LMFDB - Embedded newform 1190.2.e.g.239.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1190,2,Mod(239,1190)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1190, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1190.239"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1190 = 2 \cdot 5 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1190.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,-14,-2,-4,0,0,-14,4,-14,0,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$9.50219784053$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 28x^{12} + 292x^{10} + 1457x^{8} + 3664x^{6} + 4360x^{4} + 1856x^{2} + 16 $ x^14 + 28x^12 + 292x^10 + 1457x^8 + 3664x^6 + 4360x^4 + 1856x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.7
Root			$2.54179i$ of defining polynomial
Character	$\chi$	$=$	1190.239
Dual form			1190.2.e.g.239.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +2.54179i q^{3} -1.00000 q^{4} +(-2.22979 + 0.167414i) q^{5} +2.54179 q^{6} +1.00000i q^{7} +1.00000i q^{8} -3.46070 q^{9} +(0.167414 + 2.22979i) q^{10} -5.72650 q^{11} -2.54179i q^{12} -3.48296i q^{13} +1.00000 q^{14} +(-0.425531 - 5.66767i) q^{15} +1.00000 q^{16} +1.00000i q^{17} +3.46070i q^{18} +4.55477 q^{19} +(2.22979 - 0.167414i) q^{20} -2.54179 q^{21} +5.72650i q^{22} -8.26551i q^{23} -2.54179 q^{24} +(4.94395 - 0.746596i) q^{25} -3.48296 q^{26} -1.17101i q^{27} -1.00000i q^{28} +0.990385 q^{29} +(-5.66767 + 0.425531i) q^{30} -3.99132 q^{31} -1.00000i q^{32} -14.5556i q^{33} +1.00000 q^{34} +(-0.167414 - 2.22979i) q^{35} +3.46070 q^{36} -1.96580i q^{37} -4.55477i q^{38} +8.85296 q^{39} +(-0.167414 - 2.22979i) q^{40} +7.88545 q^{41} +2.54179i q^{42} +12.2804i q^{43} +5.72650 q^{44} +(7.71665 - 0.579370i) q^{45} -8.26551 q^{46} -8.49457i q^{47} +2.54179i q^{48} -1.00000 q^{49} +(-0.746596 - 4.94395i) q^{50} -2.54179 q^{51} +3.48296i q^{52} -10.3317i q^{53} -1.17101 q^{54} +(12.7689 - 0.958695i) q^{55} -1.00000 q^{56} +11.5773i q^{57} -0.990385i q^{58} +10.1278 q^{59} +(0.425531 + 5.66767i) q^{60} -0.952226 q^{61} +3.99132i q^{62} -3.46070i q^{63} -1.00000 q^{64} +(0.583096 + 7.76628i) q^{65} -14.5556 q^{66} +3.87612i q^{67} -1.00000i q^{68} +21.0092 q^{69} +(-2.22979 + 0.167414i) q^{70} -6.23006 q^{71} -3.46070i q^{72} -7.07022i q^{73} -1.96580 q^{74} +(1.89769 + 12.5665i) q^{75} -4.55477 q^{76} -5.72650i q^{77} -8.85296i q^{78} -13.5580 q^{79} +(-2.22979 + 0.167414i) q^{80} -7.40565 q^{81} -7.88545i q^{82} -15.3925i q^{83} +2.54179 q^{84} +(-0.167414 - 2.22979i) q^{85} +12.2804 q^{86} +2.51735i q^{87} -5.72650i q^{88} -14.4517 q^{89} +(-0.579370 - 7.71665i) q^{90} +3.48296 q^{91} +8.26551i q^{92} -10.1451i q^{93} -8.49457 q^{94} +(-10.1562 + 0.762532i) q^{95} +2.54179 q^{96} -17.5462i q^{97} +1.00000i q^{98} +19.8177 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{4} - 2 q^{5} - 4 q^{6} - 14 q^{9} + 4 q^{10} - 14 q^{11} + 14 q^{14} + 2 q^{15} + 14 q^{16} + 4 q^{19} + 2 q^{20} + 4 q^{21} + 4 q^{24} + 14 q^{25} + 2 q^{26} + 20 q^{29} - 2 q^{30} - 36 q^{31}+ \cdots + 88 q^{99}+O(q^{100}) $ 14 * q - 14 * q^4 - 2 * q^5 - 4 * q^6 - 14 * q^9 + 4 * q^10 - 14 * q^11 + 14 * q^14 + 2 * q^15 + 14 * q^16 + 4 * q^19 + 2 * q^20 + 4 * q^21 + 4 * q^24 + 14 * q^25 + 2 * q^26 + 20 * q^29 - 2 * q^30 - 36 * q^31 + 14 * q^34 - 4 * q^35 + 14 * q^36 + 50 * q^39 - 4 * q^40 + 34 * q^41 + 14 * q^44 + 8 * q^45 - 54 * q^46 - 14 * q^49 + 8 * q^50 + 4 * q^51 + 34 * q^54 - 16 * q^55 - 14 * q^56 - 2 * q^60 + 2 * q^61 - 14 * q^64 - 32 * q^65 - 16 * q^66 - 6 * q^69 - 2 * q^70 - 22 * q^71 + 24 * q^74 - 40 * q^75 - 4 * q^76 + 52 * q^79 - 2 * q^80 + 22 * q^81 - 4 * q^84 - 4 * q^85 - 14 * q^86 - 42 * q^89 - 38 * q^90 - 2 * q^91 + 16 * q^94 - 46 * q^95 - 4 * q^96 + 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1190\mathbb{Z}\right)^\times$.

$n$	$71$	$171$	$477$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			2.54179i			1.46750i	0.679417	+	0.733752i	$0.262233\pi$
$3$			2.54179i			1.46750i	−0.679417	+	0.733752i	$0.737767\pi$
$4$	−1.00000			−0.500000
$5$	−2.22979	+	0.167414i	−0.997193	+	0.0748698i
$5$	−2.22979	+	0.167414i	−0.997193	+	0.0748698i
$6$	2.54179			1.03768
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.00000i			0.353553i
$9$	−3.46070			−1.15357
$10$	0.167414	+	2.22979i	0.0529409	+	0.705122i
$11$	−5.72650			−1.72660			−0.863302	−	0.504688i	$-0.831607\pi$
$11$	−5.72650			−1.72660			−0.863302	+	0.504688i	$0.831607\pi$
$12$		−	2.54179i		−	0.733752i
$13$		−	3.48296i		−	0.966000i	−0.875620	−	0.483000i	$-0.839547\pi$
$13$		−	3.48296i		−	0.966000i	0.875620	−	0.483000i	$-0.160453\pi$
$14$	1.00000			0.267261
$15$	−0.425531	−	5.66767i	−0.109872	−	1.46339i
$16$	1.00000			0.250000
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$			3.46070i			0.815695i
$19$	4.55477			1.04494			0.522468	−	0.852659i	$-0.325011\pi$
$19$	4.55477			1.04494			0.522468	+	0.852659i	$0.325011\pi$
$20$	2.22979	−	0.167414i	0.498597	−	0.0374349i
$21$	−2.54179			−0.554664
$22$			5.72650i			1.22089i
$23$		−	8.26551i		−	1.72348i	−0.507352	−	0.861739i	$-0.669375\pi$
$23$		−	8.26551i		−	1.72348i	0.507352	−	0.861739i	$-0.330625\pi$
$24$	−2.54179			−0.518841
$25$	4.94395	−	0.746596i	0.988789	−	0.149319i
$26$	−3.48296			−0.683065
$27$		−	1.17101i		−	0.225361i
$28$		−	1.00000i		−	0.188982i
$29$	0.990385			0.183910			0.0919550	−	0.995763i	$-0.470688\pi$
$29$	0.990385			0.183910			0.0919550	+	0.995763i	$0.470688\pi$
$30$	−5.66767	+	0.425531i	−1.03477	+	0.0776910i
$31$	−3.99132			−0.716862			−0.358431	−	0.933556i	$-0.616688\pi$
$31$	−3.99132			−0.716862			−0.358431	+	0.933556i	$0.616688\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	14.5556i		−	2.53380i
$34$	1.00000			0.171499
$35$	−0.167414	−	2.22979i	−0.0282981	−	0.376904i
$36$	3.46070			0.576784
$37$		−	1.96580i		−	0.323176i	−0.986858	−	0.161588i	$-0.948338\pi$
$37$		−	1.96580i		−	0.323176i	0.986858	−	0.161588i	$-0.0516615\pi$
$38$		−	4.55477i		−	0.738881i
$39$	8.85296			1.41761
$40$	−0.167414	−	2.22979i	−0.0264705	−	0.352561i
$41$	7.88545			1.23150			0.615750	−	0.787941i	$-0.288853\pi$
$41$	7.88545			1.23150			0.615750	+	0.787941i	$0.288853\pi$
$42$			2.54179i			0.392207i
$43$			12.2804i			1.87274i	0.351011	+	0.936371i	$0.385838\pi$
$43$			12.2804i			1.87274i	−0.351011	+	0.936371i	$0.614162\pi$
$44$	5.72650			0.863302
$45$	7.71665	−	0.579370i	1.15033	−	0.0863673i
$46$	−8.26551			−1.21868
$47$		−	8.49457i		−	1.23906i	−0.784973	−	0.619530i	$-0.787323\pi$
$47$		−	8.49457i		−	1.23906i	0.784973	−	0.619530i	$-0.212677\pi$
$48$			2.54179i			0.366876i
$49$	−1.00000			−0.142857
$50$	−0.746596	−	4.94395i	−0.105585	−	0.699179i
$51$	−2.54179			−0.355922
$52$			3.48296i			0.483000i
$53$		−	10.3317i		−	1.41917i	−0.704619	−	0.709585i	$-0.748882\pi$
$53$		−	10.3317i		−	1.41917i	0.704619	−	0.709585i	$-0.251118\pi$
$54$	−1.17101			−0.159354
$55$	12.7689	−	0.958695i	1.72176	−	0.129270i
$56$	−1.00000			−0.133631
$57$			11.5773i			1.53345i
$58$		−	0.990385i		−	0.130044i
$59$	10.1278			1.31852			0.659262	−	0.751913i	$-0.270869\pi$
$59$	10.1278			1.31852			0.659262	+	0.751913i	$0.270869\pi$
