+	0.151521i
$551$	−9.95431			−0.424068
$552$	66.3139	+	8.47063i	2.82251	+	0.360534i
$553$	12.0355			0.511802
$554$	14.0689	+	26.9416i	0.597731	+	1.14464i
$555$		−	29.6012i		−	1.25650i
$556$	10.0948	+	7.02991i	0.428116	+	0.298135i
$557$			6.69684i			0.283754i	0.989884	+	0.141877i	$0.0453138\pi$
$557$			6.69684i			0.283754i	−0.989884	+	0.141877i	$0.954686\pi$
$558$	32.3396	−	16.8877i	1.36904	−	0.714915i
$559$	12.6691			0.535844
$560$	12.4532	−	4.60518i	0.526245	−	0.194604i
$561$	−20.7754			−0.877140
$562$	−8.86445	+	4.62902i	−0.373924	+	0.195263i
$563$		−	5.11081i		−	0.215395i	−0.994184	−	0.107697i	$-0.965652\pi$
$563$		−	5.11081i		−	0.215395i	0.994184	−	0.107697i	$-0.0343478\pi$
$564$	2.50727	+	1.74603i	0.105575	+	0.0735212i
$565$		−	10.1330i		−	0.426297i
$566$	−13.9888	−	26.7882i	−0.587993	−	1.12599i
$567$	−1.14971			−0.0482833
$568$	2.14982	−	16.8302i	0.0902042	−	0.706180i
$569$	5.42508			0.227431			0.113716	−	0.993513i	$-0.463725\pi$
$569$	5.42508			0.227431			0.113716	+	0.993513i	$0.463725\pi$
$570$	1.84056	+	3.52463i	0.0770927	+	0.147631i
$571$			12.7480i			0.533487i	0.963768	+	0.266743i	$0.0859476\pi$
$571$			12.7480i			0.533487i	−0.963768	+	0.266743i	$0.914052\pi$
$572$	−17.1146	+	24.5762i	−0.715596	+	1.02758i
$573$		−	37.0784i		−	1.54897i
$574$	−39.1375	+	20.4376i	−1.63357	+	0.853049i
$575$	8.40647			0.350574
$576$	37.9827	+	9.86443i	1.58261	+	0.411018i
$577$	30.0526			1.25111			0.625554	−	0.780181i	$-0.284873\pi$
$577$	30.0526			1.25111			0.625554	+	0.780181i	$0.284873\pi$
$578$	12.7930	−	6.68052i	0.532120	−	0.277873i
$579$		−	4.23663i		−	0.176068i
$580$	−11.3772	+	16.3375i	−0.472412	+	0.678376i
$581$		−	19.1445i		−	0.794248i
$582$	−2.70823	−	5.18618i	−0.112260	−	0.214974i
$583$	−2.12275			−0.0879155
$584$	3.03373	−	23.7501i	0.125536	−	0.982785i
$585$	−25.9126			−1.07135
$586$	−21.4281	−	41.0343i	−0.885186	−	1.69511i
$587$			25.0796i			1.03514i	0.855640	+	0.517572i	$0.173164\pi$
$587$			25.0796i			1.03514i	−0.855640	+	0.517572i	$0.826836\pi$
$588$	18.5421	+	12.9125i	0.764665	+	0.532503i
$589$		−	5.25911i		−	0.216698i
$590$	−15.0698	+	7.86943i	−0.620412	+	0.323979i
$591$	−2.36701			−0.0973657
$592$	−39.4981	+	14.6063i	−1.62336	+	0.600316i
$593$	−20.4193			−0.838519			−0.419260	−	0.907866i	$-0.637710\pi$
$593$	−20.4193			−0.838519			−0.419260	+	0.907866i	$0.637710\pi$
$594$	−19.0365	+	9.94087i	−0.781078	+	0.407879i
$595$			8.65254i			0.354720i
$596$	35.1052	+	24.4468i	1.43796	+	1.00138i
$597$			6.71271i			0.274733i
$598$	29.0700	+	55.6683i	1.18876	+	2.27645i
$599$	37.1592			1.51828			0.759142	−	0.650925i	$-0.225619\pi$
$599$	37.1592			1.51828			0.759142	+	0.650925i	$0.225619\pi$
$600$	7.88844	+	1.00763i	0.322044	+	0.0411364i
$601$	28.3830			1.15777			0.578884	−	0.815410i	$-0.303488\pi$
$601$	28.3830			1.15777			0.578884	+	0.815410i	$0.303488\pi$
$602$	−5.21132	−	9.97954i	−0.212397	−	0.406736i
$603$			24.5834i			1.00111i
$604$	10.2703	−	14.7479i	0.417891	−	0.600084i
$605$		−	2.96472i		−	0.120533i
$606$	68.4935	−	35.7673i	2.78236	−	1.45295i
$607$	−15.2365			−0.618432			−0.309216	−	0.950992i	$-0.600067\pi$
$607$	−15.2365			−0.618432			−0.309216	+	0.950992i	$0.600067\pi$
$608$	3.79486	−	4.19512i	0.153902	−	0.170135i
$609$	−92.9021			−3.76458
$610$	10.6606	−	5.56697i	0.431635	−	0.225400i
$611$			2.87018i			0.116115i
