LMFDB - Embedded newform 280.2.h.a.251.1

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			251.1
Root			$-1.38133 + 0.303194i$ of defining polynomial
Character	$\chi$	$=$	280.251
Dual form			280.2.h.a.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38133 - 0.303194i) q^{2} +1.34113i q^{3} +(1.81615 + 0.837621i) q^{4} -1.00000 q^{5} +(0.406623 - 1.85255i) q^{6} +(1.28003 - 2.31550i) q^{7} +(-2.25474 - 1.70768i) q^{8} +1.20136 q^{9} +O(q^{10})$	\(q+(-1.38133 - 0.303194i) q^{2} +1.34113i q^{3} +(1.81615 + 0.837621i) q^{4} -1.00000 q^{5} +(0.406623 - 1.85255i) q^{6} +(1.28003 - 2.31550i) q^{7} +(-2.25474 - 1.70768i) q^{8} +1.20136 q^{9} +(1.38133 + 0.303194i) q^{10} +2.44809 q^{11} +(-1.12336 + 2.43569i) q^{12} +1.57090 q^{13} +(-2.47019 + 2.81037i) q^{14} -1.34113i q^{15} +(2.59678 + 3.04249i) q^{16} -1.11987i q^{17} +(-1.65948 - 0.364245i) q^{18} +8.44773i q^{19} +(-1.81615 - 0.837621i) q^{20} +(3.10539 + 1.71669i) q^{21} +(-3.38161 - 0.742244i) q^{22} +2.62959i q^{23} +(2.29022 - 3.02390i) q^{24} +1.00000 q^{25} +(-2.16994 - 0.476288i) q^{26} +5.63459i q^{27} +(4.26423 - 3.13310i) q^{28} -3.43282i q^{29} +(-0.406623 + 1.85255i) q^{30} +9.70304 q^{31} +(-2.66455 - 4.99001i) q^{32} +3.28321i q^{33} +(-0.339538 + 1.54691i) q^{34} +(-1.28003 + 2.31550i) q^{35} +(2.18185 + 1.00629i) q^{36} -6.22712i q^{37} +(2.56130 - 11.6691i) q^{38} +2.10679i q^{39} +(2.25474 + 1.70768i) q^{40} -3.13128i q^{41} +(-3.76908 - 3.31285i) q^{42} +7.45492 q^{43} +(4.44608 + 2.05057i) q^{44} -1.20136 q^{45} +(0.797275 - 3.63233i) q^{46} -9.40956 q^{47} +(-4.08038 + 3.48263i) q^{48} +(-3.72304 - 5.92781i) q^{49} +(-1.38133 - 0.303194i) q^{50} +1.50190 q^{51} +(2.85299 + 1.31582i) q^{52} +11.6067i q^{53} +(1.70837 - 7.78322i) q^{54} -2.44809 q^{55} +(-6.84025 + 3.03496i) q^{56} -11.3295 q^{57} +(-1.04081 + 4.74186i) q^{58} -6.16041i q^{59} +(1.12336 - 2.43569i) q^{60} -9.44231 q^{61} +(-13.4031 - 2.94190i) q^{62} +(1.53778 - 2.78175i) q^{63} +(2.16769 + 7.70072i) q^{64} -1.57090 q^{65} +(0.995448 - 4.53519i) q^{66} -2.15461 q^{67} +(0.938029 - 2.03385i) q^{68} -3.52663 q^{69} +(2.47019 - 2.81037i) q^{70} +7.87185i q^{71} +(-2.70876 - 2.05154i) q^{72} -12.6145i q^{73} +(-1.88802 + 8.60171i) q^{74} +1.34113i q^{75} +(-7.07600 + 15.3423i) q^{76} +(3.13362 - 5.66853i) q^{77} +(0.638766 - 2.91017i) q^{78} -7.70558i q^{79} +(-2.59678 - 3.04249i) q^{80} -3.95264 q^{81} +(-0.949384 + 4.32533i) q^{82} -0.813234i q^{83} +(4.20191 + 5.71890i) q^{84} +1.11987i q^{85} +(-10.2977 - 2.26029i) q^{86} +4.60387 q^{87} +(-5.51979 - 4.18054i) q^{88} -5.12287i q^{89} +(1.65948 + 0.364245i) q^{90} +(2.01081 - 3.63742i) q^{91} +(-2.20260 + 4.77572i) q^{92} +13.0131i q^{93} +(12.9977 + 2.85292i) q^{94} -8.44773i q^{95} +(6.69226 - 3.57352i) q^{96} +0.833955i q^{97} +(3.34548 + 9.31707i) q^{98} +2.94104 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 $

$2$	−1.38133	−	0.303194i	−0.976748	−	0.214390i
$2$	−1.38133	−	0.303194i	−0.976748	−	0.214390i
$3$			1.34113i			0.774303i	0.922016	+	0.387152i	$0.126541\pi$
$3$			1.34113i			0.774303i	−0.922016	+	0.387152i	$0.873459\pi$
$4$	1.81615	+	0.837621i	0.908074	+	0.418811i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.406623	−	1.85255i	0.166003	−	0.756299i
$7$	1.28003	−	2.31550i	0.483806	−	0.875175i
$7$	1.28003	−	2.31550i	0.483806	−	0.875175i
$8$	−2.25474	−	1.70768i	−0.797170	−	0.603755i
$9$	1.20136			0.400454
$10$	1.38133	+	0.303194i	0.436815	+	0.0958783i
$11$	2.44809			0.738125			0.369063	−	0.929404i	$-0.379679\pi$
$11$	2.44809			0.738125			0.369063	+	0.929404i	$0.379679\pi$
$12$	−1.12336	+	2.43569i	−0.324287	+	0.703125i
$13$	1.57090			0.435690			0.217845	−	0.975983i	$-0.430097\pi$
$13$	1.57090			0.435690			0.217845	+	0.975983i	$0.430097\pi$
$14$	−2.47019	+	2.81037i	−0.660186	+	0.751102i
$15$		−	1.34113i		−	0.346279i
$16$	2.59678	+	3.04249i	0.649195	+	0.760622i
$17$		−	1.11987i		−	0.271609i	−0.990736	−	0.135804i	$-0.956638\pi$
$17$		−	1.11987i		−	0.271609i	0.990736	−	0.135804i	$-0.0433619\pi$
$18$	−1.65948	−	0.364245i	−0.391143	−	0.0858535i
$19$			8.44773i			1.93804i	0.246978	+	0.969021i	$0.420563\pi$
$19$			8.44773i			1.93804i	−0.246978	+	0.969021i	$0.579437\pi$
$20$	−1.81615	−	0.837621i	−0.406103	−	0.187298i
$21$	3.10539	+	1.71669i	0.677651	+	0.374613i
$22$	−3.38161	−	0.742244i	−0.720963	−	0.158247i
$23$			2.62959i			0.548307i	0.961686	+	0.274154i	$0.0883977\pi$
$23$			2.62959i			0.548307i	−0.961686	+	0.274154i	$0.911602\pi$
$24$	2.29022	−	3.02390i	0.467489	−	0.617252i
$25$	1.00000			0.200000
$26$	−2.16994	−	0.476288i	−0.425560	−	0.0934078i
$27$			5.63459i			1.08438i
$28$	4.26423	−	3.13310i	0.805864	−	0.592100i
$29$		−	3.43282i		−	0.637458i	−0.947846	−	0.318729i	$-0.896744\pi$
$29$		−	3.43282i		−	0.637458i	0.947846	−	0.318729i	$-0.103256\pi$
$30$	−0.406623	+	1.85255i	−0.0742389	+	0.338227i
$31$	9.70304			1.74272			0.871359	−	0.490647i	$-0.163239\pi$
$31$	9.70304			1.74272			0.871359	+	0.490647i	$0.163239\pi$
$32$	−2.66455	−	4.99001i	−0.471030	−	0.882117i
$33$			3.28321i			0.571533i
$34$	−0.339538	+	1.54691i	−0.0582303	+	0.265294i
$35$	−1.28003	+	2.31550i	−0.216365	+	0.391390i
$36$	2.18185	+	1.00629i	0.363642	+	0.167714i
$37$		−	6.22712i		−	1.02373i	−0.859065	−	0.511866i	$-0.828954\pi$
$37$		−	6.22712i		−	1.02373i	0.859065	−	0.511866i	$-0.171046\pi$
$38$	2.56130	−	11.6691i	0.415497	−	1.89298i
$39$			2.10679i			0.337357i
$40$	2.25474	+	1.70768i	0.356505	+	0.270007i
$41$		−	3.13128i		−	0.489024i	−0.969646	−	0.244512i	$-0.921372\pi$
$41$		−	3.13128i		−	0.489024i	0.969646	−	0.244512i	$-0.0786277\pi$
$42$	−3.76908	−	3.31285i	−0.581581	−	0.511184i
$43$	7.45492			1.13687			0.568433	−	0.822730i	$-0.307550\pi$
$43$	7.45492			1.13687			0.568433	+	0.822730i	$0.307550\pi$
$44$	4.44608	+	2.05057i	0.670272	+	0.309135i
$45$	−1.20136			−0.179089
$46$	0.797275	−	3.63233i	0.117552	−	0.535558i
$47$	−9.40956			−1.37253			−0.686263	−	0.727354i	$-0.740750\pi$
$47$	−9.40956			−1.37253			−0.686263	+	0.727354i	$0.740750\pi$
$48$	−4.08038	+	3.48263i	−0.588952	+	0.502674i
$49$	−3.72304	−	5.92781i	−0.531863	−	0.846830i
$50$	−1.38133	−	0.303194i	−0.195350	−	0.0428781i
$51$	1.50190			0.210308
$52$	2.85299	+	1.31582i	0.395639	+	0.182472i
$53$			11.6067i			1.59430i	0.603778	+	0.797152i	$0.293661\pi$
$53$			11.6067i			1.59430i	−0.603778	+	0.797152i	$0.706339\pi$
$54$	1.70837	−	7.78322i	0.232480	−	1.05916i
$55$	−2.44809			−0.330100
$56$	−6.84025	+	3.03496i	−0.914067	+	0.405563i
$57$	−11.3295			−1.50063
$58$	−1.04081	+	4.74186i	−0.136665	+	0.622636i
$59$		−	6.16041i		−	0.802017i	−0.916074	−	0.401009i	$-0.868660\pi$
$59$		−	6.16041i		−	0.802017i	0.916074	−	0.401009i	$-0.131340\pi$
$60$	1.12336	−	2.43569i	0.145025	−	0.314447i
$61$	−9.44231			−1.20896			−0.604482	−	0.796619i	$-0.706620\pi$
$61$	−9.44231			−1.20896			−0.604482	+	0.796619i	$0.706620\pi$
$62$	−13.4031	−	2.94190i	−1.70220	−	0.373622i
$63$	1.53778	−	2.78175i	0.193742	−	0.350468i
$64$	2.16769	+	7.70072i	0.270961	+	0.962590i
$65$	−1.57090			−0.194847
$66$	0.995448	−	4.53519i	0.122531	−	0.558244i
$67$	−2.15461			−0.263228			−0.131614	−	0.991301i	$-0.542016\pi$
$67$	−2.15461			−0.263228			−0.131614	+	0.991301i	$0.542016\pi$
$68$	0.938029	−	2.03385i	0.113753	−	0.246641i
$69$	−3.52663			−0.424556
$70$	2.47019	−	2.81037i	0.295244	−	0.335903i
$71$			7.87185i			0.934217i	0.884200	+	0.467108i	$0.154704\pi$
$71$			7.87185i			0.934217i	−0.884200	+	0.467108i	$0.845296\pi$
$72$	−2.70876	−	2.05154i	−0.319230	−	0.241776i
$73$		−	12.6145i		−	1.47642i	−0.674571	−	0.738210i	$-0.735671\pi$
$73$		−	12.6145i		−	1.47642i	0.674571	−	0.738210i	$-0.264329\pi$
$74$	−1.88802	+	8.60171i	−0.219478	+	0.999929i
$75$			1.34113i			0.154861i
$76$	−7.07600	+	15.3423i	−0.811673	+	1.75989i
$77$	3.13362	−	5.66853i	0.357110	−	0.645989i
$78$	0.638766	−	2.91017i	0.0723260	−	0.329512i
