LMFDB - Embedded newform 280.2.h.b.251.8

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			251.8
Root			$-0.275585 - 1.38710i$ of defining polynomial
Character	$\chi$	$=$	280.251
Dual form			280.2.h.b.251.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.275585 + 1.38710i) q^{2} +3.19977i q^{3} +(-1.84811 - 0.764529i) q^{4} +1.00000 q^{5} +(-4.43840 - 0.881807i) q^{6} +(-2.59303 - 0.525543i) q^{7} +(1.56979 - 2.35282i) q^{8} -7.23851 q^{9} +O(q^{10})$	\(q+(-0.275585 + 1.38710i) q^{2} +3.19977i q^{3} +(-1.84811 - 0.764529i) q^{4} +1.00000 q^{5} +(-4.43840 - 0.881807i) q^{6} +(-2.59303 - 0.525543i) q^{7} +(1.56979 - 2.35282i) q^{8} -7.23851 q^{9} +(-0.275585 + 1.38710i) q^{10} -3.34588 q^{11} +(2.44631 - 5.91351i) q^{12} +3.90251 q^{13} +(1.44358 - 3.45197i) q^{14} +3.19977i q^{15} +(2.83099 + 2.82586i) q^{16} +2.92992i q^{17} +(1.99482 - 10.0406i) q^{18} +6.33672i q^{19} +(-1.84811 - 0.764529i) q^{20} +(1.68161 - 8.29709i) q^{21} +(0.922074 - 4.64108i) q^{22} +3.44642i q^{23} +(7.52847 + 5.02296i) q^{24} +1.00000 q^{25} +(-1.07547 + 5.41319i) q^{26} -13.5622i q^{27} +(4.39040 + 2.95370i) q^{28} -2.68130i q^{29} +(-4.43840 - 0.881807i) q^{30} -2.52241 q^{31} +(-4.69994 + 3.14811i) q^{32} -10.7060i q^{33} +(-4.06411 - 0.807443i) q^{34} +(-2.59303 - 0.525543i) q^{35} +(13.3775 + 5.53405i) q^{36} -4.70905i q^{37} +(-8.78968 - 1.74630i) q^{38} +12.4871i q^{39} +(1.56979 - 2.35282i) q^{40} +5.59232i q^{41} +(11.0455 + 4.61912i) q^{42} +8.62439 q^{43} +(6.18354 + 2.55802i) q^{44} -7.23851 q^{45} +(-4.78054 - 0.949782i) q^{46} -0.506742 q^{47} +(-9.04209 + 9.05851i) q^{48} +(6.44761 + 2.72550i) q^{49} +(-0.275585 + 1.38710i) q^{50} -9.37508 q^{51} +(-7.21226 - 2.98358i) q^{52} +11.4136i q^{53} +(18.8122 + 3.73755i) q^{54} -3.34588 q^{55} +(-5.30702 + 5.27594i) q^{56} -20.2760 q^{57} +(3.71924 + 0.738926i) q^{58} -0.802275i q^{59} +(2.44631 - 5.91351i) q^{60} -7.97236 q^{61} +(0.695136 - 3.49883i) q^{62} +(18.7697 + 3.80415i) q^{63} +(-3.07152 - 7.38686i) q^{64} +3.90251 q^{65} +(14.8504 + 2.95042i) q^{66} +6.37503 q^{67} +(2.24001 - 5.41481i) q^{68} -11.0278 q^{69} +(1.44358 - 3.45197i) q^{70} +1.11901i q^{71} +(-11.3629 + 17.0309i) q^{72} +5.91619i q^{73} +(6.53194 + 1.29774i) q^{74} +3.19977i q^{75} +(4.84460 - 11.7109i) q^{76} +(8.67597 + 1.75840i) q^{77} +(-17.3209 - 3.44126i) q^{78} -10.5412i q^{79} +(2.83099 + 2.82586i) q^{80} +21.6805 q^{81} +(-7.75712 - 1.54116i) q^{82} +4.29261i q^{83} +(-9.45117 + 14.0483i) q^{84} +2.92992i q^{85} +(-2.37675 + 11.9629i) q^{86} +8.57954 q^{87} +(-5.25233 + 7.87226i) q^{88} +2.00722i q^{89} +(1.99482 - 10.0406i) q^{90} +(-10.1193 - 2.05094i) q^{91} +(2.63489 - 6.36936i) q^{92} -8.07111i q^{93} +(0.139650 - 0.702903i) q^{94} +6.33672i q^{95} +(-10.0732 - 15.0387i) q^{96} -6.06903i q^{97} +(-5.55741 + 8.19239i) q^{98} +24.2192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9	$ 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) $ 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9 + q^10 - 4 * q^11 + 14 * q^12 - q^14 + 9 * q^16 - 15 * q^18 + q^20 - 4 * q^21 + 6 * q^22 + 22 * q^24 + 16 * q^25 - 20 * q^26 + q^28 - 16 * q^31 - 19 * q^32 - 14 * q^34 + 15 * q^36 - 30 * q^38 + q^40 + 44 * q^42 - 4 * q^43 - 20 * q^44 - 16 * q^45 + 6 * q^46 - 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 - 38 * q^52 + 26 * q^54 - 4 * q^55 + 33 * q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 - 8 * q^61 + 28 * q^62 + 28 * q^63 - 23 * q^64 + 46 * q^66 + 20 * q^67 + 12 * q^68 - 40 * q^69 - q^70 - 13 * q^72 - 28 * q^74 + 34 * q^76 - 4 * q^77 - 6 * q^78 + 9 * q^80 + 24 * q^81 - 16 * q^82 - 42 * q^84 - 24 * q^86 + 72 * q^87 - 44 * q^88 - 15 * q^90 - 32 * q^91 - 30 * q^92 - 58 * q^94 - 30 * q^96 + 5 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.275585	+	1.38710i	−0.194868	+	0.980830i
$2$	−0.275585	+	1.38710i	−0.194868	+	0.980830i
$3$			3.19977i			1.84739i	0.383133	+	0.923693i	$0.374845\pi$
$3$			3.19977i			1.84739i	−0.383133	+	0.923693i	$0.625155\pi$
$4$	−1.84811	−	0.764529i	−0.924053	−	0.382264i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−4.43840	−	0.881807i	−1.81197	−	0.359996i
$7$	−2.59303	−	0.525543i	−0.980073	−	0.198637i
$7$	−2.59303	−	0.525543i	−0.980073	−	0.198637i
$8$	1.56979	−	2.35282i	0.555004	−	0.831847i
$9$	−7.23851			−2.41284
$10$	−0.275585	+	1.38710i	−0.0871476	+	0.438640i
$11$	−3.34588			−1.00882			−0.504411	−	0.863464i	$-0.668290\pi$
$11$	−3.34588			−1.00882			−0.504411	+	0.863464i	$0.668290\pi$
$12$	2.44631	−	5.91351i	0.706190	−	1.70708i
$13$	3.90251			1.08236			0.541181	−	0.840906i	$-0.317977\pi$
$13$	3.90251			1.08236			0.541181	+	0.840906i	$0.317977\pi$
$14$	1.44358	−	3.45197i	0.385813	−	0.922577i
$15$			3.19977i			0.826176i
$16$	2.83099	+	2.82586i	0.707748	+	0.706465i
$17$			2.92992i			0.710611i	0.934750	+	0.355306i	$0.115623\pi$
$17$			2.92992i			0.710611i	−0.934750	+	0.355306i	$0.884377\pi$
$18$	1.99482	−	10.0406i	0.470184	−	2.36658i
$19$			6.33672i			1.45374i	0.686774	+	0.726871i	$0.259026\pi$
$19$			6.33672i			1.45374i	−0.686774	+	0.726871i	$0.740974\pi$
$20$	−1.84811	−	0.764529i	−0.413249	−	0.170954i
$21$	1.68161	−	8.29709i	0.366958	−	1.81057i
$22$	0.922074	−	4.64108i	0.196587	−	0.989481i
$23$			3.44642i			0.718629i	0.933216	+	0.359315i	$0.116990\pi$
$23$			3.44642i			0.718629i	−0.933216	+	0.359315i	$0.883010\pi$
$24$	7.52847	+	5.02296i	1.53674	+	1.02531i
$25$	1.00000			0.200000
$26$	−1.07547	+	5.41319i	−0.210918	+	1.06161i
$27$		−	13.5622i		−	2.61005i
$28$	4.39040	+	2.95370i	0.829708	+	0.558198i
$29$		−	2.68130i		−	0.497905i	−0.968516	−	0.248952i	$-0.919914\pi$
$29$		−	2.68130i		−	0.497905i	0.968516	−	0.248952i	$-0.0800863\pi$
$30$	−4.43840	−	0.881807i	−0.810338	−	0.160995i
$31$	−2.52241			−0.453037			−0.226519	−	0.974007i	$-0.572734\pi$
$31$	−2.52241			−0.453037			−0.226519	+	0.974007i	$0.572734\pi$
$32$	−4.69994	+	3.14811i	−0.830839	+	0.556513i
$33$		−	10.7060i		−	1.86368i
$34$	−4.06411	−	0.807443i	−0.696988	−	0.138475i
$35$	−2.59303	−	0.525543i	−0.438302	−	0.0888330i
$36$	13.3775	+	5.53405i	2.22959	+	0.922341i
$37$		−	4.70905i		−	0.774164i	−0.922045	−	0.387082i	$-0.873483\pi$
$37$		−	4.70905i		−	0.774164i	0.922045	−	0.387082i	$-0.126517\pi$
$38$	−8.78968	−	1.74630i	−1.42587	−	0.283288i
$39$			12.4871i			1.99954i
$40$	1.56979	−	2.35282i	0.248206	−	0.372013i
$41$			5.59232i			0.873374i	0.899614	+	0.436687i	$0.143848\pi$
$41$			5.59232i			0.873374i	−0.899614	+	0.436687i	$0.856152\pi$
$42$	11.0455	+	4.61912i	1.70436	+	0.712746i
$43$	8.62439			1.31521			0.657604	−	0.753364i	$-0.271570\pi$
$43$	8.62439			1.31521			0.657604	+	0.753364i	$0.271570\pi$
$44$	6.18354	+	2.55802i	0.932204	+	0.385636i
$45$	−7.23851			−1.07905
$46$	−4.78054	−	0.949782i	−0.704853	−	0.140038i
$47$	−0.506742			−0.0739159			−0.0369580	−	0.999317i	$-0.511767\pi$
$47$	−0.506742			−0.0739159			−0.0369580	+	0.999317i	$0.511767\pi$
$48$	−9.04209	+	9.05851i	−1.30511	+	1.30748i
$49$	6.44761	+	2.72550i	0.921087	+	0.389357i
$50$	−0.275585	+	1.38710i	−0.0389736	+	0.196166i
$51$	−9.37508			−1.31277
$52$	−7.21226	−	2.98358i	−1.00016	−	0.413749i
$53$			11.4136i			1.56777i	0.620904	+	0.783886i	$0.286765\pi$
$53$			11.4136i			1.56777i	−0.620904	+	0.783886i	$0.713235\pi$
$54$	18.8122	+	3.73755i	2.56002	+	0.508616i
$55$	−3.34588			−0.451159
$56$	−5.30702	+	5.27594i	−0.709180	+	0.705027i
$57$	−20.2760			−2.68562
$58$	3.71924	+	0.738926i	0.488360	+	0.0970257i
$59$		−	0.802275i		−	0.104447i	−0.998635	−	0.0522236i	$-0.983369\pi$
$59$		−	0.802275i		−	0.104447i	0.998635	−	0.0522236i	$-0.0166309\pi$
$60$	2.44631	−	5.91351i	0.315818	−	0.763431i
$61$	−7.97236			−1.02076			−0.510378	−	0.859950i	$-0.670494\pi$
$61$	−7.97236			−1.02076			−0.510378	+	0.859950i	$0.670494\pi$
$62$	0.695136	−	3.49883i	0.0882824	−	0.444352i
$63$	18.7697	+	3.80415i	2.36476	+	0.479277i
$64$	−3.07152	−	7.38686i	−0.383940	−	0.923358i
$65$	3.90251			0.484047
$66$	14.8504	+	2.95042i	1.82795	+	0.363172i
$67$	6.37503			0.778834			0.389417	−	0.921062i	$-0.372677\pi$