$612$	−14.6145	+	20.9861i	−0.590755	+	0.848314i
$613$			48.0846i			1.94212i	0.238840	+	0.971059i	$0.423233\pi$
$613$			48.0846i			1.94212i	−0.238840	+	0.971059i	$0.576767\pi$
$614$	−4.26296	−	8.16346i	−0.172039	−	0.329450i
$615$	−26.4451			−1.06637
$616$	26.3989	+	3.37207i	1.06364	+	0.135865i
$617$	36.1598			1.45574			0.727870	−	0.685716i	$-0.240511\pi$
$617$	36.1598			1.45574			0.727870	+	0.685716i	$0.240511\pi$
$618$	−0.562940	−	1.07802i	−0.0226448	−	0.0433642i
$619$			11.2173i			0.450862i	0.974259	+	0.225431i	$0.0723790\pi$
$619$			11.2173i			0.450862i	−0.974259	+	0.225431i	$0.927621\pi$
$620$	−8.63148	−	6.01085i	−0.346649	−	0.241402i
$621$			45.0347i			1.80718i
$622$	9.37152	−	4.89381i	0.375764	−	0.196224i
$623$	−1.15671			−0.0463425
$624$	20.6060	+	55.7223i	0.824900	+	2.23068i
$625$	1.00000			0.0400000
$626$	30.0481	−	15.6911i	1.20096	−	0.627143i
$627$			7.97005i			0.318293i
$628$	20.9099	+	14.5614i	0.834397	+	0.581063i
$629$		−	27.4434i		−	1.09424i
$630$	10.6589	+	20.4116i	0.424662	+	0.813217i
$631$	−39.9837			−1.59172			−0.795862	−	0.605478i	$-0.792982\pi$
$631$	−39.9837			−1.59172			−0.795862	+	0.605478i	$0.792982\pi$
$632$	1.29943	−	10.1728i	0.0516884	−	0.404652i
$633$	−35.1695			−1.39786
$634$	3.25037	+	6.22438i	0.129089	+	0.247202i
$635$			19.0142i			0.754557i
$636$	−2.40649	+	3.45568i	−0.0954234	+	0.137026i
$637$			21.2260i			0.841004i
$638$	−35.3724	+	18.4715i	−1.40041	+	0.731293i
$639$	29.4258			1.16407
$640$	−2.54792	−	11.0231i	−0.100715	−	0.435725i
$641$	45.4061			1.79343			0.896717	−	0.442605i	$-0.145945\pi$
$641$	45.4061			1.79343			0.896717	+	0.442605i	$0.145945\pi$
$642$	54.3813	−	28.3979i	2.14626	−	1.12078i
$643$		−	24.4753i		−	0.965212i	−0.875838	−	0.482606i	$-0.839690\pi$
$643$		−	24.4753i		−	0.965212i	0.875838	−	0.482606i	$-0.160310\pi$
$644$	31.8927	−	45.7974i	1.25675	−	1.80467i
$645$		−	6.74316i		−	0.265512i
$646$	1.70640	+	3.26770i	0.0671372	+	0.128566i
$647$	−7.35538			−0.289170			−0.144585	−	0.989492i	$-0.546185\pi$
$647$	−7.35538			−0.289170			−0.144585	+	0.989492i	$0.546185\pi$
$648$	−0.124130	+	0.971772i	−0.00487628	+	0.0381748i
$649$	−34.0764			−1.33762
$650$	3.45805	+	6.62208i	0.135636	+	0.259739i
$651$		−	49.0825i		−	1.92370i
$652$	−24.0831	−	16.7711i	−0.943166	−	0.656808i
$653$			17.7124i			0.693138i	0.938024	+	0.346569i	$0.112653\pi$
$653$			17.7124i			0.693138i	−0.938024	+	0.346569i	$0.887347\pi$
$654$	6.10619	−	3.18865i	0.238771	−	0.124686i
$655$	−4.68843			−0.183192
$656$	13.0490	+	35.2868i	0.509478	+	1.37772i
$657$	41.5244			1.62002
$658$	2.26087	−	1.18063i	0.0881378	−	0.0460256i
$659$			16.7955i			0.654259i	0.944980	+	0.327129i	$0.106081\pi$
$659$			16.7955i			0.654259i	−0.944980	+	0.327129i	$0.893919\pi$
$660$	13.0808	+	9.10930i	0.509169	+	0.354579i
$661$		−	24.1089i		−	0.937729i	−0.883270	−	0.468864i	$-0.844663\pi$
$661$		−	24.1089i		−	0.937729i	0.883270	−	0.468864i	$-0.155337\pi$
$662$	12.1229	+	23.2151i	0.471171	+	0.902280i
$663$	−38.7161			−1.50361
$664$	−16.1816	−	2.06696i	−0.627966	−	0.0802136i
$665$	3.31936			0.128719
$666$	−33.8072	−	64.7398i	−1.31000	−	2.50862i
$667$			83.6805i			3.24012i
$668$	−6.25305	+	8.97927i	−0.241938	+	0.347418i
$669$			18.2386i			0.705146i
$670$	6.28239	−	3.28066i	0.242710	−	0.126743i
$671$	24.1062			0.930610
$672$	35.4169	−	39.1525i	1.36624	−	1.51034i
