LMFDB - Embedded newform 357.2.f.a.169.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(169,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.169"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			169.3
Root			$1.45161 - 1.45161i$ of defining polynomial
Character	$\chi$	$=$	357.169
Dual form			357.2.f.a.169.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.688892 q^{2} -1.00000i q^{3} -1.52543 q^{4} +3.21432i q^{5} -0.688892i q^{6} +1.00000i q^{7} -2.42864 q^{8} -1.00000 q^{9} +2.21432i q^{10} +3.90321i q^{11} +1.52543i q^{12} -2.59210 q^{13} +0.688892i q^{14} +3.21432 q^{15} +1.37778 q^{16} +(0.214320 + 4.11753i) q^{17} -0.688892 q^{18} +2.31111 q^{19} -4.90321i q^{20} +1.00000 q^{21} +2.68889i q^{22} -3.62222i q^{23} +2.42864i q^{24} -5.33185 q^{25} -1.78568 q^{26} +1.00000i q^{27} -1.52543i q^{28} +2.90321i q^{29} +2.21432 q^{30} +1.59210i q^{31} +5.80642 q^{32} +3.90321 q^{33} +(0.147643 + 2.83654i) q^{34} -3.21432 q^{35} +1.52543 q^{36} -1.73975i q^{37} +1.59210 q^{38} +2.59210i q^{39} -7.80642i q^{40} -2.31111i q^{41} +0.688892 q^{42} -4.18421 q^{43} -5.95407i q^{44} -3.21432i q^{45} -2.49532i q^{46} +11.2652 q^{47} -1.37778i q^{48} -1.00000 q^{49} -3.67307 q^{50} +(4.11753 - 0.214320i) q^{51} +3.95407 q^{52} -6.49532 q^{53} +0.688892i q^{54} -12.5462 q^{55} -2.42864i q^{56} -2.31111i q^{57} +2.00000i q^{58} +6.96989 q^{59} -4.90321 q^{60} +0.0809666i q^{61} +1.09679i q^{62} -1.00000i q^{63} +1.24443 q^{64} -8.33185i q^{65} +2.68889 q^{66} -15.0049 q^{67} +(-0.326929 - 6.28100i) q^{68} -3.62222 q^{69} -2.21432 q^{70} -5.03657i q^{71} +2.42864 q^{72} -11.2859i q^{73} -1.19850i q^{74} +5.33185i q^{75} -3.52543 q^{76} -3.90321 q^{77} +1.78568i q^{78} +17.1590i q^{79} +4.42864i q^{80} +1.00000 q^{81} -1.59210i q^{82} +14.2351 q^{83} -1.52543 q^{84} +(-13.2351 + 0.688892i) q^{85} -2.88247 q^{86} +2.90321 q^{87} -9.47949i q^{88} +1.67307 q^{89} -2.21432i q^{90} -2.59210i q^{91} +5.52543i q^{92} +1.59210 q^{93} +7.76049 q^{94} +7.42864i q^{95} -5.80642i q^{96} +5.57136i q^{97} -0.688892 q^{98} -3.90321i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{2} + 4 q^{4} + 12 q^{8} - 6 q^{9} - 2 q^{13} + 6 q^{15} + 8 q^{16} - 12 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{21} + 8 q^{25} - 24 q^{26} + 8 q^{32} + 10 q^{33} - 12 q^{34} - 6 q^{35} - 4 q^{36}+ \cdots - 4 q^{98}+O(q^{100}) $ 6 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 - 6 * q^9 - 2 * q^13 + 6 * q^15 + 8 * q^16 - 12 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^21 + 8 * q^25 - 24 * q^26 + 8 * q^32 + 10 * q^33 - 12 * q^34 - 6 * q^35 - 4 * q^36 - 4 * q^38 + 4 * q^42 + 2 * q^43 + 28 * q^47 - 6 * q^49 + 4 * q^50 - 2 * q^51 - 16 * q^52 - 12 * q^53 - 22 * q^55 + 28 * q^59 - 16 * q^60 + 8 * q^64 + 16 * q^66 - 24 * q^67 - 28 * q^68 - 22 * q^69 - 12 * q^72 - 8 * q^76 - 10 * q^77 + 6 * q^81 + 32 * q^83 + 4 * q^84 - 26 * q^85 - 44 * q^86 + 4 * q^87 - 16 * q^89 - 4 * q^93 - 20 * q^94 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.688892			0.487120			0.243560	−	0.969886i	$-0.421685\pi$
$2$	0.688892			0.487120			0.243560	+	0.969886i	$0.421685\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.52543			−0.762714
$5$			3.21432i			1.43749i	0.695275	+	0.718744i	$0.255283\pi$
$5$			3.21432i			1.43749i	−0.695275	+	0.718744i	$0.744717\pi$
$6$		−	0.688892i		−	0.281239i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.42864			−0.858654
$9$	−1.00000			−0.333333
$10$			2.21432i			0.700229i
$11$			3.90321i			1.17686i	0.808547	+	0.588431i	$0.200254\pi$
$11$			3.90321i			1.17686i	−0.808547	+	0.588431i	$0.799746\pi$
$12$			1.52543i			0.440353i
$13$	−2.59210			−0.718920			−0.359460	−	0.933160i	$-0.617039\pi$
$13$	−2.59210			−0.718920			−0.359460	+	0.933160i	$0.617039\pi$
$14$			0.688892i			0.184114i
$15$	3.21432			0.829934
$16$	1.37778			0.344446
$17$	0.214320	+	4.11753i	0.0519802	+	0.998648i
$17$	0.214320	+	4.11753i	0.0519802	+	0.998648i
$18$	−0.688892			−0.162373
$19$	2.31111			0.530204			0.265102	−	0.964220i	$-0.414594\pi$
$19$	2.31111			0.530204			0.265102	+	0.964220i	$0.414594\pi$
$20$		−	4.90321i		−	1.09639i
$21$	1.00000			0.218218
$22$			2.68889i			0.573274i
$23$		−	3.62222i		−	0.755284i	−0.925952	−	0.377642i	$-0.876735\pi$
$23$		−	3.62222i		−	0.755284i	0.925952	−	0.377642i	$-0.123265\pi$
$24$			2.42864i			0.495744i
$25$	−5.33185			−1.06637
$26$	−1.78568			−0.350201
$27$			1.00000i			0.192450i
$28$		−	1.52543i		−	0.288279i
$29$			2.90321i			0.539113i	0.962985	+	0.269556i	$0.0868771\pi$
$29$			2.90321i			0.539113i	−0.962985	+	0.269556i	$0.913123\pi$
$30$	2.21432			0.404278
$31$			1.59210i			0.285950i	0.989726	+	0.142975i	$0.0456669\pi$
$31$			1.59210i			0.285950i	−0.989726	+	0.142975i	$0.954333\pi$
$32$	5.80642			1.02644
$33$	3.90321			0.679462
$34$	0.147643	+	2.83654i	0.0253206	+	0.486462i
$35$	−3.21432			−0.543319
$36$	1.52543			0.254238
$37$		−	1.73975i		−	0.286013i	−0.989722	−	0.143006i	$-0.954323\pi$
$37$		−	1.73975i		−	0.286013i	0.989722	−	0.143006i	$-0.0456769\pi$
$38$	1.59210			0.258273
$39$			2.59210i			0.415069i
$40$		−	7.80642i		−	1.23430i
$41$		−	2.31111i		−	0.360934i	−0.983581	−	0.180467i	$-0.942239\pi$
$41$		−	2.31111i		−	0.360934i	0.983581	−	0.180467i	$-0.0577610\pi$
$42$	0.688892			0.106298
$43$	−4.18421			−0.638086			−0.319043	−	0.947740i	$-0.603361\pi$
$43$	−4.18421			−0.638086			−0.319043	+	0.947740i	$0.603361\pi$
$44$		−	5.95407i		−	0.897609i
$45$		−	3.21432i		−	0.479162i
$46$		−	2.49532i		−	0.367914i
$47$	11.2652			1.64319			0.821597	−	0.570068i	$-0.193083\pi$
$47$	11.2652			1.64319			0.821597	+	0.570068i	$0.193083\pi$
$48$		−	1.37778i		−	0.198866i
$49$	−1.00000			−0.142857
$50$	−3.67307			−0.519451
$51$	4.11753	−	0.214320i	0.576570	−	0.0300108i
$52$	3.95407			0.548330
$53$	−6.49532			−0.892200			−0.446100	−	0.894983i	$-0.647187\pi$
$53$	−6.49532			−0.892200			−0.446100	+	0.894983i	$0.647187\pi$
$54$			0.688892i			0.0937464i
$55$	−12.5462			−1.69173
$56$		−	2.42864i		−	0.324541i
$57$		−	2.31111i		−	0.306114i
$58$			2.00000i			0.262613i
$59$	6.96989			0.907402			0.453701	−	0.891154i	$-0.350103\pi$
$59$	6.96989			0.907402			0.453701	+	0.891154i	$0.350103\pi$
$60$	−4.90321			−0.633002
$61$			0.0809666i			0.0103667i	0.999987	+	0.00518336i	$0.00164992\pi$
$61$			0.0809666i			0.0103667i	−0.999987	+	0.00518336i	$0.998350\pi$
$62$			1.09679i			0.139292i
$63$		−	1.00000i		−	0.125988i
$64$	1.24443			0.155554
$65$		−	8.33185i		−	1.03344i
$66$	2.68889			0.330980
$67$	−15.0049			−1.83314			−0.916572	−	0.399871i	$-0.869055\pi$
$67$	−15.0049			−1.83314			−0.916572	+	0.399871i	$0.869055\pi$