$67$	6.37503			0.778834			0.389417	+	0.921062i	$0.372677\pi$
$68$	2.24001	−	5.41481i	0.271641	−	0.656642i
$69$	−11.0278			−1.32759
$70$	1.44358	−	3.45197i	0.172541	−	0.412589i
$71$			1.11901i			0.132802i	0.997793	+	0.0664011i	$0.0211517\pi$
$71$			1.11901i			0.132802i	−0.997793	+	0.0664011i	$0.978848\pi$
$72$	−11.3629	+	17.0309i	−1.33913	+	2.00711i
$73$			5.91619i			0.692438i	0.938154	+	0.346219i	$0.112535\pi$
$73$			5.91619i			0.692438i	−0.938154	+	0.346219i	$0.887465\pi$
$74$	6.53194	+	1.29774i	0.759323	+	0.150860i
$75$			3.19977i			0.369477i
$76$	4.84460	−	11.7109i	0.555714	−	1.34334i
$77$	8.67597	+	1.75840i	0.988719	+	0.200389i
$78$	−17.3209	−	3.44126i	−1.96121	−	0.389646i
$79$		−	10.5412i		−	1.18598i	−0.805211	−	0.592989i	$-0.797948\pi$
$79$		−	10.5412i		−	1.18598i	0.805211	−	0.592989i	$-0.202052\pi$
$80$	2.83099	+	2.82586i	0.316515	+	0.315941i
$81$	21.6805			2.40894
$82$	−7.75712	−	1.54116i	−0.856631	−	0.170192i
$83$			4.29261i			0.471175i	0.971853	+	0.235588i	$0.0757014\pi$
$83$			4.29261i			0.471175i	−0.971853	+	0.235588i	$0.924299\pi$
$84$	−9.45117	+	14.0483i	−1.03121	+	1.53279i
$85$			2.92992i			0.317795i
$86$	−2.37675	+	11.9629i	−0.256292	+	1.28999i
$87$	8.57954			0.919823
$88$	−5.25233	+	7.87226i	−0.559900	+	0.839185i
$89$			2.00722i			0.212764i	0.994325	+	0.106382i	$0.0339267\pi$
$89$			2.00722i			0.212764i	−0.994325	+	0.106382i	$0.966073\pi$
$90$	1.99482	−	10.0406i	0.210273	−	1.05837i
$91$	−10.1193	−	2.05094i	−1.06079	−	0.214997i
$92$	2.63489	−	6.36936i	0.274706	−	0.664052i
$93$		−	8.07111i		−	0.836935i
$94$	0.139650	−	0.702903i	0.0144038	−	0.0724989i
$95$			6.33672i			0.650134i
$96$	−10.0732	−	15.0387i	−1.02809	−	1.53488i
$97$		−	6.06903i		−	0.616217i	−0.951351	−	0.308108i	$-0.900304\pi$
$97$		−	6.06903i		−	0.616217i	0.951351	−	0.308108i	$-0.0996959\pi$
$98$	−5.55741	+	8.19239i	−0.561383	+	0.827556i
$99$	24.2192			2.43412
$100$	−1.84811	−	0.764529i	−0.184811	−	0.0764529i
$101$	11.2324			1.11767			0.558834	−	0.829279i	$-0.311249\pi$
$101$	11.2324			1.11767			0.558834	+	0.829279i	$0.311249\pi$
$102$	2.58363	−	13.0042i	0.255817	−	1.28761i
$103$	0.403587			0.0397667			0.0198833	−	0.999802i	$-0.493671\pi$
$103$	0.403587			0.0397667			0.0198833	+	0.999802i	$0.493671\pi$
$104$	6.12613	−	9.18191i	0.600716	−	0.900361i
$105$	1.68161	−	8.29709i	0.164109	−	0.809713i
$106$	−15.8318	−	3.14540i	−1.53772	−	0.305508i
$107$	17.9070			1.73114			0.865568	−	0.500791i	$-0.166957\pi$
$107$	17.9070			1.73114			0.865568	+	0.500791i	$0.166957\pi$
$108$	−10.3687	+	25.0645i	−0.997730	+	2.41183i
$109$		−	14.4062i		−	1.37986i	−0.723874	−	0.689932i	$-0.757641\pi$
$109$		−	14.4062i		−	1.37986i	0.723874	−	0.689932i	$-0.242359\pi$
$110$	0.922074	−	4.64108i	0.0879163	−	0.442510i
$111$	15.0679			1.43018
$112$	−5.85574	−	8.81535i	−0.553315	−	0.832972i
$113$	−6.85909			−0.645249			−0.322625	−	0.946527i	$-0.604565\pi$
$113$	−6.85909			−0.645249			−0.322625	+	0.946527i	$0.604565\pi$
$114$	5.58776	−	28.1249i	0.523342	−	2.63414i
$115$			3.44642i			0.321381i
$116$	−2.04993	+	4.95533i	−0.190331	+	0.460091i
$117$	−28.2484			−2.61156
$118$	1.11284	+	0.221095i	0.102445	+	0.0203534i
$119$	1.53980	−	7.59738i	0.141153	−	0.696451i
$120$	7.52847	+	5.02296i	0.687253	+	0.458531i
$121$	0.194920			0.0177200
$122$	2.19706	−	11.0585i	0.198913	−	1.00119i
$123$	−17.8941			−1.61346
$124$	4.66167	+	1.92845i	0.418630	+	0.173180i
$125$	1.00000			0.0894427
$126$	−10.4494	+	24.9871i	−0.930904	+	2.22603i
$127$			5.87400i			0.521233i	0.965442	+	0.260617i	$0.0839259\pi$
$127$			5.87400i			0.521233i	−0.965442	+	0.260617i	$0.916074\pi$
$128$	11.0928	−	2.22481i	0.980474	−	0.196647i
$129$			27.5960i			2.42970i
$130$	−1.07547	+	5.41319i	−0.0943253	+	0.474768i
$131$			4.47680i			0.391139i	0.980690	+	0.195570i	$0.0626556\pi$
$131$			4.47680i			0.391139i	−0.980690	+	0.195570i	$0.937344\pi$
$132$	−8.18507	+	19.7859i	−0.712419	+	1.72214i
$133$	3.33022	−	16.4313i	0.288767	−	1.42477i
$134$	−1.75686	+	8.84282i	−0.151770	+	0.763903i
$135$		−	13.5622i		−	1.16725i
$136$	6.89358	+	4.59936i	0.591120	+	0.394392i
$137$	7.90390			0.675276			0.337638	−	0.941276i	$-0.390372\pi$
$137$	7.90390			0.675276			0.337638	+	0.941276i	$0.390372\pi$
$138$	3.03908	−	15.2966i	0.258704	−	1.30214i
$139$		−	9.80123i		−	0.831329i	−0.909518	−	0.415665i	$-0.863549\pi$
$139$		−	9.80123i		−	0.831329i	0.909518	−	0.415665i	$-0.136451\pi$
$140$	4.39040	+	2.95370i	0.371057	+	0.249634i
$141$		−	1.62146i		−	0.136551i
$142$	−1.55218	−	0.308382i	−0.130256	−	0.0258789i
$143$	−13.0573			−1.09191
$144$	−20.4922	−	20.4550i	−1.70768	−	1.70458i
$145$		−	2.68130i		−	0.222670i
$146$	−8.20636	−	1.63041i	−0.679164	−	0.134934i
$147$	−8.72096	+	20.6308i	−0.719292	+	1.70160i
$148$	−3.60021	+	8.70283i	−0.295935	+	0.715368i
$149$			11.5613i			0.947135i	0.880758	+	0.473567i	$0.157034\pi$
$149$			11.5613i			0.947135i	−0.880758	+	0.473567i	$0.842966\pi$
$150$	−4.43840	−	0.881807i	−0.362394	−	0.0719992i
$151$			0.509248i			0.0414420i	0.999785	+	0.0207210i	$0.00659617\pi$
$151$			0.509248i			0.0414420i	−0.999785	+	0.0207210i	$0.993404\pi$
$152$	14.9092	+	9.94731i	1.20929	+	0.806834i
$153$		−	21.2083i		−	1.71459i
$154$	−4.83005	+	11.5499i	−0.389217	+	0.930715i
$155$	−2.52241			−0.202604
$156$	9.54677	−	23.0776i	0.764354	−	1.84768i
$157$	9.98993			0.797283			0.398642	−	0.917107i	$-0.369482\pi$
$157$	9.98993			0.797283			0.398642	+	0.917107i	$0.369482\pi$
$158$	14.6217	+	2.90500i	1.16324	+	0.231109i
$159$	−36.5207			−2.89628
$160$	−4.69994	+	3.14811i	−0.371563	+	0.248880i
$161$	1.81124	−	8.93668i	0.142746	−	0.704309i
$162$	−5.97481	+	30.0730i	−0.469425	+	2.36276i
$163$	19.7736			1.54879			0.774393	−	0.632705i	$-0.218056\pi$
$163$	19.7736			1.54879			0.774393	+	0.632705i	$0.218056\pi$
$164$	4.27549	−	10.3352i	0.333860	−	0.807044i
$165$		−	10.7060i		−	0.833464i
$166$	−5.95429	−	1.18298i	−0.462142	−	0.0918169i
$167$	−20.6423			−1.59735			−0.798673	−	0.601765i	$-0.794464\pi$
$167$	−20.6423			−1.59735			−0.798673	+	0.601765i	$0.794464\pi$
$168$	−16.8818	−	16.9812i	−1.30246	−	1.31013i
$169$	2.22962			0.171509
$170$	−4.06411	−	0.807443i	−0.311703	−	0.0619280i
$171$		−	45.8684i		−	3.50764i
$172$	−15.9388	−	6.59360i	−1.21532	−	0.502757i
$173$	12.1166			0.921205			0.460602	−	0.887607i	$-0.347633\pi$
$173$	12.1166			0.921205			0.460602	+	0.887607i	$0.347633\pi$
$174$	−2.36439	+	11.9007i	−0.179244	+	0.902189i
$175$	−2.59303	−	0.525543i	−0.196015	−	0.0397273i
$176$	−9.47216	−	9.45499i	−0.713991	−	0.712697i
$177$	2.56709			0.192954
$178$	−2.78421	−	0.553158i	−0.208686	−	0.0414610i
$179$	−14.6327			−1.09370			−0.546851	−	0.837230i	$-0.684173\pi$
$179$	−14.6327			−1.09370			−0.546851	+	0.837230i	$0.684173\pi$
$180$	13.3775	+	5.53405i	0.997102	+	0.412483i
$181$	23.1384			1.71986			0.859932	−	0.510408i	$-0.170506\pi$
$181$	23.1384			1.71986			0.859932	+	0.510408i	$0.170506\pi$
$182$	5.63360	−	13.4713i	0.417590	−	0.998563i
$183$		−	25.5097i		−	1.88573i
$184$	8.10882	+	5.41016i	0.597790	+	0.398842i
$185$		−	4.70905i		−	0.346217i
$186$	11.1955	+	2.22427i	0.820890	+	0.163092i
$187$		−	9.80318i		−	0.716879i
$188$	0.936513	+	0.387419i	0.0683022	+	0.0282554i
$189$	−7.12754	+	35.1673i	−0.518452	+	2.55804i
$190$	−8.78968	−	1.74630i	−0.637670	−	0.126690i
$191$		−	2.41554i		−	0.174782i	−0.996174	−	0.0873911i	$-0.972147\pi$
$191$		−	2.41554i		−	0.174782i	0.996174	−	0.0873911i	$-0.0278530\pi$
$192$	23.6362	−	9.82816i	1.70580	−	0.709286i
$193$	−7.38549			−0.531619			−0.265810	−	0.964026i	$-0.585639\pi$
$193$	−7.38549			−0.531619			−0.265810	+	0.964026i	$0.585639\pi$
$194$	8.41837	+	1.67253i	0.604403	+	0.120081i
$195$			12.4871i			0.894222i
$196$	−9.83214	−	9.96639i	−0.702296	−	0.711885i
$197$			20.9305i			1.49124i	0.666372	+	0.745619i	$0.267846\pi$
$197$			20.9305i			1.49124i	−0.666372	+	0.745619i	$0.732154\pi$
$198$	−6.67444	+	33.5945i	−0.474332	+	2.38746i
$199$	−4.89644			−0.347099			−0.173550	−	0.984825i	$-0.555524\pi$
$199$	−4.89644			−0.347099			−0.173550	+	0.984825i	$0.555524\pi$
$200$	1.56979	−	2.35282i	0.111001	−	0.166369i
$201$			20.3986i			1.43881i
