LMFDB - Embedded newform 471.2.b.a.313.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(313,471)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("471.313");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.b (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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 15x^{10} + 77x^{8} + 158x^{6} + 111x^{4} + 21x^{2} + 1 $ x^12 + 15x^10 + 77x^8 + 158x^6 + 111x^4 + 21*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			313.7
Root			$0.269982i$ of defining polynomial
Character	$\chi$	$=$	471.313
Dual form			471.2.b.a.313.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.269982i q^{2} -1.00000 q^{3} +1.92711 q^{4} +3.43396i q^{5} -0.269982i q^{6} +1.97607i q^{7} +1.06025i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.269982i q^{2} -1.00000 q^{3} +1.92711 q^{4} +3.43396i q^{5} -0.269982i q^{6} +1.97607i q^{7} +1.06025i q^{8} +1.00000 q^{9} -0.927110 q^{10} -5.22414 q^{11} -1.92711 q^{12} -0.533505 q^{13} -0.533505 q^{14} -3.43396i q^{15} +3.56797 q^{16} -2.09513 q^{17} +0.269982i q^{18} -1.00634 q^{19} +6.61762i q^{20} -1.97607i q^{21} -1.41043i q^{22} -6.53200i q^{23} -1.06025i q^{24} -6.79211 q^{25} -0.144037i q^{26} -1.00000 q^{27} +3.80811i q^{28} +4.47072i q^{29} +0.927110 q^{30} +9.35374 q^{31} +3.08379i q^{32} +5.22414 q^{33} -0.565649i q^{34} -6.78577 q^{35} +1.92711 q^{36} -4.75130 q^{37} -0.271695i q^{38} +0.533505 q^{39} -3.64086 q^{40} +8.72136i q^{41} +0.533505 q^{42} +9.75764i q^{43} -10.0675 q^{44} +3.43396i q^{45} +1.76352 q^{46} +12.1684 q^{47} -3.56797 q^{48} +3.09513 q^{49} -1.83375i q^{50} +2.09513 q^{51} -1.02812 q^{52} +11.9638i q^{53} -0.269982i q^{54} -17.9395i q^{55} -2.09513 q^{56} +1.00634 q^{57} -1.20702 q^{58} -8.86578i q^{59} -6.61762i q^{60} -15.3978i q^{61} +2.52534i q^{62} +1.97607i q^{63} +6.30337 q^{64} -1.83204i q^{65} +1.41043i q^{66} -4.31560 q^{67} -4.03755 q^{68} +6.53200i q^{69} -1.83204i q^{70} +5.06567 q^{71} +1.06025i q^{72} +9.73633i q^{73} -1.28277i q^{74} +6.79211 q^{75} -1.93933 q^{76} -10.3233i q^{77} +0.144037i q^{78} +1.66535i q^{79} +12.2523i q^{80} +1.00000 q^{81} -2.35461 q^{82} -1.76822i q^{83} -3.80811i q^{84} -7.19461i q^{85} -2.63439 q^{86} -4.47072i q^{87} -5.53889i q^{88} +15.1720 q^{89} -0.927110 q^{90} -1.05425i q^{91} -12.5879i q^{92} -9.35374 q^{93} +3.28525i q^{94} -3.45575i q^{95} -3.08379i q^{96} -1.25385i q^{97} +0.835631i q^{98} -5.22414 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9	$ 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9} + 18 q^{10} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} + 10 q^{16} + 2 q^{17} + 4 q^{19} + 12 q^{25} - 12 q^{27} - 18 q^{30} + 2 q^{31} + 2 q^{33} - 4 q^{35} - 6 q^{36} - 2 q^{37} - 4 q^{39} - 40 q^{40} - 4 q^{42} - 36 q^{44} + 34 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{51} - 6 q^{52} + 2 q^{56} - 4 q^{57} + 24 q^{58} + 28 q^{64} - 38 q^{67} + 32 q^{68} - 26 q^{71} - 12 q^{75} - 28 q^{76} + 12 q^{81} - 50 q^{82} + 6 q^{86} - 4 q^{89} + 18 q^{90} - 2 q^{93} - 2 q^{99}+O(q^{100}) $ 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9 + 18 * q^10 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 + 10 * q^16 + 2 * q^17 + 4 * q^19 + 12 * q^25 - 12 * q^27 - 18 * q^30 + 2 * q^31 + 2 * q^33 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^39 - 40 * q^40 - 4 * q^42 - 36 * q^44 + 34 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^51 - 6 * q^52 + 2 * q^56 - 4 * q^57 + 24 * q^58 + 28 * q^64 - 38 * q^67 + 32 * q^68 - 26 * q^71 - 12 * q^75 - 28 * q^76 + 12 * q^81 - 50 * q^82 + 6 * q^86 - 4 * q^89 + 18 * q^90 - 2 * q^93 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$-1$

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 $

$2$			0.269982i			0.190906i	0.995434	+	0.0954532i	$0.0304300\pi$
$2$			0.269982i			0.190906i	−0.995434	+	0.0954532i	$0.969570\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.92711			0.963555
$5$			3.43396i			1.53572i	0.640620	+	0.767858i	$0.278677\pi$
$5$			3.43396i			1.53572i	−0.640620	+	0.767858i	$0.721323\pi$
$6$		−	0.269982i		−	0.110220i
$7$			1.97607i			0.746886i	0.927653	+	0.373443i	$0.121823\pi$
$7$			1.97607i			0.746886i	−0.927653	+	0.373443i	$0.878177\pi$
$8$			1.06025i			0.374855i
$9$	1.00000			0.333333
$10$	−0.927110			−0.293178
$11$	−5.22414			−1.57514			−0.787569	−	0.616227i	$-0.788660\pi$
$11$	−5.22414			−1.57514			−0.787569	+	0.616227i	$0.788660\pi$
$12$	−1.92711			−0.556309
$13$	−0.533505			−0.147968			−0.0739838	−	0.997259i	$-0.523571\pi$
$13$	−0.533505			−0.147968			−0.0739838	+	0.997259i	$0.523571\pi$
$14$	−0.533505			−0.142585
$15$		−	3.43396i		−	0.886646i
$16$	3.56797			0.891993
$17$	−2.09513			−0.508144			−0.254072	−	0.967185i	$-0.581770\pi$
$17$	−2.09513			−0.508144			−0.254072	+	0.967185i	$0.581770\pi$
$18$			0.269982i			0.0636354i
$19$	−1.00634			−0.230871			−0.115435	−	0.993315i	$-0.536826\pi$
$19$	−1.00634			−0.230871			−0.115435	+	0.993315i	$0.536826\pi$
$20$			6.61762i			1.47975i
$21$		−	1.97607i		−	0.431215i
$22$		−	1.41043i		−	0.300704i
$23$		−	6.53200i		−	1.36202i	−0.732276	−	0.681008i	$-0.761542\pi$
$23$		−	6.53200i		−	1.36202i	0.732276	−	0.681008i	$-0.238458\pi$
$24$		−	1.06025i		−	0.216423i
$25$	−6.79211			−1.35842
$26$		−	0.144037i		−	0.0282480i
$27$	−1.00000			−0.192450
$28$			3.80811i			0.719665i
$29$			4.47072i			0.830192i	0.909778	+	0.415096i	$0.136252\pi$
$29$			4.47072i			0.830192i	−0.909778	+	0.415096i	$0.863748\pi$
$30$	0.927110			0.169266
$31$	9.35374			1.67998			0.839990	−	0.542601i	$-0.182561\pi$
$31$	9.35374			1.67998			0.839990	+	0.542601i	$0.182561\pi$
$32$			3.08379i			0.545142i
$33$	5.22414			0.909406
$34$		−	0.565649i		−	0.0970080i
$35$	−6.78577			−1.14700
$36$	1.92711			0.321185
$37$	−4.75130			−0.781109			−0.390555	−	0.920580i	$-0.627717\pi$
$37$	−4.75130			−0.781109			−0.390555	+	0.920580i	$0.627717\pi$
$38$		−	0.271695i		−	0.0440747i
$39$	0.533505			0.0854292
$40$	−3.64086			−0.575671
$41$			8.72136i			1.36205i	0.732262	+	0.681024i	$0.238465\pi$
$41$			8.72136i			1.36205i	−0.732262	+	0.681024i	$0.761535\pi$
$42$	0.533505			0.0823216
$43$			9.75764i			1.48803i	0.668165	+	0.744013i	$0.267080\pi$
$43$			9.75764i			1.48803i	−0.668165	+	0.744013i	$0.732920\pi$
$44$	−10.0675			−1.51773
$45$			3.43396i			0.511905i
$46$	1.76352			0.260017
$47$	12.1684			1.77494			0.887470	−	0.460866i	$-0.152461\pi$
$47$	12.1684			1.77494			0.887470	+	0.460866i	$0.152461\pi$
$48$	−3.56797			−0.514992
$49$	3.09513			0.442162
$50$		−	1.83375i		−	0.259331i
$51$	2.09513			0.293377
$52$	−1.02812			−0.142575
