LMFDB - Embedded newform 280.2.n.b.139.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(139,280)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			139.16
Character	$\chi$	$=$	280.139
Dual form			280.2.n.b.139.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.510308 + 1.31893i) q^{2} +0.857983 q^{3} +(-1.47917 - 1.34612i) q^{4} +(-1.33029 - 1.79731i) q^{5} +(-0.437835 + 1.13162i) q^{6} +(2.41097 - 1.08959i) q^{7} +(2.53028 - 1.26399i) q^{8} -2.26387 q^{9} +O(q^{10})$	\(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} +(0.206764 + 3.73594i) 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} +(-5.03297 - 1.63377i) 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} +(-5.16563 - 2.88380i) 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} +(0.177400 + 3.20537i) 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} +(4.72320 - 5.80443i) 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} +(6.43960 - 5.34149i) 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} +(-4.31820 - 1.40175i) 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} +(4.56916 + 8.78196i) q^{98} -6.92135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{4} + 40 q^{9}+O(q^{10}) $ 40 * q - 12 * q^4 + 40 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.420332\pi$
$3$	0.857983			0.495356			0.247678	+	0.968842i	$0.420332\pi$
$4$	−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	$-0.145620\pi$
$14$	0.206764	+	3.73594i	0.0552600	+	0.998472i
$15$	−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	$-0.141051\pi$
$17$	7.44976			1.80683			0.903417	+	0.428764i	$0.141051\pi$
$18$	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
$28$	−5.03297	−	1.63377i	−0.951142	−	0.308754i
$29$			2.41421i			0.448307i	0.974554	+	0.224154i	$0.0719617\pi$
$29$			2.41421i			0.448307i	−0.974554	+	0.224154i	$0.928038\pi$
$30$	2.61633	−	0.718454i	0.477674	−	0.131171i
$31$	−5.14028			−0.923221			−0.461610	−	0.887083i	$-0.652728\pi$
$31$	−5.14028			−0.923221			−0.461610	+	0.887083i	$0.652728\pi$
$32$	−5.44421	−	1.53642i	−0.962409	−	0.271603i
$33$	2.62312			0.456627
$34$	−3.80167	+	9.82574i	−0.651982	+	1.68510i
$35$	−5.16563	−	2.88380i	−0.873150	−	0.487451i
$36$	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	$0.858313\pi$
$42$	0.177400	+	3.20537i	0.0273734	+	0.494600i
$43$		−	4.21172i		−	0.642282i	−0.947031	−	0.321141i	$-0.895934\pi$
$43$		−	4.21172i		−	0.642282i	0.947031	−	0.321141i	$-0.104066\pi$
$44$	−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
$56$	4.72320	−	5.80443i	0.631164	−	0.775649i
$57$		−	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	$-0.709440\pi$
$61$	−9.55219			−1.22303			−0.611516	+	0.791232i	$0.709440\pi$
$62$	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	$-0.989904\pi$
$67$		−	0.519160i		−	0.0634255i	0.999497	−	0.0317128i	$-0.0100962\pi$
$68$	−11.0195	−	10.0283i	−1.33631	−	1.21611i
$69$	−0.608133			−0.0732107
$70$	6.43960	−	5.34149i	0.769680	−	0.638430i
$71$			10.9754i			1.30254i	0.758848	+	0.651268i	$0.225763\pi$
$71$			10.9754i			1.30254i	−0.758848	+	0.651268i	$0.774237\pi$
$72$	−5.72822	+	2.86151i	−0.675077	+	0.337232i
$73$	2.32017			0.271555			0.135778	−	0.990739i	$-0.456647\pi$
$73$	2.32017			0.271555			0.135778	+	0.990739i	$0.456647\pi$
$74$	−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	$-0.810106\pi$
$79$		−	9.98693i		−	1.12362i	0.827267	−	0.561808i	$-0.189894\pi$
$80$	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	$-0.659139\pi$
$83$	−8.73474			−0.958762			−0.479381	+	0.877607i	$0.659139\pi$
$84$	−4.31820	−	1.40175i	−0.471154	−	0.152943i