$202$	−3.09549	+	15.5805i	−0.217798	+	1.09624i
$203$	−1.40914	+	6.95269i	−0.0989021	+	0.487983i
$204$	17.3261	+	7.16751i	1.21307	+	0.501826i
$205$			5.59232i			0.390585i
$206$	−0.111223	+	0.559817i	−0.00774924	+	0.0390043i
$207$		−	24.9470i		−	1.73393i
$208$	11.0480	+	11.0280i	0.766040	+	0.764651i
$209$		−	21.2019i		−	1.46657i
$210$	11.0455	+	4.61912i	0.762211	+	0.318750i
$211$	2.25447			0.155204			0.0776020	−	0.996984i	$-0.475274\pi$
$211$	2.25447			0.155204			0.0776020	+	0.996984i	$0.475274\pi$
$212$	8.72599	−	21.0935i	0.599303	−	1.44870i
$213$	−3.58058			−0.245337
$214$	−4.93490	+	24.8389i	−0.337343	+	1.69795i
$215$	8.62439			0.588179
$216$	−31.9095	−	21.2899i	−2.17117	−	1.44859i
$217$	6.54067	+	1.32563i	0.444010	+	0.0899898i
$218$	19.9829	+	3.97013i	1.35341	+	0.268891i
$219$	−18.9304			−1.27920
$220$	6.18354	+	2.55802i	0.416894	+	0.172462i
$221$			11.4341i			0.769139i
$222$	−4.15248	+	20.9007i	−0.278696	+	1.40276i
$223$	24.4820			1.63944			0.819718	−	0.572768i	$-0.194130\pi$
$223$	24.4820			1.63944			0.819718	+	0.572768i	$0.194130\pi$
$224$	13.8415	−	5.69313i	0.924827	−	0.380388i
$225$	−7.23851			−0.482567
$226$	1.89026	−	9.51426i	0.125738	−	0.632879i
$227$		−	5.16178i		−	0.342599i	−0.985219	−	0.171300i	$-0.945203\pi$
$227$		−	5.16178i		−	0.342599i	0.985219	−	0.171300i	$-0.0547966\pi$
$228$	37.4722	+	15.5016i	2.48166	+	1.02662i
$229$	9.48995			0.627114			0.313557	−	0.949569i	$-0.398479\pi$
$229$	9.48995			0.627114			0.313557	+	0.949569i	$0.398479\pi$
$230$	−4.78054	−	0.949782i	−0.315220	−	0.0626268i
$231$	−5.62648	+	27.7611i	−0.370195	+	1.82655i
$232$	−6.30862	−	4.20908i	−0.414181	−	0.276339i
$233$	−2.55217			−0.167198			−0.0835991	−	0.996499i	$-0.526642\pi$
$233$	−2.55217			−0.167198			−0.0835991	+	0.996499i	$0.526642\pi$
$234$	7.78482	−	39.1834i	0.508910	−	2.56150i
$235$	−0.506742			−0.0330562
$236$	−0.613362	+	1.48269i	−0.0399265	+	0.0965148i
$237$	33.7294			2.19096
$238$	10.1140	+	4.22958i	0.655593	+	0.274163i
$239$			8.15573i			0.527550i	0.964584	+	0.263775i	$0.0849677\pi$
$239$			8.15573i			0.527550i	−0.964584	+	0.263775i	$0.915032\pi$
$240$	−9.04209	+	9.05851i	−0.583665	+	0.584725i
$241$		−	2.66753i		−	0.171831i	−0.996302	−	0.0859155i	$-0.972619\pi$
$241$		−	2.66753i		−	0.171831i	0.996302	−	0.0859155i	$-0.0273815\pi$
$242$	−0.0537170	+	0.270374i	−0.00345306	+	0.0173803i
$243$			28.6857i			1.84019i
$244$	14.7338	+	6.09510i	0.943233	+	0.390199i
$245$	6.44761	+	2.72550i	0.411923	+	0.174126i
$246$	4.93135	−	24.8210i	0.314411	−	1.58253i
$247$			24.7291i			1.57348i
$248$	−3.95964	+	5.93476i	−0.251438	+	0.376858i
$249$	−13.7353			−0.870442
$250$	−0.275585	+	1.38710i	−0.0174295	+	0.0877281i
$251$			8.52244i			0.537932i	0.963150	+	0.268966i	$0.0866819\pi$
$251$			8.52244i			0.537932i	−0.963150	+	0.268966i	$0.913318\pi$
$252$	−31.7800	−	21.3804i	−2.00195	−	1.34684i
$253$		−	11.5313i		−	0.724968i
$254$	−8.14784	−	1.61879i	−0.511241	−	0.101572i
$255$	−9.37508			−0.587090
$256$	0.0290305	+	16.0000i	0.00181440	+	0.999998i
$257$			14.1473i			0.882487i	0.897387	+	0.441244i	$0.145462\pi$
$257$			14.1473i			0.882487i	−0.897387	+	0.441244i	$0.854538\pi$
$258$	−38.2785	−	7.60505i	−2.38312	−	0.473470i
$259$	−2.47481	+	12.2107i	−0.153777	+	0.758737i
$260$	−7.21226	−	2.98358i	−0.447285	−	0.185034i
$261$			19.4086i			1.20136i
$262$	−6.20977	−	1.23374i	−0.383641	−	0.0762205i
$263$		−	31.1418i		−	1.92029i	−0.279510	−	0.960143i	$-0.590172\pi$
$263$		−	31.1418i		−	1.92029i	0.279510	−	0.960143i	$-0.409828\pi$
$264$	−25.1894	−	16.8062i	−1.55030	−	1.03435i
$265$			11.4136i			0.701129i
$266$	21.8741	+	9.14757i	1.34119	+	0.560874i
$267$	−6.42262			−0.393058
$268$	−11.7817	−	4.87389i	−0.719684	−	0.297720i
$269$	−1.39567			−0.0850956			−0.0425478	−	0.999094i	$-0.513547\pi$
$269$	−1.39567			−0.0850956			−0.0425478	+	0.999094i	$0.513547\pi$
$270$	18.8122	+	3.73755i	1.14487	+	0.227460i
$271$	−22.4663			−1.36473			−0.682366	−	0.731011i	$-0.739049\pi$
$271$	−22.4663			−1.36473			−0.682366	+	0.731011i	$0.739049\pi$
$272$	−8.27956	+	8.29459i	−0.502022	+	0.502934i
$273$	6.56253	−	32.3795i	0.397182	−	1.95970i
$274$	−2.17820	+	10.9635i	−0.131590	+	0.662331i
$275$	−3.34588			−0.201764
$276$	20.3805	+	8.43103i	1.22676	+	0.507489i
$277$		−	12.0828i		−	0.725985i	−0.931792	−	0.362993i	$-0.881755\pi$
$277$		−	12.0828i		−	0.725985i	0.931792	−	0.362993i	$-0.118245\pi$
$278$	13.5953	+	2.70107i	0.815392	+	0.161999i
$279$	18.2584			1.09310
$280$	−5.30702	+	5.27594i	−0.317155	+	0.315298i
$281$	−5.84893			−0.348918			−0.174459	−	0.984664i	$-0.555818\pi$
$281$	−5.84893			−0.348918			−0.174459	+	0.984664i	$0.555818\pi$
$282$	2.24913	+	0.446849i	0.133933	+	0.0266094i
$283$			10.1804i			0.605164i	0.953123	+	0.302582i	$0.0978486\pi$
$283$			10.1804i			0.605164i	−0.953123	+	0.302582i	$0.902151\pi$
$284$	0.855516	−	2.06805i	0.0507655	−	0.122716i
$285$	−20.2760			−1.20105
$286$	3.59841	−	18.1119i	0.212778	−	1.07098i
$287$	2.93900	−	14.5011i	0.173484	−	0.855970i
$288$	34.0205	−	22.7876i	2.00468	−	1.34277i
$289$	8.41554			0.495032
$290$	3.71924	+	0.738926i	0.218401	+	0.0433912i
$291$	19.4195			1.13839
$292$	4.52310	−	10.9338i	0.264694	−	0.639849i
$293$	−30.6832			−1.79253			−0.896266	−	0.443518i	$-0.853730\pi$
$293$	−30.6832			−1.79253			−0.896266	+	0.443518i	$0.853730\pi$
$294$	−26.2137	−	17.7824i	−1.52882	−	1.03709i
$295$		−	0.802275i		−	0.0467102i
$296$	−11.0796	−	7.39222i	−0.643986	−	0.429664i
$297$			45.3776i			2.63308i
$298$	−16.0366	−	3.18611i	−0.928978	−	0.184566i
$299$			13.4497i			0.777817i
$300$	2.44631	−	5.91351i	0.141238	−	0.341417i
$301$	−22.3633	−	4.53249i	−1.28900	−	0.261248i
$302$	−0.706379	−	0.140341i	−0.0406475	−	0.00807571i
$303$			35.9412i			2.06477i
$304$	−17.9067	+	17.9392i	−1.02702	+	1.02888i
$305$	−7.97236			−0.456496
$306$	29.4181	+	5.84468i	1.68172	+	0.334118i
$307$		−	25.8632i		−	1.47609i	−0.674750	−	0.738046i	$-0.735749\pi$
$307$		−	25.8632i		−	1.47609i	0.674750	−	0.738046i	$-0.264251\pi$
$308$	−14.6898	−	9.88275i	−0.837027	−	0.563122i
$309$			1.29139i			0.0734644i
$310$	0.695136	−	3.49883i	0.0394811	−	0.198720i
$311$	10.8246			0.613806			0.306903	−	0.951741i	$-0.400707\pi$
$311$	10.8246			0.613806			0.306903	+	0.951741i	$0.400707\pi$
$312$	29.3800	+	19.6022i	1.66331	+	1.10975i
$313$		−	27.8999i		−	1.57699i	−0.615038	−	0.788497i	$-0.710859\pi$
$313$		−	27.8999i		−	1.57699i	0.615038	−	0.788497i	$-0.289141\pi$
$314$	−2.75307	+	13.8571i	−0.155365	+	0.781999i
$315$	18.7697	+	3.80415i	1.05755	+	0.214339i
$316$	−8.05905	+	19.4813i	−0.453357	+	1.09591i
$317$			7.49682i			0.421064i	0.977587	+	0.210532i	$0.0675195\pi$
$317$			7.49682i			0.421064i	−0.977587	+	0.210532i	$0.932480\pi$
$318$	10.0646	−	50.6580i	0.564392	−	2.84076i
$319$			8.97131i			0.502297i
$320$	−3.07152	−	7.38686i	−0.171703	−	0.412938i
$321$			57.2983i			3.19808i
$322$	11.8969	+	4.97520i	0.662991	+	0.277257i
$323$	−18.5661			−1.03305
$324$	−40.0678	−	16.5753i	−2.22599	−	0.920852i
$325$	3.90251			0.216473
$326$	−5.44930	+	27.4280i	−0.301809	+	1.51909i
$327$	46.0965			2.54914
$328$	13.1577	+	8.77876i	0.726514	+	0.484726i
$329$	1.31400	+	0.266315i	0.0724430	+	0.0146824i
$330$	14.8504	+	2.95042i	0.817486	+	0.162415i
$331$	12.3429			0.678429			0.339214	−	0.940709i	$-0.389839\pi$
$331$	12.3429			0.678429			0.339214	+	0.940709i	$0.389839\pi$
$332$	3.28182	−	7.93320i	0.180113	−	0.435391i
$333$			34.0865i			1.86793i
$334$	5.68869	−	28.6329i	0.311271	−	1.56672i
$335$	6.37503			0.348305
$336$	28.2071	−	18.7370i	1.53882	−	1.02219i
$337$	30.1764			1.64382			0.821908	−	0.569620i	$-0.192910\pi$
$337$	30.1764			1.64382			0.821908	+	0.569620i	$0.192910\pi$
$338$	−0.614449	+	3.09271i	−0.0334216	+	0.168221i
$339$		−	21.9475i		−	1.19202i
$340$	2.24001	−	5.41481i	0.121482	−	0.293659i
$341$	8.43967			0.457034
$342$	63.6241	+	12.6406i	3.44040	+	0.683527i
$343$	−15.2865	−	10.4558i	−0.825392	−	0.564560i
$344$	13.5385	−	20.2916i	0.729946	−	1.09405i
$345$	−11.0278			−0.593714
$346$	−3.33914	+	16.8069i	−0.179513	+	0.903545i
$347$	−21.3398			−1.14558			−0.572789	−	0.819703i	$-0.694139\pi$
