LMFDB - Embedded newform 280.2.l.a.29.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(29,280)]

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([0, 1, 1, 0]))

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

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

chi := DirichletCharacter("280.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.l (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:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.7
Character	$\chi$	$=$	280.29
Dual form			280.2.l.a.29.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23615 - 0.686976i) q^{2} -0.359051 q^{3} +(1.05613 + 1.69841i) q^{4} +(0.565870 + 2.16328i) q^{5} +(0.443841 + 0.246660i) q^{6} +1.00000i q^{7} +(-0.138765 - 2.82502i) q^{8} -2.87108 q^{9} +O(q^{10})$	\(q+(-1.23615 - 0.686976i) q^{2} -0.359051 q^{3} +(1.05613 + 1.69841i) q^{4} +(0.565870 + 2.16328i) q^{5} +(0.443841 + 0.246660i) q^{6} +1.00000i q^{7} +(-0.138765 - 2.82502i) q^{8} -2.87108 q^{9} +(0.786624 - 3.06288i) q^{10} +1.56633i q^{11} +(-0.379204 - 0.609816i) q^{12} -6.61390 q^{13} +(0.686976 - 1.23615i) q^{14} +(-0.203176 - 0.776730i) q^{15} +(-1.76919 + 3.58747i) q^{16} +2.81650i q^{17} +(3.54908 + 1.97236i) q^{18} -5.37478i q^{19} +(-3.07651 + 3.24578i) q^{20} -0.359051i q^{21} +(1.07603 - 1.93621i) q^{22} +5.85959i q^{23} +(0.0498236 + 1.01433i) q^{24} +(-4.35958 + 2.44827i) q^{25} +(8.17577 + 4.54359i) q^{26} +2.10802 q^{27} +(-1.69841 + 1.05613i) q^{28} +6.75241i q^{29} +(-0.282438 + 1.09973i) q^{30} +9.18842 q^{31} +(4.65149 - 3.21926i) q^{32} -0.562392i q^{33} +(1.93487 - 3.48161i) q^{34} +(-2.16328 + 0.565870i) q^{35} +(-3.03223 - 4.87627i) q^{36} +2.55059 q^{37} +(-3.69235 + 6.64403i) q^{38} +2.37473 q^{39} +(6.03280 - 1.89878i) q^{40} -7.93914 q^{41} +(-0.246660 + 0.443841i) q^{42} -7.16596 q^{43} +(-2.66026 + 1.65424i) q^{44} +(-1.62466 - 6.21096i) q^{45} +(4.02540 - 7.24333i) q^{46} +5.24048i q^{47} +(0.635230 - 1.28809i) q^{48} -1.00000 q^{49} +(7.07100 - 0.0315008i) q^{50} -1.01127i q^{51} +(-6.98513 - 11.2331i) q^{52} +7.46352 q^{53} +(-2.60583 - 1.44816i) q^{54} +(-3.38841 + 0.886337i) q^{55} +(2.82502 - 0.138765i) q^{56} +1.92982i q^{57} +(4.63875 - 8.34699i) q^{58} -3.87153i q^{59} +(1.10462 - 1.16540i) q^{60} -4.69888i q^{61} +(-11.3583 - 6.31222i) q^{62} -2.87108i q^{63} +(-7.96149 + 0.784026i) q^{64} +(-3.74261 - 14.3077i) q^{65} +(-0.386350 + 0.695200i) q^{66} +9.92629 q^{67} +(-4.78357 + 2.97458i) q^{68} -2.10390i q^{69} +(3.06288 + 0.786624i) q^{70} +11.4198 q^{71} +(0.398405 + 8.11087i) q^{72} +3.67765i q^{73} +(-3.15291 - 1.75220i) q^{74} +(1.56531 - 0.879056i) q^{75} +(9.12858 - 5.67646i) q^{76} -1.56633 q^{77} +(-2.93552 - 1.63138i) q^{78} -8.46205 q^{79} +(-8.76185 - 1.79721i) q^{80} +7.85636 q^{81} +(9.81395 + 5.45400i) q^{82} +1.20987 q^{83} +(0.609816 - 0.379204i) q^{84} +(-6.09289 + 1.59377i) q^{85} +(8.85819 + 4.92284i) q^{86} -2.42446i q^{87} +(4.42491 - 0.217351i) q^{88} -4.21600 q^{89} +(-2.25846 + 8.79377i) q^{90} -6.61390i q^{91} +(-9.95199 + 6.18848i) q^{92} -3.29912 q^{93} +(3.60009 - 6.47802i) q^{94} +(11.6272 - 3.04143i) q^{95} +(-1.67012 + 1.15588i) q^{96} -5.89207i q^{97} +(1.23615 + 0.686976i) q^{98} -4.49705i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.23615	−	0.686976i	−0.874089	−	0.485765i
$2$	−1.23615	−	0.686976i	−0.874089	−	0.485765i
$3$	−0.359051			−0.207298			−0.103649	−	0.994614i	$-0.533052\pi$
$3$	−0.359051			−0.207298			−0.103649	+	0.994614i	$0.533052\pi$
$4$	1.05613	+	1.69841i	0.528064	+	0.849205i
$5$	0.565870	+	2.16328i	0.253065	+	0.967449i
$5$	0.565870	+	2.16328i	0.253065	+	0.967449i
$6$	0.443841	+	0.246660i	0.181197	+	0.100698i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−0.138765	−	2.82502i	−0.0490607	−	0.998796i
$9$	−2.87108			−0.957027
$10$	0.786624	−	3.06288i	0.248752	−	0.968567i
$11$			1.56633i			0.472265i	0.971721	+	0.236133i	$0.0758800\pi$
$11$			1.56633i			0.472265i	−0.971721	+	0.236133i	$0.924120\pi$
$12$	−0.379204	−	0.609816i	−0.109467	−	0.176039i
$13$	−6.61390			−1.83437			−0.917183	−	0.398465i	$-0.869543\pi$
$13$	−6.61390			−1.83437			−0.917183	+	0.398465i	$0.869543\pi$
$14$	0.686976	−	1.23615i	0.183602	−	0.330375i
$15$	−0.203176	−	0.776730i	−0.0524599	−	0.200551i
$16$	−1.76919	+	3.58747i	−0.442297	+	0.896869i
$17$			2.81650i			0.683102i	0.939863	+	0.341551i	$0.110952\pi$
$17$			2.81650i			0.683102i	−0.939863	+	0.341551i	$0.889048\pi$
$18$	3.54908	+	1.97236i	0.836527	+	0.464891i
$19$		−	5.37478i		−	1.23306i	−0.787331	−	0.616530i	$-0.788538\pi$
$19$		−	5.37478i		−	1.23306i	0.787331	−	0.616530i	$-0.211462\pi$
$20$	−3.07651	+	3.24578i	−0.687928	+	0.725779i
$21$		−	0.359051i		−	0.0783515i
$22$	1.07603	−	1.93621i	0.229410	−	0.412802i
$23$			5.85959i			1.22181i	0.791704	+	0.610905i	$0.209194\pi$
$23$			5.85959i			1.22181i	−0.791704	+	0.610905i	$0.790806\pi$
$24$	0.0498236	+	1.01433i	0.0101702	+	0.207049i
$25$	−4.35958	+	2.44827i	−0.871917	+	0.489655i
$26$	8.17577	+	4.54359i	1.60340	+	0.891072i
$27$	2.10802			0.405689
$28$	−1.69841	+	1.05613i	−0.320969	+	0.199589i
$29$			6.75241i			1.25389i	0.779063	+	0.626946i	$0.215695\pi$
$29$			6.75241i			1.25389i	−0.779063	+	0.626946i	$0.784305\pi$
$30$	−0.282438	+	1.09973i	−0.0515660	+	0.200782i
$31$	9.18842			1.65029			0.825144	−	0.564922i	$-0.191094\pi$
$31$	9.18842			1.65029			0.825144	+	0.564922i	$0.191094\pi$
$32$	4.65149	−	3.21926i	0.822275	−	0.569091i
$33$		−	0.562392i		−	0.0978999i
$34$	1.93487	−	3.48161i	0.331827	−	0.597092i
$35$	−2.16328	+	0.565870i	−0.365661	+	0.0956495i
$36$	−3.03223	−	4.87627i	−0.505372	−	0.812712i
$37$	2.55059			0.419315			0.209657	−	0.977775i	$-0.432765\pi$
$37$	2.55059			0.419315			0.209657	+	0.977775i	$0.432765\pi$
$38$	−3.69235	+	6.64403i	−0.598978	+	1.07780i
$39$	2.37473			0.380261
$40$	6.03280	−	1.89878i	0.953869	−	0.300224i
$41$	−7.93914			−1.23988			−0.619942	−	0.784647i	$-0.712844\pi$
$41$	−7.93914			−1.23988			−0.619942	+	0.784647i	$0.712844\pi$
$42$	−0.246660	+	0.443841i	−0.0380604	+	0.0684862i
$43$	−7.16596			−1.09280			−0.546399	−	0.837525i	$-0.684002\pi$
$43$	−7.16596			−1.09280			−0.546399	+	0.837525i	$0.684002\pi$
$44$	−2.66026	+	1.65424i	−0.401050	+	0.249386i
$45$	−1.62466	−	6.21096i	−0.242190	−	0.925875i
$46$	4.02540	−	7.24333i	0.593513	−	1.06797i
$47$			5.24048i			0.764403i	0.924079	+	0.382202i	$0.124834\pi$
$47$			5.24048i			0.764403i	−0.924079	+	0.382202i	$0.875166\pi$
$48$	0.635230	−	1.28809i	0.0916875	−	0.185919i
$49$	−1.00000			−0.142857
$50$	7.07100	−	0.0315008i	0.999990	−	0.00445489i
$51$		−	1.01127i		−	0.141606i
$52$	−6.98513	−	11.2331i	−0.968663	−	1.55775i
$53$	7.46352			1.02519			0.512597	−	0.858630i	$-0.328684\pi$
$53$	7.46352			1.02519			0.512597	+	0.858630i	$0.328684\pi$
$54$	−2.60583	−	1.44816i	−0.354608	−	0.197070i
$55$	−3.38841	+	0.886337i	−0.456893	+	0.119514i
$56$	2.82502	−	0.138765i	0.377509	−	0.0185432i
$57$			1.92982i			0.255611i
$58$	4.63875	−	8.34699i	0.609097	−	1.09601i
$59$		−	3.87153i		−	0.504030i	−0.967723	−	0.252015i	$-0.918907\pi$
$59$		−	3.87153i		−	0.504030i	0.967723	−	0.252015i	$-0.0810932\pi$
$60$	1.10462	−	1.16540i	0.142606	−	0.150453i
$61$		−	4.69888i		−	0.601630i	−0.953682	−	0.300815i	$-0.902741\pi$
$61$		−	4.69888i		−	0.601630i	0.953682	−	0.300815i	$-0.0972587\pi$
$62$	−11.3583	−	6.31222i	−1.44250	−	0.801653i
$63$		−	2.87108i		−	0.361722i
$64$	−7.96149	+	0.784026i	−0.995186	+	0.0980032i
$65$	−3.74261	−	14.3077i	−0.464214	−	1.77466i
$66$	−0.386350	+	0.695200i	−0.0475564	+	0.0855732i
$67$	9.92629			1.21269			0.606345	−	0.795202i	$-0.292635\pi$
$67$	9.92629			1.21269			0.606345	+	0.795202i	$0.292635\pi$
$68$	−4.78357	+	2.97458i	−0.580093	+	0.360721i
$69$		−	2.10390i		−	0.253279i
$70$	3.06288	+	0.786624i	0.366084	+	0.0940195i
$71$	11.4198			1.35528			0.677641	−	0.735393i	$-0.263002\pi$
$71$	11.4198			1.35528			0.677641	+	0.735393i	$0.263002\pi$
$72$	0.398405	+	8.11087i	0.0469524	+	0.955875i
$73$			3.67765i			0.430436i	0.976566	+	0.215218i	$0.0690463\pi$
