LMFDB - Embedded newform 760.2.f.b.381.38

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)

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);

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")

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			381.38
Character	$\chi$	$=$	760.381
Dual form			760.2.f.b.381.37

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30675 + 0.540742i) q^{2} -3.43603i q^{3} +(1.41520 + 1.41323i) q^{4} +1.00000i q^{5} +(1.85801 - 4.49004i) q^{6} +3.17203 q^{7} +(1.08511 + 2.61200i) q^{8} -8.80634 q^{9} +(-0.540742 + 1.30675i) q^{10} -3.55591i q^{11} +(4.85591 - 4.86266i) q^{12} -3.89826i q^{13} +(4.14506 + 1.71525i) q^{14} +3.43603 q^{15} +(0.00555789 + 4.00000i) q^{16} +2.19369 q^{17} +(-11.5077 - 4.76196i) q^{18} +1.00000i q^{19} +(-1.41323 + 1.41520i) q^{20} -10.8992i q^{21} +(1.92283 - 4.64669i) q^{22} +5.09453 q^{23} +(8.97491 - 3.72849i) q^{24} -1.00000 q^{25} +(2.10795 - 5.09405i) q^{26} +19.9508i q^{27} +(4.48905 + 4.48281i) q^{28} -4.27024i q^{29} +(4.49004 + 1.85801i) q^{30} -2.70355 q^{31} +(-2.15570 + 5.23000i) q^{32} -12.2182 q^{33} +(2.86661 + 1.18622i) q^{34} +3.17203i q^{35} +(-12.4627 - 12.4454i) q^{36} +0.572056i q^{37} +(-0.540742 + 1.30675i) q^{38} -13.3945 q^{39} +(-2.61200 + 1.08511i) q^{40} -2.34229 q^{41} +(5.89367 - 14.2426i) q^{42} +0.256294i q^{43} +(5.02533 - 5.03231i) q^{44} -8.80634i q^{45} +(6.65728 + 2.75483i) q^{46} -7.32127 q^{47} +(13.7441 - 0.0190971i) q^{48} +3.06179 q^{49} +(-1.30675 - 0.540742i) q^{50} -7.53761i q^{51} +(5.50914 - 5.51680i) q^{52} +7.59072i q^{53} +(-10.7882 + 26.0707i) q^{54} +3.55591 q^{55} +(3.44202 + 8.28534i) q^{56} +3.43603 q^{57} +(2.30910 - 5.58014i) q^{58} +9.58791i q^{59} +(4.86266 + 4.85591i) q^{60} +11.0779i q^{61} +(-3.53287 - 1.46193i) q^{62} -27.9340 q^{63} +(-5.64505 + 5.66863i) q^{64} +3.89826 q^{65} +(-15.9662 - 6.60692i) q^{66} -11.6238i q^{67} +(3.10450 + 3.10019i) q^{68} -17.5050i q^{69} +(-1.71525 + 4.14506i) q^{70} +4.55159 q^{71} +(-9.55588 - 23.0021i) q^{72} +4.26714 q^{73} +(-0.309335 + 0.747534i) q^{74} +3.43603i q^{75} +(-1.41323 + 1.41520i) q^{76} -11.2795i q^{77} +(-17.5033 - 7.24300i) q^{78} +16.6654 q^{79} +(-4.00000 + 0.00555789i) q^{80} +42.1325 q^{81} +(-3.06079 - 1.26658i) q^{82} +12.9625i q^{83} +(15.4031 - 15.4245i) q^{84} +2.19369i q^{85} +(-0.138589 + 0.334912i) q^{86} -14.6727 q^{87} +(9.28803 - 3.85857i) q^{88} -17.2015 q^{89} +(4.76196 - 11.5077i) q^{90} -12.3654i q^{91} +(7.20976 + 7.19974i) q^{92} +9.28950i q^{93} +(-9.56708 - 3.95892i) q^{94} -1.00000 q^{95} +(17.9705 + 7.40707i) q^{96} +11.0366 q^{97} +(4.00100 + 1.65564i) q^{98} +31.3146i 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 $

$2$	1.30675	+	0.540742i	0.924012	+	0.382362i
$2$	1.30675	+	0.540742i	0.924012	+	0.382362i
$3$		−	3.43603i		−	1.98380i	−0.127038	−	0.991898i	$-0.540547\pi$
$3$		−	3.43603i		−	1.98380i	0.127038	−	0.991898i	$-0.459453\pi$
$4$	1.41520	+	1.41323i	0.707598	+	0.706615i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	1.85801	−	4.49004i	0.758529	−	1.83305i
$7$	3.17203			1.19892			0.599458	−	0.800406i	$-0.295383\pi$
$7$	3.17203			1.19892			0.599458	+	0.800406i	$0.295383\pi$
$8$	1.08511	+	2.61200i	0.383646	+	0.923480i
$9$	−8.80634			−2.93545
$10$	−0.540742	+	1.30675i	−0.170998	+	0.413231i
$11$		−	3.55591i		−	1.07215i	−0.844171	−	0.536074i	$-0.819907\pi$
$11$		−	3.55591i		−	1.07215i	0.844171	−	0.536074i	$-0.180093\pi$
$12$	4.85591	−	4.86266i	1.40178	−	1.40373i
$13$		−	3.89826i		−	1.08118i	−0.841286	−	0.540591i	$-0.818201\pi$
$13$		−	3.89826i		−	1.08118i	0.841286	−	0.540591i	$-0.181799\pi$
$14$	4.14506	+	1.71525i	1.10781	+	0.458420i
$15$	3.43603			0.887180
$16$	0.00555789	+	4.00000i	0.00138947	+	0.999999i
$17$	2.19369			0.532049			0.266024	−	0.963966i	$-0.414290\pi$
$17$	2.19369			0.532049			0.266024	+	0.963966i	$0.414290\pi$
$18$	−11.5077	−	4.76196i	−2.71239	−	1.12240i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−1.41323	+	1.41520i	−0.316008	+	0.316447i
$21$		−	10.8992i		−	2.37840i
$22$	1.92283	−	4.64669i	0.409949	−	0.990678i
$23$	5.09453			1.06228			0.531141	−	0.847283i	$-0.321763\pi$
$23$	5.09453			1.06228			0.531141	+	0.847283i	$0.321763\pi$
$24$	8.97491	−	3.72849i	1.83200	−	0.761075i
$25$	−1.00000			−0.200000
$26$	2.10795	−	5.09405i	0.413403	−	0.999025i
$27$			19.9508i			3.83953i
$28$	4.48905	+	4.48281i	0.848350	+	0.847172i
$29$		−	4.27024i		−	0.792964i	−0.918042	−	0.396482i	$-0.870231\pi$
$29$		−	4.27024i		−	0.792964i	0.918042	−	0.396482i	$-0.129769\pi$
$30$	4.49004	+	1.85801i	0.819766	+	0.339224i
$31$	−2.70355			−0.485572			−0.242786	−	0.970080i	$-0.578061\pi$
$31$	−2.70355			−0.485572			−0.242786	+	0.970080i	$0.578061\pi$
$32$	−2.15570	+	5.23000i	−0.381078	+	0.924543i
$33$	−12.2182			−2.12692
$34$	2.86661	+	1.18622i	0.491620	+	0.203435i
$35$			3.17203i			0.536171i
$36$	−12.4627	−	12.4454i	−2.07711	−	2.07423i
$37$			0.572056i			0.0940454i	0.998894	+	0.0470227i	$0.0149733\pi$
$37$			0.572056i			0.0940454i	−0.998894	+	0.0470227i	$0.985027\pi$
$38$	−0.540742	+	1.30675i	−0.0877200	+	0.211983i
$39$	−13.3945			−2.14484
$40$	−2.61200	+	1.08511i	−0.412993	+	0.171572i
$41$	−2.34229			−0.365805			−0.182902	−	0.983131i	$-0.558549\pi$
$41$	−2.34229			−0.365805			−0.182902	+	0.983131i	$0.558549\pi$
$42$	5.89367	−	14.2426i	0.909412	−	2.19767i
$43$			0.256294i			0.0390844i	0.999809	+	0.0195422i	$0.00622087\pi$
$43$			0.256294i			0.0390844i	−0.999809	+	0.0195422i	$0.993779\pi$
$44$	5.02533	−	5.03231i	0.757596	−	0.758650i
$45$		−	8.80634i		−	1.31277i
$46$	6.65728	+	2.75483i	0.981562	+	0.406177i
$47$	−7.32127			−1.06792			−0.533959	−	0.845511i	$-0.679296\pi$
$47$	−7.32127			−1.06792			−0.533959	+	0.845511i	$0.679296\pi$
$48$	13.7441	−	0.0190971i	1.98379	−	0.00275643i
$49$	3.06179			0.437399
$50$	−1.30675	−	0.540742i	−0.184802	−	0.0764725i
$51$		−	7.53761i		−	1.05548i
$52$	5.50914	−	5.51680i	0.763980	−	0.765042i
$53$			7.59072i			1.04267i	0.853353	+	0.521333i	$0.174565\pi$
$53$			7.59072i			1.04267i	−0.853353	+	0.521333i	$0.825435\pi$
$54$	−10.7882	+	26.0707i	−1.46809	+	3.54777i
$55$	3.55591			0.479479
$56$	3.44202	+	8.28534i	0.459959	+	1.10718i
$57$	3.43603			0.455114
$58$	2.30910	−	5.58014i	0.303200	−	0.732709i
$59$			9.58791i			1.24824i	0.781329	+	0.624120i	$0.214542\pi$
$59$			9.58791i			1.24824i	−0.781329	+	0.624120i	$0.785458\pi$
$60$	4.86266	+	4.85591i	0.627767	+	0.626895i
$61$			11.0779i			1.41838i	0.705020	+	0.709188i	$0.250938\pi$
$61$			11.0779i			1.41838i	−0.705020	+	0.709188i	$0.749062\pi$
$62$	−3.53287	−	1.46193i	−0.448675	−	0.185665i
$63$	−27.9340			−3.51935
$64$	−5.64505	+	5.66863i	−0.705631	+	0.708579i
$65$	3.89826			0.483519
$66$	−15.9662	−	6.60692i	−1.96530	−	0.813255i
$67$		−	11.6238i		−	1.42007i	−0.704164	−	0.710037i	$-0.748678\pi$
$67$		−	11.6238i		−	1.42007i	0.704164	−	0.710037i	$-0.251322\pi$
$68$	3.10450	+	3.10019i	0.376477	+	0.375954i
$69$		−	17.5050i		−	2.10735i
$70$	−1.71525	+	4.14506i	−0.205012	+	0.495429i
$71$	4.55159			0.540174			0.270087	−	0.962836i	$-0.412948\pi$
$71$	4.55159			0.540174			0.270087	+	0.962836i	$0.412948\pi$
$72$	−9.55588	−	23.0021i	−1.12617	−	2.71083i
$73$	4.26714			0.499431			0.249716	−	0.968319i	$-0.419663\pi$
$73$	4.26714			0.499431			0.249716	+	0.968319i	$0.419663\pi$
$74$	−0.309335	+	0.747534i	−0.0359594	+	0.0868991i
$75$			3.43603i			0.396759i
$76$	−1.41323	+	1.41520i	−0.162109	+	0.162334i
$77$		−	11.2795i		−	1.28542i
$78$	−17.5033	−	7.24300i	−1.98186	−	0.820108i
$79$	16.6654			1.87501			0.937504	−	0.347976i	$-0.113131\pi$
