LMFDB - Embedded newform 280.2.h.a.251.12

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			251.12
Root			$1.07046 - 0.924187i$ of defining polynomial
Character	$\chi$	$=$	280.251
Dual form			280.2.h.a.251.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07046 + 0.924187i) q^{2} +2.99734i q^{3} +(0.291758 + 1.97860i) q^{4} -1.00000 q^{5} +(-2.77010 + 3.20852i) q^{6} +(-0.183359 - 2.63939i) q^{7} +(-1.51629 + 2.38765i) q^{8} -5.98405 q^{9} +O(q^{10})$	\(q+(1.07046 + 0.924187i) q^{2} +2.99734i q^{3} +(0.291758 + 1.97860i) q^{4} -1.00000 q^{5} +(-2.77010 + 3.20852i) q^{6} +(-0.183359 - 2.63939i) q^{7} +(-1.51629 + 2.38765i) q^{8} -5.98405 q^{9} +(-1.07046 - 0.924187i) q^{10} +4.87706 q^{11} +(-5.93055 + 0.874498i) q^{12} +2.42800 q^{13} +(2.24301 - 2.99481i) q^{14} -2.99734i q^{15} +(-3.82975 + 1.15455i) q^{16} +3.92955i q^{17} +(-6.40567 - 5.53038i) q^{18} -5.24043i q^{19} +(-0.291758 - 1.97860i) q^{20} +(7.91115 - 0.549588i) q^{21} +(5.22068 + 4.50731i) q^{22} +0.114122i q^{23} +(-7.15660 - 4.54482i) q^{24} +1.00000 q^{25} +(2.59907 + 2.24393i) q^{26} -8.94421i q^{27} +(5.16881 - 1.13286i) q^{28} +3.60881i q^{29} +(2.77010 - 3.20852i) q^{30} -4.62694 q^{31} +(-5.16661 - 2.30351i) q^{32} +14.6182i q^{33} +(-3.63164 + 4.20642i) q^{34} +(0.183359 + 2.63939i) q^{35} +(-1.74589 - 11.8401i) q^{36} +7.83800i q^{37} +(4.84313 - 5.60965i) q^{38} +7.27754i q^{39} +(1.51629 - 2.38765i) q^{40} -10.4815i q^{41} +(8.97647 + 6.72307i) q^{42} +2.76350 q^{43} +(1.42292 + 9.64977i) q^{44} +5.98405 q^{45} +(-0.105470 + 0.122163i) q^{46} +12.0817 q^{47} +(-3.46057 - 11.4791i) q^{48} +(-6.93276 + 0.967910i) q^{49} +(1.07046 + 0.924187i) q^{50} -11.7782 q^{51} +(0.708388 + 4.80405i) q^{52} -0.668088i q^{53} +(8.26612 - 9.57439i) q^{54} -4.87706 q^{55} +(6.57997 + 3.56427i) q^{56} +15.7073 q^{57} +(-3.33521 + 3.86307i) q^{58} -1.37541i q^{59} +(5.93055 - 0.874498i) q^{60} +1.17808 q^{61} +(-4.95294 - 4.27615i) q^{62} +(1.09723 + 15.7942i) q^{63} +(-3.40175 - 7.24072i) q^{64} -2.42800 q^{65} +(-13.5099 + 15.6482i) q^{66} +2.57766 q^{67} +(-7.77504 + 1.14648i) q^{68} -0.342063 q^{69} +(-2.24301 + 2.99481i) q^{70} -9.43699i q^{71} +(9.07353 - 14.2878i) q^{72} -5.62623i q^{73} +(-7.24377 + 8.39024i) q^{74} +2.99734i q^{75} +(10.3687 - 1.52894i) q^{76} +(-0.894251 - 12.8725i) q^{77} +(-6.72581 + 7.79030i) q^{78} -11.8804i q^{79} +(3.82975 - 1.15455i) q^{80} +8.85669 q^{81} +(9.68687 - 11.2200i) q^{82} -5.52348i q^{83} +(3.39556 + 15.4927i) q^{84} -3.92955i q^{85} +(2.95821 + 2.55399i) q^{86} -10.8168 q^{87} +(-7.39501 + 11.6447i) q^{88} +6.21826i q^{89} +(6.40567 + 5.53038i) q^{90} +(-0.445195 - 6.40844i) q^{91} +(-0.225803 + 0.0332961i) q^{92} -13.8685i q^{93} +(12.9329 + 11.1657i) q^{94} +5.24043i q^{95} +(6.90442 - 15.4861i) q^{96} +7.85094i q^{97} +(-8.31575 - 5.37106i) q^{98} -29.1845 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} + 7 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} - 3 q^{28} + 16 q^{31} - 19 q^{32} + 14 q^{34} + 15 q^{36} + 30 q^{38} - q^{40} + 20 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} + 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} - 7 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} + 10 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} - 39 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 + 7 * 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 - 3 * q^28 + 16 * q^31 - 19 * q^32 + 14 * q^34 + 15 * q^36 + 30 * q^38 - q^40 + 20 * 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 + 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 - 7 * 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 + 10 * 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 - 39 * 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 $

$2$	1.07046	+	0.924187i	0.756928	+	0.653499i
$2$	1.07046	+	0.924187i	0.756928	+	0.653499i
$3$			2.99734i			1.73052i	0.501328	+	0.865258i	$0.332845\pi$
$3$			2.99734i			1.73052i	−0.501328	+	0.865258i	$0.667155\pi$
$4$	0.291758	+	1.97860i	0.145879	+	0.989302i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−2.77010	+	3.20852i	−1.13089	+	1.30987i
$7$	−0.183359	−	2.63939i	−0.0693031	−	0.997596i
$7$	−0.183359	−	2.63939i	−0.0693031	−	0.997596i
$8$	−1.51629	+	2.38765i	−0.536088	+	0.844162i
$9$	−5.98405			−1.99468
$10$	−1.07046	−	0.924187i	−0.338508	−	0.292253i
$11$	4.87706			1.47049			0.735244	−	0.677803i	$-0.237068\pi$
$11$	4.87706			1.47049			0.735244	+	0.677803i	$0.237068\pi$
$12$	−5.93055	+	0.874498i	−1.71200	+	0.252446i
$13$	2.42800			0.673406			0.336703	−	0.941611i	$-0.390688\pi$
$13$	2.42800			0.673406			0.336703	+	0.941611i	$0.390688\pi$
$14$	2.24301	−	2.99481i	0.599470	−	0.800397i
$15$		−	2.99734i		−	0.773910i
$16$	−3.82975	+	1.15455i	−0.957439	+	0.288637i
$17$			3.92955i			0.953057i	0.879159	+	0.476528i	$0.158105\pi$
$17$			3.92955i			0.953057i	−0.879159	+	0.476528i	$0.841895\pi$
$18$	−6.40567	−	5.53038i	−1.50983	−	1.30352i
$19$		−	5.24043i		−	1.20224i	−0.799160	−	0.601118i	$-0.794722\pi$
$19$		−	5.24043i		−	1.20224i	0.799160	−	0.601118i	$-0.205278\pi$
$20$	−0.291758	−	1.97860i	−0.0652391	−	0.442430i
$21$	7.91115	−	0.549588i	1.72635	−	0.119930i
$22$	5.22068	+	4.50731i	1.11305	+	0.960962i
$23$			0.114122i			0.0237961i	0.999929	+	0.0118981i	$0.00378736\pi$
$23$			0.114122i			0.0237961i	−0.999929	+	0.0118981i	$0.996213\pi$
$24$	−7.15660	−	4.54482i	−1.46084	−	0.927708i
$25$	1.00000			0.200000
$26$	2.59907	+	2.24393i	0.509720	+	0.440070i
$27$		−	8.94421i		−	1.72131i
$28$	5.16881	−	1.13286i	0.976814	−	0.214090i
$29$			3.60881i			0.670139i	0.942193	+	0.335069i	$0.108760\pi$
$29$			3.60881i			0.670139i	−0.942193	+	0.335069i	$0.891240\pi$
$30$	2.77010	−	3.20852i	0.505749	−	0.585794i
$31$	−4.62694			−0.831023			−0.415511	−	0.909588i	$-0.636397\pi$
$31$	−4.62694			−0.831023			−0.415511	+	0.909588i	$0.636397\pi$
$32$	−5.16661	−	2.30351i	−0.913336	−	0.407208i
$33$			14.6182i			2.54470i
$34$	−3.63164	+	4.20642i	−0.622821	+	0.721395i
$35$	0.183359	+	2.63939i	0.0309933	+	0.446138i
$36$	−1.74589	−	11.8401i	−0.290982	−	1.97334i
$37$			7.83800i			1.28856i	0.764790	+	0.644279i	$0.222843\pi$
$37$			7.83800i			1.28856i	−0.764790	+	0.644279i	$0.777157\pi$
$38$	4.84313	−	5.60965i	0.785660	−	0.910006i
$39$			7.27754i			1.16534i
$40$	1.51629	−	2.38765i	0.239746	−	0.377521i
$41$		−	10.4815i		−	1.63694i	−0.574552	−	0.818468i	$-0.694824\pi$
$41$		−	10.4815i		−	1.63694i	0.574552	−	0.818468i	$-0.305176\pi$
$42$	8.97647	+	6.72307i	1.38510	+	1.03739i
$43$	2.76350			0.421430			0.210715	−	0.977548i	$-0.432421\pi$
$43$	2.76350			0.421430			0.210715	+	0.977548i	$0.432421\pi$
$44$	1.42292	+	9.64977i	0.214513	+	1.45476i
$45$	5.98405			0.892049
$46$	−0.105470	+	0.122163i	−0.0155507	+	0.0180119i
$47$	12.0817			1.76229			0.881145	−	0.472846i	$-0.156773\pi$
$47$	12.0817			1.76229			0.881145	+	0.472846i	$0.156773\pi$
$48$	−3.46057	−	11.4791i	−0.499490	−	1.65686i
$49$	−6.93276	+	0.967910i	−0.990394	+	0.138273i
$50$	1.07046	+	0.924187i	0.151386	+	0.130700i
$51$	−11.7782			−1.64928
$52$	0.708388	+	4.80405i	0.0982358	+	0.666202i
$53$		−	0.668088i		−	0.0917689i	−0.998947	−	0.0458845i	$-0.985389\pi$
$53$		−	0.668088i		−	0.0917689i	0.998947	−	0.0458845i	$-0.0146106\pi$
$54$	8.26612	−	9.57439i	1.12488	−	1.30291i
$55$	−4.87706			−0.657622
$56$	6.57997	+	3.56427i	0.879285	+	0.476296i
$57$	15.7073			2.08049
$58$	−3.33521	+	3.86307i	−0.437935	+	0.507246i
$59$		−	1.37541i		−	0.179063i	−0.995984	−	0.0895314i	$-0.971463\pi$
$59$		−	1.37541i		−	0.179063i	0.995984	−	0.0895314i	$-0.0285369\pi$
$60$	5.93055	−	0.874498i	0.765631	−	0.112897i
$61$	1.17808			0.150837			0.0754186	−	0.997152i	$-0.475971\pi$
$61$	1.17808			0.150837			0.0754186	+	0.997152i	$0.475971\pi$
$62$	−4.95294	−	4.27615i	−0.629024	−	0.543072i
$63$	1.09723	+	15.7942i	0.138238	+	1.98989i
$64$	−3.40175	−	7.24072i	−0.425219	−	0.905090i
$65$	−2.42800			−0.301156
$66$	−13.5099	+	15.6482i	−1.66296	+	1.92615i
$67$	2.57766			0.314911			0.157456	−	0.987526i	$-0.449671\pi$
$67$	2.57766			0.314911			0.157456	+	0.987526i	$0.449671\pi$
$68$	−7.77504	+	1.14648i	−0.942862	+	0.139031i
