LMFDB - Embedded newform 731.2.d.c.560.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(560,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("731.560");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.d (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 29 x^{18} + 358 x^{16} + 2458 x^{14} + 10298 x^{12} + 27188 x^{10} + 45053 x^{8} + 44980 x^{6} + \cdots + 36 $ x^20 + 29x^18 + 358x^16 + 2458x^14 + 10298x^12 + 27188x^10 + 45053x^8 + 44980x^6 + 24400x^4 + 5448*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			560.6
Root			$-1.58374i$ of defining polynomial
Character	$\chi$	$=$	731.560
Dual form			731.2.d.c.560.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.11938 q^{2} +0.764619i q^{3} +2.49176 q^{4} +0.0168131i q^{5} -1.62052i q^{6} -2.93256i q^{7} -1.04222 q^{8} +2.41536 q^{9} +O(q^{10})$	\(q-2.11938 q^{2} +0.764619i q^{3} +2.49176 q^{4} +0.0168131i q^{5} -1.62052i q^{6} -2.93256i q^{7} -1.04222 q^{8} +2.41536 q^{9} -0.0356332i q^{10} +5.23318i q^{11} +1.90525i q^{12} +0.444316 q^{13} +6.21520i q^{14} -0.0128556 q^{15} -2.77465 q^{16} +(4.04838 - 0.781432i) q^{17} -5.11906 q^{18} -5.57095 q^{19} +0.0418941i q^{20} +2.24229 q^{21} -11.0911i q^{22} -5.04516i q^{23} -0.796905i q^{24} +4.99972 q^{25} -0.941673 q^{26} +4.14068i q^{27} -7.30724i q^{28} -4.15210i q^{29} +0.0272458 q^{30} -8.24383i q^{31} +7.96498 q^{32} -4.00139 q^{33} +(-8.58004 + 1.65615i) q^{34} +0.0493053 q^{35} +6.01849 q^{36} +5.83012i q^{37} +11.8070 q^{38} +0.339732i q^{39} -0.0175230i q^{40} +5.18552i q^{41} -4.75226 q^{42} +1.00000 q^{43} +13.0398i q^{44} +0.0406096i q^{45} +10.6926i q^{46} +0.733921 q^{47} -2.12155i q^{48} -1.59991 q^{49} -10.5963 q^{50} +(0.597497 + 3.09547i) q^{51} +1.10713 q^{52} +11.1822 q^{53} -8.77567i q^{54} -0.0879858 q^{55} +3.05639i q^{56} -4.25966i q^{57} +8.79986i q^{58} +5.63936 q^{59} -0.0320330 q^{60} +11.0175i q^{61} +17.4718i q^{62} -7.08318i q^{63} -11.3315 q^{64} +0.00747031i q^{65} +8.48045 q^{66} -4.45949 q^{67} +(10.0876 - 1.94714i) q^{68} +3.85762 q^{69} -0.104497 q^{70} -3.93942i q^{71} -2.51735 q^{72} +10.0591i q^{73} -12.3562i q^{74} +3.82288i q^{75} -13.8815 q^{76} +15.3466 q^{77} -0.720021i q^{78} -4.65614i q^{79} -0.0466504i q^{80} +4.08003 q^{81} -10.9901i q^{82} +16.1714 q^{83} +5.58725 q^{84} +(0.0131383 + 0.0680656i) q^{85} -2.11938 q^{86} +3.17477 q^{87} -5.45415i q^{88} +15.6803 q^{89} -0.0860670i q^{90} -1.30298i q^{91} -12.5713i q^{92} +6.30339 q^{93} -1.55546 q^{94} -0.0936648i q^{95} +6.09018i q^{96} -11.8561i q^{97} +3.39082 q^{98} +12.6400i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9	$ 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9} - 4 q^{13} + 26 q^{15} + 6 q^{16} + 16 q^{17} - 22 q^{18} - 4 q^{19} + 20 q^{21} - 2 q^{25} + 22 q^{26} - 72 q^{30} + 38 q^{32} - 12 q^{33} + 12 q^{34} - 30 q^{35} - 104 q^{36} - 22 q^{38} + 26 q^{42} + 20 q^{43} - 34 q^{47} + 22 q^{49} + 42 q^{50} + 52 q^{51} - 110 q^{52} + 14 q^{53} + 12 q^{55} + 20 q^{59} + 42 q^{60} - 22 q^{64} + 50 q^{66} - 12 q^{67} + 50 q^{68} - 82 q^{69} - 30 q^{70} - 50 q^{72} + 2 q^{76} + 78 q^{77} + 44 q^{81} + 20 q^{83} + 62 q^{84} + 76 q^{85} + 2 q^{86} + 12 q^{87} - 46 q^{89} + 58 q^{93} - 18 q^{94} - 62 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9 - 4 * q^13 + 26 * q^15 + 6 * q^16 + 16 * q^17 - 22 * q^18 - 4 * q^19 + 20 * q^21 - 2 * q^25 + 22 * q^26 - 72 * q^30 + 38 * q^32 - 12 * q^33 + 12 * q^34 - 30 * q^35 - 104 * q^36 - 22 * q^38 + 26 * q^42 + 20 * q^43 - 34 * q^47 + 22 * q^49 + 42 * q^50 + 52 * q^51 - 110 * q^52 + 14 * q^53 + 12 * q^55 + 20 * q^59 + 42 * q^60 - 22 * q^64 + 50 * q^66 - 12 * q^67 + 50 * q^68 - 82 * q^69 - 30 * q^70 - 50 * q^72 + 2 * q^76 + 78 * q^77 + 44 * q^81 + 20 * q^83 + 62 * q^84 + 76 * q^85 + 2 * q^86 + 12 * q^87 - 46 * q^89 + 58 * q^93 - 18 * q^94 - 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$-1$	$1$

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 $

$2$	−2.11938			−1.49863			−0.749313	−	0.662216i	$-0.769616\pi$
$2$	−2.11938			−1.49863			−0.749313	+	0.662216i	$0.769616\pi$
$3$			0.764619i			0.441453i	0.975336	+	0.220726i	$0.0708428\pi$
$3$			0.764619i			0.441453i	−0.975336	+	0.220726i	$0.929157\pi$
$4$	2.49176			1.24588
$5$			0.0168131i			0.00751903i	0.999993	+	0.00375951i	$0.00119669\pi$
$5$			0.0168131i			0.00751903i	−0.999993	+	0.00375951i	$0.998803\pi$
$6$		−	1.62052i		−	0.661573i
$7$		−	2.93256i		−	1.10840i	−0.832382	−	0.554202i	$-0.813024\pi$
$7$		−	2.93256i		−	1.10840i	0.832382	−	0.554202i	$-0.186976\pi$
$8$	−1.04222			−0.368482
$9$	2.41536			0.805119
$10$		−	0.0356332i		−	0.0112682i
$11$			5.23318i			1.57786i	0.614480	+	0.788932i	$0.289366\pi$
$11$			5.23318i			1.57786i	−0.614480	+	0.788932i	$0.710634\pi$
$12$			1.90525i			0.549997i
$13$	0.444316			0.123231			0.0616155	−	0.998100i	$-0.480375\pi$
$13$	0.444316			0.123231			0.0616155	+	0.998100i	$0.480375\pi$
$14$			6.21520i			1.66108i
$15$	−0.0128556			−0.00331930
$16$	−2.77465			−0.693663
$17$	4.04838	−	0.781432i	0.981876	−	0.189525i
$17$	4.04838	−	0.781432i	0.981876	−	0.189525i
$18$	−5.11906			−1.20657
$19$	−5.57095			−1.27806			−0.639032	−	0.769180i	$-0.720665\pi$
$19$	−5.57095			−1.27806			−0.639032	+	0.769180i	$0.720665\pi$
$20$			0.0418941i			0.00936781i
$21$	2.24229			0.489308
$22$		−	11.0911i		−	2.36463i
$23$		−	5.04516i		−	1.05199i	−0.850488	−	0.525994i	$-0.823693\pi$
$23$		−	5.04516i		−	1.05199i	0.850488	−	0.525994i	$-0.176307\pi$
$24$		−	0.796905i		−	0.162667i
$25$	4.99972			0.999943
$26$	−0.941673			−0.184677
$27$			4.14068i			0.796875i
$28$		−	7.30724i		−	1.38094i
$29$		−	4.15210i		−	0.771025i	−0.922703	−	0.385513i	$-0.874025\pi$
$29$		−	4.15210i		−	0.771025i	0.922703	−	0.385513i	$-0.125975\pi$
$30$	0.0272458			0.00497438
$31$		−	8.24383i		−	1.48064i	−0.672257	−	0.740318i	$-0.734675\pi$
$31$		−	8.24383i		−	1.48064i	0.672257	−	0.740318i	$-0.265325\pi$
$32$	7.96498			1.40802
$33$	−4.00139			−0.696553
$34$	−8.58004	+	1.65615i	−1.47146	+	0.284027i
$35$	0.0493053			0.00833412
$36$	6.01849			1.00308
$37$			5.83012i			0.958466i	0.877688	+	0.479233i	$0.159085\pi$
$37$			5.83012i			0.958466i	−0.877688	+	0.479233i	$0.840915\pi$
$38$	11.8070			1.91534
$39$			0.339732i			0.0544007i
$40$		−	0.0175230i		−	0.00277063i
$41$			5.18552i			0.809843i	0.914352	+	0.404921i	$0.132701\pi$
$41$			5.18552i			0.809843i	−0.914352	+	0.404921i	$0.867299\pi$
$42$	−4.75226			−0.733290
$43$	1.00000			0.152499
$43$	1.00000			0.152499
$44$			13.0398i			1.96583i
$45$			0.0406096i			0.00605372i
$46$			10.6926i			1.57654i
$47$	0.733921			0.107053			0.0535267	−	0.998566i	$-0.482954\pi$
$47$	0.733921			0.107053			0.0535267	+	0.998566i	$0.482954\pi$
$48$		−	2.12155i		−	0.306219i
$49$	−1.59991			−0.228559
$50$	−10.5963			−1.49854
$51$	0.597497	+	3.09547i	0.0836664	+	0.433452i