$79$	16.6654			1.87501			0.937504	+	0.347976i	$0.113131\pi$
$80$	−4.00000	+	0.00555789i	−0.447213	+	0.000621392i
$81$	42.1325			4.68139
$82$	−3.06079	−	1.26658i	−0.338008	−	0.139870i
$83$			12.9625i			1.42281i	0.702780	+	0.711407i	$0.251942\pi$
$83$			12.9625i			1.42281i	−0.702780	+	0.711407i	$0.748058\pi$
$84$	15.4031	−	15.4245i	1.68062	−	1.68295i
$85$			2.19369i			0.237939i
$86$	−0.138589	+	0.334912i	−0.0149444	+	0.0361145i
$87$	−14.6727			−1.57308
$88$	9.28803	−	3.85857i	0.990108	−	0.411325i
$89$	−17.2015			−1.82335			−0.911676	−	0.410910i	$-0.865211\pi$
$89$	−17.2015			−1.82335			−0.911676	+	0.410910i	$0.865211\pi$
$90$	4.76196	−	11.5077i	0.501954	−	1.21302i
$91$		−	12.3654i		−	1.29625i
$92$	7.20976	+	7.19974i	0.751669	+	0.750625i
$93$			9.28950i			0.963277i
$94$	−9.56708	−	3.95892i	−0.986769	−	0.408331i
$95$	−1.00000			−0.102598
$96$	17.9705	+	7.40707i	1.83410	+	0.755981i
$97$	11.0366			1.12060			0.560299	−	0.828291i	$-0.310686\pi$
$97$	11.0366			1.12060			0.560299	+	0.828291i	$0.310686\pi$
$98$	4.00100	+	1.65564i	0.404162	+	0.167245i
$99$			31.3146i			3.14723i
$100$	−1.41520	−	1.41323i	−0.141520	−	0.141323i
$101$		−	1.65421i		−	0.164600i	−0.996608	−	0.0823002i	$-0.973773\pi$
$101$		−	1.65421i		−	0.164600i	0.996608	−	0.0823002i	$-0.0262266\pi$
$102$	4.07590	−	9.84977i	0.403574	−	0.975273i
$103$	−11.3034			−1.11376			−0.556878	−	0.830594i	$-0.688001\pi$
$103$	−11.3034			−1.11376			−0.556878	+	0.830594i	$0.688001\pi$
$104$	10.1822	−	4.23006i	0.998450	−	0.414791i
$105$	10.8992			1.06365
$106$	−4.10462	+	9.91918i	−0.398676	+	0.963436i
$107$			14.9784i			1.44802i	0.689789	+	0.724011i	$0.257703\pi$
$107$			14.9784i			1.44802i	−0.689789	+	0.724011i	$0.742297\pi$
$108$	−28.1950	+	28.2342i	−2.71307	+	2.71684i
$109$		−	8.80414i		−	0.843284i	−0.906762	−	0.421642i	$-0.861454\pi$
$109$		−	8.80414i		−	0.843284i	0.906762	−	0.421642i	$-0.138546\pi$
$110$	4.64669	+	1.92283i	0.443045	+	0.183335i
$111$	1.96560			0.186567
$112$	0.0176298	+	12.6881i	0.00166586	+	1.19891i
$113$	−2.15293			−0.202531			−0.101266	−	0.994859i	$-0.532289\pi$
$113$	−2.15293			−0.202531			−0.101266	+	0.994859i	$0.532289\pi$
$114$	4.49004	+	1.85801i	0.420531	+	0.174018i
$115$			5.09453i			0.475067i
$116$	6.03484	−	6.04323i	0.560321	−	0.561100i
$117$			34.3293i			3.17375i
$118$	−5.18459	+	12.5290i	−0.477280	+	1.15339i
$119$	6.95847			0.637882
$120$	3.72849	+	8.97491i	0.340363	+	0.819294i
$121$	−1.64452			−0.149501
$122$	−5.99027	+	14.4760i	−0.542333	+	1.31060i
$123$			8.04820i			0.725681i
$124$	−3.82606	−	3.82074i	−0.343590	−	0.343113i
$125$		−	1.00000i		−	0.0894427i
$126$	−36.5028	−	15.1051i	−3.25192	−	1.34567i
$127$	−3.18254			−0.282405			−0.141202	−	0.989981i	$-0.545097\pi$
$127$	−3.18254			−0.282405			−0.141202	+	0.989981i	$0.545097\pi$
$128$	−10.4419	+	4.35497i	−0.922946	+	0.384929i
$129$	0.880634			0.0775355
$130$	5.09405	+	2.10795i	0.446778	+	0.184880i
$131$			10.2612i			0.896522i	0.893903	+	0.448261i	$0.147956\pi$
$131$			10.2612i			0.896522i	−0.893903	+	0.448261i	$0.852044\pi$
$132$	−17.2912	−	17.2672i	−1.50501	−	1.50292i
$133$			3.17203i			0.275050i
$134$	6.28548	−	15.1894i	0.542983	−	1.31217i
$135$	−19.9508			−1.71709
$136$	2.38041	+	5.72992i	0.204118	+	0.491336i
$137$	−14.7917			−1.26374			−0.631868	−	0.775076i	$-0.717712\pi$
$137$	−14.7917			−1.26374			−0.631868	+	0.775076i	$0.717712\pi$
$138$	9.46568	−	22.8746i	0.805772	−	1.94722i
$139$			3.77326i			0.320044i	0.987113	+	0.160022i	$0.0511565\pi$
$139$			3.77326i			0.320044i	−0.987113	+	0.160022i	$0.948843\pi$
$140$	−4.48281	+	4.48905i	−0.378867	+	0.379394i
$141$			25.1561i			2.11853i
$142$	5.94779	+	2.46123i	0.499127	+	0.206542i
$143$	−13.8619			−1.15919
$144$	−0.0489447	−	35.2253i	−0.00407872	−	2.93544i
$145$	4.27024			0.354624
$146$	5.57609	+	2.30742i	0.461480	+	0.190964i
$147$		−	10.5204i		−	0.867711i
$148$	−0.808447	+	0.809571i	−0.0664539	+	0.0665463i
$149$			20.0386i			1.64163i	0.571194	+	0.820815i	$0.306480\pi$
$149$			20.0386i			1.64163i	−0.571194	+	0.820815i	$0.693520\pi$
$150$	−1.85801	+	4.49004i	−0.151706	+	0.366610i
$151$	13.9175			1.13259			0.566295	−	0.824202i	$-0.308376\pi$
$151$	13.9175			1.13259			0.566295	+	0.824202i	$0.308376\pi$
$152$	−2.61200	+	1.08511i	−0.211861	+	0.0880144i
$153$	−19.3184			−1.56180
$154$	6.09929	−	14.7395i	0.491495	−	1.18774i
$155$		−	2.70355i		−	0.217155i
$156$	−18.9559	−	18.9296i	−1.51769	−	1.51558i
$157$		−	5.09197i		−	0.406384i	−0.979139	−	0.203192i	$-0.934868\pi$
$157$		−	5.09197i		−	0.406384i	0.979139	−	0.203192i	$-0.0651315\pi$
$158$	21.7776	+	9.01170i	1.73253	+	0.716932i
$159$	26.0820			2.06844
$160$	−5.23000	−	2.15570i	−0.413468	−	0.170423i
$161$	16.1600			1.27359
$162$	55.0567	+	22.7828i	4.32566	+	1.78999i
$163$			2.70054i			0.211522i	0.994392	+	0.105761i	$0.0337279\pi$
$163$			2.70054i			0.211522i	−0.994392	+	0.105761i	$0.966272\pi$
$164$	−3.31480	−	3.31020i	−0.258842	−	0.258483i
$165$		−	12.2182i		−	0.951189i
$166$	−7.00935	+	16.9387i	−0.544031	+	1.31470i
$167$	5.17113			0.400154			0.200077	−	0.979780i	$-0.435881\pi$
$167$	5.17113			0.400154			0.200077	+	0.979780i	$0.435881\pi$
$168$	28.4687	−	11.8269i	2.19641	−	0.912465i
$169$	−2.19640			−0.168954
$170$	−1.18622	+	2.86661i	−0.0909791	+	0.219859i
$171$		−	8.80634i		−	0.673437i
$172$	−0.362202	+	0.362706i	−0.0276176	+	0.0276560i
$173$		−	15.5280i		−	1.18057i	−0.807195	−	0.590285i	$-0.799016\pi$
$173$		−	15.5280i		−	1.18057i	0.807195	−	0.590285i	$-0.200984\pi$
$174$	−19.1736	−	7.93415i	−1.45354	−	0.601486i
$175$	−3.17203			−0.239783
$176$	14.2236	−	0.0197634i	1.07215	−	0.00148972i
$177$	32.9444			2.47625
$178$	−22.4780	−	9.30156i	−1.68480	−	0.697181i
$179$		−	25.5098i		−	1.90669i	−0.301880	−	0.953346i	$-0.597614\pi$
$179$		−	25.5098i		−	1.90669i	0.301880	−	0.953346i	$-0.402386\pi$
$180$	12.4454	−	12.4627i	0.927624	−	0.928914i
$181$		−	0.322469i		−	0.0239690i	−0.999928	−	0.0119845i	$-0.996185\pi$
$181$		−	0.322469i		−	0.0239690i	0.999928	−	0.0119845i	$-0.00381487\pi$
$182$	6.68649	−	16.1585i	0.495636	−	1.19775i
$183$	38.0639			2.81377
$184$	5.52815	+	13.3069i	0.407540	+	0.980997i
$185$	−0.572056			−0.0420584
$186$	−5.02323	+	12.1391i	−0.368321	+	0.890079i
$187$		−	7.80058i		−	0.570435i
$188$	−10.3610	−	10.3466i	−0.755656	−	0.754607i
$189$			63.2845i			4.60327i
$190$	−1.30675	−	0.540742i	−0.0948017	−	0.0392296i
$191$	−16.5576			−1.19806			−0.599032	−	0.800725i	$-0.704448\pi$
$191$	−16.5576			−1.19806			−0.599032	+	0.800725i	$0.704448\pi$
$192$	19.4776	+	19.3966i	1.40568	+	1.39983i
$193$	10.2572			0.738332			0.369166	−	0.929364i	$-0.379643\pi$
$193$	10.2572			0.738332			0.369166	+	0.929364i	$0.379643\pi$
$194$	14.4221	+	5.96796i	1.03545	+	0.428474i
$195$		−	13.3945i		−	0.959203i
$196$	4.33304	+	4.32702i	0.309503	+	0.309073i
$197$		−	3.19544i		−	0.227666i	−0.993500	−	0.113833i	$-0.963687\pi$
$197$		−	3.19544i		−	0.227666i	0.993500	−	0.113833i	$-0.0363128\pi$
$198$	−16.9331	+	40.9203i	−1.20338	+	2.90808i
$199$	9.69079			0.686962			0.343481	−	0.939160i	$-0.388394\pi$
$199$	9.69079			0.686962			0.343481	+	0.939160i	$0.388394\pi$
$200$	−1.08511	−	2.61200i	−0.0767292	−	0.184696i
$201$	−39.9398			−2.81714
$202$	0.894503	−	2.16165i	0.0629370	−	0.152093i
$203$		−	13.5454i		−	0.950697i
$204$	10.6524	−	10.6672i	0.745815	−	0.746852i
$205$		−	2.34229i		−	0.163593i
$206$	−14.7707	−	6.11222i	−1.02912	−	0.425859i
$207$	−44.8641			−3.11827
$208$	15.5930	−	0.0216661i	1.08118	−	0.00150227i
$209$	3.55591			0.245968
$210$	14.2426	+	5.89367i	0.982830	+	0.406702i
$211$		−	17.0734i		−	1.17538i	−0.809086	−	0.587690i	$-0.800037\pi$