$53$			11.9638i			1.64336i	0.569951	+	0.821678i	$0.306962\pi$
$53$			11.9638i			1.64336i	−0.569951	+	0.821678i	$0.693038\pi$
$54$		−	0.269982i		−	0.0367399i
$55$		−	17.9395i		−	2.41896i
$56$	−2.09513			−0.279974
$57$	1.00634			0.133293
$58$	−1.20702			−0.158489
$59$		−	8.86578i		−	1.15423i	−0.816664	−	0.577113i	$-0.804179\pi$
$59$		−	8.86578i		−	1.15423i	0.816664	−	0.577113i	$-0.195821\pi$
$60$		−	6.61762i		−	0.854332i
$61$		−	15.3978i		−	1.97148i	−0.168264	−	0.985742i	$-0.553816\pi$
$61$		−	15.3978i		−	1.97148i	0.168264	−	0.985742i	$-0.446184\pi$
$62$			2.52534i			0.320719i
$63$			1.97607i			0.248962i
$64$	6.30337			0.787922
$65$		−	1.83204i		−	0.227236i
$66$			1.41043i			0.173611i
$67$	−4.31560			−0.527234			−0.263617	−	0.964627i	$-0.584915\pi$
$67$	−4.31560			−0.527234			−0.263617	+	0.964627i	$0.584915\pi$
$68$	−4.03755			−0.489625
$69$			6.53200i			0.786360i
$70$		−	1.83204i		−	0.218970i
$71$	5.06567			0.601185			0.300592	−	0.953753i	$-0.402816\pi$
$71$	5.06567			0.601185			0.300592	+	0.953753i	$0.402816\pi$
$72$			1.06025i			0.124952i
$73$			9.73633i			1.13955i	0.821800	+	0.569776i	$0.192970\pi$
$73$			9.73633i			1.13955i	−0.821800	+	0.569776i	$0.807030\pi$
$74$		−	1.28277i		−	0.149119i
$75$	6.79211			0.784285
$76$	−1.93933			−0.222457
$77$		−	10.3233i		−	1.17645i
$78$			0.144037i			0.0163090i
$79$			1.66535i			0.187367i	0.995602	+	0.0936833i	$0.0298641\pi$
$79$			1.66535i			0.187367i	−0.995602	+	0.0936833i	$0.970136\pi$
$80$			12.2523i			1.36985i
$81$	1.00000			0.111111
$82$	−2.35461			−0.260023
$83$		−	1.76822i		−	0.194088i	−0.995280	−	0.0970439i	$-0.969061\pi$
$83$		−	1.76822i		−	0.194088i	0.995280	−	0.0970439i	$-0.0309387\pi$
$84$		−	3.80811i		−	0.415499i
$85$		−	7.19461i		−	0.780365i
$86$	−2.63439			−0.284073
$87$		−	4.47072i		−	0.479312i
$88$		−	5.53889i		−	0.590448i
$89$	15.1720			1.60823			0.804117	−	0.594471i	$-0.202639\pi$
$89$	15.1720			1.60823			0.804117	+	0.594471i	$0.202639\pi$
$90$	−0.927110			−0.0977259
$91$		−	1.05425i		−	0.110515i
$92$		−	12.5879i		−	1.31238i
$93$	−9.35374			−0.969937
$94$			3.28525i			0.338847i
$95$		−	3.45575i		−	0.354552i
$96$		−	3.08379i		−	0.314738i
$97$		−	1.25385i		−	0.127310i	−0.997972	−	0.0636548i	$-0.979724\pi$
$97$		−	1.25385i		−	0.127310i	0.997972	−	0.0636548i	$-0.0202757\pi$
$98$			0.835631i			0.0844115i
$99$	−5.22414			−0.525046
$100$	−13.0891			−1.30891
$101$	6.25226			0.622123			0.311062	−	0.950390i	$-0.399315\pi$
$101$	6.25226			0.622123			0.311062	+	0.950390i	$0.399315\pi$
$102$			0.565649i			0.0560076i
$103$		−	9.36762i		−	0.923019i	−0.887135	−	0.461509i	$-0.847308\pi$
$103$		−	9.36762i		−	0.923019i	0.887135	−	0.461509i	$-0.152692\pi$
$104$		−	0.565649i		−	0.0554664i
$105$	6.78577			0.662223
$106$	−3.23002			−0.313727
$107$		−	9.95391i		−	0.962281i	−0.876644	−	0.481140i	$-0.840223\pi$
$107$		−	9.95391i		−	0.962281i	0.876644	−	0.481140i	$-0.159777\pi$
$108$	−1.92711			−0.185436
$109$	5.40439			0.517646			0.258823	−	0.965925i	$-0.416665\pi$
$109$	5.40439			0.517646			0.258823	+	0.965925i	$0.416665\pi$
$110$	4.84335			0.461795
$111$	4.75130			0.450974
$112$			7.05057i			0.666216i
$113$	−10.5679			−0.994140			−0.497070	−	0.867710i	$-0.665591\pi$
$113$	−10.5679			−0.994140			−0.497070	+	0.867710i	$0.665591\pi$
$114$			0.271695i			0.0254465i
$115$	22.4307			2.09167
$116$			8.61557i			0.799935i
$117$	−0.533505			−0.0493226
$118$	2.39360			0.220349
$119$		−	4.14014i		−	0.379526i
$120$	3.64086			0.332364
$121$	16.2916			1.48106
$122$	4.15713			0.376369
$123$		−	8.72136i		−	0.786378i
$124$	18.0257			1.61875
$125$		−	6.15404i		−	0.550434i
$126$	−0.533505			−0.0475284
$127$	−2.40950			−0.213809			−0.106904	−	0.994269i	$-0.534094\pi$
$127$	−2.40950			−0.213809			−0.106904	+	0.994269i	$0.534094\pi$
$128$			7.86938i			0.695561i
$129$		−	9.75764i		−	0.859112i
$130$	0.494618			0.0433808
$131$			3.08121i			0.269206i	0.990900	+	0.134603i	$0.0429760\pi$
$131$			3.08121i			0.269206i	−0.990900	+	0.134603i	$0.957024\pi$
$132$	10.0675			0.876262
$133$		−	1.98861i		−	0.172434i
$134$		−	1.16513i		−	0.100652i
$135$		−	3.43396i		−	0.295549i
$136$		−	2.22136i		−	0.190480i
$137$			4.55593i			0.389239i	0.980879	+	0.194620i	$0.0623472\pi$
$137$			4.55593i			0.389239i	−0.980879	+	0.194620i	$0.937653\pi$
$138$	−1.76352			−0.150121
$139$		−	6.40428i		−	0.543204i	−0.962410	−	0.271602i	$-0.912447\pi$
$139$		−	6.40428i		−	0.543204i	0.962410	−	0.271602i	$-0.0875535\pi$
$140$	−13.0769			−1.10520
$141$	−12.1684			−1.02476
$142$			1.36764i			0.114770i
$143$	2.78710			0.233069
$144$	3.56797			0.297331
$145$	−15.3523			−1.27494
$146$	−2.62864			−0.217548
$147$	−3.09513			−0.255282
$148$	−9.15628			−0.752641
$149$		−	8.50846i		−	0.697040i	−0.937301	−	0.348520i	$-0.886684\pi$
$149$		−	8.50846i		−	0.697040i	0.937301	−	0.348520i	$-0.113316\pi$
$150$			1.83375i			0.149725i
$151$			14.2880i			1.16274i	0.813640	+	0.581369i	$0.197483\pi$
$151$			14.2880i			1.16274i	−0.813640	+	0.581369i	$0.802517\pi$
$152$		−	1.06698i		−	0.0865431i
$153$	−2.09513			−0.169381
$154$	2.78710			0.224591
$155$			32.1204i			2.57997i
$156$	1.02812			0.0823157
$157$	6.85278	+	10.4900i	0.546911	+	0.837191i
$157$	6.85278	+	10.4900i	0.546911	+	0.837191i
$158$	−0.449615			−0.0357695
$159$		−	11.9638i		−	0.948793i
$160$	−10.5896			−0.837183
$161$	12.9077			1.01727
$162$			0.269982i			0.0212118i
$163$			0.0331476i			0.00259632i	0.999999	+	0.00129816i	$0.000413218\pi$
$163$			0.0331476i			0.00259632i	−0.999999	+	0.00129816i	$0.999587\pi$
$164$			16.8070i			1.31241i
$165$			17.9395i			1.39659i
$166$	0.477389			0.0370526
$167$	−19.9457			−1.54345			−0.771724	−	0.635958i	$-0.780605\pi$
$167$	−19.9457			−1.54345			−0.771724	+	0.635958i	$0.780605\pi$
$168$	2.09513			0.161643
$169$	−12.7154			−0.978106
$170$	1.94242			0.148977
$171$	−1.00634			−0.0769570
$172$			18.8040i			1.43379i
$173$	7.40553			0.563032			0.281516	−	0.959557i	$-0.409163\pi$
$173$	7.40553			0.563032			0.281516	+	0.959557i	$0.409163\pi$
$174$	1.20702			0.0915036
$175$		−	13.4217i		−	1.01459i
$176$	−18.6396			−1.40501
$177$			8.86578i			0.666393i
$178$			4.09618i			0.307022i
$179$		−	17.1917i		−	1.28497i	−0.766299	−	0.642484i	$-0.777904\pi$
$179$		−	17.1917i		−	1.28497i	0.766299	−	0.642484i	$-0.222096\pi$
$180$			6.61762i			0.493249i
$181$		−	5.82964i		−	0.433314i	−0.976248	−	0.216657i	$-0.930485\pi$
$181$		−	5.82964i		−	0.433314i	0.976248	−	0.216657i	$-0.0695153\pi$
$182$	0.284628			0.0210980
$183$			15.3978i			1.13824i
$184$	6.92555			0.510559
$185$		−	16.3158i		−	1.19956i
$186$		−	2.52534i		−	0.185167i
$187$	10.9453			0.800397
$188$	23.4498			1.71025
$189$		−	1.97607i		−	0.143738i