$79$		−	7.70558i		−	0.866946i	−0.901167	−	0.433473i	$-0.857288\pi$
$79$		−	7.70558i		−	0.866946i	0.901167	−	0.433473i	$-0.142712\pi$
$80$	−2.59678	−	3.04249i	−0.290329	−	0.340160i
$81$	−3.95264			−0.439182
$82$	−0.949384	+	4.32533i	−0.104842	+	0.477653i
$83$		−	0.813234i		−	0.0892640i	−0.999003	−	0.0446320i	$-0.985788\pi$
$83$		−	0.813234i		−	0.0892640i	0.999003	−	0.0446320i	$-0.0142115\pi$
$84$	4.20191	+	5.71890i	0.458465	+	0.623983i
$85$			1.11987i			0.121467i
$86$	−10.2977	−	2.26029i	−1.11043	−	0.243733i
$87$	4.60387			0.493586
$88$	−5.51979	−	4.18054i	−0.588412	−	0.445647i
$89$		−	5.12287i		−	0.543023i	−0.962435	−	0.271512i	$-0.912476\pi$
$89$		−	5.12287i		−	0.543023i	0.962435	−	0.271512i	$-0.0875235\pi$
$90$	1.65948	+	0.364245i	0.174924	+	0.0383948i
$91$	2.01081	−	3.63742i	0.210790	−	0.381305i
$92$	−2.20260	+	4.77572i	−0.229637	+	0.497903i
$93$			13.0131i			1.34939i
$94$	12.9977	+	2.85292i	1.34061	+	0.294256i
$95$		−	8.44773i		−	0.866719i
$96$	6.69226	−	3.57352i	0.683026	−	0.364720i
$97$			0.833955i			0.0846753i	0.999103	+	0.0423377i	$0.0134805\pi$
$97$			0.833955i			0.0846753i	−0.999103	+	0.0423377i	$0.986519\pi$
$98$	3.34548	+	9.31707i	0.337944	+	0.941166i
$99$	2.94104			0.295585
$100$	1.81615	+	0.837621i	0.181615	+	0.0837621i
$101$	−5.52401			−0.549660			−0.274830	−	0.961493i	$-0.588622\pi$
$101$	−5.52401			−0.549660			−0.274830	+	0.961493i	$0.588622\pi$
$102$	−2.07462	−	0.455366i	−0.205418	−	0.0450879i
$103$	−11.7675			−1.15949			−0.579745	−	0.814798i	$-0.696848\pi$
$103$	−11.7675			−1.15949			−0.579745	+	0.814798i	$0.696848\pi$
$104$	−3.54198	−	2.68260i	−0.347319	−	0.263050i
$105$	−3.10539	−	1.71669i	−0.303055	−	0.167532i
$106$	3.51908	−	16.0327i	0.341803	−	1.55723i
$107$	−1.38992			−0.134369			−0.0671844	−	0.997741i	$-0.521402\pi$
$107$	−1.38992			−0.134369			−0.0671844	+	0.997741i	$0.521402\pi$
$108$	−4.71965	+	10.2332i	−0.454148	+	0.984694i
$109$		−	1.07524i		−	0.102990i	−0.998673	−	0.0514949i	$-0.983601\pi$
$109$		−	1.07524i		−	0.102990i	0.998673	−	0.0514949i	$-0.0163986\pi$
$110$	3.38161	+	0.742244i	0.322424	+	0.0707702i
$111$	8.35140			0.792680
$112$	10.3688	−	2.11836i	0.979762	−	0.200166i
$113$	11.1967			1.05329			0.526647	−	0.850084i	$-0.323449\pi$
$113$	11.1967			1.05329			0.526647	+	0.850084i	$0.323449\pi$
$114$	15.6498	+	3.43504i	1.46574	+	0.321721i
$115$		−	2.62959i		−	0.245210i
$116$	2.87540	−	6.23450i	0.266974	−	0.578859i
$117$	1.88722			0.174474
$118$	−1.86780	+	8.50956i	−0.171945	+	0.783369i
$119$	−2.59306	−	1.43347i	−0.237705	−	0.131406i
$120$	−2.29022	+	3.02390i	−0.209068	+	0.276043i
$121$	−5.00688			−0.455171
$122$	13.0429	+	2.86285i	1.18085	+	0.259190i
$123$	4.19946			0.378653
$124$	17.6221	+	8.12747i	1.58252	+	0.729868i
$125$	−1.00000			−0.0894427
$126$	−2.96759	+	3.37627i	−0.264374	+	0.300782i
$127$			16.4186i			1.45692i	0.685089	+	0.728459i	$0.259763\pi$
$127$			16.4186i			1.45692i	−0.685089	+	0.728459i	$0.740237\pi$
$128$	−0.659479	−	11.2945i	−0.0582903	−	0.998300i
$129$			9.99804i			0.880279i
$130$	2.16994	+	0.476288i	0.190316	+	0.0417732i
$131$		−	2.00348i		−	0.175045i	−0.996163	−	0.0875223i	$-0.972105\pi$
$131$		−	2.00348i		−	0.175045i	0.996163	−	0.0875223i	$-0.0278949\pi$
$132$	−2.75008	+	5.96279i	−0.239364	+	0.518994i
$133$	19.5607	+	10.8134i	1.69613	+	0.937637i
$134$	2.97623	+	0.653264i	0.257107	+	0.0564334i
$135$		−	5.63459i		−	0.484948i
$136$	−1.91238	+	2.52502i	−0.163985	+	0.216519i
$137$	4.20941			0.359634			0.179817	−	0.983700i	$-0.442449\pi$
$137$	4.20941			0.359634			0.179817	+	0.983700i	$0.442449\pi$
$138$	4.87144	+	1.06925i	0.414684	+	0.0910207i
$139$		−	4.20658i		−	0.356798i	−0.983958	−	0.178399i	$-0.942908\pi$
$139$		−	4.20658i		−	0.356798i	0.983958	−	0.178399i	$-0.0570917\pi$
$140$	−4.26423	+	3.13310i	−0.360393	+	0.264795i
$141$		−	12.6195i		−	1.06275i
$142$	2.38669	−	10.8736i	0.200287	−	0.912494i
$143$	3.84571			0.321594
$144$	3.11968	+	3.65513i	0.259973	+	0.304594i
$145$			3.43282i			0.285080i
$146$	−3.82465	+	17.4249i	−0.316530	+	1.44209i
$147$	7.94998	−	4.99310i	0.655704	−	0.411824i
$148$	5.21597	−	11.3094i	0.428750	−	0.929625i
$149$		−	19.1438i		−	1.56832i	−0.620560	−	0.784159i	$-0.713094\pi$
$149$		−	19.1438i		−	1.56832i	0.620560	−	0.784159i	$-0.286906\pi$
$150$	0.406623	−	1.85255i	0.0332006	−	0.151260i
$151$			2.73232i			0.222353i	0.993801	+	0.111177i	$0.0354619\pi$
$151$			2.73232i			0.222353i	−0.993801	+	0.111177i	$0.964538\pi$
$152$	14.4260	−	19.0474i	1.17010	−	1.54495i
$153$		−	1.34537i		−	0.108767i
$154$	−6.04723	+	6.88002i	−0.487300	+	0.554408i
$155$	−9.70304			−0.779367
$156$	−1.76469	+	3.82624i	−0.141289	+	0.306345i
$157$	−13.5441			−1.08094			−0.540468	−	0.841365i	$-0.681753\pi$
$157$	−13.5441			−1.08094			−0.540468	+	0.841365i	$0.681753\pi$
$158$	−2.33628	+	10.6440i	−0.185865	+	0.846788i
$159$	−15.5661			−1.23448
$160$	2.66455	+	4.99001i	0.210651	+	0.394495i
$161$	6.08880	+	3.36595i	0.479865	+	0.265274i
$162$	5.45990	+	1.19842i	0.428971	+	0.0941565i
$163$	−18.5317			−1.45151			−0.725756	−	0.687953i	$-0.758510\pi$
$163$	−18.5317			−1.45151			−0.725756	+	0.687953i	$0.758510\pi$
$164$	2.62283	−	5.68687i	0.204808	−	0.444070i
$165$		−	3.28321i		−	0.255597i
$166$	−0.246567	+	1.12334i	−0.0191373	+	0.0871884i
$167$	7.74592			0.599397			0.299699	−	0.954034i	$-0.403114\pi$
$167$	7.74592			0.599397			0.299699	+	0.954034i	$0.403114\pi$
$168$	−4.07028	−	9.17369i	−0.314029	−	0.707765i
$169$	−10.5323			−0.810174
$170$	0.339538	−	1.54691i	0.0260414	−	0.118643i
$171$			10.1488i			0.776097i
$172$	13.5392	+	6.24440i	1.03236	+	0.476131i
$173$	13.6112			1.03484			0.517421	−	0.855731i	$-0.326892\pi$
$173$	13.6112			1.03484			0.517421	+	0.855731i	$0.326892\pi$
$174$	−6.35946	−	1.39586i	−0.482109	−	0.105820i
$175$	1.28003	−	2.31550i	0.0967612	−	0.175035i
$176$	6.35714	+	7.44827i	0.479188	+	0.561434i
$177$	8.26193			0.621005
$178$	−1.55322	+	7.07638i	−0.116419	+	0.530397i
$179$	−17.3370			−1.29583			−0.647914	−	0.761714i	$-0.724358\pi$
$179$	−17.3370			−1.29583			−0.647914	+	0.761714i	$0.724358\pi$
$180$	−2.18185	−	1.00629i	−0.162626	−	0.0750042i
$181$	−11.8268			−0.879076			−0.439538	−	0.898224i	$-0.644858\pi$
$181$	−11.8268			−0.879076			−0.439538	+	0.898224i	$0.644858\pi$
$182$	−3.88043	+	4.41482i	−0.287637	+	0.327248i
$183$		−	12.6634i		−	0.936105i
$184$	4.49049	−	5.92903i	0.331043	−	0.437094i
$185$			6.22712i			0.457827i
$186$	3.94548	−	17.9753i	0.289297	−	1.31802i
$187$		−	2.74154i		−	0.200481i
$188$	−17.0892	−	7.88165i	−1.24635	−	0.574828i
$189$	13.0469	+	7.21244i	0.949019	+	0.524628i
$190$	−2.56130	+	11.6691i	−0.185816	+	0.846566i
$191$			20.5823i			1.48929i	0.667463	+	0.744643i	$0.267380\pi$
$191$			20.5823i			1.48929i	−0.667463	+	0.744643i	$0.732620\pi$
$192$	−10.3277	+	2.90715i	−0.745337	+	0.209806i
$193$	10.0690			0.724781			0.362391	−	0.932026i	$-0.381961\pi$
$193$	10.0690			0.724781			0.362391	+	0.932026i	$0.381961\pi$
$194$	0.252850	−	1.15197i	0.0181536	−	0.0827065i
$195$		−	2.10679i		−	0.150870i
$196$	−1.79634	−	13.8843i	−0.128310	−	0.991734i
$197$			4.59538i			0.327407i	0.986510	+	0.163704i	$0.0523441\pi$
$197$			4.59538i			0.327407i	−0.986510	+	0.163704i	$0.947656\pi$
$198$	−4.06254	−	0.891704i	−0.288712	−	0.0633706i
$199$	2.15447			0.152727			0.0763633	−	0.997080i	$-0.475669\pi$
$199$	2.15447			0.152727			0.0763633	+	0.997080i	$0.475669\pi$
$200$	−2.25474	−	1.70768i	−0.159434	−	0.120751i
$201$		−	2.88962i		−	0.203818i
$202$	7.63049	+	1.67485i	0.536879	+	0.117842i
$203$	−7.94868	−	4.39411i	−0.557888	−	0.308406i
$204$	2.72767	+	1.25802i	0.190975	+	0.0880791i
$205$			3.13128i			0.218698i
$206$	16.2549	+	3.56784i	1.13253	+	0.248583i
$207$			3.15909i			0.219572i
$208$	4.07929	+	4.77946i	0.282848	+	0.331396i
$209$			20.6808i			1.43052i
$210$	3.76908	+	3.31285i	0.260091	+	0.228608i
$211$	−11.7444			−0.808515			−0.404258	−	0.914645i	$-0.632470\pi$