$211$		−	17.0734i		−	1.17538i	0.809086	−	0.587690i	$-0.199963\pi$
$212$	−10.7274	+	10.7424i	−0.736764	+	0.737788i
$213$		−	15.6394i		−	1.07159i
$214$	−8.09948	+	19.5731i	−0.553669	+	1.33799i
$215$	−0.256294			−0.0174791
$216$	−52.1113	+	21.6489i	−3.54573	+	1.47302i
$217$	−8.57576			−0.582161
$218$	4.76077	−	11.5048i	0.322440	−	0.779205i
$219$		−	14.6620i		−	0.990769i
$220$	5.03231	+	5.02533i	0.339278	+	0.338807i
$221$		−	8.55158i		−	0.575241i
$222$	2.56855	+	1.06288i	0.172390	+	0.0713361i
$223$	2.02927			0.135890			0.0679450	−	0.997689i	$-0.478356\pi$
$223$	2.02927			0.135890			0.0679450	+	0.997689i	$0.478356\pi$
$224$	−6.83796	+	16.5897i	−0.456881	+	1.10845i
$225$	8.80634			0.587089
$226$	−2.81335	−	1.16418i	−0.187141	−	0.0774403i
$227$			24.2142i			1.60715i	0.595201	+	0.803577i	$0.297072\pi$
$227$			24.2142i			1.60715i	−0.595201	+	0.803577i	$0.702928\pi$
$228$	4.86266	+	4.85591i	0.322038	+	0.321590i
$229$		−	5.57019i		−	0.368089i	−0.982918	−	0.184044i	$-0.941081\pi$
$229$		−	5.57019i		−	0.368089i	0.982918	−	0.184044i	$-0.0589190\pi$
$230$	−2.75483	+	6.65728i	−0.181648	+	0.438968i
$231$	−38.7567			−2.55000
$232$	11.1539	−	4.63370i	0.732287	−	0.304218i
$233$	−8.03878			−0.526638			−0.263319	−	0.964709i	$-0.584817\pi$
$233$	−8.03878			−0.526638			−0.263319	+	0.964709i	$0.584817\pi$
$234$	−18.5633	+	44.8599i	−1.21352	+	2.93258i
$235$		−	7.32127i		−	0.477587i
$236$	−13.5499	+	13.5688i	−0.882025	+	0.883251i
$237$		−	57.2630i		−	3.71963i
$238$	9.09298	+	3.76274i	0.589410	+	0.243902i
$239$	1.31933			0.0853406			0.0426703	−	0.999089i	$-0.486413\pi$
$239$	1.31933			0.0853406			0.0426703	+	0.999089i	$0.486413\pi$
$240$	0.0190971	+	13.7441i	0.00123271	+	0.887180i
$241$	−15.2205			−0.980436			−0.490218	−	0.871600i	$-0.663083\pi$
$241$	−15.2205			−0.980436			−0.490218	+	0.871600i	$0.663083\pi$
$242$	−2.14897	−	0.889259i	−0.138141	−	0.0571637i
$243$		−	84.9165i		−	5.44740i
$244$	−15.6556	+	15.6773i	−1.00225	+	1.00364i
$245$			3.06179i			0.195611i
$246$	−4.35200	+	10.5170i	−0.277473	+	0.670539i
$247$	3.89826			0.248040
$248$	−2.93367	−	7.06167i	−0.186288	−	0.448417i
$249$	44.5395			2.82257
$250$	0.540742	−	1.30675i	0.0341995	−	0.0826462i
$251$			12.4716i			0.787203i	0.919281	+	0.393602i	$0.128771\pi$
$251$			12.4716i			0.787203i	−0.919281	+	0.393602i	$0.871229\pi$
$252$	−39.5321	−	39.4772i	−2.49029	−	2.48683i
$253$		−	18.1157i		−	1.13892i
$254$	−4.15879	−	1.72093i	−0.260945	−	0.107981i
$255$	7.53761			0.472023
$256$	−15.9999	+	0.0444631i	−0.999996	+	0.00277894i
$257$	−11.2331			−0.700700			−0.350350	−	0.936619i	$-0.613937\pi$
$257$	−11.2331			−0.700700			−0.350350	+	0.936619i	$0.613937\pi$
$258$	1.15077	+	0.476196i	0.0716437	+	0.0296467i
$259$			1.81458i			0.112752i
$260$	5.51680	+	5.50914i	0.342137	+	0.341662i
$261$			37.6052i			2.32770i
$262$	−5.54864	+	13.4088i	−0.342796	+	0.828397i
$263$	−5.31570			−0.327780			−0.163890	−	0.986479i	$-0.552404\pi$
$263$	−5.31570			−0.327780			−0.163890	+	0.986479i	$0.552404\pi$
$264$	−13.2582	−	31.9140i	−0.815985	−	1.96417i
$265$	−7.59072			−0.466294
$266$	−1.71525	+	4.14506i	−0.105169	+	0.254150i
$267$			59.1048i			3.61716i
$268$	16.4271	−	16.4500i	1.00345	−	1.00484i
$269$		−	19.1343i		−	1.16664i	−0.812242	−	0.583320i	$-0.801753\pi$
$269$		−	19.1343i		−	1.16664i	0.812242	−	0.583320i	$-0.198247\pi$
$270$	−26.0707	−	10.7882i	−1.58661	−	0.656550i
$271$	−11.6218			−0.705972			−0.352986	−	0.935629i	$-0.614834\pi$
$271$	−11.6218			−0.705972			−0.352986	+	0.935629i	$0.614834\pi$
$272$	0.0121923	+	8.77476i	0.000739268	+	0.532048i
$273$	−42.4879			−2.57149
$274$	−19.3290	−	7.99847i	−1.16771	−	0.483205i
$275$			3.55591i			0.214430i
$276$	24.7386	−	24.7730i	1.48909	−	1.49116i
$277$			6.04042i			0.362934i	0.983397	+	0.181467i	$0.0580845\pi$
$277$			6.04042i			0.362934i	−0.983397	+	0.181467i	$0.941916\pi$
$278$	−2.04036	+	4.93071i	−0.122373	+	0.295725i
$279$	23.8084			1.42537
$280$	−8.28534	+	3.44202i	−0.495144	+	0.205700i
$281$	14.6782			0.875629			0.437814	−	0.899065i	$-0.355753\pi$
$281$	14.6782			0.875629			0.437814	+	0.899065i	$0.355753\pi$
$282$	−13.6030	+	32.8728i	−0.810046	+	1.95755i
$283$			10.9007i			0.647977i	0.946061	+	0.323989i	$0.105024\pi$
$283$			10.9007i			0.647977i	−0.946061	+	0.323989i	$0.894976\pi$
$284$	6.44139	+	6.43244i	0.382226	+	0.381695i
$285$			3.43603i			0.203533i
$286$	−18.1140	−	7.49569i	−1.07110	−	0.443230i
$287$	−7.42983			−0.438569
$288$	18.9839	−	46.0572i	1.11863	−	2.71394i
$289$	−12.1877			−0.716924
$290$	5.58014	+	2.30910i	0.327677	+	0.135595i
$291$		−	37.9222i		−	2.22304i
$292$	6.03884	+	6.03045i	0.353396	+	0.352906i
$293$		−	26.9466i		−	1.57423i	−0.616803	−	0.787117i	$-0.711573\pi$
$293$		−	26.9466i		−	1.57423i	0.616803	−	0.787117i	$-0.288427\pi$
$294$	5.68884	−	13.7476i	0.331780	−	0.801775i
$295$	−9.58791			−0.558229
$296$	−1.49421	+	0.620746i	−0.0868490	+	0.0360801i
$297$	70.9432			4.11654
$298$	−10.8357	+	26.1855i	−0.627698	+	1.51689i
$299$		−	19.8598i		−	1.14852i
$300$	−4.85591	+	4.86266i	−0.280356	+	0.280746i
$301$			0.812972i			0.0468589i
$302$	18.1867	+	7.52578i	1.04653	+	0.433060i
$303$	−5.68394			−0.326534
$304$	−4.00000	+	0.00555789i	−0.229416	+	0.000318767i
$305$	−11.0779			−0.634317
$306$	−25.2443	−	10.4463i	−1.44312	−	0.597174i
$307$		−	6.29461i		−	0.359252i	−0.983735	−	0.179626i	$-0.942511\pi$
$307$		−	6.29461i		−	0.359252i	0.983735	−	0.179626i	$-0.0574888\pi$
$308$	15.9405	−	15.9627i	0.908294	−	0.909557i
$309$			38.8389i			2.20947i
$310$	1.46193	−	3.53287i	0.0830318	−	0.200654i
$311$	−1.12709			−0.0639115			−0.0319558	−	0.999489i	$-0.510174\pi$
$311$	−1.12709			−0.0639115			−0.0319558	+	0.999489i	$0.510174\pi$
$312$	−14.5346	−	34.9865i	−0.822861	−	1.98072i
$313$	−16.9303			−0.956955			−0.478477	−	0.878100i	$-0.658811\pi$
$313$	−16.9303			−0.956955			−0.478477	+	0.878100i	$0.658811\pi$
$314$	2.75345	−	6.65394i	0.155386	−	0.375504i
$315$		−	27.9340i		−	1.57390i
$316$	23.5848	+	23.5521i	1.32675	+	1.32491i
$317$		−	13.0664i		−	0.733883i	−0.930244	−	0.366942i	$-0.880405\pi$
$317$		−	13.0664i		−	0.733883i	0.930244	−	0.366942i	$-0.119595\pi$
$318$	34.0827	+	14.1036i	1.91126	+	0.790892i
$319$	−15.1846			−0.850175
$320$	−5.66863	−	5.64505i	−0.316886	−	0.315568i
$321$	51.4665			2.87258
$322$	21.1171	+	8.73840i	1.17681	+	0.486972i
$323$			2.19369i			0.122060i
$324$	59.6258	+	59.5430i	3.31254	+	3.30794i
$325$			3.89826i			0.216236i
$326$	−1.46029	+	3.52893i	−0.0808782	+	0.195449i
$327$	−30.2513			−1.67290
$328$	−2.54166	−	6.11806i	−0.140339	−	0.337813i
$329$	−23.2233			−1.28034
$330$	6.60692	−	15.9662i	0.363699	−	0.878910i
$331$			16.2867i			0.895198i	0.894234	+	0.447599i	$0.147721\pi$
$331$			16.2867i			0.895198i	−0.894234	+	0.447599i	$0.852279\pi$
$332$	−18.3189	+	18.3444i	−1.00538	+	1.00678i
$333$		−	5.03771i		−	0.276065i
$334$	6.75738	+	2.79625i	0.369747	+	0.153004i
$335$	11.6238			0.635077
$336$	43.5968	−	0.0605767i	2.37840	−	0.00330473i
$337$	13.8164			0.752628			0.376314	−	0.926492i	$-0.377191\pi$
$337$	13.8164			0.752628			0.376314	+	0.926492i	$0.377191\pi$
$338$	−2.87015	−	1.18769i	−0.156115	−	0.0646016i
$339$			7.39756i			0.401780i
$340$	−3.10019	+	3.10450i	−0.168132	+	0.168365i
$341$			9.61360i			0.520606i
$342$	4.76196	−	11.5077i	0.257497	−	0.622264i
$343$	−12.4921			−0.674511
$344$	−0.669438	+	0.278108i	−0.0360937	+	0.0149946i
$345$	17.5050			0.942436
$346$	8.39662	−	20.2912i	0.451405	−	1.09086i
$347$		−	12.4801i		−	0.669968i	−0.942224	−	0.334984i	$-0.891269\pi$
$347$		−	12.4801i		−	0.669968i	0.942224	−	0.334984i	$-0.108731\pi$