$52$	1.10713			0.153531
$53$	11.1822			1.53600			0.767999	−	0.640451i	$-0.221252\pi$
$53$	11.1822			1.53600			0.767999	+	0.640451i	$0.221252\pi$
$54$		−	8.77567i		−	1.19422i
$55$	−0.0879858			−0.0118640
$56$			3.05639i			0.408427i
$57$		−	4.25966i		−	0.564205i
$58$			8.79986i			1.15548i
$59$	5.63936			0.734182			0.367091	−	0.930185i	$-0.380354\pi$
$59$	5.63936			0.734182			0.367091	+	0.930185i	$0.380354\pi$
$60$	−0.0320330			−0.00413545
$61$			11.0175i			1.41065i	0.708883	+	0.705326i	$0.249199\pi$
$61$			11.0175i			1.41065i	−0.708883	+	0.705326i	$0.750801\pi$
$62$			17.4718i			2.21892i
$63$		−	7.08318i		−	0.892397i
$64$	−11.3315			−1.41644
$65$			0.00747031i			0.000926578i
$66$	8.48045			1.04387
$67$	−4.45949			−0.544814			−0.272407	−	0.962182i	$-0.587820\pi$
$67$	−4.45949			−0.544814			−0.272407	+	0.962182i	$0.587820\pi$
$68$	10.0876	−	1.94714i	1.22330	−	0.236125i
$69$	3.85762			0.464403
$70$	−0.104497			−0.0124897
$71$		−	3.93942i		−	0.467523i	−0.972294	−	0.233761i	$-0.924897\pi$
$71$		−	3.93942i		−	0.467523i	0.972294	−	0.233761i	$-0.0751034\pi$
$72$	−2.51735			−0.296672
$73$			10.0591i			1.17733i	0.808377	+	0.588665i	$0.200346\pi$
$73$			10.0591i			1.17733i	−0.808377	+	0.588665i	$0.799654\pi$
$74$		−	12.3562i		−	1.43638i
$75$			3.82288i			0.441428i
$76$	−13.8815			−1.59232
$77$	15.3466			1.74891
$78$		−	0.720021i		−	0.0815263i
$79$		−	4.65614i		−	0.523857i	−0.965087	−	0.261929i	$-0.915642\pi$
$79$		−	4.65614i		−	0.523857i	0.965087	−	0.261929i	$-0.0843585\pi$
$80$		−	0.0466504i		−	0.00521567i
$81$	4.08003			0.453337
$82$		−	10.9901i		−	1.21365i
$83$	16.1714			1.77504			0.887519	−	0.460772i	$-0.152427\pi$
$83$	16.1714			1.77504			0.887519	+	0.460772i	$0.152427\pi$
$84$	5.58725			0.609619
$85$	0.0131383	+	0.0680656i	0.00142504	+	0.00738275i
$86$	−2.11938			−0.228538
$87$	3.17477			0.340371
$88$		−	5.45415i		−	0.581415i
$89$	15.6803			1.66211			0.831057	−	0.556188i	$-0.187736\pi$
$89$	15.6803			1.66211			0.831057	+	0.556188i	$0.187736\pi$
$90$		−	0.0860670i		−	0.00907226i
$91$		−	1.30298i		−	0.136590i
$92$		−	12.5713i		−	1.31065i
$93$	6.30339			0.653631
$94$	−1.55546			−0.160433
$95$		−	0.0936648i		−	0.00960980i
$96$			6.09018i			0.621576i
$97$		−	11.8561i		−	1.20380i	−0.798570	−	0.601902i	$-0.794410\pi$
$97$		−	11.8561i		−	1.20380i	0.798570	−	0.601902i	$-0.205590\pi$
$98$	3.39082			0.342524
$99$			12.6400i			1.27037i
$100$	12.4581			1.24581
$101$	−4.65389			−0.463080			−0.231540	−	0.972825i	$-0.574376\pi$
$101$	−4.65389			−0.463080			−0.231540	+	0.972825i	$0.574376\pi$
$102$	−1.26632	−	6.56046i	−0.125385	−	0.649582i
$103$	11.8355			1.16619			0.583095	−	0.812404i	$-0.301841\pi$
$103$	11.8355			1.16619			0.583095	+	0.812404i	$0.301841\pi$
$104$	−0.463077			−0.0454084
$105$			0.0376998i			0.00367912i
$106$	−23.6994			−2.30189
$107$			17.1223i			1.65528i	0.561261	+	0.827639i	$0.310316\pi$
$107$			17.1223i			1.65528i	−0.561261	+	0.827639i	$0.689684\pi$
$108$			10.3176i			0.992811i
$109$		−	18.1393i		−	1.73743i	−0.495314	−	0.868714i	$-0.664947\pi$
$109$		−	18.1393i		−	1.73743i	0.495314	−	0.868714i	$-0.335053\pi$
$110$	0.186475			0.0177797
$111$	−4.45782			−0.423117
$112$			8.13684i			0.768859i
$113$			1.83820i			0.172923i	0.996255	+	0.0864617i	$0.0275560\pi$
$113$			1.83820i			0.172923i	−0.996255	+	0.0864617i	$0.972444\pi$
$114$			9.02782i			0.845533i
$115$	0.0848246			0.00790993
$116$		−	10.3460i		−	0.960605i
$117$	1.07318			0.0992157
$118$	−11.9519			−1.10026
$119$	−2.29160	−	11.8721i	−0.210070	−	1.08831i
$120$	0.0133984			0.00122310
$121$	−16.3862			−1.48966
$122$		−	23.3503i		−	2.11404i
$123$	−3.96495			−0.357507
$124$		−	20.5417i		−	1.84470i
$125$			0.168126i			0.0150376i
$126$			15.0119i			1.33737i
$127$	7.93526			0.704140			0.352070	−	0.935974i	$-0.385478\pi$
$127$	7.93526			0.704140			0.352070	+	0.935974i	$0.385478\pi$
$128$	8.08576			0.714687
$129$			0.764619i			0.0673209i
$130$		−	0.0158324i		−	0.00138859i
$131$		−	2.04399i		−	0.178585i	−0.996005	−	0.0892923i	$-0.971539\pi$
$131$		−	2.04399i		−	0.178585i	0.996005	−	0.0892923i	$-0.0284605\pi$
$132$	−9.97050			−0.867821
$133$			16.3372i			1.41661i
$134$	9.45135			0.816472
$135$	−0.0696176			−0.00599173
$136$	−4.21932	+	0.814428i	−0.361804	+	0.0698366i
$137$	−15.9391			−1.36177			−0.680884	−	0.732392i	$-0.738404\pi$
$137$	−15.9391			−1.36177			−0.680884	+	0.732392i	$0.738404\pi$
$138$	−8.17576			−0.695967
$139$			9.18520i			0.779078i	0.921010	+	0.389539i	$0.127366\pi$
$139$			9.18520i			0.779078i	−0.921010	+	0.389539i	$0.872634\pi$
$140$	0.122857			0.0103833
$141$			0.561170i			0.0472590i
$142$			8.34911i			0.700642i
$143$			2.32519i			0.194442i
$144$	−6.70178			−0.558482
$145$	0.0698095			0.00579736
$146$		−	21.3190i		−	1.76438i
$147$		−	1.22332i		−	0.100898i
$148$			14.5273i			1.19413i
$149$	−7.06477			−0.578769			−0.289384	−	0.957213i	$-0.593451\pi$
$149$	−7.06477			−0.578769			−0.289384	+	0.957213i	$0.593451\pi$
$150$		−	8.10212i		−	0.661535i
$151$	2.13370			0.173638			0.0868191	−	0.996224i	$-0.472330\pi$
$151$	2.13370			0.173638			0.0868191	+	0.996224i	$0.472330\pi$
$152$	5.80619			0.470944
$153$	9.77828	−	1.88744i	0.790527	−	0.152590i
$154$	−32.5253			−2.62096
$155$	0.138604			0.0111329
$156$			0.846531i			0.0677767i
$157$	9.41136			0.751108			0.375554	−	0.926801i	$-0.377452\pi$
$157$	9.41136			0.751108			0.375554	+	0.926801i	$0.377452\pi$
$158$			9.86812i			0.785066i
$159$			8.55015i			0.678071i
$160$			0.133916i			0.0105870i
$161$	−14.7952			−1.16603
$162$	−8.64712			−0.679382
$163$		−	22.7321i		−	1.78052i	−0.455455	−	0.890259i	$-0.650523\pi$
$163$		−	22.7321i		−	1.78052i	0.455455	−	0.890259i	$-0.349477\pi$
$164$			12.9211i			1.00897i
$165$		−	0.0672756i		−	0.00523740i
$166$	−34.2732			−2.66012
$167$			8.79481i			0.680563i	0.940324	+	0.340281i	$0.110522\pi$
$167$			8.79481i			0.680563i	−0.940324	+	0.340281i	$0.889478\pi$
$168$	−2.33697			−0.180301
$169$	−12.8026			−0.984814
$170$	−0.0278449	−	0.144257i	−0.00213561	−	0.0110640i
$171$	−13.4559			−1.02899
$172$	2.49176			0.189995
$173$		−	6.49853i		−	0.494074i	−0.969006	−	0.247037i	$-0.920543\pi$
$173$		−	6.49853i		−	0.494074i	0.969006	−	0.247037i	$-0.0794570\pi$
$174$	−6.72854			−0.510089
$175$		−	14.6620i		−	1.10834i
$176$		−	14.5203i		−	1.09451i
$177$			4.31196i			0.324107i
$178$	−33.2326			−2.49089
$179$	24.3200			1.81776			0.908882	−	0.417054i	$-0.136937\pi$
$179$	24.3200			1.81776			0.908882	+	0.417054i	$0.136937\pi$
$180$			0.101189i			0.00754220i
$181$		−	5.53825i		−	0.411655i	−0.978588	−	0.205828i	$-0.934011\pi$
$181$		−	5.53825i		−	0.411655i	0.978588	−	0.205828i	$-0.0659886\pi$
$182$			2.76151i			0.204697i
$183$	−8.42422			−0.622736
$184$			5.25819i			0.387639i
$185$	−0.0980222			−0.00720673
$186$	−13.3593			−0.979548
$187$	4.08938	+	21.1859i	0.299045	+	1.54927i