$68$	−0.326929	−	6.28100i	−0.0396460	−	0.761683i
$69$	−3.62222			−0.436064
$70$	−2.21432			−0.264662
$71$		−	5.03657i		−	0.597730i	−0.954295	−	0.298865i	$-0.903392\pi$
$71$		−	5.03657i		−	0.597730i	0.954295	−	0.298865i	$-0.0966081\pi$
$72$	2.42864			0.286218
$73$		−	11.2859i		−	1.32092i	−0.750863	−	0.660458i	$-0.770362\pi$
$73$		−	11.2859i		−	1.32092i	0.750863	−	0.660458i	$-0.229638\pi$
$74$		−	1.19850i		−	0.139323i
$75$			5.33185i			0.615669i
$76$	−3.52543			−0.404394
$77$	−3.90321			−0.444812
$78$			1.78568i			0.202188i
$79$			17.1590i			1.93054i	0.261254	+	0.965270i	$0.415864\pi$
$79$			17.1590i			1.93054i	−0.261254	+	0.965270i	$0.584136\pi$
$80$			4.42864i			0.495137i
$81$	1.00000			0.111111
$82$		−	1.59210i		−	0.175818i
$83$	14.2351			1.56250			0.781251	−	0.624218i	$-0.214582\pi$
$83$	14.2351			1.56250			0.781251	+	0.624218i	$0.214582\pi$
$84$	−1.52543			−0.166438
$85$	−13.2351	+	0.688892i	−1.43554	+	0.0747208i
$86$	−2.88247			−0.310825
$87$	2.90321			0.311257
$88$		−	9.47949i		−	1.01052i
$89$	1.67307			0.177345			0.0886726	−	0.996061i	$-0.471738\pi$
$89$	1.67307			0.177345			0.0886726	+	0.996061i	$0.471738\pi$
$90$		−	2.21432i		−	0.233410i
$91$		−	2.59210i		−	0.271726i
$92$			5.52543i			0.576066i
$93$	1.59210			0.165094
$94$	7.76049			0.800434
$95$			7.42864i			0.762162i
$96$		−	5.80642i		−	0.592616i
$97$			5.57136i			0.565686i	0.959166	+	0.282843i	$0.0912775\pi$
$97$			5.57136i			0.565686i	−0.959166	+	0.282843i	$0.908722\pi$
$98$	−0.688892			−0.0695886
$99$		−	3.90321i		−	0.392288i
$100$	8.13335			0.813335
$101$	14.5827			1.45104			0.725518	−	0.688203i	$-0.241600\pi$
$101$	14.5827			1.45104			0.725518	+	0.688203i	$0.241600\pi$
$102$	2.83654	−	0.147643i	0.280859	−	0.0146189i
$103$	11.5827			1.14128			0.570640	−	0.821200i	$-0.306695\pi$
$103$	11.5827			1.14128			0.570640	+	0.821200i	$0.306695\pi$
$104$	6.29529			0.617304
$105$			3.21432i			0.313685i
$106$	−4.47457			−0.434609
$107$			17.3368i			1.67601i	0.545663	+	0.838005i	$0.316278\pi$
$107$			17.3368i			1.67601i	−0.545663	+	0.838005i	$0.683722\pi$
$108$		−	1.52543i		−	0.146784i
$109$		−	15.9748i		−	1.53011i	−0.643965	−	0.765055i	$-0.722712\pi$
$109$		−	15.9748i		−	1.53011i	0.643965	−	0.765055i	$-0.277288\pi$
$110$	−8.64296			−0.824074
$111$	−1.73975			−0.165130
$112$			1.37778i			0.130188i
$113$			3.01429i			0.283561i	0.989898	+	0.141780i	$0.0452826\pi$
$113$			3.01429i			0.283561i	−0.989898	+	0.141780i	$0.954717\pi$
$114$		−	1.59210i		−	0.149114i
$115$	11.6430			1.08571
$116$		−	4.42864i		−	0.411189i
$117$	2.59210			0.239640
$118$	4.80150			0.442014
$119$	−4.11753	+	0.214320i	−0.377454	+	0.0196467i
$120$	−7.80642			−0.712626
$121$	−4.23506			−0.385006
$122$			0.0557773i			0.00504984i
$123$	−2.31111			−0.208386
$124$		−	2.42864i		−	0.218098i
$125$		−	1.06668i		−	0.0954065i
$126$		−	0.688892i		−	0.0613714i
$127$	14.3319			1.27175			0.635873	−	0.771794i	$-0.280640\pi$
$127$	14.3319			1.27175			0.635873	+	0.771794i	$0.280640\pi$
$128$	−10.7556			−0.950667
$129$			4.18421i			0.368399i
$130$		−	5.73975i		−	0.503409i
$131$			1.44938i			0.126633i	0.997993	+	0.0633166i	$0.0201678\pi$
$131$			1.44938i			0.126633i	−0.997993	+	0.0633166i	$0.979832\pi$
$132$	−5.95407			−0.518235
$133$			2.31111i			0.200398i
$134$	−10.3368			−0.892961
$135$	−3.21432			−0.276645
$136$	−0.520505	−	10.0000i	−0.0446330	−	0.857493i
$137$	−6.36196			−0.543539			−0.271770	−	0.962362i	$-0.587609\pi$
$137$	−6.36196			−0.543539			−0.271770	+	0.962362i	$0.587609\pi$
$138$	−2.49532			−0.212415
$139$			7.93978i			0.673443i	0.941604	+	0.336722i	$0.109318\pi$
$139$			7.93978i			0.673443i	−0.941604	+	0.336722i	$0.890682\pi$
$140$	4.90321			0.414397
$141$		−	11.2652i		−	0.948699i
$142$		−	3.46965i		−	0.291167i
$143$		−	10.1175i		−	0.846071i
$144$	−1.37778			−0.114815
$145$	−9.33185			−0.774968
$146$		−	7.77478i		−	0.643445i
$147$			1.00000i			0.0824786i
$148$			2.65386i			0.218146i
$149$	15.7748			1.29232			0.646160	−	0.763202i	$-0.276374\pi$
$149$	15.7748			1.29232			0.646160	+	0.763202i	$0.276374\pi$
$150$			3.67307i			0.299905i
$151$	20.9032			1.70108			0.850540	−	0.525911i	$-0.176275\pi$
$151$	20.9032			1.70108			0.850540	+	0.525911i	$0.176275\pi$
$152$	−5.61285			−0.455262
$153$	−0.214320	−	4.11753i	−0.0173267	−	0.332883i
$154$	−2.68889			−0.216677
$155$	−5.11753			−0.411050
$156$		−	3.95407i		−	0.316579i
$157$	−15.9842			−1.27568			−0.637838	−	0.770170i	$-0.720171\pi$
$157$	−15.9842			−1.27568			−0.637838	+	0.770170i	$0.720171\pi$
$158$			11.8207i			0.940406i
$159$			6.49532i			0.515112i
$160$			18.6637i			1.47550i
$161$	3.62222			0.285471
$162$	0.688892			0.0541245
$163$			17.9081i			1.40267i	0.712830	+	0.701337i	$0.247413\pi$
$163$			17.9081i			1.40267i	−0.712830	+	0.701337i	$0.752587\pi$
$164$			3.52543i			0.275290i
$165$			12.5462i			0.976718i
$166$	9.80642			0.761126
$167$		−	3.79060i		−	0.293326i	−0.989187	−	0.146663i	$-0.953147\pi$
$167$		−	3.79060i		−	0.293326i	0.989187	−	0.146663i	$-0.0468532\pi$
$168$	−2.42864			−0.187374
$169$	−6.28100			−0.483154
$170$	−9.11753	+	0.474572i	−0.699283	+	0.0363980i
$171$	−2.31111			−0.176735
$172$	6.38271			0.486677
$173$			8.20495i			0.623811i	0.950113	+	0.311905i	$0.100967\pi$
$173$			8.20495i			0.623811i	−0.950113	+	0.311905i	$0.899033\pi$
$174$	2.00000			0.151620
$175$		−	5.33185i		−	0.403050i
$176$			5.37778i			0.405366i
$177$		−	6.96989i		−	0.523889i
$178$	1.15257			0.0863884
$179$	−16.6035			−1.24100			−0.620501	−	0.784206i	$-0.713071\pi$
$179$	−16.6035			−1.24100			−0.620501	+	0.784206i	$0.713071\pi$
$180$			4.90321i			0.365464i
$181$			6.36842i			0.473361i	0.971588	+	0.236680i	$0.0760594\pi$
$181$			6.36842i			0.473361i	−0.971588	+	0.236680i	$0.923941\pi$
$182$		−	1.78568i		−	0.132363i
$183$	0.0809666			0.00598523
$184$			8.79706i			0.648528i
$185$	5.59210			0.411140
$186$	1.09679			0.0804204
$187$	−16.0716	+	0.836535i	−1.17527	+	0.0611735i
$188$	−17.1842			−1.25329
$189$	−1.00000			−0.0727393
$190$			5.11753i			0.371265i
$191$	7.61285			0.550846			0.275423	−	0.961323i	$-0.411182\pi$
$191$	7.61285			0.550846			0.275423	+	0.961323i	$0.411182\pi$
$192$		−	1.24443i		−	0.0898091i
$193$		−	3.21924i		−	0.231726i	−0.993265	−	0.115863i	$-0.963037\pi$
$193$		−	3.21924i		−	0.231726i	0.993265	−	0.115863i	$-0.0369634\pi$
$194$			3.83807i			0.275557i
$195$	−8.33185			−0.596656
$196$	1.52543			0.108959
$197$		−	6.13828i		−	0.437334i	−0.975800	−	0.218667i	$-0.929829\pi$
$197$		−	6.13828i		−	0.437334i	0.975800	−	0.218667i	$-0.0701708\pi$
$198$		−	2.68889i		−	0.191091i
$199$		−	3.65233i		−	0.258907i	−0.991586	−	0.129453i	$-0.958678\pi$
