LMFDB - Embedded newform 280.2.n.b.139.19

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			139.19
Character	$\chi$	$=$	280.139
Dual form			280.2.n.b.139.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.244900 + 1.39285i) q^{2} -2.91053 q^{3} +(-1.88005 - 0.682218i) q^{4} +(-1.83654 + 1.27559i) q^{5} +(0.712789 - 4.05392i) q^{6} +(-1.52252 + 2.16378i) q^{7} +(1.41065 - 2.45154i) q^{8} +5.47117 q^{9} +O(q^{10})$	\(q+(-0.244900 + 1.39285i) q^{2} -2.91053 q^{3} +(-1.88005 - 0.682218i) q^{4} +(-1.83654 + 1.27559i) q^{5} +(0.712789 - 4.05392i) q^{6} +(-1.52252 + 2.16378i) q^{7} +(1.41065 - 2.45154i) q^{8} +5.47117 q^{9} +(-1.32694 - 2.87041i) q^{10} -0.0929484 q^{11} +(5.47193 + 1.98561i) q^{12} -4.08979i q^{13} +(-2.64094 - 2.65055i) q^{14} +(5.34529 - 3.71264i) q^{15} +(3.06916 + 2.56520i) q^{16} +4.24008 q^{17} +(-1.33989 + 7.62050i) q^{18} -2.39835i q^{19} +(4.32301 - 1.14526i) q^{20} +(4.43134 - 6.29773i) q^{21} +(0.0227631 - 0.129463i) q^{22} -4.52148 q^{23} +(-4.10573 + 7.13529i) q^{24} +(1.74573 - 4.68534i) q^{25} +(5.69645 + 1.00159i) q^{26} -7.19241 q^{27} +(4.33858 - 3.02931i) q^{28} +4.35133i q^{29} +(3.86208 + 8.35440i) q^{30} -1.10465 q^{31} +(-4.32457 + 3.64665i) q^{32} +0.270529 q^{33} +(-1.03840 + 5.90578i) q^{34} +(0.0360703 - 5.91597i) q^{35} +(-10.2861 - 3.73253i) q^{36} -8.54612 q^{37} +(3.34054 + 0.587357i) q^{38} +11.9034i q^{39} +(0.536461 + 6.30176i) q^{40} -6.10466i q^{41} +(7.68654 + 7.71450i) q^{42} -4.60415i q^{43} +(0.174747 + 0.0634110i) q^{44} +(-10.0480 + 6.97898i) q^{45} +(1.10731 - 6.29773i) q^{46} -7.93489i q^{47} +(-8.93287 - 7.46609i) q^{48} +(-2.36386 - 6.58879i) q^{49} +(6.09843 + 3.57898i) q^{50} -12.3409 q^{51} +(-2.79013 + 7.68900i) q^{52} +14.3740 q^{53} +(1.76142 - 10.0179i) q^{54} +(0.170703 - 0.118564i) q^{55} +(3.15685 + 6.78486i) q^{56} +6.98047i q^{57} +(-6.06075 - 1.06564i) q^{58} +10.6226i q^{59} +(-12.5822 + 3.33330i) q^{60} -1.92656 q^{61} +(0.270529 - 1.53861i) q^{62} +(-8.32997 + 11.8384i) q^{63} +(-4.02014 - 6.91654i) q^{64} +(5.21690 + 7.51105i) q^{65} +(-0.0662526 + 0.376805i) q^{66} -13.1636i q^{67} +(-7.97154 - 2.89265i) q^{68} +13.1599 q^{69} +(8.23121 + 1.49906i) q^{70} -9.75994i q^{71} +(7.71790 - 13.4128i) q^{72} -6.19245 q^{73} +(2.09295 - 11.9034i) q^{74} +(-5.08100 + 13.6368i) q^{75} +(-1.63620 + 4.50902i) q^{76} +(0.141516 - 0.201119i) q^{77} +(-16.5797 - 2.91516i) q^{78} -3.42089i q^{79} +(-8.90877 - 0.796096i) q^{80} +4.52019 q^{81} +(8.50286 + 1.49503i) q^{82} +11.7848 q^{83} +(-12.6276 + 8.81690i) q^{84} +(-7.78705 + 5.40860i) q^{85} +(6.41288 + 1.12756i) q^{86} -12.6647i q^{87} +(-0.131118 + 0.227867i) q^{88} -4.46220i q^{89} +(-7.25989 - 15.7045i) q^{90} +(8.84939 + 6.22679i) q^{91} +(8.50060 + 3.08463i) q^{92} +3.21511 q^{93} +(11.0521 + 1.94326i) q^{94} +(3.05932 + 4.40466i) q^{95} +(12.5868 - 10.6137i) q^{96} -10.1447 q^{97} +(9.75609 - 1.67890i) q^{98} -0.508536 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 $

$2$	−0.244900	+	1.39285i	−0.173171	+	0.984892i
$2$	−0.244900	+	1.39285i	−0.173171	+	0.984892i
$3$	−2.91053			−1.68039			−0.840197	−	0.542281i	$-0.817561\pi$
$3$	−2.91053			−1.68039			−0.840197	+	0.542281i	$0.817561\pi$
$4$	−1.88005	−	0.682218i	−0.940024	−	0.341109i
$5$	−1.83654	+	1.27559i	−0.821324	+	0.570462i
$5$	−1.83654	+	1.27559i	−0.821324	+	0.570462i
$6$	0.712789	−	4.05392i	0.290995	−	1.65501i
$7$	−1.52252	+	2.16378i	−0.575459	+	0.817831i
$7$	−1.52252	+	2.16378i	−0.575459	+	0.817831i
$8$	1.41065	−	2.45154i	0.498740	−	0.866752i
$9$	5.47117			1.82372
$10$	−1.32694	−	2.87041i	−0.419614	−	0.907703i
$11$	−0.0929484			−0.0280250			−0.0140125	−	0.999902i	$-0.504460\pi$
$11$	−0.0929484			−0.0280250			−0.0140125	+	0.999902i	$0.504460\pi$
$12$	5.47193	+	1.98561i	1.57961	+	0.573197i
$13$		−	4.08979i		−	1.13430i	−0.823613	−	0.567152i	$-0.808045\pi$
$13$		−	4.08979i		−	1.13430i	0.823613	−	0.567152i	$-0.191955\pi$
$14$	−2.64094	−	2.65055i	−0.705822	−	0.708389i
$15$	5.34529	−	3.71264i	1.38015	−	0.958601i
$16$	3.06916	+	2.56520i	0.767290	+	0.641301i
$17$	4.24008			1.02837			0.514185	−	0.857680i	$-0.328095\pi$
$17$	4.24008			1.02837			0.514185	+	0.857680i	$0.328095\pi$
$18$	−1.33989	+	7.62050i	−0.315815	+	1.79617i
$19$		−	2.39835i		−	0.550220i	−0.961413	−	0.275110i	$-0.911286\pi$
$19$		−	2.39835i		−	0.550220i	0.961413	−	0.275110i	$-0.0887142\pi$
$20$	4.32301	−	1.14526i	0.966654	−	0.256087i
$21$	4.43134	−	6.29773i	0.966998	−	1.37428i
$22$	0.0227631	−	0.129463i	0.00485311	−	0.0276016i
$23$	−4.52148			−0.942794			−0.471397	−	0.881921i	$-0.656250\pi$
$23$	−4.52148			−0.942794			−0.471397	+	0.881921i	$0.656250\pi$
$24$	−4.10573	+	7.13529i	−0.838079	+	1.45648i
$25$	1.74573	−	4.68534i	0.349146	−	0.937068i
$26$	5.69645	+	1.00159i	1.11717	+	0.196428i
$27$	−7.19241			−1.38418
$28$	4.33858	−	3.02931i	0.819914	−	0.572486i
$29$			4.35133i			0.808023i	0.914754	+	0.404011i	$0.132384\pi$
$29$			4.35133i			0.808023i	−0.914754	+	0.404011i	$0.867616\pi$
$30$	3.86208	+	8.35440i	0.705117	+	1.52530i
$31$	−1.10465			−0.198401			−0.0992004	−	0.995067i	$-0.531628\pi$
$31$	−1.10465			−0.198401			−0.0992004	+	0.995067i	$0.531628\pi$
$32$	−4.32457	+	3.64665i	−0.764484	+	0.644643i
$33$	0.270529			0.0470930
$34$	−1.03840	+	5.90578i	−0.178083	+	1.01283i
$35$	0.0360703	−	5.91597i	0.00609700	−	0.999981i
$36$	−10.2861	−	3.73253i	−1.71434	−	0.622088i
$37$	−8.54612			−1.40497			−0.702487	−	0.711697i	$-0.747927\pi$
$37$	−8.54612			−1.40497			−0.702487	+	0.711697i	$0.747927\pi$
$38$	3.34054	+	0.587357i	0.541907	+	0.0952819i
$39$			11.9034i			1.90608i
$40$	0.536461	+	6.30176i	0.0848219	+	0.996396i
$41$		−	6.10466i		−	0.953388i	−0.879069	−	0.476694i	$-0.841835\pi$
$41$		−	6.10466i		−	0.953388i	0.879069	−	0.476694i	$-0.158165\pi$
$42$	7.68654	+	7.71450i	1.18606	+	1.19037i
$43$		−	4.60415i		−	0.702126i	−0.936352	−	0.351063i	$-0.885820\pi$
$43$		−	4.60415i		−	0.702126i	0.936352	−	0.351063i	$-0.114180\pi$
$44$	0.174747	+	0.0634110i	0.0263442	+	0.00955957i
$45$	−10.0480	+	6.97898i	−1.49787	+	1.04036i
$46$	1.10731	−	6.29773i	0.163264	−	0.928550i
$47$		−	7.93489i		−	1.15742i	−0.815533	−	0.578711i	$-0.803556\pi$
$47$		−	7.93489i		−	1.15742i	0.815533	−	0.578711i	$-0.196444\pi$
$48$	−8.93287	−	7.46609i	−1.28935	−	1.07764i
$49$	−2.36386	−	6.58879i	−0.337694	−	0.941256i
$50$	6.09843	+	3.57898i	0.862449	+	0.506144i
$51$	−12.3409			−1.72807
$52$	−2.79013	+	7.68900i	−0.386921	+	1.06627i
$53$	14.3740			1.97442			0.987209	−	0.159434i	$-0.0509670\pi$
$53$	14.3740			1.97442			0.987209	+	0.159434i	$0.0509670\pi$
$54$	1.76142	−	10.0179i	0.239699	−	1.36327i
$55$	0.170703	−	0.118564i	0.0230176	−	0.0159872i
$56$	3.15685	+	6.78486i	0.421852	+	0.906665i
$57$			6.98047i			0.924586i
$58$	−6.06075	−	1.06564i	−0.795815	−	0.139926i
$59$			10.6226i			1.38295i	0.722400	+	0.691476i	$0.243039\pi$
$59$			10.6226i			1.38295i	−0.722400	+	0.691476i	$0.756961\pi$
$60$	−12.5822	+	3.33330i	−1.62436	+	0.430327i
$61$	−1.92656			−0.246671			−0.123336	−	0.992365i	$-0.539359\pi$
$61$	−1.92656			−0.246671			−0.123336	+	0.992365i	$0.539359\pi$
$62$	0.270529	−	1.53861i	0.0343572	−	0.195403i
$63$	−8.32997	+	11.8384i	−1.04948	+	1.49150i
$64$	−4.02014	−	6.91654i	−0.502517	−	0.864567i
$65$	5.21690	+	7.51105i	0.647077	+	0.931631i
$66$	−0.0662526	+	0.376805i	−0.00815513	+	0.0463815i
$67$		−	13.1636i		−	1.60819i	−0.594499	−	0.804097i	$-0.702649\pi$
$67$		−	13.1636i		−	1.60819i	0.594499	−	0.804097i	$-0.297351\pi$
$68$	−7.97154	−	2.89265i	−0.966692	−	0.350786i
$69$	13.1599			1.58426
$70$	8.23121	+	1.49906i	0.983818	+	0.179172i
$71$		−	9.75994i		−	1.15829i	−0.815224	−	0.579146i	$-0.803386\pi$
$71$		−	9.75994i		−	1.15829i	0.815224	−	0.579146i	$-0.196614\pi$
$72$	7.71790	−	13.4128i	0.909563	−	1.58072i
$73$	−6.19245			−0.724772			−0.362386	−	0.932028i	$-0.618038\pi$
$73$	−6.19245			−0.724772			−0.362386	+	0.932028i	$0.618038\pi$
$74$	2.09295	−	11.9034i	0.243300	−	1.38375i
$75$	−5.08100	+	13.6368i	−0.586703	+	1.57464i
$76$	−1.63620	+	4.50902i	−0.187685	+	0.517220i
$77$	0.141516	−	0.201119i	0.0161272	−	0.0229197i
$78$	−16.5797	−	2.91516i	−1.87728	−	0.330077i
$79$		−	3.42089i		−	0.384880i	−0.981309	−	0.192440i	$-0.938360\pi$