$348$	−20.7647	−	20.7359i	−1.11311	−	1.11156i
$349$		−	28.5000i		−	1.52557i	−0.646651	−	0.762786i	$-0.723831\pi$
$349$		−	28.5000i		−	1.52557i	0.646651	−	0.762786i	$-0.276169\pi$
$350$	−4.14506	−	1.71525i	−0.221563	−	0.0916841i
$351$	77.7732			4.15123
$352$	18.5974	+	7.66550i	0.991247	+	0.408572i
$353$	−1.15159			−0.0612929			−0.0306465	−	0.999530i	$-0.509757\pi$
$353$	−1.15159			−0.0612929			−0.0306465	+	0.999530i	$0.509757\pi$
$354$	43.0501	+	17.8144i	2.28809	+	0.946826i
$355$			4.55159i			0.241573i
$356$	−24.3434	−	24.3096i	−1.29020	−	1.28841i
$357$		−	23.9095i		−	1.26543i
$358$	13.7942	−	33.3349i	0.729047	−	1.76181i
$359$	−13.7596			−0.726203			−0.363101	−	0.931750i	$-0.618282\pi$
$359$	−13.7596			−0.726203			−0.363101	+	0.931750i	$0.618282\pi$
$360$	23.0021	−	9.55588i	1.21232	−	0.503639i
$361$	−1.00000			−0.0526316
$362$	0.174373	−	0.421387i	0.00916483	−	0.0221476i
$363$			5.65061i			0.296580i
$364$	17.4752	−	17.4995i	0.915947	−	0.917221i
$365$			4.26714i			0.223352i
$366$	49.7401	+	20.5828i	2.59995	+	1.07588i
$367$	−22.3902			−1.16876			−0.584381	−	0.811480i	$-0.698662\pi$
$367$	−22.3902			−1.16876			−0.584381	+	0.811480i	$0.698662\pi$
$368$	0.0283149	+	20.3781i	0.00147601	+	1.06228i
$369$	20.6270			1.07380
$370$	−0.747534	−	0.309335i	−0.0388625	−	0.0160815i
$371$			24.0780i			1.25007i
$372$	−13.1282	+	13.1465i	−0.680666	+	0.681612i
$373$		−	30.0287i		−	1.55483i	−0.628990	−	0.777413i	$-0.716531\pi$
$373$		−	30.0287i		−	1.55483i	0.628990	−	0.777413i	$-0.283469\pi$
$374$	4.21810	−	10.1934i	0.218113	−	0.527089i
$375$	−3.43603			−0.177436
$376$	−7.94442	−	19.1231i	−0.409702	−	0.986200i
$377$	−16.6465			−0.857338
$378$	−34.2206	+	82.6971i	−1.76012	+	4.25348i
$379$		−	2.11947i		−	0.108870i	−0.998517	−	0.0544349i	$-0.982664\pi$
$379$		−	2.11947i		−	0.108870i	0.998517	−	0.0544349i	$-0.0173357\pi$
$380$	−1.41520	−	1.41323i	−0.0725980	−	0.0724972i
$381$			10.9353i			0.560233i
$382$	−21.6366	−	8.95338i	−1.10703	−	0.458095i
$383$	−20.7268			−1.05909			−0.529546	−	0.848281i	$-0.677638\pi$
$383$	−20.7268			−1.05909			−0.529546	+	0.848281i	$0.677638\pi$
$384$	14.9638	+	35.8789i	0.763620	+	1.83094i
$385$	11.2795			0.574855
$386$	13.4036	+	5.54652i	0.682228	+	0.282310i
$387$		−	2.25701i		−	0.114730i
$388$	15.6190	+	15.5973i	0.792932	+	0.791831i
$389$		−	12.6399i		−	0.640868i	−0.947271	−	0.320434i	$-0.896171\pi$
$389$		−	12.6399i		−	0.640868i	0.947271	−	0.320434i	$-0.103829\pi$
$390$	7.24300	−	17.5033i	0.366763	−	0.886316i
$391$	11.1758			0.565186
$392$	3.32240	+	7.99740i	0.167806	+	0.403929i
$393$	35.2577			1.77852
$394$	1.72791	−	4.17564i	0.0870508	−	0.210366i
$395$			16.6654i			0.838529i
$396$	−44.2547	+	44.3162i	−2.22388	+	2.22697i
$397$			10.5707i			0.530531i	0.964175	+	0.265265i	$0.0854596\pi$
$397$			10.5707i			0.530531i	−0.964175	+	0.265265i	$0.914540\pi$
$398$	12.6635	+	5.24022i	0.634761	+	0.262669i
$399$	10.8992			0.545643
$400$	−0.00555789	−	4.00000i	−0.000277895	−	0.200000i
$401$	−21.3800			−1.06767			−0.533833	−	0.845590i	$-0.679249\pi$
$401$	−21.3800			−1.06767			−0.533833	+	0.845590i	$0.679249\pi$
$402$	−52.1914	−	21.5971i	−2.60307	−	1.07717i
$403$			10.5391i			0.524992i
$404$	2.33779	−	2.34104i	0.116309	−	0.116471i
$405$			42.1325i			2.09358i
$406$	7.32454	−	17.7004i	0.363511	−	0.878456i
$407$	2.03418			0.100831
$408$	19.6882	−	8.17917i	0.974711	−	0.404929i
$409$	−1.08607			−0.0537026			−0.0268513	−	0.999639i	$-0.508548\pi$
$409$	−1.08607			−0.0537026			−0.0268513	+	0.999639i	$0.508548\pi$
$410$	1.26658	−	3.06079i	0.0625517	−	0.151162i
$411$			50.8246i			2.50699i
$412$	−15.9965	−	15.9743i	−0.788092	−	0.786998i
$413$			30.4132i			1.49653i
$414$	−58.6262	−	24.2599i	−2.88132	−	1.19231i
$415$	−12.9625			−0.636302
$416$	20.3879	+	8.40349i	0.999599	+	0.412015i
$417$	12.9651			0.634902
$418$	4.64669	+	1.92283i	0.227277	+	0.0940488i
$419$		−	24.3609i		−	1.19011i	−0.803686	−	0.595053i	$-0.797131\pi$
$419$		−	24.3609i		−	1.19011i	0.803686	−	0.595053i	$-0.202869\pi$
$420$	15.4245	+	15.4031i	0.752640	+	0.751595i
$421$		−	18.8340i		−	0.917914i	−0.888458	−	0.458957i	$-0.848223\pi$
$421$		−	18.8340i		−	0.917914i	0.888458	−	0.458957i	$-0.151777\pi$
$422$	9.23230	−	22.3107i	0.449421	−	1.08607i
$423$	64.4736			3.13481
$424$	−19.8269	+	8.23681i	−0.962881	+	0.400015i
$425$	−2.19369			−0.106410
$426$	8.45689	−	20.4368i	0.409738	−	0.990167i
$427$			35.1393i			1.70051i
$428$	−21.1680	+	21.1974i	−1.02319	+	1.02462i
$429$			47.6298i			2.29959i
$430$	−0.334912	−	0.138589i	−0.0161509	−	0.00668334i
$431$	31.5923			1.52175			0.760875	−	0.648899i	$-0.224770\pi$
$431$	31.5923			1.52175			0.760875	+	0.648899i	$0.224770\pi$
$432$	−79.8030	+	0.110884i	−3.83952	+	0.00533492i
$433$	8.33702			0.400651			0.200326	−	0.979729i	$-0.435800\pi$
$433$	8.33702			0.400651			0.200326	+	0.979729i	$0.435800\pi$
$434$	−11.2064	−	4.63728i	−0.537924	−	0.222596i
$435$		−	14.6727i		−	0.703502i
$436$	12.4423	−	12.4596i	0.595877	−	0.596706i
$437$			5.09453i			0.243704i
$438$	7.92839	−	19.1596i	0.378833	−	0.915483i
$439$	34.0302			1.62417			0.812085	−	0.583539i	$-0.198332\pi$
$439$	34.0302			1.62417			0.812085	+	0.583539i	$0.198332\pi$
$440$	3.85857	+	9.28803i	0.183950	+	0.442790i
$441$	−26.9632			−1.28396
$442$	4.62420	−	11.1748i	0.219951	−	0.531530i
$443$			18.2183i			0.865577i	0.901495	+	0.432789i	$0.142470\pi$
$443$			18.2183i			0.865577i	−0.901495	+	0.432789i	$0.857530\pi$
$444$	2.78171	+	2.77785i	0.132014	+	0.131831i
$445$		−	17.2015i		−	0.815428i
$446$	2.65175	+	1.09731i	0.125564	+	0.0519592i
$447$	68.8535			3.25666
$448$	−17.9063	+	17.9811i	−0.845993	+	0.849527i
$449$	−39.4027			−1.85953			−0.929764	−	0.368156i	$-0.879989\pi$
$449$	−39.4027			−1.85953			−0.929764	+	0.368156i	$0.879989\pi$
$450$	11.5077	+	4.76196i	0.542478	+	0.224481i
$451$			8.32899i			0.392197i
$452$	−3.04682	−	3.04259i	−0.143311	−	0.143112i
$453$		−	47.8210i		−	2.24683i
$454$	−13.0936	+	31.6419i	−0.614515	+	1.48503i
$455$	12.3654			0.579699
$456$	3.72849	+	8.97491i	0.174603	+	0.420289i
$457$	9.88724			0.462506			0.231253	−	0.972894i	$-0.425718\pi$
$457$	9.88724			0.462506			0.231253	+	0.972894i	$0.425718\pi$
$458$	3.01204	−	7.27885i	0.140743	−	0.340118i
$459$			43.7659i			2.04282i
$460$	−7.19974	+	7.20976i	−0.335690	+	0.336157i
$461$			15.3988i			0.717195i	0.933492	+	0.358597i	$0.116745\pi$
$461$			15.3988i			0.717195i	−0.933492	+	0.358597i	$0.883255\pi$
$462$	−50.6453	−	20.9574i	−2.35623	−	0.975025i
$463$	17.6430			0.819941			0.409970	−	0.912099i	$-0.365539\pi$
$463$	17.6430			0.819941			0.409970	+	0.912099i	$0.365539\pi$
$464$	17.0810	−	0.0237336i	0.792963	−	0.00110180i
$465$	−9.28950			−0.430790
$466$	−10.5047	−	4.34691i	−0.486620	−	0.201367i
$467$			14.2647i			0.660093i	0.943965	+	0.330047i	$0.107064\pi$
$467$			14.2647i			0.660093i	−0.943965	+	0.330047i	$0.892936\pi$
$468$	−48.5153	+	48.5827i	−2.24262	+	2.24574i
$469$		−	36.8711i		−	1.70255i
$470$	3.95892	−	9.56708i	0.182611	−	0.441296i
$471$	−17.4962			−0.806182
$472$	−25.0436	+	10.4040i	−1.15272	+	0.478882i
$473$	0.911358			0.0419043
$474$	30.9645	−	74.8285i	1.42225	−	3.43699i
$475$		−	1.00000i		−	0.0458831i
$476$	9.84759	+	9.83392i	0.451364	+	0.450737i
$477$		−	66.8465i		−	3.06069i
$478$	1.72404	+	0.713420i	0.0788558	+	0.0326311i
$479$	23.0752			1.05433			0.527166	−	0.849762i	$-0.323254\pi$
$479$	23.0752			1.05433			0.527166	+	0.849762i	$0.323254\pi$
$480$	−7.40707	+	17.9705i	−0.338085	+	0.820236i
$481$	2.23002			0.101680
$482$	−19.8893	−	8.23034i	−0.905935	−	0.374882i
$483$		−	55.5264i		−	2.52654i
$484$	−2.32731	−	2.32408i	−0.105787	−	0.105640i