$673$	−45.9583			−1.77156			−0.885780	−	0.464105i	$-0.846376\pi$
$673$	−45.9583			−1.77156			−0.885780	+	0.464105i	$0.846376\pi$
$674$	5.97853	−	3.12199i	0.230284	−	0.120255i
$675$			5.35715i			0.206197i
$676$	−17.0356	+	24.4628i	−0.655215	+	0.940878i
$677$			3.33276i			0.128088i	0.997947	+	0.0640441i	$0.0203998\pi$
$677$			3.33276i			0.128088i	−0.997947	+	0.0640441i	$0.979600\pi$
$678$	−18.6503	−	35.7149i	−0.716262	−	1.37162i
$679$	−4.88415			−0.187436
$680$	7.31341	+	0.934182i	0.280456	+	0.0358242i
$681$	−52.5386			−2.01328
$682$	−9.75894	−	18.6881i	−0.373689	−	0.715605i
$683$		−	12.8851i		−	0.493034i	−0.969139	−	0.246517i	$-0.920714\pi$
$683$		−	12.8851i		−	0.493034i	0.969139	−	0.246517i	$-0.0792860\pi$
$684$	8.05087	+	5.60652i	0.307833	+	0.214371i
$685$			9.29846i			0.355276i
$686$	−12.4078	+	6.47933i	−0.473730	+	0.247382i
$687$	−46.1947			−1.76244
$688$	−8.99767	+	3.32732i	−0.343033	+	0.126853i
$689$	−3.95586			−0.150706
$690$	29.6297	−	15.4726i	1.12798	−	0.589033i
$691$		−	3.25907i		−	0.123981i	−0.998077	−	0.0619904i	$-0.980255\pi$
$691$		−	3.25907i		−	0.123981i	0.998077	−	0.0619904i	$-0.0197448\pi$
$692$	−11.9160	−	8.29817i	−0.452980	−	0.315449i
$693$			46.1556i			1.75331i
$694$	16.6512	+	31.8866i	0.632071	+	1.21040i
$695$	6.15072			0.233310
$696$	−10.0303	+	78.5239i	−0.380197	+	2.97644i
$697$	−24.5174			−0.928664
$698$	−0.127815	−	0.244763i	−0.00483787	−	0.00926440i
$699$		−	21.8448i		−	0.826247i
$700$	3.79383	−	5.44788i	0.143393	−	0.205911i
$701$		−	20.7425i		−	0.783435i	−0.920085	−	0.391718i	$-0.871881\pi$
$701$		−	20.7425i		−	0.783435i	0.920085	−	0.391718i	$-0.128119\pi$
$702$	−35.4755	+	18.5253i	−1.33894	+	0.699192i
$703$	−10.5281			−0.397074
$704$	5.70037	−	21.9491i	0.214841	−	0.827239i
$705$	1.52766			0.0575352
$706$	−26.9052	+	14.0499i	−1.01259	+	0.528775i
$707$		−	64.5046i		−	2.42594i
$708$	−38.6311	+	55.4736i	−1.45185	+	2.08483i
$709$		−	10.5229i		−	0.395195i	−0.980283	−	0.197598i	$-0.936686\pi$
$709$		−	10.5229i		−	0.395195i	0.980283	−	0.197598i	$-0.0633139\pi$
$710$	−3.92690	−	7.51990i	−0.147374	−	0.282217i
$711$	17.7860			0.667029
$712$	−0.124885	+	0.977687i	−0.00468028	+	0.0366404i
$713$	−44.2105			−1.65570
$714$	15.9255	+	30.4970i	0.595999	+	1.14132i
$715$			14.9741i			0.560001i
$716$	−4.69583	−	3.27012i	−0.175491	−	0.122210i
$717$		−	54.5752i		−	2.03815i
$718$	1.75181	−	0.914798i	0.0653771	−	0.0341400i
$719$	−33.5457			−1.25104			−0.625521	−	0.780207i	$-0.715114\pi$
$719$	−33.5457			−1.25104			−0.625521	+	0.780207i	$0.715114\pi$
$720$	18.4033	−	6.80552i	0.685852	−	0.253627i
$721$	−1.01523			−0.0378093
$722$	1.25358	−	0.654621i	0.0466535	−	0.0243625i
$723$			41.2714i			1.53490i
$724$	−4.65677	−	3.24292i	−0.173068	−	0.120522i
$725$			9.95431i			0.369694i
$726$	−5.45675	−	10.4495i	−0.202519	−	0.387819i
$727$	−18.7931			−0.696999			−0.348499	−	0.937309i	$-0.613309\pi$
$727$	−18.7931			−0.696999			−0.348499	+	0.937309i	$0.613309\pi$
$728$	49.1956	+	6.28402i	1.82331	+	0.232901i
$729$	43.4881			1.61067
$730$	−5.54146	−	10.6118i	−0.205099	−	0.392759i
$731$		−	6.25162i		−	0.231224i
$732$	27.3283	−	39.2430i	1.01008	−	1.45046i
$733$			45.0389i			1.66355i	0.555114	+	0.831775i	$0.312675\pi$
$733$			45.0389i			1.66355i	−0.555114	+	0.831775i	$0.687325\pi$
$734$	5.29923	−	2.76726i	0.195598	−	0.102141i
$735$	11.2976			0.416719
$736$	−35.2661	−	31.9014i	−1.29993	−	1.17590i