$188$	1.82875			0.133376
$189$	12.1428			0.883259
$190$			0.198511i			0.0144015i
$191$	−22.8878			−1.65610			−0.828051	−	0.560653i	$-0.810550\pi$
$191$	−22.8878			−1.65610			−0.828051	+	0.560653i	$0.810550\pi$
$192$		−	8.66428i		−	0.625290i
$193$			13.4065i			0.965024i	0.875889	+	0.482512i	$0.160276\pi$
$193$			13.4065i			0.965024i	−0.875889	+	0.482512i	$0.839724\pi$
$194$			25.1275i			1.80405i
$195$	−0.00571194			−0.000409040
$196$	−3.98660			−0.284757
$197$			3.82070i			0.272213i	0.990694	+	0.136107i	$0.0434590\pi$
$197$			3.82070i			0.272213i	−0.990694	+	0.136107i	$0.956541\pi$
$198$		−	26.7890i		−	1.90381i
$199$		−	18.5236i		−	1.31310i	−0.754281	−	0.656551i	$-0.772015\pi$
$199$		−	18.5236i		−	1.31310i	0.754281	−	0.656551i	$-0.227985\pi$
$200$	−5.21083			−0.368461
$201$		−	3.40981i		−	0.240510i
$202$	9.86336			0.693983
$203$	−12.1763			−0.854607
$204$	1.48882	+	7.71316i	0.104238	+	0.540029i
$205$	−0.0871845			−0.00608923
$206$	−25.0840			−1.74768
$207$		−	12.1859i		−	0.846977i
$208$	−1.23282			−0.0854808
$209$		−	29.1538i		−	2.01661i
$210$		−	0.0799000i		−	0.00551363i
$211$			3.99867i			0.275280i	0.990482	+	0.137640i	$0.0439517\pi$
$211$			3.99867i			0.275280i	−0.990482	+	0.137640i	$0.956048\pi$
$212$	27.8634			1.91367
$213$	3.01215			0.206389
$214$		−	36.2887i		−	2.48064i
$215$			0.0168131i			0.00114664i
$216$		−	4.31552i		−	0.293634i
$217$	−24.1755			−1.64114
$218$			38.4440i			2.60376i
$219$	−7.69138			−0.519735
$220$	−0.219240			−0.0147811
$221$	1.79876	−	0.347203i	0.120998	−	0.0233554i
$222$	9.44780			0.634095
$223$	−1.42849			−0.0956586			−0.0478293	−	0.998856i	$-0.515230\pi$
$223$	−1.42849			−0.0956586			−0.0478293	+	0.998856i	$0.515230\pi$
$224$		−	23.3578i		−	1.56066i
$225$	12.0761			0.805074
$226$		−	3.89584i		−	0.259147i
$227$			14.9162i			0.990021i	0.868887	+	0.495011i	$0.164836\pi$
$227$			14.9162i			0.990021i	−0.868887	+	0.495011i	$0.835164\pi$
$228$		−	10.6140i		−	0.702932i
$229$	−4.02345			−0.265877			−0.132939	−	0.991124i	$-0.542441\pi$
$229$	−4.02345			−0.265877			−0.132939	+	0.991124i	$0.542441\pi$
$230$	−0.179775			−0.0118540
$231$			11.7343i			0.772061i
$232$			4.32742i			0.284109i
$233$		−	6.99745i		−	0.458418i	−0.973377	−	0.229209i	$-0.926386\pi$
$233$		−	6.99745i		−	0.458418i	0.973377	−	0.229209i	$-0.0736140\pi$
$234$	−2.27448			−0.148687
$235$			0.0123395i			0.000804938i
$236$	14.0519			0.914703
$237$	3.56017			0.231258
$238$	4.85676	+	25.1615i	0.314817	+	1.63098i
$239$	−12.8013			−0.828048			−0.414024	−	0.910266i	$-0.635877\pi$
$239$	−12.8013			−0.828048			−0.414024	+	0.910266i	$0.635877\pi$
$240$	0.0356698			0.00230247
$241$			11.7177i			0.754802i	0.926050	+	0.377401i	$0.123182\pi$
$241$			11.7177i			0.754802i	−0.926050	+	0.377401i	$0.876818\pi$
$242$	34.7286			2.23244
$243$			15.5417i			0.997002i
$244$			27.4531i			1.75750i
$245$		−	0.0268994i		−	0.00171854i
$246$	8.40322			0.535770
$247$	−2.47526			−0.157497
$248$			8.59193i			0.545588i
$249$			12.3649i			0.783595i
$250$		−	0.356322i		−	0.0225358i
$251$	−21.1212			−1.33316			−0.666581	−	0.745433i	$-0.732243\pi$
$251$	−21.1212			−1.33316			−0.666581	+	0.745433i	$0.732243\pi$
$252$		−	17.6496i		−	1.11182i
$253$	26.4023			1.65990
$254$	−16.8178			−1.05524
$255$	−0.0520442	+	0.0100458i	−0.00325914	+	0.000629090i
$256$	5.52623			0.345389
$257$	20.0108			1.24824			0.624120	−	0.781328i	$-0.285457\pi$
$257$	20.0108			1.24824			0.624120	+	0.781328i	$0.285457\pi$
$258$		−	1.62052i		−	0.100889i
$259$	17.0972			1.06237
$260$			0.0186142i			0.00115441i
$261$		−	10.0288i		−	0.620767i
$262$			4.33199i			0.267631i
$263$	−15.6319			−0.963906			−0.481953	−	0.876197i	$-0.660072\pi$
$263$	−15.6319			−0.963906			−0.481953	+	0.876197i	$0.660072\pi$
$264$	4.17035			0.256667
$265$			0.188008i			0.0115492i
$266$		−	34.6246i		−	2.12297i
$267$			11.9895i			0.733745i
$268$	−11.1120			−0.678773
$269$			25.5305i			1.55662i	0.627878	+	0.778312i	$0.283924\pi$
$269$			25.5305i			1.55662i	−0.627878	+	0.778312i	$0.716076\pi$
$270$	0.147546			0.00897936
$271$	−1.52434			−0.0925972			−0.0462986	−	0.998928i	$-0.514743\pi$
$271$	−1.52434			−0.0925972			−0.0462986	+	0.998928i	$0.514743\pi$
$272$	−11.2328	+	2.16820i	−0.681091	+	0.131467i
$273$	0.996285			0.0602979
$274$	33.7809			2.04078
$275$			26.1644i			1.57778i
$276$	9.61227			0.578591
$277$		−	13.5896i		−	0.816520i	−0.912866	−	0.408260i	$-0.866136\pi$
$277$		−	13.5896i		−	0.816520i	0.912866	−	0.408260i	$-0.133864\pi$
$278$		−	19.4669i		−	1.16755i
$279$		−	19.9118i		−	1.19209i
$280$	−0.0513872			−0.00307097
$281$	−5.13686			−0.306439			−0.153220	−	0.988192i	$-0.548964\pi$
$281$	−5.13686			−0.306439			−0.153220	+	0.988192i	$0.548964\pi$
$282$		−	1.18933i		−	0.0708236i
$283$		−	28.9574i		−	1.72134i	−0.509163	−	0.860670i	$-0.670045\pi$
$283$		−	28.9574i		−	1.72134i	0.509163	−	0.860670i	$-0.329955\pi$
$284$		−	9.81608i		−	0.582477i
$285$	0.0716178			0.00424228
$286$		−	4.92795i		−	0.291396i
$287$	15.2069			0.897632
$288$	19.2383			1.13363
$289$	15.7787	−	6.32706i	0.928161	−	0.372180i
$290$	−0.147953			−0.00868808
$291$	9.06539			0.531422
$292$			25.0649i			1.46681i
$293$	13.8847			0.811155			0.405578	−	0.914061i	$-0.367070\pi$
$293$	13.8847			0.811155			0.405578	+	0.914061i	$0.367070\pi$
$294$			2.59268i			0.151208i
$295$			0.0948149i			0.00552034i
$296$		−	6.07630i		−	0.353178i
$297$	−21.6690			−1.25736
$298$	14.9729			0.867358
$299$		−	2.24165i		−	0.129638i
$300$			9.52569i			0.549966i
$301$		−	2.93256i		−	0.169030i
$302$	−4.52212			−0.260219
$303$		−	3.55845i		−	0.204428i
$304$	15.4575			0.886546
$305$	−0.185239			−0.0106067
$306$	−20.7239	+	4.00019i	−1.18470	+	0.228676i
$307$	−34.2610			−1.95538			−0.977690	−	0.210055i	$-0.932636\pi$
$307$	−34.2610			−1.95538			−0.977690	+	0.210055i	$0.932636\pi$
$308$	38.2401			2.17893
$309$			9.04968i			0.514818i
$310$	−0.293754			−0.0166841
$311$			1.37753i			0.0781127i	0.999237	+	0.0390563i	$0.0124352\pi$
$311$			1.37753i			0.0781127i	−0.999237	+	0.0390563i	$0.987565\pi$
$312$		−	0.354077i		−	0.0200457i
$313$			3.07745i			0.173948i	0.996211	+	0.0869738i	$0.0277196\pi$
$313$			3.07745i			0.173948i	−0.996211	+	0.0869738i	$0.972280\pi$
$314$	−19.9462			−1.12563
$315$	0.119090			0.00670996
$316$		−	11.6020i		−	0.652663i
$317$			32.7342i			1.83853i	0.393634	+	0.919267i	$0.371218\pi$
$317$			32.7342i			1.83853i	−0.393634	+	0.919267i	$0.628782\pi$
$318$		−	18.1210i		−	1.01617i
$319$	21.7287			1.21657
$320$		−	0.190517i		−	0.0106502i
$321$	−13.0920			−0.730727
$322$	31.3567			1.74744
$323$	−22.5533	+	4.35332i	−1.25490	+	0.242225i
$324$	10.1665			0.564803
$325$	2.22145			0.123224
$326$			48.1780i			2.66833i
$327$	13.8696			0.766993
$328$		−	5.40448i		−	0.298413i
$329$		−	2.15227i		−	0.118658i
$330$			0.142582i			0.00784890i
$331$	−30.0375			−1.65101			−0.825506	−	0.564393i	$-0.809110\pi$