$485$			11.0366i			0.501146i
$486$	45.9180	−	110.965i	2.08288	−	5.03346i
$487$	21.9580			0.995013			0.497507	−	0.867460i	$-0.334249\pi$
$487$	21.9580			0.995013			0.497507	+	0.867460i	$0.334249\pi$
$488$	−28.9353	+	12.0208i	−1.30984	+	0.544154i
$489$	9.27914			0.419617
$490$	−1.65564	+	4.00100i	−0.0747943	+	0.180747i
$491$		−	4.20600i		−	0.189814i	−0.995486	−	0.0949070i	$-0.969745\pi$
$491$		−	4.20600i		−	0.189814i	0.995486	−	0.0949070i	$-0.0302554\pi$
$492$	−11.3740	+	11.3898i	−0.512778	+	0.513491i
$493$		−	9.36760i		−	0.421896i
$494$	5.09405	+	2.10795i	0.229192	+	0.0948412i
$495$	−31.3146			−1.40748
$496$	−0.0150261	−	10.8142i	−0.000674690	−	0.485572i
$497$	14.4378			0.647623
$498$	58.2020	+	24.0844i	2.60809	+	1.07925i
$499$		−	36.9427i		−	1.65378i	−0.562361	−	0.826892i	$-0.690107\pi$
$499$		−	36.9427i		−	1.65378i	0.562361	−	0.826892i	$-0.309893\pi$
$500$	1.41323	−	1.41520i	0.0632016	−	0.0632895i
$501$		−	17.7682i		−	0.793824i
$502$	−6.74394	+	16.2973i	−0.300997	+	0.727385i
$503$	−13.7984			−0.615242			−0.307621	−	0.951509i	$-0.599533\pi$
$503$	−13.7984			−0.615242			−0.307621	+	0.951509i	$0.599533\pi$
$504$	−30.3116	−	72.9635i	−1.35019	−	3.25005i
$505$	1.65421			0.0736116
$506$	9.79592	−	23.6727i	0.435482	−	1.05238i
$507$			7.54691i			0.335170i
$508$	−4.50392	−	4.49766i	−0.199829	−	0.199551i
$509$			6.78272i			0.300639i	0.988637	+	0.150319i	$0.0480302\pi$
$509$			6.78272i			0.300639i	−0.988637	+	0.150319i	$0.951970\pi$
$510$	9.84977	+	4.07590i	0.436155	+	0.180484i
$511$	13.5355			0.598776
$512$	−20.9320	−	8.59374i	−0.925071	−	0.379793i
$513$	−19.9508			−0.880848
$514$	−14.6788	−	6.07420i	−0.647455	−	0.267921i
$515$		−	11.3034i		−	0.498087i
$516$	1.24627	+	1.24454i	0.0548639	+	0.0547878i
$517$			26.0338i			1.14497i
$518$	−0.981220	+	2.37120i	−0.0431123	+	0.104185i
$519$	−53.3546			−2.34201
$520$	4.23006	+	10.1822i	0.185500	+	0.446520i
$521$	−12.6810			−0.555565			−0.277782	−	0.960644i	$-0.589599\pi$
$521$	−12.6810			−0.555565			−0.277782	+	0.960644i	$0.589599\pi$
$522$	−20.3347	+	49.1406i	−0.890026	+	2.15083i
$523$		−	9.56659i		−	0.418318i	−0.977882	−	0.209159i	$-0.932927\pi$
$523$		−	9.56659i		−	0.418318i	0.977882	−	0.209159i	$-0.0670726\pi$
$524$	−14.5014	+	14.5216i	−0.633496	+	0.634377i
$525$			10.8992i			0.475681i
$526$	−6.94629	−	2.87442i	−0.302873	−	0.125331i
$527$	−5.93077			−0.258348
$528$	−0.0679077	−	48.8729i	−0.00295530	−	2.12692i
$529$	2.95422			0.128444
$530$	−9.91918	−	4.10462i	−0.430862	−	0.178293i
$531$		−	84.4343i		−	3.66414i
$532$	−4.48281	+	4.48905i	−0.194355	+	0.194625i
$533$			9.13085i			0.395501i
$534$	−31.9605	+	77.2353i	−1.38307	+	3.34230i
$535$	−14.9784			−0.647575
$536$	30.3614	−	12.6132i	1.31141	−	0.544806i
$537$	−87.6525			−3.78249
$538$	10.3467	−	25.0038i	0.446080	−	1.07799i
$539$		−	10.8875i		−	0.468957i
$540$	−28.2342	−	28.1950i	−1.21501	−	1.21332i
$541$		−	25.6765i		−	1.10392i	−0.833872	−	0.551959i	$-0.813881\pi$
$541$		−	25.6765i		−	1.10392i	0.833872	−	0.551959i	$-0.186119\pi$
$542$	−15.1868	−	6.28438i	−0.652327	−	0.269937i
$543$	−1.10802			−0.0475495
$544$	−4.72895	+	11.4730i	−0.202752	+	0.491902i
$545$	8.80414			0.377128
$546$	−55.5211	−	22.9750i	−2.37609	−	0.983240i
$547$			25.9436i			1.10927i	0.832095	+	0.554634i	$0.187142\pi$
$547$			25.9436i			1.10927i	−0.832095	+	0.554634i	$0.812858\pi$
$548$	−20.9331	−	20.9040i	−0.894217	−	0.892975i
$549$		−	97.5554i		−	4.16356i
$550$	−1.92283	+	4.64669i	−0.0819898	+	0.198136i
$551$	4.27024			0.181918
$552$	45.7229	−	18.9949i	1.94610	−	0.808477i
$553$	52.8633			2.24798
$554$	−3.26631	+	7.89332i	−0.138772	+	0.335355i
$555$			1.96560i			0.0834352i
$556$	−5.33249	+	5.33991i	−0.226148	+	0.226462i
$557$			32.7815i			1.38900i	0.719494	+	0.694498i	$0.244374\pi$
$557$			32.7815i			1.38900i	−0.719494	+	0.694498i	$0.755626\pi$
$558$	31.1116	+	12.8742i	1.31706	+	0.545009i
$559$	0.999098			0.0422574
$560$	−12.6881	+	0.0176298i	−0.536171	+	0.000744996i
$561$	−26.8031			−1.13163
$562$	19.1808	+	7.93713i	0.809092	+	0.334808i
$563$			9.12702i			0.384658i	0.981330	+	0.192329i	$0.0616041\pi$
$563$			9.12702i			0.384658i	−0.981330	+	0.192329i	$0.938396\pi$
$564$	−35.5514	+	35.6009i	−1.49699	+	1.49907i
$565$		−	2.15293i		−	0.0905746i
$566$	−5.89445	+	14.2444i	−0.247762	+	0.598739i
$567$	133.646			5.61260
$568$	4.93899	+	11.8887i	0.207236	+	0.498840i
$569$	24.7194			1.03629			0.518146	−	0.855292i	$-0.326623\pi$
$569$	24.7194			1.03629			0.518146	+	0.855292i	$0.326623\pi$
$570$	−1.85801	+	4.49004i	−0.0778234	+	0.188067i
$571$			37.2686i			1.55964i	0.626002	+	0.779821i	$0.284690\pi$
$571$			37.2686i			1.55964i	−0.626002	+	0.779821i	$0.715310\pi$
$572$	−19.6172	−	19.5900i	−0.820238	−	0.819099i
$573$			56.8924i			2.37671i
$574$	−9.70893	−	4.01762i	−0.405243	−	0.167692i
$575$	−5.09453			−0.212457
$576$	49.7122	−	49.9199i	2.07134	−	2.07999i
$577$	−23.6465			−0.984416			−0.492208	−	0.870478i	$-0.663810\pi$
$577$	−23.6465			−0.984416			−0.492208	+	0.870478i	$0.663810\pi$
$578$	−15.9263	−	6.59041i	−0.662447	−	0.274125i
$579$		−	35.2442i		−	1.46470i
$580$	6.04323	+	6.03484i	0.250931	+	0.250583i
$581$			41.1173i			1.70583i
$582$	20.5061	−	49.5548i	0.850006	−	2.05411i
$583$	26.9919			1.11789
$584$	4.63034	+	11.1458i	0.191605	+	0.461215i
$585$	−34.3293			−1.41934
$586$	14.5711	−	35.2124i	0.601928	−	1.45461i
$587$		−	18.9649i		−	0.782763i	−0.920228	−	0.391382i	$-0.871997\pi$
$587$		−	18.9649i		−	0.782763i	0.920228	−	0.391382i	$-0.128003\pi$
$588$	14.8678	−	14.8885i	0.613138	−	0.613990i
$589$		−	2.70355i		−	0.111398i
$590$	−12.5290	−	5.18459i	−0.515811	−	0.213446i
$591$	−10.9796			−0.451642
$592$	−2.28822	+	0.00317942i	−0.0940453	+	0.000130674i
$593$	−33.7430			−1.38566			−0.692830	−	0.721101i	$-0.743636\pi$
$593$	−33.7430			−1.38566			−0.692830	+	0.721101i	$0.743636\pi$
$594$	92.7051	+	38.3620i	3.80374	+	1.57401i
$595$			6.95847i			0.285269i
$596$	−28.3192	+	28.3586i	−1.16000	+	1.16161i
$597$		−	33.2979i		−	1.36279i
$598$	10.7390	−	25.9518i	0.439151	−	1.06125i
$599$	32.8572			1.34251			0.671254	−	0.741227i	$-0.265756\pi$
$599$	32.8572			1.34251			0.671254	+	0.741227i	$0.265756\pi$
$600$	−8.97491	+	3.72849i	−0.366399	+	0.152215i
$601$	−15.7118			−0.640898			−0.320449	−	0.947266i	$-0.603834\pi$
$601$	−15.7118			−0.640898			−0.320449	+	0.947266i	$0.603834\pi$
$602$	−0.439608	+	1.06235i	−0.0179171	+	0.0432982i
$603$			102.363i			4.16855i
$604$	19.6960	+	19.6687i	0.801419	+	0.800306i
$605$		−	1.64452i		−	0.0668591i
$606$	−7.42749	−	3.07355i	−0.301721	−	0.124854i
$607$	−13.8213			−0.560990			−0.280495	−	0.959856i	$-0.590499\pi$
$607$	−13.8213			−0.560990			−0.280495	+	0.959856i	$0.590499\pi$
$608$	−5.23000	−	2.15570i	−0.212105	−	0.0874253i
$609$	−46.5423			−1.88599
$610$	−14.4760	−	5.99027i	−0.586116	−	0.242539i
$611$			28.5402i			1.15461i
$612$	−27.3393	−	27.3013i	−1.10513	−	1.10359i
$613$			3.38275i			0.136628i	0.997664	+	0.0683139i	$0.0217619\pi$
$613$			3.38275i			0.136628i	−0.997664	+	0.0683139i	$0.978238\pi$
$614$	3.40376	−	8.22548i	0.137365	−	0.331954i
$615$	−8.04820			−0.324535
$616$	29.4619	−	12.2395i	1.18706	−	0.493144i
$617$	4.50352			0.181305			0.0906524	−	0.995883i	$-0.471105\pi$
$617$	4.50352			0.181305			0.0906524	+	0.995883i	$0.471105\pi$
$618$	−21.0018	+	50.7527i	−0.844817	+	2.04157i
$619$		−	0.735818i		−	0.0295750i	−0.999891	−	0.0147875i	$-0.995293\pi$
$619$		−	0.735818i		−	0.0295750i	0.999891	−	0.0147875i	$-0.00470718\pi$
$620$	3.82074	−	3.82606i	0.153445	−	0.153658i
$621$			101.640i			4.07866i
$622$	−1.47283	−	0.609466i	−0.0590550	−	0.0244374i
$623$	−54.5636			−2.18605