$211$	−11.7444			−0.808515			−0.404258	+	0.914645i	$0.632470\pi$
$212$	−9.72203	+	21.0795i	−0.667712	+	1.44775i
$213$	−10.5572			−0.723367
$214$	1.91994	+	0.421416i	0.131245	+	0.0288074i
$215$	−7.45492			−0.508422
$216$	9.62205	−	12.7045i	0.654697	−	0.864433i
$217$	12.4202	−	22.4673i	0.843137	−	1.52518i
$218$	−0.326007	+	1.48527i	−0.0220800	+	0.100595i
$219$	16.9178			1.14320
$220$	−4.44608	−	2.05057i	−0.299755	−	0.138249i
$221$		−	1.75921i		−	0.118337i
$222$	−11.5360	−	2.53209i	−0.774249	−	0.169943i
$223$	6.92127			0.463482			0.231741	−	0.972777i	$-0.425558\pi$
$223$	6.92127			0.463482			0.231741	+	0.972777i	$0.425558\pi$
$224$	−14.9650	−	0.217606i	−0.999894	−	0.0145394i
$225$	1.20136			0.0800908
$226$	−15.4663	−	3.39476i	−1.02880	−	0.225816i
$227$		−	12.2022i		−	0.809890i	−0.914341	−	0.404945i	$-0.867291\pi$
$227$		−	12.2022i		−	0.809890i	0.914341	−	0.404945i	$-0.132709\pi$
$228$	−20.5761	−	9.48986i	−1.36269	−	0.628481i
$229$	−12.2581			−0.810041			−0.405021	−	0.914308i	$-0.632736\pi$
$229$	−12.2581			−0.810041			−0.405021	+	0.914308i	$0.632736\pi$
$230$	−0.797275	+	3.63233i	−0.0525707	+	0.239509i
$231$	7.60226	+	4.20261i	0.500192	+	0.276511i
$232$	−5.86214	+	7.74010i	−0.384868	+	0.508163i
$233$	−10.1521			−0.665083			−0.332542	−	0.943089i	$-0.607906\pi$
$233$	−10.1521			−0.665083			−0.332542	+	0.943089i	$0.607906\pi$
$234$	−2.60688	−	0.572195i	−0.170417	−	0.0374055i
$235$	9.40956			0.613812
$236$	5.16009	−	11.1882i	0.335893	−	0.728291i
$237$	10.3342			0.671279
$238$	3.14725	+	2.76630i	0.204006	+	0.179312i
$239$		−	5.57510i		−	0.360624i	−0.983610	−	0.180312i	$-0.942289\pi$
$239$		−	5.57510i		−	0.360624i	0.983610	−	0.180312i	$-0.0577107\pi$
$240$	4.08038	−	3.48263i	0.263387	−	0.224803i
$241$			20.9813i			1.35152i	0.737120	+	0.675762i	$0.236185\pi$
$241$			20.9813i			1.35152i	−0.737120	+	0.675762i	$0.763815\pi$
$242$	6.91615	+	1.51805i	0.444587	+	0.0975842i
$243$			11.6027i			0.744316i
$244$	−17.1486	−	7.90908i	−1.09783	−	0.506327i
$245$	3.72304	+	5.92781i	0.237857	+	0.378714i
$246$	−5.80085	−	1.27325i	−0.369848	−	0.0811795i
$247$			13.2706i			0.844386i
$248$	−21.8778	−	16.5696i	−1.38924	−	1.05217i
$249$	1.09065			0.0691174
$250$	1.38133	+	0.303194i	0.0873630	+	0.0191757i
$251$		−	22.8742i		−	1.44381i	−0.691995	−	0.721903i	$-0.743268\pi$
$251$		−	22.8742i		−	1.44381i	0.691995	−	0.721903i	$-0.256732\pi$
$252$	5.12289	−	3.76399i	0.322712	−	0.237109i
$253$			6.43746i			0.404720i
$254$	4.97803	−	22.6796i	0.312349	−	1.42304i
$255$	−1.50190			−0.0940525
$256$	−2.51345	+	15.8013i	−0.157091	+	0.987584i
$257$			28.8767i			1.80128i	0.434566	+	0.900640i	$0.356902\pi$
$257$			28.8767i			1.80128i	−0.434566	+	0.900640i	$0.643098\pi$
$258$	3.03134	−	13.8106i	0.188723	−	0.859811i
$259$	−14.4189	−	7.97091i	−0.895946	−	0.495288i
$260$	−2.85299	−	1.31582i	−0.176935	−	0.0816039i
$261$		−	4.12406i		−	0.255273i
$262$	−0.607442	+	2.76746i	−0.0375279	+	0.170974i
$263$		−	19.6017i		−	1.20869i	−0.796722	−	0.604347i	$-0.793434\pi$
$263$		−	19.6017i		−	1.20869i	0.796722	−	0.604347i	$-0.206566\pi$
$264$	5.60666	−	7.40277i	0.345066	−	0.455609i
$265$		−	11.6067i		−	0.712995i
$266$	−23.7412	−	20.8675i	−1.45567	−	1.27947i
$267$	6.87045			0.420465
$268$	−3.91309	−	1.80475i	−0.239030	−	0.110243i
$269$	−27.2431			−1.66104			−0.830520	−	0.556988i	$-0.811957\pi$
$269$	−27.2431			−1.66104			−0.830520	+	0.556988i	$0.811957\pi$
$270$	−1.70837	+	7.78322i	−0.103968	+	0.473672i
$271$	−26.0339			−1.58144			−0.790722	−	0.612175i	$-0.790295\pi$
$271$	−26.0339			−1.58144			−0.790722	+	0.612175i	$0.790295\pi$
$272$	3.40720	−	2.90806i	0.206592	−	0.176327i
$273$	4.87827	+	2.69676i	0.295246	+	0.163215i
$274$	−5.81458	−	1.27627i	−0.351272	−	0.0771020i
$275$	2.44809			0.147625
$276$	−6.40488	−	2.95398i	−0.385528	−	0.177809i
$277$		−	5.64829i		−	0.339373i	−0.985498	−	0.169687i	$-0.945724\pi$
$277$		−	5.64829i		−	0.339373i	0.985498	−	0.169687i	$-0.0542755\pi$
$278$	−1.27541	+	5.81068i	−0.0764940	+	0.348501i
$279$	11.6569			0.697878
$280$	6.84025	−	3.03496i	0.408783	−	0.181374i
$281$	25.9379			1.54733			0.773663	−	0.633598i	$-0.218422\pi$
$281$	25.9379			1.54733			0.773663	+	0.633598i	$0.218422\pi$
$282$	−3.82615	+	17.4317i	−0.227844	+	1.03804i
$283$		−	12.6062i		−	0.749358i	−0.927155	−	0.374679i	$-0.877753\pi$
$283$		−	12.6062i		−	0.749358i	0.927155	−	0.374679i	$-0.122247\pi$
$284$	−6.59363	+	14.2964i	−0.391260	+	0.848337i
$285$	11.3295			0.671103
$286$	−5.31219	−	1.16599i	−0.314116	−	0.0689467i
$287$	−7.25047	−	4.00813i	−0.427982	−	0.236593i
$288$	−3.20109	−	5.99481i	−0.188626	−	0.353247i
$289$	15.7459			0.926229
$290$	1.04081	−	4.74186i	0.0611184	−	0.278451i
$291$	−1.11844			−0.0655644
$292$	10.5662	−	22.9099i	0.618341	−	1.34070i
$293$	16.7982			0.981362			0.490681	−	0.871339i	$-0.336748\pi$
$293$	16.7982			0.981362			0.490681	+	0.871339i	$0.336748\pi$
$294$	−12.4954	+	4.48673i	−0.728748	+	0.261672i
$295$			6.16041i			0.358673i
$296$	−10.6339	+	14.0405i	−0.618083	+	0.816089i
$297$			13.7939i			0.800406i
$298$	−5.80427	+	26.4439i	−0.336232	+	1.53185i
$299$			4.13083i			0.238892i
$300$	−1.12336	+	2.43569i	−0.0648573	+	0.140625i
$301$	9.54253	−	17.2618i	0.550022	−	0.994956i
$302$	0.828423	−	3.77424i	0.0476704	−	0.217183i
$303$		−	7.40844i		−	0.425604i
$304$	−25.7021	+	21.9369i	−1.47412	+	1.25817i
$305$	9.44231			0.540665
$306$	−0.407908	+	1.85840i	−0.0233186	+	0.106238i
$307$			5.08609i			0.290279i	0.989411	+	0.145139i	$0.0463630\pi$
$307$			5.08609i			0.290279i	−0.989411	+	0.145139i	$0.953637\pi$
$308$	10.4392	−	7.67010i	0.594829	−	0.437044i
$309$		−	15.7818i		−	0.897797i
$310$	13.4031	+	2.94190i	0.761245	+	0.167089i
$311$	16.9297			0.959994			0.479997	−	0.877270i	$-0.340638\pi$
$311$	16.9297			0.959994			0.479997	+	0.877270i	$0.340638\pi$
$312$	3.59772	−	4.75026i	0.203681	−	0.268931i
$313$		−	8.30791i		−	0.469591i	−0.972045	−	0.234795i	$-0.924558\pi$
$313$		−	8.30791i		−	0.469591i	0.972045	−	0.234795i	$-0.0754420\pi$
$314$	18.7089	+	4.10648i	1.05580	+	0.231742i
$315$	−1.53778	+	2.78175i	−0.0866441	+	0.156734i
$316$	6.45436	−	13.9945i	0.363086	−	0.787251i
$317$			10.7428i			0.603376i	0.953407	+	0.301688i	$0.0975501\pi$
$317$			10.7428i			0.603376i	−0.953407	+	0.301688i	$0.902450\pi$
$318$	21.5020	+	4.71956i	1.20577	+	0.264660i
$319$		−	8.40383i		−	0.470524i
$320$	−2.16769	−	7.70072i	−0.121177	−	0.430484i
$321$		−	1.86407i		−	0.104042i
$322$	−7.39011	−	6.49558i	−0.411835	−	0.361985i
$323$	9.46038			0.526390
$324$	−7.17858	−	3.31082i	−0.398810	−	0.183934i
$325$	1.57090			0.0871381
$326$	25.5983	+	5.61868i	1.41776	+	0.311190i
$327$	1.44205			0.0797453
$328$	−5.34721	+	7.06022i	−0.295250	+	0.389835i
$329$	−12.0445	+	21.7878i	−0.664036	+	1.20120i
$330$	−0.995448	+	4.53519i	−0.0547976	+	0.249654i
$331$	12.1739			0.669140			0.334570	−	0.942371i	$-0.391409\pi$
$331$	12.1739			0.669140			0.334570	+	0.942371i	$0.391409\pi$
$332$	0.681182	−	1.47695i	0.0373847	−	0.0810583i
$333$		−	7.48103i		−	0.409958i
$334$	−10.6997	−	2.34851i	−0.585460	−	0.128505i
$335$	2.15461			0.117719
$336$	2.84100	+	13.9060i	0.154989	+	0.758633i
$337$	−11.5686			−0.630179			−0.315090	−	0.949062i	$-0.602035\pi$
$337$	−11.5686			−0.630179			−0.315090	+	0.949062i	$0.602035\pi$
$338$	14.5485	+	3.19331i	0.791336	+	0.173693i
$339$			15.0162i			0.815569i
$340$	−0.938029	+	2.03385i	−0.0508718	+	0.110301i
$341$	23.7539			1.28634
$342$	3.07705	−	14.0188i	0.166388	−	0.758051i
$343$	−18.4914	+	1.03291i	−0.998444	+	0.0557721i
$344$	−16.8089	−	12.7306i	−0.906275	−	0.686388i
$345$	3.52663			0.189867
$346$	−18.8016	−	4.12684i	−1.01078	−	0.221860i
$347$	−10.6711			−0.572854			−0.286427	−	0.958102i	$-0.592468\pi$
$347$	−10.6711			−0.572854			−0.286427	+	0.958102i	$0.592468\pi$
$348$	8.36130	+	3.85630i	0.448213	+	0.206719i
$349$	14.5060			0.776486			0.388243	−	0.921557i	$-0.373082\pi$
$349$	14.5060			0.776486			0.388243	+	0.921557i	$0.373082\pi$
