LMFDB - Embedded newform 280.2.h.a.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.a.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} +(0.0143823 + 3.74163i) 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} +(-5.19399 - 1.01119i) 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} +(11.9723 - 0.0460200i) 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} +(2.83400 - 6.92592i) 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} +(-0.0143823 - 3.74163i) 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} +(-3.23556 + 16.6195i) 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} +(2.00368 + 9.69460i) 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} + 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 $

$2$	−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	$-0.625155\pi$
$3$		−	3.19977i		−	1.84739i	0.383133	−	0.923693i	$-0.374845\pi$
$4$	−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	$-0.682023\pi$
$13$	−3.90251			−1.08236			−0.541181	+	0.840906i	$0.682023\pi$
$14$	0.0143823	+	3.74163i	0.00384383	+	0.999993i
$15$			3.19977i			0.826176i
$16$	2.83099	+	2.82586i	0.707748	+	0.706465i
$17$		−	2.92992i		−	0.710611i	−0.934750	−	0.355306i	$-0.884377\pi$
$17$		−	2.92992i		−	0.710611i	0.934750	−	0.355306i	$-0.115623\pi$
$18$	1.99482	−	10.0406i	0.470184	−	2.36658i
$19$		−	6.33672i		−	1.45374i	−0.686774	−	0.726871i	$-0.740974\pi$
$19$		−	6.33672i		−	1.45374i	0.686774	−	0.726871i	$-0.259026\pi$
$20$	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
$28$	−5.19399	−	1.01119i	−0.981571	−	0.191096i
$29$		−	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	$-0.427266\pi$
$31$	2.52241			0.453037			0.226519	+	0.974007i	$0.427266\pi$
$32$	−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	$-0.856152\pi$
$41$		−	5.59232i		−	0.873374i	0.899614	−	0.436687i	$-0.143848\pi$
$42$	11.9723	−	0.0460200i	1.84737	−	0.00710104i
$43$	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	$-0.488233\pi$
$47$	0.506742			0.0739159			0.0369580	+	0.999317i	$0.488233\pi$
$48$	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
$56$	2.83400	−	6.92592i	0.378710	−	0.925516i
$57$	−20.2760			−2.68562
$58$	3.71924	+	0.738926i	0.488360	+	0.0970257i
$59$			0.802275i			0.104447i	0.998635	+	0.0522236i	$0.0166309\pi$
$59$			0.802275i			0.104447i	−0.998635	+	0.0522236i	$0.983369\pi$
$60$	2.44631	−	5.91351i	0.315818	−	0.763431i
$61$	7.97236			1.02076			0.510378	−	0.859950i	$-0.329506\pi$
$61$	7.97236			1.02076			0.510378	+	0.859950i	$0.329506\pi$
$62$	−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
$70$	−0.0143823	−	3.74163i	−0.00171901	−	0.447210i
$71$			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	$-0.887465\pi$
$73$		−	5.91619i		−	0.692438i	0.938154	−	0.346219i	$-0.112535\pi$
$74$	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	$-0.924299\pi$
$83$		−	4.29261i		−	0.471175i	0.971853	−	0.235588i	$-0.0757014\pi$
$84$	−3.23556	+	16.6195i	−0.353029	+	1.81334i
$85$			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	$-0.966073\pi$
$89$		−	2.00722i		−	0.212764i	0.994325	−	0.106382i	$-0.0339267\pi$
$90$	−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	$0.0996959\pi$
$97$			6.06903i			0.616217i	−0.951351	+	0.308108i	$0.900304\pi$
$98$	2.00368	+	9.69460i	0.202402	+	0.979302i
$99$	24.2192			2.43412
$100$	−1.84811	−	0.764529i	−0.184811	−	0.0764529i
$101$	−11.2324			−1.11767			−0.558834	−	0.829279i	$-0.688751\pi$
$101$	−11.2324			−1.11767			−0.558834	+	0.829279i	$0.688751\pi$
$102$	2.58363	−	13.0042i	0.255817	−	1.28761i
$103$	−0.403587			−0.0397667			−0.0198833	−	0.999802i	$-0.506329\pi$
$103$	−0.403587			−0.0397667			−0.0198833	+	0.999802i	$0.506329\pi$
$104$	−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