$331$	−30.0375			−1.65101			−0.825506	+	0.564393i	$0.809110\pi$
$332$	40.2951			2.21148
$333$			14.0818i			0.771679i
$334$		−	18.6395i		−	1.01991i
$335$		−	0.0749778i		−	0.00409647i
$336$	−6.22158			−0.339415
$337$			21.5876i			1.17595i	0.808879	+	0.587975i	$0.200075\pi$
$337$			21.5876i			1.17595i	−0.808879	+	0.587975i	$0.799925\pi$
$338$	27.1335			1.47587
$339$	−1.40552			−0.0763375
$340$	0.0327374	+	0.169603i	0.00177543	+	0.00919803i
$341$	43.1415			2.33624
$342$	28.5180			1.54208
$343$		−	15.8361i		−	0.855068i
$344$	−1.04222			−0.0561930
$345$			0.0648585i			0.00349186i
$346$			13.7728i			0.740433i
$347$		−	9.66738i		−	0.518972i	−0.965747	−	0.259486i	$-0.916447\pi$
$347$		−	9.66738i		−	0.518972i	0.965747	−	0.259486i	$-0.0835532\pi$
$348$	7.91077			0.424062
$349$	−7.99940			−0.428198			−0.214099	−	0.976812i	$-0.568682\pi$
$349$	−7.99940			−0.428198			−0.214099	+	0.976812i	$0.568682\pi$
$350$			31.0743i			1.66099i
$351$			1.83977i			0.0981998i
$352$			41.6822i			2.22167i
$353$	9.83906			0.523680			0.261840	−	0.965111i	$-0.415671\pi$
$353$	9.83906			0.523680			0.261840	+	0.965111i	$0.415671\pi$
$354$		−	9.13867i		−	0.485715i
$355$	0.0662337			0.00351532
$356$	39.0717			2.07079
$357$	9.07764	−	1.75220i	0.480440	−	0.0927361i
$358$	−51.5433			−2.72415
$359$	−7.33762			−0.387265			−0.193632	−	0.981074i	$-0.562027\pi$
$359$	−7.33762			−0.387265			−0.193632	+	0.981074i	$0.562027\pi$
$360$		−	0.0423243i		−	0.00223069i
$361$	12.0355			0.633449
$362$			11.7376i			0.616917i
$363$		−	12.5292i		−	0.657613i
$364$		−	3.24672i		−	0.170174i
$365$	−0.169124			−0.00885237
$366$	17.8541			0.933248
$367$		−	15.3724i		−	0.802432i	−0.915983	−	0.401216i	$-0.868588\pi$
$367$		−	15.3724i		−	0.802432i	0.915983	−	0.401216i	$-0.131412\pi$
$368$			13.9986i			0.729726i
$369$			12.5249i			0.652020i
$370$	0.207746			0.0108002
$371$		−	32.7926i		−	1.70251i
$372$	15.7065			0.814346
$373$	−29.0572			−1.50453			−0.752263	−	0.658863i	$-0.771038\pi$
$373$	−29.0572			−1.50453			−0.752263	+	0.658863i	$0.771038\pi$
$374$	−8.66693	−	44.9009i	−0.448156	−	2.32177i
$375$	−0.128552			−0.00663841
$376$	−0.764911			−0.0394473
$377$		−	1.84484i		−	0.0950142i
$378$	−25.7352			−1.32368
$379$		−	6.97671i		−	0.358369i	−0.983815	−	0.179185i	$-0.942654\pi$
$379$		−	6.97671i		−	0.358369i	0.983815	−	0.179185i	$-0.0573460\pi$
$380$		−	0.233390i		−	0.0119727i
$381$			6.06745i			0.310845i
$382$	48.5079			2.48188
$383$	14.0579			0.718327			0.359163	−	0.933275i	$-0.383062\pi$
$383$	14.0579			0.718327			0.359163	+	0.933275i	$0.383062\pi$
$384$			6.18252i			0.315501i
$385$			0.258024i			0.0131501i
$386$		−	28.4135i		−	1.44621i
$387$	2.41536			0.122780
$388$		−	29.5425i		−	1.49979i
$389$	−9.98089			−0.506051			−0.253026	−	0.967460i	$-0.581426\pi$
$389$	−9.98089			−0.506051			−0.253026	+	0.967460i	$0.581426\pi$
$390$	0.0121058			0.000612999
$391$	−3.94245	−	20.4247i	−0.199378	−	1.03292i
$392$	1.66747			0.0842198
$393$	1.56288			0.0788366
$394$		−	8.09750i		−	0.407946i
$395$	0.0782840			0.00393890
$396$			31.4959i			1.58273i
$397$		−	39.2149i		−	1.96814i	−0.177785	−	0.984069i	$-0.556893\pi$
$397$		−	39.2149i		−	1.96814i	0.177785	−	0.984069i	$-0.443107\pi$
$398$			39.2585i			1.96785i
$399$	−12.4917			−0.625367
$400$	−13.8725			−0.693624
$401$		−	26.1299i		−	1.30486i	−0.757848	−	0.652431i	$-0.773749\pi$
$401$		−	26.1299i		−	1.30486i	0.757848	−	0.652431i	$-0.226251\pi$
$402$			7.22668i			0.360434i
$403$		−	3.66287i		−	0.182460i
$404$	−11.5964			−0.576942
$405$			0.0685978i			0.00340865i
$406$	25.8061			1.28074
$407$	−30.5101			−1.51233
$408$	−0.622727	−	3.22617i	−0.0308296	−	0.159719i
$409$	5.91820			0.292636			0.146318	−	0.989238i	$-0.453258\pi$
$409$	5.91820			0.292636			0.146318	+	0.989238i	$0.453258\pi$
$410$	0.184777			0.00912548
$411$		−	12.1873i		−	0.601156i
$412$	29.4913			1.45293
$413$		−	16.5378i		−	0.813770i
$414$			25.8265i			1.26930i
$415$			0.271890i			0.0133466i
$416$	3.53897			0.173512
$417$	−7.02317			−0.343926
$418$			61.7880i			3.02215i
$419$		−	16.1021i		−	0.786640i	−0.919402	−	0.393320i	$-0.871326\pi$
$419$		−	16.1021i		−	0.786640i	0.919402	−	0.393320i	$-0.128674\pi$
$420$			0.0939388i			0.00458374i
$421$	−23.2592			−1.13359			−0.566793	−	0.823860i	$-0.691816\pi$
$421$	−23.2592			−1.13359			−0.566793	+	0.823860i	$0.691816\pi$
$422$		−	8.47469i		−	0.412541i
$423$	1.77268			0.0861908
$424$	−11.6544			−0.565988
$425$	20.2407	−	3.90694i	0.981820	−	0.189514i
$426$	−6.38389			−0.309300
$427$	32.3096			1.56357
$428$			42.6647i			2.06228i
$429$	−1.77788			−0.0858369
$430$		−	0.0356332i		−	0.00171839i
$431$			29.8248i			1.43661i	0.695727	+	0.718306i	$0.255082\pi$
$431$			29.8248i			1.43661i	−0.695727	+	0.718306i	$0.744918\pi$
$432$		−	11.4890i		−	0.552763i
$433$	10.4883			0.504035			0.252018	−	0.967723i	$-0.418906\pi$
$433$	10.4883			0.504035			0.252018	+	0.967723i	$0.418906\pi$
$434$	51.2371			2.45946
$435$			0.0533776i			0.00255926i
$436$		−	45.1987i		−	2.16463i
$437$			28.1064i			1.34451i
$438$	16.3009			0.778889
$439$			2.68019i			0.127918i	0.997953	+	0.0639591i	$0.0203727\pi$
$439$			2.68019i			0.127918i	−0.997953	+	0.0639591i	$0.979627\pi$
$440$	0.0917010			0.00437168
$441$	−3.86436			−0.184017
$442$	−3.81225	+	0.735853i	−0.181330	+	0.0350010i
$443$	−5.73570			−0.272512			−0.136256	−	0.990674i	$-0.543507\pi$
$443$	−5.73570			−0.272512			−0.136256	+	0.990674i	$0.543507\pi$
$444$	−11.1078			−0.527154
$445$			0.263635i			0.0124975i
$446$	3.02751			0.143357
$447$		−	5.40185i		−	0.255499i
$448$			33.2303i			1.56998i
$449$		−	21.5420i		−	1.01663i	−0.861172	−	0.508314i	$-0.830269\pi$
$449$		−	21.5420i		−	1.01663i	0.861172	−	0.508314i	$-0.169731\pi$
$450$	−25.5938			−1.20650
$451$	−27.1368			−1.27782
$452$			4.58035i			0.215442i
$453$			1.63147i			0.0766531i
$454$		−	31.6130i		−	1.48367i
$455$	0.0219071			0.00102702
$456$			4.43952i			0.207900i
$457$	0.388909			0.0181924			0.00909620	−	0.999959i	$-0.497105\pi$
$457$	0.388909			0.0181924			0.00909620	+	0.999959i	$0.497105\pi$
$458$	8.52721			0.398450
$459$	3.23566	+	16.7631i	0.151028	+	0.782432i
$460$	0.211363			0.00985483
$461$	−23.6394			−1.10099			−0.550497	−	0.834837i	$-0.685562\pi$
$461$	−23.6394			−1.10099			−0.550497	+	0.834837i	$0.685562\pi$
$462$		−	24.8694i		−	1.15703i
$463$	−27.0222			−1.25583			−0.627914	−	0.778283i	$-0.716091\pi$
$463$	−27.0222			−1.25583			−0.627914	+	0.778283i	$0.716091\pi$
$464$			11.5206i			0.534832i
$465$			0.105979i			0.00491467i
$466$			14.8302i			0.686998i
$467$	−3.70724			−0.171551			−0.0857754	−	0.996315i	$-0.527337\pi$
$467$	−3.70724			−0.171551			−0.0857754	+	0.996315i	$0.527337\pi$
$468$	2.67411			0.123611
$469$			13.0777i			0.603874i
$470$		−	0.0261520i		−	0.00120630i
$471$			7.19610i			0.331579i
$472$	−5.87748			−0.270533