$347$	−21.3398			−1.14558			−0.572789	+	0.819703i	$0.694139\pi$
$348$	−15.8559	−	6.55930i	−0.849965	−	0.351615i
$349$	−16.3885			−0.877255			−0.438627	−	0.898669i	$-0.644535\pi$
$349$	−16.3885			−0.877255			−0.438627	+	0.898669i	$0.644535\pi$
$350$	1.44358	−	3.45197i	0.0771627	−	0.184515i
$351$		−	52.9268i		−	2.82502i
$352$	15.7254	−	10.5332i	0.838168	−	0.561422i
$353$		−	3.84670i		−	0.204739i	−0.994746	−	0.102370i	$-0.967358\pi$
$353$		−	3.84670i		−	0.204739i	0.994746	−	0.102370i	$-0.0326425\pi$
$354$	−0.707451	+	3.56082i	−0.0376006	+	0.189255i
$355$			1.11901i			0.0593910i
$356$	1.53457	−	3.70955i	0.0813323	−	0.196606i
$357$	24.3099	+	4.92700i	1.28661	+	0.260765i
$358$	4.03256	−	20.2971i	0.213127	−	1.07273i
$359$		−	27.6613i		−	1.45991i	−0.683495	−	0.729955i	$-0.739541\pi$
$359$		−	27.6613i		−	1.45991i	0.683495	−	0.729955i	$-0.260459\pi$
$360$	−11.3629	+	17.0309i	−0.598879	+	0.897607i
$361$	−21.1540			−1.11337
$362$	−6.37660	+	32.0954i	−0.335146	+	1.68689i
$363$			0.623698i			0.0327357i
$364$	17.1336	+	11.5269i	0.898045	+	0.604172i
$365$			5.91619i			0.309668i
$366$	35.3845	+	7.03008i	1.84958	+	0.367468i
$367$	2.94732			0.153849			0.0769244	−	0.997037i	$-0.475490\pi$
$367$	2.94732			0.153849			0.0769244	+	0.997037i	$0.475490\pi$
$368$	−9.73911	+	9.75680i	−0.507686	+	0.508608i
$369$		−	40.4801i		−	2.10731i
$370$	6.53194	+	1.29774i	0.339579	+	0.0674665i
$371$	5.99831	−	29.5957i	0.311417	−	1.53653i
$372$	−6.17059	+	14.9163i	−0.319930	+	0.773372i
$373$			12.6247i			0.653683i	0.945079	+	0.326841i	$0.105984\pi$
$373$			12.6247i			0.653683i	−0.945079	+	0.326841i	$0.894016\pi$
$374$	13.5980	+	2.70161i	0.703136	+	0.139697i
$375$			3.19977i			0.165235i
$376$	−0.795478	+	1.19227i	−0.0410236	+	0.0614868i
$377$		−	10.4638i		−	0.538914i
$378$	−46.8164	−	19.5782i	−2.40798	−	1.00699i
$379$	−20.9882			−1.07809			−0.539045	−	0.842277i	$-0.681215\pi$
$379$	−20.9882			−1.07809			−0.539045	+	0.842277i	$0.681215\pi$
$380$	4.84460	−	11.7109i	0.248523	−	0.600758i
$381$	−18.7954			−0.962919
$382$	3.35060	+	0.665686i	0.171432	+	0.0340595i
$383$	−11.4237			−0.583724			−0.291862	−	0.956460i	$-0.594275\pi$
$383$	−11.4237			−0.583724			−0.291862	+	0.956460i	$0.594275\pi$
$384$	7.11887	+	35.4944i	0.363283	+	1.81131i
$385$	8.67597	+	1.75840i	0.442168	+	0.0896166i
$386$	2.03533	−	10.2444i	0.103596	−	0.521428i
$387$	−62.4277			−3.17338
$388$	−4.63995	+	11.2162i	−0.235558	+	0.569417i
$389$		−	22.7966i		−	1.15583i	−0.816096	−	0.577917i	$-0.803866\pi$
$389$		−	22.7966i		−	1.15583i	0.816096	−	0.577917i	$-0.196134\pi$
$390$	−17.3209	−	3.44126i	−0.877080	−	0.174255i
$391$	−10.0978			−0.510666
$392$	16.5340	−	10.8916i	0.835093	−	0.550109i
$393$	−14.3247			−0.722586
$394$	−29.0328	−	5.76814i	−1.46265	−	0.290595i
$395$		−	10.5412i		−	0.530385i
$396$	−44.7596	−	18.5163i	−2.24926	−	0.930477i
$397$	−29.8779			−1.49953			−0.749763	−	0.661706i	$-0.769833\pi$
$397$	−29.8779			−1.49953			−0.749763	+	0.661706i	$0.769833\pi$
$398$	1.34938	−	6.79186i	0.0676385	−	0.340445i
$399$	52.5763	+	10.6559i	2.63211	+	0.533463i
$400$	2.83099	+	2.82586i	0.141550	+	0.141293i
$401$	−16.8397			−0.840933			−0.420467	−	0.907308i	$-0.638134\pi$
$401$	−16.8397			−0.840933			−0.420467	+	0.907308i	$0.638134\pi$
$402$	−28.2950	−	5.62154i	−1.41122	−	0.280377i
$403$	−9.84372			−0.490351
$404$	−20.7587	−	8.58752i	−1.03279	−	0.427245i
$405$	21.6805			1.07731
$406$	−9.25576	−	3.87068i	−0.459356	−	0.192098i
$407$			15.7559i			0.780993i
$408$	−14.7169	+	22.0579i	−0.728595	+	1.09203i
$409$		−	26.9755i		−	1.33385i	−0.745123	−	0.666927i	$-0.767609\pi$
$409$		−	26.9755i		−	1.33385i	0.745123	−	0.666927i	$-0.232391\pi$
$410$	−7.75712	−	1.54116i	−0.383097	−	0.0761124i
$411$			25.2906i			1.24750i
$412$	−0.745872	−	0.308554i	−0.0367465	−	0.0152014i
$413$	−0.421630	+	2.08032i	−0.0207470	+	0.102366i
$414$	34.6040	+	6.87501i	1.70069	+	0.337888i
$415$			4.29261i			0.210716i
$416$	−18.3416	+	12.2856i	−0.899269	+	0.602349i
$417$	31.3616			1.53579
$418$	29.4092	+	5.84292i	1.43845	+	0.285787i
$419$		−	15.0474i		−	0.735114i	−0.930001	−	0.367557i	$-0.880194\pi$
$419$		−	15.0474i		−	0.735114i	0.930001	−	0.367557i	$-0.119806\pi$
$420$	−9.45117	+	14.0483i	−0.461170	+	0.685485i
$421$			27.5257i			1.34152i	0.741674	+	0.670761i	$0.234032\pi$
$421$			27.5257i			1.34152i	−0.741674	+	0.670761i	$0.765968\pi$
$422$	−0.621297	+	3.12718i	−0.0302443	+	0.152229i
$423$	3.66806			0.178347
$424$	26.8540	+	17.9169i	1.30415	+	0.870121i
$425$			2.92992i			0.142122i
$426$	0.986752	−	4.96662i	0.0478083	−	0.240634i
$427$	20.6726	+	4.18982i	1.00042	+	0.202759i
$428$	−33.0941	−	13.6904i	−1.59966	−	0.661752i
$429$		−	41.7805i		−	2.01718i
$430$	−2.37675	+	11.9629i	−0.114617	+	0.576903i
$431$		−	22.5778i		−	1.08753i	−0.839236	−	0.543767i	$-0.816998\pi$
$431$		−	22.5778i		−	1.08753i	0.839236	−	0.543767i	$-0.183002\pi$
$432$	38.3250	−	38.3946i	1.84391	−	1.84726i
$433$			23.4737i			1.12808i	0.825749	+	0.564038i	$0.190753\pi$
$433$			23.4737i			1.12808i	−0.825749	+	0.564038i	$0.809247\pi$
$434$	−3.64130	+	8.70726i	−0.174788	+	0.417962i
$435$	8.57954			0.411357
$436$	−11.0140	+	26.6242i	−0.527473	+	1.27507i
$437$	−21.8390			−1.04470
$438$	5.21694	−	26.2585i	0.249275	−	1.25468i
$439$	−12.3485			−0.589363			−0.294681	−	0.955596i	$-0.595214\pi$
$439$	−12.3485			−0.589363			−0.294681	+	0.955596i	$0.595214\pi$
$440$	−5.25233	+	7.87226i	−0.250395	+	0.375295i
$441$	−46.6711	−	19.7285i	−2.22243	−	0.939454i
$442$	−15.8602	−	3.15106i	−0.754394	−	0.149880i
$443$	24.9234			1.18415			0.592074	−	0.805883i	$-0.298309\pi$
$443$	24.9234			1.18415			0.592074	+	0.805883i	$0.298309\pi$
$444$	−27.8470	−	11.5198i	−1.32156	−	0.546707i
$445$			2.00722i			0.0951512i
$446$	−6.74686	+	33.9590i	−0.319473	+	1.60801i
$447$	−36.9933			−1.74972
$448$	4.08244	+	20.7686i	0.192877	+	0.981223i
$449$	33.7360			1.59210			0.796051	−	0.605230i	$-0.206919\pi$
$449$	33.7360			1.59210			0.796051	+	0.605230i	$0.206919\pi$
$450$	1.99482	−	10.0406i	0.0940368	−	0.473316i
$451$		−	18.7112i		−	0.881078i
$452$	12.6763	+	5.24397i	0.596244	+	0.246656i
$453$	−1.62947			−0.0765594
$454$	7.15992	+	1.42251i	0.336032	+	0.0667616i
$455$	−10.1193	−	2.05094i	−0.474402	−	0.0961495i
$456$	−31.8291	+	47.7058i	−1.49053	+	2.23403i
$457$	−23.0696			−1.07915			−0.539576	−	0.841937i	$-0.681416\pi$
$457$	−23.0696			−1.07915			−0.539576	+	0.841937i	$0.681416\pi$
$458$	−2.61529	+	13.1635i	−0.122204	+	0.615092i
$459$	39.7363			1.85473
$460$	2.63489	−	6.36936i	0.122852	−	0.296973i
$461$	4.90911			0.228640			0.114320	−	0.993444i	$-0.463531\pi$
$461$	4.90911			0.228640			0.114320	+	0.993444i	$0.463531\pi$
$462$	−36.9569	−	15.4550i	−1.71939	−	0.719034i
$463$			30.9829i			1.43990i	0.694027	+	0.719949i	$0.255835\pi$
$463$			30.9829i			1.43990i	−0.694027	+	0.719949i	$0.744165\pi$
$464$	7.57698	−	7.59074i	0.351752	−	0.352391i
$465$		−	8.07111i		−	0.374289i
$466$	0.703339	−	3.54012i	0.0325815	−	0.163993i
$467$			20.4881i			0.948078i	0.880504	+	0.474039i	$0.157204\pi$
$467$			20.4881i			0.948078i	−0.880504	+	0.474039i	$0.842796\pi$
$468$	52.2060	+	21.5967i	2.41322	+	0.998308i
$469$	−16.5306	−	3.35035i	−0.763314	−	0.154705i
$470$	0.139650	−	0.702903i	0.00644159	−	0.0324225i
$471$			31.9655i			1.47289i
$472$	−1.88761	−	1.25940i	−0.0868842	−	0.0579687i
$473$	−28.8562			−1.32681
$474$	−9.29531	+	46.7861i	−0.426948	+	2.14896i
$475$			6.33672i			0.290749i
$476$	−8.65413	+	12.8635i	−0.396661	+	0.589600i
$477$		−	82.6171i		−	3.78278i
$478$	−11.3128	−	2.24759i	−0.517437	−	0.102803i
$479$	−35.1704			−1.60698			−0.803489	−	0.595319i	$-0.797026\pi$
$479$	−35.1704			−1.60698			−0.803489	+	0.595319i	$0.797026\pi$
$480$	−10.0732	−	15.0387i	−0.459778	−	0.686419i
$481$		−	18.3772i		−	0.837926i
$482$	3.70014	+	0.735132i	0.168537	+	0.0334843i
$483$	28.5953	+	5.79556i	1.30113	+	0.263707i
$484$	−0.360233	−	0.149022i	−0.0163742	−	0.00677372i
$485$		−	6.06903i		−	0.275580i
$486$	−39.7901	−	7.90535i	−1.80491	−	0.358594i
$487$			7.86977i			0.356614i	0.983975	+	0.178307i	$0.0570619\pi$