$190$	0.932990			0.0676862
$191$		−	5.96749i		−	0.431793i	−0.976416	−	0.215896i	$-0.930733\pi$
$191$		−	5.96749i		−	0.431793i	0.976416	−	0.215896i	$-0.0692673\pi$
$192$	−6.30337			−0.454907
$193$	17.4399			1.25535			0.627675	−	0.778475i	$-0.284007\pi$
$193$	17.4399			1.25535			0.627675	+	0.778475i	$0.284007\pi$
$194$	0.338518			0.0243042
$195$			1.83204i			0.131195i
$196$	5.96466			0.426047
$197$	−15.0037			−1.06897			−0.534484	−	0.845179i	$-0.679494\pi$
$197$	−15.0037			−1.06897			−0.534484	+	0.845179i	$0.679494\pi$
$198$		−	1.41043i		−	0.100235i
$199$	−16.1670			−1.14605			−0.573025	−	0.819538i	$-0.694230\pi$
$199$	−16.1670			−1.14605			−0.573025	+	0.819538i	$0.694230\pi$
$200$		−	7.20133i		−	0.509211i
$201$	4.31560			0.304399
$202$			1.68800i			0.118767i
$203$	−8.83447			−0.620058
$204$	4.03755			0.282685
$205$	−29.9488			−2.09172
$206$	2.52909			0.176210
$207$		−	6.53200i		−	0.454005i
$208$	−1.90353			−0.131986
$209$	5.25727			0.363653
$210$			1.83204i			0.126423i
$211$		−	2.44314i		−	0.168193i	−0.996458	−	0.0840964i	$-0.973200\pi$
$211$		−	2.44314i		−	0.168193i	0.996458	−	0.0840964i	$-0.0268004\pi$
$212$			23.0556i			1.58346i
$213$	−5.06567			−0.347094
$214$	2.68738			0.183705
$215$	−33.5074			−2.28518
$216$		−	1.06025i		−	0.0721409i
$217$			18.4837i			1.25475i
$218$			1.45909i			0.0988219i
$219$		−	9.73633i		−	0.657920i
$220$		−	34.5714i		−	2.33080i
$221$	1.11776			0.0751889
$222$			1.28277i			0.0860937i
$223$		−	21.2151i		−	1.42067i	−0.703864	−	0.710335i	$-0.748544\pi$
$223$		−	21.2151i		−	1.42067i	0.703864	−	0.710335i	$-0.251456\pi$
$224$	−6.09379			−0.407159
$225$	−6.79211			−0.452807
$226$		−	2.85313i		−	0.189788i
$227$		−	10.7726i		−	0.715003i	−0.933913	−	0.357502i	$-0.883629\pi$
$227$		−	10.7726i		−	0.715003i	0.933913	−	0.357502i	$-0.116371\pi$
$228$	1.93933			0.128435
$229$			14.5743i			0.963097i	0.876419	+	0.481549i	$0.159926\pi$
$229$			14.5743i			0.963097i	−0.876419	+	0.481549i	$0.840074\pi$
$230$			6.05588i			0.399313i
$231$			10.3233i			0.679222i
$232$	−4.74008			−0.311202
$233$	0.204892			0.0134229			0.00671145	−	0.999977i	$-0.497864\pi$
$233$	0.204892			0.0134229			0.00671145	+	0.999977i	$0.497864\pi$
$234$		−	0.144037i		−	0.00941599i
$235$			41.7858i			2.72580i
$236$		−	17.0853i		−	1.11216i
$237$		−	1.66535i		−	0.108176i
$238$	1.11776			0.0724538
$239$	26.2369			1.69712			0.848562	−	0.529097i	$-0.177469\pi$
$239$	26.2369			1.69712			0.848562	+	0.529097i	$0.177469\pi$
$240$		−	12.2523i		−	0.790881i
$241$		−	7.08082i		−	0.456116i	−0.973648	−	0.228058i	$-0.926762\pi$
$241$		−	7.08082i		−	0.456116i	0.973648	−	0.228058i	$-0.0732376\pi$
$242$			4.39845i			0.282743i
$243$	−1.00000			−0.0641500
$244$		−	29.6732i		−	1.89963i
$245$			10.6286i			0.679035i
$246$	2.35461			0.150125
$247$	0.536889			0.0341614
$248$			9.91730i			0.629749i
$249$			1.76822i			0.112057i
$250$	1.66148			0.105081
$251$		−	7.73410i		−	0.488172i	−0.969754	−	0.244086i	$-0.921512\pi$
$251$		−	7.73410i		−	0.488172i	0.969754	−	0.244086i	$-0.0784879\pi$
$252$			3.80811i			0.239888i
$253$			34.1241i			2.14536i
$254$		−	0.650523i		−	0.0408175i
$255$			7.19461i			0.450544i
$256$	10.4822			0.655134
$257$	10.8533			0.677007			0.338504	−	0.940965i	$-0.390079\pi$
$257$	10.8533			0.677007			0.338504	+	0.940965i	$0.390079\pi$
$258$	2.63439			0.164010
$259$		−	9.38892i		−	0.583399i
$260$		−	3.53054i		−	0.218955i
$261$			4.47072i			0.276731i
$262$	−0.831872			−0.0513932
$263$	15.6301			0.963796			0.481898	−	0.876227i	$-0.339948\pi$
$263$	15.6301			0.963796			0.481898	+	0.876227i	$0.339948\pi$
$264$			5.53889i			0.340895i
$265$	−41.0833			−2.52373
$266$	0.536889			0.0329188
$267$	−15.1720			−0.928514
$268$	−8.31663			−0.508019
$269$		−	13.6289i		−	0.830967i	−0.909601	−	0.415483i	$-0.863612\pi$
$269$		−	13.6289i		−	0.830967i	0.909601	−	0.415483i	$-0.136388\pi$
$270$	0.927110			0.0564221
$271$			23.1580i			1.40675i	0.710819	+	0.703375i	$0.248325\pi$
$271$			23.1580i			1.40675i	−0.710819	+	0.703375i	$0.751675\pi$
$272$	−7.47537			−0.453261
$273$			1.05425i			0.0638058i
$274$	−1.23002			−0.0743082
$275$	35.4829			2.13970
$276$			12.5879i			0.757701i
$277$	−19.4700			−1.16984			−0.584920	−	0.811091i	$-0.698874\pi$
$277$	−19.4700			−1.16984			−0.584920	+	0.811091i	$0.698874\pi$
$278$	1.72904			0.103701
$279$	9.35374			0.559994
$280$		−	7.19461i		−	0.429960i
$281$	3.29915			0.196811			0.0984055	−	0.995146i	$-0.468626\pi$
$281$	3.29915			0.196811			0.0984055	+	0.995146i	$0.468626\pi$
$282$		−	3.28525i		−	0.195634i
$283$	4.51039			0.268115			0.134057	−	0.990974i	$-0.457199\pi$
$283$	4.51039			0.268115			0.134057	+	0.990974i	$0.457199\pi$
$284$	9.76211			0.579274
$285$			3.45575i			0.204701i
$286$			0.752469i			0.0444944i
$287$	−17.2340			−1.01729
$288$			3.08379i			0.181714i
$289$	−12.6104			−0.741789
$290$		−	4.14485i		−	0.243394i
$291$			1.25385i			0.0735022i
$292$			18.7630i			1.09802i
$293$		−	9.34032i		−	0.545667i	−0.962061	−	0.272834i	$-0.912039\pi$
$293$		−	9.34032i		−	0.545667i	0.962061	−	0.272834i	$-0.0879608\pi$
$294$		−	0.835631i		−	0.0487350i
$295$	30.4448			1.77256
$296$		−	5.03757i		−	0.292803i
$297$	5.22414			0.303135
$298$	2.29713			0.133069
$299$			3.48485i			0.201534i
$300$	13.0891			0.755702
$301$	−19.2818			−1.11138
$302$	−3.85750			−0.221974
$303$	−6.25226			−0.359183
$304$	−3.59060			−0.205935
$305$	52.8754			3.02764
$306$		−	0.565649i		−	0.0323360i
$307$			20.0016i			1.14155i	0.821105	+	0.570777i	$0.193358\pi$
$307$			20.0016i			1.14155i	−0.821105	+	0.570777i	$0.806642\pi$
$308$		−	19.8941i		−	1.13357i
$309$			9.36762i			0.532905i
$310$	−8.67194			−0.492533
$311$	5.87722			0.333267			0.166633	−	0.986019i	$-0.446710\pi$
$311$	5.87722			0.333267			0.166633	+	0.986019i	$0.446710\pi$
$312$			0.565649i			0.0320236i
$313$	−9.85411			−0.556987			−0.278493	−	0.960438i	$-0.589835\pi$
$313$	−9.85411			−0.556987			−0.278493	+	0.960438i	$0.589835\pi$
$314$	−2.83211	+	1.85013i	−0.159825	+	0.104409i
$315$	−6.78577			−0.382335
$316$			3.20931i			0.180538i
$317$	−9.50321			−0.533754			−0.266877	−	0.963731i	$-0.585992\pi$
$317$	−9.50321			−0.533754			−0.266877	+	0.963731i	$0.585992\pi$
$318$	3.23002			0.181130
$319$		−	23.3557i		−	1.30767i
$320$			21.6456i			1.21002i
$321$			9.95391i			0.555573i
$322$			3.48485i			0.194203i
$323$	2.10842			0.117316
$324$	1.92711			0.107062
$325$	3.62362			0.201002
$326$	−0.00894927			−0.000495654
$327$	−5.40439			−0.298863
$328$	−9.24682			−0.510570
$329$			24.0456i			1.32568i
$330$	−4.84335			−0.266618
$331$	13.0247			0.715904			0.357952	−	0.933740i	$-0.383475\pi$
$331$	13.0247			0.715904			0.357952	+	0.933740i	$0.383475\pi$
