LMFDB - Embedded newform 280.2.h.b.251.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(251,280)]

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, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("280.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.h (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 $ x^16 - x^15 - 2x^12 + 6x^11 - 12x^9 + 8x^8 - 24x^7 + 48x^5 - 32x^4 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.10
Root			$0.244064 - 1.39299i$ of defining polynomial
Character	$\chi$	$=$	280.251
Dual form			280.2.h.b.251.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.244064 + 1.39299i) q^{2} -1.68420i q^{3} +(-1.88087 + 0.679959i) q^{4} +1.00000 q^{5} +(2.34608 - 0.411052i) q^{6} +(0.695780 + 2.55262i) q^{7} +(-1.40623 - 2.45408i) q^{8} +0.163484 q^{9} +O(q^{10})$	\(q+(0.244064 + 1.39299i) q^{2} -1.68420i q^{3} +(-1.88087 + 0.679959i) q^{4} +1.00000 q^{5} +(2.34608 - 0.411052i) q^{6} +(0.695780 + 2.55262i) q^{7} +(-1.40623 - 2.45408i) q^{8} +0.163484 q^{9} +(0.244064 + 1.39299i) q^{10} +1.45385 q^{11} +(1.14518 + 3.16775i) q^{12} +5.12034 q^{13} +(-3.38598 + 1.59222i) q^{14} -1.68420i q^{15} +(3.07531 - 2.55782i) q^{16} +0.313877i q^{17} +(0.0399006 + 0.227732i) q^{18} +0.250100i q^{19} +(-1.88087 + 0.679959i) q^{20} +(4.29912 - 1.17183i) q^{21} +(0.354833 + 2.02521i) q^{22} +4.27001i q^{23} +(-4.13315 + 2.36837i) q^{24} +1.00000 q^{25} +(1.24969 + 7.13260i) q^{26} -5.32793i q^{27} +(-3.04435 - 4.32804i) q^{28} -1.63961i q^{29} +(2.34608 - 0.411052i) q^{30} -8.96308 q^{31} +(4.31361 + 3.65962i) q^{32} -2.44857i q^{33} +(-0.437228 + 0.0766060i) q^{34} +(0.695780 + 2.55262i) q^{35} +(-0.307492 + 0.111163i) q^{36} +3.47842i q^{37} +(-0.348388 + 0.0610404i) q^{38} -8.62365i q^{39} +(-1.40623 - 2.45408i) q^{40} -9.88374i q^{41} +(2.68161 + 5.70265i) q^{42} -8.65164 q^{43} +(-2.73450 + 0.988561i) q^{44} +0.163484 q^{45} +(-5.94810 + 1.04216i) q^{46} -7.77853 q^{47} +(-4.30788 - 5.17943i) q^{48} +(-6.03178 + 3.55213i) q^{49} +(0.244064 + 1.39299i) q^{50} +0.528630 q^{51} +(-9.63067 + 3.48162i) q^{52} +1.90687i q^{53} +(7.42177 - 1.30036i) q^{54} +1.45385 q^{55} +(5.28592 - 5.29708i) q^{56} +0.421218 q^{57} +(2.28396 - 0.400169i) q^{58} -7.73295i q^{59} +(1.14518 + 3.16775i) q^{60} +0.415877 q^{61} +(-2.18757 - 12.4855i) q^{62} +(0.113749 + 0.417313i) q^{63} +(-4.04503 + 6.90201i) q^{64} +5.12034 q^{65} +(3.41085 - 0.597609i) q^{66} +15.2878 q^{67} +(-0.213423 - 0.590360i) q^{68} +7.19153 q^{69} +(-3.38598 + 1.59222i) q^{70} -1.50413i q^{71} +(-0.229896 - 0.401203i) q^{72} +10.7072i q^{73} +(-4.84541 + 0.848956i) q^{74} -1.68420i q^{75} +(-0.170058 - 0.470405i) q^{76} +(1.01156 + 3.71114i) q^{77} +(12.0127 - 2.10472i) q^{78} -9.36521i q^{79} +(3.07531 - 2.55782i) q^{80} -8.48282 q^{81} +(13.7680 - 2.41226i) q^{82} -3.45276i q^{83} +(-7.28927 + 5.12728i) q^{84} +0.313877i q^{85} +(-2.11155 - 12.0517i) q^{86} -2.76142 q^{87} +(-2.04445 - 3.56788i) q^{88} -9.12705i q^{89} +(0.0399006 + 0.227732i) q^{90} +(3.56263 + 13.0703i) q^{91} +(-2.90343 - 8.03131i) q^{92} +15.0956i q^{93} +(-1.89846 - 10.8354i) q^{94} +0.250100i q^{95} +(6.16351 - 7.26496i) q^{96} +16.5442i q^{97} +(-6.42024 - 7.53529i) q^{98} +0.237682 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9	$ 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) $ 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9 + q^10 - 4 * q^11 + 14 * q^12 - q^14 + 9 * q^16 - 15 * q^18 + q^20 - 4 * q^21 + 6 * q^22 + 22 * q^24 + 16 * q^25 - 20 * q^26 + q^28 - 16 * q^31 - 19 * q^32 - 14 * q^34 + 15 * q^36 - 30 * q^38 + q^40 + 44 * q^42 - 4 * q^43 - 20 * q^44 - 16 * q^45 + 6 * q^46 - 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 - 38 * q^52 + 26 * q^54 - 4 * q^55 + 33 * q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 - 8 * q^61 + 28 * q^62 + 28 * q^63 - 23 * q^64 + 46 * q^66 + 20 * q^67 + 12 * q^68 - 40 * q^69 - q^70 - 13 * q^72 - 28 * q^74 + 34 * q^76 - 4 * q^77 - 6 * q^78 + 9 * q^80 + 24 * q^81 - 16 * q^82 - 42 * q^84 - 24 * q^86 + 72 * q^87 - 44 * q^88 - 15 * q^90 - 32 * q^91 - 30 * q^92 - 58 * q^94 - 30 * q^96 + 5 * q^98 + 20 * 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 $

$2$	0.244064	+	1.39299i	0.172579	+	0.984996i
$2$	0.244064	+	1.39299i	0.172579	+	0.984996i
$3$		−	1.68420i		−	0.972371i	−0.873856	−	0.486185i	$-0.838388\pi$
$3$		−	1.68420i		−	0.972371i	0.873856	−	0.486185i	$-0.161612\pi$
$4$	−1.88087	+	0.679959i	−0.940433	+	0.339980i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	2.34608	−	0.411052i	0.957781	−	0.167811i
$7$	0.695780	+	2.55262i	0.262980	+	0.964801i
$7$	0.695780	+	2.55262i	0.262980	+	0.964801i
$8$	−1.40623	−	2.45408i	−0.497178	−	0.867649i
$9$	0.163484			0.0544947
$10$	0.244064	+	1.39299i	0.0771798	+	0.440503i
$11$	1.45385			0.438353			0.219177	−	0.975685i	$-0.429663\pi$
$11$	1.45385			0.438353			0.219177	+	0.975685i	$0.429663\pi$
$12$	1.14518	+	3.16775i	0.330586	+	0.914450i
$13$	5.12034			1.42013			0.710063	−	0.704138i	$-0.248666\pi$
$13$	5.12034			1.42013			0.710063	+	0.704138i	$0.248666\pi$
$14$	−3.38598	+	1.59222i	−0.904940	+	0.425539i
$15$		−	1.68420i		−	0.434858i
$16$	3.07531	−	2.55782i	0.768828	−	0.639456i
$17$			0.313877i			0.0761263i	0.999275	+	0.0380631i	$0.0121188\pi$
$17$			0.313877i			0.0761263i	−0.999275	+	0.0380631i	$0.987881\pi$
$18$	0.0399006	+	0.227732i	0.00940466	+	0.0536770i
$19$			0.250100i			0.0573769i	0.999588	+	0.0286884i	$0.00913307\pi$
$19$			0.250100i			0.0573769i	−0.999588	+	0.0286884i	$0.990867\pi$
$20$	−1.88087	+	0.679959i	−0.420574	+	0.152044i
$21$	4.29912	−	1.17183i	0.938145	−	0.255714i
$22$	0.354833	+	2.02521i	0.0756507	+	0.431776i
$23$			4.27001i			0.890358i	0.895442	+	0.445179i	$0.146860\pi$
$23$			4.27001i			0.890358i	−0.895442	+	0.445179i	$0.853140\pi$
$24$	−4.13315	+	2.36837i	−0.843676	+	0.483441i
$25$	1.00000			0.200000
$26$	1.24969	+	7.13260i	0.245084	+	1.39882i
$27$		−	5.32793i		−	1.02536i
$28$	−3.04435	−	4.32804i	−0.575328	−	0.817923i
$29$		−	1.63961i		−	0.304468i	−0.988345	−	0.152234i	$-0.951353\pi$
$29$		−	1.63961i		−	0.304468i	0.988345	−	0.152234i	$-0.0486467\pi$
$30$	2.34608	−	0.411052i	0.428333	−	0.0750474i
$31$	−8.96308			−1.60982			−0.804909	−	0.593399i	$-0.797786\pi$
$31$	−8.96308			−1.60982			−0.804909	+	0.593399i	$0.797786\pi$
$32$	4.31361	+	3.65962i	0.762545	+	0.646935i
$33$		−	2.44857i		−	0.426242i
$34$	−0.437228	+	0.0766060i	−0.0749841	+	0.0131378i
$35$	0.695780	+	2.55262i	0.117608	+	0.431472i
$36$	−0.307492	+	0.111163i	−0.0512486	+	0.0185271i
$37$			3.47842i			0.571848i	0.958252	+	0.285924i	$0.0923005\pi$
$37$			3.47842i			0.571848i	−0.958252	+	0.285924i	$0.907699\pi$
$38$	−0.348388	+	0.0610404i	−0.0565160	+	0.00990206i
$39$		−	8.62365i		−	1.38089i
$40$	−1.40623	−	2.45408i	−0.222345	−	0.388024i
$41$		−	9.88374i		−	1.54358i	−0.635877	−	0.771790i	$-0.719362\pi$
$41$		−	9.88374i		−	1.54358i	0.635877	−	0.771790i	$-0.280638\pi$
$42$	2.68161	+	5.70265i	0.413782	+	0.879937i
$43$	−8.65164			−1.31936			−0.659681	−	0.751545i	$-0.729309\pi$
$43$	−8.65164			−1.31936			−0.659681	+	0.751545i	$0.729309\pi$
$44$	−2.73450	+	0.988561i	−0.412242	+	0.149031i
$45$	0.163484			0.0243708
$46$	−5.94810	+	1.04216i	−0.876999	+	0.153657i
$47$	−7.77853			−1.13461			−0.567307	−	0.823506i	$-0.692015\pi$
$47$	−7.77853			−1.13461			−0.567307	+	0.823506i	$0.692015\pi$
$48$	−4.30788	−	5.17943i	−0.621789	−	0.747586i
$49$	−6.03178	+	3.55213i	−0.861683	+	0.507447i
$50$	0.244064	+	1.39299i	0.0345159	+	0.196999i
$51$	0.528630			0.0740230
$52$	−9.63067	+	3.48162i	−1.33553	+	0.482814i
$53$			1.90687i			0.261929i	0.991387	+	0.130965i	$0.0418075\pi$
$53$			1.90687i			0.261929i	−0.991387	+	0.130965i	$0.958193\pi$
$54$	7.42177	−	1.30036i	1.00998	−	0.176956i
$55$	1.45385			0.196038
$56$	5.28592	−	5.29708i	0.706361	−	0.707852i
$57$	0.421218			0.0557916
$58$	2.28396	−	0.400169i	0.299899	−	0.0525448i
$59$		−	7.73295i		−	1.00674i	−0.864070	−	0.503372i	$-0.832093\pi$
$59$		−	7.73295i		−	1.00674i	0.864070	−	0.503372i	$-0.167907\pi$
$60$	1.14518	+	3.16775i	0.147843	+	0.408954i
$61$	0.415877			0.0532475			0.0266238	−	0.999646i	$-0.491524\pi$
$61$	0.415877			0.0532475			0.0266238	+	0.999646i	$0.491524\pi$