$199$		−	3.65233i		−	0.258907i	0.991586	−	0.129453i	$-0.0413222\pi$
$200$	12.9491			0.915643
$201$			15.0049i			1.05837i
$202$	10.0459			0.706829
$203$	−2.90321			−0.203766
$204$	−6.28100	+	0.326929i	−0.439758	+	0.0228896i
$205$	7.42864			0.518839
$206$	7.97926			0.555941
$207$			3.62222i			0.251761i
$208$	−3.57136			−0.247629
$209$			9.02074i			0.623978i
$210$			2.21432i			0.152803i
$211$		−	13.4445i		−	0.925555i	−0.886475	−	0.462777i	$-0.846853\pi$
$211$		−	13.4445i		−	0.925555i	0.886475	−	0.462777i	$-0.153147\pi$
$212$	9.90813			0.680493
$213$	−5.03657			−0.345100
$214$			11.9432i			0.816418i
$215$		−	13.4494i		−	0.917240i
$216$		−	2.42864i		−	0.165248i
$217$	−1.59210			−0.108079
$218$		−	11.0049i		−	0.745347i
$219$	−11.2859			−0.762632
$220$	19.1383			1.29030
$221$	−0.555539	−	10.6731i	−0.0373696	−	0.717948i
$222$	−1.19850			−0.0804379
$223$	10.0716			0.674444			0.337222	−	0.941425i	$-0.390513\pi$
$223$	10.0716			0.674444			0.337222	+	0.941425i	$0.390513\pi$
$224$			5.80642i			0.387958i
$225$	5.33185			0.355457
$226$			2.07652i			0.138128i
$227$			22.2192i			1.47474i	0.675487	+	0.737371i	$0.263933\pi$
$227$			22.2192i			1.47474i	−0.675487	+	0.737371i	$0.736067\pi$
$228$			3.52543i			0.233477i
$229$	22.3225			1.47511			0.737556	−	0.675286i	$-0.235980\pi$
$229$	22.3225			1.47511			0.737556	+	0.675286i	$0.235980\pi$
$230$	8.02074			0.528872
$231$			3.90321i			0.256812i
$232$		−	7.05086i		−	0.462911i
$233$		−	27.5116i		−	1.80235i	−0.433460	−	0.901173i	$-0.642707\pi$
$233$		−	27.5116i		−	1.80235i	0.433460	−	0.901173i	$-0.357293\pi$
$234$	1.78568			0.116734
$235$			36.2099i			2.36207i
$236$	−10.6321			−0.692088
$237$	17.1590			1.11460
$238$	−2.83654	+	0.147643i	−0.183865	+	0.00957029i
$239$	−8.22861			−0.532265			−0.266132	−	0.963937i	$-0.585746\pi$
$239$	−8.22861			−0.532265			−0.266132	+	0.963937i	$0.585746\pi$
$240$	4.42864			0.285867
$241$			16.2953i			1.04967i	0.851203	+	0.524836i	$0.175873\pi$
$241$			16.2953i			1.04967i	−0.851203	+	0.524836i	$0.824127\pi$
$242$	−2.91750			−0.187544
$243$		−	1.00000i		−	0.0641500i
$244$		−	0.123509i		−	0.00790684i
$245$		−	3.21432i		−	0.205355i
$246$	−1.59210			−0.101509
$247$	−5.99063			−0.381175
$248$		−	3.86665i		−	0.245532i
$249$		−	14.2351i		−	0.902110i
$250$		−	0.734825i		−	0.0464744i
$251$	−28.7862			−1.81697			−0.908483	−	0.417922i	$-0.862759\pi$
$251$	−28.7862			−1.81697			−0.908483	+	0.417922i	$0.862759\pi$
$252$			1.52543i			0.0960929i
$253$	14.1383			0.888866
$254$	9.87310			0.619493
$255$	0.688892	+	13.2351i	0.0431401	+	0.828812i
$256$	−9.89829			−0.618643
$257$	15.2050			0.948459			0.474229	−	0.880401i	$-0.342727\pi$
$257$	15.2050			0.948459			0.474229	+	0.880401i	$0.342727\pi$
$258$			2.88247i			0.179455i
$259$	1.73975			0.108103
$260$			12.7096i			0.788218i
$261$		−	2.90321i		−	0.179704i
$262$			0.998469i			0.0616856i
$263$	−16.9906			−1.04769			−0.523844	−	0.851814i	$-0.675502\pi$
$263$	−16.9906			−1.04769			−0.523844	+	0.851814i	$0.675502\pi$
$264$	−9.47949			−0.583423
$265$		−	20.8780i		−	1.28253i
$266$			1.59210i			0.0976182i
$267$		−	1.67307i		−	0.102390i
$268$	22.8889			1.39816
$269$			9.49532i			0.578940i	0.957187	+	0.289470i	$0.0934790\pi$
$269$			9.49532i			0.578940i	−0.957187	+	0.289470i	$0.906521\pi$
$270$	−2.21432			−0.134759
$271$	−10.8316			−0.657974			−0.328987	−	0.944335i	$-0.606707\pi$
$271$	−10.8316			−0.657974			−0.328987	+	0.944335i	$0.606707\pi$
$272$	0.295286	+	5.67307i	0.0179044	+	0.343980i
$273$	−2.59210			−0.156881
$274$	−4.38271			−0.264769
$275$		−	20.8113i		−	1.25497i
$276$	5.52543			0.332592
$277$		−	29.3590i		−	1.76401i	−0.471236	−	0.882007i	$-0.656192\pi$
$277$		−	29.3590i		−	1.76401i	0.471236	−	0.882007i	$-0.343808\pi$
$278$			5.46965i			0.328048i
$279$		−	1.59210i		−	0.0953168i
$280$	7.80642			0.466523
$281$	−7.76494			−0.463217			−0.231609	−	0.972809i	$-0.574399\pi$
$281$	−7.76494			−0.463217			−0.231609	+	0.972809i	$0.574399\pi$
$282$		−	7.76049i		−	0.462131i
$283$		−	32.3575i		−	1.92345i	−0.274008	−	0.961727i	$-0.588350\pi$
$283$		−	32.3575i		−	1.92345i	0.274008	−	0.961727i	$-0.411650\pi$
$284$			7.68292i			0.455897i
$285$	7.42864			0.440035
$286$		−	6.96989i		−	0.412138i
$287$	2.31111			0.136420
$288$	−5.80642			−0.342147
$289$	−16.9081	+	1.76494i	−0.994596	+	0.103820i
$290$	−6.42864			−0.377503
$291$	5.57136			0.326599
$292$			17.2159i			1.00748i
$293$	−27.6731			−1.61668			−0.808339	−	0.588717i	$-0.799633\pi$
$293$	−27.6731			−1.61668			−0.808339	+	0.588717i	$0.799633\pi$
$294$			0.688892i			0.0401770i
$295$			22.4035i			1.30438i
$296$			4.22522i			0.245586i
$297$	−3.90321			−0.226487
$298$	10.8671			0.629516
$299$			9.38916i			0.542989i
$300$		−	8.13335i		−	0.469579i
$301$		−	4.18421i		−	0.241174i
$302$	14.4001			0.828630
$303$		−	14.5827i		−	0.837756i
$304$	3.18421			0.182627
$305$	−0.260253			−0.0149020
$306$	−0.147643	−	2.83654i	−0.00844020	−	0.162154i
$307$	−23.3876			−1.33480			−0.667401	−	0.744698i	$-0.732593\pi$
$307$	−23.3876			−1.33480			−0.667401	+	0.744698i	$0.732593\pi$
$308$	5.95407			0.339264
$309$		−	11.5827i		−	0.658919i
$310$	−3.52543			−0.200231
$311$			2.71408i			0.153901i	0.997035	+	0.0769507i	$0.0245184\pi$
$311$			2.71408i			0.153901i	−0.997035	+	0.0769507i	$0.975482\pi$
$312$		−	6.29529i		−	0.356400i
$313$		−	31.6019i		−	1.78625i	−0.449811	−	0.893124i	$-0.648509\pi$
$313$		−	31.6019i		−	1.78625i	0.449811	−	0.893124i	$-0.351491\pi$
$314$	−11.0114			−0.621408
$315$	3.21432			0.181106
$316$		−	26.1748i		−	1.47245i
$317$			8.91750i			0.500857i	0.968135	+	0.250428i	$0.0805715\pi$
$317$			8.91750i			0.500857i	−0.968135	+	0.250428i	$0.919429\pi$
$318$			4.47457i			0.250922i
$319$	−11.3319			−0.634462
$320$			4.00000i			0.223607i
$321$	17.3368			0.967644
$322$	2.49532			0.139059
$323$	0.495316	+	9.51606i	0.0275601	+	0.529488i
$324$	−1.52543			−0.0847460
$325$	13.8207			0.766635
$326$			12.3368i			0.683271i
$327$	−15.9748			−0.883409
$328$			5.61285i			0.309918i
$329$			11.2652i			0.621069i
$330$			8.64296i			0.475779i
$331$	11.9634			0.657570			0.328785	−	0.944405i	$-0.393361\pi$
$331$	11.9634			0.657570			0.328785	+	0.944405i	$0.393361\pi$
$332$	−21.7146			−1.19174
$333$			1.73975i			0.0953376i
$334$		−	2.61132i		−	0.142885i
$335$		−	48.2306i		−	2.63512i
$336$	1.37778			0.0751643
$337$			10.7620i			0.586245i	0.956075	+	0.293122i	$0.0946943\pi$
$337$			10.7620i			0.586245i	−0.956075	+	0.293122i	$0.905306\pi$
$338$	−4.32693			−0.235354
$339$	3.01429			0.163714
$340$	20.1891	−	1.05086i	1.09491	−	0.0569906i
$341$	−6.21432			−0.336524
$342$	−1.59210			−0.0860911