$69$	−0.342063			−0.0411795
$70$	−2.24301	+	2.99481i	−0.268091	+	0.357949i
$71$		−	9.43699i		−	1.11996i	−0.828505	−	0.559982i	$-0.810808\pi$
$71$		−	9.43699i		−	1.11996i	0.828505	−	0.559982i	$-0.189192\pi$
$72$	9.07353	−	14.2878i	1.06933	−	1.68384i
$73$		−	5.62623i		−	0.658500i	−0.944243	−	0.329250i	$-0.893204\pi$
$73$		−	5.62623i		−	0.658500i	0.944243	−	0.329250i	$-0.106796\pi$
$74$	−7.24377	+	8.39024i	−0.842072	+	0.975346i
$75$			2.99734i			0.346103i
$76$	10.3687	−	1.52894i	1.18938	−	0.175381i
$77$	−0.894251	−	12.8725i	−0.101909	−	1.46695i
$78$	−6.72581	+	7.79030i	−0.761548	+	0.882078i
$79$		−	11.8804i		−	1.33665i	−0.743872	−	0.668323i	$-0.767013\pi$
$79$		−	11.8804i		−	1.33665i	0.743872	−	0.668323i	$-0.232987\pi$
$80$	3.82975	−	1.15455i	0.428180	−	0.129082i
$81$	8.85669			0.984077
$82$	9.68687	−	11.2200i	1.06974	−	1.23904i
$83$		−	5.52348i		−	0.606280i	−0.952946	−	0.303140i	$-0.901965\pi$
$83$		−	5.52348i		−	0.606280i	0.952946	−	0.303140i	$-0.0980350\pi$
$84$	3.39556	+	15.4927i	0.370486	+	1.69039i
$85$		−	3.92955i		−	0.426220i
$86$	2.95821	+	2.55399i	0.318992	+	0.275404i
$87$	−10.8168			−1.15969
$88$	−7.39501	+	11.6447i	−0.788311	+	1.24133i
$89$			6.21826i			0.659135i	0.944132	+	0.329567i	$0.106903\pi$
$89$			6.21826i			0.659135i	−0.944132	+	0.329567i	$0.893097\pi$
$90$	6.40567	+	5.53038i	0.675217	+	0.582953i
$91$	−0.445195	−	6.40844i	−0.0466691	−	0.671787i
$92$	−0.225803	+	0.0332961i	−0.0235416	+	0.00347135i
$93$		−	13.8685i		−	1.43810i
$94$	12.9329	+	11.1657i	1.33393	+	1.15165i
$95$			5.24043i			0.537657i
$96$	6.90442	−	15.4861i	0.704679	−	1.58054i
$97$			7.85094i			0.797142i	0.917137	+	0.398571i	$0.130494\pi$
$97$			7.85094i			0.797142i	−0.917137	+	0.398571i	$0.869506\pi$
$98$	−8.31575	−	5.37106i	−0.840018	−	0.542559i
$99$	−29.1845			−2.93316
$100$	0.291758	+	1.97860i	0.0291758	+	0.197860i
$101$	10.9057			1.08516			0.542580	−	0.840004i	$-0.317448\pi$
$101$	10.9057			1.08516			0.542580	+	0.840004i	$0.317448\pi$
$102$	−12.6081	−	10.8853i	−1.24839	−	1.07780i
$103$	−15.8202			−1.55881			−0.779403	−	0.626523i	$-0.784477\pi$
$103$	−15.8202			−1.55881			−0.779403	+	0.626523i	$0.784477\pi$
$104$	−3.68154	+	5.79722i	−0.361005	+	0.568464i
$105$	−7.91115	+	0.549588i	−0.772049	+	0.0536343i
$106$	0.617438	−	0.715160i	0.0599709	−	0.0694624i
$107$	6.53444			0.631708			0.315854	−	0.948808i	$-0.397709\pi$
$107$	6.53444			0.631708			0.315854	+	0.948808i	$0.397709\pi$
$108$	17.6971	−	2.60954i	1.70290	−	0.251103i
$109$		−	10.9309i		−	1.04699i	−0.852028	−	0.523496i	$-0.824628\pi$
$109$		−	10.9309i		−	1.04699i	0.852028	−	0.523496i	$-0.175372\pi$
$110$	−5.22068	−	4.50731i	−0.497772	−	0.429755i
$111$	−23.4931			−2.22987
$112$	3.74952	+	9.89652i	0.354296	+	0.935133i
$113$	3.72004			0.349951			0.174976	−	0.984573i	$-0.444015\pi$
$113$	3.72004			0.349951			0.174976	+	0.984573i	$0.444015\pi$
$114$	16.8140	+	14.5165i	1.57478	+	1.35960i
$115$		−	0.114122i		−	0.0106419i
$116$	−7.14040	+	1.05290i	−0.662970	+	0.0977591i
$117$	−14.5293			−1.34323
$118$	1.27113	−	1.47232i	0.117017	−	0.135538i
$119$	10.3716	−	0.720518i	0.950766	−	0.0660498i
$120$	7.15660	+	4.54482i	0.653305	+	0.414884i
$121$	12.7857			1.16233
$122$	1.26108	+	1.08876i	0.114173	+	0.0985719i
$123$	31.4166			2.83274
$124$	−1.34995	−	9.15488i	−0.121229	−	0.822133i
$125$	−1.00000			−0.0894427
$126$	−13.4223	+	17.9211i	−1.19575	+	1.59654i
$127$		−	3.80326i		−	0.337485i	−0.985660	−	0.168742i	$-0.946029\pi$
$127$		−	3.80326i		−	0.337485i	0.985660	−	0.168742i	$-0.0539706\pi$
$128$	3.05035	−	10.8947i	0.269615	−	0.962968i
$129$			8.28315i			0.729291i
$130$	−2.59907	−	2.24393i	−0.227954	−	0.196805i
$131$			7.68109i			0.671100i	0.942022	+	0.335550i	$0.108922\pi$
$131$			7.68109i			0.671100i	−0.942022	+	0.335550i	$0.891078\pi$
$132$	−28.9236	+	4.26497i	−2.51748	+	0.371218i
$133$	−13.8315	+	0.960878i	−1.19935	+	0.0833187i
$134$	2.75927	+	2.38224i	0.238365	+	0.205794i
$135$			8.94421i			0.769795i
$136$	−9.38241	−	5.95833i	−0.804535	−	0.510922i
$137$	−16.9739			−1.45018			−0.725090	−	0.688655i	$-0.758202\pi$
$137$	−16.9739			−1.45018			−0.725090	+	0.688655i	$0.758202\pi$
$138$	−0.366164	−	0.316130i	−0.0311699	−	0.0269108i
$139$			2.54598i			0.215947i	0.994154	+	0.107973i	$0.0344362\pi$
$139$			2.54598i			0.215947i	−0.994154	+	0.107973i	$0.965564\pi$
$140$	−5.16881	+	1.13286i	−0.436844	+	0.0957439i
$141$			36.2128i			3.04967i
$142$	8.72154	−	10.1019i	0.731895	−	0.847732i
$143$	11.8415			0.990235
$144$	22.9174	−	6.90887i	1.90979	−	0.575739i
$145$		−	3.60881i		−	0.299695i
$146$	5.19969	−	6.02264i	0.430329	−	0.498437i
$147$	−2.90116	−	20.7798i	−0.239283	−	1.71389i
$148$	−15.5083	+	2.28680i	−1.27477	+	0.187974i
$149$			13.7925i			1.12992i	0.825118	+	0.564961i	$0.191109\pi$
$149$			13.7925i			1.12992i	−0.825118	+	0.564961i	$0.808891\pi$
$150$	−2.77010	+	3.20852i	−0.226178	+	0.261975i
$151$		−	0.128374i		−	0.0104469i	−0.999986	−	0.00522347i	$-0.998337\pi$
$151$		−	0.128374i		−	0.0104469i	0.999986	−	0.00522347i	$-0.00166269\pi$
$152$	12.5123	+	7.94599i	1.01488	+	0.644505i
$153$		−	23.5146i		−	1.90105i
$154$	10.9393	−	14.6059i	0.881513	−	1.17697i
$155$	4.62694			0.371645
$156$	−14.3994	+	2.12328i	−1.15287	+	0.169999i
$157$	−13.1585			−1.05017			−0.525083	−	0.851051i	$-0.675966\pi$
$157$	−13.1585			−1.05017			−0.525083	+	0.851051i	$0.675966\pi$
$158$	10.9797	−	12.7174i	0.873496	−	1.01174i
$159$	2.00249			0.158808
$160$	5.16661	+	2.30351i	0.408456	+	0.182109i
$161$	0.301213	−	0.0209253i	0.0237389	−	0.00164914i
$162$	9.48071	+	8.18523i	0.744875	+	0.643093i
$163$	0.158264			0.0123962			0.00619809	−	0.999981i	$-0.498027\pi$
$163$	0.158264			0.0123962			0.00619809	+	0.999981i	$0.498027\pi$
$164$	20.7388	−	3.05806i	1.61943	−	0.238795i
$165$		−	14.6182i		−	1.13802i
$166$	5.10472	−	5.91264i	0.396203	−	0.458910i
$167$	16.7105			1.29310			0.646550	−	0.762871i	$-0.276211\pi$
$167$	16.7105			1.29310			0.646550	+	0.762871i	$0.276211\pi$
$168$	−10.6833	+	19.7224i	−0.824237	+	1.52162i
$169$	−7.10482			−0.546524
$170$	3.63164	−	4.20642i	0.278534	−	0.322618i
$171$			31.3590i			2.39808i
$172$	0.806274	+	5.46788i	0.0614778	+	0.416922i
$173$	−5.19433			−0.394918			−0.197459	−	0.980311i	$-0.563269\pi$
$173$	−5.19433			−0.394918			−0.197459	+	0.980311i	$0.563269\pi$
$174$	−11.5789	−	9.99676i	−0.877798	−	0.757853i
$175$	−0.183359	−	2.63939i	−0.0138606	−	0.199519i
$176$	−18.6779	+	5.63079i	−1.40790	+	0.424437i
$177$	4.12256			0.309871
$178$	−5.74684	+	6.65639i	−0.430744	+	0.498917i
$179$	−17.3274			−1.29511			−0.647555	−	0.762019i	$-0.724208\pi$
$179$	−17.3274			−1.29511			−0.647555	+	0.762019i	$0.724208\pi$
$180$	1.74589	+	11.8401i	0.130131	+	0.882507i
$181$	−21.0585			−1.56526			−0.782631	−	0.622485i	$-0.786123\pi$
$181$	−21.0585			−1.56526			−0.782631	+	0.622485i	$0.786123\pi$
$182$	5.44603	−	7.27140i	0.403687	−	0.538992i
$183$			3.53110i			0.261026i
$184$	−0.272484	−	0.173042i	−0.0200878	−	0.0127568i
$185$		−	7.83800i		−	0.576261i
$186$	12.8171	−	14.8456i	0.939795	−	1.08854i
$187$			19.1647i			1.40146i
$188$	3.52492	+	23.9048i	0.257081	+	1.74344i
$189$	−23.6073	+	1.64000i	−1.71718	+	0.119292i
$190$	−4.84313	+	5.60965i	−0.351358	+	0.406967i
$191$		−	8.43465i		−	0.610310i	−0.952303	−	0.305155i	$-0.901292\pi$
$191$		−	8.43465i		−	0.610310i	0.952303	−	0.305155i	$-0.0987083\pi$
$192$	21.7029	−	10.1962i	1.56627	−	0.735849i
$193$	−25.6337			−1.84516			−0.922578	−	0.385811i	$-0.873922\pi$
$193$	−25.6337			−1.84516			−0.922578	+	0.385811i	$0.873922\pi$
$194$	−7.25573	+	8.40410i	−0.520931	+	0.603379i
$195$		−	7.27754i		−	0.521156i
$196$	−3.93780	−	13.4348i	−0.281271	−	0.959628i
$197$			1.78729i			0.127339i	0.997971	+	0.0636697i	$0.0202804\pi$
$197$			1.78729i			0.127339i	−0.997971	+	0.0636697i	$0.979720\pi$
$198$	−31.2408	−	26.9720i	−2.22019	−	1.91681i
$199$	−22.3178			−1.58206			−0.791032	−	0.611774i	$-0.790456\pi$
$199$	−22.3178			−1.58206			−0.791032	+	0.611774i	$0.790456\pi$
$200$	−1.51629	+	2.38765i	−0.107218	+	0.168832i
$201$			7.72612i			0.544958i
$202$	11.6741	+	10.0789i	0.821388	+	0.709151i
$203$	9.52505	−	0.661706i	0.668527	−	0.0464427i
$204$	−3.43639	−	23.3044i	−0.240595	−	1.63164i