$62$	−2.18757	−	12.4855i	−0.277821	−	1.58566i
$63$	0.113749	+	0.417313i	0.0143310	+	0.0525766i
$64$	−4.04503	+	6.90201i	−0.505629	+	0.862751i
$65$	5.12034			0.635100
$66$	3.41085	−	0.597609i	0.419847	−	0.0735606i
$67$	15.2878			1.86770			0.933848	−	0.357670i	$-0.116429\pi$
$67$	15.2878			1.86770			0.933848	+	0.357670i	$0.116429\pi$
$68$	−0.213423	−	0.590360i	−0.0258814	−	0.0715916i
$69$	7.19153			0.865759
$70$	−3.38598	+	1.59222i	−0.404702	+	0.190307i
$71$		−	1.50413i		−	0.178507i	−0.996009	−	0.0892537i	$-0.971552\pi$
$71$		−	1.50413i		−	0.178507i	0.996009	−	0.0892537i	$-0.0284482\pi$
$72$	−0.229896	−	0.401203i	−0.0270936	−	0.0472823i
$73$			10.7072i			1.25318i	0.779349	+	0.626590i	$0.215550\pi$
$73$			10.7072i			1.25318i	−0.779349	+	0.626590i	$0.784450\pi$
$74$	−4.84541	+	0.848956i	−0.563268	+	0.0986892i
$75$		−	1.68420i		−	0.194474i
$76$	−0.170058	−	0.470405i	−0.0195070	−	0.0539591i
$77$	1.01156	+	3.71114i	0.115278	+	0.422924i
$78$	12.0127	−	2.10472i	1.36017	−	0.238313i
$79$		−	9.36521i		−	1.05367i	−0.849968	−	0.526834i	$-0.823379\pi$
$79$		−	9.36521i		−	1.05367i	0.849968	−	0.526834i	$-0.176621\pi$
$80$	3.07531	−	2.55782i	0.343830	−	0.285973i
$81$	−8.48282			−0.942536
$82$	13.7680	−	2.41226i	1.52042	−	0.266390i
$83$		−	3.45276i		−	0.378989i	−0.981882	−	0.189495i	$-0.939315\pi$
$83$		−	3.45276i		−	0.378989i	0.981882	−	0.189495i	$-0.0606850\pi$
$84$	−7.28927	+	5.12728i	−0.795324	+	0.559432i
$85$			0.313877i			0.0340447i
$86$	−2.11155	−	12.0517i	−0.227695	−	1.29957i
$87$	−2.76142			−0.296055
$88$	−2.04445	−	3.56788i	−0.217940	−	0.380337i
$89$		−	9.12705i		−	0.967466i	−0.875216	−	0.483733i	$-0.839281\pi$
$89$		−	9.12705i		−	0.967466i	0.875216	−	0.483733i	$-0.160719\pi$
$90$	0.0399006	+	0.227732i	0.00420589	+	0.0240051i
$91$	3.56263	+	13.0703i	0.373465	+	1.37014i
$92$	−2.90343	−	8.03131i	−0.302704	−	0.837322i
$93$			15.0956i			1.56534i
$94$	−1.89846	−	10.8354i	−0.195811	−	1.11759i
$95$			0.250100i			0.0256597i
$96$	6.16351	−	7.26496i	0.629061	−	0.741477i
$97$			16.5442i			1.67981i	0.542732	+	0.839906i	$0.317390\pi$
$97$			16.5442i			1.67981i	−0.542732	+	0.839906i	$0.682610\pi$
$98$	−6.42024	−	7.53529i	−0.648542	−	0.761179i
$99$	0.237682			0.0238879
$100$	−1.88087	+	0.679959i	−0.188087	+	0.0679959i
$101$	−11.1440			−1.10887			−0.554437	−	0.832226i	$-0.687066\pi$
$101$	−11.1440			−1.10887			−0.554437	+	0.832226i	$0.687066\pi$
$102$	0.129019	+	0.736378i	0.0127748	+	0.0729123i
$103$	−11.5479			−1.13785			−0.568923	−	0.822391i	$-0.692640\pi$
$103$	−11.5479			−1.13785			−0.568923	+	0.822391i	$0.692640\pi$
$104$	−7.20038	−	12.5657i	−0.706055	−	1.23217i
$105$	4.29912	−	1.17183i	0.419551	−	0.114359i
$106$	−2.65627	+	0.465399i	−0.257999	+	0.0452036i
$107$	−3.37404			−0.326181			−0.163091	−	0.986611i	$-0.552146\pi$
$107$	−3.37404			−0.326181			−0.163091	+	0.986611i	$0.552146\pi$
$108$	3.62277	+	10.0211i	0.348602	+	0.964282i
$109$		−	12.6125i		−	1.20805i	−0.796964	−	0.604027i	$-0.793562\pi$
$109$		−	12.6125i		−	1.20805i	0.796964	−	0.604027i	$-0.206438\pi$
$110$	0.354833	+	2.02521i	0.0338320	+	0.193096i
$111$	5.85834			0.556049
$112$	8.66890	+	6.07043i	0.819134	+	0.573602i
$113$	13.5643			1.27602			0.638009	−	0.770029i	$-0.279758\pi$
$113$	13.5643			1.27602			0.638009	+	0.770029i	$0.279758\pi$
$114$	0.102804	+	0.586754i	0.00962848	+	0.0549545i
$115$			4.27001i			0.398180i
$116$	1.11487	+	3.08388i	0.103513	+	0.286331i
$117$	0.837094			0.0773894
$118$	10.7720	−	1.88733i	0.991639	−	0.173743i
$119$	−0.801209	+	0.218389i	−0.0734467	+	0.0200197i
$120$	−4.13315	+	2.36837i	−0.377304	+	0.216201i
$121$	−8.88631			−0.807846
$122$	0.101500	+	0.579314i	0.00918942	+	0.0524486i
$123$	−16.6461			−1.50093
$124$	16.8584	−	6.09453i	1.51392	−	0.547305i
$125$	1.00000			0.0894427
$126$	−0.553553	+	0.260303i	−0.0493144	+	0.0231896i
$127$			2.17011i			0.192566i	0.995354	+	0.0962832i	$0.0306954\pi$
$127$			2.17011i			0.192566i	−0.995354	+	0.0962832i	$0.969305\pi$
$128$	−10.6017	−	3.95017i	−0.937067	−	0.349149i
$129$			14.5711i			1.28291i
$130$	1.24969	+	7.13260i	0.109605	+	0.625571i
$131$			8.82257i			0.770832i	0.922743	+	0.385416i	$0.125942\pi$
$131$			8.82257i			0.770832i	−0.922743	+	0.385416i	$0.874058\pi$
$132$	1.66493	+	4.60544i	0.144914	+	0.400852i
$133$	−0.638411	+	0.174015i	−0.0553573	+	0.0150890i
$134$	3.73119	+	21.2958i	0.322326	+	1.83967i
$135$		−	5.32793i		−	0.458555i
$136$	0.770279	−	0.441383i	0.0660509	−	0.0378483i
$137$	0.361903			0.0309195			0.0154597	−	0.999880i	$-0.495079\pi$
$137$	0.361903			0.0309195			0.0154597	+	0.999880i	$0.495079\pi$
$138$	1.75519	+	10.0178i	0.149412	+	0.852768i
$139$			8.49740i			0.720740i	0.932809	+	0.360370i	$0.117350\pi$
$139$			8.49740i			0.720740i	−0.932809	+	0.360370i	$0.882650\pi$
$140$	−3.04435	−	4.32804i	−0.257295	−	0.365786i
$141$			13.1006i			1.10327i
$142$	2.09525	−	0.367104i	0.175829	−	0.0308067i
$143$	7.44422			0.622517
$144$	0.502764	−	0.418164i	0.0418970	−	0.0348470i
$145$		−	1.63961i		−	0.136162i
$146$	−14.9150	+	2.61323i	−1.23438	+	0.216273i
$147$	5.98248	+	10.1587i	0.493427	+	0.837875i
$148$	−2.36518	−	6.54243i	−0.194417	−	0.537785i
$149$		−	14.7688i		−	1.20991i	−0.796260	−	0.604955i	$-0.793191\pi$
$149$		−	14.7688i		−	1.20991i	0.796260	−	0.604955i	$-0.206809\pi$
$150$	2.34608	−	0.411052i	0.191556	−	0.0335622i
$151$			17.6833i			1.43905i	0.694468	+	0.719523i	$0.255640\pi$
$151$			17.6833i			1.43905i	−0.694468	+	0.719523i	$0.744360\pi$
$152$	0.613766	−	0.351698i	0.0497830	−	0.0285265i
$153$			0.0513138i			0.00414848i
$154$	−4.92271	+	2.31486i	−0.396684	+	0.186536i
$155$	−8.96308			−0.719932
$156$	5.86373	+	16.2199i	0.469475	+	1.29863i
$157$	0.628228			0.0501380			0.0250690	−	0.999686i	$-0.492019\pi$
$157$	0.628228			0.0501380			0.0250690	+	0.999686i	$0.492019\pi$
$158$	13.0457	−	2.28571i	1.03786	−	0.181841i
$159$	3.21155			0.254693
$160$	4.31361	+	3.65962i	0.341021	+	0.289318i
$161$	−10.8997	+	2.97099i	−0.859019	+	0.234147i
$162$	−2.07035	−	11.8165i	−0.162662	−	0.928393i
$163$	−15.7162			−1.23099			−0.615493	−	0.788142i	$-0.711043\pi$
$163$	−15.7162			−1.23099			−0.615493	+	0.788142i	$0.711043\pi$
$164$	6.72054	+	18.5900i	0.524786	+	1.45163i
$165$		−	2.44857i		−	0.190621i
$166$	4.80967	−	0.842693i	0.373303	−	0.0654057i
$167$	18.6731			1.44497			0.722485	−	0.691386i	$-0.243000\pi$
$167$	18.6731			1.44497			0.722485	+	0.691386i	$0.243000\pi$
$168$	−8.92132	−	8.90252i	−0.688295	−	0.686845i
$169$	13.2179			1.01676
$170$	−0.437228	+	0.0766060i	−0.0335339	+	0.00587541i
$171$			0.0408874i			0.00312674i
$172$	16.2726	−	5.88276i	1.24077	−	0.448557i
$173$	−24.7373			−1.88074			−0.940372	−	0.340147i	$-0.889523\pi$
$173$	−24.7373			−1.88074			−0.940372	+	0.340147i	$0.889523\pi$
$174$	−0.673963	−	3.84664i	−0.0510930	−	0.291613i
$175$	0.695780	+	2.55262i	0.0525960	+	0.192960i
$176$	4.47105	−	3.71870i	0.337018	−	0.280308i
$177$	−13.0238			−0.978929
$178$	12.7139	−	2.22759i	0.952950	−	0.166965i
$179$	6.86464			0.513088			0.256544	−	0.966533i	$-0.417416\pi$
$179$	6.86464			0.513088			0.256544	+	0.966533i	$0.417416\pi$
$180$	−0.307492	+	0.111163i	−0.0229191	+	0.00828557i
$181$	13.8072			1.02628			0.513141	−	0.858304i	$-0.328482\pi$
$181$	13.8072			1.02628			0.513141	+	0.858304i	$0.328482\pi$
$182$	−17.3373	+	8.15271i	−1.28513	+	0.604319i
$183$		−	0.700418i		−	0.0517764i
$184$	10.4789	−	6.00462i	0.772518	−	0.442666i
$185$			3.47842i			0.255738i
$186$	−21.0281	+	3.68429i	−1.54185	+	0.270145i
$187$			0.456331i			0.0333702i
$188$	14.6304	−	5.28908i	1.06703	−	0.385746i
$189$	13.6002	−	3.70707i	0.989269	−	0.269649i
$190$	−0.348388	+	0.0610404i	−0.0252747	+	0.00442834i
$191$			6.79373i			0.491577i	0.969324	+	0.245788i	$0.0790468\pi$
$191$			6.79373i			0.491577i	−0.969324	+	0.245788i	$0.920953\pi$
$192$	11.6243	+	6.81262i	0.838914	+	0.491659i
$193$	−6.94798			−0.500127			−0.250063	−	0.968229i	$-0.580451\pi$
$193$	−6.94798			−0.500127			−0.250063	+	0.968229i	$0.580451\pi$
$194$	−23.0460	+	4.03785i	−1.65461	+	0.289901i
$195$		−	8.62365i		−	0.617553i
$196$	8.92966	−	10.7824i	0.637833	−	0.770175i
$197$		−	25.0020i		−	1.78132i	−0.454670	−	0.890660i	$-0.650243\pi$
$197$		−	25.0020i		−	1.78132i	0.454670	−	0.890660i	$-0.349757\pi$