$487$			7.86977i			0.356614i	−0.983975	+	0.178307i	$0.942938\pi$
$488$	−12.5149	+	18.7575i	−0.566524	+	0.849113i
$489$			63.2708i			2.86121i
$490$	−5.55741	+	8.19239i	−0.251058	+	0.370094i
$491$	2.88992			0.130420			0.0652102	−	0.997872i	$-0.479228\pi$
$491$	2.88992			0.130420			0.0652102	+	0.997872i	$0.479228\pi$
$492$	33.0702	+	13.6806i	1.49092	+	0.616768i
$493$	7.85601			0.353817
$494$	−34.3018	−	6.81497i	−1.54331	−	0.306620i
$495$	24.2192			1.08857
$496$	−7.14091	−	7.12796i	−0.320636	−	0.320055i
$497$	0.588089	−	2.90163i	0.0263794	−	0.130156i
$498$	3.78525	−	19.0523i	0.169621	−	0.853756i
$499$	16.5134			0.739240			0.369620	−	0.929183i	$-0.379488\pi$
$499$	16.5134			0.739240			0.369620	+	0.929183i	$0.379488\pi$
$500$	−1.84811	−	0.764529i	−0.0826498	−	0.0341908i
$501$		−	66.0504i		−	2.95092i
$502$	−11.8215	−	2.34866i	−0.527619	−	0.104826i
$503$	−7.23320			−0.322513			−0.161256	−	0.986913i	$-0.551555\pi$
$503$	−7.23320			−0.322513			−0.161256	+	0.986913i	$0.551555\pi$
$504$	38.4149	−	38.1899i	1.71114	−	1.70112i
$505$	11.2324			0.499837
$506$	15.9951	+	3.17786i	0.711070	+	0.141273i
$507$			7.13426i			0.316843i
$508$	4.49084	−	10.8558i	0.199249	−	0.481647i
$509$	26.3986			1.17010			0.585048	−	0.810999i	$-0.301076\pi$
$509$	26.3986			1.17010			0.585048	+	0.810999i	$0.301076\pi$
$510$	2.58363	−	13.0042i	0.114405	−	0.575835i
$511$	3.10921	−	15.3409i	0.137543	−	0.678640i
$512$	−22.2016	−	4.36908i	−0.981181	−	0.193088i
$513$	85.9401			3.79435
$514$	−19.6238	−	3.89879i	−0.865569	−	0.171968i
$515$	0.403587			0.0177842
$516$	21.0980	−	51.0004i	0.928786	−	2.24517i
$517$	1.69550			0.0745679
$518$	−16.2555	−	6.79790i	−0.714226	−	0.298683i
$519$			38.7702i			1.70182i
$520$	6.12613	−	9.18191i	0.268648	−	0.402654i
$521$			29.5635i			1.29520i	0.761981	+	0.647599i	$0.224227\pi$
$521$			29.5635i			1.29520i	−0.761981	+	0.647599i	$0.775773\pi$
$522$	−26.9217	−	5.34872i	−1.17833	−	0.234107i
$523$			21.6311i			0.945862i	0.881100	+	0.472931i	$0.156804\pi$
$523$			21.6311i			0.945862i	−0.881100	+	0.472931i	$0.843196\pi$
$524$	3.42264	−	8.27359i	0.149519	−	0.361434i
$525$	1.68161	−	8.29709i	0.0733917	−	0.362115i
$526$	43.1969	+	8.58221i	1.88347	+	0.374202i
$527$		−	7.39046i		−	0.321933i
$528$	30.2538	−	30.3087i	1.31663	−	1.31902i
$529$	11.1222			0.483572
$530$	−15.8318	−	3.14540i	−0.687688	−	0.136628i
$531$			5.80727i			0.252014i
$532$	−18.7168	+	27.8207i	−0.811476	+	1.20618i
$533$			21.8241i			0.945307i
$534$	1.76998	−	8.90883i	0.0765944	−	0.385523i
$535$	17.9070			0.774188
$536$	10.0075	−	14.9993i	0.432256	−	0.647871i
$537$		−	46.8213i		−	2.02049i
$538$	0.384626	−	1.93594i	0.0165824	−	0.0834643i
$539$	−21.5729	−	9.11919i	−0.929212	−	0.392791i
$540$	−10.3687	+	25.0645i	−0.446199	+	1.07860i
$541$		−	3.88138i		−	0.166874i	−0.996513	−	0.0834368i	$-0.973410\pi$
$541$		−	3.88138i		−	0.166874i	0.996513	−	0.0834368i	$-0.0265897\pi$
$542$	6.19138	−	31.1631i	0.265942	−	1.33857i
$543$			74.0375i			3.17725i
$544$	−9.22373	−	13.7705i	−0.395464	−	0.590403i
$545$		−	14.4062i		−	0.617094i
$546$	43.1052	+	18.0262i	1.84473	+	0.771450i
$547$	−4.88320			−0.208791			−0.104395	−	0.994536i	$-0.533291\pi$
$547$	−4.88320			−0.208791			−0.104395	+	0.994536i	$0.533291\pi$
$548$	−14.6072	−	6.04276i	−0.623991	−	0.258134i
$549$	57.7080			2.46292
$550$	0.922074	−	4.64108i	0.0393174	−	0.197896i
$551$	16.9906			0.723826
$552$	−17.3113	+	25.9463i	−0.736816	+	1.10435i
$553$	−5.53985	+	27.3337i	−0.235579	+	1.16235i
$554$	16.7601	+	3.32984i	0.712068	+	0.141471i
$555$	15.0679			0.639596
$556$	−7.49332	+	18.1137i	−0.317788	+	0.768192i
$557$			44.6377i			1.89136i	0.325099	+	0.945680i	$0.394602\pi$
$557$			44.6377i			1.89136i	−0.325099	+	0.945680i	$0.605398\pi$
$558$	−5.03175	+	25.3263i	−0.213011	+	1.07215i
$559$	33.6568			1.42353
$560$	−5.85574	−	8.81535i	−0.247450	−	0.372516i
$561$	31.3679			1.32435
$562$	1.61188	−	8.11306i	0.0679928	−	0.342229i
$563$		−	28.5884i		−	1.20486i	−0.798172	−	0.602429i	$-0.794200\pi$
$563$		−	28.5884i		−	1.20486i	0.798172	−	0.602429i	$-0.205800\pi$
$564$	−1.23965	+	2.99662i	−0.0521987	+	0.126181i
$565$	−6.85909			−0.288564
$566$	−14.1213	−	2.80557i	−0.593563	−	0.117927i
$567$	−56.2181	−	11.3940i	−2.36094	−	0.478504i
$568$	2.63283	+	1.75661i	0.110471	+	0.0737058i
$569$	−5.12489			−0.214846			−0.107423	−	0.994213i	$-0.534260\pi$
$569$	−5.12489			−0.214846			−0.107423	+	0.994213i	$0.534260\pi$
$570$	5.58776	−	28.1249i	0.234046	−	1.17802i
$571$	36.7465			1.53779			0.768897	−	0.639373i	$-0.220806\pi$
$571$	36.7465			1.53779			0.768897	+	0.639373i	$0.220806\pi$
$572$	24.1314	+	9.98272i	1.00898	+	0.417398i
$573$	7.72916			0.322890
$574$	19.3045	+	8.07297i	0.805754	+	0.336959i
$575$			3.44642i			0.143726i
$576$	22.2332	+	53.4699i	0.926385	+	2.22791i
$577$			2.55301i			0.106283i	0.998587	+	0.0531417i	$0.0169235\pi$
$577$			2.55301i			0.106283i	−0.998587	+	0.0531417i	$0.983076\pi$
$578$	−2.31920	+	11.6732i	−0.0964658	+	0.485542i
$579$		−	23.6319i		−	0.982106i
$580$	−2.04993	+	4.95533i	−0.0851187	+	0.205759i
$581$	2.25595	−	11.1309i	0.0935926	−	0.461786i
$582$	−5.35171	+	26.9368i	−0.221836	+	1.11657i
$583$		−	38.1884i		−	1.58160i
$584$	13.9197	+	9.28718i	0.576003	+	0.384306i
$585$	−28.2484			−1.16793
$586$	8.45582	−	42.5607i	0.349307	−	1.75817i
$587$			33.3508i			1.37653i	0.725457	+	0.688267i	$0.241628\pi$
$587$			33.3508i			1.37653i	−0.725457	+	0.688267i	$0.758372\pi$
$588$	31.8901	−	31.4606i	1.31513	−	1.29741i
$589$		−	15.9838i		−	0.658600i
$590$	1.11284	+	0.221095i	0.0458148	+	0.00910232i
$591$	−66.9728			−2.75489
$592$	13.3071	−	13.3313i	0.546920	−	0.547913i
$593$			10.9350i			0.449048i	0.974469	+	0.224524i	$0.0720827\pi$
$593$			10.9350i			0.449048i	−0.974469	+	0.224524i	$0.927917\pi$
$594$	−62.9434	−	12.5054i	−2.58260	−	0.513102i
$595$	1.53980	−	7.59738i	0.0631257	−	0.311462i
$596$	8.83891	−	21.3664i	0.362056	−	0.875203i
$597$		−	15.6675i		−	0.641227i
$598$	−18.6561	−	3.70654i	−0.762906	−	0.151572i
$599$		−	25.8459i		−	1.05603i	−0.849234	−	0.528017i	$-0.822936\pi$
$599$		−	25.8459i		−	1.05603i	0.849234	−	0.528017i	$-0.177064\pi$
$600$	7.52847	+	5.02296i	0.307349	+	0.205061i
$601$		−	6.70199i		−	0.273380i	−0.990614	−	0.136690i	$-0.956354\pi$
$601$		−	6.70199i		−	0.273380i	0.990614	−	0.136690i	$-0.0436464\pi$
$602$	12.4500	−	29.7711i	0.507425	−	1.21338i
$603$	−46.1457			−1.87920
$604$	0.389334	−	0.941144i	0.0158418	−	0.0382946i
$605$	0.194920			0.00792462
$606$	−49.8541	−	9.90484i	−2.02518	−	0.402357i
$607$	37.4686			1.52080			0.760402	−	0.649453i	$-0.225002\pi$
$607$	37.4686			1.52080			0.760402	+	0.649453i	$0.225002\pi$
$608$	−19.9487	−	29.7822i	−0.809026	−	1.20783i
$609$	−22.2470	−	4.50891i	−0.901494	−	0.182710i
$610$	2.19706	−	11.0585i	0.0889564	−	0.447745i
$611$	−1.97757			−0.0800038
$612$	−16.2143	+	39.1952i	−0.655426	+	1.58437i
$613$		−	20.0776i		−	0.810928i	−0.914111	−	0.405464i	$-0.867110\pi$
$613$		−	20.0776i		−	0.810928i	0.914111	−	0.405464i	$-0.132890\pi$
$614$	35.8750	+	7.12751i	1.44780	+	0.287643i
$615$	−17.8941			−0.721561
$616$	17.7567	−	17.6527i	0.715436	−	0.711246i
$617$	27.8737			1.12215			0.561077	−	0.827764i	$-0.310387\pi$
$617$	27.8737			1.12215			0.561077	+	0.827764i	$0.310387\pi$
$618$	−1.79128	−	0.355886i	−0.0720560	−	0.0143158i
$619$			25.0328i			1.00615i	0.864242	+	0.503076i	$0.167798\pi$
$619$			25.0328i			1.00615i	−0.864242	+	0.503076i	$0.832202\pi$
$620$	4.66167	+	1.92845i	0.187217	+	0.0774485i
$621$	46.7412			1.87566
$622$	−2.98309	+	15.0148i	−0.119611	+	0.602039i
$623$	1.05488	−	5.20477i	0.0422628	−	0.208525i
$624$	−35.2869	+	35.3510i	−1.41261	+	1.41517i
$625$	1.00000			0.0400000
$626$	38.7000	+	7.68879i	1.54676	+	0.307306i
$627$	67.8412			2.70931
$628$	−18.4625	−	7.63759i	−0.736732	−	0.304773i
$629$	13.7972			0.550129
$630$	−10.4494	+	24.9871i	−0.416313	+	0.995509i
$631$			17.2836i			0.688048i	0.938961	+	0.344024i	$0.111790\pi$
$631$			17.2836i			0.688048i	−0.938961	+	0.344024i	$0.888210\pi$
$632$	−24.8016	−	16.5475i	−0.986553	−	0.658223i
$633$			7.21378i			0.286722i