$205$			10.4815i			0.732060i
$206$	−16.9348	−	14.6208i	−1.17990	−	1.01868i
$207$		−	0.682913i		−	0.0474657i
$208$	−9.29864	+	2.80324i	−0.644745	+	0.194370i
$209$		−	25.5579i		−	1.76787i
$210$	−8.97647	−	6.72307i	−0.619435	−	0.463936i
$211$	8.58471			0.590996			0.295498	−	0.955343i	$-0.404514\pi$
$211$	8.58471			0.590996			0.295498	+	0.955343i	$0.404514\pi$
$212$	1.32188	−	0.194920i	0.0907872	−	0.0133872i
$213$	28.2859			1.93812
$214$	6.99484	+	6.03904i	0.478157	+	0.412820i
$215$	−2.76350			−0.188469
$216$	21.3556	+	13.5620i	1.45307	+	0.922776i
$217$	0.848389	+	12.2123i	0.0575924	+	0.829024i
$218$	10.1022	−	11.7011i	0.684207	−	0.792497i
$219$	16.8637			1.13954
$220$	−1.42292	−	9.64977i	−0.0959332	−	0.650587i
$221$			9.54096i			0.641794i
$222$	−25.1484	−	21.7121i	−1.68785	−	1.45722i
$223$	14.0359			0.939916			0.469958	−	0.882689i	$-0.344269\pi$
$223$	14.0359			0.939916			0.469958	+	0.882689i	$0.344269\pi$
$224$	−5.13253	+	14.0591i	−0.342932	+	0.939360i
$225$	−5.98405			−0.398937
$226$	3.98214	+	3.43801i	0.264888	+	0.228693i
$227$			29.9063i			1.98495i	0.122442	+	0.992476i	$0.460927\pi$
$227$			29.9063i			1.98495i	−0.122442	+	0.992476i	$0.539073\pi$
$228$	4.58274	+	31.0786i	0.303500	+	2.05823i
$229$	8.92103			0.589518			0.294759	−	0.955572i	$-0.404761\pi$
$229$	8.92103			0.589518			0.294759	+	0.955572i	$0.404761\pi$
$230$	0.105470	−	0.122163i	0.00695450	−	0.00805518i
$231$	38.5831	−	2.68037i	2.53858	−	0.176356i
$232$	−8.61657	−	5.47198i	−0.565706	−	0.359253i
$233$	0.565155			0.0370245			0.0185123	−	0.999829i	$-0.494107\pi$
$233$	0.565155			0.0370245			0.0185123	+	0.999829i	$0.494107\pi$
$234$	−15.5530	−	13.4278i	−1.01673	−	0.877800i
$235$	−12.0817			−0.788120
$236$	2.72139	−	0.401286i	0.177147	−	0.0261215i
$237$	35.6095			2.31309
$238$	11.7683	+	8.81404i	0.762824	+	0.571329i
$239$		−	8.51136i		−	0.550554i	−0.961365	−	0.275277i	$-0.911230\pi$
$239$		−	8.51136i		−	0.550554i	0.961365	−	0.275277i	$-0.0887695\pi$
$240$	3.46057	+	11.4791i	0.223379	+	0.740971i
$241$			2.17523i			0.140119i	0.997543	+	0.0700595i	$0.0223189\pi$
$241$			2.17523i			0.140119i	−0.997543	+	0.0700595i	$0.977681\pi$
$242$	13.6865	+	11.8163i	0.879803	+	0.759584i
$243$		−	0.286112i		−	0.0183541i
$244$	0.343713	+	2.33095i	0.0220040	+	0.149224i
$245$	6.93276	−	0.967910i	0.442918	−	0.0618375i
$246$	33.6302	+	29.0348i	2.14418	+	1.85119i
$247$		−	12.7238i		−	0.809593i
$248$	7.01576	−	11.0475i	0.445501	−	0.701518i
$249$	16.5557			1.04918
$250$	−1.07046	−	0.924187i	−0.0677017	−	0.0584507i
$251$		−	9.41690i		−	0.594390i	−0.954817	−	0.297195i	$-0.903949\pi$
$251$		−	9.41690i		−	0.594390i	0.954817	−	0.297195i	$-0.0960511\pi$
$252$	−30.9304	+	6.77907i	−1.94843	+	0.427042i
$253$			0.556580i			0.0349919i
$254$	3.51492	−	4.07123i	0.220546	−	0.255452i
$255$	11.7782			0.737580
$256$	13.3340	−	8.84327i	0.833378	−	0.552704i
$257$		−	4.44138i		−	0.277045i	−0.990359	−	0.138523i	$-0.955765\pi$
$257$		−	4.44138i		−	0.277045i	0.990359	−	0.138523i	$-0.0442354\pi$
$258$	−7.65518	+	8.86676i	−0.476591	+	0.552021i
$259$	20.6875	−	1.43717i	1.28546	−	0.0893011i
$260$	−0.708388	−	4.80405i	−0.0439324	−	0.297935i
$261$		−	21.5953i		−	1.33671i
$262$	−7.09876	+	8.22228i	−0.438563	+	0.507974i
$263$		−	13.6247i		−	0.840132i	−0.907493	−	0.420066i	$-0.862007\pi$
$263$		−	13.6247i		−	0.840132i	0.907493	−	0.420066i	$-0.137993\pi$
$264$	−34.9031	−	22.1654i	−2.14814	−	1.36418i
$265$			0.668088i			0.0410403i
$266$	−15.6941	−	11.7543i	−0.962267	−	0.720705i
$267$	−18.6383			−1.14064
$268$	0.752052	+	5.10017i	0.0459389	+	0.311542i
$269$	10.2713			0.626253			0.313127	−	0.949711i	$-0.398624\pi$
$269$	10.2713			0.626253			0.313127	+	0.949711i	$0.398624\pi$
$270$	−8.26612	+	9.57439i	−0.503060	+	0.582679i
$271$	2.67264			0.162352			0.0811758	−	0.996700i	$-0.474132\pi$
$271$	2.67264			0.162352			0.0811758	+	0.996700i	$0.474132\pi$
$272$	−4.53686	−	15.0492i	−0.275087	−	0.912494i
$273$	19.2083	−	1.33440i	1.16254	−	0.0807616i
$274$	−18.1698	−	15.6871i	−1.09768	−	0.947690i
$275$	4.87706			0.294098
$276$	−0.0997996	−	0.676807i	−0.00600723	−	0.0407390i
$277$			28.1383i			1.69067i	0.534239	+	0.845333i	$0.320598\pi$
$277$			28.1383i			1.69067i	−0.534239	+	0.845333i	$0.679402\pi$
$278$	−2.35296	+	2.72536i	−0.141121	+	0.163456i
$279$	27.6878			1.65763
$280$	−6.57997	−	3.56427i	−0.393228	−	0.213006i
$281$	0.466842			0.0278494			0.0139247	−	0.999903i	$-0.495567\pi$
$281$	0.466842			0.0278494			0.0139247	+	0.999903i	$0.495567\pi$
$282$	−33.4674	+	38.7643i	−1.99295	+	2.30838i
$283$		−	10.8004i		−	0.642019i	−0.947076	−	0.321009i	$-0.895978\pi$
$283$		−	10.8004i		−	0.642019i	0.947076	−	0.321009i	$-0.104022\pi$
$284$	18.6721	−	2.75332i	1.10798	−	0.163379i
$285$	−15.7073			−0.930423
$286$	12.6758	+	10.9437i	0.749536	+	0.647117i
$287$	−27.6648	+	1.92188i	−1.63300	+	0.113445i
$288$	30.9172	+	13.7843i	1.82181	+	0.812250i
$289$	1.55860			0.0916824
$290$	3.33521	−	3.86307i	0.195850	−	0.226848i
$291$	−23.5319			−1.37947
$292$	11.1321	−	1.64150i	0.651456	−	0.0960613i
$293$	−7.34532			−0.429118			−0.214559	−	0.976711i	$-0.568831\pi$
$293$	−7.34532			−0.429118			−0.214559	+	0.976711i	$0.568831\pi$
$294$	16.0989	−	24.9251i	0.938906	−	1.45366i
$295$			1.37541i			0.0800793i
$296$	−18.7144	−	11.8846i	−1.08775	−	0.690781i
$297$		−	43.6214i		−	2.53117i
$298$	−12.7468	+	14.7642i	−0.738402	+	0.855269i
$299$			0.277089i			0.0160244i
$300$	−5.93055	+	0.874498i	−0.342401	+	0.0504892i
$301$	−0.506712	−	7.29396i	−0.0292064	−	0.420417i
$302$	0.118642	−	0.137419i	0.00682706	−	0.00790758i
$303$			32.6882i			1.87789i
$304$	6.05032	+	20.0696i	0.347010	+	1.15107i
$305$	−1.17808			−0.0674564
$306$	21.7319	−	25.1714i	1.24233	−	1.43895i
$307$		−	5.08078i		−	0.289975i	−0.989433	−	0.144988i	$-0.953686\pi$
$307$		−	5.08078i		−	0.289975i	0.989433	−	0.144988i	$-0.0463142\pi$
$308$	25.2086	−	5.52501i	1.43639	−	0.314817i
$309$		−	47.4184i		−	2.69754i
$310$	4.95294	+	4.27615i	0.281308	+	0.242869i
$311$	17.8319			1.01116			0.505578	−	0.862781i	$-0.331279\pi$
$311$	17.8319			1.01116			0.505578	+	0.862781i	$0.331279\pi$
$312$	−17.3762	−	11.0348i	−0.983735	−	0.624724i
$313$			3.54008i			0.200097i	0.994983	+	0.100049i	$0.0318998\pi$
$313$			3.54008i			0.200097i	−0.994983	+	0.100049i	$0.968100\pi$
$314$	−14.0857	−	12.1610i	−0.794900	−	0.686282i
$315$	−1.09723	−	15.7942i	−0.0618218	−	0.889904i
$316$	23.5065	−	3.46619i	1.32235	−	0.194988i
$317$		−	4.86360i		−	0.273167i	−0.990629	−	0.136583i	$-0.956388\pi$
$317$		−	4.86360i		−	0.273167i	0.990629	−	0.136583i	$-0.0436122\pi$
$318$	2.14358	+	1.85067i	0.120206	+	0.103781i
$319$			17.6004i			0.985431i
$320$	3.40175	+	7.24072i	0.190164	+	0.404769i
$321$			19.5859i			1.09318i
$322$	0.341774	+	0.255977i	0.0190463	+	0.0142651i
$323$	20.5925			1.14580
$324$	2.58401	+	17.5239i	0.143556	+	0.973549i
$325$	2.42800			0.134681
$326$	0.169415	+	0.146265i	0.00938301	+	0.00810088i
$327$	32.7637			1.81183
$328$	25.0262	+	15.8930i	1.38184	+	0.877542i
$329$	−2.21528	−	31.8882i	−0.122132	−	1.75805i
$330$	13.5099	−	15.6482i	0.743698	−	0.861403i
$331$	−9.38870			−0.516050			−0.258025	−	0.966138i	$-0.583072\pi$
$331$	−9.38870			−0.516050			−0.258025	+	0.966138i	$0.583072\pi$
$332$	10.9288	−	1.61152i	0.599794	−	0.0884435i
$333$		−	46.9030i		−	2.57027i
$334$	17.8879	+	15.4437i	0.978784	+	0.845040i
$335$	−2.57766			−0.140832
$336$	−29.6632	+	11.2386i	−1.61826	+	0.613115i
$337$	19.7551			1.07613			0.538064	−	0.842904i	$-0.319156\pi$
$337$	19.7551			1.07613			0.538064	+	0.842904i	$0.319156\pi$
$338$	−7.60540	−	6.56618i	−0.413679	−	0.357153i
$339$			11.1502i			0.605596i
$340$	7.77504	−	1.14648i	0.421661	−	0.0621765i
$341$	−22.5658			−1.22201
$342$	−28.9815	+	33.5684i	−1.56714	+	1.81517i
$343$	3.82587	+	18.1208i	0.206578	+	0.978430i
$344$	−4.19026	+	6.59828i	−0.225924	+	0.355755i
$345$	0.342063			0.0184161
$346$	−5.56031	−	4.80053i	−0.298924	−	0.258078i
$347$	−29.8093			−1.60025			−0.800124	−	0.599835i	$-0.795233\pi$
$347$	−29.8093			−1.60025			−0.800124	+	0.599835i	$0.795233\pi$
$348$	−3.15589	−	21.4022i	−0.169174	−	1.14728i
$349$	15.6993			0.840364			0.420182	−	0.907440i	$-0.361966\pi$