$112$	8.82596	+	5.83973i	0.833975	+	0.551803i
$113$	−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
$126$	−0.104106	−	27.0838i	−0.00927453	−	2.41282i
$127$			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	$-0.937344\pi$
$131$		−	4.47680i		−	0.391139i	0.980690	−	0.195570i	$-0.0626556\pi$
$132$	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	$0.136451\pi$
$139$			9.80123i			0.831329i	−0.909518	+	0.415665i	$0.863549\pi$
$140$	5.19399	+	1.01119i	0.438972	+	0.0854609i
$141$		−	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
$154$	−0.0481214	−	12.5190i	−0.00387774	−	1.00881i
$155$	−2.52241			−0.202604
$156$	9.54677	−	23.0776i	0.764354	−	1.84768i
$157$	−9.98993			−0.797283			−0.398642	−	0.917107i	$-0.630518\pi$
$157$	−9.98993			−0.797283			−0.398642	+	0.917107i	$0.630518\pi$
$158$	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	$-0.205536\pi$
$167$	20.6423			1.59735			0.798673	+	0.601765i	$0.205536\pi$
$168$	−22.1613	−	9.06815i	−1.70978	−	0.699623i
$169$	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	$-0.652367\pi$
$173$	−12.1166			−0.921205			−0.460602	+	0.887607i	$0.652367\pi$
$174$	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	$-0.829494\pi$
$181$	−23.1384			−1.71986			−0.859932	+	0.510408i	$0.829494\pi$
$182$	−0.0561271	−	14.6018i	−0.00416042	−	1.08235i
$183$		−	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
$196$	−13.9996	+	0.107626i	−0.999970	+	0.00768760i
$197$			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	$-0.444476\pi$
$199$	4.89644			0.347099			0.173550	+	0.984825i	$0.444476\pi$
$200$	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
$210$	−11.9723	+	0.0460200i	−0.826170	+	0.00317568i
$211$	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	$-0.805870\pi$
$223$	−24.4820			−1.63944			−0.819718	+	0.572768i	$0.805870\pi$
$224$	−10.5326	+	10.6332i	−0.703739	+	0.710458i
$225$	−7.23851			−0.482567
$226$	1.89026	−	9.51426i	0.125738	−	0.632879i
$227$			5.16178i			0.342599i	0.985219	+	0.171300i	$0.0547966\pi$
$227$			5.16178i			0.342599i	−0.985219	+	0.171300i	$0.945203\pi$
$228$	37.4722	+	15.5016i	2.48166	+	1.02662i
$229$	−9.48995			−0.627114			−0.313557	−	0.949569i	$-0.601521\pi$
$229$	−9.48995			−0.627114			−0.313557	+	0.949569i	$0.601521\pi$
$230$	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
$238$	10.9627	−	0.0421390i	0.710606	−	0.00273147i
$239$			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	$0.0273815\pi$
$241$			2.66753i			0.171831i	−0.996302	+	0.0859155i	$0.972619\pi$
$242$	−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	$-0.913318\pi$
$251$		−	8.52244i		−	0.537932i	0.963150	−	0.268966i	$-0.0866819\pi$
$252$	37.5967	+	7.31948i	2.36837	+	0.461084i
$253$		−	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	$-0.854538\pi$
$257$		−	14.1473i		−	0.882487i	0.897387	−	0.441244i	$-0.145462\pi$
$258$	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
$266$	23.7097	−	0.0911365i	1.45373	−	0.00558794i
$267$	−6.42262			−0.393058
$268$	−11.7817	−	4.87389i	−0.719684	−	0.297720i
$269$	1.39567			0.0850956			0.0425478	−	0.999094i	$-0.486453\pi$
$269$	1.39567			0.0850956			0.0425478	+	0.999094i	$0.486453\pi$
$270$	18.8122	+	3.73755i	1.14487	+	0.227460i
$271$	22.4663			1.36473			0.682366	−	0.731011i	$-0.260951\pi$
$271$	22.4663			1.36473			0.682366	+	0.731011i	$0.260951\pi$
$272$	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
$280$	−2.83400	+	6.92592i	−0.169364	+	0.413903i
$281$	−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	$-0.902151\pi$
$283$		−	10.1804i		−	0.605164i	0.953123	−	0.302582i	$-0.0978486\pi$
$284$	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	$-0.146270\pi$
$293$	30.6832			1.79253			0.896266	+	0.443518i	$0.146270\pi$