$60$	0.425531	+	5.66767i	0.0549358	+	0.731693i
$61$	−0.952226			−0.121920			−0.0609600	−	0.998140i	$-0.519416\pi$
$61$	−0.952226			−0.121920			−0.0609600	+	0.998140i	$0.519416\pi$
$62$			3.99132i			0.506898i
$63$		−	3.46070i		−	0.436008i
$64$	−1.00000			−0.125000
$65$	0.583096	+	7.76628i	0.0723242	+	0.963288i
$66$	−14.5556			−1.79167
$67$			3.87612i			0.473543i	0.971565	+	0.236772i	$0.0760893\pi$
$67$			3.87612i			0.473543i	−0.971565	+	0.236772i	$0.923911\pi$
$68$		−	1.00000i		−	0.121268i
$69$	21.0092			2.52921
$70$	−2.22979	+	0.167414i	−0.266511	+	0.0200098i
$71$	−6.23006			−0.739372			−0.369686	−	0.929157i	$-0.620535\pi$
$71$	−6.23006			−0.739372			−0.369686	+	0.929157i	$0.620535\pi$
$72$		−	3.46070i		−	0.407848i
$73$		−	7.07022i		−	0.827507i	−0.910389	−	0.413753i	$-0.864218\pi$
$73$		−	7.07022i		−	0.827507i	0.910389	−	0.413753i	$-0.135782\pi$
$74$	−1.96580			−0.228520
$75$	1.89769	+	12.5665i	0.219127	+	1.45105i
$76$	−4.55477			−0.522468
$77$		−	5.72650i		−	0.652595i
$78$		−	8.85296i		−	1.00240i
$79$	−13.5580			−1.52539			−0.762695	−	0.646759i	$-0.776124\pi$
$79$	−13.5580			−1.52539			−0.762695	+	0.646759i	$0.776124\pi$
$80$	−2.22979	+	0.167414i	−0.249298	+	0.0187174i
$81$	−7.40565			−0.822850
$82$		−	7.88545i		−	0.870802i
$83$		−	15.3925i		−	1.68955i	−0.535121	−	0.844775i	$-0.679734\pi$
$83$		−	15.3925i		−	1.68955i	0.535121	−	0.844775i	$-0.320266\pi$
$84$	2.54179			0.277332
$85$	−0.167414	−	2.22979i	−0.0181586	−	0.241855i
$86$	12.2804			1.32423
$87$			2.51735i			0.269889i
$88$		−	5.72650i		−	0.610446i
$89$	−14.4517			−1.53188			−0.765938	−	0.642915i	$-0.777725\pi$
$89$	−14.4517			−1.53188			−0.765938	+	0.642915i	$0.777725\pi$
$90$	−0.579370	−	7.71665i	−0.0610709	−	0.813406i
$91$	3.48296			0.365114
$92$			8.26551i			0.861739i
$93$		−	10.1451i		−	1.05200i
$94$	−8.49457			−0.876148
$95$	−10.1562	+	0.762532i	−1.04200	+	0.0782341i
$96$	2.54179			0.259420
$97$		−	17.5462i		−	1.78154i	−0.454452	−	0.890771i	$-0.650165\pi$
$97$		−	17.5462i		−	1.78154i	0.454452	−	0.890771i	$-0.349835\pi$
$98$			1.00000i			0.101015i
$99$	19.8177			1.99175
$100$	−4.94395	+	0.746596i	−0.494395	+	0.0746596i
$101$	−3.17217			−0.315643			−0.157821	−	0.987468i	$-0.550447\pi$
$101$	−3.17217			−0.315643			−0.157821	+	0.987468i	$0.550447\pi$
$102$			2.54179i			0.251675i
$103$		−	1.94049i		−	0.191202i	−0.995420	−	0.0956009i	$-0.969523\pi$
$103$		−	1.94049i		−	0.191202i	0.995420	−	0.0956009i	$-0.0304772\pi$
$104$	3.48296			0.341532
$105$	5.66767	−	0.425531i	0.553108	−	0.0415276i
$106$	−10.3317			−1.00351
$107$			2.05039i			0.198218i	0.995077	+	0.0991091i	$0.0315993\pi$
$107$			2.05039i			0.198218i	−0.995077	+	0.0991091i	$0.968401\pi$
$108$			1.17101i			0.112680i
$109$	19.3457			1.85298			0.926490	−	0.376320i	$-0.122811\pi$
$109$	19.3457			1.85298			0.926490	+	0.376320i	$0.122811\pi$
$110$	−0.958695	−	12.7689i	−0.0914080	−	1.21747i
$111$	4.99666			0.474262
$112$			1.00000i			0.0944911i
$113$		−	6.29785i		−	0.592452i	−0.955118	−	0.296226i	$-0.904272\pi$
$113$		−	6.29785i		−	0.592452i	0.955118	−	0.296226i	$-0.0957282\pi$
$114$	11.5773			1.08431
$115$	1.38376	+	18.4304i	0.129036	+	1.71864i
$116$	−0.990385			−0.0919550
$117$			12.0535i			1.11435i
$118$		−	10.1278i		−	0.932338i
$119$	−1.00000			−0.0916698
$120$	5.66767	−	0.425531i	0.517385	−	0.0388455i
$121$	21.7928			1.98116
$122$			0.952226i			0.0862105i
$123$			20.0432i			1.80723i
$124$	3.99132			0.358431
$125$	−10.8990	+	2.49244i	−0.974834	+	0.222931i
$126$	−3.46070			−0.308304
$127$			3.92166i			0.347991i	0.984746	+	0.173996i	$0.0556678\pi$
$127$			3.92166i			0.347991i	−0.984746	+	0.173996i	$0.944332\pi$
$128$			1.00000i			0.0883883i
$129$	−31.2142			−2.74826
$130$	7.76628	−	0.583096i	0.681148	−	0.0511409i
$131$	−9.94843			−0.869198			−0.434599	−	0.900624i	$-0.643110\pi$
$131$	−9.94843			−0.869198			−0.434599	+	0.900624i	$0.643110\pi$
$132$			14.5556i			1.26690i
$133$			4.55477i			0.394949i
$134$	3.87612			0.334846
$135$	0.196043	+	2.61111i	0.0168727	+	0.224728i
$136$	−1.00000			−0.0857493
$137$		−	21.0684i		−	1.80000i	−0.435895	−	0.899998i	$-0.643568\pi$
$137$		−	21.0684i		−	1.80000i	0.435895	−	0.899998i	$-0.356432\pi$
$138$		−	21.0092i		−	1.78842i
$139$	−1.43988			−0.122129			−0.0610643	−	0.998134i	$-0.519449\pi$
$139$	−1.43988			−0.122129			−0.0610643	+	0.998134i	$0.519449\pi$
$140$	0.167414	+	2.22979i	0.0141491	+	0.188452i
$141$	21.5914			1.81833
$142$			6.23006i			0.522815i
$143$			19.9452i			1.66790i
$144$	−3.46070			−0.288392
$145$	−2.20835	+	0.165804i	−0.183394	+	0.0137693i
$146$	−7.07022			−0.585136
$147$		−	2.54179i		−	0.209643i
$148$			1.96580i			0.161588i
$149$	−22.3068			−1.82744			−0.913722	−	0.406339i	$-0.866805\pi$
$149$	−22.3068			−1.82744			−0.913722	+	0.406339i	$0.866805\pi$
$150$	12.5665	−	1.89769i	1.02605	−	0.154946i
$151$	−8.43690			−0.686585			−0.343293	−	0.939228i	$-0.611542\pi$
$151$	−8.43690			−0.686585			−0.343293	+	0.939228i	$0.611542\pi$
$152$			4.55477i			0.369441i
$153$		−	3.46070i		−	0.279781i
$154$	−5.72650			−0.461454
$155$	8.89981	−	0.668202i	0.714850	−	0.0536713i
$156$	−8.85296			−0.708804
$157$		−	19.5520i		−	1.56042i	−0.625516	−	0.780212i	$-0.715111\pi$
$157$		−	19.5520i		−	1.56042i	0.625516	−	0.780212i	$-0.284889\pi$
$158$			13.5580i			1.07861i
$159$	26.2611			2.08264
$160$	0.167414	+	2.22979i	0.0132352	+	0.176281i
$161$	8.26551			0.651414
$162$			7.40565i			0.581843i
$163$			15.2346i			1.19326i	0.802515	+	0.596632i	$0.203495\pi$
$163$			15.2346i			1.19326i	−0.802515	+	0.596632i	$0.796505\pi$
$164$	−7.88545			−0.615750
$165$	2.43680	+	32.4559i	0.189705	+	2.52669i
$166$	−15.3925			−1.19469
$167$			1.44115i			0.111520i	0.998444	+	0.0557598i	$0.0177581\pi$
$167$			1.44115i			0.111520i	−0.998444	+	0.0557598i	$0.982242\pi$
$168$		−	2.54179i		−	0.196103i
$169$	0.868981			0.0668447
$170$	−2.22979	+	0.167414i	−0.171017	+	0.0128401i
$171$	−15.7627			−1.20540
$172$		−	12.2804i		−	0.936371i
$173$		−	0.0905351i		−	0.00688326i	−0.999994	−	0.00344163i	$-0.998904\pi$
$173$		−	0.0905351i		−	0.00688326i	0.999994	−	0.00344163i	$-0.00109551\pi$
$174$	2.51735			0.190840
$175$	0.746596	+	4.94395i	0.0564374	+	0.373727i
$176$	−5.72650			−0.431651
$177$			25.7427i			1.93494i
$178$			14.4517i			1.08320i
$179$	6.72039			0.502306			0.251153	−	0.967947i	$-0.419190\pi$
$179$	6.72039			0.502306			0.251153	+	0.967947i	$0.419190\pi$
$180$	−7.71665	+	0.579370i	−0.575165	+	0.0431837i
$181$	−20.3547			−1.51295			−0.756476	−	0.654021i	$-0.773081\pi$
$181$	−20.3547			−1.51295			−0.756476	+	0.654021i	$0.773081\pi$
$182$		−	3.48296i		−	0.258174i
$183$		−	2.42036i		−	0.178918i
$184$	8.26551			0.609342
$185$	0.329102	+	4.38333i	0.0241961	+	0.322269i
$186$	−10.1451			−0.743874
$187$		−	5.72650i		−	0.418763i
$188$			8.49457i			0.619530i
$189$	1.17101			0.0851784
$190$	0.762532	+	10.1562i	0.0553199	+	0.736808i
$191$	−5.38668			−0.389766			−0.194883	−	0.980826i	$-0.562433\pi$
$191$	−5.38668			−0.389766			−0.194883	+	0.980826i	$0.562433\pi$
$192$		−	2.54179i		−	0.183438i
$193$			0.617801i			0.0444703i	0.999753	+	0.0222351i	$0.00707825\pi$