$349$	15.6993			0.840364			0.420182	+	0.907440i	$0.361966\pi$
$350$	2.24301	−	2.99481i	0.119894	−	0.160079i
$351$		−	21.7165i		−	1.15914i
$352$	−25.1978	−	11.2344i	−1.34305	−	0.598794i
$353$		−	10.2186i		−	0.543879i	−0.962314	−	0.271939i	$-0.912335\pi$
$353$		−	10.2186i		−	0.543879i	0.962314	−	0.271939i	$-0.0876651\pi$
$354$	4.41303	+	3.81002i	0.234550	+	0.202500i
$355$			9.43699i			0.500863i
$356$	−12.3035	+	1.81423i	−0.652084	+	0.0961539i
$357$	2.15964	+	31.0873i	0.114300	+	1.64531i
$358$	−18.5482	−	16.0137i	−0.980304	−	0.846352i
$359$			23.4758i			1.23900i	0.784995	+	0.619502i	$0.212666\pi$
$359$			23.4758i			1.23900i	−0.784995	+	0.619502i	$0.787334\pi$
$360$	−9.07353	+	14.2878i	−0.478217	+	0.753034i
$361$	−8.46208			−0.445373
$362$	−22.5422	−	19.4619i	−1.18479	−	1.02290i
$363$			38.3230i			2.01144i
$364$	12.5499	−	2.75058i	0.657792	−	0.144169i
$365$			5.62623i			0.294490i
$366$	−3.26339	+	3.77989i	−0.170580	+	0.197578i
$367$	−21.5002			−1.12230			−0.561151	−	0.827714i	$-0.689641\pi$
$367$	−21.5002			−1.12230			−0.561151	+	0.827714i	$0.689641\pi$
$368$	−0.131759	−	0.437060i	−0.00686844	−	0.0227833i
$369$			62.7218i			3.26517i
$370$	7.24377	−	8.39024i	0.376586	−	0.436188i
$371$	−1.76334	+	0.122500i	−0.0915483	+	0.00635987i
$372$	27.4403	−	4.04625i	1.42271	−	0.209788i
$373$		−	0.781051i		−	0.0404413i	−0.999796	−	0.0202206i	$-0.993563\pi$
$373$		−	0.781051i		−	0.0404413i	0.999796	−	0.0202206i	$-0.00643687\pi$
$374$	−17.7117	+	20.5149i	−0.915851	+	1.06080i
$375$		−	2.99734i		−	0.154782i
$376$	−18.3192	+	28.8468i	−0.944742	+	1.48766i
$377$			8.76218i			0.451275i
$378$	−26.7862	−	20.0620i	−1.37773	−	1.03188i
$379$	4.53381			0.232886			0.116443	−	0.993197i	$-0.462851\pi$
$379$	4.53381			0.232886			0.116443	+	0.993197i	$0.462851\pi$
$380$	−10.3687	+	1.52894i	−0.531905	+	0.0784328i
$381$	11.3997			0.584023
$382$	7.79519	−	9.02893i	0.398837	−	0.461960i
$383$	36.0555			1.84235			0.921176	−	0.389147i	$-0.127230\pi$
$383$	36.0555			1.84235			0.921176	+	0.389147i	$0.127230\pi$
$384$	32.6552	+	9.14293i	1.66643	+	0.466573i
$385$	0.894251	+	12.8725i	0.0455752	+	0.656041i
$386$	−27.4398	−	23.6903i	−1.39665	−	1.20581i
$387$	−16.5369			−0.840619
$388$	−15.5339	+	2.29057i	−0.788615	+	0.116286i
$389$			21.1691i			1.07332i	0.843800	+	0.536658i	$0.180313\pi$
$389$			21.1691i			1.07332i	−0.843800	+	0.536658i	$0.819687\pi$
$390$	6.72581	−	7.79030i	0.340574	−	0.394477i
$391$	−0.448449			−0.0226791
$392$	8.20101	−	18.0206i	0.414214	−	0.910180i
$393$	−23.0228			−1.16135
$394$	−1.65179	+	1.91322i	−0.0832161	+	0.0963867i
$395$			11.8804i			0.597766i
$396$	−8.51482	−	57.7447i	−0.427886	−	2.90178i
$397$	−14.1445			−0.709891			−0.354946	−	0.934887i	$-0.615501\pi$
$397$	−14.1445			−0.709891			−0.354946	+	0.934887i	$0.615501\pi$
$398$	−23.8902	−	20.6258i	−1.19751	−	1.03388i
$399$	−2.88008	−	41.4578i	−0.144184	−	2.07549i
$400$	−3.82975	+	1.15455i	−0.191488	+	0.0577274i
$401$	17.8168			0.889729			0.444865	−	0.895598i	$-0.353252\pi$
$401$	17.8168			0.889729			0.444865	+	0.895598i	$0.353252\pi$
$402$	−7.14037	+	8.27048i	−0.356130	+	0.412494i
$403$	−11.2342			−0.559616
$404$	3.18183	+	21.5781i	0.158302	+	1.07355i
$405$	−8.85669			−0.440092
$406$	10.8077	+	8.09460i	0.536377	+	0.401728i
$407$			38.2264i			1.89481i
$408$	17.8591	−	28.1223i	0.884159	−	1.39226i
$409$		−	32.5292i		−	1.60846i	−0.594315	−	0.804232i	$-0.702577\pi$
$409$		−	32.5292i		−	1.60846i	0.594315	−	0.804232i	$-0.297423\pi$
$410$	−9.68687	+	11.2200i	−0.478400	+	0.554117i
$411$		−	50.8766i		−	2.50956i
$412$	−4.61566	−	31.3018i	−0.227397	−	1.54213i
$413$	−3.63024	+	0.252193i	−0.178632	+	0.0124096i
$414$	0.631139	−	0.731029i	0.0310188	−	0.0359281i
$415$			5.52348i			0.271137i
$416$	−12.5445	−	5.59293i	−0.615046	−	0.274216i
$417$	−7.63116			−0.373699
$418$	23.6202	−	27.3586i	1.15530	−	1.33815i
$419$			34.4793i			1.68443i	0.539146	+	0.842213i	$0.318747\pi$
$419$			34.4793i			1.68443i	−0.539146	+	0.842213i	$0.681253\pi$
$420$	−3.39556	−	15.4927i	−0.165686	−	0.755966i
$421$		−	12.2635i		−	0.597688i	−0.954302	−	0.298844i	$-0.903399\pi$
$421$		−	12.2635i		−	0.597688i	0.954302	−	0.298844i	$-0.0966010\pi$
$422$	9.18957	+	7.93388i	0.447341	+	0.386215i
$423$	−72.2972			−3.51521
$424$	1.59516	+	1.01301i	0.0774679	+	0.0491962i
$425$			3.92955i			0.190611i
$426$	30.2788	+	26.1414i	1.46701	+	1.26656i
$427$	−0.216011	−	3.10940i	−0.0104535	−	0.150475i
$428$	1.90647	+	12.9291i	0.0921529	+	0.624950i
$429$			35.4930i			1.71362i
$430$	−2.95821	−	2.55399i	−0.142658	−	0.123164i
$431$			21.7718i			1.04871i	0.851499	+	0.524357i	$0.175694\pi$
$431$			21.7718i			1.04871i	−0.851499	+	0.524357i	$0.824306\pi$
$432$	10.3265	+	34.2541i	0.496835	+	1.64805i
$433$			26.1597i			1.25715i	0.777747	+	0.628577i	$0.216362\pi$
$433$			26.1597i			1.25715i	−0.777747	+	0.628577i	$0.783638\pi$
$434$	−10.3783	+	13.8568i	−0.498173	+	0.665148i
$435$	10.8168			0.518627
$436$	21.6279	−	3.18918i	1.03579	−	0.152734i
$437$	0.598049			0.0286086
$438$	18.0519	+	15.5852i	0.862553	+	0.744691i
$439$	−29.5333			−1.40955			−0.704775	−	0.709431i	$-0.748952\pi$
$439$	−29.5333			−1.40955			−0.704775	+	0.709431i	$0.748952\pi$
$440$	7.39501	−	11.6447i	0.352543	−	0.555140i
$441$	41.4860	−	5.79202i	1.97552	−	0.275811i
$442$	−8.81763	+	10.2132i	−0.419412	+	0.485792i
$443$	−21.7915			−1.03535			−0.517673	−	0.855579i	$-0.673202\pi$
$443$	−21.7915			−1.03535			−0.517673	+	0.855579i	$0.673202\pi$
$444$	−6.85431	−	46.4837i	−0.325291	−	2.20602i
$445$		−	6.21826i		−	0.294774i
$446$	15.0249	+	12.9718i	0.711449	+	0.614234i
$447$	−41.3407			−1.95535
$448$	−18.4873	+	10.3062i	−0.873445	+	0.486923i
$449$	−1.75711			−0.0829231			−0.0414615	−	0.999140i	$-0.513201\pi$
$449$	−1.75711			−0.0829231			−0.0414615	+	0.999140i	$0.513201\pi$
$450$	−6.40567	−	5.53038i	−0.301966	−	0.260705i
$451$		−	51.1189i		−	2.40709i
$452$	1.08535	+	7.36048i	0.0510506	+	0.346208i
$453$	0.384781			0.0180786
$454$	−27.6390	+	32.0134i	−1.29716	+	1.50246i
$455$	0.445195	+	6.40844i	0.0208711	+	0.300432i
$456$	−23.8168	+	37.5037i	−1.11532	+	1.75627i
$457$	3.78856			0.177221			0.0886106	−	0.996066i	$-0.471757\pi$
$457$	3.78856			0.177221			0.0886106	+	0.996066i	$0.471757\pi$
$458$	9.54958	+	8.24470i	0.446223	+	0.385249i
$459$	35.1468			1.64051
$460$	0.225803	−	0.0332961i	0.0105281	−	0.00155244i
$461$	−32.3541			−1.50688			−0.753439	−	0.657517i	$-0.771607\pi$
$461$	−32.3541			−1.50688			−0.753439	+	0.657517i	$0.771607\pi$
$462$	43.7787	+	32.7888i	2.03677	+	1.52547i
$463$			31.2530i			1.45245i	0.687456	+	0.726226i	$0.258727\pi$
$463$			31.2530i			1.45245i	−0.687456	+	0.726226i	$0.741273\pi$
$464$	−4.16654	−	13.8208i	−0.193427	−	0.641617i
$465$			13.8685i			0.643137i
$466$	0.604974	+	0.522309i	0.0280249	+	0.0241955i
$467$			22.6800i			1.04950i	0.851255	+	0.524752i	$0.175842\pi$
$467$			22.6800i			1.04950i	−0.851255	+	0.524752i	$0.824158\pi$
$468$	−4.23903	−	28.7477i	−0.195949	−	1.32886i
$469$	−0.472636	−	6.80344i	−0.0218243	−	0.314154i
$470$	−12.9329	−	11.1657i	−0.596550	−	0.515035i
$471$		−	39.4406i		−	1.81733i
$472$	3.28399	+	2.08551i	0.151158	+	0.0959934i
$473$	13.4777			0.619708
$474$	38.1184	+	32.9098i	1.75084	+	1.51160i
$475$		−	5.24043i		−	0.240447i
$476$	4.45163	+	20.3111i	0.204040	+	0.930959i
$477$			3.99787i			0.183050i
$478$	7.86608	−	9.11104i	0.359786	−	0.416729i
$479$	−12.8639			−0.587765			−0.293883	−	0.955842i	$-0.594947\pi$
$479$	−12.8639			−0.587765			−0.293883	+	0.955842i	$0.594947\pi$
$480$	−6.90442	+	15.4861i	−0.315142	+	0.706839i
$481$			19.0307i			0.867723i
$482$	−2.01032	+	2.32849i	−0.0915675	+	0.106060i
$483$	0.0627202	+	0.902838i	0.00285387	+	0.0410805i
$484$	3.73032	+	25.2978i	0.169560	+	1.14990i
$485$		−	7.85094i		−	0.356493i
$486$	0.264421	−	0.306271i	0.0119944	−	0.0138927i
$487$		−	20.3133i		−	0.920483i	−0.887794	−	0.460241i	$-0.847763\pi$
$487$		−	20.3133i		−	0.920483i	0.887794	−	0.460241i	$-0.152237\pi$
$488$	−1.78630	+	2.81283i	−0.0808620	+	0.127331i
$489$			0.474370i			0.0214518i
$490$	8.31575	+	5.37106i	0.375667	+	0.242640i
$491$	16.4582			0.742746			0.371373	−	0.928484i	$-0.378887\pi$
$491$	16.4582			0.742746			0.371373	+	0.928484i	$0.378887\pi$