$73$			3.67765i			0.430436i	−0.976566	+	0.215218i	$0.930954\pi$
$74$	−3.15291	−	1.75220i	−0.366519	−	0.203689i
$75$	1.56531	−	0.879056i	0.180747	−	0.101505i
$76$	9.12858	−	5.67646i	1.04712	−	0.651134i
$77$	−1.56633			−0.178500
$78$	−2.93552	−	1.63138i	−0.332382	−	0.184718i
$79$	−8.46205			−0.952055			−0.476028	−	0.879430i	$-0.657924\pi$
$79$	−8.46205			−0.952055			−0.476028	+	0.879430i	$0.657924\pi$
$80$	−8.76185	−	1.79721i	−0.979605	−	0.200934i
$81$	7.85636			0.872929
$82$	9.81395	+	5.45400i	1.08377	+	0.602293i
$83$	1.20987			0.132801			0.0664003	−	0.997793i	$-0.478849\pi$
$83$	1.20987			0.132801			0.0664003	+	0.997793i	$0.478849\pi$
$84$	0.609816	−	0.379204i	0.0665364	−	0.0413746i
$85$	−6.09289	+	1.59377i	−0.660866	+	0.172869i
$86$	8.85819	+	4.92284i	0.955203	+	0.530844i
$87$		−	2.42446i		−	0.259930i
$88$	4.42491	−	0.217351i	0.471697	−	0.0231697i
$89$	−4.21600			−0.446895			−0.223448	−	0.974716i	$-0.571731\pi$
$89$	−4.21600			−0.446895			−0.223448	+	0.974716i	$0.571731\pi$
$90$	−2.25846	+	8.79377i	−0.238063	+	0.926945i
$91$		−	6.61390i		−	0.693326i
$92$	−9.95199	+	6.18848i	−1.03757	+	0.645194i
$93$	−3.29912			−0.342102
$94$	3.60009	−	6.47802i	0.371321	−	0.668157i
$95$	11.6272	−	3.04143i	1.19292	−	0.312044i
$96$	−1.67012	+	1.15588i	−0.170456	+	0.117972i
$97$		−	5.89207i		−	0.598249i	−0.954214	−	0.299125i	$-0.903305\pi$
$97$		−	5.89207i		−	0.598249i	0.954214	−	0.299125i	$-0.0966947\pi$
$98$	1.23615	+	0.686976i	0.124870	+	0.0693951i
$99$		−	4.49705i		−	0.451971i
$100$	−8.76245	−	4.81867i	−0.876245	−	0.481867i
$101$			11.5085i			1.14514i	0.819857	+	0.572568i	$0.194053\pi$
$101$			11.5085i			1.14514i	−0.819857	+	0.572568i	$0.805947\pi$
$102$	−0.694717	+	1.25008i	−0.0687873	+	0.123776i
$103$		−	16.0392i		−	1.58039i	−0.612856	−	0.790194i	$-0.709980\pi$
$103$		−	16.0392i		−	1.58039i	0.612856	−	0.790194i	$-0.290020\pi$
$104$	0.917776	+	18.6844i	0.0899953	+	1.83216i
$105$	0.776730	−	0.203176i	0.0758011	−	0.0198280i
$106$	−9.22602	−	5.12726i	−0.896110	−	0.498003i
$107$	7.93103			0.766722			0.383361	−	0.923599i	$-0.374767\pi$
$107$	7.93103			0.766722			0.383361	+	0.923599i	$0.374767\pi$
$108$	2.22634	+	3.58028i	0.214230	+	0.344513i
$109$			14.1011i			1.35064i	0.737524	+	0.675321i	$0.235995\pi$
$109$			14.1011i			1.35064i	−0.737524	+	0.675321i	$0.764005\pi$
$110$	4.79747	+	1.23211i	0.457421	+	0.117477i
$111$	−0.915794			−0.0869233
$112$	−3.58747	−	1.76919i	−0.338984	−	0.167173i
$113$		−	5.03990i		−	0.474114i	−0.971496	−	0.237057i	$-0.923817\pi$
$113$		−	5.03990i		−	0.474114i	0.971496	−	0.237057i	$-0.0761828\pi$
$114$	1.32574	−	2.38555i	0.124167	−	0.223427i
$115$	−12.6760	+	3.31577i	−1.18204	+	0.309197i
$116$	−11.4684	+	7.13141i	−1.06481	+	0.662135i
$117$	18.9891			1.75554
$118$	−2.65965	+	4.78578i	−0.244840	+	0.440567i
$119$	−2.81650			−0.258188
$120$	−2.16608	+	0.681760i	−0.197736	+	0.0622359i
$121$	8.54662			0.776965
$122$	−3.22802	+	5.80852i	−0.292251	+	0.525879i
$123$	2.85056			0.257026
$124$	9.70414	+	15.6057i	0.871458	+	1.40143i
$125$	−7.76326	−	8.04560i	−0.694367	−	0.719621i
$126$	−1.97236	+	3.54908i	−0.175712	+	0.316178i
$127$			15.6041i			1.38464i	0.721589	+	0.692322i	$0.243412\pi$
$127$			15.6041i			1.38464i	−0.721589	+	0.692322i	$0.756588\pi$
$128$	10.3802	+	4.50018i	0.917488	+	0.397763i
$129$	2.57295			0.226535
$130$	−5.20266	+	20.2576i	−0.456303	+	1.77671i
$131$			8.89546i			0.777200i	0.921406	+	0.388600i	$0.127041\pi$
$131$			8.89546i			0.777200i	−0.921406	+	0.388600i	$0.872959\pi$
$132$	0.955172	−	0.593958i	0.0831370	−	0.0516974i
$133$	5.37478			0.466053
$134$	−12.2704	−	6.81912i	−1.06000	−	0.589083i
$135$	1.19287	+	4.56024i	0.102666	+	0.392483i
$136$	7.95667	−	0.390831i	0.682279	−	0.0335134i
$137$			3.41574i			0.291827i	0.989297	+	0.145913i	$0.0466121\pi$
$137$			3.41574i			0.291827i	−0.989297	+	0.145913i	$0.953388\pi$
$138$	−1.44533	+	2.60073i	−0.123034	+	0.221389i
$139$		−	7.45387i		−	0.632229i	−0.948721	−	0.316115i	$-0.897622\pi$
$139$		−	7.45387i		−	0.632229i	0.948721	−	0.316115i	$-0.102378\pi$
$140$	−3.24578	−	3.07651i	−0.274319	−	0.260012i
$141$		−	1.88160i		−	0.158460i
$142$	−14.1166	−	7.84514i	−1.18464	−	0.658349i
$143$		−	10.3595i		−	0.866308i
$144$	5.07948	−	10.2999i	0.423290	−	0.858328i
$145$	−14.6074	+	3.82099i	−1.21308	+	0.317316i
$146$	2.52646	−	4.54612i	0.209091	−	0.376240i
$147$	0.359051			0.0296141
$148$	2.69375	+	4.33195i	0.221425	+	0.356084i
$149$			8.29609i			0.679643i	0.940490	+	0.339821i	$0.110367\pi$
$149$			8.29609i			0.679643i	−0.940490	+	0.339821i	$0.889633\pi$
$150$	−2.53885	+	0.0113104i	−0.207296	+	0.000923492i
$151$	−12.9015			−1.04991			−0.524953	−	0.851131i	$-0.675917\pi$
$151$	−12.9015			−1.04991			−0.524953	+	0.851131i	$0.675917\pi$
$152$	−15.1839	+	0.745830i	−1.23158	+	0.0604948i
$153$		−	8.08640i		−	0.653747i
$154$	1.93621	+	1.07603i	0.156025	+	0.0867089i
$155$	5.19945	+	19.8771i	0.417630	+	1.59657i
$156$	2.50802	+	4.03327i	0.200802	+	0.322920i
$157$	0.966723			0.0771529			0.0385765	−	0.999256i	$-0.487718\pi$
$157$	0.966723			0.0771529			0.0385765	+	0.999256i	$0.487718\pi$
$158$	10.4604	+	5.81323i	0.832181	+	0.462475i
$159$	−2.67979			−0.212521
$160$	9.59631	+	8.24080i	0.758655	+	0.651493i
$161$	−5.85959			−0.461801
$162$	−9.71163	−	5.39713i	−0.763018	−	0.424039i
$163$	8.61603			0.674859			0.337430	−	0.941351i	$-0.390442\pi$
$163$	8.61603			0.674859			0.337430	+	0.941351i	$0.390442\pi$
$164$	−8.38474	−	13.4839i	−0.654738	−	1.05292i
$165$	1.21661	−	0.318241i	0.0947132	−	0.0247750i
$166$	−1.49558	−	0.831153i	−0.116080	−	0.0645100i
$167$		−	9.95401i		−	0.770264i	−0.922861	−	0.385132i	$-0.874156\pi$
$167$		−	9.95401i		−	0.770264i	0.922861	−	0.385132i	$-0.125844\pi$
$168$	−1.01433	+	0.0498236i	−0.0782571	+	0.00384398i
$169$	30.7437			2.36490
$170$	8.62660	+	2.21553i	0.661630	+	0.169923i
$171$			15.4314i			1.18007i
$172$	−7.56817	−	12.1707i	−0.577067	−	0.928009i
$173$	−4.45378			−0.338614			−0.169307	−	0.985563i	$-0.554153\pi$
$173$	−4.45378			−0.338614			−0.169307	+	0.985563i	$0.554153\pi$
$174$	−1.66555	+	2.99700i	−0.126265	+	0.227202i
$175$	−2.44827	−	4.35958i	−0.185072	−	0.329553i
$176$	−5.61916	−	2.77113i	−0.423560	−	0.208882i
$177$			1.39008i			0.104485i
$178$	5.21161	+	2.89629i	0.390626	+	0.217086i
$179$		−	1.65935i		−	0.124025i	−0.998075	−	0.0620127i	$-0.980248\pi$
$179$		−	1.65935i		−	0.124025i	0.998075	−	0.0620127i	$-0.0197519\pi$
$180$	8.83291	−	9.31890i	0.658366	−	0.694590i
$181$		−	4.87763i		−	0.362551i	−0.983432	−	0.181276i	$-0.941977\pi$
$181$		−	4.87763i		−	0.362551i	0.983432	−	0.181276i	$-0.0580226\pi$
$182$	−4.54359	+	8.17577i	−0.336794	+	0.606028i
$183$			1.68714i			0.124717i
$184$	16.5535	−	0.813104i	1.22034	−	0.0599428i
$185$	1.44330	+	5.51765i	0.106114	+	0.405666i
$186$	4.07820	+	2.26641i	0.299028	+	0.166181i
$187$	−4.41156			−0.322605
$188$	−8.90049	+	5.53462i	−0.649135	+	0.403654i
$189$			2.10802i			0.153336i
$190$	−16.4623	−	4.22793i	−1.19430	−	0.306727i
$191$	−6.29965			−0.455827			−0.227913	−	0.973681i	$-0.573190\pi$
$191$	−6.29965			−0.455827			−0.227913	+	0.973681i	$0.573190\pi$
$192$	2.85858	−	0.281506i	0.206301	−	0.0203159i
$193$			10.8912i			0.783968i	0.919972	+	0.391984i	$0.128211\pi$
$193$			10.8912i			0.783968i	−0.919972	+	0.391984i	$0.871789\pi$
$194$	−4.04771	+	7.28348i	−0.290609	+	0.522923i
$195$	1.34379	+	5.13722i	0.0962308	+	0.367884i
$196$	−1.05613	−	1.69841i	−0.0754377	−	0.121315i
$197$	4.00610			0.285423			0.142711	−	0.989764i	$-0.454418\pi$
$197$	4.00610			0.285423			0.142711	+	0.989764i	$0.454418\pi$
$198$	−3.08937	+	5.55903i	−0.219552	+	0.395063i
$199$	−7.12881			−0.505348			−0.252674	−	0.967551i	$-0.581310\pi$
$199$	−7.12881			−0.505348			−0.252674	+	0.967551i	$0.581310\pi$
$200$	7.52138	+	11.9762i	0.531842	+	0.846844i
$201$	−3.56405			−0.251389
$202$	7.90605	−	14.2262i	0.556268	−	1.00095i
$203$	−6.75241			−0.473926
$204$	1.71755	−	1.06803i	0.120252	−	0.0747770i
$205$	−4.49252	−	17.1746i	−0.313771	−	1.19953i
$206$	−11.0185	+	19.8268i	−0.767698	+	1.38140i