$193$			0.617801i			0.0444703i	−0.999753	+	0.0222351i	$0.992922\pi$
$194$	−17.5462			−1.25974
$195$	−19.7403	+	1.48211i	−1.41363	+	0.106136i
$196$	1.00000			0.0714286
$197$			8.90420i			0.634398i	0.948359	+	0.317199i	$0.102742\pi$
$197$			8.90420i			0.634398i	−0.948359	+	0.317199i	$0.897258\pi$
$198$		−	19.8177i		−	1.40838i
$199$	−2.74906			−0.194876			−0.0974380	−	0.995242i	$-0.531065\pi$
$199$	−2.74906			−0.194876			−0.0974380	+	0.995242i	$0.531065\pi$
$200$	0.746596	+	4.94395i	0.0527923	+	0.349590i
$201$	−9.85228			−0.694926
$202$			3.17217i			0.223193i
$203$			0.990385i			0.0695114i
$204$	2.54179			0.177961
$205$	−17.5829	+	1.32013i	−1.22804	+	0.0922022i
$206$	−1.94049			−0.135200
$207$			28.6045i			1.98815i
$208$		−	3.48296i		−	0.241500i
$209$	−26.0829			−1.80419
$210$	−0.425531	−	5.66767i	−0.0293644	−	0.391106i
$211$	−9.35373			−0.643937			−0.321969	−	0.946750i	$-0.604345\pi$
$211$	−9.35373			−0.643937			−0.321969	+	0.946750i	$0.604345\pi$
$212$			10.3317i			0.709585i
$213$		−	15.8355i		−	1.08503i
$214$	2.05039			0.140161
$215$	−2.05591	−	27.3827i	−0.140212	−	1.86749i
$216$	1.17101			0.0796771
$217$		−	3.99132i		−	0.270948i
$218$		−	19.3457i		−	1.31025i
$219$	17.9710			1.21437
$220$	−12.7689	+	0.958695i	−0.860879	+	0.0646352i
$221$	3.48296			0.234289
$222$		−	4.99666i		−	0.335354i
$223$		−	0.946770i		−	0.0634004i	−0.999497	−	0.0317002i	$-0.989908\pi$
$223$		−	0.946770i		−	0.0634004i	0.999497	−	0.0317002i	$-0.0100922\pi$
$224$	1.00000			0.0668153
$225$	−17.1095	+	2.58375i	−1.14063	+	0.172250i
$226$	−6.29785			−0.418927
$227$			12.3408i			0.819085i	0.912291	+	0.409543i	$0.134312\pi$
$227$			12.3408i			0.819085i	−0.912291	+	0.409543i	$0.865688\pi$
$228$		−	11.5773i		−	0.766724i
$229$	13.3470			0.881993			0.440996	−	0.897509i	$-0.354625\pi$
$229$	13.3470			0.881993			0.440996	+	0.897509i	$0.354625\pi$
$230$	18.4304	−	1.38376i	1.21526	−	0.0912425i
$231$	14.5556			0.957685
$232$			0.990385i			0.0650220i
$233$			23.2229i			1.52138i	0.649114	+	0.760691i	$0.275140\pi$
$233$			23.2229i			1.52138i	−0.649114	+	0.760691i	$0.724860\pi$
$234$	12.0535			0.787961
$235$	1.42211	+	18.9411i	0.0927682	+	1.23558i
$236$	−10.1278			−0.659262
$237$		−	34.4615i		−	2.23851i
$238$			1.00000i			0.0648204i
$239$	−10.8663			−0.702880			−0.351440	−	0.936210i	$-0.614308\pi$
$239$	−10.8663			−0.702880			−0.351440	+	0.936210i	$0.614308\pi$
$240$	−0.425531	−	5.66767i	−0.0274679	−	0.365846i
$241$	9.61298			0.619226			0.309613	−	0.950863i	$-0.399800\pi$
$241$	9.61298			0.619226			0.309613	+	0.950863i	$0.399800\pi$
$242$		−	21.7928i		−	1.40089i
$243$		−	22.3366i		−	1.43290i
$244$	0.952226			0.0609600
$245$	2.22979	−	0.167414i	0.142456	−	0.0106957i
$246$	20.0432			1.27791
$247$		−	15.8641i		−	1.00941i
$248$		−	3.99132i		−	0.253449i
$249$	39.1246			2.47942
$250$	2.49244	+	10.8990i	0.157636	+	0.689312i
$251$	13.6959			0.864477			0.432239	−	0.901759i	$-0.357724\pi$
$251$	13.6959			0.864477			0.432239	+	0.901759i	$0.357724\pi$
$252$			3.46070i			0.218004i
$253$			47.3324i			2.97576i
$254$	3.92166			0.246067
$255$	5.66767	−	0.425531i	0.354923	−	0.0266478i
$256$	1.00000			0.0625000
$257$			19.2766i			1.20244i	0.799082	+	0.601222i	$0.205319\pi$
$257$			19.2766i			1.20244i	−0.799082	+	0.601222i	$0.794681\pi$
$258$			31.2142i			1.94331i
$259$	1.96580			0.122149
$260$	−0.583096	−	7.76628i	−0.0361621	−	0.481644i
$261$	−3.42743			−0.212153
$262$			9.94843i			0.614616i
$263$		−	15.4341i		−	0.951706i	−0.879525	−	0.475853i	$-0.842139\pi$
$263$		−	15.4341i		−	0.951706i	0.879525	−	0.475853i	$-0.157861\pi$
$264$	14.5556			0.895833
$265$	1.72967	+	23.0376i	0.106253	+	1.41519i
$266$	4.55477			0.279271
$267$		−	36.7332i		−	2.24803i
$268$		−	3.87612i		−	0.236772i
$269$	−18.7045			−1.14044			−0.570218	−	0.821494i	$-0.693141\pi$
$269$	−18.7045			−1.14044			−0.570218	+	0.821494i	$0.693141\pi$
$270$	2.61111	−	0.196043i	0.158907	−	0.0119308i
$271$	27.6242			1.67805			0.839026	−	0.544092i	$-0.183126\pi$
$271$	27.6242			1.67805			0.839026	+	0.544092i	$0.183126\pi$
$272$			1.00000i			0.0606339i
$273$			8.85296i			0.535806i
$274$	−21.0684			−1.27279
$275$	−28.3115	+	4.27538i	−1.70725	+	0.257815i
$276$	−21.0092			−1.26461
$277$		−	2.15313i		−	0.129369i	−0.997906	−	0.0646846i	$-0.979396\pi$
$277$		−	2.15313i		−	0.129369i	0.997906	−	0.0646846i	$-0.0206041\pi$
$278$			1.43988i			0.0863580i
$279$	13.8128			0.826948
$280$	2.22979	−	0.167414i	0.133256	−	0.0100049i
$281$	3.87390			0.231098			0.115549	−	0.993302i	$-0.463137\pi$
$281$	3.87390			0.231098			0.115549	+	0.993302i	$0.463137\pi$
$282$		−	21.5914i		−	1.28575i
$283$		−	5.48685i		−	0.326160i	−0.986613	−	0.163080i	$-0.947857\pi$
$283$		−	5.48685i		−	0.326160i	0.986613	−	0.163080i	$-0.0521428\pi$
$284$	6.23006			0.369686
$285$	−1.93820	−	25.8149i	−0.114809	−	1.52914i
$286$	19.9452			1.17938
$287$			7.88545i			0.465463i
$288$			3.46070i			0.203924i
$289$	−1.00000			−0.0588235
$290$	0.165804	+	2.20835i	0.00973636	+	0.129679i
$291$	44.5987			2.61442
$292$			7.07022i			0.413753i
$293$		−	21.7657i		−	1.27156i	−0.771869	−	0.635782i	$-0.780678\pi$
$293$		−	21.7657i		−	1.27156i	0.771869	−	0.635782i	$-0.219322\pi$
$294$	−2.54179			−0.148240
$295$	−22.5828	+	1.69553i	−1.31482	+	0.0987176i
$296$	1.96580			0.114260
$297$			6.70578i			0.389109i
$298$			22.3068i			1.29220i
$299$	−28.7885			−1.66488
$300$	−1.89769	−	12.5665i	−0.109563	−	0.725526i
$301$	−12.2804			−0.707830
$302$			8.43690i			0.485489i
$303$		−	8.06299i		−	0.463207i
$304$	4.55477			0.261234
$305$	2.12327	−	0.159416i	0.121578	−	0.00912812i
$306$	−3.46070			−0.197835
$307$			13.1008i			0.747704i	0.927488	+	0.373852i	$0.121963\pi$
$307$			13.1008i			0.747704i	−0.927488	+	0.373852i	$0.878037\pi$
$308$			5.72650i			0.326297i
$309$	4.93231			0.280589
$310$	−0.668202	−	8.89981i	−0.0379513	−	0.505475i
$311$	−4.20193			−0.238270			−0.119135	−	0.992878i	$-0.538012\pi$
$311$	−4.20193			−0.238270			−0.119135	+	0.992878i	$0.538012\pi$
$312$			8.85296i			0.501200i
$313$		−	11.6520i		−	0.658612i	−0.944223	−	0.329306i	$-0.893185\pi$
$313$		−	11.6520i		−	0.658612i	0.944223	−	0.329306i	$-0.106815\pi$
$314$	−19.5520			−1.10339
$315$	0.579370	+	7.71665i	0.0326438	+	0.434784i
$316$	13.5580			0.762695
$317$			3.45462i			0.194031i	0.995283	+	0.0970155i	$0.0309296\pi$
$317$			3.45462i			0.194031i	−0.995283	+	0.0970155i	$0.969070\pi$
$318$		−	26.2611i		−	1.47265i
$319$	−5.67144			−0.317540
$320$	2.22979	−	0.167414i	0.124649	−	0.00935872i
$321$	−5.21165			−0.290886
$322$		−	8.26551i		−	0.460619i
$323$			4.55477i			0.253434i
$324$	7.40565			0.411425
$325$	−2.60037	−	17.2196i	−0.144242	−	0.955170i
$326$	15.2346			0.843766
$327$			49.1727i			2.71925i
$328$			7.88545i			0.435401i
$329$	8.49457			0.468321
$330$	32.4559	−	2.43680i	1.78664	−	0.134142i
$331$	12.4973			0.686911			0.343456	−	0.939169i	$-0.388403\pi$
$331$	12.4973			0.686911			0.343456	+	0.939169i	$0.388403\pi$
$332$			15.3925i			0.844775i
$333$			6.80305i			0.372805i
$334$	1.44115			0.0788562
$335$	−0.648916	−	8.64294i	−0.0354541	−	0.472214i
$336$	−2.54179			−0.138666