$737$	14.2060			0.523285
$738$	−57.8373	+	30.2027i	−2.12902	+	1.11178i
$739$			13.2938i			0.489019i	0.969647	+	0.244509i	$0.0786269\pi$
$739$			13.2938i			0.489019i	−0.969647	+	0.244509i	$0.921373\pi$
$740$	−12.0330	+	17.2791i	−0.442341	+	0.635194i
$741$			14.8526i			0.545623i
$742$	1.62721	+	3.11607i	0.0597368	+	0.114394i
$743$	15.3277			0.562319			0.281159	−	0.959661i	$-0.409281\pi$
$743$	15.3277			0.562319			0.281159	+	0.959661i	$0.409281\pi$
$744$	−41.4861	−	5.29925i	−1.52096	−	0.194280i
$745$	21.3894			0.783645
$746$	10.5329	+	20.1702i	0.385637	+	0.738485i
$747$		−	28.2917i		−	1.03514i
$748$	12.1273	+	8.44528i	0.443417	+	0.308790i
$749$		−	51.2142i		−	1.87133i
$750$	3.52463	−	1.84056i	0.128701	−	0.0672078i
$751$	−47.2604			−1.72456			−0.862278	−	0.506436i	$-0.830963\pi$
$751$	−47.2604			−1.72456			−0.862278	+	0.506436i	$0.830963\pi$
$752$	−0.753806	−	2.03843i	−0.0274885	−	0.0743337i
$753$	36.2589			1.32135
$754$	−65.9182	+	34.4225i	−2.40060	+	1.25359i
$755$		−	8.98581i		−	0.327027i
$756$	29.1851	+	20.3241i	1.06145	+	0.739182i
$757$		−	18.8829i		−	0.686312i	−0.939279	−	0.343156i	$-0.888504\pi$
$757$		−	18.8829i		−	0.686312i	0.939279	−	0.343156i	$-0.111496\pi$
$758$	5.32751	+	10.2021i	0.193504	+	0.370555i
$759$	66.9999			2.43194
$760$	0.358379	−	2.80563i	0.0129998	−	0.101771i
$761$	−52.4552			−1.90150			−0.950749	−	0.309961i	$-0.899684\pi$
$761$	−52.4552			−1.90150			−0.950749	+	0.309961i	$0.899684\pi$
$762$	34.9969	+	67.0181i	1.26780	+	2.42781i
$763$		−	5.75057i		−	0.208185i
$764$	−15.0725	+	21.6438i	−0.545303	+	0.783046i
$765$			12.7867i			0.462304i
$766$	24.6538	−	12.8742i	0.890776	−	0.465164i
$767$	−63.5030			−2.29296
$768$	−29.2691	−	34.1626i	−1.05616	−	1.23274i
$769$	−7.79501			−0.281095			−0.140548	−	0.990074i	$-0.544886\pi$
$769$	−7.79501			−0.281095			−0.140548	+	0.990074i	$0.544886\pi$
$770$	11.7953	−	6.15949i	0.425072	−	0.221973i
$771$		−	68.9270i		−	2.48235i
$772$	−1.72220	+	2.47305i	−0.0619834	+	0.0890071i
$773$			1.94467i			0.0699447i	0.999388	+	0.0349724i	$0.0111343\pi$
$773$			1.94467i			0.0699447i	−0.999388	+	0.0349724i	$0.988866\pi$
$774$	−7.70127	−	14.7477i	−0.276817	−	0.530097i
$775$	−5.25911			−0.188913
$776$	−0.527322	+	4.12824i	−0.0189298	+	0.148195i
$777$	−98.2570			−3.52495
$778$	1.41574	+	2.71111i	0.0507569	+	0.0971981i
$779$			9.40558i			0.336990i
$780$	24.3767	+	16.9756i	0.872826	+	0.607825i
$781$		−	17.0043i		−	0.608463i
$782$	27.4698	−	14.3448i	0.982319	−	0.512967i
$783$	−53.3267			−1.90574
$784$	−5.57466	−	15.0749i	−0.199095	−	0.538388i
$785$	12.7403			0.454720
$786$	−16.5250	+	8.62935i	−0.589427	+	0.307799i
$787$			7.81971i			0.278742i	0.990240	+	0.139371i	$0.0445081\pi$
$787$			7.81971i			0.278742i	−0.990240	+	0.139371i	$0.955492\pi$
$788$	1.38170	+	0.962196i	0.0492209	+	0.0342768i
$789$		−	33.4087i		−	1.18938i
$790$	−2.37356	−	4.54530i	−0.0844474	−	0.161715i
$791$	−33.6349			−1.19592
$792$	39.0122	+	4.98324i	1.38624	+	0.177072i
$793$	44.9231			1.59527
$794$	−8.44291	−	16.1680i	−0.299628	−	0.573779i
$795$			2.10552i			0.0746751i
$796$	2.72874	−	3.91842i	0.0967175	−	0.138885i
$797$			6.59089i			0.233461i	0.993164	+	0.116731i	$0.0372414\pi$
$797$			6.59089i			0.233461i	−0.993164	+	0.116731i	$0.962759\pi$
$798$	11.6995	−	6.10949i	0.414158	−	0.216274i
$799$	1.41631			0.0501053