$79$		−	3.42089i		−	0.384880i	0.981309	−	0.192440i	$-0.0616401\pi$
$80$	−8.90877	−	0.796096i	−0.996031	−	0.0890062i
$81$	4.52019			0.502243
$82$	8.50286	+	1.49503i	0.938984	+	0.165099i
$83$	11.7848			1.29355			0.646774	−	0.762682i	$-0.276118\pi$
$83$	11.7848			1.29355			0.646774	+	0.762682i	$0.276118\pi$
$84$	−12.6276	+	8.81690i	−1.37778	+	0.962002i
$85$	−7.78705	+	5.40860i	−0.844624	+	0.586646i
$86$	6.41288	+	1.12756i	0.691519	+	0.121588i
$87$		−	12.6647i		−	1.35780i
$88$	−0.131118	+	0.227867i	−0.0139772	+	0.0242907i
$89$		−	4.46220i		−	0.472992i	−0.971632	−	0.236496i	$-0.924001\pi$
$89$		−	4.46220i		−	0.472992i	0.971632	−	0.236496i	$-0.0759991\pi$
$90$	−7.25989	−	15.7045i	−0.765260	−	1.65540i
$91$	8.84939	+	6.22679i	0.927668	+	0.652745i
$92$	8.50060	+	3.08463i	0.886249	+	0.321595i
$93$	3.21511			0.333391
$94$	11.0521	+	1.94326i	1.13994	+	0.200432i
$95$	3.05932	+	4.40466i	0.313879	+	0.451909i
$96$	12.5868	−	10.6137i	1.28463	−	1.08325i
$97$	−10.1447			−1.03004			−0.515021	−	0.857177i	$-0.672216\pi$
$97$	−10.1447			−1.03004			−0.515021	+	0.857177i	$0.672216\pi$
$98$	9.75609	−	1.67890i	0.985514	−	0.169594i
$99$	−0.508536			−0.0511098
$100$	−6.47848	+	7.61770i	−0.647848	+	0.761770i
$101$	−7.27752			−0.724140			−0.362070	−	0.932151i	$-0.617930\pi$
$101$	−7.27752			−0.724140			−0.362070	+	0.932151i	$0.617930\pi$
$102$	3.02228	−	17.1889i	0.299250	−	1.70196i
$103$			8.57425i			0.844846i	0.906399	+	0.422423i	$0.138820\pi$
$103$			8.57425i			0.844846i	−0.906399	+	0.422423i	$0.861180\pi$
$104$	−10.0263	−	5.76926i	−0.983160	−	0.565722i
$105$	−0.104984	+	17.2186i	−0.0102454	+	1.68036i
$106$	−3.52019	+	20.0208i	−0.341911	+	1.94459i
$107$			7.51221i			0.726233i	0.931744	+	0.363117i	$0.118287\pi$
$107$			7.51221i			0.726233i	−0.931744	+	0.363117i	$0.881713\pi$
$108$	13.5221	+	4.90679i	1.30116	+	0.472156i
$109$		−	10.1050i		−	0.967886i	−0.875100	−	0.483943i	$-0.839204\pi$
$109$		−	10.1050i		−	0.967886i	0.875100	−	0.483943i	$-0.160796\pi$
$110$	0.123337	+	0.266800i	0.0117597	+	0.0254384i
$111$	24.8737			2.36091
$112$	−10.2234	+	2.73540i	−0.966019	+	0.258471i
$113$			2.22783i			0.209577i	0.994495	+	0.104788i	$0.0334165\pi$
$113$			2.22783i			0.209577i	−0.994495	+	0.104788i	$0.966583\pi$
$114$	−9.72273	−	1.70952i	−0.910617	−	0.160111i
$115$	8.30386	−	5.76756i	0.774339	−	0.537828i
$116$	2.96856	−	8.18072i	0.275624	−	0.759560i
$117$		−	22.3759i		−	2.06866i
$118$	−14.7957	−	2.60149i	−1.36206	−	0.239487i
$119$	−6.45560	+	9.17458i	−0.591784	+	0.841032i
$120$	−1.56138	−	18.3415i	−0.142534	−	1.67434i
$121$	−10.9914			−0.999215
$122$	0.471816	−	2.68341i	0.0427162	−	0.242945i
$123$			17.7678i			1.60207i
$124$	2.07679	+	0.753610i	0.186501	+	0.0676762i
$125$	2.77048	+	10.8316i	0.247799	+	0.968811i
$126$	−14.4491	−	14.5016i	−1.28722	−	1.29191i
$127$	7.92857			0.703547			0.351773	−	0.936085i	$-0.385579\pi$
$127$	7.92857			0.703547			0.351773	+	0.936085i	$0.385579\pi$
$128$	10.6182	−	3.90558i	0.938526	−	0.345207i
$129$			13.4005i			1.17985i
$130$	−11.7394	+	5.42689i	−1.02961	+	0.475970i
$131$		−	7.55609i		−	0.660179i	−0.943950	−	0.330089i	$-0.892921\pi$
$131$		−	7.55609i		−	0.660179i	0.943950	−	0.330089i	$-0.107079\pi$
$132$	−0.508607	−	0.184559i	−0.0442685	−	0.0160638i
$133$	5.18950	+	3.65154i	0.449987	+	0.316629i
$134$	18.3349	+	3.22378i	1.58390	+	0.278492i
$135$	13.2091	−	9.17458i	1.13686	−	0.789622i
$136$	5.98126	−	10.3947i	0.512889	−	0.891341i
$137$			18.2856i			1.56225i	0.624377	+	0.781123i	$0.285353\pi$
$137$			18.2856i			1.56225i	−0.624377	+	0.781123i	$0.714647\pi$
$138$	−3.22286	+	18.3297i	−0.274348	+	1.56033i
$139$		−	1.58667i		−	0.134579i	−0.997733	−	0.0672897i	$-0.978565\pi$
$139$		−	1.58667i		−	0.134579i	0.997733	−	0.0672897i	$-0.0214352\pi$
$140$	−4.10379	+	11.0977i	−0.346834	+	0.937927i
$141$			23.0947i			1.94493i
$142$	13.5941	+	2.39021i	1.14079	+	0.200582i
$143$			0.380139i			0.0317888i
$144$	16.7919	+	14.0347i	1.39932	+	1.16956i
$145$	−5.55053	−	7.99138i	−0.460946	−	0.663648i
$146$	1.51653	−	8.62514i	0.125509	−	0.713822i
$147$	6.88007	+	19.1769i	0.567459	+	1.58168i
$148$	16.0671	+	5.83032i	1.32071	+	0.479249i
$149$		−	11.2114i		−	0.918476i	−0.888313	−	0.459238i	$-0.848123\pi$
$149$		−	11.2114i		−	0.918476i	0.888313	−	0.459238i	$-0.151877\pi$
$150$	−17.7497	−	10.4167i	−1.44925	−	0.850521i
$151$		−	2.14351i		−	0.174436i	−0.996189	−	0.0872180i	$-0.972202\pi$
$151$		−	2.14351i		−	0.174436i	0.996189	−	0.0872180i	$-0.0277977\pi$
$152$	−5.87967	−	3.38323i	−0.476904	−	0.274416i
$153$	23.1982			1.87546
$154$	0.245471	+	0.246364i	0.0197807	+	0.0198526i
$155$	2.02873	−	1.40908i	0.162951	−	0.113180i
$156$	8.12074	−	22.3790i	0.650180	−	1.79176i
$157$			6.74329i			0.538173i	0.963116	+	0.269087i	$0.0867218\pi$
$157$			6.74329i			0.538173i	−0.963116	+	0.269087i	$0.913278\pi$
$158$	4.76477	+	0.837776i	0.379065	+	0.0666499i
$159$	−41.8358			−3.31780
$160$	3.29060	−	12.2136i	0.260145	−	0.965570i
$161$	6.88405	−	9.78347i	0.542539	−	0.771046i
$162$	−1.10700	+	6.29594i	−0.0869738	+	0.494655i
$163$		−	7.51221i		−	0.588402i	−0.955744	−	0.294201i	$-0.904946\pi$
$163$		−	7.51221i		−	0.588402i	0.955744	−	0.294201i	$-0.0950535\pi$
$164$	−4.16471	+	11.4771i	−0.325209	+	0.896207i
$165$	−0.496836	+	0.345084i	−0.0386786	+	0.0268648i
$166$	−2.88610	+	16.4144i	−0.224005	+	1.27401i
$167$		−	8.57425i		−	0.663496i	−0.943368	−	0.331748i	$-0.892362\pi$
$167$		−	8.57425i		−	0.663496i	0.943368	−	0.331748i	$-0.107638\pi$
$168$	−9.18810	−	19.7475i	−0.708877	−	1.52355i
$169$	−3.72638			−0.286645
$170$	−5.62631	−	12.1707i	−0.431518	−	0.933454i
$171$		−	13.1218i		−	1.00345i
$172$	−3.14103	+	8.65602i	−0.239501	+	0.660016i
$173$		−	23.9145i		−	1.81819i	−0.416590	−	0.909094i	$-0.636775\pi$
$173$		−	23.9145i		−	1.81819i	0.416590	−	0.909094i	$-0.363225\pi$
$174$	17.6400	+	3.10158i	1.33728	+	0.235130i
$175$	7.48012	+	10.9109i	0.565444	+	0.824787i
$176$	−0.285273	−	0.238431i	−0.0215033	−	0.0179724i
$177$		−	30.9175i		−	2.32390i
$178$	6.21516	+	1.09279i	0.465846	+	0.0819084i
$179$	−11.5489			−0.863207			−0.431603	−	0.902064i	$-0.642052\pi$
$179$	−11.5489			−0.863207			−0.431603	+	0.902064i	$0.642052\pi$
$180$	23.6519	−	6.26589i	1.76291	−	0.467032i
$181$	−10.8919			−0.809590			−0.404795	−	0.914407i	$-0.632657\pi$
$181$	−10.8919			−0.809590			−0.404795	+	0.914407i	$0.632657\pi$
$182$	−10.8402	+	10.8009i	−0.803528	+	0.800617i
$183$	5.60732			0.414505
$184$	−6.37822	+	11.0846i	−0.470209	+	0.817168i
$185$	15.6953	−	10.9014i	1.15394	−	0.801484i
$186$	−0.787381	+	4.47816i	−0.0577336	+	0.328354i
$187$	−0.394108			−0.0288200
$188$	−5.41332	+	14.9180i	−0.394807	+	1.08800i
$189$	10.9506	−	15.5628i	0.796538	−	1.13202i
$190$	−6.88425	+	3.18246i	−0.499436	+	0.230880i
$191$			3.42089i			0.247527i	0.992312	+	0.123763i	$0.0394964\pi$
$191$			3.42089i			0.247527i	−0.992312	+	0.123763i	$0.960504\pi$
$192$	11.7007	+	20.1308i	0.844427	+	1.45281i
$193$		−	18.1232i		−	1.30454i	−0.757987	−	0.652270i	$-0.773817\pi$
$193$		−	18.1232i		−	1.30454i	0.757987	−	0.652270i	$-0.226183\pi$
$194$	2.48445	−	14.1301i	0.178373	−	1.01448i
$195$	−15.1839	−	21.8611i	−1.08734	−	1.56551i
$196$	−0.0508232	+	13.9999i	−0.00363023	+	0.999993i
$197$	−18.9251			−1.34836			−0.674179	−	0.738568i	$-0.735503\pi$
$197$	−18.9251			−1.34836			−0.674179	+	0.738568i	$0.735503\pi$
$198$	0.124541	−	0.708313i	0.00885072	−	0.0503376i
$199$	6.52608			0.462622			0.231311	−	0.972880i	$-0.425699\pi$
$199$	6.52608			0.462622			0.231311	+	0.972880i	$0.425699\pi$
$200$	−9.02371	−	10.8891i	−0.638072	−	0.769976i
$201$			38.3131i			2.70240i
$202$	1.78227	−	10.1365i	0.125400	−	0.713200i
$203$	−9.41532	−	6.62500i	−0.660826	−	0.464984i
$204$	23.2014	+	8.41915i	1.62442	+	0.589458i
$205$	7.78705	+	11.2114i	0.543871	+	0.783040i
$206$	−11.9426	−	2.09984i	−0.832082	−	0.146303i
$207$	−24.7378			−1.71939
$208$	10.4911	−	12.5522i	0.727430	−	0.870339i
$209$			0.222923i			0.0154199i
$210$	−23.9572	−	4.36307i	−1.65320	−	0.301080i
$211$	−4.66349			−0.321048			−0.160524	−	0.987032i	$-0.551318\pi$
$211$	−4.66349			−0.321048			−0.160524	+	0.987032i	$0.551318\pi$
$212$	−27.0238	−	9.80618i	−1.85600	−	0.673491i
$213$			28.4066i			1.94639i
$214$	−10.4634	−	1.83974i	−0.715261	−	0.125762i
