LMFDB - Embedded newform 280.2.n.b.139.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [280,2,Mod(139,280)] 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("280.139"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(280, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.n (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.13
Character	$\chi$	$=$	280.139
Dual form			280.2.n.b.139.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.510308 - 1.31893i) q^{2} -0.857983 q^{3} +(-1.47917 + 1.34612i) q^{4} +(1.33029 - 1.79731i) q^{5} +(0.437835 + 1.13162i) q^{6} +(2.41097 - 1.08959i) q^{7} +(2.53028 + 1.26399i) q^{8} -2.26387 q^{9} +(-3.04939 - 0.837376i) q^{10} +3.05732 q^{11} +(1.26910 - 1.15495i) q^{12} -3.18505i q^{13} +(-2.66744 - 2.62388i) q^{14} +(-1.14136 + 1.54206i) q^{15} +(0.375896 - 3.98230i) q^{16} -7.44976 q^{17} +(1.15527 + 2.98589i) q^{18} -4.61892i q^{19} +(0.451687 + 4.44927i) q^{20} +(-2.06857 + 0.934853i) q^{21} +(-1.56017 - 4.03240i) q^{22} -0.708794 q^{23} +(-2.17094 - 1.08448i) q^{24} +(-1.46068 - 4.78189i) q^{25} +(-4.20087 + 1.62536i) q^{26} +4.51631 q^{27} +(-2.09951 + 4.85717i) q^{28} -2.41421i q^{29} +(2.61633 + 0.718454i) q^{30} +5.14028 q^{31} +(-5.44421 + 1.53642i) q^{32} -2.62312 q^{33} +(3.80167 + 9.82574i) q^{34} +(1.24894 - 5.78275i) q^{35} +(3.34865 - 3.04745i) q^{36} +2.07192 q^{37} +(-6.09205 + 2.35707i) q^{38} +2.73272i q^{39} +(5.63779 - 2.86624i) q^{40} +5.51396i q^{41} +(2.28862 + 2.25125i) q^{42} +4.21172i q^{43} +(-4.52229 + 4.11553i) q^{44} +(-3.01159 + 4.06888i) q^{45} +(0.361703 + 0.934853i) q^{46} +6.55463i q^{47} +(-0.322513 + 3.41674i) q^{48} +(4.62557 - 5.25396i) q^{49} +(-5.56159 + 4.36677i) q^{50} +6.39177 q^{51} +(4.28748 + 4.71124i) q^{52} +3.75594 q^{53} +(-2.30471 - 5.95671i) q^{54} +(4.06711 - 5.49496i) q^{55} +(7.47768 + 0.290465i) q^{56} +3.96296i q^{57} +(-3.18418 + 1.23199i) q^{58} -3.11915i q^{59} +(-0.387540 - 3.81739i) q^{60} +9.55219 q^{61} +(-2.62312 - 6.77968i) q^{62} +(-5.45812 + 2.46669i) q^{63} +(4.80466 + 6.39651i) q^{64} +(-5.72454 - 4.23703i) q^{65} +(1.33860 + 3.45973i) q^{66} +0.519160i q^{67} +(11.0195 - 10.0283i) q^{68} +0.608133 q^{69} +(-8.26440 + 1.30371i) q^{70} -10.9754i q^{71} +(-5.72822 - 2.86151i) q^{72} -2.32017 q^{73} +(-1.05732 - 2.73272i) q^{74} +(1.25323 + 4.10277i) q^{75} +(6.21765 + 6.83218i) q^{76} +(7.37110 - 3.33123i) q^{77} +(3.60428 - 1.39453i) q^{78} +9.98693i q^{79} +(-6.65739 - 5.97320i) q^{80} +2.91669 q^{81} +(7.27255 - 2.81382i) q^{82} +8.73474 q^{83} +(1.80134 - 4.16736i) q^{84} +(-9.91032 + 13.3896i) q^{85} +(5.55498 - 2.14928i) q^{86} +2.07135i q^{87} +(7.73587 + 3.86442i) q^{88} +18.5697i q^{89} +(6.90342 + 1.89571i) q^{90} +(-3.47042 - 7.67907i) q^{91} +(1.04843 - 0.954126i) q^{92} -4.41027 q^{93} +(8.64512 - 3.34488i) q^{94} +(-8.30166 - 6.14449i) q^{95} +(4.67104 - 1.31822i) q^{96} +1.58285 q^{97} +(-9.29009 - 3.41968i) q^{98} -6.92135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65}+ \cdots - 128 q^{99}+O(q^{100}) $ 40 * q - 12 * q^4 + 40 * q^9 - 12 * q^14 - 28 * q^16 + 16 * q^25 - 28 * q^30 + 16 * q^35 - 28 * q^36 - 8 * q^44 - 32 * q^46 + 8 * q^49 + 4 * q^50 - 32 * q^51 - 4 * q^56 + 12 * q^60 - 84 * q^64 - 24 * q^65 + 40 * q^70 + 80 * q^74 - 72 * q^81 - 8 * q^84 + 80 * q^86 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−0.510308	−	1.31893i	−0.360842	−	0.932627i
$2$	−0.510308	−	1.31893i	−0.360842	−	0.932627i
$3$	−0.857983			−0.495356			−0.247678	−	0.968842i	$-0.579668\pi$
$3$	−0.857983			−0.495356			−0.247678	+	0.968842i	$0.579668\pi$
$4$	−1.47917	+	1.34612i	−0.739586	+	0.673062i
$5$	1.33029	−	1.79731i	0.594922	−	0.803783i
$5$	1.33029	−	1.79731i	0.594922	−	0.803783i
$6$	0.437835	+	1.13162i	0.178746	+	0.461983i
$7$	2.41097	−	1.08959i	0.911262	−	0.411828i
$7$	2.41097	−	1.08959i	0.911262	−	0.411828i
$8$	2.53028	+	1.26399i	0.894590	+	0.446888i
$9$	−2.26387			−0.754622
$10$	−3.04939	−	0.837376i	−0.964303	−	0.264801i
$11$	3.05732			0.921815			0.460908	−	0.887448i	$-0.347524\pi$
$11$	3.05732			0.921815			0.460908	+	0.887448i	$0.347524\pi$
$12$	1.26910	−	1.15495i	0.366359	−	0.333406i
$13$		−	3.18505i		−	0.883375i	−0.897169	−	0.441687i	$-0.854380\pi$
$13$		−	3.18505i		−	0.883375i	0.897169	−	0.441687i	$-0.145620\pi$
$14$	−2.66744	−	2.62388i	−0.712903	−	0.701262i
$15$	−1.14136	+	1.54206i	−0.294699	+	0.398159i
$16$	0.375896	−	3.98230i	0.0939741	−	0.995575i
$17$	−7.44976			−1.80683			−0.903417	−	0.428764i	$-0.858949\pi$
$17$	−7.44976			−1.80683			−0.903417	+	0.428764i	$0.858949\pi$
$18$	1.15527	+	2.98589i	0.272299	+	0.703781i
$19$		−	4.61892i		−	1.05965i	−0.848106	−	0.529827i	$-0.822257\pi$
$19$		−	4.61892i		−	1.05965i	0.848106	−	0.529827i	$-0.177743\pi$
$20$	0.451687	+	4.44927i	0.101000	+	0.994886i
$21$	−2.06857	+	0.934853i	−0.451399	+	0.204002i
$22$	−1.56017	−	4.03240i	−0.332630	−	0.859710i
$23$	−0.708794			−0.147794			−0.0738969	−	0.997266i	$-0.523544\pi$
$23$	−0.708794			−0.147794			−0.0738969	+	0.997266i	$0.523544\pi$
$24$	−2.17094	−	1.08448i	−0.443141	−	0.221369i
$25$	−1.46068	−	4.78189i	−0.292135	−	0.956377i
$26$	−4.20087	+	1.62536i	−0.823859	+	0.318759i
$27$	4.51631			0.869163
$28$	−2.09951	+	4.85717i	−0.396770	+	0.917918i
$29$		−	2.41421i		−	0.448307i	−0.974554	−	0.224154i	$-0.928038\pi$
$29$		−	2.41421i		−	0.448307i	0.974554	−	0.224154i	$-0.0719617\pi$
$30$	2.61633	+	0.718454i	0.477674	+	0.131171i
$31$	5.14028			0.923221			0.461610	−	0.887083i	$-0.347272\pi$
$31$	5.14028			0.923221			0.461610	+	0.887083i	$0.347272\pi$
$32$	−5.44421	+	1.53642i	−0.962409	+	0.271603i
$33$	−2.62312			−0.456627
$34$	3.80167	+	9.82574i	0.651982	+	1.68510i
$35$	1.24894	−	5.78275i	0.211109	−	0.977462i
$36$	3.34865	−	3.04745i	0.558108	−	0.507908i
$37$	2.07192			0.340621			0.170311	−	0.985390i	$-0.445523\pi$
$37$	2.07192			0.340621			0.170311	+	0.985390i	$0.445523\pi$
$38$	−6.09205	+	2.35707i	−0.988261	+	0.382368i
$39$			2.73272i			0.437586i
$40$	5.63779	−	2.86624i	0.891413	−	0.453193i
$41$			5.51396i			0.861136i	0.902558	+	0.430568i	$0.141687\pi$
$41$			5.51396i			0.861136i	−0.902558	+	0.430568i	$0.858313\pi$
$42$	2.28862	+	2.25125i	0.353141	+	0.347375i
$43$			4.21172i			0.642282i	0.947031	+	0.321141i	$0.104066\pi$
$43$			4.21172i			0.642282i	−0.947031	+	0.321141i	$0.895934\pi$
$44$	−4.52229	+	4.11553i	−0.681762	+	0.620439i
$45$	−3.01159	+	4.06888i	−0.448941	+	0.606553i
$46$	0.361703	+	0.934853i	0.0533303	+	0.137837i
$47$			6.55463i			0.956091i	0.878335	+	0.478045i	$0.158655\pi$
$47$			6.55463i			0.956091i	−0.878335	+	0.478045i	$0.841345\pi$
$48$	−0.322513	+	3.41674i	−0.0465507	+	0.493164i
$49$	4.62557	−	5.25396i	0.660796	−	0.750566i
$50$	−5.56159	+	4.36677i	−0.786528	+	0.617554i
$51$	6.39177			0.895027
$52$	4.28748	+	4.71124i	0.594566	+	0.653332i
$53$	3.75594			0.515918			0.257959	−	0.966156i	$-0.416950\pi$
$53$	3.75594			0.515918			0.257959	+	0.966156i	$0.416950\pi$
$54$	−2.30471	−	5.95671i	−0.313631	−	0.810605i
$55$	4.06711	−	5.49496i	0.548408	−	0.740940i
$56$	7.47768	+	0.290465i	0.999246	+	0.0388150i
$57$			3.96296i			0.524906i
$58$	−3.18418	+	1.23199i	−0.418103	+	0.161768i
$59$		−	3.11915i		−	0.406079i	−0.979171	−	0.203040i	$-0.934918\pi$
$59$		−	3.11915i		−	0.406079i	0.979171	−	0.203040i	$-0.0650820\pi$
$60$	−0.387540	−	3.81739i	−0.0500312	−	0.492823i
$61$	9.55219			1.22303			0.611516	−	0.791232i	$-0.290560\pi$
$61$	9.55219			1.22303			0.611516	+	0.791232i	$0.290560\pi$
$62$	−2.62312	−	6.77968i	−0.333137	−	0.861020i
$63$	−5.45812	+	2.46669i	−0.687658	+	0.310774i
$64$	4.80466	+	6.39651i	0.600582	+	0.799563i
$65$	−5.72454	−	4.23703i	−0.710042	−	0.525539i
$66$	1.33860	+	3.45973i	0.164770	+	0.425863i
$67$			0.519160i			0.0634255i	0.999497	+	0.0317128i	$0.0100962\pi$
$67$			0.519160i			0.0634255i	−0.999497	+	0.0317128i	$0.989904\pi$
$68$	11.0195	−	10.0283i	1.33631	−	1.21611i
$69$	0.608133			0.0732107
$70$	−8.26440	+	1.30371i	−0.987785	+	0.155823i
$71$		−	10.9754i		−	1.30254i	−0.758848	−	0.651268i	$-0.774237\pi$
$71$		−	10.9754i		−	1.30254i	0.758848	−	0.651268i	$-0.225763\pi$
$72$	−5.72822	−	2.86151i	−0.675077	−	0.337232i
$73$	−2.32017			−0.271555			−0.135778	−	0.990739i	$-0.543353\pi$
$73$	−2.32017			−0.271555			−0.135778	+	0.990739i	$0.543353\pi$