$624$	−0.0744455	−	53.5781i	−0.00298020	−	2.14484i
$625$	1.00000			0.0400000
$626$	−22.1236	−	9.15491i	−0.884238	−	0.365904i
$627$		−	12.2182i		−	0.487950i
$628$	7.19613	−	7.20614i	0.287157	−	0.287556i
$629$			1.25491i			0.0500367i
$630$	15.1051	−	36.5028i	0.601801	−	1.45430i
$631$	−18.0615			−0.719016			−0.359508	−	0.933142i	$-0.617055\pi$
$631$	−18.0615			−0.719016			−0.359508	+	0.933142i	$0.617055\pi$
$632$	18.0839	+	43.5300i	0.719339	+	1.73153i
$633$	−58.6647			−2.33171
$634$	7.06557	−	17.0746i	0.280609	−	0.678117i
$635$		−	3.18254i		−	0.126295i
$636$	36.9111	+	36.8599i	1.46362	+	1.46159i
$637$		−	11.9357i		−	0.472908i
$638$	−19.8425	−	8.21096i	−0.785572	−	0.325075i
$639$	−40.0828			−1.58565
$640$	−4.35497	−	10.4419i	−0.172145	−	0.412754i
$641$	−31.9018			−1.26004			−0.630022	−	0.776577i	$-0.716954\pi$
$641$	−31.9018			−1.26004			−0.630022	+	0.776577i	$0.716954\pi$
$642$	67.2539	+	27.8301i	2.65430	+	1.09837i
$643$			9.49545i			0.374464i	0.982316	+	0.187232i	$0.0599516\pi$
$643$			9.49545i			0.374464i	−0.982316	+	0.187232i	$0.940048\pi$
$644$	22.8696	+	22.8378i	0.901188	+	0.899936i
$645$			0.880634i			0.0346749i
$646$	−1.18622	+	2.86661i	−0.0466713	+	0.112785i
$647$	36.2811			1.42636			0.713180	−	0.700981i	$-0.247254\pi$
$647$	36.2811			1.42636			0.713180	+	0.700981i	$0.247254\pi$
$648$	45.7186	+	110.050i	1.79600	+	4.32317i
$649$	34.0938			1.33830
$650$	−2.10795	+	5.09405i	−0.0826807	+	0.199805i
$651$			29.4666i			1.15489i
$652$	−3.81648	+	3.82179i	−0.149465	+	0.149673i
$653$		−	7.15546i		−	0.280015i	−0.990150	−	0.140007i	$-0.955287\pi$
$653$		−	7.15546i		−	0.280015i	0.990150	−	0.140007i	$-0.0447127\pi$
$654$	−39.5310	−	16.3582i	−1.54578	−	0.639655i
$655$	−10.2612			−0.400937
$656$	−0.0130182	−	9.36916i	−0.000508276	−	0.365804i
$657$	−37.5779			−1.46605
$658$	−30.3471	−	12.5578i	−1.18305	−	0.489555i
$659$			1.20453i			0.0469217i	0.999725	+	0.0234609i	$0.00746851\pi$
$659$			1.20453i			0.0469217i	−0.999725	+	0.0234609i	$0.992531\pi$
$660$	17.2672	−	17.2912i	0.672125	−	0.673059i
$661$		−	2.37847i		−	0.0925118i	−0.998930	−	0.0462559i	$-0.985271\pi$
$661$		−	2.37847i		−	0.0925118i	0.998930	−	0.0462559i	$-0.0147290\pi$
$662$	−8.80691	+	21.2827i	−0.342290	+	0.827174i
$663$	−29.3835			−1.14116
$664$	−33.8579	+	14.0658i	−1.31394	+	0.545857i
$665$	−3.17203			−0.123006
$666$	2.72410	−	6.58304i	0.105557	−	0.255087i
$667$		−	21.7549i		−	0.842352i
$668$	7.31816	+	7.30800i	0.283148	+	0.282755i
$669$		−	6.97264i		−	0.269578i
$670$	15.1894	+	6.28548i	0.586819	+	0.242829i
$671$	39.3919			1.52071
$672$	57.0029	+	23.4955i	2.19894	+	0.906358i
$673$	21.0551			0.811613			0.405806	−	0.913959i	$-0.366991\pi$
$673$	21.0551			0.811613			0.405806	+	0.913959i	$0.366991\pi$
$674$	18.0546	+	7.47112i	0.695438	+	0.287777i
$675$		−	19.9508i		−	0.767905i
$676$	−3.10834	−	3.10402i	−0.119551	−	0.119385i
$677$			6.45872i			0.248229i	0.992268	+	0.124114i	$0.0396090\pi$
$677$			6.45872i			0.248229i	−0.992268	+	0.124114i	$0.960391\pi$
$678$	−4.00017	+	9.66677i	−0.153626	+	0.371250i
$679$	35.0085			1.34350
$680$	−5.72992	+	2.38041i	−0.219732	+	0.0912845i
$681$	83.2009			3.18826
$682$	−5.19848	+	12.5626i	−0.199060	+	0.481046i
$683$			4.62399i			0.176932i	0.996079	+	0.0884661i	$0.0281965\pi$
$683$			4.62399i			0.176932i	−0.996079	+	0.0884661i	$0.971804\pi$
$684$	12.4454	−	12.4627i	0.475861	−	0.476523i
$685$		−	14.7917i		−	0.565160i
$686$	−16.3241	−	6.75502i	−0.623257	−	0.257908i
$687$	−19.1394			−0.730212
$688$	−1.02517	+	0.00142445i	−0.0390844	+	5.43068e-5i
$689$	29.5906			1.12731
$690$	22.8746	+	9.46568i	0.870823	+	0.360352i
$691$		−	34.0866i		−	1.29672i	−0.761336	−	0.648358i	$-0.775456\pi$
$691$		−	34.0866i		−	1.29672i	0.761336	−	0.648358i	$-0.224544\pi$
$692$	21.9446	−	21.9751i	0.834208	−	0.835368i
$693$			99.3308i			3.77327i
$694$	6.74853	−	16.3084i	0.256171	−	0.619059i
$695$	−3.77326			−0.143128
$696$	−15.9216	−	38.3251i	−0.603505	−	1.45271i
$697$	−5.13827			−0.194626
$698$	15.4112	−	37.2424i	0.583321	−	1.40965i
$699$			27.6215i			1.04474i
$700$	−4.48905	−	4.48281i	−0.169670	−	0.169434i
$701$			6.64815i			0.251097i	0.992087	+	0.125549i	$0.0400691\pi$
$701$			6.64815i			0.251097i	−0.992087	+	0.125549i	$0.959931\pi$
$702$	101.630	+	42.0553i	3.83579	+	1.58727i
$703$	−0.572056			−0.0215755
$704$	20.1572	+	20.0733i	0.759702	+	0.756541i
$705$	−25.1561			−0.947435
$706$	−1.50484	−	0.622713i	−0.0566354	−	0.0234361i
$707$		−	5.24722i		−	0.197342i
$708$	46.6227	+	46.5580i	1.75219	+	1.74976i
$709$		−	31.6102i		−	1.18715i	−0.804780	−	0.593574i	$-0.797717\pi$
$709$		−	31.6102i		−	1.18715i	0.804780	−	0.593574i	$-0.202283\pi$
$710$	−2.46123	+	5.94779i	−0.0923685	+	0.223217i
$711$	−146.761			−5.50398
$712$	−18.6656	−	44.9302i	−0.699522	−	1.68383i
$713$	−13.7733			−0.515815
$714$	12.9289	−	31.2438i	0.483852	−	1.16927i
$715$		−	13.8619i		−	0.518404i
$716$	36.0512	−	36.1014i	1.34730	−	1.34917i
$717$		−	4.53328i		−	0.169298i
$718$	−17.9803	−	7.44038i	−0.671020	−	0.277673i
$719$	47.5177			1.77211			0.886055	−	0.463580i	$-0.153435\pi$
$719$	47.5177			1.77211			0.886055	+	0.463580i	$0.153435\pi$
$720$	35.2253	−	0.0489447i	1.31277	−	0.00182406i
$721$	−35.8547			−1.33530
$722$	−1.30675	−	0.540742i	−0.0486322	−	0.0201243i
$723$			52.2980i			1.94498i
$724$	0.455724	−	0.456357i	0.0169368	−	0.0169604i
$725$			4.27024i			0.158593i
$726$	−3.05552	+	7.38394i	−0.113401	+	0.274044i
$727$	11.4234			0.423670			0.211835	−	0.977305i	$-0.432056\pi$
$727$	11.4234			0.423670			0.211835	+	0.977305i	$0.432056\pi$
$728$	32.2984	−	13.4179i	1.19706	−	0.497300i
$729$	−165.379			−6.12513
$730$	−2.30742	+	5.57609i	−0.0854016	+	0.206380i
$731$			0.562230i			0.0207948i
$732$	53.8679	+	53.7931i	1.99101	+	1.98825i
$733$		−	13.3588i		−	0.493420i	−0.969089	−	0.246710i	$-0.920650\pi$
$733$		−	13.3588i		−	0.493420i	0.969089	−	0.246710i	$-0.0793495\pi$
$734$	−29.2585	−	12.1073i	−1.07995	−	0.446890i
$735$	10.5204			0.388052
$736$	−10.9823	+	26.6444i	−0.404813	+	0.982126i
$737$	−41.3333			−1.52253
$738$	26.9544	+	11.1539i	0.992204	+	0.410580i
$739$			34.3533i			1.26371i	0.775088	+	0.631853i	$0.217705\pi$
$739$			34.3533i			1.26371i	−0.775088	+	0.631853i	$0.782295\pi$
$740$	−0.809571	−	0.808447i	−0.0297604	−	0.0297191i
$741$		−	13.3945i		−	0.492061i
$742$	−13.0200	+	31.4640i	−0.477979	+	1.15508i
$743$	−35.8483			−1.31515			−0.657573	−	0.753391i	$-0.728417\pi$
$743$	−35.8483			−1.31515			−0.657573	+	0.753391i	$0.728417\pi$
$744$	−24.2641	+	10.0802i	−0.889567	+	0.369557i
$745$	−20.0386			−0.734159
$746$	16.2378	−	39.2400i	0.594507	−	1.43668i
$747$		−	114.152i		−	4.17659i
$748$	11.0240	−	11.0393i	0.403078	−	0.403639i
$749$			47.5121i			1.73606i
$750$	−4.49004	−	1.85801i	−0.163953	−	0.0678449i
$751$	−25.1799			−0.918828			−0.459414	−	0.888222i	$-0.651941\pi$
$751$	−25.1799			−0.918828			−0.459414	+	0.888222i	$0.651941\pi$
$752$	−0.0406908	−	29.2851i	−0.00148384	−	1.06792i
$753$	42.8530			1.56165
$754$	−21.7528	−	9.00147i	−0.792191	−	0.327814i
$755$			13.9175i			0.506510i
$756$	−89.4356	+	89.5600i	−3.25274	+	3.25726i
$757$			42.5485i			1.54645i	0.634130	+	0.773226i	$0.281358\pi$
$757$			42.5485i			1.54645i	−0.634130	+	0.773226i	$0.718642\pi$
$758$	1.14609	−	2.76962i	0.0416277	−	0.100597i
$759$	−62.2462			−2.25939
$760$	−1.08511	−	2.61200i	−0.0393612	−	0.0947471i
$761$	20.6747			0.749459			0.374729	−	0.927134i	$-0.377736\pi$
$761$	20.6747			0.749459			0.374729	+	0.927134i	$0.377736\pi$
$762$	−5.91319	+	14.2897i	−0.214212	+	0.517662i
$763$		−	27.9270i		−	1.01103i
$764$	−23.4322	−	23.3997i	−0.847747	−	0.846570i