$350$	−2.47019	+	2.81037i	−0.132037	+	0.150220i
$351$			8.85139i			0.472452i
$352$	−6.52305	−	12.2160i	−0.347680	−	0.651113i
$353$			33.2031i			1.76722i	0.468221	+	0.883611i	$0.344895\pi$
$353$			33.2031i			1.76722i	−0.468221	+	0.883611i	$0.655105\pi$
$354$	−11.4125	−	2.50496i	−0.606565	−	0.133137i
$355$		−	7.87185i		−	0.417794i
$356$	4.29103	−	9.30389i	0.227424	−	0.493105i
$357$	1.92247	−	3.47764i	0.101748	−	0.184056i
$358$	23.9481	+	5.25646i	1.26570	+	0.277813i
$359$		−	13.3218i		−	0.703097i	−0.936170	−	0.351549i	$-0.885655\pi$
$359$		−	13.3218i		−	0.703097i	0.936170	−	0.351549i	$-0.114345\pi$
$360$	2.70876	+	2.05154i	0.142764	+	0.108126i
$361$	−52.3642			−2.75601
$362$	16.3367	+	3.58580i	0.858636	+	0.188465i
$363$		−	6.71489i		−	0.352440i
$364$	6.69870	−	4.92180i	0.351107	−	0.257972i
$365$			12.6145i			0.660275i
$366$	−3.83946	+	17.4923i	−0.200692	+	0.914338i
$367$	25.9412			1.35412			0.677059	−	0.735929i	$-0.263254\pi$
$367$	25.9412			1.35412			0.677059	+	0.735929i	$0.263254\pi$
$368$	−8.00049	+	6.82847i	−0.417054	+	0.355958i
$369$		−	3.76180i		−	0.195832i
$370$	1.88802	−	8.60171i	0.0981537	−	0.447182i
$371$	26.8753	+	14.8569i	1.39530	+	0.771334i
$372$	−10.9000	+	23.6336i	−0.565140	+	1.22535i
$373$			30.5923i			1.58401i	0.610515	+	0.792005i	$0.290963\pi$
$373$			30.5923i			1.58401i	−0.610515	+	0.792005i	$0.709037\pi$
$374$	−0.831218	+	3.78698i	−0.0429813	+	0.195820i
$375$		−	1.34113i		−	0.0692558i
$376$	21.2161	+	16.0685i	1.09414	+	0.828669i
$377$		−	5.39263i		−	0.277734i
$378$	−15.8353	−	13.9185i	−0.814478	−	0.715890i
$379$	−10.6930			−0.549262			−0.274631	−	0.961550i	$-0.588556\pi$
$379$	−10.6930			−0.549262			−0.274631	+	0.961550i	$0.588556\pi$
$380$	7.07600	−	15.3423i	0.362991	−	0.787045i
$381$	−22.0196			−1.12810
$382$	6.24044	−	28.4310i	0.319288	−	1.45466i
$383$	−9.36792			−0.478679			−0.239339	−	0.970936i	$-0.576931\pi$
$383$	−9.36792			−0.478679			−0.239339	+	0.970936i	$0.576931\pi$
$384$	15.1474	−	0.884449i	0.772987	−	0.0451343i
$385$	−3.13362	+	5.66853i	−0.159704	+	0.288895i
$386$	−13.9086	−	3.05285i	−0.707929	−	0.155386i
$387$	8.95606			0.455262
$388$	−0.698539	+	1.51459i	−0.0354629	+	0.0768914i
$389$		−	2.30373i		−	0.116804i	−0.998293	−	0.0584019i	$-0.981399\pi$
$389$		−	2.30373i		−	0.116804i	0.998293	−	0.0584019i	$-0.0186005\pi$
$390$	−0.638766	+	2.91017i	−0.0323452	+	0.147362i
$391$	2.94480			0.148925
$392$	−1.72829	+	19.7234i	−0.0872920	+	0.996183i
$393$	2.68693			0.135538
$394$	1.39329	−	6.34774i	0.0701929	−	0.319794i
$395$			7.70558i			0.387710i
$396$	5.34136	+	2.46348i	0.268413	+	0.123794i
$397$	−1.77718			−0.0891942			−0.0445971	−	0.999005i	$-0.514200\pi$
$397$	−1.77718			−0.0891942			−0.0445971	+	0.999005i	$0.514200\pi$
$398$	−2.97604	−	0.653222i	−0.149175	−	0.0327431i
$399$	−14.5021	+	26.2335i	−0.726015	+	1.31332i
$400$	2.59678	+	3.04249i	0.129839	+	0.152124i
$401$	17.8159			0.889682			0.444841	−	0.895609i	$-0.353260\pi$
$401$	17.8159			0.889682			0.444841	+	0.895609i	$0.353260\pi$
$402$	−0.876114	+	3.99152i	−0.0436966	+	0.199079i
$403$	15.2425			0.759285
$404$	−10.0324	−	4.62703i	−0.499132	−	0.230203i
$405$	3.95264			0.196408
$406$	9.64748	+	8.47971i	0.478796	+	0.420841i
$407$		−	15.2445i		−	0.755643i
$408$	−3.38639	−	2.56475i	−0.167651	−	0.126974i
$409$		−	37.8691i		−	1.87250i	−0.351329	−	0.936252i	$-0.614270\pi$
$409$		−	37.8691i		−	1.87250i	0.351329	−	0.936252i	$-0.385730\pi$
$410$	0.949384	−	4.32533i	0.0468868	−	0.213613i
$411$			5.64538i			0.278466i
$412$	−21.3716	−	9.85674i	−1.05290	−	0.485606i
$413$	−14.2644	−	7.88551i	−0.701906	−	0.388021i
$414$	0.957816	−	4.36375i	0.0470741	−	0.214466i
$415$			0.813234i			0.0399201i
$416$	−4.18575	−	7.83882i	−0.205223	−	0.384330i
$417$	5.64159			0.276270
$418$	6.27028	−	28.5670i	0.306689	−	1.39726i
$419$		−	3.11076i		−	0.151971i	−0.997109	−	0.0759854i	$-0.975790\pi$
$419$		−	3.11076i		−	0.151971i	0.997109	−	0.0759854i	$-0.0242102\pi$
$420$	−4.20191	−	5.71890i	−0.205032	−	0.279054i
$421$		−	18.8952i		−	0.920893i	−0.887687	−	0.460447i	$-0.847689\pi$
$421$		−	18.8952i		−	0.920893i	0.887687	−	0.460447i	$-0.152311\pi$
$422$	16.2228	+	3.56082i	0.789716	+	0.173338i
$423$	−11.3043			−0.549634
$424$	19.8205	−	26.1701i	0.962569	−	1.27093i
$425$		−	1.11987i		−	0.0543218i
$426$	14.5830	+	3.20088i	0.706548	+	0.155083i
$427$	−12.0864	+	21.8636i	−0.584904	+	1.05805i
$428$	−2.52430	−	1.16423i	−0.122017	−	0.0562751i
$429$			5.15760i			0.249011i
$430$	10.2977	+	2.26029i	0.496600	+	0.109001i
$431$			38.2730i			1.84355i	0.387730	+	0.921773i	$0.373259\pi$
$431$			38.2730i			1.84355i	−0.387730	+	0.921773i	$0.626741\pi$
$432$	−17.1432	+	14.6318i	−0.824800	+	0.703972i
$433$			1.50589i			0.0723684i	0.999345	+	0.0361842i	$0.0115203\pi$
$433$			1.50589i			0.0723684i	−0.999345	+	0.0361842i	$0.988480\pi$
$434$	−23.9683	+	27.2691i	−1.15052	+	1.30896i
$435$	−4.60387			−0.220738
$436$	0.900648	−	1.95280i	0.0431332	−	0.0935223i
$437$	−22.2141			−1.06264
$438$	−23.3690	−	5.12936i	−1.11662	−	0.245090i
$439$	5.00779			0.239009			0.119504	−	0.992834i	$-0.461869\pi$
$439$	5.00779			0.239009			0.119504	+	0.992834i	$0.461869\pi$
$440$	5.51979	+	4.18054i	0.263146	+	0.199299i
$441$	−4.47272	−	7.12145i	−0.212987	−	0.339117i
$442$	−0.533382	+	2.43005i	−0.0253704	+	0.115586i
$443$	−24.9714			−1.18643			−0.593213	−	0.805046i	$-0.702141\pi$
$443$	−24.9714			−1.18643			−0.593213	+	0.805046i	$0.702141\pi$
$444$	15.1674	+	6.99531i	0.719812	+	0.331983i
$445$			5.12287i			0.242847i
$446$	−9.56056	−	2.09848i	−0.452706	−	0.0993661i
$447$	25.6743			1.21435
$448$	20.6057	+	4.83789i	0.973528	+	0.228569i
$449$	−4.85721			−0.229226			−0.114613	−	0.993410i	$-0.536563\pi$
$449$	−4.85721			−0.229226			−0.114613	+	0.993410i	$0.536563\pi$
$450$	−1.65948	−	0.364245i	−0.0782286	−	0.0171707i
$451$		−	7.66564i		−	0.360961i
$452$	20.3348	+	9.37857i	0.956468	+	0.441131i
$453$	−3.66441			−0.172169
$454$	−3.69964	+	16.8553i	−0.173633	+	0.791059i
$455$	−2.01081	+	3.63742i	−0.0942680	+	0.170525i
$456$	25.5451	+	19.3472i	1.19626	+	0.906014i
$457$	−21.1002			−0.987025			−0.493513	−	0.869739i	$-0.664287\pi$
$457$	−21.1002			−0.987025			−0.493513	+	0.869739i	$0.664287\pi$
$458$	16.9326	+	3.71659i	0.791206	+	0.173665i
$459$	6.31002			0.294526
$460$	2.20260	−	4.77572i	0.102697	−	0.222669i
$461$	11.2426			0.523620			0.261810	−	0.965119i	$-0.415681\pi$
$461$	11.2426			0.523620			0.261810	+	0.965119i	$0.415681\pi$
$462$	−9.22702	−	8.11014i	−0.429280	−	0.377318i
$463$		−	39.4199i		−	1.83200i	−0.401179	−	0.916000i	$-0.631399\pi$
$463$		−	39.4199i		−	1.83200i	0.401179	−	0.916000i	$-0.368601\pi$
$464$	10.4443	−	8.91428i	0.484865	−	0.413835i
$465$		−	13.0131i		−	0.603466i
$466$	14.0233	+	3.07804i	0.649619	+	0.142587i
$467$		−	26.4941i		−	1.22600i	−0.790083	−	0.613000i	$-0.789963\pi$
$467$		−	26.4941i		−	1.22600i	0.790083	−	0.613000i	$-0.210037\pi$
$468$	3.42748	+	1.58078i	0.158435	+	0.0730716i
$469$	−2.75797	+	4.98899i	−0.127351	+	0.230370i
$470$	−12.9977	−	2.85292i	−0.599540	−	0.131595i
$471$		−	18.1644i		−	0.836973i
$472$	−10.5200	+	13.8901i	−0.484222	+	0.639344i
$473$	18.2503			0.839149
$474$	−14.2750	−	3.13327i	−0.655671	−	0.143916i
$475$			8.44773i			0.387608i
$476$	−3.50867	−	4.77540i	−0.160820	−	0.218880i
$477$			13.9439i			0.638446i
$478$	−1.69034	+	7.70106i	−0.0773142	+	0.352238i
$479$	35.7827			1.63495			0.817477	−	0.575961i	$-0.195372\pi$
$479$	35.7827			1.63495			0.817477	+	0.575961i	$0.195372\pi$
$480$	−6.69226	+	3.57352i	−0.305459	+	0.163108i
$481$		−	9.78221i		−	0.446031i
$482$	6.36140	−	28.9821i	0.289754	−	1.32010i
$483$	−4.51419	+	8.16590i	−0.205403	+	0.371561i
$484$	−9.09323	−	4.19387i	−0.413329	−	0.190630i
$485$		−	0.833955i		−	0.0378680i
$486$	3.51788	−	16.0272i	0.159574	−	0.727009i
$487$			12.4491i			0.564125i	0.959396	+	0.282062i	$0.0910185\pi$