$473$			5.23318i			0.240622i
$474$	−7.54535			−0.346569
$475$	−27.8532			−1.27799
$476$	−5.71011	−	29.5825i	−0.261722	−	1.35591i
$477$	27.0091			1.23666
$478$	27.1308			1.24093
$479$			25.6350i			1.17130i	0.810566	+	0.585648i	$0.199160\pi$
$479$			25.6350i			1.17130i	−0.810566	+	0.585648i	$0.800840\pi$
$480$	−0.102394			−0.00467365
$481$			2.59042i			0.118113i
$482$		−	24.8342i		−	1.13117i
$483$		−	11.3127i		−	0.514746i
$484$	−40.8305			−1.85593
$485$	0.199337			0.00905144
$486$		−	32.9388i		−	1.49413i
$487$			32.6430i			1.47919i	0.673050	+	0.739597i	$0.264984\pi$
$487$			32.6430i			1.47919i	−0.673050	+	0.739597i	$0.735016\pi$
$488$		−	11.4828i		−	0.519800i
$489$	17.3814			0.786015
$490$			0.0570100i			0.00257545i
$491$	4.40945			0.198996			0.0994979	−	0.995038i	$-0.468276\pi$
$491$	4.40945			0.198996			0.0994979	+	0.995038i	$0.468276\pi$
$492$	−9.87970			−0.445411
$493$	−3.24458	−	16.8093i	−0.146129	−	0.757051i
$494$	5.24602			0.236029
$495$	−0.212517			−0.00955194
$496$			22.8738i			1.02706i
$497$	−11.5526			−0.518204
$498$		−	26.2059i		−	1.17432i
$499$			32.9796i			1.47637i	0.674599	+	0.738184i	$0.264317\pi$
$499$			32.9796i			1.47637i	−0.674599	+	0.738184i	$0.735683\pi$
$500$			0.418929i			0.0187351i
$501$	−6.72467			−0.300436
$502$	44.7639			1.99791
$503$		−	37.0567i		−	1.65228i	−0.563466	−	0.826139i	$-0.690532\pi$
$503$		−	37.0567i		−	1.65228i	0.563466	−	0.826139i	$-0.309468\pi$
$504$			7.38227i			0.328833i
$505$		−	0.0782462i		−	0.00348191i
$506$	−55.9563			−2.48756
$507$		−	9.78909i		−	0.434749i
$508$	19.7728			0.877274
$509$	−14.5099			−0.643139			−0.321570	−	0.946886i	$-0.604210\pi$
$509$	−14.5099			−0.643139			−0.321570	+	0.946886i	$0.604210\pi$
$510$	0.110301	−	0.0212908i	0.00488423	−	0.000942770i
$511$	29.4989			1.30496
$512$	−27.8837			−1.23230
$513$		−	23.0676i		−	1.01846i
$514$	−42.4105			−1.87065
$515$			0.198992i			0.00876862i
$516$			1.90525i			0.0838738i
$517$			3.84074i			0.168916i
$518$	−36.2354			−1.59209
$519$	4.96890			0.218110
$520$		−	0.00778574i		−	0.000341427i
$521$			20.4015i			0.893807i	0.894582	+	0.446904i	$0.147473\pi$
$521$			20.4015i			0.893807i	−0.894582	+	0.446904i	$0.852527\pi$
$522$			21.2548i			0.930298i
$523$	23.4758			1.02653			0.513263	−	0.858231i	$-0.328437\pi$
$523$	23.4758			1.02653			0.513263	+	0.858231i	$0.328437\pi$
$524$		−	5.09314i		−	0.222495i
$525$	11.2108			0.489280
$526$	33.1300			1.44453
$527$	−6.44199	−	33.3742i	−0.280618	−	1.45380i
$528$	11.1025			0.483173
$529$	−2.45365			−0.106680
$530$		−	0.398459i		−	0.0173080i
$531$	13.6211			0.591104
$532$			40.7083i			1.76493i
$533$			2.30401i			0.0997978i
$534$		−	25.4102i		−	1.09961i
$535$	−0.287879			−0.0124461
$536$	4.64780			0.200754
$537$			18.5955i			0.802457i
$538$		−	54.1088i		−	2.33280i
$539$		−	8.37263i		−	0.360635i
$540$	−0.173470			−0.00746497
$541$			24.1711i			1.03920i	0.854410	+	0.519599i	$0.173919\pi$
$541$			24.1711i			1.03920i	−0.854410	+	0.519599i	$0.826081\pi$
$542$	3.23066			0.138769
$543$	4.23465			0.181726
$544$	32.2453	−	6.22409i	1.38250	−	0.266856i
$545$	0.304977			0.0130638
$546$	−2.11150			−0.0903641
$547$		−	42.9163i		−	1.83497i	−0.397771	−	0.917485i	$-0.630216\pi$
$547$		−	42.9163i		−	1.83497i	0.397771	−	0.917485i	$-0.369784\pi$
$548$	−39.7164			−1.69660
$549$			26.6113i			1.13574i
$550$		−	55.4523i		−	2.36449i
$551$			23.1311i			0.985420i
$552$	−4.02051			−0.171124
$553$	−13.6544			−0.580645
$554$			28.8015i			1.22366i
$555$		−	0.0749496i		−	0.00318143i
$556$			22.8873i			0.970638i
$557$	4.56358			0.193365			0.0966825	−	0.995315i	$-0.469177\pi$
$557$	4.56358			0.193365			0.0966825	+	0.995315i	$0.469177\pi$
$558$			42.2006i			1.78650i
$559$	0.444316			0.0187926
$560$	−0.136805			−0.00578107
$561$	−16.1991	+	3.12681i	−0.683928	+	0.132014i
$562$	10.8869			0.459238
$563$	−14.7206			−0.620399			−0.310199	−	0.950672i	$-0.600396\pi$
$563$	−14.7206			−0.620399			−0.310199	+	0.950672i	$0.600396\pi$
$564$			1.39830i			0.0588791i
$565$	−0.0309058			−0.00130022
$566$			61.3717i			2.57965i
$567$		−	11.9649i		−	0.502480i
$568$			4.10576i			0.172274i
$569$	−32.5275			−1.36363			−0.681813	−	0.731527i	$-0.738808\pi$
$569$	−32.5275			−1.36363			−0.681813	+	0.731527i	$0.738808\pi$
$570$	−0.151785			−0.00635758
$571$			20.2976i			0.849426i	0.905328	+	0.424713i	$0.139625\pi$
$571$			20.2976i			0.849426i	−0.905328	+	0.424713i	$0.860375\pi$
$572$			5.79381i			0.242251i
$573$		−	17.5004i		−	0.731091i
$574$	−32.2291			−1.34522
$575$		−	25.2244i		−	1.05193i
$576$	−27.3696			−1.14040
$577$	26.1701			1.08948			0.544738	−	0.838606i	$-0.316629\pi$
$577$	26.1701			1.08948			0.544738	+	0.838606i	$0.316629\pi$
$578$	−33.4411	+	13.4094i	−1.39097	+	0.557759i
$579$	−10.2509			−0.426013
$580$	0.173948			0.00722282
$581$		−	47.4235i		−	1.96746i
$582$	−19.2130			−0.796404
$583$			58.5187i			2.42360i
$584$		−	10.4838i		−	0.433825i
$585$			0.0180435i			0.000746006i
$586$	−29.4270			−1.21562
$587$	−26.1579			−1.07965			−0.539827	−	0.841776i	$-0.681510\pi$
$587$	−26.1579			−1.07965			−0.539827	+	0.841776i	$0.681510\pi$
$588$		−	3.04823i		−	0.125707i
$589$			45.9260i			1.89235i
$590$		−	0.200949i		−	0.00827292i
$591$	−2.92138			−0.120169
$592$		−	16.1766i		−	0.664852i
$593$	−17.8275			−0.732089			−0.366045	−	0.930597i	$-0.619288\pi$
$593$	−17.8275			−0.732089			−0.366045	+	0.930597i	$0.619288\pi$
$594$	45.9247			1.88431
$595$	0.199607	−	0.0385287i	0.00818307	−	0.00157952i
$596$	−17.6037			−0.721076
$597$	14.1635			0.579673
$598$			4.75089i			0.194278i
$599$	14.3499			0.586320			0.293160	−	0.956063i	$-0.405293\pi$
$599$	14.3499			0.586320			0.293160	+	0.956063i	$0.405293\pi$
$600$		−	3.98430i		−	0.162658i
$601$			44.8220i			1.82833i	0.405343	+	0.914165i	$0.367152\pi$
$601$			44.8220i			1.82833i	−0.405343	+	0.914165i	$0.632848\pi$
$602$			6.21520i			0.253313i
$603$	−10.7713			−0.438640
$604$	5.31667			0.216332
$605$		−	0.275502i		−	0.0112008i
$606$			7.54171i			0.306361i
$607$		−	1.67604i		−	0.0680283i	−0.999421	−	0.0340141i	$-0.989171\pi$
$607$		−	1.67604i		−	0.0680283i	0.999421	−	0.0340141i	$-0.0108291\pi$
$608$	−44.3726			−1.79955
$609$		−	9.31021i		−	0.377269i
$610$	0.392590			0.0158955
$611$	0.326093			0.0131923
$612$	24.3651	−	4.70304i	0.984902	−	0.190109i
$613$	−3.67527			−0.148443			−0.0742214	−	0.997242i	$-0.523647\pi$
$613$	−3.67527			−0.148443			−0.0742214	+	0.997242i	$0.523647\pi$
$614$	72.6120			2.93038
$615$		−	0.0666629i		−	0.00268811i
$616$	−15.9946			−0.644442
$617$			6.34213i			0.255324i	0.991818	+	0.127662i	$0.0407473\pi$
$617$			6.34213i			0.255324i	−0.991818	+	0.127662i	$0.959253\pi$
$618$		−	19.1797i		−	0.771520i
$619$			31.1259i			1.25105i	0.780202	+	0.625527i	$0.215116\pi$
$619$			31.1259i			1.25105i	−0.780202	+	0.625527i	$0.784884\pi$
$620$	0.345368			0.0138703
$621$	20.8904			0.838304