$85$	−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	$-0.525606\pi$
$97$	−1.58285			−0.160714			−0.0803568	+	0.996766i	$0.525606\pi$
$98$	4.56916	+	8.78196i	0.461555	+	0.887112i
$99$	−6.92135			−0.695622
$100$	8.59760	−	5.10698i	0.859760	−	0.510698i
$101$	13.5493			1.34820			0.674101	−	0.738639i	$-0.264531\pi$
$101$	13.5493			1.34820			0.674101	+	0.738639i	$0.264531\pi$
$102$	−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
$105$	−4.43202	−	2.47425i	−0.432521	−	0.241462i
$106$	−1.91669	+	4.95383i	−0.186165	+	0.481159i
$107$		−	17.5187i		−	1.69359i	−0.531916	−	0.846797i	$-0.678528\pi$
$107$		−	17.5187i		−	1.69359i	0.531916	−	0.846797i	$-0.321472\pi$
$108$	6.68039	+	6.07951i	0.642821	+	0.585001i
$109$			15.6899i			1.50282i	0.659834	+	0.751412i	$0.270627\pi$
$109$			15.6899i			1.50282i	−0.659834	+	0.751412i	$0.729373\pi$
$110$	9.32296	−	2.56012i	0.888909	−	0.244098i
$111$	1.77767			0.168729
$112$	5.24536	+	9.19163i	0.495640	+	0.868528i
$113$			12.3864i			1.16521i	0.812754	+	0.582607i	$0.197967\pi$
$113$			12.3864i			1.16521i	−0.812754	+	0.582607i	$0.802033\pi$
$114$	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
$126$	−0.468086	−	8.45767i	−0.0417004	−	0.753469i
$127$	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	$-0.838117\pi$
$137$		−	11.3987i		−	0.973857i	0.873442	−	0.486928i	$-0.161883\pi$
$138$	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	$0.891126\pi$
$140$	3.75889	+	11.2192i	0.317684	+	0.948197i
$141$			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	$0.0971400\pi$
$149$			7.33515i			0.600919i	−0.953795	+	0.300459i	$0.902860\pi$
$150$	−4.77175	−	3.74661i	−0.389612	−	0.305910i
$151$		−	8.24264i		−	0.670776i	−0.942080	−	0.335388i	$-0.891133\pi$
$151$		−	8.24264i		−	0.670776i	0.942080	−	0.335388i	$-0.108867\pi$
$152$	−5.83828	−	11.6872i	−0.473547	−	0.947955i
$153$	−16.8653			−1.36348
$154$	0.632143	+	11.4219i	0.0509395	+	0.920407i
$155$	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	$0.240672\pi$
$163$			17.5187i			1.37217i	−0.727522	+	0.686084i	$0.759328\pi$
$164$	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	$-0.141270\pi$
$168$	4.05243	−	4.98010i	0.312651	−	0.384223i
$169$	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
$175$	1.68866	+	13.1205i	0.127651	+	0.991819i
$176$	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	$-0.476009\pi$
$181$	2.02611			0.150600			0.0752999	+	0.997161i	$0.476009\pi$
$182$	11.8992	−	0.658555i	0.882025	−	0.0488153i
$183$	−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	$0.117672\pi$
$191$			9.98693i			0.722629i	−0.932444	+	0.361314i	$0.882328\pi$
$192$	4.12231	−	5.48809i	0.297502	−	0.396069i
$193$		−	6.58851i		−	0.474252i	−0.971479	−	0.237126i	$-0.923795\pi$
$193$		−	6.58851i		−	0.474252i	0.971479	−	0.237126i	$-0.0762053\pi$
$194$	0.807739	−	2.08767i	0.0579923	−	0.149886i
$195$	−4.91156	+	3.63530i	−0.351724	+	0.260329i
$196$	−13.9145	+	1.54492i	−0.993893	+	0.110351i
$197$	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	$-0.694013\pi$
$199$	−16.1512			−1.14493			−0.572465	+	0.819929i	$0.694013\pi$
$200$	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
$210$	5.52507	−	4.58291i	0.381266	−	0.316251i
$211$	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	$-0.0896946\pi$
$224$	−14.7999	+	2.22772i	−0.988860	+	0.148846i
$225$	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	$-0.566924\pi$
$227$	−6.28883			−0.417404			−0.208702	+	0.977979i	$0.566924\pi$
$228$	−5.33463	+	5.86189i	−0.353295	+	0.388213i
$229$	−23.8298			−1.57472			−0.787359	−	0.616495i	$-0.788552\pi$
$229$	−23.8298			−1.57472			−0.787359	+	0.616495i	$0.788552\pi$