$332$		−	3.40756i		−	0.187014i
$333$	−4.75130			−0.260370
$334$		−	5.38500i		−	0.294654i
$335$		−	14.8196i		−	0.809681i
$336$		−	7.05057i		−	0.384640i
$337$			21.1025i			1.14953i	0.818320	+	0.574763i	$0.194906\pi$
$337$			21.1025i			1.14953i	−0.818320	+	0.574763i	$0.805094\pi$
$338$		−	3.43293i		−	0.186727i
$339$	10.5679			0.573967
$340$		−	13.8648i		−	0.751924i
$341$	−48.8652			−2.64620
$342$		−	0.271695i		−	0.0146916i
$343$			19.9487i			1.07713i
$344$	−10.3455			−0.557794
$345$	−22.4307			−1.20763
$346$			1.99936i			0.107486i
$347$	21.5729			1.15809			0.579046	−	0.815295i	$-0.303425\pi$
$347$	21.5729			1.15809			0.579046	+	0.815295i	$0.303425\pi$
$348$		−	8.61557i		−	0.461843i
$349$	28.8024			1.54176			0.770878	−	0.636983i	$-0.219818\pi$
$349$	28.8024			1.54176			0.770878	+	0.636983i	$0.219818\pi$
$350$	3.62362			0.193691
$351$	0.533505			0.0284764
$352$		−	16.1101i		−	0.858673i
$353$	15.0998			0.803683			0.401842	−	0.915709i	$-0.368370\pi$
$353$	15.0998			0.803683			0.401842	+	0.915709i	$0.368370\pi$
$354$	−2.39360			−0.127219
$355$			17.3953i			0.923249i
$356$	29.2382			1.54962
$357$			4.14014i			0.219119i
$358$	4.64145			0.245308
$359$		−	37.7068i		−	1.99009i	−0.0994437	−	0.995043i	$-0.531706\pi$
$359$		−	37.7068i		−	1.99009i	0.0994437	−	0.995043i	$-0.468294\pi$
$360$	−3.64086			−0.191890
$361$	−17.9873			−0.946699
$362$	1.57390			0.0827224
$363$	−16.2916			−0.855089
$364$		−	2.03165i		−	0.106487i
$365$	−33.4342			−1.75003
$366$	−4.15713			−0.217297
$367$		−	3.92190i		−	0.204721i	−0.994747	−	0.102361i	$-0.967360\pi$
$367$		−	3.92190i		−	0.204721i	0.994747	−	0.102361i	$-0.0326396\pi$
$368$		−	23.3060i		−	1.21491i
$369$			8.72136i			0.454016i
$370$	4.40498			0.229004
$371$	−23.6414			−1.22740
$372$	−18.0257			−0.934588
$373$			9.77912i			0.506343i	0.967421	+	0.253172i	$0.0814738\pi$
$373$			9.77912i			0.506343i	−0.967421	+	0.253172i	$0.918526\pi$
$374$			2.95503i			0.152801i
$375$			6.15404i			0.317793i
$376$			12.9015i			0.665345i
$377$		−	2.38515i		−	0.122842i
$378$	0.533505			0.0274405
$379$		−	4.09618i		−	0.210407i	−0.994451	−	0.105203i	$-0.966451\pi$
$379$		−	4.09618i		−	0.210407i	0.994451	−	0.105203i	$-0.0335494\pi$
$380$		−	6.65960i		−	0.341630i
$381$	2.40950			0.123443
$382$	1.61112			0.0824319
$383$		−	11.0626i		−	0.565273i	−0.959227	−	0.282636i	$-0.908791\pi$
$383$		−	11.0626i		−	0.565273i	0.959227	−	0.282636i	$-0.0912090\pi$
$384$		−	7.86938i		−	0.401582i
$385$	35.4498			1.80669
$386$			4.70846i			0.239654i
$387$			9.75764i			0.496008i
$388$		−	2.41631i		−	0.122670i
$389$	−23.4365			−1.18828			−0.594139	−	0.804363i	$-0.702507\pi$
$389$	−23.4365			−1.18828			−0.594139	+	0.804363i	$0.702507\pi$
$390$	−0.494618			−0.0250459
$391$			13.6854i			0.692101i
$392$			3.28161i			0.165747i
$393$		−	3.08121i		−	0.155426i
$394$		−	4.05073i		−	0.204073i
$395$	−5.71876			−0.287742
$396$	−10.0675			−0.505910
$397$			19.3932i			0.973316i	0.873592	+	0.486658i	$0.161784\pi$
$397$			19.3932i			0.973316i	−0.873592	+	0.486658i	$0.838216\pi$
$398$		−	4.36481i		−	0.218788i
$399$			1.98861i			0.0995549i
$400$	−24.2340			−1.21170
$401$		−	5.80128i		−	0.289702i	−0.989453	−	0.144851i	$-0.953730\pi$
$401$		−	5.80128i		−	0.289702i	0.989453	−	0.144851i	$-0.0462703\pi$
$402$			1.16513i			0.0581116i
$403$	−4.99026			−0.248583
$404$	12.0488			0.599450
$405$			3.43396i			0.170635i
$406$		−	2.38515i		−	0.118373i
$407$	24.8215			1.23035
$408$			2.22136i			0.109974i
$409$		−	25.2540i		−	1.24873i	−0.781133	−	0.624365i	$-0.785358\pi$
$409$		−	25.2540i		−	1.24873i	0.781133	−	0.624365i	$-0.214642\pi$
$410$		−	8.08565i		−	0.399322i
$411$		−	4.55593i		−	0.224727i
$412$		−	18.0524i		−	0.889379i
$413$	17.5194			0.862075
$414$	1.76352			0.0866725
$415$	6.07202			0.298063
$416$		−	1.64522i		−	0.0806634i
$417$			6.40428i			0.313619i
$418$			1.41937i			0.0694237i
$419$	2.05861			0.100570			0.0502849	−	0.998735i	$-0.483987\pi$
$419$	2.05861			0.100570			0.0502849	+	0.998735i	$0.483987\pi$
$420$	13.0769			0.638088
$421$		−	27.6297i		−	1.34659i	−0.739374	−	0.673295i	$-0.764878\pi$
$421$		−	27.6297i		−	1.34659i	0.739374	−	0.673295i	$-0.235122\pi$
$422$	0.659605			0.0321091
$423$	12.1684			0.591646
$424$	−12.6846			−0.616021
$425$	14.2304			0.690274
$426$		−	1.36764i		−	0.0662625i
$427$	30.4272			1.47247
$428$		−	19.1823i		−	0.927210i
$429$	−2.78710			−0.134563
$430$		−	9.04640i		−	0.436256i
$431$	−0.896863			−0.0432004			−0.0216002	−	0.999767i	$-0.506876\pi$
$431$	−0.896863			−0.0432004			−0.0216002	+	0.999767i	$0.506876\pi$
$432$	−3.56797			−0.171664
$433$		−	17.9395i		−	0.862118i	−0.902324	−	0.431059i	$-0.858140\pi$
$433$		−	17.9395i		−	0.862118i	0.902324	−	0.431059i	$-0.141860\pi$
$434$	−4.99026			−0.239540
$435$	15.3523			0.736086
$436$	10.4148			0.498780
$437$			6.57343i			0.314450i
$438$	2.62864			0.125601
$439$		−	20.4232i		−	0.974748i	−0.873193	−	0.487374i	$-0.837955\pi$
$439$		−	20.4232i		−	0.974748i	0.873193	−	0.487374i	$-0.162045\pi$
$440$	19.0204			0.906760
$441$	3.09513			0.147387
$442$			0.301776i			0.0143540i
$443$		−	19.8396i		−	0.942609i	−0.881971	−	0.471304i	$-0.843783\pi$
$443$		−	19.8396i		−	0.942609i	0.881971	−	0.471304i	$-0.156217\pi$
$444$	9.15628			0.434538
$445$			52.1003i			2.46979i
$446$	5.72771			0.271215
$447$			8.50846i			0.402436i
$448$			12.4559i			0.588487i
$449$		−	6.96032i		−	0.328478i	−0.986421	−	0.164239i	$-0.947483\pi$
$449$		−	6.96032i		−	0.328478i	0.986421	−	0.164239i	$-0.0525168\pi$
$450$		−	1.83375i		−	0.0864438i
$451$		−	45.5616i		−	2.14541i
$452$	−20.3654			−0.957909
$453$		−	14.2880i		−	0.671307i
$454$	2.90841			0.136499
$455$	3.62024			0.169719
$456$			1.06698i			0.0499657i
$457$	23.2038			1.08543			0.542715	−	0.839917i	$-0.317396\pi$
$457$	23.2038			1.08543			0.542715	+	0.839917i	$0.317396\pi$
$458$	−3.93481			−0.183861
$459$	2.09513			0.0977924
$460$	43.2263			2.01544
$461$	−3.29915			−0.153657			−0.0768284	−	0.997044i	$-0.524479\pi$
$461$	−3.29915			−0.153657			−0.0768284	+	0.997044i	$0.524479\pi$
$462$	−2.78710			−0.129668
$463$		−	10.5560i		−	0.490581i	−0.969450	−	0.245290i	$-0.921117\pi$
$463$		−	10.5560i		−	0.490581i	0.969450	−	0.245290i	$-0.0788833\pi$
$464$			15.9514i			0.740525i
$465$		−	32.1204i		−	1.48955i
$466$			0.0553171i			0.00256252i
$467$	−11.8415			−0.547961			−0.273980	−	0.961735i	$-0.588340\pi$
$467$	−11.8415			−0.547961			−0.273980	+	0.961735i	$0.588340\pi$
$468$	−1.02812			−0.0475250
$469$		−	8.52794i		−	0.393783i
$470$	−11.2814			−0.520373
$471$	−6.85278	−	10.4900i	−0.315759	−	0.483352i
$472$	9.39995			0.432668
$473$		−	50.9752i		−	2.34384i
$474$	0.449615			0.0206515