$765$		−	19.3184i		−	0.698458i
$766$	−27.0848	−	11.2079i	−0.978613	−	0.404957i
$767$	37.3761			1.34957
$768$	0.152777	+	54.9763i	0.00551286	+	1.98379i
$769$	53.6971			1.93637			0.968183	−	0.250243i	$-0.0805105\pi$
$769$	53.6971			1.93637			0.968183	+	0.250243i	$0.0805105\pi$
$770$	14.7395	+	6.09929i	0.531173	+	0.219803i
$771$			38.5972i			1.39005i
$772$	14.5160	+	14.4958i	0.522442	+	0.521717i
$773$			26.8933i			0.967286i	0.875265	+	0.483643i	$0.160687\pi$
$773$			26.8933i			0.967286i	−0.875265	+	0.483643i	$0.839313\pi$
$774$	1.22046	−	2.94935i	0.0438685	−	0.106012i
$775$	2.70355			0.0971145
$776$	11.9760	+	28.8276i	0.429913	+	1.03485i
$777$	6.23496			0.223678
$778$	6.83492	−	16.5172i	0.245044	−	0.592170i
$779$		−	2.34229i		−	0.0839213i
$780$	18.9296	−	18.9559i	0.677788	−	0.678730i
$781$		−	16.1850i		−	0.579146i
$782$	14.6040	+	6.04324i	0.522239	+	0.216106i
$783$	85.1946			3.04461
$784$	0.0170171	+	12.2472i	0.000607755	+	0.437399i
$785$	5.09197			0.181740
$786$	46.0730	+	19.0653i	1.64337	+	0.680038i
$787$		−	17.6372i		−	0.628700i	−0.949307	−	0.314350i	$-0.898214\pi$
$787$		−	17.6372i		−	0.628700i	0.949307	−	0.314350i	$-0.101786\pi$
$788$	4.51589	−	4.52217i	0.160872	−	0.161096i
$789$			18.2649i			0.650248i
$790$	−9.01170	+	21.7776i	−0.320622	+	0.774811i
$791$	−6.82918			−0.242818
$792$	−81.7935	+	33.9799i	−2.90641	+	1.20742i
$793$	43.1843			1.53352
$794$	−5.71605	+	13.8133i	−0.202855	+	0.490217i
$795$			26.0820i			0.925033i
$796$	13.7144	+	13.6953i	0.486093	+	0.485418i
$797$		−	39.0071i		−	1.38170i	−0.722996	−	0.690852i	$-0.757236\pi$
$797$		−	39.0071i		−	1.38170i	0.722996	−	0.690852i	$-0.242764\pi$
$798$	14.2426	+	5.89367i	0.504181	+	0.208634i
$799$	−16.0606			−0.568184
$800$	2.15570	−	5.23000i	0.0762156	−	0.184909i
$801$	151.482			5.35235
$802$	−27.9383	−	11.5611i	−0.986536	−	0.408235i
$803$		−	15.1736i		−	0.535464i
$804$	−56.5227	−	56.4442i	−1.99340	−	1.99063i
$805$			16.1600i			0.569566i
$806$	−5.69896	+	13.7720i	−0.200737	+	0.485099i
$807$	−65.7462			−2.31438
$808$	4.32080	−	1.79501i	0.152005	−	0.0631483i
$809$	−16.3415			−0.574536			−0.287268	−	0.957850i	$-0.592747\pi$
$809$	−16.3415			−0.574536			−0.287268	+	0.957850i	$0.592747\pi$
$810$	−22.7828	+	55.0567i	−0.800507	+	1.93450i
$811$		−	51.7929i		−	1.81870i	−0.416036	−	0.909348i	$-0.636581\pi$
$811$		−	51.7929i		−	1.81870i	0.416036	−	0.909348i	$-0.363419\pi$
$812$	19.1427	−	19.1693i	0.671777	−	0.672711i
$813$			39.9328i			1.40050i
$814$	2.65817	+	1.09997i	0.0931687	+	0.0385538i
$815$	−2.70054			−0.0945957
$816$	30.1504	−	0.0418932i	1.05547	−	0.00146656i
$817$	−0.256294			−0.00896658
$818$	−1.41922	−	0.587283i	−0.0496219	−	0.0205339i
$819$			108.894i			3.80506i
$820$	3.31020	−	3.31480i	0.115597	−	0.115758i
$821$		−	2.14965i		−	0.0750233i	−0.999296	−	0.0375117i	$-0.988057\pi$
$821$		−	2.14965i		−	0.0750233i	0.999296	−	0.0375117i	$-0.0119431\pi$
$822$	−27.4830	+	66.4151i	−0.958581	+	2.31649i
$823$	−21.5839			−0.752367			−0.376183	−	0.926545i	$-0.622764\pi$
$823$	−21.5839			−0.752367			−0.376183	+	0.926545i	$0.622764\pi$
$824$	−12.2655	−	29.5244i	−0.427288	−	1.02853i
$825$	12.2182			0.425385
$826$	−16.4457	+	39.7424i	−0.572218	+	1.38282i
$827$			50.0918i			1.74186i	0.491404	+	0.870932i	$0.336484\pi$
$827$			50.0918i			1.74186i	−0.491404	+	0.870932i	$0.663516\pi$
$828$	−63.4915	−	63.4034i	−2.20648	−	2.20342i
$829$		−	26.7817i		−	0.930168i	−0.885267	−	0.465084i	$-0.846024\pi$
$829$		−	26.7817i		−	0.930168i	0.885267	−	0.465084i	$-0.153976\pi$
$830$	−16.9387	−	7.00935i	−0.587951	−	0.243298i
$831$	20.7551			0.719986
$832$	22.0978	+	22.0059i	0.766103	+	0.762916i
$833$	6.71664			0.232718
$834$	16.9421	+	7.01076i	0.586657	+	0.242763i
$835$			5.17113i			0.178954i
$836$	5.03231	+	5.02533i	0.174046	+	0.173805i
$837$		−	53.9380i		−	1.86437i
$838$	13.1730	−	31.8336i	0.455052	−	1.09967i
$839$	18.8381			0.650363			0.325181	−	0.945652i	$-0.394575\pi$
$839$	18.8381			0.650363			0.325181	+	0.945652i	$0.394575\pi$
$840$	11.8269	+	28.4687i	0.408067	+	0.982264i
$841$	10.7650			0.371208
$842$	10.1843	−	24.6114i	0.350976	−	0.848164i
$843$		−	50.4348i		−	1.73707i
$844$	24.1286	−	24.1622i	0.830542	−	0.831697i
$845$		−	2.19640i		−	0.0755585i
$846$	84.2509	+	34.8636i	2.89660	+	1.19863i
$847$	−5.21646			−0.179240
$848$	−30.3629	+	0.0421884i	−1.04266	+	0.00144876i
$849$	37.4551			1.28545
$850$	−2.86661	−	1.18622i	−0.0983239	−	0.0406871i
$851$			2.91435i			0.0999028i
$852$	22.1021	−	22.1328i	0.757205	−	0.758258i
$853$			0.774647i			0.0265234i	0.999912	+	0.0132617i	$0.00422145\pi$
$853$			0.774647i			0.0265234i	−0.999912	+	0.0132617i	$0.995779\pi$
$854$	−19.0013	+	45.9184i	−0.650212	+	1.57129i
$855$	8.80634			0.301170
$856$	−39.1237	+	16.2533i	−1.33722	+	0.555528i
$857$	13.4855			0.460656			0.230328	−	0.973113i	$-0.426020\pi$
$857$	13.4855			0.460656			0.230328	+	0.973113i	$0.426020\pi$
$858$	−25.7555	+	62.2403i	−0.879277	+	2.12485i
$859$			1.95595i			0.0667360i	0.999443	+	0.0333680i	$0.0106233\pi$
$859$			1.95595i			0.0667360i	−0.999443	+	0.0333680i	$0.989377\pi$
$860$	−0.362706	−	0.362202i	−0.0123682	−	0.0123510i
$861$			25.5291i			0.870031i
$862$	41.2833	+	17.0833i	1.40612	+	0.581860i
$863$	39.1386			1.33229			0.666147	−	0.745821i	$-0.267942\pi$
$863$	39.1386			1.33229			0.666147	+	0.745821i	$0.267942\pi$
$864$	−104.343	−	43.0080i	−3.54981	−	1.46316i
$865$	15.5280			0.527967
$866$	10.8944	+	4.50818i	0.370207	+	0.153194i
$867$			41.8774i			1.42223i
$868$	−12.1364	−	12.1195i	−0.411936	−	0.411364i
$869$		−	59.2608i		−	2.01029i
$870$	7.93415	−	19.1736i	0.268993	−	0.650045i
$871$	−45.3126			−1.53536
$872$	22.9964	−	9.55350i	0.778756	−	0.323522i
$873$	−97.1920			−3.28945
$874$	−2.75483	+	6.65728i	−0.0931834	+	0.225186i
$875$		−	3.17203i		−	0.107234i
$876$	20.7209	−	20.7497i	0.700093	−	0.701066i
$877$		−	21.0431i		−	0.710575i	−0.934757	−	0.355287i	$-0.884383\pi$
$877$		−	21.0431i		−	0.710575i	0.934757	−	0.355287i	$-0.115617\pi$
$878$	44.4689	+	18.4015i	1.50075	+	0.621022i
$879$	−92.5893			−3.12296
$880$	0.0197634	+	14.2236i	0.000666224	+	0.479479i
$881$	27.5240			0.927307			0.463653	−	0.886017i	$-0.346538\pi$
$881$	27.5240			0.927307			0.463653	+	0.886017i	$0.346538\pi$
$882$	−35.2342	−	14.5801i	−1.18640	−	0.490939i
$883$		−	12.3668i		−	0.416175i	−0.978110	−	0.208088i	$-0.933276\pi$
$883$		−	12.3668i		−	0.416175i	0.978110	−	0.208088i	$-0.0667239\pi$
$884$	12.0854	−	12.1022i	0.406474	−	0.407040i
$885$			32.9444i			1.10741i
$886$	−9.85140	+	23.8068i	−0.330964	+	0.799804i
$887$	−5.53534			−0.185858			−0.0929292	−	0.995673i	$-0.529623\pi$
$887$	−5.53534			−0.185858			−0.0929292	+	0.995673i	$0.529623\pi$
$888$	2.13290	+	5.13415i	0.0715756	+	0.172291i
$889$	−10.0951			−0.338579
$890$	9.30156	−	22.4780i	0.311789	−	0.753465i
$891$		−	149.820i		−	5.01915i
$892$	2.87181	+	2.86783i	0.0961555	+	0.0960220i
$893$		−	7.32127i		−	0.244997i
$894$	89.9743	+	37.2320i	3.00919	+	1.24522i
$895$	25.5098			0.852698
$896$	−33.1222	+	13.8141i	−1.10653	+	0.461497i
$897$	−68.2389			−2.27843
$898$	−51.4895	−	21.3067i	−1.71823	−	0.711014i
$899$			11.5448i			0.385042i
$900$	12.4627	+	12.4454i	0.415423	+	0.414846i
$901$			16.6517i			0.554749i
$902$	−4.50383	+	10.8839i	−0.149961	+	0.362395i
$903$	2.79340			0.0929585
$904$	−2.33618	−	5.62346i	−0.0777002	−	0.187033i
$905$	0.322469			0.0107192
$906$	25.8589	−	62.4902i	0.859103	−	2.07610i
$907$			6.97326i			0.231543i	0.993276	+	0.115772i	$0.0369341\pi$
$907$			6.97326i			0.231543i	−0.993276	+	0.115772i	$0.963066\pi$
$908$	−34.2203	+	34.2678i	−1.13564	+	1.13722i