$230$	−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	$-0.939178\pi$
$233$		−	5.79789i		−	0.379832i	0.981800	−	0.189916i	$-0.0608216\pi$
$234$	−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
$238$	1.54034	+	27.8319i	0.0998456	+	1.80407i
$239$		−	22.2759i		−	1.44091i	−0.693502	−	0.720454i	$-0.743933\pi$
$239$		−	22.2759i		−	1.44091i	0.693502	−	0.720454i	$-0.256067\pi$
$240$	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
$245$	−15.5964	−	1.32433i	−0.996414	−	0.0846082i
$246$	−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	$-0.167671\pi$
$252$	11.3940	+	3.69864i	0.717753	+	0.232992i
$253$	−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	$-0.401975\pi$
$257$	9.71846			0.606221			0.303110	+	0.952955i	$0.401975\pi$
$258$	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
$266$	17.2560	−	0.955027i	1.05803	−	0.0585565i
$267$			15.9325i			0.975054i
$268$	−0.698854	+	0.767927i	−0.0426893	+	0.0469086i
$269$	4.80691			0.293083			0.146541	−	0.989205i	$-0.453186\pi$
$269$	4.80691			0.293083			0.146541	+	0.989205i	$0.453186\pi$
$270$	−13.7720	+	3.78184i	−0.838137	+	0.230156i
$271$	12.0056			0.729286			0.364643	−	0.931147i	$-0.381191\pi$
$271$	12.0056			0.729286			0.364643	+	0.931147i	$0.381191\pi$
$272$	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
$280$	−16.7156	−	0.767528i	−0.998947	−	0.0458686i
$281$	−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	$-0.461745\pi$
$283$	4.03383			0.239786			0.119893	+	0.992787i	$0.461745\pi$
$284$	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	$0.853779\pi$
$294$	3.92026	+	7.53477i	0.228634	+	0.439437i
$295$	−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	$-0.351544\pi$
$307$	15.7575			0.899329			0.449664	+	0.893198i	$0.351544\pi$
$308$	−15.3874	−	4.99496i	−0.876777	−	0.284614i
$309$			9.52168i			0.541669i
$310$	−15.6747	+	4.30434i	−0.890265	+	0.244470i
$311$	−27.2794			−1.54687			−0.773436	−	0.633874i	$-0.781464\pi$
$311$	−27.2794			−1.54687			−0.773436	+	0.633874i	$0.781464\pi$
$312$	−3.45413	−	6.91455i	−0.195552	−	0.391460i
$313$	−7.37828			−0.417045			−0.208523	−	0.978018i	$-0.566865\pi$
$313$	−7.37828			−0.417045			−0.208523	+	0.978018i	$0.566865\pi$
$314$	−22.2750	−	8.61840i	−1.25705	−	0.486365i
$315$	11.6943	+	6.52854i	0.658898	+	0.367842i
$316$	−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
$322$	−0.146553	−	2.64801i	−0.00816709	−	0.147568i
$323$		−	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
$336$	4.50043	+	7.88626i	0.245519	+	0.430231i
$337$		−	2.07740i		−	0.113163i	−0.998398	−	0.0565816i	$-0.981980\pi$
$337$		−	2.07740i		−	0.113163i	0.998398	−	0.0565816i	$-0.0180201\pi$
$338$	−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	$0.0135561\pi$
$347$			1.58617i			0.0851499i	−0.999093	+	0.0425749i	$0.986444\pi$
$348$	2.78829	−	3.06388i	0.149468	−	0.164241i
$349$	−0.0939008			−0.00502640			−0.00251320	−	0.999997i	$-0.500800\pi$
$349$	−0.0939008			−0.00502640			−0.00251320	+	0.999997i	$0.500800\pi$
$350$	−18.1669	−	4.46828i	−0.971059	−	0.238839i
$351$			14.3847i			0.767797i
$352$	−16.6447	−	4.69731i	−0.887164	−	0.250367i
$353$	16.6771			0.887634			0.443817	−	0.896117i	$-0.353624\pi$
$353$	16.6771			0.887634			0.443817	+	0.896117i	$0.353624\pi$
$354$	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	$-0.825499\pi$
$359$		−	19.7492i		−	1.04232i	0.853458	−	0.521162i	$-0.174501\pi$
$360$	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
$364$	−5.20365	+	16.0303i	−0.272745	+	0.840215i
$365$	−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