$492$	9.16606	+	62.1611i	0.413238	+	2.80244i
$493$	−14.1810			−0.638680
$494$	11.7591	−	13.6202i	0.529068	−	0.612804i
$495$	29.1845			1.31175
$496$	17.7200	−	5.34202i	0.795653	−	0.239864i
$497$	−24.9079	+	1.73035i	−1.11727	+	0.0776170i
$498$	17.7222	+	15.3006i	0.794151	+	0.685636i
$499$	18.7483			0.839291			0.419645	−	0.907688i	$-0.362154\pi$
$499$	18.7483			0.839291			0.419645	+	0.907688i	$0.362154\pi$
$500$	−0.291758	−	1.97860i	−0.0130478	−	0.0884859i
$501$			50.0872i			2.23773i
$502$	8.70298	−	10.0804i	0.388433	−	0.449910i
$503$	−19.5629			−0.872269			−0.436134	−	0.899882i	$-0.643653\pi$
$503$	−19.5629			−0.872269			−0.436134	+	0.899882i	$0.643653\pi$
$504$	−39.3748	−	21.3288i	−1.75389	−	0.950059i
$505$	−10.9057			−0.485298
$506$	−0.514384	+	0.595795i	−0.0228672	+	0.0264863i
$507$		−	21.2956i		−	0.945769i
$508$	7.52515	−	1.10963i	0.333875	−	0.0492320i
$509$	19.9845			0.885797			0.442898	−	0.896572i	$-0.353950\pi$
$509$	19.9845			0.885797			0.442898	+	0.896572i	$0.353950\pi$
$510$	12.6081	+	10.8853i	0.558295	+	0.482008i
$511$	−14.8498	+	1.03162i	−0.656917	+	0.0456361i
$512$	22.4464	+	2.85680i	0.991998	+	0.126254i
$513$	−46.8715			−2.06943
$514$	4.10466	−	4.75430i	0.181049	−	0.209703i
$515$	15.8202			0.697119
$516$	−16.3891	+	2.41668i	−0.721489	+	0.106388i
$517$	58.9229			2.59143
$518$	23.4733	+	17.5807i	1.03136	+	0.772452i
$519$		−	15.5692i		−	0.683411i
$520$	3.68154	−	5.79722i	0.161446	−	0.254225i
$521$		−	1.35111i		−	0.0591932i	−0.999562	−	0.0295966i	$-0.990578\pi$
$521$		−	1.35111i		−	0.0591932i	0.999562	−	0.0295966i	$-0.00942226\pi$
$522$	19.9581	−	23.1168i	0.873541	−	1.01180i
$523$		−	28.1452i		−	1.23071i	−0.788252	−	0.615353i	$-0.789014\pi$
$523$		−	28.1452i		−	1.23071i	0.788252	−	0.615353i	$-0.210986\pi$
$524$	−15.1978	+	2.24102i	−0.663921	+	0.0978994i
$525$	7.91115	−	0.549588i	0.345271	−	0.0239860i
$526$	12.5917	−	14.5846i	0.549025	−	0.635919i
$527$		−	18.1818i		−	0.792012i
$528$	−16.8774	−	55.9841i	−0.734495	−	2.43640i
$529$	22.9870			0.999434
$530$	−0.617438	+	0.715160i	−0.0268198	+	0.0310645i
$531$			8.23051i			0.357174i
$532$	−5.93666	−	27.0868i	−0.257387	−	1.17436i
$533$		−	25.4491i		−	1.10232i
$534$	−19.9515	−	17.2252i	−0.863384	−	0.745408i
$535$	−6.53444			−0.282508
$536$	−3.90847	+	6.15455i	−0.168820	+	0.265836i
$537$		−	51.9360i		−	2.24121i
$538$	10.9950	+	9.49262i	0.474028	+	0.409256i
$539$	−33.8115	+	4.72055i	−1.45636	+	0.203329i
$540$	−17.6971	+	2.60954i	−0.761560	+	0.112297i
$541$			0.0636523i			0.00273663i	0.999999	+	0.00136831i	$0.000435548\pi$
$541$			0.0636523i			0.00273663i	−0.999999	+	0.00136831i	$0.999564\pi$
$542$	2.86095	+	2.47002i	0.122888	+	0.106096i
$543$		−	63.1194i		−	2.70871i
$544$	9.05179	−	20.3025i	0.388092	−	0.870461i
$545$			10.9309i			0.468229i
$546$	21.7949	+	16.3236i	0.932734	+	0.698586i
$547$	26.6632			1.14004			0.570018	−	0.821632i	$-0.306936\pi$
$547$	26.6632			1.14004			0.570018	+	0.821632i	$0.306936\pi$
$548$	−4.95227	−	33.5847i	−0.211551	−	1.43467i
$549$	−7.04966			−0.300872
$550$	5.22068	+	4.50731i	0.222611	+	0.192192i
$551$	18.9117			0.805665
$552$	0.518665	−	0.816727i	0.0220759	−	0.0347622i
$553$	−31.3569	+	2.17837i	−1.33343	+	0.0926336i
$554$	−26.0050	+	30.1208i	−1.10485	+	1.27971i
$555$	23.4931			0.997228
$556$	−5.03748	+	0.742809i	−0.213637	+	0.0315021i
$557$		−	9.81678i		−	0.415950i	−0.978134	−	0.207975i	$-0.933313\pi$
$557$		−	9.81678i		−	0.415950i	0.978134	−	0.207975i	$-0.0666873\pi$
$558$	29.6386	+	25.5887i	1.25470	+	1.08326i
$559$	6.70978			0.283794
$560$	−3.74952	−	9.89652i	−0.158446	−	0.418204i
$561$	−57.4430			−2.42525
$562$	0.499734	+	0.431449i	0.0210800	+	0.0181996i
$563$			30.8680i			1.30093i	0.759535	+	0.650466i	$0.225426\pi$
$563$			30.8680i			1.30093i	−0.759535	+	0.650466i	$0.774574\pi$
$564$	−71.6509	+	10.5654i	−3.01705	+	0.444883i
$565$	−3.72004			−0.156503
$566$	9.98161	−	11.5614i	0.419558	−	0.485962i
$567$	−1.62395	−	23.3763i	−0.0681995	−	0.981711i
$568$	22.5322	+	14.3092i	0.945432	+	0.600400i
$569$	30.9000			1.29540			0.647698	−	0.761897i	$-0.275732\pi$
$569$	30.9000			1.29540			0.647698	+	0.761897i	$0.275732\pi$
$570$	−16.8140	−	14.5165i	−0.704263	−	0.608030i
$571$	−37.5033			−1.56946			−0.784732	−	0.619835i	$-0.787199\pi$
$571$	−37.5033			−1.56946			−0.784732	+	0.619835i	$0.787199\pi$
$572$	3.45485	+	23.4296i	0.144455	+	0.979642i
$573$	25.2815			1.05615
$574$	−31.3901	−	23.5101i	−1.31020	−	0.981294i
$575$			0.114122i			0.00475922i
$576$	20.3563	+	43.3288i	0.848178	+	1.80537i
$577$			17.4216i			0.725272i	0.931931	+	0.362636i	$0.118123\pi$
$577$			17.4216i			0.725272i	−0.931931	+	0.362636i	$0.881877\pi$
$578$	1.66842	+	1.44044i	0.0693969	+	0.0599143i
$579$		−	76.8330i		−	3.19307i
$580$	7.14040	−	1.05290i	0.296489	−	0.0437192i
$581$	−14.5786	+	1.01278i	−0.604822	+	0.0420171i
$582$	−25.1899	−	21.7479i	−1.04416	−	0.901479i
$583$		−	3.25830i		−	0.134945i
$584$	13.4335	+	8.53097i	0.555881	+	0.353014i
$585$	14.5293			0.600711
$586$	−7.86286	−	6.78845i	−0.324812	−	0.280428i
$587$		−	12.4270i		−	0.512918i	−0.966555	−	0.256459i	$-0.917444\pi$
$587$		−	12.4270i		−	0.512918i	0.966555	−	0.256459i	$-0.0825558\pi$
$588$	40.2687	−	11.8029i	1.66065	−	0.486744i
$589$			24.2471i			0.999086i
$590$	−1.27113	+	1.47232i	−0.0523317	+	0.0606143i
$591$	−5.35713			−0.220363
$592$	−9.04934	−	30.0176i	−0.371926	−	1.23372i
$593$			13.7257i			0.563646i	0.959466	+	0.281823i	$0.0909391\pi$
$593$			13.7257i			0.563646i	−0.959466	+	0.281823i	$0.909061\pi$
$594$	40.3143	−	46.6948i	1.65412	−	1.91591i
$595$	−10.3716	+	0.720518i	−0.425195	+	0.0295384i
$596$	−27.2898	+	4.02406i	−1.11783	+	0.164832i
$597$		−	66.8940i		−	2.73779i
$598$	−0.256082	+	0.296612i	−0.0104720	+	0.0121293i
$599$		−	27.7947i		−	1.13566i	−0.823146	−	0.567829i	$-0.807783\pi$
$599$		−	27.7947i		−	1.13566i	0.823146	−	0.567829i	$-0.192217\pi$
$600$	−7.15660	−	4.54482i	−0.292167	−	0.185542i
$601$		−	38.9855i		−	1.59025i	−0.606443	−	0.795127i	$-0.707404\pi$
$601$		−	38.9855i		−	1.59025i	0.606443	−	0.795127i	$-0.292596\pi$
$602$	6.19857	−	8.27617i	0.252635	−	0.337311i
$603$	−15.4248			−0.628148
$604$	0.254002	−	0.0374542i	0.0103352	−	0.00152399i
$605$	−12.7857			−0.519811
$606$	−30.2100	+	34.9913i	−1.22720	+	1.42142i
$607$	11.7981			0.478872			0.239436	−	0.970912i	$-0.423038\pi$
$607$	11.7981			0.478872			0.239436	+	0.970912i	$0.423038\pi$
$608$	−12.0714	+	27.0752i	−0.489560	+	1.09805i
$609$	1.98336	+	28.5498i	0.0803697	+	1.15690i
$610$	−1.26108	−	1.08876i	−0.0510597	−	0.0440827i
$611$	29.3342			1.18674
$612$	46.5262	−	6.86058i	1.88071	−	0.277323i
$613$			13.4628i			0.543756i	0.962332	+	0.271878i	$0.0876447\pi$
$613$			13.4628i			0.543756i	−0.962332	+	0.271878i	$0.912355\pi$
$614$	4.69559	−	5.43876i	0.189498	−	0.219490i
$615$	−31.4166			−1.26684
$616$	32.0909	+	17.3832i	1.29298	+	0.700387i
$617$	−15.2924			−0.615650			−0.307825	−	0.951443i	$-0.599601\pi$
$617$	−15.2924			−0.615650			−0.307825	+	0.951443i	$0.599601\pi$
$618$	43.8234	−	50.7594i	1.76284	−	2.04184i
$619$			3.76548i			0.151347i	0.997133	+	0.0756736i	$0.0241107\pi$
$619$			3.76548i			0.151347i	−0.997133	+	0.0756736i	$0.975889\pi$
$620$	1.34995	+	9.15488i	0.0542151	+	0.367669i
$621$	1.02073			0.0409606
$622$	19.0883	+	16.4800i	0.765372	+	0.660789i
$623$	16.4124	−	1.14017i	0.657550	−	0.0456801i
$624$	−8.40227	−	27.8712i	−0.336360	−	1.11574i
$625$	1.00000			0.0400000
$626$	−3.27169	+	3.78950i	−0.130763	+	0.151459i
$627$	76.6056			3.05933
$628$	−3.83911	−	26.0356i	−0.153197	−	1.03893i
$629$	−30.7998			−1.22807
$630$	13.4223	−	17.9211i	0.534757	−	0.713994i
$631$			21.1777i			0.843070i	0.906812	+	0.421535i	$0.138508\pi$
$631$			21.1777i			0.843070i	−0.906812	+	0.421535i	$0.861492\pi$
$632$	28.3662	+	18.0140i	1.12835	+	0.716560i
$633$			25.7313i			1.02273i
$634$	4.49487	−	5.20627i	0.178514	−	0.206768i
$635$			3.80326i			0.150928i
$636$	0.584241	+	3.96213i	0.0231667	+	0.157109i
$637$	−16.8327	+	2.35009i	−0.666937	+	0.0931138i
$638$	−16.2660	+	18.8404i	−0.643978	+	0.745900i
$639$			56.4714i			2.23397i
$640$	−3.05035	+	10.8947i	−0.120576	+	0.430652i
$641$	29.5569			1.16743			0.583713	−	0.811960i	$-0.301599\pi$