$475$	6.83519			0.313620
$476$		−	7.97850i		−	0.365694i
$477$			11.9638i			0.547786i
$478$			7.08350i			0.323992i
$479$			29.1274i			1.33087i	0.746458	+	0.665433i	$0.231753\pi$
$479$			29.1274i			1.33087i	−0.746458	+	0.665433i	$0.768247\pi$
$480$	10.5896			0.483348
$481$	2.53484			0.115579
$482$	1.91170			0.0870754
$483$	−12.9077			−0.587321
$484$	31.3957			1.42708
$485$	4.30569			0.195511
$486$		−	0.269982i		−	0.0122466i
$487$	−13.3696			−0.605834			−0.302917	−	0.953017i	$-0.597960\pi$
$487$	−13.3696			−0.605834			−0.302917	+	0.953017i	$0.597960\pi$
$488$	16.3255			0.739021
$489$		−	0.0331476i		−	0.00149899i
$490$	−2.86953			−0.129632
$491$			29.0824i			1.31247i	0.754555	+	0.656236i	$0.227853\pi$
$491$			29.0824i			1.31247i	−0.754555	+	0.656236i	$0.772147\pi$
$492$		−	16.8070i		−	0.757719i
$493$		−	9.36675i		−	0.421857i
$494$			0.144951i			0.00652163i
$495$		−	17.9395i		−	0.806321i
$496$	33.3739			1.49853
$497$			10.0101i			0.449016i
$498$	−0.477389			−0.0213923
$499$			33.4132i			1.49578i	0.663822	+	0.747891i	$0.268933\pi$
$499$			33.4132i			1.49578i	−0.663822	+	0.747891i	$0.731067\pi$
$500$		−	11.8595i		−	0.530373i
$501$	19.9457			0.891110
$502$	2.08807			0.0931951
$503$			22.0230i			0.981957i	0.871172	+	0.490979i	$0.163361\pi$
$503$			22.0230i			0.981957i	−0.871172	+	0.490979i	$0.836639\pi$
$504$	−2.09513			−0.0933246
$505$			21.4700i			0.955404i
$506$	−9.21290			−0.409563
$507$	12.7154			0.564710
$508$	−4.64338			−0.206017
$509$		−	30.0778i		−	1.33318i	−0.745426	−	0.666588i	$-0.767754\pi$
$509$		−	30.0778i		−	1.33318i	0.745426	−	0.666588i	$-0.232246\pi$
$510$	−1.94242			−0.0860117
$511$	−19.2397			−0.851115
$512$			18.5687i			0.820631i
$513$	1.00634			0.0444311
$514$			2.93019i			0.129245i
$515$	32.1681			1.41749
$516$		−	18.8040i		−	0.827801i
$517$	−63.5693			−2.79577
$518$	2.53484			0.111375
$519$	−7.40553			−0.325067
$520$	1.94242			0.0851806
$521$			2.76142i			0.120980i	0.998169	+	0.0604899i	$0.0192663\pi$
$521$			2.76142i			0.120980i	−0.998169	+	0.0604899i	$0.980734\pi$
$522$	−1.20702			−0.0528296
$523$	−0.386395			−0.0168959			−0.00844793	−	0.999964i	$-0.502689\pi$
$523$	−0.386395			−0.0168959			−0.00844793	+	0.999964i	$0.502689\pi$
$524$			5.93783i			0.259395i
$525$			13.4217i			0.585771i
$526$			4.21986i			0.183995i
$527$	−19.5973			−0.853673
$528$	18.6396			0.811183
$529$	−19.6670			−0.855088
$530$		−	11.0918i		−	0.481796i
$531$		−	8.86578i		−	0.384742i
$532$		−	3.83226i		−	0.166150i
$533$		−	4.65289i		−	0.201539i
$534$		−	4.09618i		−	0.177259i
$535$	34.1814			1.47779
$536$		−	4.57561i		−	0.197636i
$537$			17.1917i			0.741876i
$538$	3.67955			0.158637
$539$	−16.1694			−0.696465
$540$		−	6.61762i		−	0.284777i
$541$			19.2245i			0.826527i	0.910612	+	0.413263i	$0.135611\pi$
$541$			19.2245i			0.826527i	−0.910612	+	0.413263i	$0.864389\pi$
$542$	−6.25226			−0.268558
$543$			5.82964i			0.250174i
$544$		−	6.46095i		−	0.277011i
$545$			18.5585i			0.794957i
$546$	−0.284628			−0.0121809
$547$	−19.1850			−0.820289			−0.410145	−	0.912020i	$-0.634522\pi$
$547$	−19.1850			−0.820289			−0.410145	+	0.912020i	$0.634522\pi$
$548$			8.77977i			0.375053i
$549$		−	15.3978i		−	0.657161i
$550$			9.57976i			0.408482i
$551$		−	4.49908i		−	0.191667i
$552$	−6.92555			−0.294771
$553$	−3.29086			−0.139941
$554$		−	5.25656i		−	0.223330i
$555$			16.3158i			0.692567i
$556$		−	12.3418i		−	0.523407i
$557$	−8.66177			−0.367011			−0.183506	−	0.983019i	$-0.558745\pi$
$557$	−8.66177			−0.367011			−0.183506	+	0.983019i	$0.558745\pi$
$558$			2.52534i			0.106906i
$559$		−	5.20575i		−	0.220180i
$560$	−24.2114			−1.02312
$561$	−10.9453			−0.462109
$562$			0.890713i			0.0375725i
$563$			29.0361i			1.22373i	0.790964	+	0.611863i	$0.209580\pi$
$563$			29.0361i			1.22373i	−0.790964	+	0.611863i	$0.790420\pi$
$564$	−23.4498			−0.987414
$565$		−	36.2896i		−	1.52672i
$566$			1.21772i			0.0511848i
$567$			1.97607i			0.0829873i
$568$			5.37088i			0.225357i
$569$		−	19.2553i		−	0.807223i	−0.914930	−	0.403612i	$-0.867755\pi$
$569$		−	19.2553i		−	0.807223i	0.914930	−	0.403612i	$-0.132245\pi$
$570$	−0.932990			−0.0390787
$571$	−29.3377			−1.22774			−0.613871	−	0.789406i	$-0.710389\pi$
$571$	−29.3377			−1.22774			−0.613871	+	0.789406i	$0.710389\pi$
$572$	5.37105			0.224575
$573$			5.96749i			0.249296i
$574$		−	4.65289i		−	0.194208i
$575$			44.3661i			1.85019i
$576$	6.30337			0.262641
$577$	−22.9618			−0.955912			−0.477956	−	0.878384i	$-0.658622\pi$
$577$	−22.9618			−0.955912			−0.477956	+	0.878384i	$0.658622\pi$
$578$		−	3.40459i		−	0.141612i
$579$	−17.4399			−0.724777
$580$	−29.5856			−1.22847
$581$	3.49414			0.144961
$582$	−0.338518			−0.0140320
$583$		−	62.5006i		−	2.58851i
$584$	−10.3229			−0.427167
$585$		−	1.83204i		−	0.0757454i
$586$	2.52172			0.104171
$587$		−	13.0424i		−	0.538317i	−0.963096	−	0.269158i	$-0.913254\pi$
$587$		−	13.0424i		−	0.538317i	0.963096	−	0.269158i	$-0.0867455\pi$
$588$	−5.96466			−0.245978
$589$	−9.41307			−0.387859
$590$			8.21955i			0.338394i
$591$	15.0037			0.617169
$592$	−16.9525			−0.696743
$593$	−35.8248			−1.47115			−0.735575	−	0.677444i	$-0.763088\pi$
$593$	−35.8248			−1.47115			−0.735575	+	0.677444i	$0.763088\pi$
$594$			1.41043i			0.0578704i
$595$	14.2171			0.582843
$596$		−	16.3967i		−	0.671637i
$597$	16.1670			0.661673
$598$	−0.940849			−0.0384742
$599$			10.2960i			0.420681i	0.977628	+	0.210341i	$0.0674573\pi$
$599$			10.2960i			0.420681i	−0.977628	+	0.210341i	$0.932543\pi$
$600$			7.20133i			0.293993i
$601$	2.92572			0.119343			0.0596714	−	0.998218i	$-0.480995\pi$
$601$	2.92572			0.119343			0.0596714	+	0.998218i	$0.480995\pi$
$602$		−	5.20575i		−	0.212170i
$603$	−4.31560			−0.175745
$604$			27.5345i			1.12036i
$605$			55.9449i			2.27448i
$606$		−	1.68800i		−	0.0685703i
$607$		−	42.6959i		−	1.73297i	−0.499200	−	0.866487i	$-0.666373\pi$
$607$		−	42.6959i		−	1.73297i	0.499200	−	0.866487i	$-0.333627\pi$
$608$		−	3.10335i		−	0.125857i
$609$	8.83447			0.357991
$610$			14.2754i			0.577995i
$611$	−6.49189			−0.262634
$612$	−4.03755			−0.163208
$613$		−	33.1950i		−	1.34073i	−0.742030	−	0.670366i	$-0.766137\pi$
$613$		−	33.1950i		−	1.34073i	0.742030	−	0.670366i	$-0.233863\pi$
$614$	−5.40008			−0.217930
$615$	29.9488			1.20765
$616$	10.9453			0.440997
$617$	13.9059			0.559830			0.279915	−	0.960025i	$-0.409694\pi$
$617$	13.9059			0.559830			0.279915	+	0.960025i	$0.409694\pi$
$618$	−2.52909			−0.101735
$619$	36.2605			1.45743			0.728717	−	0.684815i	$-0.240117\pi$
$619$	36.2605			1.45743			0.728717	+	0.684815i	$0.240117\pi$
$620$			61.8995i			2.48594i
$621$			6.53200i			0.262120i
$622$			1.58675i			0.0636227i