$343$		−	1.00000i		−	0.0539949i
$344$	10.1619			0.547895
$345$		−	11.6430i		−	0.626836i
$346$			5.65233i			0.303871i
$347$		−	14.4844i		−	0.777564i	−0.921330	−	0.388782i	$-0.872896\pi$
$347$		−	14.4844i		−	0.777564i	0.921330	−	0.388782i	$-0.127104\pi$
$348$	−4.42864			−0.237400
$349$	31.7402			1.69902			0.849508	−	0.527576i	$-0.176899\pi$
$349$	31.7402			1.69902			0.849508	+	0.527576i	$0.176899\pi$
$350$		−	3.67307i		−	0.196334i
$351$		−	2.59210i		−	0.138356i
$352$			22.6637i			1.20798i
$353$	3.32540			0.176993			0.0884965	−	0.996076i	$-0.471794\pi$
$353$	3.32540			0.176993			0.0884965	+	0.996076i	$0.471794\pi$
$354$		−	4.80150i		−	0.255197i
$355$	16.1891			0.859230
$356$	−2.55215			−0.135264
$357$	0.214320	+	4.11753i	0.0113430	+	0.217923i
$358$	−11.4380			−0.604517
$359$	17.5462			0.926051			0.463026	−	0.886345i	$-0.346764\pi$
$359$	17.5462			0.926051			0.463026	+	0.886345i	$0.346764\pi$
$360$			7.80642i			0.411435i
$361$	−13.6588			−0.718883
$362$			4.38715i			0.230584i
$363$			4.23506i			0.222283i
$364$			3.95407i			0.207249i
$365$	36.2766			1.89880
$366$	0.0557773			0.00291553
$367$		−	29.5941i		−	1.54480i	−0.635136	−	0.772400i	$-0.719056\pi$
$367$		−	29.5941i		−	1.54480i	0.635136	−	0.772400i	$-0.280944\pi$
$368$		−	4.99063i		−	0.260155i
$369$			2.31111i			0.120311i
$370$	3.85236			0.200274
$371$		−	6.49532i		−	0.337220i
$372$	−2.42864			−0.125919
$373$	−7.85236			−0.406580			−0.203290	−	0.979119i	$-0.565163\pi$
$373$	−7.85236			−0.406580			−0.203290	+	0.979119i	$0.565163\pi$
$374$	−11.0716	+	0.576283i	−0.572499	+	0.0297989i
$375$	−1.06668			−0.0550829
$376$	−27.3590			−1.41094
$377$		−	7.52543i		−	0.387579i
$378$	−0.688892			−0.0354328
$379$			5.22570i			0.268426i	0.990953	+	0.134213i	$0.0428506\pi$
$379$			5.22570i			0.268426i	−0.990953	+	0.134213i	$0.957149\pi$
$380$		−	11.3319i		−	0.581312i
$381$		−	14.3319i		−	0.734243i
$382$	5.24443			0.268328
$383$	22.3575			1.14242			0.571208	−	0.820805i	$-0.306475\pi$
$383$	22.3575			1.14242			0.571208	+	0.820805i	$0.306475\pi$
$384$			10.7556i			0.548868i
$385$		−	12.5462i		−	0.639412i
$386$		−	2.21771i		−	0.112878i
$387$	4.18421			0.212695
$388$		−	8.49871i		−	0.431456i
$389$	38.4385			1.94891			0.974454	−	0.224586i	$-0.0721030\pi$
$389$	38.4385			1.94891			0.974454	+	0.224586i	$0.0721030\pi$
$390$	−5.73975			−0.290643
$391$	14.9146	−	0.776312i	0.754263	−	0.0392598i
$392$	2.42864			0.122665
$393$	1.44938			0.0731117
$394$		−	4.22861i		−	0.213034i
$395$	−55.1546			−2.77513
$396$			5.95407i			0.299203i
$397$		−	24.2973i		−	1.21945i	−0.792614	−	0.609723i	$-0.791281\pi$
$397$		−	24.2973i		−	1.21945i	0.792614	−	0.609723i	$-0.208719\pi$
$398$		−	2.51606i		−	0.126119i
$399$	2.31111			0.115700
$400$	−7.34614			−0.367307
$401$		−	14.0651i		−	0.702380i	−0.936304	−	0.351190i	$-0.885777\pi$
$401$		−	14.0651i		−	0.702380i	0.936304	−	0.351190i	$-0.114223\pi$
$402$			10.3368i			0.515551i
$403$		−	4.12690i		−	0.205576i
$404$	−22.2449			−1.10673
$405$			3.21432i			0.159721i
$406$	−2.00000			−0.0992583
$407$	6.79060			0.336598
$408$	−10.0000	+	0.520505i	−0.495074	+	0.0257689i
$409$	−18.7353			−0.926401			−0.463201	−	0.886254i	$-0.653299\pi$
$409$	−18.7353			−0.926401			−0.463201	+	0.886254i	$0.653299\pi$
$410$	5.11753			0.252737
$411$			6.36196i			0.313812i
$412$	−17.6686			−0.870471
$413$			6.96989i			0.342966i
$414$			2.49532i			0.122638i
$415$			45.7560i			2.24608i
$416$	−15.0509			−0.737929
$417$	7.93978			0.388813
$418$			6.21432i			0.303952i
$419$			34.2908i			1.67522i	0.546271	+	0.837609i	$0.316047\pi$
$419$			34.2908i			1.67522i	−0.546271	+	0.837609i	$0.683953\pi$
$420$		−	4.90321i		−	0.239252i
$421$	−6.07805			−0.296226			−0.148113	−	0.988970i	$-0.547320\pi$
$421$	−6.07805			−0.296226			−0.148113	+	0.988970i	$0.547320\pi$
$422$		−	9.26178i		−	0.450857i
$423$	−11.2652			−0.547732
$424$	15.7748			0.766091
$425$	−1.14272	−	21.9541i	−0.0554301	−	1.06493i
$426$	−3.46965			−0.168105
$427$	−0.0809666			−0.00391825
$428$		−	26.4460i		−	1.27832i
$429$	−10.1175			−0.488479
$430$		−	9.26517i		−	0.446806i
$431$			1.04101i			0.0501437i	0.999686	+	0.0250719i	$0.00798146\pi$
$431$			1.04101i			0.0501437i	−0.999686	+	0.0250719i	$0.992019\pi$
$432$			1.37778i			0.0662887i
$433$	0.771390			0.0370706			0.0185353	−	0.999828i	$-0.494100\pi$
$433$	0.771390			0.0370706			0.0185353	+	0.999828i	$0.494100\pi$
$434$	−1.09679			−0.0526475
$435$			9.33185i			0.447428i
$436$			24.3684i			1.16704i
$437$		−	8.37133i		−	0.400455i
$438$	−7.77478			−0.371493
$439$		−	16.9097i		−	0.807054i	−0.914968	−	0.403527i	$-0.867784\pi$
$439$		−	16.9097i		−	0.807054i	0.914968	−	0.403527i	$-0.132216\pi$
$440$	30.4701			1.45261
$441$	1.00000			0.0476190
$442$	−0.382707	−	7.35260i	−0.0182035	−	0.349727i
$443$	−8.40345			−0.399260			−0.199630	−	0.979871i	$-0.563974\pi$
$443$	−8.40345			−0.399260			−0.199630	+	0.979871i	$0.563974\pi$
$444$	2.65386			0.125947
$445$			5.37778i			0.254931i
$446$	6.93825			0.328535
$447$		−	15.7748i		−	0.746122i
$448$			1.24443i			0.0587939i
$449$			8.44293i			0.398446i	0.979954	+	0.199223i	$0.0638419\pi$
$449$			8.44293i			0.398446i	−0.979954	+	0.199223i	$0.936158\pi$
$450$	3.67307			0.173150
$451$	9.02074			0.424770
$452$		−	4.59808i		−	0.216276i
$453$		−	20.9032i		−	0.982119i
$454$			15.3067i			0.718377i
$455$	8.33185			0.390603
$456$			5.61285i			0.262846i
$457$	−35.4558			−1.65855			−0.829277	−	0.558838i	$-0.811247\pi$
$457$	−35.4558			−1.65855			−0.829277	+	0.558838i	$0.811247\pi$
$458$	15.3778			0.718557
$459$	−4.11753	+	0.214320i	−0.192190	+	0.0100036i
$460$	−17.7605			−0.828087
$461$	−14.3763			−0.669569			−0.334784	−	0.942295i	$-0.608663\pi$
$461$	−14.3763			−0.669569			−0.334784	+	0.942295i	$0.608663\pi$
$462$			2.68889i			0.125099i
$463$	35.0464			1.62874			0.814372	−	0.580343i	$-0.197081\pi$
$463$	35.0464			1.62874			0.814372	+	0.580343i	$0.197081\pi$
$464$			4.00000i			0.185695i
$465$			5.11753i			0.237320i
$466$		−	18.9525i		−	0.877959i
$467$	28.4701			1.31744			0.658720	−	0.752388i	$-0.271098\pi$
$467$	28.4701			1.31744			0.658720	+	0.752388i	$0.271098\pi$
$468$	−3.95407			−0.182777
$469$		−	15.0049i		−	0.692863i
$470$			24.9447i			1.15061i
$471$			15.9842i			0.736512i
$472$	−16.9273			−0.779144
$473$		−	16.3319i		−	0.750939i
$474$	11.8207			0.542943
$475$	−12.3225			−0.565394
$476$	6.28100	−	0.326929i	0.287889	−	0.0149848i
$477$	6.49532			0.297400
$478$	−5.66862			−0.259277
$479$			3.12690i			0.142872i	0.997445	+	0.0714358i	$0.0227581\pi$
$479$			3.12690i			0.142872i	−0.997445	+	0.0714358i	$0.977242\pi$
$480$	18.6637			0.851878
$481$			4.50961i			0.205620i