$487$			12.4491i			0.564125i	−0.959396	+	0.282062i	$0.908982\pi$
$488$	21.2899	+	16.1244i	0.963750	+	0.729917i
$489$		−	24.8534i		−	1.12391i
$490$	−3.34548	−	9.31707i	−0.151133	−	0.420902i
$491$	−14.4396			−0.651649			−0.325824	−	0.945430i	$-0.605642\pi$
$491$	−14.4396			−0.651649			−0.325824	+	0.945430i	$0.605642\pi$
$492$	7.62684	+	3.51756i	0.343845	+	0.158584i
$493$	−3.84432			−0.173139
$494$	4.02355	−	18.3310i	0.181028	−	0.824753i
$495$	−2.94104			−0.132190
$496$	25.1967	+	29.5214i	1.13136	+	1.32555i
$497$	18.2272	+	10.0762i	0.817603	+	0.451980i
$498$	−1.50655	−	0.330680i	−0.0675103	−	0.0148181i
$499$	22.0969			0.989195			0.494597	−	0.869122i	$-0.335315\pi$
$499$	22.0969			0.989195			0.494597	+	0.869122i	$0.335315\pi$
$500$	−1.81615	−	0.837621i	−0.0812206	−	0.0374596i
$501$			10.3883i			0.464116i
$502$	−6.93531	+	31.5968i	−0.309538	+	1.41023i
$503$	−21.8311			−0.973401			−0.486701	−	0.873569i	$-0.661800\pi$
$503$	−21.8311			−0.973401			−0.486701	+	0.873569i	$0.661800\pi$
$504$	−8.21762	+	3.64609i	−0.366042	+	0.162410i
$505$	5.52401			0.245815
$506$	1.95180	−	8.89226i	0.0867679	−	0.395309i
$507$		−	14.1252i		−	0.627320i
$508$	−13.7526	+	29.8187i	−0.610173	+	1.32299i
$509$	30.6514			1.35860			0.679300	−	0.733861i	$-0.262284\pi$
$509$	30.6514			1.35860			0.679300	+	0.733861i	$0.262284\pi$
$510$	2.07462	+	0.455366i	0.0918656	+	0.0201639i
$511$	−29.2089	−	16.1470i	−1.29213	−	0.714301i
$512$	8.26278	−	21.0648i	0.365167	−	0.930942i
$513$	−47.5995			−2.10157
$514$	8.75524	−	39.8883i	0.386177	−	1.75940i
$515$	11.7675			0.518539
$516$	−8.37457	+	18.1579i	−0.368670	+	0.799358i
$517$	−23.0354			−1.01310
$518$	17.5005	+	15.3822i	0.768928	+	0.675854i
$519$			18.2545i			0.801282i
$520$	3.54198	+	2.68260i	0.155326	+	0.117640i
$521$		−	7.13741i		−	0.312696i	−0.987702	−	0.156348i	$-0.950028\pi$
$521$		−	7.13741i		−	0.312696i	0.987702	−	0.156348i	$-0.0499721\pi$
$522$	−1.25039	+	5.69669i	−0.0547280	+	0.249337i
$523$			31.6160i			1.38247i	0.722630	+	0.691235i	$0.242933\pi$
$523$			31.6160i			1.38247i	−0.722630	+	0.691235i	$0.757067\pi$
$524$	1.67816	−	3.63861i	0.0733105	−	0.158953i
$525$	3.10539	+	1.71669i	0.135530	+	0.0749225i
$526$	−5.94311	+	27.0764i	−0.259132	+	1.18059i
$527$		−	10.8662i		−	0.473338i
$528$	−9.98912	+	8.52577i	−0.434721	+	0.371037i
$529$	16.0853			0.699359
$530$	−3.51908	+	16.0327i	−0.152859	+	0.696416i
$531$		−	7.40088i		−	0.321171i
$532$	26.4676	+	36.0231i	1.14752	+	1.56180i
$533$		−	4.91894i		−	0.213063i
$534$	−9.49036	−	2.08308i	−0.410688	−	0.0901436i
$535$	1.38992			0.0600916
$536$	4.85808	+	3.67938i	0.209837	+	0.158925i
$537$		−	23.2512i		−	1.00336i
$538$	37.6317	+	8.25993i	1.62242	+	0.356111i
$539$	−9.11433	−	14.5118i	−0.392582	−	0.625067i
$540$	4.71965	−	10.2332i	0.203101	−	0.440368i
$541$		−	39.5347i		−	1.69973i	−0.526999	−	0.849866i	$-0.676683\pi$
$541$		−	39.5347i		−	1.69973i	0.526999	−	0.849866i	$-0.323317\pi$
$542$	35.9614	+	7.89330i	1.54467	+	0.339046i
$543$		−	15.8613i		−	0.680672i
$544$	−5.58817	+	2.98396i	−0.239591	+	0.127936i
$545$			1.07524i			0.0460584i
$546$	−5.92086	−	5.20417i	−0.253389	−	0.222718i
$547$	27.6549			1.18244			0.591218	−	0.806512i	$-0.298647\pi$
$547$	27.6549			1.18244			0.591218	+	0.806512i	$0.298647\pi$
$548$	7.64491	+	3.52589i	0.326574	+	0.150619i
$549$	−11.3436			−0.484134
$550$	−3.38161	−	0.742244i	−0.144193	−	0.0316494i
$551$	28.9995			1.23542
$552$	7.95162	+	6.02234i	0.338444	+	0.256328i
$553$	−17.8422	−	9.86338i	−0.758730	−	0.419434i
$554$	−1.71253	+	7.80216i	−0.0727583	+	0.331482i
$555$	−8.35140			−0.354497
$556$	3.52352	−	7.63977i	0.149431	−	0.323999i
$557$		−	29.2830i		−	1.24076i	−0.784301	−	0.620380i	$-0.786978\pi$
$557$		−	29.2830i		−	1.24076i	0.784301	−	0.620380i	$-0.213022\pi$
$558$	−16.1020	−	3.53429i	−0.681651	−	0.149618i
$559$	11.7110			0.495321
$560$	−10.3688	+	2.11836i	−0.438163	+	0.0895171i
$561$	3.67677			0.155234
$562$	−35.8288	−	7.86421i	−1.51135	−	0.331732i
$563$			5.22412i			0.220170i	0.993922	+	0.110085i	$0.0351124\pi$
$563$			5.22412i			0.220170i	−0.993922	+	0.110085i	$0.964888\pi$
$564$	10.5703	−	22.9188i	0.445092	−	0.965057i
$565$	−11.1967			−0.471047
$566$	−3.82211	+	17.4133i	−0.160655	+	0.731934i
$567$	−5.05950	+	9.15233i	−0.212479	+	0.384362i
$568$	13.4426	−	17.7490i	0.564038	−	0.744730i
$569$	11.8297			0.495925			0.247963	−	0.968770i	$-0.420239\pi$
$569$	11.8297			0.495925			0.247963	+	0.968770i	$0.420239\pi$
$570$	−15.6498	−	3.43504i	−0.655499	−	0.143878i
$571$	−22.3223			−0.934158			−0.467079	−	0.884216i	$-0.654694\pi$
$571$	−22.3223			−0.934158			−0.467079	+	0.884216i	$0.654694\pi$
$572$	6.98437	+	3.22125i	0.292031	+	0.134687i
$573$	−27.6037			−1.15316
$574$	8.80005	+	7.73485i	0.367307	+	0.322847i
$575$			2.62959i			0.109661i
$576$	2.60418	+	9.25136i	0.108507	+	0.385473i
$577$		−	25.4830i		−	1.06087i	−0.847725	−	0.530436i	$-0.822028\pi$
$577$		−	25.4830i		−	1.06087i	0.847725	−	0.530436i	$-0.177972\pi$
$578$	−21.7503	−	4.77405i	−0.904692	−	0.198574i
$579$			13.5038i			0.561201i
$580$	−2.87540	+	6.23450i	−0.119395	+	0.258874i
$581$	−1.88304	−	1.04096i	−0.0781216	−	0.0431865i
$582$	1.54494	+	0.339105i	0.0640399	+	0.0140564i
$583$			28.4142i			1.17680i
$584$	−21.5416	+	28.4425i	−0.891396	+	1.17696i
$585$	−1.88722			−0.0780271
$586$	−23.2039	−	5.09311i	−0.958543	−	0.210394i
$587$			27.1365i			1.12004i	0.828478	+	0.560021i	$0.189207\pi$
$587$			27.1365i			1.12004i	−0.828478	+	0.560021i	$0.810793\pi$
$588$	18.6207	−	2.40912i	0.767903	−	0.0993506i
$589$			81.9687i			3.37746i
$590$	1.86780	−	8.50956i	0.0768960	−	0.350333i
$591$	−6.16301			−0.253512
$592$	18.9459	−	16.1705i	0.778673	−	0.664602i
$593$		−	33.7929i		−	1.38771i	−0.720116	−	0.693853i	$-0.755912\pi$
$593$		−	33.7929i		−	1.38771i	0.720116	−	0.693853i	$-0.244088\pi$
$594$	4.18224	−	19.0540i	0.171599	−	0.781795i
$595$	2.59306	+	1.43347i	0.106305	+	0.0587666i
$596$	16.0352	−	34.7679i	0.656829	−	1.42415i
$597$			2.88943i			0.118257i
$598$	1.25244	−	5.70604i	0.0512162	−	0.233337i
$599$			26.0094i			1.06271i	0.847148	+	0.531357i	$0.178318\pi$
$599$			26.0094i			1.06271i	−0.847148	+	0.531357i	$0.821682\pi$
$600$	2.29022	−	3.02390i	0.0934979	−	0.123450i
$601$		−	25.5296i		−	1.04137i	−0.853747	−	0.520687i	$-0.825676\pi$
$601$		−	25.5296i		−	1.04137i	0.853747	−	0.520687i	$-0.174324\pi$
$602$	−18.4151	+	20.9511i	−0.750542	+	0.853902i
$603$	−2.58847			−0.105411
$604$	−2.28865	+	4.96230i	−0.0931239	+	0.201913i
$605$	5.00688			0.203559
$606$	−2.24619	+	10.2335i	−0.0912453	+	0.415708i
$607$	−21.2033			−0.860615			−0.430307	−	0.902682i	$-0.641595\pi$
$607$	−21.2033			−0.860615			−0.430307	+	0.902682i	$0.641595\pi$
$608$	42.1542	−	22.5094i	1.70958	−	0.912877i
$609$	5.89309	−	10.6602i	0.238800	−	0.431974i
$610$	−13.0429	−	2.86285i	−0.528093	−	0.115913i
$611$	−14.7815			−0.597996
$612$	1.12691	−	2.44339i	0.0455527	−	0.0987684i
$613$		−	0.381509i		−	0.0154090i	−0.999970	−	0.00770450i	$-0.997548\pi$
$613$		−	0.381509i		−	0.0154090i	0.999970	−	0.00770450i	$-0.00245244\pi$
$614$	1.54207	−	7.02557i	0.0622329	−	0.283529i
$615$	−4.19946			−0.169339
$616$	−16.7455	+	7.42984i	−0.674696	+	0.299357i
$617$	−23.7394			−0.955714			−0.477857	−	0.878438i	$-0.658586\pi$
$617$	−23.7394			−0.955714			−0.477857	+	0.878438i	$0.658586\pi$
$618$	−4.78495	+	21.7999i	−0.192479	+	0.876921i
$619$			3.66231i			0.147201i	0.997288	+	0.0736004i	$0.0234489\pi$
$619$			3.66231i			0.147201i	−0.997288	+	0.0736004i	$0.976551\pi$
$620$	−17.6221	−	8.12747i	−0.707722	−	0.326407i
$621$	−14.8166			−0.594571
$622$	−23.3855	−	5.13297i	−0.937672	−	0.205813i
$623$	−11.8620	−	6.55743i	−0.475240	−	0.262718i
$624$	−6.40988	+	5.47088i	−0.256601	+	0.219010i
$625$	1.00000			0.0400000
$626$	−2.51890	+	11.4760i	−0.100676	+	0.458672i
$627$	−27.7357			−1.10766
$628$	−24.5981	−	11.3448i	−0.981569	−	0.452707i
$629$	−6.97358			−0.278055
$630$	2.96759	−	3.37627i	0.118232	−	0.134514i