$198$	0.0580096	+	0.331090i	0.00412256	+	0.0235295i
$199$	8.86022			0.628084			0.314042	−	0.949409i	$-0.398317\pi$
$199$	8.86022			0.628084			0.314042	+	0.949409i	$0.398317\pi$
$200$	−1.40623	−	2.45408i	−0.0994355	−	0.173530i
$201$		−	25.7476i		−	1.81609i
$202$	−2.71986	−	15.5236i	−0.191369	−	1.09224i
$203$	4.18530	−	1.14081i	0.293751	−	0.0800689i
$204$	−0.994282	+	0.359447i	−0.0696136	+	0.0251663i
$205$		−	9.88374i		−	0.690310i
$206$	−2.81842	−	16.0861i	−0.196369	−	1.12077i
$207$			0.698079i			0.0485198i
$208$	15.7466	−	13.0969i	1.09183	−	0.908109i
$209$			0.363609i			0.0251514i
$210$	2.68161	+	5.70265i	0.185049	+	0.393520i
$211$	13.6470			0.939501			0.469751	−	0.882799i	$-0.344344\pi$
$211$	13.6470			0.939501			0.469751	+	0.882799i	$0.344344\pi$
$212$	−1.29660	−	3.58657i	−0.0890507	−	0.246327i
$213$	−2.53325			−0.173576
$214$	−0.823483	−	4.70002i	−0.0562921	−	0.321287i
$215$	−8.65164			−0.590037
$216$	−13.0752	+	7.49230i	−0.889652	+	0.509786i
$217$	−6.23634	−	22.8794i	−0.423350	−	1.55315i
$218$	17.5691	−	3.07825i	1.18993	−	0.208485i
$219$	18.0330			1.21856
$220$	−2.73450	+	0.988561i	−0.184360	+	0.0666488i
$221$			1.60716i			0.108109i
$222$	1.42981	+	8.16063i	0.0959625	+	0.547705i
$223$	7.67172			0.513737			0.256868	−	0.966446i	$-0.417309\pi$
$223$	7.67172			0.513737			0.256868	+	0.966446i	$0.417309\pi$
$224$	−6.34030	+	13.5573i	−0.423629	+	0.905836i
$225$	0.163484			0.0108989
$226$	3.31055	+	18.8949i	0.220214	+	1.25687i
$227$		−	18.4879i		−	1.22708i	−0.789662	−	0.613542i	$-0.789744\pi$
$227$		−	18.4879i		−	1.22708i	0.789662	−	0.613542i	$-0.210256\pi$
$228$	−0.792254	+	0.286411i	−0.0524683	+	0.0189680i
$229$	−22.6715			−1.49817			−0.749087	−	0.662472i	$-0.769507\pi$
$229$	−22.6715			−1.49817			−0.749087	+	0.662472i	$0.769507\pi$
$230$	−5.94810	+	1.04216i	−0.392206	+	0.0687177i
$231$	6.25029	−	1.70367i	0.411239	−	0.112093i
$232$	−4.02373	+	2.30567i	−0.264171	+	0.151375i
$233$	25.4680			1.66847			0.834234	−	0.551411i	$-0.185910\pi$
$233$	25.4680			1.66847			0.834234	+	0.551411i	$0.185910\pi$
$234$	0.204305	+	1.16607i	0.0133558	+	0.0762282i
$235$	−7.77853			−0.507415
$236$	5.25809	+	14.5446i	0.342273	+	0.946775i
$237$	−15.7728			−1.02456
$238$	−0.499761	−	1.06278i	−0.0323947	−	0.0688897i
$239$			17.5044i			1.13227i	0.824314	+	0.566134i	$0.191561\pi$
$239$			17.5044i			1.13227i	−0.824314	+	0.566134i	$0.808439\pi$
$240$	−4.30788	−	5.17943i	−0.278072	−	0.334330i
$241$			20.7733i			1.33813i	0.743206	+	0.669063i	$0.233304\pi$
$241$			20.7733i			1.33813i	−0.743206	+	0.669063i	$0.766696\pi$
$242$	−2.16883	−	12.3786i	−0.139418	−	0.795725i
$243$		−	1.69705i		−	0.108866i
$244$	−0.782208	+	0.282779i	−0.0500757	+	0.0181031i
$245$	−6.03178	+	3.55213i	−0.385356	+	0.226937i
$246$	−4.06272	−	23.1880i	−0.259030	−	1.47841i
$247$			1.28060i			0.0814825i
$248$	12.6042	+	21.9961i	0.800365	+	1.39676i
$249$	−5.81512			−0.368518
$250$	0.244064	+	1.39299i	0.0154360	+	0.0881007i
$251$		−	18.9279i		−	1.19472i	−0.801973	−	0.597361i	$-0.796216\pi$
$251$		−	18.9279i		−	1.19472i	0.801973	−	0.597361i	$-0.203784\pi$
$252$	−0.497703	−	0.707566i	−0.0313523	−	0.0445725i
$253$			6.20797i			0.390292i
$254$	−3.02295	+	0.529646i	−0.189677	+	0.0332330i
$255$	0.528630			0.0331041
$256$	2.91507	−	15.7322i	0.182192	−	0.983263i
$257$		−	4.31841i		−	0.269375i	−0.990888	−	0.134688i	$-0.956997\pi$
$257$		−	4.31841i		−	0.269375i	0.990888	−	0.134688i	$-0.0430031\pi$
$258$	−20.2974	+	3.55627i	−1.26366	+	0.221404i
$259$	−8.87909	+	2.42021i	−0.551720	+	0.150385i
$260$	−9.63067	+	3.48162i	−0.597269	+	0.215921i
$261$		−	0.268050i		−	0.0165919i
$262$	−12.2898	+	2.15327i	−0.759266	+	0.133030i
$263$		−	1.43331i		−	0.0883814i	−0.999023	−	0.0441907i	$-0.985929\pi$
$263$		−	1.43331i		−	0.0883814i	0.999023	−	0.0441907i	$-0.0140709\pi$
$264$	−6.00900	+	3.44326i	−0.369828	+	0.211918i
$265$			1.90687i			0.117138i
$266$	−0.398215	−	0.846833i	−0.0244161	−	0.0519226i
$267$	−15.3717			−0.940736
$268$	−28.7542	+	10.3951i	−1.75644	+	0.634979i
$269$	−12.1457			−0.740537			−0.370268	−	0.928925i	$-0.620734\pi$
$269$	−12.1457			−0.740537			−0.370268	+	0.928925i	$0.620734\pi$
$270$	7.42177	−	1.30036i	0.451675	−	0.0791371i
$271$	−6.48716			−0.394067			−0.197034	−	0.980397i	$-0.563131\pi$
$271$	−6.48716			−0.394067			−0.197034	+	0.980397i	$0.563131\pi$
$272$	0.802841	+	0.965268i	0.0486794	+	0.0585280i
$273$	22.0129	−	6.00017i	1.33228	−	0.363147i
$274$	0.0883275	+	0.504129i	0.00533606	+	0.0304555i
$275$	1.45385			0.0876707
$276$	−13.5263	+	4.88995i	−0.814188	+	0.294340i
$277$			23.8861i			1.43518i	0.696467	+	0.717589i	$0.254754\pi$
$277$			23.8861i			1.43518i	−0.696467	+	0.717589i	$0.745246\pi$
$278$	−11.8368	+	2.07391i	−0.709926	+	0.124385i
$279$	−1.46532			−0.0877265
$280$	5.28592	−	5.29708i	0.315894	−	0.316561i
$281$	−14.4015			−0.859120			−0.429560	−	0.903038i	$-0.641331\pi$
$281$	−14.4015			−0.859120			−0.429560	+	0.903038i	$0.641331\pi$
$282$	−18.2490	+	3.19737i	−1.08671	+	0.190401i
$283$		−	24.0556i		−	1.42996i	−0.699146	−	0.714979i	$-0.746436\pi$
$283$		−	24.0556i		−	1.42996i	0.699146	−	0.714979i	$-0.253564\pi$
$284$	1.02275	+	2.82907i	0.0606889	+	0.167874i
$285$	0.421218			0.0249508
$286$	1.81687	+	10.3698i	0.107434	+	0.613177i
$287$	25.2295	−	6.87691i	1.48925	−	0.405931i
$288$	0.705206	+	0.598289i	0.0415547	+	0.0352545i
$289$	16.9015			0.994205
$290$	2.28396	−	0.400169i	0.134119	−	0.0234987i
$291$	27.8637			1.63340
$292$	−7.28044	−	20.1387i	−0.426055	−	1.17853i
$293$	−4.78803			−0.279720			−0.139860	−	0.990171i	$-0.544665\pi$
$293$	−4.78803			−0.279720			−0.139860	+	0.990171i	$0.544665\pi$
$294$	−12.6909	+	10.8129i	−0.740148	+	0.630623i
$295$		−	7.73295i		−	0.450230i
$296$	8.53632	−	4.89146i	0.496163	−	0.284310i
$297$		−	7.74603i		−	0.449470i
$298$	20.5729	−	3.60454i	1.19176	−	0.208805i
$299$			21.8639i			1.26442i
$300$	1.14518	+	3.16775i	0.0661173	+	0.182890i
$301$	−6.01964	−	22.0844i	−0.346966	−	1.27292i
$302$	−24.6327	+	4.31586i	−1.41745	+	0.248350i
$303$			18.7688i			1.07824i
$304$	0.639712	+	0.769135i	0.0366900	+	0.0441129i
$305$	0.415877			0.0238130
$306$	−0.0714799	+	0.0125239i	−0.00408623	+	0.000715942i
$307$			23.6121i			1.34762i	0.738907	+	0.673808i	$0.235342\pi$
$307$			23.6121i			1.34762i	−0.738907	+	0.673808i	$0.764658\pi$
$308$	−4.42604	−	6.29234i	−0.252197	−	0.358539i
$309$			19.4489i			1.10641i
$310$	−2.18757	−	12.4855i	−0.124245	−	0.709130i
$311$	23.6203			1.33939			0.669693	−	0.742638i	$-0.266426\pi$
$311$	23.6203			1.33939			0.669693	+	0.742638i	$0.266426\pi$
$312$	−21.1631	+	12.1269i	−1.19813	+	0.686548i
$313$		−	20.6514i		−	1.16728i	−0.812011	−	0.583642i	$-0.801627\pi$
$313$		−	20.6514i		−	1.16728i	0.812011	−	0.583642i	$-0.198373\pi$
$314$	0.153328	+	0.875117i	0.00865278	+	0.0493857i
$315$	0.113749	+	0.417313i	0.00640903	+	0.0235130i
$316$	6.36796	+	17.6147i	0.358226	+	0.990904i
$317$		−	13.1857i		−	0.740580i	−0.928916	−	0.370290i	$-0.879258\pi$
$317$		−	13.1857i		−	0.740580i	0.928916	−	0.370290i	$-0.120742\pi$
$318$	0.783824	+	4.47367i	0.0439547	+	0.250871i
$319$		−	2.38375i		−	0.133464i
$320$	−4.04503	+	6.90201i	−0.226124	+	0.385834i
$321$			5.68255i			0.317169i
$322$	−6.79880	−	14.4581i	−0.378882	−	0.805721i
$323$	−0.0785006			−0.00436789
$324$	15.9550	−	5.76797i	0.886391	−	0.320443i
$325$	5.12034			0.284025
$326$	−3.83575	−	21.8926i	−0.212443	−	1.21252i
$327$	−21.2419			−1.17468
$328$	−24.2555	+	13.8988i	−1.33929	+	0.767434i
$329$	−5.41214	−	19.8557i	−0.298381	−	1.09468i
$330$	3.41085	−	0.597609i	0.187761	−	0.0328973i
$331$	4.29166			0.235891			0.117945	−	0.993020i	$-0.462369\pi$
$331$	4.29166			0.235891			0.117945	+	0.993020i	$0.462369\pi$
$332$	2.34773	+	6.49417i	0.128849	+	0.356414i
$333$			0.568666i			0.0311627i
$334$	4.55744	+	26.0116i	0.249372	+	1.42329i
$335$	15.2878			0.835259
$336$	10.2238	−	14.6001i	0.557754	−	0.796503i
$337$	−23.8194			−1.29752			−0.648762	−	0.760991i	$-0.724713\pi$
$337$	−23.8194			−1.29752			−0.648762	+	0.760991i	$0.724713\pi$
$338$	3.22601	+	18.4124i	0.175472	+	1.00150i
$339$		−	22.8449i		−	1.24076i
$340$	−0.213423	−	0.590360i	−0.0115745	−	0.0320168i
$341$	−13.0310			−0.705669