$337$			8.93416i			0.486675i	0.969942	+	0.243337i	$0.0782422\pi$
$337$			8.93416i			0.486675i	−0.969942	+	0.243337i	$0.921758\pi$
$338$		−	0.868981i		−	0.0472663i
$339$	16.0078			0.869426
$340$	0.167414	+	2.22979i	0.00907929	+	0.120927i
$341$	22.8563			1.23774
$342$			15.7627i			0.852350i
$343$		−	1.00000i		−	0.0539949i
$344$	−12.2804			−0.662115
$345$	−46.8462	+	3.51723i	−2.52211	+	0.189361i
$346$	−0.0905351			−0.00486720
$347$			19.0850i			1.02454i	0.858825	+	0.512269i	$0.171195\pi$
$347$			19.0850i			1.02454i	−0.858825	+	0.512269i	$0.828805\pi$
$348$		−	2.51735i		−	0.134944i
$349$	−15.3497			−0.821652			−0.410826	−	0.911714i	$-0.634760\pi$
$349$	−15.3497			−0.821652			−0.410826	+	0.911714i	$0.634760\pi$
$350$	4.94395	−	0.746596i	0.264265	−	0.0399073i
$351$	−4.07858			−0.217698
$352$			5.72650i			0.305223i
$353$		−	3.33185i		−	0.177337i	−0.996061	−	0.0886684i	$-0.971739\pi$
$353$		−	3.33185i		−	0.177337i	0.996061	−	0.0886684i	$-0.0282611\pi$
$354$	25.7427			1.36821
$355$	13.8917	−	1.04300i	0.737297	−	0.0553566i
$356$	14.4517			0.765938
$357$		−	2.54179i		−	0.134526i
$358$		−	6.72039i		−	0.355184i
$359$	10.1746			0.536995			0.268498	−	0.963280i	$-0.413473\pi$
$359$	10.1746			0.536995			0.268498	+	0.963280i	$0.413473\pi$
$360$	0.579370	+	7.71665i	0.0305355	+	0.406703i
$361$	1.74594			0.0918915
$362$			20.3547i			1.06982i
$363$			55.3926i			2.90736i
$364$	−3.48296			−0.182557
$365$	1.18365	+	15.7651i	0.0619553	+	0.825184i
$366$	−2.42036			−0.126514
$367$		−	11.2202i		−	0.585688i	−0.956160	−	0.292844i	$-0.905398\pi$
$367$		−	11.2202i		−	0.585688i	0.956160	−	0.292844i	$-0.0946017\pi$
$368$		−	8.26551i		−	0.430870i
$369$	−27.2892			−1.42062
$370$	4.38333	−	0.329102i	0.227878	−	0.0171092i
$371$	10.3317			0.536396
$372$			10.1451i			0.525999i
$373$		−	19.7975i		−	1.02508i	−0.858665	−	0.512538i	$-0.828705\pi$
$373$		−	19.7975i		−	1.02508i	0.858665	−	0.512538i	$-0.171295\pi$
$374$	−5.72650			−0.296110
$375$	−6.33526	−	27.7029i	−0.327152	−	1.43057i
$376$	8.49457			0.438074
$377$		−	3.44947i		−	0.177657i
$378$		−	1.17101i		−	0.0602302i
$379$	33.0938			1.69992			0.849958	−	0.526851i	$-0.176627\pi$
$379$	33.0938			1.69992			0.849958	+	0.526851i	$0.176627\pi$
$380$	10.1562	−	0.762532i	0.521002	−	0.0391171i
$381$	−9.96804			−0.510678
$382$			5.38668i			0.275606i
$383$		−	17.2749i		−	0.882706i	−0.897333	−	0.441353i	$-0.854499\pi$
$383$		−	17.2749i		−	0.882706i	0.897333	−	0.441353i	$-0.145501\pi$
$384$	−2.54179			−0.129710
$385$	0.958695	+	12.7689i	0.0488596	+	0.650763i
$386$	0.617801			0.0314452
$387$		−	42.4988i		−	2.16034i
$388$			17.5462i			0.890771i
$389$	−5.88067			−0.298162			−0.149081	−	0.988825i	$-0.547631\pi$
$389$	−5.88067			−0.298162			−0.149081	+	0.988825i	$0.547631\pi$
$390$	1.48211	+	19.7403i	0.0750495	+	0.999587i
$391$	8.26551			0.418005
$392$		−	1.00000i		−	0.0505076i
$393$		−	25.2868i		−	1.27555i
$394$	8.90420			0.448587
$395$	30.2314	−	2.26979i	1.52111	−	0.114206i
$396$	−19.8177			−0.995877
$397$			17.3518i			0.870859i	0.900223	+	0.435430i	$0.143404\pi$
$397$			17.3518i			0.870859i	−0.900223	+	0.435430i	$0.856596\pi$
$398$			2.74906i			0.137798i
$399$	−11.5773			−0.579589
$400$	4.94395	−	0.746596i	0.247197	−	0.0373298i
$401$	−19.9909			−0.998299			−0.499149	−	0.866516i	$-0.666354\pi$
$401$	−19.9909			−0.998299			−0.499149	+	0.866516i	$0.666354\pi$
$402$			9.85228i			0.491387i
$403$			13.9016i			0.692488i
$404$	3.17217			0.157821
$405$	16.5131	−	1.23981i	0.820540	−	0.0616066i
$406$	0.990385			0.0491520
$407$			11.2572i			0.557996i
$408$		−	2.54179i		−	0.125837i
$409$	−35.3383			−1.74737			−0.873683	−	0.486495i	$-0.838275\pi$
$409$	−35.3383			−1.74737			−0.873683	+	0.486495i	$0.838275\pi$
$410$	1.32013	+	17.5829i	0.0651968	+	0.868358i
$411$	53.5515			2.64150
$412$			1.94049i			0.0956009i
$413$			10.1278i			0.498355i
$414$	28.6045			1.40583
$415$	2.57693	+	34.3222i	0.126496	+	1.68481i
$416$	−3.48296			−0.170766
$417$		−	3.65986i		−	0.179224i
$418$			26.0829i			1.27576i
$419$	27.0860			1.32324			0.661619	−	0.749841i	$-0.269870\pi$
$419$	27.0860			1.32324			0.661619	+	0.749841i	$0.269870\pi$
$420$	−5.66767	+	0.425531i	−0.276554	+	0.0207638i
$421$	12.6808			0.618025			0.309013	−	0.951058i	$-0.400001\pi$
$421$	12.6808			0.618025			0.309013	+	0.951058i	$0.400001\pi$
$422$			9.35373i			0.455332i
$423$			29.3972i			1.42934i
$424$	10.3317			0.501753
$425$	0.746596	+	4.94395i	0.0362152	+	0.239817i
$426$	−15.8355			−0.767233
$427$		−	0.952226i		−	0.0460814i
$428$		−	2.05039i		−	0.0991091i
$429$	−50.6964			−2.44765
$430$	−27.3827	+	2.05591i	−1.32051	+	0.0991447i
$431$	−2.22147			−0.107005			−0.0535023	−	0.998568i	$-0.517038\pi$
$431$	−2.22147			−0.107005			−0.0535023	+	0.998568i	$0.517038\pi$
$432$		−	1.17101i		−	0.0563402i
$433$		−	29.8916i		−	1.43650i	−0.695786	−	0.718249i	$-0.744944\pi$
$433$		−	29.8916i		−	1.43650i	0.695786	−	0.718249i	$-0.255056\pi$
$434$	−3.99132			−0.191589
$435$	−0.421440	−	5.61317i	−0.0202065	−	0.269131i
$436$	−19.3457			−0.926490
$437$		−	37.6475i		−	1.80092i
$438$		−	17.9710i		−	0.858689i
$439$	14.5552			0.694683			0.347342	−	0.937739i	$-0.387084\pi$
$439$	14.5552			0.694683			0.347342	+	0.937739i	$0.387084\pi$
$440$	0.958695	+	12.7689i	0.0457040	+	0.608733i
$441$	3.46070			0.164795
$442$		−	3.48296i		−	0.165668i
$443$		−	6.99922i		−	0.332543i	−0.986080	−	0.166271i	$-0.946827\pi$
$443$		−	6.99922i		−	0.332543i	0.986080	−	0.166271i	$-0.0531728\pi$
$444$	−4.99666			−0.237131
$445$	32.2242	−	2.41941i	1.52758	−	0.114691i
$446$	−0.946770			−0.0448309
$447$		−	56.6992i		−	2.68178i
$448$		−	1.00000i		−	0.0472456i
$449$	4.29546			0.202715			0.101358	−	0.994850i	$-0.467681\pi$
$449$	4.29546			0.202715			0.101358	+	0.994850i	$0.467681\pi$
$450$	2.58375	+	17.1095i	0.121799	+	0.806551i
$451$	−45.1560			−2.12631
$452$			6.29785i			0.296226i
$453$		−	21.4448i		−	1.00757i
$454$	12.3408			0.579181
$455$	−7.76628	+	0.583096i	−0.364089	+	0.0273360i
$456$	−11.5773			−0.542156
$457$			0.936921i			0.0438273i	0.999760	+	0.0219137i	$0.00697589\pi$
$457$			0.936921i			0.0438273i	−0.999760	+	0.0219137i	$0.993024\pi$
$458$		−	13.3470i		−	0.623663i
$459$	1.17101			0.0546580
$460$	−1.38376	−	18.4304i	−0.0645182	−	0.859321i
$461$	24.6279			1.14704			0.573518	−	0.819193i	$-0.305578\pi$
$461$	24.6279			1.14704			0.573518	+	0.819193i	$0.305578\pi$
$462$		−	14.5556i		−	0.677186i
$463$		−	29.9356i		−	1.39122i	−0.718418	−	0.695612i	$-0.755133\pi$
$463$		−	29.9356i		−	1.39122i	0.718418	−	0.695612i	$-0.244867\pi$
$464$	0.990385			0.0459775
$465$	1.69843	+	22.6214i	0.0787628	+	1.04904i
$466$	23.2229			1.07578
$467$			9.31665i			0.431123i	0.976490	+	0.215562i	$0.0691582\pi$
$467$			9.31665i			0.431123i	−0.976490	+	0.215562i	$0.930842\pi$
$468$		−	12.0535i		−	0.557173i
$469$	−3.87612			−0.178982
$470$	18.9411	−	1.42211i	0.873689	−	0.0655970i
$471$	49.6972			2.28993
$472$			10.1278i			0.466169i
$473$		−	70.3236i		−	3.23348i
$474$	−34.4615			−1.58287
$475$	22.5185	−	3.40058i	1.03322	−	0.156029i
$476$	1.00000			0.0458349
$477$			35.7550i			1.63711i
$478$			10.8663i			0.497011i