$215$	5.87302	+	8.45569i	0.400536	+	0.576673i
$216$	−10.1460	+	17.6325i	−0.690345	+	1.19974i
$217$	1.68185	−	2.39021i	0.114171	−	0.162258i
$218$	14.0748	+	2.47472i	0.953263	+	0.167609i
$219$	18.0233			1.21790
$220$	−0.401816	+	0.106450i	−0.0270905	+	0.00717683i
$221$		−	17.3410i		−	1.16648i
$222$	−6.09158	+	34.6453i	−0.408840	+	2.32524i
$223$		−	8.18714i		−	0.548252i	−0.961694	−	0.274126i	$-0.911612\pi$
$223$		−	8.18714i		−	0.548252i	0.961694	−	0.274126i	$-0.0883885\pi$
$224$	−1.30628	−	14.9095i	−0.0872795	−	0.996184i
$225$	9.55120	−	25.6343i	0.636746	−	1.70895i
$226$	−3.10303	−	0.545597i	−0.206410	−	0.0362925i
$227$	−0.687619			−0.0456389			−0.0228195	−	0.999740i	$-0.507264\pi$
$227$	−0.687619			−0.0456389			−0.0228195	+	0.999740i	$0.507264\pi$
$228$	4.76220	−	13.1236i	0.315384	−	0.869133i
$229$	5.06822			0.334918			0.167459	−	0.985879i	$-0.446444\pi$
$229$	5.06822			0.334918			0.167459	+	0.985879i	$0.446444\pi$
$230$	5.99971	+	12.9785i	0.395609	+	0.855776i
$231$	−0.411886	+	0.585364i	−0.0271001	+	0.0385141i
$232$	10.6675	+	6.13821i	0.700355	+	0.402993i
$233$			15.8954i			1.04134i	0.853757	+	0.520672i	$0.174318\pi$
$233$			15.8954i			1.04134i	−0.853757	+	0.520672i	$0.825682\pi$
$234$	31.1663	+	5.47987i	2.03740	+	0.358231i
$235$	10.1217	+	14.5727i	0.660265	+	0.950619i
$236$	7.24696	−	19.9711i	0.471737	−	1.30001i
$237$			9.95658i			0.646750i
$238$	−11.1978	−	11.2385i	−0.725846	−	0.728486i
$239$		−	12.2302i		−	0.791106i	−0.918443	−	0.395553i	$-0.870553\pi$
$239$		−	12.2302i		−	0.791106i	0.918443	−	0.395553i	$-0.129447\pi$
$240$	25.9292	+	2.31706i	1.67372	+	0.149565i
$241$			3.80710i			0.245237i	0.992454	+	0.122618i	$0.0391291\pi$
$241$			3.80710i			0.245237i	−0.992454	+	0.122618i	$0.960871\pi$
$242$	2.69179	−	15.3093i	0.173035	−	0.984118i
$243$	8.42108			0.540213
$244$	3.62203	+	1.31434i	0.231877	+	0.0841418i
$245$	12.7459	+	9.08524i	0.814307	+	0.580435i
$246$	−24.7478	−	4.35133i	−1.57786	−	0.277431i
$247$	−9.80876			−0.624116
$248$	−1.55827	+	2.70809i	−0.0989503	+	0.171964i
$249$	−34.2999			−2.17367
$250$	−15.7653	+	1.20619i	−0.997086	+	0.0762859i
$251$			11.5411i			0.728468i	0.931307	+	0.364234i	$0.118669\pi$
$251$			11.5411i			0.728468i	−0.931307	+	0.364234i	$0.881331\pi$
$252$	23.7371	−	16.5739i	1.49530	−	1.04406i
$253$	0.420264			0.0264218
$254$	−1.94171	+	11.0433i	−0.121834	+	0.692917i
$255$	22.6644	−	15.7419i	1.41930	−	0.985796i
$256$	2.83947	+	15.7460i	0.177467	+	0.984127i
$257$	−20.9753			−1.30840			−0.654201	−	0.756321i	$-0.726995\pi$
$257$	−20.9753			−1.30840			−0.654201	+	0.756321i	$0.726995\pi$
$258$	−18.6649	−	3.28179i	−1.16202	−	0.204315i
$259$	13.0117	−	18.4919i	0.808505	−	1.14903i
$260$	−4.68386	−	17.6802i	−0.290480	−	1.09648i
$261$			23.8069i			1.47361i
$262$	10.5245	+	1.85049i	0.650205	+	0.114324i
$263$	−1.08584			−0.0669558			−0.0334779	−	0.999439i	$-0.510658\pi$
$263$	−1.08584			−0.0669558			−0.0334779	+	0.999439i	$0.510658\pi$
$264$	0.381621	−	0.663213i	0.0234872	−	0.0408179i
$265$	−26.3983	+	18.3353i	−1.62164	+	1.12633i
$266$	−6.35695	+	6.33392i	−0.389770	+	0.388357i
$267$			12.9874i			0.794813i
$268$	−8.98046	+	24.7482i	−0.548569	+	1.51174i
$269$	6.22378			0.379470			0.189735	−	0.981835i	$-0.439237\pi$
$269$	6.22378			0.379470			0.189735	+	0.981835i	$0.439237\pi$
$270$	9.54387	+	20.6451i	0.580821	+	1.25642i
$271$	−28.3667			−1.72316			−0.861578	−	0.507624i	$-0.830524\pi$
$271$	−28.3667			−1.72316			−0.861578	+	0.507624i	$0.830524\pi$
$272$	13.0135	+	10.8767i	0.789057	+	0.659494i
$273$	−25.7564	−	18.1232i	−1.55885	−	1.09687i
$274$	−25.4691	−	4.47816i	−1.53864	−	0.270535i
$275$	−0.162263	+	0.435495i	−0.00978482	+	0.0262613i
$276$	−24.7412	−	8.97791i	−1.48925	−	0.540407i
$277$	0.917100			0.0551032			0.0275516	−	0.999620i	$-0.491229\pi$
$277$	0.917100			0.0551032			0.0275516	+	0.999620i	$0.491229\pi$
$278$	2.20999	+	0.388576i	0.132546	+	0.0233052i
$279$	−6.04372			−0.361828
$280$	−14.4524	−	8.43379i	−0.863695	−	0.504015i
$281$	−11.8342			−0.705969			−0.352984	−	0.935629i	$-0.614833\pi$
$281$	−11.8342			−0.705969			−0.352984	+	0.935629i	$0.614833\pi$
$282$	−32.1674	−	5.65590i	−1.91554	−	0.336804i
$283$	−22.0343			−1.30980			−0.654901	−	0.755715i	$-0.727290\pi$
$283$	−22.0343			−1.30980			−0.654901	+	0.755715i	$0.727290\pi$
$284$	−6.65840	+	18.3492i	−0.395103	+	1.08882i
$285$	−8.90423	−	12.8199i	−0.527441	−	0.759385i
$286$	−0.529476	−	0.0930962i	−0.0313086	−	0.00550489i
$287$	13.2091	+	9.29447i	0.779710	+	0.548635i
$288$	−23.6605	+	19.9514i	−1.39421	+	1.17565i
$289$	0.978238			0.0575434
$290$	12.4901	−	5.77394i	0.733444	−	0.339058i
$291$	29.5265			1.73088
$292$	11.6421	+	4.22460i	0.681303	+	0.247226i
$293$			16.2092i			0.946953i	0.880807	+	0.473476i	$0.157001\pi$
$293$			16.2092i			0.946953i	−0.880807	+	0.473476i	$0.842999\pi$
$294$	−28.3954	+	4.88647i	−1.65605	+	0.284985i
$295$	−13.5502	−	19.5089i	−0.788921	−	1.13585i
$296$	−12.0556	+	20.9512i	−0.700716	+	1.21776i
$297$	0.668522			0.0387916
$298$	15.6158	+	2.74568i	0.904600	+	0.159053i
$299$			18.4919i			1.06941i
$300$	18.8558	−	22.1715i	1.08864	−	1.28007i
$301$	9.96235	+	7.00992i	0.574220	+	0.404045i
$302$	2.98558	+	0.524945i	0.171801	+	0.0302072i
$303$	21.1814			1.21684
$304$	6.15226	−	7.36092i	0.352856	−	0.422178i
$305$	3.53821	−	2.45751i	0.202597	−	0.140717i
$306$	−5.68124	+	32.3115i	−0.324775	+	1.84713i
$307$	5.56962			0.317875			0.158938	−	0.987289i	$-0.449193\pi$
$307$	5.56962			0.317875			0.158938	+	0.987289i	$0.449193\pi$
$308$	−0.403264	+	0.281570i	−0.0229781	+	0.0160439i
$309$		−	24.9556i		−	1.41967i
$310$	1.46580	+	3.17079i	0.0832517	+	0.180089i
$311$	8.31354			0.471418			0.235709	−	0.971824i	$-0.424259\pi$
$311$	8.31354			0.471418			0.235709	+	0.971824i	$0.424259\pi$
$312$	29.1818	+	16.7916i	1.65210	+	0.950636i
$313$	0.184481			0.0104275			0.00521375	−	0.999986i	$-0.498340\pi$
$313$	0.184481			0.0104275			0.00521375	+	0.999986i	$0.498340\pi$
$314$	−9.39237	−	1.65143i	−0.530042	−	0.0931958i
$315$	0.197347	−	32.3673i	0.0111192	−	1.82369i
$316$	−2.33379	+	6.43143i	−0.131286	+	0.361796i
$317$	0.135906			0.00763321			0.00381661	−	0.999993i	$-0.498785\pi$
$317$	0.135906			0.00763321			0.00381661	+	0.999993i	$0.498785\pi$
$318$	10.2456	−	58.2709i	0.574545	−	3.26767i
$319$		−	0.404449i		−	0.0226448i
$320$	16.2058	+	7.57442i	0.905932	+	0.423423i
$321$		−	21.8645i		−	1.22036i
$322$	11.9410	+	11.9844i	0.665445	+	0.667865i
$323$		−	10.1692i		−	0.565829i
$324$	−8.49817	−	3.08375i	−0.472121	−	0.171320i
$325$	−19.1621	−	7.13968i	−1.06292	−	0.396038i
$326$	10.4634	+	1.83974i	0.579512	+	0.101894i
$327$			29.4109i			1.62643i
$328$	−14.9658	−	8.61153i	−0.826350	−	0.475492i
$329$	17.1693	+	12.0810i	0.946575	+	0.666049i
$330$	−0.358974	−	0.776528i	−0.0197609	−	0.0427464i
$331$	26.0751			1.43322			0.716609	−	0.697475i	$-0.245693\pi$
$331$	26.0751			1.43322			0.716609	+	0.697475i	$0.245693\pi$
$332$	−22.1560	−	8.03979i	−1.21597	−	0.441241i
$333$	−46.7573			−2.56228
$334$	11.9426	+	2.09984i	0.653471	+	0.114898i
$335$	16.7914	+	24.1755i	0.917413	+	1.32085i
$336$	29.7554	−	7.96145i	1.62329	−	0.434333i
$337$			3.87932i			0.211320i	0.994402	+	0.105660i	$0.0336955\pi$
$337$			3.87932i			0.211320i	−0.994402	+	0.105660i	$0.966305\pi$
$338$	0.912592	−	5.19028i	0.0496385	−	0.282314i
$339$		−	6.48416i		−	0.352171i
$340$	18.3299	−	4.85597i	0.994077	−	0.263352i
$341$	0.102675			0.00556018
$342$	18.2767	+	3.21353i	0.988288	+	0.173768i
$343$	17.8557	+	4.91671i	0.964117	+	0.265478i
$344$	−11.2873	−	6.49484i	−0.608569	−	0.350178i
$345$	−24.1686	+	16.7866i	−1.30119	+	0.903763i
$346$	33.3093	+	5.85668i	1.79072	+	0.314857i
$347$		−	20.4996i		−	1.10047i	−0.835008	−	0.550237i	$-0.814537\pi$
$347$		−	20.4996i		−	1.10047i	0.835008	−	0.550237i	$-0.185463\pi$
$348$	−8.64007	+	23.8102i	−0.463156	+	1.27636i
$349$	14.2823			0.764512			0.382256	−	0.924056i	$-0.375147\pi$
$349$	14.2823			0.764512			0.382256	+	0.924056i	$0.375147\pi$
$350$	−17.0291	+	7.74658i	−0.910244	+	0.414072i
$351$			29.4154i			1.57008i
$352$	0.401962	−	0.338950i	0.0214246	−	0.0180661i
$353$	−17.7313			−0.943740			−0.471870	−	0.881668i	$-0.656421\pi$
$353$	−17.7313			−0.943740			−0.471870	+	0.881668i	$0.656421\pi$