$342$	−0.0569559	+	0.00997914i	−0.00307982	+	0.000539610i
$343$	−13.2640	−	12.9254i	−0.716191	−	0.697904i
$344$	12.1662	+	21.2318i	0.655958	+	1.14474i
$345$	7.19153			0.387179
$346$	−6.03749	−	34.4590i	−0.324578	−	1.85253i
$347$	−1.81968			−0.0976858			−0.0488429	−	0.998806i	$-0.515553\pi$
$347$	−1.81968			−0.0976858			−0.0488429	+	0.998806i	$0.515553\pi$
$348$	5.19386	−	1.87765i	0.278420	−	0.100653i
$349$	8.94236			0.478673			0.239337	−	0.970937i	$-0.423070\pi$
$349$	8.94236			0.478673			0.239337	+	0.970937i	$0.423070\pi$
$350$	−3.38598	+	1.59222i	−0.180988	+	0.0851078i
$351$		−	27.2808i		−	1.45614i
$352$	6.27135	+	5.32055i	0.334264	+	0.283586i
$353$			16.0890i			0.856331i	0.903700	+	0.428165i	$0.140840\pi$
$353$			16.0890i			0.856331i	−0.903700	+	0.428165i	$0.859160\pi$
$354$	−3.17864	−	18.1421i	−0.168943	−	0.964240i
$355$		−	1.50413i		−	0.0798310i
$356$	6.20603	+	17.1668i	0.328919	+	0.909837i
$357$	0.367810	+	1.34939i	0.0194666	+	0.0714175i
$358$	1.67541	+	9.56241i	0.0885483	+	0.505389i
$359$		−	10.1838i		−	0.537481i	−0.963213	−	0.268740i	$-0.913393\pi$
$359$		−	10.1838i		−	0.537481i	0.963213	−	0.268740i	$-0.0866073\pi$
$360$	−0.229896	−	0.401203i	−0.0121166	−	0.0211453i
$361$	18.9374			0.996708
$362$	3.36984	+	19.2334i	0.177115	+	1.01088i
$363$			14.9663i			0.785526i
$364$	−15.5881	−	22.1610i	−0.817039	−	1.16155i
$365$			10.7072i			0.560439i
$366$	0.975678	−	0.170947i	0.0509995	−	0.00893553i
$367$	−3.78238			−0.197438			−0.0987192	−	0.995115i	$-0.531475\pi$
$367$	−3.78238			−0.197438			−0.0987192	+	0.995115i	$0.531475\pi$
$368$	10.9219	+	13.1316i	0.569345	+	0.684532i
$369$		−	1.61583i		−	0.0841169i
$370$	−4.84541	+	0.848956i	−0.251901	+	0.0441351i
$371$	−4.86753	+	1.32677i	−0.252710	+	0.0688822i
$372$	−10.2644	−	28.3928i	−0.532184	−	1.47210i
$373$			2.84339i			0.147225i	0.997287	+	0.0736127i	$0.0234529\pi$
$373$			2.84339i			0.147225i	−0.997287	+	0.0736127i	$0.976547\pi$
$374$	−0.635666	+	0.111374i	−0.0328695	+	0.00575901i
$375$		−	1.68420i		−	0.0869715i
$376$	10.9384	+	19.0891i	0.564105	+	0.984447i
$377$		−	8.39535i		−	0.432383i
$378$	8.48324	+	18.0402i	0.436331	+	0.927889i
$379$	5.22176			0.268224			0.134112	−	0.990966i	$-0.457182\pi$
$379$	5.22176			0.268224			0.134112	+	0.990966i	$0.457182\pi$
$380$	−0.170058	−	0.470405i	−0.00872379	−	0.0241312i
$381$	3.65490			0.187246
$382$	−9.46362	+	1.65810i	−0.484201	+	0.0848360i
$383$	25.8702			1.32191			0.660953	−	0.750428i	$-0.270152\pi$
$383$	25.8702			1.32191			0.660953	+	0.750428i	$0.270152\pi$
$384$	−6.65286	+	17.8553i	−0.339502	+	0.911177i
$385$	1.01156	+	3.71114i	0.0515540	+	0.189137i
$386$	−1.69575	−	9.67850i	−0.0863115	−	0.492623i
$387$	−1.41441			−0.0718983
$388$	−11.2494	−	31.1175i	−0.571102	−	1.57975i
$389$			26.1792i			1.32734i	0.748025	+	0.663670i	$0.231002\pi$
$389$			26.1792i			1.32734i	−0.748025	+	0.663670i	$0.768998\pi$
$390$	12.0127	−	2.10472i	0.608287	−	0.106577i
$391$	−1.34026			−0.0677797
$392$	17.1993	+	9.80736i	0.868695	+	0.495347i
$393$	14.8589			0.749534
$394$	34.8277	−	6.10209i	1.75459	−	0.307419i
$395$		−	9.36521i		−	0.471215i
$396$	−0.447048	+	0.161614i	−0.0224650	+	0.00812141i
$397$	30.6192			1.53674			0.768368	−	0.640009i	$-0.221069\pi$
$397$	30.6192			1.53674			0.768368	+	0.640009i	$0.221069\pi$
$398$	2.16246	+	12.3422i	0.108394	+	0.618660i
$399$	0.293075	+	1.07521i	0.0146721	+	0.0538278i
$400$	3.07531	−	2.55782i	0.153766	−	0.127891i
$401$	−32.6992			−1.63292			−0.816461	−	0.577401i	$-0.804067\pi$
$401$	−32.6992			−1.63292			−0.816461	+	0.577401i	$0.804067\pi$
$402$	35.8662	−	6.28406i	1.78884	−	0.313420i
$403$	−45.8940			−2.28614
$404$	20.9604	−	7.57750i	1.04282	−	0.376995i
$405$	−8.48282			−0.421515
$406$	2.61062	+	5.55167i	0.129563	+	0.275525i
$407$			5.05711i			0.250672i
$408$	−0.743376	−	1.29730i	−0.0368026	−	0.0642259i
$409$		−	15.2212i		−	0.752642i	−0.926489	−	0.376321i	$-0.877189\pi$
$409$		−	15.2212i		−	0.752642i	0.926489	−	0.376321i	$-0.122811\pi$
$410$	13.7680	−	2.41226i	0.679952	−	0.119133i
$411$		−	0.609516i		−	0.0300652i
$412$	21.7200	−	7.85209i	1.07007	−	0.386845i
$413$	19.7393	−	5.38043i	0.971308	−	0.264754i
$414$	−0.972419	+	0.170376i	−0.0477918	+	0.00837351i
$415$		−	3.45276i		−	0.169489i
$416$	22.0871	+	18.7385i	1.08291	+	0.918730i
$417$	14.3113			0.700827
$418$	−0.506505	+	0.0887438i	−0.0247740	+	0.00434060i
$419$			1.51292i			0.0739111i	0.999317	+	0.0369555i	$0.0117660\pi$
$419$			1.51292i			0.0739111i	−0.999317	+	0.0369555i	$0.988234\pi$
$420$	−7.28927	+	5.12728i	−0.355680	+	0.250186i
$421$		−	4.42587i		−	0.215704i	−0.994167	−	0.107852i	$-0.965603\pi$
$421$		−	4.42587i		−	0.215704i	0.994167	−	0.107852i	$-0.0343973\pi$
$422$	3.33075	+	19.0103i	0.162138	+	0.925405i
$423$	−1.27167			−0.0618305
$424$	4.67963	−	2.68151i	0.227263	−	0.130225i
$425$			0.313877i			0.0152253i
$426$	−0.618275	−	3.52880i	−0.0299555	−	0.170971i
$427$	0.289359	+	1.06158i	0.0140030	+	0.0513733i
$428$	6.34612	−	2.29421i	0.306751	−	0.110895i
$429$		−	12.5375i		−	0.605318i
$430$	−2.11155	−	12.0517i	−0.101828	−	0.581184i
$431$			15.7807i			0.760128i	0.924960	+	0.380064i	$0.124098\pi$
$431$			15.7807i			0.760128i	−0.924960	+	0.380064i	$0.875902\pi$
$432$	−13.6279	−	16.3850i	−0.655673	−	0.788325i
$433$			38.5048i			1.85042i	0.379452	+	0.925211i	$0.376112\pi$
$433$			38.5048i			1.85042i	−0.379452	+	0.925211i	$0.623888\pi$
$434$	30.3488	−	14.2712i	1.45679	−	0.685040i
$435$	−2.76142			−0.132400
$436$	8.57596	+	23.7223i	0.410714	+	1.13609i
$437$	−1.06793			−0.0510860
$438$	4.40120	+	25.1198i	0.210297	+	1.20027i
$439$	8.16215			0.389558			0.194779	−	0.980847i	$-0.437601\pi$
$439$	8.16215			0.389558			0.194779	+	0.980847i	$0.437601\pi$
$440$	−2.04445	−	3.56788i	−0.0974655	−	0.170092i
$441$	−0.986100	+	0.580717i	−0.0469572	+	0.0276532i
$442$	−2.23876	+	0.392249i	−0.106487	+	0.0186574i
$443$	14.4962			0.688735			0.344368	−	0.938835i	$-0.388093\pi$
$443$	14.4962			0.688735			0.344368	+	0.938835i	$0.388093\pi$
$444$	−11.0187	+	3.98343i	−0.522926	+	0.189045i
$445$		−	9.12705i		−	0.432664i
$446$	1.87239	+	10.6867i	0.0886603	+	0.506028i
$447$	−24.8736			−1.17648
$448$	−20.4327	−	5.52316i	−0.965354	−	0.260945i
$449$	−26.2203			−1.23741			−0.618705	−	0.785623i	$-0.712342\pi$
$449$	−26.2203			−1.23741			−0.618705	+	0.785623i	$0.712342\pi$
$450$	0.0399006	+	0.227732i	0.00188093	+	0.0107354i
$451$		−	14.3695i		−	0.676634i
$452$	−25.5126	+	9.22315i	−1.20001	+	0.433820i
$453$	29.7821			1.39929
$454$	25.7535	−	4.51222i	1.20867	−	0.211769i
$455$	3.56263	+	13.0703i	0.167019	+	0.612745i
$456$	−0.592329	−	1.03370i	−0.0277384	−	0.0484075i
$457$	−10.8518			−0.507624			−0.253812	−	0.967254i	$-0.581684\pi$
$457$	−10.8518			−0.507624			−0.253812	+	0.967254i	$0.581684\pi$
$458$	−5.53329	−	31.5812i	−0.258554	−	1.47569i
$459$	1.67231			0.0780568
$460$	−2.90343	−	8.03131i	−0.135373	−	0.374462i
$461$	−10.9727			−0.511049			−0.255525	−	0.966803i	$-0.582248\pi$
$461$	−10.9727			−0.511049			−0.255525	+	0.966803i	$0.582248\pi$
$462$	3.89867	+	8.29081i	0.181383	+	0.385724i
$463$		−	12.8266i		−	0.596102i	−0.954550	−	0.298051i	$-0.903663\pi$
$463$		−	12.8266i		−	0.596102i	0.954550	−	0.298051i	$-0.0963365\pi$
$464$	−4.19383	−	5.04230i	−0.194694	−	0.234083i
$465$			15.0956i			0.700041i
$466$	6.21583	+	35.4768i	0.287943	+	1.64343i
$467$			27.2475i			1.26087i	0.776244	+	0.630433i	$0.217122\pi$
$467$			27.2475i			1.26087i	−0.776244	+	0.630433i	$0.782878\pi$
$468$	−1.57446	+	0.569190i	−0.0727795	+	0.0263108i
$469$	10.6369	+	39.0239i	0.491167	+	1.80196i
$470$	−1.89846	−	10.8354i	−0.0875693	−	0.499802i
$471$		−	1.05806i		−	0.0487527i
$472$	−18.9773	+	10.8743i	−0.873500	+	0.500531i
$473$	−12.5782			−0.578347
$474$	−3.84958	−	21.9715i	−0.176817	−	1.00918i
$475$			0.250100i			0.0114754i
$476$	1.35847	−	0.955550i	0.0622654	−	0.0437976i
$477$			0.311744i			0.0142738i
$478$	−24.3836	+	4.27220i	−1.11528	+	0.195406i
$479$	−5.93280			−0.271076			−0.135538	−	0.990772i	$-0.543276\pi$
$479$	−5.93280			−0.271076			−0.135538	+	0.990772i	$0.543276\pi$
$480$	6.16351	−	7.26496i	0.281325	−	0.331599i
$481$			17.8107i			0.812097i
$482$	−28.9371	+	5.07002i	−1.31805	+	0.230933i
$483$	5.00372	+	18.3573i	0.227677	+	0.835285i