$294$	31.0205	−	6.41131i	1.80915	−	0.373915i
$295$		−	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	$0.264251\pi$
$307$			25.8632i			1.47609i	−0.674750	+	0.738046i	$0.735749\pi$
$308$	17.3785	+	3.38331i	0.990230	+	0.192782i
$309$			1.29139i			0.0734644i
$310$	0.695136	−	3.49883i	0.0394811	−	0.198720i
$311$	−10.8246			−0.613806			−0.306903	−	0.951741i	$-0.599293\pi$
$311$	−10.8246			−0.613806			−0.306903	+	0.951741i	$0.599293\pi$
$312$	29.3800	+	19.6022i	1.66331	+	1.10975i
$313$			27.8999i			1.57699i	0.615038	+	0.788497i	$0.289141\pi$
$313$			27.8999i			1.57699i	−0.615038	+	0.788497i	$0.710859\pi$
$314$	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
$322$	−12.8952	+	0.0495675i	−0.718624	+	0.00276229i
$323$	−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
$336$	18.6858	−	28.2410i	1.01939	−	1.54067i
$337$	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	$-0.355465\pi$
$349$	16.3885			0.877255			0.438627	+	0.898669i	$0.355465\pi$
$350$	0.0143823	+	3.74163i	0.000768766	+	0.199999i
$351$		−	52.9268i		−	2.82502i
$352$	15.7254	−	10.5332i	0.838168	−	0.561422i
$353$			3.84670i			0.204739i	0.994746	+	0.102370i	$0.0326425\pi$
$353$			3.84670i			0.204739i	−0.994746	+	0.102370i	$0.967358\pi$
$354$	−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
$364$	20.2696	+	3.94617i	1.06242	+	0.206836i
$365$			5.91619i			0.309668i
$366$	35.3845	+	7.03008i	1.84958	+	0.367468i
$367$	−2.94732			−0.153849			−0.0769244	−	0.997037i	$-0.524510\pi$
$367$	−2.94732			−0.153849			−0.0769244	+	0.997037i	$0.524510\pi$
$368$	−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
$378$	−50.7449	+	0.195056i	−2.61003	+	0.0100326i
$379$	−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	$-0.405725\pi$
$383$	11.4237			0.583724			0.291862	+	0.956460i	$0.405725\pi$
$384$	−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
$392$	3.70878	−	19.4485i	0.187322	−	0.982299i
$393$	−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	$-0.230167\pi$
$397$	29.8779			1.49953			0.749763	+	0.661706i	$0.230167\pi$
$398$	−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
$406$	10.0324	−	0.0385632i	0.497901	−	0.00191386i
$407$			15.7559i			0.780993i
$408$	−14.7169	+	22.0579i	−0.728595	+	1.09203i
$409$			26.9755i			1.33385i	0.745123	+	0.666927i	$0.232391\pi$
$409$			26.9755i			1.33385i	−0.745123	+	0.666927i	$0.767609\pi$
$410$	−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	$0.119806\pi$
$419$			15.0474i			0.735114i	−0.930001	+	0.367557i	$0.880194\pi$
$420$	3.23556	−	16.6195i	0.157879	−	0.810951i
$421$			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	$-0.809247\pi$
$433$		−	23.4737i		−	1.12808i	0.825749	−	0.564038i	$-0.190753\pi$
$434$	0.0362780	+	9.43791i	0.00174140	+	0.453034i
$435$	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	$-0.404786\pi$
$439$	12.3485			0.589363			0.294681	+	0.955596i	$0.404786\pi$
$440$	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
$448$	−11.8467	−	17.5401i	−0.559702	−	0.828694i
$449$	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	$-0.536469\pi$
$461$	−4.90911			−0.228640			−0.114320	+	0.993444i	$0.536469\pi$
$462$	−40.0580	+	0.153977i	−1.86367	+	0.00716367i
$463$			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	$-0.842796\pi$
$467$		−	20.4881i		−	0.948078i	0.880504	−	0.474039i	$-0.157204\pi$
$468$	−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
$476$	−2.96270	+	15.2180i	−0.135795	+	0.697515i
$477$		−	82.6171i		−	3.78278i
$478$	−11.3128	−	2.24759i	−0.517437	−	0.102803i
$479$	35.1704			1.60698			0.803489	−	0.595319i	$-0.202974\pi$
$479$	35.1704			1.60698			0.803489	+	0.595319i	$0.202974\pi$
$480$	−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
$490$	−2.00368	−	9.69460i	−0.0905171	−	0.437957i