$800$	−4.19512	−	3.79486i	−0.148320	−	0.134169i
$801$	−1.70938			−0.0603980
$802$	26.5580	−	13.8686i	0.937795	−	0.489717i
$803$		−	23.9958i		−	0.846793i
$804$	16.1048	−	23.1263i	0.567973	−	0.815600i
$805$		−	27.9041i		−	0.983490i
$806$	−18.1863	−	34.8262i	−0.640584	−	1.22670i
$807$	20.1614			0.709715
$808$	−54.5213	−	6.96431i	−1.91805	−	0.245004i
$809$	5.89457			0.207242			0.103621	−	0.994617i	$-0.466957\pi$
$809$	5.89457			0.207242			0.103621	+	0.994617i	$0.466957\pi$
$810$	0.226738	+	0.434197i	0.00796676	+	0.0152561i
$811$		−	35.8912i		−	1.26031i	−0.776469	−	0.630156i	$-0.782991\pi$
$811$		−	35.8912i		−	1.26031i	0.776469	−	0.630156i	$-0.217009\pi$
$812$	54.2299	+	37.7650i	1.90310	+	1.32529i
$813$			53.3998i			1.87281i
$814$	−37.4113	+	19.5362i	−1.31126	+	0.684743i
$815$	−14.6737			−0.513996
$816$	27.4965	−	10.1681i	0.962569	−	0.355956i
$817$	−2.39830			−0.0839058
$818$	−31.7360	+	16.5725i	−1.10962	+	0.579445i
$819$			86.0132i			3.00555i
$820$	15.4369	+	10.7500i	0.539078	+	0.375407i
$821$			35.6458i			1.24405i	0.782999	+	0.622023i	$0.213689\pi$
$821$			35.6458i			1.24405i	−0.782999	+	0.622023i	$0.786311\pi$
$822$	17.1144	+	32.7736i	0.596933	+	1.14311i
$823$	14.0411			0.489444			0.244722	−	0.969593i	$-0.421303\pi$
$823$	14.0411			0.489444			0.244722	+	0.969593i	$0.421303\pi$
$824$	−0.109611	+	0.858109i	−0.00381848	+	0.0298936i
$825$	7.97005			0.277481
$826$	26.1215	+	50.0219i	0.908882	+	1.74049i
$827$			6.38058i			0.221874i	0.993827	+	0.110937i	$0.0353853\pi$
$827$			6.38058i			0.221874i	−0.993827	+	0.110937i	$0.964615\pi$
$828$	47.1310	−	67.6794i	1.63792	−	2.35202i
$829$		−	20.3087i		−	0.705351i	−0.935746	−	0.352675i	$-0.885272\pi$
$829$		−	20.3087i		−	0.705351i	0.935746	−	0.352675i	$-0.114728\pi$
$830$	−7.23008	+	3.77555i	−0.250960	+	0.131051i
$831$	60.4269			2.09619
$832$	10.6229	−	40.9033i	0.368283	−	1.41807i
$833$	10.4741			0.362905
$834$	21.6790	−	11.3208i	0.750683	−	0.392007i
$835$			5.47101i			0.189332i
$836$	3.23985	−	4.65237i	0.112052	−	0.160905i
$837$		−	28.1738i		−	0.973830i
$838$	−10.6092	−	20.3164i	−0.366490	−	0.701819i
$839$	10.2876			0.355168			0.177584	−	0.984106i	$-0.443172\pi$
$839$	10.2876			0.355168			0.177584	+	0.984106i	$0.443172\pi$
$840$	3.34470	−	26.1846i	0.115403	−	0.903453i
$841$	−70.0882			−2.41683
$842$	7.35407	+	14.0829i	0.253438	+	0.485327i
$843$			19.8819i			0.684771i
$844$	20.5295	+	14.2965i	0.706655	+	0.492106i
$845$			14.9050i			0.512749i
$846$	3.34110	−	1.74473i	0.114870	−	0.0599849i
$847$	−9.84097			−0.338140
$848$	2.80948	−	1.03894i	0.0964781	−	0.0356774i
$849$	−60.0828			−2.06204
$850$	3.26770	−	1.70640i	0.112081	−	0.0585289i
$851$			88.5039i			3.03387i
$852$	−27.6817	−	19.2772i	−0.948360	−	0.660425i
$853$		−	20.5672i		−	0.704208i	−0.935961	−	0.352104i	$-0.885466\pi$
$853$		−	20.5672i		−	0.704208i	0.935961	−	0.352104i	$-0.114534\pi$
$854$	−18.4788	−	35.3864i	−0.632331	−	1.21090i
$855$	4.90534			0.167759
$856$	−43.2879	−	5.52940i	−1.47955	−	0.188991i
$857$	26.6763			0.911245			0.455623	−	0.890173i	$-0.349417\pi$
$857$	26.6763			0.911245			0.455623	+	0.890173i	$0.349417\pi$
$858$	27.5608	+	52.7783i	0.940912	+	1.80182i
$859$		−	5.04151i		−	0.172014i	−0.996295	−	0.0860071i	$-0.972589\pi$
$859$		−	5.04151i		−	0.172014i	0.996295	−	0.0860071i	$-0.0274108\pi$
$860$	−2.74111	+	3.93619i	−0.0934712	+	0.134223i