$484$	16.7140	−	6.04233i	0.759725	−	0.274651i
$485$			16.5442i			0.751235i
$486$	2.36398	−	0.414189i	0.107232	−	0.0187880i
$487$			0.799878i			0.0362459i	0.999836	+	0.0181230i	$0.00576903\pi$
$487$			0.799878i			0.0362459i	−0.999836	+	0.0181230i	$0.994231\pi$
$488$	−0.584819	−	1.02059i	−0.0264735	−	0.0462002i
$489$			26.4691i			1.19698i
$490$	−6.42024	−	7.53529i	−0.290037	−	0.340410i
$491$	35.4782			1.60111			0.800555	−	0.599259i	$-0.204538\pi$
$491$	35.4782			1.60111			0.800555	+	0.599259i	$0.204538\pi$
$492$	31.3092	−	11.3187i	1.41153	−	0.510287i
$493$	0.514635			0.0231780
$494$	−1.78386	+	0.312548i	−0.0802599	+	0.0140622i
$495$	0.237682			0.0106830
$496$	−27.5643	+	22.9260i	−1.23767	+	1.02941i
$497$	3.83948	−	1.04654i	0.172224	−	0.0469439i
$498$	−1.41926	−	8.10043i	−0.0635986	−	0.362989i
$499$	−13.8343			−0.619306			−0.309653	−	0.950850i	$-0.600213\pi$
$499$	−13.8343			−0.619306			−0.309653	+	0.950850i	$0.600213\pi$
$500$	−1.88087	+	0.679959i	−0.0841149	+	0.0304087i
$501$		−	31.4492i		−	1.40505i
$502$	26.3665	−	4.61963i	1.17680	−	0.206184i
$503$	−24.9750			−1.11358			−0.556790	−	0.830653i	$-0.687967\pi$
$503$	−24.9750			−1.11358			−0.556790	+	0.830653i	$0.687967\pi$
$504$	0.864164	−	0.865988i	0.0384929	−	0.0385742i
$505$	−11.1440			−0.495903
$506$	−8.64766	+	1.51514i	−0.384436	+	0.0673562i
$507$		−	22.2615i		−	0.988668i
$508$	−1.47559	−	4.08169i	−0.0654687	−	0.181096i
$509$	−6.97858			−0.309320			−0.154660	−	0.987968i	$-0.549428\pi$
$509$	−6.97858			−0.309320			−0.154660	+	0.987968i	$0.549428\pi$
$510$	0.129019	+	0.736378i	0.00571308	+	0.0326074i
$511$	−27.3314	+	7.44983i	−1.20907	+	0.329561i
$512$	22.6263	+	0.221009i	0.999952	+	0.00976731i
$513$	1.33251			0.0588320
$514$	6.01552	−	1.05397i	0.265333	−	0.0464886i
$515$	−11.5479			−0.508860
$516$	−9.90773	−	27.4062i	−0.436163	−	1.20649i
$517$	−11.3088			−0.497362
$518$	−5.53841	−	11.7778i	−0.243344	−	0.517488i
$519$			41.6625i			1.82878i
$520$	−7.20038	−	12.5657i	−0.315758	−	0.551044i
$521$			16.4401i			0.720253i	0.932904	+	0.360126i	$0.117266\pi$
$521$			16.4401i			0.720253i	−0.932904	+	0.360126i	$0.882734\pi$
$522$	0.373392	−	0.0654213i	0.0163429	−	0.00286341i
$523$			23.0349i			1.00725i	0.863923	+	0.503624i	$0.168000\pi$
$523$			23.0349i			1.00725i	−0.863923	+	0.503624i	$0.832000\pi$
$524$	−5.99899	−	16.5941i	−0.262067	−	0.724915i
$525$	4.29912	−	1.17183i	0.187629	−	0.0511429i
$526$	1.99659	−	0.349818i	0.0870553	−	0.0152528i
$527$		−	2.81330i		−	0.122549i
$528$	−6.26302	−	7.53013i	−0.272563	−	0.327707i
$529$	4.76703			0.207262
$530$	−2.65627	+	0.465399i	−0.115381	+	0.0202157i
$531$		−	1.26421i		−	0.0548622i
$532$	1.08244	−	0.761392i	0.0469299	−	0.0330105i
$533$		−	50.6081i		−	2.19208i
$534$	−3.75169	−	21.4128i	−0.162351	−	0.926620i
$535$	−3.37404			−0.145873
$536$	−21.4981	−	37.5174i	−0.928577	−	1.62050i
$537$		−	11.5614i		−	0.498911i
$538$	−2.96433	−	16.9189i	−0.127801	−	0.729425i
$539$	−8.76933	+	5.16428i	−0.377722	+	0.222441i
$540$	3.62277	+	10.0211i	0.155899	+	0.431240i
$541$			12.6920i			0.545671i	0.962061	+	0.272835i	$0.0879615\pi$
$541$			12.6920i			0.545671i	−0.962061	+	0.272835i	$0.912039\pi$
$542$	−1.58328	−	9.03658i	−0.0680078	−	0.388154i
$543$		−	23.2540i		−	0.997926i
$544$	−1.14867	+	1.35394i	−0.0492488	+	0.0580497i
$545$		−	12.6125i		−	0.540258i
$546$	13.7308	+	29.1995i	0.587623	+	1.24962i
$547$	21.0334			0.899321			0.449661	−	0.893199i	$-0.351545\pi$
$547$	21.0334			0.899321			0.449661	+	0.893199i	$0.351545\pi$
$548$	−0.680691	+	0.246079i	−0.0290777	+	0.0105120i
$549$	0.0679892			0.00290171
$550$	0.354833	+	2.02521i	0.0151301	+	0.0863552i
$551$	0.410066			0.0174694
$552$	−10.1130	−	17.6486i	−0.430436	−	0.751174i
$553$	23.9059	−	6.51613i	1.01658	−	0.277094i
$554$	−33.2732	+	5.82974i	−1.41364	+	0.247682i
$555$	5.85834			0.248672
$556$	−5.77789	−	15.9825i	−0.245037	−	0.677808i
$557$		−	0.724648i		−	0.0307043i	−0.999882	−	0.0153522i	$-0.995113\pi$
$557$		−	0.724648i		−	0.0307043i	0.999882	−	0.0153522i	$-0.00488694\pi$
$558$	−0.357632	−	2.04118i	−0.0151398	−	0.0864102i
$559$	−44.2993			−1.87366
$560$	8.66890	+	6.07043i	0.366328	+	0.256522i
$561$	0.768550			0.0324482
$562$	−3.51488	−	20.0612i	−0.148266	−	0.846230i
$563$		−	8.62465i		−	0.363486i	−0.983346	−	0.181743i	$-0.941826\pi$
$563$		−	8.62465i		−	0.363486i	0.983346	−	0.181743i	$-0.0581739\pi$
$564$	−8.90785	−	24.6404i	−0.375088	−	1.03755i
$565$	13.5643			0.570653
$566$	33.5093	−	5.87111i	1.40850	−	0.246781i
$567$	−5.90218	−	21.6535i	−0.247868	−	0.909360i
$568$	−3.69126	+	2.11516i	−0.154882	+	0.0887499i
$569$	2.20005			0.0922311			0.0461155	−	0.998936i	$-0.485316\pi$
$569$	2.20005			0.0922311			0.0461155	+	0.998936i	$0.485316\pi$
$570$	0.102804	+	0.586754i	0.00430599	+	0.0245764i
$571$	22.8120			0.954654			0.477327	−	0.878726i	$-0.341606\pi$
$571$	22.8120			0.954654			0.477327	+	0.878726i	$0.341606\pi$
$572$	−14.0016	+	5.06177i	−0.585436	+	0.211643i
$573$	11.4420			0.477995
$574$	15.7371	+	33.4661i	0.656854	+	1.39685i
$575$			4.27001i			0.178072i
$576$	−0.661298	+	1.12837i	−0.0275541	+	0.0470154i
$577$			19.6510i			0.818081i	0.912516	+	0.409040i	$0.134136\pi$
$577$			19.6510i			0.818081i	−0.912516	+	0.409040i	$0.865864\pi$
$578$	4.12504	+	23.5437i	0.171579	+	0.979287i
$579$			11.7018i			0.486309i
$580$	1.11487	+	3.08388i	0.0462923	+	0.128051i
$581$	8.81359	−	2.40236i	0.365649	−	0.0996667i
$582$	6.80053	+	38.8140i	0.281891	+	1.60889i
$583$			2.77232i			0.114818i
$584$	26.2763	−	15.0568i	1.08732	−	0.623053i
$585$	0.837094			0.0346096
$586$	−1.16859	−	6.66970i	−0.0482738	−	0.275523i
$587$			24.2904i			1.00257i	0.865281	+	0.501287i	$0.167140\pi$
$587$			24.2904i			1.00257i	−0.865281	+	0.501287i	$0.832860\pi$
$588$	−18.1598	−	15.0393i	−0.748895	−	0.620210i
$589$		−	2.24167i		−	0.0923663i
$590$	10.7720	−	1.88733i	0.443474	−	0.0777003i
$591$	−42.1083			−1.73210
$592$	8.89718	+	10.6972i	0.365672	+	0.439653i
$593$			25.4337i			1.04444i	0.852811	+	0.522219i	$0.174896\pi$
$593$			25.4337i			1.04444i	−0.852811	+	0.522219i	$0.825104\pi$
$594$	10.7902	−	1.89053i	0.442726	−	0.0775692i
$595$	−0.801209	+	0.218389i	−0.0328464	+	0.00895308i
$596$	10.0422	+	27.7782i	0.411345	+	1.13784i
$597$		−	14.9223i		−	0.610731i
$598$	−30.4563	+	5.33619i	−1.24545	+	0.218213i
$599$		−	4.24448i		−	0.173425i	−0.996233	−	0.0867124i	$-0.972364\pi$
$599$		−	4.24448i		−	0.173425i	0.996233	−	0.0867124i	$-0.0276361\pi$
$600$	−4.13315	+	2.36837i	−0.168735	+	0.0966882i
$601$			1.00464i			0.0409800i	0.999790	+	0.0204900i	$0.00652263\pi$
$601$			1.00464i			0.0409800i	−0.999790	+	0.0204900i	$0.993477\pi$
$602$	29.2942	−	13.7753i	1.19394	−	0.561440i
$603$	2.49930			0.101780
$604$	−12.0239	−	33.2599i	−0.489247	−	1.35333i
$605$	−8.88631			−0.361280
$606$	−26.1448	+	4.58078i	−1.06206	+	0.186081i
$607$	−31.5181			−1.27928			−0.639640	−	0.768675i	$-0.720917\pi$
$607$	−31.5181			−1.27928			−0.639640	+	0.768675i	$0.720917\pi$
$608$	−0.915270	+	1.07883i	−0.0371191	+	0.0437525i
$609$	−1.92134	−	7.04887i	−0.0778567	−	0.285635i
$610$	0.101500	+	0.579314i	0.00410963	+	0.0234557i
$611$	−39.8287			−1.61130
$612$	−0.0348913	−	0.0965145i	−0.00141040	−	0.00390137i
$613$		−	22.3851i		−	0.904126i	−0.891986	−	0.452063i	$-0.850688\pi$
$613$		−	22.3851i		−	0.904126i	0.891986	−	0.452063i	$-0.149312\pi$
$614$	−32.8916	+	5.76287i	−1.32740	+	0.232570i
$615$	−16.6461			−0.671237
$616$	7.68495	−	7.70118i	0.309636	−	0.310289i
$617$	27.1721			1.09391			0.546954	−	0.837163i	$-0.315787\pi$
$617$	27.1721			1.09391			0.546954	+	0.837163i	$0.315787\pi$
$618$	−27.0922	+	4.74677i	−1.08981	+	0.190943i
$619$			16.7190i			0.671993i	0.941863	+	0.335997i	$0.109073\pi$
$619$			16.7190i			0.671993i	−0.941863	+	0.335997i	$0.890927\pi$
$620$	16.8584	−	6.09453i	0.677048	−	0.244762i
$621$	22.7503			0.912938
$622$	5.76487	+	32.9030i	0.231150	+	1.31929i
$623$	23.2979	−	6.35042i	0.933412	−	0.254424i
$624$	−22.0578	−	26.5204i	−0.883018	−	1.06167i
$625$	1.00000			0.0400000
$626$	28.7672	−	5.04026i	1.14977	−	0.201449i
$627$	0.612389			0.0244564
$628$	−1.18161	+	0.427169i	−0.0471514	+	0.0170459i
$629$	−1.09179			−0.0435327
$630$	−0.553553	+	0.260303i	−0.0220541	+	0.0103707i