$354$	43.0634	+	7.57171i	2.28879	+	0.402432i
$355$	12.4497	+	17.9245i	0.660761	+	0.951333i
$356$	−3.04419	+	8.38915i	−0.161342	+	0.444624i
$357$	18.7892	−	26.7029i	0.994431	−	1.41326i
$358$	2.82833	−	16.0859i	0.149482	−	0.850165i
$359$			28.2157i			1.48917i	0.667528	+	0.744585i	$0.267353\pi$
$359$			28.2157i			1.48917i	−0.667528	+	0.744585i	$0.732647\pi$
$360$	2.93507	+	34.4780i	0.154692	+	1.81715i
$361$	13.2479			0.697258
$362$	2.66743	−	15.1708i	0.140197	−	0.797359i
$363$	31.9907			1.67907
$364$	−12.3893	−	17.7439i	−0.649373	−	0.930032i
$365$	11.3727	−	7.89904i	0.595273	−	0.413455i
$366$	−1.37323	+	7.81014i	−0.0717801	+	0.408243i
$367$		−	26.3739i		−	1.37670i	−0.725377	−	0.688352i	$-0.758334\pi$
$367$		−	26.3739i		−	1.37670i	0.725377	−	0.688352i	$-0.241666\pi$
$368$	−13.8771	−	11.5985i	−0.723396	−	0.604614i
$369$		−	33.3996i		−	1.73872i
$370$	11.3402	+	24.5309i	0.589547	+	1.27530i
$371$	−21.8847	+	31.1021i	−1.13620	+	1.61474i
$372$	−6.04456	−	2.19340i	−0.313396	−	0.113723i
$373$	−0.213804			−0.0110704			−0.00553518	−	0.999985i	$-0.501762\pi$
$373$	−0.213804			−0.0110704			−0.00553518	+	0.999985i	$0.501762\pi$
$374$	0.0965172	−	0.548932i	0.00499078	−	0.0283846i
$375$	−8.06356	−	31.5258i	−0.416401	−	1.62798i
$376$	−19.4527	−	11.1933i	−1.00320	−	0.577253i
$377$	17.7960			0.916543
$378$	18.9948	+	19.0638i	0.976985	+	0.980538i
$379$	0.508536			0.0261218			0.0130609	−	0.999915i	$-0.495842\pi$
$379$	0.508536			0.0261218			0.0130609	+	0.999915i	$0.495842\pi$
$380$	−2.74673	−	10.3681i	−0.140904	−	0.531872i
$381$	−23.0763			−1.18224
$382$	−4.76477	−	0.837776i	−0.243787	−	0.0428644i
$383$		−	24.8242i		−	1.26846i	−0.773146	−	0.634228i	$-0.781318\pi$
$383$		−	24.8242i		−	1.26846i	0.773146	−	0.634228i	$-0.218682\pi$
$384$	−30.9046	+	11.3673i	−1.57709	+	0.580084i
$385$	−0.00335268	+	0.549880i	−0.000170868	+	0.0280245i
$386$	25.2429	+	4.43839i	1.28483	+	0.225908i
$387$		−	25.1901i		−	1.28048i
$388$	19.0726	+	6.92092i	0.968264	+	0.351356i
$389$			18.9060i			0.958570i	0.877659	+	0.479285i	$0.159104\pi$
$389$			18.9060i			0.958570i	−0.877659	+	0.479285i	$0.840896\pi$
$390$	34.1677	−	15.7951i	1.73015	−	0.799817i
$391$	−19.1714			−0.969540
$392$	−19.4873	−	3.49937i	−0.984257	−	0.176745i
$393$			21.9922i			1.10936i
$394$	4.63477	−	26.3598i	0.233496	−	1.32799i
$395$	4.36365	+	6.28258i	0.219559	+	0.316111i
$396$	0.956072	+	0.346932i	0.0480444	+	0.0174340i
$397$			17.2079i			0.863640i	0.901960	+	0.431820i	$0.142128\pi$
$397$			17.2079i			0.863640i	−0.901960	+	0.431820i	$0.857872\pi$
$398$	−1.59824	+	9.08984i	−0.0801125	+	0.455632i
$399$	−15.1042	−	10.6279i	−0.756155	−	0.532061i
$400$	17.3768	−	9.90190i	0.868839	−	0.495095i
$401$	11.6687			0.582708			0.291354	−	0.956615i	$-0.405894\pi$
$401$	11.6687			0.582708			0.291354	+	0.956615i	$0.405894\pi$
$402$	−53.3643	−	9.38289i	−2.66157	−	0.467976i
$403$			4.51778i			0.225047i
$404$	13.6821	+	4.96485i	0.680709	+	0.247011i
$405$	−8.30149	+	5.76592i	−0.412505	+	0.286511i
$406$	11.5334	−	11.4916i	0.572394	−	0.570320i
$407$	0.794348			0.0393744
$408$	−17.4086	+	30.2542i	−0.861855	+	1.49780i
$409$		−	12.8644i		−	0.636105i	−0.948073	−	0.318052i	$-0.896971\pi$
$409$		−	12.8644i		−	0.636105i	0.948073	−	0.318052i	$-0.103029\pi$
$410$	−17.5229	+	8.10049i	−0.865392	+	0.400055i
$411$		−	53.2208i		−	2.62519i
$412$	5.84951	−	16.1200i	0.288184	−	0.794176i
$413$	−22.9850	−	16.1732i	−1.13102	−	0.795832i
$414$	6.05829	−	34.4560i	0.297749	−	1.69342i
$415$	−21.6432	+	15.0326i	−1.06242	+	0.737920i
$416$	14.9140	+	17.6866i	0.731221	+	0.867157i
$417$			4.61804i			0.226147i
$418$	−0.310498	−	0.0545939i	−0.0151869	−	0.00267027i
$419$		−	4.44166i		−	0.216989i	−0.994097	−	0.108495i	$-0.965397\pi$
$419$		−	4.44166i		−	0.216989i	0.994097	−	0.108495i	$-0.0346030\pi$
$420$	11.9442	−	32.3002i	0.582817	−	1.57609i
$421$		−	30.4133i		−	1.48226i	−0.671364	−	0.741128i	$-0.734291\pi$
$421$		−	30.4133i		−	1.48226i	0.671364	−	0.741128i	$-0.265709\pi$
$422$	1.14209	−	6.49554i	0.0555961	−	0.316198i
$423$		−	43.4131i		−	2.11082i
$424$	20.2766	−	35.2384i	0.984720	−	1.71133i
$425$	7.40203	−	19.8662i	0.359051	−	0.963652i
$426$	−39.5660	−	6.95678i	−1.91698	−	0.337057i
$427$	2.93324	−	4.16866i	0.141949	−	0.201735i
$428$	5.12496	−	14.1233i	0.247724	−	0.682676i
$429$		−	1.10641i		−	0.0534178i
$430$	−13.2158	+	6.10941i	−0.637322	+	0.294622i
$431$		−	18.1648i		−	0.874968i	−0.899226	−	0.437484i	$-0.855870\pi$
$431$		−	18.1648i		−	0.874968i	0.899226	−	0.437484i	$-0.144130\pi$
$432$	−22.0746	−	18.4500i	−1.06207	−	0.887675i
$433$	17.4153			0.836926			0.418463	−	0.908234i	$-0.362569\pi$
$433$	17.4153			0.836926			0.418463	+	0.908234i	$0.362569\pi$
$434$	2.91732	+	2.92792i	0.140036	+	0.140545i
$435$	16.1550	+	23.2591i	0.774571	+	1.11519i
$436$	−6.89382	+	18.9979i	−0.330154	+	0.909836i
$437$			10.8441i			0.518744i
$438$	−4.41391	+	25.1037i	−0.210905	+	1.19950i
$439$	34.2855			1.63636			0.818180	−	0.574962i	$-0.194983\pi$
$439$	34.2855			1.63636			0.818180	+	0.574962i	$0.194983\pi$
$440$	−0.0498631	−	0.585738i	−0.00237713	−	0.0279240i
$441$	−12.9331	−	36.0484i	−0.615860	−	1.71659i
$442$	24.1534	+	4.24682i	1.14886	+	0.202001i
$443$			12.2027i			0.579769i	0.957062	+	0.289885i	$0.0936170\pi$
$443$			12.2027i			0.579769i	−0.957062	+	0.289885i	$0.906383\pi$
$444$	−46.7638	−	16.9693i	−2.21931	−	0.805327i
$445$	5.69194	+	8.19499i	0.269824	+	0.388480i
$446$	11.4034	+	2.00503i	0.539969	+	0.0949411i
$447$			32.6312i			1.54340i
$448$	21.0866	+	1.83190i	0.996248	+	0.0865489i
$449$	12.3919			0.584809			0.292405	−	0.956295i	$-0.405545\pi$
$449$	12.3919			0.584809			0.292405	+	0.956295i	$0.405545\pi$
$450$	33.3656	+	19.5812i	1.57287	+	0.923067i
$451$			0.567418i			0.0267187i
$452$	1.51987	−	4.18843i	0.0714885	−	0.197007i
$453$			6.23873i			0.293121i
$454$	0.168398	−	0.957749i	0.00790332	−	0.0449494i
$455$	−24.1951	−	0.147520i	−1.13428	−	0.00691585i
$456$	17.1129	+	9.84699i	0.801386	+	0.461128i
$457$		−	10.6974i		−	0.500404i	−0.968194	−	0.250202i	$-0.919503\pi$
$457$		−	10.6974i		−	0.500404i	0.968194	−	0.250202i	$-0.0804970\pi$
$458$	−1.24121	+	7.05926i	−0.0579979	+	0.329858i
$459$	−30.4964			−1.42345
$460$	−19.5464	+	5.17825i	−0.911355	+	0.241437i
$461$	−15.0677			−0.701775			−0.350887	−	0.936418i	$-0.614120\pi$
$461$	−15.0677			−0.701775			−0.350887	+	0.936418i	$0.614120\pi$
$462$	−0.714451	−	0.717050i	−0.0332393	−	0.0333602i
$463$	−19.4135			−0.902222			−0.451111	−	0.892468i	$-0.648972\pi$
$463$	−19.4135			−0.902222			−0.451111	+	0.892468i	$0.648972\pi$
$464$	−11.1621	+	13.3549i	−0.518185	+	0.619987i
$465$	−5.90467	+	4.10117i	−0.273822	+	0.190187i
$466$	−22.1399	−	3.89279i	−1.02561	−	0.180330i
$467$	−24.7528			−1.14542			−0.572712	−	0.819756i	$-0.694109\pi$
$467$	−24.7528			−1.14542			−0.572712	+	0.819756i	$0.694109\pi$
$468$	−15.2653	+	42.0678i	−0.705637	+	1.94459i
$469$	28.4832	+	20.0419i	1.31523	+	0.925449i
$470$	−22.7764	+	10.5291i	−1.05060	+	0.485671i
$471$		−	19.6265i		−	0.904343i
$472$	26.0419	+	14.9848i	1.19868	+	0.689733i
$473$			0.427948i			0.0196771i
$474$	−13.8680	−	2.43837i	−0.636978	−	0.111998i
$475$	−11.2371	−	4.18688i	−0.515593	−	0.192107i
$476$	18.3959	−	12.8445i	0.843175	−	0.588727i
$477$	78.6425			3.60079
$478$	17.0348	+	2.99518i	0.779154	+	0.136996i
$479$	−4.13772			−0.189057			−0.0945285	−	0.995522i	$-0.530134\pi$
$479$	−4.13772			−0.189057			−0.0945285	+	0.995522i	$0.530134\pi$
$480$	−9.57738	+	35.5480i	−0.437146	+	1.62254i
$481$			34.9518i			1.59367i
$482$	−5.30271	−	0.932359i	−0.241532	−	0.0424678i
$483$	−20.0362	+	28.4751i	−0.911679	+	1.29566i
$484$	20.6643	+	7.49850i	0.939286	+	0.340841i
$485$	18.6312	−	12.9405i	0.845999	−	0.587600i
$486$	−2.06233	+	11.7293i	−0.0935490	+	0.532051i
$487$	28.8687			1.30816			0.654082	−	0.756424i	$-0.273055\pi$
$487$	28.8687			1.30816			0.654082	+	0.756424i	$0.273055\pi$
$488$	−2.71771	+	4.72306i	−0.123025	+	0.213803i
$489$			21.8645i			0.988747i
$490$	−15.7758	+	15.5281i	−0.712679	+	0.701490i
$491$	−31.0586			−1.40165			−0.700827	−	0.713331i	$-0.747186\pi$
$491$	−31.0586			−1.40165			−0.700827	+	0.713331i	$0.747186\pi$
$492$	12.1215	−	33.4043i	0.546479	−	1.50598i
$493$			18.4500i			0.830946i