$491$	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	$-0.448445\pi$
$503$	7.23320			0.322513			0.161256	+	0.986913i	$0.448445\pi$
$504$	−20.5140	+	50.1334i	−0.913764	+	2.23312i
$505$	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	$-0.698924\pi$
$509$	−26.3986			−1.17010			−0.585048	+	0.810999i	$0.698924\pi$
$510$	−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
$518$	17.6195	−	0.0677270i	0.774158	−	0.00297575i
$519$			38.7702i			1.70182i
$520$	6.12613	−	9.18191i	0.268648	−	0.402654i
$521$		−	29.5635i		−	1.29520i	−0.761981	−	0.647599i	$-0.775773\pi$
$521$		−	29.5635i		−	1.29520i	0.761981	−	0.647599i	$-0.224227\pi$
$522$	−26.9217	−	5.34872i	−1.17833	−	0.234107i
$523$		−	21.6311i		−	0.945862i	−0.881100	−	0.472931i	$-0.843196\pi$
$523$		−	21.6311i		−	0.945862i	0.881100	−	0.472931i	$-0.156804\pi$
$524$	−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
$532$	−6.40760	+	32.9128i	−0.277805	+	1.42695i
$533$			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
$546$	−46.7222	+	0.179594i	−1.99953	+	0.00768590i
$547$	−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
$560$	−8.82596	−	5.83973i	−0.372965	−	0.246774i
$561$	31.3679			1.32435
$562$	1.61188	−	8.11306i	0.0679928	−	0.342229i
$563$			28.5884i			1.20486i	0.798172	+	0.602429i	$0.205800\pi$
$563$			28.5884i			1.20486i	−0.798172	+	0.602429i	$0.794200\pi$
$564$	−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
$574$	20.9244	−	0.0804304i	0.873367	−	0.00335710i
$575$			3.44642i			0.143726i
$576$	22.2332	+	53.4699i	0.926385	+	2.22791i
$577$		−	2.55301i		−	0.106283i	−0.998587	−	0.0531417i	$-0.983076\pi$
$577$		−	2.55301i		−	0.106283i	0.998587	−	0.0531417i	$-0.0169235\pi$
$578$	−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	$-0.758372\pi$
$587$		−	33.3508i		−	1.37653i	0.725457	−	0.688267i	$-0.241628\pi$
$588$	0.344379	+	44.7954i	0.0142020	+	1.84733i
$589$		−	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	$-0.927917\pi$
$593$		−	10.9350i		−	0.449048i	0.974469	−	0.224524i	$-0.0720827\pi$
$594$	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	$0.0436464\pi$
$601$			6.70199i			0.273380i	−0.990614	+	0.136690i	$0.956354\pi$
$602$	0.124039	+	32.2693i	0.00505543	+	1.31520i
$603$	−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	$-0.774998\pi$
$607$	−37.4686			−1.52080			−0.760402	+	0.649453i	$0.774998\pi$
$608$	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
$616$	−9.48224	+	23.1733i	−0.382050	+	0.933680i
$617$	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	$-0.832202\pi$
$619$		−	25.0328i		−	1.00615i	0.864242	−	0.503076i	$-0.167798\pi$
$620$	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
$630$	0.104106	+	27.0838i	0.00414769	+	1.07905i
$631$			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	$0.0537024\pi$
$643$			8.51562i			0.335823i	−0.985802	+	0.167912i	$0.946298\pi$
$644$	3.48498	−	17.9007i	0.137327	−	0.705386i
$645$			27.5960i			1.08659i
$646$	5.11654	−	25.7531i	0.201307	−	1.01324i
$647$	−9.29106			−0.365269			−0.182635	−	0.983181i	$-0.558463\pi$
$647$	−9.29106			−0.365269			−0.182635	+	0.983181i	$0.558463\pi$
$648$	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
$658$	0.00728811	+	1.89604i	0.000284120	+	0.0739154i
$659$	−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	$-0.311912\pi$
$661$	28.6462			1.11421			0.557104	+	0.830443i	$0.311912\pi$
$662$	−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
$672$	34.0237	+	33.7019i	1.31249	+	1.30008i
$673$	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	$-0.351803\pi$
$677$	23.3619			0.897870			0.448935	+	0.893564i	$0.351803\pi$
$678$	−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
$686$	10.2905	+	24.0854i	0.392894	+	0.919584i