$74$	−1.05732	−	2.73272i	−0.122910	−	0.317672i
$75$	1.25323	+	4.10277i	0.144711	+	0.473748i
$76$	6.21765	+	6.83218i	0.713213	+	0.783705i
$77$	7.37110	−	3.33123i	0.840015	−	0.379629i
$78$	3.60428	−	1.39453i	0.408104	−	0.157899i
$79$			9.98693i			1.12362i	0.827267	+	0.561808i	$0.189894\pi$
$79$			9.98693i			1.12362i	−0.827267	+	0.561808i	$0.810106\pi$
$80$	−6.65739	−	5.97320i	−0.744319	−	0.667824i
$81$	2.91669			0.324076
$82$	7.27255	−	2.81382i	0.803119	−	0.310734i
$83$	8.73474			0.958762			0.479381	−	0.877607i	$-0.340861\pi$
$83$	8.73474			0.958762			0.479381	+	0.877607i	$0.340861\pi$
$84$	1.80134	−	4.16736i	0.196543	−	0.454697i
$85$	−9.91032	+	13.3896i	−1.07493	+	1.45230i
$86$	5.55498	−	2.14928i	0.599009	−	0.231762i
$87$			2.07135i			0.222072i
$88$	7.73587	+	3.86442i	0.824647	+	0.411948i
$89$			18.5697i			1.96839i	0.177093	+	0.984194i	$0.443331\pi$
$89$			18.5697i			1.96839i	−0.177093	+	0.984194i	$0.556669\pi$
$90$	6.90342	+	1.89571i	0.727684	+	0.199825i
$91$	−3.47042	−	7.67907i	−0.363798	−	0.804986i
$92$	1.04843	−	0.954126i	0.109306	−	0.0994745i
$93$	−4.41027			−0.457323
$94$	8.64512	−	3.34488i	0.891676	−	0.344998i
$95$	−8.30166	−	6.14449i	−0.851732	−	0.630411i
$96$	4.67104	−	1.31822i	0.476736	−	0.134540i
$97$	1.58285			0.160714			0.0803568	−	0.996766i	$-0.474394\pi$
$97$	1.58285			0.160714			0.0803568	+	0.996766i	$0.474394\pi$
$98$	−9.29009	−	3.41968i	−0.938441	−	0.345440i
$99$	−6.92135			−0.695622
$100$	8.59760	+	5.10698i	0.859760	+	0.510698i
$101$	−13.5493			−1.34820			−0.674101	−	0.738639i	$-0.735469\pi$
$101$	−13.5493			−1.34820			−0.674101	+	0.738639i	$0.735469\pi$
$102$	−3.26177	−	8.43032i	−0.322963	−	0.834726i
$103$			11.0978i			1.09349i	0.837298	+	0.546747i	$0.184134\pi$
$103$			11.0978i			1.09349i	−0.837298	+	0.546747i	$0.815866\pi$
$104$	4.02588	−	8.05908i	0.394770	−	0.790258i
$105$	−1.07157	+	4.96150i	−0.104574	+	0.484192i
$106$	−1.91669	−	4.95383i	−0.186165	−	0.481159i
$107$			17.5187i			1.69359i	0.531916	+	0.846797i	$0.321472\pi$
$107$			17.5187i			1.69359i	−0.531916	+	0.846797i	$0.678528\pi$
$108$	−6.68039	+	6.07951i	−0.642821	+	0.585001i
$109$		−	15.6899i		−	1.50282i	−0.659834	−	0.751412i	$-0.729373\pi$
$109$		−	15.6899i		−	1.50282i	0.659834	−	0.751412i	$-0.270627\pi$
$110$	−9.32296	−	2.56012i	−0.888909	−	0.244098i
$111$	−1.77767			−0.168729
$112$	−3.43281	−	10.0108i	−0.324370	−	0.945930i
$113$		−	12.3864i		−	1.16521i	−0.812754	−	0.582607i	$-0.802033\pi$
$113$		−	12.3864i		−	1.16521i	0.812754	−	0.582607i	$-0.197967\pi$
$114$	5.22688	−	2.02233i	0.489542	−	0.189408i
$115$	−0.942900	+	1.27393i	−0.0879258	+	0.118794i
$116$	3.24982	+	3.57103i	0.301739	+	0.331562i
$117$			7.21053i			0.666614i
$118$	−4.11395	+	1.59173i	−0.378720	+	0.146530i
$119$	−17.9612	+	8.11722i	−1.64650	+	0.744104i
$120$	−4.83712	+	2.45919i	−0.441567	+	0.224492i
$121$	−1.65282			−0.150256
$122$	−4.87456	−	12.5987i	−0.441322	−	1.14063i
$123$		−	4.73088i		−	0.426569i
$124$	−7.60335	+	6.91945i	−0.682801	+	0.621385i
$125$	−10.5377	−	3.73598i	−0.942518	−	0.334156i
$126$	6.03873	+	5.94012i	0.537973	+	0.529188i
$127$	17.2814			1.53348			0.766739	−	0.641959i	$-0.221878\pi$
$127$	17.2814			1.53348			0.766739	+	0.641959i	$0.221878\pi$
$128$	5.98471	−	9.60121i	0.528979	−	0.848635i
$129$		−	3.61358i		−	0.318158i
$130$	−2.66709	+	9.71248i	−0.233919	+	0.851841i
$131$			12.6396i			1.10433i	0.833736	+	0.552164i	$0.186198\pi$
$131$			12.6396i			1.10433i	−0.833736	+	0.552164i	$0.813802\pi$
$132$	3.88005	−	3.53105i	0.337715	−	0.307339i
$133$	−5.03275	−	11.1361i	−0.436395	−	0.965622i
$134$	0.684738	−	0.264932i	0.0591523	−	0.0228866i
$135$	6.00798	−	8.11722i	0.517085	−	0.698619i
$136$	−18.8500	−	9.41643i	−1.61637	−	0.807452i
$137$			11.3987i			0.973857i	0.873442	+	0.486928i	$0.161883\pi$
$137$			11.3987i			0.973857i	−0.873442	+	0.486928i	$0.838117\pi$
$138$	−0.310335	−	0.802087i	−0.0264175	−	0.0682782i
$139$			7.90877i			0.670813i	0.942073	+	0.335407i	$0.108874\pi$
$139$			7.90877i			0.670813i	−0.942073	+	0.335407i	$0.891126\pi$
$140$	5.93690	+	10.2349i	0.501760	+	0.865007i
$141$		−	5.62376i		−	0.473606i
$142$	−14.4758	+	5.60081i	−1.21478	+	0.470010i
$143$		−	9.73772i		−	0.814309i
$144$	−0.850979	+	9.01539i	−0.0709149	+	0.751282i
$145$	−4.33909	−	3.21159i	−0.360342	−	0.266708i
$146$	1.18400	+	3.06015i	0.0979887	+	0.253260i
$147$	−3.96866	+	4.50781i	−0.327329	+	0.371798i
$148$	−3.06472	+	2.78906i	−0.251918	+	0.229259i
$149$		−	7.33515i		−	0.600919i	−0.953795	−	0.300459i	$-0.902860\pi$
$149$		−	7.33515i		−	0.600919i	0.953795	−	0.300459i	$-0.0971400\pi$
$150$	4.77175	−	3.74661i	0.389612	−	0.305910i
$151$			8.24264i			0.670776i	0.942080	+	0.335388i	$0.108867\pi$
$151$			8.24264i			0.670776i	−0.942080	+	0.335388i	$0.891133\pi$
$152$	5.83828	−	11.6872i	0.473547	−	0.947955i
$153$	16.8653			1.36348
$154$	−8.15521	−	8.02204i	−0.657165	−	0.646434i
$155$	6.83804	−	9.23869i	0.549244	−	0.742069i
$156$	−3.67858	−	4.04216i	−0.294522	−	0.323632i
$157$			16.8886i			1.34786i	0.738795	+	0.673930i	$0.235395\pi$
$157$			16.8886i			1.34786i	−0.738795	+	0.673930i	$0.764605\pi$
$158$	13.1721	−	5.09641i	1.04792	−	0.405448i
$159$	−3.22253			−0.255563
$160$	−4.48094	+	11.8288i	−0.354249	+	0.935151i
$161$	−1.70888	+	0.772298i	−0.134679	+	0.0608656i
$162$	−1.48841	−	3.84691i	−0.116940	−	0.302242i
$163$		−	17.5187i		−	1.37217i	−0.727522	−	0.686084i	$-0.759328\pi$
$163$		−	17.5187i		−	1.37217i	0.727522	−	0.686084i	$-0.240672\pi$
$164$	−7.42248	−	8.15609i	−0.579598	−	0.636884i
$165$	−3.48951	+	4.71458i	−0.271658	+	0.367029i
$166$	−4.45741	−	11.5205i	−0.345962	−	0.894167i
$167$		−	11.0978i		−	0.858770i	−0.903122	−	0.429385i	$-0.858730\pi$
$167$		−	11.0978i		−	0.858770i	0.903122	−	0.429385i	$-0.141270\pi$
$168$	−6.41572	−	0.249214i	−0.494983	−	0.0192273i
$169$	2.85543			0.219649
$170$	22.7173	+	6.23825i	1.74233	+	0.478452i
$171$			10.4566i			0.799638i
$172$	−5.66950	−	6.22986i	−0.432296	−	0.475022i
$173$			0.430852i			0.0327571i	0.999866	+	0.0163785i	$0.00521369\pi$
$173$			0.430852i			0.0327571i	−0.999866	+	0.0163785i	$0.994786\pi$
$174$	2.73197	−	1.05703i	0.207110	−	0.0801329i
$175$	−8.73196	−	9.93745i	−0.660074	−	0.751200i
$176$	1.14923	−	12.1751i	0.0866268	−	0.917736i
$177$			2.67618i			0.201154i
$178$	24.4922	−	9.47629i	1.83577	−	0.710278i
$179$	−14.7547			−1.10282			−0.551410	−	0.834234i	$-0.685910\pi$
$179$	−14.7547			−1.10282			−0.551410	+	0.834234i	$0.685910\pi$
$180$	−1.02256	−	10.0725i	−0.0762171	−	0.750763i
$181$	−2.02611			−0.150600			−0.0752999	−	0.997161i	$-0.523991\pi$
$181$	−2.02611			−0.150600			−0.0752999	+	0.997161i	$0.523991\pi$
$182$	−8.35721	+	8.49594i	−0.619477	+	0.629761i
$183$	−8.19561			−0.605837
$184$	−1.79345	−	0.895910i	−0.132215	−	0.0660473i
$185$	2.75624	−	3.72389i	0.202643	−	0.273786i
$186$	2.25059	+	5.81685i	0.165022	+	0.426512i
$187$	−22.7763			−1.66557
$188$	−8.82334	−	9.69542i	−0.643509	−	0.707111i
$189$	10.8887	−	4.92094i	0.792035	−	0.357946i
$190$	−3.86777	+	14.0849i	−0.280598	+	1.02183i
$191$		−	9.98693i		−	0.722629i	−0.932444	−	0.361314i	$-0.882328\pi$
$191$		−	9.98693i		−	0.722629i	0.932444	−	0.361314i	$-0.117672\pi$
$192$	−4.12231	−	5.48809i	−0.297502	−	0.396069i
$193$			6.58851i			0.474252i	0.971479	+	0.237126i	$0.0762053\pi$
$193$			6.58851i			0.474252i	−0.971479	+	0.237126i	$0.923795\pi$
$194$	−0.807739	−	2.08767i	−0.0579923	−	0.149886i
$195$	4.91156	+	3.63530i	0.351724	+	0.260329i
$196$	0.230477	+	13.9981i	0.0164626	+	0.999864i
$197$	12.1374			0.864755			0.432378	−	0.901693i	$-0.357675\pi$
$197$	12.1374			0.864755			0.432378	+	0.901693i	$0.357675\pi$
$198$	3.53202	+	9.12880i	0.251010	+	0.648756i
$199$	16.1512			1.14493			0.572465	−	0.819929i	$-0.305987\pi$
$199$	16.1512			1.14493			0.572465	+	0.819929i	$0.305987\pi$
$200$	2.34833	−	13.9458i	0.166052	−	0.986117i
$201$		−	0.445430i		−	0.0314182i
$202$	6.91429	+	17.8706i	0.486488	+	1.25737i
$203$	−2.63051	−	5.82059i	−0.184625	−	0.408525i
$204$	−9.45452	+	8.60412i	−0.661949	+	0.602409i
$205$	9.91032	+	7.33515i	0.692167	+	0.512309i
$206$	14.6372	−	5.66327i	1.01982	−	0.394579i
$207$	1.60462			0.111528
$208$	−12.6838	−	1.19725i	−0.879466	−	0.0830144i
$209$		−	14.1215i		−	0.976805i
$210$	7.09071	−	1.11856i	0.489306	−	0.0771882i