$479$	−12.2197			−0.558333			−0.279167	−	0.960243i	$-0.590058\pi$
$479$	−12.2197			−0.558333			−0.279167	+	0.960243i	$0.590058\pi$
$480$	−5.66767	+	0.425531i	−0.258692	+	0.0194228i
$481$	−6.84681			−0.312188
$482$		−	9.61298i		−	0.437859i
$483$			21.0092i			0.955952i
$484$	−21.7928			−0.990580
$485$	2.93747	+	39.1243i	0.133384	+	1.77654i
$486$	−22.3366			−1.01321
$487$			2.11355i			0.0957739i	0.998853	+	0.0478870i	$0.0152487\pi$
$487$			2.11355i			0.0957739i	−0.998853	+	0.0478870i	$0.984751\pi$
$488$		−	0.952226i		−	0.0431052i
$489$	−38.7231			−1.75112
$490$	−0.167414	−	2.22979i	−0.00756299	−	0.100732i
$491$	−6.35587			−0.286836			−0.143418	−	0.989662i	$-0.545809\pi$
$491$	−6.35587			−0.286836			−0.143418	+	0.989662i	$0.545809\pi$
$492$		−	20.0432i		−	0.903616i
$493$			0.990385i			0.0446047i
$494$	−15.8641			−0.713759
$495$	−44.1893	+	3.31776i	−1.98616	+	0.149122i
$496$	−3.99132			−0.179215
$497$		−	6.23006i		−	0.279456i
$498$		−	39.1246i		−	1.75322i
$499$	−42.4519			−1.90041			−0.950204	−	0.311627i	$-0.899126\pi$
$499$	−42.4519			−1.90041			−0.950204	+	0.311627i	$0.899126\pi$
$500$	10.8990	−	2.49244i	0.487417	−	0.111465i
$501$	−3.66310			−0.163655
$502$		−	13.6959i		−	0.611278i
$503$		−	20.9628i		−	0.934683i	−0.884077	−	0.467342i	$-0.845212\pi$
$503$		−	20.9628i		−	0.934683i	0.884077	−	0.467342i	$-0.154788\pi$
$504$	3.46070			0.154152
$505$	7.07328	−	0.531065i	0.314757	−	0.0236321i
$506$	47.3324			2.10418
$507$			2.20877i			0.0980948i
$508$		−	3.92166i		−	0.173996i
$509$	3.66956			0.162650			0.0813251	−	0.996688i	$-0.474085\pi$
$509$	3.66956			0.162650			0.0813251	+	0.996688i	$0.474085\pi$
$510$	−0.425531	−	5.66767i	−0.0188428	−	0.250968i
$511$	7.07022			0.312768
$512$		−	1.00000i		−	0.0441942i
$513$		−	5.33368i		−	0.235488i
$514$	19.2766			0.850256
$515$	0.324864	+	4.32688i	0.0143152	+	0.190665i
$516$	31.2142			1.37413
$517$			48.6441i			2.13937i
$518$		−	1.96580i		−	0.0863723i
$519$	0.230121			0.0101012
$520$	−7.76628	+	0.583096i	−0.340574	+	0.0255705i
$521$	21.8630			0.957836			0.478918	−	0.877860i	$-0.341029\pi$
$521$	21.8630			0.957836			0.478918	+	0.877860i	$0.341029\pi$
$522$			3.42743i			0.150014i
$523$		−	2.31826i		−	0.101370i	−0.998715	−	0.0506852i	$-0.983859\pi$
$523$		−	2.31826i		−	0.101370i	0.998715	−	0.0506852i	$-0.0161405\pi$
$524$	9.94843			0.434599
$525$	−12.5665	+	1.89769i	−0.548446	+	0.0828221i
$526$	−15.4341			−0.672958
$527$		−	3.99132i		−	0.173864i
$528$		−	14.5556i		−	0.633449i
$529$	−45.3187			−1.97038
$530$	23.0376	−	1.72967i	1.00069	−	0.0751322i
$531$	−35.0492			−1.52101
$532$		−	4.55477i		−	0.197474i
$533$		−	27.4647i		−	1.18963i
$534$	−36.7332			−1.58960
$535$	−0.343263	−	4.57193i	−0.0148406	−	0.197662i
$536$	−3.87612			−0.167423
$537$			17.0818i			0.737136i
$538$			18.7045i			0.806409i
$539$	5.72650			0.246658
$540$	−0.196043	−	2.61111i	−0.00843636	−	0.112364i
$541$	−26.3538			−1.13304			−0.566520	−	0.824048i	$-0.691711\pi$
$541$	−26.3538			−1.13304			−0.566520	+	0.824048i	$0.691711\pi$
$542$		−	27.6242i		−	1.18656i
$543$		−	51.7374i		−	2.22026i
$544$	1.00000			0.0428746
$545$	−43.1368	+	3.23873i	−1.84778	+	0.138732i
$546$	8.85296			0.378872
$547$		−	20.5567i		−	0.878943i	−0.898257	−	0.439471i	$-0.855166\pi$
$547$		−	20.5567i		−	0.878943i	0.898257	−	0.439471i	$-0.144834\pi$
$548$			21.0684i			0.899998i
$549$	3.29537			0.140643
$550$	4.27538	+	28.3115i	0.182303	+	1.20721i
$551$	4.51098			0.192174
$552$			21.0092i			0.894211i
$553$		−	13.5580i		−	0.576543i
$554$	−2.15313			−0.0914778
$555$	−11.1415	+	0.836510i	−0.472931	+	0.0355079i
$556$	1.43988			0.0610643
$557$			30.1050i			1.27559i	0.770207	+	0.637794i	$0.220153\pi$
$557$			30.1050i			1.27559i	−0.770207	+	0.637794i	$0.779847\pi$
$558$		−	13.8128i		−	0.584741i
$559$	42.7721			1.80907
$560$	−0.167414	−	2.22979i	−0.00707453	−	0.0942259i
$561$	14.5556			0.614536
$562$		−	3.87390i		−	0.163411i
$563$		−	13.4551i		−	0.567065i	−0.958963	−	0.283532i	$-0.908494\pi$
$563$		−	13.4551i		−	0.567065i	0.958963	−	0.283532i	$-0.0915063\pi$
$564$	−21.5914			−0.909163
$565$	1.05435	+	14.0429i	0.0443568	+	0.590789i
$566$	−5.48685			−0.230630
$567$		−	7.40565i		−	0.311008i
$568$		−	6.23006i		−	0.261407i
$569$	−14.1962			−0.595135			−0.297567	−	0.954701i	$-0.596175\pi$
$569$	−14.1962			−0.595135			−0.297567	+	0.954701i	$0.596175\pi$
$570$	−25.8149	+	1.93820i	−1.08127	+	0.0811821i
$571$	4.06927			0.170294			0.0851469	−	0.996368i	$-0.472864\pi$
$571$	4.06927			0.170294			0.0851469	+	0.996368i	$0.472864\pi$
$572$		−	19.9452i		−	0.833949i
$573$		−	13.6918i		−	0.571984i
$574$	7.88545			0.329132
$575$	−6.17100	−	40.8642i	−0.257349	−	1.70416i
$576$	3.46070			0.144196
$577$		−	23.0464i		−	0.959433i	−0.877424	−	0.479716i	$-0.840740\pi$
$577$		−	23.0464i		−	0.959433i	0.877424	−	0.479716i	$-0.159260\pi$
$578$			1.00000i			0.0415945i
$579$	−1.57032			−0.0652603
$580$	2.20835	−	0.165804i	0.0916969	−	0.00688465i
$581$	15.3925			0.638590
$582$		−	44.5987i		−	1.84867i
$583$			59.1645i			2.45035i
$584$	7.07022			0.292568
$585$	−2.01792	−	26.8768i	−0.0834308	−	1.11122i
$586$	−21.7657			−0.899131
$587$		−	9.46700i		−	0.390745i	−0.980729	−	0.195372i	$-0.937408\pi$
$587$		−	9.46700i		−	0.390745i	0.980729	−	0.195372i	$-0.0625916\pi$
$588$			2.54179i			0.104822i
$589$	−18.1795			−0.749075
$590$	1.69553	+	22.5828i	0.0698039	+	0.929721i
$591$	−22.6326			−0.930981
$592$		−	1.96580i		−	0.0807939i
$593$			0.297927i			0.0122344i	0.999981	+	0.00611719i	$0.00194717\pi$
$593$			0.297927i			0.0122344i	−0.999981	+	0.00611719i	$0.998053\pi$
$594$	6.70578			0.275141
$595$	2.22979	−	0.167414i	0.0914126	−	0.00686330i
$596$	22.3068			0.913722
$597$		−	6.98754i		−	0.285981i
$598$			28.7885i			1.17725i
$599$	−30.4804			−1.24539			−0.622697	−	0.782463i	$-0.713963\pi$
$599$	−30.4804			−1.24539			−0.622697	+	0.782463i	$0.713963\pi$
$600$	−12.5665	+	1.89769i	−0.513024	+	0.0774730i
$601$	−11.4524			−0.467154			−0.233577	−	0.972338i	$-0.575043\pi$
$601$	−11.4524			−0.467154			−0.233577	+	0.972338i	$0.575043\pi$
$602$			12.2804i			0.500512i
$603$		−	13.4141i		−	0.546264i
$604$	8.43690			0.343293
$605$	−48.5933	+	3.64841i	−1.97560	+	0.148329i
$606$	−8.06299			−0.327537
$607$			16.7894i			0.681461i	0.940161	+	0.340730i	$0.110674\pi$
$607$			16.7894i			0.681461i	−0.940161	+	0.340730i	$0.889326\pi$
$608$		−	4.55477i		−	0.184720i
$609$	−2.51735			−0.102008
$610$	−0.159416	−	2.12327i	−0.00645456	−	0.0859685i
$611$	−29.5863			−1.19693
$612$			3.46070i			0.139891i
$613$			4.05568i			0.163808i	0.996640	+	0.0819038i	$0.0261000\pi$
$613$			4.05568i			0.163808i	−0.996640	+	0.0819038i	$0.973900\pi$
$614$	13.1008			0.528707
$615$	−3.35551	−	44.6921i	−0.135307	−	1.80216i
$616$	5.72650			0.230727
$617$		−	31.7150i		−	1.27680i	−0.769706	−	0.638399i	$-0.779597\pi$
$617$		−	31.7150i		−	1.27680i	0.769706	−	0.638399i	$-0.220403\pi$
$618$		−	4.93231i		−	0.198407i
$619$	10.3777			0.417114			0.208557	−	0.978010i	$-0.433123\pi$
$619$	10.3777			0.417114			0.208557	+	0.978010i	$0.433123\pi$
$620$	−8.89981	+	0.668202i	−0.357425	+	0.0268356i
$621$	−9.67899			−0.388405