$641$	29.5569			1.16743			0.583713	+	0.811960i	$0.301599\pi$
$642$	−18.1011	+	20.9659i	−0.714392	+	0.827458i
$643$		−	19.8063i		−	0.781085i	−0.920585	−	0.390543i	$-0.872287\pi$
$643$		−	19.8063i		−	0.781085i	0.920585	−	0.390543i	$-0.127713\pi$
$644$	0.129284	+	0.589876i	0.00509451	+	0.0232444i
$645$		−	8.28315i		−	0.326149i
$646$	22.0434	+	19.0314i	0.867288	+	0.748779i
$647$	−12.4755			−0.490461			−0.245231	−	0.969465i	$-0.578864\pi$
$647$	−12.4755			−0.490461			−0.245231	+	0.969465i	$0.578864\pi$
$648$	−13.4293	+	21.1467i	−0.527552	+	0.830720i
$649$		−	6.70794i		−	0.263310i
$650$	2.59907	+	2.24393i	0.101944	+	0.0880140i
$651$	−36.6044	+	2.54291i	−1.43464	+	0.0996646i
$652$	0.0461747	+	0.313141i	0.00180834	+	0.0122636i
$653$			9.99757i			0.391235i	0.980680	+	0.195618i	$0.0626712\pi$
$653$			9.99757i			0.391235i	−0.980680	+	0.195618i	$0.937329\pi$
$654$	35.0721	+	30.2797i	1.37143	+	1.18403i
$655$		−	7.68109i		−	0.300125i
$656$	12.1014	+	40.1416i	0.472480	+	1.56727i
$657$			33.6676i			1.31350i
$658$	27.0993	−	36.1823i	1.05644	−	1.41053i
$659$	27.2870			1.06295			0.531475	−	0.847074i	$-0.321638\pi$
$659$	27.2870			1.06295			0.531475	+	0.847074i	$0.321638\pi$
$660$	28.9236	−	4.26497i	1.12585	−	0.166014i
$661$	38.2384			1.48730			0.743650	−	0.668569i	$-0.233093\pi$
$661$	38.2384			1.48730			0.743650	+	0.668569i	$0.233093\pi$
$662$	−10.0502	−	8.67691i	−0.390612	−	0.337238i
$663$	−28.5975			−1.11063
$664$	13.1881	+	8.37517i	0.511799	+	0.325020i
$665$	13.8315	−	0.960878i	0.536364	−	0.0372613i
$666$	43.3471	−	50.2076i	1.67967	−	1.94551i
$667$	−0.411845			−0.0159467
$668$	4.87543	+	33.0636i	0.188636	+	1.27927i
$669$			42.0705i			1.62654i
$670$	−2.75927	−	2.38224i	−0.106600	−	0.0920338i
$671$	5.74554			0.221804
$672$	−42.1398	−	15.3839i	−1.62558	−	0.593448i
$673$	8.47579			0.326718			0.163359	−	0.986567i	$-0.447767\pi$
$673$	8.47579			0.326718			0.163359	+	0.986567i	$0.447767\pi$
$674$	21.1470	+	18.2574i	0.814552	+	0.703249i
$675$		−	8.94421i		−	0.344263i
$676$	−2.07289	−	14.0576i	−0.0797264	−	0.540678i
$677$	−23.2065			−0.891897			−0.445948	−	0.895059i	$-0.647134\pi$
$677$	−23.2065			−0.891897			−0.445948	+	0.895059i	$0.647134\pi$
$678$	−10.3049	+	11.9358i	−0.395756	+	0.458393i
$679$	20.7217	−	1.43954i	0.795225	−	0.0552444i
$680$	9.38241	+	5.95833i	0.359799	+	0.228491i
$681$	−89.6394			−3.43499
$682$	−24.1558	−	20.8550i	−0.924972	−	0.798581i
$683$	−25.7680			−0.985986			−0.492993	−	0.870033i	$-0.664097\pi$
$683$	−25.7680			−0.985986			−0.492993	+	0.870033i	$0.664097\pi$
$684$	−62.0470	+	9.14923i	−2.37243	+	0.349830i
$685$	16.9739			0.648540
$686$	−12.6515	+	22.9333i	−0.483038	+	0.875599i
$687$			26.7394i			1.02017i
$688$	−10.5835	+	3.19059i	−0.403493	+	0.121640i
$689$		−	1.62212i		−	0.0617978i
$690$	0.366164	+	0.316130i	0.0139396	+	0.0120349i
$691$			24.5498i			0.933917i	0.884279	+	0.466958i	$0.154650\pi$
$691$			24.5498i			0.933917i	−0.884279	+	0.466958i	$0.845350\pi$
$692$	−1.51549	−	10.2775i	−0.0576102	−	0.390693i
$693$	5.35124	+	77.0294i	0.203277	+	2.92610i
$694$	−31.9096	−	27.5494i	−1.21127	−	1.04576i
$695$		−	2.54598i		−	0.0965744i
$696$	16.4014	−	25.8268i	0.621693	−	0.978962i
$697$	41.1877			1.56009
$698$	16.8054	+	14.5091i	0.636095	+	0.549177i
$699$			1.69396i			0.0640715i
$700$	5.16881	−	1.13286i	0.195363	−	0.0428180i
$701$			2.33837i			0.0883188i	0.999024	+	0.0441594i	$0.0140610\pi$
$701$			2.33837i			0.0883188i	−0.999024	+	0.0441594i	$0.985939\pi$
$702$	20.0701	−	23.2466i	0.757498	−	0.877387i
$703$	41.0745			1.54915
$704$	−16.5905	−	35.3134i	−0.625280	−	1.33092i
$705$		−	36.2128i		−	1.36385i
$706$	9.44386	−	10.9385i	0.355424	−	0.411677i
$707$	−1.99966	−	28.7845i	−0.0752049	−	1.08255i
$708$	1.20279	+	8.15693i	0.0452037	+	0.306556i
$709$		−	36.8318i		−	1.38325i	−0.722257	−	0.691624i	$-0.756895\pi$
$709$		−	36.8318i		−	1.38325i	0.722257	−	0.691624i	$-0.243105\pi$
$710$	−8.72154	+	10.1019i	−0.327314	+	0.379117i
$711$			71.0927i			2.66618i
$712$	−14.8470	−	9.42867i	−0.556417	−	0.353354i
$713$		−	0.528036i		−	0.0197751i
$714$	−26.4187	+	35.2735i	−0.988694	+	1.32008i
$715$	−11.8415			−0.442847
$716$	−5.05540	−	34.2840i	−0.188929	−	1.28125i
$717$	25.5114			0.952742
$718$	−21.6960	+	25.1298i	−0.809688	+	0.937837i
$719$	−33.8925			−1.26398			−0.631989	−	0.774978i	$-0.717761\pi$
$719$	−33.8925			−1.26398			−0.631989	+	0.774978i	$0.717761\pi$
$720$	−22.9174	+	6.90887i	−0.854082	+	0.257478i
$721$	2.90076	+	41.7556i	0.108030	+	1.55506i
$722$	−9.05830	−	7.82055i	−0.337115	−	0.291051i
$723$	−6.51991			−0.242478
$724$	−6.14397	−	41.6664i	−0.228339	−	1.54852i
$725$			3.60881i			0.134028i
$726$	−35.4176	+	41.0231i	−1.31447	+	1.52251i
$727$	4.28102			0.158774			0.0793871	−	0.996844i	$-0.474704\pi$
$727$	4.28102			0.158774			0.0793871	+	0.996844i	$0.474704\pi$
$728$	15.9762	+	8.65405i	0.592116	+	0.320741i
$729$	27.4276			1.01584
$730$	−5.19969	+	6.02264i	−0.192449	+	0.222908i
$731$			10.8593i			0.401647i
$732$	−6.98664	+	1.03023i	−0.258234	+	0.0380782i
$733$	38.0426			1.40513			0.702567	−	0.711618i	$-0.252037\pi$
$733$	38.0426			1.40513			0.702567	+	0.711618i	$0.252037\pi$
$734$	−23.0151	−	19.8702i	−0.849501	−	0.733422i
$735$	2.90116	+	20.7798i	0.107011	+	0.766476i
$736$	0.262882	−	0.589624i	0.00968996	−	0.0217338i
$737$	12.5714			0.463073
$738$	−57.9667	+	67.1411i	−2.13378	+	2.47150i
$739$	9.93398			0.365427			0.182714	−	0.983166i	$-0.441512\pi$
$739$	9.93398			0.365427			0.182714	+	0.983166i	$0.441512\pi$
$740$	15.5083	−	2.28680i	0.570096	−	0.0840644i
$741$	38.1374			1.40101
$742$	−2.00080	−	1.49853i	−0.0734516	−	0.0550127i
$743$			1.68905i			0.0619651i	0.999520	+	0.0309826i	$0.00986363\pi$
$743$			1.68905i			0.0619651i	−0.999520	+	0.0309826i	$0.990136\pi$
$744$	33.1132	+	21.0286i	1.21399	+	0.770947i
$745$		−	13.7925i		−	0.505316i
$746$	0.721837	−	0.836082i	0.0264283	−	0.0306111i
$747$			33.0527i			1.20934i
$748$	−37.9193	+	5.59144i	−1.38647	+	0.204443i
$749$	−1.19815	−	17.2469i	−0.0437793	−	0.630189i
$750$	2.77010	−	3.20852i	0.101150	−	0.117159i
$751$		−	36.9451i		−	1.34815i	−0.738664	−	0.674073i	$-0.764543\pi$
$751$		−	36.9451i		−	1.34815i	0.738664	−	0.674073i	$-0.235457\pi$
$752$	−46.2698	+	13.9488i	−1.68728	+	0.508662i
$753$	28.2257			1.02860
$754$	−8.09789	+	9.37954i	−0.294908	+	0.341583i
$755$			0.128374i			0.00467202i
$756$	−10.1325	−	46.2309i	−0.368516	−	1.68140i
$757$		−	45.8391i		−	1.66605i	−0.553235	−	0.833025i	$-0.686607\pi$
$757$		−	45.8391i		−	1.66605i	0.553235	−	0.833025i	$-0.313393\pi$
$758$	4.85325	+	4.19009i	0.176278	+	0.152191i
$759$	−1.66826			−0.0605540
$760$	−12.5123	−	7.94599i	−0.453869	−	0.288231i
$761$			19.9588i			0.723506i	0.932274	+	0.361753i	$0.117822\pi$
$761$			19.9588i			0.723506i	−0.932274	+	0.361753i	$0.882178\pi$
$762$	12.2029	+	10.5354i	0.442063	+	0.381658i
$763$	−28.8509	+	2.00428i	−1.04447	+	0.0725597i
$764$	16.6888	−	2.46088i	0.603781	−	0.0890314i
$765$			23.5146i			0.850174i
$766$	38.5959	+	33.3220i	1.39453	+	1.20397i
$767$		−	3.33949i		−	0.120582i
$768$	26.5063	+	39.9667i	0.956463	+	1.44217i
$769$		−	13.9529i		−	0.503153i	−0.967837	−	0.251576i	$-0.919051\pi$
$769$		−	13.9529i		−	0.503153i	0.967837	−	0.251576i	$-0.0809490\pi$
$770$	−10.9393	+	14.6059i	−0.394225	+	0.526359i
$771$	13.3123			0.479431
$772$	−7.47884	−	50.7190i	−0.269169	−	1.82542i
$773$	−33.8775			−1.21849			−0.609245	−	0.792982i	$-0.708527\pi$
$773$	−33.8775			−1.21849			−0.609245	+	0.792982i	$0.708527\pi$
$774$	−17.7021	−	15.2832i	−0.636288	−	0.549344i
$775$	−4.62694			−0.166205
$776$	−18.7453	−	11.9043i	−0.672917	−	0.427338i
$777$	4.30767	+	62.0076i	0.154537	+	2.22451i
$778$	−19.5642	+	22.6606i	−0.701410	+	0.812422i
$779$	−54.9276			−1.96798
$780$	14.3994	−	2.12328i	0.515581	−	0.0760256i
$781$		−	46.0247i		−	1.64689i
$782$	−0.480046	−	0.414451i	−0.0171664	−	0.0148207i
$783$	32.2779			1.15352
$784$	25.4333	−	11.7111i	0.908331	−	0.418252i
$785$	13.1585			0.469649
$786$	−24.6450	−	21.2774i	−0.879057	−	0.758940i
$787$		−	8.07748i		−	0.287931i	−0.989583	−	0.143965i	$-0.954015\pi$
$787$		−	8.07748i		−	0.287931i	0.989583	−	0.143965i	$-0.0459854\pi$