$631$		−	25.9280i		−	1.03218i	−0.856535	−	0.516090i	$-0.827387\pi$
$631$		−	25.9280i		−	1.03218i	0.856535	−	0.516090i	$-0.172613\pi$
$632$	−22.9830	+	13.1696i	−0.914214	+	0.523860i
$633$		−	22.9843i		−	0.913544i
$634$	18.3675	−	3.21814i	0.729468	−	0.127809i
$635$			2.17011i			0.0861183i
$636$	−6.04049	+	2.18372i	−0.239521	+	0.0865903i
$637$	−30.8848	+	18.1881i	−1.22370	+	0.720639i
$638$	3.32055	−	0.581788i	0.131462	−	0.0230332i
$639$		−	0.245901i		−	0.00972771i
$640$	−10.6017	−	3.95017i	−0.419069	−	0.156144i
$641$	40.1639			1.58638			0.793189	−	0.608975i	$-0.208419\pi$
$641$	40.1639			1.58638			0.793189	+	0.608975i	$0.208419\pi$
$642$	−7.91576	+	1.38691i	−0.312410	+	0.0547368i
$643$		−	40.5245i		−	1.59813i	−0.601244	−	0.799065i	$-0.705328\pi$
$643$		−	40.5245i		−	1.59813i	0.601244	−	0.799065i	$-0.294672\pi$
$644$	18.4808	−	12.9994i	0.728244	−	0.512248i
$645$			14.5711i			0.573735i
$646$	−0.0191592	−	0.109351i	−0.000753807	−	0.00430235i
$647$	14.3559			0.564387			0.282193	−	0.959358i	$-0.408938\pi$
$647$	14.3559			0.564387			0.282193	+	0.959358i	$0.408938\pi$
$648$	11.9288	+	20.8175i	0.468608	+	0.817790i
$649$		−	11.2426i		−	0.441310i
$650$	1.24969	+	7.13260i	0.0490169	+	0.279764i
$651$	−38.5334	+	10.5032i	−1.51024	+	0.411653i
$652$	29.5600	−	10.6864i	1.15766	−	0.418510i
$653$			34.5999i			1.35400i	0.735984	+	0.676999i	$0.236720\pi$
$653$			34.5999i			1.35400i	−0.735984	+	0.676999i	$0.763280\pi$
$654$	−5.18437	−	29.5898i	−0.202725	−	1.15705i
$655$			8.82257i			0.344726i
$656$	−25.2809	−	30.3956i	−0.987052	−	1.18675i
$657$			1.75045i			0.0682916i
$658$	26.3379	−	12.3851i	1.02676	−	0.482823i
$659$	−10.6325			−0.414185			−0.207092	−	0.978321i	$-0.566400\pi$
$659$	−10.6325			−0.414185			−0.207092	+	0.978321i	$0.566400\pi$
$660$	1.66493	+	4.60544i	0.0648074	+	0.179266i
$661$	16.0278			0.623410			0.311705	−	0.950179i	$-0.399100\pi$
$661$	16.0278			0.623410			0.311705	+	0.950179i	$0.399100\pi$
$662$	1.04744	+	5.97825i	0.0407099	+	0.232351i
$663$	2.70676			0.105122
$664$	−8.47334	+	4.85537i	−0.328830	+	0.188425i
$665$	−0.638411	+	0.174015i	−0.0247565	+	0.00674800i
$666$	−0.792148	+	0.138791i	−0.0306951	+	0.00537804i
$667$	7.00114			0.271085
$668$	−35.1217	+	12.6970i	−1.35890	+	0.491261i
$669$		−	12.9207i		−	0.499542i
$670$	3.73119	+	21.2958i	0.144148	+	0.822727i
$671$	0.604624			0.0233412
$672$	22.8332	+	10.6783i	0.880808	+	0.411925i
$673$	−24.0119			−0.925591			−0.462796	−	0.886465i	$-0.653154\pi$
$673$	−24.0119			−0.925591			−0.462796	+	0.886465i	$0.653154\pi$
$674$	−5.81345	−	33.1803i	−0.223926	−	1.27806i
$675$		−	5.32793i		−	0.205072i
$676$	−24.8610	+	8.98762i	−0.956194	+	0.345678i
$677$	32.1429			1.23535			0.617676	−	0.786432i	$-0.288074\pi$
$677$	32.1429			1.23535			0.617676	+	0.786432i	$0.288074\pi$
$678$	31.8228	−	5.57561i	1.22215	−	0.214130i
$679$	−42.2312	+	11.5111i	−1.62068	+	0.441757i
$680$	0.770279	−	0.441383i	0.0295388	−	0.0169263i
$681$	−31.1372			−1.19318
$682$	−3.18040	−	18.1521i	−0.121784	−	0.695081i
$683$	−2.97604			−0.113875			−0.0569374	−	0.998378i	$-0.518134\pi$
$683$	−2.97604			−0.113875			−0.0569374	+	0.998378i	$0.518134\pi$
$684$	−0.0278018	−	0.0769037i	−0.00106303	−	0.00294049i
$685$	0.361903			0.0138276
$686$	14.7677	−	21.6314i	0.563833	−	0.825889i
$687$			38.1832i			1.45678i
$688$	−26.6065	+	22.1294i	−1.01436	+	0.843675i
$689$			9.76385i			0.371973i
$690$	1.75519	+	10.0178i	0.0668191	+	0.381370i
$691$		−	13.7448i		−	0.522877i	−0.965220	−	0.261439i	$-0.915803\pi$
$691$		−	13.7448i		−	0.522877i	0.965220	−	0.261439i	$-0.0841969\pi$
$692$	46.5276	−	16.8204i	1.76871	−	0.639415i
$693$	0.165374	+	0.606713i	0.00628205	+	0.0230471i
$694$	−0.444120	−	2.53481i	−0.0168585	−	0.0962201i
$695$			8.49740i			0.322325i
$696$	3.88320	+	6.77675i	0.147192	+	0.256872i
$697$	3.10227			0.117507
$698$	2.18251	+	12.4567i	0.0826091	+	0.471491i
$699$		−	42.8932i		−	1.62237i
$700$	−3.04435	−	4.32804i	−0.115066	−	0.163585i
$701$			49.8152i			1.88149i	0.339111	+	0.940746i	$0.389874\pi$
$701$			49.8152i			1.88149i	−0.339111	+	0.940746i	$0.610126\pi$
$702$	38.0020	−	6.65826i	1.43429	−	0.251300i
$703$	−0.869952			−0.0328109
$704$	−5.88088	+	10.0345i	−0.221644	+	0.378190i
$705$			13.1006i			0.493396i
$706$	−22.4119	+	3.92674i	−0.843482	+	0.147785i
$707$	−7.75380	−	28.4466i	−0.291612	−	1.06984i
$708$	24.4960	−	8.85565i	0.920617	−	0.332816i
$709$			5.24482i			0.196973i	0.995138	+	0.0984867i	$0.0314002\pi$
$709$			5.24482i			0.196973i	−0.995138	+	0.0984867i	$0.968600\pi$
$710$	2.09525	−	0.367104i	0.0786332	−	0.0137772i
$711$		−	1.53106i		−	0.0574193i
$712$	−22.3985	+	12.8347i	−0.839420	+	0.481002i
$713$		−	38.2724i		−	1.43331i
$714$	−1.78993	+	0.841696i	−0.0669864	+	0.0314997i
$715$	7.44422			0.278398
$716$	−12.9115	+	4.66768i	−0.482524	+	0.174439i
$717$	29.4809			1.10098
$718$	14.1860	−	2.48550i	0.529416	−	0.0927580i
$719$	35.6884			1.33095			0.665476	−	0.746419i	$-0.268229\pi$
$719$	35.6884			1.33095			0.665476	+	0.746419i	$0.268229\pi$
$720$	0.502764	−	0.418164i	0.0187369	−	0.0155840i
$721$	−8.03479	−	29.4774i	−0.299231	−	1.09780i
$722$	4.62195	+	26.3798i	0.172011	+	0.981753i
$723$	34.9863			1.30116
$724$	−25.9695	+	9.38834i	−0.965149	+	0.348915i
$725$		−	1.63961i		−	0.0608935i
$726$	−20.8479	+	3.65273i	−0.773740	+	0.135566i
$727$	49.5564			1.83794			0.918972	−	0.394322i	$-0.129020\pi$
$727$	49.5564			1.83794			0.918972	+	0.394322i	$0.129020\pi$
$728$	27.0657	−	27.1228i	1.00312	−	1.00524i
$729$	−28.3066			−1.04839
$730$	−14.9150	+	2.61323i	−0.552030	+	0.0967201i
$731$		−	2.71555i		−	0.100438i
$732$	0.476256	+	1.31739i	0.0176029	+	0.0486922i
$733$	−9.76884			−0.360820			−0.180410	−	0.983591i	$-0.557743\pi$
$733$	−9.76884			−0.360820			−0.180410	+	0.983591i	$0.557743\pi$
$734$	−0.923141	−	5.26883i	−0.0340738	−	0.194476i
$735$	5.98248	+	10.1587i	0.220667	+	0.374709i
$736$	−15.6266	+	18.4191i	−0.576004	+	0.678938i
$737$	22.2262			0.818711
$738$	2.25085	−	0.394367i	0.0828548	−	0.0145168i
$739$	−28.7691			−1.05829			−0.529145	−	0.848531i	$-0.677487\pi$
$739$	−28.7691			−1.05829			−0.529145	+	0.848531i	$0.677487\pi$
$740$	−2.36518	−	6.54243i	−0.0869458	−	0.240505i
$741$	2.15678			0.0792312
$742$	−3.03617	−	6.45663i	−0.111461	−	0.237030i
$743$		−	34.3244i		−	1.25924i	−0.776903	−	0.629620i	$-0.783211\pi$
$743$		−	34.3244i		−	1.25924i	0.776903	−	0.629620i	$-0.216789\pi$
$744$	37.0458	−	21.2279i	1.35816	−	0.778252i
$745$		−	14.7688i		−	0.541088i
$746$	−3.96083	+	0.693970i	−0.145016	+	0.0254081i
$747$		−	0.564471i		−	0.0206529i
$748$	−0.310286	−	0.858297i	−0.0113452	−	0.0313824i
$749$	−2.34759	−	8.61267i	−0.0857792	−	0.314700i
$750$	2.34608	−	0.411052i	0.0856666	−	0.0150095i
$751$		−	40.8689i		−	1.49133i	−0.666323	−	0.745663i	$-0.732133\pi$
$751$		−	40.8689i		−	1.49133i	0.666323	−	0.745663i	$-0.267867\pi$
$752$	−23.9214	+	19.8961i	−0.872323	+	0.725536i
$753$	−31.8784			−1.16171
$754$	11.6947	−	2.04900i	0.425895	−	0.0746203i
$755$			17.6833i			0.643561i
$756$	−23.0595	+	16.2201i	−0.838665	+	0.589918i
$757$		−	35.1958i		−	1.27921i	−0.768703	−	0.639606i	$-0.779098\pi$
$757$		−	35.1958i		−	1.27921i	0.768703	−	0.639606i	$-0.220902\pi$
$758$	1.27444	+	7.27388i	0.0462898	+	0.264199i
$759$	10.4554			0.379508
$760$	0.613766	−	0.351698i	0.0222636	−	0.0127574i
$761$		−	9.03383i		−	0.327476i	−0.986504	−	0.163738i	$-0.947645\pi$
$761$		−	9.03383i		−	0.327476i	0.986504	−	0.163738i	$-0.0523552\pi$
$762$	0.892028	+	5.09125i	0.0323148	+	0.184436i
$763$	32.1949	−	8.77550i	1.16553	−	0.317694i
$764$	−4.61946	−	12.7781i	−0.167126	−	0.462295i
$765$			0.0513138i			0.00185526i
$766$	6.31398	+	36.0370i	0.228134	+	1.30207i
$767$		−	39.5953i		−	1.42970i
$768$	−26.4961	−	4.90955i	−0.956096	−	0.177158i
$769$			16.4068i			0.591645i	0.955243	+	0.295823i	$0.0955937\pi$
$769$			16.4068i			0.591645i	−0.955243	+	0.295823i	$0.904406\pi$
$770$	−4.92271	+	2.31486i	−0.177402	+	0.0834217i
$771$	−7.27305			−0.261933
$772$	13.0682	−	4.72435i	0.470336	−	0.170033i
$773$	−9.49352			−0.341458			−0.170729	−	0.985318i	$-0.554612\pi$
$773$	−9.49352			−0.341458			−0.170729	+	0.985318i	$0.554612\pi$
$774$	−0.345205	−	1.97026i	−0.0124082	−	0.0708195i
$775$	−8.96308			−0.321963
$776$	40.6009	−	23.2650i	1.45749	−	0.835165i