$494$	2.40217	−	13.6621i	0.108079	−	0.614687i
$495$	0.933945	−	0.648685i	0.0419777	−	0.0291562i
$496$	−3.39034	−	2.83365i	−0.152231	−	0.127235i
$497$	21.1183	+	14.8597i	0.947286	+	0.666549i
$498$	8.40007	−	47.7746i	0.376416	−	2.14083i
$499$	16.9068			0.756854			0.378427	−	0.925631i	$-0.376465\pi$
$499$	16.9068			0.756854			0.378427	+	0.925631i	$0.376465\pi$
$500$	2.18090	−	22.2541i	0.0975327	−	0.995232i
$501$			24.9556i			1.11493i
$502$	−16.0750	−	2.82642i	−0.717463	−	0.126149i
$503$		−	8.24998i		−	0.367848i	−0.982940	−	0.183924i	$-0.941120\pi$
$503$		−	8.24998i		−	0.367848i	0.982940	−	0.183924i	$-0.0588801\pi$
$504$	17.2717	+	37.1211i	0.769341	+	1.65351i
$505$	13.3654	−	9.28315i	0.594754	−	0.413095i
$506$	−0.102923	+	0.585364i	−0.00457548	+	0.0260226i
$507$	10.8457			0.481676
$508$	−14.9061	−	5.40901i	−0.661351	−	0.239986i
$509$	24.1632			1.07102			0.535508	−	0.844530i	$-0.320120\pi$
$509$	24.1632			1.07102			0.535508	+	0.844530i	$0.320120\pi$
$510$	16.3755	+	35.4233i	0.725121	+	1.56857i
$511$	9.42814	−	13.3991i	0.417077	−	0.592741i
$512$	−22.6272	+	0.0987371i	−0.999990	+	0.00436360i
$513$			17.2499i			0.761603i
$514$	5.13685	−	29.2153i	0.226577	−	1.28863i
$515$	−10.9372	−	15.7469i	−0.481953	−	0.693893i
$516$	9.14206	−	25.1936i	0.402457	−	1.10909i
$517$			0.737535i			0.0324367i
$518$	22.5698	+	22.6519i	0.991662	+	0.995268i
$519$			69.6039i			3.05527i
$520$	25.7729	−	2.19401i	1.13022	−	0.0962138i
$521$			36.8884i			1.61611i	0.589108	+	0.808055i	$0.299479\pi$
$521$			36.8884i			1.61611i	−0.589108	+	0.808055i	$0.700521\pi$
$522$	−33.1594	−	5.83032i	−1.45135	−	0.255186i
$523$	6.36172			0.278179			0.139089	−	0.990280i	$-0.455582\pi$
$523$	6.36172			0.278179			0.139089	+	0.990280i	$0.455582\pi$
$524$	−5.15490	+	14.2058i	−0.225193	+	0.620584i
$525$	−21.7711	−	31.7565i	−0.950168	−	1.38597i
$526$	0.265923	−	1.51241i	0.0115948	−	0.0659442i
$527$	−4.68379			−0.204029
$528$	0.830296	+	0.693961i	0.0361340	+	0.0302008i
$529$	−2.55622			−0.111140
$530$	−19.0733	−	41.2592i	−0.828493	−	1.79218i
$531$			58.1183i			2.52212i
$532$	−7.26536	−	10.4054i	−0.314993	−	0.451133i
$533$	−24.9668			−1.08143
$534$	−18.0894	−	3.18061i	−0.782805	−	0.137638i
$535$	−9.58252	−	13.7965i	−0.414288	−	0.596473i
$536$	−32.2712	−	18.5693i	−1.39390	−	0.802070i
$537$	33.6134			1.45053
$538$	−1.52420	+	8.66877i	−0.0657131	+	0.373737i
$539$	0.219717	+	0.612417i	0.00946387	+	0.0263787i
$540$	−31.0928	+	8.23715i	−1.33802	+	0.354470i
$541$		−	31.6568i		−	1.36103i	−0.732733	−	0.680516i	$-0.761756\pi$
$541$		−	31.6568i		−	1.36103i	0.732733	−	0.680516i	$-0.238244\pi$
$542$	6.94702	−	39.5105i	0.298400	−	1.69712i
$543$	31.7012			1.36043
$544$	−18.3365	+	15.4621i	−0.786172	+	0.662931i
$545$	12.8899	+	18.5582i	0.552142	+	0.794948i
$546$	31.5507	−	31.4363i	1.35024	−	1.34535i
$547$			40.1397i			1.71625i	0.513441	+	0.858125i	$0.328371\pi$
$547$			40.1397i			1.71625i	−0.513441	+	0.858125i	$0.671629\pi$
$548$	12.4748	−	34.3779i	0.532896	−	1.46855i
$549$	−10.5406			−0.449860
$550$	−0.566839	−	0.332660i	−0.0241701	−	0.0141847i
$551$	10.4360			0.444590
$552$	18.5640	−	32.2621i	0.790136	−	1.37316i
$553$	7.40203	+	5.20837i	0.314767	+	0.221483i
$554$	−0.224598	+	1.27738i	−0.00954226	+	0.0542707i
$555$	−45.6815	+	31.7287i	−1.93907	+	1.34681i
$556$	−1.08245	+	2.98301i	−0.0459062	+	0.126508i
$557$	0.601042			0.0254670			0.0127335	−	0.999919i	$-0.495947\pi$
$557$	0.601042			0.0254670			0.0127335	+	0.999919i	$0.495947\pi$
$558$	1.48011	−	8.41798i	0.0626580	−	0.356361i
$559$	−18.8300			−0.796424
$560$	15.2864	−	18.0645i	0.645967	−	0.763365i
$561$	1.14706			0.0484290
$562$	2.89820	−	16.4832i	0.122253	−	0.695303i
$563$	−25.0288			−1.05484			−0.527419	−	0.849605i	$-0.676840\pi$
$563$	−25.0288			−1.05484			−0.527419	+	0.849605i	$0.676840\pi$
$564$	15.7556	−	43.4191i	0.663431	−	1.82828i
$565$	−2.84180	−	4.09149i	−0.119556	−	0.172130i
$566$	5.39620	−	30.6904i	0.226819	−	1.29001i
$567$	−6.88209	+	9.78068i	−0.289020	+	0.410750i
$568$	−23.9269	−	13.7679i	−1.00395	−	0.577686i
$569$	14.2638			0.597969			0.298984	−	0.954258i	$-0.403352\pi$
$569$	14.2638			0.597969			0.298984	+	0.954258i	$0.403352\pi$
$570$	20.0368	−	9.26264i	0.839249	−	0.387969i
$571$	−25.2375			−1.05616			−0.528079	−	0.849196i	$-0.677087\pi$
$571$	−25.2375			−1.05616			−0.528079	+	0.849196i	$0.677087\pi$
$572$	0.259338	−	0.714680i	0.0108435	−	0.0298823i
$573$		−	9.95658i		−	0.415942i
$574$	−16.1807	+	16.1221i	−0.675369	+	0.672922i
$575$	−7.89329	+	21.1847i	−0.329173	+	0.883462i
$576$	−21.9949	−	37.8416i	−0.916452	−	1.57673i
$577$	8.46289			0.352315			0.176157	−	0.984362i	$-0.443633\pi$
$577$	8.46289			0.352315			0.176157	+	0.984362i	$0.443633\pi$
$578$	−0.239571	+	1.36254i	−0.00996483	+	0.0566740i
$579$			52.7482i			2.19214i
$580$	4.98339	+	18.8108i	0.206924	+	0.781078i
$581$	−17.9426	+	25.4996i	−0.744384	+	1.05790i
$582$	−7.23106	+	41.1260i	−0.299737	+	1.70473i
$583$	−1.33604			−0.0553330
$584$	−8.73538	+	15.1811i	−0.361473	+	0.628197i
$585$	28.5426	+	41.0942i	1.18009	+	1.69904i
$586$	−22.5770	−	3.96964i	−0.932646	−	0.163984i
$587$	−12.5948			−0.519843			−0.259922	−	0.965630i	$-0.583697\pi$
$587$	−12.5948			−0.519843			−0.259922	+	0.965630i	$0.583697\pi$
$588$	0.147922	−	40.7471i	0.00610022	−	1.68038i
$589$			2.64934i			0.109164i
$590$	30.4913	−	14.0956i	1.25531	−	0.580306i
$591$	55.0821			2.26577
$592$	−26.2294	−	21.9225i	−1.07802	−	0.901011i
$593$	23.8425			0.979096			0.489548	−	0.871976i	$-0.337162\pi$
$593$	23.8425			0.979096			0.489548	+	0.871976i	$0.337162\pi$
$594$	−0.163721	+	0.931150i	−0.00671757	+	0.0382055i
$595$	0.152941	−	25.0842i	0.00626997	−	1.02835i
$596$	−7.64863	+	21.0780i	−0.313300	+	0.863389i
$597$	−18.9943			−0.777387
$598$	−25.7564	−	4.52867i	−1.05326	−	0.185191i
$599$			30.8246i			1.25946i	0.776814	+	0.629730i	$0.216834\pi$
$599$			30.8246i			1.25946i	−0.776814	+	0.629730i	$0.783166\pi$
$600$	26.2637	+	31.6931i	1.07221	+	1.29386i
$601$		−	30.7889i		−	1.25591i	−0.778251	−	0.627953i	$-0.783893\pi$
$601$		−	30.7889i		−	1.25591i	0.778251	−	0.627953i	$-0.216107\pi$
$602$	−12.2035	+	12.1593i	−0.497379	+	0.495576i
$603$		−	72.0204i		−	2.93290i
$604$	−1.46234	+	4.02989i	−0.0595017	+	0.163974i
$605$	20.1860	−	14.0205i	0.820679	−	0.570014i
$606$	−5.18734	+	29.5025i	−0.210721	+	1.19846i
$607$			25.4974i			1.03491i	0.855712	+	0.517453i	$0.173120\pi$
$607$			25.4974i			1.03491i	−0.855712	+	0.517453i	$0.826880\pi$
$608$	8.74595	+	10.3719i	0.354695	+	0.420634i
$609$	27.4035	+	19.2822i	1.11045	+	0.781356i
$610$	2.55643	+	5.53003i	0.103507	+	0.223904i
$611$	−32.4520			−1.31287
$612$	−43.6137	−	15.8262i	−1.76298	−	0.639736i
$613$	26.9818			1.08978			0.544891	−	0.838507i	$-0.316571\pi$
$613$	26.9818			1.08978			0.544891	+	0.838507i	$0.316571\pi$
$614$	−1.36400	+	7.75763i	−0.0550467	+	0.313073i
$615$	−22.6644	−	32.6312i	−0.913918	−	1.31582i
$616$	−0.293424	−	0.630641i	−0.0118224	−	0.0254093i
$617$			1.03337i			0.0416019i	0.999784	+	0.0208010i	$0.00662163\pi$
$617$			1.03337i			0.0416019i	−0.999784	+	0.0208010i	$0.993378\pi$
$618$	34.7593	+	6.11163i	1.39823	+	0.245846i
$619$		−	6.16501i		−	0.247793i	−0.992295	−	0.123896i	$-0.960461\pi$
$619$		−	6.16501i		−	0.247793i	0.992295	−	0.123896i	$-0.0395391\pi$
$620$	−4.77540	+	1.26510i	−0.191785	+	0.0508078i
$621$	32.5203			1.30500
$622$	−2.03599	+	11.5795i	−0.0816358	+	0.464296i
$623$	9.65520	+	6.79379i	0.386828	+	0.272188i
$624$	−30.5348	+	36.5336i	−1.22237	+	1.46251i
$625$	−18.9048	−	16.3587i	−0.756194	−	0.654348i
$626$	−0.0451796	+	0.256954i	−0.00180574	+	0.0102700i
$627$		−	0.648823i		−	0.0259115i
$628$	4.60039	−	12.6777i	0.183576	−	0.505896i
$629$	−36.2362			−1.44483
$630$	45.0343	+	8.20163i	1.79421	+	0.326761i
$631$		−	1.30635i		−	0.0520048i	−0.999662	−	0.0260024i	$-0.991722\pi$
$631$		−	1.30635i		−	0.0520048i	0.999662	−	0.0260024i	$-0.00827776\pi$
$632$	−8.38645	−	4.82567i	−0.333595	−	0.191955i
$633$	13.5732			0.539487
$634$	−0.0332833	+	0.189296i	−0.00132185	+	0.00751789i
$635$	−14.5611	+	10.1136i	−0.577840	+	0.401347i
$636$	78.6534	+	28.5411i	3.11881	+	1.13173i
$637$	−26.9468	+	9.66768i	−1.06767	+	0.383048i
$638$	0.563336	+	0.0990498i	0.0223027	+	0.00392142i
$639$		−	53.3983i		−	2.11240i