$207$		−	16.8234i		−	1.16931i
$208$	11.7012	−	23.7272i	0.811335	−	1.64519i
$209$	8.41867			0.582332
$210$	−1.09973	−	0.282438i	−0.0758886	−	0.0194901i
$211$		−	1.53304i		−	0.105539i	−0.998607	−	0.0527693i	$-0.983195\pi$
$211$		−	1.53304i		−	0.105539i	0.998607	−	0.0527693i	$-0.0168048\pi$
$212$	7.88243	+	12.6761i	0.541368	+	0.870599i
$213$	−4.10030			−0.280948
$214$	−9.80393	−	5.44843i	−0.670183	−	0.372447i
$215$	−4.05500	−	15.5020i	−0.276549	−	1.05723i
$216$	−0.292519	−	5.95520i	−0.0199034	−	0.405200i
$217$			9.18842i			0.623751i
$218$	9.68712	−	17.4311i	0.656095	−	1.18058i
$219$		−	1.32047i		−	0.0892288i
$220$	−5.08396	−	4.81882i	−0.342760	−	0.324885i
$221$		−	18.6281i		−	1.25306i
$222$	1.13206	+	0.629129i	0.0759787	+	0.0422243i
$223$			20.9653i			1.40394i	0.712205	+	0.701971i	$0.247697\pi$
$223$			20.9653i			1.40394i	−0.712205	+	0.701971i	$0.752303\pi$
$224$	3.21926	+	4.65149i	0.215096	+	0.310791i
$225$	12.5167	−	7.02919i	0.834448	−	0.468613i
$226$	−3.46229	+	6.23007i	−0.230308	+	0.414418i
$227$	−5.85839			−0.388835			−0.194417	−	0.980919i	$-0.562282\pi$
$227$	−5.85839			−0.388835			−0.194417	+	0.980919i	$0.562282\pi$
$228$	−3.27763	+	2.03814i	−0.217066	+	0.134979i
$229$		−	10.2545i		−	0.677636i	−0.940852	−	0.338818i	$-0.889973\pi$
$229$		−	10.2545i		−	0.677636i	0.940852	−	0.338818i	$-0.110027\pi$
$230$	17.9472	+	4.60930i	1.18341	+	0.303928i
$231$	0.562392			0.0370027
$232$	19.0757	−	0.936996i	1.25238	−	0.0615168i
$233$		−	24.1699i		−	1.58342i	−0.610894	−	0.791712i	$-0.709190\pi$
$233$		−	24.1699i		−	1.58342i	0.610894	−	0.791712i	$-0.290810\pi$
$234$	−23.4733	−	13.0450i	−1.53450	−	0.852780i
$235$	−11.3366	+	2.96543i	−0.739521	+	0.193443i
$236$	6.57544	−	4.08883i	0.428024	−	0.266160i
$237$	3.03831			0.197360
$238$	3.48161	+	1.93487i	0.225680	+	0.125419i
$239$	8.33008			0.538828			0.269414	−	0.963024i	$-0.413170\pi$
$239$	8.33008			0.538828			0.269414	+	0.963024i	$0.413170\pi$
$240$	3.14596	+	0.645291i	0.203071	+	0.0416534i
$241$	−2.03927			−0.131361			−0.0656806	−	0.997841i	$-0.520922\pi$
$241$	−2.03927			−0.131361			−0.0656806	+	0.997841i	$0.520922\pi$
$242$	−10.5649	−	5.87132i	−0.679137	−	0.377423i
$243$	−9.14490			−0.586646
$244$	7.98063	−	4.96262i	0.510907	−	0.317699i
$245$	−0.565870	−	2.16328i	−0.0361521	−	0.138207i
$246$	−3.52371	−	1.95827i	−0.224664	−	0.124854i
$247$			35.5483i			2.26188i
$248$	−1.27503	−	25.9575i	−0.0809643	−	1.64830i
$249$	−0.434406			−0.0275294
$250$	4.06941	+	15.2787i	0.257372	+	0.966312i
$251$		−	7.23870i		−	0.456903i	−0.973555	−	0.228451i	$-0.926634\pi$
$251$		−	7.23870i		−	0.456903i	0.973555	−	0.228451i	$-0.0733662\pi$
$252$	4.87627	−	3.03223i	0.307176	−	0.191013i
$253$	−9.17804			−0.577019
$254$	10.7197	−	19.2890i	0.672612	−	1.21030i
$255$	2.18766	−	0.572247i	0.136997	−	0.0358355i
$256$	−9.73995	−	12.6938i	−0.608747	−	0.793365i
$257$			13.6418i			0.850950i	0.904970	+	0.425475i	$0.139893\pi$
$257$			13.6418i			0.850950i	−0.904970	+	0.425475i	$0.860107\pi$
$258$	−3.18055	−	1.76755i	−0.198012	−	0.110043i
$259$			2.55059i			0.158486i
$260$	20.3477	−	21.4673i	1.26191	−	1.33134i
$261$		−	19.3867i		−	1.20001i
$262$	6.11097	−	10.9961i	0.377537	−	0.679342i
$263$			11.1870i			0.689823i	0.938635	+	0.344911i	$0.112091\pi$
$263$			11.1870i			0.689823i	−0.938635	+	0.344911i	$0.887909\pi$
$264$	−1.58877	+	0.0780401i	−0.0977820	+	0.00480304i
$265$	4.22338	+	16.1457i	0.259440	+	0.991823i
$266$	−6.64403	−	3.69235i	−0.407372	−	0.226392i
$267$	1.51376			0.0926407
$268$	10.4834	+	16.8589i	0.640378	+	1.02982i
$269$			15.7803i			0.962141i	0.876682	+	0.481071i	$0.159752\pi$
$269$			15.7803i			0.962141i	−0.876682	+	0.481071i	$0.840248\pi$
$270$	1.65822	−	6.45661i	0.100916	−	0.392937i
$271$	−23.7523			−1.44285			−0.721424	−	0.692494i	$-0.756512\pi$
$271$	−23.7523			−1.44285			−0.721424	+	0.692494i	$0.756512\pi$
$272$	−10.1041	−	4.98292i	−0.612653	−	0.302134i
$273$			2.37473i			0.143725i
$274$	2.34653	−	4.22237i	0.141759	−	0.255083i
$275$	−3.83480	−	6.82853i	−0.231247	−	0.411776i
$276$	3.57328	−	2.22198i	0.215086	−	0.133748i
$277$	4.68755			0.281647			0.140824	−	0.990035i	$-0.455025\pi$
$277$	4.68755			0.281647			0.140824	+	0.990035i	$0.455025\pi$
$278$	−5.12063	+	9.21409i	−0.307115	+	0.552625i
$279$	−26.3807			−1.57937
$280$	1.89878	+	6.03280i	0.113474	+	0.360529i
$281$	−7.98089			−0.476100			−0.238050	−	0.971253i	$-0.576508\pi$
$281$	−7.98089			−0.476100			−0.238050	+	0.971253i	$0.576508\pi$
$282$	−1.29262	+	2.32594i	−0.0769742	+	0.138508i
$283$	2.41657			0.143650			0.0718250	−	0.997417i	$-0.477118\pi$
$283$	2.41657			0.143650			0.0718250	+	0.997417i	$0.477118\pi$
$284$	12.0608	+	19.3955i	0.715676	+	1.15091i
$285$	−4.17475	+	1.09203i	−0.247291	+	0.0646862i
$286$	−7.11675	+	12.8059i	−0.420822	+	0.757231i
$287$		−	7.93914i		−	0.468632i
$288$	−13.3548	+	9.24277i	−0.786940	+	0.544635i
$289$	9.06732			0.533372
$290$	20.6818	+	5.31161i	1.21448	+	0.311908i
$291$			2.11556i			0.124016i
$292$	−6.24616	+	3.88407i	−0.365529	+	0.227298i
$293$	17.1719			1.00319			0.501596	−	0.865102i	$-0.332746\pi$
$293$	17.1719			1.00319			0.501596	+	0.865102i	$0.332746\pi$
$294$	−0.443841	−	0.246660i	−0.0258853	−	0.0143855i
$295$	8.37521	−	2.19078i	0.487623	−	0.127552i
$296$	−0.353932	−	7.20548i	−0.0205719	−	0.418810i
$297$			3.30185i			0.191593i
$298$	5.69922	−	10.2552i	0.330147	−	0.594068i
$299$		−	38.7548i		−	2.24125i
$300$	3.14617	+	1.73015i	0.181644	+	0.0998902i
$301$		−	7.16596i		−	0.413039i
$302$	15.9481	+	8.86300i	0.917712	+	0.510008i
$303$		−	4.13214i		−	0.237385i
$304$	19.2819	+	9.50900i	1.10589	+	0.545379i
$305$	10.1650	−	2.65896i	0.582047	−	0.152251i
$306$	−5.55517	+	9.99600i	−0.317568	+	0.571433i
$307$	4.00966			0.228844			0.114422	−	0.993432i	$-0.463498\pi$
$307$	4.00966			0.228844			0.114422	+	0.993432i	$0.463498\pi$
$308$	−1.65424	−	2.66026i	−0.0942592	−	0.151583i
$309$			5.75890i			0.327612i
$310$	7.22783	−	28.1430i	0.410513	−	1.59842i
$311$	13.6406			0.773487			0.386744	−	0.922187i	$-0.373600\pi$
$311$	13.6406			0.773487			0.386744	+	0.922187i	$0.373600\pi$
$312$	−0.329529	−	6.70867i	−0.0186559	−	0.379804i
$313$			23.4781i			1.32706i	0.748150	+	0.663529i	$0.230942\pi$
$313$			23.4781i			1.32706i	−0.748150	+	0.663529i	$0.769058\pi$
$314$	−1.19501	−	0.664116i	−0.0674385	−	0.0374782i
$315$	6.21096	−	1.62466i	0.349948	−	0.0915392i
$316$	−8.93701	−	14.3720i	−0.502746	−	0.808490i
$317$	−30.6963			−1.72407			−0.862037	−	0.506846i	$-0.830811\pi$
$317$	−30.6963			−1.72407			−0.862037	+	0.506846i	$0.830811\pi$
$318$	3.31262	+	1.84095i	0.185762	+	0.103235i
$319$	−10.5765			−0.592170
$320$	−6.20124	−	16.7793i	−0.346660	−	0.937991i
$321$	−2.84765			−0.158940
$322$	7.24333	+	4.02540i	0.403655	+	0.224327i
$323$	15.1381			0.842306
$324$	8.29732	+	13.3433i	0.460962	+	0.741295i
$325$	28.8339	−	16.1926i	1.59941	−	0.898206i
$326$	−10.6507	−	5.91901i	−0.589887	−	0.327823i
$327$		−	5.06302i		−	0.279986i
$328$	1.10167	+	22.4282i	0.0608296	+	1.23839i
$329$	−5.24048			−0.288917
$330$	−1.72254	−	0.442391i	−0.0948226	−	0.0243528i
$331$			24.2915i			1.33518i	0.744529	+	0.667591i	$0.232674\pi$
$331$			24.2915i			1.33518i	−0.744529	+	0.667591i	$0.767326\pi$
$332$	1.27778	+	2.05486i	0.0701272	+	0.112775i
$333$	−7.32296			−0.401296
$334$	−6.83817	+	12.3046i	−0.374168	+	0.673280i
$335$	5.61699	+	21.4734i	0.306889	+	1.17322i
$336$	1.28809	+	0.635230i	0.0702710	+	0.0346546i
$337$			17.5721i			0.957211i	0.878030	+	0.478606i	$0.158858\pi$
$337$			17.5721i			0.957211i	−0.878030	+	0.478606i	$0.841142\pi$
$338$	−38.0038	−	21.1202i	−2.06714	−	1.14879i
$339$			1.80958i			0.0982831i
$340$	−9.14175	−	8.66499i	−0.495781	−	0.469925i
$341$			14.3921i			0.779374i
$342$	10.6010	−	19.0756i	0.573238	−	1.03149i
$343$		−	1.00000i		−	0.0539949i
$344$	0.994381	+	20.2440i	0.0536134	+	1.09148i
$345$	4.55132	−	1.19053i	0.245035	−	0.0640961i
$346$	5.50553	+	3.05964i	0.295979	+	0.164487i
$347$	−15.8828			−0.852632			−0.426316	−	0.904574i	$-0.640189\pi$