$687$			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	$0.265118\pi$
$691$			38.8983i			1.47976i	−0.672738	+	0.739881i	$0.734882\pi$
$692$	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
$700$	−5.19399	−	1.01119i	−0.196314	−	0.0382193i
$701$		−	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
$714$	−0.134835	−	35.0781i	−0.00504607	−	1.31276i
$715$	−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	$-0.699697\pi$
$719$	−31.4806			−1.17403			−0.587014	+	0.809577i	$0.699697\pi$
$720$	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	$-0.488352\pi$
$727$	1.97285			0.0731689			0.0365844	+	0.999331i	$0.488352\pi$
$728$	−11.0597	+	27.0285i	−0.409901	+	1.00174i
$729$	−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	$-0.506141\pi$
$733$	−1.04466			−0.0385855			−0.0192928	+	0.999814i	$0.506141\pi$
$734$	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
$742$	−42.7053	+	0.164153i	−1.56776	+	0.00602625i
$743$		−	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
$756$	13.7140	−	70.4421i	0.498772	−	2.56195i
$757$		−	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	$0.0556543\pi$
$761$			9.59745i			0.347907i	−0.984754	+	0.173954i	$0.944346\pi$
$762$	−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	$0.312008\pi$
$769$			46.0671i			1.66122i	−0.556854	+	0.830610i	$0.687992\pi$
$770$	0.0481214	+	12.5190i	0.00173418	+	0.451155i
$771$	−45.2682			−1.63029
$772$	13.6492	+	5.64642i	0.491244	+	0.203219i
$773$	7.98484			0.287195			0.143597	−	0.989636i	$-0.454133\pi$
$773$	7.98484			0.287195			0.143597	+	0.989636i	$0.454133\pi$
$774$	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
$784$	25.9550	+	10.5042i	0.926964	+	0.375149i
$785$	9.98993			0.356556
$786$	3.94767	−	19.8698i	0.140809	−	0.708733i
$787$			56.0482i			1.99790i	0.0457828	+	0.998951i	$0.485422\pi$
$787$			56.0482i			1.99790i	−0.0457828	+	0.998951i	$0.514578\pi$
$788$	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	$-0.361900\pi$
$797$	23.7352			0.840744			0.420372	+	0.907352i	$0.361900\pi$
$798$	−0.291616	−	75.8654i	−0.0103231	−	2.68560i
$799$		−	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	$-0.901335\pi$
$811$		−	17.3731i		−	0.610054i	0.952344	−	0.305027i	$-0.0986655\pi$
$812$	−2.71129	+	13.9266i	−0.0951478	+	0.488729i
$813$		−	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
$826$	−3.00181	+	0.0115385i	−0.104446	+	0.000401477i
$827$	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	$-0.475405\pi$
$829$	4.44507			0.154384			0.0771919	+	0.997016i	$0.475405\pi$
$830$	−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	$-0.550947\pi$
$839$	−9.23265			−0.318746			−0.159373	+	0.987218i	$0.550947\pi$
$840$	22.1613	+	9.06815i	0.764639	+	0.312881i
$841$	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	$-0.529112\pi$
$853$	−5.33487			−0.182662			−0.0913312	+	0.995821i	$0.529112\pi$
$854$	0.114661	+	29.8296i	0.00392361	+	1.02075i
$855$		−	45.8684i		−	1.56867i
$856$	28.1102	−	42.1320i	0.960788	−	1.44004i
$857$		−	3.81449i		−	0.130301i	−0.997875	−	0.0651503i	$-0.979247\pi$
$857$		−	3.81449i		−	0.130301i	0.997875	−	0.0651503i	$-0.0207527\pi$
$858$	57.9538	+	11.5141i	1.97851	+	0.393084i
$859$		−	40.9650i		−	1.39771i	−0.715264	−	0.698854i	$-0.753694\pi$
$859$		−	40.9650i		−	1.39771i	0.715264	−	0.698854i	$-0.246306\pi$
$860$	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
$868$	−13.1013	−	2.55062i	−0.444688	−	0.0865738i
$869$			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	$0.102824\pi$
$881$			18.8445i			0.634887i	−0.948277	+	0.317443i	$0.897176\pi$
$882$	−14.5037	−	70.1744i	−0.488364	−	2.36290i
$883$	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	$-0.617972\pi$
$887$	−21.5740			−0.724385			−0.362193	+	0.932103i	$0.617972\pi$