$861$			87.7809i			2.99157i
$862$	−7.79035	+	4.06812i	−0.265341	+	0.138561i
$863$	29.8424			1.01585			0.507923	−	0.861402i	$-0.330413\pi$
$863$	29.8424			1.01585			0.507923	+	0.861402i	$0.330413\pi$
$864$	20.3296	−	22.4739i	0.691628	−	0.764577i
$865$	−7.26036			−0.246860
$866$	9.04754	−	4.72463i	0.307448	−	0.160549i
$867$		−	28.6933i		−	0.974476i
$868$	−19.9522	+	28.6510i	−0.677221	+	0.972478i
$869$		−	10.2780i		−	0.348659i
$870$	18.3215	+	35.0852i	0.621158	+	1.18950i
$871$	26.4736			0.897024
$872$	−4.86057	−	0.620867i	−0.164600	−	0.0210252i
$873$	−7.21778			−0.244285
$874$	−5.50305	−	10.5382i	−0.186144	−	0.356460i
$875$		−	3.31936i		−	0.112215i
$876$	−39.0632	−	27.2031i	−1.31982	−	0.919108i
$877$			38.9434i			1.31502i	0.753444	+	0.657512i	$0.228391\pi$
$877$			38.9434i			1.31502i	−0.753444	+	0.657512i	$0.771609\pi$
$878$	−14.6744	+	7.66299i	−0.495238	+	0.258613i
$879$	−92.0352			−3.10427
$880$	−3.93271	−	10.6348i	−0.132572	−	0.358498i
$881$	−5.08894			−0.171451			−0.0857253	−	0.996319i	$-0.527321\pi$
$881$	−5.08894			−0.171451			−0.0857253	+	0.996319i	$0.527321\pi$
$882$	24.7086	−	12.9029i	0.831983	−	0.434462i
$883$		−	32.1786i		−	1.08290i	−0.840734	−	0.541448i	$-0.817876\pi$
$883$		−	32.1786i		−	1.08290i	0.840734	−	0.541448i	$-0.182124\pi$
$884$	22.5998	+	15.7382i	0.760113	+	0.529333i
$885$			33.7997i			1.13617i
$886$	3.61643	+	6.92538i	0.121496	+	0.232663i
$887$	11.3435			0.380877			0.190439	−	0.981699i	$-0.439009\pi$
$887$	11.3435			0.380877			0.190439	+	0.981699i	$0.439009\pi$
$888$	−10.6084	+	83.0500i	−0.355996	+	2.78698i
$889$	63.1151			2.11681
$890$	0.228118	+	0.436840i	0.00764653	+	0.0146429i
$891$			0.981826i			0.0328924i
$892$	7.41406	−	10.6465i	0.248241	−	0.356470i
$893$		−	0.543335i		−	0.0181820i
$894$	75.3896	−	39.3684i	2.52140	−	1.31668i
$895$	−2.86114			−0.0956374
$896$	−36.5895	+	8.45746i	−1.22237	+	0.282544i
$897$	124.858			4.16888
$898$	−35.4651	+	18.5199i	−1.18349	+	0.618016i
$899$		−	52.3508i		−	1.74600i
$900$	5.60652	−	8.05087i	0.186884	−	0.268362i
$901$			1.95204i			0.0650319i
$902$	17.4532	+	33.4225i	0.581130	+	1.11285i
$903$	−22.3830			−0.744858
$904$	−3.63143	+	28.4293i	−0.120780	+	0.945545i
$905$	−2.83734			−0.0943164
$906$	−16.5389	−	31.6716i	−0.549469	−	1.05222i
$907$		−	28.4150i		−	0.943504i	−0.881731	−	0.471752i	$-0.843622\pi$
$907$		−	28.4150i		−	0.943504i	0.881731	−	0.471752i	$-0.156378\pi$
$908$	30.6684	+	21.3571i	1.01777	+	0.708761i
$909$		−	95.3247i		−	3.16172i
$910$	21.9811	−	11.4785i	0.728666	−	0.380509i
$911$	−36.4986			−1.20925			−0.604627	−	0.796509i	$-0.706678\pi$
$911$	−36.4986			−1.20925			−0.604627	+	0.796509i	$0.706678\pi$
$912$	−3.90079	−	10.5484i	−0.129168	−	0.349293i
$913$	−16.3490			−0.541072
$914$	−30.3042	+	15.8249i	−1.00238	+	0.523441i
$915$		−	23.9105i		−	0.790457i
$916$	26.9653	+	18.7783i	0.890958	+	0.620452i
$917$			15.5626i			0.513922i
$918$	9.14141	+	17.5056i	0.301712	+	0.577770i
$919$	−7.16571			−0.236375			−0.118187	−	0.992991i	$-0.537708\pi$
$919$	−7.16571			−0.236375			−0.118187	+	0.992991i	$0.537708\pi$
$920$	−23.5854	−	3.01270i	−0.777589	−	0.0993257i
$921$	−18.3097			−0.603326
$922$	10.7946	+	20.6714i	0.355502	+	0.680778i
$923$		−	31.6884i		−	1.04304i
$924$	30.2370	−	43.4199i	0.994726	−	1.42841i
$925$			10.5281i			0.346161i
$926$	22.0673	−	11.5236i	0.725178	−	0.378688i
$927$	−1.50031			−0.0492767