$347$	−15.8828			−0.852632			−0.426316	+	0.904574i	$0.640189\pi$
$348$	4.11773	−	2.56054i	0.220734	−	0.137260i
$349$			7.84033i			0.419684i	0.977735	+	0.209842i	$0.0672949\pi$
$349$			7.84033i			0.419684i	−0.977735	+	0.209842i	$0.932705\pi$
$350$	0.0315008	+	7.07100i	0.00168379	+	0.377961i
$351$	−13.9422			−0.744182
$352$	5.04242	+	7.28575i	0.268762	+	0.388332i
$353$			33.6793i			1.79257i	0.443481	+	0.896284i	$0.353743\pi$
$353$			33.6793i			1.79257i	−0.443481	+	0.896284i	$0.646257\pi$
$354$	0.954950	−	1.71834i	0.0507550	−	0.0913289i
$355$	6.46213	+	24.7043i	0.342974	+	1.31117i
$356$	−4.45264	−	7.16050i	−0.235989	−	0.379506i
$357$	1.01127			0.0535220
$358$	−1.13993	+	2.05120i	−0.0602473	+	0.108409i
$359$	−8.15061			−0.430173			−0.215086	−	0.976595i	$-0.569003\pi$
$359$	−8.15061			−0.430173			−0.215086	+	0.976595i	$0.569003\pi$
$360$	−17.3207	+	5.45156i	−0.912879	+	0.287322i
$361$	−9.88830			−0.520437
$362$	−3.35081	+	6.02947i	−0.176115	+	0.316902i
$363$	−3.06868			−0.161064
$364$	11.2331	−	6.98513i	0.588775	−	0.366120i
$365$	−7.95580	+	2.08107i	−0.416425	+	0.108928i
$366$	1.15903	−	2.08556i	0.0605832	−	0.109014i
$367$		−	15.6223i		−	0.815476i	−0.913099	−	0.407738i	$-0.866318\pi$
$367$		−	15.6223i		−	0.815476i	0.913099	−	0.407738i	$-0.133682\pi$
$368$	−21.0211	−	10.3667i	−1.09580	−	0.540403i
$369$	22.7939			1.18660
$370$	2.00636	−	7.81216i	0.104306	−	0.406135i
$371$			7.46352i			0.387487i
$372$	−3.48429	−	5.60325i	−0.180652	−	0.290515i
$373$	−16.3917			−0.848731			−0.424365	−	0.905491i	$-0.639503\pi$
$373$	−16.3917			−0.848731			−0.424365	+	0.905491i	$0.639503\pi$
$374$	5.45335	+	3.03064i	0.281986	+	0.156711i
$375$	2.78741	+	2.88879i	0.143941	+	0.149176i
$376$	14.8045	−	0.727194i	0.763483	−	0.0375021i
$377$		−	44.6598i		−	2.30010i
$378$	1.44816	−	2.60583i	0.0744853	−	0.134029i
$379$			8.01328i			0.411614i	0.978593	+	0.205807i	$0.0659820\pi$
$379$			8.01328i			0.411614i	−0.978593	+	0.205807i	$0.934018\pi$
$380$	17.4454	+	16.5356i	0.894929	+	0.848257i
$381$		−	5.60269i		−	0.287034i
$382$	7.78731	+	4.32771i	0.398433	+	0.221425i
$383$			3.07386i			0.157067i	0.996911	+	0.0785334i	$0.0250237\pi$
$383$			3.07386i			0.157067i	−0.996911	+	0.0785334i	$0.974976\pi$
$384$	−3.72702	−	1.61580i	−0.190194	−	0.0824558i
$385$	−0.886337	−	3.38841i	−0.0451719	−	0.172689i
$386$	7.48201	−	13.4632i	0.380824	−	0.685258i
$387$	20.5740			1.04584
$388$	10.0072	−	6.22278i	0.508036	−	0.315914i
$389$			21.7340i			1.10196i	0.834519	+	0.550979i	$0.185745\pi$
$389$			21.7340i			1.10196i	−0.834519	+	0.550979i	$0.814255\pi$
$390$	1.86802	−	7.27351i	0.0945909	−	0.368309i
$391$	−16.5036			−0.834621
$392$	0.138765	+	2.82502i	0.00700867	+	0.142685i
$393$		−	3.19393i		−	0.161112i
$394$	−4.95213	−	2.75209i	−0.249485	−	0.138649i
$395$	−4.78842	−	18.3058i	−0.240932	−	0.921065i
$396$	7.63784	−	4.74946i	0.383816	−	0.238670i
$397$	−7.59409			−0.381136			−0.190568	−	0.981674i	$-0.561033\pi$
$397$	−7.59409			−0.381136			−0.190568	+	0.981674i	$0.561033\pi$
$398$	8.81227	+	4.89732i	0.441719	+	0.245481i
$399$	−1.92982			−0.0966120
$400$	−1.07019	−	19.9713i	−0.0535097	−	0.998567i
$401$	−8.08109			−0.403551			−0.201775	−	0.979432i	$-0.564671\pi$
$401$	−8.08109			−0.403551			−0.201775	+	0.979432i	$0.564671\pi$
$402$	4.40570	+	2.44842i	0.219736	+	0.122116i
$403$	−60.7713			−3.02724
$404$	−19.5461	+	12.1544i	−0.972455	+	0.604705i
$405$	4.44568	+	16.9955i	0.220907	+	0.844514i
$406$	8.34699	+	4.63875i	0.414254	+	0.230217i
$407$			3.99506i			0.198028i
$408$	−2.85686	+	0.140328i	−0.141435	+	0.00694729i
$409$	7.52128			0.371903			0.185952	−	0.982559i	$-0.440463\pi$
$409$	7.52128			0.371903			0.185952	+	0.982559i	$0.440463\pi$
$410$	−6.24511	+	24.3166i	−0.308424	+	1.20091i
$411$		−	1.22643i		−	0.0604952i
$412$	27.2411	−	16.9394i	1.34207	−	0.834546i
$413$	3.87153			0.190505
$414$	−11.5573	+	20.7962i	−0.568008	+	1.02208i
$415$	0.684630	+	2.61729i	0.0336072	+	0.128478i
$416$	−30.7645	+	21.2919i	−1.50835	+	1.04392i
$417$			2.67632i			0.131060i
$418$	−10.4067	−	5.78342i	−0.509010	−	0.282877i
$419$		−	12.7649i		−	0.623608i	−0.950146	−	0.311804i	$-0.899067\pi$
$419$		−	12.7649i		−	0.623608i	0.950146	−	0.311804i	$-0.100933\pi$
$420$	1.16540	+	1.10462i	0.0568658	+	0.0539002i
$421$			7.85070i			0.382620i	0.981530	+	0.191310i	$0.0612735\pi$
$421$			7.85070i			0.382620i	−0.981530	+	0.191310i	$0.938726\pi$
$422$	−1.05316	+	1.89506i	−0.0512670	+	0.0922502i
$423$		−	15.0459i		−	0.731555i
$424$	−1.03567	−	21.0846i	−0.0502967	−	1.02396i
$425$	−6.89556	−	12.2788i	−0.334484	−	0.595608i
$426$	5.06858	+	2.81681i	0.245574	+	0.136475i
$427$	4.69888			0.227395
$428$	8.37618	+	13.4701i	0.404878	+	0.651104i
$429$			3.71961i			0.179584i
$430$	−5.63691	+	21.9485i	−0.271836	+	1.05845i
$431$	34.5571			1.66456			0.832279	−	0.554357i	$-0.187036\pi$
$431$	34.5571			1.66456			0.832279	+	0.554357i	$0.187036\pi$
$432$	−3.72949	+	7.56247i	−0.179435	+	0.363850i
$433$		−	18.1662i		−	0.873012i	−0.899701	−	0.436506i	$-0.856216\pi$
$433$		−	18.1662i		−	0.873012i	0.899701	−	0.436506i	$-0.143784\pi$
$434$	6.31222	−	11.3583i	0.302996	−	0.545214i
$435$	5.24480	−	1.37193i	0.251469	−	0.0657790i
$436$	−23.9495	+	14.8926i	−1.14697	+	0.713225i
$437$	31.4941			1.50657
$438$	−0.907128	+	1.63229i	−0.0433443	+	0.0779939i
$439$	25.9865			1.24027			0.620135	−	0.784495i	$-0.287078\pi$
$439$	25.9865			1.24027			0.620135	+	0.784495i	$0.287078\pi$
$440$	2.97411	+	9.44933i	0.141785	+	0.450479i
$441$	2.87108			0.136718
$442$	−12.7970	+	23.0271i	−0.608693	+	1.09529i
$443$	23.9751			1.13909			0.569547	−	0.821959i	$-0.307119\pi$
$443$	23.9751			1.13909			0.569547	+	0.821959i	$0.307119\pi$
$444$	−0.967196	−	1.55539i	−0.0459011	−	0.0738157i
$445$	−2.38571	−	9.12041i	−0.113093	−	0.432349i
$446$	14.4027	−	25.9163i	0.681987	−	1.22717i
$447$		−	2.97873i		−	0.140889i
$448$	−0.784026	−	7.96149i	−0.0370417	−	0.376145i
$449$	−19.3165			−0.911600			−0.455800	−	0.890082i	$-0.650647\pi$
$449$	−19.3165			−0.911600			−0.455800	+	0.890082i	$0.650647\pi$
$450$	−20.3014	+	0.0904415i	−0.957018	+	0.00426345i
$451$		−	12.4353i		−	0.585555i
$452$	8.55982	−	5.32278i	0.402620	−	0.250363i
$453$	4.63229			0.217644
$454$	7.24184	+	4.02457i	0.339876	+	0.188883i
$455$	14.3077	−	3.74261i	0.670757	−	0.175456i
$456$	5.45179	−	0.267791i	0.255304	−	0.0125405i
$457$		−	30.6094i		−	1.43185i	−0.698178	−	0.715924i	$-0.746006\pi$
$457$		−	30.6094i		−	1.43185i	0.698178	−	0.715924i	$-0.253994\pi$
$458$	−7.04459	+	12.6761i	−0.329172	+	0.592314i
$459$			5.93724i			0.277127i
$460$	−19.0190	−	18.0271i	−0.886764	−	0.840517i
$461$		−	7.78457i		−	0.362563i	−0.983431	−	0.181282i	$-0.941975\pi$
$461$		−	7.78457i		−	0.362563i	0.983431	−	0.181282i	$-0.0580246\pi$
$462$	−0.695200	−	0.386350i	−0.0323436	−	0.0179746i
$463$		−	0.248984i		−	0.0115713i	−0.999983	−	0.00578563i	$-0.998158\pi$
$463$		−	0.248984i		−	0.0115713i	0.999983	−	0.00578563i	$-0.00184163\pi$
$464$	−24.2241	−	11.9463i	−1.12458	−	0.554592i
$465$	−1.86687	−	7.13692i	−0.0865740	−	0.330967i
$466$	−16.6042	+	29.8776i	−0.769173	+	1.38405i
$467$	−28.3836			−1.31344			−0.656719	−	0.754136i	$-0.728056\pi$
$467$	−28.3836			−1.31344			−0.656719	+	0.754136i	$0.728056\pi$
$468$	20.0549	+	32.2512i	0.927037	+	1.49081i
$469$			9.92629i			0.458354i
$470$	16.0510	+	4.12229i	0.740376	+	0.190147i
$471$	−0.347103			−0.0159937
$472$	−10.9371	+	0.537231i	−0.503423	+	0.0247280i
$473$		−	11.2242i		−	0.516091i
$474$	−3.75581	−	2.08725i	−0.172510	−	0.0958704i
$475$	13.1589	+	23.4318i	0.603773	+	1.07513i
$476$	−2.97458	−	4.78357i	−0.136340	−	0.219255i
$477$	−21.4284			−0.981138
$478$	−10.2972	−	5.72257i	−0.470984	−	0.261744i
$479$	2.61364			0.119420			0.0597102	−	0.998216i	$-0.480982\pi$
$479$	2.61364			0.119420			0.0597102	+	0.998216i	$0.480982\pi$
$480$	−3.44557	−	2.95887i	−0.157268	−	0.135053i
$481$	−16.8694			−0.769177
$482$	2.52085	+	1.40093i	0.114821	+	0.0638107i
$483$	2.10390			0.0957306
$484$	9.02632	+	14.5157i	0.410287	+	0.659803i
$485$	12.7462	−	3.33415i	0.578776	−	0.151396i