$623$			29.9811i			1.20117i
$624$	1.90353			0.0762022
$625$	−12.8278			−0.513112
$626$		−	2.66043i		−	0.106332i
$627$	−5.25727			−0.209955
$628$	13.2061	+	20.2153i	0.526979	+	0.806679i
$629$	9.95460			0.396916
$630$		−	1.83204i		−	0.0729901i
$631$	−40.2442			−1.60210			−0.801049	−	0.598599i	$-0.795724\pi$
$631$	−40.2442			−1.60210			−0.801049	+	0.598599i	$0.795724\pi$
$632$	−1.76569			−0.0702353
$633$			2.44314i			0.0971062i
$634$		−	2.56570i		−	0.101897i
$635$		−	8.27415i		−	0.328350i
$636$		−	23.0556i		−	0.914214i
$637$	−1.65127			−0.0654256
$638$	6.30562			0.249642
$639$	5.06567			0.200395
$640$	−27.0232			−1.06818
$641$	13.5550			0.535392			0.267696	−	0.963503i	$-0.413738\pi$
$641$	13.5550			0.535392			0.267696	+	0.963503i	$0.413738\pi$
$642$	−2.68738			−0.106062
$643$		−	40.6096i		−	1.60149i	−0.599007	−	0.800744i	$-0.704438\pi$
$643$		−	40.6096i		−	1.60149i	0.599007	−	0.800744i	$-0.295562\pi$
$644$	24.8746			0.980196
$645$	33.5074			1.31935
$646$			0.569237i			0.0223963i
$647$	−18.3865			−0.722847			−0.361424	−	0.932402i	$-0.617709\pi$
$647$	−18.3865			−0.722847			−0.361424	+	0.932402i	$0.617709\pi$
$648$			1.06025i			0.0416506i
$649$			46.3161i			1.81807i
$650$			0.978314i			0.0383726i
$651$		−	18.4837i		−	0.724432i
$652$			0.0638791i			0.00250170i
$653$	15.2460			0.596623			0.298312	−	0.954469i	$-0.403577\pi$
$653$	15.2460			0.596623			0.298312	+	0.954469i	$0.403577\pi$
$654$		−	1.45909i		−	0.0570549i
$655$	−10.5808			−0.413425
$656$			31.1175i			1.21494i
$657$			9.73633i			0.379850i
$658$	−6.49189			−0.253080
$659$	−29.9417			−1.16636			−0.583181	−	0.812342i	$-0.698192\pi$
$659$	−29.9417			−1.16636			−0.583181	+	0.812342i	$0.698192\pi$
$660$			34.5714i			1.34569i
$661$	−3.76446			−0.146421			−0.0732104	−	0.997317i	$-0.523324\pi$
$661$	−3.76446			−0.146421			−0.0732104	+	0.997317i	$0.523324\pi$
$662$			3.51645i			0.136671i
$663$	−1.11776			−0.0434103
$664$	1.87476			0.0727548
$665$	6.82881			0.264810
$666$		−	1.28277i		−	0.0497062i
$667$	29.2027			1.13073
$668$	−38.4376			−1.48720
$669$			21.2151i			0.820224i
$670$	4.00103			0.154573
$671$			80.4402i			3.10536i
$672$	6.09379			0.235073
$673$			15.9076i			0.613194i	0.951839	+	0.306597i	$0.0991904\pi$
$673$			15.9076i			0.613194i	−0.951839	+	0.306597i	$0.900810\pi$
$674$	−5.69730			−0.219452
$675$	6.79211			0.261428
$676$	−24.5039			−0.942458
$677$	8.75397			0.336442			0.168221	−	0.985749i	$-0.446198\pi$
$677$	8.75397			0.336442			0.168221	+	0.985749i	$0.446198\pi$
$678$			2.85313i			0.109574i
$679$	2.47771			0.0950857
$680$	7.62809			0.292524
$681$			10.7726i			0.412807i
$682$		−	13.1927i		−	0.505176i
$683$			11.4501i			0.438126i	0.975711	+	0.219063i	$0.0703000\pi$
$683$			11.4501i			0.438126i	−0.975711	+	0.219063i	$0.929700\pi$
$684$	−1.93933			−0.0741522
$685$	−15.6449			−0.597760
$686$	−5.38580			−0.205631
$687$		−	14.5743i		−	0.556045i
$688$			34.8150i			1.32731i
$689$		−	6.38276i		−	0.243164i
$690$		−	6.05588i		−	0.230543i
$691$		−	4.37307i		−	0.166359i	−0.996535	−	0.0831797i	$-0.973492\pi$
$691$		−	4.37307i		−	0.166359i	0.996535	−	0.0831797i	$-0.0265076\pi$
$692$	14.2713			0.542512
$693$		−	10.3233i		−	0.392149i
$694$			5.82429i			0.221087i
$695$	21.9921			0.834207
$696$	4.74008			0.179672
$697$		−	18.2724i		−	0.692116i
$698$			7.77613i			0.294331i
$699$	−0.204892			−0.00774972
$700$		−	25.8651i		−	0.977609i
$701$			30.0866i			1.13635i	0.822906	+	0.568177i	$0.192351\pi$
$701$			30.0866i			1.13635i	−0.822906	+	0.568177i	$0.807649\pi$
$702$			0.144037i			0.00543632i
$703$	4.78144			0.180335
$704$	−32.9297			−1.24108
$705$		−	41.7858i		−	1.57374i
$706$			4.07669i			0.153428i
$707$			12.3549i			0.464655i
$708$			17.0853i			0.642106i
$709$	32.4070			1.21707			0.608536	−	0.793526i	$-0.291757\pi$
$709$	32.4070			1.21707			0.608536	+	0.793526i	$0.291757\pi$
$710$	−4.69643			−0.176254
$711$			1.66535i			0.0624556i
$712$			16.0862i			0.602855i
$713$		−	61.0986i		−	2.28816i
$714$	−1.11776			−0.0418312
$715$			9.57081i			0.357928i
$716$		−	33.1303i		−	1.23814i
$717$	−26.2369			−0.979835
$718$	10.1802			0.379920
$719$			29.3611i			1.09499i	0.836810	+	0.547493i	$0.184418\pi$
$719$			29.3611i			1.09499i	−0.836810	+	0.547493i	$0.815582\pi$
$720$			12.2523i			0.456616i
$721$	18.5111			0.689390
$722$		−	4.85625i		−	0.180731i
$723$			7.08082i			0.263339i
$724$		−	11.2344i		−	0.417522i
$725$		−	30.3656i		−	1.12775i
$726$		−	4.39845i		−	0.163242i
$727$	−27.9292			−1.03584			−0.517919	−	0.855430i	$-0.673293\pi$
$727$	−27.9292			−1.03584			−0.517919	+	0.855430i	$0.673293\pi$
$728$	1.11776			0.0414271
$729$	1.00000			0.0370370
$730$		−	9.02665i		−	0.334091i
$731$		−	20.4435i		−	0.756132i
$732$			29.6732i			1.09675i
$733$	50.5655			1.86768			0.933839	−	0.357693i	$-0.116437\pi$
$733$	50.5655			1.86768			0.933839	+	0.357693i	$0.116437\pi$
$734$	1.05884			0.0390826
$735$		−	10.6286i		−	0.392041i
$736$	20.1433			0.742492
$737$	22.5453			0.830466
$738$	−2.35461			−0.0866745
$739$	−22.8127			−0.839180			−0.419590	−	0.907714i	$-0.637826\pi$
$739$	−22.8127			−0.839180			−0.419590	+	0.907714i	$0.637826\pi$
$740$		−	31.4423i		−	1.15584i
$741$	−0.536889			−0.0197231
$742$		−	6.38276i		−	0.234318i
$743$	−8.59295			−0.315245			−0.157622	−	0.987499i	$-0.550383\pi$
$743$	−8.59295			−0.315245			−0.157622	+	0.987499i	$0.550383\pi$
$744$		−	9.91730i		−	0.363586i
$745$	29.2178			1.07046
$746$	−2.64019			−0.0966642
$747$		−	1.76822i		−	0.0646959i
$748$	21.0927			0.771226
$749$	19.6697			0.718714
$750$	−1.66148			−0.0606687
$751$			50.5343i			1.84402i	0.387161	+	0.922012i	$0.373456\pi$
$751$			50.5343i			1.84402i	−0.387161	+	0.922012i	$0.626544\pi$
$752$	43.4164			1.58323
$753$			7.73410i			0.281846i
$754$	0.643949			0.0234512
$755$	−49.0644			−1.78563
$756$		−	3.80811i		−	0.138500i
$757$			38.4091i			1.39600i	0.716096	+	0.698001i	$0.245927\pi$
$757$			38.4091i			1.39600i	−0.716096	+	0.698001i	$0.754073\pi$
$758$	1.10590			0.0401680
$759$		−	34.1241i		−	1.23863i
$760$	3.66395			0.132906
$761$			38.0158i			1.37807i	0.724728	+	0.689035i	$0.241966\pi$
$761$			38.0158i			1.37807i	−0.724728	+	0.689035i	$0.758034\pi$
$762$			0.650523i			0.0235660i
$763$			10.6795i			0.386623i
$764$		−	11.5000i		−	0.416056i
$765$		−	7.19461i		−	0.260122i
$766$	2.98671			0.107914
$767$			4.72994i			0.170788i
$768$	−10.4822			−0.378242
$769$	30.9446			1.11589			0.557946	−	0.829877i	$-0.311590\pi$
$769$	30.9446			1.11589			0.557946	+	0.829877i	$0.311590\pi$
$770$			9.57081i			0.344908i
$771$	−10.8533			−0.390870
$772$	33.6086			1.20960
$773$	38.2410			1.37543			0.687717	−	0.725979i	$-0.258613\pi$