$640$	−14.5188	+	20.7172i	−0.573907	+	0.818921i
$641$	24.5606			0.970084			0.485042	−	0.874491i	$-0.338804\pi$
$641$	24.5606			0.970084			0.485042	+	0.874491i	$0.338804\pi$
$642$	30.4539	+	5.35462i	1.20192	+	0.211330i
$643$	−13.0725			−0.515530			−0.257765	−	0.966208i	$-0.582986\pi$
$643$	−13.0725			−0.515530			−0.257765	+	0.966208i	$0.582986\pi$
$644$	−19.6168	+	13.6970i	−0.773010	+	0.539736i
$645$	−17.0936	−	24.6105i	−0.673059	−	0.969038i
$646$	14.1641	+	2.49044i	0.557280	+	0.0979850i
$647$			13.2349i			0.520318i	0.965566	+	0.260159i	$0.0837750\pi$
$647$			13.2349i			0.520318i	−0.965566	+	0.260159i	$0.916225\pi$
$648$	6.37640	−	11.0814i	0.250489	−	0.435320i
$649$		−	0.987358i		−	0.0387572i
$650$	14.6373	−	24.9413i	0.574121	−	0.978279i
$651$	−4.89507	+	6.95678i	−0.191853	+	0.272658i
$652$	−5.12496	+	14.1233i	−0.200709	+	0.553112i
$653$	14.5528			0.569495			0.284748	−	0.958603i	$-0.408090\pi$
$653$	14.5528			0.569495			0.284748	+	0.958603i	$0.408090\pi$
$654$	−40.9650	−	7.20275i	−1.60186	−	0.281650i
$655$	9.63848	+	13.8770i	0.376607	+	0.542221i
$656$	15.6597	−	18.7362i	0.611408	−	0.731524i
$657$	−33.8800			−1.32178
$658$	−21.0318	+	20.9556i	−0.819905	+	0.816934i
$659$	−7.39396			−0.288028			−0.144014	−	0.989576i	$-0.546001\pi$
$659$	−7.39396			−0.288028			−0.144014	+	0.989576i	$0.546001\pi$
$660$	1.16950	−	0.309825i	0.0455226	−	0.0120599i
$661$	2.37065			0.0922074			0.0461037	−	0.998937i	$-0.485320\pi$
$661$	2.37065			0.0922074			0.0461037	+	0.998937i	$0.485320\pi$
$662$	−6.38581	+	36.3187i	−0.248191	+	1.41157i
$663$			50.4715i			1.96015i
$664$	16.6242	−	28.8909i	0.645144	−	1.12119i
$665$	−14.1886	−	0.0865094i	−0.550209	−	0.00335469i
$666$	11.4509	−	65.1258i	0.443712	−	2.52357i
$667$		−	19.6745i		−	0.761799i
$668$	−5.84951	+	16.1200i	−0.226324	+	0.623702i
$669$			23.8289i			0.921279i
$670$	−37.7850	+	17.4673i	−1.45976	+	0.674820i
$671$	0.179071			0.00691296
$672$	3.80197	+	43.3946i	0.146664	+	1.67398i
$673$			11.4258i			0.440431i	0.975451	+	0.220216i	$0.0706761\pi$
$673$			11.4258i			0.440431i	−0.975451	+	0.220216i	$0.929324\pi$
$674$	−5.40330	−	0.950046i	−0.208127	−	0.0365944i
$675$	−12.5560	+	33.6989i	−0.483281	+	1.29707i
$676$	7.00577	+	2.54220i	0.269453	+	0.0977770i
$677$		−	5.36512i		−	0.206198i	−0.994671	−	0.103099i	$-0.967124\pi$
$677$		−	5.36512i		−	0.206198i	0.994671	−	0.103099i	$-0.0328759\pi$
$678$	9.03145	+	1.58797i	0.346851	+	0.0609858i
$679$	15.4456	−	21.9510i	0.592747	−	0.842400i
$680$	2.27463	+	26.7199i	0.0872282	+	1.02466i
$681$	2.00134			0.0766913
$682$	−0.0251452	+	0.143011i	−0.000962860	+	0.00547617i
$683$			7.24957i			0.277397i	0.990335	+	0.138699i	$0.0442919\pi$
$683$			7.24957i			0.277397i	−0.990335	+	0.138699i	$0.955708\pi$
$684$	−8.95192	+	24.6696i	−0.342285	+	0.943266i
$685$	−23.3250	−	33.5822i	−0.891202	−	1.28311i
$686$	−11.2211	+	23.6662i	−0.428424	+	0.903578i
$687$	−14.7512			−0.562794
$688$	11.8106	−	14.1309i	0.450274	−	0.538734i
$689$		−	58.7865i		−	2.23959i
$690$	−17.4623	−	37.7743i	−0.664780	−	1.43804i
$691$		−	48.8381i		−	1.85789i	−0.370220	−	0.928944i	$-0.620718\pi$
$691$		−	48.8381i		−	1.85789i	0.370220	−	0.928944i	$-0.379282\pi$
$692$	−16.3149	+	44.9605i	−0.620200	+	1.70914i
$693$	0.774257	−	1.10036i	0.0294116	−	0.0417992i
$694$	28.5528	+	5.02035i	1.08385	+	0.190570i
$695$	2.02394	+	2.91398i	0.0767725	+	0.110533i
$696$	−31.0480	−	17.8654i	−1.17687	−	0.677187i
$697$		−	25.8842i		−	0.980435i
$698$	−3.49773	+	19.8930i	−0.132391	+	0.752962i
$699$		−	46.2640i		−	1.74987i
$700$	−6.61937	−	25.6161i	−0.250189	−	0.968197i
$701$			5.22242i			0.197248i	0.995125	+	0.0986240i	$0.0314441\pi$
$701$			5.22242i			0.197248i	−0.995125	+	0.0986240i	$0.968556\pi$
$702$	−40.9712	−	7.20385i	−1.54636	−	0.271892i
$703$			20.4966i			0.773044i
$704$	0.373665	+	0.642881i	0.0140830	+	0.0242295i
$705$	−29.4594	−	42.4143i	−1.10951	−	1.59741i
$706$	4.34239	−	24.6969i	0.163428	−	0.929481i
$707$	11.0802	−	15.7469i	0.416713	−	0.592224i
$708$	−21.0925	+	58.1264i	−0.792704	+	2.18452i
$709$		−	31.5014i		−	1.18306i	−0.806283	−	0.591530i	$-0.798524\pi$
$709$		−	31.5014i		−	1.18306i	0.806283	−	0.591530i	$-0.201476\pi$
$710$	−28.0150	+	12.9508i	−1.05138	+	0.486035i
$711$		−	18.7163i		−	0.701914i
$712$	−10.9393	−	6.29460i	−0.409967	−	0.235900i
$713$	4.99465			0.187051
$714$	32.5915	+	32.7100i	1.21971	+	1.22414i
$715$	−0.484902	−	0.698140i	−0.0181343	−	0.0261089i
$716$	21.7125	+	7.87887i	0.811435	+	0.294447i
$717$			35.5964i			1.32937i
$718$	−39.3002	−	6.91004i	−1.46667	−	0.257881i
$719$	−7.20252			−0.268609			−0.134304	−	0.990940i	$-0.542880\pi$
$719$	−7.20252			−0.268609			−0.134304	+	0.990940i	$0.542880\pi$
$720$	−48.7414	−	4.35558i	−1.81649	−	0.162323i
$721$	−18.5528	−	13.0545i	−0.690941	−	0.486174i
$722$	−3.24442	+	18.4523i	−0.120745	+	0.686724i
$723$		−	11.0807i		−	0.412094i
$724$	20.4773	+	7.43066i	0.761034	+	0.276158i
$725$	20.3875	+	7.59626i	0.757172	+	0.282118i
$726$	−7.83452	+	44.5581i	−0.290766	+	1.65371i
$727$		−	20.0473i		−	0.743515i	−0.928330	−	0.371757i	$-0.878755\pi$
$727$		−	20.0473i		−	0.743515i	0.928330	−	0.371757i	$-0.121245\pi$
$728$	27.7486	−	12.9109i	1.02843	−	0.478508i
$729$	−38.0704			−1.41001
$730$	8.21699	+	17.7749i	0.304125	+	0.657877i
$731$		−	19.5219i		−	0.722045i
$732$	−10.5420	−	3.82541i	−0.389645	−	0.141391i
$733$			9.51770i			0.351544i	0.984431	+	0.175772i	$0.0562422\pi$
$733$			9.51770i			0.351544i	−0.984431	+	0.175772i	$0.943758\pi$
$734$	36.7348	+	6.45896i	1.35590	+	0.238405i
$735$	−37.0973	−	26.4428i	−1.36836	−	0.975359i
$736$	19.5535	−	16.4883i	0.720751	−	0.607765i
$737$			1.22354i			0.0450696i
$738$	46.5206	+	8.17958i	1.71245	+	0.301094i
$739$	−36.0009			−1.32432			−0.662158	−	0.749364i	$-0.730359\pi$
$739$	−36.0009			−1.32432			−0.662158	+	0.749364i	$0.730359\pi$
$740$	−36.9450	+	9.78750i	−1.35812	+	0.359796i
$741$	28.5487			1.04876
$742$	−37.9609	−	38.0989i	−1.39359	−	1.39866i
$743$	−30.4574			−1.11737			−0.558686	−	0.829379i	$-0.688694\pi$
$743$	−30.4574			−1.11737			−0.558686	+	0.829379i	$0.688694\pi$
$744$	4.53539	−	7.88198i	0.166276	−	0.288968i
$745$	14.3012	+	20.5902i	0.523956	+	0.754366i
$746$	0.0523607	−	0.297797i	0.00191706	−	0.0109031i
$747$	64.4766			2.35907
$748$	0.740942	+	0.268867i	0.0270915	+	0.00983077i
$749$	−16.2548	−	11.4375i	−0.593936	−	0.417917i
$750$	45.8854	−	3.51064i	1.67550	−	0.128190i
$751$			36.5140i			1.33241i	0.745767	+	0.666207i	$0.232083\pi$
$751$			36.5140i			1.33241i	−0.745767	+	0.666207i	$0.767917\pi$
$752$	20.3546	−	24.3534i	0.742256	−	0.888078i
$753$		−	33.5907i		−	1.22411i
$754$	−4.35826	+	24.7872i	−0.158718	+	0.902696i
$755$	2.73424	+	3.93663i	0.0995091	+	0.143269i
$756$	−31.2048	+	21.7881i	−1.13491	+	0.792424i
$757$	−37.9558			−1.37953			−0.689763	−	0.724035i	$-0.742285\pi$
$757$	−37.9558			−1.37953			−0.689763	+	0.724035i	$0.742285\pi$
$758$	−0.124541	+	0.708313i	−0.00452352	+	0.0257271i
$759$	−1.22319			−0.0443990
$760$	15.1138	−	1.28662i	0.548237	−	0.0466707i
$761$		−	8.65361i		−	0.313693i	−0.987623	−	0.156846i	$-0.949867\pi$
$761$		−	8.65361i		−	0.313693i	0.987623	−	0.156846i	$-0.0501328\pi$
$762$	5.65140	−	32.1418i	0.204729	−	1.16437i
$763$	21.8650	+	15.3851i	0.791567	+	0.556978i
$764$	2.33379	−	6.43143i	0.0844335	−	0.232681i
$765$	−42.6043	+	29.5914i	−1.54036	+	1.06988i
$766$	34.5763	+	6.07945i	1.24929	+	0.219659i
$767$	43.4444			1.56869
$768$	−8.26435	−	45.8292i	−0.298214	−	1.65372i
$769$			19.0593i			0.687297i	0.939098	+	0.343648i	$0.111663\pi$
$769$			19.0593i			0.687297i	−0.939098	+	0.343648i	$0.888337\pi$
$770$	−0.765077	−	0.139335i	−0.0275715	−	0.00502130i
$771$	61.0491			2.19863
$772$	−12.3640	+	34.0726i	−0.444990	+	1.22630i
$773$		−	31.6953i		−	1.14000i	−0.821645	−	0.570000i	$-0.806943\pi$
$773$		−	31.6953i		−	1.14000i	0.821645	−	0.570000i	$-0.193057\pi$
$774$	35.0860	+	6.16906i	1.26114	+	0.221742i
$775$	−1.92842	+	5.17565i	−0.0692709	+	0.185915i
$776$	−14.3107	+	24.8703i	−0.513723	+	0.892791i
$777$	−37.8708	+	53.8212i	−1.35861	+	1.93082i
$778$	−26.3331	−	4.63008i	−0.944088	−	0.165996i
$779$	−14.6411			−0.524573
$780$	13.6325	+	51.4587i	0.488121	+	1.84252i
$781$			0.907170i			0.0324611i
$782$	4.69509	−	26.7029i	0.167896	−	0.954892i