$211$	1.35578			0.0933360			0.0466680	−	0.998910i	$-0.485140\pi$
$211$	1.35578			0.0933360			0.0466680	+	0.998910i	$0.485140\pi$
$212$	−5.55568	+	5.05596i	−0.381566	+	0.347245i
$213$			9.41667i			0.645219i
$214$	23.1060	−	8.93992i	1.57949	−	0.611120i
$215$	7.56979	+	5.60280i	0.516255	+	0.382108i
$216$	11.4275	+	5.70857i	0.777545	+	0.388419i
$217$	12.3931	−	5.60081i	0.841296	−	0.380208i
$218$	−20.6940	+	8.00670i	−1.40157	+	0.542282i
$219$	1.99067			0.134517
$220$	1.38095	+	13.6028i	0.0931037	+	0.917102i
$221$			23.7279i			1.59611i
$222$	0.907159	+	2.34463i	0.0608845	+	0.157361i
$223$		−	8.30493i		−	0.556139i	−0.960561	−	0.278070i	$-0.910305\pi$
$223$		−	8.30493i		−	0.556139i	0.960561	−	0.278070i	$-0.0896946\pi$
$224$	−11.4518	+	9.63624i	−0.765153	+	0.643848i
$225$	3.30678	+	10.8255i	0.220452	+	0.721703i
$226$	−16.3368	+	6.32088i	−1.08671	+	0.420459i
$227$	6.28883			0.417404			0.208702	−	0.977979i	$-0.433076\pi$
$227$	6.28883			0.417404			0.208702	+	0.977979i	$0.433076\pi$
$228$	−5.33463	−	5.86189i	−0.353295	−	0.388213i
$229$	23.8298			1.57472			0.787359	−	0.616495i	$-0.211448\pi$
$229$	23.8298			1.57472			0.787359	+	0.616495i	$0.211448\pi$
$230$	2.16139	+	0.593527i	0.142518	+	0.0391360i
$231$	−6.32428	+	2.85814i	−0.416107	+	0.188052i
$232$	3.05154	−	6.10863i	0.200343	−	0.401051i
$233$			5.79789i			0.379832i	0.981800	+	0.189916i	$0.0608216\pi$
$233$			5.79789i			0.379832i	−0.981800	+	0.189916i	$0.939178\pi$
$234$	9.51022	−	3.67959i	0.621702	−	0.240543i
$235$	11.7807	+	8.71953i	0.768490	+	0.568799i
$236$	4.19877	+	4.61376i	0.273317	+	0.300330i
$237$		−	8.56861i		−	0.556591i
$238$	19.8718	+	19.5473i	1.28810	+	1.26706i
$239$			22.2759i			1.44091i	0.693502	+	0.720454i	$0.256067\pi$
$239$			22.2759i			1.44091i	−0.693502	+	0.720454i	$0.743933\pi$
$240$	5.71193	+	5.12490i	0.368703	+	0.330811i
$241$		−	22.0893i		−	1.42290i	−0.702739	−	0.711448i	$-0.748040\pi$
$241$		−	22.0893i		−	1.42290i	0.702739	−	0.711448i	$-0.251960\pi$
$242$	0.843447	+	2.17996i	0.0542188	+	0.140133i
$243$	−16.0514			−1.02970
$244$	−14.1293	+	12.8584i	−0.904537	+	0.823177i
$245$	−3.28969	−	15.3029i	−0.210170	−	0.977665i
$246$	−6.23972	+	2.41421i	−0.397830	+	0.153924i
$247$	−14.7115			−0.936072
$248$	13.0063	+	6.49726i	0.825904	+	0.412576i
$249$	−7.49425			−0.474929
$250$	0.449944	+	15.8050i	0.0284570	+	0.999595i
$251$		−	15.9294i		−	1.00546i	−0.864444	−	0.502729i	$-0.832329\pi$
$251$		−	15.9294i		−	1.00546i	0.864444	−	0.502729i	$-0.167671\pi$
$252$	4.75301	−	10.9960i	0.299412	−	0.692681i
$253$	−2.16701			−0.136239
$254$	−8.81885	−	22.7930i	−0.553344	−	1.43016i
$255$	8.50288	−	11.4880i	0.532471	−	0.719407i
$256$	−15.7174	−	2.99386i	−0.982338	−	0.187116i
$257$	−9.71846			−0.606221			−0.303110	−	0.952955i	$-0.598025\pi$
$257$	−9.71846			−0.606221			−0.303110	+	0.952955i	$0.598025\pi$
$258$	−4.76608	+	1.84404i	−0.296723	+	0.114805i
$259$	4.99533	−	2.25755i	0.310395	−	0.140277i
$260$	14.1712	−	1.43865i	0.878858	−	0.0892212i
$261$			5.46544i			0.338302i
$262$	16.6708	−	6.45009i	1.02993	−	0.398488i
$263$	8.90441			0.549069			0.274535	−	0.961577i	$-0.411476\pi$
$263$	8.90441			0.549069			0.274535	+	0.961577i	$0.411476\pi$
$264$	−6.63724	−	3.31560i	−0.408494	−	0.204061i
$265$	4.99647	−	6.75060i	0.306931	−	0.414686i
$266$	−12.1195	+	12.3207i	−0.743095	+	0.755431i
$267$		−	15.9325i		−	0.975054i
$268$	−0.698854	−	0.767927i	−0.0426893	−	0.0469086i
$269$	−4.80691			−0.293083			−0.146541	−	0.989205i	$-0.546814\pi$
$269$	−4.80691			−0.293083			−0.146541	+	0.989205i	$0.546814\pi$
$270$	−13.7720	−	3.78184i	−0.838137	−	0.230156i
$271$	−12.0056			−0.729286			−0.364643	−	0.931147i	$-0.618809\pi$
$271$	−12.0056			−0.729286			−0.364643	+	0.931147i	$0.618809\pi$
$272$	−2.80034	+	29.6672i	−0.169796	+	1.79884i
$273$	2.97756	+	6.58851i	0.180210	+	0.398755i
$274$	15.0341	−	5.81685i	0.908245	−	0.351409i
$275$	−4.46575	−	14.6197i	−0.269295	−	0.881603i
$276$	−0.899533	+	0.818623i	−0.0541456	+	0.0492753i
$277$	1.32250			0.0794612			0.0397306	−	0.999210i	$-0.487350\pi$
$277$	1.32250			0.0794612			0.0397306	+	0.999210i	$0.487350\pi$
$278$	10.4311	−	4.03591i	0.625618	−	0.242058i
$279$	−11.6369			−0.696683
$280$	10.4695	−	13.0533i	0.625673	−	0.780086i
$281$	−13.6055			−0.811636			−0.405818	−	0.913954i	$-0.633013\pi$
$281$	−13.6055			−0.811636			−0.405818	+	0.913954i	$0.633013\pi$
$282$	−7.41736	+	2.86985i	−0.441697	+	0.170897i
$283$	−4.03383			−0.239786			−0.119893	−	0.992787i	$-0.538255\pi$
$283$	−4.03383			−0.239786			−0.119893	+	0.992787i	$0.538255\pi$
$284$	14.7742	+	16.2344i	0.876688	+	0.963337i
$285$	7.12268	+	5.27187i	0.421911	+	0.312278i
$286$	−12.8434	+	4.96923i	−0.759446	+	0.293837i
$287$	6.00798	+	13.2940i	0.354640	+	0.784720i
$288$	12.3250	−	3.47824i	0.726255	−	0.204957i
$289$	38.4990			2.26465
$290$	−2.02160	+	7.36187i	−0.118712	+	0.432304i
$291$	−1.35805			−0.0796106
$292$	3.43193	−	3.12324i	0.200839	−	0.182774i
$293$			15.1789i			0.886759i	0.896334	+	0.443379i	$0.146221\pi$
$293$			15.1789i			0.886759i	−0.896334	+	0.443379i	$0.853779\pi$
$294$	7.97074	+	2.93403i	0.464863	+	0.171116i
$295$	−5.60610	−	4.14937i	−0.326400	−	0.241585i
$296$	5.24253	+	2.61888i	0.304716	+	0.152220i
$297$	13.8078			0.801208
$298$	−9.67457	+	3.74318i	−0.560433	+	0.216837i
$299$			2.25755i			0.130557i
$300$	−7.37660	−	4.38170i	−0.425888	−	0.252977i
$301$	4.58907	+	10.1543i	0.264509	+	0.585287i
$302$	10.8715	−	4.20628i	0.625584	−	0.242044i
$303$	11.6250			0.667840
$304$	−18.3939	−	1.73624i	−1.05496	−	0.0995800i
$305$	12.7071	−	17.1683i	0.727609	−	0.983053i
$306$	−8.60648	−	22.2442i	−0.492000	−	1.27161i
$307$	−15.7575			−0.899329			−0.449664	−	0.893198i	$-0.648456\pi$
$307$	−15.7575			−0.899329			−0.449664	+	0.893198i	$0.648456\pi$
$308$	−6.41887	+	14.8499i	−0.365749	+	0.846151i
$309$		−	9.52168i		−	0.541669i
$310$	−15.6747	−	4.30434i	−0.890265	−	0.244470i
$311$	27.2794			1.54687			0.773436	−	0.633874i	$-0.218536\pi$
$311$	27.2794			1.54687			0.773436	+	0.633874i	$0.218536\pi$
$312$	−3.45413	+	6.91455i	−0.195552	+	0.391460i
$313$	7.37828			0.417045			0.208523	−	0.978018i	$-0.433135\pi$
$313$	7.37828			0.417045			0.208523	+	0.978018i	$0.433135\pi$
$314$	22.2750	−	8.61840i	1.25705	−	0.486365i
$315$	−2.82743	+	13.0914i	−0.159308	+	0.737615i
$316$	−13.4436	−	14.7724i	−0.756264	−	0.831011i
$317$	−27.5478			−1.54724			−0.773619	−	0.633651i	$-0.781556\pi$
$317$	−27.5478			−1.54724			−0.773619	+	0.633651i	$0.781556\pi$
$318$	1.64448	+	4.25030i	0.0922180	+	0.238345i
$319$		−	7.38099i		−	0.413256i
$320$	17.8881	−	0.126290i	0.999975	−	0.00705984i
$321$		−	15.0307i		−	0.838933i
$322$	1.89067	+	1.85979i	0.105363	+	0.103642i
$323$			34.4099i			1.91462i
$324$	−4.31428	+	3.92622i	−0.239682	+	0.218123i
$325$	−15.2306	+	4.65233i	−0.844840	+	0.258065i
$326$	−23.1060	+	8.93992i	−1.27972	+	0.495136i
$327$			13.4617i			0.744433i
$328$	−6.96960	+	13.9519i	−0.384832	+	0.770364i
$329$	7.14188	+	15.8030i	0.393745	+	0.871249i
$330$	7.99894	+	2.19654i	0.440327	+	0.120916i
$331$	−30.0660			−1.65258			−0.826288	−	0.563248i	$-0.809552\pi$
$331$	−30.0660			−1.65258			−0.826288	+	0.563248i	$0.809552\pi$
$332$	−12.9202	+	11.7580i	−0.709087	+	0.645307i
$333$	−4.69054			−0.257040
$334$	−14.6372	+	5.66327i	−0.800912	+	0.309881i
$335$	0.933094	+	0.690632i	0.0509804	+	0.0377332i
$336$	2.94529	+	8.58908i	0.160679	+	0.468573i
$337$			2.07740i			0.113163i	0.998398	+	0.0565816i	$0.0180201\pi$
$337$			2.07740i			0.113163i	−0.998398	+	0.0565816i	$0.981980\pi$
$338$	−1.45715	−	3.76613i	−0.0792585	−	0.204850i
$339$			10.6273i			0.577197i
$340$	−3.36496	−	33.1460i	−0.182491	−	1.79759i
$341$	15.7154			0.851039
$342$	13.7916	−	5.33610i	0.745764	−	0.288543i
$343$	5.42743	−	17.7071i	0.293054	−	0.956096i
$344$	−5.32358	+	10.6568i	−0.287028	+	0.574579i
$345$	0.808991	−	1.09301i	0.0435546	−	0.0588455i
$346$	0.568265	−	0.219867i	0.0305501	−	0.0118201i
$347$		−	1.58617i		−	0.0851499i	−0.999093	−	0.0425749i	$-0.986444\pi$
$347$		−	1.58617i		−	0.0851499i	0.999093	−	0.0425749i	$-0.0135561\pi$
$348$	−2.78829	−	3.06388i	−0.149468	−	0.164241i
$349$	0.0939008			0.00502640			0.00251320	−	0.999997i	$-0.499200\pi$
$349$	0.0939008			0.00502640			0.00251320	+	0.999997i	$0.499200\pi$
$350$	−8.65084	+	16.5880i	−0.462407	+	0.886668i