$773$	38.2410			1.37543			0.687717	+	0.725979i	$0.258613\pi$
$774$	−2.63439			−0.0946912
$775$	−63.5316			−2.28212
$776$	1.32940			0.0477226
$777$			9.38892i			0.336826i
$778$		−	6.32744i		−	0.226850i
$779$		−	8.77667i		−	0.314457i
$780$			3.53054i			0.126413i
$781$	−26.4638			−0.946948
$782$	−3.69482			−0.132126
$783$		−	4.47072i		−	0.159771i
$784$	11.0433			0.394405
$785$	−36.0222	+	23.5322i	−1.28569	+	0.839900i
$786$	0.831872			0.0296719
$787$			3.73369i			0.133092i	0.997783	+	0.0665458i	$0.0211978\pi$
$787$			3.73369i			0.133092i	−0.997783	+	0.0665458i	$0.978802\pi$
$788$	−28.9137			−1.03001
$789$	−15.6301			−0.556448
$790$		−	1.54396i		−	0.0549317i
$791$		−	20.8829i		−	0.742509i
$792$		−	5.53889i		−	0.196816i
$793$			8.21479i			0.291716i
$794$	−5.23582			−0.185812
$795$	41.0833			1.45708
$796$	−31.1556			−1.10428
$797$	13.8103			0.489187			0.244593	−	0.969626i	$-0.421346\pi$
$797$	13.8103			0.489187			0.244593	+	0.969626i	$0.421346\pi$
$798$	−0.536889			−0.0190057
$799$	−25.4944			−0.901925
$800$		−	20.9454i		−	0.740533i
$801$	15.1720			0.536078
$802$	1.56624			0.0553060
$803$		−	50.8640i		−	1.79495i
$804$	8.31663			0.293305
$805$			44.3246i			1.56224i
$806$		−	1.34728i		−	0.0474560i
$807$			13.6289i			0.479759i
$808$			6.62896i			0.233206i
$809$		−	52.5134i		−	1.84627i	−0.384474	−	0.923136i	$-0.625617\pi$
$809$		−	52.5134i		−	1.84627i	0.384474	−	0.923136i	$-0.374383\pi$
$810$	−0.927110			−0.0325753
$811$			6.30705i			0.221470i	0.993850	+	0.110735i	$0.0353206\pi$
$811$			6.30705i			0.221470i	−0.993850	+	0.110735i	$0.964679\pi$
$812$	−17.0250			−0.597460
$813$		−	23.1580i		−	0.812188i
$814$			6.70135i			0.234882i
$815$	−0.113828			−0.00398721
$816$	7.47537			0.261690
$817$		−	9.81953i		−	0.343542i
$818$	6.81813			0.238390
$819$		−	1.05425i		−	0.0368383i
$820$	−57.7147			−2.01548
$821$	−52.1412			−1.81974			−0.909870	−	0.414893i	$-0.863819\pi$
$821$	−52.1412			−1.81974			−0.909870	+	0.414893i	$0.863819\pi$
$822$	1.23002			0.0429019
$823$		−	29.0074i		−	1.01114i	−0.862787	−	0.505568i	$-0.831283\pi$
$823$		−	29.0074i		−	1.01114i	0.862787	−	0.505568i	$-0.168717\pi$
$824$	9.93202			0.345998
$825$	−35.4829			−1.23536
$826$			4.72994i			0.164576i
$827$	−41.4786			−1.44235			−0.721176	−	0.692752i	$-0.756398\pi$
$827$	−41.4786			−1.44235			−0.721176	+	0.692752i	$0.756398\pi$
$828$		−	12.5879i		−	0.437459i
$829$	3.30476			0.114779			0.0573895	−	0.998352i	$-0.481722\pi$
$829$	3.30476			0.114779			0.0573895	+	0.998352i	$0.481722\pi$
$830$			1.63934i			0.0569022i
$831$	19.4700			0.675407
$832$	−3.36288			−0.116587
$833$	−6.48471			−0.224682
$834$	−1.72904			−0.0598719
$835$		−	68.4930i		−	2.37030i
$836$	10.1313			0.350400
$837$	−9.35374			−0.323312
$838$			0.555789i			0.0191994i
$839$			44.6737i			1.54231i	0.636650	+	0.771153i	$0.280320\pi$
$839$			44.6737i			1.54231i	−0.636650	+	0.771153i	$0.719680\pi$
$840$			7.19461i			0.248238i
$841$	9.01266			0.310781
$842$	7.45954			0.257073
$843$	−3.29915			−0.113629
$844$		−	4.70820i		−	0.162063i
$845$		−	43.6641i		−	1.50209i
$846$			3.28525i			0.112949i
$847$			32.1935i			1.10618i
$848$			42.6865i			1.46586i
$849$	−4.51039			−0.154796
$850$			3.84195i			0.131778i
$851$			31.0355i			1.06388i
$852$	−9.76211			−0.334444
$853$	36.6543			1.25502			0.627510	−	0.778609i	$-0.284074\pi$
$853$	36.6543			1.25502			0.627510	+	0.778609i	$0.284074\pi$
$854$			8.21479i			0.281104i
$855$		−	3.45575i		−	0.118184i
$856$	10.5536			0.360716
$857$			5.65579i			0.193198i	0.995323	+	0.0965991i	$0.0307965\pi$
$857$			5.65579i			0.193198i	−0.995323	+	0.0965991i	$0.969204\pi$
$858$		−	0.752469i		−	0.0256889i
$859$			30.8285i			1.05185i	0.850530	+	0.525927i	$0.176282\pi$
$859$			30.8285i			1.05185i	−0.850530	+	0.525927i	$0.823718\pi$
$860$	−64.5724			−2.20190
$861$	17.2340			0.587335
$862$		−	0.242137i		−	0.00824723i
$863$		−	12.7523i		−	0.434094i	−0.976161	−	0.217047i	$-0.930357\pi$
$863$		−	12.7523i		−	0.434094i	0.976161	−	0.217047i	$-0.0696426\pi$
$864$		−	3.08379i		−	0.104913i
$865$			25.4303i			0.864657i
$866$	4.84335			0.164584
$867$	12.6104			0.428272
$868$			35.6201i			1.20902i
$869$		−	8.70003i		−	0.295128i
$870$			4.14485i			0.140523i
$871$	2.30239			0.0780136
$872$			5.73000i			0.194042i
$873$		−	1.25385i		−	0.0424365i
$874$	−1.77471			−0.0600305
$875$	12.1608			0.411111
$876$		−	18.7630i		−	0.633942i
$877$		−	19.5832i		−	0.661276i	−0.943758	−	0.330638i	$-0.892736\pi$
$877$		−	19.5832i		−	0.661276i	0.943758	−	0.330638i	$-0.107264\pi$
$878$	5.51391			0.186086
$879$			9.34032i			0.315041i
$880$		−	64.0076i		−	2.15770i
$881$			12.9453i			0.436137i	0.975933	+	0.218069i	$0.0699757\pi$
$881$			12.9453i			0.436137i	−0.975933	+	0.218069i	$0.930024\pi$
$882$			0.835631i			0.0281372i
$883$		−	36.8186i		−	1.23904i	−0.784979	−	0.619522i	$-0.787326\pi$
$883$		−	36.8186i		−	1.23904i	0.784979	−	0.619522i	$-0.212674\pi$
$884$	2.15405			0.0724486
$885$	−30.4448			−1.02339
$886$	5.35635			0.179950
$887$			24.5149i			0.823130i	0.911380	+	0.411565i	$0.135018\pi$
$887$			24.5149i			0.823130i	−0.911380	+	0.411565i	$0.864982\pi$
$888$			5.03757i			0.169050i
$889$		−	4.76136i		−	0.159691i
$890$	−14.0662			−0.471498
$891$	−5.22414			−0.175015
$892$		−	40.8839i		−	1.36889i
$893$	−12.2456			−0.409782
$894$	−2.29713			−0.0768277
$895$	59.0356			1.97334
$896$	−15.5505			−0.519505
$897$		−	3.48485i		−	0.116356i
$898$	1.87916			0.0627085
$899$			41.8179i			1.39471i
$900$	−13.0891			−0.436305
$901$		−	25.0658i		−	0.835062i
$902$	12.3008			0.409573
$903$	19.2818			0.641658
$904$		−	11.2046i		−	0.372659i
$905$	20.0188			0.665447
$906$	3.85750			0.128157
$907$	−24.8754			−0.825974			−0.412987	−	0.910737i	$-0.635515\pi$
$907$	−24.8754			−0.825974			−0.412987	+	0.910737i	$0.635515\pi$
$908$		−	20.7600i		−	0.688945i
$909$	6.25226			0.207374
$910$			0.977401i			0.0324005i
$911$	7.02729			0.232825			0.116412	−	0.993201i	$-0.462861\pi$
$911$	7.02729			0.232825			0.116412	+	0.993201i	$0.462861\pi$
$912$	3.59060			0.118897
$913$			9.23744i			0.305715i
$914$			6.26463i			0.207215i
$915$	−52.8754			−1.74801
$916$			28.0863i			0.927997i
$917$	−6.08870			−0.201066
$918$			0.565649i			0.0186692i
$919$		−	31.2503i		−	1.03085i	−0.856934	−	0.515427i	$-0.827633\pi$
$919$		−	31.2503i		−	1.03085i	0.856934	−	0.515427i	$-0.172367\pi$
$920$			23.7821i			0.784073i
$921$		−	20.0016i		−	0.659076i
$922$		−	0.890713i		−	0.0293341i
$923$	−2.70256			−0.0889559
$924$			19.8941i			0.654468i
$925$	32.2714			1.06108
$926$	2.84994			0.0936550
$927$		−	9.36762i		−	0.307673i
$928$	−13.7868			−0.452573
$929$	13.1043			0.429938			0.214969	−	0.976621i	$-0.431035\pi$