$486$	11.3045	+	6.28233i	0.512781	+	0.284972i
$487$		−	31.2422i		−	1.41572i	−0.706354	−	0.707859i	$-0.749661\pi$
$487$		−	31.2422i		−	1.41572i	0.706354	−	0.707859i	$-0.250339\pi$
$488$	−13.2744	+	0.652039i	−0.600906	+	0.0295164i
$489$	−3.09360			−0.139897
$490$	−0.786624	+	3.06288i	−0.0355360	+	0.138367i
$491$			14.3064i			0.645639i	0.946461	+	0.322820i	$0.104631\pi$
$491$			14.3064i			0.645639i	−0.946461	+	0.322820i	$0.895369\pi$
$492$	3.01055	+	4.84142i	0.135726	+	0.218268i
$493$	−19.0182			−0.856535
$494$	24.4208	−	43.9430i	1.09875	−	1.97709i
$495$	9.72840	−	2.54475i	0.437259	−	0.114378i
$496$	−16.2560	+	32.9632i	−0.729918	+	1.48009i
$497$			11.4198i			0.512249i
$498$	0.536991	+	0.298427i	0.0240631	+	0.0133728i
$499$			3.17323i			0.142053i	0.997474	+	0.0710266i	$0.0226275\pi$
$499$			3.17323i			0.142053i	−0.997474	+	0.0710266i	$0.977372\pi$
$500$	5.46573	−	21.6824i	0.244435	−	0.969666i
$501$			3.57400i			0.159675i
$502$	−4.97282	+	8.94812i	−0.221948	+	0.399374i
$503$			5.14356i			0.229340i	0.993404	+	0.114670i	$0.0365811\pi$
$503$			5.14356i			0.229340i	−0.993404	+	0.114670i	$0.963419\pi$
$504$	−8.11087	+	0.398405i	−0.361287	+	0.0177463i
$505$	−24.8961	+	6.51230i	−1.10786	+	0.289794i
$506$	11.3454	+	6.30510i	0.504366	+	0.280296i
$507$	−11.0386			−0.490241
$508$	−26.5022	+	16.4800i	−1.17585	+	0.731180i
$509$		−	19.4810i		−	0.863481i	−0.901998	−	0.431740i	$-0.857900\pi$
$509$		−	19.4810i		−	0.863481i	0.901998	−	0.431740i	$-0.142100\pi$
$510$	−3.09739	−	0.795488i	−0.137155	−	0.0352248i
$511$	−3.67765			−0.162690
$512$	3.31966	+	22.3826i	0.146710	+	0.989180i
$513$		−	11.3302i		−	0.500239i
$514$	9.37156	−	16.8632i	0.413362	−	0.743806i
$515$	34.6973	−	9.07610i	1.52895	−	0.399941i
$516$	2.71736	+	4.36992i	0.119625	+	0.192375i
$517$	−8.20831			−0.361001
$518$	1.75220	−	3.15291i	0.0769871	−	0.138531i
$519$	1.59914			0.0701942
$520$	−39.9003	+	12.5584i	−1.74975	+	0.550720i
$521$	5.14371			0.225350			0.112675	−	0.993632i	$-0.464058\pi$
$521$	5.14371			0.225350			0.112675	+	0.993632i	$0.464058\pi$
$522$	−13.3182	+	23.9649i	−0.582923	+	1.04891i
$523$	28.4662			1.24474			0.622371	−	0.782722i	$-0.286170\pi$
$523$	28.4662			1.24474			0.622371	+	0.782722i	$0.286170\pi$
$524$	−15.1081	+	9.39475i	−0.660002	+	0.410411i
$525$	0.879056	+	1.56531i	0.0383651	+	0.0683159i
$526$	7.68523	−	13.8289i	0.335092	−	0.602967i
$527$			25.8792i			1.12732i
$528$	2.01757	+	0.994977i	0.0878033	+	0.0433008i
$529$	−11.3349			−0.492820
$530$	5.87098	−	22.8599i	0.255019	−	0.992969i
$531$			11.1155i			0.482370i
$532$	5.67646	+	9.12858i	0.246106	+	0.395774i
$533$	52.5087			2.27440
$534$	−1.87124	−	1.03992i	−0.0809763	−	0.0450017i
$535$	4.48793	+	17.1571i	0.194030	+	0.741764i
$536$	−1.37742	−	28.0420i	−0.0594954	−	1.21123i
$537$			0.595791i			0.0257103i
$538$	10.8407	−	19.5068i	0.467375	−	0.840997i
$539$		−	1.56633i		−	0.0674665i
$540$	−6.48534	+	6.84217i	−0.279085	+	0.294440i
$541$			24.7536i			1.06424i	0.846669	+	0.532120i	$0.178605\pi$
$541$			24.7536i			1.06424i	−0.846669	+	0.532120i	$0.821395\pi$
$542$	29.3613	+	16.3172i	1.26118	+	0.700885i
$543$			1.75132i			0.0751563i
$544$	9.06706	+	13.1009i	0.388747	+	0.561697i
$545$	−30.5047	+	7.97939i	−1.30668	+	0.341800i
$546$	1.63138	−	2.93552i	0.0698168	−	0.125629i
$547$	5.27405			0.225502			0.112751	−	0.993623i	$-0.464034\pi$
$547$	5.27405			0.225502			0.112751	+	0.993623i	$0.464034\pi$
$548$	−5.80133	+	3.60746i	−0.247821	+	0.154103i
$549$			13.4909i			0.575777i
$550$	0.0493406	+	11.0755i	0.00210389	+	0.472261i
$551$	36.2928			1.54612
$552$	−5.94355	+	0.291946i	−0.252974	+	0.0124261i
$553$		−	8.46205i		−	0.359843i
$554$	−5.79451	−	3.22023i	−0.246185	−	0.136815i
$555$	−0.518220	−	1.98112i	−0.0219972	−	0.0840939i
$556$	12.6597	−	7.87224i	0.536892	−	0.333857i
$557$	−30.0692			−1.27407			−0.637037	−	0.770834i	$-0.719840\pi$
$557$	−30.0692			−1.27407			−0.637037	+	0.770834i	$0.719840\pi$
$558$	32.6105	+	18.1229i	1.38051	+	0.767204i
$559$	47.3949			2.00459
$560$	1.79721	−	8.76185i	0.0759460	−	0.370256i
$561$	1.58398			0.0668756
$562$	9.86556	+	5.48268i	0.416154	+	0.231273i
$563$	44.4092			1.87163			0.935813	−	0.352497i	$-0.114667\pi$
$563$	44.4092			1.87163			0.935813	+	0.352497i	$0.114667\pi$
$564$	3.19573	−	1.98721i	0.134565	−	0.0836768i
$565$	10.9027	−	2.85193i	0.458681	−	0.119982i
$566$	−2.98724	−	1.66012i	−0.125563	−	0.0697802i
$567$			7.85636i			0.329936i
$568$	−1.58467	−	32.2612i	−0.0664911	−	1.35365i
$569$	−13.2587			−0.555835			−0.277917	−	0.960605i	$-0.589644\pi$
$569$	−13.2587			−0.555835			−0.277917	+	0.960605i	$0.589644\pi$
$570$	5.91082	+	1.51805i	0.247577	+	0.0635839i
$571$		−	45.2484i		−	1.89359i	−0.321844	−	0.946793i	$-0.604303\pi$
$571$		−	45.2484i		−	1.89359i	0.321844	−	0.946793i	$-0.395697\pi$
$572$	17.5947	−	10.9410i	0.735673	−	0.457466i
$573$	2.26190			0.0944922
$574$	−5.45400	+	9.81395i	−0.227645	+	0.409627i
$575$	−14.3459	−	25.5454i	−0.598265	−	1.06532i
$576$	22.8581	−	2.25100i	0.952420	−	0.0937918i
$577$			6.60929i			0.275148i	0.990491	+	0.137574i	$0.0439305\pi$
$577$			6.60929i			0.275148i	−0.990491	+	0.137574i	$0.956069\pi$
$578$	−11.2086	−	6.22903i	−0.466215	−	0.259094i
$579$		−	3.91051i		−	0.162515i
$580$	−21.9169	−	20.7739i	−0.910048	−	0.862587i
$581$			1.20987i			0.0501939i
$582$	1.45334	−	2.61514i	0.0602428	−	0.108401i
$583$			11.6903i			0.484163i
$584$	10.3894	−	0.510328i	0.429918	−	0.0211175i
$585$	10.7453	+	41.0787i	0.444265	+	1.69840i
$586$	−21.2270	−	11.7967i	−0.876879	−	0.487316i
$587$	9.60737			0.396539			0.198269	−	0.980148i	$-0.436468\pi$
$587$	9.60737			0.396539			0.198269	+	0.980148i	$0.436468\pi$
$588$	0.379204	+	0.609816i	0.0156381	+	0.0251484i
$589$		−	49.3858i		−	2.03491i
$590$	−11.8580	−	3.04544i	−0.488187	−	0.125379i
$591$	−1.43840			−0.0591677
$592$	−4.51248	+	9.15019i	−0.185462	+	0.376070i
$593$		−	8.03743i		−	0.330057i	−0.986289	−	0.165029i	$-0.947228\pi$
$593$		−	8.03743i		−	0.330057i	0.986289	−	0.165029i	$-0.0527717\pi$
$594$	2.26829	−	4.08158i	0.0930691	−	0.167469i
$595$	−1.59377	−	6.09289i	−0.0653383	−	0.249784i
$596$	−14.0902	+	8.76174i	−0.577156	+	0.358895i
$597$	2.55961			0.104758
$598$	−26.6236	+	47.9067i	−1.08872	+	1.95905i
$599$	−17.3922			−0.710628			−0.355314	−	0.934747i	$-0.615626\pi$
$599$	−17.3922			−0.710628			−0.355314	+	0.934747i	$0.615626\pi$
$600$	−2.70056	−	4.30006i	−0.110250	−	0.175549i
$601$	35.8044			1.46049			0.730246	−	0.683184i	$-0.239405\pi$
$601$	35.8044			1.46049			0.730246	+	0.683184i	$0.239405\pi$
$602$	−4.92284	+	8.85819i	−0.200640	+	0.361033i
$603$	−28.4992			−1.16058
$604$	−13.6256	−	21.9120i	−0.554418	−	0.891585i
$605$	4.83627	+	18.4888i	0.196623	+	0.751675i
$606$	−2.83868	+	5.10794i	−0.115313	+	0.207496i
$607$		−	26.4530i		−	1.07369i	−0.843680	−	0.536847i	$-0.819615\pi$
$607$		−	26.4530i		−	1.07369i	0.843680	−	0.536847i	$-0.180385\pi$
$608$	−17.3028	−	25.0007i	−0.701723	−	1.01391i
$609$	2.42446			0.0982442
$610$	−14.3921	−	3.69625i	−0.582719	−	0.149657i
$611$		−	34.6601i		−	1.40220i
$612$	13.7340	−	8.54028i	0.555165	−	0.345220i
$613$	25.8688			1.04483			0.522415	−	0.852692i	$-0.325031\pi$
$613$	25.8688			1.04483			0.522415	+	0.852692i	$0.325031\pi$
$614$	−4.95654	−	2.75454i	−0.200030	−	0.111164i
$615$	1.61305	+	6.16656i	0.0650443	+	0.248660i
$616$	0.217351	+	4.42491i	0.00875731	+	0.178285i
$617$		−	18.3970i		−	0.740636i	−0.928905	−	0.370318i	$-0.879249\pi$
$617$		−	18.3970i		−	0.740636i	0.928905	−	0.370318i	$-0.120751\pi$
$618$	3.95622	−	7.11885i	0.159143	−	0.286362i
$619$		−	7.67375i		−	0.308434i	−0.988037	−	0.154217i	$-0.950715\pi$
$619$		−	7.67375i		−	0.308434i	0.988037	−	0.154217i	$-0.0492855\pi$
$620$	−28.2682	+	29.8236i	−1.13528	+	1.19774i
$621$			12.3521i			0.495675i
$622$	−16.8618	−	9.37077i	−0.676097	−	0.375733i
$623$		−	4.21600i		−	0.168911i
$624$	−4.20135	+	8.51929i	−0.168189	+	0.341045i
$625$	13.0119	−	21.3469i	0.520477	−	0.853876i
$626$	16.1289	−	29.0224i	0.644639	−	1.15997i
$627$	−3.02274			−0.120716
$628$	1.02098	+	1.64189i	0.0407417	+	0.0655186i