$482$			11.2257i			0.511316i
$483$		−	3.62222i		−	0.164817i
$484$	6.46028			0.293649
$485$	−17.9081			−0.813166
$486$		−	0.688892i		−	0.0312488i
$487$			10.2667i			0.465229i	0.972569	+	0.232614i	$0.0747280\pi$
$487$			10.2667i			0.465229i	−0.972569	+	0.232614i	$0.925272\pi$
$488$		−	0.196639i		−	0.00890142i
$489$	17.9081			0.809834
$490$		−	2.21432i		−	0.100033i
$491$	−0.663703			−0.0299525			−0.0149762	−	0.999888i	$-0.504767\pi$
$491$	−0.663703			−0.0299525			−0.0149762	+	0.999888i	$0.504767\pi$
$492$	3.52543			0.158939
$493$	−11.9541	+	0.622216i	−0.538384	+	0.0280232i
$494$	−4.12690			−0.185678
$495$	12.5462			0.563908
$496$			2.19358i			0.0984945i
$497$	5.03657			0.225921
$498$		−	9.80642i		−	0.439436i
$499$		−	3.99355i		−	0.178776i	−0.995997	−	0.0893878i	$-0.971509\pi$
$499$		−	3.99355i		−	0.178776i	0.995997	−	0.0893878i	$-0.0284911\pi$
$500$			1.62714i			0.0727678i
$501$	−3.79060			−0.169352
$502$	−19.8306			−0.885081
$503$			14.8588i			0.662522i	0.943539	+	0.331261i	$0.107474\pi$
$503$			14.8588i			0.662522i	−0.943539	+	0.331261i	$0.892526\pi$
$504$			2.42864i			0.108180i
$505$			46.8736i			2.08585i
$506$	9.73975			0.432985
$507$			6.28100i			0.278949i
$508$	−21.8622			−0.969978
$509$	−12.5018			−0.554131			−0.277066	−	0.960851i	$-0.589362\pi$
$509$	−12.5018			−0.554131			−0.277066	+	0.960851i	$0.589362\pi$
$510$	0.474572	+	9.11753i	0.0210144	+	0.403731i
$511$	11.2859			0.499260
$512$	14.6923			0.649313
$513$			2.31111i			0.102038i
$514$	10.4746			0.462014
$515$			37.2306i			1.64058i
$516$		−	6.38271i		−	0.280983i
$517$			43.9704i			1.93381i
$518$	1.19850			0.0526590
$519$	8.20495			0.360157
$520$			20.2351i			0.887366i
$521$			29.5970i			1.29667i	0.761356	+	0.648335i	$0.224534\pi$
$521$			29.5970i			1.29667i	−0.761356	+	0.648335i	$0.775466\pi$
$522$		−	2.00000i		−	0.0875376i
$523$	27.8163			1.21632			0.608160	−	0.793814i	$-0.291908\pi$
$523$	27.8163			1.21632			0.608160	+	0.793814i	$0.291908\pi$
$524$		−	2.21093i		−	0.0965849i
$525$	−5.33185			−0.232701
$526$	−11.7047			−0.510350
$527$	−6.55554	+	0.341219i	−0.285564	+	0.0148637i
$528$	5.37778			0.234038
$529$	9.87955			0.429546
$530$		−	14.3827i		−	0.624745i
$531$	−6.96989			−0.302467
$532$		−	3.52543i		−	0.152847i
$533$			5.99063i			0.259483i
$534$		−	1.15257i		−	0.0498764i
$535$	−55.7259			−2.40924
$536$	36.4415			1.57404
$537$			16.6035i			0.716493i
$538$			6.54125i			0.282013i
$539$		−	3.90321i		−	0.168123i
$540$	4.90321			0.211001
$541$		−	3.18421i		−	0.136900i	−0.997655	−	0.0684499i	$-0.978195\pi$
$541$		−	3.18421i		−	0.136900i	0.997655	−	0.0684499i	$-0.0218053\pi$
$542$	−7.46181			−0.320512
$543$	6.36842			0.273295
$544$	1.24443	+	23.9081i	0.0533546	+	1.02505i
$545$	51.3481			2.19951
$546$	−1.78568			−0.0764201
$547$			11.8415i			0.506304i	0.967426	+	0.253152i	$0.0814673\pi$
$547$			11.8415i			0.506304i	−0.967426	+	0.253152i	$0.918533\pi$
$548$	9.70471			0.414565
$549$		−	0.0809666i		−	0.00345557i
$550$		−	14.3368i		−	0.611322i
$551$			6.70964i			0.285840i
$552$	8.79706			0.374428
$553$	−17.1590			−0.729676
$554$		−	20.2252i		−	0.859287i
$555$		−	5.59210i		−	0.237372i
$556$		−	12.1116i		−	0.513644i
$557$	10.4035			0.440808			0.220404	−	0.975409i	$-0.429262\pi$
$557$	10.4035			0.440808			0.220404	+	0.975409i	$0.429262\pi$
$558$		−	1.09679i		−	0.0464307i
$559$	10.8459			0.458733
$560$	−4.42864			−0.187144
$561$	0.836535	+	16.0716i	0.0353186	+	0.678543i
$562$	−5.34920			−0.225643
$563$	23.3176			0.982718			0.491359	−	0.870957i	$-0.336500\pi$
$563$	23.3176			0.982718			0.491359	+	0.870957i	$0.336500\pi$
$564$			17.1842i			0.723586i
$565$	−9.68889			−0.407615
$566$		−	22.2908i		−	0.936954i
$567$			1.00000i			0.0419961i
$568$			12.2320i			0.513243i
$569$	−18.7239			−0.784948			−0.392474	−	0.919763i	$-0.628381\pi$
$569$	−18.7239			−0.784948			−0.392474	+	0.919763i	$0.628381\pi$
$570$	5.11753			0.214350
$571$			33.7431i			1.41211i	0.708159	+	0.706053i	$0.249526\pi$
$571$			33.7431i			1.41211i	−0.708159	+	0.706053i	$0.750474\pi$
$572$			15.4336i			0.645310i
$573$		−	7.61285i		−	0.318031i
$574$	1.59210			0.0664531
$575$			19.3131i			0.805413i
$576$	−1.24443			−0.0518513
$577$	−34.9101			−1.45333			−0.726664	−	0.686993i	$-0.758930\pi$
$577$	−34.9101			−1.45333			−0.726664	+	0.686993i	$0.758930\pi$
$578$	−11.6479	+	1.21585i	−0.484488	+	0.0505727i
$579$	−3.21924			−0.133787
$580$	14.2351			0.591079
$581$			14.2351i			0.590570i
$582$	3.83807			0.159093
$583$		−	25.3526i		−	1.05000i
$584$			27.4094i			1.13421i
$585$			8.33185i			0.344480i
$586$	−19.0638			−0.787517
$587$	27.1635			1.12116			0.560578	−	0.828102i	$-0.310579\pi$
$587$	27.1635			1.12116			0.560578	+	0.828102i	$0.310579\pi$
$588$		−	1.52543i		−	0.0629076i
$589$			3.67952i			0.151612i
$590$			15.4336i			0.635390i
$591$	−6.13828			−0.252495
$592$		−	2.39700i		−	0.0985160i
$593$	−23.6019			−0.969216			−0.484608	−	0.874731i	$-0.661038\pi$
$593$	−23.6019			−0.969216			−0.484608	+	0.874731i	$0.661038\pi$
$594$	−2.68889			−0.110327
$595$	−0.688892	−	13.2351i	−0.0282418	−	0.542585i
$596$	−24.0633			−0.985671
$597$	−3.65233			−0.149480
$598$			6.46812i			0.264501i
$599$	−31.2257			−1.27585			−0.637924	−	0.770100i	$-0.720206\pi$
$599$	−31.2257			−1.27585			−0.637924	+	0.770100i	$0.720206\pi$
$600$		−	12.9491i		−	0.528647i
$601$		−	20.1541i		−	0.822103i	−0.911612	−	0.411051i	$-0.865162\pi$
$601$		−	20.1541i		−	0.822103i	0.911612	−	0.411051i	$-0.134838\pi$
$602$		−	2.88247i		−	0.117481i
$603$	15.0049			0.611048
$604$	−31.8863			−1.29744
$605$		−	13.6128i		−	0.553441i
$606$		−	10.0459i		−	0.408088i
$607$		−	34.1354i		−	1.38551i	−0.721172	−	0.692756i	$-0.756396\pi$
$607$		−	34.1354i		−	1.38551i	0.721172	−	0.692756i	$-0.243604\pi$
$608$	13.4193			0.544223
$609$			2.90321i			0.117644i
$610$	−0.179286			−0.00725908
$611$	−29.2005			−1.18133
$612$	0.326929	+	6.28100i	0.0132153	+	0.253894i
$613$	−16.0923			−0.649964			−0.324982	−	0.945720i	$-0.605358\pi$
$613$	−16.0923			−0.649964			−0.324982	+	0.945720i	$0.605358\pi$
$614$	−16.1116			−0.650209
$615$		−	7.42864i		−	0.299552i
$616$	9.47949			0.381940
$617$		−	23.8020i		−	0.958232i	−0.877752	−	0.479116i	$-0.840957\pi$
$617$		−	23.8020i		−	0.958232i	0.877752	−	0.479116i	$-0.159043\pi$
$618$		−	7.97926i		−	0.320973i
$619$			6.58274i			0.264583i	0.991211	+	0.132291i	$0.0422334\pi$
$619$			6.58274i			0.264583i	−0.991211	+	0.132291i	$0.957767\pi$
$620$	7.80642			0.313514
$621$	3.62222			0.145355
$622$			1.86971i			0.0749685i
$623$			1.67307i			0.0670302i
$624$			3.57136i			0.142969i
$625$	−23.2306			−0.929225
$626$		−	21.7703i		−	0.870118i
$627$	9.02074			0.360254