$777$	4.07611	+	14.9541i	0.146230	+	0.536476i
$778$	−36.4675	+	6.38941i	−1.30742	+	0.229071i
$779$	2.47192			0.0885658
$780$	5.86373	+	16.2199i	0.209955	+	0.580767i
$781$		−	2.18679i		−	0.0782494i
$782$	−0.327108	−	1.86697i	−0.0116974	−	0.0667627i
$783$	−8.73571			−0.312189
$784$	−9.46387	+	26.3521i	−0.337995	+	0.941148i
$785$	0.628228			0.0224224
$786$	3.62653	+	20.6984i	0.129354	+	0.738288i
$787$			2.43467i			0.0867866i	0.999058	+	0.0433933i	$0.0138169\pi$
$787$			2.43467i			0.0867866i	−0.999058	+	0.0433933i	$0.986183\pi$
$788$	17.0004	+	47.0254i	0.605613	+	1.67521i
$789$	−2.41397			−0.0859395
$790$	13.0457	−	2.28571i	0.464145	−	0.0813219i
$791$	9.43774	+	34.6245i	0.335568	+	1.23110i
$792$	−0.334236	−	0.583291i	−0.0118766	−	0.0207263i
$793$	2.12943			0.0756182
$794$	7.47305	+	42.6524i	0.265209	+	1.51368i
$795$	3.21155			0.113902
$796$	−16.6649	+	6.02459i	−0.590671	+	0.213536i
$797$	−18.3689			−0.650660			−0.325330	−	0.945601i	$-0.605475\pi$
$797$	−18.3689			−0.650660			−0.325330	+	0.945601i	$0.605475\pi$
$798$	−1.42623	+	0.670672i	−0.0504881	+	0.0237415i
$799$		−	2.44150i		−	0.0863740i
$800$	4.31361	+	3.65962i	0.152509	+	0.129387i
$801$		−	1.49213i		−	0.0527218i
$802$	−7.98070	−	45.5498i	−0.281808	−	1.60842i
$803$			15.5667i			0.549335i
$804$	17.5073	+	48.4277i	0.617435	+	1.70791i
$805$	−10.8997	+	2.97099i	−0.384165	+	0.104714i
$806$	−11.2011	−	63.9301i	−0.394541	−	2.25184i
$807$			20.4557i			0.720076i
$808$	15.6711	+	27.3484i	0.551307	+	0.962113i
$809$	18.8508			0.662759			0.331379	−	0.943498i	$-0.392486\pi$
$809$	18.8508			0.662759			0.331379	+	0.943498i	$0.392486\pi$
$810$	−2.07035	−	11.8165i	−0.0727447	−	0.415190i
$811$			7.40501i			0.260025i	0.991512	+	0.130013i	$0.0415018\pi$
$811$			7.40501i			0.260025i	−0.991512	+	0.130013i	$0.958498\pi$
$812$	−7.09629	+	4.99154i	−0.249031	+	0.175169i
$813$			10.9257i			0.383179i
$814$	−7.04452	+	1.23426i	−0.246910	+	0.0432607i
$815$	−15.7162			−0.550514
$816$	1.62570	−	1.35214i	0.0569109	−	0.0473344i
$817$		−	2.16378i		−	0.0757009i
$818$	21.2031	−	3.71496i	0.741349	−	0.129890i
$819$	0.582433	+	2.13679i	0.0203519	+	0.0746654i
$820$	6.72054	+	18.5900i	0.234691	+	0.649190i
$821$			16.2192i			0.566054i	0.959112	+	0.283027i	$0.0913385\pi$
$821$			16.2192i			0.566054i	−0.959112	+	0.283027i	$0.908661\pi$
$822$	0.849052	−	0.148761i	0.0296141	−	0.00518863i
$823$		−	31.7375i		−	1.10630i	−0.833081	−	0.553150i	$-0.813425\pi$
$823$		−	31.7375i		−	1.10630i	0.833081	−	0.553150i	$-0.186575\pi$
$824$	16.2390	+	28.3394i	0.565712	+	0.987251i
$825$		−	2.44857i		−	0.0852484i
$826$	12.3126	+	26.1836i	0.428409	+	0.911043i
$827$	35.1357			1.22179			0.610894	−	0.791713i	$-0.290810\pi$
$827$	35.1357			1.22179			0.610894	+	0.791713i	$0.290810\pi$
$828$	−0.474665	−	1.31299i	−0.0164958	−	0.0456296i
$829$	30.5400			1.06070			0.530350	−	0.847779i	$-0.322061\pi$
$829$	30.5400			1.06070			0.530350	+	0.847779i	$0.322061\pi$
$830$	4.80967	−	0.842693i	0.166946	−	0.0292503i
$831$	40.2289			1.39553
$832$	−20.7119	+	35.3406i	−0.718057	+	1.22522i
$833$	−1.11493	−	1.89324i	−0.0386301	−	0.0655967i
$834$	3.49287	+	19.9355i	0.120948	+	0.690312i
$835$	18.6731			0.646211
$836$	−0.247239	−	0.683900i	−0.00855095	−	0.0236532i
$837$			47.7547i			1.65064i
$838$	−2.10749	+	0.369250i	−0.0728021	+	0.0127555i
$839$	12.5696			0.433950			0.216975	−	0.976177i	$-0.430381\pi$
$839$	12.5696			0.433950			0.216975	+	0.976177i	$0.430381\pi$
$840$	−8.92132	−	8.90252i	−0.307815	−	0.307166i
$841$	26.3117			0.907299
$842$	6.16522	−	1.08020i	0.212467	−	0.0372260i
$843$			24.2549i			0.835384i
$844$	−25.6683	+	9.27944i	−0.883538	+	0.319411i
$845$	13.2179			0.454709
$846$	−0.310368	−	1.77142i	−0.0106707	−	0.0609028i
$847$	−6.18292	−	22.6834i	−0.212448	−	0.779411i
$848$	4.87745	+	5.86423i	0.167492	+	0.201379i
$849$	−40.5143			−1.39045
$850$	−0.437228	+	0.0766060i	−0.0149968	+	0.00262756i
$851$	−14.8529			−0.509150
$852$	4.76470	−	1.72251i	0.163236	−	0.0590121i
$853$	2.56221			0.0877284			0.0438642	−	0.999038i	$-0.486033\pi$
$853$	2.56221			0.0877284			0.0438642	+	0.999038i	$0.486033\pi$
$854$	−1.40815	+	0.662168i	−0.0481858	+	0.0226589i
$855$			0.0408874i			0.00139832i
$856$	4.74469	+	8.28018i	0.162170	+	0.283011i
$857$			50.0346i			1.70915i	0.519329	+	0.854574i	$0.326182\pi$
$857$			50.0346i			1.70915i	−0.519329	+	0.854574i	$0.673818\pi$
$858$	17.4647	−	3.05996i	0.596235	−	0.104465i
$859$		−	38.9502i		−	1.32896i	−0.747304	−	0.664482i	$-0.768652\pi$
$859$		−	38.9502i		−	1.32896i	0.747304	−	0.664482i	$-0.231348\pi$
$860$	16.2726	−	5.88276i	0.554890	−	0.200601i
$861$	−11.5821	−	42.4914i	−0.394716	−	1.44810i
$862$	−21.9824	+	3.85149i	−0.748723	+	0.131182i
$863$			18.6149i			0.633657i	0.948483	+	0.316828i	$0.102618\pi$
$863$			18.6149i			0.633657i	−0.948483	+	0.316828i	$0.897382\pi$
$864$	19.4982	−	22.9826i	0.663341	−	0.781883i
$865$	−24.7373			−0.841095
$866$	−53.6370	+	9.39763i	−1.82266	+	0.319345i
$867$		−	28.4654i		−	0.966736i
$868$	27.2868	+	38.7926i	0.926173	+	1.31671i
$869$		−	13.6156i		−	0.461879i
$870$	−0.673963	−	3.84664i	−0.0228495	−	0.130413i
$871$	78.2785			2.65237
$872$	−30.9520	+	17.7360i	−1.04817	+	0.600618i
$873$			2.70472i			0.0915408i
$874$	−0.260643	−	1.48762i	−0.00881638	−	0.0503195i
$875$	0.695780	+	2.55262i	0.0235217	+	0.0862944i
$876$	−33.9176	+	12.2617i	−1.14597	+	0.414284i
$877$			26.4153i			0.891982i	0.895037	+	0.445991i	$0.147149\pi$
$877$			26.4153i			0.891982i	−0.895037	+	0.445991i	$0.852851\pi$
$878$	1.99209	+	11.3698i	0.0672297	+	0.383713i
$879$			8.06398i			0.271991i
$880$	4.47105	−	3.71870i	0.150719	−	0.125357i
$881$		−	27.3582i		−	0.921722i	−0.887472	−	0.460861i	$-0.847541\pi$
$881$		−	27.3582i		−	0.921722i	0.887472	−	0.460861i	$-0.152459\pi$
$882$	−1.04961	−	1.23190i	−0.0353421	−	0.0414802i
$883$	15.3050			0.515053			0.257526	−	0.966271i	$-0.417093\pi$
$883$	15.3050			0.515053			0.257526	+	0.966271i	$0.417093\pi$
$884$	−1.09280	−	3.02284i	−0.0367548	−	0.101669i
$885$	−13.0238			−0.437790
$886$	3.53800	+	20.1931i	0.118861	+	0.678401i
$887$	4.33168			0.145444			0.0727218	−	0.997352i	$-0.476831\pi$
$887$	4.33168			0.145444			0.0727218	+	0.997352i	$0.476831\pi$
$888$	−8.23817	−	14.3768i	−0.276455	−	0.482455i
$889$	−5.53948	+	1.50992i	−0.185788	+	0.0506411i
$890$	12.7139	−	2.22759i	0.426172	−	0.0746688i
$891$	−12.3328			−0.413164
$892$	−14.4295	+	5.21646i	−0.483135	+	0.174660i
$893$		−	1.94541i		−	0.0651007i
$894$	−6.07075	−	34.6488i	−0.203036	−	1.15883i
$895$	6.86464			0.229460
$896$	2.70684	−	29.8106i	0.0904292	−	0.995903i
$897$	36.8231			1.22949
$898$	−6.39942	−	36.5247i	−0.213551	−	1.21884i
$899$			14.6959i			0.490137i
$900$	−0.307492	+	0.111163i	−0.0102497	+	0.00370542i
$901$	−0.598523			−0.0199397
$902$	20.0166	−	3.50708i	0.666481	−	0.116773i
$903$	−37.1944	+	10.1383i	−1.23775	+	0.337380i
$904$	−19.0745	−	33.2878i	−0.634408	−	1.10714i
$905$	13.8072			0.458967
$906$	7.26875	+	41.4863i	0.241488	+	1.37829i
$907$	38.3842			1.27453			0.637263	−	0.770646i	$-0.280066\pi$
$907$	38.3842			1.27453			0.637263	+	0.770646i	$0.280066\pi$
$908$	12.5710	+	34.7732i	0.417183	+	1.15399i
$909$	−1.82187			−0.0604277
$910$	−17.3373	+	8.15271i	−0.574727	+	0.270260i
$911$		−	21.1601i		−	0.701065i	−0.936551	−	0.350533i	$-0.886001\pi$
$911$		−	21.1601i		−	0.701065i	0.936551	−	0.350533i	$-0.113999\pi$
$912$	1.29537	−	1.07740i	0.0428941	−	0.0356763i
$913$		−	5.01980i		−	0.166131i
$914$	−2.64852	−	15.1164i	−0.0876053	−	0.500007i
$915$		−	0.700418i		−	0.0231551i
$916$	42.6420	−	15.4157i	1.40893	−	0.509349i
$917$	−22.5207	+	6.13857i	−0.743699	+	0.202713i
$918$	0.408151	+	2.32952i	0.0134710	+	0.0768856i
$919$			11.5795i			0.381971i	0.981593	+	0.190986i	$0.0611684\pi$
$919$			11.5795i			0.381971i	−0.981593	+	0.190986i	$0.938832\pi$
$920$	10.4789	−	6.00462i	0.345481	−	0.197966i
$921$	39.7674			1.31038
$922$	−2.67804	−	15.2849i	−0.0881965	−	0.503381i
$923$		−	7.70166i		−	0.253503i
$924$	−10.5975	+	7.45432i	−0.348633	+	0.245229i
$925$			3.47842i			0.114370i
$926$	17.8674	−	3.13051i	0.587158	−	0.102875i
$927$	−1.88789			−0.0620066
$928$	6.00034	−	7.07262i	0.196971	−	0.232170i
$929$		−	16.9537i		−	0.556232i	−0.960547	−	0.278116i	$-0.910290\pi$