$634$	−10.3989	−	2.06601i	−0.412992	−	0.0820518i
$635$			5.87400i			0.233103i
$636$	67.4942	+	27.9211i	2.67632	+	1.10714i
$637$	25.1619	+	10.6363i	0.996950	+	0.421425i
$638$	−12.4441	−	2.47236i	−0.492668	−	0.0978815i
$639$		−	8.09997i		−	0.320430i
$640$	11.0928	−	2.22481i	0.438481	−	0.0879433i
$641$	−5.40646			−0.213542			−0.106771	−	0.994284i	$-0.534051\pi$
$641$	−5.40646			−0.213542			−0.106771	+	0.994284i	$0.534051\pi$
$642$	−79.4786	−	15.7905i	−3.13677	−	0.623203i
$643$		−	8.51562i		−	0.335823i	−0.985802	−	0.167912i	$-0.946298\pi$
$643$		−	8.51562i		−	0.335823i	0.985802	−	0.167912i	$-0.0537024\pi$
$644$	−10.1797	+	15.1312i	−0.401137	+	0.596252i
$645$			27.5960i			1.08659i
$646$	5.11654	−	25.7531i	0.201307	−	1.01324i
$647$	9.29106			0.365269			0.182635	−	0.983181i	$-0.441537\pi$
$647$	9.29106			0.365269			0.182635	+	0.983181i	$0.441537\pi$
$648$	34.0338	−	51.0102i	1.33697	−	2.00387i
$649$			2.68432i			0.105369i
$650$	−1.07547	+	5.41319i	−0.0421835	+	0.212323i
$651$	−4.24171	+	20.9286i	−0.166246	+	0.820257i
$652$	−36.5437	−	15.1175i	−1.43116	−	0.592045i
$653$		−	13.4994i		−	0.528272i	−0.964486	−	0.264136i	$-0.914913\pi$
$653$		−	13.4994i		−	0.528272i	0.964486	−	0.264136i	$-0.0850867\pi$
$654$	−12.7035	+	63.9405i	−0.496746	+	2.50027i
$655$			4.47680i			0.174923i
$656$	−15.8031	+	15.8318i	−0.617008	+	0.618128i
$657$		−	42.8244i		−	1.67074i
$658$	−0.731523	+	1.74926i	−0.0285177	+	0.0681931i
$659$	−32.9215			−1.28244			−0.641219	−	0.767358i	$-0.721571\pi$
$659$	−32.9215			−1.28244			−0.641219	+	0.767358i	$0.721571\pi$
$660$	−8.18507	+	19.7859i	−0.318604	+	0.770165i
$661$	−28.6462			−1.11421			−0.557104	−	0.830443i	$-0.688088\pi$
$661$	−28.6462			−1.11421			−0.557104	+	0.830443i	$0.688088\pi$
$662$	−3.40152	+	17.1209i	−0.132204	+	0.665423i
$663$	−36.5864			−1.42090
$664$	10.0997	+	6.73849i	0.391946	+	0.261504i
$665$	3.33022	−	16.4313i	0.129140	−	0.637179i
$666$	−47.2815	−	9.39373i	−1.83212	−	0.364000i
$667$	9.24090			0.357809
$668$	38.1491	+	15.7816i	1.47603	+	0.610608i
$669$			78.3367i			3.02867i
$670$	−1.75686	+	8.84282i	−0.0678735	+	0.341628i
$671$	26.6746			1.02976
$672$	18.2167	+	44.2897i	0.702724	+	1.70851i
$673$	4.30988			0.166134			0.0830669	−	0.996544i	$-0.473528\pi$
$673$	4.30988			0.166134			0.0830669	+	0.996544i	$0.473528\pi$
$674$	−8.31617	+	41.8578i	−0.320327	+	1.61230i
$675$		−	13.5622i		−	0.522011i
$676$	−4.12057	−	1.70461i	−0.158483	−	0.0655618i
$677$	−23.3619			−0.897870			−0.448935	−	0.893564i	$-0.648197\pi$
$677$	−23.3619			−0.897870			−0.448935	+	0.893564i	$0.648197\pi$
$678$	30.4434	+	6.04840i	1.16917	+	0.232287i
$679$	−3.18954	+	15.7372i	−0.122403	+	0.603937i
$680$	6.89358	+	4.59936i	0.264357	+	0.176378i
$681$	16.5165			0.632913
$682$	−2.32584	+	11.7067i	−0.0890612	+	0.448272i
$683$	40.0020			1.53063			0.765317	−	0.643653i	$-0.222582\pi$
$683$	40.0020			1.53063			0.765317	+	0.643653i	$0.222582\pi$
$684$	−35.0677	+	84.7696i	−1.34085	+	3.24125i
$685$	7.90390			0.301993
$686$	18.7160	−	18.3225i	0.714579	−	0.699554i
$687$			30.3656i			1.15852i
$688$	24.4156	+	24.3713i	0.930835	+	0.929148i
$689$			44.5416i			1.69690i
$690$	3.03908	−	15.2966i	0.115696	−	0.582333i
$691$		−	38.8983i		−	1.47976i	−0.672738	−	0.739881i	$-0.734882\pi$
$691$		−	38.8983i		−	1.47976i	0.672738	−	0.739881i	$-0.265118\pi$
$692$	−22.3927	−	9.26346i	−0.851242	−	0.352144i
$693$	−62.8011	−	12.7282i	−2.38562	−	0.483505i
$694$	5.88091	−	29.6004i	0.223236	−	1.12362i
$695$		−	9.80123i		−	0.371782i
$696$	13.4681	−	20.1861i	0.510506	−	0.765152i
$697$	−16.3851			−0.620629
$698$	4.51641	−	22.7325i	0.170949	−	0.860437i
$699$		−	8.16634i		−	0.308880i
$700$	4.39040	+	2.95370i	0.165942	+	0.111640i
$701$		−	3.06613i		−	0.115806i	−0.998322	−	0.0579031i	$-0.981559\pi$
$701$		−	3.06613i		−	0.115806i	0.998322	−	0.0579031i	$-0.0184415\pi$
$702$	73.4149	+	14.5858i	2.77087	+	0.550507i
$703$	29.8400			1.12544
$704$	10.2769	+	24.7156i	0.387327	+	0.931503i
$705$		−	1.62146i		−	0.0610676i
$706$	5.33577	+	1.06009i	0.200814	+	0.0398971i
$707$	−29.1260	−	5.90313i	−1.09540	−	0.222010i
$708$	−4.74426	−	1.96261i	−0.178300	−	0.0737596i
$709$		−	38.5857i		−	1.44912i	−0.689214	−	0.724558i	$-0.742044\pi$
$709$		−	38.5857i		−	1.44912i	0.689214	−	0.724558i	$-0.257956\pi$
$710$	−1.55218	−	0.308382i	−0.0582524	−	0.0115734i
$711$			76.3026i			2.86157i
$712$	4.72262	+	3.15091i	0.176988	+	0.118085i
$713$		−	8.69328i		−	0.325566i
$714$	−13.5337	+	32.3624i	−0.506485	+	1.21113i
$715$	−13.0573			−0.488317
$716$	27.0428	+	11.1871i	1.01064	+	0.418083i
$717$	−26.0964			−0.974589
$718$	38.3691	+	7.62305i	1.43192	+	0.284490i
$719$	31.4806			1.17403			0.587014	−	0.809577i	$-0.300303\pi$
$719$	31.4806			1.17403			0.587014	+	0.809577i	$0.300303\pi$
$720$	−20.4922	−	20.4550i	−0.763698	−	0.762313i
$721$	−1.04651	−	0.212103i	−0.0389742	−	0.00789911i
$722$	5.82972	−	29.3428i	0.216960	−	1.09202i
$723$	8.53548			0.317438
$724$	−42.7622	−	17.6900i	−1.58925	−	0.657443i
$725$		−	2.68130i		−	0.0995810i
$726$	−0.865133	−	0.171882i	−0.0321081	−	0.00637913i
$727$	−1.97285			−0.0731689			−0.0365844	−	0.999331i	$-0.511648\pi$
$727$	−1.97285			−0.0731689			−0.0365844	+	0.999331i	$0.511648\pi$
$728$	−20.7107	+	20.5894i	−0.767590	+	0.763095i
$729$	−26.7463			−0.990603
$730$	−8.20636	−	1.63041i	−0.303731	−	0.0603443i
$731$			25.2688i			0.934601i
$732$	−19.5029	+	47.1446i	−0.720847	+	1.74251i
$733$	1.04466			0.0385855			0.0192928	−	0.999814i	$-0.493859\pi$
$733$	1.04466			0.0385855			0.0192928	+	0.999814i	$0.493859\pi$
$734$	−0.812236	+	4.08823i	−0.0299802	+	0.150899i
$735$	−8.72096	+	20.6308i	−0.321677	+	0.760980i
$736$	−10.8497	−	16.1980i	−0.399926	−	0.597065i
$737$	−21.3301			−0.785704
$738$	56.1500	+	11.1557i	2.06691	+	0.410646i
$739$	−33.3529			−1.22691			−0.613454	−	0.789730i	$-0.710220\pi$
$739$	−33.3529			−1.22691			−0.613454	+	0.789730i	$0.710220\pi$
$740$	−3.60021	+	8.70283i	−0.132346	+	0.319922i
$741$	−79.1275			−2.90682
$742$	39.3992	+	16.4764i	1.44639	+	0.604868i
$743$		−	2.33616i		−	0.0857054i	−0.999081	−	0.0428527i	$-0.986355\pi$
$743$		−	2.33616i		−	0.0857054i	0.999081	−	0.0428527i	$-0.0136446\pi$
$744$	−18.9899	−	12.6699i	−0.696202	−	0.464503i
$745$			11.5613i			0.423572i
$746$	−17.5118	−	3.47918i	−0.641151	−	0.127382i
$747$		−	31.0721i		−	1.13687i
$748$	−7.49481	+	18.1173i	−0.274037	+	0.662435i
$749$	−46.4334	−	9.41091i	−1.69664	−	0.343867i
$750$	−4.43840	−	0.881807i	−0.162068	−	0.0321990i
$751$		−	22.6980i		−	0.828261i	−0.910218	−	0.414130i	$-0.864086\pi$
$751$		−	22.6980i		−	0.828261i	0.910218	−	0.414130i	$-0.135914\pi$
$752$	−1.43458	−	1.43198i	−0.0523138	−	0.0522190i
$753$	−27.2698			−0.993768
$754$	14.5144	+	2.88367i	0.528583	+	0.105017i
$755$			0.509248i			0.0185334i
$756$	40.0588	−	59.5437i	1.45693	−	2.16558i
$757$		−	0.859830i		−	0.0312510i	−0.999878	−	0.0156255i	$-0.995026\pi$
$757$		−	0.859830i		−	0.0312510i	0.999878	−	0.0156255i	$-0.00497396\pi$
$758$	5.78402	−	29.1128i	0.210085	−	1.05742i
$759$	36.8976			1.33930
$760$	14.9092	+	9.94731i	0.540812	+	0.360827i
$761$		−	9.59745i		−	0.347907i	−0.984754	−	0.173954i	$-0.944346\pi$
$761$		−	9.59745i		−	0.347907i	0.984754	−	0.173954i	$-0.0556543\pi$
$762$	5.17974	−	26.0712i	0.187642	−	0.944460i
$763$	−7.57108	+	37.3557i	−0.274091	+	1.35237i
$764$	−1.84675	+	4.46417i	−0.0668130	+	0.161508i
$765$		−	21.2083i		−	0.766787i
$766$	3.14820	−	15.8458i	0.113749	−	0.572533i
$767$		−	3.13089i		−	0.113050i
$768$	−51.1962	+	0.0928907i	−1.84738	+	0.00335191i
$769$		−	46.0671i		−	1.66122i	−0.556854	−	0.830610i	$-0.687992\pi$
$769$		−	46.0671i		−	1.66122i	0.556854	−	0.830610i	$-0.312008\pi$
$770$	−4.83005	+	11.5499i	−0.174063	+	0.416228i
$771$	−45.2682			−1.63029
$772$	13.6492	+	5.64642i	0.491244	+	0.203219i
$773$	−7.98484			−0.287195			−0.143597	−	0.989636i	$-0.545867\pi$
$773$	−7.98484			−0.287195			−0.143597	+	0.989636i	$0.545867\pi$
$774$	17.2041	−	86.5937i	0.618390	−	3.11254i
$775$	−2.52241			−0.0906075
$776$	−14.2793	−	9.52710i	−0.512598	−	0.342003i
$777$	−39.0715	−	7.91882i	−1.40168	−	0.284086i
$778$	31.6212	+	6.28240i	1.13368	+	0.225235i