$783$		−	31.2966i		−	1.11845i
$784$	9.64653	−	26.2858i	0.344519	−	0.938779i
$785$	−8.60168	−	12.3843i	−0.307007	−	0.442015i
$786$	−30.6318	−	5.38590i	−1.09260	−	0.192109i
$787$	−1.34681			−0.0480085			−0.0240043	−	0.999712i	$-0.507642\pi$
$787$	−1.34681			−0.0480085			−0.0240043	+	0.999712i	$0.507642\pi$
$788$	35.5801	+	12.9110i	1.26749	+	0.459937i
$789$	3.16037			0.112512
$790$	−9.81934	+	4.53930i	−0.349356	+	0.161501i
$791$	−4.82053	−	3.39192i	−0.171398	−	0.120603i
$792$	−0.717366	+	1.24670i	−0.0254905	+	0.0442995i
$793$			7.87925i			0.279800i
$794$	−23.9680	−	4.21422i	−0.850592	−	0.149557i
$795$	76.8330	−	53.3655i	2.72499	−	1.89268i
$796$	−12.2693	−	4.45221i	−0.434876	−	0.157804i
$797$			44.1264i			1.56304i	0.623882	+	0.781519i	$0.285555\pi$
$797$			44.1264i			1.56304i	−0.623882	+	0.781519i	$0.714445\pi$
$798$	18.5021	−	18.4350i	0.654967	−	0.652593i
$799$		−	33.6445i		−	1.19026i
$800$	9.53625	+	26.6282i	0.337157	+	0.941448i
$801$		−	24.4135i		−	0.862607i
$802$	−2.85767	+	16.2527i	−0.100908	+	0.573904i
$803$	0.575578			0.0203117
$804$	26.1379	−	72.0305i	0.921812	−	2.54032i
$805$	−0.163091	+	26.7489i	−0.00574821	+	0.942776i
$806$	−6.29258	−	1.10641i	−0.221647	−	0.0389715i
$807$	−18.1145			−0.637660
$808$	−10.2660	+	17.8412i	−0.361158	+	0.627650i
$809$	−22.6554			−0.796521			−0.398261	−	0.917272i	$-0.630386\pi$
$809$	−22.6554			−0.796521			−0.398261	+	0.917272i	$0.630386\pi$
$810$	−5.99800	−	12.9748i	−0.210748	−	0.455888i
$811$			23.8620i			0.837909i	0.908007	+	0.418954i	$0.137603\pi$
$811$			23.8620i			0.837909i	−0.908007	+	0.418954i	$0.862397\pi$
$812$	13.1816	+	18.8786i	0.462582	+	0.662509i
$813$	82.5622			2.89558
$814$	−0.194536	+	1.10641i	−0.00681849	+	0.0387795i
$815$	9.58252	+	13.7965i	0.335661	+	0.483269i
$816$	−37.8760	−	31.6568i	−1.32593	−	1.10821i
$817$	−11.0424			−0.386324
$818$	17.9182	+	3.15050i	0.626494	+	0.110155i
$819$	48.4165	+	34.0678i	1.69181	+	1.19043i
$820$	−6.99140	−	26.3905i	−0.244150	−	0.921596i
$821$		−	26.3396i		−	0.919260i	−0.888111	−	0.459630i	$-0.847982\pi$
$821$		−	26.3396i		−	0.919260i	0.888111	−	0.459630i	$-0.152018\pi$
$822$	74.1285	+	13.0338i	2.58553	+	0.454606i
$823$	−16.2057			−0.564896			−0.282448	−	0.959283i	$-0.591147\pi$
$823$	−16.2057			−0.564896			−0.282448	+	0.959283i	$0.591147\pi$
$824$	21.0202	+	12.0953i	0.732272	+	0.421359i
$825$	0.472271	−	1.26752i	0.0164424	−	0.0441294i
$826$	28.1559	−	28.0538i	0.979668	−	0.976118i
$827$		−	10.3304i		−	0.359222i	−0.983738	−	0.179611i	$-0.942516\pi$
$827$		−	10.3304i		−	0.359222i	0.983738	−	0.179611i	$-0.0574840\pi$
$828$	46.5082	+	16.8765i	1.61627	+	0.586501i
$829$	−48.5037			−1.68460			−0.842302	−	0.539007i	$-0.818800\pi$
$829$	−48.5037			−1.68460			−0.842302	+	0.539007i	$0.818800\pi$
$830$	−15.6377	−	33.8271i	−0.542791	−	1.17416i
$831$	−2.66924			−0.0925951
$832$	−28.2872	+	16.4415i	−0.980682	+	0.570007i
$833$	−10.0229	−	27.9370i	−0.347274	−	0.967959i
$834$	−6.43223	−	1.13096i	−0.222730	−	0.0391620i
$835$	10.9372	+	15.7469i	0.378499	+	0.544945i
$836$	0.152082	−	0.419106i	0.00525986	−	0.0144951i
$837$	7.94508			0.274622
$838$	6.18655	+	1.08776i	0.213711	+	0.0375762i
$839$	25.6975			0.887176			0.443588	−	0.896231i	$-0.353705\pi$
$839$	25.6975			0.887176			0.443588	+	0.896231i	$0.353705\pi$
$840$	42.0640	+	24.5468i	1.45135	+	0.846944i
$841$	10.0659			0.347100
$842$	42.3611	+	7.44824i	1.45986	+	0.256683i
$843$	34.4437			1.18631
$844$	8.76759	+	3.18152i	0.301793	+	0.109512i
$845$	6.84363	−	4.75334i	0.235428	−	0.163520i
$846$	60.4678	+	10.6319i	2.07893	+	0.365532i
$847$	16.7346	−	23.7828i	0.575007	−	0.817188i
$848$	44.1160	+	36.8722i	1.51495	+	1.26620i
$849$	64.1314			2.20098
$850$	25.8578	+	15.1751i	0.886916	+	0.520503i
$851$	38.6411			1.32460
$852$	19.3795	−	53.4057i	0.663929	−	1.82965i
$853$		−	36.3693i		−	1.24526i	−0.782516	−	0.622630i	$-0.786064\pi$
$853$		−	36.3693i		−	1.24526i	0.782516	−	0.622630i	$-0.213936\pi$
$854$	5.08795	+	5.10645i	0.174106	+	0.174739i
$855$	16.7380	+	24.0986i	0.572429	+	0.824156i
$856$	18.4165	+	10.5971i	0.629464	+	0.362201i
$857$	7.87431			0.268981			0.134491	−	0.990915i	$-0.457060\pi$
$857$	7.87431			0.268981			0.134491	+	0.990915i	$0.457060\pi$
$858$	1.54105	+	0.270959i	0.0526107	+	0.00925039i
$859$		−	6.61172i		−	0.225589i	−0.993618	−	0.112795i	$-0.964020\pi$
$859$		−	6.61172i		−	0.225589i	0.993618	−	0.112795i	$-0.0359802\pi$
$860$	−5.27293	−	19.9038i	−0.179805	−	0.678713i
$861$	−38.4455	−	27.0518i	−1.31022	−	0.921924i
$862$	25.3008	+	4.44857i	0.861749	+	0.151519i
$863$	−52.1673			−1.77580			−0.887898	−	0.460040i	$-0.847835\pi$
$863$	−52.1673			−1.77580			−0.887898	+	0.460040i	$0.847835\pi$
$864$	31.1041	−	26.2282i	1.05818	−	0.892301i
$865$	30.5052	+	43.9199i	1.03721	+	1.49332i
$866$	−4.26502	+	24.2569i	−0.144931	+	0.824282i
$867$	−2.84719			−0.0966956
$868$	−4.79260	+	3.34632i	−0.162672	+	0.113582i
$869$			0.317966i			0.0107863i
$870$	−36.3528	+	16.8052i	−1.23248	+	0.569750i
$871$	−53.8365			−1.82418
$872$	−24.7729	−	14.2546i	−0.838917	−	0.482723i
$873$	−55.5036			−1.87851
$874$	−15.1042	−	2.65572i	−0.510906	−	0.0898312i
$875$	−27.6554	−	10.4967i	−0.934922	−	0.354853i
$876$	−33.8847	−	12.2958i	−1.14486	−	0.415437i
$877$	28.4925			0.962125			0.481063	−	0.876686i	$-0.340251\pi$
$877$	28.4925			0.962125			0.481063	+	0.876686i	$0.340251\pi$
$878$	−8.39654	+	47.7545i	−0.283369	+	1.61164i
$879$		−	47.1774i		−	1.59125i
$880$	0.828056	+	0.0739958i	0.0279138	+	0.00249440i
$881$		−	33.0865i		−	1.11471i	−0.830274	−	0.557356i	$-0.811816\pi$
$881$		−	33.0865i		−	1.11471i	0.830274	−	0.557356i	$-0.188184\pi$
$882$	53.3772	−	9.18553i	1.79730	−	0.309293i
$883$		−	13.6397i		−	0.459013i	−0.973307	−	0.229506i	$-0.926289\pi$
$883$		−	13.6397i		−	0.459013i	0.973307	−	0.229506i	$-0.0737112\pi$
$884$	−11.8303	+	32.6019i	−0.397898	+	1.09652i
$885$	39.4381	+	56.7811i	1.32570	+	1.90868i
$886$	−16.9965	−	2.98845i	−0.571010	−	0.100399i
$887$		−	14.1834i		−	0.476233i	−0.971237	−	0.238116i	$-0.923470\pi$
$887$		−	14.1834i		−	0.476233i	0.971237	−	0.238116i	$-0.0765300\pi$
$888$	35.0881	−	60.9790i	1.17748	−	2.04632i
$889$	−12.0714	+	17.1557i	−0.404862	+	0.575382i
$890$	−12.8083	+	5.92105i	−0.429336	+	0.198474i
$891$	−0.420144			−0.0140754
$892$	−5.58541	+	15.3922i	−0.187013	+	0.515370i
$893$	−19.0307			−0.636837
$894$	−45.4502	−	7.99138i	−1.52008	−	0.267272i
$895$	21.2100	−	14.7317i	0.708972	−	0.492427i
$896$	−7.71566	+	28.9218i	−0.257762	+	0.966208i
$897$		−	53.8212i		−	1.79704i
$898$	−3.03478	+	17.2600i	−0.101272	+	0.575974i
$899$		−	4.80669i		−	0.160312i
$900$	−35.4449	+	41.6777i	−1.18150	+	1.38926i
$901$	60.9467			2.03043
$902$	−0.790327	−	0.138961i	−0.0263150	−	0.00462689i
$903$	−28.9957	−	20.4026i	−0.964917	−	0.678955i
$904$	5.46163	+	3.14269i	0.181651	+	0.104524i
$905$	20.0034	−	13.8936i	0.664936	−	0.461840i
$906$	−8.68960	−	1.52787i	−0.288693	−	0.0507600i
$907$			43.9936i			1.46078i	0.683029	+	0.730391i	$0.260662\pi$
$907$			43.9936i			1.46078i	−0.683029	+	0.730391i	$0.739338\pi$
$908$	1.29276	+	0.469106i	0.0429017	+	0.0155678i
$909$	−39.8166			−1.32063
$910$	6.13085	−	33.6639i	0.203236	−	1.11595i
$911$		−	16.0145i		−	0.530584i	−0.964168	−	0.265292i	$-0.914532\pi$
$911$		−	16.0145i		−	0.530584i	0.964168	−	0.265292i	$-0.0854684\pi$
$912$	−17.9063	+	21.4242i	−0.592938	+	0.709425i
$913$	−1.09538			−0.0362517
$914$	14.8999	+	2.61980i	0.492843	+	0.0866552i
$915$	−10.2980	+	7.15265i	−0.340443	+	0.236459i
$916$	−9.52850	−	3.45763i	−0.314831	−	0.114243i
$917$	16.3497	+	11.5043i	0.539914	+	0.379906i
$918$	7.46857	−	42.4768i	0.246499	−	1.40194i
$919$			8.04985i			0.265540i	0.991147	+	0.132770i	$0.0423872\pi$
$919$			8.04985i			0.265540i	−0.991147	+	0.132770i	$0.957613\pi$
$920$	−2.42560	−	28.4933i	−0.0799695	−	0.939396i
$921$	−16.2105			−0.534155
$922$	3.69010	−	20.9871i	0.121527	−	0.691172i
$923$	−39.9161			−1.31385
$924$	1.17371	−	0.819516i	0.0386122	−	0.0269601i
$925$	−14.9192	+	40.0415i	−0.490542	+	1.31656i
$926$	4.75437	−	27.0400i	0.156238	−	0.888591i
$927$			46.9112i			1.54077i
$928$	−15.8678	−	18.8177i	−0.520886	−	0.617720i
$929$			24.7127i			0.810798i	0.914140	+	0.405399i	$0.132867\pi$