$622$		−	2.91951i		−	0.117062i
$623$		−	45.9836i		−	1.84229i
$624$		−	0.942639i		−	0.0377358i
$625$	24.9958			0.999830
$626$		−	6.52227i		−	0.260682i
$627$	22.2916			0.890239
$628$	23.4508			0.935790
$629$	4.55584	+	23.6025i	0.181653	+	0.941094i
$630$	−0.252397			−0.0100557
$631$	−12.9059			−0.513777			−0.256888	−	0.966441i	$-0.582697\pi$
$631$	−12.9059			−0.513777			−0.256888	+	0.966441i	$0.582697\pi$
$632$			4.85275i			0.193032i
$633$	−3.05746			−0.121523
$634$		−	69.3761i		−	2.75528i
$635$			0.133416i			0.00529445i
$636$			21.3049i			0.844795i
$637$	−0.710866			−0.0281655
$638$	−46.0513			−1.82319
$639$		−	9.51510i		−	0.376412i
$640$			0.135946i			0.00537375i
$641$		−	20.0658i		−	0.792550i	−0.918132	−	0.396275i	$-0.870303\pi$
$641$		−	20.0658i		−	0.792550i	0.918132	−	0.396275i	$-0.129697\pi$
$642$	27.7470			1.09509
$643$		−	4.09990i		−	0.161684i	−0.996727	−	0.0808422i	$-0.974239\pi$
$643$		−	4.09990i		−	0.161684i	0.996727	−	0.0808422i	$-0.0257610\pi$
$644$	−36.8662			−1.45273
$645$	−0.0128556			−0.000506188
$646$	47.7990	−	9.22633i	1.88063	−	0.363005i
$647$	12.8543			0.505355			0.252677	−	0.967551i	$-0.418689\pi$
$647$	12.8543			0.505355			0.252677	+	0.967551i	$0.418689\pi$
$648$	−4.25231			−0.167047
$649$			29.5118i			1.15844i
$650$	−4.70810			−0.184667
$651$		−	18.4851i		−	0.724487i
$652$		−	56.6430i		−	2.21831i
$653$		−	36.3914i		−	1.42411i	−0.702126	−	0.712053i	$-0.747766\pi$
$653$		−	36.3914i		−	1.42411i	0.702126	−	0.712053i	$-0.252234\pi$
$654$	−29.3950			−1.14943
$655$	0.0343658			0.00134278
$656$		−	14.3880i		−	0.561758i
$657$			24.2963i			0.947891i
$658$			4.56147i			0.177825i
$659$	−28.5390			−1.11172			−0.555861	−	0.831275i	$-0.687611\pi$
$659$	−28.5390			−1.11172			−0.555861	+	0.831275i	$0.687611\pi$
$660$		−	0.167635i		−	0.00652517i
$661$	−20.0473			−0.779750			−0.389875	−	0.920868i	$-0.627482\pi$
$661$	−20.0473			−0.779750			−0.389875	+	0.920868i	$0.627482\pi$
$662$	63.6609			2.47425
$663$	0.265478	+	1.37536i	0.0103103	+	0.0534147i
$664$	−16.8542			−0.654069
$665$	−0.274678			−0.0106515
$666$		−	29.8447i		−	1.15646i
$667$	−20.9480			−0.811110
$668$			21.9146i			0.847899i
$669$		−	1.09225i		−	0.0422288i
$670$			0.158906i			0.00613908i
$671$	−57.6568			−2.22582
$672$	17.8598			0.688957
$673$		−	46.8243i		−	1.80494i	−0.430750	−	0.902472i	$-0.641751\pi$
$673$		−	46.8243i		−	1.80494i	0.430750	−	0.902472i	$-0.358249\pi$
$674$		−	45.7522i		−	1.76231i
$675$			20.7022i			0.796830i
$676$	−31.9010			−1.22696
$677$			11.3503i			0.436229i	0.975923	+	0.218114i	$0.0699906\pi$
$677$			11.3503i			0.436229i	−0.975923	+	0.218114i	$0.930009\pi$
$678$	2.97883			0.114401
$679$	−34.7687			−1.33430
$680$	−0.0136930	−	0.0709397i	−0.000525103	−	0.00272041i
$681$	−11.4052			−0.437048
$682$	−91.4331			−3.50115
$683$			39.9165i			1.52736i	0.645594	+	0.763680i	$0.276610\pi$
$683$			39.9165i			1.52736i	−0.645594	+	0.763680i	$0.723390\pi$
$684$	−33.5287			−1.28200
$685$		−	0.267985i		−	0.0102392i
$686$			33.5626i			1.28143i
$687$		−	3.07641i		−	0.117372i
$688$	−2.77465			−0.105783
$689$	4.96845			0.189283
$690$		−	0.137460i		−	0.00523300i
$691$		−	15.4564i		−	0.587989i	−0.955807	−	0.293994i	$-0.905015\pi$
$691$		−	15.4564i		−	0.587989i	0.955807	−	0.293994i	$-0.0949847\pi$
$692$		−	16.1928i		−	0.615557i
$693$	37.0676			1.40808
$694$			20.4888i			0.777745i
$695$	−0.154431			−0.00585791
$696$	−3.30883			−0.125421
$697$	4.05213	+	20.9930i	0.153485	+	0.795165i
$698$	16.9538			0.641709
$699$	5.35038			0.202370
$700$		−	36.5341i		−	1.38086i
$701$	−49.4859			−1.86906			−0.934528	−	0.355890i	$-0.884178\pi$
$701$	−49.4859			−1.86906			−0.934528	+	0.355890i	$0.884178\pi$
$702$		−	3.89917i		−	0.147165i
$703$		−	32.4793i		−	1.22498i
$704$		−	59.2998i		−	2.23495i
$705$	−0.00943498			−0.000355342
$706$	−20.8527			−0.784801
$707$			13.6478i			0.513279i
$708$			10.7444i			0.403798i
$709$			2.46436i			0.0925510i	0.998929	+	0.0462755i	$0.0147352\pi$
$709$			2.46436i			0.0925510i	−0.998929	+	0.0462755i	$0.985265\pi$
$710$	−0.140374			−0.00526815
$711$		−	11.2463i		−	0.421767i
$712$	−16.3424			−0.612459
$713$	−41.5915			−1.55761
$714$	−19.2389	+	3.71357i	−0.719999	+	0.138977i
$715$	−0.0390935			−0.00146201
$716$	60.5997			2.26472
$717$		−	9.78812i		−	0.365544i
$718$	15.5512			0.580365
$719$			25.6991i			0.958415i	0.877702	+	0.479207i	$0.159076\pi$
$719$			25.6991i			0.958415i	−0.877702	+	0.479207i	$0.840924\pi$
$720$		−	0.112677i		−	0.00419924i
$721$		−	34.7084i		−	1.29261i
$722$	−25.5078			−0.949303
$723$	−8.95956			−0.333210
$724$		−	13.8000i		−	0.512873i
$725$		−	20.7593i		−	0.770982i
$726$			26.5541i			0.985515i
$727$	17.6550			0.654787			0.327393	−	0.944888i	$-0.393830\pi$
$727$	17.6550			0.654787			0.327393	+	0.944888i	$0.393830\pi$
$728$			1.35800i			0.0503309i
$729$	0.356604			0.0132075
$730$	0.358438			0.0132664
$731$	4.04838	−	0.781432i	0.149735	−	0.0289023i
$732$	−20.9911			−0.775854
$733$	16.3716			0.604699			0.302349	−	0.953197i	$-0.402229\pi$
$733$	16.3716			0.604699			0.302349	+	0.953197i	$0.402229\pi$
$734$			32.5799i			1.20255i
$735$	0.0205678			0.000758654
$736$		−	40.1846i		−	1.48123i
$737$		−	23.3374i		−	0.859643i
$738$		−	26.5450i		−	0.977134i
$739$	3.87722			0.142626			0.0713130	−	0.997454i	$-0.477281\pi$
$739$	3.87722			0.142626			0.0713130	+	0.997454i	$0.477281\pi$
$740$	−0.244248			−0.00897872
$741$		−	1.89263i		−	0.0695276i
$742$			69.4999i			2.55142i
$743$			5.86275i			0.215083i	0.994201	+	0.107542i	$0.0342979\pi$
$743$			5.86275i			0.215083i	−0.994201	+	0.107542i	$0.965702\pi$
$744$	−6.56955			−0.240851
$745$		−	0.118780i		−	0.00435178i
$746$	61.5833			2.25472
$747$	39.0596			1.42912
$748$	10.1897	+	52.7902i	0.372574	+	1.93020i
$749$	50.2123			1.83472
$750$	0.272451			0.00994849
$751$		−	5.00328i		−	0.182572i	−0.995825	−	0.0912861i	$-0.970902\pi$
$751$		−	5.00328i		−	0.182572i	0.995825	−	0.0912861i	$-0.0290978\pi$
$752$	−2.03638			−0.0742590
$753$		−	16.1497i		−	0.588528i
$754$			3.90992i			0.142391i
$755$			0.0358741i			0.00130559i
$756$	30.2570			1.10043
$757$	11.0721			0.402422			0.201211	−	0.979548i	$-0.435512\pi$
$757$	11.0721			0.402422			0.201211	+	0.979548i	$0.435512\pi$
$758$			14.7863i			0.537062i
$759$			20.1877i			0.732765i
$760$			0.0976198i			0.00354104i
$761$	36.1036			1.30875			0.654377	−	0.756169i	$-0.272931\pi$
$761$	36.1036			1.30875			0.654377	+	0.756169i	$0.272931\pi$
$762$		−	12.8592i		−	0.465840i
$763$	−53.1945			−1.92577
$764$	−57.0309			−2.06330
$765$	0.0317336	+	0.164403i	0.00114733	+	0.00594400i
$766$	−29.7941			−1.07650
$767$	2.50566			0.0904741
$768$			4.22546i			0.152473i
$769$	−3.15770			−0.113870			−0.0569348	−	0.998378i	$-0.518133\pi$
$769$	−3.15770			−0.113870			−0.0569348	+	0.998378i	$0.518133\pi$
$770$		−	0.546850i		−	0.0197071i
$771$			15.3006i			0.551039i