$631$		−	10.6277i		−	0.423080i	−0.977369	−	0.211540i	$-0.932152\pi$
$631$		−	10.6277i		−	0.423080i	0.977369	−	0.211540i	$-0.0678479\pi$
$632$	−13.1586	+	17.3741i	−0.523423	+	0.691103i
$633$		−	15.7508i		−	0.626036i
$634$	3.25715	−	14.8394i	0.129358	−	0.589347i
$635$		−	16.4186i		−	0.651554i
$636$	−28.2704	−	13.0385i	−1.12099	−	0.517011i
$637$	−5.84854	−	9.31202i	−0.231728	−	0.368956i
$638$	−2.54799	+	11.6085i	−0.100876	+	0.459584i
$639$			9.45694i			0.374111i
$640$	0.659479	+	11.2945i	0.0260682	+	0.446453i
$641$	−31.4300			−1.24141			−0.620705	−	0.784044i	$-0.713154\pi$
$641$	−31.4300			−1.24141			−0.620705	+	0.784044i	$0.713154\pi$
$642$	−0.565174	+	2.57490i	−0.0223057	+	0.101623i
$643$		−	7.82074i		−	0.308420i	−0.988038	−	0.154210i	$-0.950717\pi$
$643$		−	7.82074i		−	0.308420i	0.988038	−	0.154210i	$-0.0492832\pi$
$644$	8.23877	+	11.2132i	0.324653	+	0.441861i
$645$		−	9.99804i		−	0.393673i
$646$	−13.0679	−	2.86833i	−0.514150	−	0.112853i
$647$	−27.3346			−1.07463			−0.537317	−	0.843381i	$-0.680562\pi$
$647$	−27.3346			−1.07463			−0.537317	+	0.843381i	$0.680562\pi$
$648$	8.91217	+	6.74983i	0.350103	+	0.265158i
$649$		−	15.0812i		−	0.591989i
$650$	−2.16994	−	0.476288i	−0.0851119	−	0.0186816i
$651$	30.1317	+	16.6571i	1.18095	+	0.652844i
$652$	−33.6562	−	15.5225i	−1.31808	−	0.607908i
$653$		−	19.6566i		−	0.769221i	−0.923079	−	0.384611i	$-0.874336\pi$
$653$		−	19.6566i		−	0.769221i	0.923079	−	0.384611i	$-0.125664\pi$
$654$	−1.99194	−	0.437219i	−0.0778911	−	0.0170966i
$655$			2.00348i			0.0782823i
$656$	9.52688	−	8.13125i	0.371962	−	0.317472i
$657$		−	15.1546i		−	0.591239i
$658$	23.2434	−	26.4443i	0.906122	−	1.03091i
$659$	14.1522			0.551293			0.275647	−	0.961259i	$-0.411108\pi$
$659$	14.1522			0.551293			0.275647	+	0.961259i	$0.411108\pi$
$660$	2.75008	−	5.96279i	0.107047	−	0.232101i
$661$	7.32100			0.284754			0.142377	−	0.989812i	$-0.454525\pi$
$661$	7.32100			0.284754			0.142377	+	0.989812i	$0.454525\pi$
$662$	−16.8162	−	3.69106i	−0.653581	−	0.143457i
$663$	2.35934			0.0916291
$664$	−1.38874	+	1.83363i	−0.0538935	+	0.0711586i
$665$	−19.5607	−	10.8134i	−0.758531	−	0.419324i
$666$	−2.26820	+	10.3338i	−0.0878910	+	0.400426i
$667$	9.02690			0.349523
$668$	14.0677	+	6.48815i	0.544297	+	0.251034i
$669$			9.28234i			0.358876i
$670$	−2.97623	−	0.653264i	−0.114982	−	0.0252378i
$671$	−23.1156			−0.892367
$672$	0.291839	−	20.0701i	0.0112579	−	0.774222i
$673$	21.5006			0.828786			0.414393	−	0.910098i	$-0.363994\pi$
$673$	21.5006			0.828786			0.414393	+	0.910098i	$0.363994\pi$
$674$	15.9800	+	3.50751i	0.615527	+	0.135104i
$675$			5.63459i			0.216875i
$676$	−19.1281	−	8.82205i	−0.735698	−	0.339309i
$677$	41.7438			1.60434			0.802172	−	0.597093i	$-0.203678\pi$
$677$	41.7438			1.60434			0.802172	+	0.597093i	$0.203678\pi$
$678$	4.55282	−	20.7424i	0.174850	−	0.796606i
$679$	1.93102	+	1.06749i	0.0741057	+	0.0409664i
$680$	1.91238	−	2.52502i	0.0733364	−	0.0968300i
$681$	16.3648			0.627101
$682$	−32.8119	−	7.20202i	−1.25643	−	0.275780i
$683$	26.9066			1.02955			0.514777	−	0.857324i	$-0.327875\pi$
$683$	26.9066			1.02955			0.514777	+	0.857324i	$0.327875\pi$
$684$	−8.50084	+	18.4317i	−0.325038	+	0.704753i
$685$	−4.20941			−0.160833
$686$	25.8560	+	4.17969i	0.987185	+	0.159581i
$687$		−	16.4398i		−	0.627218i
$688$	19.3588	+	22.6815i	0.738048	+	0.864724i
$689$			18.2330i			0.694623i
$690$	−4.87144	−	1.06925i	−0.185453	−	0.0407057i
$691$			17.3610i			0.660443i	0.943904	+	0.330221i	$0.107123\pi$
$691$			17.3610i			0.660443i	−0.943904	+	0.330221i	$0.892877\pi$
$692$	24.7200	+	11.4010i	0.939713	+	0.433403i
$693$	3.76462	−	6.80996i	0.143006	−	0.258689i
$694$	14.7403	+	3.23541i	0.559534	+	0.122814i
$695$			4.20658i			0.159565i
$696$	−10.3805	−	7.86191i	−0.393472	−	0.298005i
$697$	−3.50663			−0.132823
$698$	−20.0375	−	4.39811i	−0.758431	−	0.166471i
$699$		−	13.6153i		−	0.514976i
$700$	4.26423	−	3.13310i	0.161173	−	0.118420i
$701$			31.9368i			1.20624i	0.797651	+	0.603119i	$0.206076\pi$
$701$			31.9368i			1.20624i	−0.797651	+	0.603119i	$0.793924\pi$
$702$	2.68369	−	12.2267i	0.101289	−	0.461467i
$703$	52.6051			1.98404
$704$	5.30668	+	18.8520i	0.200003	+	0.710513i
$705$			12.6195i			0.475277i
$706$	10.0670	−	45.8644i	0.378875	−	1.72613i
$707$	−7.07091	+	12.7908i	−0.265929	+	0.481049i
$708$	15.0049	+	6.92037i	0.563918	+	0.260083i
$709$			1.65295i			0.0620777i	0.999518	+	0.0310389i	$0.00988157\pi$
$709$			1.65295i			0.0620777i	−0.999518	+	0.0310389i	$0.990118\pi$
$710$	−2.38669	+	10.8736i	−0.0895711	+	0.408080i
$711$		−	9.25720i		−	0.347172i
$712$	−8.74820	+	11.5507i	−0.327853	+	0.432882i
$713$			25.5150i			0.955544i
$714$	−3.70997	+	4.22089i	−0.138842	+	0.157963i
$715$	−3.84571			−0.143821
$716$	−31.4865	−	14.5218i	−1.17671	−	0.542706i
$717$	7.47696			0.279232
$718$	−4.03908	+	18.4018i	−0.150737	+	0.686749i
$719$	16.0007			0.596725			0.298363	−	0.954453i	$-0.403560\pi$
$719$	16.0007			0.596725			0.298363	+	0.954453i	$0.403560\pi$
$720$	−3.11968	−	3.65513i	−0.116263	−	0.136219i
$721$	−15.0628	+	27.2477i	−0.560968	+	1.01476i
$722$	72.3322	+	15.8765i	2.69193	+	0.590861i
$723$	−28.1387			−1.04649
$724$	−21.4791	−	9.90634i	−0.798266	−	0.368166i
$725$		−	3.43282i		−	0.127492i
$726$	−2.03591	+	9.27548i	−0.0755598	+	0.344245i
$727$	7.28793			0.270294			0.135147	−	0.990826i	$-0.456849\pi$
$727$	7.28793			0.270294			0.135147	+	0.990826i	$0.456849\pi$
$728$	−10.7454	+	4.76763i	−0.398250	+	0.176700i
$729$	−27.4187			−1.01551
$730$	3.82465	−	17.4249i	0.141557	−	0.644923i
$731$		−	8.34856i		−	0.308783i
$732$	10.6071	−	22.9986i	0.392051	−	0.850052i
$733$	4.79246			0.177013			0.0885067	−	0.996076i	$-0.471791\pi$
$733$	4.79246			0.177013			0.0885067	+	0.996076i	$0.471791\pi$
$734$	−35.8333	−	7.86519i	−1.32263	−	0.290310i
$735$	−7.94998	+	4.99310i	−0.293240	+	0.184173i
$736$	13.1217	−	7.00667i	0.483671	−	0.258269i
$737$	−5.27467			−0.194295
$738$	−1.14055	+	5.19629i	−0.0419844	+	0.191278i
$739$	37.3432			1.37369			0.686845	−	0.726804i	$-0.258995\pi$
$739$	37.3432			1.37369			0.686845	+	0.726804i	$0.258995\pi$
$740$	−5.21597	+	11.3094i	−0.191743	+	0.415741i
$741$	−17.7976			−0.653811
$742$	−32.6191	−	28.6708i	−1.19749	−	1.05254i
$743$			14.9317i			0.547789i	0.961760	+	0.273895i	$0.0883119\pi$
$743$			14.9317i			0.547789i	−0.961760	+	0.273895i	$0.911688\pi$
$744$	22.2221	−	29.3410i	0.814702	−	1.07570i
$745$			19.1438i			0.701373i
$746$	9.27539	−	42.2581i	0.339596	−	1.54718i
$747$		−	0.976988i		−	0.0357461i
$748$	2.29637	−	4.97905i	0.0839638	−	0.182052i
$749$	−1.77914	+	3.21836i	−0.0650085	+	0.117596i
$750$	−0.406623	+	1.85255i	−0.0148478	+	0.0676455i
$751$		−	32.2962i		−	1.17851i	−0.807948	−	0.589253i	$-0.799422\pi$
$751$		−	32.2962i		−	1.17851i	0.807948	−	0.589253i	$-0.200578\pi$
$752$	−24.4346	−	28.6285i	−0.891037	−	1.04397i
$753$	30.6773			1.11794
$754$	−1.63501	+	7.44900i	−0.0595436	+	0.271277i
$755$		−	2.73232i		−	0.0994394i
$756$	17.6537	+	24.0272i	0.642060	+	0.873860i
$757$		−	21.1662i		−	0.769299i	−0.923063	−	0.384650i	$-0.874322\pi$
$757$		−	21.1662i		−	0.769299i	0.923063	−	0.384650i	$-0.125678\pi$
$758$	14.7705	+	3.24205i	0.536490	+	0.117756i
$759$	−8.63349			−0.313376
$760$	−14.4260	+	19.0474i	−0.523286	+	0.690922i
$761$			8.98517i			0.325712i	0.986650	+	0.162856i	$0.0520706\pi$
$761$			8.98517i			0.325712i	−0.986650	+	0.162856i	$0.947929\pi$
$762$	30.4163	+	6.67620i	1.10187	+	0.241853i
$763$	−2.48972	−	1.37635i	−0.0901341	−	0.0498271i
$764$	−17.2402	+	37.3806i	−0.623729	+	1.35238i
$765$			1.34537i			0.0486420i
$766$	12.9402	+	2.84030i	0.467548	+	0.102624i
$767$		−	9.67741i		−	0.349431i
$768$	−21.1917	−	3.37088i	−0.764690	−	0.121636i
$769$			38.3718i			1.38372i	0.722031	+	0.691861i	$0.243209\pi$
$769$			38.3718i			1.38372i	−0.722031	+	0.691861i	$0.756791\pi$
$770$	6.04723	−	6.88002i	0.217927	−	0.247939i
$771$	−38.7275			−1.39474