$351$		−	14.3847i		−	0.767797i
$352$	−16.6447	+	4.69731i	−0.887164	+	0.250367i
$353$	−16.6771			−0.887634			−0.443817	−	0.896117i	$-0.646376\pi$
$353$	−16.6771			−0.887634			−0.443817	+	0.896117i	$0.646376\pi$
$354$	3.52970	−	1.36568i	0.187602	−	0.0725848i
$355$	−19.7262	−	14.6004i	−1.04696	−	0.774907i
$356$	−24.9972	−	27.4678i	−1.32485	−	1.45579i
$357$	15.4104	−	6.96443i	0.815603	−	0.368597i
$358$	7.52945	+	19.4605i	0.397944	+	1.02852i
$359$			19.7492i			1.04232i	0.853458	+	0.521162i	$0.174501\pi$
$359$			19.7492i			1.04232i	−0.853458	+	0.521162i	$0.825499\pi$
$360$	−12.7632	+	6.48879i	−0.672679	+	0.341989i
$361$	−2.33445			−0.122866
$362$	1.03394	+	2.67231i	0.0543427	+	0.140453i
$363$	1.41809			0.0744305
$364$	15.4703	+	6.68706i	0.810866	+	0.350497i
$365$	−3.08649	+	4.17008i	−0.161554	+	0.218272i
$366$	4.18229	+	10.8095i	0.218612	+	0.565020i
$367$		−	28.2305i		−	1.47362i	−0.676101	−	0.736809i	$-0.736332\pi$
$367$		−	28.2305i		−	1.47362i	0.676101	−	0.736809i	$-0.263668\pi$
$368$	−0.266433	+	2.82263i	−0.0138888	+	0.147140i
$369$		−	12.4829i		−	0.649832i
$370$	−6.31809	−	1.73497i	−0.328462	−	0.0901969i
$371$	9.05546	−	4.09245i	0.470136	−	0.212469i
$372$	6.52354	−	5.93677i	0.338230	−	0.307807i
$373$	11.2527			0.582643			0.291321	−	0.956625i	$-0.405905\pi$
$373$	11.2527			0.582643			0.291321	+	0.956625i	$0.405905\pi$
$374$	11.6229	+	30.0404i	0.601007	+	1.55335i
$375$	9.04114	+	3.20541i	0.466882	+	0.165527i
$376$	−8.28499	+	16.5851i	−0.427266	+	0.855309i
$377$	−7.68938			−0.396023
$378$	−12.0470	−	11.8503i	−0.619630	−	0.609511i
$379$	6.92135			0.355526			0.177763	−	0.984073i	$-0.443114\pi$
$379$	6.92135			0.355526			0.177763	+	0.984073i	$0.443114\pi$
$380$	20.5508	−	2.08631i	1.05424	−	0.107025i
$381$	−14.8272			−0.759618
$382$	−13.1721	+	5.09641i	−0.673943	+	0.260755i
$383$			11.7492i			0.600357i	0.953883	+	0.300178i	$0.0970462\pi$
$383$			11.7492i			0.600357i	−0.953883	+	0.300178i	$0.902954\pi$
$384$	−5.13478	+	8.23767i	−0.262033	+	0.420377i
$385$	3.81840	−	17.6797i	0.194604	−	0.901040i
$386$	8.68981	−	3.36217i	0.442300	−	0.171130i
$387$		−	9.53477i		−	0.484680i
$388$	−2.34130	+	2.13071i	−0.118862	+	0.108170i
$389$		−	37.4556i		−	1.89907i	−0.313654	−	0.949537i	$-0.601553\pi$
$389$		−	37.4556i		−	1.89907i	0.313654	−	0.949537i	$-0.398447\pi$
$390$	2.28831	−	8.33314i	0.115873	−	0.421965i
$391$	5.28035			0.267039
$392$	18.3450	−	7.44733i	0.926560	−	0.376147i
$393$		−	10.8446i		−	0.547036i
$394$	−6.19382	−	16.0085i	−0.312040	−	0.806494i
$395$	17.9496	+	13.2855i	0.903145	+	0.668465i
$396$	10.2379	−	9.31700i	0.514472	−	0.468197i
$397$		−	26.0150i		−	1.30565i	−0.757507	−	0.652827i	$-0.773583\pi$
$397$		−	26.0150i		−	1.30565i	0.757507	−	0.652827i	$-0.226417\pi$
$398$	−8.24211	−	21.3024i	−0.413139	−	1.06779i
$399$	4.31801	+	9.55457i	0.216171	+	0.478327i
$400$	−19.5920	+	4.01936i	−0.979598	+	0.200968i
$401$	−10.3832			−0.518510			−0.259255	−	0.965809i	$-0.583477\pi$
$401$	−10.3832			−0.518510			−0.259255	+	0.965809i	$0.583477\pi$
$402$	−0.587493	+	0.227307i	−0.0293015	+	0.0113370i
$403$		−	16.3721i		−	0.815550i
$404$	20.0417	−	18.2390i	0.997111	−	0.907424i
$405$	3.88003	−	5.24220i	0.192800	−	0.260487i
$406$	−6.33460	+	6.43975i	−0.314381	+	0.319600i
$407$	6.33450			0.313990
$408$	16.1730	+	8.07914i	0.800682	+	0.399977i
$409$			7.50838i			0.371265i	0.982619	+	0.185633i	$0.0594335\pi$
$409$			7.50838i			0.371265i	−0.982619	+	0.185633i	$0.940567\pi$
$410$	4.61726	−	16.8142i	0.228030	−	0.830396i
$411$		−	9.77989i		−	0.482406i
$412$	−14.9390	−	16.4155i	−0.735990	−	0.808733i
$413$	−3.39861	−	7.52019i	−0.167235	−	0.370044i
$414$	−0.818848	−	2.11638i	−0.0402442	−	0.104014i
$415$	11.6197	−	15.6991i	0.570389	−	0.770637i
$416$	4.89357	+	17.3401i	0.239927	+	0.850168i
$417$		−	6.78559i		−	0.332292i
$418$	−18.6253	+	7.20632i	−0.910995	+	0.352473i
$419$		−	22.3526i		−	1.09200i	−0.837786	−	0.545999i	$-0.816150\pi$
$419$		−	22.3526i		−	1.09200i	0.837786	−	0.545999i	$-0.183850\pi$
$420$	−5.09376	−	8.78137i	−0.248550	−	0.428487i
$421$			1.24732i			0.0607905i	0.999538	+	0.0303953i	$0.00967660\pi$
$421$			1.24732i			0.0607905i	−0.999538	+	0.0303953i	$0.990323\pi$
$422$	−0.691868	−	1.78819i	−0.0336796	−	0.0870477i
$423$		−	14.8388i		−	0.721487i
$424$	9.50359	+	4.74747i	0.461535	+	0.230558i
$425$	10.8817	+	35.6239i	0.527840	+	1.72801i
$426$	12.4200	−	4.80540i	0.601749	−	0.232822i
$427$	23.0301	−	10.4080i	1.11450	−	0.503679i
$428$	−23.5823	−	25.9131i	−1.13989	−	1.25256i
$429$			8.35479i			0.403373i
$430$	3.52679	−	12.8432i	0.170077	−	0.619354i
$431$			8.69462i			0.418805i	0.977830	+	0.209402i	$0.0671519\pi$
$431$			8.69462i			0.418805i	−0.977830	+	0.209402i	$0.932848\pi$
$432$	1.69766	−	17.9853i	0.0816789	−	0.865317i
$433$	−25.0439			−1.20353			−0.601767	−	0.798672i	$-0.705536\pi$
$433$	−25.0439			−1.20353			−0.601767	+	0.798672i	$0.705536\pi$
$434$	−13.7114	−	13.4875i	−0.658167	−	0.647420i
$435$	3.72286	+	2.75549i	0.178498	+	0.132115i
$436$	21.1206	+	23.2081i	1.01149	+	1.11147i
$437$			3.27387i			0.156610i
$438$	−1.01585	−	2.62556i	−0.0485393	−	0.125454i
$439$	−37.3313			−1.78173			−0.890864	−	0.454270i	$-0.849900\pi$
$439$	−37.3313			−1.78173			−0.890864	+	0.454270i	$0.849900\pi$
$440$	17.2365	−	8.76301i	0.821718	−	0.417760i
$441$	−10.4717	+	11.8943i	−0.498651	+	0.566393i
$442$	31.2955	−	12.1085i	1.48858	−	0.575944i
$443$			25.4673i			1.20999i	0.796230	+	0.604994i	$0.206824\pi$
$443$			25.4673i			1.20999i	−0.796230	+	0.604994i	$0.793176\pi$
$444$	2.62948	−	2.39296i	0.124789	−	0.113565i
$445$	33.3756	+	24.7031i	1.58216	+	1.17104i
$446$	−10.9536	+	4.23807i	−0.518670	+	0.200678i
$447$			6.29343i			0.297669i
$448$	18.5535	+	10.1867i	0.876570	+	0.481275i
$449$	−4.73840			−0.223619			−0.111810	−	0.993730i	$-0.535665\pi$
$449$	−4.73840			−0.223619			−0.111810	+	0.993730i	$0.535665\pi$
$450$	12.5907	−	9.88578i	0.593531	−	0.466020i
$451$			16.8579i			0.793808i
$452$	16.6736	+	18.3216i	0.784262	+	0.861776i
$453$		−	7.07204i		−	0.332273i
$454$	−3.20924	−	8.29455i	−0.150617	−	0.389282i
$455$	−18.4184	−	3.97794i	−0.863466	−	0.186489i
$456$	−5.00914	+	10.0274i	−0.234574	+	0.469576i
$457$			11.9469i			0.558850i	0.960167	+	0.279425i	$0.0901439\pi$
$457$			11.9469i			0.558850i	−0.960167	+	0.279425i	$0.909856\pi$
$458$	−12.1605	−	31.4299i	−0.568225	−	1.46862i
$459$	−33.6454			−1.57043
$460$	−0.320154	−	3.15362i	−0.0149272	−	0.147038i
$461$	−32.0778			−1.49401			−0.747005	−	0.664818i	$-0.768509\pi$
$461$	−32.0778			−1.49401			−0.747005	+	0.664818i	$0.768509\pi$
$462$	6.99703	+	6.88277i	0.325531	+	0.320215i
$463$	−21.3332			−0.991438			−0.495719	−	0.868483i	$-0.665095\pi$
$463$	−21.3332			−0.991438			−0.495719	+	0.868483i	$0.665095\pi$
$464$	−9.61409	−	0.907492i	−0.446323	−	0.0421293i
$465$	−5.86692	+	7.92664i	−0.272072	+	0.367589i
$466$	7.64703	−	2.95871i	0.354242	−	0.137060i
$467$	38.4098			1.77739			0.888696	−	0.458497i	$-0.151612\pi$
$467$	38.4098			1.77739			0.888696	+	0.458497i	$0.151612\pi$
$468$	−9.70628	−	10.6656i	−0.448673	−	0.493018i
$469$	0.565674	+	1.25168i	0.0261204	+	0.0577972i
$470$	5.48868	−	19.9876i	0.253174	−	0.921961i
$471$		−	14.4902i		−	0.667671i
$472$	3.94258	−	7.89233i	0.181472	−	0.363274i
$473$			12.8766i			0.592065i
$474$	−11.3014	+	4.37263i	−0.519092	+	0.200842i
$475$	−22.0872	+	6.74675i	−1.01343	+	0.309562i
$476$	15.6409	−	36.1847i	0.716898	−	1.65852i
$477$	−8.50294			−0.389323
$478$	29.3804	−	11.3676i	1.34383	−	0.519941i
$479$	2.77227			0.126668			0.0633342	−	0.997992i	$-0.479827\pi$
$479$	2.77227			0.126668			0.0633342	+	0.997992i	$0.479827\pi$
$480$	3.84456	−	10.1489i	0.175480	−	0.463233i
$481$		−	6.59917i		−	0.300896i
$482$	−29.1343	+	11.2723i	−1.32703	+	0.513441i
$483$	1.46619	−	0.662619i	0.0667141	−	0.0301502i
$484$	2.44480	−	2.22490i	0.111127	−	0.101132i
$485$	2.10564	−	2.84487i	0.0956121	−	0.129179i
$486$	8.19115	+	21.1707i	0.371558	+	0.960323i
$487$	−15.3310			−0.694712			−0.347356	−	0.937733i	$-0.612921\pi$
$487$	−15.3310			−0.694712			−0.347356	+	0.937733i	$0.612921\pi$
$488$	24.1697	+	12.0739i	1.09411	+	0.546559i
$489$			15.0307i			0.679713i
$490$	−18.5047	+	12.1481i	−0.835958	+	0.548793i
$491$	3.59438			0.162212			0.0811061	−	0.996705i	$-0.474155\pi$
$491$	3.59438			0.162212			0.0811061	+	0.996705i	$0.474155\pi$