$378$	−0.933810	−	16.8726i	−0.0480300	−	0.867835i
$379$	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
$385$	−15.7929	−	8.81669i	−0.804883	−	0.449340i
$386$	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	$0.398447\pi$
$389$			37.4556i			1.89907i	−0.313654	+	0.949537i	$0.601553\pi$
$390$	−2.28831	−	8.33314i	−0.115873	−	0.421965i
$391$	−5.28035			−0.267039
$392$	5.06304	−	19.1407i	0.255722	−	0.966750i
$393$			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
$406$	−9.01933	+	0.499171i	−0.447622	+	0.0247735i
$407$	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	$-0.183850\pi$
$420$	3.22506	+	9.62589i	0.157367	+	0.469695i
$421$		−	1.24732i		−	0.0607905i	−0.999538	−	0.0303953i	$-0.990323\pi$
$421$		−	1.24732i		−	0.0607905i	0.999538	−	0.0303953i	$-0.00967660\pi$
$422$	−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	$-0.932848\pi$
$431$		−	8.69462i		−	0.418805i	0.977830	−	0.209402i	$-0.0671519\pi$
$432$	−1.69766	−	17.9853i	−0.0816789	−	0.865317i
$433$	25.0439			1.20353			0.601767	−	0.798672i	$-0.294464\pi$
$433$	25.0439			1.20353			0.601767	+	0.798672i	$0.294464\pi$
$434$	−1.06282	−	19.2038i	−0.0510172	−	0.921810i
$435$	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	$-0.150100\pi$
$439$	37.3313			1.78173			0.890864	+	0.454270i	$0.150100\pi$
$440$	−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	$-0.793176\pi$
$443$		−	25.4673i		−	1.20999i	0.796230	−	0.604994i	$-0.206824\pi$
$444$	−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
$448$	4.61429	−	20.6569i	0.218005	−	0.975948i
$449$	−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
$455$	−9.18506	+	16.4528i	−0.430602	+	0.771319i
$456$	−5.00914	−	10.0274i	−0.234574	−	0.469576i
$457$		−	11.9469i		−	0.558850i	−0.960167	−	0.279425i	$-0.909856\pi$
$457$		−	11.9469i		−	0.558850i	0.960167	−	0.279425i	$-0.0901439\pi$
$458$	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	$-0.231491\pi$
$461$	32.0778			1.49401			0.747005	+	0.664818i	$0.231491\pi$
$462$	0.542368	+	9.79983i	0.0252332	+	0.455930i
$463$	−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	$-0.848388\pi$
$467$	−38.4098			−1.77739			−0.888696	+	0.458497i	$0.848388\pi$
$468$	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
$476$	−37.4944	−	12.1712i	−1.71855	−	0.557867i
$477$	−8.50294			−0.389323
$478$	29.3804	+	11.3676i	1.34383	+	0.519941i
$479$	−2.77227			−0.126668			−0.0633342	−	0.997992i	$-0.520173\pi$
$479$	−2.77227			−0.126668			−0.0633342	+	0.997992i	$0.520173\pi$
$480$	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
$490$	9.70564	−	19.8947i	0.438456	−	0.898753i
$491$	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	$0.860151\pi$
$504$	−10.6927	+	13.1404i	−0.476291	+	0.585322i
$505$	−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	$-0.535777\pi$
$509$	−5.06084			−0.224318			−0.112159	+	0.993690i	$0.535777\pi$
$510$	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
$518$	0.428398	+	7.74056i	0.0188227	+	0.340101i
$519$			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	$-0.671351\pi$
$523$	−23.4497			−1.02538			−0.512691	+	0.858573i	$0.671351\pi$
$524$	17.0145	−	18.6961i	0.743281	−	0.816745i
$525$	1.44884	+	11.2572i	0.0632328	+	0.491304i
$526$	−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
$532$	−7.54627	+	23.2469i	−0.327172	+	1.00788i
$533$	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	$0.184297\pi$
$541$			25.4539i			1.09435i	−0.837018	+	0.547175i	$0.815703\pi$
$542$	−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
$546$	10.2093	−	0.565028i	0.436917	−	0.0241810i
$547$			13.6735i			0.584636i	0.956321	+	0.292318i	$0.0944266\pi$