$772$	18.2868	+	8.43399i	0.658155	+	0.303546i
$773$	−5.61383			−0.201916			−0.100958	−	0.994891i	$-0.532191\pi$
$773$	−5.61383			−0.201916			−0.100958	+	0.994891i	$0.532191\pi$
$774$	−12.3713	−	2.71542i	−0.444677	−	0.0976038i
$775$	9.70304			0.348543
$776$	1.42413	−	1.88035i	0.0511231	−	0.0675006i
$777$	10.6900	−	19.3376i	0.383503	−	0.693734i
$778$	−0.698477	+	3.18222i	−0.0250416	+	0.114088i
$779$	26.4522			0.947749
$780$	1.76469	−	3.82624i	0.0631861	−	0.137001i
$781$			19.2710i			0.689569i
$782$	−4.06775	−	0.892846i	−0.145462	−	0.0319281i
$783$	19.3425			0.691245
$784$	8.36736	−	26.7205i	0.298834	−	0.954305i
$785$	13.5441			0.483409
$786$	−3.71154	−	0.814660i	−0.132386	−	0.0290580i
$787$			13.1424i			0.468474i	0.972180	+	0.234237i	$0.0752592\pi$
$787$			13.1424i			0.468474i	−0.972180	+	0.234237i	$0.924741\pi$
$788$	−3.84919	+	8.34588i	−0.137122	+	0.297310i
$789$	26.2885			0.935895
$790$	2.33628	−	10.6440i	0.0831213	−	0.378695i
$791$	14.3321	−	25.9258i	0.509590	−	0.921817i
$792$	−6.63127	−	5.02234i	−0.235632	−	0.178461i
$793$	−14.8330			−0.526734
$794$	2.45488	+	0.538831i	0.0871203	+	0.0191224i
$795$	15.5661			0.552074
$796$	3.91284	+	1.80463i	0.138687	+	0.0639635i
$797$	−26.8837			−0.952269			−0.476134	−	0.879373i	$-0.657962\pi$
$797$	−26.8837			−0.952269			−0.476134	+	0.879373i	$0.657962\pi$
$798$	27.9861	−	31.8401i	0.990696	−	1.12713i
$799$			10.5375i			0.372790i
$800$	−2.66455	−	4.99001i	−0.0942061	−	0.176423i
$801$		−	6.15442i		−	0.217456i
$802$	−24.6096	−	5.40166i	−0.868996	−	0.190739i
$803$		−	30.8815i		−	1.08978i
$804$	2.42041	−	5.24797i	0.0853612	−	0.185082i
$805$	−6.08880	−	3.36595i	−0.214602	−	0.118634i
$806$	−21.0550	−	4.62144i	−0.741630	−	0.162783i
$807$		−	36.5366i		−	1.28615i
$808$	12.4552	+	9.43323i	0.438173	+	0.331860i
$809$	9.28389			0.326404			0.163202	−	0.986593i	$-0.447818\pi$
$809$	9.28389			0.326404			0.163202	+	0.986593i	$0.447818\pi$
$810$	−5.45990	−	1.19842i	−0.191841	−	0.0421080i
$811$			47.2011i			1.65745i	0.559653	+	0.828727i	$0.310935\pi$
$811$			47.2011i			1.65745i	−0.559653	+	0.828727i	$0.689065\pi$
$812$	−10.7554	−	14.6383i	−0.377439	−	0.513705i
$813$		−	34.9149i		−	1.22452i
$814$	−4.62204	+	21.0577i	−0.162003	+	0.738073i
$815$	18.5317			0.649136
$816$	3.90010	+	4.56950i	0.136531	+	0.159965i
$817$			62.9772i			2.20329i
$818$	−11.4817	+	52.3097i	−0.401447	+	1.82896i
$819$	2.41571	−	4.36986i	0.0844116	−	0.152695i
$820$	−2.62283	+	5.68687i	−0.0915931	+	0.198594i
$821$			28.6713i			1.00063i	0.865842	+	0.500317i	$0.166783\pi$
$821$			28.6713i			1.00063i	−0.865842	+	0.500317i	$0.833217\pi$
$822$	1.71164	−	7.79813i	0.0597004	−	0.271991i
$823$			15.8578i			0.552769i	0.961047	+	0.276385i	$0.0891364\pi$
$823$			15.8578i			0.552769i	−0.961047	+	0.276385i	$0.910864\pi$
$824$	26.5327	+	20.0951i	0.924310	+	0.700047i
$825$			3.28321i			0.114307i
$826$	17.3130	+	15.2174i	0.602397	+	0.529480i
$827$	9.33173			0.324496			0.162248	−	0.986750i	$-0.448126\pi$
$827$	9.33173			0.324496			0.162248	+	0.986750i	$0.448126\pi$
$828$	−2.64612	+	5.73737i	−0.0919590	+	0.199387i
$829$	50.2966			1.74687			0.873436	−	0.486939i	$-0.161887\pi$
$829$	50.2966			1.74687			0.873436	+	0.486939i	$0.161887\pi$
$830$	0.246567	−	1.12334i	0.00855847	−	0.0389918i
$831$	7.57511			0.262778
$832$	3.40523	+	12.0971i	0.118055	+	0.419391i
$833$	−6.63839	+	4.16933i	−0.230007	+	0.144459i
$834$	−7.79290	−	1.71049i	−0.269846	−	0.0592295i
$835$	−7.74592			−0.268059
$836$	−17.3226	+	37.5593i	−0.599116	+	1.29902i
$837$			54.6726i			1.88976i
$838$	−0.943164	+	4.29699i	−0.0325811	+	0.148437i
$839$	−39.0155			−1.34697			−0.673483	−	0.739203i	$-0.735203\pi$
$839$	−39.0155			−1.34697			−0.673483	+	0.739203i	$0.735203\pi$
$840$	4.07028	+	9.17369i	0.140438	+	0.316522i
$841$	17.2158			0.593647
$842$	−5.72889	+	26.1004i	−0.197431	+	0.899481i
$843$			34.7862i			1.19810i
$844$	−21.3295	−	9.83733i	−0.734192	−	0.338615i
$845$	10.5323			0.362321
$846$	15.6150	+	3.42739i	0.536854	+	0.117836i
$847$	−6.40896	+	11.5934i	−0.220214	+	0.398354i
$848$	−35.3133	+	30.1401i	−1.21266	+	1.03501i
$849$	16.9065			0.580231
$850$	−0.339538	+	1.54691i	−0.0116461	+	0.0530587i
$851$	16.3748			0.561320
$852$	−19.1734	−	8.84293i	−0.656871	−	0.302954i
$853$	11.1812			0.382836			0.191418	−	0.981509i	$-0.438691\pi$
$853$	11.1812			0.382836			0.191418	+	0.981509i	$0.438691\pi$
$854$	23.3243	−	26.5364i	0.798140	−	0.908055i
$855$		−	10.1488i		−	0.347081i
$856$	3.13391	+	2.37354i	0.107115	+	0.0811258i
$857$			36.5484i			1.24847i	0.781236	+	0.624235i	$0.214589\pi$
$857$			36.5484i			1.24847i	−0.781236	+	0.624235i	$0.785411\pi$
$858$	1.56375	−	7.12436i	0.0533856	−	0.243221i
$859$			6.59801i			0.225121i	0.993645	+	0.112561i	$0.0359052\pi$
$859$			6.59801i			0.225121i	−0.993645	+	0.112561i	$0.964095\pi$
$860$	−13.5392	−	6.24440i	−0.461684	−	0.212932i
$861$	5.37544	−	9.72384i	0.183195	−	0.331388i
$862$	11.6041	−	52.8677i	0.395238	−	1.80068i
$863$			6.48314i			0.220689i	0.993893	+	0.110344i	$0.0351954\pi$
$863$			6.48314i			0.220689i	−0.993893	+	0.110344i	$0.964805\pi$
$864$	28.1166	−	15.0136i	0.956547	−	0.510774i
$865$	−13.6112			−0.462795
$866$	0.456576	−	2.08013i	0.0155151	−	0.0706857i
$867$			21.1173i			0.717182i
$868$	41.3760	−	30.4006i	1.40439	−	1.03186i
$869$		−	18.8639i		−	0.639915i
$870$	6.35946	+	1.39586i	0.215606	+	0.0473242i
$871$	−3.38469			−0.114686
$872$	−1.83617	+	2.42439i	−0.0621805	+	0.0821004i
$873$			1.00188i			0.0339086i
$874$	30.6850	+	6.73516i	1.03793	+	0.227820i
$875$	−1.28003	+	2.31550i	−0.0432729	+	0.0782781i
$876$	30.7252	+	14.1707i	1.03811	+	0.478783i
$877$		−	23.0472i		−	0.778248i	−0.921185	−	0.389124i	$-0.872778\pi$
$877$		−	23.0472i		−	0.778248i	0.921185	−	0.389124i	$-0.127222\pi$
$878$	−6.91741	−	1.51833i	−0.233451	−	0.0512412i
$879$			22.5286i			0.759872i
$880$	−6.35714	−	7.44827i	−0.214299	−	0.251081i
$881$			35.8703i			1.20850i	0.796794	+	0.604251i	$0.206528\pi$
$881$			35.8703i			1.20850i	−0.796794	+	0.604251i	$0.793472\pi$
$882$	4.01913	+	11.1932i	0.135331	+	0.376894i
$883$	50.9029			1.71302			0.856509	−	0.516131i	$-0.172628\pi$
$883$	50.9029			1.71302			0.856509	+	0.516131i	$0.172628\pi$
$884$	1.47355	−	3.19499i	0.0495610	−	0.107459i
$885$	−8.26193			−0.277722
$886$	34.4937	+	7.57116i	1.15884	+	0.254358i
$887$	26.6009			0.893172			0.446586	−	0.894741i	$-0.352640\pi$
$887$	26.6009			0.893172			0.446586	+	0.894741i	$0.352640\pi$
$888$	−18.8302	−	14.2615i	−0.631901	−	0.478584i
$889$	38.0173	+	21.0164i	1.27506	+	0.704866i
$890$	1.55322	−	7.07638i	0.0520641	−	0.237201i
$891$	−9.67640			−0.324172
$892$	12.5700	+	5.79740i	0.420876	+	0.194111i
$893$		−	79.4895i		−	2.66001i
$894$	−35.4647	−	7.78430i	−1.18612	−	0.260346i
$895$	17.3370			0.579511
$896$	−26.9965	−	12.9302i	−0.901888	−	0.431969i
$897$	−5.54000			−0.184975
$898$	6.70942	+	1.47268i	0.223896	+	0.0491438i
$899$		−	33.3088i		−	1.11091i
$900$	2.18185	+	1.00629i	0.0727284	+	0.0335429i
$901$	12.9980			0.433027
$902$	−2.32417	+	10.5888i	−0.0773865	+	0.352568i
$903$	23.1504	+	12.7978i	0.770398	+	0.425884i
$904$	−25.2456	−	19.1203i	−0.839655	−	0.635931i
$905$	11.8268			0.393135
$906$	5.06176	+	1.11103i	0.168166	+	0.0369113i
$907$	−27.7572			−0.921662			−0.460831	−	0.887488i	$-0.652449\pi$
$907$	−27.7572			−0.921662			−0.460831	+	0.887488i	$0.652449\pi$
$908$	10.2208	−	22.1610i	0.339191	−	0.735440i
$909$	−6.63634			−0.220114
$910$	3.88043	−	4.41482i	0.128635	−	0.146350i
$911$			2.35676i			0.0780829i	0.999238	+	0.0390414i	$0.0124304\pi$
$911$			2.35676i			0.0780829i	−0.999238	+	0.0390414i	$0.987570\pi$
$912$	−29.4203	−	34.4699i	−0.974204	−	1.14141i
$913$		−	1.99087i		−	0.0658880i
$914$	29.1463	+	6.39744i	0.964075	+	0.211609i
$915$			12.6634i			0.418639i
$916$	−22.2626	−	10.2677i	−0.735577	−	0.339254i
$917$	−4.63904	−	2.56451i	−0.153195	−	0.0846876i
$918$	−8.71622	−	1.91316i	−0.287678	−	0.0631436i