$772$			33.4059i			1.20230i
$773$	−8.21909			−0.295620			−0.147810	−	0.989016i	$-0.547222\pi$
$773$	−8.21909			−0.295620			−0.147810	+	0.989016i	$0.547222\pi$
$774$	−5.11906			−0.184001
$775$		−	41.2168i		−	1.48055i
$776$			12.3567i			0.443580i
$777$			13.0728i			0.468985i
$778$	21.1533			0.758382
$779$		−	28.8883i		−	1.03503i
$780$	−0.0142328			−0.000509615
$781$	20.6157			0.737687
$782$	8.35554	+	43.2877i	0.298793	+	1.54796i
$783$	17.1925			0.614411
$784$	4.43920			0.158543
$785$			0.158234i			0.00564760i
$786$	−3.31232			−0.118147
$787$		−	43.5813i		−	1.55350i	−0.629806	−	0.776752i	$-0.716866\pi$
$787$		−	43.5813i		−	1.55350i	0.629806	−	0.776752i	$-0.283134\pi$
$788$			9.52026i			0.339145i
$789$		−	11.9525i		−	0.425519i
$790$	−0.165913			−0.00590293
$791$	5.39063			0.191669
$792$		−	13.1737i		−	0.468108i
$793$			4.89527i			0.173836i
$794$			83.1111i			2.94950i
$795$	−0.143754			−0.00509843
$796$		−	46.1564i		−	1.63597i
$797$	43.4495			1.53906			0.769530	−	0.638610i	$-0.220490\pi$
$797$	43.4495			1.53906			0.769530	+	0.638610i	$0.220490\pi$
$798$	26.4746			0.937191
$799$	2.97119	−	0.573509i	0.105113	−	0.0202893i
$800$	39.8227			1.40794
$801$	37.8737			1.33820
$802$			55.3790i			1.95550i
$803$	−52.6411			−1.85767
$804$		−	8.49643i		−	0.299646i
$805$		−	0.248753i		−	0.00876740i
$806$			7.76300i			0.273440i
$807$	−19.5211			−0.687176
$808$	4.85040			0.170637
$809$			20.0933i			0.706444i	0.935540	+	0.353222i	$0.114914\pi$
$809$			20.0933i			0.706444i	−0.935540	+	0.353222i	$0.885086\pi$
$810$		−	0.145385i		−	0.00510830i
$811$			19.7767i			0.694455i	0.937781	+	0.347227i	$0.112877\pi$
$811$			19.7767i			0.694455i	−0.937781	+	0.347227i	$0.887123\pi$
$812$	−30.3404			−1.06474
$813$		−	1.16554i		−	0.0408773i
$814$	64.6624			2.26642
$815$	0.382197			0.0133878
$816$	−1.65785	−	8.58884i	−0.0580363	−	0.300670i
$817$	−5.57095			−0.194903
$818$	−12.5429			−0.438552
$819$		−	3.14717i		−	0.109971i
$820$	−0.217243			−0.00758645
$821$		−	50.2265i		−	1.75292i	−0.481479	−	0.876458i	$-0.659900\pi$
$821$		−	50.2265i		−	1.75292i	0.481479	−	0.876458i	$-0.340100\pi$
$822$			25.8295i			0.900908i
$823$			5.50536i			0.191905i	0.995386	+	0.0959525i	$0.0305897\pi$
$823$			5.50536i			0.191905i	−0.995386	+	0.0959525i	$0.969410\pi$
$824$	−12.3353			−0.429720
$825$	−20.0058			−0.696513
$826$			35.0498i			1.21954i
$827$			14.9663i			0.520429i	0.965551	+	0.260214i	$0.0837932\pi$
$827$			14.9663i			0.520429i	−0.965551	+	0.260214i	$0.916207\pi$
$828$		−	30.3643i		−	1.05523i
$829$	24.7945			0.861147			0.430574	−	0.902555i	$-0.358311\pi$
$829$	24.7945			0.861147			0.430574	+	0.902555i	$0.358311\pi$
$830$		−	0.576238i		−	0.0200015i
$831$	10.3909			0.360455
$832$	−5.03477			−0.174549
$833$	−6.47705	+	1.25022i	−0.224416	+	0.0433176i
$834$	14.8848			0.515417
$835$	−0.147868			−0.00511717
$836$		−	72.6443i		−	2.51246i
$837$	34.1351			1.17988
$838$			34.1265i			1.17888i
$839$			39.9875i			1.38052i	0.723560	+	0.690261i	$0.242504\pi$
$839$			39.9875i			1.38052i	−0.723560	+	0.690261i	$0.757496\pi$
$840$		−	0.0392916i		−	0.00135569i
$841$	11.7601			0.405520
$842$	49.2951			1.69882
$843$		−	3.92774i		−	0.135278i
$844$			9.96372i			0.342966i
$845$		−	0.215251i		−	0.00740485i
$846$	−3.75698			−0.129168
$847$			48.0536i			1.65114i
$848$	−31.0268			−1.06547
$849$	22.1414			0.759891
$850$	−42.8978	+	8.28027i	−1.47138	+	0.284011i
$851$	29.4139			1.00830
$852$	7.50556			0.257136
$853$		−	12.0452i		−	0.412420i	−0.978508	−	0.206210i	$-0.933887\pi$
$853$		−	12.0452i		−	0.412420i	0.978508	−	0.206210i	$-0.0661130\pi$
$854$	−68.4762			−2.34321
$855$		−	0.226234i		−	0.00773704i
$856$		−	17.8453i		−	0.609940i
$857$			24.2411i			0.828059i	0.910264	+	0.414029i	$0.135879\pi$
$857$			24.2411i			0.828059i	−0.910264	+	0.414029i	$0.864121\pi$
$858$	3.76800			0.128637
$859$	35.2684			1.20334			0.601672	−	0.798743i	$-0.294501\pi$
$859$	35.2684			1.20334			0.601672	+	0.798743i	$0.294501\pi$
$860$			0.0418941i			0.00142858i
$861$			11.6274i			0.396262i
$862$		−	63.2101i		−	2.15294i
$863$	11.4483			0.389706			0.194853	−	0.980832i	$-0.437577\pi$
$863$	11.4483			0.389706			0.194853	+	0.980832i	$0.437577\pi$
$864$			32.9805i			1.12202i
$865$	0.109260			0.00371496
$866$	−22.2286			−0.755360
$867$	4.83779	+	12.0647i	0.164300	+	0.409739i
$868$	−60.2397			−2.04467
$869$	24.3665			0.826575
$870$		−	0.113127i		−	0.00383538i
$871$	−1.98142			−0.0671380
$872$			18.9052i			0.640211i
$873$		−	28.6367i		−	0.969206i
$874$		−	59.5680i		−	2.01492i
$875$	0.493039			0.0166678
$876$	−19.1651			−0.647528
$877$		−	13.5404i		−	0.457228i	−0.973517	−	0.228614i	$-0.926581\pi$
$877$		−	13.5404i		−	0.457228i	0.973517	−	0.228614i	$-0.0734193\pi$
$878$		−	5.68033i		−	0.191702i
$879$			10.6165i			0.358087i
$880$	0.244130			0.00822962
$881$		−	29.8111i		−	1.00436i	−0.864763	−	0.502181i	$-0.832531\pi$
$881$		−	29.8111i		−	1.00436i	0.864763	−	0.502181i	$-0.167469\pi$
$882$	8.19004			0.275773
$883$	1.49267			0.0502325			0.0251162	−	0.999685i	$-0.492004\pi$
$883$	1.49267			0.0502325			0.0251162	+	0.999685i	$0.492004\pi$
$884$	4.48208	−	0.865145i	0.150749	−	0.0290980i
$885$	−0.0724973			−0.00243697
$886$	12.1561			0.408393
$887$			22.4831i			0.754909i	0.926028	+	0.377455i	$0.123201\pi$
$887$			22.4831i			0.754909i	−0.926028	+	0.377455i	$0.876799\pi$
$888$	4.64605			0.155911
$889$		−	23.2706i		−	0.780472i
$890$		−	0.558741i		−	0.0187291i
$891$			21.3516i			0.715304i
$892$	−3.55945			−0.119179
$893$	−4.08864			−0.136821
$894$			11.4486i			0.382897i
$895$			0.408894i			0.0136678i
$896$		−	23.7120i		−	0.792162i
$897$	1.71400			0.0572289
$898$			45.6556i			1.52355i
$899$	−34.2292			−1.14161
$900$	30.0908			1.00303
$901$	45.2699	−	8.73815i	1.50816	−	0.291110i
$902$	57.5131			1.91498
$903$	2.24229			0.0746188
$904$		−	1.91582i		−	0.0637192i
$905$	0.0931150			0.00309525
$906$		−	3.45770i		−	0.114874i
$907$		−	25.3670i		−	0.842297i	−0.906992	−	0.421149i	$-0.861627\pi$
$907$		−	25.3670i		−	0.842297i	0.906992	−	0.421149i	$-0.138373\pi$
$908$			37.1675i			1.23345i
$909$	−11.2408			−0.372834
$910$	−0.0464295			−0.00153912
$911$			14.6320i			0.484781i	0.970179	+	0.242390i	$0.0779315\pi$
$911$			14.6320i			0.484781i	−0.970179	+	0.242390i	$0.922069\pi$
$912$			11.8191i			0.391368i
$913$			84.6277i			2.80077i
$914$	−0.824245			−0.0272636
$915$		−	0.141637i		−	0.00468237i
$916$	−10.0255			−0.331251
$917$	−5.99413			−0.197944
$918$	−6.85759	−	35.5272i	−0.226334	−	1.17257i
$919$	16.1513			0.532782			0.266391	−	0.963865i	$-0.414169\pi$
$919$	16.1513			0.532782			0.266391	+	0.963865i	$0.414169\pi$
$920$	−0.0884063			−0.00291467
$921$		−	26.1966i		−	0.863208i
$922$	50.1007			1.64998
$923$		−	1.75035i		−	0.0576133i
$924$			29.2391i			0.961896i
$925$			29.1490i			0.958412i
$926$	57.2702			1.88202
$927$	28.5871			0.938923
$928$		−	33.0714i		−	1.08562i