$492$	6.36836	+	6.99779i	0.287108	+	0.315485i
$493$			17.9853i			0.810016i
$494$	7.50741	+	19.4035i	0.337774	+	0.873005i
$495$	−9.20738	+	12.4398i	−0.413841	+	0.559129i
$496$	1.93221	−	20.4701i	0.0867589	−	0.919135i
$497$	−11.9587	−	26.4613i	−0.536420	−	1.18695i
$498$	3.82438	+	9.88442i	0.171374	+	0.442931i
$499$	14.2057			0.635933			0.317966	−	0.948102i	$-0.397000\pi$
$499$	14.2057			0.635933			0.317966	+	0.948102i	$0.397000\pi$
$500$	20.6161	−	8.65886i	0.921981	−	0.387236i
$501$			9.52168i			0.425397i
$502$	−21.0099	+	8.12893i	−0.937717	+	0.362812i
$503$			19.0792i			0.850698i	0.905029	+	0.425349i	$0.139849\pi$
$503$			19.0792i			0.850698i	−0.905029	+	0.425349i	$0.860151\pi$
$504$	−16.9285	−	0.657574i	−0.754053	−	0.0292907i
$505$	−18.0244	+	24.3523i	−0.802075	+	1.08366i
$506$	1.10584	+	2.85814i	0.0491607	+	0.127060i
$507$	−2.44991			−0.108804
$508$	−25.5622	+	23.2629i	−1.13414	+	1.03213i
$509$	5.06084			0.224318			0.112159	−	0.993690i	$-0.464223\pi$
$509$	5.06084			0.224318			0.112159	+	0.993690i	$0.464223\pi$
$510$	−19.4910	−	5.35231i	−0.863077	−	0.237004i
$511$	−5.59387	+	2.52804i	−0.247458	+	0.111834i
$512$	4.07201	+	22.2580i	0.179959	+	0.983674i
$513$		−	20.8605i		−	0.921012i
$514$	4.95941	+	12.8180i	0.218750	+	0.565378i
$515$	19.9462	+	14.7632i	0.878932	+	0.650544i
$516$	4.86434	+	5.34511i	0.214140	+	0.235305i
$517$			20.0396i			0.881339i
$518$	−5.52671	−	5.43647i	−0.242830	−	0.238865i
$519$		−	0.369664i		−	0.0162264i
$520$	−9.12914	−	17.9567i	−0.400339	−	0.787452i
$521$			36.4725i			1.59789i	0.601404	+	0.798945i	$0.294608\pi$
$521$			36.4725i			1.59789i	−0.601404	+	0.798945i	$0.705392\pi$
$522$	7.20855	−	2.78906i	0.315510	−	0.122074i
$523$	23.4497			1.02538			0.512691	−	0.858573i	$-0.328649\pi$
$523$	23.4497			1.02538			0.512691	+	0.858573i	$0.328649\pi$
$524$	−17.0145	−	18.6961i	−0.743281	−	0.816745i
$525$	7.49187	+	8.52616i	0.326972	+	0.372112i
$526$	−4.54399	−	11.7443i	−0.198127	−	0.512077i
$527$	−38.2938			−1.66811
$528$	−0.986023	+	10.4461i	−0.0429111	+	0.454607i
$529$	−22.4976			−0.978157
$530$	−11.4533	−	3.14513i	−0.497501	−	0.136616i
$531$			7.06134i			0.306436i
$532$	22.4349	+	9.69748i	0.972675	+	0.420439i
$533$	17.5623			0.760706
$534$	−21.0139	+	8.13049i	−0.909361	+	0.351841i
$535$	31.4866	+	23.3049i	1.36128	+	1.00756i
$536$	−0.656214	+	1.31362i	−0.0283441	+	0.0567398i
$537$	12.6593			0.546289
$538$	2.45301	+	6.34000i	0.105757	+	0.273337i
$539$	14.1418	−	16.0630i	0.609132	−	0.691883i
$540$	2.03996	+	20.0942i	0.0877858	+	0.864719i
$541$		−	25.4539i		−	1.09435i	−0.837018	−	0.547175i	$-0.815703\pi$
$541$		−	25.4539i		−	1.09435i	0.837018	−	0.547175i	$-0.184297\pi$
$542$	6.12654	+	15.8345i	0.263157	+	0.680152i
$543$	1.73837			0.0746006
$544$	40.5581	−	11.4459i	1.73891	−	0.490741i
$545$	−28.1997	−	20.8721i	−1.20794	−	0.894063i
$546$	7.17034	−	7.28937i	0.306862	−	0.311956i
$547$		−	13.6735i		−	0.584636i	−0.956321	−	0.292318i	$-0.905573\pi$
$547$		−	13.6735i		−	0.584636i	0.956321	−	0.292318i	$-0.0944266\pi$
$548$	−15.3441	−	16.8606i	−0.655466	−	0.720251i
$549$	−21.6249			−0.922927
$550$	−17.0035	+	13.3506i	−0.725034	+	0.569271i
$551$	−11.1510			−0.475050
$552$	1.53875	+	0.768675i	0.0654935	+	0.0327170i
$553$	10.8817	+	24.0782i	0.462737	+	1.02391i
$554$	−0.674881	−	1.74429i	−0.0286729	−	0.0741076i
$555$	−2.36481	+	3.19503i	−0.100381	+	0.135621i
$556$	−10.6462	−	11.6984i	−0.451499	−	0.496124i
$557$	−25.2870			−1.07144			−0.535722	−	0.844395i	$-0.679960\pi$
$557$	−25.2870			−1.07144			−0.535722	+	0.844395i	$0.679960\pi$
$558$	5.93840	+	15.3483i	0.251393	+	0.649745i
$559$	13.4146			0.567376
$560$	−22.5591	−	7.14737i	−0.953298	−	0.302031i
$561$	19.5417			0.825049
$562$	6.94299	+	17.9447i	0.292872	+	0.756953i
$563$	17.9372			0.755962			0.377981	−	0.925813i	$-0.376618\pi$
$563$	17.9372			0.755962			0.377981	+	0.925813i	$0.376618\pi$
$564$	7.57028	+	8.31850i	0.318766	+	0.350272i
$565$	−22.2623	−	16.4775i	−0.936580	−	0.693212i
$566$	2.05850	+	5.32036i	0.0865251	+	0.223631i
$567$	7.03205	−	3.17800i	0.295318	−	0.133464i
$568$	13.8728	−	27.7708i	0.582088	−	1.16524i
$569$	−12.5418			−0.525781			−0.262891	−	0.964826i	$-0.584676\pi$
$569$	−12.5418			−0.525781			−0.262891	+	0.964826i	$0.584676\pi$
$570$	3.31848	−	12.0846i	0.138996	−	0.506169i
$571$	27.0229			1.13088			0.565438	−	0.824791i	$-0.308707\pi$
$571$	27.0229			1.13088			0.565438	+	0.824791i	$0.308707\pi$
$572$	13.1082	+	14.4038i	0.548081	+	0.602251i
$573$			8.56861i			0.357959i
$574$	14.4680	−	14.7082i	0.603882	−	0.613907i
$575$	1.03532	+	3.38937i	0.0431758	+	0.141347i
$576$	−10.8771	−	14.4808i	−0.453212	−	0.603368i
$577$	−13.9759			−0.581825			−0.290912	−	0.956750i	$-0.593959\pi$
$577$	−13.9759			−0.581825			−0.290912	+	0.956750i	$0.593959\pi$
$578$	−19.6463	−	50.7776i	−0.817180	−	2.11207i
$579$		−	5.65283i		−	0.234924i
$580$	10.7415	−	1.09047i	0.446015	−	0.0452792i
$581$	21.0592	−	9.51732i	0.873683	−	0.394845i
$582$	0.693026	+	1.79118i	0.0287269	+	0.0742470i
$583$	11.4831			0.475581
$584$	−5.87069	−	2.93267i	−0.242931	−	0.121355i
$585$	12.9596	+	9.59208i	0.535813	+	0.396584i
$586$	20.0199	−	7.74590i	0.827015	−	0.319980i
$587$	28.5757			1.17945			0.589723	−	0.807605i	$-0.299237\pi$
$587$	28.5757			1.17945			0.589723	+	0.807605i	$0.299237\pi$
$588$	−0.197745	−	12.0101i	−0.00815487	−	0.495289i
$589$		−	23.7425i		−	0.978294i
$590$	−2.61190	+	9.51152i	−0.107530	+	0.391583i
$591$	−10.4137			−0.428362
$592$	0.778826	−	8.25099i	0.0320096	−	0.339114i
$593$	0.693990			0.0284987			0.0142494	−	0.999898i	$-0.495464\pi$
$593$	0.693990			0.0284987			0.0142494	+	0.999898i	$0.495464\pi$
$594$	−7.04622	−	18.2115i	−0.289110	−	0.747228i
$595$	−9.30431	+	43.0801i	−0.381439	+	1.76611i
$596$	9.87402	+	10.8499i	0.404456	+	0.444431i
$597$	−13.8575			−0.567149
$598$	2.97756	−	1.15205i	0.121761	−	0.0471106i
$599$		−	30.4359i		−	1.24358i	−0.783185	−	0.621789i	$-0.786406\pi$
$599$		−	30.4359i		−	1.24358i	0.783185	−	0.621789i	$-0.213594\pi$
$600$	−2.01483	+	11.9653i	−0.0822551	+	0.488479i
$601$			22.1088i			0.901835i	0.892566	+	0.450917i	$0.148903\pi$
$601$			22.1088i			0.901835i	−0.892566	+	0.450917i	$0.851097\pi$
$602$	11.0511	−	11.2345i	0.450408	−	0.457885i
$603$		−	1.17531i		−	0.0478623i
$604$	−11.0956	−	12.1923i	−0.451474	−	0.496097i
$605$	−2.19872	+	2.97064i	−0.0893908	+	0.120774i
$606$	−5.93234	−	15.3326i	−0.240985	−	0.622846i
$607$		−	0.411826i		−	0.0167155i	−0.999965	−	0.00835774i	$-0.997340\pi$
$607$		−	0.411826i		−	0.0167155i	0.999965	−	0.00835774i	$-0.00266038\pi$
$608$	7.09659	+	25.1464i	0.287805	+	1.01982i
$609$	2.25693	+	4.99396i	0.0914554	+	0.202366i
$610$	−29.1284	−	7.99877i	−1.17937	−	0.323861i
$611$	20.8768			0.844586
$612$	−24.9466	+	22.7028i	−1.00841	+	0.917704i
$613$	−38.0372			−1.53631			−0.768155	−	0.640264i	$-0.778825\pi$
$613$	−38.0372			−1.53631			−0.768155	+	0.640264i	$0.778825\pi$
$614$	8.04118	+	20.7831i	0.324516	+	0.838738i
$615$	−8.50288	−	6.29343i	−0.342869	−	0.253776i
$616$	22.8616	+	0.888044i	0.921121	+	0.0357803i
$617$		−	11.2523i		−	0.452999i	−0.974011	−	0.226499i	$-0.927272\pi$
$617$		−	11.2523i		−	0.452999i	0.974011	−	0.226499i	$-0.0727281\pi$
$618$	−12.5585	+	4.85899i	−0.505175	+	0.195457i
$619$			15.2620i			0.613433i	0.951801	+	0.306716i	$0.0992303\pi$
$619$			15.2620i			0.613433i	−0.951801	+	0.306716i	$0.900770\pi$
$620$	2.32180	+	22.8705i	0.0932456	+	0.918500i
$621$	−3.20113			−0.128457
$622$	−13.9209	−	35.9797i	−0.558177	−	1.44265i
$623$	20.2335	+	44.7711i	0.810637	+	1.79372i
$624$	10.8825	+	1.02722i	0.435649	+	0.0411217i
$625$	−20.7328	+	13.9696i	−0.829314	+	0.558783i
$626$	−3.76520	−	9.73146i	−0.150488	−	0.388948i
$627$			12.1160i			0.483867i
$628$	−22.7342	−	24.9812i	−0.907194	−	0.996858i
$629$	−15.4353			−0.615445
$630$	18.7095	−	2.95143i	0.745404	−	0.117588i
$631$			41.5945i			1.65585i	0.560839	+	0.827925i	$0.310479\pi$
$631$			41.5945i			1.65585i	−0.560839	+	0.827925i	$0.689521\pi$
$632$	−12.6234	+	25.2697i	−0.502131	+	1.00518i
$633$	−1.16324			−0.0462346
$634$	14.0579	+	36.3337i	0.558309	+	1.44300i
$635$	22.9892	−	31.0601i	0.912300	−	1.23258i
$636$	4.76668	−	4.33793i	0.189011	−	0.172010i
$637$	−16.7341	−	14.7327i	−0.663031	−	0.583730i
$638$	−9.73504	+	3.76658i	−0.385414	+	0.149120i