$788$	−3.53635	+	0.521457i	−0.125977	+	0.0185761i
$789$	40.8377			1.45386
$790$	−10.9797	+	12.7174i	−0.390639	+	0.452466i
$791$	−0.682101	−	9.81862i	−0.0242527	−	0.349110i
$792$	44.2521	−	69.6825i	1.57243	−	2.47606i
$793$	2.86037			0.101575
$794$	−15.1411	−	13.0721i	−0.537337	−	0.463913i
$795$	−2.00249			−0.0710209
$796$	−6.51139	−	44.1580i	−0.230790	−	1.56514i
$797$	−30.9873			−1.09763			−0.548813	−	0.835945i	$-0.684920\pi$
$797$	−30.9873			−1.09763			−0.548813	+	0.835945i	$0.684920\pi$
$798$	35.2318	−	47.0405i	1.24719	−	1.66522i
$799$			47.4755i			1.67956i
$800$	−5.16661	−	2.30351i	−0.182667	−	0.0814415i
$801$		−	37.2104i		−	1.31476i
$802$	19.0721	+	16.4661i	0.673461	+	0.581437i
$803$		−	27.4394i		−	0.968316i
$804$	−15.2869	+	2.25416i	−0.539129	+	0.0794980i
$805$	−0.301213	+	0.0209253i	−0.0106164	+	0.000737520i
$806$	−12.0257	−	10.3825i	−0.423588	−	0.365708i
$807$			30.7866i			1.08374i
$808$	−16.5362	+	26.0391i	−0.581741	+	0.916051i
$809$	−52.5895			−1.84895			−0.924474	−	0.381245i	$-0.875495\pi$
$809$	−52.5895			−1.84895			−0.924474	+	0.381245i	$0.875495\pi$
$810$	−9.48071	−	8.18523i	−0.333118	−	0.287600i
$811$			37.3872i			1.31284i	0.754395	+	0.656421i	$0.227931\pi$
$811$			37.3872i			1.31284i	−0.754395	+	0.656421i	$0.772069\pi$
$812$	4.08826	+	18.6533i	0.143470	+	0.654601i
$813$			8.01082i			0.280952i
$814$	−35.3283	+	40.9197i	−1.23826	+	1.43423i
$815$	−0.158264			−0.00554374
$816$	45.1077	−	13.5985i	1.57908	−	0.476043i
$817$		−	14.4819i		−	0.506659i
$818$	30.0630	−	34.8211i	1.05113	−	1.21749i
$819$	2.66407	+	38.3484i	0.0930901	+	1.34000i
$820$	−20.7388	+	3.05806i	−0.724229	+	0.106792i
$821$			23.1500i			0.807941i	0.914772	+	0.403970i	$0.132370\pi$
$821$			23.1500i			0.807941i	−0.914772	+	0.403970i	$0.867630\pi$
$822$	47.0195	−	54.4612i	1.63999	−	1.89955i
$823$			10.1543i			0.353957i	0.984215	+	0.176979i	$0.0566323\pi$
$823$			10.1543i			0.353957i	−0.984215	+	0.176979i	$0.943368\pi$
$824$	23.9879	−	37.7730i	0.835657	−	1.31588i
$825$			14.6182i			0.508940i
$826$	−4.11909	−	3.08506i	−0.143321	−	0.107343i
$827$	−25.7346			−0.894881			−0.447440	−	0.894314i	$-0.647664\pi$
$827$	−25.7346			−0.894881			−0.447440	+	0.894314i	$0.647664\pi$
$828$	1.35121	−	0.199245i	0.0469579	−	0.00692425i
$829$	29.2920			1.01735			0.508677	−	0.860958i	$-0.330135\pi$
$829$	29.2920			1.01735			0.508677	+	0.860958i	$0.330135\pi$
$830$	−5.10472	+	5.91264i	−0.177187	+	0.205231i
$831$	−84.3400			−2.92572
$832$	−8.25946	−	17.5805i	−0.286345	−	0.609493i
$833$	−3.80346	−	27.2427i	−0.131782	−	0.943902i
$834$	−8.16883	−	7.05261i	−0.282863	−	0.244212i
$835$	−16.7105			−0.578292
$836$	50.5689	−	7.45671i	1.74896	−	0.257896i
$837$			41.3843i			1.43045i
$838$	−31.8653	+	36.9086i	−1.10077	+	1.27499i
$839$	11.5479			0.398676			0.199338	−	0.979931i	$-0.436121\pi$
$839$	11.5479			0.398676			0.199338	+	0.979931i	$0.436121\pi$
$840$	10.6833	−	19.7224i	0.368610	−	0.680487i
$841$	15.9765			0.550914
$842$	11.3338	−	13.1276i	0.390588	−	0.452407i
$843$			1.39928i			0.0481939i
$844$	2.50466	+	16.9858i	0.0862139	+	0.584674i
$845$	7.10482			0.244413
$846$	−77.3911	−	66.8161i	−2.66076	−	2.29718i
$847$	−2.34436	−	33.7464i	−0.0805533	−	1.15954i
$848$	0.771339	+	2.55861i	0.0264879	+	0.0878631i
$849$	32.3726			1.11102
$850$	−3.63164	+	4.20642i	−0.124564	+	0.144279i
$851$	−0.894489			−0.0306627
$852$	8.25263	+	55.9666i	0.282730	+	1.91738i
$853$	−35.5827			−1.21833			−0.609164	−	0.793045i	$-0.708495\pi$
$853$	−35.5827			−1.21833			−0.609164	+	0.793045i	$0.708495\pi$
$854$	2.64244	−	3.52812i	0.0904224	−	0.120730i
$855$		−	31.3590i		−	1.07245i
$856$	−9.90808	+	15.6020i	−0.338651	+	0.533264i
$857$		−	1.71368i		−	0.0585383i	−0.999572	−	0.0292691i	$-0.990682\pi$
$857$		−	1.71368i		−	0.0585383i	0.999572	−	0.0292691i	$-0.00931799\pi$
$858$	−32.8021	+	37.9937i	−1.11985	+	1.29708i
$859$		−	14.7176i		−	0.502158i	−0.967967	−	0.251079i	$-0.919215\pi$
$859$		−	14.7176i		−	0.502158i	0.967967	−	0.251079i	$-0.0807855\pi$
$860$	−0.806274	−	5.46788i	−0.0274937	−	0.186453i
$861$	−5.76052	−	82.9208i	−0.196318	−	2.82593i
$862$	−20.1213	+	23.3058i	−0.685333	+	0.793800i
$863$		−	37.4241i		−	1.27393i	−0.770892	−	0.636966i	$-0.780189\pi$
$863$		−	37.4241i		−	1.27393i	0.770892	−	0.636966i	$-0.219811\pi$
$864$	−20.6031	+	46.2112i	−0.700932	+	1.57214i
$865$	5.19433			0.176612
$866$	−24.1764	+	28.0028i	−0.821549	+	0.951575i
$867$			4.67166i			0.158658i
$868$	−23.9158	+	5.24166i	−0.811754	+	0.177914i
$869$		−	57.9412i		−	1.96552i
$870$	11.5789	+	9.99676i	0.392563	+	0.338922i
$871$	6.25855			0.212063
$872$	26.0992	+	16.5744i	0.883830	+	0.561279i
$873$		−	46.9804i		−	1.59005i
$874$	0.640186	+	0.552709i	0.0216546	+	0.0186957i
$875$	0.183359	+	2.63939i	0.00619866	+	0.0892277i
$876$	4.92013	+	33.3666i	0.166236	+	1.12735i
$877$			24.9933i			0.843965i	0.906604	+	0.421982i	$0.138666\pi$
$877$			24.9933i			0.843965i	−0.906604	+	0.421982i	$0.861334\pi$
$878$	−31.6142	−	27.2943i	−1.06693	−	0.921139i
$879$		−	22.0164i		−	0.742596i
$880$	18.6779	−	5.63079i	0.629633	−	0.189814i
$881$			27.7020i			0.933303i	0.884441	+	0.466651i	$0.154540\pi$
$881$			27.7020i			0.933303i	−0.884441	+	0.466651i	$0.845460\pi$
$882$	49.7619	+	32.1407i	1.67557	+	1.08223i
$883$	3.66299			0.123269			0.0616347	−	0.998099i	$-0.480369\pi$
$883$	3.66299			0.123269			0.0616347	+	0.998099i	$0.480369\pi$
$884$	−18.8778	+	2.78365i	−0.634929	+	0.0936243i
$885$	−4.12256			−0.138579
$886$	−23.3269	−	20.1394i	−0.783682	−	0.676597i
$887$	40.0849			1.34592			0.672960	−	0.739679i	$-0.265022\pi$
$887$	40.0849			1.34592			0.672960	+	0.739679i	$0.265022\pi$
$888$	35.6223	−	56.0934i	1.19541	−	1.88237i
$889$	−10.0383	+	0.697361i	−0.336674	+	0.0233887i
$890$	5.74684	−	6.65639i	0.192634	−	0.223123i
$891$	43.1946			1.44707
$892$	4.09510	+	27.7716i	0.137114	+	0.929862i
$893$		−	63.3130i		−	2.11869i
$894$	−44.2534	−	38.2065i	−1.48006	−	1.27782i
$895$	17.3274			0.579190
$896$	−29.3148	−	6.05341i	−0.979338	−	0.202230i
$897$	−0.830529			−0.0277306
$898$	−1.88091	−	1.62390i	−0.0627668	−	0.0541901i
$899$		−	16.6977i		−	0.556900i
$900$	−1.74589	−	11.8401i	−0.0581965	−	0.394669i
$901$	2.62529			0.0874610
$902$	47.2434	−	54.7206i	1.57303	−	1.82200i
$903$	21.8625	−	1.51879i	0.727538	−	0.0505421i
$904$	−5.64064	+	8.88215i	−0.187605	+	0.295416i
$905$	21.0585			0.700007
$906$	0.411892	+	0.355610i	0.0136842	+	0.0118143i
$907$	−33.0878			−1.09866			−0.549331	−	0.835605i	$-0.685117\pi$
$907$	−33.0878			−1.09866			−0.549331	+	0.835605i	$0.685117\pi$
$908$	−59.1728	+	8.72540i	−1.96372	+	0.289563i
$909$	−65.2604			−2.16455
$910$	−5.44603	+	7.27140i	−0.180534	+	0.241045i
$911$			41.4259i			1.37250i	0.727365	+	0.686250i	$0.240745\pi$
$911$			41.4259i			1.37250i	−0.727365	+	0.686250i	$0.759255\pi$
$912$	−60.1553	+	18.1349i	−1.99194	+	0.600506i
$913$		−	26.9383i		−	0.891527i
$914$	4.05549	+	3.50133i	0.134144	+	0.115814i
$915$		−	3.53110i		−	0.116734i
$916$	2.60278	+	17.6512i	0.0859983	+	0.583212i
$917$	20.2734	−	1.40840i	0.669487	−	0.0465093i
$918$	37.6231	+	32.4822i	1.24175	+	1.07207i
$919$		−	2.61219i		−	0.0861682i	−0.999071	−	0.0430841i	$-0.986282\pi$
$919$		−	2.61219i		−	0.0861682i	0.999071	−	0.0430841i	$-0.0137183\pi$
$920$	0.272484	+	0.173042i	0.00898353	+	0.00570502i
$921$	15.2288			0.501807
$922$	−34.6336	−	29.9012i	−1.14060	−	0.984743i
$923$		−	22.9130i		−	0.754191i
$924$	16.5603	+	75.5587i	0.544795	+	2.48570i
$925$			7.83800i			0.257712i
$926$	−28.8836	+	33.4551i	−0.949176	+	1.09940i
$927$	94.6686			3.10932
$928$	8.31294	−	18.6453i	0.272886	−	0.612061i
$929$		−	29.7850i		−	0.977213i	−0.872504	−	0.488606i	$-0.837505\pi$
$929$		−	29.7850i		−	0.977213i	0.872504	−	0.488606i	$-0.162495\pi$
$930$	−12.8171	+	14.8456i	−0.420289	+	0.486808i
$931$	5.07226	+	36.3306i	0.166237	+	1.19069i
$932$	0.164888	+	1.11822i	0.00540110	+	0.0366285i
$933$			53.4484i			1.74982i
$934$	−20.9605	+	24.2780i	−0.685850	+	0.794399i
$935$		−	19.1647i		−	0.626751i
$936$	22.0305	−	34.6908i	0.720090	−	1.13391i
$937$			20.9620i			0.684800i	0.939554	+	0.342400i	$0.111240\pi$
$937$			20.9620i			0.684800i	−0.939554	+	0.342400i	$0.888760\pi$
$938$	5.78172	−	7.71960i	0.188780	−	0.252054i