$547$			13.6735i			0.584636i	−0.956321	+	0.292318i	$0.905573\pi$
$548$	−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
$560$	9.54242	−	21.6551i	0.403241	−	0.915094i
$561$	19.5417			0.825049
$562$	6.94299	−	17.9447i	0.292872	−	0.756953i
$563$	−17.9372			−0.755962			−0.377981	−	0.925813i	$-0.623382\pi$
$563$	−17.9372			−0.755962			−0.377981	+	0.925813i	$0.623382\pi$
$564$	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
$574$	−20.5998	+	1.14009i	−0.859820	+	0.0475864i
$575$	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	$-0.406041\pi$
$577$	13.9759			0.581825			0.290912	+	0.956750i	$0.406041\pi$
$578$	−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	$-0.700763\pi$
$587$	−28.5757			−1.17945			−0.589723	+	0.807605i	$0.700763\pi$
$588$	−11.9384	+	1.32551i	−0.492331	+	0.0546632i
$589$			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	$-0.504536\pi$
$593$	−0.693990			−0.0284987			−0.0142494	+	0.999898i	$0.504536\pi$
$594$	7.04622	−	18.2115i	0.289110	−	0.747228i
$595$	−38.4827	−	21.4836i	−1.57764	−	0.880743i
$596$	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	$0.213594\pi$
$599$			30.4359i			1.24358i	−0.783185	+	0.621789i	$0.786406\pi$
$600$	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	$0.851097\pi$
$602$	15.7347	−	0.870833i	0.641300	−	0.0354925i
$603$			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
$616$	14.4403	−	17.7460i	0.581817	−	0.715005i
$617$			11.2523i			0.452999i	0.974011	+	0.226499i	$0.0727281\pi$
$617$			11.2523i			0.452999i	−0.974011	+	0.226499i	$0.927272\pi$
$618$	−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
$630$	−14.5784	+	12.0924i	−0.580817	+	0.481773i
$631$		−	41.5945i		−	1.65585i	−0.560839	−	0.827925i	$-0.689521\pi$
$631$		−	41.5945i		−	1.65585i	0.560839	−	0.827925i	$-0.310479\pi$
$632$	−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	$-0.510348\pi$
$643$	−1.64849			−0.0650100			−0.0325050	+	0.999472i	$0.510348\pi$
$644$	3.56734	+	1.15801i	0.140573	+	0.0456319i
$645$	−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
$658$	−24.4877	+	1.35526i	−0.954630	+	0.0528336i
$659$	−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	$-0.589689\pi$
$661$	−14.2975			−0.556107			−0.278054	+	0.960566i	$0.589689\pi$
$662$	15.3429	−	39.6550i	0.596319	−	1.54124i
$663$		−	20.3581i		−	0.790644i
$664$	−22.1013	+	11.0406i	−0.857699	+	0.428459i
$665$	−13.3201	+	23.8596i	−0.516530	+	0.925237i
$666$	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
$672$	−12.6981	+	1.91135i	−0.489838	+	0.0737318i
$673$			27.1433i			1.04630i	0.852242	+	0.523149i	$0.175243\pi$
$673$			27.1433i			1.04630i	−0.852242	+	0.523149i	$0.824757\pi$
$674$	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	$0.0616180\pi$
$683$			10.0550i			0.384744i	−0.981322	+	0.192372i	$0.938382\pi$
$684$	14.0759	−	15.4671i	0.538206	−	0.591401i
$685$	−20.4871	+	15.1635i	−0.782770	+	0.579369i
$686$	20.5849	+	16.1945i	0.785935	+	0.618310i
$687$	−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
$700$	15.1641	−	21.6807i	0.573147	−	0.819452i
$701$		−	2.49209i		−	0.0941251i	−0.998892	−	0.0470625i	$-0.985014\pi$
$701$		−	2.49209i		−	0.0941251i	0.998892	−	0.0470625i	$-0.0149860\pi$
$702$	−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	$-0.735560\pi$
$709$		−	39.3253i		−	1.47689i	0.674312	−	0.738447i	$-0.264440\pi$
$710$	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
$714$	1.32159	+	23.8793i	0.0494592	+	0.893659i
$715$	−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	$-0.656202\pi$
$719$	−25.2731			−0.942528			−0.471264	+	0.881992i	$0.656202\pi$