$779$	−35.4370			−1.26966
$780$	9.54677	−	23.0776i	0.341829	−	0.826309i
$781$		−	3.74408i		−	0.133974i
$782$	2.78279	−	14.0066i	0.0995124	−	0.500876i
$783$	−36.3644			−1.29956
$784$	10.5513	+	25.9359i	0.376831	+	0.926282i
$785$	9.98993			0.356556
$786$	3.94767	−	19.8698i	0.140809	−	0.708733i
$787$		−	56.0482i		−	1.99790i	−0.0457828	−	0.998951i	$-0.514578\pi$
$787$		−	56.0482i		−	1.99790i	0.0457828	−	0.998951i	$-0.485422\pi$
$788$	16.0020	−	38.6818i	0.570047	−	1.37798i
$789$	99.6465			3.54751
$790$	14.6217	+	2.90500i	0.520218	+	0.103355i
$791$	17.7858	+	3.60475i	0.632391	+	0.128170i
$792$	38.0190	−	56.9834i	1.35095	−	2.02482i
$793$	−31.1122			−1.10483
$794$	8.23388	−	41.4436i	0.292210	−	1.47078i
$795$	−36.5207			−1.29526
$796$	9.04914	+	3.74347i	0.320738	+	0.132684i
$797$	−23.7352			−0.840744			−0.420372	−	0.907352i	$-0.638100\pi$
$797$	−23.7352			−0.840744			−0.420372	+	0.907352i	$0.638100\pi$
$798$	−29.2701	+	69.9921i	−1.03615	+	2.47770i
$799$		−	1.48472i		−	0.0525255i
$800$	−4.69994	+	3.14811i	−0.166168	+	0.111303i
$801$		−	14.5292i		−	0.513366i
$802$	4.64076	−	23.3584i	0.163871	−	0.824812i
$803$		−	19.7949i		−	0.698546i
$804$	15.5953	−	37.6988i	0.550004	−	1.32953i
$805$	1.81124	−	8.93668i	0.0638380	−	0.314977i
$806$	2.71278	−	13.6542i	0.0955536	−	0.480950i
$807$		−	4.46582i		−	0.157204i
$808$	17.6326	−	26.4279i	0.620311	−	0.929730i
$809$	22.4179			0.788172			0.394086	−	0.919074i	$-0.371061\pi$
$809$	22.4179			0.788172			0.394086	+	0.919074i	$0.371061\pi$
$810$	−5.97481	+	30.0730i	−0.209933	+	1.05666i
$811$			17.3731i			0.610054i	0.952344	+	0.305027i	$0.0986655\pi$
$811$			17.3731i			0.610054i	−0.952344	+	0.305027i	$0.901335\pi$
$812$	7.91977	−	11.7720i	0.277929	−	0.413116i
$813$		−	71.8870i		−	2.52119i
$814$	−21.8551	−	4.34210i	−0.766021	−	0.152190i
$815$	19.7736			0.692638
$816$	−26.5408	−	26.4927i	−0.929113	−	0.927428i
$817$			54.6503i			1.91197i
$818$	37.4178	+	7.43405i	1.30828	+	0.259925i
$819$	73.2489	+	14.8457i	2.55952	+	0.518752i
$820$	4.27549	−	10.3352i	0.149307	−	0.360921i
$821$			32.6279i			1.13872i	0.822088	+	0.569361i	$0.192809\pi$
$821$			32.6279i			1.13872i	−0.822088	+	0.569361i	$0.807191\pi$
$822$	−35.0807	−	6.96972i	−1.22358	−	0.243097i
$823$			6.06037i			0.211251i	0.994406	+	0.105626i	$0.0336845\pi$
$823$			6.06037i			0.211251i	−0.994406	+	0.105626i	$0.966315\pi$
$824$	0.633547	−	0.949569i	0.0220707	−	0.0330798i
$825$		−	10.7060i		−	0.372736i
$826$	−2.76942	−	1.15815i	−0.0963606	−	0.0402971i
$827$	21.7214			0.755328			0.377664	−	0.925943i	$-0.376727\pi$
$827$	21.7214			0.755328			0.377664	+	0.925943i	$0.376727\pi$
$828$	−19.0727	+	46.1047i	−0.662821	+	1.60225i
$829$	−4.44507			−0.154384			−0.0771919	−	0.997016i	$-0.524595\pi$
$829$	−4.44507			−0.154384			−0.0771919	+	0.997016i	$0.524595\pi$
$830$	−5.95429	−	1.18298i	−0.206676	−	0.0410618i
$831$	38.6622			1.34118
$832$	−11.9867	−	28.8273i	−0.415563	−	0.999408i
$833$	−7.98550	+	18.8910i	−0.276681	+	0.654535i
$834$	−8.64279	+	43.5018i	−0.299275	+	1.50634i
$835$	−20.6423			−0.714355
$836$	−16.2095	+	39.1834i	−0.560616	+	1.35519i
$837$			34.2095i			1.18245i
$838$	20.8723	+	4.14684i	0.721022	+	0.143250i
$839$	9.23265			0.318746			0.159373	−	0.987218i	$-0.449053\pi$
$839$	9.23265			0.318746			0.159373	+	0.987218i	$0.449053\pi$
$840$	−16.8818	−	16.9812i	−0.582477	−	0.585908i
$841$	21.8106			0.752091
$842$	−38.1810	−	7.58567i	−1.31580	−	0.261419i
$843$		−	18.7152i		−	0.644586i
$844$	−4.16650	−	1.72361i	−0.143417	−	0.0593290i
$845$	2.22962			0.0767012
$846$	−1.01086	+	5.08797i	−0.0347541	+	0.174928i
$847$	−0.505433	−	0.102439i	−0.0173669	−	0.00351984i
$848$	−32.2531	+	32.3117i	−1.10758	+	1.10959i
$849$	−32.5750			−1.11797
$850$	−4.06411	−	0.807443i	−0.139398	−	0.0276951i
$851$	16.2294			0.556337
$852$	6.61728	+	2.73745i	0.226704	+	0.0937836i
$853$	5.33487			0.182662			0.0913312	−	0.995821i	$-0.470888\pi$
$853$	5.33487			0.182662			0.0913312	+	0.995821i	$0.470888\pi$
$854$	−11.5087	+	27.5203i	−0.393821	+	0.941726i
$855$		−	45.8684i		−	1.56867i
$856$	28.1102	−	42.1320i	0.960788	−	1.44004i
$857$			3.81449i			0.130301i	0.997875	+	0.0651503i	$0.0207527\pi$
$857$			3.81449i			0.130301i	−0.997875	+	0.0651503i	$0.979247\pi$
$858$	57.9538	+	11.5141i	1.97851	+	0.393084i
$859$			40.9650i			1.39771i	0.715264	+	0.698854i	$0.246306\pi$
$859$			40.9650i			1.39771i	−0.715264	+	0.698854i	$0.753694\pi$
$860$	−15.9388	−	6.59360i	−0.543508	−	0.224840i
$861$	46.4000	+	9.40413i	1.58131	+	0.320492i
$862$	31.3177	+	6.22209i	1.06668	+	0.211925i
$863$		−	20.2817i		−	0.690399i	−0.938529	−	0.345199i	$-0.887811\pi$
$863$		−	20.2817i		−	0.690399i	0.938529	−	0.345199i	$-0.112189\pi$
$864$	42.6954	+	63.7416i	1.45253	+	2.16853i
$865$	12.1166			0.411975
$866$	−32.5605	−	6.46900i	−1.10645	−	0.219826i
$867$			26.9278i			0.914515i
$868$	−11.0744	−	7.45044i	−0.375889	−	0.252884i
$869$			35.2696i			1.19644i
$870$	−2.36439	+	11.9007i	−0.0801603	+	0.403471i
$871$	24.8786			0.842980
$872$	−33.8952	−	22.6147i	−1.14784	−	0.765830i
$873$			43.9307i			1.48683i
$874$	6.01850	−	30.2930i	0.203579	−	1.02467i
$875$	−2.59303	−	0.525543i	−0.0876604	−	0.0177666i
$876$	34.9855	+	14.4729i	1.18205	+	0.488993i
$877$			42.3958i			1.43160i	0.698304	+	0.715802i	$0.253938\pi$
$877$			42.3958i			1.43160i	−0.698304	+	0.715802i	$0.746062\pi$
$878$	3.40307	−	17.1287i	0.114848	−	0.578065i
$879$		−	98.1791i		−	3.31150i
$880$	−9.47216	−	9.45499i	−0.319307	−	0.318728i
$881$		−	18.8445i		−	0.634887i	−0.948277	−	0.317443i	$-0.897176\pi$
$881$		−	18.8445i		−	0.634887i	0.948277	−	0.317443i	$-0.102824\pi$
$882$	40.2273	−	59.3007i	1.35452	−	1.99676i
$883$	36.2096			1.21855			0.609274	−	0.792959i	$-0.291461\pi$
$883$	36.2096			1.21855			0.609274	+	0.792959i	$0.291461\pi$
$884$	8.74168	−	21.1314i	0.294014	−	0.710725i
$885$	2.56709			0.0862918
$886$	−6.86852	+	34.5714i	−0.230753	+	1.16145i
$887$	21.5740			0.724385			0.362193	−	0.932103i	$-0.382028\pi$
$887$	21.5740			0.724385			0.362193	+	0.932103i	$0.382028\pi$
$888$	23.6534	−	35.4520i	0.793756	−	1.18969i
$889$	3.08704	−	15.2315i	0.103536	−	0.510847i
$890$	−2.78421	−	0.553158i	−0.0933271	−	0.0185419i
$891$	−72.5403			−2.43019
$892$	−45.2453	−	18.7172i	−1.51492	−	0.626698i
$893$		−	3.21108i		−	0.107455i
$894$	10.1948	−	51.3135i	0.340965	−	1.71618i
$895$	−14.6327			−0.489118
$896$	−29.9332	−	0.0607475i	−0.999998	−	0.00202943i
$897$	−43.0360			−1.43693
$898$	−9.29714	+	46.7953i	−0.310250	+	1.56158i
$899$			6.76332i			0.225570i
$900$	13.3775	+	5.53405i	0.445918	+	0.184468i
$901$	−33.4409			−1.11408
$902$	25.9544	+	5.15653i	0.864187	+	0.171694i
$903$	14.5029	−	71.5574i	0.482627	−	2.38128i
$904$	−10.7673	+	16.1382i	−0.358116	+	0.536749i
$905$	23.1384			0.769147
$906$	0.449058	−	2.26025i	0.0149190	−	0.0750917i
$907$	−35.3694			−1.17442			−0.587210	−	0.809435i	$-0.699774\pi$
$907$	−35.3694			−1.17442			−0.587210	+	0.809435i	$0.699774\pi$
$908$	−3.94633	+	9.53952i	−0.130964	+	0.316580i
$909$	−81.3061			−2.69675
$910$	5.63360	−	13.4713i	0.186752	−	0.446571i
$911$		−	59.3513i		−	1.96640i	−0.182540	−	0.983199i	$-0.558432\pi$
$911$		−	59.3513i		−	1.96640i	0.182540	−	0.983199i	$-0.441568\pi$
$912$	−57.4013	−	57.2972i	−1.90075	−	1.89730i
$913$		−	14.3626i		−	0.475331i
$914$	6.35764	−	32.0000i	0.210292	−	1.05846i
$915$		−	25.5097i		−	0.843324i
$916$	−17.5384	−	7.25534i	−0.579486	−	0.239723i
$917$	2.35275	−	11.6085i	0.0776946	−	0.383345i
$918$	−10.9507	+	55.1184i	−0.361428	+	1.81918i
$919$			54.6687i			1.80335i	0.432411	+	0.901677i	$0.357663\pi$
$919$			54.6687i			1.80335i	−0.432411	+	0.901677i	$0.642337\pi$
$920$	8.10882	+	5.41016i	0.267340	+	0.178368i
$921$	82.7563			2.72691
$922$	−1.35288	+	6.80943i	−0.0445546	+	0.224257i
$923$			4.36696i			0.143740i
$924$	31.6225	−	47.0038i	1.04030	−	1.54631i
$925$		−	4.70905i		−	0.154833i
$926$	−42.9765	−	8.53842i	−1.41229	−	0.280590i
$927$	−2.92137			−0.0959504
$928$	8.44103	+	12.6019i	0.277090	+	0.413679i
$929$			37.8759i			1.24267i	0.783546	+	0.621334i	$0.213409\pi$
$929$			37.8759i			1.24267i	−0.783546	+	0.621334i	$0.786591\pi$