$628$	24.3827			0.972976
$629$	7.16346	−	0.372862i	0.285626	−	0.0148670i
$630$	2.21432			0.0882206
$631$	3.20648			0.127648			0.0638240	−	0.997961i	$-0.479670\pi$
$631$	3.20648			0.127648			0.0638240	+	0.997961i	$0.479670\pi$
$632$		−	41.6731i		−	1.65767i
$633$	−13.4445			−0.534369
$634$			6.14320i			0.243978i
$635$			46.0672i			1.82812i
$636$		−	9.90813i		−	0.392883i
$637$	2.59210			0.102703
$638$	−7.80642			−0.309059
$639$			5.03657i			0.199243i
$640$		−	34.5718i		−	1.36657i
$641$			28.7275i			1.13467i	0.823488	+	0.567333i	$0.192025\pi$
$641$			28.7275i			1.13467i	−0.823488	+	0.567333i	$0.807975\pi$
$642$	11.9432			0.471359
$643$		−	39.2543i		−	1.54804i	−0.633163	−	0.774019i	$-0.718244\pi$
$643$		−	39.2543i		−	1.54804i	0.633163	−	0.774019i	$-0.281756\pi$
$644$	−5.52543			−0.217732
$645$	−13.4494			−0.529569
$646$	0.341219	+	6.55554i	0.0134251	+	0.257924i
$647$	6.25380			0.245862			0.122931	−	0.992415i	$-0.460771\pi$
$647$	6.25380			0.245862			0.122931	+	0.992415i	$0.460771\pi$
$648$	−2.42864			−0.0954060
$649$			27.2050i			1.06789i
$650$	9.52098			0.373444
$651$			1.59210i			0.0623995i
$652$		−	27.3176i		−	1.06984i
$653$			47.5303i			1.86001i	0.367552	+	0.930003i	$0.380196\pi$
$653$			47.5303i			1.86001i	−0.367552	+	0.930003i	$0.619804\pi$
$654$	−11.0049			−0.430327
$655$	−4.65878			−0.182034
$656$		−	3.18421i		−	0.124322i
$657$			11.2859i			0.440306i
$658$			7.76049i			0.302535i
$659$	25.8227			1.00591			0.502955	−	0.864312i	$-0.332246\pi$
$659$	25.8227			1.00591			0.502955	+	0.864312i	$0.332246\pi$
$660$		−	19.1383i		−	0.744956i
$661$	−28.0672			−1.09169			−0.545843	−	0.837888i	$-0.683790\pi$
$661$	−28.0672			−1.09169			−0.545843	+	0.837888i	$0.683790\pi$
$662$	8.24152			0.320316
$663$	−10.6731	+	0.555539i	−0.414508	+	0.0215754i
$664$	−34.5718			−1.34165
$665$	−7.42864			−0.288070
$666$			1.19850i			0.0464409i
$667$	10.5161			0.407183
$668$			5.78229i			0.223723i
$669$		−	10.0716i		−	0.389391i
$670$		−	33.2257i		−	1.28362i
$671$	−0.316030			−0.0122002
$672$	5.80642			0.223988
$673$		−	23.3907i		−	0.901645i	−0.892614	−	0.450822i	$-0.851131\pi$
$673$		−	23.3907i		−	0.901645i	0.892614	−	0.450822i	$-0.148869\pi$
$674$			7.41387i			0.285572i
$675$		−	5.33185i		−	0.205223i
$676$	9.58120			0.368508
$677$		−	3.46674i		−	0.133237i	−0.997779	−	0.0666187i	$-0.978779\pi$
$677$		−	3.46674i		−	0.133237i	0.997779	−	0.0666187i	$-0.0212211\pi$
$678$	2.07652			0.0797483
$679$	−5.57136			−0.213809
$680$	32.1432	−	1.67307i	1.23264	−	0.0641593i
$681$	22.2192			0.851443
$682$	−4.28100			−0.163928
$683$		−	42.7101i		−	1.63426i	−0.576456	−	0.817129i	$-0.695565\pi$
$683$		−	42.7101i		−	1.63426i	0.576456	−	0.817129i	$-0.304435\pi$
$684$	3.52543			0.134798
$685$		−	20.4494i		−	0.781331i
$686$		−	0.688892i		−	0.0263020i
$687$		−	22.3225i		−	0.851656i
$688$	−5.76494			−0.219786
$689$	16.8365			0.641421
$690$		−	8.02074i		−	0.305344i
$691$			30.1037i			1.14520i	0.819835	+	0.572600i	$0.194065\pi$
$691$			30.1037i			1.14520i	−0.819835	+	0.572600i	$0.805935\pi$
$692$		−	12.5161i		−	0.475789i
$693$	3.90321			0.148271
$694$		−	9.97820i		−	0.378767i
$695$	−25.5210			−0.968066
$696$	−7.05086			−0.267262
$697$	9.51606	−	0.495316i	0.360446	−	0.0187614i
$698$	21.8656			0.827625
$699$	−27.5116			−1.04058
$700$			8.13335i			0.307412i
$701$	−6.32693			−0.238965			−0.119482	−	0.992836i	$-0.538124\pi$
$701$	−6.32693			−0.238965			−0.119482	+	0.992836i	$0.538124\pi$
$702$		−	1.78568i		−	0.0673962i
$703$		−	4.02074i		−	0.151645i
$704$			4.85728i			0.183066i
$705$	36.2099			1.36374
$706$	2.29084			0.0862169
$707$			14.5827i			0.548440i
$708$			10.6321i			0.399577i
$709$			2.48886i			0.0934712i	0.998907	+	0.0467356i	$0.0148818\pi$
$709$			2.48886i			0.0934712i	−0.998907	+	0.0467356i	$0.985118\pi$
$710$	11.1526			0.418548
$711$		−	17.1590i		−	0.643513i
$712$	−4.06329			−0.152278
$713$	5.76694			0.215974
$714$	0.147643	+	2.83654i	0.00552541	+	0.106155i
$715$	32.5210			1.21622
$716$	25.3274			0.946530
$717$			8.22861i			0.307303i
$718$	12.0874			0.451099
$719$			25.6113i			0.955141i	0.878593	+	0.477570i	$0.158482\pi$
$719$			25.6113i			0.955141i	−0.878593	+	0.477570i	$0.841518\pi$
$720$		−	4.42864i		−	0.165046i
$721$			11.5827i			0.431364i
$722$	−9.40943			−0.350183
$723$	16.2953			0.606028
$724$		−	9.71456i		−	0.361039i
$725$		−	15.4795i		−	0.574894i
$726$			2.91750i			0.108279i
$727$	−0.612371			−0.0227116			−0.0113558	−	0.999936i	$-0.503615\pi$
$727$	−0.612371			−0.0227116			−0.0113558	+	0.999936i	$0.503615\pi$
$728$			6.29529i			0.233319i
$729$	−1.00000			−0.0370370
$730$	24.9906			0.924945
$731$	−0.896758	−	17.2286i	−0.0331678	−	0.637223i
$732$	−0.123509			−0.00456502
$733$	33.9496			1.25396			0.626979	−	0.779036i	$-0.284291\pi$
$733$	33.9496			1.25396			0.626979	+	0.779036i	$0.284291\pi$
$734$		−	20.3872i		−	0.752504i
$735$	−3.21432			−0.118562
$736$		−	21.0321i		−	0.775254i
$737$		−	58.5674i		−	2.15736i
$738$			1.59210i			0.0586062i
$739$	14.3907			0.529370			0.264685	−	0.964335i	$-0.414732\pi$
$739$	14.3907			0.529370			0.264685	+	0.964335i	$0.414732\pi$
$740$	−8.53035			−0.313582
$741$			5.99063i			0.220071i
$742$		−	4.47457i		−	0.164267i
$743$		−	45.4938i		−	1.66901i	−0.551004	−	0.834503i	$-0.685755\pi$
$743$		−	45.4938i		−	1.66901i	0.551004	−	0.834503i	$-0.314245\pi$
$744$	−3.86665			−0.141758
$745$			50.7052i			1.85769i
$746$	−5.40943			−0.198053
$747$	−14.2351			−0.520834
$748$	24.5161	−	1.27607i	0.896396	−	0.0466579i
$749$	−17.3368			−0.633472
$750$	−0.734825			−0.0268320
$751$		−	39.9017i		−	1.45603i	−0.685560	−	0.728017i	$-0.740442\pi$
$751$		−	39.9017i		−	1.45603i	0.685560	−	0.728017i	$-0.259558\pi$
$752$	15.5210			0.565992
$753$			28.7862i			1.04903i
$754$		−	5.18421i		−	0.188798i
$755$			67.1896i			2.44528i
$756$	1.52543			0.0554793
$757$	−23.1388			−0.840992			−0.420496	−	0.907294i	$-0.638144\pi$
$757$	−23.1388			−0.840992			−0.420496	+	0.907294i	$0.638144\pi$
$758$			3.59994i			0.130756i
$759$		−	14.1383i		−	0.513187i
$760$		−	18.0415i		−	0.654434i
$761$	−31.2958			−1.13447			−0.567235	−	0.823556i	$-0.691987\pi$
$761$	−31.2958			−1.13447			−0.567235	+	0.823556i	$0.691987\pi$
$762$		−	9.87310i		−	0.357665i
$763$	15.9748			0.578327
$764$	−11.6128			−0.420138
$765$	13.2351	−	0.688892i	0.478515	−	0.0249069i
$766$	15.4019			0.556494
$767$	−18.0667			−0.652350
$768$			9.89829i			0.357174i
$769$	19.3446			0.697584			0.348792	−	0.937200i	$-0.386592\pi$
$769$	19.3446			0.697584			0.348792	+	0.937200i	$0.386592\pi$
$770$		−	8.64296i		−	0.311471i
$771$		−	15.2050i		−	0.547593i
$772$			4.91072i			0.176741i