$720$	−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	$0.958020\pi$
$728$	−18.4874	−	15.0437i	−0.685189	−	0.557555i
$729$	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
$735$	−13.3814	−	1.13625i	−0.493580	−	0.0419112i
$736$	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
$742$	0.776593	+	14.0320i	0.0285096	+	0.515130i
$743$	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	$-0.956072\pi$
$751$		−	7.53982i		−	0.275132i	0.990493	−	0.137566i	$-0.0439279\pi$
$752$	−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
$756$	22.7304	+	7.37861i	0.826698	+	0.268358i
$757$	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	$0.887994\pi$
$770$	19.6879	−	16.3306i	0.709503	−	0.588515i
$771$	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
$784$	22.6616	+	16.4455i	0.809342	+	0.587338i
$785$	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	$-0.552611\pi$
$787$	−9.23137			−0.329063			−0.164531	+	0.986372i	$0.552611\pi$
$788$	−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	$-0.00706969\pi$
$798$	14.8054	−	0.819397i	0.524104	−	0.0290063i
$799$			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
$805$	3.66137	+	2.04402i	0.129046	+	0.0720423i
$806$	−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	$0.915333\pi$
$812$	3.94426	−	12.1506i	0.138417	−	0.426404i
$813$	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	$0.00175984\pi$
$821$			0.316827i			0.0110574i	−0.999985	+	0.00552868i	$0.998240\pi$
$822$	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
$826$	11.6530	−	0.644929i	0.405459	−	0.0224399i
$827$			35.9961i			1.25171i	0.779941	+	0.625853i	$0.215249\pi$
$827$			35.9961i			1.25171i	−0.779941	+	0.625853i	$0.784751\pi$
$828$	−2.37350	−	2.16001i	−0.0824849	−	0.0750656i
$829$	22.2653			0.773305			0.386652	−	0.922225i	$-0.373631\pi$
$829$	22.2653			0.773305			0.386652	+	0.922225i	$0.373631\pi$
$830$	−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	$-0.560088\pi$
$839$	−10.8709			−0.375305			−0.187652	+	0.982236i	$0.560088\pi$
$840$	−14.3417	−	0.658526i	−0.494835	−	0.0227213i
$841$	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	$-0.140417\pi$
$854$	−1.97505	−	35.6864i	−0.0675848	−	1.22116i
$855$	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	$-0.580857\pi$
$857$	−14.7132			−0.502594			−0.251297	+	0.967910i	$0.580857\pi$
$858$	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
$868$	25.8709	+	8.39804i	0.878114	+	0.285048i
$869$		−	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
$875$	21.3353	−	20.4891i	0.721265	−	0.692659i
$876$	−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	$0.970286\pi$
$882$	−10.3440	−	19.8812i	−0.348299	−	0.669434i
$883$		−	36.9558i		−	1.24366i	−0.783151	−	0.621831i	$-0.786389\pi$
$883$		−	36.9558i		−	1.24366i	0.783151	−	0.621831i	$-0.213611\pi$
$884$	−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
$896$	24.8904	+	16.6273i	0.831530	+	0.555480i
$897$			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	$-0.789023\pi$
$907$		−	37.0631i		−	1.23066i	0.788270	−	0.615329i	$-0.210977\pi$
$908$	9.30226	+	8.46555i	0.308706	+	0.280939i
$909$	−30.6737			−1.01738
$910$	−17.0129	−	20.5105i	−0.563973	−	0.679916i
$911$			2.17495i			0.0720593i	0.999351	+	0.0360297i	$0.0114711\pi$
$911$			2.17495i			0.0720593i	−0.999351	+	0.0360297i	$0.988529\pi$
$912$	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	$0.0701354\pi$
$919$			13.2512i			0.437117i	−0.975824	+	0.218558i	$0.929865\pi$
$920$	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
$924$	−13.2021	−	4.28559i	−0.434317	−	0.140985i
$925$	−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	$-0.470735\pi$