$929$		−	45.2046i		−	1.48312i	−0.670889	−	0.741558i	$-0.734087\pi$
$929$		−	45.2046i		−	1.48312i	0.670889	−	0.741558i	$-0.265913\pi$
$930$		−	0.224610i		−	0.00736525i
$931$	8.91303			0.292113
$932$		−	17.4360i		−	0.571134i
$933$	−1.05329			−0.0344830
$934$	7.85705			0.257090
$935$	−0.356200	+	0.0687549i	−0.0116490	+	0.00224853i
$936$	−1.11850			−0.0365592
$937$	−0.887949			−0.0290080			−0.0145040	−	0.999895i	$-0.504617\pi$
$937$	−0.887949			−0.0290080			−0.0145040	+	0.999895i	$0.504617\pi$
$938$		−	27.7167i		−	0.904981i
$939$	−2.35307			−0.0767897
$940$			0.0307470i			0.00100286i
$941$		−	34.5488i		−	1.12626i	−0.826369	−	0.563129i	$-0.809597\pi$
$941$		−	34.5488i		−	1.12626i	0.826369	−	0.563129i	$-0.190403\pi$
$942$		−	15.2512i		−	0.496912i
$943$	26.1618			0.851945
$944$	−15.6473			−0.509275
$945$			0.204158i			0.00664125i
$946$		−	11.0911i		−	0.360602i
$947$		−	33.5275i		−	1.08950i	−0.838599	−	0.544749i	$-0.816625\pi$
$947$		−	33.5275i		−	1.08950i	0.838599	−	0.544749i	$-0.183375\pi$
$948$	8.87110			0.288120
$949$			4.46942i			0.145084i
$950$	59.0314			1.91523
$951$	−25.0292			−0.811626
$952$	2.38836	+	12.3734i	0.0774071	+	0.401025i
$953$	18.6434			0.603918			0.301959	−	0.953321i	$-0.402359\pi$
$953$	18.6434			0.603918			0.301959	+	0.953321i	$0.402359\pi$
$954$	−57.2425			−1.85329
$955$		−	0.384814i		−	0.0124523i
$956$	−31.8978			−1.03165
$957$			16.6142i			0.537060i
$958$		−	54.3303i		−	1.75533i
$959$			46.7423i			1.50939i
$960$	0.145673			0.00470158
$961$	−36.9608			−1.19228
$962$		−	5.49007i		−	0.177007i
$963$			41.3566i			1.33270i
$964$			29.1977i			0.940393i
$965$	−0.225405			−0.00725604
$966$			23.9759i			0.771412i
$967$	0.857645			0.0275800			0.0137900	−	0.999905i	$-0.495610\pi$
$967$	0.857645			0.0275800			0.0137900	+	0.999905i	$0.495610\pi$
$968$	17.0781			0.548912
$969$	−3.32863	−	17.2447i	−0.106931	−	0.553979i
$970$	−0.422471			−0.0135647
$971$	−15.4704			−0.496470			−0.248235	−	0.968700i	$-0.579850\pi$
$971$	−15.4704			−0.496470			−0.248235	+	0.968700i	$0.579850\pi$
$972$			38.7262i			1.24214i
$973$	26.9362			0.863533
$974$		−	69.1827i		−	2.21676i
$975$			1.69857i			0.0543976i
$976$		−	30.5698i		−	0.978517i
$977$	−11.7602			−0.376244			−0.188122	−	0.982146i	$-0.560240\pi$
$977$	−11.7602			−0.376244			−0.188122	+	0.982146i	$0.560240\pi$
$978$	−36.8378			−1.17794
$979$			82.0581i			2.62259i
$980$		−	0.0670269i		−	0.00214110i
$981$		−	43.8129i		−	1.39884i
$982$	−9.34530			−0.298220
$983$		−	30.3033i		−	0.966524i	−0.875476	−	0.483262i	$-0.839452\pi$
$983$		−	30.3033i		−	0.966524i	0.875476	−	0.483262i	$-0.160548\pi$
$984$	4.13237			0.131735
$985$	−0.0642376			−0.00204678
$986$	6.87649	+	35.6252i	0.218992	+	1.13454i
$987$	1.64566			0.0523821
$988$	−6.16776			−0.196223
$989$		−	5.04516i		−	0.160427i
$990$	0.450404			0.0143148
$991$			31.9305i			1.01431i	0.861856	+	0.507153i	$0.169302\pi$
$991$			31.9305i			1.01431i	−0.861856	+	0.507153i	$0.830698\pi$
$992$		−	65.6620i		−	2.08477i
$993$		−	22.9673i		−	0.728844i
$994$	24.4843			0.776594
$995$	0.311438			0.00987326
$996$			30.8104i			0.976265i
$997$		−	38.8466i		−	1.23029i	−0.788416	−	0.615143i	$-0.789098\pi$
$997$		−	38.8466i		−	1.23029i	0.788416	−	0.615143i	$-0.210902\pi$
$998$		−	69.8962i		−	2.21252i
$999$	−24.1407			−0.763777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.c.560.6	yes	20
17.16	even	2	inner	731.2.d.c.560.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.c.560.5	✓	20	17.16	even	2	inner
731.2.d.c.560.6	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.11938 q^{2} +0.764619i q^{3} +2.49176 q^{4} +0.0168131i q^{5} -1.62052i q^{6} -2.93256i q^{7} -1.04222 q^{8} +2.41536 q^{9} +O(q^{10})\)	\(q-2.11938 q^{2} +0.764619i q^{3} +2.49176 q^{4} +0.0168131i q^{5} -1.62052i q^{6} -2.93256i q^{7} -1.04222 q^{8} +2.41536 q^{9} -0.0356332i q^{10} +5.23318i q^{11} +1.90525i q^{12} +0.444316 q^{13} +6.21520i q^{14} -0.0128556 q^{15} -2.77465 q^{16} +(4.04838 - 0.781432i) q^{17} -5.11906 q^{18} -5.57095 q^{19} +0.0418941i q^{20} +2.24229 q^{21} -11.0911i q^{22} -5.04516i q^{23} -0.796905i q^{24} +4.99972 q^{25} -0.941673 q^{26} +4.14068i q^{27} -7.30724i q^{28} -4.15210i q^{29} +0.0272458 q^{30} -8.24383i q^{31} +7.96498 q^{32} -4.00139 q^{33} +(-8.58004 + 1.65615i) q^{34} +0.0493053 q^{35} +6.01849 q^{36} +5.83012i q^{37} +11.8070 q^{38} +0.339732i q^{39} -0.0175230i q^{40} +5.18552i q^{41} -4.75226 q^{42} +1.00000 q^{43} +13.0398i q^{44} +0.0406096i q^{45} +10.6926i q^{46} +0.733921 q^{47} -2.12155i q^{48} -1.59991 q^{49} -10.5963 q^{50} +(0.597497 + 3.09547i) q^{51} +1.10713 q^{52} +11.1822 q^{53} -8.77567i q^{54} -0.0879858 q^{55} +3.05639i q^{56} -4.25966i q^{57} +8.79986i q^{58} +5.63936 q^{59} -0.0320330 q^{60} +11.0175i q^{61} +17.4718i q^{62} -7.08318i q^{63} -11.3315 q^{64} +0.00747031i q^{65} +8.48045 q^{66} -4.45949 q^{67} +(10.0876 - 1.94714i) q^{68} +3.85762 q^{69} -0.104497 q^{70} -3.93942i q^{71} -2.51735 q^{72} +10.0591i q^{73} -12.3562i q^{74} +3.82288i q^{75} -13.8815 q^{76} +15.3466 q^{77} -0.720021i q^{78} -4.65614i q^{79} -0.0466504i q^{80} +4.08003 q^{81} -10.9901i q^{82} +16.1714 q^{83} +5.58725 q^{84} +(0.0131383 + 0.0680656i) q^{85} -2.11938 q^{86} +3.17477 q^{87} -5.45415i q^{88} +15.6803 q^{89} -0.0860670i q^{90} -1.30298i q^{91} -12.5713i q^{92} +6.30339 q^{93} -1.55546 q^{94} -0.0936648i q^{95} +6.09018i q^{96} -11.8561i q^{97} +3.39082 q^{98} +12.6400i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9	\( 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9} - 4 q^{13} + 26 q^{15} + 6 q^{16} + 16 q^{17} - 22 q^{18} - 4 q^{19} + 20 q^{21} - 2 q^{25} + 22 q^{26} - 72 q^{30} + 38 q^{32} - 12 q^{33} + 12 q^{34} - 30 q^{35} - 104 q^{36} - 22 q^{38} + 26 q^{42} + 20 q^{43} - 34 q^{47} + 22 q^{49} + 42 q^{50} + 52 q^{51} - 110 q^{52} + 14 q^{53} + 12 q^{55} + 20 q^{59} + 42 q^{60} - 22 q^{64} + 50 q^{66} - 12 q^{67} + 50 q^{68} - 82 q^{69} - 30 q^{70} - 50 q^{72} + 2 q^{76} + 78 q^{77} + 44 q^{81} + 20 q^{83} + 62 q^{84} + 76 q^{85} + 2 q^{86} + 12 q^{87} - 46 q^{89} + 58 q^{93} - 18 q^{94} - 62 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9 - 4 * q^13 + 26 * q^15 + 6 * q^16 + 16 * q^17 - 22 * q^18 - 4 * q^19 + 20 * q^21 - 2 * q^25 + 22 * q^26 - 72 * q^30 + 38 * q^32 - 12 * q^33 + 12 * q^34 - 30 * q^35 - 104 * q^36 - 22 * q^38 + 26 * q^42 + 20 * q^43 - 34 * q^47 + 22 * q^49 + 42 * q^50 + 52 * q^51 - 110 * q^52 + 14 * q^53 + 12 * q^55 + 20 * q^59 + 42 * q^60 - 22 * q^64 + 50 * q^66 - 12 * q^67 + 50 * q^68 - 82 * q^69 - 30 * q^70 - 50 * q^72 + 2 * q^76 + 78 * q^77 + 44 * q^81 + 20 * q^83 + 62 * q^84 + 76 * q^85 + 2 * q^86 + 12 * q^87 - 46 * q^89 + 58 * q^93 - 18 * q^94 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

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