$773$	−5.56046			−0.199996			−0.0999979	−	0.994988i	$-0.531884\pi$
$773$	−5.56046			−0.199996			−0.0999979	+	0.994988i	$0.531884\pi$
$774$	2.88247			0.103608
$775$		−	8.48886i		−	0.304929i
$776$		−	13.5308i		−	0.485728i
$777$		−	1.73975i		−	0.0624131i
$778$	26.4800			0.949353
$779$		−	5.34122i		−	0.191369i
$780$	12.7096			0.455078
$781$	19.6588			0.703446
$782$	10.2745	−	0.534795i	0.367417	−	0.0191242i
$783$	−2.90321			−0.103752
$784$	−1.37778			−0.0492066
$785$		−	51.3783i		−	1.83377i
$786$	0.998469			0.0356142
$787$			22.4177i			0.799106i	0.916710	+	0.399553i	$0.130835\pi$
$787$			22.4177i			0.799106i	−0.916710	+	0.399553i	$0.869165\pi$
$788$			9.36349i			0.333561i
$789$			16.9906i			0.604883i
$790$	−37.9956			−1.35182
$791$	−3.01429			−0.107176
$792$			9.47949i			0.336839i
$793$		−	0.209874i		−	0.00745284i
$794$		−	16.7382i		−	0.594017i
$795$	−20.8780			−0.740467
$796$			5.57136i			0.197472i
$797$	11.5812			0.410227			0.205114	−	0.978738i	$-0.434244\pi$
$797$	11.5812			0.410227			0.205114	+	0.978738i	$0.434244\pi$
$798$	1.59210			0.0563599
$799$	2.41435	+	46.3847i	0.0854135	+	1.64097i
$800$	−30.9590			−1.09457
$801$	−1.67307			−0.0591150
$802$		−	9.68937i		−	0.342143i
$803$	44.0513			1.55454
$804$		−	22.8889i		−	0.807230i
$805$			11.6430i			0.410360i
$806$		−	2.84299i		−	0.100140i
$807$	9.49532			0.334251
$808$	−35.4162			−1.24594
$809$		−	40.6084i		−	1.42772i	−0.700291	−	0.713858i	$-0.746946\pi$
$809$		−	40.6084i		−	1.42772i	0.700291	−	0.713858i	$-0.253054\pi$
$810$			2.21432i			0.0778033i
$811$			43.7431i			1.53603i	0.640432	+	0.768015i	$0.278755\pi$
$811$			43.7431i			1.53603i	−0.640432	+	0.768015i	$0.721245\pi$
$812$	4.42864			0.155415
$813$			10.8316i			0.379881i
$814$	4.67799			0.163964
$815$	−57.5625			−2.01633
$816$	5.67307	−	0.295286i	0.198597	−	0.0103371i
$817$	−9.67016			−0.338316
$818$	−12.9066			−0.451269
$819$			2.59210i			0.0905754i
$820$	−11.3319			−0.395725
$821$			21.8889i			0.763929i	0.924177	+	0.381964i	$0.124752\pi$
$821$			21.8889i			0.763929i	−0.924177	+	0.381964i	$0.875248\pi$
$822$			4.38271i			0.152864i
$823$		−	54.4449i		−	1.89783i	−0.315530	−	0.948916i	$-0.602182\pi$
$823$		−	54.4449i		−	1.89783i	0.315530	−	0.948916i	$-0.397818\pi$
$824$	−28.1303			−0.979965
$825$	−20.8113			−0.724558
$826$			4.80150i			0.167066i
$827$		−	13.6593i		−	0.474979i	−0.971390	−	0.237489i	$-0.923675\pi$
$827$		−	13.6593i		−	0.474979i	0.971390	−	0.237489i	$-0.0763245\pi$
$828$		−	5.52543i		−	0.192022i
$829$	43.2070			1.50064			0.750320	−	0.661075i	$-0.229899\pi$
$829$	43.2070			1.50064			0.750320	+	0.661075i	$0.229899\pi$
$830$			31.5210i			1.09411i
$831$	−29.3590			−1.01845
$832$	−3.22570			−0.111831
$833$	−0.214320	−	4.11753i	−0.00742574	−	0.142664i
$834$	5.46965			0.189398
$835$	12.1842			0.421652
$836$		−	13.7605i		−	0.475917i
$837$	−1.59210			−0.0550312
$838$			23.6227i			0.816032i
$839$		−	13.8352i		−	0.477643i	−0.971064	−	0.238821i	$-0.923239\pi$
$839$		−	13.8352i		−	0.477643i	0.971064	−	0.238821i	$-0.0767610\pi$
$840$		−	7.80642i		−	0.269347i
$841$	20.5714			0.709357
$842$	−4.18712			−0.144298
$843$			7.76494i			0.267439i
$844$			20.5086i			0.705933i
$845$		−	20.1891i		−	0.694527i
$846$	−7.76049			−0.266811
$847$		−	4.23506i		−	0.145518i
$848$	−8.94914			−0.307315
$849$	−32.3575			−1.11051
$850$	−0.787212	−	15.1240i	−0.0270011	−	0.518748i
$851$	−6.30174			−0.216021
$852$	7.68292			0.263212
$853$			30.7991i			1.05454i	0.849698	+	0.527270i	$0.176784\pi$
$853$			30.7991i			1.05454i	−0.849698	+	0.527270i	$0.823216\pi$
$854$	−0.0557773			−0.00190866
$855$		−	7.42864i		−	0.254054i
$856$		−	42.1048i		−	1.43911i
$857$		−	41.7877i		−	1.42744i	−0.700431	−	0.713720i	$-0.747009\pi$
$857$		−	41.7877i		−	1.42744i	0.700431	−	0.713720i	$-0.252991\pi$
$858$	−6.96989			−0.237948
$859$	32.7368			1.11697			0.558483	−	0.829516i	$-0.311384\pi$
$859$	32.7368			1.11697			0.558483	+	0.829516i	$0.311384\pi$
$860$			20.5161i			0.699592i
$861$		−	2.31111i		−	0.0787623i
$862$			0.717144i			0.0244260i
$863$	−20.7205			−0.705335			−0.352668	−	0.935749i	$-0.614725\pi$
$863$	−20.7205			−0.705335			−0.352668	+	0.935749i	$0.614725\pi$
$864$			5.80642i			0.197539i
$865$	−26.3733			−0.896720
$866$	0.531405			0.0180579
$867$	1.76494	+	16.9081i	0.0599404	+	0.574230i
$868$	2.42864			0.0824334
$869$	−66.9753			−2.27198
$870$			6.42864i			0.217951i
$871$	38.8943			1.31788
$872$			38.7971i			1.31383i
$873$		−	5.57136i		−	0.188562i
$874$		−	5.76694i		−	0.195070i
$875$	1.06668			0.0360602
$876$	17.2159			0.581670
$877$			14.1082i			0.476399i	0.971216	+	0.238199i	$0.0765572\pi$
$877$			14.1082i			0.476399i	−0.971216	+	0.238199i	$0.923443\pi$
$878$		−	11.6489i		−	0.393133i
$879$			27.6731i			0.933390i
$880$	−17.2859			−0.582708
$881$		−	0.805947i		−	0.0271531i	−0.999908	−	0.0135765i	$-0.995678\pi$
$881$		−	0.805947i		−	0.0271531i	0.999908	−	0.0135765i	$-0.00432168\pi$
$882$	0.688892			0.0231962
$883$	6.17976			0.207966			0.103983	−	0.994579i	$-0.466841\pi$
$883$	6.17976			0.207966			0.103983	+	0.994579i	$0.466841\pi$
$884$	0.847435	+	16.2810i	0.0285023	+	0.547589i
$885$	22.4035			0.753084
$886$	−5.78907			−0.194488
$887$			1.35212i			0.0453997i	0.999742	+	0.0226998i	$0.00722621\pi$
$887$			1.35212i			0.0453997i	−0.999742	+	0.0226998i	$0.992774\pi$
$888$	4.22522			0.141789
$889$			14.3319i			0.480675i
$890$			3.70471i			0.124182i
$891$			3.90321i			0.130763i
$892$	−15.3635			−0.514408
$893$	26.0350			0.871229
$894$		−	10.8671i		−	0.363451i
$895$		−	53.3689i		−	1.78393i
$896$		−	10.7556i		−	0.359318i
$897$	9.38916			0.313495
$898$			5.81627i			0.194091i
$899$	−4.62222			−0.154160
$900$	−8.13335			−0.271112
$901$	−1.39207	−	26.7447i	−0.0463767	−	0.890994i
$902$	6.21432			0.206914
$903$	−4.18421			−0.139242
$904$		−	7.32062i		−	0.243480i
$905$	−20.4701			−0.680450
$906$		−	14.4001i		−	0.478410i
$907$			9.74620i			0.323617i	0.986822	+	0.161809i	$0.0517327\pi$
$907$			9.74620i			0.323617i	−0.986822	+	0.161809i	$0.948267\pi$
$908$		−	33.8938i		−	1.12481i
$909$	−14.5827			−0.483679
$910$	5.73975			0.190271
$911$			12.1570i			0.402780i	0.979511	+	0.201390i	$0.0645458\pi$
$911$			12.1570i			0.402780i	−0.979511	+	0.201390i	$0.935454\pi$
$912$		−	3.18421i		−	0.105440i
$913$			55.5625i			1.83885i
$914$	−24.4252			−0.807915
$915$			0.260253i			0.00860369i
$916$	−34.0513			−1.12509
$917$	−1.44938			−0.0478628
$918$	−2.83654	+	0.147643i	−0.0936196	+	0.00487295i
$919$	49.8800			1.64539			0.822695	−	0.568483i	$-0.192469\pi$
$919$	49.8800			1.64539			0.822695	+	0.568483i	$0.192469\pi$
$920$	−28.2766			−0.932250
$921$			23.3876i			0.770649i