$622$			4.20193i			0.168482i
$623$		−	14.4517i		−	0.578994i
$624$	8.85296			0.354402
$625$	23.8852	−	7.38226i	0.955408	−	0.295291i
$626$	−11.6520			−0.465709
$627$		−	66.2972i		−	2.64766i
$628$			19.5520i			0.780212i
$629$	1.96580			0.0783816
$630$	7.71665	−	0.579370i	0.307439	−	0.0230826i
$631$	13.3731			0.532373			0.266187	−	0.963922i	$-0.414236\pi$
$631$	13.3731			0.532373			0.266187	+	0.963922i	$0.414236\pi$
$632$		−	13.5580i		−	0.539307i
$633$		−	23.7752i		−	0.944980i
$634$	3.45462			0.137201
$635$	−0.656540	−	8.74449i	−0.0260540	−	0.347014i
$636$	−26.2611			−1.04132
$637$			3.48296i			0.138000i
$638$			5.67144i			0.224534i
$639$	21.5604			0.852915
$640$	−0.167414	−	2.22979i	−0.00661762	−	0.0881403i
$641$	−44.6667			−1.76423			−0.882113	−	0.471037i	$-0.843880\pi$
$641$	−44.6667			−1.76423			−0.882113	+	0.471037i	$0.843880\pi$
$642$			5.21165i			0.205688i
$643$			3.96886i			0.156517i	0.996933	+	0.0782583i	$0.0249359\pi$
$643$			3.96886i			0.156517i	−0.996933	+	0.0782583i	$0.975064\pi$
$644$	−8.26551			−0.325707
$645$	69.6012	−	5.22569i	2.74054	−	0.205761i
$646$	4.55477			0.179205
$647$			8.10463i			0.318626i	0.987228	+	0.159313i	$0.0509279\pi$
$647$			8.10463i			0.318626i	−0.987228	+	0.159313i	$0.949072\pi$
$648$		−	7.40565i		−	0.290921i
$649$	−57.9967			−2.27657
$650$	−17.2196	+	2.60037i	−0.675407	+	0.101995i
$651$	10.1451			0.397618
$652$		−	15.2346i		−	0.596632i
$653$		−	14.6228i		−	0.572235i	−0.958194	−	0.286118i	$-0.907635\pi$
$653$		−	14.6228i		−	0.572235i	0.958194	−	0.286118i	$-0.0923648\pi$
$654$	49.1727			1.92280
$655$	22.1829	−	1.66551i	0.866759	−	0.0650767i
$656$	7.88545			0.307875
$657$			24.4679i			0.954585i
$658$		−	8.49457i		−	0.331153i
$659$	−10.9571			−0.426829			−0.213414	−	0.976962i	$-0.568458\pi$
$659$	−10.9571			−0.426829			−0.213414	+	0.976962i	$0.568458\pi$
$660$	−2.43680	−	32.4559i	−0.0948524	−	1.26334i
$661$	41.7506			1.62391			0.811955	−	0.583720i	$-0.198404\pi$
$661$	41.7506			1.62391			0.811955	+	0.583720i	$0.198404\pi$
$662$		−	12.4973i		−	0.485720i
$663$			8.85296i			0.343820i
$664$	15.3925			0.597346
$665$	−0.762532	−	10.1562i	−0.0295697	−	0.393840i
$666$	6.80305			0.263613
$667$		−	8.18604i		−	0.316965i
$668$		−	1.44115i		−	0.0557598i
$669$	2.40649			0.0930403
$670$	−8.64294	+	0.648916i	−0.333906	+	0.0250698i
$671$	5.45292			0.210508
$672$			2.54179i			0.0980517i
$673$		−	7.26123i		−	0.279900i	−0.990159	−	0.139950i	$-0.955306\pi$
$673$		−	7.26123i		−	0.279900i	0.990159	−	0.139950i	$-0.0446941\pi$
$674$	8.93416			0.344131
$675$	−0.874271	−	5.78941i	−0.0336507	−	0.222834i
$676$	−0.868981			−0.0334223
$677$			32.7711i			1.25950i	0.776799	+	0.629748i	$0.216842\pi$
$677$			32.7711i			1.25950i	−0.776799	+	0.629748i	$0.783158\pi$
$678$		−	16.0078i		−	0.614777i
$679$	17.5462			0.673360
$680$	2.22979	−	0.167414i	0.0855086	−	0.00642003i
$681$	−31.3676			−1.20201
$682$		−	22.8563i		−	0.875211i
$683$		−	1.54929i		−	0.0592818i	−0.999561	−	0.0296409i	$-0.990564\pi$
$683$		−	1.54929i		−	0.0592818i	0.999561	−	0.0296409i	$-0.00943637\pi$
$684$	15.7627			0.602702
$685$	3.52714	+	46.9782i	0.134765	+	1.79494i
$686$	−1.00000			−0.0381802
$687$			33.9252i			1.29433i
$688$			12.2804i			0.468186i
$689$	−35.9850			−1.37092
$690$	3.51723	+	46.8462i	0.133899	+	1.78340i
$691$	−31.3105			−1.19111			−0.595554	−	0.803315i	$-0.703068\pi$
$691$	−31.3105			−1.19111			−0.595554	+	0.803315i	$0.703068\pi$
$692$			0.0905351i			0.00344163i
$693$			19.8177i			0.752812i
$694$	19.0850			0.724457
$695$	3.21062	−	0.241055i	0.121786	−	0.00914375i
$696$	−2.51735			−0.0954200
$697$			7.88545i			0.298683i
$698$			15.3497i			0.580996i
$699$	−59.0277			−2.23263
$700$	−0.746596	−	4.94395i	−0.0282187	−	0.186864i
$701$	−26.7200			−1.00920			−0.504601	−	0.863353i	$-0.668360\pi$
$701$	−26.7200			−1.00920			−0.504601	+	0.863353i	$0.668360\pi$
$702$			4.07858i			0.153936i
$703$		−	8.95377i		−	0.337698i
$704$	5.72650			0.215825
$705$	−48.1444	+	3.61470i	−1.81322	+	0.136138i
$706$	−3.33185			−0.125396
$707$		−	3.17217i		−	0.119302i
$708$		−	25.7427i		−	0.967470i
$709$	18.5720			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$709$	18.5720			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$710$	−1.04300	−	13.8917i	−0.0391430	−	0.521348i
$711$	46.9200			1.75964
$712$		−	14.4517i		−	0.541600i
$713$			32.9903i			1.23550i
$714$	−2.54179			−0.0951241
$715$	−3.33910	−	44.4736i	−0.124875	−	1.66322i
$716$	−6.72039			−0.251153
$717$		−	27.6198i		−	1.03148i
$718$		−	10.1746i		−	0.379713i
$719$	−6.42124			−0.239472			−0.119736	−	0.992806i	$-0.538205\pi$
$719$	−6.42124			−0.239472			−0.119736	+	0.992806i	$0.538205\pi$
$720$	7.71665	−	0.579370i	0.287582	−	0.0215918i
$721$	1.94049			0.0722675
$722$		−	1.74594i		−	0.0649771i
$723$			24.4342i			0.908717i
$724$	20.3547			0.756476
$725$	4.89641	−	0.739418i	0.181848	−	0.0274613i
$726$	55.3926			2.05581
$727$			41.2275i			1.52904i	0.644598	+	0.764522i	$0.277025\pi$
$727$			41.2275i			1.52904i	−0.644598	+	0.764522i	$0.722975\pi$
$728$			3.48296i			0.129087i
$729$	34.5581			1.27993
$730$	15.7651	−	1.18365i	0.583493	−	0.0438090i
$731$	−12.2804			−0.454207
$732$			2.42036i			0.0894590i
$733$		−	16.0832i		−	0.594048i	−0.954870	−	0.297024i	$-0.904006\pi$
$733$		−	16.0832i		−	0.594048i	0.954870	−	0.297024i	$-0.0959942\pi$
$734$	−11.2202			−0.414144
$735$	0.425531	+	5.66767i	0.0156960	+	0.209055i
$736$	−8.26551			−0.304671
$737$		−	22.1966i		−	0.817621i
$738$			27.2892i			1.00453i
$739$	−24.2742			−0.892941			−0.446470	−	0.894798i	$-0.647319\pi$
$739$	−24.2742			−0.892941			−0.446470	+	0.894798i	$0.647319\pi$
$740$	−0.329102	−	4.38333i	−0.0120980	−	0.161134i
$741$	40.3232			1.48131
$742$		−	10.3317i		−	0.379289i
$743$			13.4662i			0.494027i	0.969012	+	0.247013i	$0.0794492\pi$
$743$			13.4662i			0.494027i	−0.969012	+	0.247013i	$0.920551\pi$
$744$	10.1451			0.371937
$745$	49.7395	−	3.73447i	1.82232	−	0.136820i
$746$	−19.7975			−0.724838
$747$			53.2690i			1.94901i
$748$			5.72650i			0.209381i
$749$	−2.05039			−0.0749195
$750$	−27.7029	+	6.33526i	−1.01157	+	0.231331i
$751$	38.8084			1.41614			0.708069	−	0.706144i	$-0.249567\pi$
$751$	38.8084			1.41614			0.708069	+	0.706144i	$0.249567\pi$
$752$		−	8.49457i		−	0.309765i
$753$			34.8121i			1.26862i
$754$	−3.44947			−0.125622
$755$	18.8125	−	1.41245i	0.684658	−	0.0514045i
$756$	−1.17101			−0.0425892
$757$			35.9312i			1.30594i	0.757384	+	0.652970i	$0.226477\pi$
$757$			35.9312i			1.30594i	−0.757384	+	0.652970i	$0.773523\pi$
$758$		−	33.0938i		−	1.20202i
$759$	−120.309			−4.36694
$760$	−0.762532	−	10.1562i	−0.0276599	−	0.368404i
$761$	44.4288			1.61054			0.805272	−	0.592906i	$-0.202020\pi$
$761$	44.4288			1.61054			0.805272	+	0.592906i	$0.202020\pi$
$762$			9.96804i			0.361104i
$763$			19.3457i			0.700360i
$764$	5.38668			0.194883
$765$	0.579370	+	7.71665i	0.0209472	+	0.278996i
$766$	−17.2749			−0.624168
$767$		−	35.2747i		−	1.27369i
$768$			2.54179i			0.0917190i
$769$	−0.248795			−0.00897177			−0.00448589	−	0.999990i	$-0.501428\pi$
$769$	−0.248795			−0.00897177			−0.00448589	+	0.999990i	$0.501428\pi$