$888$	−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
$896$	27.5947	−	11.5987i	0.921875	−	0.387487i
$897$	−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
$910$	0.0561271	+	14.6018i	0.00186059	+	0.484044i
$911$		−	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
$924$	10.8258	−	55.6070i	0.356143	−	1.82934i
$925$		−	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	$-0.786591\pi$
$929$		−	37.8759i		−	1.24267i	0.783546	−	0.621334i	$-0.213409\pi$
$930$	−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	$-0.633243\pi$
$937$		−	55.9352i		−	1.82732i	0.406476	−	0.913661i	$-0.366757\pi$
$938$	0.0916875	+	23.8530i	0.00299370	+	0.778828i
$939$	89.2731			2.91332
$940$	0.936513	+	0.387419i	0.0305457	+	0.0126362i
$941$	−60.3400			−1.96703			−0.983514	−	0.180831i	$-0.942121\pi$
$941$	−60.3400			−1.96703			−0.983514	+	0.180831i	$0.942121\pi$
$942$	−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
$952$	−20.2924	−	8.30342i	−0.657682	−	0.269115i
$953$	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
$966$	0.158604	+	41.2618i	0.00510301	+	1.32758i
$967$			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	$0.0466609\pi$
$971$			9.10304i			0.292130i	−0.989275	+	0.146065i	$0.953339\pi$
$972$	−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
$980$	13.9996	−	0.107626i	0.447200	−	0.00343800i
$981$			104.279i			3.32938i
$982$	−0.796419	+	4.00862i	−0.0254147	+	0.127920i
$983$	−11.4686			−0.365792			−0.182896	−	0.983132i	$-0.558547\pi$
$983$	−11.4686			−0.365792			−0.182896	+	0.983132i	$0.558547\pi$
$984$	−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
$994$	−4.18693	+	0.0160939i	−0.132801	+	0.000510469i
$995$	−4.89644			−0.155228
$996$	25.3844	+	10.5011i	0.804335	+	0.332739i
$997$	−51.3033			−1.62479			−0.812395	−	0.583107i	$-0.801837\pi$
$997$	−51.3033			−1.62479			−0.812395	+	0.583107i	$0.801837\pi$
$998$	−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.a.251.8	yes	16
4.3	odd	2		1120.2.h.a.111.16		16
7.6	odd	2		280.2.h.b.251.8	yes	16
8.3	odd	2		280.2.h.b.251.7	yes	16
8.5	even	2		1120.2.h.b.111.16		16
28.27	even	2		1120.2.h.b.111.1		16
56.13	odd	2		1120.2.h.a.111.1		16
56.27	even	2	inner	280.2.h.a.251.7	✓	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.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} +(0.0143823 + 3.74163i) 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} +(-5.19399 - 1.01119i) 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} +(11.9723 - 0.0460200i) 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} +(2.83400 - 6.92592i) 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} +(-0.0143823 - 3.74163i) 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} +(-3.23556 + 16.6195i) 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} +(2.00368 + 9.69460i) 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	\( 16 q + q^{2} + q^{4} - 16 q^{5} + q^{8} - 16 q^{9} - q^{10} - 4 q^{11} - 14 q^{12} + 7 q^{14} + 9 q^{16} - 15 q^{18} - q^{20} + 4 q^{21} + 6 q^{22} - 22 q^{24} + 16 q^{25} + 20 q^{26} - 3 q^{28} + 16 q^{31} - 19 q^{32} + 14 q^{34} + 15 q^{36} + 30 q^{38} - q^{40} + 20 q^{42} - 4 q^{43} - 20 q^{44} + 16 q^{45} + 6 q^{46} + 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} + 38 q^{52} - 26 q^{54} + 4 q^{55} + q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} + 8 q^{61} - 28 q^{62} - 28 q^{63} - 23 q^{64} - 46 q^{66} + 20 q^{67} - 12 q^{68} + 40 q^{69} - 7 q^{70} - 13 q^{72} - 28 q^{74} - 34 q^{76} + 4 q^{77} - 6 q^{78} - 9 q^{80} + 24 q^{81} + 16 q^{82} + 10 q^{84} - 24 q^{86} - 72 q^{87} - 44 q^{88} + 15 q^{90} - 32 q^{91} - 30 q^{92} + 58 q^{94} + 30 q^{96} - 39 q^{98} + 20 q^{99}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

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