$639$			24.8467i			0.982922i
$640$	−9.29501	−	23.5288i	−0.367417	−	0.930056i
$641$	19.7501			0.780080			0.390040	−	0.920798i	$-0.372461\pi$
$641$	19.7501			0.780080			0.390040	+	0.920798i	$0.372461\pi$
$642$	−19.8245	+	7.67030i	−0.782411	+	0.302722i
$643$	1.64849			0.0650100			0.0325050	−	0.999472i	$-0.489652\pi$
$643$	1.64849			0.0650100			0.0325050	+	0.999472i	$0.489652\pi$
$644$	1.48812	−	3.44273i	0.0586402	−	0.135663i
$645$	−6.49475	−	4.80710i	−0.255730	−	0.189279i
$646$	45.3844	−	17.5596i	1.78562	−	0.690875i
$647$			8.32199i			0.327171i	0.986529	+	0.163586i	$0.0523060\pi$
$647$			8.32199i			0.327171i	−0.986529	+	0.163586i	$0.947694\pi$
$648$	7.38004	+	3.68666i	0.289915	+	0.144826i
$649$		−	9.53623i		−	0.374330i
$650$	13.9084	+	17.7140i	0.545532	+	0.694799i
$651$	−10.6330	+	4.80540i	−0.416741	+	0.188339i
$652$	23.5823	+	25.9131i	0.923555	+	1.01484i
$653$	47.2746			1.85000			0.924999	−	0.379968i	$-0.124065\pi$
$653$	47.2746			1.85000			0.924999	+	0.379968i	$0.124065\pi$
$654$	17.7551	−	6.86961i	0.694279	−	0.268623i
$655$	22.7173	+	16.8143i	0.887640	+	0.656989i
$656$	21.9582	+	2.07268i	0.857325	+	0.0809245i
$657$	5.25256			0.204922
$658$	17.1986	−	17.4841i	0.670470	−	0.681600i
$659$	−23.0319			−0.897194			−0.448597	−	0.893734i	$-0.648076\pi$
$659$	−23.0319			−0.897194			−0.448597	+	0.893734i	$0.648076\pi$
$660$	−1.18483	−	11.6710i	−0.0461195	−	0.454292i
$661$	14.2975			0.556107			0.278054	−	0.960566i	$-0.410311\pi$
$661$	14.2975			0.556107			0.278054	+	0.960566i	$0.410311\pi$
$662$	15.3429	+	39.6550i	0.596319	+	1.54124i
$663$		−	20.3581i		−	0.790644i
$664$	22.1013	+	11.0406i	0.857699	+	0.428459i
$665$	−26.7101	−	5.76876i	−1.03577	−	0.223703i
$666$	2.39362	+	6.18651i	0.0927509	+	0.239723i
$667$			1.71118i			0.0662570i
$668$	14.9390	+	16.4155i	0.578006	+	0.635134i
$669$			7.12548i			0.275487i
$670$	0.434732	−	1.58312i	0.0167952	−	0.0611614i
$671$	29.2041			1.12741
$672$	9.82542	−	8.26772i	0.379024	−	0.318934i
$673$		−	27.1433i		−	1.04630i	−0.852242	−	0.523149i	$-0.824757\pi$
$673$		−	27.1433i		−	1.04630i	0.852242	−	0.523149i	$-0.175243\pi$
$674$	2.73995	−	1.06011i	0.105539	−	0.0408341i
$675$	−6.59686	−	21.5965i	−0.253913	−	0.831248i
$676$	−4.22367	+	3.84377i	−0.162449	+	0.147837i
$677$		−	11.9050i		−	0.457546i	−0.973480	−	0.228773i	$-0.926529\pi$
$677$		−	11.9050i		−	0.457546i	0.973480	−	0.228773i	$-0.0734714\pi$
$678$	14.0167	−	5.42321i	0.538309	−	0.208277i
$679$	3.81620	−	1.72466i	0.146452	−	0.0661864i
$680$	−42.0002	+	21.3528i	−1.61063	+	0.818844i
$681$	−5.39571			−0.206764
$682$	−8.01972	−	20.7276i	−0.307091	−	0.793702i
$683$		−	10.0550i		−	0.384744i	−0.981322	−	0.192372i	$-0.938382\pi$
$683$		−	10.0550i		−	0.384744i	0.981322	−	0.192372i	$-0.0616180\pi$
$684$	−14.0759	−	15.4671i	−0.538206	−	0.591401i
$685$	20.4871	+	15.1635i	0.782770	+	0.579369i
$686$	−26.1242	+	1.87768i	−0.997427	+	0.0716900i
$687$	−20.4456			−0.780047
$688$	16.7723	+	1.58317i	0.639439	+	0.0603579i
$689$		−	11.9629i		−	0.455749i
$690$	−1.85444	−	0.509236i	−0.0705972	−	0.0193863i
$691$		−	6.60195i		−	0.251150i	−0.992084	−	0.125575i	$-0.959922\pi$
$691$		−	6.60195i		−	0.251150i	0.992084	−	0.125575i	$-0.0400776\pi$
$692$	−0.579981	−	0.637304i	−0.0220476	−	0.0242267i
$693$	−16.6872	+	7.54147i	−0.633894	+	0.286477i
$694$	−2.09205	+	0.809433i	−0.0794130	+	0.0307257i
$695$	14.2145	+	10.5209i	0.539188	+	0.399082i
$696$	−2.61816	+	5.24109i	−0.0992413	+	0.198663i
$697$		−	41.0777i		−	1.55593i
$698$	−0.0479184	−	0.123849i	−0.00181374	−	0.00468775i
$699$		−	4.97449i		−	0.188152i
$700$	26.2931	+	2.94487i	0.993786	+	0.111306i
$701$			2.49209i			0.0941251i	0.998892	+	0.0470625i	$0.0149860\pi$
$701$			2.49209i			0.0941251i	−0.998892	+	0.0470625i	$0.985014\pi$
$702$	−18.9724	+	7.34062i	−0.716068	+	0.277054i
$703$		−	9.57003i		−	0.360940i
$704$	14.6893	+	19.5561i	0.553626	+	0.737050i
$705$	−10.1077	−	7.48121i	−0.380676	−	0.281758i
$706$	8.51047	+	21.9960i	0.320296	+	0.827831i
$707$	−32.6669	+	14.7632i	−1.22856	+	0.555227i
$708$	−3.60247	−	3.95853i	−0.135389	−	0.148771i
$709$			39.3253i			1.47689i	0.674312	+	0.738447i	$0.264440\pi$
$709$			39.3253i			1.47689i	−0.674312	+	0.738447i	$0.735560\pi$
$710$	−9.19050	+	33.4682i	−0.344913	+	1.25604i
$711$		−	22.6091i		−	0.847906i
$712$	−23.4720	+	46.9867i	−0.879649	+	1.76090i
$713$	−3.64340			−0.136446
$714$	−17.0497	−	16.7713i	−0.638068	−	0.627648i
$715$	−17.5017	−	12.9539i	−0.654528	−	0.484450i
$716$	21.8248	−	19.8617i	0.815630	−	0.742267i
$717$		−	19.1123i		−	0.713763i
$718$	26.0479	−	10.0782i	0.972100	−	0.376115i
$719$	25.2731			0.942528			0.471264	−	0.881992i	$-0.343798\pi$
$719$	25.2731			0.942528			0.471264	+	0.881992i	$0.343798\pi$
$720$	15.0714	+	13.5225i	0.561679	+	0.503955i
$721$	12.0920	+	26.7564i	0.450331	+	0.996459i
$722$	1.19129	+	3.07899i	0.0443352	+	0.114588i
$723$			18.9522i			0.704841i
$724$	2.99697	−	2.72740i	0.111381	−	0.101363i
$725$	−11.5445	+	3.52638i	−0.428751	+	0.130966i
$726$	−0.723663	−	1.87037i	−0.0268577	−	0.0694159i
$727$			7.09135i			0.263004i	0.991316	+	0.131502i	$0.0419799\pi$
$727$			7.09135i			0.263004i	−0.991316	+	0.131502i	$0.958020\pi$
$728$	0.925147	−	23.8168i	0.0342882	−	0.882709i
$729$	5.02175			0.185991
$730$	7.07511	+	1.94285i	0.261862	+	0.0719083i
$731$		−	31.3763i		−	1.16050i
$732$	12.1227	−	11.0323i	0.448069	−	0.407766i
$733$		−	6.53560i		−	0.241398i	−0.992689	−	0.120699i	$-0.961486\pi$
$733$		−	6.53560i		−	0.241398i	0.992689	−	0.120699i	$-0.0385136\pi$
$734$	−37.2341	+	14.4062i	−1.37434	+	0.531744i
$735$	2.82249	+	13.1296i	0.104109	+	0.484293i
$736$	3.85883	−	1.08900i	0.142238	−	0.0401412i
$737$			1.58724i			0.0584666i
$738$	−16.4641	+	6.37011i	−0.606051	+	0.234487i
$739$	14.1221			0.519490			0.259745	−	0.965677i	$-0.416361\pi$
$739$	14.1221			0.519490			0.259745	+	0.965677i	$0.416361\pi$
$740$	0.935859	+	9.21851i	0.0344029	+	0.338879i
$741$	12.6222			0.463689
$742$	−10.0187	−	9.85514i	−0.367800	−	0.361794i
$743$	2.66196			0.0976578			0.0488289	−	0.998807i	$-0.484451\pi$
$743$	2.66196			0.0976578			0.0488289	+	0.998807i	$0.484451\pi$
$744$	−11.1592	−	5.57454i	−0.409117	−	0.204372i
$745$	−13.1836	−	9.75785i	−0.483008	−	0.357500i
$746$	−5.74234	−	14.8416i	−0.210242	−	0.543388i
$747$	−19.7743			−0.723503
$748$	33.6900	−	30.6597i	1.23183	−	1.12103i
$749$	19.0882	+	42.2370i	0.697469	+	1.54331i
$750$	−0.386044	−	13.5604i	−0.0140963	−	0.495156i
$751$			7.53982i			0.275132i	0.990493	+	0.137566i	$0.0439279\pi$
$751$			7.53982i			0.275132i	−0.990493	+	0.137566i	$0.956072\pi$
$752$	26.1025	+	2.46386i	0.951859	+	0.0898478i
$753$			13.6672i			0.498060i
$754$	3.92395	+	10.1418i	0.142902	+	0.369342i
$755$	14.8146	+	10.9651i	0.539159	+	0.399060i
$756$	−9.48203	+	21.9364i	−0.344858	+	0.797821i
$757$	42.4127			1.54152			0.770759	−	0.637127i	$-0.219877\pi$
$757$	42.4127			1.54152			0.770759	+	0.637127i	$0.219877\pi$
$758$	−3.53202	−	9.12880i	−0.128289	−	0.331573i
$759$	1.85926			0.0674867
$760$	−13.2390	−	26.0405i	−0.480227	−	0.944589i
$761$		−	21.4947i		−	0.779183i	−0.920988	−	0.389591i	$-0.872616\pi$
$761$		−	21.4947i		−	0.779183i	0.920988	−	0.389591i	$-0.127384\pi$
$762$	7.56642	+	19.5560i	0.274102	+	0.708441i
$763$	−17.0957	−	37.8280i	−0.618905	−	1.36947i
$764$	13.4436	+	14.7724i	0.486374	+	0.534446i
$765$	22.4356	−	30.3122i	0.811162	−	1.09594i
$766$	15.4964	−	5.99572i	0.559909	−	0.216634i
$767$	−9.93467			−0.358720
$768$	13.4853	+	2.56868i	0.486607	+	0.0926894i
$769$			19.1155i			0.689321i	0.938727	+	0.344661i	$0.112006\pi$
$769$			19.1155i			0.689321i	−0.938727	+	0.344661i	$0.887994\pi$
$770$	−25.2669	+	3.98586i	−0.910555	+	0.143640i
$771$	8.33827			0.300295
$772$	−8.86896	−	9.74554i	−0.319201	−	0.350750i
$773$		−	25.8616i		−	0.930177i	−0.885264	−	0.465089i	$-0.846022\pi$
$773$		−	25.8616i		−	0.930177i	0.885264	−	0.465089i	$-0.153978\pi$
$774$	−12.5757	+	4.86567i	−0.452025	+	0.174893i
$775$	−7.50828	−	24.5802i	−0.269705	−	0.882947i
$776$	4.00505	+	2.00070i	0.143773	+	0.0718210i
$777$	−4.28591	+	1.93694i	−0.153756	+	0.0694872i
$778$	−49.4015	+	19.1139i	−1.77113	+	0.685266i
$779$	25.4686			0.912506
$780$	−12.1586	+	1.23434i	−0.435348	+	0.0441963i
$781$		−	33.5551i		−	1.20070i
$782$	−2.69461	−	6.96443i	−0.0963589	−	0.249048i