$929$	13.1043			0.429938			0.214969	+	0.976621i	$0.431035\pi$
$930$	8.67194			0.284364
$931$	−3.11476			−0.102082
$932$	0.394849			0.0129337
$933$	−5.87722			−0.192412
$934$		−	3.19700i		−	0.104609i
$935$			37.5856i			1.22918i
$936$		−	0.565649i		−	0.0184888i
$937$			35.0676i			1.14561i	0.819692	+	0.572804i	$0.194145\pi$
$937$			35.0676i			1.14561i	−0.819692	+	0.572804i	$0.805855\pi$
$938$	2.30239			0.0751758
$939$	9.85411			0.321577
$940$			80.5257i			2.62646i
$941$	−0.774263			−0.0252403			−0.0126201	−	0.999920i	$-0.504017\pi$
$941$	−0.774263			−0.0252403			−0.0126201	+	0.999920i	$0.504017\pi$
$942$	2.83211	−	1.85013i	0.0922750	−	0.0602804i
$943$	56.9679			1.85513
$944$		−	31.6329i		−	1.02956i
$945$	6.78577			0.220741
$946$	13.7624			0.447455
$947$		−	36.6821i		−	1.19201i	−0.802982	−	0.596004i	$-0.796754\pi$
$947$		−	36.6821i		−	1.19201i	0.802982	−	0.596004i	$-0.203246\pi$
$948$		−	3.20931i		−	0.104234i
$949$		−	5.19438i		−	0.168617i
$950$			1.84538i			0.0598721i
$951$	9.50321			0.308163
$952$	4.38958			0.142267
$953$	−0.950348			−0.0307848			−0.0153924	−	0.999882i	$-0.504900\pi$
$953$	−0.950348			−0.0307848			−0.0153924	+	0.999882i	$0.504900\pi$
$954$	−3.23002			−0.104576
$955$	20.4922			0.663110
$956$	50.5614			1.63527
$957$			23.3557i			0.754981i
$958$	−7.86389			−0.254071
$959$	−9.00285			−0.290717
$960$		−	21.6456i		−	0.698607i
$961$	56.4924			1.82234
$962$			0.684363i			0.0220647i
$963$		−	9.95391i		−	0.320760i
$964$		−	13.6455i		−	0.439493i
$965$			59.8879i			1.92786i
$966$		−	3.48485i		−	0.112123i
$967$	−21.2095			−0.682051			−0.341025	−	0.940054i	$-0.610774\pi$
$967$	−21.2095			−0.682051			−0.341025	+	0.940054i	$0.610774\pi$
$968$			17.2732i			0.555182i
$969$	−2.10842			−0.0677323
$970$			1.16246i			0.0373243i
$971$		−	29.1017i		−	0.933919i	−0.884279	−	0.466960i	$-0.845349\pi$
$971$		−	29.1017i		−	0.933919i	0.884279	−	0.466960i	$-0.154651\pi$
$972$	−1.92711			−0.0618121
$973$	12.6553			0.405711
$974$		−	3.60955i		−	0.115658i
$975$	−3.62362			−0.116049
$976$		−	54.9388i		−	1.75855i
$977$	−34.3247			−1.09814			−0.549072	−	0.835775i	$-0.685019\pi$
$977$	−34.3247			−1.09814			−0.549072	+	0.835775i	$0.685019\pi$
$978$	0.00894927			0.000286166
$979$	−79.2609			−2.53319
$980$			20.4824i			0.654287i
$981$	5.40439			0.172549
$982$	−7.85175			−0.250559
$983$		−	34.6230i		−	1.10430i	−0.833744	−	0.552151i	$-0.813807\pi$
$983$		−	34.6230i		−	1.10430i	0.833744	−	0.552151i	$-0.186193\pi$
$984$	9.24682			0.294778
$985$		−	51.5221i		−	1.64163i
$986$	2.52886			0.0805352
$987$		−	24.0456i		−	0.765380i
$988$	1.03464			0.0329164
$989$	63.7369			2.02671
$990$	4.84335			0.153932
$991$	18.7406			0.595316			0.297658	−	0.954673i	$-0.403794\pi$
$991$	18.7406			0.595316			0.297658	+	0.954673i	$0.403794\pi$
$992$			28.8450i			0.915828i
$993$	−13.0247			−0.413328
$994$	−2.70256			−0.0857200
$995$		−	55.5170i		−	1.76001i
$996$			3.40756i			0.107973i
$997$			11.4911i			0.363927i	0.983305	+	0.181963i	$0.0582452\pi$
$997$			11.4911i			0.363927i	−0.983305	+	0.181963i	$0.941755\pi$
$998$	−9.02098			−0.285554
$999$	4.75130			0.150325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.b.a.313.7	yes	12
3.2	odd	2		1413.2.b.c.784.6		12
157.156	even	2	inner	471.2.b.a.313.6	✓	12
471.470	odd	2		1413.2.b.c.784.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.b.a.313.6	✓	12	157.156	even	2	inner
471.2.b.a.313.7	yes	12	1.1	even	1	trivial
1413.2.b.c.784.6		12	3.2	odd	2
1413.2.b.c.784.7		12	471.470	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.269982i q^{2} -1.00000 q^{3} +1.92711 q^{4} +3.43396i q^{5} -0.269982i q^{6} +1.97607i q^{7} +1.06025i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.269982i q^{2} -1.00000 q^{3} +1.92711 q^{4} +3.43396i q^{5} -0.269982i q^{6} +1.97607i q^{7} +1.06025i q^{8} +1.00000 q^{9} -0.927110 q^{10} -5.22414 q^{11} -1.92711 q^{12} -0.533505 q^{13} -0.533505 q^{14} -3.43396i q^{15} +3.56797 q^{16} -2.09513 q^{17} +0.269982i q^{18} -1.00634 q^{19} +6.61762i q^{20} -1.97607i q^{21} -1.41043i q^{22} -6.53200i q^{23} -1.06025i q^{24} -6.79211 q^{25} -0.144037i q^{26} -1.00000 q^{27} +3.80811i q^{28} +4.47072i q^{29} +0.927110 q^{30} +9.35374 q^{31} +3.08379i q^{32} +5.22414 q^{33} -0.565649i q^{34} -6.78577 q^{35} +1.92711 q^{36} -4.75130 q^{37} -0.271695i q^{38} +0.533505 q^{39} -3.64086 q^{40} +8.72136i q^{41} +0.533505 q^{42} +9.75764i q^{43} -10.0675 q^{44} +3.43396i q^{45} +1.76352 q^{46} +12.1684 q^{47} -3.56797 q^{48} +3.09513 q^{49} -1.83375i q^{50} +2.09513 q^{51} -1.02812 q^{52} +11.9638i q^{53} -0.269982i q^{54} -17.9395i q^{55} -2.09513 q^{56} +1.00634 q^{57} -1.20702 q^{58} -8.86578i q^{59} -6.61762i q^{60} -15.3978i q^{61} +2.52534i q^{62} +1.97607i q^{63} +6.30337 q^{64} -1.83204i q^{65} +1.41043i q^{66} -4.31560 q^{67} -4.03755 q^{68} +6.53200i q^{69} -1.83204i q^{70} +5.06567 q^{71} +1.06025i q^{72} +9.73633i q^{73} -1.28277i q^{74} +6.79211 q^{75} -1.93933 q^{76} -10.3233i q^{77} +0.144037i q^{78} +1.66535i q^{79} +12.2523i q^{80} +1.00000 q^{81} -2.35461 q^{82} -1.76822i q^{83} -3.80811i q^{84} -7.19461i q^{85} -2.63439 q^{86} -4.47072i q^{87} -5.53889i q^{88} +15.1720 q^{89} -0.927110 q^{90} -1.05425i q^{91} -12.5879i q^{92} -9.35374 q^{93} +3.28525i q^{94} -3.45575i q^{95} -3.08379i q^{96} -1.25385i q^{97} +0.835631i q^{98} -5.22414 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9	\( 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9} + 18 q^{10} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} + 10 q^{16} + 2 q^{17} + 4 q^{19} + 12 q^{25} - 12 q^{27} - 18 q^{30} + 2 q^{31} + 2 q^{33} - 4 q^{35} - 6 q^{36} - 2 q^{37} - 4 q^{39} - 40 q^{40} - 4 q^{42} - 36 q^{44} + 34 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{51} - 6 q^{52} + 2 q^{56} - 4 q^{57} + 24 q^{58} + 28 q^{64} - 38 q^{67} + 32 q^{68} - 26 q^{71} - 12 q^{75} - 28 q^{76} + 12 q^{81} - 50 q^{82} + 6 q^{86} - 4 q^{89} + 18 q^{90} - 2 q^{93} - 2 q^{99}+O(q^{100}) \) 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9 + 18 * q^10 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 + 10 * q^16 + 2 * q^17 + 4 * q^19 + 12 * q^25 - 12 * q^27 - 18 * q^30 + 2 * q^31 + 2 * q^33 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^39 - 40 * q^40 - 4 * q^42 - 36 * q^44 + 34 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^51 - 6 * q^52 + 2 * q^56 - 4 * q^57 + 24 * q^58 + 28 * q^64 - 38 * q^67 + 32 * q^68 - 26 * q^71 - 12 * q^75 - 28 * q^76 + 12 * q^81 - 50 * q^82 + 6 * q^86 - 4 * q^89 + 18 * q^90 - 2 * q^93 - 2 * q^99

Introduction

L-functions

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