$928$	37.7752	−	41.7595i	1.24003	−	1.37082i
$929$	5.27223			0.172976			0.0864881	−	0.996253i	$-0.472436\pi$
$929$	5.27223			0.172976			0.0864881	+	0.996253i	$0.472436\pi$
$930$	−18.5364	+	9.67972i	−0.607833	+	0.317410i
$931$		−	4.01815i		−	0.131690i
$932$	−8.87998	+	12.7515i	−0.290873	+	0.417689i
$933$		−	21.0192i		−	0.688139i
$934$	−3.30776	−	6.33428i	−0.108233	−	0.207264i
$935$	7.38907			0.241649
$936$	72.7012	+	9.28652i	2.37631	+	0.303539i
$937$	0.678255			0.0221576			0.0110788	−	0.999939i	$-0.496473\pi$
$937$	0.678255			0.0221576			0.0110788	+	0.999939i	$0.496473\pi$
$938$	−10.8897	−	20.8535i	−0.355562	−	0.680891i
$939$		−	67.3945i		−	2.19934i
$940$	−0.891745	−	0.621000i	−0.0290855	−	0.0202548i
$941$		−	16.1758i		−	0.527317i	−0.964616	−	0.263658i	$-0.915071\pi$
$941$		−	16.1758i		−	0.527317i	0.964616	−	0.263658i	$-0.0849292\pi$
$942$	44.9048	−	23.4493i	1.46308	−	0.764019i
$943$	79.0677			2.57480
$944$	45.1004	−	16.6780i	1.46789	−	0.542824i
$945$	17.7823			0.578458
$946$	−8.52230	+	4.45034i	−0.277084	+	0.144693i
$947$		−	32.6924i		−	1.06236i	−0.847259	−	0.531179i	$-0.821749\pi$
$947$		−	32.6924i		−	1.06236i	0.847259	−	0.531179i	$-0.178251\pi$
$948$	−16.7318	−	11.6518i	−0.543425	−	0.378434i
$949$		−	44.7173i		−	1.45159i
$950$	−0.654621	−	1.25358i	−0.0212387	−	0.0406716i
$951$	13.9606			0.452703
$952$	3.10089	−	24.2758i	0.100500	−	0.786785i
$953$	14.0549			0.455284			0.227642	−	0.973745i	$-0.426898\pi$
$953$	14.0549			0.455284			0.227642	+	0.973745i	$0.426898\pi$
$954$	2.40469	+	4.60492i	0.0778547	+	0.149090i
$955$			13.1874i			0.426736i
$956$	−22.1850	+	31.8573i	−0.717514	+	1.03034i
$957$			79.3363i			2.56458i
$958$	34.8929	−	18.2211i	1.12734	−	0.588696i
$959$	30.8649			0.996681
$960$	−21.7709	−	5.65409i	−0.702654	−	0.182485i
$961$	−3.34178			−0.107799
$962$	−69.7178	+	36.4066i	−2.24779	+	1.17380i
$963$		−	75.6842i		−	2.43889i
$964$	16.7769	−	24.0914i	0.540349	−	0.775932i
$965$			1.50682i			0.0485061i
$966$	−51.3592	−	98.3516i	−1.65246	−	3.16441i
$967$	−1.84780			−0.0594213			−0.0297107	−	0.999559i	$-0.509459\pi$
$967$	−1.84780			−0.0594213			−0.0297107	+	0.999559i	$0.509459\pi$
$968$	−1.06249	+	8.31791i	−0.0341498	+	0.267348i
$969$	7.32908			0.235444
$970$	0.963218	+	1.84454i	0.0309271	+	0.0592245i
$971$		−	23.1458i		−	0.742785i	−0.928476	−	0.371392i	$-0.878881\pi$
$971$		−	23.1458i		−	0.742785i	0.928476	−	0.371392i	$-0.121119\pi$
$972$	−24.7788	−	17.2557i	−0.794782	−	0.553476i
$973$		−	20.4165i		−	0.654521i
$974$	13.2594	−	6.92405i	0.424858	−	0.221861i
$975$	14.8526			0.475663
$976$	−31.9048	+	11.7983i	−1.02125	+	0.377655i
$977$	32.5595			1.04167			0.520835	−	0.853657i	$-0.325621\pi$
$977$	32.5595			1.04167			0.520835	+	0.853657i	$0.325621\pi$
$978$	−51.7192	+	27.0078i	−1.65380	+	0.863614i
$979$			0.987802i			0.0315703i
$980$	−6.59477	−	4.59251i	−0.210662	−	0.146702i
$981$		−	8.49818i		−	0.271326i
$982$	11.6556	+	22.3202i	0.371946	+	0.712268i
$983$	−55.6094			−1.77366			−0.886832	−	0.462092i	$-0.847099\pi$
$983$	−55.6094			−1.77366			−0.886832	+	0.462092i	$0.847099\pi$
$984$	74.1953	+	9.47737i	2.36526	+	0.302128i
$985$	0.841859			0.0268239
$986$	16.9860	+	32.5277i	0.540944	+	1.03589i
$987$		−	5.07087i		−	0.161407i
$988$	6.03762	−	8.66991i	0.192082	−	0.275827i
$989$			20.1612i			0.641089i
$990$	17.4310	−	9.10249i	0.553995	−	0.289296i