$922$	−9.90369			−0.326161
$923$			13.0553i			0.429720i
$924$		−	5.95407i		−	0.195874i
$925$			9.27607i			0.304995i
$926$	24.1432			0.793395
$927$	−11.5827			−0.380427
$928$			16.8573i			0.553367i
$929$			6.61930i			0.217172i	0.994087	+	0.108586i	$0.0346323\pi$
$929$			6.61930i			0.217172i	−0.994087	+	0.108586i	$0.965368\pi$
$930$			3.52543i			0.115603i
$931$	−2.31111			−0.0757435
$932$			41.9670i			1.37467i
$933$	2.71408			0.0888550
$934$	19.6128			0.641752
$935$	−2.68889	−	51.6593i	−0.0879362	−	1.68944i
$936$	−6.29529			−0.205768
$937$	9.28147			0.303212			0.151606	−	0.988441i	$-0.451555\pi$
$937$	9.28147			0.303212			0.151606	+	0.988441i	$0.451555\pi$
$938$		−	10.3368i		−	0.337508i
$939$	−31.6019			−1.03129
$940$		−	55.2355i		−	1.80158i
$941$			24.7338i			0.806298i	0.915134	+	0.403149i	$0.132084\pi$
$941$			24.7338i			0.806298i	−0.915134	+	0.403149i	$0.867916\pi$
$942$			11.0114i			0.358770i
$943$	−8.37133			−0.272608
$944$	9.60300			0.312551
$945$		−	3.21432i		−	0.104562i
$946$		−	11.2509i		−	0.365798i
$947$			27.0879i			0.880238i	0.897939	+	0.440119i	$0.145064\pi$
$947$			27.0879i			0.880238i	−0.897939	+	0.440119i	$0.854936\pi$
$948$	−26.1748			−0.850119
$949$			29.2543i			0.949634i
$950$	−8.48886			−0.275415
$951$	8.91750			0.289170
$952$	10.0000	−	0.520505i	0.324102	−	0.0168697i
$953$	54.1367			1.75366			0.876831	−	0.480799i	$-0.159654\pi$
$953$	54.1367			1.75366			0.876831	+	0.480799i	$0.159654\pi$
$954$	4.47457			0.144870
$955$			24.4701i			0.791835i
$956$	12.5521			0.405965
$957$			11.3319i			0.366307i
$958$			2.15410i			0.0695957i
$959$		−	6.36196i		−	0.205438i
$960$	4.00000			0.129099
$961$	28.4652			0.918232
$962$			3.10663i			0.100162i
$963$		−	17.3368i		−	0.558670i
$964$		−	24.8573i		−	0.800599i
$965$	10.3477			0.333103
$966$		−	2.49532i		−	0.0802855i
$967$	26.4750			0.851380			0.425690	−	0.904869i	$-0.360031\pi$
$967$	26.4750			0.851380			0.425690	+	0.904869i	$0.360031\pi$
$968$	10.2854			0.330587
$969$	9.51606	−	0.495316i	0.305700	−	0.0159118i
$970$	−12.3368			−0.396110
$971$	−15.4479			−0.495745			−0.247873	−	0.968793i	$-0.579731\pi$
$971$	−15.4479			−0.495745			−0.247873	+	0.968793i	$0.579731\pi$
$972$			1.52543i			0.0489281i
$973$	−7.93978			−0.254538
$974$			7.07265i			0.226622i
$975$		−	13.8207i		−	0.442617i
$976$			0.111555i			0.00357078i
$977$	58.6321			1.87581			0.937903	−	0.346898i	$-0.112765\pi$
$977$	58.6321			1.87581			0.937903	+	0.346898i	$0.112765\pi$
$978$	12.3368			0.394487
$979$			6.53035i			0.208711i
$980$			4.90321i			0.156627i
$981$			15.9748i			0.510036i
$982$	−0.457220			−0.0145905
$983$		−	1.92396i		−	0.0613647i	−0.999529	−	0.0306823i	$-0.990232\pi$
$983$		−	1.92396i		−	0.0613647i	0.999529	−	0.0306823i	$-0.00976802\pi$
$984$	5.61285			0.178931
$985$	19.7304			0.628662
$986$	−8.23506	+	0.428639i	−0.262258	+	0.0136507i
$987$	11.2652			0.358574
$988$	9.13828			0.290727
$989$			15.1561i			0.481936i
$990$	8.64296			0.274691
$991$		−	19.6030i		−	0.622710i	−0.950294	−	0.311355i	$-0.899217\pi$
$991$		−	19.6030i		−	0.622710i	0.950294	−	0.311355i	$-0.100783\pi$
$992$			9.24443i			0.293511i
$993$		−	11.9634i		−	0.379648i
$994$	3.46965			0.110051
$995$	11.7397			0.372175
$996$			21.7146i			0.688052i
$997$		−	16.6726i		−	0.528026i	−0.964519	−	0.264013i	$-0.914954\pi$
$997$		−	16.6726i		−	0.528026i	0.964519	−	0.264013i	$-0.0850462\pi$
$998$		−	2.75112i		−	0.0870853i
$999$	1.73975			0.0550432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.f.a.169.3	✓	6
3.2	odd	2		1071.2.f.a.883.3		6
17.4	even	4		6069.2.a.k.1.2		3
17.13	even	4		6069.2.a.m.1.2		3
17.16	even	2	inner	357.2.f.a.169.4	yes	6
51.50	odd	2		1071.2.f.a.883.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.f.a.169.3	✓	6	1.1	even	1	trivial
357.2.f.a.169.4	yes	6	17.16	even	2	inner
1071.2.f.a.883.3		6	3.2	odd	2
1071.2.f.a.883.4		6	51.50	odd	2
6069.2.a.k.1.2		3	17.4	even	4
6069.2.a.m.1.2		3	17.13	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.688892 q^{2} -1.00000i q^{3} -1.52543 q^{4} +3.21432i q^{5} -0.688892i q^{6} +1.00000i q^{7} -2.42864 q^{8} -1.00000 q^{9} +2.21432i q^{10} +3.90321i q^{11} +1.52543i q^{12} -2.59210 q^{13} +0.688892i q^{14} +3.21432 q^{15} +1.37778 q^{16} +(0.214320 + 4.11753i) q^{17} -0.688892 q^{18} +2.31111 q^{19} -4.90321i q^{20} +1.00000 q^{21} +2.68889i q^{22} -3.62222i q^{23} +2.42864i q^{24} -5.33185 q^{25} -1.78568 q^{26} +1.00000i q^{27} -1.52543i q^{28} +2.90321i q^{29} +2.21432 q^{30} +1.59210i q^{31} +5.80642 q^{32} +3.90321 q^{33} +(0.147643 + 2.83654i) q^{34} -3.21432 q^{35} +1.52543 q^{36} -1.73975i q^{37} +1.59210 q^{38} +2.59210i q^{39} -7.80642i q^{40} -2.31111i q^{41} +0.688892 q^{42} -4.18421 q^{43} -5.95407i q^{44} -3.21432i q^{45} -2.49532i q^{46} +11.2652 q^{47} -1.37778i q^{48} -1.00000 q^{49} -3.67307 q^{50} +(4.11753 - 0.214320i) q^{51} +3.95407 q^{52} -6.49532 q^{53} +0.688892i q^{54} -12.5462 q^{55} -2.42864i q^{56} -2.31111i q^{57} +2.00000i q^{58} +6.96989 q^{59} -4.90321 q^{60} +0.0809666i q^{61} +1.09679i q^{62} -1.00000i q^{63} +1.24443 q^{64} -8.33185i q^{65} +2.68889 q^{66} -15.0049 q^{67} +(-0.326929 - 6.28100i) q^{68} -3.62222 q^{69} -2.21432 q^{70} -5.03657i q^{71} +2.42864 q^{72} -11.2859i q^{73} -1.19850i q^{74} +5.33185i q^{75} -3.52543 q^{76} -3.90321 q^{77} +1.78568i q^{78} +17.1590i q^{79} +4.42864i q^{80} +1.00000 q^{81} -1.59210i q^{82} +14.2351 q^{83} -1.52543 q^{84} +(-13.2351 + 0.688892i) q^{85} -2.88247 q^{86} +2.90321 q^{87} -9.47949i q^{88} +1.67307 q^{89} -2.21432i q^{90} -2.59210i q^{91} +5.52543i q^{92} +1.59210 q^{93} +7.76049 q^{94} +7.42864i q^{95} -5.80642i q^{96} +5.57136i q^{97} -0.688892 q^{98} -3.90321i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 4 q^{4} + 12 q^{8} - 6 q^{9} - 2 q^{13} + 6 q^{15} + 8 q^{16} - 12 q^{17} - 4 q^{18} + 14 q^{19} + 6 q^{21} + 8 q^{25} - 24 q^{26} + 8 q^{32} + 10 q^{33} - 12 q^{34} - 6 q^{35} - 4 q^{36}+ \cdots - 4 q^{98}+O(q^{100}) \) 6 * q + 4 * q^2 + 4 * q^4 + 12 * q^8 - 6 * q^9 - 2 * q^13 + 6 * q^15 + 8 * q^16 - 12 * q^17 - 4 * q^18 + 14 * q^19 + 6 * q^21 + 8 * q^25 - 24 * q^26 + 8 * q^32 + 10 * q^33 - 12 * q^34 - 6 * q^35 - 4 * q^36 - 4 * q^38 + 4 * q^42 + 2 * q^43 + 28 * q^47 - 6 * q^49 + 4 * q^50 - 2 * q^51 - 16 * q^52 - 12 * q^53 - 22 * q^55 + 28 * q^59 - 16 * q^60 + 8 * q^64 + 16 * q^66 - 24 * q^67 - 28 * q^68 - 22 * q^69 - 12 * q^72 - 8 * q^76 - 10 * q^77 + 6 * q^81 + 32 * q^83 + 4 * q^84 - 26 * q^85 - 44 * q^86 + 4 * q^87 - 16 * q^89 - 4 * q^93 - 20 * q^94 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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