$629$			7.18375i			0.286435i
$630$	−8.79377	−	2.25846i	−0.350352	−	0.0899793i
$631$	8.72244			0.347235			0.173617	−	0.984813i	$-0.444454\pi$
$631$	8.72244			0.347235			0.173617	+	0.984813i	$0.444454\pi$
$632$	1.17423	+	23.9055i	0.0467085	+	0.950909i
$633$			0.550439i			0.0218780i
$634$	37.9451	+	21.0876i	1.50699	+	0.837495i
$635$	−33.7562	+	8.82991i	−1.33957	+	0.350404i
$636$	−2.83020	−	4.55138i	−0.112225	−	0.180474i
$637$	6.61390			0.262052
$638$	13.0741	+	7.26579i	0.517609	+	0.287655i
$639$	−32.7872			−1.29704
$640$	−3.86132	+	25.0018i	−0.152632	+	0.988283i
$641$	−22.2480			−0.878745			−0.439372	−	0.898305i	$-0.644799\pi$
$641$	−22.2480			−0.878745			−0.439372	+	0.898305i	$0.644799\pi$
$642$	3.52012	+	1.95627i	0.138928	+	0.0772077i
$643$	22.5513			0.889338			0.444669	−	0.895695i	$-0.353321\pi$
$643$	22.5513			0.889338			0.444669	+	0.895695i	$0.353321\pi$
$644$	−6.18848	−	9.95199i	−0.243860	−	0.392163i
$645$	1.45595	+	5.56601i	0.0573281	+	0.219161i
$646$	−18.7129	−	10.3995i	−0.736250	−	0.409163i
$647$		−	24.5607i		−	0.965582i	−0.875736	−	0.482791i	$-0.839623\pi$
$647$		−	24.5607i		−	0.965582i	0.875736	−	0.482791i	$-0.160377\pi$
$648$	−1.09018	−	22.1944i	−0.0428265	−	0.871878i
$649$	6.06408			0.238036
$650$	−46.7669	+	0.208344i	−1.83435	+	0.00817191i
$651$		−	3.29912i		−	0.129303i
$652$	9.09963	+	14.6335i	0.356369	+	0.573094i
$653$	−35.0350			−1.37102			−0.685512	−	0.728061i	$-0.740422\pi$
$653$	−35.0350			−1.37102			−0.685512	+	0.728061i	$0.740422\pi$
$654$	−3.47818	+	6.25865i	−0.136007	+	0.244733i
$655$	−19.2434	+	5.03368i	−0.751902	+	0.196682i
$656$	14.0458	−	28.4815i	0.548397	−	1.11201i
$657$		−	10.5588i		−	0.411939i
$658$	6.47802	+	3.60009i	0.252539	+	0.140346i
$659$		−	48.9612i		−	1.90726i	−0.300984	−	0.953629i	$-0.597315\pi$
$659$		−	48.9612i		−	1.90726i	0.300984	−	0.953629i	$-0.402685\pi$
$660$	1.82540	+	1.73020i	0.0710537	+	0.0673481i
$661$			1.46917i			0.0571442i	0.999592	+	0.0285721i	$0.00909603\pi$
$661$			1.46917i			0.0571442i	−0.999592	+	0.0285721i	$0.990904\pi$
$662$	16.6877	−	30.0279i	0.648585	−	1.16707i
$663$			6.68843i			0.259757i
$664$	−0.167887	−	3.41791i	−0.00651529	−	0.132641i
$665$	3.04143	+	11.6272i	0.117942	+	0.450883i
$666$	9.05227	+	5.03070i	0.350768	+	0.194936i
$667$	−39.5664			−1.53202
$668$	16.9060	−	10.5127i	0.654112	−	0.406749i
$669$		−	7.52763i		−	0.291035i
$670$	7.80826	−	30.4030i	0.301659	−	1.17457i
$671$	7.35999			0.284129
$672$	−1.15588	−	1.67012i	−0.0445891	−	0.0644264i
$673$		−	48.9411i		−	1.88654i	−0.332024	−	0.943271i	$-0.607731\pi$
$673$		−	48.9411i		−	1.88654i	0.332024	−	0.943271i	$-0.392269\pi$
$674$	12.0716	−	21.7217i	0.464980	−	0.836688i
$675$	−9.19009	+	5.16101i	−0.353727	+	0.198647i
$676$	32.4693	+	52.2154i	1.24882	+	2.00829i
$677$	−18.9487			−0.728259			−0.364129	−	0.931348i	$-0.618633\pi$
$677$	−18.9487			−0.728259			−0.364129	+	0.931348i	$0.618633\pi$
$678$	1.24314	−	2.23692i	0.0477425	−	0.0859082i
$679$	5.89207			0.226117
$680$	5.34792	+	16.9914i	0.205083	+	0.651589i
$681$	2.10346			0.0806049
$682$	9.88701	−	17.7907i	0.378593	−	0.681243i
$683$	43.9995			1.68359			0.841797	−	0.539794i	$-0.181498\pi$
$683$	43.9995			1.68359			0.841797	+	0.539794i	$0.181498\pi$
$684$	−26.2089	+	16.2976i	−1.00212	+	0.623154i
$685$	−7.38922	+	1.93287i	−0.282328	+	0.0738510i
$686$	−0.686976	+	1.23615i	−0.0262289	+	0.0471964i
$687$			3.68189i			0.140473i
$688$	12.6779	−	25.7077i	0.483341	−	0.980096i
$689$	−49.3630			−1.88058
$690$	−6.44398	−	1.65498i	−0.245318	−	0.0630038i
$691$			14.7250i			0.560167i	0.959976	+	0.280083i	$0.0903621\pi$
$691$			14.7250i			0.560167i	−0.959976	+	0.280083i	$0.909638\pi$
$692$	−4.70376	−	7.56434i	−0.178810	−	0.287553i
$693$	4.49705			0.170829
$694$	19.6335	+	10.9111i	0.745276	+	0.414179i
$695$	16.1248	−	4.21792i	0.611650	−	0.159995i
$696$	−6.84916	+	0.336430i	−0.259617	+	0.0127523i
$697$		−	22.3606i		−	0.846968i
$698$	5.38612	−	9.69182i	0.203868	−	0.366841i
$699$			8.67825i			0.328242i
$700$	4.81867	−	8.76245i	0.182128	−	0.331189i
$701$			13.1503i			0.496681i	0.968673	+	0.248340i	$0.0798851\pi$
$701$			13.1503i			0.496681i	−0.968673	+	0.248340i	$0.920115\pi$
$702$	17.2347	+	9.57799i	0.650482	+	0.361498i
$703$		−	13.7089i		−	0.517040i
$704$	−1.22804	−	12.4703i	−0.0462835	−	0.469992i
$705$	4.07044	−	1.06474i	0.153302	−	0.0401005i
$706$	23.1369	−	41.6326i	0.870767	−	1.56686i
$707$	−11.5085			−0.432821
$708$	−2.36092	+	1.46810i	−0.0887288	+	0.0551745i
$709$			41.3756i			1.55389i	0.629567	+	0.776946i	$0.283232\pi$
$709$			41.3756i			1.55389i	−0.629567	+	0.776946i	$0.716768\pi$
$710$	8.98310	−	34.9775i	0.337130	−	1.31268i
$711$	24.2952			0.911143
$712$	0.585032	+	11.9103i	0.0219250	+	0.446357i
$713$			53.8404i			2.01634i
$714$	−1.25008	−	0.694717i	−0.0467830	−	0.0259991i
$715$	22.4106	−	5.86215i	0.838109	−	0.219232i
$716$	2.81825	−	1.75248i	0.105323	−	0.0654934i
$717$	−2.99093			−0.111698
$718$	10.0754	+	5.59927i	0.376009	+	0.208963i
$719$	14.9559			0.557760			0.278880	−	0.960326i	$-0.410037\pi$
$719$	14.9559			0.557760			0.278880	+	0.960326i	$0.410037\pi$
$720$	25.1560	+	5.15994i	0.937509	+	0.192300i
$721$	16.0392			0.597331
$722$	12.2234	+	6.79303i	0.454908	+	0.252810i
$723$	0.732204			0.0272310
$724$	8.28421	−	5.15140i	0.307880	−	0.191450i
$725$	−16.5317	−	29.4377i	−0.613974	−	1.09329i
$726$	3.79334	+	2.10811i	0.140784	+	0.0782392i
$727$		−	14.6166i		−	0.542101i	−0.962565	−	0.271051i	$-0.912629\pi$
$727$		−	14.6166i		−	0.542101i	0.962565	−	0.271051i	$-0.0873711\pi$
$728$	−18.6844	+	0.917776i	−0.692491	+	0.0340150i
$729$	−20.2856			−0.751318
$730$	11.2642	+	2.89293i	0.416907	+	0.107072i
$731$		−	20.1829i		−	0.746492i
$732$	−2.86546	+	1.78184i	−0.105910	+	0.0658586i
$733$	3.20519			0.118386			0.0591932	−	0.998247i	$-0.481147\pi$
$733$	3.20519			0.118386			0.0591932	+	0.998247i	$0.481147\pi$
$734$	−10.7321	+	19.3115i	−0.396130	+	0.712799i
$735$	0.203176	+	0.776730i	0.00749428	+	0.0286501i
$736$	18.8636	+	27.2558i	0.695321	+	1.00466i
$737$			15.5478i			0.572711i
$738$	−28.1767	−	15.6589i	−1.03720	−	0.576411i
$739$			42.7101i			1.57112i	0.618787	+	0.785559i	$0.287624\pi$
$739$			42.7101i			1.57112i	−0.618787	+	0.785559i	$0.712376\pi$
$740$	−7.84692	+	8.27867i	−0.288459	+	0.304330i
$741$		−	12.7637i		−	0.468885i
$742$	5.12726	−	9.22602i	0.188228	−	0.338698i
$743$			39.5490i			1.45091i	0.688268	+	0.725456i	$0.258371\pi$
$743$			39.5490i			1.45091i	−0.688268	+	0.725456i	$0.741629\pi$
$744$	0.457800	+	9.32007i	0.0167838	+	0.341690i
$745$	−17.9468	+	4.69451i	−0.657520	+	0.171994i
$746$	20.2626	+	11.2607i	0.741867	+	0.412284i
$747$	−3.47364			−0.127094
$748$	−4.65917	−	7.49264i	−0.170356	−	0.273958i
$749$			7.93103i			0.289794i
$750$	−1.46113	−	5.48585i	−0.0533528	−	0.200315i
$751$	25.3942			0.926647			0.463323	−	0.886189i	$-0.346657\pi$
$751$	25.3942			0.926647			0.463323	+	0.886189i	$0.346657\pi$
$752$	−18.8001	−	9.27140i	−0.685569	−	0.338093i
$753$			2.59907i			0.0947153i
$754$	−30.6802	+	55.2062i	−1.11731	+	2.01049i
$755$	−7.30055	−	27.9095i	−0.265694	−	1.01573i
$756$	−3.58028	+	2.22634i	−0.130214	+	0.0809712i
$757$	−18.7961			−0.683156			−0.341578	−	0.939853i	$-0.610961\pi$
$757$	−18.7961			−0.683156			−0.341578	+	0.939853i	$0.610961\pi$
$758$	5.50493	−	9.90560i	0.199948	−	0.359788i
$759$	3.29539			0.119615
$760$	−10.2055	−	32.4250i	−0.370194	−	1.17618i
$761$	8.22386			0.298115			0.149057	−	0.988829i	$-0.452376\pi$
$761$	8.22386			0.298115			0.149057	+	0.988829i	$0.452376\pi$
$762$	−3.84891	+	6.92576i	−0.139431	+	0.250894i
$763$	−14.1011			−0.510494
$764$	−6.65324	−	10.6994i	−0.240706	−	0.387090i
$765$	17.4932	−	4.57585i	0.632467	−	0.165440i
$766$	2.11167	−	3.79974i	0.0762976	−	0.137290i
$767$			25.6059i			0.924576i
$768$	3.49714	+	4.55774i	0.126192	+	0.164463i
$769$	9.60749			0.346455			0.173227	−	0.984882i	$-0.444580\pi$
$769$	9.60749			0.346455			0.173227	+	0.984882i	$0.444580\pi$
$770$	−1.23211	+	4.79747i	−0.0444022	+	0.172889i
$771$		−	4.89809i		−	0.176401i