$783$		−	10.9033i		−	0.389652i
$784$	−19.1841	−	20.3953i	−0.685147	−	0.728405i
$785$	30.3542	+	22.4667i	1.08339	+	0.801872i
$786$	−14.3033	+	5.53407i	−0.510180	+	0.197394i
$787$	9.23137			0.329063			0.164531	−	0.986372i	$-0.447389\pi$
$787$	9.23137			0.329063			0.164531	+	0.986372i	$0.447389\pi$
$788$	−17.9533	+	16.3385i	−0.639561	+	0.582034i
$789$	−7.63983			−0.271985
$790$	8.36281	−	30.4541i	0.297535	−	1.08351i
$791$	−13.4962	−	29.8633i	−0.479868	−	1.06182i
$792$	−17.5130	−	8.74853i	−0.622296	−	0.310865i
$793$		−	30.4242i		−	1.08040i
$794$	−34.3120	+	13.2756i	−1.21769	+	0.471135i
$795$	−4.28689	+	5.79190i	−0.152040	+	0.205418i
$796$	−23.8905	+	21.7416i	−0.846775	+	0.770610i
$797$		−	1.25393i		−	0.0444165i	−0.999753	−	0.0222083i	$-0.992930\pi$
$797$		−	1.25393i		−	0.0444165i	0.999753	−	0.0222083i	$-0.00706969\pi$
$798$	10.3983	−	10.5709i	0.368097	−	0.374208i
$799$		−	48.8304i		−	1.72750i
$800$	15.2992	+	23.7894i	0.540908	+	0.841082i
$801$		−	42.0394i		−	1.48539i
$802$	5.29861	+	13.6947i	0.187100	+	0.483577i
$803$	−7.09349			−0.250324
$804$	0.599605	+	0.658868i	0.0211464	+	0.0232365i
$805$	−0.885242	+	4.09878i	−0.0312007	+	0.144463i
$806$	−21.5937	+	8.35479i	−0.760604	+	0.294285i
$807$	4.12425			0.145180
$808$	−34.2834	−	17.1261i	−1.20609	−	0.602495i
$809$	−41.6114			−1.46298			−0.731489	−	0.681854i	$-0.761174\pi$
$809$	−41.6114			−1.46298			−0.731489	+	0.681854i	$0.761174\pi$
$810$	−8.89412	−	2.44236i	−0.312508	−	0.0858158i
$811$			14.9717i			0.525728i	0.964833	+	0.262864i	$0.0846671\pi$
$811$			14.9717i			0.525728i	−0.964833	+	0.262864i	$0.915333\pi$
$812$	11.7262	+	5.06865i	0.411509	+	0.177875i
$813$	10.3006			0.361257
$814$	−3.23255	−	8.35479i	−0.113301	−	0.292835i
$815$	−31.4866	−	23.3049i	−1.10293	−	0.816334i
$816$	2.40264	−	25.4539i	0.0841093	−	0.891066i
$817$	19.4536			0.680596
$818$	9.90305	−	3.83159i	0.346252	−	0.133968i
$819$	7.85656	+	17.3844i	0.274530	+	0.607460i
$820$	−24.5331	+	2.49059i	−0.856733	+	0.0869751i
$821$		−	0.316827i		−	0.0110574i	−0.999985	−	0.00552868i	$-0.998240\pi$
$821$		−	0.316827i		−	0.0110574i	0.999985	−	0.00552868i	$-0.00175984\pi$
$822$	−12.8990	+	4.99076i	−0.449905	+	0.174073i
$823$	−5.40508			−0.188409			−0.0942046	−	0.995553i	$-0.530031\pi$
$823$	−5.40508			−0.188409			−0.0942046	+	0.995553i	$0.530031\pi$
$824$	−14.0275	+	28.0804i	−0.488670	+	0.978229i
$825$	3.83154	+	12.5435i	0.133397	+	0.436708i
$826$	−8.18429	+	8.32015i	−0.284768	+	0.289495i
$827$		−	35.9961i		−	1.25171i	−0.779941	−	0.625853i	$-0.784751\pi$
$827$		−	35.9961i		−	1.25171i	0.779941	−	0.625853i	$-0.215249\pi$
$828$	−2.37350	+	2.16001i	−0.0824849	+	0.0750656i
$829$	−22.2653			−0.773305			−0.386652	−	0.922225i	$-0.626369\pi$
$829$	−22.2653			−0.773305			−0.386652	+	0.922225i	$0.626369\pi$
$830$	−26.6357	−	7.31425i	−0.924537	−	0.253881i
$831$	−1.13468			−0.0393616
$832$	20.3732	−	15.3031i	0.706314	−	0.530539i
$833$	−34.4594	+	39.1408i	−1.19395	+	1.35615i
$834$	−8.94974	+	3.46274i	−0.309904	+	0.119905i
$835$	−19.9462	−	14.7632i	−0.690265	−	0.510901i
$836$	19.0093	+	20.8881i	0.657451	+	0.722431i
$837$	23.2151			0.802430
$838$	−29.4816	+	11.4067i	−1.01843	+	0.394039i
$839$	10.8709			0.375305			0.187652	−	0.982236i	$-0.439912\pi$
$839$	10.8709			0.375305			0.187652	+	0.982236i	$0.439912\pi$
$840$	−8.98266	+	11.1995i	−0.309931	+	0.386421i
$841$	23.1716			0.799021
$842$	1.64513	−	0.636516i	0.0566949	−	0.0219358i
$843$	11.6733			0.402049
$844$	−2.00544	+	1.82505i	−0.0690300	+	0.0628210i
$845$	3.79854	−	5.13211i	0.130674	−	0.176550i
$846$	−19.5714	+	7.57236i	−0.672878	+	0.260343i
$847$	−3.98490	+	1.80090i	−0.136923	+	0.0618798i
$848$	1.41184	−	14.9573i	0.0484829	−	0.513635i
$849$	3.46096			0.118780
$850$	41.4326	−	32.5314i	1.42113	−	1.11582i
$851$	−1.46856			−0.0503417
$852$	−12.6760	−	13.9289i	−0.434273	−	0.477195i
$853$		−	24.9401i		−	0.853931i	−0.904268	−	0.426966i	$-0.859583\pi$
$853$		−	24.9401i		−	0.853931i	0.904268	−	0.426966i	$-0.140417\pi$
$854$	−25.4799	−	25.0638i	−0.871904	−	0.857667i
$855$	18.7938	+	13.9103i	0.642736	+	0.475722i
$856$	−22.1434	+	44.3272i	−0.756847	+	1.51507i
$857$	14.7132			0.502594			0.251297	−	0.967910i	$-0.419143\pi$
$857$	14.7132			0.502594			0.251297	+	0.967910i	$0.419143\pi$
$858$	11.0194	−	4.26352i	0.376197	−	0.145554i
$859$		−	21.0920i		−	0.719651i	−0.933020	−	0.359825i	$-0.882836\pi$
$859$		−	21.0920i		−	0.719651i	0.933020	−	0.359825i	$-0.117164\pi$
$860$	−18.7391	+	1.90238i	−0.638997	+	0.0648707i
$861$	−5.15474	−	11.4060i	−0.175673	−	0.388716i
$862$	11.4676	−	4.43693i	0.390589	−	0.151123i
$863$	−13.6813			−0.465715			−0.232858	−	0.972511i	$-0.574808\pi$
$863$	−13.6813			−0.465715			−0.232858	+	0.972511i	$0.574808\pi$
$864$	−24.5877	+	6.93893i	−0.836491	+	0.236067i
$865$	0.774377	+	0.573157i	0.0263296	+	0.0194879i
$866$	12.7801	+	33.0312i	0.434286	+	1.12245i
$867$	−33.0315			−1.12181
$868$	−10.7921	+	24.9672i	−0.366307	+	0.847441i
$869$			30.5332i			1.03577i
$870$	1.73450	−	6.31636i	0.0588049	−	0.214145i
$871$	1.65355			0.0560285
$872$	19.8319	−	39.7000i	0.671594	−	1.34441i
$873$	−3.58335			−0.121278
$874$	4.31801	−	1.67068i	0.146059	−	0.0565116i
$875$	−29.4767	+	2.47443i	−0.996495	+	0.0836511i
$876$	−2.94454	+	2.67969i	−0.0994867	+	0.0905382i
$877$	−41.6633			−1.40687			−0.703435	−	0.710759i	$-0.748351\pi$
$877$	−41.6633			−1.40687			−0.703435	+	0.710759i	$0.748351\pi$
$878$	19.0505	+	49.2376i	0.642923	+	1.66169i
$879$		−	13.0232i		−	0.439262i
$880$	−20.3537	−	18.2620i	−0.686125	−	0.615611i
$881$			5.53343i			0.186426i	0.995646	+	0.0932131i	$0.0297138\pi$
$881$			5.53343i			0.186426i	−0.995646	+	0.0932131i	$0.970286\pi$
$882$	21.0315	+	7.74170i	0.708168	+	0.260676i
$883$			36.9558i			1.24366i	0.783151	+	0.621831i	$0.213611\pi$
$883$			36.9558i			1.24366i	−0.783151	+	0.621831i	$0.786389\pi$
$884$	−31.9407	−	35.0976i	−1.07428	−	1.18046i
$885$	4.80993	+	3.56008i	0.161684	+	0.119671i
$886$	33.5897	−	12.9962i	1.12847	−	0.436615i
$887$		−	52.2816i		−	1.75545i	−0.479169	−	0.877723i	$-0.659062\pi$
$887$		−	52.2816i		−	1.75545i	0.479169	−	0.877723i	$-0.340938\pi$
$888$	−4.49800	−	2.24696i	−0.150943	−	0.0754029i
$889$	41.6650	−	18.8297i	1.39740	−	0.631529i
$890$	15.5498	−	56.6264i	0.521232	−	1.89812i
$891$	8.91723			0.298738
$892$	11.1795	+	12.2844i	0.374316	+	0.411313i
$893$	30.2753			1.01312
$894$	8.30061	−	3.21159i	0.277614	−	0.107412i
$895$	−19.6280	+	26.5189i	−0.656092	+	0.886428i
$896$	3.96755	−	29.6692i	0.132547	−	0.991177i
$897$		−	1.93694i		−	0.0646725i
$898$	2.41805	+	6.24964i	0.0806912	+	0.208553i
$899$		−	12.4097i		−	0.413886i
$900$	−19.4638	−	11.5615i	−0.648794	−	0.385384i
$901$	−27.9809			−0.932178
$902$	22.2345	−	8.60273i	0.740327	−	0.286440i
$903$	−3.93734	−	8.71225i	−0.131026	−	0.289926i
$904$	15.6563	−	31.3411i	0.520721	−	1.04239i
$905$	−2.69531	+	3.64156i	−0.0895951	+	0.121050i
$906$	−9.32755	+	3.60892i	−0.309887	+	0.119898i
$907$			37.0631i			1.23066i	0.788270	+	0.615329i	$0.210977\pi$
$907$			37.0631i			1.23066i	−0.788270	+	0.615329i	$0.789023\pi$
$908$	−9.30226	+	8.46555i	−0.308706	+	0.280939i
$909$	30.6737			1.01738
$910$	4.15240	+	26.3226i	0.137651	+	0.872584i
$911$		−	2.17495i		−	0.0720593i	−0.999351	−	0.0360297i	$-0.988529\pi$
$911$		−	2.17495i		−	0.0720593i	0.999351	−	0.0360297i	$-0.0114711\pi$
$912$	15.7817	+	1.48966i	0.522583	+	0.0493276i
$913$	26.7048			0.883801
$914$	15.7571	−	6.09658i	0.521199	−	0.201657i
$915$	−10.9025	+	14.7301i	−0.360426	+	0.486962i
$916$	−35.2484	+	32.0779i	−1.16464	+	1.05988i
$917$	13.7720	+	30.4737i	0.454793	+	1.00633i
$918$	17.1695	+	44.3761i	0.566679	+	1.46463i
$919$		−	13.2512i		−	0.437117i	−0.975824	−	0.218558i	$-0.929865\pi$
$919$		−	13.2512i		−	0.437117i	0.975824	−	0.218558i	$-0.0701354\pi$
$920$	−3.99603	+	2.03158i	−0.131745	+	0.0669791i
$921$	13.5197			0.445488
$922$	16.3695	+	42.3084i	0.539102	+	1.39335i
$923$	−34.9571			−1.15063
$924$	5.50728	−	12.7409i	0.181176	−	0.419146i
$925$	−3.02640	−	9.90767i	−0.0995074	−	0.325762i
$926$	10.8865	+	28.1371i	0.357753	+	0.924642i
$927$		−	25.1238i		−	0.825175i
$928$	3.70923	+	13.1435i	0.121761	+	0.431455i
$929$			7.96007i			0.261161i	0.991438	+	0.130581i	$0.0416842\pi$
$929$			7.96007i			0.261161i	−0.991438	+	0.130581i	$0.958316\pi$