$919$		−	5.11186i		−	0.168625i	−0.996439	−	0.0843124i	$-0.973131\pi$
$919$		−	5.11186i		−	0.168625i	0.996439	−	0.0843124i	$-0.0268694\pi$
$920$	−4.49049	+	5.92903i	−0.148047	+	0.195474i
$921$	−6.82113			−0.224764
$922$	−15.5297	−	3.40868i	−0.511445	−	0.112259i
$923$			12.3659i			0.407029i
$924$	10.2866	+	14.0004i	0.338405	+	0.460578i
$925$		−	6.22712i		−	0.204747i
$926$	−11.9519	+	54.4520i	−0.392763	+	1.78940i
$927$	−14.1371			−0.464322
$928$	−17.1298	+	9.14691i	−0.562313	+	0.300262i
$929$		−	49.8134i		−	1.63432i	−0.576408	−	0.817162i	$-0.695546\pi$
$929$		−	49.8134i		−	1.63432i	0.576408	−	0.817162i	$-0.304454\pi$
$930$	−3.94548	+	17.9753i	−0.129377	+	0.589435i
$931$	50.0766	−	31.4513i	1.64119	−	1.03077i
$932$	−18.4376	−	8.50358i	−0.603945	−	0.278544i
$933$			22.7049i			0.743326i
$934$	−8.03283	+	36.5971i	−0.262842	+	1.19749i
$935$			2.74154i			0.0896580i
$936$	−4.25520	−	3.22277i	−0.139085	−	0.105339i
$937$			15.7887i			0.515794i	0.966172	+	0.257897i	$0.0830296\pi$
$937$			15.7887i			0.515794i	−0.966172	+	0.257897i	$0.916970\pi$
$938$	5.32229	−	6.05525i	0.173779	−	0.197711i
$939$	11.1420			0.363606
$940$	17.0892	+	7.88165i	0.557387	+	0.257071i
$941$	−2.58455			−0.0842538			−0.0421269	−	0.999112i	$-0.513413\pi$
$941$	−2.58455			−0.0842538			−0.0421269	+	0.999112i	$0.513413\pi$
$942$	−5.50734	+	25.0911i	−0.179439	+	0.817511i
$943$	8.23398			0.268135
$944$	18.7430	−	15.9972i	0.610032	−	0.520666i
$945$	−13.0469	−	7.21244i	−0.424414	−	0.234621i
$946$	−25.2097	−	5.53337i	−0.819637	−	0.179905i
$947$	17.5390			0.569940			0.284970	−	0.958536i	$-0.408016\pi$
$947$	17.5390			0.569940			0.284970	+	0.958536i	$0.408016\pi$
$948$	18.7685	+	8.65616i	0.609571	+	0.281139i
$949$		−	19.8162i		−	0.643262i
$950$	2.56130	−	11.6691i	0.0830995	−	0.378596i
$951$	−14.4075			−0.467196
$952$	3.39877	+	7.66021i	0.110155	+	0.248269i
$953$	−25.0362			−0.811001			−0.405501	−	0.914095i	$-0.632903\pi$
$953$	−25.0362			−0.811001			−0.405501	+	0.914095i	$0.632903\pi$
$954$	4.22769	−	19.2611i	0.136877	−	0.623601i
$955$		−	20.5823i		−	0.666029i
$956$	4.66983	−	10.1252i	0.151033	−	0.327473i
$957$	11.2707			0.364329
$958$	−49.4277	−	10.8491i	−1.59694	−	0.350518i
$959$	5.38817	−	9.74687i	0.173993	−	0.314743i
$960$	10.3277	−	2.90715i	0.333325	−	0.0938280i
$961$	63.1490			2.03706
$962$	−2.96590	+	13.5125i	−0.0956246	+	0.435659i
$963$	−1.66980			−0.0538086
$964$	−17.5744	+	38.1051i	−0.566033	+	1.22728i
$965$	−10.0690			−0.324132
$966$	8.71144	−	9.91112i	0.280286	−	0.318885i
$967$		−	18.7066i		−	0.601564i	−0.953693	−	0.300782i	$-0.902752\pi$
$967$		−	18.7066i		−	0.601564i	0.953693	−	0.300782i	$-0.0972477\pi$
$968$	11.2892	+	8.55013i	0.362849	+	0.274811i
$969$			12.6876i			0.407585i
$970$	−0.252850	+	1.15197i	−0.00811852	+	0.0369875i
$971$		−	32.0975i		−	1.03006i	−0.857173	−	0.515029i	$-0.827781\pi$
$971$		−	32.0975i		−	1.03006i	0.857173	−	0.515029i	$-0.172219\pi$
$972$	−9.71870	+	21.0723i	−0.311727	+	0.675894i
$973$	−9.74033	−	5.38455i	−0.312261	−	0.172621i
$974$	3.77450	−	17.1964i	0.120943	−	0.551008i
$975$			2.10679i			0.0674713i
$976$	−24.5196	−	28.7281i	−0.784853	−	0.919564i
$977$	5.17448			0.165546			0.0827731	−	0.996568i	$-0.473622\pi$
$977$	5.17448			0.165546			0.0827731	+	0.996568i	$0.473622\pi$
$978$	−7.53540	+	34.3308i	−0.240955	+	1.09778i
$979$		−	12.5412i		−	0.400819i
$980$	1.79634	+	13.8843i	0.0573818	+	0.443517i
$981$		−	1.29176i		−	0.0412427i
$982$	19.9458	+	4.37799i	0.636497	+	0.139707i
$983$	−25.3909			−0.809843			−0.404921	−	0.914352i	$-0.632701\pi$
$983$	−25.3909			−0.809843			−0.404921	+	0.914352i	$0.632701\pi$
$984$	−9.46869	−	7.17132i	−0.301851	−	0.228613i
$985$		−	4.59538i		−	0.146421i
$986$	5.31027	+	1.16557i	0.169114	+	0.0371194i
$987$	−29.2203	−	16.1533i	−0.930094	−	0.514166i
$988$	−11.1157	+	24.1013i	−0.353638	+	0.766765i
$989$			19.6034i			0.623351i
$990$	4.06254	+	0.891704i	0.129116	+	0.0283402i
$991$		−	37.1976i		−	1.18162i	−0.806810	−	0.590810i	$-0.798808\pi$
$991$		−	37.1976i		−	1.18162i	0.806810	−	0.590810i	$-0.201192\pi$
$992$	−25.8542	−	48.4182i	−0.820873	−	1.53728i
$993$			16.3269i			0.518117i
$994$	−22.1228	−	19.4450i	−0.701692	−	0.616756i
$995$	−2.15447			−0.0683014
$996$	1.98079	+	0.913555i	0.0627637	+	0.0289471i
$997$	45.0979			1.42827			0.714133	−	0.700011i	$-0.246821\pi$
$997$	45.0979			1.42827			0.714133	+	0.700011i	$0.246821\pi$
$998$	−30.5232	−	6.69965i	−0.966194	−	0.212074i
$999$	35.0873			1.11011

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.h.a.251.1	✓	16
4.3	odd	2		1120.2.h.a.111.6		16
7.6	odd	2		280.2.h.b.251.1	yes	16
8.3	odd	2		280.2.h.b.251.2	yes	16
8.5	even	2		1120.2.h.b.111.6		16
28.27	even	2		1120.2.h.b.111.11		16
56.13	odd	2		1120.2.h.a.111.11		16
56.27	even	2	inner	280.2.h.a.251.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.h.a.251.1	✓	16	1.1	even	1	trivial
280.2.h.a.251.2	yes	16	56.27	even	2	inner
280.2.h.b.251.1	yes	16	7.6	odd	2
280.2.h.b.251.2	yes	16	8.3	odd	2
1120.2.h.a.111.6		16	4.3	odd	2
1120.2.h.a.111.11		16	56.13	odd	2
1120.2.h.b.111.6		16	8.5	even	2
1120.2.h.b.111.11		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)

\(f(q)\)	\(=\)	\(q+(-1.38133 - 0.303194i) q^{2} +1.34113i q^{3} +(1.81615 + 0.837621i) q^{4} -1.00000 q^{5} +(0.406623 - 1.85255i) q^{6} +(1.28003 - 2.31550i) q^{7} +(-2.25474 - 1.70768i) q^{8} +1.20136 q^{9} +O(q^{10})\)	\(q+(-1.38133 - 0.303194i) q^{2} +1.34113i q^{3} +(1.81615 + 0.837621i) q^{4} -1.00000 q^{5} +(0.406623 - 1.85255i) q^{6} +(1.28003 - 2.31550i) q^{7} +(-2.25474 - 1.70768i) q^{8} +1.20136 q^{9} +(1.38133 + 0.303194i) q^{10} +2.44809 q^{11} +(-1.12336 + 2.43569i) q^{12} +1.57090 q^{13} +(-2.47019 + 2.81037i) q^{14} -1.34113i q^{15} +(2.59678 + 3.04249i) q^{16} -1.11987i q^{17} +(-1.65948 - 0.364245i) q^{18} +8.44773i q^{19} +(-1.81615 - 0.837621i) q^{20} +(3.10539 + 1.71669i) q^{21} +(-3.38161 - 0.742244i) q^{22} +2.62959i q^{23} +(2.29022 - 3.02390i) q^{24} +1.00000 q^{25} +(-2.16994 - 0.476288i) q^{26} +5.63459i q^{27} +(4.26423 - 3.13310i) q^{28} -3.43282i q^{29} +(-0.406623 + 1.85255i) q^{30} +9.70304 q^{31} +(-2.66455 - 4.99001i) q^{32} +3.28321i q^{33} +(-0.339538 + 1.54691i) q^{34} +(-1.28003 + 2.31550i) q^{35} +(2.18185 + 1.00629i) q^{36} -6.22712i q^{37} +(2.56130 - 11.6691i) q^{38} +2.10679i q^{39} +(2.25474 + 1.70768i) q^{40} -3.13128i q^{41} +(-3.76908 - 3.31285i) q^{42} +7.45492 q^{43} +(4.44608 + 2.05057i) q^{44} -1.20136 q^{45} +(0.797275 - 3.63233i) q^{46} -9.40956 q^{47} +(-4.08038 + 3.48263i) q^{48} +(-3.72304 - 5.92781i) q^{49} +(-1.38133 - 0.303194i) q^{50} +1.50190 q^{51} +(2.85299 + 1.31582i) q^{52} +11.6067i q^{53} +(1.70837 - 7.78322i) q^{54} -2.44809 q^{55} +(-6.84025 + 3.03496i) q^{56} -11.3295 q^{57} +(-1.04081 + 4.74186i) q^{58} -6.16041i q^{59} +(1.12336 - 2.43569i) q^{60} -9.44231 q^{61} +(-13.4031 - 2.94190i) q^{62} +(1.53778 - 2.78175i) q^{63} +(2.16769 + 7.70072i) q^{64} -1.57090 q^{65} +(0.995448 - 4.53519i) q^{66} -2.15461 q^{67} +(0.938029 - 2.03385i) q^{68} -3.52663 q^{69} +(2.47019 - 2.81037i) q^{70} +7.87185i q^{71} +(-2.70876 - 2.05154i) q^{72} -12.6145i q^{73} +(-1.88802 + 8.60171i) q^{74} +1.34113i q^{75} +(-7.07600 + 15.3423i) q^{76} +(3.13362 - 5.66853i) q^{77} +(0.638766 - 2.91017i) q^{78} -7.70558i q^{79} +(-2.59678 - 3.04249i) q^{80} -3.95264 q^{81} +(-0.949384 + 4.32533i) q^{82} -0.813234i q^{83} +(4.20191 + 5.71890i) q^{84} +1.11987i q^{85} +(-10.2977 - 2.26029i) q^{86} +4.60387 q^{87} +(-5.51979 - 4.18054i) q^{88} -5.12287i q^{89} +(1.65948 + 0.364245i) q^{90} +(2.01081 - 3.63742i) q^{91} +(-2.20260 + 4.77572i) q^{92} +13.0131i q^{93} +(12.9977 + 2.85292i) q^{94} -8.44773i q^{95} +(6.69226 - 3.57352i) q^{96} +0.833955i q^{97} +(3.34548 + 9.31707i) q^{98} +2.94104 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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