$937$	5.62068			0.183620			0.0918099	+	0.995777i	$0.470735\pi$
$938$	1.93955	−	0.107344i	0.0633286	−	0.00350489i
$939$	−6.33044			−0.206586
$940$	−29.1633	−	2.96064i	−0.951201	−	0.0965655i
$941$	−10.7839			−0.351546			−0.175773	−	0.984431i	$-0.556242\pi$
$941$	−10.7839			−0.351546			−0.175773	+	0.984431i	$0.556242\pi$
$942$	−19.1115	−	7.39444i	−0.622688	−	0.240924i
$943$		−	3.90827i		−	0.127271i
$944$	12.4214	−	1.17248i	0.404282	−	0.0381609i
$945$	23.3295	+	13.0241i	0.758910	+	0.423675i
$946$	16.9833	+	6.57101i	0.552176	+	0.213642i
$947$			32.8524i			1.06756i	0.845623	+	0.533780i	$0.179229\pi$
$947$			32.8524i			1.06756i	−0.845623	+	0.533780i	$0.820771\pi$
$948$	−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
$952$	35.1867	−	43.2416i	1.14041	−	1.40147i
$953$			8.51329i			0.275772i	0.990448	+	0.137886i	$0.0440308\pi$
$953$			8.51329i			0.275772i	−0.990448	+	0.137886i	$0.955969\pi$
$954$	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
$966$	−0.125740	−	2.27195i	−0.00404562	−	0.0730988i
$967$	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	$0.0751195\pi$
$977$			14.6164i			0.467621i	−0.972282	+	0.233810i	$0.924880\pi$
$978$	−19.8245	−	7.67030i	−0.633918	−	0.245269i
$979$			56.7735i			1.81449i
$980$	21.2870	+	22.9535i	0.679987	+	0.733224i
$981$		−	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	$-0.898692\pi$
$991$		−	19.7017i		−	0.625845i	0.949779	−	0.312923i	$-0.101308\pi$
$992$	27.9847	+	7.89760i	0.888516	+	0.250749i
$993$	−25.7961			−0.818614
$994$	−41.0033	+	2.26931i	−1.30055	+	0.0719781i
$995$	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.139.16	yes	40
4.3	odd	2		1120.2.n.b.559.18		40
5.4	even	2	inner	280.2.n.b.139.25	yes	40
7.6	odd	2	inner	280.2.n.b.139.15	yes	40
8.3	odd	2	inner	280.2.n.b.139.28	yes	40
8.5	even	2		1120.2.n.b.559.17		40
20.19	odd	2		1120.2.n.b.559.24		40
28.27	even	2		1120.2.n.b.559.22		40
35.34	odd	2	inner	280.2.n.b.139.26	yes	40
40.19	odd	2	inner	280.2.n.b.139.13	✓	40
40.29	even	2		1120.2.n.b.559.23		40
56.13	odd	2		1120.2.n.b.559.21		40
56.27	even	2	inner	280.2.n.b.139.27	yes	40
140.139	even	2		1120.2.n.b.559.20		40
280.69	odd	2		1120.2.n.b.559.19		40
280.139	even	2	inner	280.2.n.b.139.14	yes	40

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

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

\(f(q)\)	\(=\)	\(q+(-0.510308 + 1.31893i) q^{2} +0.857983 q^{3} +(-1.47917 - 1.34612i) q^{4} +(-1.33029 - 1.79731i) q^{5} +(-0.437835 + 1.13162i) q^{6} +(2.41097 - 1.08959i) q^{7} +(2.53028 - 1.26399i) q^{8} -2.26387 q^{9} +O(q^{10})\)	\(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} +(0.206764 + 3.73594i) 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} +(-5.03297 - 1.63377i) 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} +(-5.16563 - 2.88380i) 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} +(0.177400 + 3.20537i) 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} +(4.72320 - 5.80443i) 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} +(6.43960 - 5.34149i) 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} +(-4.31820 - 1.40175i) 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} +(4.56916 + 8.78196i) q^{98} -6.92135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{4} + 40 q^{9}+O(q^{10}) \) 40 * q - 12 * q^4 + 40 * q^9	\( 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65} + 40 q^{70} + 80 q^{74} - 72 q^{81} - 8 q^{84} + 80 q^{86} - 128 q^{99}+O(q^{100}) \) 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

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