$930$	13.4486	+	3.69305i	0.440998	+	0.121100i
$931$	−24.2676	−	21.3652i	−0.795340	−	0.700215i
$932$	−7.80468	−	8.57607i	−0.255651	−	0.280919i
$933$	−23.4052			−0.766253
$934$	−19.6008	−	50.6599i	−0.641358	−	1.65764i
$935$	−30.2990	+	40.9361i	−0.990883	+	1.33875i
$936$	−9.11405	+	18.2447i	−0.297902	+	0.596346i
$937$	−5.62068			−0.183620			−0.0918099	−	0.995777i	$-0.529265\pi$
$937$	−5.62068			−0.183620			−0.0918099	+	0.995777i	$0.529265\pi$
$938$	1.36222	−	1.38483i	0.0444779	−	0.0452163i
$939$	−6.33044			−0.206586
$940$	−29.1633	+	2.96064i	−0.951201	+	0.0965655i
$941$	10.7839			0.351546			0.175773	−	0.984431i	$-0.443758\pi$
$941$	10.7839			0.351546			0.175773	+	0.984431i	$0.443758\pi$
$942$	−19.1115	+	7.39444i	−0.622688	+	0.240924i
$943$		−	3.90827i		−	0.127271i
$944$	−12.4214	−	1.17248i	−0.404282	−	0.0381609i
$945$	5.64059	−	26.1166i	0.183489	−	0.849575i
$946$	16.9833	−	6.57101i	0.552176	−	0.213642i
$947$		−	32.8524i		−	1.06756i	−0.845623	−	0.533780i	$-0.820771\pi$
$947$		−	32.8524i		−	1.06756i	0.845623	−	0.533780i	$-0.179229\pi$
$948$	11.5344	+	12.6744i	0.374620	+	0.411647i
$949$			7.38987i			0.239885i
$950$	20.1698	+	25.6886i	0.654394	+	0.833447i
$951$	23.6355			0.766435
$952$	−55.7069	−	2.16390i	−1.80547	−	0.0701323i
$953$		−	8.51329i		−	0.275772i	−0.990448	−	0.137886i	$-0.955969\pi$
$953$		−	8.51329i		−	0.275772i	0.990448	−	0.137886i	$-0.0440308\pi$
$954$	4.33912	+	11.2148i	0.140484	+	0.363093i
$955$	−17.9496	−	13.2855i	−0.580837	−	0.429908i
$956$	−29.9861	−	32.9499i	−0.969821	−	1.06568i
$957$			6.33276i			0.204709i
$958$	−1.41471	−	3.65644i	−0.0457073	−	0.118134i
$959$	12.4200	+	27.4820i	0.401061	+	0.887438i
$960$	−15.3477	+	0.108355i	−0.495344	+	0.00349714i
$961$	−4.57757			−0.147663
$962$	−8.70386	+	3.36761i	−0.280624	+	0.108576i
$963$		−	39.6599i		−	1.27802i
$964$	29.7349	+	32.6738i	0.957697	+	1.05235i
$965$	11.8416	+	8.76461i	0.381195	+	0.282143i
$966$	−1.62216	−	1.59567i	−0.0521921	−	0.0513399i
$967$	34.3758			1.10545			0.552726	−	0.833363i	$-0.313588\pi$
$967$	34.3758			1.10545			0.552726	+	0.833363i	$0.313588\pi$
$968$	−4.18210	−	2.08915i	−0.134418	−	0.0671478i
$969$		−	29.5231i		−	0.948418i
$970$	−4.82672	−	1.32544i	−0.154977	−	0.0425572i
$971$			57.5759i			1.84770i	0.382755	+	0.923850i	$0.374975\pi$
$971$			57.5759i			1.84770i	−0.382755	+	0.923850i	$0.625025\pi$
$972$	23.7427	−	21.6072i	0.761549	−	0.693050i
$973$	8.61735	+	19.0678i	0.276260	+	0.611286i
$974$	7.82352	+	20.2205i	0.250682	+	0.647907i
$975$	13.0676	−	3.99162i	0.418497	−	0.127834i
$976$	3.59063	−	38.0397i	0.114933	−	1.21762i
$977$		−	14.6164i		−	0.467621i	−0.972282	−	0.233810i	$-0.924880\pi$
$977$		−	14.6164i		−	0.467621i	0.972282	−	0.233810i	$-0.0751195\pi$
$978$	19.8245	−	7.67030i	0.633918	−	0.245269i
$979$			56.7735i			1.81449i
$980$	25.4656	+	18.2072i	0.813468	+	0.581609i
$981$			35.5199i			1.13406i
$982$	−1.83424	−	4.74075i	−0.0585330	−	0.151283i
$983$			30.3916i			0.969342i	0.874696	+	0.484671i	$0.161061\pi$
$983$			30.3916i			0.969342i	−0.874696	+	0.484671i	$0.838939\pi$
$984$	5.97979	−	11.9705i	0.190629	−	0.381605i
$985$	16.1462	−	21.8148i	0.514462	−	0.695076i
$986$	23.7214	−	9.17803i	0.755443	−	0.292288i
$987$	−6.12761	−	13.5587i	−0.195044	−	0.431579i
$988$	21.7609	−	19.8035i	0.692305	−	0.630035i
$989$		−	2.98525i		−	0.0949253i
$990$	21.1059	+	5.79577i	0.670790	+	0.184202i
$991$			19.7017i			0.625845i	0.949779	+	0.312923i	$0.101308\pi$
$991$			19.7017i			0.625845i	−0.949779	+	0.312923i	$0.898692\pi$
$992$	−27.9847	+	7.89760i	−0.888516	+	0.250749i
$993$	25.7961			0.818614
$994$	−28.7981	+	29.2761i	−0.913419	+	0.928582i
$995$	21.4858	−	29.0288i	0.681145	−	0.920276i
$996$	11.0853	−	10.0882i	0.351251	−	0.319657i
$997$			36.7474i			1.16380i	0.813260	+	0.581901i	$0.197691\pi$
$997$			36.7474i			1.16380i	−0.813260	+	0.581901i	$0.802309\pi$
$998$	−7.24926	−	18.7363i	−0.229471	−	0.593088i
$999$	9.35741			0.296055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.n.b.139.13	✓	40
4.3	odd	2		1120.2.n.b.559.23		40
5.4	even	2	inner	280.2.n.b.139.28	yes	40
7.6	odd	2	inner	280.2.n.b.139.14	yes	40
8.3	odd	2	inner	280.2.n.b.139.25	yes	40
8.5	even	2		1120.2.n.b.559.24		40
20.19	odd	2		1120.2.n.b.559.17		40
28.27	even	2		1120.2.n.b.559.19		40
35.34	odd	2	inner	280.2.n.b.139.27	yes	40
40.19	odd	2	inner	280.2.n.b.139.16	yes	40
40.29	even	2		1120.2.n.b.559.18		40
56.13	odd	2		1120.2.n.b.559.20		40
56.27	even	2	inner	280.2.n.b.139.26	yes	40
140.139	even	2		1120.2.n.b.559.21		40
280.69	odd	2		1120.2.n.b.559.22		40
280.139	even	2	inner	280.2.n.b.139.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.n.b.139.13	✓	40	1.1	even	1	trivial
280.2.n.b.139.14	yes	40	7.6	odd	2	inner
280.2.n.b.139.15	yes	40	280.139	even	2	inner
280.2.n.b.139.16	yes	40	40.19	odd	2	inner
280.2.n.b.139.25	yes	40	8.3	odd	2	inner
280.2.n.b.139.26	yes	40	56.27	even	2	inner
280.2.n.b.139.27	yes	40	35.34	odd	2	inner
280.2.n.b.139.28	yes	40	5.4	even	2	inner
1120.2.n.b.559.17		40	20.19	odd	2
1120.2.n.b.559.18		40	40.29	even	2
1120.2.n.b.559.19		40	28.27	even	2
1120.2.n.b.559.20		40	56.13	odd	2
1120.2.n.b.559.21		40	140.139	even	2
1120.2.n.b.559.22		40	280.69	odd	2
1120.2.n.b.559.23		40	4.3	odd	2
1120.2.n.b.559.24		40	8.5	even	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.510308 - 1.31893i) q^{2} -0.857983 q^{3} +(-1.47917 + 1.34612i) q^{4} +(1.33029 - 1.79731i) q^{5} +(0.437835 + 1.13162i) q^{6} +(2.41097 - 1.08959i) q^{7} +(2.53028 + 1.26399i) q^{8} -2.26387 q^{9} +(-3.04939 - 0.837376i) q^{10} +3.05732 q^{11} +(1.26910 - 1.15495i) q^{12} -3.18505i q^{13} +(-2.66744 - 2.62388i) q^{14} +(-1.14136 + 1.54206i) q^{15} +(0.375896 - 3.98230i) q^{16} -7.44976 q^{17} +(1.15527 + 2.98589i) q^{18} -4.61892i q^{19} +(0.451687 + 4.44927i) q^{20} +(-2.06857 + 0.934853i) q^{21} +(-1.56017 - 4.03240i) q^{22} -0.708794 q^{23} +(-2.17094 - 1.08448i) q^{24} +(-1.46068 - 4.78189i) q^{25} +(-4.20087 + 1.62536i) q^{26} +4.51631 q^{27} +(-2.09951 + 4.85717i) q^{28} -2.41421i q^{29} +(2.61633 + 0.718454i) q^{30} +5.14028 q^{31} +(-5.44421 + 1.53642i) q^{32} -2.62312 q^{33} +(3.80167 + 9.82574i) q^{34} +(1.24894 - 5.78275i) q^{35} +(3.34865 - 3.04745i) q^{36} +2.07192 q^{37} +(-6.09205 + 2.35707i) q^{38} +2.73272i q^{39} +(5.63779 - 2.86624i) q^{40} +5.51396i q^{41} +(2.28862 + 2.25125i) q^{42} +4.21172i q^{43} +(-4.52229 + 4.11553i) q^{44} +(-3.01159 + 4.06888i) q^{45} +(0.361703 + 0.934853i) q^{46} +6.55463i q^{47} +(-0.322513 + 3.41674i) q^{48} +(4.62557 - 5.25396i) q^{49} +(-5.56159 + 4.36677i) q^{50} +6.39177 q^{51} +(4.28748 + 4.71124i) q^{52} +3.75594 q^{53} +(-2.30471 - 5.95671i) q^{54} +(4.06711 - 5.49496i) q^{55} +(7.47768 + 0.290465i) q^{56} +3.96296i q^{57} +(-3.18418 + 1.23199i) q^{58} -3.11915i q^{59} +(-0.387540 - 3.81739i) q^{60} +9.55219 q^{61} +(-2.62312 - 6.77968i) q^{62} +(-5.45812 + 2.46669i) q^{63} +(4.80466 + 6.39651i) q^{64} +(-5.72454 - 4.23703i) q^{65} +(1.33860 + 3.45973i) q^{66} +0.519160i q^{67} +(11.0195 - 10.0283i) q^{68} +0.608133 q^{69} +(-8.26440 + 1.30371i) q^{70} -10.9754i q^{71} +(-5.72822 - 2.86151i) q^{72} -2.32017 q^{73} +(-1.05732 - 2.73272i) q^{74} +(1.25323 + 4.10277i) q^{75} +(6.21765 + 6.83218i) q^{76} +(7.37110 - 3.33123i) q^{77} +(3.60428 - 1.39453i) q^{78} +9.98693i q^{79} +(-6.65739 - 5.97320i) q^{80} +2.91669 q^{81} +(7.27255 - 2.81382i) q^{82} +8.73474 q^{83} +(1.80134 - 4.16736i) q^{84} +(-9.91032 + 13.3896i) q^{85} +(5.55498 - 2.14928i) q^{86} +2.07135i q^{87} +(7.73587 + 3.86442i) q^{88} +18.5697i q^{89} +(6.90342 + 1.89571i) q^{90} +(-3.47042 - 7.67907i) q^{91} +(1.04843 - 0.954126i) q^{92} -4.41027 q^{93} +(8.64512 - 3.34488i) q^{94} +(-8.30166 - 6.14449i) q^{95} +(4.67104 - 1.31822i) q^{96} +1.58285 q^{97} +(-9.29009 - 3.41968i) q^{98} -6.92135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65}+ \cdots - 128 q^{99}+O(q^{100}) \) 40 * q - 12 * q^4 + 40 * q^9 - 12 * q^14 - 28 * q^16 + 16 * q^25 - 28 * q^30 + 16 * q^35 - 28 * q^36 - 8 * q^44 - 32 * q^46 + 8 * q^49 + 4 * q^50 - 32 * q^51 - 4 * q^56 + 12 * q^60 - 84 * q^64 - 24 * q^65 + 40 * q^70 + 80 * q^74 - 72 * q^81 - 8 * q^84 + 80 * q^86 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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