$929$			24.7127i			0.810798i	−0.914140	+	0.405399i	$0.867133\pi$
$930$	−4.26624	−	9.22867i	−0.139896	−	0.302620i
$931$	−15.8022	+	5.66936i	−0.517898	+	0.185806i
$932$	10.8441	−	29.8841i	0.355211	−	0.978888i
$933$	−24.1968			−0.792168
$934$	6.06198	−	34.4769i	0.198354	−	1.12812i
$935$	0.723794	−	0.502721i	0.0236706	−	0.0164407i
$936$	−54.8556	−	31.5646i	−1.79301	−	1.03172i
$937$	11.4286			0.373356			0.186678	−	0.982421i	$-0.440228\pi$
$937$	11.4286			0.373356			0.186678	+	0.982421i	$0.440228\pi$
$938$	−34.8908	+	34.7644i	−1.13923	+	1.13510i
$939$	−0.536938			−0.0175223
$940$	−9.08747	−	34.3026i	−0.296401	−	1.11883i
$941$	46.2213			1.50677			0.753385	−	0.657580i	$-0.228420\pi$
$941$	46.2213			1.50677			0.753385	+	0.657580i	$0.228420\pi$
$942$	27.3368	+	4.80654i	0.890680	+	0.156606i
$943$			27.6021i			0.898848i
$944$	−27.2493	+	32.6026i	−0.886888	+	1.06112i
$945$	−0.259433	+	42.5501i	−0.00843934	+	1.38415i
$946$	−0.596067	−	0.104805i	−0.0193798	−	0.00340749i
$947$		−	29.3217i		−	0.952827i	−0.879221	−	0.476413i	$-0.841937\pi$
$947$		−	29.3217i		−	0.952827i	0.879221	−	0.476413i	$-0.158063\pi$
$948$	6.79256	−	18.7189i	0.220612	−	0.607960i
$949$			25.3258i			0.822111i
$950$	8.58365	−	14.6262i	0.278490	−	0.474536i
$951$	−0.395557			−0.0128268
$952$	13.3853	+	28.7683i	0.433820	+	0.932386i
$953$			53.3364i			1.72773i	0.503719	+	0.863867i	$0.331965\pi$
$953$			53.3364i			1.72773i	−0.503719	+	0.863867i	$0.668035\pi$
$954$	−19.2596	+	109.537i	−0.623551	+	3.54639i
$955$	−4.36365	−	6.28258i	−0.141205	−	0.203300i
$956$	−8.34366	+	22.9934i	−0.269853	+	0.743659i
$957$			1.17716i			0.0380522i
$958$	1.01333	−	5.76321i	0.0327391	−	0.186201i
$959$	−39.5660	−	27.8403i	−1.27765	−	0.899009i
$960$	−47.1674	−	22.0456i	−1.52232	−	0.711517i
$961$	−29.7798			−0.960637
$962$	−48.6826	−	8.55972i	−1.56959	−	0.275976i
$963$			41.1006i			1.32445i
$964$	2.59727	−	7.15752i	0.0836524	−	0.230528i
$965$	23.1179	+	33.2840i	0.744190	+	1.07145i
$966$	−34.7545	−	34.8809i	−1.11821	−	1.12228i
$967$	49.6379			1.59625			0.798123	−	0.602494i	$-0.205826\pi$
$967$	49.6379			1.59625			0.798123	+	0.602494i	$0.205826\pi$
$968$	−15.5050	+	26.9458i	−0.498348	+	0.866071i
$969$			29.5977i			0.950816i
$970$	13.4614	+	29.1195i	0.432220	+	0.934972i
$971$		−	9.69938i		−	0.311268i	−0.987815	−	0.155634i	$-0.950258\pi$
$971$		−	9.69938i		−	0.311268i	0.987815	−	0.155634i	$-0.0497421\pi$
$972$	−15.8320	−	5.74501i	−0.507813	−	0.184271i
$973$	3.43320	+	2.41574i	0.110063	+	0.0774450i
$974$	−7.06995	+	40.2096i	−0.226536	+	1.28840i
$975$	55.7717	+	20.7802i	1.78612	+	0.665500i
$976$	−5.91293	−	4.94203i	−0.189268	−	0.158191i
$977$		−	40.7439i		−	1.30351i	−0.758428	−	0.651757i	$-0.774032\pi$
$977$		−	40.7439i		−	1.30351i	0.758428	−	0.651757i	$-0.225968\pi$
$978$	−30.4539	−	5.35462i	−0.973809	−	0.171222i
$979$			0.414754i			0.0132556i
$980$	−17.7648	−	25.7762i	−0.567477	−	0.823390i
$981$		−	55.2863i		−	1.76516i
$982$	7.60626	−	43.2599i	0.242726	−	1.38048i
$983$			1.23527i			0.0393990i	0.999806	+	0.0196995i	$0.00627095\pi$
$983$			1.23527i			0.0393990i	−0.999806	+	0.0196995i	$0.993729\pi$
$984$	43.5585	+	25.0641i	1.38859	+	0.799014i
$985$	34.7567	−	24.1407i	1.10744	−	0.769187i
$986$	−25.6980	−	4.51841i	−0.818392	−	0.143895i
$987$	−49.9718	−	35.1622i	−1.59062	−	1.11922i
$988$	18.4409	+	6.69171i	0.586684	+	0.212892i
$989$			20.8176i			0.661960i
$990$	0.674795	+	1.45971i	0.0214464	+	0.0463925i
$991$			49.1076i			1.55995i	0.625808	+	0.779977i	$0.284769\pi$
$991$			49.1076i			1.55995i	−0.625808	+	0.779977i	$0.715231\pi$
$992$	4.77713	−	4.02827i	0.151674	−	0.127898i
$993$	−75.8924			−2.40837
$994$	−25.8692	+	25.7755i	−0.820521	+	0.817548i
$995$	−11.9854	+	8.32462i	−0.379962	+	0.263908i
$996$	64.4855	+	23.4000i	2.04330	+	0.741458i
$997$		−	24.6133i		−	0.779512i	−0.920918	−	0.389756i	$-0.872559\pi$
$997$		−	24.6133i		−	0.779512i	0.920918	−	0.389756i	$-0.127441\pi$
$998$	−4.14049	+	23.5487i	−0.131065	+	0.745420i
$999$	61.4672			1.94474

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.n.b.139.19	yes	40
4.3	odd	2		1120.2.n.b.559.39		40
5.4	even	2	inner	280.2.n.b.139.22	yes	40
7.6	odd	2	inner	280.2.n.b.139.20	yes	40
8.3	odd	2	inner	280.2.n.b.139.23	yes	40
8.5	even	2		1120.2.n.b.559.40		40
20.19	odd	2		1120.2.n.b.559.4		40
28.27	even	2		1120.2.n.b.559.2		40
35.34	odd	2	inner	280.2.n.b.139.21	yes	40
40.19	odd	2	inner	280.2.n.b.139.18	yes	40
40.29	even	2		1120.2.n.b.559.3		40
56.13	odd	2		1120.2.n.b.559.1		40
56.27	even	2	inner	280.2.n.b.139.24	yes	40
140.139	even	2		1120.2.n.b.559.37		40
280.69	odd	2		1120.2.n.b.559.38		40
280.139	even	2	inner	280.2.n.b.139.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.n.b.139.17	✓	40	280.139	even	2	inner
280.2.n.b.139.18	yes	40	40.19	odd	2	inner
280.2.n.b.139.19	yes	40	1.1	even	1	trivial
280.2.n.b.139.20	yes	40	7.6	odd	2	inner
280.2.n.b.139.21	yes	40	35.34	odd	2	inner
280.2.n.b.139.22	yes	40	5.4	even	2	inner
280.2.n.b.139.23	yes	40	8.3	odd	2	inner
280.2.n.b.139.24	yes	40	56.27	even	2	inner
1120.2.n.b.559.1		40	56.13	odd	2
1120.2.n.b.559.2		40	28.27	even	2
1120.2.n.b.559.3		40	40.29	even	2
1120.2.n.b.559.4		40	20.19	odd	2
1120.2.n.b.559.37		40	140.139	even	2
1120.2.n.b.559.38		40	280.69	odd	2
1120.2.n.b.559.39		40	4.3	odd	2
1120.2.n.b.559.40		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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.244900 + 1.39285i) q^{2} -2.91053 q^{3} +(-1.88005 - 0.682218i) q^{4} +(-1.83654 + 1.27559i) q^{5} +(0.712789 - 4.05392i) q^{6} +(-1.52252 + 2.16378i) q^{7} +(1.41065 - 2.45154i) q^{8} +5.47117 q^{9} +O(q^{10})\)	\(q+(-0.244900 + 1.39285i) q^{2} -2.91053 q^{3} +(-1.88005 - 0.682218i) q^{4} +(-1.83654 + 1.27559i) q^{5} +(0.712789 - 4.05392i) q^{6} +(-1.52252 + 2.16378i) q^{7} +(1.41065 - 2.45154i) q^{8} +5.47117 q^{9} +(-1.32694 - 2.87041i) q^{10} -0.0929484 q^{11} +(5.47193 + 1.98561i) q^{12} -4.08979i q^{13} +(-2.64094 - 2.65055i) q^{14} +(5.34529 - 3.71264i) q^{15} +(3.06916 + 2.56520i) q^{16} +4.24008 q^{17} +(-1.33989 + 7.62050i) q^{18} -2.39835i q^{19} +(4.32301 - 1.14526i) q^{20} +(4.43134 - 6.29773i) q^{21} +(0.0227631 - 0.129463i) q^{22} -4.52148 q^{23} +(-4.10573 + 7.13529i) q^{24} +(1.74573 - 4.68534i) q^{25} +(5.69645 + 1.00159i) q^{26} -7.19241 q^{27} +(4.33858 - 3.02931i) q^{28} +4.35133i q^{29} +(3.86208 + 8.35440i) q^{30} -1.10465 q^{31} +(-4.32457 + 3.64665i) q^{32} +0.270529 q^{33} +(-1.03840 + 5.90578i) q^{34} +(0.0360703 - 5.91597i) q^{35} +(-10.2861 - 3.73253i) q^{36} -8.54612 q^{37} +(3.34054 + 0.587357i) q^{38} +11.9034i q^{39} +(0.536461 + 6.30176i) q^{40} -6.10466i q^{41} +(7.68654 + 7.71450i) q^{42} -4.60415i q^{43} +(0.174747 + 0.0634110i) q^{44} +(-10.0480 + 6.97898i) q^{45} +(1.10731 - 6.29773i) q^{46} -7.93489i q^{47} +(-8.93287 - 7.46609i) q^{48} +(-2.36386 - 6.58879i) q^{49} +(6.09843 + 3.57898i) q^{50} -12.3409 q^{51} +(-2.79013 + 7.68900i) q^{52} +14.3740 q^{53} +(1.76142 - 10.0179i) q^{54} +(0.170703 - 0.118564i) q^{55} +(3.15685 + 6.78486i) q^{56} +6.98047i q^{57} +(-6.06075 - 1.06564i) q^{58} +10.6226i q^{59} +(-12.5822 + 3.33330i) q^{60} -1.92656 q^{61} +(0.270529 - 1.53861i) q^{62} +(-8.32997 + 11.8384i) q^{63} +(-4.02014 - 6.91654i) q^{64} +(5.21690 + 7.51105i) q^{65} +(-0.0662526 + 0.376805i) q^{66} -13.1636i q^{67} +(-7.97154 - 2.89265i) q^{68} +13.1599 q^{69} +(8.23121 + 1.49906i) q^{70} -9.75994i q^{71} +(7.71790 - 13.4128i) q^{72} -6.19245 q^{73} +(2.09295 - 11.9034i) q^{74} +(-5.08100 + 13.6368i) q^{75} +(-1.63620 + 4.50902i) q^{76} +(0.141516 - 0.201119i) q^{77} +(-16.5797 - 2.91516i) q^{78} -3.42089i q^{79} +(-8.90877 - 0.796096i) q^{80} +4.52019 q^{81} +(8.50286 + 1.49503i) q^{82} +11.7848 q^{83} +(-12.6276 + 8.81690i) q^{84} +(-7.78705 + 5.40860i) q^{85} +(6.41288 + 1.12756i) q^{86} -12.6647i q^{87} +(-0.131118 + 0.227867i) q^{88} -4.46220i q^{89} +(-7.25989 - 15.7045i) q^{90} +(8.84939 + 6.22679i) q^{91} +(8.50060 + 3.08463i) q^{92} +3.21511 q^{93} +(11.0521 + 1.94326i) q^{94} +(3.05932 + 4.40466i) q^{95} +(12.5868 - 10.6137i) q^{96} -10.1447 q^{97} +(9.75609 - 1.67890i) q^{98} -0.508536 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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