$772$	−18.4978	+	11.5025i	−0.665749	+	0.413985i
$773$	−17.2543			−0.620595			−0.310298	−	0.950639i	$-0.600429\pi$
$773$	−17.2543			−0.620595			−0.310298	+	0.950639i	$0.600429\pi$
$774$	−25.4326	−	14.1339i	−0.914155	−	0.508032i
$775$	−40.0577	+	22.4958i	−1.43891	+	0.808071i
$776$	−16.6452	+	0.817611i	−0.597529	+	0.0293505i
$777$		−	0.915794i		−	0.0328539i
$778$	14.9307	−	26.8664i	0.535293	−	0.963209i
$779$			42.6711i			1.52885i
$780$	−7.30588	+	7.70786i	−0.261593	+	0.275986i
$781$			17.8872i			0.640053i
$782$	20.4008	+	11.3375i	0.729533	+	0.405430i
$783$			14.2342i			0.508690i
$784$	1.76919	−	3.58747i	0.0631853	−	0.128124i
$785$	0.547040	+	2.09130i	0.0195247	+	0.0746416i
$786$	−2.19415	+	3.94817i	−0.0782628	+	0.140827i
$787$	−41.0653			−1.46382			−0.731910	−	0.681401i	$-0.761371\pi$
$787$	−41.0653			−1.46382			−0.731910	+	0.681401i	$0.761371\pi$
$788$	4.23095	+	6.80400i	0.150721	+	0.242382i
$789$		−	4.01672i		−	0.142999i
$790$	−6.65645	+	25.9182i	−0.236826	+	0.922129i
$791$	5.03990			0.179198
$792$	−12.7043	+	0.624032i	−0.451427	+	0.0221740i
$793$			31.0780i			1.10361i
$794$	9.38742	+	5.21696i	0.333147	+	0.185143i
$795$	−1.51641	−	5.79714i	−0.0537816	−	0.205603i
$796$	−7.52893	−	12.1076i	−0.266856	−	0.429144i
$797$	−38.8789			−1.37716			−0.688581	−	0.725159i	$-0.741766\pi$
$797$	−38.8789			−1.37716			−0.688581	+	0.725159i	$0.741766\pi$
$798$	2.38555	+	1.32574i	0.0844475	+	0.0469308i
$799$	−14.7598			−0.522165
$800$	−12.3969	+	25.4228i	−0.438297	+	0.898830i
$801$	12.1045			0.427691
$802$	9.98943	+	5.55152i	0.352739	+	0.196031i
$803$	−5.76040			−0.203280
$804$	−3.76409	−	6.05321i	−0.132749	−	0.213480i
$805$	−3.31577	−	12.6760i	−0.116865	−	0.446769i
$806$	75.1224	+	41.7484i	2.64607	+	1.47053i
$807$		−	5.66594i		−	0.199450i
$808$	32.5117	−	1.59697i	1.14376	−	0.0561812i
$809$	−2.62281			−0.0922129			−0.0461065	−	0.998937i	$-0.514681\pi$
$809$	−2.62281			−0.0922129			−0.0461065	+	0.998937i	$0.514681\pi$
$810$	6.18000	−	24.0631i	0.217143	−	0.845490i
$811$			37.5496i			1.31854i	0.751905	+	0.659272i	$0.229135\pi$
$811$			37.5496i			1.31854i	−0.751905	+	0.659272i	$0.770865\pi$
$812$	−7.13141	−	11.4684i	−0.250263	−	0.402461i
$813$	8.52829			0.299100
$814$	2.74451	−	4.93849i	0.0961951	−	0.173094i
$815$	4.87555	+	18.6389i	0.170783	+	0.652892i
$816$	3.62790	+	1.78912i	0.127002	+	0.0626319i
$817$			38.5155i			1.34749i
$818$	−9.29742	−	5.16694i	−0.325077	−	0.180658i
$819$			18.9891i			0.663532i
$820$	24.4248	−	25.7687i	0.852952	−	0.899882i
$821$		−	22.5533i		−	0.787115i	−0.919300	−	0.393557i	$-0.871244\pi$
$821$		−	22.5533i		−	0.787115i	0.919300	−	0.393557i	$-0.128756\pi$
$822$	−0.842527	+	1.51605i	−0.0293865	+	0.0528782i
$823$		−	19.6368i		−	0.684494i	−0.939610	−	0.342247i	$-0.888812\pi$
$823$		−	19.6368i		−	0.684494i	0.939610	−	0.342247i	$-0.111188\pi$
$824$	−45.3111	+	2.22567i	−1.57849	+	0.0775349i
$825$	1.37689	+	2.45179i	0.0479371	+	0.0853605i
$826$	−4.78578	−	2.65965i	−0.166519	−	0.0925409i
$827$	21.2476			0.738853			0.369426	−	0.929260i	$-0.379554\pi$
$827$	21.2476			0.738853			0.369426	+	0.929260i	$0.379554\pi$
$828$	28.5730	−	17.7676i	0.992980	−	0.617468i
$829$		−	5.14096i		−	0.178553i	−0.996007	−	0.0892765i	$-0.971545\pi$
$829$		−	5.14096i		−	0.178553i	0.996007	−	0.0892765i	$-0.0284555\pi$
$830$	0.951714	−	3.70569i	0.0330345	−	0.128626i
$831$	−1.68307			−0.0583851
$832$	52.6565	−	5.18547i	1.82554	−	0.179774i
$833$		−	2.81650i		−	0.0975860i
$834$	1.83857	−	3.30833i	0.0636645	−	0.114558i
$835$	21.5333	−	5.63267i	0.745192	−	0.194927i
$836$	8.89119	+	14.2983i	0.307508	+	0.494519i
$837$	19.3694			0.669504
$838$	−8.76921	+	15.7794i	−0.302927	+	0.545089i
$839$	4.86710			0.168031			0.0840154	−	0.996464i	$-0.473225\pi$
$839$	4.86710			0.168031			0.0840154	+	0.996464i	$0.473225\pi$
$840$	−0.681760	−	2.16608i	−0.0235230	−	0.0747370i
$841$	−16.5951			−0.572244
$842$	5.39324	−	9.70463i	0.185863	−	0.334444i
$843$	2.86555			0.0986947
$844$	2.60373	−	1.61908i	0.0896239	−	0.0557312i
$845$	17.3970	+	66.5074i	0.598473	+	2.28792i
$846$	−10.3361	+	18.5989i	−0.355364	+	0.639444i
$847$			8.54662i			0.293665i
$848$	−13.2044	+	26.7752i	−0.453440	+	0.919464i
$849$	−0.867672			−0.0297784
$850$	0.0887221	+	19.9155i	0.00304314	+	0.683095i
$851$			14.9454i			0.512323i
$852$	−4.33044	−	6.96399i	−0.148358	−	0.238582i
$853$	−1.98339			−0.0679101			−0.0339550	−	0.999423i	$-0.510810\pi$
$853$	−1.98339			−0.0679101			−0.0339550	+	0.999423i	$0.510810\pi$
$854$	−5.80852	−	3.22802i	−0.198763	−	0.110461i
$855$	−33.3826	+	8.73219i	−1.14166	+	0.298635i
$856$	−1.10055	−	22.4053i	−0.0376159	−	0.765798i
$857$		−	36.3305i		−	1.24103i	−0.784196	−	0.620513i	$-0.786924\pi$
$857$		−	36.3305i		−	1.24103i	0.784196	−	0.620513i	$-0.213076\pi$
$858$	2.55528	−	4.59799i	0.0872359	−	0.156973i
$859$		−	24.3863i		−	0.832049i	−0.909353	−	0.416025i	$-0.863423\pi$
$859$		−	24.3863i		−	0.832049i	0.909353	−	0.416025i	$-0.136577\pi$
$860$	22.0461	−	23.2591i	0.751767	−	0.793130i
$861$			2.85056i			0.0971468i
$862$	−42.7177	−	23.7399i	−1.45497	−	0.808585i
$863$			12.0631i			0.410634i	0.978696	+	0.205317i	$0.0658225\pi$
$863$			12.0631i			0.410634i	−0.978696	+	0.205317i	$0.934177\pi$
$864$	9.80543	−	6.78627i	0.333588	−	0.230874i
$865$	−2.52026	−	9.63478i	−0.0856914	−	0.327592i
$866$	−12.4798	+	22.4561i	−0.424079	+	0.763091i
$867$	−3.25564			−0.110567
$868$	−15.6057	+	9.70414i	−0.529692	+	0.329380i
$869$		−	13.2543i		−	0.449623i
$870$	−7.42584	−	1.90714i	−0.251759	−	0.0646581i
$871$	−65.6515			−2.22452
$872$	39.8359	−	1.95673i	1.34901	−	0.0662634i
$873$			16.9166i			0.572541i
$874$	−38.9313	−	21.6357i	−1.31687	−	0.731837i
$875$	8.04560	−	7.76326i	0.271991	−	0.262446i
$876$	2.24269	−	1.39458i	0.0757735	−	0.0471185i
$877$	49.1360			1.65920			0.829602	−	0.558355i	$-0.188567\pi$
$877$	49.1360			1.65920			0.829602	+	0.558355i	$0.188567\pi$
$878$	−32.1232	−	17.8521i	−1.08411	−	0.602480i
$879$	−6.16559			−0.207960
$880$	2.81502	−	13.7239i	0.0948943	−	0.462633i
$881$	11.2810			0.380068			0.190034	−	0.981778i	$-0.439140\pi$
$881$	11.2810			0.380068			0.190034	+	0.981778i	$0.439140\pi$
$882$	−3.54908	−	1.97236i	−0.119504	−	0.0664130i
$883$	−28.1865			−0.948550			−0.474275	−	0.880377i	$-0.657290\pi$
$883$	−28.1865			−0.948550			−0.474275	+	0.880377i	$0.657290\pi$
$884$	31.6381	−	19.6736i	1.06410	−	0.661695i
$885$	−3.00713	+	0.786603i	−0.101084	+	0.0264414i
$886$	−29.6368	−	16.4703i	−0.995669	−	0.553332i
$887$			43.1316i			1.44822i	0.689686	+	0.724109i	$0.257749\pi$
$887$			43.1316i			1.44822i	−0.689686	+	0.724109i	$0.742251\pi$
$888$	0.127080	+	2.58714i	0.00426452	+	0.0868187i
$889$	−15.6041			−0.523346
$890$	−3.31641	+	12.9131i	−0.111166	+	0.432848i
$891$			12.3056i			0.412254i
$892$	−35.6077	+	22.1421i	−1.19223	+	0.741371i
$893$	28.1665			0.942555
$894$	−2.04631	+	3.68215i	−0.0684389	+	0.123149i
$895$	3.58964	−	0.938975i	0.119988	−	0.0313865i
$896$	−4.50018	+	10.3802i	−0.150340	+	0.346778i
$897$			13.9150i			0.464607i
$898$	23.8780	+	13.2700i	0.796820	+	0.442824i
$899$			62.0440i			2.06928i
$900$	25.1577	+	13.8348i	0.838590	+	0.461160i
$901$			21.0210i			0.700311i
$902$	−8.54274	+	15.3719i	−0.284442	+	0.511827i
$903$			2.57295i			0.0856223i
$904$	−14.2378	+	0.699360i	−0.473543	+	0.0232604i
$905$	10.5517	−	2.76010i	0.350750	−	0.0917489i
$906$	−5.72620	−	3.18227i	−0.190240	−	0.105724i
$907$	15.7874			0.524212			0.262106	−	0.965039i	$-0.415583\pi$
$907$	15.7874			0.524212			0.262106	+	0.965039i	$0.415583\pi$
$908$	−6.18721	−	9.94994i	−0.205330	−	0.330200i
$909$		−	33.0418i		−	1.09593i
$910$	−20.2576	−	5.20266i	−0.671532	−	0.172466i
$911$	−41.8647			−1.38704			−0.693519	−	0.720438i	$-0.743941\pi$
$911$	−41.8647			−1.38704			−0.693519	+	0.720438i	$0.743941\pi$
$912$	−6.92319	−	3.41422i	−0.229250	−	0.113056i
$913$			1.89505i			0.0627172i
$914$	−21.0279	+	37.8378i	−0.695542	+	1.25156i
$915$	−3.64976	+	0.954702i	−0.120657	+	0.0315615i
$916$	17.4163	−	10.8301i	0.575451	−	0.357835i
$917$	−8.89546			−0.293754
$918$	4.07874	−	7.33931i	0.134619	−	0.242233i