$939$	−10.6108			−0.346271
$940$	−3.52492	−	23.9048i	−0.114970	−	0.779689i
$941$	21.3589			0.696280			0.348140	−	0.937443i	$-0.386813\pi$
$941$	21.3589			0.696280			0.348140	+	0.937443i	$0.386813\pi$
$942$	36.4505	−	42.2195i	1.18762	−	1.37559i
$943$	1.19617			0.0389527
$944$	1.58797	+	5.26747i	0.0516841	+	0.171442i
$945$	23.6073	−	1.64000i	0.767944	−	0.0533492i
$946$	14.4274	+	12.4560i	0.469074	+	0.404978i
$947$	−54.2008			−1.76129			−0.880645	−	0.473777i	$-0.842890\pi$
$947$	−54.2008			−1.76129			−0.880645	+	0.473777i	$0.842890\pi$
$948$	10.3894	+	70.4571i	0.337430	+	2.28834i
$949$		−	13.6605i		−	0.443438i
$950$	4.84313	−	5.60965i	0.157132	−	0.182001i
$951$	14.5779			0.472719
$952$	−14.0060	+	25.8563i	−0.453937	+	0.838009i
$953$	26.3943			0.854994			0.427497	−	0.904017i	$-0.359395\pi$
$953$	26.3943			0.854994			0.427497	+	0.904017i	$0.359395\pi$
$954$	−3.69478	+	4.27955i	−0.119623	+	0.138556i
$955$			8.43465i			0.272939i
$956$	16.8406	−	2.48326i	0.544664	−	0.0803142i
$957$	−52.7542			−1.70530
$958$	−13.7702	−	11.8886i	−0.444896	−	0.384104i
$959$	3.11231	+	44.8008i	0.100502	+	1.44669i
$960$	−21.7029	+	10.1962i	−0.700458	+	0.329081i
$961$	−9.59145			−0.309402
$962$	−17.5879	+	20.3715i	−0.567056	+	0.656804i
$963$	−39.1024			−1.26006
$964$	−4.30392	+	0.634641i	−0.138620	+	0.0204404i
$965$	25.6337			0.825179
$966$	−0.767251	+	1.02441i	−0.0246859	+	0.0329600i
$967$		−	32.9216i		−	1.05869i	−0.848408	−	0.529343i	$-0.822438\pi$
$967$		−	32.9216i		−	1.05869i	0.848408	−	0.529343i	$-0.177562\pi$
$968$	−19.3867	+	30.5277i	−0.623113	+	0.981198i
$969$			61.7229i			1.98282i
$970$	7.25573	−	8.40410i	0.232968	−	0.269839i
$971$			32.2598i			1.03527i	0.855603	+	0.517633i	$0.173187\pi$
$971$			32.2598i			1.03527i	−0.855603	+	0.517633i	$0.826813\pi$
$972$	0.566103	−	0.0834756i	0.0181578	−	0.00267748i
$973$	6.71982	−	0.466827i	0.215428	−	0.0149658i
$974$	18.7733	−	21.7445i	0.601534	−	0.696739i
$975$			7.27754i			0.233068i
$976$	−4.51174	+	1.36014i	−0.144417	+	0.0435372i
$977$	−21.3881			−0.684265			−0.342132	−	0.939652i	$-0.611149\pi$
$977$	−21.3881			−0.684265			−0.342132	+	0.939652i	$0.611149\pi$
$978$	−0.438407	+	0.507793i	−0.0140187	+	0.0162374i
$979$			30.3268i			0.969249i
$980$	3.93780	+	13.4348i	0.125788	+	0.429159i
$981$			65.4111i			2.08842i
$982$	17.6178	+	15.2104i	0.562205	+	0.485384i
$983$	−18.6503			−0.594852			−0.297426	−	0.954745i	$-0.596128\pi$
$983$	−18.6503			−0.594852			−0.297426	+	0.954745i	$0.596128\pi$
$984$	−47.6366	+	75.0120i	−1.51860	+	2.39129i
$985$		−	1.78729i		−	0.0569479i
$986$	−15.1802	−	13.1059i	−0.483435	−	0.417377i
$987$	95.5798	−	6.63994i	3.04234	−	0.211351i
$988$	25.1753	−	3.71226i	0.800933	−	0.118103i
$989$			0.315377i			0.0100284i
$990$	31.2408	+	26.9720i	0.992898	+	0.857225i
$991$		−	13.5821i		−	0.431448i	−0.976454	−	0.215724i	$-0.930789\pi$
$991$		−	13.5821i		−	0.431448i	0.976454	−	0.215724i	$-0.0692112\pi$
$992$	23.9056	+	10.6582i	0.759002	+	0.338399i
$993$		−	28.1411i		−	0.893032i
$994$	−28.2620	−	21.1673i	−0.896417	−	0.671385i
$995$	22.3178			0.707521
$996$	4.83027	+	32.7573i	0.153053	+	1.03795i
$997$	−25.3616			−0.803210			−0.401605	−	0.915813i	$-0.631548\pi$
$997$	−25.3616			−0.803210			−0.401605	+	0.915813i	$0.631548\pi$
$998$	20.0693	+	17.3270i	0.635282	+	0.548475i
$999$	70.1047			2.21801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.h.a.251.12	yes	16
4.3	odd	2		1120.2.h.a.111.2		16
7.6	odd	2		280.2.h.b.251.12	yes	16
8.3	odd	2		280.2.h.b.251.11	yes	16
8.5	even	2		1120.2.h.b.111.2		16
28.27	even	2		1120.2.h.b.111.15		16
56.13	odd	2		1120.2.h.a.111.15		16
56.27	even	2	inner	280.2.h.a.251.11	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.h.a.251.11	✓	16	56.27	even	2	inner
280.2.h.a.251.12	yes	16	1.1	even	1	trivial
280.2.h.b.251.11	yes	16	8.3	odd	2
280.2.h.b.251.12	yes	16	7.6	odd	2
1120.2.h.a.111.2		16	4.3	odd	2
1120.2.h.a.111.15		16	56.13	odd	2
1120.2.h.b.111.2		16	8.5	even	2
1120.2.h.b.111.15		16	28.27	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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07046 + 0.924187i) q^{2} +2.99734i q^{3} +(0.291758 + 1.97860i) q^{4} -1.00000 q^{5} +(-2.77010 + 3.20852i) q^{6} +(-0.183359 - 2.63939i) q^{7} +(-1.51629 + 2.38765i) q^{8} -5.98405 q^{9} +O(q^{10})\)	\(q+(1.07046 + 0.924187i) q^{2} +2.99734i q^{3} +(0.291758 + 1.97860i) q^{4} -1.00000 q^{5} +(-2.77010 + 3.20852i) q^{6} +(-0.183359 - 2.63939i) q^{7} +(-1.51629 + 2.38765i) q^{8} -5.98405 q^{9} +(-1.07046 - 0.924187i) q^{10} +4.87706 q^{11} +(-5.93055 + 0.874498i) q^{12} +2.42800 q^{13} +(2.24301 - 2.99481i) q^{14} -2.99734i q^{15} +(-3.82975 + 1.15455i) q^{16} +3.92955i q^{17} +(-6.40567 - 5.53038i) q^{18} -5.24043i q^{19} +(-0.291758 - 1.97860i) q^{20} +(7.91115 - 0.549588i) q^{21} +(5.22068 + 4.50731i) q^{22} +0.114122i q^{23} +(-7.15660 - 4.54482i) q^{24} +1.00000 q^{25} +(2.59907 + 2.24393i) q^{26} -8.94421i q^{27} +(5.16881 - 1.13286i) q^{28} +3.60881i q^{29} +(2.77010 - 3.20852i) q^{30} -4.62694 q^{31} +(-5.16661 - 2.30351i) q^{32} +14.6182i q^{33} +(-3.63164 + 4.20642i) q^{34} +(0.183359 + 2.63939i) q^{35} +(-1.74589 - 11.8401i) q^{36} +7.83800i q^{37} +(4.84313 - 5.60965i) q^{38} +7.27754i q^{39} +(1.51629 - 2.38765i) q^{40} -10.4815i q^{41} +(8.97647 + 6.72307i) q^{42} +2.76350 q^{43} +(1.42292 + 9.64977i) q^{44} +5.98405 q^{45} +(-0.105470 + 0.122163i) q^{46} +12.0817 q^{47} +(-3.46057 - 11.4791i) q^{48} +(-6.93276 + 0.967910i) q^{49} +(1.07046 + 0.924187i) q^{50} -11.7782 q^{51} +(0.708388 + 4.80405i) q^{52} -0.668088i q^{53} +(8.26612 - 9.57439i) q^{54} -4.87706 q^{55} +(6.57997 + 3.56427i) q^{56} +15.7073 q^{57} +(-3.33521 + 3.86307i) q^{58} -1.37541i q^{59} +(5.93055 - 0.874498i) q^{60} +1.17808 q^{61} +(-4.95294 - 4.27615i) q^{62} +(1.09723 + 15.7942i) q^{63} +(-3.40175 - 7.24072i) q^{64} -2.42800 q^{65} +(-13.5099 + 15.6482i) q^{66} +2.57766 q^{67} +(-7.77504 + 1.14648i) q^{68} -0.342063 q^{69} +(-2.24301 + 2.99481i) q^{70} -9.43699i q^{71} +(9.07353 - 14.2878i) q^{72} -5.62623i q^{73} +(-7.24377 + 8.39024i) q^{74} +2.99734i q^{75} +(10.3687 - 1.52894i) q^{76} +(-0.894251 - 12.8725i) q^{77} +(-6.72581 + 7.79030i) q^{78} -11.8804i q^{79} +(3.82975 - 1.15455i) q^{80} +8.85669 q^{81} +(9.68687 - 11.2200i) q^{82} -5.52348i q^{83} +(3.39556 + 15.4927i) q^{84} -3.92955i q^{85} +(2.95821 + 2.55399i) q^{86} -10.8168 q^{87} +(-7.39501 + 11.6447i) q^{88} +6.21826i q^{89} +(6.40567 + 5.53038i) q^{90} +(-0.445195 - 6.40844i) q^{91} +(-0.225803 + 0.0332961i) q^{92} -13.8685i q^{93} +(12.9329 + 11.1657i) q^{94} +5.24043i q^{95} +(6.90442 - 15.4861i) q^{96} +7.85094i q^{97} +(-8.31575 - 5.37106i) q^{98} -29.1845 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	\( 16 q + q^{2} + q^{4} - 16 q^{5} + q^{8} - 16 q^{9} - q^{10} - 4 q^{11} - 14 q^{12} + 7 q^{14} + 9 q^{16} - 15 q^{18} - q^{20} + 4 q^{21} + 6 q^{22} - 22 q^{24} + 16 q^{25} + 20 q^{26} - 3 q^{28} + 16 q^{31} - 19 q^{32} + 14 q^{34} + 15 q^{36} + 30 q^{38} - q^{40} + 20 q^{42} - 4 q^{43} - 20 q^{44} + 16 q^{45} + 6 q^{46} + 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} + 38 q^{52} - 26 q^{54} + 4 q^{55} + q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} + 8 q^{61} - 28 q^{62} - 28 q^{63} - 23 q^{64} - 46 q^{66} + 20 q^{67} - 12 q^{68} + 40 q^{69} - 7 q^{70} - 13 q^{72} - 28 q^{74} - 34 q^{76} + 4 q^{77} - 6 q^{78} - 9 q^{80} + 24 q^{81} + 16 q^{82} + 10 q^{84} - 24 q^{86} - 72 q^{87} - 44 q^{88} + 15 q^{90} - 32 q^{91} - 30 q^{92} + 58 q^{94} + 30 q^{96} - 39 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^4 - 16 * q^5 + q^8 - 16 * q^9 - q^10 - 4 * q^11 - 14 * q^12 + 7 * 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 - 3 * q^28 + 16 * q^31 - 19 * q^32 + 14 * q^34 + 15 * q^36 + 30 * q^38 - q^40 + 20 * 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 + 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 - 7 * 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 + 10 * 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 - 39 * q^98 + 20 * q^99

Introduction

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