$991$	21.1785			0.672756			0.336378	−	0.941727i	$-0.390798\pi$
$991$	21.1785			0.672756			0.336378	+	0.941727i	$0.390798\pi$
$992$	22.0626	+	19.9576i	0.700488	+	0.633654i
$993$	52.0688			1.65235
$994$	−24.9613	+	13.0348i	−0.791723	+	0.413438i
$995$		−	2.38747i		−	0.0756878i
$996$	−18.5342	+	26.6148i	−0.587279	+	0.843323i
$997$			10.7365i			0.340028i	0.985442	+	0.170014i	$0.0543814\pi$
$997$			10.7365i			0.340028i	−0.985442	+	0.170014i	$0.945619\pi$
$998$	−4.23202	−	8.10421i	−0.133962	−	0.256534i
$999$	−56.4005			−1.78443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.f.b.381.8	yes	44
4.3	odd	2		3040.2.f.b.1521.6		44
8.3	odd	2		3040.2.f.b.1521.39		44
8.5	even	2	inner	760.2.f.b.381.7	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.f.b.381.7	✓	44	8.5	even	2	inner
760.2.f.b.381.8	yes	44	1.1	even	1	trivial
3040.2.f.b.1521.6		44	4.3	odd	2
3040.2.f.b.1521.39		44	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25358 + 0.654621i) q^{2} +2.81164i q^{3} +(1.14294 - 1.64124i) q^{4} -1.00000i q^{5} +(-1.84056 - 3.52463i) q^{6} -3.31936 q^{7} +(-0.358379 + 2.80563i) q^{8} -4.90534 q^{9} +(0.654621 + 1.25358i) q^{10} +2.83466i q^{11} +(4.61460 + 3.21355i) q^{12} +5.28252i q^{13} +(4.16109 - 2.17292i) q^{14} +2.81164 q^{15} +(-1.38737 - 3.75169i) q^{16} +2.60669 q^{17} +(6.14926 - 3.21114i) q^{18} -1.00000i q^{19} +(-1.64124 - 1.14294i) q^{20} -9.33286i q^{21} +(-1.85563 - 3.55348i) q^{22} -8.40647 q^{23} +(-7.88844 - 1.00763i) q^{24} -1.00000 q^{25} +(-3.45805 - 6.62208i) q^{26} -5.35715i q^{27} +(-3.79383 + 5.44788i) q^{28} -9.95431i q^{29} +(-3.52463 + 1.84056i) q^{30} +5.25911 q^{31} +(4.19512 + 3.79486i) q^{32} -7.97005 q^{33} +(-3.26770 + 1.70640i) q^{34} +3.31936i q^{35} +(-5.60652 + 8.05087i) q^{36} -10.5281i q^{37} +(0.654621 + 1.25358i) q^{38} -14.8526 q^{39} +(2.80563 + 0.358379i) q^{40} -9.40558 q^{41} +(6.10949 + 11.6995i) q^{42} -2.39830i q^{43} +(4.65237 + 3.23985i) q^{44} +4.90534i q^{45} +(10.5382 - 5.50305i) q^{46} +0.543335 q^{47} +(10.5484 - 3.90079i) q^{48} +4.01815 q^{49} +(1.25358 - 0.654621i) q^{50} +7.32908i q^{51} +(8.66991 + 6.03762i) q^{52} +0.748858i q^{53} +(3.50690 + 6.71563i) q^{54} +2.83466 q^{55} +(1.18959 - 9.31290i) q^{56} +2.81164 q^{57} +(6.51630 + 12.4786i) q^{58} +12.0213i q^{59} +(3.21355 - 4.61460i) q^{60} -8.50410i q^{61} +(-6.59273 + 3.44272i) q^{62} +16.2826 q^{63} +(-7.74313 - 2.01096i) q^{64} +5.28252 q^{65} +(9.99112 - 5.21736i) q^{66} -5.01155i q^{67} +(2.97929 - 4.27822i) q^{68} -23.6360i q^{69} +(-2.17292 - 4.16109i) q^{70} -5.99873 q^{71} +(1.75797 - 13.7626i) q^{72} -8.46514 q^{73} +(6.89190 + 13.1978i) q^{74} -2.81164i q^{75} +(-1.64124 - 1.14294i) q^{76} -9.40925i q^{77} +(18.6189 - 9.72281i) q^{78} -3.62585 q^{79} +(-3.75169 + 1.38737i) q^{80} +0.346365 q^{81} +(11.7907 - 6.15709i) q^{82} +5.76753i q^{83} +(-15.3175 - 10.6669i) q^{84} -2.60669i q^{85} +(1.56998 + 3.00646i) q^{86} +27.9880 q^{87} +(-7.95300 - 1.01588i) q^{88} +0.348473 q^{89} +(-3.21114 - 6.14926i) q^{90} -17.5346i q^{91} +(-9.60810 + 13.7971i) q^{92} +14.7867i q^{93} +(-0.681115 + 0.355679i) q^{94} -1.00000 q^{95} +(-10.6698 + 11.7952i) q^{96} +1.47141 q^{97} +(-5.03709 + 2.63037i) q^{98} -13.9050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

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