$919$	56.3907			1.86016			0.930078	−	0.367362i	$-0.119739\pi$
$919$	56.3907			1.86016			0.930078	+	0.367362i	$0.119739\pi$
$920$	11.1261	+	35.3497i	0.366816	+	1.16545i
$921$	−1.43968			−0.0474389
$922$	−5.34781	+	9.62288i	−0.176121	+	0.316913i
$923$	−75.5296			−2.48609
$924$	0.593958	+	0.955172i	0.0195398	+	0.0314228i
$925$	−11.1195	+	6.24455i	−0.365608	+	0.205319i
$926$	−0.171046	+	0.307781i	−0.00562091	+	0.0101143i
$927$			46.0498i			1.51247i
$928$	21.7378	+	31.4088i	0.713578	+	1.03104i
$929$	39.0302			1.28054			0.640270	−	0.768150i	$-0.278823\pi$
$929$	39.0302			1.28054			0.640270	+	0.768150i	$0.278823\pi$
$930$	−2.59516	+	10.1048i	−0.0850987	+	0.331349i
$931$			5.37478i			0.176151i
$932$	41.0504	−	25.5265i	1.34465	−	0.836149i
$933$	−4.89768			−0.160343
$934$	35.0864	+	19.4989i	1.14806	+	0.638022i
$935$	−2.49637	−	9.54345i	−0.0816400	−	0.312104i
$936$	−2.63501	−	53.6445i	−0.0861280	−	1.75343i
$937$			18.0230i			0.588785i	0.955685	+	0.294393i	$0.0951173\pi$
$937$			18.0230i			0.588785i	−0.955685	+	0.294393i	$0.904883\pi$
$938$	6.81912	−	12.2704i	0.222652	−	0.400642i
$939$		−	8.42983i		−	0.275097i
$940$	−17.0095	−	16.1224i	−0.554788	−	0.525854i
$941$		−	57.8886i		−	1.88712i	−0.331209	−	0.943558i	$-0.607456\pi$
$941$		−	57.8886i		−	1.88712i	0.331209	−	0.943558i	$-0.392544\pi$
$942$	0.429072	+	0.238452i	0.0139799	+	0.00776918i
$943$		−	46.5201i		−	1.51490i
$944$	13.8890	+	6.84946i	0.452049	+	0.222931i
$945$	−4.56024	+	1.19287i	−0.148345	+	0.0388039i
$946$	−7.71078	+	13.8748i	−0.250699	+	0.451109i
$947$	−20.3787			−0.662220			−0.331110	−	0.943592i	$-0.607423\pi$
$947$	−20.3787			−0.662220			−0.331110	+	0.943592i	$0.607423\pi$
$948$	3.20885	+	5.16030i	0.104218	+	0.167599i
$949$		−	24.3236i		−	0.789578i
$950$	−0.169310	−	38.0051i	−0.00549315	−	1.23305i
$951$	11.0215			0.357398
$952$	0.390831	+	7.95667i	0.0126669	+	0.257877i
$953$			20.7044i			0.670681i	0.942097	+	0.335340i	$0.108851\pi$
$953$			20.7044i			0.670681i	−0.942097	+	0.335340i	$0.891149\pi$
$954$	26.4887	+	14.7208i	0.857602	+	0.476603i
$955$	−3.56478	−	13.6279i	−0.115354	−	0.440989i
$956$	8.79763	+	14.1479i	0.284536	+	0.457576i
$957$	3.79750			0.122756
$958$	−3.23085	−	1.79551i	−0.104384	−	0.0580103i
$959$	−3.41574			−0.110300
$960$	2.22656	+	6.02463i	0.0718620	+	0.194444i
$961$	53.4270			1.72345
$962$	20.8531	+	11.5889i	0.672330	+	0.373640i
$963$	−22.7706			−0.733774
$964$	−2.15373	−	3.46352i	−0.0693671	−	0.111553i
$965$	−23.5608	+	6.16302i	−0.758449	+	0.198395i
$966$	−2.60073	−	1.44533i	−0.0836771	−	0.0465026i
$967$		−	21.7862i		−	0.700598i	−0.936638	−	0.350299i	$-0.886080\pi$
$967$		−	21.7862i		−	0.700598i	0.936638	−	0.350299i	$-0.113920\pi$
$968$	−1.18597	−	24.1444i	−0.0381185	−	0.776030i
$969$	−5.43535			−0.174609
$970$	−18.0467	−	4.63485i	−0.579445	−	0.148816i
$971$			13.3648i			0.428896i	0.976735	+	0.214448i	$0.0687952\pi$
$971$			13.3648i			0.428896i	−0.976735	+	0.214448i	$0.931205\pi$
$972$	−9.65818	−	15.5318i	−0.309786	−	0.498182i
$973$	7.45387			0.238960
$974$	−21.4626	+	38.6200i	−0.687707	+	1.23746i
$975$	−10.3528	+	5.81399i	−0.331556	+	0.186197i
$976$	16.8571	+	8.31321i	0.539583	+	0.266099i
$977$		−	2.01269i		−	0.0643916i	−0.999482	−	0.0321958i	$-0.989750\pi$
$977$		−	2.01269i		−	0.0643916i	0.999482	−	0.0321958i	$-0.0102500\pi$
$978$	3.82415	+	2.12523i	0.122283	+	0.0679573i
$979$		−	6.60364i		−	0.211053i
$980$	3.07651	−	3.24578i	0.0982754	−	0.103683i
$981$		−	40.4854i		−	1.29260i
$982$	9.82816	−	17.6849i	0.313629	−	0.564346i
$983$		−	44.1602i		−	1.40849i	−0.709956	−	0.704246i	$-0.751285\pi$
$983$		−	44.1602i		−	1.40849i	0.709956	−	0.704246i	$-0.248715\pi$
$984$	−0.395557	−	8.05289i	−0.0126099	−	0.256717i
$985$	2.26693	+	8.66632i	0.0722304	+	0.276132i
$986$	23.5093	+	13.0650i	0.748688	+	0.416075i
$987$	1.88160			0.0598921
$988$	−60.3756	+	37.5436i	−1.92080	+	1.19442i
$989$		−	41.9896i		−	1.33519i
$990$	−13.7739	−	3.53749i	−0.437764	−	0.112429i
$991$	−5.53076			−0.175690			−0.0878451	−	0.996134i	$-0.527998\pi$
$991$	−5.53076			−0.175690			−0.0878451	+	0.996134i	$0.527998\pi$
$992$	42.7398	−	29.5799i	1.35699	−	0.939164i
$993$		−	8.72190i		−	0.276781i
$994$	7.84514	−	14.1166i	0.248833	−	0.447751i
$995$	−4.03398	−	15.4216i	−0.127886	−	0.488899i
$996$	−0.458788	−	0.737800i	−0.0145373	−	0.0233781i
$997$	−21.0515			−0.666709			−0.333355	−	0.942802i	$-0.608181\pi$
$997$	−21.0515			−0.666709			−0.333355	+	0.942802i	$0.608181\pi$
$998$	2.17993	−	3.92258i	0.0690045	−	0.124167i
$999$	5.37670			0.170111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.l.a.29.7	✓	36
4.3	odd	2		1120.2.l.a.1009.21		36
5.4	even	2	inner	280.2.l.a.29.30	yes	36
8.3	odd	2		1120.2.l.a.1009.16		36
8.5	even	2	inner	280.2.l.a.29.29	yes	36
20.19	odd	2		1120.2.l.a.1009.15		36
40.19	odd	2		1120.2.l.a.1009.22		36
40.29	even	2	inner	280.2.l.a.29.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.l.a.29.7	✓	36	1.1	even	1	trivial
280.2.l.a.29.8	yes	36	40.29	even	2	inner
280.2.l.a.29.29	yes	36	8.5	even	2	inner
280.2.l.a.29.30	yes	36	5.4	even	2	inner
1120.2.l.a.1009.15		36	20.19	odd	2
1120.2.l.a.1009.16		36	8.3	odd	2
1120.2.l.a.1009.21		36	4.3	odd	2
1120.2.l.a.1009.22		36	40.19	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.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23615 - 0.686976i) q^{2} -0.359051 q^{3} +(1.05613 + 1.69841i) q^{4} +(0.565870 + 2.16328i) q^{5} +(0.443841 + 0.246660i) q^{6} +1.00000i q^{7} +(-0.138765 - 2.82502i) q^{8} -2.87108 q^{9} +O(q^{10})\)	\(q+(-1.23615 - 0.686976i) q^{2} -0.359051 q^{3} +(1.05613 + 1.69841i) q^{4} +(0.565870 + 2.16328i) q^{5} +(0.443841 + 0.246660i) q^{6} +1.00000i q^{7} +(-0.138765 - 2.82502i) q^{8} -2.87108 q^{9} +(0.786624 - 3.06288i) q^{10} +1.56633i q^{11} +(-0.379204 - 0.609816i) q^{12} -6.61390 q^{13} +(0.686976 - 1.23615i) q^{14} +(-0.203176 - 0.776730i) q^{15} +(-1.76919 + 3.58747i) q^{16} +2.81650i q^{17} +(3.54908 + 1.97236i) q^{18} -5.37478i q^{19} +(-3.07651 + 3.24578i) q^{20} -0.359051i q^{21} +(1.07603 - 1.93621i) q^{22} +5.85959i q^{23} +(0.0498236 + 1.01433i) q^{24} +(-4.35958 + 2.44827i) q^{25} +(8.17577 + 4.54359i) q^{26} +2.10802 q^{27} +(-1.69841 + 1.05613i) q^{28} +6.75241i q^{29} +(-0.282438 + 1.09973i) q^{30} +9.18842 q^{31} +(4.65149 - 3.21926i) q^{32} -0.562392i q^{33} +(1.93487 - 3.48161i) q^{34} +(-2.16328 + 0.565870i) q^{35} +(-3.03223 - 4.87627i) q^{36} +2.55059 q^{37} +(-3.69235 + 6.64403i) q^{38} +2.37473 q^{39} +(6.03280 - 1.89878i) q^{40} -7.93914 q^{41} +(-0.246660 + 0.443841i) q^{42} -7.16596 q^{43} +(-2.66026 + 1.65424i) q^{44} +(-1.62466 - 6.21096i) q^{45} +(4.02540 - 7.24333i) q^{46} +5.24048i q^{47} +(0.635230 - 1.28809i) q^{48} -1.00000 q^{49} +(7.07100 - 0.0315008i) q^{50} -1.01127i q^{51} +(-6.98513 - 11.2331i) q^{52} +7.46352 q^{53} +(-2.60583 - 1.44816i) q^{54} +(-3.38841 + 0.886337i) q^{55} +(2.82502 - 0.138765i) q^{56} +1.92982i q^{57} +(4.63875 - 8.34699i) q^{58} -3.87153i q^{59} +(1.10462 - 1.16540i) q^{60} -4.69888i q^{61} +(-11.3583 - 6.31222i) q^{62} -2.87108i q^{63} +(-7.96149 + 0.784026i) q^{64} +(-3.74261 - 14.3077i) q^{65} +(-0.386350 + 0.695200i) q^{66} +9.92629 q^{67} +(-4.78357 + 2.97458i) q^{68} -2.10390i q^{69} +(3.06288 + 0.786624i) q^{70} +11.4198 q^{71} +(0.398405 + 8.11087i) q^{72} +3.67765i q^{73} +(-3.15291 - 1.75220i) q^{74} +(1.56531 - 0.879056i) q^{75} +(9.12858 - 5.67646i) q^{76} -1.56633 q^{77} +(-2.93552 - 1.63138i) q^{78} -8.46205 q^{79} +(-8.76185 - 1.79721i) q^{80} +7.85636 q^{81} +(9.81395 + 5.45400i) q^{82} +1.20987 q^{83} +(0.609816 - 0.379204i) q^{84} +(-6.09289 + 1.59377i) q^{85} +(8.85819 + 4.92284i) q^{86} -2.42446i q^{87} +(4.42491 - 0.217351i) q^{88} -4.21600 q^{89} +(-2.25846 + 8.79377i) q^{90} -6.61390i q^{91} +(-9.95199 + 6.18848i) q^{92} -3.29912 q^{93} +(3.60009 - 6.47802i) q^{94} +(11.6272 - 3.04143i) q^{95} +(-1.67012 + 1.15588i) q^{96} -5.89207i q^{97} +(1.23615 + 0.686976i) q^{98} -4.49705i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more