$770$	12.7689	−	0.958695i	0.460159	−	0.0345490i
$771$	−48.9972			−1.76459
$772$		−	0.617801i		−	0.0222351i
$773$			13.7137i			0.493248i	0.969111	+	0.246624i	$0.0793212\pi$
$773$			13.7137i			0.493248i	−0.969111	+	0.246624i	$0.920679\pi$
$774$	−42.4988			−1.52759
$775$	−19.7328	+	2.97990i	−0.708825	+	0.107041i
$776$	17.5462			0.629870
$777$			4.99666i			0.179254i
$778$			5.88067i			0.210832i
$779$	35.9164			1.28684
$780$	19.7403	−	1.48211i	0.706815	−	0.0530680i
$781$	35.6764			1.27660
$782$		−	8.26551i		−	0.295574i
$783$		−	1.15975i		−	0.0414461i
$784$	−1.00000			−0.0357143
$785$	3.27328	+	43.5970i	0.116829	+	1.55604i
$786$	−25.2868			−0.901951
$787$		−	39.3773i		−	1.40365i	−0.712350	−	0.701824i	$-0.752369\pi$
$787$		−	39.3773i		−	1.40365i	0.712350	−	0.701824i	$-0.247631\pi$
$788$		−	8.90420i		−	0.317199i
$789$	39.2302			1.39663
$790$	−2.26979	−	30.2314i	−0.0807555	−	1.07559i
$791$	6.29785			0.223926
$792$			19.8177i			0.704191i
$793$			3.31657i			0.117775i
$794$	17.3518			0.615791
$795$	−58.5567	+	4.39647i	−2.07679	+	0.155927i
$796$	2.74906			0.0974380
$797$			28.4245i			1.00685i	0.864039	+	0.503424i	$0.167927\pi$
$797$			28.4245i			1.00685i	−0.864039	+	0.503424i	$0.832073\pi$
$798$			11.5773i			0.409831i
$799$	8.49457			0.300516
$800$	−0.746596	−	4.94395i	−0.0263962	−	0.174795i
$801$	50.0130			1.76712
$802$			19.9909i			0.705904i
$803$			40.4876i			1.42878i
$804$	9.85228			0.347463
$805$	−18.4304	+	1.38376i	−0.649585	+	0.0487712i
$806$	13.9016			0.489663
$807$		−	47.5430i		−	1.67359i
$808$		−	3.17217i		−	0.111597i
$809$	36.4046			1.27992			0.639958	−	0.768410i	$-0.278952\pi$
$809$	36.4046			1.27992			0.639958	+	0.768410i	$0.278952\pi$
$810$	−1.23981	−	16.5131i	−0.0435624	−	0.580209i
$811$	29.5590			1.03796			0.518978	−	0.854787i	$-0.326312\pi$
$811$	29.5590			1.03796			0.518978	+	0.854787i	$0.326312\pi$
$812$		−	0.990385i		−	0.0347557i
$813$			70.2150i			2.46255i
$814$	11.2572			0.394563
$815$	−2.55048	−	33.9700i	−0.0893395	−	1.18992i
$816$	−2.54179			−0.0889805
$817$			55.9344i			1.95690i
$818$			35.3383i			1.23557i
$819$	−12.0535			−0.421183
$820$	17.5829	−	1.32013i	0.614022	−	0.0461011i
$821$	−7.70862			−0.269033			−0.134516	−	0.990911i	$-0.542948\pi$
$821$	−7.70862			−0.269033			−0.134516	+	0.990911i	$0.542948\pi$
$822$		−	53.5515i		−	1.86782i
$823$		−	28.4869i		−	0.992990i	−0.868040	−	0.496495i	$-0.834620\pi$
$823$		−	28.4869i		−	0.992990i	0.868040	−	0.496495i	$-0.165380\pi$
$824$	1.94049			0.0676000
$825$	−10.8671	−	71.9619i	−0.378345	−	2.50539i
$826$	10.1278			0.352390
$827$			34.5262i			1.20060i	0.799777	+	0.600298i	$0.204951\pi$
$827$			34.5262i			1.20060i	−0.799777	+	0.600298i	$0.795049\pi$
$828$		−	28.6045i		−	0.994074i
$829$	19.5009			0.677293			0.338647	−	0.940914i	$-0.390031\pi$
$829$	19.5009			0.677293			0.338647	+	0.940914i	$0.390031\pi$
$830$	34.3222	−	2.57693i	1.19134	−	0.0894464i
$831$	5.47281			0.189850
$832$			3.48296i			0.120750i
$833$		−	1.00000i		−	0.0346479i
$834$	−3.65986			−0.126731
$835$	−0.241269	−	3.21347i	−0.00834945	−	0.111207i
$836$	26.0829			0.902095
$837$			4.67387i			0.161553i
$838$		−	27.0860i		−	0.935670i
$839$	33.4690			1.15548			0.577738	−	0.816222i	$-0.303935\pi$
$839$	33.4690			1.15548			0.577738	+	0.816222i	$0.303935\pi$
$840$	0.425531	+	5.66767i	0.0146822	+	0.195553i
$841$	−28.0191			−0.966177
$842$		−	12.6808i		−	0.437010i
$843$			9.84665i			0.339137i
$844$	9.35373			0.321969
$845$	−1.93765	+	0.145479i	−0.0666570	+	0.00500464i
$846$	29.3972			1.01070
$847$			21.7928i			0.748808i
$848$		−	10.3317i		−	0.354793i
$849$	13.9464			0.478641
$850$	4.94395	−	0.746596i	0.169576	−	0.0256080i
$851$	−16.2484			−0.556986
$852$			15.8355i			0.542516i
$853$		−	13.7146i		−	0.469580i	−0.972046	−	0.234790i	$-0.924560\pi$
$853$		−	13.7146i		−	0.469580i	0.972046	−	0.234790i	$-0.0754402\pi$
$854$	−0.952226			−0.0325845
$855$	35.1476	−	2.63890i	1.20202	−	0.0902484i
$856$	−2.05039			−0.0700807
$857$		−	42.1511i		−	1.43986i	−0.694049	−	0.719928i	$-0.744175\pi$
$857$		−	42.1511i		−	1.43986i	0.694049	−	0.719928i	$-0.255825\pi$
$858$			50.6964i			1.73075i
$859$	−45.9832			−1.56893			−0.784463	−	0.620176i	$-0.787061\pi$
$859$	−45.9832			−1.56893			−0.784463	+	0.620176i	$0.787061\pi$
$860$	2.05591	+	27.3827i	0.0701059	+	0.933743i
$861$	−20.0432			−0.683069
$862$			2.22147i			0.0756637i
$863$			21.0234i			0.715644i	0.933790	+	0.357822i	$0.116481\pi$
$863$			21.0234i			0.715644i	−0.933790	+	0.357822i	$0.883519\pi$
$864$	−1.17101			−0.0398385
$865$	0.0151568	+	0.201874i	0.000515348	+	0.00686394i
$866$	−29.8916			−1.01576
$867$		−	2.54179i		−	0.0863238i
$868$			3.99132i			0.135474i
$869$	77.6396			2.63374
$870$	−5.61317	+	0.421440i	−0.190304	+	0.0142882i
$871$	13.5004			0.457443
$872$			19.3457i			0.655127i
$873$			60.7220i			2.05513i
$874$	−37.6475			−1.27345
$875$	−2.49244	−	10.8990i	−0.0842598	−	0.368453i
$876$	−17.9710			−0.607185
$877$			3.93131i			0.132751i	0.997795	+	0.0663754i	$0.0211435\pi$
$877$			3.93131i			0.132751i	−0.997795	+	0.0663754i	$0.978857\pi$
$878$		−	14.5552i		−	0.491215i
$879$	55.3238			1.86602
$880$	12.7689	−	0.958695i	0.430439	−	0.0323176i
$881$	5.41729			0.182513			0.0912566	−	0.995827i	$-0.470912\pi$
$881$	5.41729			0.182513			0.0912566	+	0.995827i	$0.470912\pi$
$882$		−	3.46070i		−	0.116528i
$883$			33.5752i			1.12990i	0.825127	+	0.564948i	$0.191104\pi$
$883$			33.5752i			1.12990i	−0.825127	+	0.564948i	$0.808896\pi$
$884$	−3.48296			−0.117145
$885$	−4.30969	−	57.4009i	−0.144868	−	1.92951i
$886$	−6.99922			−0.235143
$887$			2.92415i			0.0981834i	0.998794	+	0.0490917i	$0.0156327\pi$
$887$			2.92415i			0.0981834i	−0.998794	+	0.0490917i	$0.984367\pi$
$888$			4.99666i			0.167677i
$889$	−3.92166			−0.131528
$890$	−2.41941	−	32.2242i	−0.0810989	−	1.08016i
$891$	42.4084			1.42073
$892$			0.946770i			0.0317002i
$893$		−	38.6908i		−	1.29474i
$894$	−56.6992			−1.89631
$895$	−14.9851	+	1.12509i	−0.500896	+	0.0376075i
$896$	−1.00000			−0.0334077
$897$		−	73.1742i		−	2.44322i
$898$		−	4.29546i		−	0.143341i
$899$	−3.95294			−0.131838
$900$	17.1095	−	2.58375i	0.570317	−	0.0861249i
$901$	10.3317			0.344199
$902$			45.1560i			1.50353i
$903$		−	31.2142i		−	1.03874i
$904$	6.29785			0.209464
$905$	45.3867	−	3.40766i	1.50871	−	0.113274i
$906$	−21.4448			−0.712457
$907$		−	27.5005i		−	0.913138i	−0.889688	−	0.456569i	$-0.849078\pi$
$907$		−	27.5005i		−	0.913138i	0.889688	−	0.456569i	$-0.150922\pi$
$908$		−	12.3408i		−	0.409543i
$909$	10.9779			0.364115
$910$	0.583096	+	7.76628i	0.0193294	+	0.257450i
$911$	−5.75095			−0.190537			−0.0952687	−	0.995452i	$-0.530371\pi$
$911$	−5.75095			−0.190537			−0.0952687	+	0.995452i	$0.530371\pi$
$912$			11.5773i			0.383362i
$913$			88.1453i			2.91718i
$914$	0.936921			0.0309906
$915$	0.405202	+	5.39690i	0.0133956	+	0.178416i
$916$	−13.3470			−0.440996
$917$		−	9.94843i		−	0.328526i
$918$		−	1.17101i		−	0.0386491i
$919$	6.18604			0.204059			0.102029	−	0.994781i	$-0.467466\pi$
$919$	6.18604			0.204059			0.102029	+	0.994781i	$0.467466\pi$
$920$	−18.4304	+	1.38376i	−0.607631	+	0.0456213i
$921$	−33.2996			−1.09726