$929$		−	16.9537i		−	0.556232i	0.960547	−	0.278116i	$-0.0897100\pi$
$930$	−21.0281	+	3.68429i	−0.689537	+	0.120813i
$931$	−0.888388	−	1.50855i	−0.0291157	−	0.0494407i
$932$	−47.9020	+	17.3172i	−1.56908	+	0.567245i
$933$		−	39.7813i		−	1.30238i
$934$	−37.9556	+	6.65014i	−1.24195	+	0.217599i
$935$			0.456331i			0.0149236i
$936$	−1.17715	−	2.05430i	−0.0384763	−	0.0671468i
$937$		−	36.4798i		−	1.19174i	−0.803079	−	0.595872i	$-0.796807\pi$
$937$		−	36.4798i		−	1.19174i	0.803079	−	0.595872i	$-0.203193\pi$
$938$	−51.7640	+	24.3415i	−1.69015	+	0.794778i
$939$	−34.7810			−1.13503
$940$	14.6304	−	5.28908i	0.477190	−	0.172511i
$941$	−9.71945			−0.316845			−0.158423	−	0.987371i	$-0.550641\pi$
$941$	−9.71945			−0.316845			−0.158423	+	0.987371i	$0.550641\pi$
$942$	1.47387	−	0.258234i	0.0480212	−	0.00841371i
$943$	42.2036			1.37434
$944$	−19.7795	−	23.7812i	−0.643769	−	0.774013i
$945$	13.6002	−	3.70707i	0.442414	−	0.120591i
$946$	−3.06989	−	17.5214i	−0.0998107	−	0.569669i
$947$	−32.8605			−1.06782			−0.533911	−	0.845541i	$-0.679278\pi$
$947$	−32.8605			−1.06782			−0.533911	+	0.845541i	$0.679278\pi$
$948$	29.6666	−	10.7249i	0.963527	−	0.348328i
$949$			54.8243i			1.77967i
$950$	−0.348388	+	0.0610404i	−0.0113032	+	0.00198041i
$951$	−22.2072			−0.720118
$952$	1.66263	+	1.65913i	0.0538861	+	0.0537726i
$953$	−52.0838			−1.68716			−0.843580	−	0.537003i	$-0.819556\pi$
$953$	−52.0838			−1.68716			−0.843580	+	0.537003i	$0.819556\pi$
$954$	−0.434257	+	0.0760854i	−0.0140596	+	0.00246336i
$955$			6.79373i			0.219840i
$956$	−11.9023	−	32.9235i	−0.384948	−	1.06482i
$957$	−4.01470			−0.129777
$958$	−1.44798	−	8.26435i	−0.0467822	−	0.267009i
$959$	0.251805	+	0.923803i	0.00813121	+	0.0298311i
$960$	11.6243	+	6.81262i	0.375174	+	0.219876i
$961$	49.3369			1.59151
$962$	−24.8102	+	4.34694i	−0.799912	+	0.140151i
$963$	−0.551603			−0.0177751
$964$	−14.1250	−	39.0718i	−0.454936	−	1.25842i
$965$	−6.94798			−0.223663
$966$	−24.3503	+	11.4505i	−0.783460	+	0.368414i
$967$			53.8786i			1.73262i	0.499509	+	0.866309i	$0.333514\pi$
$967$			53.8786i			1.73262i	−0.499509	+	0.866309i	$0.666486\pi$
$968$	12.4962	+	21.8077i	0.401643	+	0.700927i
$969$			0.132210i			0.00424721i
$970$	−23.0460	+	4.03785i	−0.739963	+	0.129648i
$971$			41.7861i			1.34098i	0.741919	+	0.670490i	$0.233916\pi$
$971$			41.7861i			1.34098i	−0.741919	+	0.670490i	$0.766084\pi$
$972$	1.15392	+	3.19192i	0.0370121	+	0.102381i
$973$	−21.6907	+	5.91232i	−0.695371	+	0.189540i
$974$	−1.11423	+	0.195221i	−0.0357021	+	0.00625530i
$975$		−	8.62365i		−	0.276178i
$976$	1.27895	−	1.06374i	0.0409382	−	0.0340495i
$977$	−11.1568			−0.356939			−0.178469	−	0.983945i	$-0.557115\pi$
$977$	−11.1568			−0.356939			−0.178469	+	0.983945i	$0.557115\pi$
$978$	−36.8713	+	6.46016i	−1.17902	+	0.206573i
$979$		−	13.2694i		−	0.424092i
$980$	8.92966	−	10.7824i	0.285248	−	0.344433i
$981$		−	2.06194i		−	0.0658326i
$982$	8.65896	+	49.4210i	0.276318	+	1.57709i
$983$	−6.51094			−0.207667			−0.103833	−	0.994595i	$-0.533111\pi$
$983$	−6.51094			−0.207667			−0.103833	+	0.994595i	$0.533111\pi$
$984$	23.4083	+	40.8510i	0.746230	+	1.30228i
$985$		−	25.0020i		−	0.796631i
$986$	0.125604	+	0.716883i	0.00400004	+	0.0228302i
$987$	−33.4408	+	9.11511i	−1.06443	+	0.290137i
$988$	−0.870754	−	2.40863i	−0.0277024	−	0.0766288i
$989$		−	36.9426i		−	1.17471i
$990$	0.0580096	+	0.331090i	0.00184367	+	0.0105227i
$991$			41.7400i			1.32591i	0.748658	+	0.662957i	$0.230699\pi$
$991$			41.7400i			1.32591i	−0.748658	+	0.662957i	$0.769301\pi$
$992$	−38.6632	−	32.8014i	−1.22756	−	1.04145i
$993$		−	7.22799i		−	0.229373i
$994$	2.39491	+	5.09295i	0.0759619	+	0.161539i
$995$	8.86022			0.280888
$996$	10.9375	−	3.95404i	0.346567	−	0.125289i
$997$	13.1237			0.415632			0.207816	−	0.978168i	$-0.433365\pi$
$997$	13.1237			0.415632			0.207816	+	0.978168i	$0.433365\pi$
$998$	−3.37644	−	19.2710i	−0.106879	−	0.610014i
$999$	18.5327			0.586350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.h.b.251.10	yes	16
4.3	odd	2		1120.2.h.b.111.13		16
7.6	odd	2		280.2.h.a.251.10	yes	16
8.3	odd	2		280.2.h.a.251.9	✓	16
8.5	even	2		1120.2.h.a.111.13		16
28.27	even	2		1120.2.h.a.111.4		16
56.13	odd	2		1120.2.h.b.111.4		16
56.27	even	2	inner	280.2.h.b.251.9	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.h.a.251.9	✓	16	8.3	odd	2
280.2.h.a.251.10	yes	16	7.6	odd	2
280.2.h.b.251.9	yes	16	56.27	even	2	inner
280.2.h.b.251.10	yes	16	1.1	even	1	trivial
1120.2.h.a.111.4		16	28.27	even	2
1120.2.h.a.111.13		16	8.5	even	2
1120.2.h.b.111.4		16	56.13	odd	2
1120.2.h.b.111.13		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.244064 + 1.39299i) q^{2} -1.68420i q^{3} +(-1.88087 + 0.679959i) q^{4} +1.00000 q^{5} +(2.34608 - 0.411052i) q^{6} +(0.695780 + 2.55262i) q^{7} +(-1.40623 - 2.45408i) q^{8} +0.163484 q^{9} +O(q^{10})\)	\(q+(0.244064 + 1.39299i) q^{2} -1.68420i q^{3} +(-1.88087 + 0.679959i) q^{4} +1.00000 q^{5} +(2.34608 - 0.411052i) q^{6} +(0.695780 + 2.55262i) q^{7} +(-1.40623 - 2.45408i) q^{8} +0.163484 q^{9} +(0.244064 + 1.39299i) q^{10} +1.45385 q^{11} +(1.14518 + 3.16775i) q^{12} +5.12034 q^{13} +(-3.38598 + 1.59222i) q^{14} -1.68420i q^{15} +(3.07531 - 2.55782i) q^{16} +0.313877i q^{17} +(0.0399006 + 0.227732i) q^{18} +0.250100i q^{19} +(-1.88087 + 0.679959i) q^{20} +(4.29912 - 1.17183i) q^{21} +(0.354833 + 2.02521i) q^{22} +4.27001i q^{23} +(-4.13315 + 2.36837i) q^{24} +1.00000 q^{25} +(1.24969 + 7.13260i) q^{26} -5.32793i q^{27} +(-3.04435 - 4.32804i) q^{28} -1.63961i q^{29} +(2.34608 - 0.411052i) q^{30} -8.96308 q^{31} +(4.31361 + 3.65962i) q^{32} -2.44857i q^{33} +(-0.437228 + 0.0766060i) q^{34} +(0.695780 + 2.55262i) q^{35} +(-0.307492 + 0.111163i) q^{36} +3.47842i q^{37} +(-0.348388 + 0.0610404i) q^{38} -8.62365i q^{39} +(-1.40623 - 2.45408i) q^{40} -9.88374i q^{41} +(2.68161 + 5.70265i) q^{42} -8.65164 q^{43} +(-2.73450 + 0.988561i) q^{44} +0.163484 q^{45} +(-5.94810 + 1.04216i) q^{46} -7.77853 q^{47} +(-4.30788 - 5.17943i) q^{48} +(-6.03178 + 3.55213i) q^{49} +(0.244064 + 1.39299i) q^{50} +0.528630 q^{51} +(-9.63067 + 3.48162i) q^{52} +1.90687i q^{53} +(7.42177 - 1.30036i) q^{54} +1.45385 q^{55} +(5.28592 - 5.29708i) q^{56} +0.421218 q^{57} +(2.28396 - 0.400169i) q^{58} -7.73295i q^{59} +(1.14518 + 3.16775i) q^{60} +0.415877 q^{61} +(-2.18757 - 12.4855i) q^{62} +(0.113749 + 0.417313i) q^{63} +(-4.04503 + 6.90201i) q^{64} +5.12034 q^{65} +(3.41085 - 0.597609i) q^{66} +15.2878 q^{67} +(-0.213423 - 0.590360i) q^{68} +7.19153 q^{69} +(-3.38598 + 1.59222i) q^{70} -1.50413i q^{71} +(-0.229896 - 0.401203i) q^{72} +10.7072i q^{73} +(-4.84541 + 0.848956i) q^{74} -1.68420i q^{75} +(-0.170058 - 0.470405i) q^{76} +(1.01156 + 3.71114i) q^{77} +(12.0127 - 2.10472i) q^{78} -9.36521i q^{79} +(3.07531 - 2.55782i) q^{80} -8.48282 q^{81} +(13.7680 - 2.41226i) q^{82} -3.45276i q^{83} +(-7.28927 + 5.12728i) q^{84} +0.313877i q^{85} +(-2.11155 - 12.0517i) q^{86} -2.76142 q^{87} +(-2.04445 - 3.56788i) q^{88} -9.12705i q^{89} +(0.0399006 + 0.227732i) q^{90} +(3.56263 + 13.0703i) q^{91} +(-2.90343 - 8.03131i) q^{92} +15.0956i q^{93} +(-1.89846 - 10.8354i) q^{94} +0.250100i q^{95} +(6.16351 - 7.26496i) q^{96} +16.5442i q^{97} +(-6.42024 - 7.53529i) q^{98} +0.237682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9	\( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9 + q^10 - 4 * q^11 + 14 * q^12 - q^14 + 9 * q^16 - 15 * q^18 + q^20 - 4 * q^21 + 6 * q^22 + 22 * q^24 + 16 * q^25 - 20 * q^26 + q^28 - 16 * q^31 - 19 * q^32 - 14 * q^34 + 15 * q^36 - 30 * q^38 + q^40 + 44 * q^42 - 4 * q^43 - 20 * q^44 - 16 * q^45 + 6 * q^46 - 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 - 38 * q^52 + 26 * q^54 - 4 * q^55 + 33 * q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 - 8 * q^61 + 28 * q^62 + 28 * q^63 - 23 * q^64 + 46 * q^66 + 20 * q^67 + 12 * q^68 - 40 * q^69 - q^70 - 13 * q^72 - 28 * q^74 + 34 * q^76 - 4 * q^77 - 6 * q^78 + 9 * q^80 + 24 * q^81 - 16 * q^82 - 42 * q^84 - 24 * q^86 + 72 * q^87 - 44 * q^88 - 15 * q^90 - 32 * q^91 - 30 * q^92 - 58 * q^94 - 30 * q^96 + 5 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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