$909$			14.5676i			0.483176i
$910$	16.1585	+	6.68649i	0.535649	+	0.221655i
$911$	54.8323			1.81668			0.908338	−	0.418237i	$-0.137352\pi$
$911$	54.8323			1.81668			0.908338	+	0.418237i	$0.137352\pi$
$912$	0.0190971	+	13.7441i	0.000632369	+	0.455113i
$913$	46.0934			1.52547
$914$	12.9202	+	5.34645i	0.427361	+	0.176845i
$915$			38.0639i			1.25835i
$916$	7.87196	−	7.88291i	0.260097	−	0.260459i
$917$			32.5487i			1.07485i
$918$	−23.6660	+	57.1911i	−0.781096	+	1.88759i
$919$	34.2473			1.12972			0.564858	−	0.825188i	$-0.308931\pi$
$919$	34.2473			1.12972			0.564858	+	0.825188i	$0.308931\pi$
$920$	−13.3069	+	5.52815i	−0.438715	+	0.182258i
$921$	−21.6285			−0.712683
$922$	−8.32679	+	20.1224i	−0.274228	+	0.662697i
$923$		−	17.7432i		−	0.584026i
$924$	−54.8483	−	54.7721i	−1.80438	−	1.80187i
$925$		−	0.572056i		−	0.0188091i
$926$	23.0550	+	9.54033i	0.757635	+	0.313515i
$927$	99.5415			3.26937
$928$	22.3334	+	9.20538i	0.733129	+	0.302181i
$929$	−31.3912			−1.02991			−0.514955	−	0.857217i	$-0.672192\pi$
$929$	−31.3912			−1.02991			−0.514955	+	0.857217i	$0.672192\pi$
$930$	−12.1391	−	5.02323i	−0.398056	−	0.164718i
$931$			3.06179i			0.100346i
$932$	−11.3764	−	11.3606i	−0.372648	−	0.372130i
$933$			3.87273i			0.126787i
$934$	−7.71355	+	18.6405i	−0.252395	+	0.609934i
$935$	7.80058			0.255106
$936$	−89.6681	+	37.2513i	−2.93089	+	1.21760i
$937$	−7.52591			−0.245861			−0.122930	−	0.992415i	$-0.539229\pi$
$937$	−7.52591			−0.245861			−0.122930	+	0.992415i	$0.539229\pi$
$938$	19.9378	−	48.1814i	0.650991	−	1.57318i
$939$			58.1730i			1.89840i
$940$	10.3466	−	10.3610i	0.337470	−	0.337940i
$941$			16.3023i			0.531440i	0.964050	+	0.265720i	$0.0856096\pi$
$941$			16.3023i			0.531440i	−0.964050	+	0.265720i	$0.914390\pi$
$942$	−22.8632	−	9.46093i	−0.744922	−	0.308254i
$943$	−11.9329			−0.388588
$944$	−38.3516	+	0.0532886i	−1.24824	+	0.00173440i
$945$	−63.2845			−2.05865
$946$	1.19092	+	0.492810i	0.0387201	+	0.0160226i
$947$			20.0256i			0.650745i	0.945586	+	0.325372i	$0.105490\pi$
$947$			20.0256i			0.650745i	−0.945586	+	0.325372i	$0.894510\pi$
$948$	80.9258	−	81.0383i	2.62835	−	2.63200i
$949$		−	16.6344i		−	0.539976i
$950$	0.540742	−	1.30675i	0.0175440	−	0.0423966i
$951$	−44.8967			−1.45587
$952$	7.55073	+	18.1755i	0.244721	+	0.589071i
$953$	−44.2155			−1.43228			−0.716140	−	0.697957i	$-0.754093\pi$
$953$	−44.2155			−1.43228			−0.716140	+	0.697957i	$0.754093\pi$
$954$	36.1467	−	87.3517i	1.17029	−	2.82811i
$955$		−	16.5576i		−	0.535790i
$956$	1.86712	+	1.86452i	0.0603868	+	0.0603030i
$957$			52.1749i			1.68657i
$958$	30.1535	+	12.4777i	0.974217	+	0.403137i
$959$	−46.9196			−1.51511
$960$	−19.3966	+	19.4776i	−0.626022	+	0.628637i
$961$	−23.6908			−0.764219
$962$	2.91408	+	1.20587i	0.0939537	+	0.0388787i
$963$		−	131.905i		−	4.25059i
$964$	−21.5399	−	21.5100i	−0.693754	−	0.692791i
$965$			10.2572i			0.330192i
$966$	30.0255	−	72.5591i	0.966053	−	2.33455i
$967$	49.0693			1.57796			0.788981	−	0.614418i	$-0.210609\pi$
$967$	49.0693			1.57796			0.788981	+	0.614418i	$0.210609\pi$
$968$	−1.78449	−	4.29547i	−0.0573556	−	0.138062i
$969$	7.53761			0.242143
$970$	−5.96796	+	14.4221i	−0.191620	+	0.463065i
$971$			1.20151i			0.0385582i	0.999814	+	0.0192791i	$0.00613711\pi$
$971$			1.20151i			0.0385582i	−0.999814	+	0.0192791i	$0.993863\pi$
$972$	120.007	−	120.174i	3.84922	−	3.85457i
$973$			11.9689i			0.383706i
$974$	28.6937	+	11.8736i	0.919405	+	0.380456i
$975$	13.3945			0.428969
$976$	−44.3114	+	0.0615696i	−1.41837	+	0.00197079i
$977$	−17.4709			−0.558942			−0.279471	−	0.960154i	$-0.590159\pi$
$977$	−17.4709			−0.558942			−0.279471	+	0.960154i	$0.590159\pi$
$978$	12.1255	+	5.01762i	0.387731	+	0.160446i
$979$			61.1669i			1.95490i
$980$	−4.32702	+	4.33304i	−0.138222	+	0.138414i
$981$			77.5322i			2.47541i
$982$	2.27436	−	5.49619i	0.0725778	−	0.175391i
$983$	−14.6484			−0.467210			−0.233605	−	0.972332i	$-0.575052\pi$
$983$	−14.6484			−0.467210			−0.233605	+	0.972332i	$0.575052\pi$
$984$	−21.0219	+	8.73322i	−0.670152	+	0.278405i
$985$	3.19544			0.101815
$986$	5.06546	−	12.2411i	0.161317	−	0.389837i
$987$			79.7961i			2.53994i
$988$	5.51680	+	5.50914i	0.175513	+	0.175269i
$989$			1.30570i			0.0415187i
$990$	−40.9203	−	16.9331i	−1.30053	−	0.538169i
$991$	39.8960			1.26734			0.633668	−	0.773605i	$-0.281548\pi$
$991$	39.8960			1.26734			0.633668	+	0.773605i	$0.281548\pi$
$992$	5.82806	−	14.1396i	0.185041	−	0.448933i
$993$	55.9617			1.77589
$994$	18.8666	+	7.80712i	0.598412	+	0.247627i
$995$			9.69079i			0.307219i
$996$	63.0320	+	62.9445i	1.99725	+	1.99447i
$997$			9.17278i			0.290505i	0.989395	+	0.145252i	$0.0463994\pi$
$997$			9.17278i			0.290505i	−0.989395	+	0.145252i	$0.953601\pi$
$998$	19.9765	−	48.2749i	0.632345	−	1.52812i
$999$	−11.4130			−0.361090

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.f.b.381.38	yes	44
4.3	odd	2		3040.2.f.b.1521.44		44
8.3	odd	2		3040.2.f.b.1521.1		44
8.5	even	2	inner	760.2.f.b.381.37	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.f.b.381.37	✓	44	8.5	even	2	inner
760.2.f.b.381.38	yes	44	1.1	even	1	trivial
3040.2.f.b.1521.1		44	8.3	odd	2
3040.2.f.b.1521.44		44	4.3	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+(1.30675 + 0.540742i) q^{2} -3.43603i q^{3} +(1.41520 + 1.41323i) q^{4} +1.00000i q^{5} +(1.85801 - 4.49004i) q^{6} +3.17203 q^{7} +(1.08511 + 2.61200i) q^{8} -8.80634 q^{9} +(-0.540742 + 1.30675i) q^{10} -3.55591i q^{11} +(4.85591 - 4.86266i) q^{12} -3.89826i q^{13} +(4.14506 + 1.71525i) q^{14} +3.43603 q^{15} +(0.00555789 + 4.00000i) q^{16} +2.19369 q^{17} +(-11.5077 - 4.76196i) q^{18} +1.00000i q^{19} +(-1.41323 + 1.41520i) q^{20} -10.8992i q^{21} +(1.92283 - 4.64669i) q^{22} +5.09453 q^{23} +(8.97491 - 3.72849i) q^{24} -1.00000 q^{25} +(2.10795 - 5.09405i) q^{26} +19.9508i q^{27} +(4.48905 + 4.48281i) q^{28} -4.27024i q^{29} +(4.49004 + 1.85801i) q^{30} -2.70355 q^{31} +(-2.15570 + 5.23000i) q^{32} -12.2182 q^{33} +(2.86661 + 1.18622i) q^{34} +3.17203i q^{35} +(-12.4627 - 12.4454i) q^{36} +0.572056i q^{37} +(-0.540742 + 1.30675i) q^{38} -13.3945 q^{39} +(-2.61200 + 1.08511i) q^{40} -2.34229 q^{41} +(5.89367 - 14.2426i) q^{42} +0.256294i q^{43} +(5.02533 - 5.03231i) q^{44} -8.80634i q^{45} +(6.65728 + 2.75483i) q^{46} -7.32127 q^{47} +(13.7441 - 0.0190971i) q^{48} +3.06179 q^{49} +(-1.30675 - 0.540742i) q^{50} -7.53761i q^{51} +(5.50914 - 5.51680i) q^{52} +7.59072i q^{53} +(-10.7882 + 26.0707i) q^{54} +3.55591 q^{55} +(3.44202 + 8.28534i) q^{56} +3.43603 q^{57} +(2.30910 - 5.58014i) q^{58} +9.58791i q^{59} +(4.86266 + 4.85591i) q^{60} +11.0779i q^{61} +(-3.53287 - 1.46193i) q^{62} -27.9340 q^{63} +(-5.64505 + 5.66863i) q^{64} +3.89826 q^{65} +(-15.9662 - 6.60692i) q^{66} -11.6238i q^{67} +(3.10450 + 3.10019i) q^{68} -17.5050i q^{69} +(-1.71525 + 4.14506i) q^{70} +4.55159 q^{71} +(-9.55588 - 23.0021i) q^{72} +4.26714 q^{73} +(-0.309335 + 0.747534i) q^{74} +3.43603i q^{75} +(-1.41323 + 1.41520i) q^{76} -11.2795i q^{77} +(-17.5033 - 7.24300i) q^{78} +16.6654 q^{79} +(-4.00000 + 0.00555789i) q^{80} +42.1325 q^{81} +(-3.06079 - 1.26658i) q^{82} +12.9625i q^{83} +(15.4031 - 15.4245i) q^{84} +2.19369i q^{85} +(-0.138589 + 0.334912i) q^{86} -14.6727 q^{87} +(9.28803 - 3.85857i) q^{88} -17.2015 q^{89} +(4.76196 - 11.5077i) q^{90} -12.3654i q^{91} +(7.20976 + 7.19974i) q^{92} +9.28950i q^{93} +(-9.56708 - 3.95892i) q^{94} -1.00000 q^{95} +(17.9705 + 7.40707i) q^{96} +11.0366 q^{97} +(4.00100 + 1.65564i) q^{98} +31.3146i 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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