$922$		−	24.6279i		−	0.811077i
$923$			21.6991i			0.714233i
$924$	−14.5556			−0.478843
$925$	−1.46766	−	9.71881i	−0.0482564	−	0.319553i
$926$	−29.9356			−0.983744
$927$			6.71544i			0.220564i
$928$		−	0.990385i		−	0.0325110i
$929$	−44.0088			−1.44388			−0.721941	−	0.691955i	$-0.756750\pi$
$929$	−44.0088			−1.44388			−0.721941	+	0.691955i	$0.756750\pi$
$930$	22.6214	−	1.69843i	0.741786	−	0.0556937i
$931$	−4.55477			−0.149277
$932$		−	23.2229i		−	0.760691i
$933$		−	10.6804i		−	0.349662i
$934$	9.31665			0.304850
$935$	0.958695	+	12.7689i	0.0313527	+	0.417588i
$936$	−12.0535			−0.393981
$937$			27.3208i			0.892533i	0.894900	+	0.446266i	$0.147247\pi$
$937$			27.3208i			0.892533i	−0.894900	+	0.446266i	$0.852753\pi$
$938$			3.87612i			0.126560i
$939$	29.6170			0.966515
$940$	−1.42211	−	18.9411i	−0.0463841	−	0.617791i
$941$	44.8806			1.46306			0.731532	−	0.681807i	$-0.238806\pi$
$941$	44.8806			1.46306			0.731532	+	0.681807i	$0.238806\pi$
$942$		−	49.6972i		−	1.61922i
$943$		−	65.1773i		−	2.12246i
$944$	10.1278			0.329631
$945$	−2.61111	+	0.196043i	−0.0849393	+	0.00637729i
$946$	−70.3236			−2.28642
$947$			32.0215i			1.04056i	0.853996	+	0.520279i	$0.174172\pi$
$947$			32.0215i			1.04056i	−0.853996	+	0.520279i	$0.825828\pi$
$948$			34.4615i			1.11926i
$949$	−24.6253			−0.799371
$950$	−3.40058	−	22.5185i	−0.110329	−	0.730598i
$951$	−8.78093			−0.284741
$952$		−	1.00000i		−	0.0324102i
$953$		−	6.66420i		−	0.215875i	−0.994158	−	0.107937i	$-0.965575\pi$
$953$		−	6.66420i		−	0.215875i	0.994158	−	0.107937i	$-0.0344246\pi$
$954$	35.7550			1.15761
$955$	12.0112	−	0.901805i	0.388672	−	0.0291817i
$956$	10.8663			0.351440
$957$		−	14.4156i		−	0.465991i
$958$			12.2197i			0.394801i
$959$	21.0684			0.680334
$960$	0.425531	+	5.66767i	0.0137340	+	0.182923i
$961$	−15.0694			−0.486109
$962$			6.84681i			0.220750i
$963$		−	7.09577i		−	0.228658i
$964$	−9.61298			−0.309613
$965$	−0.103428	−	1.37757i	−0.00332948	−	0.0443455i
$966$	21.0092			0.675960
$967$			32.3370i			1.03989i	0.854200	+	0.519944i	$0.174047\pi$
$967$			32.3370i			1.03989i	−0.854200	+	0.519944i	$0.825953\pi$
$968$			21.7928i			0.700446i
$969$	−11.5773			−0.371916
$970$	39.1243	−	2.93747i	1.25621	−	0.0943165i
$971$	26.8528			0.861747			0.430873	−	0.902412i	$-0.358206\pi$
$971$	26.8528			0.861747			0.430873	+	0.902412i	$0.358206\pi$
$972$			22.3366i			0.716448i
$973$		−	1.43988i		−	0.0461603i
$974$	2.11355			0.0677224
$975$	43.7686	−	6.60959i	1.40172	−	0.211676i
$976$	−0.952226			−0.0304800
$977$		−	14.3089i		−	0.457783i	−0.973452	−	0.228892i	$-0.926490\pi$
$977$		−	14.3089i		−	0.457783i	0.973452	−	0.228892i	$-0.0735102\pi$
$978$			38.7231i			1.23823i
$979$	82.7575			2.64494
$980$	−2.22979	+	0.167414i	−0.0712281	+	0.00534784i
$981$	−66.9496			−2.13754
$982$			6.35587i			0.202824i
$983$		−	10.9246i		−	0.348442i	−0.984707	−	0.174221i	$-0.944259\pi$
$983$		−	10.9246i		−	0.348442i	0.984707	−	0.174221i	$-0.0557407\pi$
$984$	−20.0432			−0.638953
$985$	−1.49069	−	19.8545i	−0.0474972	−	0.632617i
$986$	0.990385			0.0315403
$987$			21.5914i			0.687262i
$988$			15.8641i			0.504704i
$989$	101.504			3.22763
$990$	3.31776	+	44.1893i	0.105445	+	1.40443i
$991$	46.6895			1.48314			0.741570	−	0.670876i	$-0.234082\pi$
$991$	46.6895			1.48314			0.741570	+	0.670876i	$0.234082\pi$
$992$			3.99132i			0.126724i
$993$			31.7654i			1.00804i
$994$	−6.23006			−0.197605
$995$	6.12984	−	0.460231i	0.194329	−	0.0145903i
$996$	−39.1246			−1.23971
$997$			7.52339i			0.238268i	0.992878	+	0.119134i	$0.0380119\pi$
$997$			7.52339i			0.238268i	−0.992878	+	0.119134i	$0.961988\pi$
$998$			42.4519i			1.34379i
$999$	−2.30197			−0.0728312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1190.2.e.g.239.7	✓	14
5.2	odd	4		5950.2.a.cc.1.7		7
5.3	odd	4		5950.2.a.cb.1.1		7
5.4	even	2	inner	1190.2.e.g.239.8	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1190.2.e.g.239.7	✓	14	1.1	even	1	trivial
1190.2.e.g.239.8	yes	14	5.4	even	2	inner
5950.2.a.cb.1.1		7	5.3	odd	4
5950.2.a.cc.1.7		7	5.2	odd	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:	\( N \)	\(=\)	\( 1190 = 2 \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1190.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.54179i q^{3} -1.00000 q^{4} +(-2.22979 + 0.167414i) q^{5} +2.54179 q^{6} +1.00000i q^{7} +1.00000i q^{8} -3.46070 q^{9} +(0.167414 + 2.22979i) q^{10} -5.72650 q^{11} -2.54179i q^{12} -3.48296i q^{13} +1.00000 q^{14} +(-0.425531 - 5.66767i) q^{15} +1.00000 q^{16} +1.00000i q^{17} +3.46070i q^{18} +4.55477 q^{19} +(2.22979 - 0.167414i) q^{20} -2.54179 q^{21} +5.72650i q^{22} -8.26551i q^{23} -2.54179 q^{24} +(4.94395 - 0.746596i) q^{25} -3.48296 q^{26} -1.17101i q^{27} -1.00000i q^{28} +0.990385 q^{29} +(-5.66767 + 0.425531i) q^{30} -3.99132 q^{31} -1.00000i q^{32} -14.5556i q^{33} +1.00000 q^{34} +(-0.167414 - 2.22979i) q^{35} +3.46070 q^{36} -1.96580i q^{37} -4.55477i q^{38} +8.85296 q^{39} +(-0.167414 - 2.22979i) q^{40} +7.88545 q^{41} +2.54179i q^{42} +12.2804i q^{43} +5.72650 q^{44} +(7.71665 - 0.579370i) q^{45} -8.26551 q^{46} -8.49457i q^{47} +2.54179i q^{48} -1.00000 q^{49} +(-0.746596 - 4.94395i) q^{50} -2.54179 q^{51} +3.48296i q^{52} -10.3317i q^{53} -1.17101 q^{54} +(12.7689 - 0.958695i) q^{55} -1.00000 q^{56} +11.5773i q^{57} -0.990385i q^{58} +10.1278 q^{59} +(0.425531 + 5.66767i) q^{60} -0.952226 q^{61} +3.99132i q^{62} -3.46070i q^{63} -1.00000 q^{64} +(0.583096 + 7.76628i) q^{65} -14.5556 q^{66} +3.87612i q^{67} -1.00000i q^{68} +21.0092 q^{69} +(-2.22979 + 0.167414i) q^{70} -6.23006 q^{71} -3.46070i q^{72} -7.07022i q^{73} -1.96580 q^{74} +(1.89769 + 12.5665i) q^{75} -4.55477 q^{76} -5.72650i q^{77} -8.85296i q^{78} -13.5580 q^{79} +(-2.22979 + 0.167414i) q^{80} -7.40565 q^{81} -7.88545i q^{82} -15.3925i q^{83} +2.54179 q^{84} +(-0.167414 - 2.22979i) q^{85} +12.2804 q^{86} +2.51735i q^{87} -5.72650i q^{88} -14.4517 q^{89} +(-0.579370 - 7.71665i) q^{90} +3.48296 q^{91} +8.26551i q^{92} -10.1451i q^{93} -8.49457 q^{94} +(-10.1562 + 0.762532i) q^{95} +2.54179 q^{96} -17.5462i q^{97} +1.00000i q^{98} +19.8177 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{4} - 2 q^{5} - 4 q^{6} - 14 q^{9} + 4 q^{10} - 14 q^{11} + 14 q^{14} + 2 q^{15} + 14 q^{16} + 4 q^{19} + 2 q^{20} + 4 q^{21} + 4 q^{24} + 14 q^{25} + 2 q^{26} + 20 q^{29} - 2 q^{30} - 36 q^{31}+ \cdots + 88 q^{99}+O(q^{100}) \) 14 * q - 14 * q^4 - 2 * q^5 - 4 * q^6 - 14 * q^9 + 4 * q^10 - 14 * q^11 + 14 * q^14 + 2 * q^15 + 14 * q^16 + 4 * q^19 + 2 * q^20 + 4 * q^21 + 4 * q^24 + 14 * q^25 + 2 * q^26 + 20 * q^29 - 2 * q^30 - 36 * q^31 + 14 * q^34 - 4 * q^35 + 14 * q^36 + 50 * q^39 - 4 * q^40 + 34 * q^41 + 14 * q^44 + 8 * q^45 - 54 * q^46 - 14 * q^49 + 8 * q^50 + 4 * q^51 + 34 * q^54 - 16 * q^55 - 14 * q^56 - 2 * q^60 + 2 * q^61 - 14 * q^64 - 32 * q^65 - 16 * q^66 - 6 * q^69 - 2 * q^70 - 22 * q^71 + 24 * q^74 - 40 * q^75 - 4 * q^76 + 52 * q^79 - 2 * q^80 + 22 * q^81 - 4 * q^84 - 4 * q^85 - 14 * q^86 - 42 * q^89 - 38 * q^90 - 2 * q^91 + 16 * q^94 - 46 * q^95 - 4 * q^96 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more