$930$	11.1955	+	2.22427i	0.367113	+	0.0729368i
$931$	−17.2707	+	40.8567i	−0.566025	+	1.33902i
$932$	4.71668	+	1.95121i	0.154500	+	0.0639139i
$933$			34.6361i			1.13394i
$934$	−28.4192	−	5.64622i	−0.929903	−	0.184750i
$935$		−	9.80318i		−	0.320598i
$936$	−44.3440	+	66.4633i	−1.44943	+	2.17242i
$937$			55.9352i			1.82732i	0.406476	+	0.913661i	$0.366757\pi$
$937$			55.9352i			1.82732i	−0.406476	+	0.913661i	$0.633243\pi$
$938$	9.20287	−	22.0064i	0.300484	−	0.718534i
$939$	89.2731			2.91332
$940$	0.936513	+	0.387419i	0.0305457	+	0.0126362i
$941$	60.3400			1.96703			0.983514	−	0.180831i	$-0.0578787\pi$
$941$	60.3400			1.96703			0.983514	+	0.180831i	$0.0578787\pi$
$942$	−44.3394	−	8.80919i	−1.44465	−	0.287019i
$943$	−19.2735			−0.627632
$944$	2.26712	−	2.27123i	0.0737883	−	0.0739223i
$945$	−7.12754	+	35.1673i	−0.231859	+	1.14399i
$946$	7.95233	−	40.0265i	0.258552	−	1.30137i
$947$	22.0376			0.716126			0.358063	−	0.933697i	$-0.383437\pi$
$947$	22.0376			0.716126			0.358063	+	0.933697i	$0.383437\pi$
$948$	−62.3355	−	25.7871i	−2.02456	−	0.837526i
$949$			23.0880i			0.749469i
$950$	−8.78968	−	1.74630i	−0.285175	−	0.0566576i
$951$	−23.9881			−0.777867
$952$	−15.4581	−	15.5492i	−0.501000	−	0.503951i
$953$	21.2857			0.689511			0.344756	−	0.938693i	$-0.387962\pi$
$953$	21.2857			0.689511			0.344756	+	0.938693i	$0.387962\pi$
$954$	114.598	+	22.7680i	3.71026	+	0.737142i
$955$		−	2.41554i		−	0.0781650i
$956$	6.23529	−	15.0726i	0.201664	−	0.487484i
$957$	−28.7061			−0.927937
$958$	9.69244	−	48.7850i	0.313148	−	1.57617i
$959$	−20.4951	−	4.15384i	−0.661820	−	0.134134i
$960$	23.6362	−	9.82816i	0.762856	−	0.317202i
$961$	−24.6375			−0.794757
$962$	25.4910	+	5.06446i	0.821863	+	0.163285i
$963$	−129.620			−4.17695
$964$	−2.03941	+	4.92988i	−0.0656848	+	0.158781i
$965$	−7.38549			−0.237747
$966$	−15.9195	+	38.0674i	−0.512200	+	1.22480i
$967$			29.9897i			0.964405i	0.876060	+	0.482203i	$0.160163\pi$
$967$			29.9897i			0.964405i	−0.876060	+	0.482203i	$0.839837\pi$
$968$	0.305983	−	0.458611i	0.00983467	−	0.0147403i
$969$		−	59.4072i		−	1.90843i
$970$	8.41837	+	1.67253i	0.270297	+	0.0537018i
$971$		−	9.10304i		−	0.292130i	−0.989275	−	0.146065i	$-0.953339\pi$
$971$		−	9.10304i		−	0.292130i	0.989275	−	0.146065i	$-0.0466609\pi$
$972$	21.9311	−	53.0143i	0.703440	−	1.70043i
$973$	−5.15097	+	25.4149i	−0.165132	+	0.814764i
$974$	−10.9162	−	2.16879i	−0.349777	−	0.0694925i
$975$			12.4871i			0.399908i
$976$	−22.5697	−	22.5288i	−0.722438	−	0.721128i
$977$	−38.3437			−1.22672			−0.613362	−	0.789802i	$-0.710183\pi$
$977$	−38.3437			−1.22672			−0.613362	+	0.789802i	$0.710183\pi$
$978$	−87.7631	−	17.4365i	−2.80635	−	0.557557i
$979$		−	6.71591i		−	0.214641i
$980$	−9.83214	−	9.96639i	−0.314076	−	0.318365i
$981$			104.279i			3.32938i
$982$	−0.796419	+	4.00862i	−0.0254147	+	0.127920i
$983$	11.4686			0.365792			0.182896	−	0.983132i	$-0.441453\pi$
$983$	11.4686			0.365792			0.182896	+	0.983132i	$0.441453\pi$
$984$	−28.0900	+	42.1016i	−0.895476	+	1.34215i
$985$			20.9305i			0.666902i
$986$	−2.16500	+	10.8971i	−0.0689475	+	0.347034i
$987$	−0.852145	+	4.20448i	−0.0271241	+	0.133830i
$988$	18.9061	−	45.7021i	0.601484	−	1.45398i
$989$			29.7233i			0.945147i
$990$	−6.67444	+	33.5945i	−0.212128	+	1.06770i
$991$			27.8094i			0.883395i	0.897164	+	0.441697i	$0.145624\pi$
$991$			27.8094i			0.883395i	−0.897164	+	0.441697i	$0.854376\pi$
$992$	11.8551	−	7.94081i	0.376401	−	0.252121i
$993$			39.4945i			1.25332i
$994$	3.86279	+	1.61538i	0.122520	+	0.0512369i
$995$	−4.89644			−0.155228
$996$	25.3844	+	10.5011i	0.804335	+	0.332739i
$997$	51.3033			1.62479			0.812395	−	0.583107i	$-0.198163\pi$
$997$	51.3033			1.62479			0.812395	+	0.583107i	$0.198163\pi$
$998$	−4.55083	+	22.9057i	−0.144054	+	0.725068i
$999$	−63.8653			−2.02061

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.h.b.251.8	yes	16
4.3	odd	2		1120.2.h.b.111.1		16
7.6	odd	2		280.2.h.a.251.8	yes	16
8.3	odd	2		280.2.h.a.251.7	✓	16
8.5	even	2		1120.2.h.a.111.1		16
28.27	even	2		1120.2.h.a.111.16		16
56.13	odd	2		1120.2.h.b.111.16		16
56.27	even	2	inner	280.2.h.b.251.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.h.a.251.7	✓	16	8.3	odd	2
280.2.h.a.251.8	yes	16	7.6	odd	2
280.2.h.b.251.7	yes	16	56.27	even	2	inner
280.2.h.b.251.8	yes	16	1.1	even	1	trivial
1120.2.h.a.111.1		16	8.5	even	2
1120.2.h.a.111.16		16	28.27	even	2
1120.2.h.b.111.1		16	4.3	odd	2
1120.2.h.b.111.16		16	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.275585 + 1.38710i) q^{2} +3.19977i q^{3} +(-1.84811 - 0.764529i) q^{4} +1.00000 q^{5} +(-4.43840 - 0.881807i) q^{6} +(-2.59303 - 0.525543i) q^{7} +(1.56979 - 2.35282i) q^{8} -7.23851 q^{9} +O(q^{10})\)	\(q+(-0.275585 + 1.38710i) q^{2} +3.19977i q^{3} +(-1.84811 - 0.764529i) q^{4} +1.00000 q^{5} +(-4.43840 - 0.881807i) q^{6} +(-2.59303 - 0.525543i) q^{7} +(1.56979 - 2.35282i) q^{8} -7.23851 q^{9} +(-0.275585 + 1.38710i) q^{10} -3.34588 q^{11} +(2.44631 - 5.91351i) q^{12} +3.90251 q^{13} +(1.44358 - 3.45197i) q^{14} +3.19977i q^{15} +(2.83099 + 2.82586i) q^{16} +2.92992i q^{17} +(1.99482 - 10.0406i) q^{18} +6.33672i q^{19} +(-1.84811 - 0.764529i) q^{20} +(1.68161 - 8.29709i) q^{21} +(0.922074 - 4.64108i) q^{22} +3.44642i q^{23} +(7.52847 + 5.02296i) q^{24} +1.00000 q^{25} +(-1.07547 + 5.41319i) q^{26} -13.5622i q^{27} +(4.39040 + 2.95370i) q^{28} -2.68130i q^{29} +(-4.43840 - 0.881807i) q^{30} -2.52241 q^{31} +(-4.69994 + 3.14811i) q^{32} -10.7060i q^{33} +(-4.06411 - 0.807443i) q^{34} +(-2.59303 - 0.525543i) q^{35} +(13.3775 + 5.53405i) q^{36} -4.70905i q^{37} +(-8.78968 - 1.74630i) q^{38} +12.4871i q^{39} +(1.56979 - 2.35282i) q^{40} +5.59232i q^{41} +(11.0455 + 4.61912i) q^{42} +8.62439 q^{43} +(6.18354 + 2.55802i) q^{44} -7.23851 q^{45} +(-4.78054 - 0.949782i) q^{46} -0.506742 q^{47} +(-9.04209 + 9.05851i) q^{48} +(6.44761 + 2.72550i) q^{49} +(-0.275585 + 1.38710i) q^{50} -9.37508 q^{51} +(-7.21226 - 2.98358i) q^{52} +11.4136i q^{53} +(18.8122 + 3.73755i) q^{54} -3.34588 q^{55} +(-5.30702 + 5.27594i) q^{56} -20.2760 q^{57} +(3.71924 + 0.738926i) q^{58} -0.802275i q^{59} +(2.44631 - 5.91351i) q^{60} -7.97236 q^{61} +(0.695136 - 3.49883i) q^{62} +(18.7697 + 3.80415i) q^{63} +(-3.07152 - 7.38686i) q^{64} +3.90251 q^{65} +(14.8504 + 2.95042i) q^{66} +6.37503 q^{67} +(2.24001 - 5.41481i) q^{68} -11.0278 q^{69} +(1.44358 - 3.45197i) q^{70} +1.11901i q^{71} +(-11.3629 + 17.0309i) q^{72} +5.91619i q^{73} +(6.53194 + 1.29774i) q^{74} +3.19977i q^{75} +(4.84460 - 11.7109i) q^{76} +(8.67597 + 1.75840i) q^{77} +(-17.3209 - 3.44126i) q^{78} -10.5412i q^{79} +(2.83099 + 2.82586i) q^{80} +21.6805 q^{81} +(-7.75712 - 1.54116i) q^{82} +4.29261i q^{83} +(-9.45117 + 14.0483i) q^{84} +2.92992i q^{85} +(-2.37675 + 11.9629i) q^{86} +8.57954 q^{87} +(-5.25233 + 7.87226i) q^{88} +2.00722i q^{89} +(1.99482 - 10.0406i) q^{90} +(-10.1193 - 2.05094i) q^{91} +(2.63489 - 6.36936i) q^{92} -8.07111i q^{93} +(0.139650 - 0.702903i) q^{94} +6.33672i q^{95} +(-10.0732 - 15.0387i) q^{96} -6.06903i q^{97} +(-5.55741 + 8.19239i) q^{98} +24.2192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9	\( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^4 + 16 * q^5 + q^8 - 16 * q^9 + q^10 - 4 * q^11 + 14 * q^12 - q^14 + 9 * q^16 - 15 * q^18 + q^20 - 4 * q^21 + 6 * q^22 + 22 * q^24 + 16 * q^25 - 20 * q^26 + q^28 - 16 * q^31 - 19 * q^32 - 14 * q^34 + 15 * q^36 - 30 * q^38 + q^40 + 44 * q^42 - 4 * q^43 - 20 * q^44 - 16 * q^45 + 6 * q^46 - 34 * q^48 - 8 * q^49 + q^50 - 40 * q^51 - 38 * q^52 + 26 * q^54 - 4 * q^55 + 33 * q^56 - 16 * q^57 + 18 * q^58 + 14 * q^60 - 8 * q^61 + 28 * q^62 + 28 * q^63 - 23 * q^64 + 46 * q^66 + 20 * q^67 + 12 * q^68 - 40 * q^69 - q^70 - 13 * q^72 - 28 * q^74 + 34 * q^76 - 4 * q^77 - 6 * q^78 + 9 * q^80 + 24 * q^81 - 16 * q^82 - 42 * q^84 - 24 * q^86 + 72 * q^87 - 44 * q^88 - 15 * q^90 - 32 * q^91 - 30 * q^92 - 58 * q^94 - 30 * q^96 + 5 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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